{ "2009": { "0607_s09_qp_1.pdf": { "1": " this document consists of 10 printed pages and 2 blank pages. ib09 06_0607_01/4rp \u00a9 ucles 2009 [turn over *5853680123* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/01 paper 1 (core) may/june 2009 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total of the marks for this paper is 40. ", "2": "2 \u00a9 ucles 2009 0607/01/m/j/09 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2009 0607/01/m/j/09 [turn over for examiner's use answer all the questions. 1 (a) list all six factors of 18. answer (a) , , , , , [1] (b) find the highest common factor of 18 and 24. answer (b) [2] 2 (a) work out 2 + 3 \u00d7 4. answer (a) [1] (b) the lowest temperature in geneva one year was \u221215 \u00b0c. the highest temperature the same year was 50 \u00b0c above this. what was the highest temperature? answer (b) \u00b0c [1] (c) gerry and danos share $450. danos receives 2 5 of this amount. work out how much danos receives. answer (c) $ [1] ", "4": "4 \u00a9 ucles 2009 0607/01/m/j/09 for examiner's use 3 (a) write 5\u00d75\u00d75\u00d75 as a power of 5. answer (a) [1] (b) simplify. 2 x 5 \u00d7 3x2 answer (b) [2] 4 25 20 15 10 5 0 busnumber of students cycletravel survey car foot 50 students took part in a survey on how they travelled to school. what fraction of the students travelled by car? give your answer in its lowest terms. answer [2] ", "5": "5 \u00a9 ucles 2009 0607/01/m/j/09 [turn over for examiner's use 5 (a) put a ring around the letters below that have line symmetry. [2] (b) put a ring around the letters below that have rotational symmetry. [2] 6 (a) factorise completely. 3p 2 \u2212 12p answer (a) [2] (b) expand and simplify. 3(2x + y) \u2212 2(x \u2212 3 y) answer (b) [2] ", "6": "6 \u00a9 ucles 2009 0607/01/m/j/09 for examiner's use 7 solve the simultaneous equations. x \u2212 y = 4 3x + 2y = 17 answer x = y = [3] 8 the first four terms of a sequence are 2, 7, 12, 17. (a) write down the next two terms of the sequence. answer (a) , [1] (b) find the nth term of the sequence. answer (b) [2] ", "7": "7 \u00a9 ucles 2009 0607/01/m/j/09 [turn over for examiner's use 9 describe fully the single transformation that maps triangle p onto triangle q in each diagram below. (a) y x \u20133 \u20132 \u20131 1 2 3 3 2 1 \u20131 \u20132 0 pq answer (a) [2] (b) py x \u20133 \u20132 \u20131 1 2 3 3 2 1 \u20131 \u20132 0 q answer (b) [2] ", "8": " 8 \u00a9 ucles 2009 0607/01/m/j/09 for examiner's use 10 the masses of a number of athletes were recorded. the results are shown in the cumulative frequency diagram. 100 90 8070605040302010 0 70 60 80 90 100 110 120 130 mass (kg)cumulative frequency (a) how many masses were recorded altogether? answer (a) [1] (b) how many athletes had a mass less than 80 kg? answer (b) [1] (c) find the median mass. answer (c) kg [1] ", "9": "9 \u00a9 ucles 2009 0607/01/m/j/09 [turn over for examiner's use 11 find the values of x, y and z in the diagrams below. (a) 150\u00b0 x\u00b0not to scale answer (a) x = [1] (b) y\u00b0 70\u00b0not to scale answer (b) y = [2] (c) 120\u00b0 100\u00b0 150\u00b0100\u00b0100\u00b0 z\u00b0 not to scale answer (c) z = [2] question 12 is on the next page ", "10": "10 \u00a9 ucles 2009 0607/01/m/j/09 for examiner's use 12 b 15 m50 m 10 m not to scale d a e c the diagram shows a tower bc of height 50 m. the tower is 15 m from a flagpole de. the flagpole is 10 m from a point a on horizontal ground. find the height, de, of the flagpole. answer de = m [3] ", "11": "11 0607/01/m/j/09 blank page", "12": "12 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. 0607/01/m/j/09 blank page " }, "0607_s09_qp_2.pdf": { "1": " this document consists of 8 printed pages. ib09 06_0607_02/5rp \u00a9 ucles 2009 [turn over *6634783498* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/02 paper 2 (extended) may/june 2009 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total of the marks for this paper is 40. ", "2": "2 \u00a9 ucles 2009 0607/02/m/j/09 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2009 0607/02/m/j/09 [turn over for examiner's use answer all the questions. 1 the distance from the earth to the moon is 3.8 \u00d7 105 km. a spacecraft travels this distance four times. calculate the total distance travelled. give your answer in standard form. answer km [2] 2 for the function f(x) = 2sin 3x write down (a) the amplitude, answer (a) [1] (b) the period. answer (b) [1] 3 o d a z\u00b0y\u00b0b c 20\u00b0x\u00b0not to scale a , b, c and d lie on a circle, centre o. ac is a diameter and angle acd = 20\u00b0. ab = bc. find the values of x, y and z. answer x = [1] y = [1] z = [1] ", "4": "4 \u00a9 ucles 2009 0607/02/m/j/09 for examiner's use 4 write the following as algebraic expressions. (a) one-third of the sum of p and q. answer (a) [1] (b) the square root of the product of x and y. answer (b) [1] 5 list the elements of the following sets. (a) a = { x | x\u2208w, \u2013 4 < x y1} answer (a) [1] (b) b = {prime numbers between 25 and 35} answer (b) [1] (c) c = { x | x\u2208o, | x | = 4} answer (c) [1] 6 (a) write as a single logarithm. log6 + log3 \u2013 log2 answer (a) [1] (b) simplify. _98 50 + 8 answer (b) [2] ", "5": "5 \u00a9 ucles 2009 0607/02/m/j/09 [turn over for examiner's use 7 the first five terms of a sequence are 0, 3, 8, 15, 24. (a) write down the next two terms of the sequence. answer (a) , [1] (b) find the nth term of the sequence. answer (b) [2] 8 y x \u20133 \u20134 \u20132 \u20131 1 2 3 43 21 \u20131\u20132\u201330f the diagram shows a flag f . (a) translate flag f by \uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec \uf8ed\uf8eb 2_3 . label the image p. [2] (b) reflect flag f in the line x = 1. label the image q. [2] ", "6": "6 \u00a9 ucles 2009 0607/02/m/j/09 for examiner's use 9 solve the simultaneous equations. 2 x + 3y = 7 5 x \u2013 4y = \u201317 answer x = y = [4] 10 make t the subject of the formula. =_ 2ay t answer t = [3] ", "7": "7 \u00a9 ucles 2009 0607/02/m/j/09 [turn over for examiner's use 11 the points a(\u22123, 5) and b(3, 2) are shown on the diagram below. y x 0a bnot to scale (a) (i) write down the vector ab in component form. answer (a)(i) \uf8f7\uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec\uf8ec \uf8ed\uf8eb [1] (ii) find \uf8e6 ab\uf8e6 leaving your answer in surd form. answer (a)(ii) [2] (b) calculate the gradient of the line ab. answer (b) [2] (c) calculate the co-ordinates of the midpoint of the line ab. answer (c) ( , ) [1] (d) find the equation of the perpendicular bisector of the line ab. answer (d) [2] question 12 is on the next page. ", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2009 0607/02/m/j/09 for examiner's use 12 find the value of the following. (a) 23 16 answer (a) [1] (b) (cos 30\u00b0)2 answer (b) [2] " }, "0607_s09_qp_3.pdf": { "1": " this document consists of 16 printed pages. ib09 06_0607_03/3rp \u00a9 ucles 2009 [turn over *5760555781* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/03 paper 3 (core) may/june 2009 1 hour 45 minutes candidates answer on the question paper additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of the marks for this paper is 96. ", "2": "2 \u00a9 ucles 2009 0607/03/m/j/09 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2009 0607/03/m/j/09 [turn over for examiner's use answer all the questions. 1 55 7 27wcu 11 100 students are asked if they walk ( w) or cycle (c) as part of their regular exercise. the venn diagram shows this information. (a) how many students (i) walk and cycle, answer (a)(i) [1] (ii) cycle but do not walk, answer (a)(ii) [1] (iii) do not walk and do not cycle? answer (a)(iii) [1] (b) write down the value of (i) n(w), answer (b)(i) [1] (ii) n(c\u2032). answer (b)(ii) [1] (c) one of the students is chosen at random. find the probability that this student does at least one of these types of exercise. answer (c) [1] (d) a school has 2000 students. use your results to predict the number of students from the school who do at least one of these types of exercise. answer (d) [1] ", "4": "4 \u00a9 ucles 2009 0607/03/m/j/09 for examiner's use 2 konrad keeps a record of the marks he receives in ten tests. mark 7 8 9 10 frequency 5 2 2 1 (a) find (i) the mode, answer (a)(i) [1] (ii) the median, answer (a)(ii) [1] (iii) the mean, answer (a)(iii) [1] (iv) the range, answer (a)(iv) [1] (v) the upper quartile. answer (a)(v) [1] (b) a pie chart to show this information has been started below. complete and label the pie chart accurately . 7 marks 8 marks [2] ", "5": "5 \u00a9 ucles 2009 0607/03/m/j/09 [turn over for examiner's use (c) 6 543210 8 71 0 9 frequency mark on the grid above, draw a bar chart to show konrad\u2019s marks. [3] (d) work out the percentage of the ten tests in which konrad\u2019s marks were 9 or 10. answer (d) % [2] ", "6": "6 \u00a9 ucles 2009 0607/03/m/j/09 for examiner's use 3 (a) the ratio of abdul\u2019s height to babar\u2019s height is abdul : babar = 6 : 5 abdul\u2019s height is 180 cm. calculate babar\u2019s height. answer (a) cm [2] (b) the masses of abdul and babar are in the same ratio as their heights. the total of their masses is 121 kg. show that abdul\u2019s mass is 66 kg. [2] (c) last year abdul\u2019s mass was 63 kg. it is now 66 kg. calculate the percentage increase in abdul\u2019s mass. answer (c) % [2] ", "7": "7 \u00a9 ucles 2009 0607/03/m/j/09 [turn over for examiner's use (d) convert 63 kg into grams. give your answer in standard form. answer (d) g [3] (e) abdul and babar run 100 metres. (i) abdul runs at a steady speed of 7 metres per second. find the time taken for abdul to run the 100 metres. answer (e)(i) seconds [2] (ii) babar takes 14.5 seconds to run the 100 metres. find his speed, in metres per second. answer (e)(ii) m/s [2] ", "8": "8 \u00a9 ucles 2009 0607/03/m/j/09 for examiner's use 4 0\u2013223 \u20131y x the diagram shows a sketch of the graph of the function y = 3 \u2013 x 2. (a) on the diagram, sketch the graph of the function y = 2x + 2 for \u22122 y x y=2. [2] (b) solve the equation 3 \u2212 x2 = 2x + 2. give your answers correct to 4 decimal places. answer (b) x = or [2] (c) on the diagram, sketch the straight line y = 4. from your diagram, explain why the equation 3 \u2013 x 2 = 4 has no solutions. [1] ", "9": "9 \u00a9 ucles 2009 0607/03/m/j/09 [turn over for examiner's use 5 75\u00b035\u00b06 cm 12 cmdc b a7 cmnot to scale abcd is a trapezium with ab parallel to dc. ab = 12 cm, dc = 6 cm and the height of the trapezium is 7 cm. angle dab = 75\u00b0 and angle cdb = 35\u00b0. calculate (a) the area of triangle abd , answer (a) cm2 [2] (b) the area of the trapezium, answer (b) cm2 [2] (c) angle adc, answer (c) [1] (d) angle abd . answer (d) [1] ", "10": "10 \u00a9 ucles 2009 0607/03/m/j/09 for examiner's use 6 each day lavinia records the number of glasses of water and the number of cups of coffee she drinks. the results for one week are shown in the table. day sun mon tue wed thu fri sat number of glasses of water 8 5 6 3 7 7 6 number of cups of coffee 2 4 4 6 2 1 2 (a) on the grid, draw a scatter diagram to show this information. 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 number of glasses of waternumber of cups of coffee [3] (b) which of these words (positive, negative, none) describes the correlation between the number of glasses of water and the number of cups of coffee? answer (b) [1] (c) (i) calculate the mean number of cups of coffee. answer (c)(i) [1] (ii) the mean number of glasses of water is 6. draw the line of best fit for this data. [2] ", "11": "11 \u00a9 ucles 2009 0607/03/m/j/09 [turn over for examiner's use 7 4 cmnot to scale 3 cm5 cm the diagram shows a solid cone of height 4 cm and radius 3cm. the length of the sloping edge of the cone is 5 cm. (a) (i) calculate the volume of the cone. answer (a) (i) cm3 [2] (ii) the cone is made of metal. 1 cm3 of the metal has a mass of 7.5 g. calculate the mass of the cone. answer (a) (ii) g [2] (b) (i) calculate the total surface area of the cone. answer (b) (i) cm2 [3] (ii) change your answer into square metres. answer (b) (ii) m2 [1] (iii) one pot of paint covers 7 m2. how many of these cones can be painted using one pot of paint? answer (b) (iii) [2] ", "12": "12 \u00a9 ucles 2009 0607/03/m/j/09 for examiner's use 8 7 \u20136\u20132 4y x0 (a) on the diagram, sketch the graph of the function y = 3 3x \u2212 x2 + 1 for \u22122 y x y=4. [4] (b) find the value of y when (i) x = 0 answer (b)(i) [1] (ii) x = 3.5 answer (b)(ii) [1] (c) find the three values of x when y = 0. answer (c) x = , , [3] (d) find the co-ordinates of the local minimum point. answer (d) ( , ) [2] (e) find the value of x when 3 3x \u2212 x2 + 1 = \u22122 answer (e) [1] (f) the domain of the function f( x) = 3 3x \u2212 x2 + 1 is \u22122 y x y=4. find the range of the function. answer (f) [2] ", "13": "13 \u00a9 ucles 2009 0607/03/m/j/09 [turn over for examiner's use 9 op qt 70\u00b0not to scale the diagram shows a circle, centre o. tp and tq are tangents to the circle at p and q. angle ptq = 70\u00b0. (a) calculate (i) angle tpq , answer (a)(i) [2] (ii) angle poq. answer (a)(ii) [2] (b) another circle can be drawn through the points o, p, t and q. complete the statement. \u201cot is a of this new circle.\u201d [1] ", "14": "14 \u00a9 ucles 2009 0607/03/m/j/09 for examiner's use 10 0 l (1,2)m (1,6) k (8,2)y xnot to scale the diagram shows triangle klm on a co-ordinate grid. the diagram is not to scale so do not measure any lengths or angles. (a) write down the equation of the straight line which passes through l and m. answer (a) [1] (b) find the gradient of the line mk. answer (b) [2] ", "15": "15 \u00a9 ucles 2009 0607/03/m/j/09 [turn over for examiner's use (c) find the co-ordinates of the midpoint of the line mk. answer (c) ( , ) [2] (d) calculate the length of mk. answer (d) [2] (e) use trigonometry to calculate the size of angle lkm. answer (e) [2] question 11 is printed on the next page. ", "16": "16 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. 0607/03/m/j/09 for examiner's use 11 (a) find the value of 2_ 5 2xy when x = 7 and y = 4. give your answer as a fraction in its lowest terms. answer (a) [2] (b) 2 52xy\u2212 can be written as a single fraction 10x y \u2212. fill in the two missing values. [2] (c) 2 52xy\u2212 = 1 and y = 14. find the value of x. answer (c) x = [2] (d) 2 52xy\u2212 = 1. find y in terms of x. answer (d) y = [2] " }, "0607_s09_qp_4.pdf": { "1": " this document consists of 23 printed pages and 1 blank page. ib09 06_0607_04/4rp \u00a9 ucles 2009 [turn over *6816953946* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/04 paper 4 (extended) may/june 2009 2 hours 15 minutes candidates answer on the question paper additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of the marks for this paper is 120. ", "2": "2 \u00a9 ucles 2009 0607/04/m/j/09 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2009 0607/04/m/j/09 [turn over for examiner's use answer all the questions. 1 katharine and lucas share a gift of $200 in the ratio katharine : lucas = 11 : 9 (a) show that katharine receives $110. [2] (b) katharine spends $60. she then invests the remaining $50 for 3 years at 5% simple interest per year. find the amount katharine has after 3 years. answer (b) $ [2] (c) lucas receives $90 and spends $30. he invests the remaining $60 for 3 years at 4% compound interest per year. find the amount lucas has after 3 years. give your answer correct to 2 decimal places. answer (c) $ [3] ", "4": "4 \u00a9 ucles 2009 0607/04/m/j/09 for examiner's use 2 davinia records the shoe sizes of the girls in her class. shoe size 35 36 37 38 39 40 frequency 2 7 6 4 3 2 find (a) the mean, answer (a) [1] (b) the median, answer (b) [1] (c) the mode, answer (c) [1] (d) the lower quartile, answer (d) [1] (e) the inter-quartile range. answer (e) [1] 3 (a) factorise completely 2 x + 4y + px +2py. answer (a) [2] (b) solve the equation 2 x2 + 2x \u2212 5 = 0. give your answers correct to 2 decimal places. answer (b) x = or [4] ", "5": "5 \u00a9 ucles 2009 0607/04/m/j/09 [turn over for examiner's use (c) y varies as the square root of w. when w = 9, y = 4. find the value of y when w = 36. answer (c) y= [3] 4 (a) k l shade k \u2229 l\u2032 on the diagram. [1] (b) a b c shade ( a \u2229 b) \u222a c on the diagram. [2] (c) there are 20 students in helena\u2019s class. 6 students have fair hair. 10 students have long hair. 8 students do not have fair hair and do not have long hair. how many students have fair hair and long hair? answer (c) [2] ", "6": "6 \u00a9 ucles 2009 0607/04/m/j/09 for examiner's use 5 200 \u201330 \u20133 5 0y x (a) for o3 y x y 5, sketch the following graphs on the diagram above. (i) y = x 4 o 4x3 [2] (ii) y = \uf8e640 o 17x\uf8e6 [2] (b) solve the equation x4 o 4x3 = 0. answer (b) x = or [2] (c) find the co-ordinates of the local minimum point on the graph of y = x4 o 4x3. answer (c) ( , ) [2] (d) solve the equation x4 \u2212 4x3 = \uf8e640 o 17x \uf8e6. answer (d) x = or [2] ", "7": "7 \u00a9 ucles 2009 0607/04/m/j/09 [turn over for examiner's use 6 (a) farooz cycles 35 kilometres in 21 2 hours. she then walks for 13 4 hours at 4 km/h. calculate farooz\u2019s average speed for the whole journey. answer (a) km/h [3] (b) basil runs 10 kilometres at an average speed of 12.6 km/h. (i) find the time, in minutes, basil takes. answer (b)(i) minutes [2] (ii) basil\u2019s speed of 12.6 km/h is 5% faster than his speed in a previous run. find basil\u2019s speed in his previous run. answer (b)(ii) km/h [2] ", "8": "8 \u00a9 ucles 2009 0607/04/m/j/09 for examiner's use 7 (a) 2 1.5 1 0.5 \u20130.5 \u20131 \u20131.5 \u201320 \u20131 1 2 \u20132 \u20131.5 \u20130.5 0.5 1.5y x the graph shows y = f(x ), where f( x) = 2 x o 1. (i) find the inverse function, f \u22121(x). answer (a)(i) f \u22121(x) = [2] (ii) sketch the graph of y = f \u22121(x) on the diagram above. [1] ", "9": "9 \u00a9 ucles 2009 0607/04/m/j/09 [turn over for examiner's use (b) 2 1.5 1 0.5 \u20130.5 \u20131 \u20131.5 \u201320 \u20131 1 2 \u20132 \u20131.5 \u20130.5 0.5 1.5y x the graph shows y = g(x), where g( x) = x3. (i) find the inverse function, g\u22121(x). answer (b)(i) g \u22121 (x) = [1] (ii) sketch the graph of y = g\u22121 (x) on the diagram above. [2] (iii) describe fully the single transformation which maps the graph of y = g(x) onto the graph of y = g\u22121 (x). answer (b)(iii) [2] ", "10": "10 \u00a9 ucles 2009 0607/04/m/j/09 for examiner's use 8 ap b 7 km5 km 3 km northnorth north not to scale sunil walks 15 kilometres along three straight paths pa, ab and bp. pa = 3 km, ab = 7 km and bp = 5 km. (a) calculate (i) angle apb, answer (a)(i) [3] (ii) the area of triangle apb. answer (a)(ii) km2 [2] ", "11": "11 \u00a9 ucles 2009 0607/04/m/j/09 [turn over for examiner's use (b) the bearing of a from p is 220\u00b0. find (i) the bearing of p from a, answer (b)(i) [1] (ii) the bearing sunil uses when walking from b to p. answer (b)(ii) [2] 9 \u20132 3y x0 f(x) = x3 \u2212 x2 \u2212 7x \u2212 1 for the domain \u22122 y x y 3 (a) sketch the graph of y = f( x), [2] (b) find the range of the function f( x). answer (b) [2] ", "12": "12 \u00a9 ucles 2009 0607/04/m/j/09 for examiner's use 10 a football team plays 28 games. the table shows the results. result win (w) draw (d) lose (l) frequency 14 5 9 (a) one of the games is chosen at random. what is the probability that the team (i) wins, answer (a)(i) [1] (ii) draws, answer (a)(ii) [1] (iii) loses? answer (a)(iii) [1] ", "13": "13 \u00a9 ucles 2009 0607/04/m/j/09 [turn over for examiner's use (b) the football team plays two more games. the tree diagram shows the possible outcomes. first game second game w d l w d l w d lw d l using the probabilities you have worked out in part (a) for both of these games, find the probability that the team (i) wins both games, answer (b)(i) [2] (ii) wins one game and draws the other, answer (b)(ii) [2] (iii) does not lose both games. answer (b)(iii) [2] ", "14": "14 \u00a9 ucles 2009 0607/04/m/j/09 for examiner's use 11 y x t u q6 cm 2.5 cm 3 cm not to scale in the diagram, xy and tu are parallel. yt and xu intersect at q. (a) complete the statement. \u201ctriangle xqy is to triangle uqt. \u201d [1] (b) yq = 2.5 cm, xq = 3 cm and qu = 6 cm. (i) calculate the length of qt. answer (b)(i) cm [2] ", "15": "15 \u00a9 ucles 2009 0607/04/m/j/09 [turn over for examiner's use (ii) the area of triangle xqy is 2.8 cm2. calculate the area of triangle uqt. answer (b)(ii) cm2 [2] (iii) angle xyq = 26.5\u00b0. use the sine rule to calculate angle qxy . answer (b)(iii) [3] ", "16": "16 \u00a9 ucles 2009 0607/04/m/j/09 for examiner's use 12 o c l q k p 30\u00b0 30\u00b0 12 cm 3 cm 12 cm not to scale the diagram shows a slice of cake. okl and cpq are identical sectors of radius 12 cm and angle 30\u00b0. okl is vertically above cpq and co = ql = pk = 3 cm. calculate (a) the length of the arc kl, answer (a) cm [2] (b) the area of the sector okl, answer (b) cm2 [2] ", "17": "17 \u00a9 ucles 2009 0607/04/m/j/09 [turn over for examiner's use (c) the volume of the slice of cake, answer (c) cm3 [2] (d) the total surface area of the slice of cake. answer (d) cm2 [4] ", "18": "18 \u00a9 ucles 2009 0607/04/m/j/09 for examiner's use 13 ten players in a basketball club want to find out if there is any correlation between a person\u2019s height (h centimetres) and the number of points ( p) scored in a month. player fred greg andy bill chris dave ed hans ian jim height (h) 185 190 183 186 165 185 175 170 190 170 points (p) 50 59 52 53 47 55 50 51 63 52 (a) on the grid below, draw a scatter diagram to show the information in the table. p h height (cm)number of points scored65 60 55 50 45 160 165 170 175 180 185 190 0 [3] (b) describe any correlation between the height and the number of points scored. answer (b) [1] ", "19": "19 \u00a9 ucles 2009 0607/04/m/j/09 [turn over for examiner's use (c) find (i) the mean height, answer (c)(i) cm [1] (ii) the mean number of points scored. answer (c)(ii) [1] (d) (i) find the equation of the line of regression, which gives p in terms of h. answer (d)(i) p = [2] (ii) draw the line of regression accurately on the grid. [2] (iii) predict the number of points a player of height 178 cm would score. answer (d)(iii) [1] ", "20": "20 \u00a9 ucles 2009 0607/04/m/j/09 for examiner's use 14 y x10 9 87654321 0 1 2 3 4 5 6 7 8 9 10 (a) on the grid above draw the following lines. y = 2x, for 0 y x y 5 x + y = 10, for 0 y x y 10 2x + y = 10, for 0 y x y 5 [3] (b) show, by shading the unwanted regions, the region, t, containing the points which satisfy the three inequalities y [ 2 x, x + y y 10 and 2x + y [ 10 [1] ", "21": "21 \u00a9 ucles 2009 0607/04/m/j/09 [turn over for examiner's use (c) find the greatest value of x in the region, t, when (i) x \u2208 o, answer (c)(i) x = [1] (ii) x \u2208 k. answer (c)(ii) x = [1] (d) (x, y) lies in the region t. find all pairs of integer values of x and y when 2x + y = 11 answer (d) [2] ", "22": "22 \u00a9 ucles 2009 0607/04/m/j/09 for examiner's use 15 (a) (i) red pencils cost 12 cents each. what is the greatest number of red pencils you can buy for 360 cents? answer (a)(i) [1] (ii) blue pencils cost x cents each. write down, in terms of x, the greatest number of blue pencils you can buy for 360 cents. answer (a)(ii) [1] (iii) yellow pencils cost ( x + 8) cents each. write down, in terms of x, the greatest number of yellow pencils you can buy for 360 cents. answer (a)(iii) [1] (b) the number of blue pencils in part (a)(ii) is 16 more than the number of yellow pencils in part (a)(iii) . (i) write down an equation in x and show that it simplifies to x 2 + 8x \u2212 180 = 0. [4] ", "23": "23 \u00a9 ucles 2009 0607/04/m/j/09 for examiner's use (ii) factorise. x2 + 8x \u2212 180 answer (b)(ii) [2] (iii) solve the equation. x2 + 8x \u2212 180 = 0 answer (b)(iii) x= or [1] (iv) write down the cost of a blue pencil. answer (b)(iv) cents [1] ", "24": "24 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. 0607/04/m/j/09 blank page " }, "0607_s09_qp_5.pdf": { "1": " this document consists of 3 printed pages and 1 blank page. ib09 06_0607_05/5rp \u00a9 ucles 2009 [turn over *9267088157* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/05 paper 5 (core) may/june 2009 1 hour additional materials: answer booklet/paper graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. answer all the questions. you must show all relevant working to gain full mark s for correct methods, including sketches, even if your answer is incorrect. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of the marks for this paper is 24. ", "2": "2 \u00a9 ucles 2009 0607/05/m/j/09 answer all questions. investigation removing discs 652 10 71 43 89 the diagram shows ten discs, numbered 1 to 10, arranged in a circle. you remove the disc numbered 1, and, going clockwise, le ave the next one, remove the one after that, leave the next one, and so on until only one disc remains. the discs which you remove are, in order, numbered 1, 3, 5, 7, 9, 2, 6, 10, 8. the remaining disc is numbered 4. 1 copy and complete the table showing the number on the remaining disc when you have 2 discs, 3 discs, 4 discs, \u2026., 20 discs in the circle. you may find it useful to draw some more diagrams to help you. number of discs in the circle number on the remaining disc 2 2 3 2 4 4 5 6 7 8 8 9 10 4 11 6 12 8 13 10 14 15 14 16 16 17 18 19 6 20 8 ", "3": "3 \u00a9 ucles 2009 0607/05/m/j/09 2 when you have 2, 4, 8, 16 or 32 discs in the circle, the number on the remaining disc is always the same as the total number of discs in the circle. assume this pattern continues. write down the next two numbers when this happens. 3 use question 2, and any patterns you see in y our table, to find the number on the remaining disc when the circle contains (a) 33 discs, (b) 31 discs, (c) 68 discs, (d) 127 discs, (e) 200 discs. 4 how many discs are there when (a) the remaining disc is numbered 14 and there are between 20 and 30 discs in the circle , (b) the remaining disc is numbered 24 and there are between 30 and 50 discs in the circle? 5 consider the original ten discs again. remove the disc numbered 10, and going anticlockwise , leave the next one, remove the one after that, leave the next one, and so on until only one disc remains. you should finish with the disc numbered 7. (a) write down the numbers on the discs in the order in which you remove them. (b) when you started with the disc numbered 1 and worked clockwise, the order was 1 3 5 7 9 2 6 10 8 compare this order with the order you have written down in part (a) . explain how the two orders are related. (c) when there are 700 discs and you work clockwise, first removing the disc numbered 1, the remaining disc is the disc numbered 376. find the number on the remaining disc when you work anticlockwise, first removing the disc numbered 700. ", "4": "4 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. 0607/05/m/j/09 blank page " }, "0607_s09_qp_6.pdf": { "1": "this document consists of 4 printed pages. ib09 06_0607_06/5rp \u00a9 ucles 2009 [ turn over *7384524122*u niversity of cambridge international examinations international general certificate of secondary education c ambridge international mathematics 0607/06 paper 6 (extended) may/june 2009 1 hour 30 minutes additional materials: answer booklet/paper graphics calculator r ead these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. answer both parts a and b. you must show all relevant working to gain full mark s for correct methods, including sketches, even if your answer is incorrect. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of the marks for this paper is 40. ", "2": "2 \u00a9 ucles 2009 0607/06/m/j/09 answer both parts a and b. a. investigation removing discs 24 marks 652 10 71 43 89 t en discs, numbered 1 to 10, form a circle. you remove the disc numbered 1, and, going clockwise, le ave the next one, remove the one after that, leave the next one, and so on until only one disc remains. the discs which you remove are, in order, numbered 1, 3, 5, 7, 9, 2, 6, 10, 8. the remaining disc is numbered 4. 1 copy and complete the table showing the number on the remaining disc when you have 2 discs, 3 discs, 4 discs, \u2026., 20 discs in the circle. number of discs in the circle number on the remaining disc 2 2 3 2 4 4 5 6 7 8 8 9 10 4 11 6 12 8 13 10 14 15 14 16 16 17 18 19 6 20 8", "3": "3 \u00a9 ucles 2009 0607/06/m/j/09 [turn over2 when you have 2, 4, 8 or 16 discs in the circle, the number on the remaining disc is always the same as the total number of discs in the circle. assume this pattern continues. write down the next three numbers when this happens. 3 use question 2, and any patterns you see in your table, to find the number on the remaining disc when the circle contains (a) 65 discs, (b) 125 discs, (c) 200 discs, (d) 100 000 discs. 4 find an algebraic expression for the number of discs in the circle, when the remaining disc is numbered 10. 5 consider the original ten discs again. remove the disc numbered 10, and going anticlockwise , leave the next one, remove the one after that, leave the next one, and so on until only one disc remains. you should finish with the disc numbered 7. (a) (i) write down the numbers on the discs in the order in which you remove them. (ii) when you started with the disc numbered 1 and worked clockwise, the order was 1 3 5 7 9 2 6 10 8 compare this order with the order you have written down in part (a) (i). explain how the two orders are related. (b) (i) when you have n discs in the circle and work clockwise from the disc numbered 1, the number on the remaining disc is x. when you work anticlockwise from the disc numbered n, the number on the remaining disc is y. find a rule connecting x, y and n. (ii) find the number on the remaining disc when there are 100 discs and you work anticlockwise by first removing the disc numbered 100. part b is on the next page. ", "4": "4 b. modelling hanging chain 16 marks pqy 0x a b not to scale t he diagram shows two vertical poles ( ap and bq) that support the ends ( a and b) of a hanging chain. the chain is symmetrical about the y-axis. the poles are each 7.52 metres high and are 4 metres apart. the lowest point of the chain is 2 metres above the horizontal ground ( pq). the units are in metres. 1 write down the co-ordinates of a, b and the lowest point of the chain. 2 the scientist galileo chose one of the following models for the shape of a hanging chain. which model best fits the hanging chain in the diagram? y = ax + b y = | ax + b | y = ax2 + b y = a sin x + b 3 use the co-ordinates of the lowest point of the chain to find the value of b in your chosen model. 4 find the value of a in your chosen model. 5 according to your model, how high is the cha in above a point on the ground that is 50 cm from one of the poles? 6 today, engineers use the model y = k \uf8f7 \uf8f8\uf8f6\uf8ec \uf8ed\uf8eb+xwxw1, w > 1, for a hanging chain. (a) use the co-ordinates of the lowest point of the chain to find the value of k. (b) find the value of w for this model. 7 the two models give heights for the hanging chain. the difference in these heights is h. (a) sketch the graph of h against x. (b) find the greatest difference in height between the two models. permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. 0607/06/m/j/09" } }, "2010": { "0607_s10_qp_1.pdf": { "1": " this document consists of 8 printed pages. ib10 06_0607_01/2rp \u00a9 ucles 2010 [turn over *9521008140* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/01 paper 1 (core) may/june 2010 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2010 0607/01/m/j/10 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2010 0607/01/m/j/10 [turn over for examiner's use answer all the questions. 1 write down the value of (a) 23, answer(a) [1] (b) 2 0. answer(b) [1] 2 simplify 48 48+ \u00d7. give your answer as a fraction in its lowest terms. answer [2] 3 p = 2 \u00d7 10 5 find the value of 6 p, giving your answer in standard form. answer [2] ", "4": "4 \u00a9 ucles 2010 0607/01/m/j/10 for examiner's use 4 the heights of 20 buildings are measured. (a) state whether the data is discrete or continuous. answer(a) [1] (b) the heights, correct to the nearest metre, are shown below. 12 10 15 18 8 9 23 26 14 21 11 16 20 21 22 13 22 25 17 19 draw an ordered stem-and-leaf diagram to show this information. [3] (c) work out the range of the heights. answer(c) m [1] ", "5": "5 \u00a9 ucles 2010 0607/01/m/j/10 [turn over for examiner's use 5 (a) simplify 5p2 \u00d7 3p3. answer(a) [2] (b) factorise completely 2x 2 + 6xy . answer(b) [2] 6 (a) plot the points a(\u22121, 5) and b(3, 7) on the grid. y x8 7654321 \u20131\u20132 \u20131 \u20132 1 0 2345678 [2] (b) write down the coordinates of the midpoint of the line joining a and b. answer(b) ( , ) [1] ", "6": "6 \u00a9 ucles 2010 0607/01/m/j/10 for examiner's use 7 all measurements in this question are in centimetres. three rectangles are placed together to form the shape below. 2 23 46not to scale (a) calculate the area of this shape. answer(a) cm2 [2] (b) the shape is projected onto a screen and the enlargement is shown below. 24 xnot to scale find the value of x. answer(b) x = cm [2] ", "7": "7 \u00a9 ucles 2010 0607/01/m/j/10 [turn over for examiner's use 8 the probability that it is windy is 0.3 . (a) write down the probability that it is not windy. answer(a) [1] (b) anita plans to go sailing. if it is windy, the probability that she will go sailing is 0.8 . if it is not windy, the probability that she will go sailing is 0.1 . (i) complete the tree diagram. 0.3 ..0.8 ..windy not windysailing not sailing 0.1 ..sailing not sailing [2] (ii) find the probability that it is windy and anita goes sailing. answer(b)(ii) [2] 9 (a) solve the inequality 3( x \u2013 1) < 6. answer(a) [2] (b) show your solution on the number line below. \u20134 \u20133 \u20132 \u20131 0 1 2 3 4x [2] ", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2010 0607/01/m/j/10 for examiner's use 10 the venn diagram shows the numbers 1 to 9 placed in different regions. u ab 5 7 94 83 61 2 complete the following statements. (a) n(a) = [1] (b) a \u2229b = { } [1] (c) (a\u222ab) ' = { } [1] (d) a number in the venn diagram is chosen at random. find the probability that the number is in a. answer(d) [1] 11 \u22122, 1, 4, 7, 10, \u2026.. (a) write down the next term of the sequence. answer(a) [1] (b) find the nth term of the sequence. answer(b) [2] (c) is the number 296 a term of the sequence? you must show your working. [2] " }, "0607_s10_qp_2.pdf": { "1": " this document consists of 10 printed pages and 2 blank pages. ib10 06_0607_02/2rp \u00a9 ucles 2010 [turn over *0414909462* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/02 paper 2 (extended) may/june 2010 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2010 0607/02/m/j/10 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2010 0607/02/m/j/10 [turn over for examiner's use answer all the questions. 1 write 36 000 in standard form. answer [1] 2 (a) find the value of (i) 3 0, answer(a)(i) [1] (ii) 1 236. answer(a)(ii) [1] (b) 28 \u00f7 2 = 2x find the value of x. answer(b) x = [1] 3 factorise completely 3x 2y \u2013 12y3. answer [2] ", "4": "4 \u00a9 ucles 2010 0607/02/m/j/10 for examiner's use 4 4 321 \u20131\u20132\u20133\u201340 \u201390\u00b0 90\u00b0 180\u00b0 270\u00b0 360\u00b0 \u2013180\u00b0y x the diagram shows the graph of y = f( x), where f( x) = asin(bx). find the values of a and b. answer a = [1] answer b = [1] ", "5": "5 \u00a9 ucles 2010 0607/02/m/j/10 [turn over for examiner's use 5 (a) factorise 2 x2 + x \u2013 6. answer(a) [2] (b) solve the equation. 2 x 2 = 6 \u2013 x answer(b) x = or x = [2] 6 (a) 3log2 + 2log3 = log k find the value of k. answer(a) k = [2] (b) find the value of log 25 log 5. answer(b) [1] ", "6": "6 \u00a9 ucles 2010 0607/02/m/j/10 for examiner's use 7 p = 5 1\uf8eb\uf8f6\uf8ec\uf8f7\uf8ed\uf8f8 and q = 4 2\u2212\uf8eb\uf8f6\uf8ec\uf8f7\uf8ed\uf8f8 (a) write 2 p \u2212 1 2q as a column vector. answer(a) \uf8eb\uf8f6 \uf8ec\uf8f7 \uf8ec\uf8f7\uf8ec\uf8f7\uf8ed\uf8f8[2] (b) find \u2502q\u2502 leaving your answer in surd form. answer(b) [2] 8 (a) simplify 72 50\u2212 . answer(a) [2] (b) write 1 23\u2212 in its simplest form by rationalising the denominator. answer(b) [2] ", "7": "7 \u00a9 ucles 2010 0607/02/m/j/10 [turn over for examiner's use 9 b a8 642 \u20132\u20134\u20136\u201380y x \u20132 2 4 6 8 \u20134 \u20136 \u20138 (a) describe fully the single transformation which maps shape a onto shape b. [3] (b) draw the image of shape a after a stretch, with y-axis invariant and scale factor 2. [2] ", "8": "8 \u00a9 ucles 2010 0607/02/m/j/10 for examiner's use 10 bo c eda 55\u00b0 20\u00b0not to scale the points a, b, c and d lie on a circle, centre o. ab is a diameter, angle bad = 55\u00b0 and angle bdc = 20\u00b0. abe and dce are straight lines. find (a) angle abd , answer(a) [1] (b) angle bcd, answer(b) [1] (c) angle aed . answer(c) [1] ", "9": "9 \u00a9 ucles 2010 0607/02/m/j/10 [turn over for examiner's use 11 0y xp qlnot to scale the diagram shows a line, l, which passes through the points p(0, 4) and q(2, 0). (a) find the equation of the line l. answer(a) [2] (b) find the equation of the line which is perpendicular to l and passes through the midpoint of pq. answer(b) [4] ", "10": "10 \u00a9 ucles 2010 0607/02/m/j/10 for examiner's use 12 700 600500400300200100 010 20 30 40 50y x the graph shows the result of an experiment measuring x and y. it is known that y is directly proportional to the square of x. find the equation connecting y and x. answer [3] ", "11": "11 \u00a9 ucles 2010 0607/02/m/j/10 blank page ", "12": "12 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2010 0607/02/m/j/10 blank page " }, "0607_s10_qp_3.pdf": { "1": " this document consists of 17 printed pages and 3 blank pages. ib10 06_0607_03/2rp \u00a9 ucles 2010 [turn over *3843129279* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/03 paper 3 (core) may/june 2010 1 hour 45 minutes candidates answer on the question paper additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96. ", "2": "2 \u00a9 ucles 2010 0607/03/m/j/10 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2010 0607/03/m/j/10 [turn over for examiner's use answer all the questions. 1 (a) sangita and asha share $140 in the ratio sangita : asha = 4 : 3. show that sangita receives $80. [2] (b) sangita spends 7 16 of her $80 on clothes. (i) calculate how much she spends on clothes. answer(b)(i) $ [2] (ii) after sangita has bought her clothes, the money remaining from the $80 is 9 11 of the price of an electronic game. calculate the price of this game. answer(b)(ii) $ [2] (c) asha invests her $60 for two years at 6% per year compound interest. calculate the amount asha has after the two years. give your answer correct to 2 decimal places. answer(c) $ [3] ", "4": "4 \u00a9 ucles 2010 0607/03/m/j/10 for examiner's use 2 (a) y = 2x \u2013 3 (i) find the value of y when x = \u2013 1. answer(a)(i) [1] (ii) make x the subject of the formula. answer(a)(ii) x = [2] (iii) find the value of x when y = 6. answer(a)(iii) [1] (b) solve the simultaneous equations y = 2x \u2013 3 and y = 9 \u2013 x. answer(b) x = y = [3] ", "5": "5 \u00a9 ucles 2010 0607/03/m/j/10 [turn over for examiner's use 3 t bay x6 54321 \u20131\u20132\u20133\u20134\u20135\u201360 \u20136 \u20135 \u20134 \u20133 \u20132 \u2013 1 123456 (a) describe fully the single transformation that maps (i) triangle t onto triangle a, [2] (ii) triangle t onto triangle b. [3] (b) on the grid, draw the enlargement of triangle t, centre (0, 0), scale factor 2. [2] ", "6": "6 \u00a9 ucles 2010 0607/03/m/j/10 for examiner's use 4 ahmed\u2019s football team has played 20 games. the number of goals scored in these games is shown in the table. number of goals 0 1 2 3 4 5 frequency 4 9 3 2 1 1 (a) ahmed begins to draw a pie chart to show this information. complete the pie chart accurately and label each sector. 5 goals 4 goals 3 goals [3] (b) find (i) the mode, answer(b)(i) [1] (ii) the mean, answer(b)(ii) [1] (iii) the range, answer(b)(iii) [1] ", "7": "7 \u00a9 ucles 2010 0607/03/m/j/10 [turn over for examiner's use (iv) the lower quartile, answer(b)(iv) [1] (v) the upper quartile. answer(b)(v) [1] (c) a game is picked at random. find the probability that in this game (i) 1 goal was scored, answer(c)(i) [1] (ii) 6 goals were scored, answer(c)(ii) [1] (iii) more than one goal was scored. answer(c)(iii) [1] ", "8": "8 \u00a9 ucles 2010 0607/03/m/j/10 for examiner's use 5 6 54321 \u20131\u20132\u20133\u20134\u20135\u20136\u20137\u20138\u20139 \u201310\u20132 \u20131 1 20y x (a) on the diagram, sketch the graphs of (i) y = 31 x, for \u2212 2 y x y 2, x \u2260 0, [2] (ii) y = x3 \u2212 2, for \u2212 2 y x y 2. [2] ", "9": "9 \u00a9 ucles 2010 0607/03/m/j/10 [turn over for examiner's use (b) the graph of y = 31 x has two asymptotes. write down the equation of each asymptote. answer(b) [2] (c) (i) the graphs of 31yx= and y = x3 \u2212 2 intersect at two points. write down the co-ordinates of these two points. give each answer correct to 4 decimal places. answer(c)(i) ( , ) ( , ) [2] (ii) solve the equation 3 312 xx=\u2212 . give each answer correct to 4 decimal places. answer(c)(ii) x = or x = [1] (d) the graph of y = x3 \u2212 2 is a single transformation of the graph of y = x3. describe fully this single transformation. [2] ", "10": "10 \u00a9 ucles 2010 0607/03/m/j/10 for examiner's use 6 0y xa (2, 3)b (10, 9) cnot to scale in the right-angled triangle abc, a is the point (2, 3) and b is the point (10, 9). (a) write down the co-ordinates of the point c. answer(a) ( , ) [1] (b) calculate the length of ab. answer(b) [3] (c) (i) find the gradient of ab. answer(c)(i) [2] (ii) the line l is parallel to ab and passes through the origin. write down the equation of l. answer(c)(ii) [1] ", "11": "11 \u00a9 ucles 2010 0607/03/m/j/10 [turn over for examiner's use 7 each day a train leaves paris at 20 32 and arrives in barcelona at 08 24 the next day. the distance between paris and barcelona is 1150 km. (a) (i) find the time taken for the journey, in hours and minutes. answer(a)(i) h min [2] (ii) calculate the average speed of the train, in kilometres per hour. answer(a)(ii) km/h [3] (b) one day the average speed of the train was 95 km/h. as a result the train was late arriving in barcelona. calculate by how many minutes the train was late. give your answer correct to the nearest minute. answer(b) min [3] ", "12": "12 \u00a9 ucles 2010 0607/03/m/j/10 for examiner's use 8 o ab m 56\u00b0 8 cmnot to scale oab is a sector of a circle, centre o, radius 8 cm. angle aob = 56\u00b0. m is the midpoint of the chord ab. om is perpendicular to the chord ab. calculate (a) the length of the arc ab, answer(a) cm [2] (b) the length of the chord ab, answer(b) cm [3] (c) the perimeter of the shaded region. answer(c) cm [1] ", "13": "13 \u00a9 ucles 2010 0607/03/m/j/10 [turn over for examiner's use 9 b acnorth north 12 km17 kmnot to scale b is 12 km from a on a bearing of 320\u00b0. c is 17 km from a. angle bac = 90\u00b0. (a) find the bearing of c from a. answer(a) [1] (b) use trigonometry to calculate angle abc. answer(b) [2] (c) calculate the bearing of c from b. answer(c) [2] ", "14": "14 \u00a9 ucles 2010 0607/03/m/j/10 for examiner's use 10 a sphere has a radius of 8 cm. (a) calculate the surface area. answer(a) cm2 [2] (b) calculate the volume. answer(b) cm3 [2] (c) the sphere is solid and is made of iron. 1cm3 of iron has a mass of 7.87 g. calculate the mass of the sphere in (i) grams, answer(c)(i) g [2] (ii) kilograms. answer(c)(ii) kg [1] (d) the sphere is melted down and made into a cube. use your answer to part (b) to calculate the length of a side of the cube. answer(d) cm [2] ", "15": "15 \u00a9 ucles 2010 0607/03/m/j/10 [turn over for examiner's use 11 t a wopb q 38\u00b0not to scale a, b, p and q are points on the circumference of a circle, centre o. ab is a diameter. taw is a tangent to the circle at a. aq = qb and angle pat = 38\u00b0. (a) find the size of (i) angle apb, answer(a)(i) [1] (ii) angle pba, answer(a)(ii) [1] (iii) angle baq . answer(a)(iii) [1] (b) use answers from part (a) to explain why the lines pb and aq are not parallel. [1] ", "16": "16 \u00a9 ucles 2010 0607/03/m/j/10 for examiner's use 12 the table shows information about the heights of 120 flowers. height (h cm) 0 y h i 10 10 y h i 20 20 y h i 30 30 y h i 40 frequency 19 37 47 17 (a) calculate the percentage of the flowers with a height of less than 10 cm. answer(a) % [2] (b) find the fraction of the flowers with a height of at least 20 cm. give your answer in its lowest terms. answer(b) [2] (c) calculate an estimate of the mean height of the flowers. answer(c) cm [2] (d) (i) complete the cumulative frequency table. height (h cm) h i 10 h i 20 h i 30 h i 40 cumulative frequency 19 120 [2] ", "17": "17 \u00a9 ucles 2010 0607/03/m/j/10 for examiner's use (ii) 120 100 80604020 010 20 30 40cumulative frequency height (cm) on the grid, draw the cumulative frequency curve from the information in your table in part (d)(i) . the points (0, 0) and (10, 19) have been plotted for you. [3] (iii) use your cumulative frequency curve to find the median height. answer(d)(iii) cm [1] ", "18": "18 \u00a9 ucles 2010 0607/03/m/j/10 blank page ", "19": "19 \u00a9 ucles 2010 0607/03/m/j/10 blank page ", "20": "20 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders , but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2010 0607/03/m/j/10 blank page " }, "0607_s10_qp_4.pdf": { "1": " this document consists of 18 printed pages and 2 blank pages. ib10 06_0607_04/2rp \u00a9 ucles 2010 [turn over *6828773900* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/04 paper 4 (extended) may/june 2010 2 hours 15 minutes candidates answer on the question paper additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120. ", "2": "2 \u00a9 ucles 2010 0607/04/m/j/10 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2010 0607/04/m/j/10 [turn over for examiner's use answer all the questions. 1 (a) samia buys 8 kg of oranges, which cost $1.55 per kilogram. she pays with a $20 note. calculate how much change she receives. answer(a) $ [2] (b) $1.55 per kilogram is $0.05 more than the cost per kilogram last year. calculate the percentage increase on last year\u2019s cost per kilogram. answer(b) % [2] (c) the cost of melons is $0.84 per kilogram. this is an increase of 12% on last year\u2019s cost per kilogram. calculate last year\u2019s cost per kilogram. answer(c) $ [2] (d) the cost of bananas is $0.75 per kilogram. the cost increases by 6% each year. how many complete years will it take for the cost to become greater than $1 per kilogram? answer(d) [3] ", "4": "4 \u00a9 ucles 2010 0607/04/m/j/10 for examiner's use 2 (a) show clearly that (x2 \u2013 x + 1)(x + 1) = x3 + 1 [2] (b) show that x 2 \u2013 x + 1 = 0 has no solutions. [3] (c) f(x) = x 3 + 1 (i) find f(2). answer(c)(i) [1] (ii) find f(\u20131). answer(c)(ii) [1] (iii) find f \u20131(x). answer(c)(iii) f \u22121(x) = [3] (iv) solve the equation f \u20131(x) = 3 . answer(c)(iv) x = [1] ", "5": "5 \u00a9 ucles 2010 0607/04/m/j/10 [turn over for examiner's use 3 u = { x | 0 i x y 12, x \u2208 w} a = {multiples of 3} b = {factors of 30} c = { x=| 6 y x y 11, x \u2208 w } (a) list the elements of the sets. a = { } b = { } c = { } [3] (b) u ab c put the 12 elements of u in the correct regions of the venn diagram. [2] (c) complete the following statements. (i) a \u2229 b = { } [1] (ii) a \u222a c = { } [1] (iii) (a \u222a c ) \u2229 b = { } [1] (iv) b ' = { } [1] (v) n (a \u2229 b \u2229 c ) ' = [1] ", "6": "6 \u00a9 ucles 2010 0607/04/m/j/10 for examiner's use 4 the masses of 100 bags of flour are given in the table. mass (m grams) frequency 980ymi 990 4 990ymi 1000 10 1000ymi 1005 50 1005ymi 1010 20 1010ymi 1020 8 1020ymi 1040 8 (a) calculate an estimate of the mean mass of a bag of flour, correct to the nearest gram. answer(a) g [3] (b) (i) complete the frequency density column in this table. mass (m grams) frequency frequency density 980ymi 990 4 990ymi 1000 10 1000ymi 1005 50 1005ymi 1010 20 1010ymi 1020 8 1020ymi 1040 8 [3] (ii) on the grid opposite, draw an accurate histogram to show this information. ", "7": "7 \u00a9 ucles 2010 0607/04/m/j/10 [turn over for examiner's use 10 9 87654321 980 990 1000 1010 1020 1030 1040 mass (grams)frequency density m 0 [4] ", "8": "8 \u00a9 ucles 2010 0607/04/m/j/10 for examiner's use 5 (a) on the axes, sketch the graph of y = f( x) where f(x) = 21. (2 3 )xx\u2212\u2212 [3] (b) write down the equations of the three asymptotes. answer(b) , , [3] (c) write down the co-ordinates of the local maximum point. answer(c) ( , ) [2] (d) write down the domain and range of f( x). answer(d) domain range [4] (e) how many solutions are there to these equations? (i) f(x) = 0.5 answer(e)(i) [1] (ii) |f(x)| = 0.5 answer(e)(ii) [1] 3 21 \u20131\u20132\u20133 \u20133\u2013 2\u2013 1 1 2 3 4 50y x", "9": "9 \u00a9 ucles 2010 0607/04/m/j/10 [turn over for examiner's use 6 (a) a car uses fuel at a rate of 5.6 litres per 100 km. calculate the distance travelled when the car has used 14 litres of fuel. answer(a) km [2] (b) the car passes a post at a speed of 72 km/h. (i) change 72 km/h into m/s. answer(b)(i) m/s [2] (ii) the car has a length of 4.5 metres. calculate, in seconds, the time the car takes to pass the post completely. answer(b)(ii) s [2] ", "10": "10 \u00a9 ucles 2010 0607/04/m/j/10 for examiner's use 7 (a) one day zak sold some books at $5 each. he received a total of $ x. write down, in terms of x, the number of books he sold. answer(a) [1] (b) the next day zak reduced the price of each book to $4. he received $13 more than on the first day. (i) write down, in terms of x, the number of books he sold on this day. answer(b)(i) [1] (ii) he sold a total of 46 books during the 2 days. write down an equation in x to show this information. answer(b)(ii) [1] (iii) solve your equation. answer(b)(iii) x = [3] (c) calculate the mean price of a book during these two days. give your answer correct to 2 decimal places. answer(c) $ [2] ", "11": "11 \u00a9 ucles 2010 0607/04/m/j/10 [turn over for examiner's use 8 a student investigates the monthly rainfall ( r) and the monthly temperature ( t) of ten cities. monthly rainfall ( r mm) 1 3 4 5 8 10 13 15 17 20 monthly temperature ( t\u00b0 c) 2 6 9 3 11 16 15 20 25 23 (a) without doing any calculations, underline the word tha t best describes the correlation between rainfall and temperature. none negative positive [1] (b) find (i) the mean rainfall, answer(b)(i) mm [1] (ii) the interquartile range of the rainfall. answer(b)(ii) mm [1] (c) find the equation of the linear regression line, giving t in terms of r. answer(c) t = [2] ", "12": "12 \u00a9 ucles 2010 0607/04/m/j/10 for examiner's use 9 8.6\u00b058.3\u00b082.5\u00b0t d a k770 km1410 km 180 kmnot to scale the diagram shows the cities of amman ( a), damascus ( d), tehran (t) and kuwait (k). ad =180 km, dt = 1410 km and tk = 770 km. angle adk = 82.5\u00b0, angle akd = 8.6\u00b0 and angle dtk = 58.3\u00b0. (a) use the sine rule in triangle adk to calculate the distance ak. answer(a) km [3] (b) use the cosine rule in triangle dkt to calculate the distance dk. answer(b) km [3] ", "13": "13 \u00a9 ucles 2010 0607/04/m/j/10 [turn over for examiner's use (c) calculate the area of the quadrilateral adtk. answer(c) km2 [3] (d) calculate the distance at. answer(d) km [5] (e) a map is drawn to a scale of 1: 5 000 000. calculate the length of dt on the map, in centimetres. answer(e) cm [2] ", "14": "14 \u00a9 ucles 2010 0607/04/m/j/10 for examiner's use 10 not to scale d a b c 4 cm3 cm 8 cm 1.5 cm the diagram shows a gold bar of length 8 cm. the cross-section of the bar, abcd, is an isosceles trapezium. ab = 4 cm, dc = 3 cm and these parallel edges are 1.5 cm apart. (a) write down the mathematical name for this solid. [1] (b) (i) calculate the area of the trapezium. answer(b)(i) cm2 [2] (ii) one cubic centimetre of gold has a mass of 19.3 g. calculate the mass of the gold bar. answer(b)(ii) g [3] ", "15": "15 \u00a9 ucles 2010 0607/04/m/j/10 [turn over for examiner's use (iii) calculate the total surface area of the gold bar. answer(b)(iii) cm2 [4] (c) a box can hold a maximum of 20 kg. find the largest number of gold bars that can be put in the box. answer(c) [3] ", "16": "16 \u00a9 ucles 2010 0607/04/m/j/10 for examiner's use 11 a school bus picks up students at the town centre and takes them to the school. on any day the probability that the bus is on time at the town centre is 5 6. (a) write down the probability that the bus is not on time at the town centre. answer(a) [1] (b) if the bus is on time at the town centre, the probability that it is on time at the school is 7 8. if the bus is not on time at the town centre then the probability that it is on time at the school is 1 4. (i) draw a tree diagram and write the correct probability against each branch. [4] ", "17": "17 \u00a9 ucles 2010 0607/04/m/j/10 [turn over for examiner's use (ii) calculate the probability that the bus is on time at the school. answer(b)(ii) [3] (iii) calculate the probability that the bus is never on time at the school in a week of 5 school days. give your answer as a decimal, correct to 2 significant figures. answer(b)(iii) [2] (iv) there are 192 days in this school\u2019s year. on how many days is the bus expected to be on time at the school? answer(b)(iv) [1] ", "18": "18 \u00a9 ucles 2010 0607/04/m/j/10 for examiner's use 12 find the next term and the nth term in each of the sequences. (a) 6, 12, 24, 48, 96, \u2026\u2026\u2026 answer(a) next term = [1] nth term = [2] (b) \u20131, 0, 3, 8, 15, \u2026\u2026\u2026 answer(b) next term = [1] nth term = [3] ", "19": "19 \u00a9 ucles 2010 0607/04/m/j/10 blank page ", "20": "20 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2010 0607/04/m/j/10 blank page " }, "0607_s10_qp_5.pdf": { "1": " this document consists of 4 printed pages. ib10 06_0607_05/5rp \u00a9 ucles 2010 [turn over *8483854260**8483854260* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/05 paper 5 (core) may/june 2010 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of the marks for this paper is 24. ", "2": "2 \u00a9 ucles 2010 0607/05/m/j/10 for examiner's use answer all questions. investigation fermat\u2019s little theorem the division 46 \u00f7 5 gives 9 with a remainder of 1. a method for finding the remainder is 46 \u00f7 5 = 9.2 because 9 \u00d7 5 = 45, the remainder is 46 \u2013 45 = 1. the division 921 \u00f7 7 gives a remainder of 4. a method for finding the remainder is 921 \u00f7 7 =131.571\u2026.. because 131 \u00d7 7 = 917, the remainder is 921 \u2013 917 = 4. the division 2 11 \u00f7 13 gives a remainder of 7. a method for finding the remainder is 211 \u00f7 13 = 157.5384\u2026.. because 157 \u00d7 13 = 2041, the remainder is 211 \u2013 2041 = 7. note: to calculate the value of 25 either use the appropriate calculator key or use 25 = 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2. the value of 25 is 32. 1 find the remainder in these divisions. (a) 57 \u00f7 6 (b) 579 \u00f7 13 (c) 25 \u00f7 7 (d) 29 \u00f7 17 ", "3": "3 \u00a9 ucles 2010 0607/05/m/j/10 [turn over for examiner's use 2 in 1640 the french mathematician fermat found something interesting about the remainder when dividing by a prime number. some of his results are shown in the table below. prime division remainder division remainder division remainder 3 22 \u00f7 3 5 24 \u00f7 5 34 \u00f7 5 44 \u00f7 5 7 26 \u00f7 7 1 36 \u00f7 7 46 \u00f7 7 11 210 \u00f7 11 310 \u00f7 11 410 \u00f7 11 1 212 \u00f7 13 complete the unshaded boxes in this table. you may use the space below to show any working. 3 use the patterns you have found in your table to complete the following statements. (a) 712 \u00f7 has a remainder of . (b) 316 \u00f7 has a remainder of . 4 from the table 26 \u00f7 7 has a remainder of 1. this means that 26 \u2013 1 will divide by 7 exactly. so 26 \u2013 1 has a prime factor of 7. (a) complete the following statements to show why 712 \u2013 1 has a prime factor of 13. has a remainder of 1. this means that will divide by exactly. so 7 12 \u2013 1 has a prime factor of 13. (b) write down a prime factor of 316 \u2013 1. the investigation continues on the next page.", "4": "4 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. 0607/05/m/j/10 for examiner's use 5 complete the general statement below. a p-1 \u2013 1 has a prime factor of . this is called fermat\u2019s little theorem. 6 when p > 25 and a = 3, write down a statement using fermat\u2019s little theorem. 7 write down a prime factor, other than 3, of 4 194 303. [2 22 = 4 194 304] " }, "0607_s10_qp_6.pdf": { "1": " this document consists of 7 printed pages and 1 blank page. ib10 06_0607_06/5rp \u00a9 ucles 2010 [turn over *0661845285**0661845285* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/06 paper 6 (extended) may/june 2010 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. answer both parts a and b. you are advised to spend 45 minutes on part a and 45 minutes on part b. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of the marks for this paper is 40. ", "2": "2 \u00a9 ucles 2010 0607/06/m/j/10 for examiner's use answer both parts a and b. a. investigation fermat\u2019s little theorem (20 marks) you are advised to spend 45 minutes on part a. the division 46 \u00f7 5 gives 9 with a remainder of 1. a method for finding the remainder is 46 \u00f7 5 = 9.2 because 9 \u00d7 5 = 45, the remainder is 46 \u2013 45 = 1. the division 921 \u00f7 7 gives a remainder of 4. a method for finding the remainder is 921 \u00f7 7 = 131.571\u2026. because 131 \u00d7 7 = 917, the remainder is 921 \u2013 917 = 4. the division 2 11 \u00f7 13 gives a remainder of 7. a method for finding the remainder is 211 \u00f7 13 = 157.5384\u2026. because 157 \u00d7 13 = 2041, the remainder is 211 \u2013 2041 = 7. 1 find the remainder in these divisions. (a) 1234 \u00f7 7 (b) 29 \u00f7 9 ", "3": "3 \u00a9 ucles 2010 0607/06/m/j/10 [turn over for examiner's use 2 in 1640 the french mathematician fermat found something interesting about the remainder when dividing by a prime number. some of his results are shown in the table below. prime division remainder division remainder division remainder 3 23 \u00f7 3 5 25 \u00f7 5 35 \u00f7 5 45 \u00f7 5 7 27 \u00f7 7 2 37 \u00f7 7 47 \u00f7 7 11 211 \u00f7 11 complete the unshaded boxes in this table. you may use the space below to show any working. 3 use the patterns you have found in your table to complete the following statements. (a) 7 11 \u00f7 has a remainder of . (b) 817 \u00f7 has a remainder of . 4 from the table 27 \u00f7 7 has a remainder of 2. so 27 \u2013 2 has a prime factor of 7. because 27 \u2013 2 = 2(26 \u2013 1) and 7 is not a factor of 2, 26 \u2013 1 has a prime factor of 7. (a) complete the following statements to show why 5 12 \u2013 1 has a prime factor of 13. has a remainder of 5. so 513 \u2013 5 has a prime factor of . because 513 \u2013 5 = and is not a factor of 5, 512 \u2013 1 has a prime factor of 13. (b) write down a prime factor of 816 \u2013 1. part a continues on page 4.", "4": "4 \u00a9 ucles 2010 0607/06/m/j/10 for examiner's use 5 complete the general statement below. a p-1 \u2013 1 has a prime factor of . this is known as fermat\u2019s little theorem. 6 fermat noted that p must not be a factor of a. give an example to show the result is not true when p is a factor of a. 7 by writing 7 24 \u2013 1 in different ways, you can use fermat\u2019s little theorem to find prime factors. examples: 7 24 \u2013 1 = ( )1247 \u2013 1 = ( )21247\u2212 \u2013 1 using fermat\u2019s little theorem with p = 2, 724 \u2013 1 has a prime factor of 2. 7 24 \u2013 1 = ()387 \u2013 1 = ()4187\u2212 \u2013 1 fermat\u2019s little theorem with p = 4 cannot be used because 4 is not a prime number. use the above method to find as many prime factors as you can of 7 24 \u2013 1. remember: p must not be a factor of a. show all your working. ", "5": "5 \u00a9 ucles 2010 0607/06/m/j/10 [turn over for examiner's use blank page part b starts on page 6.", "6": "6 \u00a9 ucles 2010 0607/06/m/j/10 for examiner's use b. modelling change of average speed (20 marks) you are advised to spend 45 minutes on part b. sam makes a journey in two stages. in stage 1, he cycles at 10 km/h for one hour. in stage 2, he cycles at 20 km/h. 1 in stage 2, sam cycles for 30 minutes. (a) find the total distance he travels. km (b) show that his average speed for the whole journey is 13.3 km/h. 2 if, in stage 2, he cycles for 15 minutes, show that his average speed is now 12 km/h. 3 if, in stage 2, he cycles for 12 minutes, find his average speed. km/h 4 (a) in stage 2, sam cycles for x minutes. write down a formula for s, the average speed, in km/h. (b) your formula is a mathematical model for the average speed. show that it simplifies to s = 600 + 20 60 +x x. ", "7": "7 \u00a9 ucles 2010 0607/06/m/j/10 [turn over for examiner's use 5 use the model to find sam\u2019s average speed if, in stage 2, he cycles for 13 minutes. km/h 6 on the axes below, sketch the graph of s against x for 0 y x y 500. show any important details on your sketch. s x 00 500 7 find how many minutes sam must cycle in stage 2 to have an average speed of 13 km/h. min part b continues on page 8.", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2010 0607/06/m/j/10 for examiner's use 8 in stage 2, instead of 20 km/h, sam cycles at y km/h for x minutes. (a) modify the model in question 4(b) . (b) find y if, after 24 minutes in stage 2, sam\u2019s average speed is 8 km/h. y = (c) on the axes below sketch the graph of s against x if he stops for x minutes at the end of stage 1. s x 00 " }, "0607_w10_qp_1.pdf": { "1": " this document consists of 10 printed pages and 2 blank pages. ib10 11_0607_01/2rp \u00a9 ucles 2010 [turn over *5564235406* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/01 paper 1 (core) october/november 2010 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2010 0607/01/o/n/10 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2010 0607/01/o/n/10 [turn over for examiner's use answer all the questions. 1 (a) find the lowest common multiple of 6 and 9. answer(a) [1] (b) work out 5 2 \u2013 23. answer(b) [2] 2 (a) samir and josef divide $250 in the ratio 2 : 3. calculate how much money each receives. answer(a) samir $ josef $ [2] (b) a recipe for 3 people needs 600 g of pasta. work out how much pasta is needed for 8 people. answer(b) g [2] ", "4": "4 \u00a9 ucles 2010 0607/01/o/n/10 for examiner's use 3 p(2, 3) and q(4, 7) are two points. (a) find the gradient of the line joining p and q. answer(a) [2] (b) find the co-ordinates of the midpoint of the line joining p and q. answer(b) ( , ) [1] 4 60\u00b0 not to scale o a circle, centre o, has an area of 600 cm2. find the area of the shaded sector. answer cm2 [2] ", "5": "5 \u00a9 ucles 2010 0607/01/o/n/10 [turn over for examiner's use 5 the heights of a number of students were measured. the results are shown in the cumulative frequency diagram. 120 110 100 90 8070605040302010 0 155 150 160 165 170 175 180 185 190 height (cm)cumulative frequency (a) how many students were measured? answer(a) [1] (b) find the interquartile range. answer(b) cm [2] ", "6": "6 \u00a9 ucles 2010 0607/01/o/n/10 for examiner's use 6 diagram 1 diagram 2 diagram 3 diagram 4 (a) draw diagram 4 in this sequence. [1] (b) (i) write down, as a sequence, the number of dots in each diagram. answer(b)(i) , , , [1] (ii) write down the nth term of this sequence. answer(b)(ii) [1] 7 solve the simultaneous equations 2 x = y + 8 and 3 x + 2y = 5 . answer x = y = [4] ", "7": "7 \u00a9 ucles 2010 0607/01/o/n/10 [turn over for examiner's use 8 (a) bda 70\u00b0e cx\u00b0 not to scale in the diagram de is parallel to bc. ad = de and angle abc = 70\u00b0. find the value of x. answer(a) x = [2] (b) y\u00b020\u00b0 z\u00b0oq pnot to scale the diagram shows a circle, centre o, with a tangent drawn at p. angle oqp = 20\u00b0. find the values of y and z. answer(b) y = [1] z = [1] ", "8": "8 \u00a9 ucles 2010 0607/01/o/n/10 for examiner's use 9 (a) expand the brackets and simplify. 3(x \u2013 y) \u2013 2( x \u2013 5y ) answer(a) [2] (b) factorise completely. 3 x2 + 9xy2 answer(b) [2] (c) write as a single fraction. 2 35x x\u2212 answer(c) [2] ", "9": "9 \u00a9 ucles 2010 0607/01/o/n/10 [turn over for examiner's use 10 5 m5 m4 mnot to scale a cuboid has a square base of side 5 m and a height of 4 m. (a) calculate the volume of the cuboid. answer(a) m3 [1] (b) calculate the total surface area of the cuboid. answer(b) m2 [2] ", "10": "10 \u00a9 ucles 2010 0607/01/o/n/10 for examiner's use 11 student a b c d e f g h test 1 25 20 40 25 50 20 30 40 test 2 30 25 35 25 40 30 35 40 the table shows the marks scored by 8 students in two mathematics tests. the marks for students a to f are shown on the scatter diagram below. test 2 test 140 302010 10 20 30 40 500 (a) on the diagram, plot the marks for students g and h. [1] (b) the mean for test 1 is 31.25. calculate the mean for test 2. answer(b) [2] (c) plot the mean point on the scatter diagram. [1] (d) draw the line of best fit on the scatter diagram. [1] ", "11": "11 \u00a9 ucles 2010 0607/01/o/n/10 blank page ", "12": "12 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2010 0607/01/o/n/10 blank page " }, "0607_w10_qp_2.pdf": { "1": " this document consists of 10 printed pages and 2 blank pages. ib10 11_0607_02/2rp \u00a9 ucles 2010 [turn over *9648538625* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/02 paper 2 (extended) october/november 2010 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2010 0607/02/o/n/10 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2010 0607/02/o/n/10 [turn over for examiner's use answer all the questions. 1 (a) simplify 75. answer(a) [2] (b) find the value of log 101000. answer(b) [1] 2 factorise completely. 2 ac \u2013 5bc + 6a \u2013 15b answer [2] 3 the gradient of the line joining the points (2, 1) and (6, a) is 3 2. find the value of a. answer a = [3] ", "4": "4 \u00a9 ucles 2010 0607/02/o/n/10 for examiner's use 4 the cumulative frequency curve shows the heights of 200 plants measured correct to the nearest centimetre. 200 190180170160150140130120 110 100 908070605040302010 20 10 30 40 50 60 70 80 height (cm)cumulative frequency 0 (a) use the graph to find (i) the median, answer(a)(i) cm [1] (ii) the interquartile range. answer(a)(ii) cm [2] (b) find the percentage of plants with heights greater than 50 cm. answer(b) % [2] ", "5": "5 \u00a9 ucles 2010 0607/02/o/n/10 [turn over for examiner's use 5 a cuboid has a square base of side x cm and a height of y cm. find, in terms of x and y, (a) the volume of the cuboid, answer(a) cm3 [1] (b) the total surface area of the cuboid. answer(b) cm2 [2] 6 the distance between towns a and b is 50 km. the bearing of a from b is 210\u00b0. (a) sketch the positions of a and b showing clearly the angle of 210\u00b0. north [1] (b) calculate how far west a is from b. answer(b) km [2] ", "6": "6 \u00a9 ucles 2010 0607/02/o/n/10 for examiner's use 7 a = 3 2\u2212\uf8eb\uf8f6\uf8ec\uf8f7\uf8ed\uf8f8 b = 2 5\u2212\uf8eb\uf8f6\uf8ec\uf8f7\uf8ed\uf8f8 when 2a + kb = 2 16\u2212\uf8eb\uf8f6\uf8ec\uf8f7\uf8ed\uf8f8 find the value of k. answer [3] 8 f( x) = 2x \u2013 1 g(x) = 3x 2 + 1 find (a) g(2), answer(a) [1] (b) g(f(x)), answer(b) [2] (c) the inverse function f -1(x). answer(c) [2] ", "7": "7 \u00a9 ucles 2010 0607/02/o/n/10 [turn over for examiner's use 9 the table shows the marks ( x) gained by 100 students in an examination. mark (x) 0 y x i 10 10 y x i 20 20 y x i 40 40 y x i 45 45 y x i 60 frequency 20 10 10 30 30 use this information to draw a histogram on the grid below. 6 54321 010 20 30 40 50 60frequency density markx [3] ", "8": "8 \u00a9 ucles 2010 0607/02/o/n/10 for examiner's use 10 in hurghada the probability that the sun will shine on any day is 0.8. if the sun shines, the probability ahmed will go to the beach is 0.9. if the sun does not shine, the probability he will go to the beach is 0.5. (a) complete the tree diagram. 0.8 ..0.9 ..the sun shines the sun does not shinegoes to beach does not go to beach .. ..goes to beach does not go to beach [2] (b) find the probability that ahmed will go to the beach on a given day. answer(b) [2] ", "9": "9 \u00a9 ucles 2010 0607/02/o/n/10 [turn over for examiner's use 11 the diagram shows part of the graph of y = f(x), where f(x) = ax2 + bx \u2013 6. y x8 642 \u20132\u20134\u20136\u201380 \u20133 \u2013 2 \u2013 1 1234 find the values of a and b. answer a = b = [3] ", "10": "10 \u00a9 ucles 2010 0607/02/o/n/10 for examiner's use 12 which of the following functions are shown by the graphs below? in each case k > 1. write the correct letter under each graph. a y = k x b y = | x + k | c y = kx d y = | x \u2212 k | e y = k \u2212x f y = x k y x0 .. y x0 ..y x0 .. [3] ", "11": "11 \u00a9 ucles 2010 0607/02/o/n/10 blank page ", "12": "12 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2010 0607/02/o/n/10 blank page " }, "0607_w10_qp_3.pdf": { "1": " this document consists of 14 printed pages and 2 blank pages. ib10 11_0607_03/3rp \u00a9 ucles 2010 [turn over *9269295756* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/03 paper 3 (core) october/november 2010 1 hour 45 minutes candidates answer on the question paper additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96. ", "2": "2 \u00a9 ucles 2010 0607/03/o/n/10 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2010 0607/03/o/n/10 [turn over for examiner's use answer all the questions. 1 in 2008 the population of a city was 276 000. (a) write 276 000 in standard form. answer(a) [1] (b) 197 400 of the population were male. calculate the number of males in the population. answer(b) [2] (c) a year later the population of 276 000 had increased by 4 %. (i) calculate the new population. answer(c)(i) [2] (ii) write your answer to part (c)(i) correct to the nearest ten thousand. answer(c)(ii) [1] ", "4": "4 \u00a9 ucles 2010 0607/03/o/n/10 for examiner's use 2 20 students answered questions in a quiz. the number of correct answers for each student is shown in the table. 25 21 24 25 29 18 24 30 25 25 29 17 15 15 19 25 23 21 16 19 (a) (i) complete the stem-and-leaf plot to show this information. the numbers in the first row of the table above have been plotted. stem leaf 1 8 2 5 1 4 5 9 4 5 5 3 0 key 1 | 8 = 18 [2] (ii) complete the ordered stem-and-leaf plot. stem leaf 1 2 3 key 1 | 8 = 18 [1] (iii) use your stem-and-leaf plot in part(a)(ii) to find the median. answer(a)(iii) [1] ", "5": "5 \u00a9 ucles 2010 0607/03/o/n/10 [turn over for examiner's use (b) complete the bar chart, which has already been started for you. 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 306 543210number of students number of correct answers [3] (c) calculate the percentage of students who scored 29 correct answers. answer(c) % [2] ", "6": "6 \u00a9 ucles 2010 0607/03/o/n/10 for examiner's use 3 y x8 7654321 \u20131\u20132\u20133\u20134\u20135\u20136\u20137\u201380 \u20138 \u20137 \u20136 \u20135 \u20134 \u20133 \u20132 \u2013 1 12345678t v (a) on the grid, (i) draw the translation of triangle t by 4 2\uf8eb\uf8f6\uf8ec\uf8f7\uf8ed\uf8f8, [2] (ii) draw the reflection of triangle t in the y-axis, [2] (iii) draw the rotation of triangle t about (0, 0) through 180\u00b0. [2] (b) describe fully the single transformation that maps triangle t onto triangle v. [3] ", "7": "7 \u00a9 ucles 2010 0607/03/o/n/10 [turn over for examiner's use 4 farah takes 19 minutes to walk from home to school. the distance from her home to school is 850 metres. (a) she leaves home at 07 51. at what time does she arrive at school? answer(a) [1] (b) calculate her average speed in (i) metres per minute, answer(b)(i) m/min [2] (ii) kilometres per hour. answer(b)(ii) km/h [2] (c) each day, in a week of 5 school days, farah walks to and from school. calculate the total distance farah walks. give your answer in kilometres. answer(c) km [2] ", "8": "8 \u00a9 ucles 2010 0607/03/o/n/10 for examiner's use 5 09 \u20131\u2013 4 4y x f(x) = x2 g(x) = ( x \u2013 1)2 (a) sketch the graphs of y = f( x) and y = g( x) on the axes above. [4] (b) describe fully the single transformation that maps the graph of y = f( x) onto the graph of y = g(x). [2] (c) the graph of y = h(x) is a translation of the graph of y = f( x) by the vector 0 3\uf8eb\uf8f6\uf8ec\uf8f7\uf8ed\uf8f8. write down h(x) in terms of x. answer(c) h( x) = [2] ", "9": "9 \u00a9 ucles 2010 0607/03/o/n/10 [turn over for examiner's use 6 8 7654321 012345678y x (a) (i) on the grid, draw accurately the line y = 1 2x + 2, for 0 y x y 8. [2] (ii) p is the point where the line cuts the y-axis. q is the point on the line where x = 6. mark the points p and q on the grid. [2] (b) mark the point r (6, 2) on the grid and draw the triangle qpr . [1] (c) use trigonometry to calculate angle qpr . give your answer correct to 1 decimal place. answer(c) angle qpr = [3] ", "10": "10 \u00a9 ucles 2010 0607/03/o/n/10 for examiner's use 7 d e ac bxnot to scale 108\u00b0 the diagram shows a five-sided polygon abcde, with the side ab extended to x. (a) write down the geometrical name of the polygon abcde. answer(a) [1] (b) ae is parallel to bc and angle eab = 108\u00b0. write down the size of angle cbx. answer(b) [1] (c) calculate the sum of the five interior angles of the polygon abcde. answer(c) [2] (d) the angles bcd, cde and dea are equal. calculate the size of one of these angles. answer(d) [2] (e) (i) on the diagram, extend the sides cd and ae until they meet at f. [1] (ii) write down the special name of the quadrilateral abcf. answer(e)(ii) [1] (iii) calculate the size of angle dfe . answer(e)(iii) [2] (iv) write down the special name of the triangle def . answer(e)(iv) [1] ", "11": "11 \u00a9 ucles 2010 0607/03/o/n/10 [turn over for examiner's use 8 u pq gc dbe fa the venn diagram shows a universal set, u = { a, b, c, d, e, f, g}, and the sets p and q . (a) complete the following statements. (i) p = { } [1] (ii) = { b, c, d, g } [1] (iii) p\u2229q = { } [1] (iv) n(p\u222aq) = [1] (b) on the venn diagram, shade the region p \u2229q\u2032. [1] (c) an element is chosen at random from u. (i) write down the probability that the element is e. answer(c)(i) [1] (ii) write down the probability that the element is h. answer(c)(ii) [1] (d) an element is chosen at random from set p. write down the probability that the element is e. answer(d) [1] (e) 70 students are asked to choose a letter at random from u. how many students would you expect to choose a letter from set p? answer(e) [2] ", "12": "12 \u00a9 ucles 2010 0607/03/o/n/10 for examiner's use 9 fahran counted the number of steps it took each student to walk across the sports hall. the results for the 100 students are shown in the table. number of steps 18 19 20 21 22 23 24 frequency 3 7 9 11 20 31 19 (a) calculate the fraction of students who took 22 steps. give your answer in its lowest terms. answer(a) [2] (b) find (i) the range, answer(b)(i) [1] (ii) the mean, answer(b)(ii) [1] (iii) the median, answer(b)(iii) [1] (iv) the mode. answer(b)(iv) [1] (c) fahran planned to draw a pie chart to show his results. calculate the sector angle for the number of students who took 23 steps. do not draw the pie chart. answer(c) [2] ", "13": "13 \u00a9 ucles 2010 0607/03/o/n/10 [turn over for examiner's use 10 (a) 1 hectare (ha) = 10 000 m2 calculate the number of hectares in 1 km2. answer(a) [1] (b) ed abc0.4 km 0.8 km 1.2 km0.3 kmnot to scale the diagram shows a field abcde. calculate the area of the field (i) in km 2, answer(b)(i) km2 [3] (ii) in hectares. answer(b)(ii) ha [1] (c) (i) there is a fence around the field abcde. calculate the length of the fence. answer(c)(i) km [4] (ii) the cost of the fence is $450 per kilometre. calculate the total cost of the fence. answer(c)(ii) $ [1] ", "14": "14 \u00a9 ucles 2010 0607/03/o/n/10 for examiner's use 11 4 \u20134\u2013360y x f(x) = 2x x\u2212, x \u2260 2 (a) on the diagram, sketch the graph of y = 2x x\u2212. [3] (b) the graph has two asymptotes. write down the equation of each asymptote. answer(b) [2] (c) write down the range of f(x). answer(c) [2] (d) (i) on the same diagram, sketch the graph of y = 2x. [1] (ii) solve the equation 2x x\u2212 = 2x. answer(d)(ii) x = or x = [2] ", "15": "15 \u00a9 ucles 2010 0607/03/o/n/10 blank page", "16": "16 permission to reproduce items where t hird-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2010 0607/03/o/n/10 blank page " }, "0607_w10_qp_4.pdf": { "1": " this document consists of 18 printed pages and 2 blank pages. ib10 11_0607_04/3rp \u00a9 ucles 2010 [turn over *9202671358* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/04 paper 4 (extended) october/november 2010 2 hours 15 minutes candidates answer on the question paper additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120. ", "2": "2 \u00a9 ucles 2010 0607/04/o/n/10 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2010 0607/04/o/n/10 [turn over for examiner's use answer all the questions. 1 a train from picton to christchurch leaves picton at 13 00. the length of the journey is 340 km. (a) the train arrives at christchurch at 18 21. show that the average speed is 63.55 km/h, correct to 2 decimal places. [4] (b) one day the weather is bad and the average speed of 63.55 km/h is reduced by 15 %. (i) calculate the new average speed. answer(b)(i) km/h [2] (ii) calculate the new time of arrival at christchurch. give your answer to the nearest minute. answer(b)(ii) [3] ", "4": "4 \u00a9 ucles 2010 0607/04/o/n/10 for examiner's use 2 (a) (i) find the value of 27 \u00d7 36. answer(a)(i) [1] (ii) write your answer to part (i) in standard form. answer(a)(ii) [1] (b) find the value of ()31 22, giving your answer in standard form. answer(b) [2] (c) m5 = 2000. find the value of m. answer(c) [1] (d) 5 n = 2000. find the value of n. answer(d) [2] ", "5": "5 \u00a9 ucles 2010 0607/04/o/n/10 [turn over for examiner's use 3 (a) solve the equation x2 + 2x \u2013 4 = 0. give your answers correct to 2 decimal places. answer(a) x = or x = [3] (b) solve the inequality x2 + 2x \u2013 4 y 0. answer(b) [2] ", "6": "6 \u00a9 ucles 2010 0607/04/o/n/10 for examiner's use 4 05 5y x (a) on the diagram above, sketch the lines (i) x + y = 5, [1] (ii) y = 1, [1] (iii) y = 2x. [1] (b) write r in the region where x [ 0, y [ 1, y [ 2x and x + y y 5. [1] ", "7": "7 \u00a9 ucles 2010 0607/04/o/n/10 [turn over for examiner's use 5 the numbers of passengers in 72 taxis arriving at a city centre were recorded. the table shows the results. number of passengers 1 2 3 4 5 6 frequency 7 27 19 8 9 2 (a) find (i) the range, answer(a)(i) [1] (ii) the mode, answer(a)(ii) [1] (iii) the median, answer(a)(iii) [1] (iv) the mean, answer(a)(iv) [1] (v) the upper quartile. answer(a)(v) [1] (b) the probability that a taxi, chosen at random, had n passengers is 3 8. find the value of n. answer(b) [2] (c) (i) a taxi was chosen at random. calculate the probability that it had 5 passengers. give your answer as a fraction, in its lowest terms. answer(c)(i) [2] (ii) later, when 360 taxis have arrived at the city centre, how many would be expected to have 5 passengers? answer(c)(ii) [1] ", "8": "8 \u00a9 ucles 2010 0607/04/o/n/10 for examiner's use 6 (a) potatoes cost $ t per kilogram and carrots cost $(3 t \u2013 1) per kilogram. the total cost of 20 kg of potatoes and 8 kg of carrots is $42.60. find the value t. answer(a) [3] (b) peas cost $ y per kilogram and beans cost $( y + 2) per kilogram. anna spends $15 on peas and $9 on beans. the total mass of the peas and the beans is 8 kg. (i) write an equation in terms of y and show that it simplifies to 4 y2 \u2013 4y \u2013 15 = 0. [4] (ii) factorise the expression 4 y 2 \u2013 4y \u2013 15. answer(b)(ii) [2] (iii) find the cost of 1 kg of peas. answer(b)(iii) $ [1] ", "9": "9 \u00a9 ucles 2010 0607/04/o/n/10 [turn over for examiner's use 7 f(x) = sinx\u00b0 g(x) = 2sin x\u00b0 h(x) = 3sin(4 x)\u00b0 k(x) = sin( x + 60)\u00b0 (a) write down the domain of f(x). answer(a) [1] (b) write down the amplitude and period of h( x). answer(b) amplitude = period = [2] (c) describe fully a single transformation that maps the graph of y = f( x) onto the graph of (i) y = g(x), [3] (ii) y = k(x). [2] ", "10": "10 \u00a9 ucles 2010 0607/04/o/n/10 for examiner's use 8 u ty x6 54321 \u20131\u20132\u20133\u20134\u20135\u201360 \u20136 \u20135 \u20134 \u20133 \u20132 \u2013 1 123456 (a) on the grid, (i) draw the translation of triangle t by ()6 3\u2212, [2] (ii) draw the reflection of triangle t in the line y = \u2013 x. [2] (b) describe fully the single transformation that maps triangle t onto triangle u. [3] (c) write down the inverse of the transformation in part (a)(i) . [2] ", "11": "11 \u00a9 ucles 2010 0607/04/o/n/10 [turn over for examiner's use 9 u a b c u = {prime numbers less than 20} a = {factors of 12} b = {factors of 70} c = {factors of 91} (a) list the 8 elements of set u. (1 is not a prime number.) answer(a) { } [1] (b) write all the elements of u in the correct parts of the venn diagram above. [3] (c) list the elements of ( b \u222ac)'. answer(c) { } [1] (d) write down the value of n((b \u222ac)\u2229a' ). answer(d ) [1] (e) on the venn diagram, shade the region b\u2229a'\u2229c '. [1] ", "12": "12 \u00a9 ucles 2010 0607/04/o/n/10 for examiner's use 10 (a) a b x dcnot to scale a , b, c and d lie on a circle. ac and bd intersect at x. (i) explain why triangles abx and dcx are similar. [3] (ii) bx = 2 cm, cx = 4 cm and the area of triangle abx is 4.5 cm2. calculate the area of triangle dcx. answer(a)(ii) cm2 [2] ", "13": "13 \u00a9 ucles 2010 0607/04/o/n/10 [turn over for examiner's use (b) 50\u00b032\u00b0s pyr q8 cmnot to scale pqrs is a cyclic quadrilateral. angle rsq = 32\u00b0 and angle prq = 50\u00b0. (i) find angle psq. answer(b)(i) [1] (ii) calculate angle pqr . answer(b)(ii) [2] (iii) pr and qs intersect at right angles at y and qr = 8 cm. calculate the length of ry. answer(b)(iii) cm [2] (iv) write down the size of the radius of the circle that can be drawn through q, r and y. answer(b)(iv) cm [1] ", "14": "14 \u00a9 ucles 2010 0607/04/o/n/10 for examiner's use 11 during one week a caf\u00e9 records the number of hot drinks ( x) and cold drinks ( y) it sells each day. the table shows the results. day mon tues wed thurs fri sat sun number of hot drinks (x ) 55 29 40 45 65 80 60 number of cold drinks (y) 30 46 35 27 20 15 25 (a) complete the scatter diagram by plotting the points for friday, saturday and sunday. the first four points have been plotted for you. 60 5040302010 010 20 30 40 50 60 70 80y x number of hot drinksnumber of cold drinks [2] (b) describe any correlation between x and y. [1] (c) (i) find the equation of the line of regression, giving y in terms of x. answer(c)(i) y = [2] (ii) 50 hot drinks are sold on one day in the following week. how many cold drinks would you expect to be sold on this day? answer(c)(ii) [2] ", "15": "15 \u00a9 ucles 2010 0607/04/o/n/10 [turn over for examiner's use 12 in triangle abc, ab = 10 cm, bc = 6 cm and angle bac = 30\u00b0. (a) calculate the sine of angle acb. give your answer correct to 4 decimal places. answer(a) [3] (b) to draw triangle abc accurately, the line ab and an angle 30\u00b0 have been drawn. a b30\u00b0 (i) on the diagram, mark the two possible positions of c, so that bc = 6 cm. label them c 1 and c 2. [2] (ii) use your answer to part (a) to calculate the sizes of angle ac 1b and angle ac 2b. give your answers correct to 1 decimal place. answer(b)(ii) angle ac 1b = angle ac 2b = [2] (iii) calculate the size of angle c 1bc 2. answer(b)(iii) angle c1bc 2= [1] ", "16": "16 \u00a9 ucles 2010 0607/04/o/n/10 for examiner's use 13 10 cm3 m25 cm po qa bnot to scale the diagram shows a water trough in the shape of a prism. the cross-section is a semicircle, centre o, radius 25 cm. the length of the trough is 3 metres . (a) calculate the area of the semicircle. answer(a) cm2 [2] (b) calculate the volume of the trough, giving your answer in cm 3. answer(b) cm3 [2] ", "17": "17 \u00a9 ucles 2010 0607/04/o/n/10 [turn over for examiner's use (c) the diagram also shows water in the trough. the depth pq is 10 cm. ab is horizontal and opq is vertical. (i) calculate angle aob . answer(c)(i) [3] (ii) calculate the area of triangle aob . answer(c)(ii) cm2 [2] (iii) calculate the area of the sector aob . answer(c)(iii) cm2 [2] (iv) calculate the shaded area apbq . answer(c)(iv) cm2 [1] (v) calculate the volume of water in the trough. give your answer in litres. answer(c)(v) litres [2] ", "18": "18 \u00a9 ucles 2010 0607/04/o/n/10 for examiner's use 14 20 \u2013201.5 \u20130.50y x f(x) = 2 21 26x xx+ ++ (a) on the axes above, sketch the graph of y = f( x) for \u201320 y x y 20. (note that \u20130.5 y y y 1.5) [3] (b) find the co-ordinates of the local maximum point. answer(b) ( , ) [2] (c) find the range of f( x). answer(c) [3] (d) the graph has one asymptote. write down the equation of this asymptote. answer(d) [1] (e) solve the equation 2 215 26 5xx xx++= ++ . answer(e) x = [2] ", "19": "19 \u00a9 ucles 2010 0607/04/o/n/10 blank page ", "20": "20 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2010 0607/04/o/n/10 blank page " }, "0607_w10_qp_5.pdf": { "1": " this document consists of 6 printed pages and 2 blank pages. ib10 11_0607_05/3rp \u00a9 ucles 2010 [turn over *3620551787* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/05 paper 5 (core) october/november 2010 1 hour candidates answer on the question paper additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24. ", "2": "2 \u00a9 ucles 2010 0607/05/o/n/10 for examiner's use answer all questions. investigation the fibonacci sequence the fibonacci sequence is a sequence of numbers that is found in many real-life situations. the fibonacci sequence begins 1 1 2 3 5 \u2026\u2026. where, apart from the first two terms, each term is the sum of the previous two terms. for example 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5 and so on. 1 complete the table for the first 15 fibonacci numbers. you must show your working. term position 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 fibonacci number 1 1 2 3 5 8 13 21 34 55 89 144 233 ", "3": "3 \u00a9 ucles 2010 0607/05/o/n/10 [turn over for examiner's use 2 (a) the table shows fibonacci numbers that are multiples of 2. complete the table. term position 3 9 fibonacci number 2 8 notice that: 2 is the third term in the fibonacci sequence, 8 is the sixth term in the fibonacci sequence, and so on. every third term in the fibonacci sequence is a multiple of 2 . (b) the next two tables show other patterns. complete the tables and the statements that follow. (i) term position 4 8 12 fibonacci number 3 3 is the term in the fibonacci sequence. every term in the fibonacci sequence is a multiple of 3. (ii) term position 20 fibonacci number 5 55 6 765 5 is the term in the fibonacci sequence. every term in the fibonacci sequence is a multiple of . (c) complete the following statement. every term in the fibonacci sequence is a multiple of 8. ", "4": "4 \u00a9 ucles 2010 0607/05/o/n/10 for examiner's use 3 a golden rectangle is a rectangle with width and length that are consecutive fibonacci numbers. 2 3 5 etc.35 8 when a golden rectangle is divided into the least number of squares, the length of the side of each square is a fibonacci number. 3 21 11 the diagram above shows the 2 by 3 golden rectangle. the least number of squares it can be divided into is three. these squares have sides 1, 1 and 2. 5 3 the diagram above shows the 3 by 5 golden rectangle. the least number of squares it can be divided into is four. these squares have sides 1, 1, 2 and 3. ", "5": "5 \u00a9 ucles 2010 0607/05/o/n/10 [turn over for examiner's use (a) on the grid below, draw the 5 by 8 golden rectangle. show how this can be divided into the least number of squares. these squares have sides 1, 1, 2, 3 and 5. (b) on the grid below, draw the 8 by 13 golden rectangle. show how this can be divided into the least number of squares. ", "6": "6 \u00a9 ucles 2010 0607/05/o/n/10 for examiner's use (c) (i) complete the table to show the least number of squares in each of the first six golden rectangles. size of rectangle 1 by 1 1 by 2 2 by 3 3 by 5 5 by 8 8 by 13 least number of squares 1 4 (ii) write down the least number of squares there are in the 21 by 34 golden rectangle. (iii) when the least number of squares is 11, write down the width and the length of this golden rectangle. and (d) when the width and the length of a golden rectangle are the ( no1)th and the nth terms of the fibonacci sequence, write down the least number of squares in terms of n. ", "7": "7 \u00a9 ucles 2010 0607/05/o/n/10 blank page ", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2010 0607/05/o/n/10 blank page " }, "0607_w10_qp_6.pdf": { "1": " this document consists of 10 printed pages and 2 blank pages. ib10 11_0607_06/4rp \u00a9 ucles 2010 [turn over *6357012477* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/06 paper 6 (extended) october/november 2010 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. answer both parts a and b. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2010 0607/06/o/n/10 for examiner's use answer both parts a and b. a investigation the fibonacci sequence 24 marks you are advised to spend no more than 55 minutes on this part. the fibonacci sequence is a sequence of numbers that is found in many real-life situations. the fibonacci sequence begins 1 1 2 3 5 \u2026\u2026. where, apart from the first two terms, each term is the sum of the previous two terms. for example 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5 and so on. 1 complete the table for the first 15 fibonacci numbers. you must show your working. term position 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 fibonacci number 1 1 2 3 5 8 13 21 34 55 89 144 233 ", "3": "3 \u00a9 ucles 2010 0607/06/o/n/10 [turn over for examiner's use 2 (a) the table shows fibonacci numbers that are multiples of 2. complete the table. term position 3 9 fibonacci number 2 8 notice that: 2 is the third term in the fibonacci sequence, 8 is the sixth term in the fibonacci sequence, and so on. every third term in the fibonacci sequence is a multiple of 2 . (b) the next two tables show other patterns. complete the tables and the statements that follow. (i) term position 4 8 12 fibonacci number 3 3 is the term in the fibonacci sequence. every term in the fibonacci sequence is a multiple of 3. (ii) term position 20 fibonacci number 5 55 6 765 5 is the term in the fibonacci sequence. every term in the fibonacci sequence is a multiple of . (c) complete the following statement. every term in the fibonacci sequence is a multiple of 8. ", "4": "4 \u00a9 ucles 2010 0607/06/o/n/10 for examiner's use 3 a golden rectangle is a rectangle with width and length that are consecutive fibonacci numbers. 2 3 5 etc.35 8 when a golden rectangle is divided into the least number of squares, the length of the side of each square is a fibonacci number. 3 21 11 the diagram above shows the 2 by 3 golden rectangle. the least number of squares it can be divided into is three. these squares have sides 1, 1 and 2. 5 3 the diagram above shows the 3 by 5 golden rectangle. the least number of squares it can be divided into is four. these squares have sides 1, 1, 2 and 3. ", "5": "5 \u00a9 ucles 2010 0607/06/o/n/10 [turn over for examiner's use (a) on the grid below, draw the 5 by 8 golden rectangle. show how this can be divided into the least number of squares. these squares have sides 1, 1, 2, 3 and 5. (b) on the grid below, draw the 8 by 13 golden rectangle. show how this can be divided into the least number of squares. ", "6": "6 \u00a9 ucles 2010 0607/06/o/n/10 for examiner's use (c) (i) complete the table to show the least number of squares in each of the first six golden rectangles. size of rectangle 1 by 1 1 by 2 2 by 3 3 by 5 5 by 8 8 by 13 least number of squares 1 4 (ii) write down the least number of squares there are in the 21 by 34 golden rectangle. (iii) when the least number of squares is 11, write down the width and the length of this golden rectangle. and (d) when the width and the length of a golden rectangle are the ( no1)th and the nth terms of the fibonacci sequence, write down the least number of squares in terms of n. ", "7": "7 \u00a9 ucles 2010 0607/06/o/n/10 [turn over for examiner's use (e) in this part, numbers that are two positions apart in the fibonacci sequence are used for the width and length of a rectangle. for example, 1 by 2, 1 by 3, 2 by 5, 3 by 8 and so on. 112358 . . .1 fibonacci numberterm position 23456 . . . write down, in words, the connection between the term positions of the two fibonacci numbers used for the width and length of a rectangle and the least number of squares in the rectangle. ", "8": "8 \u00a9 ucles 2010 0607/06/o/n/10 for examiner's use b modelling the solar system 16 marks you are advised to spend no more than 35 minutes on this part. logarithms to base 10 are written as log. 1 the table below shows information about seven planets in the solar system. planet distance from the sun ( s km) time to orbit the sun ( t days) log s log t mercury 5.79 x 107 88 7.8 1.9 venus 1.08 x 108 225 8.0 2.4 earth 1.50 x 108 365 8.2 2.6 mars 2.28 x 108 687 jupiter 7.78 x 108 4 330 saturn 1.43 x 109 10 800 pluto 5.91 x 109 90 800 9.8 5.0 complete the table of values for log s and log t. give each value correct to 2 significant figures. 2 (a) on the grid opposite, plot the seven points (log s, log t). (b) plot the mean point (8.6, 3.2) and use this to draw a line of best fit. (do this by eye. do not use your calculator.) 3 the time taken for the planet uranus to orbit the sun is 30 685 days. use your graph to estimate the distance of uranus from the sun. give your answer correct to 2 significant figures. km 4 let x = log s and y = log t. the equation of the line of best fit is y = mx + c. use your calculator to find the values of m and c. give each answer correct to 2 significant figures. m = c = 5 a model for this is log t = mlog s + c. the distance of the planet neptune from the sun is 4.50 x 10 9 km. use the model to find the time taken for neptune to orbit the sun. give your answer in standard form correct to 2 significant figures. days ", "9": "9 \u00a9 ucles 2010 0607/06/o/n/10 [turn over for examiner's use 789 1 05 4 3 2 1 0 log slog t question 6 is on the next page. ", "10": "10 \u00a9 ucles 2010 0607/06/o/n/10 for examiner's use 6 writing c as log k, the model can be written as log t = m log s + log k. (a) show that t = ksm. (b) find the value of k. k = (c) write the model t = ks m using your values of k and m. use the data for earth to test this model. ", "11": "11 \u00a9 ucles 2010 0607/06/o/n/10 blank page ", "12": "12 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2010 0607/06/o/n/10 blank page " } }, "2011": { "0607_s11_qp_11.pdf": { "1": " this document consists of 8 printed pages. ib11 06_0607_11/2rp \u00a9 ucles 2011 [turn over *5403601149* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/11 paper 1 (core) may/june 2011 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2011 0607/11/m/j/11 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2011 0607/11/m/j/11 [turn over for examiner's use answer all the questions. 1 (a) write 6.149 correct to 1 decimal place. answer(a) [1] (b) write 206 correct to 2 significant figures. answer(b) [1] (c) write 0.0023 in standard form. answer(c) [1] 2 (a) list all four factors of 15. answer(a) , , , [1] (b) find the highest common factor of 15 and 21. answer(b) [2] 3 (a) write down the number of lines of symmetry of a regular pentagon. answer(a) [1] (b) a quadrilateral has rotational symmetry of order 2 and no lines of symmetry. write down the mathematical name of this quadrilateral. answer(b) [1] ", "4": "4 \u00a9 ucles 2011 0607/11/m/j/11 for examiner's use 4 (a) solve the equation 2(3 x \u2013 5) = x + 10 . answer(a) x = [3] (b) \u22123 y x i 4 show this inequality on the number line below. \u20134 \u20135 \u20133 \u20132 \u20131 0 1 2 3 4 5x [2] 5 the nth term of a sequence is 2 n \u2013 3. (a) write down the first term and the second term of this sequence. answer(a) , [2] (b) write down the 100th term of this sequence. answer(b) [1] (c) paulo says that the number 44 is in the sequence. is he correct? you must show your working. [2] ", "5": "5 \u00a9 ucles 2011 0607/11/m/j/11 [turn over for examiner's use 6 shade the required regions in the venn diagrams below. (a) p \u222a q [1] (b) p\u2032 \u2229 q [1] 7 the diagram shows two triangles. (a) write down the value of x. answer(a) x = [1] (b) complete the following statement. the two triangles are [1] (c) find the value of y. answer(c) y = [2] 95\u00b0 30\u00b015 cmy cm 95\u00b0x\u00b0 30\u00b05 cm2.5 cmnot to scaleu pq u pq", "6": "6 \u00a9 ucles 2011 0607/11/m/j/11 for examiner's use 8 (a) find the gradient of the line 2 y = x + 3. answer(a) [2] (b) write down the gradient of a line parallel to the line 2 y = x + 3. answer(b) [1] 9 ox\u00b0not to scale the area of the circle, centre o, is 100 cm2. the area of the shaded sector is 20 cm2. find the value of x. answer x = [2] ", "7": "7 \u00a9 ucles 2011 0607/11/m/j/11 [turn over for examiner's use 10 (a) work out 327. answer(a) [1] (b) factorise completely. 3y 2 \u2013 15y answer(b) [2] 11 u tb 264 3 the venn diagram shows the number of students who play tennis ( t), basketball ( b), both tennis and basketball or neither of these games. (a) how many students play basketball only? answer(a) [1] (b) how many students do not play tennis? answer(b) [1] (c) find the probability that a student chosen at random plays tennis. answer(c) [2] ", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the p ublisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2011 0607/11/m/j/11 for examiner's use 12 (a) graph b is a transformation of graph a. the equation of graph a is y = x 3. write down the equation of graph b. y x 0 ay x 03 b answer(a) [2] (b) graph d is a transformation of graph c. the equation of graph c is y = x2. write down the equation of graph d. y x 0 cy x 0 3 d answer(b) [2] " }, "0607_s11_qp_12.pdf": { "1": " this document consists of 10 printed pages and 2 blank pages. ib11 06_0607_12/2rp \u00a9 ucles 2011 [turn over *4075771834* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/12 paper 1 (core) may/june 2011 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2011 0607/12/m/j/11 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2011 0607/12/m/j/11 [turn over for examiner's use answer all the questions. 1 (a) write 2490 correct to 1 significant figure. answer(a) [1] (b) write 356 000 in standard form. answer(b) [1] 2 (a) solve the equation. 6 x \u2013 10 = x + 5 answer(a) x = [2] (b) expand and simplify. 3(2x + 1) \u2013 2x answer(b) [2] ", "4": "4 \u00a9 ucles 2011 0607/12/m/j/11 for examiner's use 3 (a) aob cd30\u00b0not to scale points a, b and c lie on the circumference of a circle, centre o. the line aoc is extended to d. angle bac = 30\u00b0. calculate the size of angle bcd. answer(a) angle bcd = [2] (b) north 50\u00b080\u00b0 30\u00b0ab c dnot to scale the diagram shows a school field abc. the point d is due south of a. angle dac = 50\u00b0, angle acb = 30\u00b0 and angle cba = 80\u00b0. find the bearing of b from a. answer(b) [2] ", "5": "5 \u00a9 ucles 2011 0607/12/m/j/11 [turn over for examiner's use 4 4 m3 m2 m not to scale the diagram shows the cross-section of a hut. the width of the hut is 4 m and the total height is 5 m. (a) find the area of the cross-section of the hut. answer(a) m2 [3] (b) a house is similar in shape to the hut and has a total height of 15 m. calculate the width of the house. answer(b) m [2] ", "6": "6 \u00a9 ucles 2011 0607/12/m/j/11 for examiner's use 5 (a) work out 3\u20132. answer(a) [1] (b) factorise completely. 8 pq \u2013 4q 2 answer(b) [2] (c) simplify. 6 3x x answer(c) [1] 6 a train leaves geneva at 09 10 and arrives in verona at 14 10. the distance from geneva to verona is 390 km. calculate the average speed of the train in km/h. answer km/h [3] ", "7": "7 \u00a9 ucles 2011 0607/12/m/j/11 [turn over for examiner's use 7 7 654321 12345670y x ad b the points a, b and d are three vertices of a parallelogram abcd. (a) draw the parallelogram abcd. [1] (b) write down the coordinates of c. answer(b) ( , ) [1] (c) find the gradient of the line ab. answer(c) [1] ", "8": "8 \u00a9 ucles 2011 0607/12/m/j/11 for examiner's use 8 the mapping diagram shows the function f( x) = 3 x \u2013 2. x 2 5q3x \u2013 2 4p 19 (a) find the values of p and q. answer(a) p = q = [2] (b) write down the range of f(x). answer(b) [1] 9 the nth term of a sequence is 2 n \u2013 5. (a) write down the first term of this sequence. answer(a) [1] (b) write down the 60th term of this sequence. answer(b) [1] ", "9": "9 \u00a9 ucles 2011 0607/12/m/j/11 [turn over for examiner's use 10 y x6 54321 \u20131\u20132\u20133\u20134\u20135\u201360 \u20136\u2013 5\u2013 4\u2013 3\u2013 2\u2013 1 1 2 3 4 5 6a c b (a) describe fully the single transformation which maps flag a onto flag b. [2] (b) describe fully the single transformation which maps flag a onto flag c. [3] (c) on the diagram above draw the image of flag a after a reflection in the line x = 3. [2] ", "10": "10 \u00a9 ucles 2011 0607/12/m/j/11 for examiner's use 11 100 90 8070605040302010 0 17 18 19 20 21 22 23 24 25 26number of hot drinks sold temperature (\u00b0c) the scatter diagram shows the correlation between the number of hot drinks sold and the temperature each day during a 12 day period. (a) use one word to describe the correlation. answer(a) [1] (b) the mean temperature was 22 \u00b0c and the mean number of hot drinks sold was 65. (i) plot the mean point on the scatter diagram above. [1] (ii) draw the line of best fit on the scatter diagram. [1] ", "11": "11 \u00a9 ucles 2011 0607/12/m/j/11 blank page ", "12": "12 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2011 0607/12/m/j/11 blank page " }, "0607_s11_qp_21.pdf": { "1": " this document consists of 8 printed pages. ib11 06_0607_21/4rp \u00a9 ucles 2011 [turn over *4380945812* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/21 paper 2 (extended) may/june 2011 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2011 0607/21/m/j/11 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2011 0607/21/m/j/11 [turn over for examiner's use answer all the questions. 1 (a) simplify 75. answer(a) [1] (b) simplify 2 53\u2212 by rationalising the denominator. answer(b) [2] 2 the first four terms of a sequence are 0, 3, 8, 15. (a) write down the next two terms of this sequence. answer(a) , [1] (b) find an expression for the nth term of this sequence. answer(b) [2] 3 solve the equation 17 \u2013 2 x = 4x \u2013 7. answer x = [2] ", "4": "4 \u00a9 ucles 2011 0607/21/m/j/11 for examiner's use 4 p = 2 3\uf8eb\uf8f6\uf8ec\uf8f7\uf8ed\uf8f8 q = 4 3\u2212\uf8eb\uf8f6\uf8ec\uf8f7\uf8ed\uf8f8 (a) find 2p \u2013 3q. answer(a) \uf8eb\uf8f6 \uf8ec\uf8f7 \uf8ec\uf8f7\uf8ec\uf8f7\uf8ed\uf8f8 [2] (b) calculate \u2502 q\u2502. answer(b) [2] 5 (a) factorise x 2 \u2013 3x \u2013 4. answer(a) [2] (b) solve for x. 10 i 2(6 \u2013 x) answer(b) [2] ", "5": "5 \u00a9 ucles 2011 0607/21/m/j/11 [turn over for examiner's use 6 using set notation describe the regions shaded on the venn diagrams. (a) u ab answer(a) [1] (b) u ab answer(b) [1] 7 f varies inversely as the square of d. when f = 9, d = 2. (a) find f in terms of d. answer(a) f = [2] (b) find the value of f when d is 3. answer(b) f = [1] ", "6": "6 \u00a9 ucles 2011 0607/21/m/j/11 for examiner's use 8 simplify. (a) log 9 + 3 log 2 \u2013 2 log 6 answer(a) [3] (b) 3 4 81 16\u2212\uf8eb\uf8f6 \uf8ec\uf8f7\uf8ed\uf8f8 answer(b) [2] 9 dx c xcd+= \u2212 find x in terms of c and d. answer x = [3] ", "7": "7 \u00a9 ucles 2011 0607/21/m/j/11 [turn over for examiner's use 10 all the students in a class of 20 took tests in mathematics and chemistry. the following table shows the results of these two tests. pass fail mathematics 12 8 chemistry 11 9 m is the set of students who passed the mathematics test. c is the set of students who passed the chemistry test. x is the number of students who passed both tests. (a) write 3 expressions in terms of x to complete the venn diagram. u m x .. .. ..c [3] (b) two pupils failed both mathematics and chemistry. find the value of x, the number of students who passed both tests. answer(b) x = [2] 11 for 0\u00b0 i x i 360\u00b0 find the values of x that satisfy the equation cos x = \u2013 1 2. answer x = and x = [2] ", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2011 0607/21/m/j/11 for examiner's use 12 y x3 21 \u20131\u20132\u201330 \u2013180\u00b0 \u201390\u00b0 90\u00b0 180\u00b0 270\u00b0 360\u00b0 (a) write down the equation of the graph. answer(a) [2] (b) on the same axes above sketch the graph of y = 2 sin x for \u2212180\u00b0 y x y 360\u00b0. [2] " }, "0607_s11_qp_22.pdf": { "1": " this document consists of 8 printed pages. ib11 06_0607_22/3rp \u00a9 ucles 2011 [turn over *9433607138* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/22 paper 2 (extended) may/june 2011 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": " 2 \u00a9 ucles 2011 0607/22/m/j/11 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2011 0607/22/m/j/11 [turn over for examiner's use answer all the questions. 1 (a) work out 2 327. answer(a) [1] (b) simplify 13 22(9 )cc\u00d7. answer(b) [2] 2 the first four terms of a sequence are 1, 3, 9, 27. (a) write down the next term of this sequence. answer(a) [1] (b) find an expression for the nth term of this sequence. answer(b) [2] 3 the size of one interior angle of a regular polygon is 156\u00b0. find the number of sides of the polygon. answer [2] ", "4": " 4 \u00a9 ucles 2011 0607/22/m/j/11 for examiner's use 4 u = { x | 1 y x y 16, x \u2208 k } a = { factors of 12 } b = { factors of 16 } complete the following. (a) a = { } [1] (b) n (a \u2229 b' ) = [1] 5 (a) find the value of log 2 8. answer(a) [1] (b) write the following as a single logarithm. 3log 2 \u2013 log 4 + 2log 5 answer(b) [3] ", "5": "5 \u00a9 ucles 2011 0607/22/m/j/11 [turn over for examiner's use 6 simplify fully 23 93aa aa\u00f7 \u2212\u2212. answer [3] 7 p = 2 3\u2212\uf8eb\uf8f6\uf8ec\uf8f7\uf8ed\uf8f8 q = 5 7\u2212\uf8eb\uf8f6\uf8ec\uf8f7\uf8ed\uf8f8 (a) find p + q . answer(a) \uf8eb\uf8f6 \uf8ec\uf8f7 \uf8ec\uf8f7\uf8ec\uf8f7\uf8ed\uf8f8 [2] (b) work out \u2502p + q\u2502. answer(b) [2] ", "6": " 6 \u00a9 ucles 2011 0607/22/m/j/11 for examiner's use 8 (a) simplify 8 2 + 2 8. answer(a) [2] (b) simplify by rationalising the denominator. 32 32\u2212 answer(b) [2] 9 the equation of a line passing through the point (2, 3) is ax + by = d, where a, b, d \u2208 k. this line is perpendicular to the line y = 2x + 5. find the values of a, b and d. answer a = b = d = [3] ", "7": "7 \u00a9 ucles 2011 0607/22/m/j/11 [turn over for examiner's use 10 the cost of a mango is $ m. the cost of a pineapple is $ p. (a) write an expression, in terms of m and p, for the cost of 2 mangoes and 3 pineapples. answer(a) $ [1] (b) the cost of 2 mangoes and 3 pineapples is $13. the cost of 6 mangoes and 2 pineapples is $18. write down two equations and solve them to find the cost of one mango and the cost of one pineapple. answer(b) mango = $ pineapple = $ [4] 11 x is an obtuse angle and sin x = 1 2. find the exact value of cos x. answer [2] ", "8": " 8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the p ublisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2011 0607/22/m/j/11 for examiner's use 12 the graph of y = f( x) where f( x) = ax 2 + bx + 3 crosses the x-axis at (\u22123, 0) and (1, 0). the y coordinate of the vertex is 4. (a) on the axes, sketch the graph of y = f(x), for \u20134 y x y 4. 5 \u20135\u20134 4y x 0 [2] (b) find the values of a and b. answer(b) a = [1] b = [1] (c) write down the range of f(x) when the domain is o. answer(c) [1] " }, "0607_s11_qp_31.pdf": { "1": " this document consists of 16 printed pages. ib11 06_0607_31/2rp \u00a9 ucles 2011 [turn over *9835578859* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/31 paper 3 (core) may/june 2011 1 hour 45 minutes candidates answer on the question paper additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96. ", "2": "2 \u00a9 ucles 2011 0607/31/m/j/11 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2011 0607/31/m/j/11 [turn over for examiner's use answer all the questions. 1 ali and amanda are in the same class at school. (a) in a test ali\u2019s mark is 24 and amanda\u2019s mark is 28. (i) write down the ratio. ali\u2019s mark : amanda\u2019s mark. give your answer in its simplest form. answer(a)(i) : [1] (ii) calculate amanda\u2019s mark as a percentage of ali\u2019s mark. answer(a)(ii) % [2] (b) in another test ali\u2019s mark is again 24 but the ratio of the marks changes to ali\u2019s mark : amanda\u2019s mark = 8 : 7. calculate amanda\u2019s mark. answer(b) [2] (c) ali and amanda share $35 in the ratio 3 : 4. calculate how much ali receives. answer(c) $ [2] ", "4": "4 \u00a9 ucles 2011 0607/31/m/j/11 for examiner's use 2 (a) simplify fully. (i) 4312 4x x\u00d7 answer(a)(i) [2] (ii) 31 515 3x x\u00f7 answer(a)(ii) [2] (iii) 26 3x y y t\u00d7 answer(a)(iii) [2] (b) write 2 52cd+ as a single fraction. answer(b) [2] 3 a ferry leaves calais at 23 15. it takes 1 h 55 min to reach dover. (a) write down the arrival time of the ferry at dover. answer(a) [1] (b) the distance travelled is 43 km. calculate the average speed of the journey, in km/h. answer(b) km/h [3] (c) in 2009 a ferry ticket cost \u20ac40. the cost of the ferry ticket increased each year by 5%. calculate the cost of the ferry ticket in 2011. answer(c) \u20ac [3] ", "5": "5 \u00a9 ucles 2011 0607/31/m/j/11 [turn over for examiner's use 4 5 4321 \u20131\u20132\u20133\u20134\u201350 \u20136 \u2013 5 \u2013 4 \u2013 3 \u2013 2 \u2013 1 123456y xh w g (a) describe fully the single transformation that maps triangle w onto (i) triangle g, [2] (ii) triangle h. [3] (b) on the grid, (i) draw the translation of triangle w by 1 3\u2212\uf8eb\uf8f6\uf8ec\uf8f7\uf8ed\uf8f8, [2] (ii) draw the enlargement of triangle w, centre (0, 0), scale factor 1 2 . [2] ", "6": "6 \u00a9 ucles 2011 0607/31/m/j/11 for examiner's use 5 (a) y = 3x \u2013 8 (i) find the value of y when x = \u20135. answer(a)(i) [1] (ii) make x the subject of the equation. answer(a)(ii) x = [2] (b) solve the simultaneous equations. show your method. y = 2x \u2013 7 y = 3 \u2013 2x answer(b) x = y = [3] ", "7": "7 \u00a9 ucles 2011 0607/31/m/j/11 [turn over for examiner's use 6 100 90 8070605040302010 05 1 01 52 02 53 03 54 04 55 0cumulative frequency test mark the cumulative frequency graph shows the distribution of test marks for 100 students. use the graph to find (a) the median, answer(a) [1] (b) the inter-quartile range, answer(b) [2] (c) the number of students with a mark of at least 20. answer(c) [2] ", "8": "8 \u00a9 ucles 2011 0607/31/m/j/11 for examiner's use 7 p c b ad 10 cm10 cm12 cmnot to scale m the diagram shows a pyramid with a square horizontal base abcd. the diagonals of the base intersect at m. the vertex, p, of the pyramid is vertically above m. ab = bc = 10 cm and pm = 12 cm. (a) calculate the volume of the pyramid. answer(a) cm3 [2] ", "9": "9 \u00a9 ucles 2011 0607/31/m/j/11 [turn over for examiner's use (b) p c b10 cm13 cmnot to scale the diagram shows one of the faces of the pyramid, triangle pbc. the distance from p to the midpoint of bc is 13 cm. calculate (i) the area of triangle pbc, answer(b)(i) cm2 [2] (ii) the total surface area of the pyramid. answer(b)(ii) cm2 [2] ", "10": "10 \u00a9 ucles 2011 0607/31/m/j/11 for examiner's use 8 32 students are asked how many coins they have. the results are shown in the pie chart. 45\u00b045\u00b04 coins 5 coins 0 coins 1 coin2 coins3 coins (a) (i) measure the angle which shows the number of students who have 4 coins. answer(a)(i) [1] (ii) calculate the number of students who have 4 coins. answer(a)(ii) [1] (iii) calculate the number of students who have more than one coin. answer(a)(iii) [2] (b) complete the frequency table. number of coins 0 1 2 3 4 5 number of students (frequency) 2 6 [2] (c) find (i) the mean, answer(c)(i) [1] (ii) the mode, answer(c)(ii) [1] (iii) the median. answer(c)(iii) [1] ", "11": "11 \u00a9 ucles 2011 0607/31/m/j/11 [turn over for examiner's use 9 north north 140\u00b0 120 mp s qnot to scale q is 120 m from p, on a bearing of 140\u00b0. (a) find the bearing of p from q. answer(a) [1] (b) s is due south of p and due west of q. calculate the distance sq. answer(b) m [3] (c) (i) r is also 120 m from p and is due west of s. show r and the line pr on the diagram. [1] (ii) find the bearing of r from p. answer(c)(ii) [1] ", "12": "12 \u00a9 ucles 2011 0607/31/m/j/11 for examiner's use 10 line 1 line 3 line 228 03a 8y xc bnot to scale the diagram shows three lines, line 1, line 2 and line 3. line 1 is parallel to the y-axis and passes through (3, 0). line 2 is parallel to the x-axis and passes through (0, 2). line 3 passes through (8, 0) and (0, 8). (a) find the equation of (i) line 1, answer(a)(i) [1] (ii) line 2, answer(a)(ii) [1] (iii) line 3. answer(a)(iii) [2] ", "13": "13 \u00a9 ucles 2011 0607/31/m/j/11 [turn over for examiner's use (b) the lines intersect at the points a, b and c as shown in the diagram. (i) work out the co-ordinates of b. answer(b)(i) ( , ) [2] (ii) work out the co-ordinates of the midpoint of ab. answer(b)(ii) ( , ) [1] (iii) calculate the length of bc. answer(b)(iii) [3] ", "14": "14 \u00a9 ucles 2011 0607/31/m/j/11 for examiner's use 11 ab is a diameter of a circle, centre o. t is a point on the circle and angle tab = 40\u00b0. utv is a tangent to the circle at t. (a) complete the following statements. (i) angle atb = , because [1] (ii) angle otv = , because [1] (b) find the size of (i) angle ato , answer(b)(i) [1] (ii) angle tob , answer(b)(ii) [1] (iii) angle utb . answer(b)(iii) [1] (c) ab and uv are extended to meet at x. (i) show this on the diagram. [1] (ii) calculate the size of angle txo . answer(c)(ii) [1] 40\u00b0 au vt o bnot to scale", "15": "15 \u00a9 ucles 2011 0607/31/m/j/11 [turn over for examiner's use 12 y x4 \u20134\u20132 20 (a) on the axes, sketch the graph of (i) y = x 2 \u2013 2 for \u2013 2 y x y 2, [2] (ii) y = 2 x for \u2013 2 y x y 2. [2] (b) write down the zeros of y = x2 \u2013 2. answer(b) x = and x = [2] (c) solve the equation 2x = x2 \u2013 2 for \u2013 2 y x y 2. answer(c) x = [1] (d) for the domain \u2013 2 y x y 2, write down the range of the function 2 x. answer(d) [2] ", "16": "16 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2011 0607/31/m/j/11 for examiner's use 13 a bag contains 7 white beads and 4 black beads. two beads are taken out of the bag at random (without replacement). (a) complete the tree diagram by putting the probabilities in the spaces. first bead second bead white blackwhite black blackwhite7 116 10 [2] (b) calculate the probability that (i) both beads are white, answer(b)(i) [2] (ii) exactly one bead is white. answer(b)(ii) [3] " }, "0607_s11_qp_32.pdf": { "1": " this document consists of 17 printed pages and 3 blank pages. ib11 06_0607_32/3rp \u00a9 ucles 2011 [turn over *5871924244* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/32 paper 3 (core) may/june 2011 1 hour 45 minutes candidates answer on the question paper additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96. ", "2": "2 \u00a9 ucles 2011 0607/32/m/j/11 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2011 0607/32/m/j/11 [turn over for examiner's use answer all the questions. 1 (a) write the ratio 12 : 20 in its simplest form. answer(a) : [1] (b) x : 8 = 3 : 2. find the value of x. answer(b) x = [1] (c) divide $30 in the ratio 3 : 7. answer(c) $ : $ [2] (d) write the fraction 26 3xy xy in its lowest terms. answer(d) [2] (e) work out 7 19 of $570. answer(e) $ [1] (f) calculate 15% of 60 kg. answer(f) kg [2] (g) sam spends $6 at a shop. this is 3 25 of sam\u2019s pocket money. calculate sam\u2019s pocket money. answer(g) $ [2] ", "4": "4 \u00a9 ucles 2011 0607/32/m/j/11 for examiner's use 2 ten students have the following shoe sizes. 33 36 36 33 35 37 33 32 38 38 (a) find (i) the mode, answer(a)(i) [1] (ii) the median, answer(a)(ii) [1] (iii) the range, answer(a)(iii) [1] (iv) the upper quartile, answer(a)(iv) [1] (v) the mean. answer(a)(v) [1] (b) 3 210 shoe sizefrequency on the grid, draw an accurate bar graph to show the frequencies of the shoe sizes. [3] ", "5": "5 \u00a9 ucles 2011 0607/32/m/j/11 [turn over for examiner's use (c) 35 3233 complete the pie chart accurately to show the frequencies of the remaining shoe sizes. label your sectors clearly. [3] (d) find the probability that a student chosen at random has a shoe size (i) greater than 36, answer(d)(i) [1] (ii) greater than 30. answer(d)(ii) [1] (e) find the percentage of those students with a shoe size greater than 32 who have a shoe size greater than 33. answer(e) % [2] ", "6": "6 \u00a9 ucles 2011 0607/32/m/j/11 for examiner's use 3 u = { x | 1 y x y 10, x \u2208 w } a = { even numbers } b = { factors of 36 } (a) u ab write the ten members of u in the correct regions of the venn diagram. [3] (b) complete the following. (i) a \u2229 b = { } [1] (ii) a \u222a b = { } [1] (iii) a' \u2229 b = { } [1] (iv) n (b' ) = [1] ", "7": "7 \u00a9 ucles 2011 0607/32/m/j/11 [turn over for examiner's use 4 b au wt 9 m 6.5 m 57\u00b0 8 mnot to scale the diagram shows a vertical flagpole standing on horizontal ground. two straight wires at and bu are attached to the flagpole as shown. (a) u is 6.5 m above the ground and bu = 9 m. calculate the angle between bu and the ground. answer(a) [2] (b) the point w is vertically below the point t. aw = 8 m and angle wat = 57\u00b0. calculate tw, the height of the flagpole. answer(b) m [2] ", "8": "8 \u00a9 ucles 2011 0607/32/m/j/11 for examiner's use 5 b o a 6 cm6 cmnot to scale the diagram shows a sector oab of a circle, radius 6 cm. angle aob = 90\u00b0. (a) calculate (i) the area of triangle oab , answer(a)(i) cm2 [2] (ii) the area of the sector oab , answer(a)(ii) cm2 [2] (iii) the area of the region shaded in the diagram. answer(a)(iii) cm2 [1] ", "9": "9 \u00a9 ucles 2011 0607/32/m/j/11 [turn over for examiner's use (b) calculate (i) the length of ab, answer(b)(i) cm [2] (ii) the perimeter of the region shaded in the diagram. answer(b)(ii) cm [3] ", "10": "10 \u00a9 ucles 2011 0607/32/m/j/11 for examiner's use 6 d aceb q 80\u00b0not to scale in the diagram, deq is parallel to ac. de = be and angle acb = 80\u00b0. (a) (i) write down the size of angle ceq. answer(a)(i) angle ceq = [1] (ii) give a reason for your answer. [1] (b) find the size of (i) angle beq , answer(b)(i) angle beq = [1] (ii) angle dbe , answer(b)(ii) angle dbe = [1] (iii) angle bac. answer(b)(iii) angle bac = [1] ", "11": "11 \u00a9 ucles 2011 0607/32/m/j/11 [turn over for examiner's use 7 y x4 321 \u20131\u20132\u20133\u20134 \u20134\u2013 3\u2013 2\u2013 1 1 02 3 4 abcl (a) write down the co-ordinates of the point a. answer(a) ( , ) [1] (b) write the vector ab\uf8e7\uf8e7 \u2192 in component form. answer(b) \uf8eb\uf8f6 \uf8ec\uf8f7 \uf8ec\uf8f7\uf8ec\uf8f7\uf8ed\uf8f8 [1] (c) the line l passes through b and c. (i) find the gradient of the line l. answer(c)(i) [2] (ii) find the equation of the line l. answer(c)(ii) [2] ", "12": "12 \u00a9 ucles 2011 0607/32/m/j/11 for examiner's use 8 y x20 \u201320\u20134 60 (a) on the axes, sketch the graph of 10 3y x= \u2212, between x = \u2013 4 and x = 6. (the graph has two separate parts.) [3] (b) the graph has two asymptotes. (i) on the axes, sketch the asymptote which is parallel to the y-axis. [1] (ii) write down the equation of this asymptote. answer(b)(ii) [1] (c) (i) on the axes, sketch the graph of 2 2xy= . [1] (ii) solve the equation 210 32x x= \u2212. answer(c)(ii) x = [1] ", "13": "13 \u00a9 ucles 2011 0607/32/m/j/11 [turn over for examiner's use 9 6 cm16 cmnot to scale the diagram shows a glass jug. the jug is a cylinder of radius 6 cm and height 16 cm. (a) calculate the volume of the jug (i) in cm 3, answer(a)(i) cm3 [2] (ii) in litres. answer(a)(ii) litres [1] (b) there are 1500 cm 3 of water in the jug. (i) calculate the height of the water in the jug. answer(b)(i) cm [2] (ii) how many 25 cl glasses can be filled from the 1500 cm 3 of water in the jug? answer(b)(ii) [2] ", "14": "14 \u00a9 ucles 2011 0607/32/m/j/11 for examiner's use 10 (a) \u20133 \u20132 \u20131 0 1 2x write down the inequality shown in the diagram. answer(a) [2] (b) solve the simultaneous equations. show your method. 2 x + y = 1 y = 2x \u2013 5 answer(b) x = y = [3] (c) the perimeter, p, of a semicircle of radius r, is given by the following formula. p = \u03c0r + 2r (i) factorise \u03c0 r + 2r. answer(c)(i) [1] (ii) rearrange the formula p = \u03c0r + 2r to give r in terms of \u03c0 and p. answer(c)(ii) r = [1] ", "15": "15 \u00a9 ucles 2011 0607/32/m/j/11 [turn over for examiner's use 11 on any day, in february, the probability that it will rain in hokitika is 3 7. (a) for how many of the 28 days in february, would you expect it to rain? answer(a) [1] (b) (i) complete the tree diagram for two consecutive days by putting the probabilities in the spaces. first day second day rain no rainrain no rain no rainrain3 737 [2] (ii) calculate the probability that it will rain on two consecutive days. answer(b)(ii) [2] (iii) calculate the probability that it will rain on exactly one of the two days. answer(b)(iii) [3] (iv) complete the statement. the probability that [1] is 16 49. ", "16": "16 \u00a9 ucles 2011 0607/32/m/j/11 for examiner's use 12 100 students estimate the length, l, of a piece of string. the results are shown in the table. length (l cm) 0 y l i 30 30 y l i 40 40 y l i 50 50 y l i 60 60 y l i 70 70 y l i 100 frequency 3 12 30 35 18 2 (a) using the mid-values of the class intervals, calculate an estimate of the mean. answer(a) cm [2] (b) (i) complete the cumulative frequency table. length (l cm) l i 30 l i 40 l i 50 l i 60 l i 70 l i 100 cumulative frequency 3 15 98 100 [2] (ii) on the grid opposite, complete the cumulative frequency curve. ", "17": "17 \u00a9 ucles 2011 0607/32/m/j/11 for examiner's use 100 90 8070605040302010 10 20 30 40 50 60 70 80 90 1000cumulative frequency length (l cm) [2] (iii) use your cumulative frequency curve to find the inter-quartile range. answer(b)(iii) cm [2] ", "18": "18 \u00a9 ucles 2011 0607/32/m/j/11 blank page ", "19": "19 \u00a9 ucles 2011 0607/32/m/j/11 blank page ", "20": "20 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2011 0607/32/m/j/11 blank page " }, "0607_s11_qp_41.pdf": { "1": " this document consists of 20 printed pages. ib11 06_0607_41/4rp \u00a9 ucles 2011 [turn over *6342947190* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/41 paper 4 (extended) may/june 2011 2 hours 15 minutes candidates answer on the question paper additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120. ", "2": "2 \u00a9 ucles 2011 0607/41/m/j/11 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2011 0607/41/m/j/11 [turn over for examiner's use answer all the questions. 1 (a) in 2009 the height of a tree was 25.2 m. a year later, the height was 28 m. calculate the percentage increase in height. answer(a) % [3] (b) the height of 25.2 m was a 20% increase of the height in 2008. calculate the height in 2008. answer(b) m [3] (c) the height of the tree is expected to increase by 5% of its value each year. the height is now 30 m. (i) calculate the expected height in 3 years time. answer(c)(i) m [3] (ii) calculate the number of years it will take for the tree to reach a height of 40 m. answer(c)(ii) [2] ", "4": "4 \u00a9 ucles 2011 0607/41/m/j/11 for examiner's use 2 20 \u2013200\u20132 4y x (a) on the axes, sketch the graph of y = x 3 \u2013 3x2. [3] (b) write down the zeros of y = x 3 \u2013 3x2. answer(b) x = x = [1] (c) write down the co-ordinates of any local maximum or local minimum points. answer(c) [2] ", "5": "5 \u00a9 ucles 2011 0607/41/m/j/11 [turn over for examiner's use 3 6 54321 \u20131\u20132\u20133\u20134\u20135\u201360 \u20136 \u2013 5 \u2013 4 \u2013 3 \u2013 2 \u2013 1 123456y x vp u (a) describe fully the single transformation that maps triangle p onto (i) triangle u, answer(a)(i) [3] (ii) triangle v. answer(a)(ii) [2] (b) on the grid above, draw the following transformations of triangle p. (i) translation by 6 2\u2212\uf8eb\uf8f6\uf8ec\uf8f7\uf8ed\uf8f8. [2] (ii) stretch by a scale factor 1.5 with the y-axis invariant. [2] ", "6": "6 \u00a9 ucles 2011 0607/41/m/j/11 for examiner's use 4 (a) abcde is a pentagon with angle eab = 120\u00b0, angle abc = 140\u00b0 and angle bcd = 85\u00b0. ab is parallel to ed and ea = ab. (i) calculate the size of angle aed . answer(a)(i) [1] (ii) calculate the size of angle edc . answer(a)(ii) [2] (iii) on the diagram above, draw the line eb and calculate the size of angle ebc. answer(a)(iii) [1] (b) 150\u00b0o p qrsnot to scale p, q, r and s lie on a circle, centre o. angle por = 150\u00b0. calculate the size of (i) angle psr, answer(b)(i) [1] (ii) angle pqr . answer(b)(ii) [1] e a bcd 120\u00b0 140\u00b085\u00b0 not to scale", "7": "7 \u00a9 ucles 2011 0607/41/m/j/11 [turn over for examiner's use 5 y b xa l6 08not to scale the diagram shows the line, l, which passes through the points a (8, 0) and b (0, 6). (a) the line l also passes through the point ( h, 9). find the value of h. answer(a) h = [2] (b) find the equation of the line which is perpendicular to l and which passes through the mid-point of the line ab. answer(b) [4] ", "8": "8 \u00a9 ucles 2011 0607/41/m/j/11 for examiner's use 6 (a) northnorth a bc7 cm 9 cm110\u00b0not to scale in triangle abc, ab = 9 cm, ac = 7 cm and angle bac = 110\u00b0. (i) calculate the area of triangle abc. answer(a)(i) cm2 [2] (ii) calculate the length of bc. answer(a)(ii) cm [3] (iii) the bearing of a from b is 050\u00b0. find the bearing of c from a. answer(a)(iii) [2] ", "9": "9 \u00a9 ucles 2011 0607/41/m/j/11 [turn over for examiner's use (b) p qs r7 cm 4 cm 11 cm75\u00b0 not to scale in the quadrilateral pqrs , pq = 4 cm, ps = 7 cm and qr = 11 cm. angle qps = 90\u00b0 and angle qsr = 75\u00b0. calculate the size of angle qrs. answer(b) [5] ", "10": "10 \u00a9 ucles 2011 0607/41/m/j/11 for examiner's use 7 nyali sells cakes and ice creams. she records the number of cakes ( c) and the number of ice creams ( i) she sells each day for 10 days. the results are shown in the table. number of cakes ( c) 48 60 52 40 60 36 70 20 44 50 number of ice creams ( i) 50 18 38 50 30 54 14 70 46 50 (a) complete the scatter diagram. the first 6 points have been plotted for you. 80 70605040302010 10 20 30 40 50 60 70 800number of ice creams number of cakesi c [2] ", "11": "11 \u00a9 ucles 2011 0607/41/m/j/11 [turn over for examiner's use (b) write down one word to describe the correlation between c and i. answer(b) [1] (c) find the equation of the line of regression, writing i in terms of c. answer(c) i = [2] (d) use your equation to estimate the number of ice creams nyali sells on a day when she sells 67 cakes. answer(d) [1] ", "12": "12 \u00a9 ucles 2011 0607/41/m/j/11 for examiner's use 8 8 cm 6 cm 12 cmnot to scale the diagram shows two similar containers. the top of the large container has diameter 8 cm. the top of the small container has diameter 6 cm. (a) the height of the large container is 12 cm. calculate the height of the small container. answer(a) cm [2] (b) the volume of the large container is 550 cm3. calculate the volume of the small container. answer(b) cm3 [3] (c) write 550 cm3 in litres. answer(c) litres [1] ", "13": "13 \u00a9 ucles 2011 0607/41/m/j/11 [turn over for examiner's use 9 y x1.5 \u20131\u201310 100 (a) (i) on the axes, sketch the graph of y = f(x), where f(x) = log x for 0 i x y 10. [2] (ii) write down the co-ordinates of the point where the graph of y = f(x ) crosses the x-axis. answer(a)(ii) ( , ) [1] (iii) write down the equation of the asymptote of the graph of y = f(x). answer(a)(iii) [1] (iv) find the range of f( x) for the domain 0 i x y 10. answer(a)(iv) [2] (b) solve the equation 10log 20xx\u2212= . answer(b) x = [2] (c) 10g( ) 20xx\u2212= find the range of g( x) for the domain \u201310 y x y 10.= answer(c) [2] (d) on the axes, sketch the graph of y = f(x + 1). [2] ", "14": "14 \u00a9 ucles 2011 0607/41/m/j/11 for examiner's use 10 40 cm 70 cmnot to scale the diagram shows a water tank which is open at the top. the tank is in the shape of a cylinder with radius 40 cm and height 70 cm. (a) (i) calculate the total surface area of the cylinder. answer(a)(i) cm2 [2] (ii) the cylinder is made of metal which costs $2.40 per square metre. calculate the cost of the metal. answer(a)(ii) $ [3] ", "15": "15 \u00a9 ucles 2011 0607/41/m/j/11 [turn over for examiner's use (b) (i) calculate the volume of the cylinder. answer(b)(i) cm3 [2] (ii) water is poured into the empty cylinder at a rate of 8 cm3 per second. calculate the time taken to fill the cylinder. give your answer in hours and minutes, correct to the nearest minute. answer(b)(ii) h min [4] ", "16": "16 \u00a9 ucles 2011 0607/41/m/j/11 for examiner's use 11 1 7 8 12 15 19 19 the diagram shows seven numbered cards. (a) a card is chosen at random. (i) write down the probability that it is numbered 12 or 15. answer(a)(i) [1] (ii) the probability that the number on the card is greater than x is 5 7. write down the value of x. answer(a)(ii) [1] (b) two cards are chosen at random, without replacement, from the seven numbered cards. (i) when the first card chosen is numbered 1 9, write down the probability that the second card is also numbered 19. answer(b)(i) [1] (ii) first card second card numbered 19 not numbered 19numbered 19 not numbere d 19 numbered 19 not numbere d 192 7 complete the tree diagram, by writing the probabilities in the spaces. [2] ", "17": "17 \u00a9 ucles 2011 0607/41/m/j/11 [turn over for examiner's use (iii) find the probability that both cards are numbered 19. answer(b)(iii) [2] (iv) find the probability that exactly one card is numbered 19. answer(b)(iv) [3] (c) cards are chosen at random, without replacement, from the seven numbered cards, until a card that is numbered 19 is chosen. find the probability that this happens with the third card. answer(c) [2] ", "18": "18 \u00a9 ucles 2011 0607/41/m/j/11 for examiner's use 12 m12 10 8642 10 20 30 40 50 60 70 80 90 1000frequency density mass (m grams) the histogram shows numbers of apples and their masses ( m grams). (a) complete the frequency table using the information in the histogram. mass (m grams) 0 y m i 30 30 y m i 50 50 y m i 60 60 y m i 70 70 y m i 100 frequency 60 110 [3] (b) calculate an estimate of the mean mass of the apples. answer(b) g [2] (c) complete the cumulative frequency table using the information in your frequency table. mass (m grams) m i 30 m i 50 m i 60 m i 70 m i 100 cumulative frequency 60 560 [2] ", "19": "19 \u00a9 ucles 2011 0607/41/m/j/11 [turn over for examiner's use (d) on the grid below, complete the cumulative frequency curve. 600 500400300200100 10 20 30 40 50 60 70 80 90 1000cumulative frequency mass (m grams) [3] (e) use your cumulative frequency curve to find (i) the median, answer(e)(i) g [1] (ii) the lower quartile, answer(e)(ii) g [1] (iii) the inter-quartile range, answer(e)(iii) g [1] (iv) the number of apples with a mass of at least 40 g. answer(e)(iv) [2] ", "20": "20 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2011 0607/41/m/j/11 for examiner's use 13 w\u00b0 x + 2 xxx + 1not to scale the area of the right-angled triangle is equal to the area of the square. (a) show that x 2 \u2013 3x \u2013 2 = 0. [3] (b) solve the equation x 2 \u2013 3x \u2013 2 = 0. give your answers correct to 2 decimal places. answer(b) x = or x = [3] (c) calculate the value of w. answer(c) w = [2] " }, "0607_s11_qp_42.pdf": { "1": " this document consists of 16 printed pages. ib11 06_0607_42/3rp \u00a9 ucles 2011 [turn over *0755012000* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/42 paper 4 (extended) may/june 2011 2 hours 15 minutes candidates answer on the question paper additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120. ", "2": "2 \u00a9 ucles 2011 0607/42/m/j/11 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2011 0607/42/m/j/11 [turn over for examiner's use answer all the questions. 1 (a) (i) the population of a village is 4620. the ratio children : women : men = 5 : 7 : 8. show that the number of women in the village is 1617. [2] (ii) during the last ten years, the number of women has increased from 1475 to 1617. calculate the percentage increase in the number of women. answer(a)(ii) % [3] (b) the population of 4620 is expected to decrease by 5%. calculate the population following this decrease. answer(b) [2] (c) the number of children is now 1155. this is an increase of 65% on the number of children twenty years ago. calculate the number of children twenty years ago. answer(c) [3] ", "4": "4 \u00a9 ucles 2011 0607/42/m/j/11 for examiner's use 2 (a) describe fully the single transformation that maps (i) shape q onto shape g, [2] (ii) shape q onto shape h. [2] (b) on the grid, draw the enlargement of shape q, centre (2, 5), scale factor 3. [2] (c) use one mathematical word to complete the statement. the shapes g and h and the image drawn in part (b) are all to shape q. [1] g q h7 654321 \u20131\u20132\u20133\u20134\u20135\u20136\u201370 \u20136 \u20137 \u2013 5 \u2013 4 \u2013 3 \u2013 2 \u2013 1 123456 7y x", "5": "5 \u00a9 ucles 2011 0607/42/m/j/11 [turn over for examiner's use 3 100 students are asked which science subjects they study. the venn diagram shows how many students study biology ( b), chemistry (c) and physics (p). (a) write down the number of students that study (i) all three subjects, answer(a)(i) [1] (ii) biology and chemistry, answer(a)(ii) [1] (iii) physics but not chemistry, answer(a)(iii) [1] (iv) exactly one of the three subjects. answer(a)(iv) [1] (b) find (i) n ( ) pc\u222a , answer(b)(i) [1] (ii) n()c'. answer(b)(ii) [1] (c) from the 100 students, one student is chosen at random. write down the probability that this student studies physics. answer(c) [1] (d) from the students who study chemistry, one student is chosen at random. find the probability that this student also studies physics. answer(d) [2] u bc p21307 210 45 3", "6": "6 \u00a9 ucles 2011 0607/42/m/j/11 for examiner's use 4 q pr100 m 130 m80 mnot to scale pierre ran around an exercise course. the three exercise points p, q and r are shown on the diagram. pq = 80 m, qr = 100 m and rp = 130 m. (a) (i) pierre ran from p to q at 2.5 m/s. calculate the time taken. answer(a)(i) s [2] (ii) the table shows some of the times pierre took to complete each part of the course. time taken run from p to q exercise at q 5 min 20 s run from q to r 50 s exercise at r 4 min 28 s run from r to p 50 s pierre started from p at 14 55. at what time did he arrive back at p? answer(a)(ii) [2] ", "7": "7 \u00a9 ucles 2011 0607/42/m/j/11 [turn over for examiner's use (b) calculate angle pqr . show all your working and show that your answer rounds to 91.8\u00b0, correct to 1 decimal place. [3] (c) calculate the area of triangle pqr . show all your working. answer(c) m2 [2] (d) a new exercise point, s, is put on the line qr, so that angle qps = 20\u00b0. (i) on the diagram, sketch the line ps and label the point s. [1] (ii) find the size of angle psq. answer(d)(ii) [1] (iii) calculate the distance qs. answer(d)(iii) m [3] ", "8": "8 \u00a9 ucles 2011 0607/42/m/j/11 for examiner's use 5 ten students take part in two quizzes. the scores in quiz 1 and quiz 2 are shown by the values x and y in the table. quiz 1 (x) 7 1 1 5 6 4 7 6 5 3 quiz 2 (y) 6 2 1 5 5 5 6 6 4 4 (a) which word best describes the correlation between x and y? answer(a) [1] (b) the line of best fit on a scatter diagram goes through the mean point. find the co-ordinates of this point. answer(b) ( , ) [2] (c) find the equation of the line of regression, writing y in terms of x. answer(c) y = [2] (d) (i) how many students scored more than 5 in both quizzes? answer(d)(i) [1] (ii) two of the ten students are chosen at random. calculate the probability that they both scored more than 5 in both quizzes. answer(d)(ii) [3] ", "9": "9 \u00a9 ucles 2011 0607/42/m/j/11 [turn over for examiner's use 6 y x4 \u20134\u20135 50 (a) on the axes sketch the graph of y = f( x), where f(x) = 2 24x x\u2212 , between x = \u2013 5 and x = 5. (the graph has three separate parts.) [5] (b) the graph has three asymptotes. write down their equations. answer(b) [3] (c) write down the co-ordinates of the local maximum point. answer(c) ( , ) [1] (d) (i) write down the range of f(x) for x \u2208 o. answer(d)(i) [2] (ii) the equation f(x) = k, where k \u2208 o has no solutions. write down a possible value of k. answer(d)(ii) k = [1] ", "10": "10 \u00a9 ucles 2011 0607/42/m/j/11 for examiner's use 7 6 mm 15 mmnot to scale the diagram shows a solid made from a cylinder of radius 6 mm, length 15 mm and two hemispheres of radius 6 mm. (a) calculate the total surface area of the solid (i) in mm 2, answer(a)(i) mm2 [3] (ii) in cm 2. answer(a)(ii) cm2 [1] (b) (i) calculate the total volume of the solid. give your answer in mm 3. answer(b)(i) mm3 [3] (ii) the solid is made of gold. 1 mm3 of gold has a mass of 0.0193 g. one gram of gold has a value of $31.80. calculate the value of the solid. answer(b)(ii) $ [3] ", "11": "11 \u00a9 ucles 2011 0607/42/m/j/11 [turn over for examiner's use 8 64\u00b0 100\u00b0 110\u00b0q\u00b0 r\u00b0p\u00b0cu d t a bonot to scale the diagram shows a cyclic quadrilateral abcd, centre o. angle dab = 110\u00b0 and angle abc = 100\u00b0. ta and td are tangents at a and d. td is extended to u and angle udc = 64\u00b0. (a) calculate the values of p, q and r. answer(a) p = [1] q = [1] r = [2] (b) calculate (i) angle odc, answer(b)(i) angle odc = [1] (ii) angle dac. answer(b)(ii) angle dac = [1] ", "12": "12 \u00a9 ucles 2011 0607/42/m/j/11 for examiner's use 9 veronica and tiago walk 9 km. the first 5 km of the walk is up a hill. (a) veronica walks the first 5 km at a speed of 2 km/h. she then walks the remaining 4 km at a speed of 4 km/h. calculate the average speed of veronica\u2019s journey. answer(a) km/h [4] (b) tiago walks the first 5 km at a speed of x km/h. he then increases his speed by 2 km/h for the remaining 4 km. (i) find, in terms of x, the total time of tiago\u2019s journey. answer(b)(i) h [2] (ii) the average speed for tiago\u2019s journey is 4.5 km/h. show that 2 x 2 \u2013 5x \u2013 10 = 0. [3] ", "13": "13 \u00a9 ucles 2011 0607/42/m/j/11 [turn over for examiner's use (iii) solve the equation 2 x2 \u2013 5x \u2013 10 = 0. give your answers correct to 2 decimal places. answer(b)(iii) x = or x = [3] (iv) work out the time tiago took to walk the first 5 km. answer(b)(iv) h [1] 10 100 students record how far they can run in one minute. the results are shown in the table. distance ( d metres) 0 y d i 200 200 y d i 250 250 y d i 300 300 y d i 400 frequency 5 20 56 19 (a) write down the interval in which the median lies. answer(a) [1] (b) calculate an estimate of the mean. answer(b) m [2] (c) calculate the frequency density of (i) the interval 250 y d i 300, answer(c)(i) [1] (ii) the interval 0 y d i 250. answer(c)(ii) [1] ", "14": "14 \u00a9 ucles 2011 0607/42/m/j/11 for examiner's use 11 y varies inversely as the square root of x. when x = 9, y = 2. (a) find y in terms of x. answer(a) y = [2] (b) find y when x = 36. answer(b) y = [1] (c) write x in terms of y. answer(c) x = [3] (d) when y is multiplied by 0.5, x is multiplied by k. find the value of k. answer(d) [2] ", "15": "15 \u00a9 ucles 2011 0607/42/m/j/11 [turn over for examiner's use 12 s p adqr c b5 cm5 cm 10 cmnot to scale the diagram shows a cuboid of length 10 cm, with a square cross-section of side 5 cm. calculate (a) the length ar, answer(a) ar = cm [3] (b) angle rac, answer(b) angle rac = [2] (c) the angle between the plane pbcs and the base abcd. answer(c) [2] ", "16": "16 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2011 0607/42/m/j/11 for examiner's use 13 f(x) = x 2 (a) write down the value of f(\u20132). answer(a) [1] (b) find x when f( x) = 9. answer(b) x = or x = [1] (c) on the axes, sketch and label the graph of (i) y = f(x ), [1] (ii) y = f(x \u2013 1), [1] (iii) y = 2f(x). [1] (d) describe fully the single transformation that maps (i) the graph of y = f(x) onto the graph of y = f(x \u2013 1), [2] (ii) the graph of y = f(x) onto the graph of y = 2f(x). [3] y x10 \u20132\u20133 30" }, "0607_s11_qp_5.pdf": { "1": " this document consists of 5 printed pages and 3 blank pages. ib11 06_0607_05/4rp \u00a9 ucles 2011 [turn over *9892833728* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/05 paper 5 (core) may/june 2011 1 hour candidates answer on the question paper additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24. ", "2": "2 \u00a9 ucles 2011 0607/05/m/j/11 for examiner's use answer all the questions. investigation pick\u2019s equation in 1899 the austrian mathematician georg pick found a method to work out the area of any polygon that has its vertices (corners) on a square grid. his method used the number of dots ( p) on the perimeter of the polygon and the number of dots ( i) inside the polygon. in the polygon shown, p = 7 and i = 4. 1 the diagram below shows 9 polygons, labelled q to y. for the rectangle r, p = 10 and i = 2. its area is a = length \u00d7 width = 3 \u00d7 2 = 6 squares. for the triangle x, p = 8 and i = 1. its area is a = 1 2 \u00d7 base \u00d7 height = 1 2 \u00d7 2 \u00d7 4 = 4 squares. q r s t u v w xy ", "3": "3 \u00a9 ucles 2011 0607/05/m/j/11 [turn over for examiner's use complete the table below. polygon dots on perimeter p dots inside i area a p + 2i \u2013 2 q 0 2 r 10 2 6 12 s 14 20 t 2 5 u 8 16 v 16 12 w 18 2 x 8 1 4 8 y 41 2 9 2 use the table to write down an equation connecting p + 2i \u2013 2 with a. this is pick\u2019s equation . 3 show that pick\u2019s equation gives the correct value for the area of this polygon. ", "4": "4 \u00a9 ucles 2011 0607/05/m/j/11 for examiner's use 4 use pick\u2019s equation to find the area of this polygon. area = squares 5 a polygon has an area a equal to 4 squares. (a) using pick\u2019s equation, a possible pair of values for p and i is p = 6 and i = 2. find another possible pair of values for p and i. p = and i = ", "5": "5 \u00a9 ucles 2011 0607/05/m/j/11 for examiner's use (b) the diagram below shows a quadrilateral with a = 4, p = 6 and i = 2. draw, on the square grid below, a quadrilateral with a = 4 and the pair of values for p and i that you found in part (a) . 6 for any polygon, explain why the value of p is greater than 2. 7 use pick\u2019s equation to show all the possible pairs of values for p and i when a polygon has an area a = 6. ", "6": "6 \u00a9 ucles 2011 0607/05/m/j/11 blank page ", "7": "7 \u00a9 ucles 2011 0607/05/m/j/11 blank page ", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2011 0607/05/m/j/11 blank page " }, "0607_s11_qp_6.pdf": { "1": " this document consists of 8 printed pages. ib11 06_0607_06/4rp \u00a9 ucles 2011 [turn over *5529328366* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/06 paper 6 (extended) may/june 2011 1 hour 30 minutes candidates answer on the question paper additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2011 0607/06/m/j/11 for examiner's use answer both parts a and b. a investigation pick\u2019s equation (20 marks) you are advised to spend 45 minutes on part a. in 1899 the austrian mathematician georg pick found a method to work out the area of any polygon that has its vertices on a square grid. his method used the number of dots ( p) on the perimeter of the polygon and the number of dots ( i) inside the polygon. in the polygon shown, p = 7 and i = 4. 1 (a) the diagram below shows the first three triangles of a sequence with i = 0. for the first triangle in the sequence p = 4. its area is a = 1 2 \u00d7 base \u00d7 height = 1 2 \u00d7 2 \u00d7 1 = 1 square. complete the table for the first 6 triangles in this sequence. area ( a) 1 number of dots on the perimeter (p) 4 6 (b) find a formula for p in terms of a. p = (c) make a the subject of the formula. a = ", "3": "3 \u00a9 ucles 2011 0607/06/m/j/11 [turn over for examiner's use (d) show that your formula for a gives the correct value of the area for this triangle. 2 the diagram below shows a sequence of triangles, each with p = 4. the number of dots (i) inside the polygon increases by one each time. (a) the area of the first triangle is 1. find the area, a, of each of the other three triangles. , , (b) explain how the connection between the increase in i and the increase in a changes your answer in question 1(c) to give a = 1 2p + i \u2013 1. this is pick\u2019s equation which works for all polygons. (c) write down the range of possible values for p. ", "4": "4 \u00a9 ucles 2011 0607/06/m/j/11 for examiner's use 3 show that pick\u2019s equation gives the correct value for the area of this polygon. 4 use pick\u2019s equation to find the area of this polygon. area = squares ", "5": "5 \u00a9 ucles 2011 0607/06/m/j/11 [turn over for examiner's use 5 a polygon has an area, a, of 4 squares. (a) using pick\u2019s equation, a possible pair of values for p and i is p = 6 and i = 2. use pick\u2019s equation to find all the other possible pairs of values. (b) the diagram below shows a quadrilateral with a = 4, p = 6 and i = 2. draw, on the square grid below, a quadrilateral with a = 4 for each of the pairs of values of p and i that you found in part (a) . ", "6": "6 \u00a9 ucles 2011 0607/06/m/j/11 for examiner's use b modelling the doubling time (20 marks) you are advised to spend 45 minutes on part b. 1 $1000 is invested at a rate of 5% compound interest per year. (a) (i) explain why, after 10 years, the total amount of money is $1000 \u00d7 1.05 10. (ii) calculate this total amount. $ (b) write down the total amount of money after y years. $ (c) (i) when y is the number of years it takes for the investment of $1000 to double, show that 1.05 y = 2. (ii) show how you can use logarithms to solve the equation 1.05y = 2 to give y = 14.2, correct to 3 significant figures. (d) (i) when the rate is x% (instead of 5% ) show, by referring to question 1(c) , that the time to double is given by the following model. log2 log 1 100yx= +\uf8eb\uf8f6 \uf8ec\uf8f7\uf8ed\uf8f8 ", "7": "7 \u00a9 ucles 2011 0607/06/m/j/11 [turn over for examiner's use (ii) using the axes given, sketch the graph of y against x for 0 i x y 100. y 0x 10010 2 (a) there is a different model for y, the time for the investment to double. which of the following approximates the model in question 1? a y = kx b y = k x c y = kx2 d y = kcosx e y = k \u2013 x (b) in question 1 , x = 5 and y = 14.2. use this information in your model to find k, correct to the nearest 10. write down your model. y = 3 use your model to write down the doubling time for a rate of 2%. years 4 (a) find the doubling time for a rate of 7% using (i) the model in question 1 , years (ii) your model. years (b) write down the difference between the times given by these two models. years ", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2011 0607/06/m/j/11 for examiner's use 5 the difference between the times given by the models is (a) on the axes, sketch the graph of d against x for 2 y x y 100. d 0x 100 2 (b) find the maximum value of d for 2 y x y 100. 6 the model in question 1 is accurate for 0 i x y 100. comment on the accuracy of your model for 0 i x y 100. ( )log 2your model log 1 100dx=\u2212 +\uf8eb\uf8f6\uf8ec\uf8f7\uf8ed\uf8f8 " }, "0607_w11_qp_1.pdf": { "1": " this document consists of 8 printed pages. ib11 11_0607_01/3rp \u00a9 ucles 2011 [turn over *0759742191* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/01 paper 1 (core) october/november 2011 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2011 0607/01/o/n/11 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2011 0607/01/o/n/11 [turn over for examiner's use answer all the questions. 1 write down the next term in the following sequence. 0, 3, 8, 15, 24, ... answer [1] 2 a football stadium holds 62 700 spectators. (a) write 62 700 in standard form. answer(a) [1] (b) write 62 700 correct to the nearest thousand. answer(b) [1] 3 (a) complete the list of factors of 45. answer(a) 1, , , , , 45 [2] (b) find the highest common factor of 36 and 45. answer(b) [1] 4 (a) work out. (i) 2 3 answer(a)(i) [1] (ii) 2(3 + 4) \u2013 5 answer(a)(ii) [1] (b) x= 4 find the value of x. answer(b) x = [1] ", "4": "4 \u00a9 ucles 2011 0607/01/o/n/11 for examiner's use 5 u ab q rps t u the elements p, q, r, s, t and u are shown in the venn diagram. complete the following. (a) a \u2229 b = { } [1] (b) a' = { } [1] (c) n ( a \u222a b ) = [1] 6 the graph of 8y x= is drawn below. \u20131 \u20132 \u20133 \u20134 \u20135 \u20136 \u20137 \u201388 7 6 5 4 3 2 1 0y x8 7654321 \u20131\u20132\u20133\u20134\u20135\u20136\u20137\u20138 on the grid, draw the two lines of symmetry of the graph. [2] ", "5": "5 \u00a9 ucles 2011 0607/01/o/n/11 [turn over for examiner's use 7 the stem and leaf diagram shows the heights of 14 plants. 0 7 8 8 9 1 1 3 6 7 9 2 0 1 2 3 2 4 key 1 3 means 13 cm (a) find the median. answer(a) cm [2] (b) find the interquartile range. answer(b) cm [2] 8 simplify. (a) 2 34x x\u2212 answer(a) [2] (b) 2c 2 \u00d7 3c3 answer(b) [2] (c) 5 26 2x x answer(c) [2] ", "6": "6 \u00a9 ucles 2011 0607/01/o/n/11 for examiner's use 9 (a) find the sum of the interior angles of a hexagon. answer(a) [1] (b) a hexagon has 4 angles of 100\u00b0 each and 2 angles of x\u00b0 each. 100\u00b0 100\u00b0 100\u00b0100\u00b0x\u00b0 x\u00b0 not to scale find the value of x. answer(b) x = [2] 10 = 6 2\uf8eb\uf8f6\uf8ec\uf8f7\uf8ed\uf8f8 and = 1 4\uf8eb\uf8f6\uf8ec\uf8f7\uf8ed\uf8f8 where o is the point (0, 0). (a) on the grid, plot the points a and c. [2] (b) oabc is a parallelogram. (i) on the grid, draw this parallelogram. [1] (ii) write down the co-ordinates of the point b. answer(b)(ii) ( , ) [1] 8 7654321 012345678xy", "7": "7 \u00a9 ucles 2011 0607/01/o/n/11 [turn over for examiner's use 11 a straight line joins the points a(1, 2) and b(3, 8). (a) find the co-ordinates of the midpoint of the line ab. answer(a) ( , ) [2] (b) find the gradient of the line ab. answer(b) [2] (c) find the equation of the line ab. answer(c) [3] question 12 is printed on the next page.", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2011 0607/01/o/n/11 for examiner's use 12 6 cm 1 cm 3 cmb c adenot to scale in the diagram de is parallel to bc. ae = 3 cm, ec = 1 cm and bc = 6 cm. find the length of de. answer cm [2] " }, "0607_w11_qp_2.pdf": { "1": " this document consists of 8 printed pages. ib11 11_0607_02/3rp \u00a9 ucles 2011 [turn over *0721467745* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/02 paper 2 (extended) october/november 2011 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2011 0607/02/o/n/11 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2011 0607/02/o/n/11 [turn over for examiner's use answer all the questions. 1 (a) write 375 \u00d7 1012 in standard form. answer(a) [1] (b) calculate 75% of $2.40. answer(b) $ [2] (c) solve the equation | x + 1 | = 2. answer(c) x = or x = [2] 2 ua b (a) n(u) = 20, n( a) = 10, n( b) = 7, n( a \u222a b) = 13. find (i) n(a \u222a b)', answer(a)(i) [1] (ii) n(a \u2229 b). answer(a)(ii) [1] (b) on the venn diagram, shade the region a \u222a b'. [1] ", "4": "4 \u00a9 ucles 2011 0607/02/o/n/11 for examiner's use 3 the equation of a straight line is 3 x + 4y = 12. write the equation in the form y = mx + c. answer y = [2] 4 the volume of a sphere of radius 3 cm is k\u03c0 cm 3. find the value of k. answer k = [2] 5 (a) simplify 125. answer(a) [1] (b) simplify 1 63\u2212 by rationalising the denominator. answer(b) [2] ", "5": "5 \u00a9 ucles 2011 0607/02/o/n/11 [turn over for examiner's use 6 6, 12, 24, 48, 96, ... (a) write down the next term in the sequence. answer(a) [1] (b) find the 8th term in the sequence. answer(b) [1] (c) find an expression for the nth term of the sequence. answer(c) [2] 7 factorise completely. (a) x 2 \u2013 2x \u2013 24 answer(a) [2] (b) xy 2 \u2013 4xz2 answer(b) [2] ", "6": "6 \u00a9 ucles 2011 0607/02/o/n/11 for examiner's use 8 qq opr pnot to scale the diagram shows the vectors = p and = q. r is on qp such that qr = 1 4qp. find the following vectors in terms of p and q. give each answer in its simplest form. (a) answer(a) = [1] (b) answer(b) = [2] 9 06 1 the die in the diagram has a number on each face. the numbers are 0, 0, 1, 2, 4, 6. the die is rolled until it shows 0 on the top face. find the probability that this happens for the first time on the third roll. answer [2] ", "7": "7 \u00a9 ucles 2011 0607/02/o/n/11 [turn over for examiner's use 10 solve the following equation. 21 19 32xx+++= answer x = [3] 11 (a) 3 = log p 8 write down the value of p. answer(a) p = [2] (b) log12 + log9 = qlog2 + rlog3 find the values of q and r. answer(b) q = r = [3] question 12 is printed on the next page.", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2011 0607/02/o/n/11 for examiner's use 12 an object moves in a circle with speed v. the force on the object is f. f varies directly as v2. when v = 5, f = 200. (a) find a formula for f in terms of v. answer(a) f = [2] (b) (i) find f when v = 2. answer(b)(i) f = [1] (ii) find v when f = 968. answer(b)(ii) v = [1] " }, "0607_w11_qp_3.pdf": { "1": " this document consists of 16 printed pages. ib11 11_0607_03/3rp \u00a9 ucles 2011 [turn over *6553972045* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/03 paper 3 (core) october/november 2011 1 hour 45 minutes candidates answer on the question paper additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96. ", "2": "2 \u00a9 ucles 2011 0607/03/o/n/11 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2011 0607/03/o/n/11 [turn over for examiner's use answer all the questions. 1 a bookcase is full of books. one shelf holds exactly 35 books. each book is 3.2 cm wide. (a) calculate l, the length of one shelf. answer(a) l = cm [1] (b) the bookcase contains 6 of these shelves. calculate the total number of books in the bookcase. answer(b) [1] (c) the books cost $6 each or $9 each. the ratio of $6 books to $9 books in the bookcase is 6 : 9. (i) write this ratio in its simplest form. answer(c)(i) : [1] (ii) find the number of $6 books in the bookcase. answer(c)(ii) [2] (iii) find the total cost of all the books in the bookcase. answer(c)(iii) $ [2] l", "4": "4 \u00a9 ucles 2011 0607/03/o/n/11 for examiner's use 2 the monthly wages, in dollars, of 10 people are listed below. 1000 1400 1100 900 1050 1500 900 800 950 1300 (a) calculate the mean. answer(a) $ [1] (b) write down the mode. answer(b) $ [1] (c) find the range. answer(c) $ [1] (d) calculate the percentage of these people with wages greater than $1100. answer(d) % [2] (e) one person is chosen at random. find the probability that this person\u2019s wage is less than $1100. answer(e) [1] (f) the largest wages, $1500, $1400 and $1300 are removed from the list. find the median of the remaining seven wages. answer(f) $ [1] ", "5": "5 \u00a9 ucles 2011 0607/03/o/n/11 [turn over for examiner's use 3 (a) expand and simplify. 2(x \u2013 3) + 3(2x + 4) answer(a) [3] (b) factorise completely. 3x 2 \u2013 9xy answer(b) [2] (c) solve the equation. 3x + 5 = x + 12 answer(c) x = [2] (d) if a = 3 and b = \u22122 find the value of 2a \u2013 3b. answer(d) [2] ", "6": "6 \u00a9 ucles 2011 0607/03/o/n/11 for examiner's use 4 (a) on the axes, sketch the graph of the function y = x2 \u2013 4 for \u2013 3 y x y 3 . 5 \u20135\u20133 3 0xy [2] (b) write down the co-ordinates of the minimum point of this graph. answer(b) ( , ) [1] (c) write down the equation of the line of symmetry of this graph. answer(c) [1] (d) write down the range of this function. answer(d) [1] (e) write down the co-ordinates of the zeros of this function. answer(e) ( , ) and ( , ) [2] ", "7": "7 \u00a9 ucles 2011 0607/03/o/n/11 [turn over for examiner's use (f) on the same axes, sketch the graph of y = 1 2x+ 2 for \u2013 3 y x y 3 . [1] (g) find the co-ordinates of the points where x2 \u2013 4 = 1 2x+ 2 . give each answer correct to 2 decimal places. answer(g) ( , ) ( , ) [2] 5 surya has $5000 in her bank account. the bank pays interest at a rate of 3% each year. (a) find how much interest surya receives at the end of the first year. answer(a) $ [2] (b) surya does not remove the interest from her account. show that the total amount of money in her account at the end of the second year is $5304.50 . [2] (c) surya does not remove any money from her account. (i) calculate the total amount of money in her account at the end of the fourth year. answer(c)(i) $ [2] (ii) find the total interest she receives. answer(c)(ii) $ [1] ", "8": "8 \u00a9 ucles 2011 0607/03/o/n/11 for examiner's use 6 one kilogram of apples costs $ x. one kilogram of oranges costs $ y. (a) write down the cost, in terms of x, of 6 kg of apples. answer(a) $ [1] (b) sami buys 6 kg of apples and 4 kg of oranges. the total cost is $27. use this information to write down an equation in x and y. answer(b) [1] (c) terri buys 2 kg of apples and 3 kg of oranges. the total cost is $14. use this information to write down an equation in x and y. answer(c) [1] (d) solve the two equations to find the cost of 1 kg of apples and the cost of 1 kg of oranges. show all your working. answer(d) 1 kg of apples costs $ 1 kg of oranges costs $ [3] ", "9": "9 \u00a9 ucles 2011 0607/03/o/n/11 [turn over for examiner's use 7 a ship sails 50 km from a point s to a point a on a bearing of 040\u00b0. northnorth sa not to scale 40\u00b050 km (a) the ship took 2 hours 30 minutes to sail from s to a. find the average speed of the ship in km/h. answer(a) km/h [1] (b) calculate the distance that a is north of s. answer(b) km [3] (c) find the bearing of s from a. answer(c) [1] ", "10": "10 \u00a9 ucles 2011 0607/03/o/n/11 for examiner's use 8 (a) c a d bp qy\u00b0 x\u00b0 60\u00b0 140\u00b0not to scale the diagram shows a triangle abc. ab is parallel to pq and abd is a straight line. angle cab = 60\u00b0 and angle cbd = 140\u00b0. find the values of x and y. answer(a) x = y = [2] (b) a bo t 30\u00b0q\u00b0 p\u00b0not to scale ta and tb are tangents at a and b to the circle, centre o. angle atb = 30\u00b0. find the values of p and q. answer(b) p = q = [2] ", "11": "11 \u00a9 ucles 2011 0607/03/o/n/11 [turn over for examiner's use (c) e d c b ao60\u00b040\u00b0not to scale the straight lines ad and be cross at o. angle cod = 40\u00b0 and angle doe = 60\u00b0. find the size of (i) angle aob , answer(c)(i) [1] (ii) angle aoe , answer(c)(ii) [1] (iii) angle boc. answer(c)(iii) [1] (d) ab o6 cm10 cmnot to scale the diagram shows a circle, radius 10 cm, centre o. a chord ab is drawn so that its midpoint is 6 cm from o. calculate the length of the chord ab. answer(d) cm [4] ", "12": "12 \u00a9 ucles 2011 0607/03/o/n/11 for examiner's use 9 the cumulative frequency curve shows the marks that students scored in an examination. 160 140120100 80604020 010 20 30 40 50 60 70 80 90 100cumulative frequency marks (a) write down how many students took the examination. answer(a) [1] (b) find how many students scored less than 60 marks. answer(b) [1] (c) the top 10% of students received a prize. (i) find how many students received a prize. answer(c)(i) [1] (ii) find the lowest possible mark for receiving a prize. answer(c)(ii) [2] ", "13": "13 \u00a9 ucles 2011 0607/03/o/n/11 [turn over for examiner's use 10 a quadrilateral p is drawn on the grid. (a) write down the geometrical name for the quadrilateral p. answer(a) [1] (b) describe fully the single transformation that maps p onto q. [2] (c) describe fully the single transformation that maps p onto r. [2] (d) on the grid, draw the image of p after a rotation of 90\u00b0 anticlockwise about (0, 0). [2] (e) on the grid, draw the image of p after an enlargement centre (0, 0), scale factor 2. [2] \u20131 \u20132 \u20133 \u20134 \u20135 \u20136 \u20137 \u20138 \u20139 \u201310 8 9 107 6 5 4 3 2 1 0y x10 9 87654321 \u20131\u20132\u20133\u20134\u20135\u20136\u20137\u20138\u20139 \u201310p q r", "14": "14 \u00a9 ucles 2011 0607/03/o/n/11 for examiner's use 11 7 m 6 mx mnot to scale a train tunnel is in the shape of a semicircle on top of a rectangle. the width of the tunnel is 6 m. the total height of the tunnel is 7 m. (a) (i) find the radius of the semicircle. answer(a)(i) m [1] (ii) find the value of x. answer(a)(ii) x = [1] (b) calculate the area of the rectangle. answer(b) m2 [1] (c) calculate the area of the semicircle. give your answer correct to 2 significant figures. answer(c) m2 [3] ", "15": "15 \u00a9 ucles 2011 0607/03/o/n/11 [turn over for examiner's use (d) the length of the tunnel is 35 kilometres. calculate the volume of earth, in cubic metres , that was removed to make the tunnel. answer(d) m3 [2] (e) a train travels at an average speed of 105 km/h through the tunnel. (i) calculate the time, in minutes, it takes the train to travel through the tunnel. answer(e)(i) minutes [2] (ii) the train enters the tunnel at 11 10. it arrives at the next station at 12 02. find the number of minutes between the train leaving the tunnel and arriving at the station. answer(e)(ii) minutes [2] question 12 is printed on the next page.", "16": "16 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2011 0607/03/o/n/11 for examiner's use 12 a bag contains 4 green beads and 8 red beads. one bead is chosen at random from the bag. (a) find the probability that the bead chosen is red. answer(a) [1] (b) the bead is not returned to the bag. find the probability that a second bead chosen at random from the bag is also red. answer(b) [2] (c) use your answers to parts (a) and (b) to help you complete the tree diagram. 1st choice 2nd choice red greenred green greenred.. .. .. .. [2] (d) calculate the probability that two beads chosen at random are different colours. answer(d) [3] " }, "0607_w11_qp_4.pdf": { "1": " this document consists of 18 printed pages and 2 blank pages. ib11 11_0607_04/2rp \u00a9 ucles 2011 [turn over *8251556869* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/04 paper 4 (extended) october/november 2011 2 hours 15 minutes candidates answer on the question paper additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120. ", "2": "2 \u00a9 ucles 2011 0607/04/o/n/11 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2011 0607/04/o/n/11 [turn over for examiner's use answer all the questions. 1 alessandro travels from a village in france to his home in italy. (a) his flight from paris to rome takes 1 hour 57 minutes. (i) the departure time is 10 25. write down the arrival time. answer(a)(i) [1] (ii) write down the flight time in hours. answer(a)(ii) h [1] (iii) the distance between paris and rome is 1120 km. calculate the average speed of the flight. give your answer in km/h. answer(a)(iii) km/h [2] (b) the flight time of 1 hour 57 minutes is 26% of alessandro\u2019s total journey time. calculate alessandro\u2019s total journey time. give your answer in hours and minutes. answer(b) h min [3] ", "4": "4 \u00a9 ucles 2011 0607/04/o/n/11 for examiner's use 2 d axb cnot to scale7 cm4 cm 6 cm in the circle, the chords ab and cd intersect at x. (a) complete the statement. angle adx is equal to angle [1] (b) ax = 6 cm, dx = 4 cm and xb = 7 cm. calculate the length of xc. answer(b) cm [2] (c) the area of triangle bxc is 32.7 cm2. calculate the area of triangle dxa . answer(c) cm2 [2] ", "5": "5 \u00a9 ucles 2011 0607/04/o/n/11 [turn over for examiner's use 3 maria invests $480 at a rate of 2.6% per year compound interest. (a) calculate the interest maria receives after 5 years. answer(a) $ [4] (b) calculate the number of years it takes for the total amount to exceed $800. show your working and give your answer to the nearest integer. answer(b) [3] ", "6": "6 \u00a9 ucles 2011 0607/04/o/n/11 for examiner's use 4 d a c b48\u00b0 95\u00b011 cm 12 cm7 cmnot to scale in the quadrilateral abcd, ad = 11 cm, dc = 7 cm and ac = 12 cm. angle bac = 48\u00b0 and angle abc = 95\u00b0. (a) calculate the length of bc. answer(a) cm [3] (b) calculate angle adc. answer(b) [3] ", "7": "7 \u00a9 ucles 2011 0607/04/o/n/11 [turn over for examiner's use 5 f(x) = 2x2 \u2013 3x \u2013 3 (a) solve the equation f( x) = 0. give your answers correct to 2 decimal places. answer(a) x = or x = [3] (b) f(2 x \u2013 3) = 8x 2 \u2013 kx + 24 find the value of k. answer(b) k = [3] ", "8": "8 \u00a9 ucles 2011 0607/04/o/n/11 for examiner's use 6 260\u00b0 4.7 mnot to scale the diagram shows the cross-section of a tunnel. this cross-section is made up of a triangle and a sector of radius 4.7 m and angle 260\u00b0. (a) calculate the area of the cross-section. answer(a) m2 [5] (b) the tunnel has a length of 2.4 km. calculate the volume of earth that was removed to make the tunnel. give your answer in cubic metres. answer(b) m3 [2] ", "9": "9 \u00a9 ucles 2011 0607/04/o/n/11 [turn over for examiner's use (c) one cubic metre of earth has a mass of 1530 kg. calculate the total mass of the earth that was removed. give your answer in tonnes and correct to 2 significant figures. answer(c) tonnes [3] 7 5 4321 050 70 100 150frequencydensity mass (grams)m the histogram shows information about the masses of some apples. (a) complete the frequency table. mass (m grams) 0 y m i 70 70 y m i 100 100 y m i 150 frequency 210 [2] (b) calculate an estimate of the mean mass of the apples. answer(b) g [2] ", "10": "10 \u00a9 ucles 2011 0607/04/o/n/11 for examiner's use 8 in this question, answers which are not exact should be given correct to 4 significant figures. (a) f(x) = x4 \u2013 x2 (i) on the axes, sketch the graph of y = f(x), for \u20131.5 y x y 1.5 . 3 \u20131.5\u20131.5 1.5 0xy [2] (ii) write down the co-ordinates of the points where the graph meets the axes. answer(a)(ii) ( , ) , ( , ) , ( , ) [2] (iii) write down the equation of the line of symmetry of this graph. answer(a)(iii) [1] (iv) find the co-ordinates of the minimum points. answer(a)(iv) ( , ) , ( , ) [2] (v) write down the range of f( x) when the domain is o. answer(a)(v) [1] ", "11": "11 \u00a9 ucles 2011 0607/04/o/n/11 [turn over for examiner's use (b) (i) on the axes, sketch the graph of y = g( x), where g(x) = 2x \u2013 1.6 . [2] (ii) solve the equation 2x \u2013 1.6 = 0 . answer(b)(ii) x = [1] (c) (i) solve the equation x4 \u2013 x2 = 2x \u2013 1.6, for \u20131.5 y x y 1.5 . answer(c)(i) x = or x = [2] (ii) solve the inequality f( x) i g( x). answer(c)(ii) [1] 9 sr c b ap dq 12 cm10 cm7 cm not to scale the diagram shows a cuboid which measures 12 cm by 10 cm by 7 cm. (a) calculate the total surface area of the cuboid. answer(a) cm2 [2] (b) calculate angle rbc. answer(b) [2] (c) calculate the length bs. answer(c) cm [3] ", "12": "12 \u00a9 ucles 2011 0607/04/o/n/11 for examiner's use 10 e a bcd 84\u00b0110\u00b0not to scale in the pentagon abcde, ab is parallel to ed, bc is parallel to ae and bc = cd. angle eab = 84\u00b0 and angle bcd = 110\u00b0. (a) (i) find the size of angle aed . answer(a)(i) [1] (ii) find the size of angle cde. answer(a)(ii) [2] (b) draw the line bd and find the size of angle abd . answer(b) [2] (c) extend ed and bc to meet at x. (i) write down the mathematical name of the shape abxe . answer(c)(i) [1] (ii) write down the size of angle cxd. answer(c)(ii) [1] (d) extend ab and dc to meet at y. (i) find the size of angle byc. answer(d)(i) [1] (ii) give a reason why it is not possible to draw a circle through b, y, x and d. answer(d)(ii) [1] ", "13": "13 \u00a9 ucles 2011 0607/04/o/n/11 [turn over for examiner's use 11 y x4 321 \u20131\u20132\u20133\u201340 \u2013 4 \u2013 3 \u2013 2 \u2013 1 1234 f( x) = x2 g( x) = ( x + 2)2 h( x) = 2 x2 k(x) = \u2013 x2 (a) on the grid, sketch the graph of each function. label each graph clearly. [4] (b) describe fully the single transformation that maps (i) the graph of y = f(x) onto the graph of y = g( x), answer(b)(i) [2] (ii) the graph of y = f(x) onto the graph of y = h( x), answer(b)(ii) [3] (iii) the graph of y = f(x) onto the graph of y = k( x). answer(b)(iii) [2] ", "14": "14 \u00a9 ucles 2011 0607/04/o/n/11 for examiner's use 12 on any day, the probability that it rains is 0.15 . if it rains, the probability that claudia rides her bike is 0.3 . if it does not rain, the probability that claudia rides her bike is 0.9 . (a) draw a tree diagram to show this information. write the probabilities on all the branches. [4] (b) find the probability that (i) it does not rain and claudia rides her bike, answer(b)(i) [2] (ii) claudia rides her bike. answer(b)(ii) [2] (c) during a period of 15 days, on how many days would claudia expect to ride her bike? answer(c) [1] ", "15": "15 \u00a9 ucles 2011 0607/04/o/n/11 [turn over for examiner's use 13 r4 \u2013443 0xline 1 line 2line 3 not to scaley (a) line 1 is parallel to the x-axis and passes through the point (0, 3). write down the equation of line 1. answer(a) [1] (b) line 2 passes through the points (0, 4) and (4, 0). find the equation of line 2. answer(b) [2] (c) line 3 passes through the point (0, \u2013 4) and has a gradient of 2. write down the equation of line 3. answer(c) [2] (d) find the co-ordinates of the point of intersection of line 2 and line 3. answer(d) ( , ) [2] (e) write down the three inequalities that define the region r, shaded in the diagram. answer(e) , , [2] ", "16": "16 \u00a9 ucles 2011 0607/04/o/n/11 for examiner's use 14 ten students take a mental arithmetic test and a calculator test. the table shows the results. student a b c d e f g h i j mental arithmetic test score ( x) 15 8 20 19 13 7 10 20 17 9 calculator test score ( y) 12 8 18 20 11 9 11 20 15 8 (a) complete the scatter diagram to show this information. the information for students a to f has already been plotted. 20 1816141210 8642 02 4 6 8 10 12 14 16 18 20y x mental arithmetic test scorecalculator test score [2] (b) underline one word which best describes the correlation between the scores on each test. none positive negative [1] ", "17": "17 \u00a9 ucles 2011 0607/04/o/n/11 [turn over for examiner's use (c) (i) the mean score for the mental arithmetic test is 13.8 . find the mean score for the calculator test. answer(c)(i) [1] (ii) find the equation of the line of regression, giving y in terms of x. answer(c)(ii) y = [2] (iii) draw the line of regression on the scatter diagram. [2] (iv) a student scores 18 in the mental arithmetic test. predict this student\u2019s score in the calculator test. answer(c)(iv) [1] ", "18": "18 \u00a9 ucles 2011 0607/04/o/n/11 for examiner's use 15 (a) (i) a circle is cut into n equal sectors. write down, in terms of n, the angle at the centre of each sector. answer(a)(i) [1] (ii) a circle is cut into n + 3 equal sectors. write down, in terms of n, the angle at the centre of each sector. answer(a)(ii) [1] (b) the angle in part(a)(ii) is 4\u00b0 smaller than the angle in part(a)(i) . write down an equation in n and find the value of n. answer(b) n = [5] ", "19": "19 \u00a9 ucles 2011 0607/04/o/n/11 blank page ", "20": "20 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2011 0607/04/o/n/11 blank page " }, "0607_w11_qp_5.pdf": { "1": " this document consists of 6 printed pages and 2 blank pages. ib11 11_0607_05/2rp \u00a9 ucles 2011 [turn over *4924094545* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/05 paper 5 (core) october/november 2011 1 hour candidates answer on the question paper additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24. ", "2": "2 \u00a9 ucles 2011 0607/05/o/n/11 for examiner's use answer all questions. investigation maximising the perimeter identical shapes can be joined to make larger shapes. 1 squares of side 1 cm may be joined edge to edge, for example but not like this. (a) the diagram below shows a shape made of 3 squares and a shape made of 4 squares. draw a different shape made of 3 squares and a different shape made of 4 squares. (b) (i) the diagram below shows a shape, made of 5 squares, with a perimeter of 10 cm. draw two different shapes each made of 5 squares and each with a perimeter greater than 10 cm. ", "3": "3 \u00a9 ucles 2011 0607/05/o/n/11 [turn over for examiner's use (ii) the diagram below shows a shape, made of 6 squares, with a perimeter of 12 cm. draw two different shapes each made of 6 squares and each with a perimeter greater than 12 cm. (c) find the greatest perimeter for shapes made of (i) 4 squares, cm (ii) 5 squares, cm (iii) 6 squares. cm you may use the grid below to draw your shapes. ", "4": "4 \u00a9 ucles 2011 0607/05/o/n/11 for examiner's use (d) (i) complete this table. number of squares 2 3 4 5 6 7 8 9 10 greatest perimeter (cm) 6 16 22 (ii) write down the greatest perimeter for a shape made of 17 squares. cm (iii) how many squares make the shape when the greatest perimeter is 32 cm? (e) look at your table to help you complete the following statements. (i) to find the greatest perimeter for a shape made of 2 squares, multiply 2 by 2, then add (ii) to find the greatest perimeter for a shape made of 7 squares, multiply 7 by , then add (f) write down an expression, in terms of x, for the greatest perimeter for a shape made of x squares. ", "5": "5 \u00a9 ucles 2011 0607/05/o/n/11 [turn over for examiner's use 2 equilateral triangles of side 1 cm may be joined edge to edge, for example but not like this. (a) find the greatest perimeter for a shape made of 6 equilateral triangles. cm you may use the grid below to help you. (b) (i) complete this table. number of equilateral triangles 2 3 4 5 6 7 8 greatest perimeter (cm) 4 10 (ii) write down the greatest perimeter for a shape made of 10 equilateral triangles. cm (iii) how many equilateral triangles make the shape when the greatest perimeter is 18 cm? (c) write down an expression, in terms of x, for the greatest perimeter for a shape made of x equilateral triangles. ", "6": "6 \u00a9 ucles 2011 0607/05/o/n/11 for examiner's use 3 find an expression, in terms of x, for the greatest perimeter for a shape made of x regular hexagons. ", "7": "7 \u00a9 ucles 2011 0607/05/o/n/11 blank page ", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2011 0607/05/o/n/11 blank page " }, "0607_w11_qp_6.pdf": { "1": " this document consists of 12 printed pages. ib11 11_0607_06/3rp \u00a9 ucles 2011 [turn over *1866204662* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/06 paper 6 (extended) october/november 2011 1 hour 30 minutes candidates answer on the question paper additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2011 0607/06/o/n/11 for examiner's use answer both parts a and b. a investigation maximising the perimeter (20 marks) identical shapes can be joined to make larger shapes. 1 equilateral triangles of side 1 cm may be joined edge to edge, for example but not like this. (a) the diagram below shows a shape made of 4 equilateral triangles and a shape made of 5 equilateral triangles. draw a different shape made of 4 equilateral triangles and a different shape made of 5 equilateral triangles. (b) (i) the diagram below shows a shape, made of 6 equilateral triangles, with a perimeter of 6 cm. draw a different shape, made of 6 equilateral triangles, with a perimeter greater than 6 cm. ", "3": "3 \u00a9 ucles 2011 0607/06/o/n/11 [turn over for examiner's use (ii) the diagram below shows a shape, made of 7 equilateral triangles, with a perimeter of 7 cm. draw a different shape, made of 7 equilateral triangles, with a perimeter greater than 7 cm. (c) (i) this table shows the greatest possible perimeters for shapes made of equilateral triangles. complete the table. number of equilateral triangles 2 3 4 5 6 7 8 greatest perimeter (cm) 4 10 you may use the grid below to help you. ", "4": "4 \u00a9 ucles 2011 0607/06/o/n/11 for examiner's use (ii) write down the greatest perimeter for a shape made of 20 equilateral triangles. cm (iii) how many equilateral triangles make the shape when the greatest perimeter is 32 cm? (d) write down an expression, in terms of x, for the greatest perimeter for a shape made of x equilateral triangles. 2 squares of side 1 cm may be joined edge to edge, for example but not like this. (a) find the greatest perimeter for a shape made of 6 squares. cm you may use the grid opposite to help you. ", "5": "5 \u00a9 ucles 2011 0607/06/o/n/11 [turn over for examiner's use (b) (i) complete this table. number of squares 2 3 4 5 6 7 8 9 10 greatest perimeter (cm) 6 12 22 (ii) write down the greatest perimeter for a shape made of 17 squares. cm (iii) how many squares make the shape when the greatest perimeter is 32 cm? (c) write down an expression, in terms of x, for the greatest perimeter for a shape made of x squares. ", "6": "6 \u00a9 ucles 2011 0607/06/o/n/11 for examiner's use 3 (a) this table shows the greatest perimeters for shapes made of regular hexagons of side 1 cm. complete the table. number of regular hexagons 2 3 4 5 6 greatest perimeter (cm) 26 (b) write down an expression, in terms of x, for the greatest perimeter for a shape made of x regular hexagons. 4 find an expression, in terms of x, for the greatest perimeter for a shape made of x regular octagons. ", "7": "7 \u00a9 ucles 2011 0607/06/o/n/11 [turn over for examiner's use 5 (a) write down an expression, in terms of x and y, for the greatest perimeter for a shape made of x regular polygons each with y sides. (b) the greatest perimeter for a shape made of x regular polygons, each with y sides is 26 cm. find three possible pairs of values of x and y. x = y = x = y = x = y = ", "8": "8 \u00a9 ucles 2011 0607/06/o/n/11 for examiner's use b modelling covering cakes (20 marks) different shaped cakes are made each with a volume of 4000 cm 3. the top and sides of each cake are covered in chocolate. 1 a square-based cake measures x cm by x cm by y cm, as shown in the diagram. x cmx cm y cm (a) show that 24000y x= . (b) the area covered in chocolate is s cm 2. by finding an expression for s in terms of x and y show that 216000sx x=+ . ", "9": "9 \u00a9 ucles 2011 0607/06/o/n/11 [turn over for examiner's use (c) sketch the graph of s against x for 2 y x y 40 and 0 y s y 10000 on the axes below. s 0 x 40 10000 (d) find the minimum surface area to be covered in chocolate. write down the values of x and y. minimum surface area = cm2 x = y = ", "10": "10 \u00a9 ucles 2011 0607/06/o/n/11 for examiner's use 2 a circular-based (cylindrical) cake has a radius of x cm and a height of y cm. the area to be covered in chocolate is s cm2 and the volume of the cake is 4000 cm3. y cmx cm (a) show that 28000sx x\u03c0=+ . (b) sketch the graph of s against x for 1 y x y 20 and 0 y s y 10000 on the axes below. s 0 x 20 10000 ", "11": "11 \u00a9 ucles 2011 0607/06/o/n/11 [turn over for examiner's use (c) find the minimum surface area to be covered in chocolate. write down the values of x and y. minimum surface area = cm2 x = y = 3 216000sx x=+ and 28000sx x\u03c0=+ are models for the amount of chocolate required to cover the top and sides of each cake. (a) explain how you could use these models for surface area to find the volume of chocolate required. (b) comment on whether the models give realistic results for the volume of chocolate. question 4 is printed on the next page", "12": "12 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2011 0607/06/o/n/11 for examiner's use 4 for a cake with minimum surface area, bakers use the following rule: test this rule on both cakes. show your working. there is twice as much chocolate on the sides as on the top. " } }, "2012": { "0607_s12_qp_11.pdf": { "1": " this document consists of 9 printed pages and 3 blank pages. ib12 06_0607_11/rp \u00a9 ucles 2012 [turn over *4459401971* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/11 paper 1 (core) may/june 2012 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. for examiner's use ", "2": "2 \u00a9 ucles 2012 0607/11/m/j/12 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2012 0607/11/m/j/12 [turn over for examiner's use answer all the questions. 1 (a) work out (4 \u2013 7)2. answer (a) [1] (b) write down the value of 144. answer (b) [1] 2 (a) write 0.00724538 correct to 3 significant figures. answer (a) [1] (b) write your answer to part (a) in standard form. answer (b) [1] 3 (a) write down the first three multiples of 6. answer (a) , , [1] (b) find the lowest common multiple of 6 and 15. answer (b) [2] ", "4": "4 \u00a9 ucles 2012 0607/11/m/j/12 for examiner's use 4in the venn diagram shade the region a \u2229 bv. u a b [1] 5 peter buys one ticket in the school raffle. the school sells 1000 tickets. the winning ticket is drawn at random. what is the probability that peter does not have the winning ticket? answer [2] ", "5": "5 \u00a9 ucles 2012 0607/11/m/j/12 [turn over for examiner's use 6 (a) simplify. 7(x \u2013 2) \u2013 3(3 + x) answer (a) [2] (b) solve the inequality. 7(x \u2013 2) \u2013 3(3 + x) < 1 answer (b) [2] (c) show your answer to part (b) on the number line below. \u20136 \u20138 \u20134 \u20132 0 2 4 6 8 [2] ", "6": "6 \u00a9 ucles 2012 0607/11/m/j/12 for examiner's use 7 (a) write as a single fraction. 43x + 3x answer (a) [2] (b) simplify. 57 618 xx answer (b) [2] 8the first five terms of a sequence are 2, 5, 10, 17, 26. (a) write down the next term in this sequence. answer (a) [1] (b) find the nth term of this sequence. answer (b) [3] ", "7": "7 \u00a9 ucles 2012 0607/11/m/j/12 [turn over for examiner's use 9 alice takes examinations in german and french. the probability that she passes german is 0.3 . the probability that she passes french is 0.6 . (a) complete the tree diagram. german passpass fail... ...0.3 ...failpass fail... ...french [2] (b) work out the probability that alice passes german and fails french. answer (b) [2] ", "8": "8 \u00a9 ucles 2012 0607/11/m/j/12 for examiner's use 10 lucy counts the number of words in each sentence of a film review. the number of words in each sentence is shown below. 7 8 12 7 9 11 4 12 8 12 find (a) the mode, answer (a) [1] (b) the mean, answer (b) [2] (c) the range. answer (c) [1] 11 one lap of the melbourne grand prix circuit is 5200 metres. a racing driver completes a lap in 1.3 minutes. calculate his average speed in kilometres per hour . answer km/h [3] ", "9": "9 \u00a9 ucles 2012 0607/11/m/j/12 for examiner's use 12 \u20136 \u20138 \u201310 \u20136 \u20138 \u201310\u20134 \u201320 2 4 6 8 10 \u20134\u20132246810 xay (a) reflect triangle a in the x-axis. label it b. [1] (b) translate triangle a by the vector \uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec \uf8ed\uf8eb \u2212\u2212 106. label it c. [2] (c) rotate triangle a 90o anti-clockwise about centre (2, 2). label it d. [2] ", "10": "10 \u00a9 ucles 2012 0607/11/m/j/12 blank page", "11": "11 \u00a9 ucles 2012 0607/11/m/j/12 blank page", "12": "12 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2012 0607/11/m/j/12 blank page " }, "0607_s12_qp_12.pdf": { "1": " this document consists of 9 printed pages and 3 blank pages. ib12 06_0607_12/rp \u00a9 ucles 2012 [turn over *0613595201* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/12 paper 1 (core) may/june 2012 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. for examiner's use ", "2": "2 \u00a9 ucles 2012 0607/12/m/j/12 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2012 0607/12/m/j/12 [turn over for examiner's use answer all the questions. 1 (a) work out (4 \u2013 7)2. answer (a) [1] (b) write down the value of 144. answer (b) [1] 2 (a) write 0.00724538 correct to 3 significant figures. answer (a) [1] (b) write your answer to part (a) in standard form. answer (b) [1] 3 (a) write down the first three multiples of 6. answer (a) , , [1] (b) find the lowest common multiple of 6 and 15. answer (b) [2] ", "4": "4 \u00a9 ucles 2012 0607/12/m/j/12 for examiner's use 4in the venn diagram shade the region a \u2229 bv. u a b [1] 5 peter buys one ticket in the school raffle. the school sells 1000 tickets. the winning ticket is drawn at random. what is the probability that peter does not have the winning ticket? answer [2] ", "5": "5 \u00a9 ucles 2012 0607/12/m/j/12 [turn over for examiner's use 6 (a) simplify. 7 ( x \u2013 2) \u2013 3(3 + x) answer (a) [2] (b) solve the inequality. 7 ( x \u2013 2) \u2013 3(3 + x) < 1 answer (b) [2] (c) show your answer to part (b) on the number line below. \u20136 \u20138 \u20134 \u20132 0 2 4 6 8 [2] ", "6": "6 \u00a9 ucles 2012 0607/12/m/j/12 for examiner's use 7 (a) write as a single fraction. 43x + 3x answer (a) [2] (b) simplify. 57 618 xx answer (b) [2] 8the first five terms of a sequence are 2, 5, 10, 17, 26. (a) write down the next term in this sequence. answer (a) [1] (b) find the nth term of this sequence. answer (b) [3] ", "7": "7 \u00a9 ucles 2012 0607/12/m/j/12 [turn over for examiner's use 9 alice takes examinations in german and french. the probability that she passes german is 0.3 . the probability that she passes french is 0.6 . (a) complete the tree diagram. german passpass fail... ...0.3 ...failpass fail... ...french [2] (b) work out the probability that alice passes german and fails french. answer (b) [2] ", "8": "8 \u00a9 ucles 2012 0607/12/m/j/12 for examiner's use 10 lucy counts the number of words in each sentence of a film review. the number of words in each sentence is shown below. 7 8 12 7 9 11 4 12 8 12 find (a) the mode, answer (a) [1] (b) the mean, answer (b) [2] (c) the range. answer (c) [1] 11 one lap of the melbourne grand prix circuit is 5200 metres. a racing driver completes a lap in 1.3 minutes. calculate his average speed in kilometres per hour . answer km/h [3] ", "9": "9 \u00a9 ucles 2012 0607/12/m/j/12 for examiner's use 12 \u20136 \u20138 \u201310 \u20136 \u20138 \u201310\u20134 \u201320 2 4 6 8 10 \u20134\u20132246810 xay (a) reflect triangle a in the x-axis. label it b. [1] (b) translate triangle a by the vector \uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec \uf8ed\uf8eb \u2212\u2212 106. label it c. [2] (c) rotate triangle a 90o anti-clockwise about centre (2, 2). label it d. [2] ", "10": "10 \u00a9 ucles 2012 0607/12/m/j/12 blank page ", "11": "11 \u00a9 ucles 2012 0607/12/m/j/12 blank page", "12": "12 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2012 0607/12/m/j/12 blank page " }, "0607_s12_qp_13.pdf": { "1": " this document consists of 9 printed pages and 3 blank pages. ib12 06_0607_13/rp \u00a9 ucles 2012 [turn over *8151451650* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/13 paper 1 (core) may/june 2012 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2012 0607/13/m/j/12 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2012 0607/13/m/j/12 [turn over for examiner's use answer all the questions 1 (a) work out 0.2 \u00d7 0.4 . answer (a) [1] (b) write these in order, smallest first. 0.85 89% 0.9 0.745 answer (b) < < < [1] 2work out 15% of $160 . answer $ [2] 3 (a) write 0.007582 correct to 3 significant figures. answer (a) [1] (b) write 209 as a decimal. answer (b) [1] ", "4": "4 \u00a9 ucles 2012 0607/13/m/j/12 for examiner's use 4 work out. 243 + 332 answer [3] 5 (a) find the value of 70 . answer (a) [1] (b) simplify. 7 x2 \u00d7 3x5 answer (b) [2] ", "5": "5 \u00a9 ucles 2012 0607/13/m/j/12 [turn over for examiner's use 6 (a) factorise. 3 a \u2013 a2 answer (a) [1] (b) expand and simplify. ( x \u2013 5)(x + 1) answer (b) [2] 7 under each shape write the correct letter from the table. l line symmetry only r rotational symmetry only b both line and rotational symmetry n no symmetry \u2260 \u03b8 p \u00a7 \u263a [3] ", "6": "6 \u00a9 ucles 2012 0607/13/m/j/12 for examiner's use 8 f(x) = 3x + 2 (a) find f(5) . answer (a) [1] (b) find x when f( x) = 14 . answer (b) [2] 9 a class of 21 students took a mathematics test. here are their results. 29 34 18 28 43 49 8 29 45 32 28 17 46 32 26 17 42 39 21 38 47 draw an ordered stem-and-leaf diagram to show these results. 0 1 2 3 4 key: /paseq means [3] ", "7": "7 \u00a9 ucles 2012 0607/13/m/j/12 [turn over for examiner's use 10 (a) solve. 5 x \u2013 2 < 3x + 5 answer (a) [2] (b) simplify. xy7 \u00f7 yx 23 answer (b) [2] ", "8": "8 \u00a9 ucles 2012 0607/13/m/j/12 for examiner's use 11 u = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} p = {prime numbers} f = {factors of 6} (a) complete the venn diagram to show this information. u pf [3] (b) a number is chosen at random from the 14 elements in u. write down the probability that this number is an element of (i) (p \u2229 f ), answer (b)(i) [1] (ii) (p \u222a f ) v. answer (b)(ii) [1] ", "9": "9 \u00a9 ucles 2012 0607/13/m/j/12 for examiner's use 12 not to scale m (1, \u20131) a (\u20135, \u20134)b the diagram shows three points a(\u2013 5, \u2013 4), m (1, \u20131) and b. m is the midpoint of the line ab. (a) find the co-ordinates of b. answer (a) ( , ) [2] (b) find the gradient of the line ab. answer (b) [2] (c) 04 1 15y xnot to scale cd find the length of the line cd. answer (c) [3] ", "10": "10 \u00a9 ucles 2012 0607/13/m/j/12 blank page", "11": "11 \u00a9 ucles 2012 0607/13/m/j/12 blank page", "12": "12 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2012 0607/13/m/j/12 blank page " }, "0607_s12_qp_21.pdf": { "1": " this document consists of 8 printed pages. ib12 06_0607_21/4rp \u00a9 ucles 2012 [turn over *6989037045* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/21 paper 2 (extended) may/june 2012 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2012 0607/21/m/j/12 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2012 0607/21/m/j/12 [turn over for examiner's use answer all the questions. 1 solve the simultaneous equations. 7 2= \u2212y x 3 2= +y x answer x = answer y = [2] 2 a bus leaves afford at 07 55. it travels 15 km to beetown at a speed of 50 km/h. find the time the bus arrives in beetown. answer [3] 3 the area of a semicircle is given by the formula 22r \u03c0a = . make r the subject of the formula. answer r = [3] ", "4": "4 \u00a9 ucles 2012 0607/21/m/j/12 for examiner's use 4 (a) h4not to scale6 find the exact value of h. answer(a) [2] (b) g 12\u03b8not to scale sin32=\u03b8 , cos 35=\u03b8 , tan 52=\u03b8 . find the exact value of g. answer(b) [2] 5 0y x the sketch shows the graph of y = f(x). using the same axes, sketch the graph of y = 2f(x). [2] ", "5": "5 \u00a9 ucles 2012 0607/21/m/j/12 [turn over for examiner's use 6 (a) find the two possible values of y x+ when 42=x and 1=y . answer(a) , [2] (b) expand and simplify ( )( )1 2 3 1 2\u2212 +. answer(b) [2] 7 sara records some information about the number of cars in a car park. u = {cars in the car park} f = {5-door cars} s = {silver cars} fs u you may use the venn diagram to help you answer the following questions. (a) n(u) = 12, n(f) = 7, 2 ) n( = \u2229s f , 11) n( = \u222as f . find (i) n(s), answer(a)(i) [1] (ii) ) n(f s\u2032\u222a . answer(a)(ii) [1] (b) sara chooses a car from the car park at random. find the probability that it is a 5-door car. answer(b) [1] (c) sara chooses a silver car at random. find the probability that it is a 5-door car. answer(c) [1] ", "6": "6 \u00a9 ucles 2012 0607/21/m/j/12 for examiner's use 8 factorise completely. (a) 48 22\u2212 +x x answer(a) [2] (b) z y xz xy 6 3 2\u2212 \u2212 + answer(b) [2] 9 xy1\u221d when x = 4, y = 3. find y when x = 25. answer [3] ", "7": "7 \u00a9 ucles 2012 0607/21/m/j/12 [turn over for examiner's use 10 the first five terms of a sequence are \u2013 2, 1, 6, 13, 22. (a) write down the next term in the sequence. answer(a) [1] (b) find an expression, in terms of n, for the nth term of the sequence. answer(b) [3] 11 two mathematically similar containers have heights of 3 cm and 6 cm. the larger container, when full, can hold 320 ml of water. calculate how much water the smaller container can hold when full. answer ml [2] question 12 is on the next page. ", "8": "8 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2012 0607/21/m/j/12 for examiner's use 12 (a) (i) 81 3=p write down the value of p. answer(a)(i) [1] (ii) 812=q write down the value of q. answer(a)(ii) [1] (b) 2log5 3 log2 log + = y find the value of y. answer(b) [3] " }, "0607_s12_qp_22.pdf": { "1": " this document consists of 8 printed pages. ib12 06_0607_22/5rp \u00a9 ucles 2012 [turn over *0334232765* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/22 paper 2 (extended) may/june 2012 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2012 0607/22/m/j/12 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2012 0607/22/m/j/12 [turn over for examiner's use answer all the questions. 1 (a) find the value of 21 49\u2212. answer(a) [1] (b) when 42=\u2212x write down the values of x. answer(b) x = or x = [2] 2 (a) factorise 2 62\u2212 \u2212x x . answer(a) [2] (b) solve the equation 0 2 62= \u2212 \u2212 x x . answer(b) x = or x = [1] ", "4": "4 \u00a9 ucles 2012 0607/22/m/j/12 for examiner's use 3 p = \uf8f7 \uf8f8\uf8f6\uf8ec \uf8ed\uf8eb 32 q = \uf8f7 \uf8f8\uf8f6\uf8ec \uf8ed\uf8eb\u2212 53 find (a) 2p \u2013 3q, answer(a) \uf8f7\uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec\uf8ec \uf8ed\uf8eb [2] (b) p . answer(b) [2] 4 find the next two terms in this sequence. 1, 2, 6, 15, 31, .. answer , [2] ", "5": "5 \u00a9 ucles 2012 0607/22/m/j/12 [turn over for examiner's use 5 factorise completely. (a) qx xy py pq \u2212 + \u2212 answer(a) [2] (b) 2 250 32d c\u2212 answer(b) [2] 6 (a) for the function x y2 sin 3 = write down (i) the amplitude, answer(a)(i) [1] (ii) the period. answer(a)(ii) [1] (b) sketch the graph of x y2 sin 3 = on the axes below for o0 y x y o360 . y x4 0 \u2013490\u00b0 180\u00b0 270\u00b0 360\u00b0 [2] ", "6": "6 \u00a9 ucles 2012 0607/22/m/j/12 for examiner's use 7 solve the simultaneous equations. 3 p + 4q = 7 5p + 6q = 10 answer p = q = [4] 8 y varies directly as 2x, where x is a positive integer. when x = 3, y = 108. calculate the value of x when y = 300. answer x = [3] ", "7": "7 \u00a9 ucles 2012 0607/22/m/j/12 [turn over for examiner's use 9 joe is training for a triathlon. during one training session he \u007f swims 1 km in 15 minutes, \u007f cycles 20 km at a speed of 20 km/h, \u007f runs at a speed of 8 km/h for 45 minutes. calculate joe\u2019s average speed for the training session. give your answer in kilometres per hour. answer km/h [3] 10 solve the equation. 1141) 3( 73=\u2212\u2212+ x x answer x = [3] questions 11 and 12 are on the next page. ", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2012 0607/22/m/j/12 for examiner's use 11 (a) write as a single logarithm. 2log4log3log \u2212 + answer(a) [1] (b) make x the subject of x y3log= . answer(b) x = [1] (c) simplify completely. 327 answer(c) [1] 12 the co-ordinates of three points are a(\u22122, 6), b(6, 2) and c(\u22122, \u22122). (a) find the gradient of ab. answer(a) [1] (b) d is the midpoint of ab. by using gradients show that the straight lines ab and cd are not perpendicular. [3] " }, "0607_s12_qp_23.pdf": { "1": " this document consists of 8 printed pages. ib12 06_0607_23/fp \u00a9 ucles 2012 [turn over *2686818862* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/23 paper 2 (extended) may/june 2012 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2012 0607/23/m/j/12 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2012 0607/23/m/j/12 [turn over for examiner's use answer all the questions. 1 (a) find the value of 21 49\u2212. answer(a) [1] (b) when 42=\u2212x write down the values of x. answer(b) x = or x = [2] 2 (a) factorise 2 62\u2212 \u2212x x . answer(a) [2] (b) solve the equation 0 2 62= \u2212 \u2212 x x . answer(b) x = or x = [1] ", "4": "4 \u00a9 ucles 2012 0607/23/m/j/12 for examiner's use 3 p = \uf8f7 \uf8f8\uf8f6\uf8ec \uf8ed\uf8eb 32 q = \uf8f7 \uf8f8\uf8f6\uf8ec \uf8ed\uf8eb\u2212 53 find (a) 2p \u2013 3q, answer(a) \uf8f7\uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec\uf8ec \uf8ed\uf8eb [2] (b) p . answer(b) [2] 4 find the next two terms in this sequence. 1, 2, 6, 15, 31, .. answer , [2] ", "5": "5 \u00a9 ucles 2012 0607/23/m/j/12 [turn over for examiner's use 5 factorise completely. (a) qx xy py pq \u2212 + \u2212 answer(a) [2] (b) 2 250 32d c\u2212 answer(b) [2] 6 (a) for the function x y2 sin 3 = write down (i) the amplitude, answer(a)(i) [1] (ii) the period. answer(a)(ii) [1] (b) sketch the graph of x y2 sin 3 = on the axes below for o0 y x y o360 . y x4 0 \u2013490\u00b0 180\u00b0 270\u00b0 360\u00b0 [2] ", "6": "6 \u00a9 ucles 2012 0607/23/m/j/12 for examiner's use 7 solve the simultaneous equations. 3 p + 4q = 7 5p + 6q = 10 answer p = q = [4] 8 y varies directly as 2x, where x is a positive integer. when x = 3, y = 108. calculate the value of x when y = 300. answer x = [3] ", "7": "7 \u00a9 ucles 2012 0607/23/m/j/12 [turn over for examiner's use 9 joe is training for a triathlon. during one training session he \u007f swims 1 km in 15 minutes, \u007f cycles 20 km at a speed of 20 km/h, \u007f runs at a speed of 8 km/h for 45 minutes. calculate joe\u2019s average speed for the training session. give your answer in kilometres per hour. answer km/h [3] 10 solve the equation. 1141) 3( 73=\u2212\u2212+ x x answer x = [3] questions 11 and 12 are on the next page. ", "8": "8 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2012 0607/23/m/j/12 for examiner's use 11 (a) write as a single logarithm. 2log4log3log \u2212 + answer(a) [1] (b) make x the subject of x y3log= . answer(b) x = [1] (c) simplify completely. 327 answer(c) [1] 12 the co-ordinates of three points are a(\u22122, 6), b(6, 2) and c(\u22122, \u22122). (a) find the gradient of ab. answer(a) [1] (b) d is the midpoint of ab. by using gradients show that the straight lines ab and cd are not perpendicular. [3] " }, "0607_s12_qp_31.pdf": { "1": " this document consists of 18 printed pages and 2 blank pages. ib12 06_0607_31/4rp \u00a9 ucles 2012 [turn over *0252844276* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/31 paper 3 (core) may/june 2012 1 hour 45 minutes candidates answer on the question paper additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96. ", "2": "2 \u00a9 ucles 2012 0607/31/m/j/12 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2012 0607/31/m/j/12 [turn over for examiner's use answer all the questions. 1 some information about 20 students is shown in the venn diagram. each student is represented by a letter. u swim (s) tennis (t) a m b c ld kenf g r whi p u v qj (a) list the students who swim only. answer(a) [1] (b) write down n ) (t s\u2229 . answer(b) [1] (c) calculate the percentage of the 20 students who do not swim and do not play tennis. answer(c) % [2] (d) one of the 20 students is chosen at random. find the probability that the student plays tennis but does not swim. answer(d) [1] (e) a student is chosen at random from those students who swim. find the probability that this student also plays tennis. answer(e) [1] ", "4": "4 \u00a9 ucles 2012 0607/31/m/j/12 for examiner's use 2 mrs edge, mr ray and dr surd teach mathematics at imbright academy. they spend $7000 on equipment in the ratio mrs edge : mr ray : dr surd = 33 : 35 : 32 . (a) (i) show that mrs edge spends $2310. [2] (ii) work out how much mr ray and dr surd spend. answer(a)(ii) mr ray $ dr surd $ [2] (b) mrs edge spends all her $2310 on 22 calculators. find the cost of one calculator. answer(b) $ [1] (c) dr surd buys a laptop computer for her class. the laptop costs $1320. find how much dr surd has left to spend. answer(c) $ [1] (d) mr ray spends 70% of his money on text books. find how much mr ray spends on text books. answer(d) $ [2] ", "5": "5 \u00a9 ucles 2012 0607/31/m/j/12 [turn over for examiner's use 3 (a) solve the simultaneous equations x + 5y = 9 and 3 x + 2y = 1 . show all your working. answer(a) x = y = [3] (b) (i) factorise completely. 2 \u03c0r2 + 2\u03c0rh answer(b)(i) [2] (ii) make h the subject of this formula. s = 2 \u03c0r2 + 2\u03c0rh answer(b)(ii) h = [2] (c) simplify. 3 x \u00d7 2x 2 answer(c) [2] ", "6": "6 \u00a9 ucles 2012 0607/31/m/j/12 for examiner's use 4 8 7654321 012345678y x (a) on the grid, plot the points p (2, 3) and r (4, 7). [2] (b) draw the straight line pr. find the co-ordinates of m, the midpoint of pr. answer(b) ( , ) [1] (c) write in component form. answer(c) \uf8f7\uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec\uf8ec \uf8ed\uf8eb [1] (d) calculate the gradient of pr. answer(d) [2] ", "7": "7 \u00a9 ucles 2012 0607/31/m/j/12 [turn over for examiner's use (e) write down the gradient of a line parallel to pr. answer(e) [1] (f) find the equation of the straight line through the point (5, 3) which is parallel to pr. answer(f) [2] ", "8": "8 \u00a9 ucles 2012 0607/31/m/j/12 for examiner's use 5 25 201510 50 40 45 50 55 60 65 70 75cumulative frequency mass (kg) all the members of a zumba club were weighed and their masses recorded. the results are shown on the cumulative frequency graph. (a) find (i) the number of members in the zumba club, answer(a)(i) [1] (ii) the median, answer(a)(ii) kg [1] (iii) the inter-quartile range. answer(a)(iii) kg [2] (b) a member of the zumba club is selected at random. find the probability that this member has a mass less than 55kg. answer(b) [2] ", "9": "9 \u00a9 ucles 2012 0607/31/m/j/12 [turn over for examiner's use 6 (a) ab e c d51\u00b0 82\u00b0not to scale ac and db are the diagonals of the quadrilateral abcd. ab is parallel to dc. angle dce = 82\u00b0 and angle aeb = 51\u00b0. (i) write down the mathematical name for the quadrilateral abcd. answer(a)(i) [1] (ii) find angle dec. answer(a)(ii) [1] (iii) find angle eab. answer(a)(iii) [1] (iv) find angle aed . answer(a)(iv) [1] (b) calculate the size of one interior angle of a regular pentagon. answer(b) [3] ", "10": "10 \u00a9 ucles 2012 0607/31/m/j/12 for examiner's use 7 c b ae do10.6 cm 5.3 cm 35\u00b0not to scale de is a tangent at a to the circle, centre o, diameter 10.6 cm. angle oab = 35\u00b0. (a) find (i) angle abc, answer(a)(i) [1] (ii) angle cad, answer(a)(ii) [1] (iii) angle aob . answer(a)(iii) [1] (b) calculate the length of the arc ab. answer(b) cm [2] (c) use trigonometry to calculate the length of the chord cb. answer(c) cm [2] ", "11": "11 \u00a9 ucles 2012 0607/31/m/j/12 [turn over for examiner's use 8 18 cm30 cm not to scale the diagram shows the paper used to cover a triangular prism. the paper is made up of a rectangle, 30 cm by 18 cm, and two equilateral triangles. (a) find (i) the length of a side of one of the equilateral triangles, answer(a)(i) cm [1] (ii) the total perimeter of the paper. answer(a)(ii) cm [2] (b) the area of each equilateral triangle is 15.6 cm2, correct to 3 significant figures. calculate the total area of the paper. answer(b) cm2 [2] ", "12": "12 \u00a9 ucles 2012 0607/31/m/j/12 for examiner's use 9 2.8 cm 9.8 cm not to scale l cm the diagram shows an ice cream cornet. the cornet is made from a cone and a hemisphere. the cone has a base radius of 2.8 cm and a height of 9.8 cm. the hemisphere has a radius of 2.8 cm. (a) calculate the volume of the hemisphere. answer(a) cm3 [2] (b) the hemisphere is made of ice cream. the curved surface area of the hemisphere is covered in chocolate. calculate the surface area covered in chocolate. answer(b) cm2 [2] ", "13": "13 \u00a9 ucles 2012 0607/31/m/j/12 [turn over for examiner's use (c) calculate the length of the sloping edge, l, of the cone. answer(c) cm [2] (d) calculate the curved surface area of the cone. answer(d) cm2 [2] (e) the radius of the hemisphere in a similar ice cream cornet is 2 cm. calculate the height of the cone used to make this ice cream cornet. answer(e) cm [2] ", "14": "14 \u00a9 ucles 2012 0607/31/m/j/12 for examiner's use 10 to find some hidden treasure, zareen is given the following instructions. from p, walk 200 metres on a bearing of 030\u00b0. then walk 80 metres on a bearing of 120\u00b0. here lies the treasure. (a) show this information on a sketch of zareen\u2019s route to the treasure. north p [2] (b) use trigonometry to calculate the bearing of the treasure from p. answer(b) [4] ", "15": "15 \u00a9 ucles 2012 0607/31/m/j/12 [turn over for examiner's use 11 4 4 \u20134 \u201340y x (a) sketch the graph of y = 0.1 x3 + 0.15x2 \u2013 0.6x for \u2013 4 y x y 4 . [3] (b) write down the co-ordinates of the local maximum point and the local minimum point. answer(b) maximum ( , ) minimum ( , ) [2] (c) one of the zeros of y = 0.1x 3 + 0.15x2 \u2013 0.6x is \u2013 3.31. write down the other two zeros. answer(c) x = and x = [2] (d) using the same axes, sketch the graph of y = 0.1x3 + 0.15x2 \u2013 0.6x + 3 . [1] ", "16": "16 \u00a9 ucles 2012 0607/31/m/j/12 for examiner's use 12 the lung capacity of 35 males was measured using a machine. the machine\u2019s readings are shown in the table. lung capacity reading (cm 3) frequency 3300 3 3400 1 3500 3 3600 4 3700 3 3800 6 3900 4 4000 3 4100 2 4200 2 4300 3 4400 1 (a) calculate the mean lung capacity. answer(a) cm3 [1] (b) find the median lung capacity. answer(b) cm3 [1] (c) write down the fraction of males with a reading greater than 3800 cm3. give your answer in its lowest term. answer(c) [2] ", "17": "17 \u00a9 ucles 2012 0607/31/m/j/12 [turn over for examiner's use (d) the scatter diagram shows the heights and lung capacity readings of the 35 males. 150 160 170 180 190 2004500 400035003000lung capacity reading (cm3) height (cm)0 (i) describe the correlation between height and lung capacity reading. answer(d)(i) [1] (ii) the mean height of the 35 males is 180 cm. using your answer to part (a) , draw a line of best fit on the diagram. [2] (iii) estimate the lung capacity reading for a male of height 165 cm. answer(d)(iii) cm3 [1] ", "18": "18 \u00a9 ucles 2012 0607/31/m/j/12 for examiner's use 13 5 6 \u20132 \u201350y x (a) sketch the graph of ) 2 (3 \u2212=xy for \u2013 2 y x y 6. [2] (b) write down the equations of the two asymptotes. answer(b) [2] (c) using the same axes, sketch the line y = x \u2013 3. [1] (d) write down the co-ordinates of the points of intersection of ) 2 (3 \u2212=xy and y = x \u2013 3. answer(d) ( , ) and ( , ) [2] ", "19": "19 \u00a9 ucles 2012 0607/31/m/j/12 blank page", "20": "20 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publis her (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2012 0607/31/m/j/12 blank page " }, "0607_s12_qp_32.pdf": { "1": " this document consists of 18 printed pages and 2 blank pages. ib12 06_0607_32/fp \u00a9 ucles 2012 [turn over *5691435795* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/32 paper 3 (core) may/june 2012 1 hour 45 minutes candidates answer on the question paper additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96. ", "2": "2 \u00a9 ucles 2012 0607/32/m/j/12 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2012 0607/32/m/j/12 [turn over for examiner's use answer all the questions. 1 some information about 20 students is shown in the venn diagram. each student is represented by a letter. u swim (s) tennis (t) a m b c ld kenf g r whi p u v qj (a) list the students who swim only. answer(a) [1] (b) write down n ) (t s\u2229 . answer(b) [1] (c) calculate the percentage of the 20 students who do not swim and do not play tennis. answer(c) % [2] (d) one of the 20 students is chosen at random. find the probability that the student plays tennis but does not swim. answer(d) [1] (e) a student is chosen at random from those students who swim. find the probability that this student also plays tennis. answer(e) [1] ", "4": "4 \u00a9 ucles 2012 0607/32/m/j/12 for examiner's use 2 mrs edge, mr ray and dr surd teach mathematics at imbright academy. they spend $7000 on equipment in the ratio mrs edge : mr ray : dr surd = 33 : 35 : 32 . (a) (i) show that mrs edge spends $2310. [2] (ii) work out how much mr ray and dr surd spend. answer(a)(ii) mr ray $ dr surd $ [2] (b) mrs edge spends all her $2310 on 22 calculators. find the cost of one calculator. answer(b) $ [1] (c) dr surd buys a laptop computer for her class. the laptop costs $1320. find how much dr surd has left to spend. answer(c) $ [1] (d) mr ray spends 70% of his money on text books. find how much mr ray spends on text books. answer(d) $ [2] ", "5": "5 \u00a9 ucles 2012 0607/32/m/j/12 [turn over for examiner's use 3 (a) solve the simultaneous equations x + 5y = 9 and 3 x + 2y = 1 . show all your working. answer(a) x = y = [3] (b) (i) factorise completely. 2 \u03c0r2 + 2\u03c0rh answer(b)(i) [2] (ii) make h the subject of this formula. s = 2 \u03c0r2 + 2\u03c0rh answer(b)(ii) h = [2] (c) simplify. 3 x \u00d7 2x 2 answer(c) [2] ", "6": "6 \u00a9 ucles 2012 0607/32/m/j/12 for examiner's use 4 8 7654321 012345678y x (a) on the grid, plot the points p (2, 3) and r (4, 7). [2] (b) draw the straight line pr. find the co-ordinates of m, the midpoint of pr. answer(b) ( , ) [1] (c) write in component form. answer(c) \uf8f7\uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec\uf8ec \uf8ed\uf8eb [1] (d) calculate the gradient of pr. answer(d) [2] ", "7": "7 \u00a9 ucles 2012 0607/32/m/j/12 [turn over for examiner's use (e) write down the gradient of a line parallel to pr. answer(e) [1] (f) find the equation of the straight line through the point (5, 3) which is parallel to pr. answer(f) [2] ", "8": "8 \u00a9 ucles 2012 0607/32/m/j/12 for examiner's use 5 25 201510 50 40 45 50 55 60 65 70 75cumulative frequency mass (kg) all the members of a zumba club were weighed and their masses recorded. the results are shown on the cumulative frequency graph. (a) find (i) the number of members in the zumba club, answer(a)(i) [1] (ii) the median, answer(a)(ii) kg [1] (iii) the inter-quartile range. answer(a)(iii) kg [2] (b) a member of the zumba club is selected at random. find the probability that this member has a mass less than 55kg. answer(b) [2] ", "9": "9 \u00a9 ucles 2012 0607/32/m/j/12 [turn over for examiner's use 6 (a) ab e c d51\u00b0 82\u00b0not to scale ac and db are the diagonals of the quadrilateral abcd. ab is parallel to dc. angle dce = 82\u00b0 and angle aeb = 51\u00b0. (i) write down the mathematical name for the quadrilateral abcd. answer(a)(i) [1] (ii) find angle dec. answer(a)(ii) [1] (iii) find angle eab. answer(a)(iii) [1] (iv) find angle aed . answer(a)(iv) [1] (b) calculate the size of one interior angle of a regular pentagon. answer(b) [3] ", "10": "10 \u00a9 ucles 2012 0607/32/m/j/12 for examiner's use 7 c b ae do10.6 cm 5.3 cm 35\u00b0not to scale de is a tangent at a to the circle, centre o, diameter 10.6 cm. angle oab = 35\u00b0. (a) find (i) angle abc, answer(a)(i) [1] (ii) angle cad, answer(a)(ii) [1] (iii) angle aob . answer(a)(iii) [1] (b) calculate the length of the arc ab. answer(b) cm [2] (c) use trigonometry to calculate the length of the chord cb. answer(c) cm [2] ", "11": "11 \u00a9 ucles 2012 0607/32/m/j/12 [turn over for examiner's use 8 18 cm30 cm not to scale the diagram shows the paper used to cover a triangular prism. the paper is made up of a rectangle, 30 cm by 18 cm, and two equilateral triangles. (a) find (i) the length of a side of one of the equilateral triangles, answer(a)(i) cm [1] (ii) the total perimeter of the paper. answer(a)(ii) cm [2] (b) the area of each equilateral triangle is 15.6 cm2, correct to 3 significant figures. calculate the total area of the paper. answer(b) cm2 [2] ", "12": "12 \u00a9 ucles 2012 0607/32/m/j/12 for examiner's use 9 2.8 cm 9.8 cm not to scale l cm the diagram shows an ice cream cornet. the cornet is made from a cone and a hemisphere. the cone has a base radius of 2.8 cm and a height of 9.8 cm. the hemisphere has a radius of 2.8 cm. (a) calculate the volume of the hemisphere. answer(a) cm3 [2] (b) the hemisphere is made of ice cream. the curved surface area of the hemisphere is covered in chocolate. calculate the surface area covered in chocolate. answer(b) cm2 [2] ", "13": "13 \u00a9 ucles 2012 0607/32/m/j/12 [turn over for examiner's use (c) calculate the length of the sloping edge, l, of the cone. answer(c) cm [2] (d) calculate the curved surface area of the cone. answer(d) cm2 [2] (e) the radius of the hemisphere in a similar ice cream cornet is 2 cm. calculate the height of the cone used to make this ice cream cornet. answer(e) cm [2] ", "14": "14 \u00a9 ucles 2012 0607/32/m/j/12 for examiner's use 10 to find some hidden treasure, zareen is given the following instructions. from p, walk 200 metres on a bearing of 030\u00b0. then walk 80 metres on a bearing of 120\u00b0. here lies the treasure. (a) show this information on a sketch of zareen\u2019s route to the treasure. north p [2] (b) use trigonometry to calculate the bearing of the treasure from p. answer(b) [4] ", "15": "15 \u00a9 ucles 2012 0607/31/m/j/12 [turn over for examiner's use 11 4 4 \u20134 \u201340y x (a) sketch the graph of y = 0.1 x3 + 0.15x2 \u2013 0.6x for \u2013 4 y x y 4 . [3] (b) write down the co-ordinates of the local maximum point and the local minimum point. answer(b) maximum ( , ) minimum ( , ) [2] (c) one of the zeros of y = 0.1x 3 + 0.15x2 \u2013 0.6x is \u2013 3.31. write down the other two zeros. answer(c) x = and x = [2] (d) using the same axes, sketch the graph of y = 0.1x3 + 0.15x2 \u2013 0.6x + 3 . [1] ", "16": "16 \u00a9 ucles 2012 0607/32/m/j/12 for examiner's use 12 the lung capacity of 35 males was measured using a machine. the machine\u2019s readings are shown in the table. lung capacity reading (cm 3) frequency 3300 3 3400 1 3500 3 3600 4 3700 3 3800 6 3900 4 4000 3 4100 2 4200 2 4300 3 4400 1 (a) calculate the mean lung capacity. answer(a) cm3 [1] (b) find the median lung capacity. answer(b) cm3 [1] (c) write down the fraction of males with a reading greater than 3800 cm3. give your answer in its lowest term. answer(c) [2] ", "17": "17 \u00a9 ucles 2012 0607/31/m/j/12 [turn over for examiner's use (d) the scatter diagram shows the heights and lung capacity readings of the 35 males. 150 160 170 180 190 2004500 400035003000lung capacity reading (cm3) height (cm)0 (i) describe the correlation between height and lung capacity reading. answer(d)(i) [1] (ii) the mean height of the 35 males is 180 cm. using your answer to part (a) , draw a line of best fit on the diagram. [2] (iii) estimate the lung capacity reading for a male of height 165 cm. answer(d)(iii) cm3 [1] ", "18": "18 \u00a9 ucles 2012 0607/32/m/j/12 for examiner's use 13 5 6 \u20132 \u201350y x (a) sketch the graph of ) 2 (3 \u2212=xy for \u2013 2 y x y 6. [2] (b) write down the equations of the two asymptotes. answer(b) [2] (c) using the same axes, sketch the line y = x \u2013 3. [1] (d) write down the co-ordinates of the points of intersection of ) 2 (3 \u2212=xy and y = x \u2013 3. answer(d) ( , ) and ( , ) [2] ", "19": "19 \u00a9 ucles 2012 0607/32/m/j/12 blank page", "20": "20 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publis her (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2012 0607/32/m/j/12 blank page " }, "0607_s12_qp_33.pdf": { "1": " this document consists of 19 printed pages and 1 blank page. ib12 06_0607_33/3rp \u00a9 ucles 2012 [turn over *9977619076* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/33 paper 3 (core) may/june 2012 1 hour 45 minutes candidates answer on the question paper additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96. ", "2": "2 \u00a9 ucles 2012 0607/33/m/j/12 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2012 0607/33/m/j/12 [turn over for examiner's use answer all the questions. 1 mr and mrs habib and their two children are going on holiday from dubai to london. (a) their flight leaves at 14 20. they need to be at the airport 212 hours before take-off. the journey from home to the airport takes 35 minutes. what is the latest time they can leave home? answer(a) [2] (b) the flight leaves on time at 14 20 and takes 7 hours 30 minutes. the time in london is 4 hours behind the time in dubai. what time is it in london when they arrive? answer(b) [2] (c) the price of each ticket is 1600 dirhams. they must also pay 28% in taxes. calculate the total cost of all the tickets including taxes. answer(c) dirhams [3] (d) in london mrs habib changes 3000 dirhams to pounds, \u00a3. the exchange rate is \u00a31 = 5.50 dirhams. calculate the amount she receives. give your answer correct to 2 decimal places. answer(d) \u00a3 [2] ", "4": "4 \u00a9 ucles 2012 0607/33/m/j/12 for examiner's use 2 david has a farm on which he keeps chickens and goats. (a) the probability that a chicken will lay an egg on any day is 0.8 . (i) find the probability that a chicken will not lay an egg on any day. answer(a)(i) [1] (ii) calculate the probability that a chicken will lay an egg on two consecutive days. answer(a)(ii) [2] (b) david records the number of eggs he collects each day for 90 days. the results are shown in this table. number of eggs collected in one day 55 56 57 58 59 60 number of days 11 23 20 16 14 6 find (i) the mode, answer(b)(i) [1] (ii) the median, answer(b)(ii) [1] (iii) the upper quartile, answer(b)(iii) [1] (iv) the total number of eggs collected in the 90 days. answer(b)(iv) [1] ", "5": "5 \u00a9 ucles 2012 0607/33/m/j/12 [turn over for examiner's use (c) david records the amount of milk the goats produce over the same 90 days. the results are shown in this table. amount of milk (m, litres) 30 y m < 40 40 y m < 50 50 y m < 60 60 y m < 70 70 y m < 80 number of days 10 17 19 26 18 calculate an estimate of the mean amount of milk produced per day. answer(c) litres [2] ", "6": "6 \u00a9 ucles 2012 0607/33/m/j/12 for examiner's use 3 all the measurements on the diagram are in centimetres. a n e p dbc17 58 910 10not to scale the diagram shows a flag abcde. an = 8 cm, nc = 5 cm, cb = 10 cm, ab = 17 cm, en = 9 cm and pd = 10 cm. (a) calculate the total area of the flag. answer(a) cm2 [4] (b) the outside edge of the flag is shown by the solid lines. (i) calculate the length of cd. answer(b)(i) cm [2] (ii) calculate the total length of the outside edge of the flag. answer(b)(ii) cm [2] ", "7": "7 \u00a9 ucles 2012 0607/33/m/j/12 [turn over for examiner's use 4 bacy x \u20136\u2013 5\u2013 4\u2013 3\u2013 2\u2013 1 0 1234566 54321 \u20131\u20132\u20133\u20134\u20135\u20136 (a) describe fully the single transformation that maps triangle a onto triangle b. answer(a) [2] (b) describe fully the single transformation that maps triangle a onto triangle c. answer(b) [3] (c) draw the image of triangle a after an enlargement, centre (3, 6) with scale factor 2. [2] ", "8": "8 \u00a9 ucles 2012 0607/33/m/j/12 for examiner's use 5 (a) in 2010 the men\u2019s world record for running 400 metres was 43.18 seconds. calculate the average speed of this runner. answer(a) m/s [2] (b) r m s m the diagram shows the edge of a running track. there are two straight sections each s metres long and two semicircular ends of radius r metres. the formula for the distance around the track, d metres, is d = 2s + 2 \u03c0r . (i) calculate the distance around the track when s = 75 and r = 30 . answer(b)(i) m [2] (ii) rearrange d = 2s + 2 \u03c0r to make r the subject. answer(b)(ii) r = [2] (iii) when d = 400 and s = 85, show that r = 36.6 correct to 3 significant figures. [1] ", "9": "9 \u00a9 ucles 2012 0607/33/m/j/12 [turn over for examiner's use 6 y x12 \u20136\u2013203 (a) sketch the graph of y = 3x \u2013 5x for \u2013 2 y x y 3 . [2] (b) find the co-ordinates of the local minimum point. answer(b) ( , ) [2] (c) on the same diagram sketch the graph of y = 4x \u2013 5 . [2] (d) write down the solutions to the equation 3 x \u2013 5x = 4x \u2013 5 . answer(d) x = or x = [2] ", "10": "10 \u00a9 ucles 2012 0607/33/m/j/12 for examiner's use 7 a child\u2019s toy is made using a cone and a hemisphere. h 11 cm 6 cmnot to scale the hemisphere and the base of the cone each have a radius of 6 cm. the sloping edge of the cone is 11 cm. (a) (i) calculate the height of the cone, h. answer(a)(i) cm [3] (ii) calculate the volume of the cone. answer(a)(ii) cm3 [2] ", "11": "11 \u00a9 ucles 2012 0607/33/m/j/12 [turn over for examiner's use (b) (i) calculate the curved surface area of the cone. answer(b)(i) cm2 [2] (ii) calculate the total surface area of the toy. answer(b)(ii) cm2 [3] ", "12": "12 \u00a9 ucles 2012 0607/33/m/j/12 for examiner's use 8 6 6 \u20136 \u201360y x (a) (i) sketch the graph of ) 2 () 3 ( \u2212+=xxy for \u2013 6 y x y 6 . [2] (ii) write down the co-ordinates of the point where the curve crosses the x-axis. answer(a)(ii) ( , ) [1] (iii) write down the co-ordinates of the point where the curve crosses the y-axis. answer(a)(iii) ( , ) [1] (iv) write down the equations of the two asymptotes. answer(a)(iv) and [2] ", "13": "13 \u00a9 ucles 2012 0607/33/m/j/12 [turn over for examiner's use (b) the graph of y = x2 is shown on the axes below. 12 9 63 \u201330 36 \u20136\u2013 3y x (i) using the same axes, sketch the graph of 2) 3 (+ =x y . [1] (ii) describe fully the single transformation that maps the graph of y = x2 onto the graph of y = (x + 3)2 . answer(b)(ii) [2] ", "14": "14 \u00a9 ucles 2012 0607/33/m/j/12 for examiner's use 9 north 70\u00b0 a pb 8 kmnot to scale a ship sails on a bearing of 070\u00b0 from a to b. ab = 8 km. (a) use trigonometry to calculate (i) ap, the distance b is east of a, answer(a)(i) km [2] (ii) bp, the distance b is north of a. answer(a)(ii) km [2] ", "15": "15 \u00a9 ucles 2012 0607/33/m/j/12 [turn over for examiner's use (b) the ship then sails from b to c. north 70\u00b0 a prqc b 8 km5 km6 kmnot to scale bq = 5 km and cq = 6 km. (i) find the distances ar and cr. answer(b)(i) ar = km cr = km [1] (ii) north a rc not to scale another ship sails directly from a to c. using your answers to part (b)(i) , calculate the bearing of c from a. answer(b)(ii) km [3] ", "16": "16 \u00a9 ucles 2012 0607/33/m/j/12 for examiner's use 10 a teacher recorded some information about 10 of his students. the results are shown in the table. number days absent 5 1 12 22 3 24 5 46 44 30 mark in a test 74 92 62 68 83 56 87 50 38 62 (a) complete the scatter diagram. the first 7 points in the table have been plotted for you. 100 90 8070605040302010 0 0 1 02 03 04 05 0mark in test number of days absent [2] (b) describe the type of correlation. answer(b) [1] (c) calculate the mean number of days absent, d. answer(c) d = [1] ", "17": "17 \u00a9 ucles 2012 0607/33/m/j/12 [turn over for examiner's use (d) the mean mark in the test, t, is 67.2 . on the scatter diagram plot the point ( d, t). [1] (e) draw a line of best fit on your scatter diagram. [1] (f) a student who had 36 days absent missed the test. use your line of best fit to estimate a test mark for that student. answer(f) [1] ", "18": "18 \u00a9 ucles 2012 0607/33/m/j/12 for examiner's use 11 (a) these are the first 5 terms of a sequence. 7 11 15 19 23 (i) write down the next two terms in the sequence. answer(a)(i) , [2] (ii) find an expression for the nth term of the sequence. answer(a)(ii) [2] (b) write down the nth term of this sequence. 1, 4, 9, 16, 25, answer(b) [1] (c) here is another sequence. 8, 15, 24, 35, 48, (i) write down the next term of this sequence. answer(c)(i) [1] (ii) use your answers to part (a)(ii) and part (b) to find the nth term of this sequence. answer(c)(ii) [1] ", "19": "19 \u00a9 ucles 2012 0607/33/m/j/12 for examiner's use 12 o36\u00b094\u00b0 56\u00b05.4 cm 3.8 cm 8.1 cma b dcnot to scale the diagonals of the trapezium abcd intersect at o. ab is parallel to dc. angle abd = 36\u00b0, angle dbc = 94\u00b0 and angle aod = 56\u00b0. (a) find (i) angle bac, answer(a)(i) [2] (ii) angle bdc, answer(a)(ii) [1] (iii) angle bcd, answer(a)(iii) [1] (iv) angle bca. answer(a)(iv) [1] (b) ab = 5.4 cm, cd = 8.1 cm and ao = 3.8 cm. triangles aob and cod are similar. calculate the length of co. answer(b) cm [2] ", "20": "20 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2012 0607/33/m/j/12 blank page " }, "0607_s12_qp_41.pdf": { "1": " this document consists of 19 printed pages and 1 blank page. ib12 06_0607_41/4rp \u00a9 ucles 2012 [turn over *2207603078* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/41 paper 4 (extended) may/june 2012 2 hours 15 minutes candidates answer on the question paper additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120. ", "2": "2 \u00a9 ucles 2012 0607/41/m/j/12 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2012 0607/41/m/j/12 [turn over for examiner's use answer all the questions. 1 in july 2009, the population of the world was 6.78 \u00d7 109. (a) the population of bangladesh was 2.39% of the world population. (i) calculate the population of bangladesh. give your answer correct to 2 significant figures. answer(a)(i) [2] (ii) write your answer to part(a)(i) in standard form. answer(a)(ii) [1] (b) the population of uganda was 3.27 \u00d7 107. calculate the population of uganda as a percentage of the world population . answer(b) % [2] (c) the world population of 6.78 \u00d7 10 9 was an increase of 169% on the population in 1950. calculate the population in 1950. give your answer correct to the nearest million. answer(c) [3] ", "4": "4 \u00a9 ucles 2012 0607/41/m/j/12 for examiner's use 2 42\u00b0 25\u00b0sr q p9 cm18 cmnot to scale in the quadrilateral pqrs , pr = 18 cm and ps = 9 cm. angle prq = 90\u00b0, angle rpq = 25\u00b0 and angle spr = 42\u00b0. (a) calculate qr. answer(a) cm [2] (b) calculate the area of the quadrilateral pqrs . answer(b) cm2 [3] (c) calculate sr. answer(c) cm [3] ", "5": "5 \u00a9 ucles 2012 0607/41/m/j/12 [turn over for examiner's use 3 \u20136 \u20138 \u20134 \u20132y x 02 4 6 8 1 08 642 \u20132a b pqr (a) (i) write down the column vector . answer(a)(i) \uf8f7\uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec\uf8ec \uf8ed\uf8eb [1] (ii) calculate . answer(a)(ii) [2] (b) describe fully the single transformation that maps (i) p onto q, answer(b)(i) [2] (ii) p onto r. answer(b)(ii) [3] ", "6": "6 \u00a9 ucles 2012 0607/41/m/j/12 for examiner's use 4 100 students take part in a reaction time test. the table shows their results. reaction time (t seconds) 0 y t < 20 20 y t < 30 30 y t < 40 40 y t < 80 number of students 20 36 32 12 (a) calculate an estimate of the mean reaction time. answer(a) seconds [2] (b) 20040 60 80100 80 604020cumulative frequency reaction time (seconds)t on the grid, complete the cumulative frequency curve to show the information in the table. [3] ", "7": "7 \u00a9 ucles 2012 0607/41/m/j/12 [turn over for examiner's use (c) use your cumulative frequency curve to find (i) the median, answer(c)(i) seconds [1] (ii) the inter-quartile range, answer(c)(ii) seconds [2] (iii) the number of students with a reaction time of at least 25 seconds. answer(c)(iii) [2] ", "8": "8 \u00a9 ucles 2012 0607/41/m/j/12 for examiner's use 5 11 cm 8 cmnot to scale the diagram shows a solid made up of a cone and a hemisphere. the hemisphere has a radius of 8 cm. the cone has a base radius of 8 cm and a height of 11 cm. (a) (i) calculate the volume of the solid. answer(a)(i) cm3 [3] (ii) the solid is made of plastic and 1 cm3 of plastic has a mass of 1.15 g. calculate the mass of the solid. give your answer in kilograms. answer(a)(ii) kg [2] ", "9": "9 \u00a9 ucles 2012 0607/41/m/j/12 [turn over for examiner's use (b) (i) calculate the surface area of the solid. answer(b)(i) cm2 [4] (ii) the surface is painted with silver paint. the cost of all the paint used is $81.50 . calculate the cost per square centimetre. give your answer correct to 2 decimal places. answer(b)(ii) $ [2] ", "10": "10 \u00a9 ucles 2012 0607/41/m/j/12 for examiner's use 6 94\u00b0d c baonot to scale abcd is a cyclic quadrilateral in the circle, centre o. angle dcb = 94\u00b0. (a) calculate (i) angle dab , answer(a)(i) [1] (ii) the reflex angle dob , answer(a)(ii) [1] (iii) angle obd . answer(a)(iii) [2] (b) angle bdc = 40\u00b0. calculate angle dac. answer(b) [2] ", "11": "11 \u00a9 ucles 2012 0607/41/m/j/12 [turn over for examiner's use 7 abcnot to scale the diagram shows anne\u2019s car journey from a to c. the total distance from a to c is 720 km. there is a motorway from a to b and other roads from b to c. anne travels on the motorway for 7.5 hours and on the other roads for 3 hours. (a) calculate the average speed of her journey. answer(a) km/h [2] (b) anne\u2019s average speed from a to b is x km/h. her average speed from b to c is 2x km/h. (i) find an expression, in terms of x, for the total distance from a to c. give your answer in its simplest form. answer(b)(i) [2] (ii) find anne\u2019s average speed on the motorway. answer(b)(ii) km/h [1] (c) find the ratio anne\u2019s distance travelled on the motorway : anne\u2019s distance travelled on the other roads. answer(c) : [2] ", "12": "12 \u00a9 ucles 2012 0607/41/m/j/12 for examiner's use 8 g(x) = x5 \u2013 x3 (a) (i) sketch the graph of y = g(x) for \u20131.1 y x y 1.1 . 0.3 \u20130.3\u20131.1 1.10y x [2] (ii) write down the zeros of g(x). answer(a)(ii) x = or x = or x = [3] (iii) find the co-ordinates of the local minimum point. answer(a)(iii) ( , ) [2] (iv) the point (\u20130.5, 0.09375) is on the graph of y = g(x). complete the following statement. the point ( , \u20130.09375) is also on the graph of y = g(x). [1] (v) describe the symmetry of the graph of y = g(x). [3] ", "13": "13 \u00a9 ucles 2012 0607/41/m/j/12 [turn over for examiner's use (b) 053 5= + \u2212xx x this equation can be solved by drawing a suitable straight line on the diagram opposite. (i) write down the equation of this straight line. answer(b)(i) [1] (ii) on the diagram in part(a)(i) , sketch this straight line. [1] (iii) two of the solutions to this equation are x = \u2013 0.526 and x = 0.526 . find the other three solutions. answer(b)(iii) x = or x = or x = [2] ", "14": "14 \u00a9 ucles 2012 0607/41/m/j/12 for examiner's use 9 ab the diagram shows 2 boxes, a and b. box a contains 2 black marbles and 3 white marbles. box b contains 4 black marbles and 2 white marbles. (a) carlene takes out one marble at random from each box. calculate the probability that she takes out 2 black marbles. answer(a) [2] (b) carlene returns the marbles to the boxes she took them from. ricky then chooses a box and takes out 2 marbles at random. the probability that he chooses box a is 32. calculate the probability that ricky takes out 2 black marbles. answer(b) [3] (c) ricky returns the marbles to the box he took them from. ali takes marbles out of box b at random until she gets a white marble. the probability that this is the nth marble taken out is 51. find the value of n. answer(c) [3] ", "15": "15 \u00a9 ucles 2012 0607/41/m/j/12 [turn over for examiner's use 10 f(x) = 2x \u2013 3 (a) sketch the graph of y = f( x), for \u20133 y x y 3. y x6 \u20134\u20133 30 [2] (b) write down the equation of the asymptote of the graph of y = f(x). answer(b) [1] (c) write down the range of f(x) for (i) \u20132 y x y 2, answer(c)(i) [2] (ii) \u2208xo. answer(c)(ii) [1] (d) find the exact solution of the equation 2x \u2013 3 = 0. answer(d) x= [2] ", "16": "16 \u00a9 ucles 2012 0607/41/m/j/12 for examiner's use 11 f(x) = 2x + 3 g(x) = x \u2013 1 h(x) = x2 + 1 (a) find f(g(\u2013 5)). answer(a) [2] (b) find x when f( x) = g( x). answer(b) x = [2] (c) find x when f( x) = h( x). give your answers correct to 2 decimal places. answer(c) x = or x = [4] (d) find f \u2013 1(x). answer(d) [2] (e) find ) ( g1 ) ( f1 x x+ in terms of x. give your answer as a single fraction. answer(e) [3] ", "17": "17 \u00a9 ucles 2012 0607/41/m/j/12 [turn over for examiner's use 12 \u20136\u2013 4\u2013 2\u20135 \u20133 \u20131y x 0 246 1356 54321 \u20131 \u20132\u20133\u20134\u20135\u20136 (a) on the grid, draw the lines (i) x = 5, [1] (ii) y = \u2013 x, [1] (iii) y = 4 \u2013 2x. [1] (b) the region r is defined by y y 0, x y 5, y [ \u2013x and y [ 4 \u2013 2x. on the grid, label the region r. [2] (c) the point (h, k) is in the region r. h and k are integers and h + 3k = 0. find the value of h and the value of k. answer(c) h = k = [2] ", "18": "18 \u00a9 ucles 2012 0607/41/m/j/12 for examiner's use 13 issa sells newspapers and magazines. the table shows the number of newspapers ( x) and the number of magazines ( y) sold during a period of 10 days. number of newspapers ( x) 50 35 60 55 50 40 30 50 55 45 number of magazines ( y) 10 15 10 8 12 15 18 8 10 13 (a) complete the scatter diagram. the first seven points in the table have been plotted for you. y x20 1510 5number of magazines 300 35 40 45 50 55 60 number of newspapers [2] (b) complete the sentence to make a correct statement about the information on the scatter diagram. there is between the number of newspapers sold and the number of magazines sold. [1] (c) find the mean number of (i) newspapers sold, answer(c)(i) [1] (ii) magazines sold. answer(c)(ii) [1] ", "19": "19 \u00a9 ucles 2012 0607/41/m/j/12 for examiner's use (d) find the equation of the line of regression for the number of magazines sold ( y) and the number of newspapers sold (x). write your answer in the form y = mx + c. answer(d) y = [2] (e) find the value of y when x = 32. answer(e) [1] (f) draw the line of regression accurately on the scatter diagram. [2] (g) use your graph to predict the number of magazines sold when 43 newspapers are sold. answer(g) [1] ", "20": "20 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2012 0607/41/m/j/12 blank page " }, "0607_s12_qp_42.pdf": { "1": " this document consists of 20 printed pages. ib12 06_0607_42/4rp \u00a9 ucles 2012 [turn over *4601814779* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/42 paper 4 (extended) may/june 2012 2 hours 15 minutes candidates answer on the question paper additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120. ", "2": "2 \u00a9 ucles 2012 0607/42/m/j/12 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2012 0607/42/m/j/12 [turn over for examiner's use answer all the questions. 1 (a) a farmer sows 600 tomato seeds. 85% of the seeds grow into plants. find the number of seeds that grow into plants. answer(a) [2] (b) (i) the farmer sows 20 000 carrot seeds. 17 500 of these seeds grow into plants. calculate the percentage which did not grow into plants. answer(b)(i) % [2] (ii) in one season the farmer sells 161.2 tonnes of carrots. this is 4% more than he expected to sell. calculate the number of tonnes he expected to sell. answer(b)(ii) tonnes [3] (c) the farmer sows broccoli seeds, cabbage seeds and pumpkin seeds in the ratio broccoli seeds : cabbage seeds : pumpkin seeds = 2 : 5 : 7 . the total number of seeds sown is 8 400. find the number of cabbage seeds sown. answer(c) [2] ", "4": "4 \u00a9 ucles 2012 0607/42/m/j/12 for examiner's use 2 (a) d a bc 55\u00b0not to scale c and d are points on the circumference of a circle. ab is a diameter of the circle and angle abc = 55\u00b0. find (i) angle adc, answer(a)(i) [1] (ii) angle cab. answer(a)(ii) [1] (b) pqr st150\u00b0110\u00b0not to scale in the diagram angle pqr = 110\u00b0 and angle rst = 150\u00b0. pq = qr and pq is parallel to st. find (i) angle prq , answer(b)(i) [1] (ii) angle qrs. answer(b)(ii) [2] ", "5": "5 \u00a9 ucles 2012 0607/42/m/j/12 [turn over for examiner's use (c) 140\u00b0o ba ct not to scale ta and tb are tangents to a circle centre o. c is a point on the circumference and angle aob = 140\u00b0. (i) find angle atb. answer(c)(i) [2] (ii) find angle acb. answer(c)(ii) [2] (iii) on the diagram, draw the chord ab. the radius of the circle is 5 cm. calculate the length of the chord ab. answer(c)(iii) cm [3] ", "6": "6 \u00a9 ucles 2012 0607/42/m/j/12 for examiner's use 3 in a scientific experiment the following six masses, in grams, were recorded. 9.6 \u00d7 10\u20135 1.01 \u00d7 10\u20134 9.3 \u00d7 10\u20135 1.04 \u00d7 10\u20134 1.03 \u00d7 10\u20134 9.8 \u00d7 10\u20135 (a) find the median. answer(a) g [1] (b) find the range. answer(b) g [1] (c) calculate the mean. give your answer correct to 2 significant figures. answer(c) g [2] (d) another mass, x grams, is recorded. the mean of the seven masses is now 410 0 . 1\u2212\u00d7 g. find the value of x. answer(d) x = g [3] ", "7": "7 \u00a9 ucles 2012 0607/42/m/j/12 [turn over for examiner's use 4 f(x) = x2 \u2013 5 g(x) = x \u2013 2 (a) find the value of f(\u22122). answer(a) [1] (b) solve f( x) = 4. answer(b) x = [2] (c) show that f(g( x)) = 1 42\u2212 \u2212x x . [2] (d) solve f(g( x)) = f( x). answer(d) x = [2] ", "8": "8 \u00a9 ucles 2012 0607/42/m/j/12 for examiner's use 5 f e a b18 m 12 mnot to scale ef is a vertical flagpole. two ropes, af and bf, keep the flagpole in position. the points a, e and b all lie in a straight line on horizontal ground. af = 18 m and ae = 12 m. (a) (i) calculate the height of the flagpole, ef. answer(a)(i) m [2] (ii) calculate the size of angle fae. answer(a)(ii) [2] ", "9": "9 \u00a9 ucles 2012 0607/42/m/j/12 [turn over for examiner's use (b) angle fae = 2 \u00d7 angle fbe. show that be = 30.0 m, correct to 1 decimal place. [3] (c) calculate the length of rope, bf. answer(c) m [2] (d) p is on bf so that bp = 20 m. another rope, ep, joins e to p. use the cosine rule to calculate the length of the rope, ep. answer(d) m [3] ", "10": "10 \u00a9 ucles 2012 0607/42/m/j/12 for examiner's use 6 f(x) = 16 52 \u2212+ \u2212 xx x , for \u22128 y x y 8. (a) on the diagram, sketch the graph of y = f( x). 10 \u201313\u20138 8 0y x [3] (b) write down the equation of the vertical asymptote. answer(b) [1] (c) find the range of f( x) for the domain \u22128 y x y 8. answer(c) [2] ", "11": "11 \u00a9 ucles 2012 0607/42/m/j/12 [turn over for examiner's use (d) solve f( x) = 0. answer(d) x = or x = [1] (e) on the diagram, sketch the graph of y = 3x \u2013 2. [2] (f) write down the co-ordinates of the points where 2 316 52 \u2212 =\u2212+ \u2212xxx x. give each answer correct to 3 decimal places. answer(f) ( , ) ( , ) [2] ", "12": "12 \u00a9 ucles 2012 0607/42/m/j/12 for examiner's use 7 (a) rajiv invests $525 at x% per year simple interest. after 3 years he has $588. find the value of x. answer(a) x = [3] (b) a company\u2019s profits increase by 5% each year. in 2002 the profit was $10 000. find the profit in 2010. give your answer correct to the nearest $100. answer(b) $ [3] 8 (a) the venn diagram shows the number of athletes ( a) and the number of basketball players ( b) in a class. u ab 573 2 use the venn diagram to complete the following. (i) n(a) = [1] (ii) n()b a\u2032\u2229 = [1] (iii) n ) (\u2032 \u2229b a = [1] ", "13": "13 \u00a9 ucles 2012 0607/42/m/j/12 [turn over for examiner's use (b) each student in a school orchestra can play at least one of the piano, the violin and the trumpet. 24 students play the piano 24 students play the violin 13 students play the trumpet 12 students play both the piano and the violin 7 students play both the piano and the trumpet 2 students play both the violin and the trumpet no student plays all three instruments (i) use this information to complete the venn diagram below where p = {students who play the piano}, v = {students who play the violin}, t = {students who play the trumpet}. u pv t [3] (ii) how many students are there in this orchestra? answer(b)(ii) [1] ", "14": "14 \u00a9 ucles 2012 0607/42/m/j/12 for examiner's use 9 8 cm12 cmnot to scale the diagram shows a large mug in the shape of a cylinder, open at the top. the internal radius of the mug is 8 cm and the internal height is 12 cm. (a) calculate the volume of water the mug holds when filled to the top. answer(a) cm3 [2] (b) calculate the total surface area of the inside of the mug. answer(b) cm2 [3] ", "15": "15 \u00a9 ucles 2012 0607/42/m/j/12 [turn over for examiner's use (c) 500 cm3 of water is poured into the mug. calculate the depth of water in the mug. give your answer in centimetres correct to the nearest millimetre. answer(c) cm [3] (d) the mug shown in the diagram is mathematically similar to a smaller mug. the volume of the smaller mug is 81 of the volume of the larger one. find the radius of the smaller mug. answer(d) cm [2] ", "16": "16 \u00a9 ucles 2012 0607/42/m/j/12 for examiner's use 10 the lengths of 30 fish caught in a competition are recorded. the length of each fish is measured correct to the nearest centimetre. the results are shown in the ordered stem and leaf diagram. 1 1 1 2 4 5 6 7 8 9 2 0 4 5 7 9 3 2 6 7 8 9 4 3 4 6 7 8 5 2 4 5 6 3 4 9 key 3 f 2 means 32 cm (a) find the inter-quartile range. answer(a) cm [2] (b) complete the table for the lengths of the 30 fish. class interval frequency frequency density 9.5 y x < 14.5 0.8 14.5 y x < 19.5 19.5 y x < 39.5 39.5 y x < 49.5 49.5 y x < 69.5 [4] (c) on the grid, draw a histogram to show this information. 1.0 0.80.60.40.20.0 0 1 02 03 04 05 06 07 0frequency density length (cm)x [3] ", "17": "17 \u00a9 ucles 2012 0607/42/m/j/12 [turn over for examiner's use 11 gemma has these four cards. i h l l they are shuffled and placed face down on a table. the cards are turned over, one at a time. find the probability that, (a) the first card turned over is h , answer(a) [1] (b) the first two cards turned over are l l , answer(b) [2] (c) the second card turned over is h , answer(c) [3] (d) the cards are turned over in this order. h i l l answer(d) [2] ", "18": "18 \u00a9 ucles 2012 0607/42/m/j/12 for examiner's use 12 a quadrilateral has vertices p(0, 0), q(4, 0), r(6, 4) and s(0, 2). (a) on the grid, draw the quadrilateral pqrs . \u2013 6 \u2013 5 \u2013 4 \u2013 3 \u2013 2 \u2013 1 0 123456786 54321 \u20131\u20132\u20133\u20134\u20135\u20136y x [1] (b) on the same diagram, (i) reflect pqrs in x = 0, [1] (ii) translate pqrs using the vector \uf8f7 \uf8f8\uf8f6\uf8ec \uf8ed\uf8eb \u221232, [2] (iii) enlarge pqrs, centre (0, 0), scale factor21. [3] ", "19": "19 \u00a9 ucles 2012 0607/42/m/j/12 [turn over for examiner's use 13 opq x \u00b0 10 cmnot to scale the diagram shows a circle, centre o, radius 10 cm. pq is a chord and angle poq = x\u00b0. (a) write down, in terms of x and \u03c0, an expression for the area of the sector poq . answer(a) cm2 [2] (b) write down, in terms of x, an expression for the area of the triangle poq . answer(b) cm2 [2] (c) write down, in terms of x and \u03c0, an expression for the area of the shaded segment. answer(c) cm2 [1] (d) the area of the triangle poq is 25 cm 2. angle poq is obtuse. show that x = 150. [3] (e) find the area of the shaded segment. answer(e) cm2 [2] question 14 is on the next page. ", "20": "20 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2012 0607/42/m/j/12 for examiner's use 14 a regular pentagon is drawn inside a circle so that its vertices lie on the circumference of the circle. the length of each side of the pentagon is 4 cm. (a) sketch a diagram to show this information. [1] (b) calculate the radius of the circle. answer(b) cm [4] " }, "0607_s12_qp_43.pdf": { "1": " this document consists of 20 printed pages. ib12 06_0607_43/fp \u00a9 ucles 2012 [turn over *8967578522* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/43 paper 4 (extended) may/june 2012 2 hours 15 minutes candidates answer on the question paper additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120. ", "2": "2 \u00a9 ucles 2012 0607/43/m/j/12 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2012 0607/43/m/j/12 [turn over for examiner's use answer all the questions. 1 (a) a farmer sows 600 tomato seeds. 85% of the seeds grow into plants. find the number of seeds that grow into plants. answer(a) [2] (b) (i) the farmer sows 20 000 carrot seeds. 17 500 of these seeds grow into plants. calculate the percentage which did not grow into plants. answer(b)(i) % [2] (ii) in one season the farmer sells 161.2 tonnes of carrots. this is 4% more than he expected to sell. calculate the number of tonnes he expected to sell. answer(b)(ii) tonnes [3] (c) the farmer sows broccoli seeds, cabbage seeds and pumpkin seeds in the ratio broccoli seeds : cabbage seeds : pumpkin seeds = 2 : 5 : 7 . the total number of seeds sown is 8 400. find the number of cabbage seeds sown. answer(c) [2] ", "4": "4 \u00a9 ucles 2012 0607/43/m/j/12 for examiner's use 2 (a) d a bc 55\u00b0not to scale c and d are points on the circumference of a circle. ab is a diameter of the circle and angle abc = 55\u00b0. find (i) angle adc, answer(a)(i) [1] (ii) angle cab. answer(a)(ii) [1] (b) pqr st150\u00b0110\u00b0not to scale in the diagram angle pqr = 110\u00b0 and angle rst = 150\u00b0. pq = qr and pq is parallel to st. find (i) angle prq , answer(b)(i) [1] (ii) angle qrs. answer(b)(ii) [2] ", "5": "5 \u00a9 ucles 2012 0607/43/m/j/12 [turn over for examiner's use (c) 140\u00b0o ba ct not to scale ta and tb are tangents to a circle centre o. c is a point on the circumference and angle aob = 140\u00b0. (i) find angle atb. answer(c)(i) [2] (ii) find angle acb. answer(c)(ii) [2] (iii) on the diagram, draw the chord ab. the radius of the circle is 5 cm. calculate the length of the chord ab. answer(c)(iii) cm [3] ", "6": "6 \u00a9 ucles 2012 0607/43/m/j/12 for examiner's use 3 in a scientific experiment the following six masses, in grams, were recorded. 9.6 \u00d7 10\u20135 1.01 \u00d7 10\u20134 9.3 \u00d7 10\u20135 1.04 \u00d7 10\u20134 1.03 \u00d7 10\u20134 9.8 \u00d7 10\u20135 (a) find the median. answer(a) g [1] (b) find the range. answer(b) g [1] (c) calculate the mean. give your answer correct to 2 significant figures. answer(c) g [2] (d) another mass, x grams, is recorded. the mean of the seven masses is now 410 0 . 1\u2212\u00d7 g. find the value of x. answer(d) x = g [3] ", "7": "7 \u00a9 ucles 2012 0607/43/m/j/12 [turn over for examiner's use 4 f(x) = x2 \u2013 5 g(x) = x \u2013 2 (a) find the value of f(\u22122). answer(a) [1] (b) solve f( x) = 4. answer(b) x = [2] (c) show that f(g( x)) = 1 42\u2212 \u2212x x . [2] (d) solve f(g( x)) = f( x). answer(d) x = [2] ", "8": "8 \u00a9 ucles 2012 0607/43/m/j/12 for examiner's use 5 f e a b18 m 12 mnot to scale ef is a vertical flagpole. two ropes, af and bf, keep the flagpole in position. the points a, e and b all lie in a straight line on horizontal ground. af = 18 m and ae = 12 m. (a) (i) calculate the height of the flagpole, ef. answer(a)(i) m [2] (ii) calculate the size of angle fae. answer(a)(ii) [2] ", "9": "9 \u00a9 ucles 2012 0607/43/m/j/12 [turn over for examiner's use (b) angle fae = 2 \u00d7 angle fbe. show that be = 30.0 m, correct to 1 decimal place. [3] (c) calculate the length of rope, bf. answer(c) m [2] (d) p is on bf so that bp = 20 m. another rope, ep, joins e to p. use the cosine rule to calculate the length of the rope, ep. answer(d) m [3] ", "10": "10 \u00a9 ucles 2012 0607/43/m/j/12 for examiner's use 6 f(x) = 16 52 \u2212+ \u2212 xx x , for \u22128 y x y 8. (a) on the diagram, sketch the graph of y = f( x). 10 \u201313\u20138 8 0y x [3] (b) write down the equation of the vertical asymptote. answer(b) [1] (c) find the range of f( x) for the domain \u22128 y x y 8. answer(c) [2] ", "11": "11 \u00a9 ucles 2012 0607/43/m/j/12 [turn over for examiner's use (d) solve f( x) = 0. answer(d) x = or x = [1] (e) on the diagram, sketch the graph of y = 3x \u2013 2. [2] (f) write down the co-ordinates of the points where 2 316 52 \u2212 =\u2212+ \u2212xxx x. give each answer correct to 3 decimal places. answer(f) ( , ) ( , ) [2] ", "12": "12 \u00a9 ucles 2012 0607/43/m/j/12 for examiner's use 7 (a) rajiv invests $525 at x% per year simple interest. after 3 years he has $588. find the value of x. answer(a) x = [3] (b) a company\u2019s profits increase by 5% each year. in 2002 the profit was $10 000. find the profit in 2010. give your answer correct to the nearest $100. answer(b) $ [3] 8 (a) the venn diagram shows the number of athletes ( a) and the number of basketball players ( b) in a class. u ab 573 2 use the venn diagram to complete the following. (i) n(a) = [1] (ii) n()b a\u2032\u2229 = [1] (iii) n ) (\u2032 \u2229b a = [1] ", "13": "13 \u00a9 ucles 2012 0607/43/m/j/12 [turn over for examiner's use (b) each student in a school orchestra can play at least one of the piano, the violin and the trumpet. 24 students play the piano 24 students play the violin 13 students play the trumpet 12 students play both the piano and the violin 7 students play both the piano and the trumpet 2 students play both the violin and the trumpet no student plays all three instruments (i) use this information to complete the venn diagram below where p = {students who play the piano}, v = {students who play the violin}, t = {students who play the trumpet}. u pv t [3] (ii) how many students are there in this orchestra? answer(b)(ii) [1] ", "14": "14 \u00a9 ucles 2012 0607/43/m/j/12 for examiner's use 9 8 cm12 cmnot to scale the diagram shows a large mug in the shape of a cylinder, open at the top. the internal radius of the mug is 8 cm and the internal height is 12 cm. (a) calculate the volume of water the mug holds when filled to the top. answer(a) cm3 [2] (b) calculate the total surface area of the inside of the mug. answer(b) cm2 [3] ", "15": "15 \u00a9 ucles 2012 0607/43/m/j/12 [turn over for examiner's use (c) 500 cm3 of water is poured into the mug. calculate the depth of water in the mug. give your answer in centimetres correct to the nearest millimetre. answer(c) cm [3] (d) the mug shown in the diagram is mathematically similar to a smaller mug. the volume of the smaller mug is 81 of the volume of the larger one. find the radius of the smaller mug. answer(d) cm [2] ", "16": "16 \u00a9 ucles 2012 0607/43/m/j/12 for examiner's use 10 the lengths of 30 fish caught in a competition are recorded. the length of each fish is measured correct to the nearest centimetre. the results are shown in the ordered stem and leaf diagram. 1 1 1 2 4 5 6 7 8 9 2 0 4 5 7 9 3 2 6 7 8 9 4 3 4 6 7 8 5 2 4 5 6 3 4 9 key 3 f 2 means 32 cm (a) find the inter-quartile range. answer(a) cm [2] (b) complete the table for the lengths of the 30 fish. class interval frequency frequency density 9.5 y x < 14.5 0.8 14.5 y x < 19.5 19.5 y x < 39.5 39.5 y x < 49.5 49.5 y x < 69.5 [4] (c) on the grid, draw a histogram to show this information. 1.0 0.80.60.40.20.0 0 1 02 03 04 05 06 07 0frequency density length (cm)x [3] ", "17": "17 \u00a9 ucles 2012 0607/43/m/j/12 [turn over for examiner's use 11 gemma has these four cards. i h l l they are shuffled and placed face down on a table. the cards are turned over, one at a time. find the probability that, (a) the first card turned over is h , answer(a) [1] (b) the first two cards turned over are l l , answer(b) [2] (c) the second card turned over is h , answer(c) [3] (d) the cards are turned over in this order. h i l l answer(d) [2] ", "18": "18 \u00a9 ucles 2012 0607/43/m/j/12 for examiner's use 12 a quadrilateral has vertices p(0, 0), q(4, 0), r(6, 4) and s(0, 2). (a) on the grid, draw the quadrilateral pqrs . \u2013 6 \u2013 5 \u2013 4 \u2013 3 \u2013 2 \u2013 1 0 123456786 54321 \u20131\u20132\u20133\u20134\u20135\u20136y x [1] (b) on the same diagram, (i) reflect pqrs in x = 0, [1] (ii) translate pqrs using the vector \uf8f7 \uf8f8\uf8f6\uf8ec \uf8ed\uf8eb \u221232, [2] (iii) enlarge pqrs, centre (0, 0), scale factor21. [3] ", "19": "19 \u00a9 ucles 2012 0607/43/m/j/12 [turn over for examiner's use 13 opq x \u00b0 10 cmnot to scale the diagram shows a circle, centre o, radius 10 cm. pq is a chord and angle poq = x\u00b0. (a) write down, in terms of x and \u03c0, an expression for the area of the sector poq . answer(a) cm2 [2] (b) write down, in terms of x, an expression for the area of the triangle poq . answer(b) cm2 [2] (c) write down, in terms of x and \u03c0, an expression for the area of the shaded segment. answer(c) cm2 [1] (d) the area of the triangle poq is 25 cm 2. angle poq is obtuse. show that x = 150. [3] (e) find the area of the shaded segment. answer(e) cm2 [2] question 14 is on the next page. ", "20": "20 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2012 0607/43/m/j/12 for examiner's use 14 a regular pentagon is drawn inside a circle so that its vertices lie on the circumference of the circle. the length of each side of the pentagon is 4 cm. (a) sketch a diagram to show this information. [1] (b) calculate the radius of the circle. answer(b) cm [4] " }, "0607_s12_qp_5.pdf": { "1": " this document consists of 5 printed pages and 3 blank pages. ib12 06_0607_05/4rp \u00a9 ucles 2012 [turn over *7158128086* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/05 paper 5 (core) may/june 2012 1 hour candidates answer on the question paper additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24. ", "2": "2 \u00a9 ucles 2012 0607/05/m/j/12 for examiner's use answer all the questions. investigation addition triples an addition triple has three different numbers. the numbers (8, 10, 18) form an addition triple because 8 + 10 = 18. some other addition triples are (10, 11, 21) and (21, 24, 45). this investigation explores patterns with addition triples. 1 nine addition triples can be found from the list of integers 1, 2, 3, 4, 5, 6, 7. one of these triples is (3, 4, 7). write down the other eight addition triples in the spaces provided. [note that (3, 4, 7) and (4, 3, 7) are the same addition triple.] ( , , ) ( , , ) ( , , ) ( , , ) ( , , ) ( , , ) ( , , ) ( , , ) ( 3 , 4 , 7 ) ", "3": "3 \u00a9 ucles 2012 0607/05/m/j/12 [turn over for examiner's use 2 complete the table, showing the addition triples for each list of integers. in the last column write the total number of triples. number of integers list of integers addition triples total number of addition triples 3 1, 2, 3 (1, 2, 3) 1 4 1, 2, 3, 4 2 5 1, 2, 3, 4, 5 6 1, 2, 3, 4, 5, 6 7 1, 2, 3, 4, 5, 6, 7 leave this blank \u2013 do not write your answer to question 1 again. 9 8 1, 2, 3, 4, 5, 6, 7, 8 12 ", "4": "4 \u00a9 ucles 2012 0607/05/m/j/12 for examiner's use 3 look at the pattern in the last column in the table on page 3. use it to complete the following table. number of integers 3 4 5 6 7 8 9 10 11 12 13 14 15 number of addition triples 1 2 9 12 16 20 30 36 4 using question 3, complete the following table. number of integers 3 5 7 9 11 13 15 17 number of addition triples 1 = 12 9 = 32 16 = 42 36 = 62 5 how many integers are in the list when there are 100 addition triples? ", "5": "5 \u00a9 ucles 2012 0607/05/m/j/12 for examiner's use 6 (a) is it possible to have 225 addition triples? explain your answer. (b) explain why it is not possible to have 900 000 addition triples. 7 (a) the numbers in the second row of the table in question 4 form a sequence. find the number of addition triples when there are 99 integers in the list. show how you do this. (b) the numbers in the second row of the table in question 3 form a sequence. find the number of addition triples when there are 100 integers in the list. show how you do this. ", "6": "6 \u00a9 ucles 2012 0607/05/m/j/12 blank page", "7": "7 \u00a9 ucles 2012 0607/05/m/j/12 blank page", "8": "8 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2012 0607/05/m/j/12 blank page " }, "0607_s12_qp_6.pdf": { "1": " this document consists of 11 printed pages and 1 blank page. ib12 06_0607_06/5rp \u00a9 ucles 2012 [turn over *4119238411* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/06 paper 6 (extended) may/june 2012 1 hour 30 minutes candidates answer on the question paper additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2012 0607/06/m/j/12 for examiner's use answer both parts a and b. a investigation additional triples (20 marks) you are advised to spend 45 minutes on part a. an addition triple has three different numbers. the numbers (8, 10, 18) form an addition triple because 8 + 10 = 18. some other addition triples are (10, 11, 21) and (21, 24, 45). this investigation explores patterns with addition triples. 1 nine addition triples can be found from the list of integers 1, 2, 3, 4, 5, 6, 7. one of these triples is (3, 4, 7). write down the other eight addition triples in the spaces provided. [note that (3, 4, 7) and (4, 3, 7) are the same addition triple.] ( , , ) ( , , ) ( , , ) ( , , ) ( , , ) ( , , ) ( , , ) ( , , ) ( 3 , 4 , 7 ) ", "3": "3 \u00a9 ucles 2012 0607/06/m/j/12 [turn over for examiner's use 2 complete the table, showing the addition triples for each list of integers. in the last column write the total number of triples. number of integers list of integers addition triples total number of addition triples 3 1, 2, 3 (1, 2, 3) 1 4 1, 2, 3, 4 2 5 1, 2, 3, 4, 5 6 1, 2, 3, 4, 5, 6 7 1, 2, 3, 4, 5, 6, 7 leave this blank \u2013 do not write your answer to question 1 again. 9 8 1, 2, 3, 4, 5, 6, 7, 8 12 ", "4": "4 \u00a9 ucles 2012 0607/06/m/j/12 for examiner's use 3 look at the pattern in the last column in the table on page 3. use it to complete the following table. number of integers 3 4 5 6 7 8 9 10 11 12 13 14 15 number of addition triples 1 2 9 12 16 20 30 4 using question 3, complete the following table when there is an odd number of integers in the list. number of integers 3 5 7 9 11 13 15 number of addition triples 1 9 16 5 for the table in question 4, the same three arithmetic operations always take you from the number of integers in the list to the corresponding number of addition triples. the first operation is subtract 1 . find the other two operations. show that these three operations take you from 7 integers in the list to 9 addition triples, and from 9 integers in the list to 16 addition triples. ", "5": "5 \u00a9 ucles 2012 0607/06/m/j/12 [turn over for examiner's use 6 using question 5, find (a) the number of addition triples when there are 101 integers in the list, (b) the number of integers in the list when there are 11 449 addition triples, (c) an expression for the number of addition triples when the list has n integers and n is odd. ", "6": "6 \u00a9 ucles 2012 0607/06/m/j/12 for examiner's use 7 using patterns in the table in question 3, find (a) the number of addition triples when there are 100 integers in the list, (b) the number of integers in the list when there are 1332 addition triples, (c) an expression for the number of addition triples when the list has n integers and n is even. ", "7": "7 \u00a9 ucles 2012 0607/06/m/j/12 [turn over blank page", "8": "8 \u00a9 ucles 2012 0607/06/m/j/12 for examiner's use b modelling regiomontanus\u2019 statue (20 marks) you are advised to spend 45 minutes on part b. in the 15th century the german mathematician regiomontanus worked out the best place to stand to view a statue that was on top of a column. the picture shows a statue of height one metre. the base c of the statue is one metre above the line of sight ad. angle bac is called the angle of view. the largest angle of view gives the best view of the statue. not to scaleb c dastatue column regiomontanus 1 the diagram models the picture. not to scaleb c d a1 m 1 m 3 m regiomontanus stands 3 metres from the base of the column so ad = 3 m. (a) (i) use the right-angled triangle adb to show that the length ab = 13. (ii) use this answer to write down sin abd as a fraction. (b) show that the length ac = 10. ", "9": "9 \u00a9 ucles 2012 0607/06/m/j/12 [turn over for examiner's use (c) regiomontanus wrote that, in triangle abc, bb aa sin sin= show that sin bac 1303= . 2 using the method in question 1, find sin bac when ad = 1 m. ", "10": "10 \u00a9 ucles 2012 0607/06/m/j/12 for examiner's use 3 model sin bac by letting ad = x metres. show that sin bac = ) 4 )( 1 (2 2+ +x xx. not to scaleb c d a1 m 1 m", "11": "11 \u00a9 ucles 2012 0607/06/m/j/12 [turn over for examiner's use 4 (a) using the model in question 3, sketch the graph of sin bac against x. 00.4 8sin bac x (b) find the value of x which makes sin bac a maximum. (c) find the largest angle of view. question 5 is printed on the next page.", "12": "12 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2012 0607/06/m/j/12 for examiner's use 5 (a) instead of one metre high, the statue is h metres high. the base of the statue is still one metre above the line of sight. modify the model in question 3. (b) the one metre high statue is replaced by a statue that is 2 metres high. use your model from part (a) to find the change (if any) in (i) the largest angle of view, (ii) the corresponding distance from the column. " }, "0607_w12_qp_1.pdf": { "1": " this document consists of 10 printed pages and 2 blank pages. ib12 11_0607_01/rp \u00a9 ucles 2012 [turn over *6733418139* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/01 paper 1 (core) november 2012 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. for examiner's use ", "2": "2 \u00a9 ucles 2012 0607/01/o/n/12 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3", "3": "3 \u00a9 ucles 2012 0607/01/o/n/12 [turn over for examiner's use answer all the questions. 1 (a) write 43 200 correct to the nearest thousand. answer (a) [1] (b) write 43 200 in standard form. answer (b) [1] 2 (a) complete the following. \u00d7 36 = 30 [1] (b) work out 10 + 8 \u00f72 . answer (b) [1] ", "4": "4 \u00a9 ucles 2012 0607/01/o/n/12 for examiner's use 3two adults and one child buy tickets to fly from vienna to paris. the adult ticket price is $44. the child ticket price is 43of the adult price. (a) write down the total cost of two adult tickets and one child ticket. answer (a) $ [2] (b) the aircraft leaves vienna airport at 10 45 and arrives in paris at 13 15. (i) how long, in hours and minutes, does the flight take? answer (b)(i) h min [1] (ii) the distance from vienna to paris is 1000 km. find the average speed of the aircraft. answer (b)(ii) km/h [2] ", "5": "5 \u00a9 ucles 2012 0607/01/o/n/12 [turn over for examiner's use 4the diagram shows the graph of the function y = f (x) for \u20133 y x y 3 . \u20136 \u20136\u20135 \u20134 \u20133 \u20132 \u20131 0 123456 \u20135\u20134\u20133\u20132\u20131123456y xy = f(x) (a) write down the range of y = f( x) for \u20133 y x y 3 . answer (a) [1] (b) on the same diagram, sketch the graph of y = f( x \u2013 3) . [1] (c) describe the single transformation the maps y = f(x) onto y = f(x) \u2013 3 . answer (c) [2] ", "6": "6 \u00a9 ucles 2012 0607/01/o/n/12 for examiner's use 5a bag contains yellow, blue and green discs. there are 60 discs in the bag. one disc is chosen at random. the probability that the disc is yellow is 101 . the probability that the disc is green is 103 . (a) find the probability that the disc is blue. answer (a) [2] (b) work out how many discs are green. answer (b) [1] 6 a = 232r \u03c0 make r the subject of the formula. answer r = [3] ", "7": "7 \u00a9 ucles 2012 0607/01/o/n/12 [turn over for examiner's use 7the venn diagram shows the sets a and b. ab 2 3 71115 20u (a) list the elements of set b . answer (a) [1] (b) complete the following statements. (i) 2 \u2208 [1] (ii) n( a) = [1] (iii) a \u2229 b = { } [1] ", "8": "8 \u00a9 ucles 2012 0607/01/o/n/12 for examiner's use 8the nth term of a sequence is 2n \u2013 5 . (a) find the value of the first term. answer (a) [1] (b) find the difference between the third term and the fourth term. answer (b) [2] 9 (a) factorise completely. 3 x + 13x2 answer (a) [1] (b) write as a single fraction. 54x+3y answer (b) [2] (c) write down the inequality that describes the set of numbers shown below. \u20136 \u20134 \u20132 0 2 4 6 8 answer (c) [2] ", "9": "9 \u00a9 ucles 2012 0607/01/o/n/12 [turn over for examiner's use 10 b c a14\u00b00.5 m 2 m q r p1.5 mnot to scale triangle abc is similar to triangle pqr . (a) angle bac = 14\u00b0. write down the size of angle qpr . answer (a) angle qpr = [1] (b) find the length of pr. answer (b) [2] (c) ab c d e which two triangles are congruent? answer (c) and [1] ", "10": "10 \u00a9 ucles 2012 0607/01/o/n/12 for examiner's use 11 (a) write down the gradient of the straight line y = 5x \u2013 1. answer (a) [1] (b) write down the equation of the line parallel to y = 5x \u2013 1 which passes through the point (0, 3). answer (b) [2] 12 carlos has two spinners. (a) write down the number of lines of symmetry of this spinner. answer (a) [1] (b) write down the order of rotational symmetry of this spinner. answer (b) [1] ", "11": "11 \u00a9 ucles 2012 0607/01/o/n/12 blank page ", "12": "12 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2012 0607/01/o/n/12 blank page " }, "0607_w12_qp_2.pdf": { "1": " this document consists of 8 printed pages. ib12 11_0607_02/2rp \u00a9 ucles 2012 [turn over *0841359003* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/02 paper 2 (extended) october/november 2012 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2012 0607/02/o/n/12 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2012 0607/02/o/n/12 [turn over for examiner's use answer all the questions. 1 factorise completely. yz xy6 3\u2212 answer [2] 2 (a) write 250 grams as a percentage of 2 kilograms. answer(a) % [2] (b) manuel scores 46 in a test. this is 15% more than his previous test score. calculate manuel\u2019s previous test score. answer(b) [3] 3 dariella leaves home at 07 49 and takes 24 minutes to walk to school. (a) at what time does dariella arrive at school? answer(a) [1] (b) the distance to school is 1.4 km. calculate dariella\u2019s walking speed. give your answer in kilometres per hour. answer(b) km/h [2] 4 calculate. (3.24 \u00d7 10 \u20133) \u00f7 (4 \u00d7 104) give your answer in standard form. answer [2] ", "4": "4 \u00a9 ucles 2012 0607/02/o/n/12 for examiner's use 5 (a) x8 cmp cmnot to scale 31sin =x 32 2cos =x 2 21tan =x calculate the value of p giving your answer as a simplified fraction. answer(a) p = [2] (b) 0y xq the diagram shows the graph of x y2sin3= . q is a local maximum point. find the co-ordinates of q. answer(b) ( , ) [2] ", "5": "5 \u00a9 ucles 2012 0607/02/o/n/12 [turn over for examiner's use 6 (a) simplify 3 23\u2212 \uf8f7\uf8f8\uf8f6\uf8ec\uf8ed\uf8eb. give your answer as a fraction. answer(a) [2] (b) tlog4log2 2 log3 = \u2212 find the value of t. answer(b) [2] 7 y varies inversely as the square root of x. when x = 16, y = 3. (a) find y in terms of x. answer(a) y = [2] (b) find y when x = 36. answer(b) [1] 8 write 111\u2212\u2212x as a single fraction. answer [2] ", "6": "6 \u00a9 ucles 2012 0607/02/o/n/12 for examiner's use 9 (a) y x0a bnot to scale a is the point (4, 2) and b is the point (1, \u2013 3). (i) write down the vector in component form. answer(a)(i) = \uf8f7\uf8f7\uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec\uf8ec\uf8ec \uf8ed\uf8eb [1] (ii) = \uf8f7 \uf8f8\uf8f6\uf8ec \uf8ed\uf8eb\u2212 43 write down the co-ordinates of c. answer(a)(ii) ( , ) [1] (b) rq opmr pnot to scale opqr is a parallelogram and m is the midpoint of pq. = p and = r. find in terms of p and r. answer(b) [2] ", "7": "7 \u00a9 ucles 2012 0607/02/o/n/12 [turn over for examiner's use 10 simplify the following. (a) 32 answer(a) [1] (b) 1 21 + answer(b) [2] 11 w cm 4.5 cmnot to scale the diagrams show two similar shapes. the lengths shown in the diagrams are in the ratio 2 : 1. (a) calculate the value of w. answer(a) w = [1] (b) the area of the larger shape is 56 cm 2. calculate the area of the smaller shape. answer(b) cm2 [2] question 12 is on the next page ", "8": "8 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2012 0607/02/o/n/12 for examiner's use 12 (a) a bag contains 3 white beads and 2 black beads. two beads are taken out of the bag at random, without replacement. calculate the probability that both beads are white. answer(a) [2] (b) bag a bag b bag a contains 3 white beads and 2 black beads. bag b contains 3 white beads and 4 black beads. one bead is taken out of each bag at random. calculate the probability that one bead is white and one bead is black. answer(b) [3] " }, "0607_w12_qp_3.pdf": { "1": " this document consists of 16 printed pages. ib12 11_0607_03/2rp \u00a9 ucles 2012 [turn over *9869593646* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/03 paper 3 (core) october/november 2012 1 hour 45 minutes candidates answer on the question paper additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96. ", "2": "2 \u00a9 ucles 2012 0607/03/o/n/12 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2012 0607/03/o/n/12 [turn over for examiner's use answer all the questions. 1 1000 people are asked how they travel to work. 150 walk, 450 travel by bus and 25 cycle. all the rest travel by car. (a) how many people travel to work by car? answer(a) [1] (b) find the percentage of people who walk to work. answer(b) % [1] (c) the number of people who travel by bus is in the ratio men : women = 3 : 2. calculate the number of men who travel by bus. answer(c) [2] (d) aisha draws a pie chart to show how the 1000 people travel to work. calculate the sector angle which shows the number of people who walk to work. (do not draw the pie chart.) answer(d) [2] (e) one of the 1000 people is chosen at random. what is the probability that this person travels to work by bus? give your answer as a fraction in its lowest terms. answer(e) [2] ", "4": "4 \u00a9 ucles 2012 0607/03/o/n/12 for examiner's use 2 y xa b 0not to scale the equation of the straight line through a and b is 3x + 8y = 24. the line cuts the y-axis at a and the x-axis at b. (a) find the co-ordinates of a. answer(a) ( , ) [1] (b) find the co-ordinates of b. answer(b) ( , ) [1] (c) find the gradient of ab. answer(c) [2] (d) m is the midpoint of ab. write down the co-ordinates of m. answer(d) ( , ) [2] (e) write down the vector in component form. answer(e) \uf8f7\uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec\uf8ec \uf8ed\uf8eb [1] ", "5": "5 \u00a9 ucles 2012 0607/03/o/n/12 [turn over for examiner's use 3 12 cm 12 cm12 cm 12 cmnot to scale the diagram shows a piece of wood with the cross-section shaded. (a) calculate the area of the cross-section. answer(a) cm2 [2] (b) the piece of wood is 5 metres long. (i) calculate the volume of the piece of wood in cm 3. answer(b)(i) cm3 [2] (ii) write your answer to part(b)(i) in cubic metres. answer(b)(ii) m3 [1] (c) a builder needs 200 of these 5 metre long pieces of wood to construct a house. the wood costs $9.45 per metre. calculate the total cost of the wood. answer(c) $ [2] ", "6": "6 \u00a9 ucles 2012 0607/03/o/n/12 for examiner's use 4 (a) find the value of ( p \u2013 q)2 when p = 5.2 and q = \u2212 2.3. answer(a) [2] (b) solve the simultaneous equations. 3 x + 2y = 18 4 x \u2013 2y = \u2212 4 answer(b) x = y = [2] (c) simplify 3x5 \u00d7 2x3 . answer(c) [2] (d) solve the following equation. 2(3x \u2013 5) \u2013 3( x + 1) = 5 answer(d) x = [3] (e) 2 x = 24 + 24 find the value of x. answer(e) x = [2] ", "7": "7 \u00a9 ucles 2012 0607/03/o/n/12 [turn over for examiner's use 5 the marks gained by 20 students in a quiz are shown in the table. mark 1 2 3 4 5 frequency 9 3 5 2 1 find (a) the mode, answer(a) [1] (b) the mean, answer(b) [1] (c) the median, answer(c) [1] (d) the lower quartile, answer(d) [1] (e) the range. answer(e) [1] ", "8": "8 \u00a9 ucles 2012 0607/03/o/n/12 for examiner's use 6 (a) x\u00b0110\u00b0 not to scale find the value of x. answer(a) x = [1] (b) z\u00b0y\u00b0 120\u00b0 ot nanot to scale tan is a tangent, at a, to the circle, centre o. oa is a radius. find the values of y and z. answer(b) y = z = [3] ", "9": "9 \u00a9 ucles 2012 0607/03/o/n/12 [turn over for examiner's use (c) w\u00b0w\u00b0w\u00b0 w\u00b0 w\u00b0 140\u00b0not to scale one angle in a hexagon is 140\u00b0. each of the other angles is w\u00b0. find the value of w. answer(c) w = [3] ", "10": "10 \u00a9 ucles 2012 0607/03/o/n/12 for examiner's use 7 p q r26 cm10 cm not to scale (a) calculate pr. answer(a) cm [3] (b) find the area of triangle pqr . answer(b) cm2 [2] (c) use trigonometry to calculate the size of angle prq . answer(c) [2] ", "11": "11 \u00a9 ucles 2012 0607/03/o/n/12 [turn over for examiner's use 8 f( x) = 2x(x \u2212 4) (a) on the diagram sketch the graph of y = f(x) for \u22121 y x y 6. 6x24 \u20138\u201310y [3] (b) find the co-ordinates of the minimum point of the graph. answer(b) ( , ) [1] (c) write down the equation of the line of symmetry of the graph. answer(c) [1] (d) on the same diagram sketch the graph of y = 3x \u2013 4 . [2] (e) write down the co-ordinates of the points where 2 x(x \u2013 4) = 3x \u2013 4 . give each answer correct to 3 decimal places. answer(e) ( , ) ( , ) [3] ", "12": "12 \u00a9 ucles 2012 0607/03/o/n/12 for examiner's use 9 3 4 5 6 7 8 9 10 11 (a) joachim chooses a number from the list above at random. find the probability that the number is (i) an odd number, answer(a)(i) [1] (ii) a prime number, answer(a)(ii) [1] (iii) a factor of 12, answer(a)(iii) [1] (iv) a multiple of 3, answer(a)(iv) [1] (v) a power of 2. answer(a)(v) [1] (b) x is a number in the list above where 6 < x y 9 . write down all the possible values for x. answer(b) [1] ", "13": "13 \u00a9 ucles 2012 0607/03/o/n/12 [turn over for examiner's use 10 a bank pays interest at a rate of 2.5% each year. (a) lukas invests $5000 in the bank. at the end of each year he removes the interest from his bank account. calculate the total amount of interest he has removed after 4 years. answer(a) $ [3] (b) marcus also invests $5000 in the bank. he does not remove any money from the bank for 4 years. calculate how much more interest marcus will have than lukas at the end of the 4 years. answer(b) $ [4] ", "14": "14 \u00a9 ucles 2012 0607/03/o/n/12 for examiner's use 11 15 cm the diagram shows the top of a circular pizza with a radius of 15 cm. it is cut into 6 equal slices. (a) calculate the area of the top of the whole pizza. answer(a) cm2 [2] (b) find the area of the top of one slice of pizza. answer(b) cm2 [1] (c) find the length of the curved edge of one slice. answer(c) cm [2] (d) the whole pizza costs $12 to make. each slice of pizza is sold for $2.75 . calculate the percentage profit made by selling all six slices. answer(d) % [4] ", "15": "15 \u00a9 ucles 2012 0607/03/o/n/12 [turn over for examiner's use 12 a large number of plants are grown from seeds. the probability that a plant has a red flower is 51 . (a) find the probability that a plant does not have a red flower. answer(a) [1] (b) two of these plants are chosen at random. (i) complete the tree diagram. plant 1 plant 2 red flower not red flowerredflower not red flower not red flowerred flower15 [2] (ii) find the probability that both plants have red flowers. answer(b)(ii) [2] (iii) find the probability that only one of the two plants has a red flower. answer(b)(iii) [3] question 13 is on the next page. ", "16": "16 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2012 0607/03/o/n/12 for examiner's use 13 6 54321 \u20131\u20132\u20133\u20134\u20135\u20136\u20135 \u20136 \u20137 \u2013 4\u2013 3\u2013 2\u2013 1 1 0 234567y xfp q g (a) describe fully the single transformation that maps f onto g. [2] (b) describe fully the single transformation that maps p onto q. [2] " }, "0607_w12_qp_4.pdf": { "1": " this document consists of 19 printed pages and 1 blank page. ib12 11_0607_04/2rp \u00a9 ucles 2012 [turn over *3360305085* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/04 paper 4 (extended) october/november 2012 2 hours 15 minutes candidates answer on the question paper additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120. ", "2": "2 \u00a9 ucles 2012 0607/04/o/n/12 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2012 0607/04/o/n/12 [turn over for examiner's use answer all the questions. 1 a number of students were asked how many brothers or sisters they have. the results are shown in the table. number of brothers or sisters 0 1 2 3 4 5 6 frequency 9 15 13 6 2 3 2 find (a) the number of students, answer(a) [1] (b) the median, answer(b) [1] (c) the mean, answer(c) [1] (d) the upper quartile, answer(d) [1] (e) the range, answer(e) [1] (f) the mode. answer(f) [1] ", "4": "4 \u00a9 ucles 2012 0607/04/o/n/12 for examiner's use 2 (a) mr pereira shares $200 between his two sons in the ratio pedro : jose = 3 : 2. (i) write this ratio in the form n : 1. answer(a)(i) : 1 [1] (ii) show that pedro receives $120. [1] (iii) pedro invests his $120 at a rate of 4 % per year simple interest. calculate the total amount pedro has after 2 years. answer(a)(iii) $ [2] (iv) jose invests his $80 at a rate of 3.95 % per year compound interest. calculate the total amount jose has after 2 years. answer(a)(iv) $ [2] (v) show that, over 2 years, 3.95% per year compound interest is better than 4% per year simple interest. [2] ", "5": "5 \u00a9 ucles 2012 0607/04/o/n/12 [turn over for examiner's use (b) the value of mr pereira\u2019s car is $24 000. the value of the car decreases by 10 % each year. (i) find the value of the car after 2 years. answer(b)(i) $ [2] (ii) find the number of complete years it takes for the value of the car to reduce from $24 000 to $10 000. answer(b)(ii) [2] ", "6": "6 \u00a9 ucles 2012 0607/04/o/n/12 for examiner's use 3 4.8 cm 23.7 cmnot to scale the diagram shows a solid made using a hemisphere and a cylinder. the radius of both the hemisphere and the cylinder is 4.8 cm. the height of the cylinder is 23.7 cm. (a) (i) calculate the volume of the solid. give your answer correct to the nearest cubic centimetre. answer(a)(i) cm3 [4] (ii) write your answer to part(a)(i) in cubic metres. answer(a)(ii) m3 [1] (iii) the solid is made of wood. 1 m3 of wood has a mass of 820 kg. calculate the mass of the solid. answer(a)(iii) kg [1] ", "7": "7 \u00a9 ucles 2012 0607/04/o/n/12 [turn over for examiner's use (b) the surface of the solid, including the base, is painted at a cost of 0.15 cents per square centimetre. calculate the cost of painting the solid. give your answer in dollars , correct to the nearest cent. answer(b) $ [5] ", "8": "8 \u00a9 ucles 2012 0607/04/o/n/12 for examiner's use 4 (a) each interior angle of a regular polygon with n sides is 175\u00b0. find n. answer(a) n = [2] (b) 74\u00b0 x\u00b0y\u00b0 2x\u00b0c d a bnot to scale in the diagram ba = bd = bc. angle dab = 74\u00b0, angle abd = x\u00b0, angle dbc = 2x\u00b0 and angle bcd = y\u00b0. (i) find the value of y. answer(b)(i) y = [3] (ii) explain why ad is not parallel to bc. [2] ", "9": "9 \u00a9 ucles 2012 0607/04/o/n/12 [turn over for examiner's use (c) ad c bo 150\u00b027\u00b0 not to scale in the diagram a, b, c and d lie on the circle, centre o. angle aob = 150\u00b0 and angle bdc = 27\u00b0. calculate (i) angle acb, answer(c)(i) [1] (ii) angle oac. answer(c)(ii) [3] ", "10": "10 \u00a9 ucles 2012 0607/04/o/n/12 for examiner's use 5 r qp7 cm 7.5 cm40\u00b0not to scale (a) calculate the area of triangle pqr . answer(a) cm2 [2] (b) calculate qr. answer(b) cm [3] ", "11": "11 \u00a9 ucles 2012 0607/04/o/n/12 [turn over for examiner's use 6 \u201362 \u2013260y x f(x) = 64 2\u2212 \u2212x x (a) on the diagram sketch the graph of y = f(x) for \u2013 6 y x y 6. [5] (b) write down the equations of the three asymptotes. answer(b) , , [3] (c) find the range of f( x). answer(c) [3] (d) write down the range of ) ( fx. answer(d) [1] (e) g(x) = log x (ii) solve the equation x x xlog 64 2= \u2212 \u2212 . answer(e)(ii) x = or x = [2] (iii) solve the equation x x xlog 64 2= \u2212 \u2212 . answer(e)(iii) [1] (i) on the same diagram sketch the graph of y = g(x). [2] ", "12": "12 \u00a9 ucles 2012 0607/04/o/n/12 for examiner's use 7 u p qx wt vuy n l mr the venn diagram shows three sets p, q and r. u = {l, m, n, t, u, v, w, x, y} (a) use set notation to complete each statement. (i) y r [1] (ii) q p [1] (iii) q \u2229 r = [1] (iv) p q = p [1] (b) list the elements of the following sets. (i) p = { } [1] (ii) p \u2229 q = { } [1] (iii) (p \u222a r)' = { } [1] (iv) q \u222a r { } [1] ", "13": "13 \u00a9 ucles 2012 0607/04/o/n/12 [turn over for examiner's use 8 y x3 \u20131\u20132 20 (a) sketch the following lines. (i) y = x + 1 [1] (ii) 32xy \u2212 = [1] (b) find the co-ordinates of the point of intersection, i, of the two lines in part (a) . answer(b) ( , ) [1] (c) find the area of the triangle enclosed by the lines y = x + 1, 32xy \u2212 =and x = 0. answer(c) [2] (d) find the equation of the line which passes through i and is perpendicular to the line y = x + 1. answer(d) [3] ", "14": "14 \u00a9 ucles 2012 0607/04/o/n/12 for examiner's use 9 200 students measured the distance, d metres, they walked in 5 minutes. the table shows the results. distance ( d metres) 0 y d < 200 200 y d < 300 300 y d < 350 350 y d < 400 400 y d < 500 frequency 13 19 83 70 15 (a) calculate an estimate of the mean distance walked. answer(a) m [2] (b) complete the histogram below. the bar for 400 y d < 500 has already been drawn for you. 2 1.5 1 0.5 0100 200 300 400 500frequency density distance (metres)d [4] ", "15": "15 \u00a9 ucles 2012 0607/04/o/n/12 [turn over for examiner's use 10 (a) solve the equation 6 \u2013 3 x \u2013 x2 = 0 . answer(a) x = or x = [3] (b) solve the inequality 6 \u2013 3 x \u2013 x2 y 0 . answer(b) [2] ", "16": "16 \u00a9 ucles 2012 0607/04/o/n/12 for examiner's use 11 f(x) = 2x + 3 g(x) = x2 + x + 2 (a) find f(g(2)). answer(a) [2] (b) find g(f( x)) in its simplest form. answer(b) [3] (c) find f \u20131(x). answer(c) [2] (d) (i) find the value of f(f(1)). answer(d)(i) [1] (ii) solve the equation f(f(x)) = f( x). answer(d)(ii) x = [2] ", "17": "17 \u00a9 ucles 2012 0607/04/o/n/12 [turn over for examiner's use 12 ac b5 4321 \u20131\u20132\u20133 \u20135\u2013 4\u2013 3\u2013 2\u2013 1 1 0 234567y x (a) describe fully the single transformation that maps flag a onto (i) flag b, [2] (ii) flag c. [3] (b) draw the rotation of flag a through 90\u00b0 clockwise about the point (1, \u2013 1). [2] ", "18": "18 \u00a9 ucles 2012 0607/04/o/n/12 for examiner's use 13 sara cycles 10 km at a speed of ( x + 3) km/h. she then cycles a further 4 km at a speed of x km/h. the total time taken is 1 hour. (a) (i) write down an expression in x for the time sara takes to cycle the first 10 km. answer(a)(i) hours [1] (ii) show that x 2 \u2013 11x \u2013 12 = 0. [3] (b) factorise x 2 \u2013 11x \u2013 12 . answer(b) [2] (c) find the number of minutes sara takes to cycle the first 10 km. answer(c) min [2] ", "19": "19 \u00a9 ucles 2012 0607/04/o/n/12 for examiner's use 14 y x 30\u00b0 \u201330\u00b0 0 60\u00b0 \u201360\u00b0 90\u00b0 \u201390\u00b0 120\u00b0 \u2013120\u00b0 150\u00b0 \u2013150\u00b0 180\u00b0 \u2013180\u00b06 42 \u20132\u20134\u20136 the diagram shows the graph of y = tan x for \u2013 180\u00b0 y x y 180\u00b0. (a) (i) on the diagram sketch the graph of y = tan( x \u2013 60\u00b0) for \u2013 180\u00b0 y x y 180\u00b0. [2] (ii) describe fully the single transformation that maps the graph of y = tan x onto the graph of y = tan( x \u2013 60\u00b0). [2] (b) solve the equation tan x = 3 for \u2013 180\u00b0 y x y 180\u00b0. answer(b) [2] ", "20": "20 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2012 0607/04/o/n/12 blank page " }, "0607_w12_qp_5.pdf": { "1": " this document consists of 7 printed pages and 1 blank page. ib12 11_0607_05/3rp \u00a9 ucles 2012 [turn over *5588991114* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/05 paper 5 (core) october/november 2012 1 hour candidates answer on the question paper additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24. ", "2": "2 \u00a9 ucles 2012 0607/05/o/n/12 for examiner's use answer all the questions. investigation straight lines 1 the straight lines in this diagram never cross . complete the statement. these lines are called lines. 2 in this diagram three lines cross at two points. in this diagram three lines cross at three points. this is the maximum number of crossing points for three lines. draw diagrams to show the following numbers of crossing points for four lines. put arrow symbols on all the lines that never cross. (a) three crossing points. ", "3": "3 \u00a9 ucles 2012 0607/05/o/n/12 [turn over for examiner's use (b) four crossing points. (c) five crossing points. (d) six crossing points. this is the maximum number of crossing points for four lines. ", "4": "4 \u00a9 ucles 2012 0607/05/o/n/12 for examiner's use 3 a diagram for the maximum number of crossing points for five lines is to be drawn. (a) explain how a fifth line must be drawn on your diagram in part 2 (d) to give the maximum number of crossing points. (b) draw this diagram. (c) write down the maximum number of crossing points for five lines. ", "5": "5 \u00a9 ucles 2012 0607/05/o/n/12 [turn over for examiner's use 4 complete this table. number of lines 1 2 3 4 5 6 7 8 9 maximum number of crossing points 0 3 6 15 28 5 the formula for the maximum number of crossing points is ) 1 (21\u2212n n . (a) what does the letter n represent? (b) show that this formula gives the answer in the table when eight lines cross. (c) find the number of lines when the maximum number of crossing points is 120. ", "6": "6 \u00a9 ucles 2012 0607/05/o/n/12 for examiner's use 6 straight lines can also form regions. there are four regions when two lines cross. 1 2 43 the maximum number of regions when three lines cross is seven. 1 2 3 4 5 6 7 (a) (i) draw a diagram to show the maximum number of regions when four lines cross. number the regions. (ii) write down the maximum number of regions when four lines cross. ", "7": "7 \u00a9 ucles 2012 0607/05/o/n/12 for examiner's use (b) complete this table. number of lines 1 2 3 4 5 6 7 maximum number of regions 2 4 7 16 22 (c) the maximum number of regions forms a sequence. the maximum number of regions when 21 lines cross is 232. find the maximum number of regions when 22 lines cross. show how you get your answer. (d) (i) find a formula for the maximum number of regions when n lines cross. you may use the formula in question 5 to help you. (ii) test that your formula gives the answer in the table when six lines cross. ", "8": "8 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2012 0607/05/o/n/12 blank page " }, "0607_w12_qp_6.pdf": { "1": " this document consists of 11 printed pages and 1 blank page. ib12 11_0607_06/2rp \u00a9 ucles 2012 [turn over *1208111882* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/06 paper 6 (extended) october/november 2012 1 hour 30 minutes candidates answer on the question paper additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2012 0607/06/o/n/12 for examiner's use answer both parts a and b. a investigation straight lines (20 marks) you are advised to spend no more than 45 minutes on this part. 1 the straight lines in this diagram never cross . complete the statement. these lines are called lines. 2 in this diagram three lines cross at two points. in this diagram three lines cross at three points. this is the maximum number of crossing points for three lines. draw diagrams to show the following numbers of crossing points for four lines. put arrow symbols on all the lines that never cross. (a) three crossing points. ", "3": "3 \u00a9 ucles 2012 0607/06/o/n/12 [turn over for examiner's use (b) four crossing points. (c) five crossing points. (d) six crossing points. this is the maximum number of crossing points for four lines. ", "4": "4 \u00a9 ucles 2012 0607/06/o/n/12 for examiner's use 3 a diagram for the maximum number of crossing points for five lines is to be drawn. (a) explain how a fifth line must be drawn on your diagram in part 2 (d) to give the maximum number of crossing points. (b) (i) draw this diagram. (ii) write down the maximum number of crossing points for five lines. 4 (a) complete this table. number of lines 1 2 3 4 5 6 7 8 9 maximum number of crossing points 0 3 6 15 28 ", "5": "5 \u00a9 ucles 2012 0607/06/o/n/12 [turn over for examiner's use (b) the maximum number of crossing points follows this pattern 0, odd, odd, even, even, odd, odd, and so on. explain why this pattern occurs. 5 the maximum number of crossing points forms a sequence. (a) find a formula for the nth term of this sequence. (b) use your formula to show that when 10 lines cross, the maximum number of crossing points is 45. (c) find the number of lines when the maximum number of crossing points is 120. (d) is it possible for the maximum number of crossing points to be 590? show how you get your answer. ", "6": "6 \u00a9 ucles 2012 0607/06/o/n/12 for examiner's use b modelling a swing (20 marks) you are advised to spend no more than 45 minutes on this part. the diagram shows a swing that is free to move backwards and forwards. the seat is attached to the top bar by two ropes of equal length. the length, l cm, of the ropes is changed. the time taken, t seconds, for the seat to swing backwards and forwards once is measured. the results are shown in the table. length l cm 0 50 100 150 200 250 300 350 time t seconds 0 1.4 2.3 2.4 2.8 3.2 3.5 3.8 ", "7": "7 \u00a9 ucles 2012 0607/06/o/n/12 [turn over for examiner's use 1 (a) on the grid below, plot the points for t against l, for 0 y l y 350. t l4 321 050 100 150 200 length (cm)250 300 350time (seconds) (b) one of the times in the table is incorrect. write down this time. seconds (c) (i) on the grid in part (a) , draw the graph of t against l using the seven correct points. (ii) estimate the correct time for your answer to part (b) . seconds ", "8": "8 \u00a9 ucles 2012 0607/06/o/n/12 for examiner's use 2 the relationship between t and l can be represented by a model. (a) which of the following models best fits this relationship? t = al + b t = al 2 + b t = alb (b) (i) use lengths of 50 cm and 200 cm to show that the value of b is 21. (ii) find the value of a in your model. give your answer correct to 1 decimal place. ", "9": "9 \u00a9 ucles 2012 0607/06/o/n/12 [turn over for examiner's use (iii) rewrite your model substituting your values for a and b. show that your model works when l = 250 cm. (c) use your model to find (i) the length of the rope when the time taken is 4 seconds, cm (ii) an estimate of the correct time for your answer in question 1 (b) . seconds ", "10": "10 \u00a9 ucles 2012 0607/06/o/n/12 for examiner's use 3 the model for the time, t seconds, that a pendulum of length l metres takes for one swing is 9.82\u03c0lt= . (a) sketch the graph of t against l for 0 y l y 10. 0 length (metres)lt 107 time (seconds) ", "11": "11 \u00a9 ucles 2012 0607/06/o/n/12 for examiner's use (b) (i) show how this model becomes 9.85\u03c0lt= when l is measured in centimetres . (ii) compare this model with your model in question 2 (b) (iii) . ", "12": "12 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publis her (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2012 0607/06/o/n/12 blank page " } }, "2013": { "0607_s13_qp_11.pdf": { "1": " this document consists of 11 printed pages and 1 blank page. ib13 06_0607_11/4rp \u00a9 ucles 2013 [turn over *0968513895* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/11 paper 1 (core) may/june 2013 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2012 0607/11/m/j/13 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2012 0607/11/m/j/13 [turn over for examiner's use 1 10 30 60 61 63 65 69 using only numbers from the list above, write down (a) a multiple of 7, answer (a) [1] (b) a prime number, answer (b) [1] (c) the lowest common multiple of 20 and 30. answer (c) [1] 2 write 41 as (a) a decimal, answer (a) [1] (b) a percentage. answer (b) [1] ", "4": "4 \u00a9 ucles 2012 0607/11/m/j/13 for examiner's use 3 the bar chart shows the grades obtained by a group of students in an examination. d01234 frequency grade5 c b a (a) how many students achieved an a grade? answer (a) [1] (b) write down the modal grade. answer (b) [1] (c) how many students were there altogether? answer (c) [1] (d) how many more students achieved a b grade than a d grade? answer (d) [1] ", "5": "5 \u00a9 ucles 2012 0607/11/m/j/13 [turn over for examiner's use 4 ahmed earns $2500 in may. in june, he earns 2% more. work out how much he earns in june. answer $ [2] 5 this shape is drawn on a one-centimetre square grid. (a) find the perimeter of this shape. answer (a) cm [1] (b) work out the area of this shape. answer (b) cm2 [1] ", "6": "6 \u00a9 ucles 2012 0607/11/m/j/13 for examiner's use 6 a box of chocolates contains 4 milk chocolates (m) and 6 plain chocolates (p). one chocolate is chosen at random and is not replaced. a second chocolate is chosen at random. (a) find the probability that the first chocolate chosen is a milk chocolate. answer (a) [1] (b) complete the tree diagram. mm p... ... ...pm p... .. [3] (c) find the probability that both of the chocolates chosen are milk chocolates. answer (c) [2] ", "7": "7 \u00a9 ucles 2012 0607/11/m/j/13 [turn over for examiner's use 7 \u20134 \u20133 \u20132 \u20131 0 12341234y x 5 \u201355 q p describe fully the single transformation which maps triangle p onto triangle q. [3] 8 a b c120\u00b0not to scale abc is a sector of a circle with circumference 300 cm. angle acb is 120\u00b0. find the length of the arc ab. answer cm [2] ", "8": "8 \u00a9 ucles 2012 0607/11/m/j/13 for examiner's use 9 the diagram shows the graph of the function y = f(x) for \u20131 y=x y 2 . \u20134 \u20133 \u20132 \u20131 0 1234 \u20133\u20132\u20131123y x (a) on the diagram, draw the graph of y = f(x + 3). [1] (b) on the diagram, draw the graph of y = f(x) \u2013 2 . [1] (c) describe the single transformation that maps y = f( x) onto y = f(x ) \u2013 2 . answer (c) [2] ", "9": "9 \u00a9 ucles 2012 0607/11/m/j/13 [turn over for examiner's use 10 \u20136 \u20136\u20135 \u20134 \u20133 \u20132 \u20131 0 123456 \u20135\u20134\u20133\u20132\u20131123456y x p the diagram shows the point p(\u20134, \u20132) . (a) = \uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec \uf8ed\uf8eb 28 on the grid, plot and label the point q. [1] (b) r is the midpoint of the line pq. write down the co-ordinates of r. answer (b) ( ) [1] (c) the line pq is parallel to the line y = 41x + 1 . , write down the equation of the line pq in the form y = mx + c answer (c) y = [2] ", "10": "10 \u00a9 ucles 2012 0607/11/m/j/13 for examiner's use 11 (a) simplify. (i) 5 + 3d \u2013 1 + 4d answer (a)(i) [2] (ii) t3\u00d7t answer (a) (ii) [1] (b) expand the brackets. 8(4 \u2013 3 n) answer (b) [1] (c) factorise the following expression. 9x2 \u2013 15xy answer (c) [2] ", "11": "11 \u00a9 ucles 2012 0607/11/m/j/13 for examiner's use 12 solve the following equation. 7q \u2013 5 = 6 \u2013 3q answer q = [2] ", "12": "12 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2012 0607/11/m/j/13 blank page " }, "0607_s13_qp_12.pdf": { "1": " this document consists of 12 printed pages. ib13 06_0607_12/4rp \u00a9 ucles 2013 [turn over *2077414067* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/12 paper 1 (core) may/june 2013 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2012 0607/12/m/j/13 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2012 0607/12/m/j/13 [turn over for examiner's use 1 write 5392 correct to (a) the nearest 100 , answer (a) [1] (b) the nearest 10 . answer (b) [1] 2 here is a list of numbers. 4 5 11 20 27 39 43 use the list to write down (a) a square number, answer (a) [1] (b) a factor of 20, answer (b) [1] (c) a multiple of 5, answer (c) [1] (d) a prime number. answer (d) [1] 3 write down the order of rotational symmetry of this regular hexagon. answer [1] ", "4": "4 \u00a9 ucles 2012 0607/12/m/j/13 for examiner's use 4 (a) work out 6 \u2013 2 \u00d7 2 . answer (a) [1] (b) work out 41 of 128 . answer (b) [1] (c) find the value of 2-3 . answer (c) [1] 5 write down in order of size, starting with the smallest. 31 51 0.3 25% answer i i i [2] ", "5": "5 \u00a9 ucles 2012 0607/12/m/j/13 [turn over for examiner's use 6 (a) \u20136\u20135\u20134\u20133\u20132\u20131 0 123456 \u20135\u20134\u20133\u20132\u2013112345y xa reflect triangle a in the y-axis. [1] (b) \u20136\u20135\u20134\u20133\u20132\u201310 123456 \u20135\u20134\u20133\u20132\u2013112345y xb rotate shape b through 90\u00b0 clockwise about the origin. [2] ", "6": "6 \u00a9 ucles 2012 0607/12/m/j/13 for examiner's use 7 (a) the line ab is drawn below. mark a point c so that angle abc = 124\u00b0 . a b [1] (b) not to scale 72\u00b0 pqnorth the bearing of q from p is 072\u00b0 . find the bearing of p from q. answer (b) [2] ", "7": "7 \u00a9 ucles 2012 0607/12/m/j/13 [turn over for examiner's use 8 elaine, mark and timi each spin the same spinner a number of times. they record how many times it lands on the number 4. number of spins number of times the spinner lands on 4 elaine 10 2 mark 100 26 timi 200 49 who will give the best estimate of the probability that the spinner lands on the number 4? explain your answer. because [2] ", "8": "8 \u00a9 ucles 2012 0607/12/m/j/13 for examiner's use 9 (a) the cost, in $, of hiring a machine is worked out using the formula cost = 50 + 25 \u00d7 number of days hired. work out the cost of hiring the machine for (i) 2 days, answer (a)(i) $ [1] (ii) 1 week. answer (a)(ii) $ [1] (b) simplify. 5 x + 4y + 2x \u2013 y answer (b) [2] (c) solve the following equation. 3 x + 5 = 23 answer (c) x = [2] (d) solve the following inequality. 4 x \u2013 3 y 7 answer (d) [2] ", "9": "9 \u00a9 ucles 2012 0607/12/m/j/13 [turn over for examiner's use (e) solve the simultaneous equations. 3 x + y = 19 x + y = \u22125 answer (e) x = y = [2] ", "10": "10 \u00a9 ucles 2012 0607/12/m/j/13 for examiner's use 10 2 cm 3 cmnot to scale a badge is in the shape of a square with four congruent triangles attached. the square has side 3 cm. the triangles each have a perpendicular height of 2 cm. work out the area of the badge. answer cm 2 [3] ", "11": "11 \u00a9 ucles 2012 0607/12/m/j/13 [turn over for examiner's use 11 the cumulative frequency curve shows the time, in minutes, spent by 50 customers at a supermarket checkout. 01020304050 5 10 15 20 time (min)cumulative frequency (a) use the graph to find (i) the median time, answer (a)(i) min [1] (ii) the interquartile range. answer (a)(ii) min [2] (b) how many customers spent less than 10 minutes at the checkout? answer (b) [1] question 12 is printed on the next page. ", "12": "12 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2012 0607/12/m/j/13 for examiner's use12 triangles abe and acd are similar. ae = 4 cm, eb = 6 cm and dc = 9 cm. 9 cm6 cm4 cm ba e dcnot to scale work out the length of ed. answer cm [3] " }, "0607_s13_qp_13.pdf": { "1": " this document consists of 11 printed pages and 1 blank page. ib13 06_0607_13/fp \u00a9 ucles 2013 [turn over *5740333976* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/13 paper 1 (core) may/june 2013 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2012 0607/13/m/j/13 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2012 0607/13/m/j/13 [turn over for examiner's use 1 10 30 60 61 63 65 69 using only numbers from the list above, write down (a) a multiple of 7, answer (a) [1] (b) a prime number, answer (b) [1] (c) the lowest common multiple of 20 and 30. answer (c) [1] 2 write 41 as (a) a decimal, answer (a) [1] (b) a percentage. answer (b) [1] ", "4": "4 \u00a9 ucles 2012 0607/13/m/j/13 for examiner's use 3 the bar chart shows the grades obtained by a group of students in an examination. d01234 frequency grade5 c b a (a) how many students achieved an a grade? answer (a) [1] (b) write down the modal grade. answer (b) [1] (c) how many students were there altogether? answer (c) [1] (d) how many more students achieved a b grade than a d grade? answer (d) [1] ", "5": "5 \u00a9 ucles 2012 0607/13/m/j/13 [turn over for examiner's use 4 ahmed earns $2500 in may. in june, he earns 2% more. work out how much he earns in june. answer $ [2] 5 this shape is drawn on a one-centimetre square grid. (a) find the perimeter of this shape. answer (a) cm [1] (b) work out the area of this shape. answer (b) cm2 [1] ", "6": "6 \u00a9 ucles 2012 0607/13/m/j/13 for examiner's use 6 a box of chocolates contains 4 milk chocolates (m) and 6 plain chocolates (p). one chocolate is chosen at random and is not replaced. a second chocolate is chosen at random. (a) find the probability that the first chocolate chosen is a milk chocolate. answer (a) [1] (b) complete the tree diagram. mm p... ... ...pm p... .. [3] (c) find the probability that both of the chocolates chosen are milk chocolates. answer (c) [2] ", "7": "7 \u00a9 ucles 2012 0607/13/m/j/13 [turn over for examiner's use 7 \u20134 \u20133 \u20132 \u20131 0 12341234y x 5 \u201355 q p describe fully the single transformation which maps triangle p onto triangle q. [3] 8 a b c120\u00b0not to scale abc is a sector of a circle with circumference 300 cm. angle acb is 120\u00b0. find the length of the arc ab. answer cm [2] ", "8": "8 \u00a9 ucles 2012 0607/13/m/j/13 for examiner's use 9 the diagram shows the graph of the function y = f(x) for \u20131 y=x y 2 . \u20134 \u20133 \u20132 \u20131 0 1234 \u20133\u20132\u20131123y x (a) on the diagram, draw the graph of y = f(x + 3). [1] (b) on the diagram, draw the graph of y = f(x) \u2013 2 . [1] (c) describe the single transformation that maps y = f( x) onto y = f(x ) \u2013 2 . answer (c) [2] ", "9": "9 \u00a9 ucles 2012 0607/13/m/j/13 [turn over for examiner's use 10 \u20136 \u20136\u20135 \u20134 \u20133 \u20132 \u20131 0 123456 \u20135\u20134\u20133\u20132\u20131123456y x p the diagram shows the point p(\u20134, \u20132) . (a) = \uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec \uf8ed\uf8eb 28 on the grid, plot and label the point q. [1] (b) r is the midpoint of the line pq. write down the co-ordinates of r. answer (b) ( ) [1] (c) the line pq is parallel to the line y = 41x + 1 . , write down the equation of the line pq in the form y = mx + c answer (c) y = [2] ", "10": "10 \u00a9 ucles 2012 0607/13/m/j/13 for examiner's use 11 (a) simplify. (i) 5 + 3d \u2013 1 + 4d answer (a)(i) [2] (ii) t3\u00d7t answer (a) (ii) [1] (b) expand the brackets. 8(4 \u2013 3 n) answer (b) [1] (c) factorise the following expression. 9x2 \u2013 15xy answer (c) [2] ", "11": "11 \u00a9 ucles 2012 0607/13/m/j/13 for examiner's use 12 solve the following equation. 7q \u2013 5 = 6 \u2013 3q answer q = [2] ", "12": "12 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2012 0607/13/m/j/13 blank page " }, "0607_s13_qp_21.pdf": { "1": " this document consists of 8 printed pages. ib13 06_0607_21/3rp \u00a9 ucles 2013 [turn over *1024033730* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/21 paper 2 (extended) may/june 2013 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2013 0607/21/m/j/13 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2013 0607/21/m/j/13 [turn over for examiner's use answer all the questions. 1 the population of india in 2011 was 1.21 \u00d7 109 . the population of pakistan in 2011 was 1.77 \u00d7 108 . calculate the total population of india and pakistan in 2011. give your answer in standard form. answer [2] 2 p is the point (\u20132, 5) and q is the point (4, 1). (a) find the co-ordinates of the midpoint of pq. answer(a) ( , ) [1] (b) find the gradient of pq. answer(b) [2] (c) (i) find the equation of the line perpendicular to pq which passes through the point (0, 4). answer(c)(i) [2] (ii) find the x co-ordinate of the point where this line cuts the x-axis. answer(c)(ii) x = [1] ", "4": "4 \u00a9 ucles 2013 0607/21/m/j/13 for examiner's use 3 solve these simultaneous equations. y = 2x \u2013 8 3 x + 2y = 5 answer x = answer y = [3] 4 one morning, ashad carries out a survey on the colours of 200 cars in his town. these are his results. colour silver black red blue other frequency 78 40 36 30 16 (a) complete this table of relative frequencies. colour silver black red blue other relative frequency 0.2 [2] (b) there is a total of 18 000 cars in the town. work out an estimate of the number of black cars in the town. answer(b) [2] ", "5": "5 \u00a9 ucles 2013 0607/21/m/j/13 [turn over for examiner's use 5 y\u00b0 x\u00b0130\u00b0 a bo d c enot to scale a, b, c and d are points on the circle centre o. dce is a straight line. angle aod = 130 \u00b0. find the value of (a) x, answer(a) x = [2] (b) y. answer(b) y = [2] ", "6": "6 \u00a9 ucles 2013 0607/21/m/j/13 for examiner's use 6 u pq r on the venn diagram write the elements a, b and c in the correct subsets using the following information. a \u2208 ( p \u222a q \u222a r)' b \u2208 p ' \u2229 (q \u2229 r) c \u2208 ( q \u222a r)' \u2229 p [3] 7 (a) write down the value of (i) log 1000, answer(a)(i) [1] (ii) log 0.01 . answer(a)(ii) [1] (b) find p when 2log 5 \u2013 log 2 = log p . answer(b) p = [2] ", "7": "7 \u00a9 ucles 2013 0607/21/m/j/13 [turn over for examiner's use 8 5 cmr cm160\u00b0 not to scale the diagrams show a circle with radius 5 cm and the sector of another circle with angle 160 \u00b0 and radius r cm. the circle and the sector have the same area. calculate the value of r. answer r = [4] 9 simplify. (a) 50 + 8 answer(a) [2] (b) ( 3 5+ )2 answer(b) [2] questions 10 and 11 are printed on the next page. ", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2013 0607/21/m/j/13 for examiner's use 10 rearrange this equation to make x the subject. ax \u2013 3y = b( x + 2y) answer x = [3] 11 ab p q r write the vectors p, q and r in terms of a and b. answer p = q = r = [3] " }, "0607_s13_qp_22.pdf": { "1": " this document consists of 8 printed pages. ib13 06_0607_22/rp \u00a9 ucles 2013 [turn over *4727863751* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/22 paper 2 (extended) may/june 2013 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2013 0607/22/m/j/13 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2013 0607/22/m/j/13 [turn over for examiner's use answer all the questions. 1 u 3 31 56 471b a c the venn diagram shows the number of elements in each of the sets a, b and c, and n(u) = 30. (a) find (i) n(a), answer(a)(i) [1] (ii) n ) (b c\u2032\u222a . answer(a)(ii) [1] (b) shade the region c b a\u222a \u2229) ( on the venn diagram. [1] 2 p 65\u00b0 q b raonot to scale a, p, q, b and r lie on a circle, centre o. angle apb = 65\u00b0. find (a) angle aqb , answer(a) angle aqb = [1] (b) angle aob , answer(b) angle aob = [1] (c) angle arb. answer(c) angle arb = [1] ", "4": "4 \u00a9 ucles 2013 0607/22/m/j/13 for examiner's use 3 5 4321 \u20131\u20132\u20133\u20134\u20135\u20136\u20137\u20138\u20139 \u201310\u20135 \u2013 4 \u2013 3 \u2013 2 \u2013 1 123456789 1 0y xpq 0 (a) enlarge shape p using centre (3, 4) and scale factor 3. [2] (b) describe fully the single transformation that maps shape p onto shape q. [3] 4 (a) simplify. 16 x 16 \u00f7 2x2 answer(a) [2] (b) 218=n find the value of n. answer(b) n = [2] ", "5": "5 \u00a9 ucles 2013 0607/22/m/j/13 [turn over for examiner's use 5 rationalise the denominator in each of the following. (a) 32 answer(a) [1] (b) 1 31 \u2212 answer(b) [2] 6 (a) find the value of ax 3 when a = 1200 and x = 5. give your answer in standard form. answer(a) [2] (b) make x the subject of the formula y = ax 3. answer(b) x = [2] ", "6": "6 \u00a9 ucles 2013 0607/22/m/j/13 for examiner's use 7 (a) write 2log( x + 1) \u2013 log(x \u2013 1) as a single logarithm. answer(a) [2] (b) log 3 p = 4 where p is an integer. find the value of p. answer(b) p = [2] 8 these are the first five terms of a sequence. 2 6 12 20 30 (a) find the next term. answer(a) [1] (b) find an expression for the nth term. answer(b) [3] ", "7": "7 \u00a9 ucles 2013 0607/22/m/j/13 [turn over for examiner's use 9 f( x) = 3 + 2x find (a) f(f(\u2013 4)), answer(a) [2] (b) f \u20131(x) . answer(b) [2] 10 y varies inversely as x 2. when x = 2, y = 24. find a formula for y in terms of x. answer y = [2] question 11 is printed on the next page. ", "8": "8 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2013 0607/22/m/j/13 for examiner's use 11 rrnot to scale the diagram shows a circle of radius r inside a circle of radius r. (a) find an expression, in terms of \u03c0, r and r, for the shaded area. factorise your expression completely. answer(a) [2] (b) when r = r + 3, the shaded area is 24 \u03c0. find the value of r. answer(b) r = [2] " }, "0607_s13_qp_23.pdf": { "1": " this document consists of 8 printed pages. ib13 06_0607_23/3rp \u00a9 ucles 2013 [turn over *4686246803* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/23 paper 2 (extended) may/june 2013 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2013 0607/23/m/j/13 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2013 0607/23/m/j/13 [turn over for examiner's use answer all the questions. 1 work out (1.6 \u00d7 103) \u00f7 (4 \u00d7 105). give your answer in standard form. answer [2] 2 solve the equations. (a) 2 \u2013 3(1 \u2013 2 x) = 4(2 \u2013 x) answer(a) x = [3] (b) sinx = 23\u00b1 for 0\u00b0 y x y 360\u00b0 answer(b) x = [3] ", "4": "4 \u00a9 ucles 2013 0607/23/m/j/13 for examiner's use 3 find the value of the following. (a) 40 answer(a) [1] (b) 32 27\u2212 answer(b) [2] 4 (a) simplify. 98 200\u2212 answer(a) [2] (b) rationalise the denominator. 3 511 \u2212 answer(b) [3] ", "5": "5 \u00a9 ucles 2013 0607/23/m/j/13 [turn over for examiner's use 5 the diagram shows the graph of y = f( x) for \u2013 4 y x y 3. 3 21 \u20131\u20132\u20133 \u20134\u2013 3\u2013 2\u2013 1 1 0 234y x (a) on the diagram below, sketch the graph of y = |f(x)|. 321 \u20131\u20132\u20133 \u20134\u2013 3\u2013 2\u2013 1 1 0 234y x [3] (b) on the diagram below, sketch the graph of y = f( x \u2013 1). 321 \u20131\u20132\u20133 \u20134\u2013 3\u2013 2\u2013 1 1 0 234y x [2] ", "6": "6 \u00a9 ucles 2013 0607/23/m/j/13 for examiner's use 6 make x the subject of the equation. xb xa=+3 answer x = [3] 7 od e c ba30\u00b070\u00b0 x\u00b0y\u00b0z\u00b0not to scale b, c, d and e lie on a circle, centre o. ce is a diameter, angle dac = 30\u00b0 and angle boe = 70\u00b0. find the values of x, y and z. answer x = y = z = [3] ", "7": "7 \u00a9 ucles 2013 0607/23/m/j/13 [turn over for examiner's use 8 the points a (1, 9) and b (7, 1) are shown on the diagram below. 02468 1 010 8 642y xa b (a) calculate the length ab. answer(a) [2] (b) (i) find the co-ordinates of the midpoint of the line ab. answer(b)(i) ( , ) [1] (ii) find the equation of the perpendicular bisector of the line ab. answer(b)(ii) [3] questions 9 and 10 are printed on the next page. ", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2013 0607/23/m/j/13 for examiner's use 9 wendy walks 9 km in 211 hours. she then runs 9 km in 45 minutes. find her average speed in km/h for the whole journey. answer km/h [3] 10 paulo goes to a supermarket. the probability that he buys orange juice is 0.65 . the probability that he does not buy milk is 0.30 . the probability that he buys milk but does not buy orange juice is 0.15 . (a) complete the table of probabilities. buys milk does not buy milk total buys orange juice 0.65 does not buy orange juice 0.15 total 0.30 1.00 [2] (b) find the probability that paulo buys either orange juice or milk but not both. answer(b) [2] " }, "0607_s13_qp_31.pdf": { "1": " this document consists of 16 printed pages. ib13 06_0607_31/4rp \u00a9 ucles 2013 [turn over *4127013103* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/31 paper 3 (core) may/june 2013 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96. ", "2": "2 \u00a9 ucles 2013 0607/31/m/j/13 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2013 0607/31/m/j/13 [turn over for examiner's use answer all the questions. 1 three friends go out for a meal. leon orders salmon fillet at $15.00 . jin orders vegetarian pasta at $10.60 . callum orders the chef\u2019s speciality at $17.00 . (a) calculate the total cost of the three meals. answer(a) $ [1] (b) the service charge is 10% of the total cost of the three meals. calculate the service charge. answer(b) $ [2] (c) find the total cost including the service charge. answer(c) $ [1] (d) the three friends agree to divide the total cost equally. calculate how much leon pays. answer(d) $ [1] (e) leon pays with a $20 note. find how much change he receives. answer(e) $ [1] ", "4": "4 \u00a9 ucles 2013 0607/31/m/j/13 for examiner's use 2 (a) q rpa\u00b0 42\u00b061\u00b0 b\u00b0c\u00b0not to scale in triangle pqr , angle qpr = 42\u00b0 and angle pqr = 61\u00b0. find the values of a, b and c. answer(a) a = b = c = [3] (b) the diagram shows a square. (i) draw all the lines of symmetry on the square. [2] (ii) write down the order of rotational symmetry of the square. answer(b)(ii) [1] 3 (a) s = qpr find the value of s when p = 13.2, q = 1.3 and r = 12.8 . give your answer correct to 3 decimal places. answer(a) [2] (b) write your answer to part (a) correct to 2 significant figures. answer(b) [1] (c) write your answer to part (b) in standard form. answer(c) [1] ", "5": "5 \u00a9 ucles 2013 0607/31/m/j/13 [turn over for examiner's use 4 23 girls each walked a distance of 2 kilometres. the number of minutes, correct to the nearest minute, that each girl took is recorded below. 18 19 26 36 18 25 31 43 13 36 18 23 20 20 34 32 41 33 19 17 21 25 40 (a) complete the ordered stem and leaf diagram to show this information. 1 2 3 4 key = [3] (b) for the times given in part (a) work out (i) the range, answer(b)(i) [1] (ii) the median, answer(b)(ii) [1] (iii) the lower quartile, answer(b)(iii) [1] (iv) the upper quartile. answer(b)(iv) [1] ", "6": "6 \u00a9 ucles 2013 0607/31/m/j/13 for examiner's use 5 ten children were each given a burger to eat. the table shows the number of hours since their last meal and the time, in seconds, taken to eat their burger. time since last meal, x hours 1.5 1.9 2.3 3.0 3.2 3.5 3.8 4.1 4.7 5.2 time to eat burger, y seconds 90 86 70 72 63 55 60 45 38 25 (a) complete the scatter diagram. the first six points have been plotted for you. 100 90 8070605040302010 0123 time since last meal (hours)456time to eat burger(seconds)y x [2] (b) describe the type of correlation. answer(b) [1] ", "7": "7 \u00a9 ucles 2013 0607/31/m/j/13 [turn over for examiner's use (c) (i) find the mean number of hours since the children\u2019s last meal. answer(c)(i) hours [1] (ii) find the mean number of seconds taken to eat a burger. answer(c)(ii) seconds [1] (iii) on the diagram, plot the mean point. [1] (d) on the diagram, draw the line of best fit by eye. [2] (e) jordi\u2019s last meal was 4.5 hours ago. use your line of best fit to estimate the time taken for jordi to eat a burger. answer(e) seconds [1] ", "8": "8 \u00a9 ucles 2013 0607/31/m/j/13 for examiner's use 6 c e a b d5 cm 3 cm 3 cmnot to scale 45\u00b0 the diagram shows a right-angled triangle, abc. bc is parallel to de, ae = de = 3 cm, bc = 5 cm and angle cba = 45\u00b0. (a) use the letters of this diagram to write down (i) an angle that is acute, answer(a)(i) [1] (ii) an angle that is obtuse, answer(a)(ii) [1] (iii) two lines that are perpendicular. answer(a)(iii) and [1] (b) write down the size of the following angles. (i) angle dea answer(b)(i) [1] (ii) angle dae answer(b)(ii) [1] ", "9": "9 \u00a9 ucles 2013 0607/31/m/j/13 [turn over for examiner's use 7 a zoo has three hippopotamuses (hippos), a male, a female and a baby. the hippos eat a total of 87.5 kg of food each day. (a) the hippos eat the food in proportion to their weight. the male weighs 1600 kg, the female weighs 1400 kg and the baby weighs 500 kg. (i) show that the male eats 40 kg of food each day. [2] (ii) calculate the amount of food that the female eats each day. answer(a)(ii) kg [2] (b) one kilogram of food costs 0.50 euros (\u20ac). calculate how much it costs to feed the three hippos for one year (365 days). answer(b) \u20ac [2] (c) the entrance fee to the zoo is 15 euros per person. what is the minimum number of people that need to visit the zoo to pay for feeding the three hippos for one year? answer(c) [2] ", "10": "10 \u00a9 ucles 2013 0607/31/m/j/13 for examiner's use 8 (a) piotr is making patterns with sticks. pattern 1 pattern 2 pattern 3 (i) in pattern 1 there are 3 sticks. write down the number of sticks that piotr uses to make pattern 2 and pattern 3. answer(a)(i) pattern 2 pattern 3 [2] (ii) find an expression, in terms of n, for the number of sticks used to make pattern n. answer(a)(ii) [1] (iii) find the number of sticks used to make pattern 10. answer(a)(iii) [1] (b) pawel is also making patterns with sticks. pattern 1 pattern 2 pattern 3 the number of triangles in each pattern forms the sequence 1, 3, 5, \u2026. (i) write down the next two terms in this sequence. answer(b)(i) , [2] (ii) find the number of triangles in pattern 10. answer(b)(ii) [1] (iii) find an expression, in terms of n, for the number of triangles used to make pattern n. answer(b)(iii) [2] ", "11": "11 \u00a9 ucles 2013 0607/31/m/j/13 [turn over for examiner's use 9 a polygon, q, has been drawn on the diagram. qy x8 7654321 \u20131\u20132\u20133\u20134\u20135\u20136\u20137\u201380 \u2013 1 12345678 \u20132 \u20133 \u20134 \u20135 \u20136 \u20137 \u20138 (a) draw the reflection of shape q in the y-axis. [2] (b) draw the enlargement of shape q with centre (0, 0), scale factor 2. [2] ", "12": "12 \u00a9 ucles 2013 0607/31/m/j/13 for examiner's use 10 u = {c, a, m, b, r, i, d, g, e} s = {m, a, g, i, c} t = {b, r, i, d, g, e} (a) write down the letters in the set s \u2229 t. answer(a) [1] (b) complete the venn diagram. u st [2] (c) a letter is chosen at random from u. find the probability that the letter is in the set (i) s, answer(c)(i) [1] (ii) s \u222a t, answer(c)(ii) [1] (iii) t \u2032. answer(c)(iii) [1] (d) a letter is chosen at random from the set s. find the probability that the letter is also in the set t. answer(d) [2] ", "13": "13 \u00a9 ucles 2013 0607/31/m/j/13 [turn over for examiner's use 11 faaiz competes in a three-part race. he runs 10 km, cycles 20 km and rollerblades 10 km. (a) faaiz takes 40 minutes to run the 10 km. find his average speed in kilometres per hour. answer(a) km/h [2] (b) he cycles at 25 km/h. find the time, in minutes, he takes to cycle 20 km. answer(b) minutes [2] (c) he takes 32 minutes to rollerblade 10 km. find his average speed, in km/h, for the whole race . answer(c) km/h [3] ", "14": "14 \u00a9 ucles 2013 0607/31/m/j/13 for examiner's use 12 (a) heyon is orienteering. she starts at point f and walks 500 m on a bearing of 050\u00b0 to the point g. from g she walks 1000 m on a bearing of 140\u00b0 to the point h. (i) draw a sketch to show heyon\u2019s walk. mark the points g and h. fnorth [2] (ii) on your sketch, draw a north line through the point g. on your sketch, write the values of the angles at g which show that angle fgh = 90\u00ba. [2] (b) sean walks from a to b to c. ac b200 m300 mnot to scale (i) calculate the distance ac. answer(b)(i) m [2] (ii) use trigonometry to calculate angle bac. answer(b)(ii) angle bac = [2] ", "15": "15 \u00a9 ucles 2013 0607/31/m/j/13 [turn over for examiner's use 13 (a) 0.2 mnot to scale the diagram shows a sphere of radius 0.2 m. (i) calculate the curved surface area of this sphere. answer(a)(i) m2 [2] (ii) the sphere is painted. one tin of paint covers an area of 50 m2. calculate the greatest number of these spheres that can be painted using one tin of paint. answer(a)(ii) [2] (b) 8 cm2 m not to scale the diagram shows a cylinder of radius 8 cm and length 2 m. (i) calculate the curved surface area of this cylinder. give your answer in square centimetres . answer(b)(i) cm2 [2] (ii) calculate the volume of this cylinder. give your answer in cubic centimetres. answer(b)(ii) cm3 [2] question 14 is printed on the next page. ", "16": "16 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2013 0607/31/m/j/13 for examiner's use 14 \u20134 43 \u20131y x0 (a) on the diagram, sketch the graph ) 1 (2 2+= xy for \u2013 4 y x y 4. [2] (b) write down the co-ordinates of the maximum point. answer(b) ( , ) [1] (c) write down the equation of the asymptote. answer(c) [1] (d) write down the range of ) 1 (2 2+= xy . answer(d) [3] " }, "0607_s13_qp_32.pdf": { "1": " this document consists of 16 printed pages. ib13 06_0607_32/4rp \u00a9 ucles 2013 [turn over *7157903421* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/32 paper 3 (core) may/june 2013 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96. ", "2": "2 \u00a9 ucles 2013 0607/32/m/j/13 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2013 0607/32/m/j/13 [turn over for examiner's use answer all the questions. 1 a jar is filled with 120 cream toffees, 90 liquorice toffees and 60 chocolate toffees. (a) how many more cream toffees are there than liquorice toffees? answer(a) [1] (b) find the total number of toffees in the jar. answer(b) [1] (c) one toffee is chosen at random. find the probability that it is (i) a liquorice toffee, answer(c)(i) [1] (ii) not a cream toffee, answer(c)(ii) [1] (iii) a mint toffee. answer(c)(iii) [1] (d) sid is 14 years old, ren is 15 years old and tarrik is 16 years old. they share all the toffees in the ratio of their ages. calculate the number of toffees that ren receives. answer(d) [2] ", "4": "4 \u00a9 ucles 2013 0607/32/m/j/13 for examiner's use 2 fifteen children were each given a different number of equations to solve. the number of equations solved and the time taken to solve them, to the nearest second, are shown in the table. number of equations 3 4 6 9 10 11 12 14 15 17 20 21 22 25 30 time (seconds) 8 11 12 20 21 34 28 40 41 45 60 58 61 70 82 51 0 1 5 number of equations20 25 3085 807570656055504540353025201510 5 0time (seconds) (a) complete the scatter diagram. the first eleven points have been plotted for you. [2] ", "5": "5 \u00a9 ucles 2013 0607/32/m/j/13 [turn over for examiner's use (b) describe the type of correlation. answer(b) [1] (c) (i) find the mean number of equations solved. answer(c)(i) [1] (ii) find the mean time taken. answer(c)(ii) s [1] (iii) on the diagram, plot the mean point. [1] (d) on the diagram, draw the line of best fit by eye. [2] (e) use your line of best fit to estimate the time taken to solve 8 equations. answer(e) s [1] ", "6": "6 \u00a9 ucles 2013 0607/32/m/j/13 for examiner's use 3 yana and jelle are arranging a party. the cost of one packet of crisps is $ c and the cost of one bottle of juice is $ j. yana spends a total of $10 on 12 packets of crisps and 5 bottles of juice. jelle spends a total of $11 on 6 packets of crisps and 10 bottles of juice. (a) write down two equations in c and j to show this information. answer(a) [2] (b) find the cost of one packet of crisps and the cost of one bottle of juice. answer(b) crisps $ juice $ [3] 4 a bean plant grows at a constant rate. the table shows its height above the ground each day. day 1 2 3 4 5 height above ground ( h cm) 1 3 5 (a) complete the table. [2] (b) find an expression, in terms of n, for the height of the bean plant after n days. answer(b) [2] (c) calculate the number of days it takes for the bean plant to reach a height of 83 cm. answer(c) days [2] ", "7": "7 \u00a9 ucles 2013 0607/32/m/j/13 [turn over for examiner's use 5 y x7 654321 \u20131\u20132\u20133\u20134\u201350 1 \u20131 \u20132 \u20133 \u20134 \u20135 \u20136 \u20137 2345 the diagram shows the graph of y = f( x). (a) write down the zeros of y = f(x ). answer(a) and [2] (b) on the same diagram, sketch the graphs of y = f(x ) \u2013 3, and y = f(x + 2). [2] ", "8": "8 \u00a9 ucles 2013 0607/32/m/j/13 for examiner's use 6 r tupq v s e\u00b0 f \u00b0d \u00b0 b \u00b0 c\u00b0a\u00b0 40\u00b0 51\u00b0not to scale pq, rs and tu are parallel lines and uv is a straight line. find the values of a, b, c, d, e and f. answer a = b = c = d = e = f = [6] ", "9": "9 \u00a9 ucles 2013 0607/32/m/j/13 [turn over for examiner's use 7 12 10 8642 \u20132\u20134 \u20134\u2013 2 0 2468 1 0 1 2y x (a) on the grid, plot the points a(1, 9) and b(7, \u20133). [2] (b) write down in component form. answer(b) \uf8f7\uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec\uf8ec \uf8ed\uf8eb [1] (c) find the co-ordinates of the midpoint of ab. answer(c) ( , ) [1] (d) calculate the length of ab. answer(d) [2] (e) calculate the gradient of ab. answer(e) [2] (f) find the equation of the line passing through the points a and b. give your answer in the form y = mx + c. answer(f) y = [2] ", "10": "10 \u00a9 ucles 2013 0607/32/m/j/13 for examiner's use 8 classicalcountryrap jazz popularx\u00b0 42\u00b078\u00b084\u00b054\u00b0not to scale rita asked 60 students what type of music they liked best. the pie chart shows her results. (a) find the value of x. answer(a) [1] (b) calculate the number of students who like rap best. answer(b) [2] (c) one of the students is chosen at random. find the probability that this student liked jazz best. answer(c) [1] ", "11": "11 \u00a9 ucles 2013 0607/32/m/j/13 [turn over for examiner's use 9 u = {a, b, c, d, e, f, g, h} a = {c, e, g} b = {f, g, h} (a) complete the venn diagram. u ab [2] (b) list the elements of the following sets. (i) a \u222a b answer(b)(i) [1] (ii) b\u2032 answer(b)(ii) [1] (iii) a \u2229 b answer(b)(iii) [1] (iv) a \u222a b\u2032 answer(b)(iv) [1] (c) write down n(a \u222a b). answer(c) [1] ", "12": "12 \u00a9 ucles 2013 0607/32/m/j/13 for examiner's use 10 b ac d500 cm50 cm 300 cmnot to scale the diagram shows the side view of a child\u2019s slide, abcd. (a) calculate cd. answer(a) cm [3] (b) use trigonometry to find the size of angle cda. answer(b) [2] (c) tayaab takes 3 seconds to slide from c to d. calculate his speed in metres per minute. answer(c) m/min [3] ", "13": "13 \u00a9 ucles 2013 0607/32/m/j/13 [turn over for examiner's use 11 40 \u201340\u20133 7y x0 (a) on the diagram, sketch the graph of y = x3 \u2013 5x2 \u2013 8x + 12. [2] (b) find the co-ordinates of the local maximum and the local minimum points. answer(b) ( , ) ( , ) [2] (c) on the same diagram sketch the graph of y = 2x + 3. [1] (d) find the x co-ordinates of the points where the two graphs intersect. answer(d) x = or x = or x = [3] ", "14": "14 \u00a9 ucles 2013 0607/32/m/j/13 for examiner's use 12 not to scale30 cm 30 cm a closed cylinder has a diameter of 30 cm and a height of 30 cm. (a) (i) find the total surface area of the cylinder. answer(a)(i) cm2 [3] (ii) find the volume of the cylinder. answer(a)(ii) cm3 [2] ", "15": "15 \u00a9 ucles 2013 0607/32/m/j/13 [turn over for examiner's use (b) the cylinder contains a sphere of radius 15 cm. not to scale 15 cm (i) find the volume of this sphere. answer(b)(i) cm3 [2] (ii) find the percentage of the volume of the cylinder that is not taken up by the sphere. answer(b)(ii) % [3] question 13 is printed on the next page. ", "16": "16 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2013 0607/32/m/j/13 for examiner's use 13 (a) expand and simplify. ( x \u2013 2)(2x + 3) answer(a) [2] (b) factorise completely. 10 x 2 \u2013 15x answer(b) [2] (c) simplify fully the following expressions. (i) yxy 282 answer(c)(i) [2] (ii) t ts 103 59\u00f7 answer(c)(ii) [2] (iii) 32 43 p p\u2212 answer(c)(iii) [2] (iv) (2y 2)3 answer(c)(iv) [2] " }, "0607_s13_qp_33.pdf": { "1": " this document consists of 16 printed pages. ib13 06_0607_33/fp \u00a9 ucles 2013 [turn over *5902643799* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/33 paper 3 (core) may/june 2013 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96. ", "2": "2 \u00a9 ucles 2013 0607/33/m/j/13 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2013 0607/33/m/j/13 [turn over for examiner's use answer all the questions. 1 three friends go out for a meal. leon orders salmon fillet at $15.00 . jin orders vegetarian pasta at $10.60 . callum orders the chef\u2019s speciality at $17.00 . (a) calculate the total cost of the three meals. answer(a) $ [1] (b) the service charge is 10% of the total cost of the three meals. calculate the service charge. answer(b) $ [2] (c) find the total cost including the service charge. answer(c) $ [1] (d) the three friends agree to divide the total cost equally. calculate how much leon pays. answer(d) $ [1] (e) leon pays with a $20 note. find how much change he receives. answer(e) $ [1] ", "4": "4 \u00a9 ucles 2013 0607/33/m/j/13 for examiner's use 2 (a) q rpa\u00b0 42\u00b061\u00b0 b\u00b0c\u00b0not to scale in triangle pqr , angle qpr = 42\u00b0 and angle pqr = 61\u00b0. find the values of a, b and c. answer(a) a = b = c = [3] (b) the diagram shows a square. (i) draw all the lines of symmetry on the square. [2] (ii) write down the order of rotational symmetry of the square. answer(b)(ii) [1] 3 (a) s = qpr find the value of s when p = 13.2, q = 1.3 and r = 12.8 . give your answer correct to 3 decimal places. answer(a) [2] (b) write your answer to part (a) correct to 2 significant figures. answer(b) [1] (c) write your answer to part (b) in standard form. answer(c) [1] ", "5": "5 \u00a9 ucles 2013 0607/33/m/j/13 [turn over for examiner's use 4 23 girls each walked a distance of 2 kilometres. the number of minutes, correct to the nearest minute, that each girl took is recorded below. 18 19 26 36 18 25 31 43 13 36 18 23 20 20 34 32 41 33 19 17 21 25 40 (a) complete the ordered stem and leaf diagram to show this information. 1 2 3 4 key = [3] (b) for the times given in part (a) work out (i) the range, answer(b)(i) [1] (ii) the median, answer(b)(ii) [1] (iii) the lower quartile, answer(b)(iii) [1] (iv) the upper quartile. answer(b)(iv) [1] ", "6": "6 \u00a9 ucles 2013 0607/33/m/j/13 for examiner's use 5 ten children were each given a burger to eat. the table shows the number of hours since their last meal and the time, in seconds, taken to eat their burger. time since last meal, x hours 1.5 1.9 2.3 3.0 3.2 3.5 3.8 4.1 4.7 5.2 time to eat burger, y seconds 90 86 70 72 63 55 60 45 38 25 (a) complete the scatter diagram. the first six points have been plotted for you. 100 90 8070605040302010 0123 time since last meal (hours)456time to eat burger(seconds)y x [2] (b) describe the type of correlation. answer(b) [1] ", "7": "7 \u00a9 ucles 2013 0607/33/m/j/13 [turn over for examiner's use (c) (i) find the mean number of hours since the children\u2019s last meal. answer(c)(i) hours [1] (ii) find the mean number of seconds taken to eat a burger. answer(c)(ii) seconds [1] (iii) on the diagram, plot the mean point. [1] (d) on the diagram, draw the line of best fit by eye. [2] (e) jordi\u2019s last meal was 4.5 hours ago. use your line of best fit to estimate the time taken for jordi to eat a burger. answer(e) seconds [1] ", "8": "8 \u00a9 ucles 2013 0607/33/m/j/13 for examiner's use 6 c e a b d5 cm 3 cm 3 cmnot to scale 45\u00b0 the diagram shows a right-angled triangle, abc. bc is parallel to de, ae = de = 3 cm, bc = 5 cm and angle cba = 45\u00b0. (a) use the letters of this diagram to write down (i) an angle that is acute, answer(a)(i) [1] (ii) an angle that is obtuse, answer(a)(ii) [1] (iii) two lines that are perpendicular. answer(a)(iii) and [1] (b) write down the size of the following angles. (i) angle dea answer(b)(i) [1] (ii) angle dae answer(b)(ii) [1] ", "9": "9 \u00a9 ucles 2013 0607/33/m/j/13 [turn over for examiner's use 7 a zoo has three hippopotamuses (hippos), a male, a female and a baby. the hippos eat a total of 87.5 kg of food each day. (a) the hippos eat the food in proportion to their weight. the male weighs 1600 kg, the female weighs 1400 kg and the baby weighs 500 kg. (i) show that the male eats 40 kg of food each day. [2] (ii) calculate the amount of food that the female eats each day. answer(a)(ii) kg [2] (b) one kilogram of food costs 0.50 euros (\u20ac). calculate how much it costs to feed the three hippos for one year (365 days). answer(b) \u20ac [2] (c) the entrance fee to the zoo is 15 euros per person. what is the minimum number of people that need to visit the zoo to pay for feeding the three hippos for one year? answer(c) [2] ", "10": "10 \u00a9 ucles 2013 0607/33/m/j/13 for examiner's use 8 (a) piotr is making patterns with sticks. pattern 1 pattern 2 pattern 3 (i) in pattern 1 there are 3 sticks. write down the number of sticks that piotr uses to make pattern 2 and pattern 3. answer(a)(i) pattern 2 pattern 3 [2] (ii) find an expression, in terms of n, for the number of sticks used to make pattern n. answer(a)(ii) [1] (iii) find the number of sticks used to make pattern 10. answer(a)(iii) [1] (b) pawel is also making patterns with sticks. pattern 1 pattern 2 pattern 3 the number of triangles in each pattern forms the sequence 1, 3, 5, \u2026. (i) write down the next two terms in this sequence. answer(b)(i) , [2] (ii) find the number of triangles in pattern 10. answer(b)(ii) [1] (iii) find an expression, in terms of n, for the number of triangles used to make pattern n. answer(b)(iii) [2] ", "11": "11 \u00a9 ucles 2013 0607/33/m/j/13 [turn over for examiner's use 9 a polygon, q, has been drawn on the diagram. qy x8 7654321 \u20131\u20132\u20133\u20134\u20135\u20136\u20137\u201380 \u2013 1 12345678 \u20132 \u20133 \u20134 \u20135 \u20136 \u20137 \u20138 (a) draw the reflection of shape q in the y-axis. [2] (b) draw the enlargement of shape q with centre (0, 0), scale factor 2. [2] ", "12": "12 \u00a9 ucles 2013 0607/33/m/j/13 for examiner's use 10 u = {c, a, m, b, r, i, d, g, e} s = {m, a, g, i, c} t = {b, r, i, d, g, e} (a) write down the letters in the set s \u2229 t. answer(a) [1] (b) complete the venn diagram. u st [2] (c) a letter is chosen at random from u. find the probability that the letter is in the set (i) s, answer(c)(i) [1] (ii) s \u222a t, answer(c)(ii) [1] (iii) t \u2032. answer(c)(iii) [1] (d) a letter is chosen at random from the set s. find the probability that the letter is also in the set t. answer(d) [2] ", "13": "13 \u00a9 ucles 2013 0607/33/m/j/13 [turn over for examiner's use 11 faaiz competes in a three-part race. he runs 10 km, cycles 20 km and rollerblades 10 km. (a) faaiz takes 40 minutes to run the 10 km. find his average speed in kilometres per hour. answer(a) km/h [2] (b) he cycles at 25 km/h. find the time, in minutes, he takes to cycle 20 km. answer(b) minutes [2] (c) he takes 32 minutes to rollerblade 10 km. find his average speed, in km/h, for the whole race . answer(c) km/h [3] ", "14": "14 \u00a9 ucles 2013 0607/33/m/j/13 for examiner's use 12 (a) heyon is orienteering. she starts at point f and walks 500 m on a bearing of 050\u00b0 to the point g. from g she walks 1000 m on a bearing of 140\u00b0 to the point h. (i) draw a sketch to show heyon\u2019s walk. mark the points g and h. fnorth [2] (ii) on your sketch, draw a north line through the point g. on your sketch, write the values of the angles at g which show that angle fgh = 90\u00ba. [2] (b) sean walks from a to b to c. ac b200 m300 mnot to scale (i) calculate the distance ac. answer(b)(i) m [2] (ii) use trigonometry to calculate angle bac. answer(b)(ii) angle bac = [2] ", "15": "15 \u00a9 ucles 2013 0607/33/m/j/13 [turn over for examiner's use 13 (a) 0.2 mnot to scale the diagram shows a sphere of radius 0.2 m. (i) calculate the curved surface area of this sphere. answer(a)(i) m2 [2] (ii) the sphere is painted. one tin of paint covers an area of 50 m2. calculate the greatest number of these spheres that can be painted using one tin of paint. answer(a)(ii) [2] (b) 8 cm2 m not to scale the diagram shows a cylinder of radius 8 cm and length 2 m. (i) calculate the curved surface area of this cylinder. give your answer in square centimetres . answer(b)(i) cm2 [2] (ii) calculate the volume of this cylinder. give your answer in cubic centimetres. answer(b)(ii) cm3 [2] question 14 is printed on the next page. ", "16": "16 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2013 0607/33/m/j/13 for examiner's use 14 \u20134 43 \u20131y x0 (a) on the diagram, sketch the graph ) 1 (2 2+= xy for \u2013 4 y x y 4. [2] (b) write down the co-ordinates of the maximum point. answer(b) ( , ) [1] (c) write down the equation of the asymptote. answer(c) [1] (d) write down the range of ) 1 (2 2+= xy . answer(d) [3] " }, "0607_s13_qp_41.pdf": { "1": " this document consists of 16 printed pages. ib13 06_0607_41/4rp \u00a9 ucles 2013 [turn over *1170642332* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/41 paper 4 (extended) may/june 2013 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120. ", "2": "2 \u00a9 ucles 2013 0607/41/m/j/13 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2013 0607/41/m/j/13 [turn over for examiner's use answer all the questions. 1 each year the value of a car decreases by 12%. on 1st april 2011 sami bought a car for $15 840. (a) work out (i) the value of the car on 1st april 2010, answer(a)(i) $ [3] (ii) the value of the car on 1st april 2014, answer(a)(ii) $ [3] (iii) the year in which the value of the car will first be below $5000. answer(a)(iii) [2] (b) each year sami drives 20 000 km in his car. his yearly motoring costs are \u007f fuel at $0.68 per litre, \u007f service and other repairs $950, \u007f tax and insurance $1020. the car travels 15 km on each litre of fuel. find the total yearly motoring costs as a percentage of the value of the car in 2011. answer (b) % [4] ", "4": "4 \u00a9 ucles 2013 0607/41/m/j/13 for examiner's use 2 a by x3 21 \u20131\u20132\u20133\u20134\u20135\u201360 \u2013 1 1234567 \u20132 \u20133 (a) describe fully the single transformation that maps triangle a onto triangle b. answer (a) [2] (b) (i) rotate triangle a through 180\u00b0 about the point (3, 0). label the image c. [2] (ii) enlarge triangle c with scale factor 2 and centre (6, 0). label the image d. [2] (iii) describe fully the single transformation that maps triangle a onto triangle d. answer(b)(iii) [3] ", "5": "5 \u00a9 ucles 2013 0607/41/m/j/13 [turn over for examiner's use 3 10 \u201310\u20132 40xy (a) on the diagram, sketch the graph of y = x3 \u2013 3x2 + 2 for \u20132 y x y 4. [2] (b) solve the equation x3 \u2013 3x2 + 2 = 0. answer (b) x = or x = or x = [2] (c) (i) find the co-ordinates of the local maximum and local minimum points. answer (c)(i) ( , ) ( , ) [2] (ii) the equation x 3 \u2013 3x2 + 2 = k has 3 solutions. write down the range of values for k. answer(c)(ii) [2] (d) by drawing a suitable line on your diagram show that x 3 \u2013 3x2 + 2 = 6 \u2013 3 x has only one solution. [2] ", "6": "6 \u00a9 ucles 2013 0607/41/m/j/13 for examiner's use 4 r ac bpqnot to scale the diagram shows a vertical radio mast pqr supported by 6 straight wires. a, b, c and p are on level horizontal ground. ra = rb = rc and qa = qb = qc. pq = 30 m, qr = 20 m and angle aqp = angle bqp = angle cqp = 65\u00b0. r pcq 65\u00b0 30 m20 mnot to scale (a) show that qc = 70.99 m, correct to 2 decimal places. [2] ", "7": "7 \u00a9 ucles 2013 0607/41/m/j/13 [turn over for examiner's use (b) using the cosine rule, calculate the length rc. answer(b) m [3] (c) find the total length of the 6 wires. answer(c) m [1] (d) calculate the length pc. answer(d) m [2] (e) this is a view from above showing a, b, p and c on horizontal ground. 120\u00b0pnot to scale b ca calculate the area of triangle bpc. answer(e) m2 [2] ", "8": "8 \u00a9 ucles 2013 0607/41/m/j/13 for examiner's use 5 16 15141312 11 10 987654321 123456789 1 0 1 1 1 2 1 3 1 40y x (a) on the grid, find the region satisfied by the following inequalities. label the region r. x y 4 x + y y 12 5x + 2y [ 30 [5] (b) (h, k) is a point in the region r and h and k are integers. (i) find the number of possible points ( h, k). answer(b)(i) [1] (ii) find the minimum value of h + k . answer(b)(ii) [1] ", "9": "9 \u00a9 ucles 2013 0607/41/m/j/13 [turn over for examiner's use 6 2 cm 2 cm2.5 cm5 cm 6 cmnot to scale the diagram shows a child\u2019s wooden brick. the brick is a cuboid with a semicircular hole cut in the bottom. (a) find the volume of the brick. answer(a) cm3 [3] (b) each cubic centimetre of wood has a mass of 0.8 g. find the mass of the brick. answer(b) g [1] (c) find the total surface area of the brick. answer(c) cm2 [5] ", "10": "10 \u00a9 ucles 2013 0607/41/m/j/13 for examiner's use 7 (a) the speeds, v km/h, of 140 cars were measured on road a. the cumulative frequency graph shows the speeds of these cars. 140 130120 110 100 908070605040302010 10 20 30 40 50 speed (km/h)cumulative frequency 60 70 80 90 1000v (i) find the median speed. answer(a)(i) km/h [1] (ii) find the inter-quartile range of the speeds. answer(a)(ii) km/h [2] ", "11": "11 \u00a9 ucles 2013 0607/41/m/j/13 [turn over for examiner's use (b) the speeds of another 140 cars were measured on road b. the results are shown in this table. speed (v km/h) 20 < v y 30 30 < v y 40 40 < v y 45 45 < v y 50 50 < v y 60 60 < v y 80 80 < v y 100 frequency 6 12 15 20 32 30 25 (i) complete this table of cumulative frequencies for road b. speed (v km/h) v y 20 v y 30 v y 40 v y 45 v y 50 v y 60 v y 80 v y 100 cumulative frequency 0 6 18 140 [2] (ii) on the grid in part (a) , draw the cumulative frequency curve for road b. [3] (iii) make a comparison between the distributions of speeds on roads a and b. answer(b)(iii) [2] (iv) calculate an estimate for the mean speed of the 140 cars on road b. answer(b)(iv) km/h [2] (v) on the grid below, complete the histogram to show the speeds of the cars on road b. 4 321 10 20 30 40 50 speed (km/h)frequency density 60 70 80 90 1000v [4] ", "12": "12 \u00a9 ucles 2013 0607/41/m/j/13 for examiner's use 8 the table shows the number of left-handed and right-handed girls and boys in a class. left-handed right-handed total girls 4 14 18 boys 3 11 14 total 7 25 32 (a) two students are chosen at random from the whole class. find the probability that they are both left-handed. answer(a) [2] (b) two of the girls are chosen at random. find the probability that exactly one of these girls is left-handed. answer(b) [3] (c) two of the right-handed students are chosen at random. find the probability that at least one is a girl. answer(c) [3] ", "13": "13 \u00a9 ucles 2013 0607/41/m/j/13 [turn over for examiner's use 9 the resistance, r ohms, of a standard length of wire varies inversely as the square of its diameter, d mm. (a) the resistance of a standard length of wire of diameter 0.5 mm is 0.8 ohms. (i) find a formula for r in terms of d. answer(a)(i) r = [3] (ii) find the resistance of a standard length of the same type of wire with diameter 2 mm. answer(a)(ii) ohms [1] (iii) the resistance of a standard length of the same type of wire is 4 ohms. find the diameter of this wire. answer(a)(iii) mm [2] (b) for a different type of wire the resistance of a standard length is 2 ohms. find the resistance of a standard length of this wire when the diameter is doubled. answer(b) ohms [2] ", "14": "14 \u00a9 ucles 2013 0607/41/m/j/13 for examiner's use 10 10 \u201310\u20136 30xy (a) on the diagram, sketch the graph of y = f(x), where f ( x) = ) 3 () 1 ( +\u2212 xx between x = \u20136 and x = 3. [3] (b) find the co-ordinates of the point where the graph crosses the x-axis. answer (b) ( , ) [1] (c) find the equations of the asymptotes of y = f(x). answer(c) and [2] (d) find the range of f( x) for x [ 0. answer(d) [2] (e) find the solutions to the equation ) 3 () 1 ( +\u2212 xx = \u20135 \u2013 2x . answer (e) x = or x = [3] (f) on the diagram, sketch the graph of y = f(x \u2013 3). [2] ", "15": "15 \u00a9 ucles 2013 0607/41/m/j/13 [turn over for examiner's use 11 ab c d3 cm 5 cm6 cm onot to scale the diagram shows a trapezium abcd with diagonals intersecting at o. ab is parallel to dc. (a) explain why triangle aob is similar to triangle cod. answer(a) [2] (b) calculate the length of cd. answer(b) cm [2] (c) find the value of these fractions. (i) area of triangle abo area of triangle cbo answer(c)(i) [1] (ii) area of triangle abo area of triangle cdo answer(c)(ii) [1] (iii) area of triangle abo area of trapezium abcd answer(c)(iii) [1] question 12 is printed on the next page. ", "16": "16 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publis her (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2013 0607/41/m/j/13 for examiner's use 12 an aircraft travels 5500 km from dubai to london. the average speed is x km/h. (a) write down an expression, in terms of x, for the time taken for this journey. answer(a) hours [1] (b) the return journey from london to dubai is \u007f 60 km/h faster \u007f half-an-hour shorter than the journey from dubai to london. write down an equation in x and show that it simplifies to x 2 + 60x \u2013 660 000 = 0 . [4] (c) solve the equation x 2 + 60x \u2013 660 000 = 0 . give your answers correct to the nearest whole number. answer (c) x = or x = [3] (d) the time that the aircraft leaves dubai is 09 40 local time. the time in london is 4 hours behind the time in dubai. use your answer to part (c) to find the arrival time in london. answer(d) [3] " }, "0607_s13_qp_42.pdf": { "1": " this document consists of 19 printed pages and 1 blank page. ib13 06_0607_42/2rp \u00a9 ucles 2013 [turn over *1604463664* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/42 paper 4 (extended) may/june 2013 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120. ", "2": "2 \u00a9 ucles 2013 0607/42/m/j/13 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2013 0607/42/m/j/13 [turn over for examiner's use answer all the questions. 1 (a) (i) kim\u2019s wage is $720 each month. she spends $196 each month on food. calculate $196 as a percentage of $720. answer(a)(i) % [1] (ii) she pays 25% of the $720 in taxes. find the ratio money spent on food : money paid in taxes. give your answer in its simplest form. answer(a)(ii) : [2] (iii) the $720 is an increase of 44% on kim\u2019s previous wage. calculate her previous wage. answer(a)(iii) $ [3] (iv) next year the $720 will increase by 4%. calculate next year\u2019s monthly wage. answer(a)(iv) $ [2] ( b) jay\u2019s monthly wage is $650. each year jay\u2019s monthly wage increases by 5%. calculate the number of years it will take for jay\u2019s monthly wage to exceed $1000. answer(b) [3] ", "4": "4 \u00a9 ucles 2013 0607/42/m/j/13 for examiner's use 2 (a) 2x 3x 2x + 1x + 3not to scale the areas of the rectangles are equal. find the value of x. show all your working. answer(a) x = [4] (b) \u03b8 y + 12ynot to scale find the value of y when tan \u03b8 = 31. show all your working. answer(b) y = [3] ", "5": "5 \u00a9 ucles 2013 0607/42/m/j/13 [turn over for examiner's use (c) jo walks 10 km at w kilometres per hour. sam cycles 10 km at (w + 9) kilometres per hour. the difference between the times taken by jo and sam is 212 hours. (i) show that w2 + 9w \u2013 36 = 0. [4] (ii) find the time, in hours and minutes, taken by jo to walk the 10 km. answer(c)(ii) h min [4] ", "6": "6 \u00a9 ucles 2013 0607/42/m/j/13 for examiner's use 3 y x5 4321 \u20131\u20132\u20133\u20134\u201350 \u20131 \u20132 \u20133 \u20134 \u201355 4 3 2 1 l (a) find the equation of the line l. answer(a) [2] (b) (i) on the grid, draw the line y = 2x + 4. [2] (ii) on the grid, shade the region where y [ 0 and y [ 2x + 4. [2] (c) p is the point (1, \u2013 4) and q is the point (3, 2). find the equation of the line passing through p and q. answer(c) [3] ", "7": "7 \u00a9 ucles 2013 0607/42/m/j/13 [turn over for examiner's use 4 the masses of 100 apples are measured. the results are shown in the table. mass (m grams) 20 < m y 100 100 < m y 150 150 < m y 240 frequency 28 45 27 (a) calculate an estimate of the mean mass. answer(a) g [2] (b) use the information in the table to complete the histogram. 1.0 0.90.80.70.60.50.40.30.20.1 040 80 120 mass (grams)160 200 240 20 60 100 140 180 220frequency density m [3] ", "8": "8 \u00a9 ucles 2013 0607/42/m/j/13 for examiner's use 5 b ph k998 km1060 km 1185 km988 km30\u00b0not to scale the diagram shows some straight line distances between bangkok ( b), hanoi ( h), phnom penh ( p) and kuala lumpur ( k). angle bhp = 30\u00b0. (a) calculate bp and show that it rounds to 535 km, correct to the nearest kilometre. [3] ", "9": "9 \u00a9 ucles 2013 0607/42/m/j/13 [turn over for examiner's use (b) calculate angle bkp. answer(b) [3] (c) the bearing of p from k is 020\u00b0. find the bearing of b from k. answer(c) [1] ", "10": "10 \u00a9 ucles 2013 0607/42/m/j/13 for examiner's use 6 rc a b qp 12 cm 20 cm6 cmnot to scale the diagram shows a triangular prism of length 20 cm. the cross-section of the prism is triangle abc with angle bac = 90\u00b0, ac = 6 cm and ab = 12 cm. (a) calculate the volume of the prism. answer(a) cm3 [2] ", "11": "11 \u00a9 ucles 2013 0607/42/m/j/13 [turn over for examiner's use (b) (i) calculate the total surface area of the prism. answer(b)(i) cm2 [4] (ii) the surface of the prism is painted at a cost of $0.005 per square centimetre. calculate the cost of painting the surface of the prism. answer(b)(ii) $ [1] (c) calculate the angle between the diagonal line cq and the base abqp . answer(c) [3] ", "12": "12 \u00a9 ucles 2013 0607/42/m/j/13 for examiner's use 7 a flight from london, england to auckland, new zealand departs at 14 00 on february 7th. the journey takes 2127 hours and the distance is 18 400 km. the time in new zealand is 13 hours ahead of the time in england. (a) find the time and the date that the flight arrives in auckland. answer(a) time date [3] (b) calculate the average speed of the journey. answer(b) km/h [1] (c) the cost of a ticket for the flight is 3600 pounds (\u00a3). \u00a31 = 2.09 new zealand dollars (nzd). (i) calculate the cost of the ticket in nzd. answer(c)(i) nzd [1] (ii) calculate the cost of the journey, in nzd per kilometre. give your answer correct to 2 decimal places. answer(c)(ii) nzd/km [2] ", "13": "13 \u00a9 ucles 2013 0607/42/m/j/13 [turn over for examiner's use 8 (a) solve the equation 22 3+ =xx. answer(a) x = or x = [4] (b) solve the inequality x2 [ x3 + 2 . answer(b) [3] ", "14": "14 \u00a9 ucles 2013 0607/42/m/j/13 for examiner's use 9 70\u00b08 cm not to scaleb ao ab is a chord of the circle centre o. calculate (a) the length of the chord ab, answer(a) cm [3] (b) the length of the arc ab, answer(b) cm [2] (c) the area of the shaded region. answer(c) cm2 [4] ", "15": "15 \u00a9 ucles 2013 0607/42/m/j/13 [turn over for examiner's use 10 2 \u201320180\u00b0 360\u00b0xy f ( x) = cos x g(x) = 2sin \uf8f7\uf8f8\uf8f6\uf8ec\uf8ed\uf8eb 2x (a) on the diagram, sketch the following graphs. (i) y = f(x) [2] (ii) y = g(x) [2] (b) write down the equation of the line of symmetry of the graphs. answer(b) [1] (c) write down the co-ordinates of the local minimum point on the graph of y = f(x ) for 0\u00b0 y x y 360\u00b0. answer(c) ( , ) [2] (d) write down the period and amplitude of g( x). answer(d) period = amplitude = [2] (e) write down the range of g( x) for the following domains. (i) 0\u00b0 y x y 360\u00b0 answer(e)(i) [1] (ii) o answer(e)(ii) [1] (f) solve the equation f( x) = g( x) for 0\u00b0 y x y 360\u00b0. answer(f) x = or x = [2] (g) shade the regions on the diagram where y y f( x) and y [ g( x). [1] ", "16": "16 \u00a9 ucles 2013 0607/42/m/j/13 for examiner's use 11 2 5111 10 the diagram shows a disc, with six equal sectors, and an arrow. when the disc is spun, each sector is equally likely to stop next to the arrow. (a) the disc is spun. write down the probability that the sector next to the arrow is labelled with (i) 1 or 2, answer(a)(i) [1] (ii) an even number, answer(a)(ii) [1] (iii) a number which is a factor of 10. answer(a)(iii) [1] (b) the disc is spun twice. (i) complete the tree diagram by writing the missing probabilities on each branch. 10first number second number not 1010 not 10 10 not 10 1 6 [2] ", "17": "17 \u00a9 ucles 2013 0607/42/m/j/13 [turn over for examiner's use (ii) find the probability that the arrow is next to the number 10 twice. answer(b)(ii) [2] (iii) find the probability that the arrow is next to the number 10 at least once. answer(b)(iii) [2] (c) the disc is spun n times until it stops with the number 10 next to the arrow. find n when the probability that this happens is 7776625. answer(c) n = [2] ", "18": "18 \u00a9 ucles 2013 0607/42/m/j/13 for examiner's use 12 month jan feb mar apr may jun jul aug sep oct nov dec temperature (t \u02dac) 13 13 15 16 19 23 25 26 24 20 18 13 rainfall ( r mm) 59 49 62 46 25 6 1 3 28 62 63 66 the table shows the average monthly temperature, t, and rainfall, r, in malaga, spain. (a) find the mean, median, upper quartile and range of the average monthly temperatures. answer(a) mean = \u00b0c median = \u00b0c upper quartile = \u00b0c range = \u00b0c [4] (b) (i) find the equation of the line of regression for this data, giving r in terms of t. answer(b)(i) r = [2] (ii) describe the type of correlation between r and t. answer(b)(ii) [1] (iii) calculate an estimate of the rainfall when the temperature is 22\u00b0c. answer(b)(iii) [1] ", "19": "19 \u00a9 ucles 2013 0607/42/m/j/13 for examiner's use 13 p o qyp qxnot to scale the diagram shows a triangle opq . the point x is on pq so that px : xq = 1 : 2. = p and = q. (a) find in terms of p and q. give your answer in its simplest form. answer(a) [2] (b) oqy is a straight line and oy = 2oq. find in terms of p and q. give your answer in its simplest form. answer(b) [3] (c) p = \uf8f7 \uf8f8\uf8f6\uf8ec \uf8ed\uf8eb k3 and |p| = 5. find the two possible values of k. answer(c) k = or k = [2] ", "20": "20 permission to reproduce items where third -party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2013 0607/42/m/j/13 blank page " }, "0607_s13_qp_43.pdf": { "1": " this document consists of 20 printed pages. ib13 06_0607_43/6rp \u00a9 ucles 2013 [turn over *4434452004* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/43 paper 4 (extended) may/june 2013 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120. ", "2": "2 \u00a9 ucles 2013 0607/43/m/j/13 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2013 0607/43/m/j/13 [turn over for examiner's use answer all the questions. 1 y varies inversely as the square root of x. y = 16 when x = 4. (a) find the value of y when x = 16. answer(a) y = [3] (b) find the value of x when y = 64. answer(b) x = [2] (c) find x in terms of y. answer(c) x = [3] ", "4": "4 \u00a9 ucles 2013 0607/43/m/j/13 for examiner's use 2 (a) solve the equation. 2log 6 \u2013 log 9 + log x = 3 answer(a) x = [3] (b) solve the simultaneous equations. 3x \u2013 4y = 10 5x \u2013 3y = 2 answer(b) x = y = [4] ", "5": "5 \u00a9 ucles 2013 0607/43/m/j/13 [turn over for examiner's use 3 for each venn diagram, describe the shaded region using set notation. (a) u ab c answer(a) [1] (b) u ab c answer(b) [1] (c) u ab c answer(c) [1] (d) u ab c answer(d) [2] ", "6": "6 \u00a9 ucles 2013 0607/43/m/j/13 for examiner's use 4 (a) 7 cm 4.5 cmcd e b ax8 cm not to scale in the diagram, be is parallel to cd. the perpendicular height between the lines be and cd is 8 cm. the perpendicular height from the point a to the line be is x. show that x = 14.4 cm. [2] ", "7": "7 \u00a9 ucles 2013 0607/43/m/j/13 [turn over for examiner's use (b) 7 cm 4.5 cm8 cmnot to scale the diagram shows a plastic cup. the diameter of the circular base is 4.5 cm and the diameter of the circular top is 7 cm. the height of the cup is 8 cm. using part (a) , calculate the volume of the cup. give your answer correct to the nearest cubic centimetre. answer(b) cm3 [3] ", "8": "8 \u00a9 ucles 2013 0607/43/m/j/13 for examiner's use 5 (a) solve the equation 10 x2 = 5 \u2013 x . give your answers correct to 2 decimal places. answer(a) x = or x = [4] (b) solve the inequality 10 x2 > 5 \u2013 x . answer(b) [2] 6 the transformation p is a rotation of 180\u00b0 about the origin. the transformation q is a reflection in the line y = x. (a) find the image of the point (6, 2) under the transformation p. answer(a) ( , ) [1] (b) find the image of the point (6, 2) under the transformation q. answer(b) ( , ) [1] (c) describe fully the single transformation equivalent to p followed by q. answer (c) [2] ", "9": "9 \u00a9 ucles 2013 0607/43/m/j/13 [turn over for examiner's use 7 4 4 \u20134\u201340y x (a) on the diagram, sketch the graph of y = f( x), where f ( x) = ) 4 () 1 ( 2\u2212\u2212 xx between x = \u2013 4 and x = 4 . [4] (b) write down the equations of the three asymptotes. answer(b) [3] (c) the line y = x intersects the curve ) 4 () 1 ( 2\u2212\u2212= xxy three times. find the values of the x co-ordinates of the points of intersection. answer(c) x = x = x = [3] ", "10": "10 \u00a9 ucles 2013 0607/43/m/j/13 for examiner's use 8 b a c8 cm7 cm 6 cmnot to scale the diagram shows a triangle abc. (a) use the cosine rule to find angle abc. answer(a) [3] (b) find the area of triangle abc, giving your answer correct to 2 decimal places. answer(b) cm2 [3] (c) find the length of the perpendicular line from c to the line ab. answer(c) cm [2] ", "11": "11 \u00a9 ucles 2013 0607/43/m/j/13 [turn over for examiner's use 9 the british lions squad for the 2009 tour of south africa originally contained 40 players from england, ireland, scotland and wales. the playing positions, either forward or back, of these players is shown in the table. england ireland scotland wales forward 6 5 2 6 back 3 9 2 7 (a) a player is selected at random from the squad to visit a local hospital. calculate the probability that the player chosen is (i) a forward from ireland, answer(a)(i) [1] (ii) not from wales. answer(a)(ii) [1] (b) a player is chosen at random from the backs to give a tv interview. calculate the probability that he is from england. answer(b) [2] (c) three forwards are chosen at random to take part in a \u2018tug-o-war\u2019 competition. calculate the probability they are all from wales. answer(c) [3] ", "12": "12 \u00a9 ucles 2013 0607/43/m/j/13 for examiner's use 10 (a) 1.6 cm 2.4 cmnot to scale the diagram shows a brass washer. the washer is made by removing a circular disc of diameter 1.6 cm from a circular disc of diameter 2.4 cm. (i) find the area of the top surface of the washer in square centimetres. answer(a)(i) cm2 [2] (ii) the washer is 2 mm thick. calculate the volume of the washer in cubic centimetres . answer(a)(ii) cm3 [2] ", "13": "13 \u00a9 ucles 2013 0607/43/m/j/13 [turn over for examiner's use (b) not to scale the diagram shows a globe made from brass. globes are hollow spheres. the outside diameter of this globe is 32 cm and the inside diameter is 30 cm. (i) find the volume of brass used to make this globe in cubic centimetres. answer(b)(i) cm3 [2] (ii) a number of globes are to be made by melting 1 000 000 of the brass washers in part (a) . find the maximum number of globes that can be made. answer(b)(ii) [3] ", "14": "14 \u00a9 ucles 2013 0607/43/m/j/13 for examiner's use 11 carlos delivers computers from a factory to a town that is 720 km away. when he drives at an average speed of x km/h the journey takes one hour longer than if he drives at (x +10) km/h. (a) write down an equation in x and show that it simplifies to x2 + 10x \u2013 7200 = 0 . [4] (b) (i) factorise x 2 + 10x \u2013 7200. answer(b)(i) [2] (ii) solve the equation x 2 + 10x \u2013 7200 = 0 . answer(b)(ii) x = or x = [1] (iii) carlos drives the 720 km at x km/h. work out the time of his journey. answer(b)(iii) hours [1] ", "15": "15 \u00a9 ucles 2013 0607/43/m/j/13 [turn over for examiner's use 12 \u20134 \u2013446 0y x (a) (i) on the diagram, sketch the graph of y = f( x), where f ( x) = 2 \u2013 ) 3 2 (1 +x between x = \u2013 4 and x = 4 . [2] (ii) write down the co-ordinates of the points where the graph crosses the axes. answer(a)(ii) ( , ) ( , ) [2] (iii) find f(0.25). answer(a)(iii) [1] (b) solve the inequality 2 \u2013 ) 3 2 (1 +x < 4 . answer(b) [4] (c) find f \u20131(x). answer(c) [4] (d) solve f \u20131(x) = 1 . answer(d) x = [2] ", "16": "16 \u00a9 ucles 2013 0607/43/m/j/13 for examiner's use 13 the masses of 200 tomatoes are given in the table. mass (m grams) frequency 0 < m y 20 12 20 < m y 30 34 30 < m y 40 40 40 < m y 45 60 45 < m y 50 42 50 < m y 80 12 (a) calculate an estimate of the mean mass of a tomato. give your answer correct to the nearest gram. answer(a) g [3] (b) (i) complete the frequency density column in this table. mass (m grams) frequency frequency density 0 < m y 20 12 20 < m y 30 34 30 < m y 40 40 40 < m y 45 60 45 < m y 50 42 50 < m y 80 12 [2] (ii) on the grid opposite, draw an accurate histogram to show this information. mark a suitable scale on the frequency density axis. ", "17": "17 \u00a9 ucles 2013 0607/43/m/j/13 [turn over frequency density 10 20 30 40 mass (grams)50 60 70 800m [4] ", "18": "18 \u00a9 ucles 2013 0607/43/m/j/13 for examiner's use 14 zaira works at an ice-cream shop. she wants to find out if there is a correlation between the maximum daily temperature, x \u00b0c, and the shop\u2019s daily income, $ y. zaira recorded the following results. temperature (x \u00b0c) 23 18 27 19 25 20 22 28 17 24 income ($y) 430 320 510 380 510 430 450 530 310 490 (a) (i) complete the scatter diagram. the first four points have been plotted for you. y x 10 12 14 16 18 20 temperature (\u00b0c)22 24 26 28 30 320650 600550500450400350300250income ($) [3] (ii) describe the type of correlation between the temperature and the income. answer(a)(ii) [1] ", "19": "19 \u00a9 ucles 2013 0607/43/m/j/13 [turn over for examiner's use (b) find (i) the mean temperature, answer(b)(i) \u00b0c [1] (ii) the mean income. answer(b)(ii) $ [1] (c) (i) find the equation of the regression line for y in terms of x. answer(c)(i) y = [2] (ii) estimate the income when the temperature is 21\u00b0c. answer(c)(ii) $ [1] (iii) estimate the income when the temperature is 32\u00b0c. answer(c)(iii) $ [1] (iv) explain which of your answers to parts (c)(ii) and (c)(iii) is likely to be the most reliable. [2] question 15 is printed on the next page. ", "20": "20 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2013 0607/43/m/j/13 for examiner's use 15 find the next term and the nth term in each of the following sequences. (a) 6, 18, 54, 162, 486, . answer(a) next term = nth term = [3] (b) \u20131, 1, 5, 11, 19, . answer(b) next term = nth term = [4] " }, "0607_s13_qp_5.pdf": { "1": " this document consists of 5 printed pages and 3 blank pages. ib13 06_0607_05/rp \u00a9 ucles 2013 [turn over *8732392529* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/05 paper 5 (core) may/june 2013 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24. ", "2": "2 \u00a9 ucles 2013 0607/05/m/j/13 for examiner's use answer all the questions. investigation diagonals of rectangles rectangles are drawn on a grid. the sides of each rectangle lie on gridlines and the length is greater than or equal to the width. this investigation looks for a method for calculating the number of small squares through which a diagonal passes. example the diagram shows a rectangle with length 5 and width 3. its diagonal passes through 7 small squares. 1 ab c de f g i h ", "3": "3 \u00a9 ucles 2013 0607/05/m/j/13 [turn over for examiner's use (a) complete the table for the rectangles a to i. rectangle length ( x) width (y) number of squares passed through (s) example 5 3 7 a b c d e f g h 9 4 12 i (b) write down an equation connecting x + y and s. (c) use this equation to find x and y for the three rectangles where the diagonal passes through 6 squares. x = y = x = y = x = y = ", "4": "4 \u00a9 ucles 2013 0607/05/m/j/13 for examiner's use 2 when x and y do not have a common factor, the x by y rectangle is called a basic rectangle. in question 1 , x and y did not have a common factor. in this question x and y do have a common factor. example the diagram below shows a large rectangle with x = 10 and y = 6. x and y have a common factor of 2. the basic 5 by 3 rectangle has a diagonal passing through 7 squares. so the 10 by 6 rectangle has a diagonal passing through 2 \u00d7 7 = 14 squares. complete the following table. length (x) width (y) common factor dimensions of the basic rectangle calculation to find s 10 6 2 5 by 3 2 \u00d7 7 = 14 6 2 = 8 6 = 25 15 = 13 13 = ", "5": "5 \u00a9 ucles 2013 0607/05/m/j/13 for examiner's use 3 a rectangle has an area of 18 squares. use question 1 and question 2 to find the minimum and maximum values of s. minimum = maximum = 4 the diagonal of a rectangle passes through 4 squares. use question 1 and question 2 to find the length and the width of each possible rectangle. ", "6": "6 \u00a9 ucles 2013 0607/05/m/j/13 blank page", "7": "7 \u00a9 ucles 2013 0607/05/m/j/13 blank page", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2013 0607/05/m/j/13 blank page " }, "0607_s13_qp_6.pdf": { "1": " this document consists of 8 printed pages. ib13 06_0607_06/2rp \u00a9 ucles 2013 [turn over *6915781925* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/06 paper 6 (extended) may/june 2013 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2013 0607/06/m/j/13 for examiner's use answer both parts a and b. a investigation diagonals of rectangles (20 marks) you are advised to spend 45 minutes on part a. rectangles are drawn on a grid. the sides of each rectangle lie on gridlines and the length is greater than or equal to the width. this investigation looks for a method for calculating the number of small squares through which a diagonal passes. 1 the diagram shows a rectangle with length 5 and width 3. the diagonal crosses 4 vertical gridlines inside the rectangle. write down (a) the number of horizontal gridlines that the diagonal crosses inside the rectangle, (b) the total number of gridlines that the diagonal crosses inside the rectangle. 2 a rectangle has length x and width y. x and y do not have a common factor. (a) write down an expression for (i) the number of vertical gridlines that a diagonal crosses inside the rectangle, in terms of x, (ii) the number of horizontal gridlines that a diagonal crosses inside the rectangle, in terms of y, (iii) the total number of gridlines, n, which a diagonal crosses inside the rectangle, in terms of x and y. write your answer in its simplest form. n = ", "3": "3 \u00a9 ucles 2013 0607/06/m/j/13 [turn over for examiner's use (b) s is the number of squares through which the diagonal passes. for example, the diagonal in question 1 passes through 7 squares. (i) write s in terms of n. s = (ii) write s in terms of x and y. s = (c) show that your formula for s in part (b)(ii) gives the correct value for an 8 by 5 rectangle. use the grid to show clearly how many squares the diagonal passes through. ", "4": "4 \u00a9 ucles 2013 0607/06/m/j/13 for examiner's use 3 in question 2 , x and y did not have a common factor. in this question, x and y do have a common factor. (a) (i) show clearly that your formula for s does not give the correct value for a 9 by 6 rectangle. (ii) 9 and 6 have a common factor of 3. show how you use the value of s for a 3 by 2 rectangle to calculate s for a 9 by 6 rectangle. ", "5": "5 \u00a9 ucles 2013 0607/06/m/j/13 [turn over for examiner's use (b) use your method in part (a)(ii) to find s for each of these rectangles. (i) 93 by 90 (ii) 60 by 35 4 the diagonal of a rectangle passes through 6 squares. use question 2 and question 3 to find the length and the width of each possible rectangle. ", "6": "6 \u00a9 ucles 2013 0607/06/m/j/13 for examiner's use b modelling drilling a tunnel (20 marks) you are advised to spend 45 minutes on part b. on the plan, a is south of b and c is east of b. ab = 500 metres and bc = 300 metres. engineers want to drill a tunnel from a to c. the tunnel has one or more straight sections. 1 calculate the length of the shortest possible tunnel from a to c. give your answer correct to the nearest metre. m 2 write down the length of the tunnel if the engineers drill through as little hard rock as possible. m 3 p is a point which is x metres south of b. the engineers decide to drill from a to p to c. through normal rock, from a to p, the drill moves forward at 2 metres per hour. through the hard rock, from p to c, the drill moves forward at 1 metre per hour. 300 m 500 mbc anormal rocknormalrock hardrocknot toscalenorth 300 m x m 500 mb c ap normal rocknormalrock hardrocknot toscalenorth", "7": "7 \u00a9 ucles 2013 0607/06/m/j/13 [turn over for examiner's use (a) explain why the time in hours, t, that it takes to drill the tunnel, can be modelled by this equation. 2900002500xxt + +\u2212= (b) all the measurements are accurate. write down a practical reason why the time given by the model may be different from the actual time. (c) on the diagram, sketch the graph of t against x. 400500600 time (hours)t x0500 distance (metres) (d) (i) find, to the nearest metre, the position of p which gives the minimum time to drill the tunnel. metres from b (ii) find this minimum time correct to the nearest 10 hours. hours ", "8": "8 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2013 0607/06/m/j/13 for examiner's use 4 to drill through normal rock costs 2 thousand dollars per hour. to drill through the hard rock costs 3 thousand dollars per hour. (a) the total cost of drilling the tunnel is n thousand dollars. write down a model for n in terms of x. n = (b) (i) find, to the nearest metre, the position of p which gives the minimum cost. metres from b (ii) write, in full, this minimum cost to the nearest ten thousand dollars. $ 5 the model for the time taken to drill the tunnel is 2900002500xxt + +\u2212= . (a) the position of b and c are fixed. investigate the position of p which gives the minimum time when a is more than 500 m south of b. (b) if ab = d metres explain, using part (a) , why the minimum time in hours is kdt + =2 , where k = 260 correct to 3 significant figures. " }, "0607_w13_qp_1.pdf": { "1": " this document consists of 11 printed pages and 1 blank page. ib13 11_0607_01/4rp \u00a9 ucles 2013 [turn over *2859125547* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/01 paper 1 (core) october/november 2013 45 minutes candidates answer on the question paper additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2013 0607/11/o/n/13 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2013 0607/11/o/n/13 [turn over for examiner's use 1 write 8572 (a) correct to the nearest 10 , answer (a) [1] (b) correct to the nearest 100 . answer (b) [1] 2 put one of + \u2013 \u00d7 \u00f7 in the box to make the following correct. 3 \u00d7 (11 5) = 18 [1] 3 write the following in order, starting with the smallest. 25 52 33 answer i i [2] ", "4": "4 \u00a9 ucles 2013 0607/11/o/n/13 for examiner's use 4 on the shape draw the line of symmetry. [1] 5 (a) work out 43 of $120 . answer (a) $ [1] (b) a sum of money is divided between stefan and tomas in the ratio stefan : tomas = 1 : 3. (i) what fraction of the money does stefan receive? answer (b)(i) [1] (ii) what percentage of the money does tomas receive? answer (b)(ii) % [1] ", "5": "5 \u00a9 ucles 2013 0607/11/o/n/13 [turn over for examiner's use 6 (a) jean plays golf. here are her best 10 scores. 69 71 68 70 71 66 71 72 69 70 (i) what is the range of her scores? answer (a)(i) [1] (ii) find jean\u2019s modal score. answer (a)(ii) [1] (b) anya records the shoe size of 10 of her friends. this frequency table shows her results. shoe size frequency 3 4 4 2 5 3 6 1 find the mean shoe size. answer (b) [3] ", "6": "6 \u00a9 ucles 2013 0607/11/o/n/13 for examiner's use 7 in the diagram be is the diameter of the circle and ac is a tangent to the circle at b. de bc anot to scale (a) write down the size of angle bde . answer (a) [1] (b) write down the size of angle cbe. answer (b) [1] (c) which word is the mathematical name for the line de? diameter radius sector chord circumference centre answer (c) [1] ", "7": "7 \u00a9 ucles 2013 0607/11/o/n/13 [turn over for examiner's use 8 (a) the diagram shows the graph of y = x1 . \u20134\u2013 3\u2013 2\u2013 1 0 1234 \u20134\u20133\u20132\u201311234y x write down the equations of the two asymptotes of the graph of y = x1 . answer (a) [2] (b) the diagram shows the graph of y = f( x). 1 \u20131 \u20131123y x\u20132 \u20133 20 (i) write down the domain. answer (b)(i) [1] (ii) write down the range. answer (b)(ii) [1] (iii) on the diagram, sketch the graph of y = f(x) + 1 . [1] ", "8": "8 \u00a9 ucles 2013 0607/11/o/n/13 for examiner's use 9 jimmi\u2019s pencil case only contains 3 pens and 12 pencils. (a) he chooses an object at random from his pencil case. find the probability that the object is a pencil. answer (a) [1] (b) jimmi chooses an object at random from his pencil case and then replaces it. he repeats this 100 times. how many times do you expect jimmi to choose a pen? answer (b) [2] ", "9": "9 \u00a9 ucles 2013 0607/11/o/n/13 [turn over for examiner's use 10 (a) solve the following equations. (i) 6 + 5w = 41 answer (a)(i) w = [2] (ii) 7 (3x \u2013 4) = 35 answer (a)(ii) x = [3] (b) write down two integers which satisfy the inequality 4 a \u2013 1 < 10 . answer (b) [2] ", "10": "10 \u00a9 ucles 2013 0607/11/o/n/13 for examiner's use 11 a is the point (2, \u20131) and b is the point (4, 5). 0y xnot to scale ab (a) find the co-ordinates of the midpoint of ab. answer (a) ( ) [1] (b) (i) find the gradient of ab. , answer (b)(i) [2] (ii) find the equation of the line ab. answer (b)(ii) [2] (c) write down the equation of a line parallel to ab. answer (c) [1] ", "11": "11 \u00a9 ucles 2013 0607/11/o/n/13 for examiner's use 12 15 mm 12 mm9 mmnot to scalex y write down (a) tan x, answer (a) [1] (b) cos y. answer (b) [1] ", "12": "12 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2013 0607/11/o/n/13 blank page " }, "0607_w13_qp_2.pdf": { "1": " this document consists of 8 printed pages. ib13 11_0607_02/2rp \u00a9 ucles 2013 [turn over *3859409843* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/02 paper 2 (extended) october/november 2013 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2013 0607/02/o/n/13 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2013 0607/02/o/n/13 [turn over for examiner's use answer all the questions. 1 solve the simultaneous equations. 3g \u2013 2h = 11 g \u2013 2h = 5 answer g = h = [2] 2 (a) uab n(u) = 20, n(a \u222a b) ' = 3, n(a) = 11, n( b) = 13. find n(a \u2229 b' ). answer(a) [2] (b) on each venn diagram, shade the region indicated. upq (p \u2229 q)'ust s \u222a t ' [2] 3 tiago buys a concert ticket and then sells it for $15. he makes a profit of 20%. calculate how much tiago paid for the ticket. answer $ [3] ", "4": "4 \u00a9 ucles 2013 0607/02/o/n/13 for examiner's use 4 36\u00b0 52\u00b0d c e p a b qnot to scale abcd is a parallelogram and bqpc is a rhombus. dce is a straight line. angle dab = 52\u00b0 and angle ecp = 36\u00b0. find the size of angle bpc. answer [3] 5 (a) simplify 72. answer(a) [1] (b) 2 1 22 2q p+ = \u2212+ find the values of p and q. answer(b) p = q = [3] ", "5": "5 \u00a9 ucles 2013 0607/02/o/n/13 [turn over for examiner's use 6 simplify the following. (a) 2y2 \u00d7 3y3 answer(a) [2] (b) 3 2727p answer(b) [2] 7 (a) find the amplitude and period of the function f( x) = 4cos(4x). answer(a) amplitude = period = [2] (b) g( x) = 4cos(4 x) \u2013 4 describe fully the single transformation that maps the graph of y = f(x) onto the graph of y = g(x). answer(b) [2] ", "6": "6 \u00a9 ucles 2013 0607/02/o/n/13 for examiner's use 8 (a) write down the value of 31 8. answer(a) [1] (b) find the exact value of 2 34\u2212 \uf8f7 \uf8f8\uf8f6\uf8ec \uf8ed\uf8eb. answer(b) [2] 9 not to scale x\u00b0 the diagram shows a cube of side length 1. find the value of tan x\u00b0. answer [3] ", "7": "7 \u00a9 ucles 2013 0607/02/o/n/13 [turn over for examiner's use 10 x cm 12 cm30\u00b0not to scale find the exact value of x. answer x = [3] 11 not to scaledc b aq pnm abcd is a parallelogram. dm = mc and cn = 2nb. = p and = q. (a) write down in terms of q. answer(a) [1] (b) find in terms of p and q. answer(b) [1] question 12 is printed on the next page. ", "8": "8 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2013 0607/02/o/n/13 for examiner's use 12 f(x) = 3x \u2013 1 g(x) = 12 \u2013 x find (a) f(g(8)), answer(a) [2] (b) f(g(x)), in its simplest form, answer(b) [2] (c) g \u2013 1(x). answer(c) g \u2013 1(x) = [1] " }, "0607_w13_qp_3.pdf": { "1": " this document consists of 15 printed pages and 1 blank page. ib13 11_0607_03/3rp \u00a9 ucles 2013 [turn over *7930960218* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/03 paper 3 (core) october/november 2013 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96. ", "2": "2 \u00a9 ucles 2013 0607/03/o/n/13 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2013 0607/03/o/n/13 [turn over for examiner's use answer all the questions. 1 youming asked 50 of his friends which of these items they owned. these are his results. item owned frequency calculator 48 mp3 player 22 mobile phone 50 laptop 35 car 12 bicycle 15 (a) complete the bar chart to show this information. 60 5040302010 0frequency calculator mp3 playermobile phonelaptop item ownedcar bicycle [2] (b) write down the ratio frequency of mobile phone : frequency of laptop : frequency of bicycle give your answer in its simplest form. answer(b) : : [2] (c) one of youming\u2019s 50 friends is chosen at random. write down the probability that this person owns (i) a laptop, answer(c)(i) [1] (ii) a mobile phone. answer(c)(ii) [1] ", "4": "4 \u00a9 ucles 2013 0607/03/o/n/13 for examiner's use 2 three sisters, meg, jo and pat, share $1400 . meg is 15 years old, jo is 17 and pat is 18. they divide the money in the ratio of their ages. (a) show that jo receives $476 . [2] (b) find the amount that pat receives. answer(b) $ [2] (c) work out how many more dollars pat receives than jo. answer(c) $ [1] (d) write your answer to part (c) as a percentage of the $1400. answer(d) % [2] ", "5": "5 \u00a9 ucles 2013 0607/03/o/n/13 [turn over for examiner's use 3 on any one night, the probability that jos\u00e9 plays a computer game is 0.6 . when jos\u00e9 plays a computer game, the probability that he does his homework is 0.1 . when he does not play a computer game, the probability that he does his homework is 0.8 . (a) complete the tree diagram. yesjos\u00e9 plays a computer gamejos\u00e9 does his homework noyes no noyes 0.6 [3] (b) find the probability that jos\u00e9 plays a computer game and does his homework. answer(b) [2] (c) find the probability that jos\u00e9 does not do his homework. answer(c) [3] ", "6": "6 \u00a9 ucles 2013 0607/03/o/n/13 for examiner's use 4 illyass asks 60 students how many minutes they spend on facebook each week. the information is shown in the table. number of minutes, x frequency 0 < x y=20 2 20 < x y=40 8 40 < x y=60 13 60 < x y=80 21 80 < x y=100 10 100 < x y=120 6 (a) write down the midpoint of the interval 0 < x \u011f 20. answer(a) [1] (b) calculate an estimate of the mean number of minutes spent on facebook. answer(b) min [2] (c) complete the cumulative frequency table. number of minutes, x cumulative frequency x y=20 2 x y=40 10 x y=60 x y=80 x y= 100 54 x y= 120 60 [1] ", "7": "7 \u00a9 ucles 2013 0607/03/o/n/13 [turn over for examiner's use (d) complete the cumulative frequency curve. 60 5040302010 10 20 30 40 50 60 number of minutes70 80 90 100 110 1200xcumulative frequency [2] (e) find the median. answer(e) min [1] (f) find the inter-quartile range. answer(f) min [2] ", "8": "8 \u00a9 ucles 2013 0607/03/o/n/13 for examiner's use 5 a pizza box has a height of 5 cm and a square base of side 30 cm. not to scale (a) (i) find the area of the base of the box. answer(a)(i) cm2 [1] (ii) calculate the volume of the box. answer(a)(ii) cm3 [1] (b) not to scale the radius of the circular pizza is 15 cm. (i) find the area of the base of this pizza. answer(b)(i) cm2 [1] (ii) the pizza is cut into 16 equal slices as shown in the diagram. find the size of the angle of each slice. answer(b)(ii) [1] (iii) calculate the area of one slice of pizza. answer(b)(iii) cm2 [1] (c) a mathematically similar pizza box has height 4 cm. calculate the length of the sides of the base of this pizza box. answer(c) cm [2] ", "9": "9 \u00a9 ucles 2013 0607/03/o/n/13 [turn over for examiner's use 6 hugo, ana and bella all leave home at 07 45 to travel to school. (a) hugo lives 3 km from school. he takes 20 minutes to skateboard to school. (i) find the time that hugo arrives at school. answer(a)(i) [1] (ii) find his average speed in kilometres per hour. answer(a)(ii) km/h [2] (b) ana lives 1 km from school. she walks to school at 4 km/h. find the time that ana arrives at school. answer(b) [2] (c) bella travels to school by car at an average speed of 30 km/h. she arrives at school at 08 10. find the distance bella travels to school. answer(c) km [2] (d) which of these three students arrives at school first? answer(d) [1] ", "10": "10 \u00a9 ucles 2013 0607/03/o/n/13 for examiner's use 7 ca by x6 42 \u20132\u20134\u20136\u20136 \u20134 \u20132 2 0 4 6 8 10 12 (a) describe fully the single transformation that maps (i) shape a onto shape b, [2] (ii) shape a onto shape c. [2] (b) draw the reflection of shape a in the y-axis. [2] ", "11": "11 \u00a9 ucles 2013 0607/03/o/n/13 [turn over for examiner's use 8 here are the first four terms of a sequence. 28 25 22 19 (a) write down the next two terms of this sequence. answer(a) and [2] (b) find the nth term of the sequence. answer(b) [2] 9 85\u00b0 135\u00b0 125\u00b0x\u00b0not to scale (a) write down the mathematical name for this polygon. answer(a) [1] (b) work out the sum of the interior angles of a polygon with five sides. answer(b) [2] (c) find the size of the angle marked x\u00b0 in the diagram. answer(c) [2] ", "12": "12 \u00a9 ucles 2013 0607/03/o/n/13 for examiner's use 10 u = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} a is the set of factors of 12 b = {1, 3, 6, 10} (a) write down the six elements of set a. answer(a) [1] (b) complete the venn diagram. u ab [2] (c) find the number of elements in (i) a \u2229 b, answer(c)(i) [1] (ii) a' \u2229 b, answer(c)(ii) [1] (iii) (a \u222a b) '. answer(c)(iii) [1] ", "13": "13 \u00a9 ucles 2013 0607/03/o/n/13 [turn over for examiner's use 11 the diagram shows a circular mirror, centre o and radius 25 cm. it hangs by two wires, ab and ac. ab and ac are tangents to the circular mirror. ao is 60 cm. 25 cma b c onot to scale 60 cm (a) calculate the length of ab. answer(a) cm [3] (b) use trigonometry to find the size of angle boc. answer(b) [3] (c) calculate the length of the arc bc. answer(c) cm [2] ", "14": "14 \u00a9 ucles 2013 0607/03/o/n/13 for examiner's use 12 y x16 \u201310\u20132 50 (a) on the diagram, sketch the graph of y = f( x) where f( x) = \u20132x 2 + 5x +12 . [2] (b) write down the zeros of f(x). answer(b) and [2] (c) find the co-ordinates of the maximum point. answer(c) ( , ) [2] (d) on the diagram, sketch the graph of y = 2x + 5. [1] (e) write down the x co-ordinates of the points of intersection of y = \u20132x 2 + 5x + 12 and y = 2x + 5 give your answers correct to two decimal places. answer(e) x = and x = [3] ", "15": "15 \u00a9 ucles 2013 0607/03/o/n/13 for examiner's use 13 (a) simplify the following expressions. (i) 2x \u2013 1 + 2(x + 2) answer(a)(i) [2] (ii) 5p3 \u00d7 3p4 answer(a)(ii) [2] (iii) 36 46 rr answer(a)(iii) [2] (iv) (6t4)2 answer(a)(iv) [2] (b) factorise fully. 12 p 2q + 18pq answer(b) [2] (c) make s the subject of the formula. r = 2pm + ns answer(c) s = [2] ", "16": "16 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publis her (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2013 0607/03/o/n/13 blank page " }, "0607_w13_qp_4.pdf": { "1": " this document consists of 18 printed pages and 2 blank pages. ib13 11_0607_04/2rp \u00a9 ucles 2013 [turn over *3769158093* for examiner's use university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/04 paper 4 (extended) october/november 2013 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120. ", "2": "2 \u00a9 ucles 2013 0607/04/o/n/13 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2013 0607/04/o/n/13 [turn over for examiner's use answer all the questions. 1 manuel buys a car for $8000. (a) each year the value of the car decreases by 8% of its value at the start of the year. (i) calculate the value of the car after 5 years. answer(a)(i) $ [2] (ii) calculate how many more years it takes for the value of the car to be less than $4000. answer(a)(ii) [2] (b) manuel has a journey of 235 km. the journey takes 3 h 15 min and the car uses 19.7 litres of fuel. (i) calculate the average speed of the journey in kilometres per hour. answer(b)(i) km/h [2] (ii) find the rate at which the car uses fuel. give your answer in litres per 100 km. answer(b)(ii) l/100 km [1] ", "4": "4 \u00a9 ucles 2013 0607/04/o/n/13 for examiner's use 2 w ty x5 4321 \u20131\u20132\u20133\u20134\u201350 \u2013 1 12345 \u20132 \u20133 \u20134 \u20135 (a) (i) reflect triangle t in the x-axis. label the image u. [2] (ii) rotate triangle u clockwise through 90 \u00b0 about (0, 0). label the image v. [2] (iii) describe fully the single transformation that maps triangle t onto triangle v. [2] (b) describe fully the single transformation that maps triangle t onto triangle w. [3] ", "5": "5 \u00a9 ucles 2013 0607/04/o/n/13 [turn over for examiner's use 3 north n wa 346 km 271 km493 kmnot to scale the diagram shows the straight line distances between the cities auckland ( a), napier (n) and wellington ( w) in new zealand. (a) the bearing of w from a is 179\u00b0. calculate the bearing of n from a. answer(a) [4] (b) a map shows the three cities. the scale of the map is 1 : 10 000 000. calculate the area of triangle anw on the map. give your answer in square centimetres. answer(b) cm2 [3] ", "6": "6 \u00a9 ucles 2013 0607/04/o/n/13 for examiner's use 4 o cnot to scale p14 cm 12 cm the diagram shows a hollow cone of height 12 cm and sloping edge, op, 14 cm. c is the centre of the base of the cone. (a) calculate (i) the radius of the base of the cone, answer(a)(i) cm [3] (ii) the volume of the cone. answer(a)(ii) cm3 [2] ", "7": "7 \u00a9 ucles 2013 0607/04/o/n/13 [turn over for examiner's use (b) the cone is cut along the sloping edge op and opened out to make a sector of a circle. oab not to scale (i) calculate the area of the sector and show that it rounds to 317 cm2, correct to 3 significant figures. [2] (ii) calculate the reflex angle aob . answer(b)(ii) [3] ", "8": "8 \u00a9 ucles 2013 0607/04/o/n/13 for examiner's use 5 200 students each record the number of hours, h, they spend on homework in one week. the cumulative frequency curve shows the results. 200 180160140120100 80604020 51 0 1 5 2 0 time spent on homework (hours)25 30 350h cumulative frequency (a) find (i) the median, answer(a)(i) h [1] (ii) the lower quartile, answer(a)(ii) h [1] (iii) the inter-quartile range, answer(a)(iii) h [1] (iv) the 90th percentile, answer(a)(iv) h [1] (v) the number of students who spend more than 10 hours on homework. answer(a)(v) [2] ", "9": "9 \u00a9 ucles 2013 0607/04/o/n/13 [turn over for examiner's use (b) (i) use the cumulative frequency curve to complete the frequency table. time spent on homework h hours 0 < h \u011f 10 10 < h \u011f 15 15 < h \u011f 20 20 < h \u011f 25 25 < h \u011f 35 frequency 20 20 50 [2] (ii) calculate an estimate of the mean number of hours spent on homework. answer(b)(ii) h [2] (iii) the data is used to draw a histogram. complete the frequency density table. (do not draw the histogram.) time spent on homework h hours 0 < h \u011f 15 15 < h \u011f 20 20 < h \u011f 25 25 < h \u011f 35 frequency density 10 [3] ", "10": "10 \u00a9 ucles 2013 0607/04/o/n/13 for examiner's use 6 y x 10 \u201310 \u201388 0 f( x) = ) 2 () 3 2 ( +\u2212 xx (a) on the diagram, sketch the graph of y = f(x). [3] (b) write down the value of f(0). answer(b) [1] (c) solve the equation f( x) = 0. answer(c) [1] (d) write down the equations of the asymptotes. answer(d) [2] (e) find the range of f( x) for the domain 0 \u011f x \u011f 8 . answer(e) [2] ", "11": "11 \u00a9 ucles 2013 0607/04/o/n/13 [turn over for examiner's use (f) g(x) = 3 \u2013 x (i) on the diagram, sketch the graph of y = g(x). [1] (ii) solve the equation f( x) = g( x). answer(f)(ii) x = or x = [2] (iii) show that the equation f( x) = g( x) can be re-arranged into x2 + x \u2013 9 = 0 . [3] (iv) the exact solutions of the equation x 2 + x \u2013 9 = 0 are 21 k\u00b1 \u2212 . find the value of k. answer(f)(iv) k = [2] ", "12": "12 \u00a9 ucles 2013 0607/04/o/n/13 for examiner's use 7 y x0a bnot to scale a (1, 6) is joined to b (5, 2) by the line ab. (a) calculate the length of the line ab. answer(a) [3] (b) find the equation of the straight line that passes through a and b. answer(b) [3] (c) (i) find the equation of the line which is perpendicular to ab and passes through the origin. answer(c)(i) [2] (ii) find the co-ordinates of the point of intersection of the line in part (c)(i) and the line ab. answer(c)(ii) ( , ) [1] ", "13": "13 \u00a9 ucles 2013 0607/04/o/n/13 [turn over for examiner's use 8 find the nth term of each of the following sequences. (a) 21, 17, 13, 9, 5, \u2026\u2026\u2026 answer(a) [2] (b) 3, 6, 12, 24, 48, \u2026\u2026\u2026 answer(b) [2] (c) 41, 54, 69, 716, 825, \u2026\u2026\u2026 answer(c) [2] (d) 0, 6, 24, 60, 120, \u2026\u2026\u2026 answer(d) [4] ", "14": "14 \u00a9 ucles 2013 0607/04/o/n/13 for examiner's use 9 if the weather is fine, the probability that alex goes to the beach is 109. if the weather is not fine, the probability that alex goes to the beach is 103. the probability that the weather will be fine is 65. (a) complete the tree diagram. yesweather is fine alex goes to the beach noyes no noyes [3] (b) find the probability that alex goes to the beach. answer(b) [3] (c) which combination of these events has a probability of 121? answer(c) [1] ", "15": "15 \u00a9 ucles 2013 0607/04/o/n/13 [turn over for examiner's use 10 d c b ax6x\u00b03x\u00b0x\u00b08.55 cm 2.78 cm 9.23 cmnot to scale a, b, c and d lie on the circumference of a circle. ac and bd intersect at x. (a) angle cdx = x\u00b0, angle dcx = 3x\u00b0 and angle cxd = 6x\u00b0. show that angle abx = 54\u00b0. [3] (b) (i) complete the statement triangles cdx and bax are [1] (ii) ab = 9.23 cm, dc = 8.55 cm and xc = 2.78 cm. calculate the length of bx. answer(b)(ii) cm [2] (iii) find the value of baxcdx triangle of areatriangle of area. give your answer correct to 2 decimal places. answer(b)(iii) [2] ", "16": "16 \u00a9 ucles 2013 0607/04/o/n/13 for examiner's use 11 (a) 0y xnot to scale the sketch shows the graph of y = log ax . on the same diagram, sketch the graph of y = 2log ax . [2] (b) 3log x = log16 \u2013 2log x find the value of x. answer(b) x = [3] (c) solve the equation 5 y = 100 . give your answer correct to 4 significant figures. answer(c) y = [3] ", "17": "17 \u00a9 ucles 2013 0607/04/o/n/13 [turn over for examiner's use 12 5x 2xnot to scale the diagram shows a rectangle with length 5 x and width 2 x. one of the shorter sides is joined to a semicircle with radius x. (a) find a formula, in terms of x and \u03c0, for the total area, a, of the shape. answer(a) a = [2] (b) make x the subject of your formula in part (a) . answer(b) x = [3] (c) find the value of x when a = 200. answer(c) x = [1] ", "18": "18 \u00a9 ucles 2013 0607/04/o/n/13 for examiner's use 13 (a) (i) factorise. 2 x2 \u2013 x \u2013 1 answer(a)(i) [2] (ii) write as a single fraction in its simplest form. 14 1 21 2 \u2212+ \u2212 \u2212 x x x answer(a)(ii) [3] (b) simplify. qt pt q pq p 5 5252 2 \u2212 \u2212 +\u2212 answer(b) [4] ", "19": "19 \u00a9 ucles 2013 0607/04/o/n/13 blank page", "20": "20 permission to reproduce items where third -party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2013 0607/04/o/n/13 blank page " }, "0607_w13_qp_5.pdf": { "1": " this document consists of 6 printed pages and 2 blank pages. ib13 11_0607_05/2rp \u00a9 ucles 2013 [turn over *8541720444* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/05 paper 5 (core) october/november 2013 1 hour candidates answer on the question paper additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24. ", "2": "2 \u00a9 ucles 2013 0607/05/o/n/13 for examiner's use answer all the questions. investigation sums of sequences here is the method to construct a sequence for this investigation. method example write down any two numbers for the first two terms. 3 and 7 add these two terms to make the third term. 3 + 7 = 10 add the second and third terms to make the fourth term. 7 + 10 = 17 add the third and fourth terms to make the fifth term. 10 + 17 = 27 continue in this way to construct the sequence. this example makes the sequence: 3, 7, 10, 17, 27, 44, 1 show that the sum of the first six terms in this sequence, divided by the fifth term, is 4. 2 (a) the first two terms of a new sequence are 272 and 412. (i) use the method to write down the next four terms in this sequence. 272, 412, , , , (ii) work out the sum of the first six terms in this sequence and divide it by the fifth term. ", "3": "3 \u00a9 ucles 2013 0607/05/o/n/13 [turn over for examiner's use (b) the first two terms of another sequence are 4.52 and 16.9 . (i) use the method to write down the next four terms in this sequence. do not round any of your numbers. 4.52, 16.9, , , , (ii) work out the sum of the first six terms in this sequence and divide it by the fifth term. (c) (i) choose two negative numbers to be the first two terms of a sequence. use the method to work out the next four terms in this sequence. write down the first six terms in your sequence. , , , , , (ii) work out the sum of the first six terms in your sequence and divide it by the fifth term. (d) describe the connection between the fifth term and the sum of the first six terms in each of these sequences. ", "4": "4 \u00a9 ucles 2013 0607/05/o/n/13 for examiner's use 3 the first two terms of a new sequence are p and q. the table shows the working for the first five terms. working term p p q q p + q p + q q + p + q p + 2q p + q + p + 2q 2p + 3q (a) complete the table. (b) find an expression for the sum of these first six terms. simplify your answer. (c) find an equation to connect the fifth term and the sum of the first six terms. ", "5": "5 \u00a9 ucles 2013 0607/05/o/n/13 [turn over for examiner's use 4 (a) 3, 7, 10, 17, 27, 44, (i) write down the next four terms in this sequence. 3, 7, 10, 17, 27, 44, , , , (ii) work out the sum of the first ten terms in this sequence and divide it by the seventh term. (b) (i) find the next four terms in the sequence in question 3 . 7th term 8th term 9 th term 10 th term (ii) find an expression for the sum of the first ten terms in this sequence. simplify your answer. (iii) find an equation to connect the seventh term and the sum of the first ten terms. ", "6": "6 \u00a9 ucles 2013 0607/05/o/n/13 for examiner's use 5 (a) find the next four terms in the sequence in question 4(b) . 11th term 12th term 13th term 14 th term (b) find an expression for the sum of the first fourteen terms. simplify your answer. (c) this sum is a multiple of one of the terms in question 4(b)(i) . find this multiple. (d) describe this connection using algebra. ", "7": "7 \u00a9 ucles 2013 0607/05/o/n/13 blank page ", "8": "8 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2013 0607/05/o/n/13 blank page " }, "0607_w13_qp_6.pdf": { "1": " this document consists of 11 printed pages and 1 blank page. ib13 11_0607_06/2rp \u00a9 ucles 2013 [turn over *8778931706* university of cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/06 paper 6 (extended) october/november 2013 1 hour 30 minutes candidates answer on the question paper additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use a pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2013 0607/06/o/n/13 for examiner's use answer both parts a and b. a investigation sums of sequences (20 marks) you are advised to spend no more than 45 minutes on this part. here is the method to construct a sequence for this investigation. method example write down any two numbers for the first two terms. 3 and 7 add these two terms to make the third term. 3 + 7 = 10 add the second and third terms to make the fourth term. 7 + 10 = 17 add the third and fourth terms to make the fifth term. 10 + 17 = 27 continue in this way to construct the sequence. this example makes the sequence: 3, 7, 10, 17, 27, 44, 1 show that the sum of the first six terms in this sequence, divided by the fifth term, is 4. ", "3": "3 \u00a9 ucles 2013 0607/06/o/n/13 [turn over for examiner's use 2 (a) the first two terms of another sequence are 4.52 and 16.9 . (i) use the method to write down the next four terms in this sequence. do not round any of your numbers. 4.52, 16.9, , , , (ii) work out the sum of the first six terms in this sequence and divide it by the fifth term. (b) (i) choose two negative numbers to be the first two terms of a sequence. use the method to work out the next four terms in this sequence. write down the first six terms in your sequence. , , , , , (ii) work out the sum of the first six terms in your sequence and divide it by the fifth term. ", "4": "4 \u00a9 ucles 2013 0607/06/o/n/13 for examiner's use 3 the first two terms of a new sequence are p and q. the table shows the working for the first five terms. working term p p q q p + q p + q q + p + q p + 2q p + q + p + 2q 2p + 3q (a) complete the table. (b) find an expression for the sum of these first six terms. simplify your answer. (c) find an equation to connect the fifth term and the sum of the first six terms. ", "5": "5 \u00a9 ucles 2013 0607/06/o/n/13 [turn over for examiner's use 4 (a) find the next four terms in the sequence in question 3 . 7th term 8th term 9th term 10 th term (b) find an expression for the sum of the first ten terms in this sequence. simplify your answer. (c) find an equation to connect the seventh term and the sum of the first ten terms. ", "6": "6 \u00a9 ucles 2013 0607/06/o/n/13 for examiner's use 5 (a) find the next four terms in the sequence in question 4 . 11th term 12th term 13th term 14 th term (b) find an expression for the sum of the first fourteen terms. simplify your answer. (c) this sum is a multiple of one of the terms in question 4(a) . find this multiple. (d) prove this connection. ", "7": "7 \u00a9 ucles 2013 0607/06/o/n/13 [turn over for examiner's use 6 in question 2 the connection between the sum of the six terms and the fifth term is sum of the first 6 terms = 4 times 5th term complete the following statements. sum of the first 10 terms = sum of the first 14 terms = sum of the first 18 terms = ", "8": "8 \u00a9 ucles 2013 0607/06/o/n/13 for examiner's use b modelling the earth\u2019s temperature (20 marks) you are advised to spend no more than 45 minutes on this part. logarithms to base 10 are written as log. scientists have been measuring the temperature of the earth since 1860. the table shows the increase in earth\u2019s temperature since 1860. the increases are averages for each decade (10 years) correct to 2 decimal places. final year of each decade number of years since 1860 (n) temperature increase since 1860 in \u00b0c (t) 1890 30 0.02 1900 40 0.03 1910 50 0.04 1920 60 0.06 1930 70 0.08 1940 80 0.10 1950 90 0.13 1960 100 0.18 1970 110 0.24 1980 120 0.32 1 (a) on the grid, plot the temperature increase ( t) against the number of years since 1860 ( n), for 30 \u011f n \u011f 120. draw a smooth curve that shows the increase in temperature. 0.4 0.30.20.1 0 40 30 50 60 70 80 number of years since 186090 100 110 120 130t ntemperature increase (\u00b0c) ", "9": "9 \u00a9 ucles 2013 0607/06/o/n/13 [turn over for examiner's use (b) (i) which of the following models best fits this graph? t = an + b t = asinbn t = an b t = | an + b | (ii) use the values of n and t for 1900 and 1940 in your model to write down two equations in a and b. (iii) use your equations to show that 0.3 = 0.5 b. (iv) find the value of b and show that it rounds to 1.74, correct to 3 significant figures. (v) find the value of a. give your answer correct to 2 significant figures. a = (vi) show that your model gives a suitable value of t for 1920. ", "10": "10 \u00a9 ucles 2013 0607/06/o/n/13 for examiner's use 2 (a) (i) complete the table to give the value of log t for each value of n. give each answer correct to 2 decimal places. final year of each decade number of years since 1860 (n) temperature increase since 1860 in \u00b0c (t) log t 1890 30 0.02 \u20131.70 1900 40 0.03 1910 50 0.04 1920 60 0.06 \u20131.22 1930 70 0.08 1940 80 0.10 1950 90 0.13 \u20130.89 1960 100 0.18 1970 110 0.24 \u20130.62 1980 120 0.32 \u20130.49 (ii) on the grid plot log t against n, for 30 \u011f n \u011f 120. 0.5 0 \u20130.5 \u20131 \u20131.5 \u20132 \u20132.510 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160nlog t ", "11": "11 \u00a9 ucles 2013 0607/06/o/n/13 for examiner's use (iii) the mean point is (75, \u20131.07). on the grid, draw the line of best fit. (iv) use your line of best fit to predict the temperature increase by 2020 (160 years since 1860). (b) (i) a model for the line of best fit is log t = mn + c. find the values of m and c. give your answers correct to 2 significant figures. m = c = (ii) use this model to predict the temperature increase by 2020. (iii) comment on your two predictions for the temperature increase by 2020. ", "12": "12 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of t he cambridge assessment group. ca mbridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2013 0607/06/o/n/13 blank page " } }, "2014": { "0607_s14_qp_11.pdf": { "1": " this document consists of 11 printed pages and 1 blank page. ib14 06_0607_11/5rp \u00a9 ucles 2014 [turn over *2660893404* cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/11 paper 1 (core) may/june 2014 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2014 0607/11/m/j/14 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2014 0607/11/m/j/14 [turn over 1 work out. 2.5 \u00d7 10 \u00f7 5 answer [1] 2 find 3% of $8000 . answer $ [1] 3 (a) write 46.849 correct to 1 decimal place. answer (a) [1] (b) after conversion from euros to dollars, a flight from paris to london costs $59.90235 . write this value correct to 4 significant figures. answer (b) $ [1] ", "4": "4 \u00a9 ucles 2014 0607/11/m/j/14 4 (a) arc circumference diameter radius sector segment label the diagram . use only words from the box above. .. . [3] (b) measure and write down the size of angle abc. a bc answer (b) [1] ", "5": "5 \u00a9 ucles 2014 0607/11/m/j/14 [turn over 5 \u20134 \u20133 \u20132 \u201310 1234 \u20134\u20133\u20132\u201311234y xb c (a) on the grid, plot the point (\u20133, 2). label this point a. [1] (b) write down the co-ordinates of point b. answer (b) ( , ) [1] (c) find the midpoint of bc. answer (c) ( , ) [1] ", "6": "6 \u00a9 ucles 2014 0607/11/m/j/14 6 (a) b c d e fanot to scale the diagram shows a regular hexagon. work out the size of angle abc . show all your working. answer (a) [3] (b) 135\u00b0 not to scale the diagram shows a square and four regular octagons. the interior angle of a regular octagon is 135\u00b0. use angles to explain why the square and octagons fit together with no gaps, as shown in the diagram. answe r (b) [2] ", "7": "7 \u00a9 ucles 2014 0607/11/m/j/14 [turn over 7 \u20134 \u20133 \u20132 \u201310 1234 \u20134\u20133\u20132\u201311234y xb a write ab as a column vector. answer\uf8f7\uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec\uf8ec \uf8ed\uf8eb [2] 8 a bag contains 3 red balls, 2 blue balls and 1 yellow ball. a ball is chosen at random. what is the probability that the ball is either red or blue? give your answer as a fraction. answer [1] ", "8": "8 \u00a9 ucles 2014 0607/11/m/j/14 9 (a) complete the mapping diagram for the function f : x a x2. x \u20132 \u20131 0 1 2 x 0142 [2] (b) write down the domain of the mapping in part (a) . answer (b) [1] (c) which of these phrases describes the mapping in part (a) . one-to-one one-to-many many-to-one many-to-many answer (c) [1] ", "9": "9 \u00a9 ucles 2014 0607/11/m/j/14 [turn over 10 \u20136\u20135\u20134\u20133 \u201310\u20139\u20138\u20137 \u20132\u20131 0 123456789 1 0 \u20135\u20134\u20133\u20132\u20131 \u201310\u20139\u20138\u20137\u2013612345678910y xq the diagram shows a quadrilateral q. (a) draw the reflection of q in the y-axis. [2] (b) draw the enlargement of q with centre (0, 0) and scale factor 21. [3] ", "10": "10 \u00a9 ucles 2014 0607/11/m/j/14 11 (a) 3p \u2013 5t = 8 work out the value of 12 p \u2013 20 t. answer (a) [2] (b) solve the following equations. (i) 5x \u2013 7 = 9 + 3 x answer (b) (i) x= [2] (ii) 4 (4x \u2013 5) = 28 answer (b) (ii) x= [3] ", "11": "11 \u00a9 ucles 2014 0607/11/m/j/14 12 diagram 1 diagram 2 diagram 3 diagram 4 (a) draw diagram 4, the next pattern of dots in this sequence. [1] (b) complete this table. diagram number 1 2 3 4 total number of dots 4 [2] (c) find an expression, in terms of n, for the nth term of the sequence. answer (c) [2] ", "12": "12 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge asse ssment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/11/m/j/14 blank page " }, "0607_s14_qp_12.pdf": { "1": " this document consists of 11 printed pages and 1 blank page. ib14 06_0607_12/5rp \u00a9 ucles 2014 [turn over *2400943248* cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/12 paper 1 (core) may/june 2014 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2014 0607/12/m/j/14 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2014 0607/12/m/j/14 [turn over 1 (a) write 107 as a percentage. answer (a) % [1] (b) work out . 4 \u00d7 5 \u2013 6 \u00f7 2 answer (b) [2] (c) write down the prime number in this list. 21 23 25 27 answer (c) [1] (d) write 307 000 in standard form. answer (d) [1] 2 jane chooses a sweet at random from a bag containing 7 mints and 7 toffees. choose one term from the list to best describe the probability that jane chooses a mint. impossible unlikely 50:50 likely certain answer [1] ", "4": "4 \u00a9 ucles 2014 0607/12/m/j/14 3 2x3y xnot to scale (a) write down an expression in x and y for the perimeter of the triangle. simplify your answer. answer (a) [2] (b) using your answer to part (a) find the perimeter when x = 4 and y = 2. answer (b) [2] 4 work out the upper quartile and the lower quartile of this list of numbers. 1 10 4 6 7 6 9 10 9 9 answer upper quartile lower quartile [2] ", "5": "5 \u00a9 ucles 2014 0607/12/m/j/14 [turn over 5 \u20133 \u20132 \u201310 123 \u20138\u20136 \u20137\u20135\u20134\u20133\u20132\u2013112345y x the diagram shows the line y = 3x \u2013 5. (a) on the same diagram, draw the line y = \u20132. [1] (b) write down the co-ordinates of the point of intersection of the lines y = 3x \u2013 5 and y = \u20132. answer (b) ( , ) [1] ", "6": "6 \u00a9 ucles 2014 0607/12/m/j/14 6 a cuboid measures 3 cm by 4 cm by 3 cm. 3 cm4 cm3 cmnot to scale find the volume of the cuboid. give the units of your answer. answer [3] 7 70 centilitresa 100 millilitresd 80 cubic centimetresc 0.45 litresbnot to scale the volume of each of four containers is shown above. list the containers in order of size, starting with the smallest. answer , , , [2] smallest ", "7": "7 \u00a9 ucles 2014 0607/12/m/j/14 [turn over 8 (a) complete the mapping diagram for the function f : x a x + 5. xx + 5 1 ... 27 3 ... [2] (b) here is a different mapping diagram. x 1 27 35 9 for this mapping diagram complete the statement f : x a \u2026\u2026\u2026\u2026\u2026 [2] ", "8": "8 \u00a9 ucles 2014 0607/12/m/j/14 9 work out, giving your answer as a fraction in its lowest terms. (a) 83 + 32 answer (a) [2] (b) 83 \u00d7 32 answer (b) [2] (c) 383 \u2013 132 answer (c) [3] ", "9": "9 \u00a9 ucles 2014 0607/12/m/j/14 [turn over 10 (a) factorise completely. 7 pq + 14 p \u2013 7pt answer (a) [2] (b) expand the brackets and simplify. 10( b \u2013 3a) \u2013 2( a + b) answer (b) [2] ", "10": "10 \u00a9 ucles 2014 0607/12/m/j/14 11 the diagram shows the graph of y = f(x) for \u20133 y x y 1 . \u20134 \u20135 \u20133 \u20132 \u201310 1234 \u20132\u201311234y x on the diagram sketch the graph of y = f(x \u2013 2). [2] ", "11": "11 \u00a9 ucles 2014 0607/12/m/j/14 12 a boat sails for 12 km from a to b on a bearing of 120\u00b0. the boat changes direction and sails for 5 km on a bearing of 030\u00b0 to c. north not to scale north12 km 5 kma bc (a) write down the bearing of a from b. answer (a) [1] (b) work out the distance ac. answer (b) km [3] ", "12": "12 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge asse ssment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/12/m/j/14 blank page " }, "0607_s14_qp_13.pdf": { "1": " this document consists of 10 printed pages and 2 blank pages. ib14 06_0607_13/rp \u00a9 ucles 2014 [turn over *8687489229* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/13 paper 1 (core) may/june 2014 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2014 0607/13/m/j/14 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2014 0607/13/m/j/14 [turn over 1 work out. 2.5 \u00d7 10 \u00f7 5 answer [1] 2 find 3% of $8000 . answer $ [1] 3 (a) write 46.849 correct to 1 decimal place. answer (a) [1] (b) after conversion from euros to dollars, a flight from paris to london costs $59.90235 . write this value correct to 4 significant figures. answer (b) $ [1] ", "4": "4 \u00a9 ucles 2014 0607/13/m/j/14 4 (a) arc circumference diameter radius sector segment label the diagram . use only words from the box above. .. . [3] (b) measure and write down the size of angle abc. a bc answer (b) [1] ", "5": "5 \u00a9 ucles 2014 0607/13/m/j/14 [turn over 5 \u20134 \u20133 \u20132 \u201310 1234 \u20134\u20133\u20132\u201311234y xb c (a) on the grid, plot the point (\u20133, 2). label this point a. [1] (b) write down the co-ordinates of point b. answer (b) ( , ) [1] (c) find the midpoint of bc. answer (c) ( , ) [1] ", "6": "6 \u00a9 ucles 2014 0607/13/m/j/14 6 (a) b c d e fanot to scale the diagram shows a regular hexagon. work out the size of angle abc . show all your working. answer (a) [3] (b) 135\u00b0 not to scale the diagram shows a square and four regular octagons. the interior angle of a regular octagon is 135\u00b0. use angles to explain why the square and octagons fit together with no gaps, as shown in the diagram. answer (b) [2] ", "7": "7 \u00a9 ucles 2014 0607/13/m/j/14 [turn over 7 \u20134 \u20133 \u20132 \u201310 1234 \u20134\u20133\u20132\u201311234y xb a write ab as a column vector. answer\uf8f7\uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec\uf8ec \uf8ed\uf8eb [2] 8 a bag contains 3 red balls, 2 blue balls and 1 yellow ball. a ball is chosen at random. what is the probability that the ball is either red or blue? give your answer as a fraction. answer [1] ", "8": "8 \u00a9 ucles 2014 0607/13/m/j/14 9 (a) complete the mapping diagram for the function f : x a x2. x \u20132 \u20131 0 1 2 x 0142 [2] (b) write down the domain of the mapping in part (a) . answer (b) [1] (c) which of these phrases describes the mapping in part (a) . one-to-one one-to-many many-to-one many-to-many answer (c) [1] ", "9": "9 \u00a9 ucles 2014 0607/13/m/j/14 [turn over 10 \u20136\u20135\u20134\u20133 \u201310\u20139\u20138\u20137 \u20132\u20131 0 123456789 1 0 \u20135\u20134\u20133\u20132\u20131 \u201310\u20139\u20138\u20137\u2013612345678910y xq the diagram shows a quadrilateral q. (a) draw the reflection of q in the y-axis. [2] (b) draw the enlargement of q with centre (0, 0) and scale factor 21. [3] ", "10": "10 \u00a9 ucles 2014 0607/13/m/j/14 11 (a) 3p \u2013 5t = 8 work out the value of 12 p \u2013 20 t. answer (a) [2] (b) solve the following equations. (i) 5x \u2013 7 = 9 + 3 x answer (b) (i) x= [2] (ii) 4 (4x \u2013 5) = 28 answer (b) (ii) x= [3] ", "11": "11 \u00a9 ucles 2014 0607/13/m/j/14 [turn over 12 diagram 1 diagram 2 diagram 3 diagram 4 (a) draw diagram 4, the next pattern of dots in this sequence. [1] (b) complete this table. diagram number 1 2 3 4 total number of dots 4 [2] (c) find an expression, in terms of n, for the nth term of the sequence. answer (c) [2] ", "12": "12 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge asse ssment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/13/m/j/14 blank page " }, "0607_s14_qp_21.pdf": { "1": " this document consists of 8 printed pages. ib14 06_0607_21/rp \u00a9 ucles 2014 [turn over *3698974700* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/21 paper 2 (extended) may/june 2014 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2014 0607/21/m/j/14 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2014 0607/21/m/j/14 [turn over answer all the questions. 1 (a) factorise. x2 \u2013 y2 answer(a) [1] (b) work out. 164 2 \u2013 362 answer(b) [1] 2 (a) simplify. 12 answer(a) [1] (b) solve the equation. cos x = 23 for 0 \u00b0 y x y 90\u00b0 answer(b) x = [1] (c) solve the equation. cos x = 412\u2212 for \u2013180 \u00b0 y x y 180 \u00b0 answer(c) x = or x = [2] ", "4": "4 \u00a9 ucles 2014 0607/21/m/j/14 3 find the highest common factor (hcf) in each list. (a) 24 56 72 answer(a) [1] (b) x3y4 x2y5 x4y2 answer(b) [2] 4 a manufacturer made a profit of 60% when he sold a chair for $20. find the cost of making the chair. answer $ [3] ", "5": "5 \u00a9 ucles 2014 0607/21/m/j/14 [turn over 5 a travel agent displays the following exchange rates. \u00a31 = $1.55 \u00a31 = \u00a5 9.3 (a) change \u00a3200 into dollars ($). answer(a) $ [1] (b) find the number of chinese yuan (\u00a5) received in exchange for $1. answer(b) \u00a5 [2] 6 (a) simplify. 27 75\u2212 answer(a) [2] (b) rationalise the denominator. 2 57 \u2212 answer (b) [2] ", "6": "6 \u00a9 ucles 2014 0607/21/m/j/14 7 y x02468 1 0 1 212 10 8642 (a) on the grid, draw the following lines. x = 1 y = 12 \u2013 2 x for 0 y x y 6 4y + 3x = 36 for 0 y x y 12 [5] (b) on the grid, label the region r containing the points which satisfy these three inequalities. x [ 1 y y 12 \u2013 2 x 4y + 3x [ 36 [1] (c) (i) find the minimum value of x + y in the region r. answer (c)(i) [1] (ii) find the co-ordinates of the point corresponding to this minimum value. answer (c)(ii) ( , ) [1] ", "7": "7 \u00a9 ucles 2014 0607/21/m/j/14 [turn over 8 a bag contains 10 discs, 7 are red and 3 are green. a disc is picked at random and not replaced. a second disc is then picked at random. (a) complete the tree diagram. one probability is shown on the diagram. red greenred green greenred 3 10 [2] (b) find the probability that (i) both discs are red, answer (b)(i) [2] (ii) at least one disc is red. answer (b)(ii) [3] questions 9 and 10 are printed on the next page. ", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge asse ssment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/21/m/j/14 9 in one month there were 120 new cars sold in a town. the table shows how many cars of each colour were sold. colour red blue white green silver black yellow number 17 20 24 x 28 17 x (a) find the value of x. answer(a) [1] (b) find the relative frequency of white cars, giving your answer as a fraction in its lowest terms. answer(b) [2] 10 solve the equation. 7)3 4(+x = )3 4(7 +x answe r [3] " }, "0607_s14_qp_22.pdf": { "1": " this document consists of 10 printed pages and 2 blank pages. ib14 06_0607_22/2rp \u00a9 ucles 2014 [turn over *8579531881* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/22 paper 2 (extended) may/june 2014 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2014 0607/22/m/j/14 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2014 0607/22/m/j/14 [turn over answer all the questions. 1 (a) 6 54321 \u20131\u20132\u20133\u20134 \u20134\u2013 3\u2013 2\u2013 1 1 0 23456y xb b is the point (1, 2) and = \uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec \uf8ed\uf8eb \u221234. plot the point c on the grid. [1] (b) p = \uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec \uf8ed\uf8eb 32 q = \uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec \uf8ed\uf8eb \u221214. write 2 p \u2013 q as a column vector. answer(b) \uf8f7\uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec\uf8ec \uf8ed\uf8eb [2] ", "4": "4 \u00a9 ucles 2014 0607/22/m/j/14 2 (a) shade one small square so that this shape has exactly 1 line of symmetry. [1] (b) shade three small squares so that this shape has exactly 2 lines of symmetry. [2] (c) shade two small squares so that this shape has rotational symmetry of order 4. [2] ", "5": "5 \u00a9 ucles 2014 0607/22/m/j/14 [turn over 3 in a year group of a school, students study one subject from art, music or dance. the table shows the choices of the 180 students. subject number of students art 85 music 50 dance 45 use the circle to draw a pie chart to show this information. [3] ", "6": "6 \u00a9 ucles 2014 0607/22/m/j/14 4 write each set of numbers in order starting with the smallest. (a) 31 0.3 3.0 0.29 33% answer(a) , , , , [2] smallest (b) 52 25 ()35 55 answer(b) , , , [2] smallest 5 expand the brackets and simplify. (a) 2x 2(3x + 5xy) answer(a) [2] (b) (2a \u2013 3b)(a \u2013 2b) answer (b) [3] ", "7": "7 \u00a9 ucles 2014 0607/22/m/j/14 [turn over 6 a = 34 \u00d7 52 b = 22 \u00d7 33 \u00d7 52 c = 32 \u00d7 53 \u00d7 7 (a) find (i) a, answer(a) (i) [1] (ii) ab. answer(a) (ii) [1] (b) leaving your answer as the product of prime factors, find (i) the highest common factor (hcf) of a, b and c, answer(b) (i) [1] (ii) the lowest common multiple (lcm) of a, b and c. answer(b) (ii) [2] ", "8": "8 \u00a9 ucles 2014 0607/22/m/j/14 7 ann, babar, chan and demi each throw the same biased die. they want to find the probability of throwing a six with this die. they each throw the die a different number of times. these are their results. ann babar chan demi number of throws 200 20 100 500 number of sixes 60 5 30 200 (a) complete the table below to show the relative frequencies of their results. write your answers as decimals. ann babar chan demi relative frequency of throwing a six [2] (b) give a reason why demi's result gives the best estimate of the probability of throwing a six with the biased die. answer(b) [1] (c) estimate the number of times that demi could expect to get a six if he throws the die 1600 times. answer(c) [1] ", "9": "9 \u00a9 ucles 2014 0607/22/m/j/14 [turn over 8 y is proportional to the square root of x. when x = 16, y = 10. (a) find an equation connecting x and y. answer(a) [2] (b) find the value of x when y = 1. answer(b) [2] 9 work out the following, giving your answers in standard form. (a) (4.6 \u00d7 10 \u20135) + (3 \u00d7 10\u20136) answer(a) [2] (b) (4.6 \u00d7 10\u20135) \u00d7 (3 \u00d7 10\u20136) answer(b) [2] ", "10": "10 \u00a9 ucles 2014 0607/22/m/j/14 10 write 23 +x \u2013 325 +x as a single fraction in its simplest form. answe r [3] ", "11": "11 \u00a9 ucles 2014 0607/22/m/j/14 blank page", "12": "12 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge a ssessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/22/m/j/14 blank page " }, "0607_s14_qp_23.pdf": { "1": " this document consists of 8 printed pages. ib14 06_0607_23/2rp \u00a9 ucles 2014 [turn over *8932327307* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/23 paper 2 (extended) may/june 2014 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2014 0607/23/m/j/14 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2014 0607/23/m/j/14 [turn over answer all the questions. 1 the price of a book was $7.00 . it is reduced by 20%. find the new price of the book. answer $ [2] 2 (a) write 0.0063 in standard form. answer(a) [1] (b) 5.7 \u00d7 109 + 2.4 \u00d7 108 = k \u00d7 109 find the value of k. answer(b) k = [2] 3 find the next term in each of these sequences. (a) 3, 5, 8, 12, 17, \u2026\u2026\u2026\u2026\u2026\u2026\u2026 [1] (b) 100, 91, 80, 67, 52, \u2026\u2026\u2026\u2026\u2026\u2026\u2026 [1] (c) 4, 12, 36, 108, 324, \u2026\u2026\u2026\u2026\u2026\u2026\u2026 [1] ", "4": "4 \u00a9 ucles 2014 0607/23/m/j/14 4 2y 6x a small square of side 2 y is inside a larger square of side 6 x. (a) find an expression for the shaded area, a, in terms of x and y. answer(a) a = [2] (b) rearrange your answer to part (a) to write x in terms of y and a. answer(b) x = [3] 5 (a) find 125 0 . answer(a) [1] (b) simplify 3 2727y . answer(b) [2] ", "5": "5 \u00a9 ucles 2014 0607/23/m/j/14 [turn over 6 (a) d c b ax\u00b0y\u00b0 50\u00b0 98\u00b0not to scale a, b, c and d lie on the circumference of a circle. angle abc = 98\u00b0 and angle acb = 50\u00b0. find the value of x and the value of y. answer(a) x = [1] y = [1] (b) op ts r qw\u00b0 v\u00b0not to scale65\u00b0 p, q, r and s lie on the circumference of a circle, centre o. tp is a tangent to the circle at p and pr is a diameter. find the value of v and the value of w. answer(b) v = [1] w = [1] ", "6": "6 \u00a9 ucles 2014 0607/23/m/j/14 7 y varies directly as the square of x. when x = 8, y = 40. find y when x =12. answe r [3] 8 (a) simplify )122)(223( + \u2212 . answer(a) [3] (b) rationalise the denominator of 510. answer(b) [2] ", "7": "7 \u00a9 ucles 2014 0607/23/m/j/14 [turn over 9 (a) y x2 1 \u20131 \u201320 \u20134\u2013 3\u2013 2\u2013 1 1 2 3 4 the diagram shows the graph of y = f(x). on the same diagram, sketch the graph of y = 2f( x). [1] (b) y x2 1 \u20131 \u201320 \u20134\u2013 3\u2013 2\u2013 1 1 2 3 4 the diagram shows the graph of y = f(x). on the same diagram, sketch the graph of y = f(x + 1). [1] 10 31 x find the exact value of cos x. answe r [3] questions 11 and 12 are printed on the next page.", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge a ssessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/23/m/j/14 11 u pr qa b cde the venn diagram shows the sets p, q and r. complete the following statements using set notation. (a) p \u2026\u2026.. r = { a, b, c, d, e} [1] (b) q \u2026\u2026.. r = \u2205 [1] (c) e \u2026\u2026.. r [1] (d) p \u2026\u2026.. q = p [1] 12 f( x) = x + 3 and g( x) = x12, 0\u2260x find (a) g(f (1)), answer(a) [2] (b) g \u20131(x). answer(b) [1] " }, "0607_s14_qp_31.pdf": { "1": " this document consists of 16 printed pages. ib14 06_0607_31/3rp \u00a9 ucles 2014 [turn over *1948255737* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/31 paper 3 (core) may/june 2014 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96. ", "2": "2 \u00a9 ucles 2014 0607/31/m/j/14 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2014 0607/31/m/j/14 [turn over answer all the questions. 1 21 22 23 24 25 26 27 from the list above, write down (a) a square number, answer(a) [1] (b) a multiple of 7, answer(b) [1] (c) a factor of 66, answer(c) [1] (d) a cube number, answer(d) [1] (e) a prime number. answer(e) [1] 2 2 p + 3q = r (a) find r when p = 3.1 and q = 2.5 . answer(a) r = [2] (b) find p when q = \u20131 and r = 4. answer(b) p = [2] (c) rearrange 2 p + 3q = r to make q the subject. answer(c) q = [2] ", "4": "4 \u00a9 ucles 2014 0607/31/m/j/14 3 (a) 41, 37, 33, 29, 25, \u2026\u2026 find the next two terms in this sequence. answer(a) and [2] (b) find 60. give your answer correct to 1 decimal place. answer(b) [2] (c) write 0.28 as a fraction in its simplest form. answer(c) [1] (d) divide 504 in the ratio 7 : 2 . answer(d) : [2] (e) write the following numbers in order, starting with the smallest. 81 1.3 \u00d7 10\u20131 14% 0.11 answer(e) , , , [2] smallest ", "5": "5 \u00a9 ucles 2014 0607/31/m/j/14 [turn over 4 a dc nb m20\u00b0not to scale abcd is a rectangle. amn and dcn are straight lines and angle bam = 20\u00b0. find the size of (a) angle amb , answer(a) [1] (b) angle mnc , answer(b) [1] (c) angle bmn . answer(c) [1] ", "6": "6 \u00a9 ucles 2014 0607/31/m/j/14 5 jeffrey has 30 packets of raisins. the number of raisins in each packet is shown below. 39 38 41 40 38 39 37 42 38 38 39 41 41 40 39 38 37 43 38 39 40 40 39 38 41 38 42 43 39 37 (a) complete the frequency table. number of raisins frequency 37 3 38 39 40 4 41 42 43 2 [2] (b) complete the bar chart to show this information. 10 9 8765432 1 0 frequency number of raisins in a packet37 38 39 40 41 42 43 [2] ", "7": "7 \u00a9 ucles 2014 0607/31/m/j/14 [turn over (c) find (i) the range, answer(c) (i) [1] (ii) the mode, answer(c) (ii) [1] (iii) the median, answer(c) (iii) [1] (iv) the mean. answer(c) (iv) [1] (d) jeffrey opens one packet at random. find the probability that there are more than 40 raisins in this packet. answer(d) [1] ", "8": "8 \u00a9 ucles 2014 0607/31/m/j/14 6 rana gives surfing lessons. she charges $50 per hour. (a) rana works 35 hours each week. calculate how much she earns each week. answer(a) $ [1] (b) rana spends $1300 each week. find how much she has left each week. answer(b) $ [1] (c) rana gives 10% of the money she has left to charity and saves the remainder. (i) calculate the amount that rana gives to charity each week. answer(c) (i) $ [2] (ii) calculate the amount that rana saves each week. answer(c) (ii) $ [1] (d) rana has 6 weeks holiday each year. she does not earn any money during her holiday. find the amount of money that rana saves in a year (52 weeks). answer(d) $ [2] ", "9": "9 \u00a9 ucles 2014 0607/31/m/j/14 [turn over 7 max has a die with faces numbered 1 to 6. he rolls the die 120 times. the pie chart shows the results. 5 6 1 234x\u00b030\u00b0 30\u00b0 30\u00b060\u00b0not to scale (a) find the value of x. answer(a) x = [1] (b) find the number of times that max rolled a 4. answer(b) [2] (c) is the die biased? give a reason for your answer. answer(c) because [2] ", "10": "10 \u00a9 ucles 2014 0607/31/m/j/14 8 the scatter diagram shows the age, in years, and number of heart beats per minute of 20 people. (a) describe the type of correlation. answer(a) [1] (b) the mean age of the twenty people is 42 and the mean number of heart beats per minute is 80. plot this point on the scatter diagram. [1] (c) draw the line of best fit by eye. [2] (d) heidi is 28 years old. estimate heidi\u2019s number of heart beats per minute. answer(d) [1] 100 90 8070605040302010 10 20 30 40 age (years)50 60 70 800heart beats per minute", "11": "11 \u00a9 ucles 2014 0607/31/m/j/14 [turn over 9 the distance between mumbai and ahmedabad is 494 kilometres. (a) an express train takes 6.5 hours for the journey. find the average speed of the train in kilometres per hour. answer(a) km/h [1] (b) a slow train travels at an average speed of 45 kilometres per hour. find the time that this train takes to travel the 494 kilometres. give your answer correct to the nearest minute. answer(b) h min [2] 10 marcina has a box containing 20 mathematical shapes. s is the set of shapes with equal sides. a is the set of shapes with equal angles. n( s) = 8, n( a) = 7 and n( s \u2229 a) = 3. (a) complete the venn diagram. u sa [2] (b) write down the number of shapes that do not have equal sides or equal angles. answer(b) [2] (c) write down the mathematical name for a shape that could be in the set s \u2229 a. answer(c) [1] (d) shade the region a \u2229 s\u2032. [1] ", "12": "12 \u00a9 ucles 2014 0607/31/m/j/14 11 the cost of a dress is $ d. the cost of a pair of shoes is $ s. adel buys 2 dresses and 4 pairs of shoes for $1100. so, 2 d + 4s = 1100. (a) carey buys 5 dresses and 4 pairs of shoes for $1850. write this as an equation in terms of d and s. answer(a) [1] (b) solve the equations to find the cost of one dress and the cost of one pair of shoes. answer(b) dress $ pair of shoes $ [2] ", "13": "13 \u00a9 ucles 2014 0607/31/m/j/14 [turn over 12 k ljnot to scale 11 m6 m (a) find the length jk. answer(a) m [2] (b) use trigonometry to calculate angle kjl. answer(b) [2] ", "14": "14 \u00a9 ucles 2014 0607/31/m/j/14 13 18 mm 40 mm30 mm 80 mmnot to scale a gold bar is in the shape of a prism. the cross-section is a trapezium. (a) find the area of the cross-section of the gold bar. answer(a) mm2 [3] (b) find the total surface area of the gold bar. answer(b) mm2 [5] (c) find the volume of the gold bar. answer(c) mm3 [1] (d) write your answer to part (c) in cm3. answer(d) cm3 [1] (e) the gold bar is melted and made into a cylinder with radius 2 cm. calculate the height of this cylinder. answer(e) cm [2] ", "15": "15 \u00a9 ucles 2014 0607/31/m/j/14 [turn over 14 a bto r12 cm8 cmnot to scale the diagram shows a circle, centre o, radius 8 cm. chord rt is 12 cm and atb is a tangent to the circle at t. (a) use trigonometry to calculate angle rot. answer(a) [3] (b) find angle rtb. answer(b) [2] (c) calculate the length of arc rt. answer(c) cm [2] question 15 is printed on the next page. ", "16": "16 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the p ublisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge assess ment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/31/m/j/14 15 y x 4 \u20134 \u201339 0 )1 (3)f(2 \u2212+=xxx (a) on the diagram, sketch the graph of y = f(x) between x = \u20134 and x = 4. [4] (b) find the co-ordinates of the local minimum point. answer(b) ( , ) [1] (c) write down the equation of the vertical asymptote. answer(c) [1] (d) write down the range of f( x) for x < 1. answer(d) [2] (e) g(x) = 4 x + 1 on the diagram, sketch the graph of y = g( x). [2] (f) find the x co-ordinates of the points of intersection of y = f(x) and y = g( x). answer (f) x = x = [2] " }, "0607_s14_qp_32.pdf": { "1": " this document consists of 16 printed pages. ib14 06_0607_32/3rp \u00a9 ucles 2014 [turn over *6364749909* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/32 paper 3 (core) may/june 2014 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96. ", "2": "2 \u00a9 ucles 2014 0607/32/m/j/14 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2014 0607/32/m/j/14 [turn over answer all the questions. 1 (a) round 245 to the nearest hundred. answer(a) [1] (b) write down a square number between 40 and 60. answer(b) [1] (c) write 0.01 as a percentage. answe r(c) [1] (d) write down all the factors of 18. answer(d) [2] (e) write down the lowest common multiple of 8 and 12. answer(e) [1] (f) write 2114 as a fraction in its lowest terms. answer(f) [1] (g) work out 35% of 48. answer(g) [2] (h) write down a prime number between 10 and 20. answer(h) [1] ", "4": "4 \u00a9 ucles 2014 0607/32/m/j/14 2 ab c (a) write down the mathematical name of shape a, shape b and shape c. answer(a) a b c [3] (b) on each shape, draw any lines of symmetry. [3] (c) for each shape, write down the order of rotational symmetry. answer(c) a b c [3] ", "5": "5 \u00a9 ucles 2014 0607/32/m/j/14 [turn over 3 (a) q\u00b0p\u00b0 r\u00b0 s\u00b058\u00b0 39\u00b0not to scale three straight lines cross at a point. find the values of p, q, r and s. answer(a) p = q = r = s = [4] (b) d \u00b0e\u00b0 c\u00b0 114\u00b0not to scale a straight line intersects three parallel lines. find the values of c, d and e. answer(b) c = d = e = [3] ", "6": "6 \u00a9 ucles 2014 0607/32/m/j/14 4 (a) find the value of 3p \u2013 2q when p = 1.5 and q = \u20131.2 . answer(a) [2] (b) solve the equation. 3x = 6 answer(b) x = [1] (c) solve the simultaneous equations. x \u2013 y = 10 2 x + y = 2 answer(c) x = y = [2] ", "7": "7 \u00a9 ucles 2014 0607/32/m/j/14 [turn over 5 py x8 7654321 \u20131\u20132\u20133\u20134\u20135\u20136\u20137 \u20138\u20136 \u20135 \u20138\u2013 7 \u2013 4\u2013 3\u2013 2\u2013 1 2 3 1 0 45678 the diagram shows a kite, p. (a) reflect p in the x-axis. label the image a. [1] (b) rotate p through 90 \u00b0 anticlockwise about the origin. label the image b. [2] (c) translate p by the vector \uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec \uf8ed\uf8eb \u2212\u2212 76. label the image c. [2] ", "8": "8 \u00a9 ucles 2014 0607/32/m/j/14 6 jin owns a chinese restaurant. the table shows the number of orders in one day for rice and noodles. cost ($) number of orders plain rice 1.60 20 fried rice 1.75 35 noodles 1.60 25 chinese noodles 1.85 15 (a) write down the ratio 20 : 35 : 25 : 15 in its simplest form. answer(a) : : : [2] (b) the table shows the cost of rice and noodles. calculate the total income from the orders of rice and noodles. answer(b) $ [3] (c) the total income for that day was $1500. work out the income from the rice and noodles as a percentage of the total income. answer(c) % [1] ", "9": "9 \u00a9 ucles 2014 0607/32/m/j/14 [turn over 7 ibrahim ran 12 km for charity. for each kilometre he received $8.25 . (a) find how much money ibrahim raised for charity. answer(a) $ [1] (b) ibrahim took 90 minutes to run the 12 km. find his speed in kilometres per hour. answer(b) km/h [2] 8 these are the first four numbers in a sequence. 12 19 26 33 (a) write down the next two numbers in this sequence. answer(a) , [2] (b) find the nth term of this sequence. answer(b) [2] ", "10": "10 \u00a9 ucles 2014 0607/32/m/j/14 9 ren\u00e9 has 6 oranges and 5 plums in a bag. he picks out a fruit at random and eats it. (a) find the probability that the fruit is an orange. answer(a) [1] (b) ren\u00e9 picks out a second fruit at random and eats it. complete the tree diagram. orangefirst fruit second fruit plumorange plum plumorange [3] (c) find the probability that ren\u00e9 eats two oranges. answer(c) [2] ", "11": "11 \u00a9 ucles 2014 0607/32/m/j/14 [turn over 10 y x10 \u201312\u20132 40 f( x) = 2 x2 \u2013 5x \u2013 8 (a) on the diagram, sketch the graph of y = f(x) between x = \u20132 and x = 4 . [2] (b) find the zeros of f( x). answer(b) , [2] (c) find the co-ordinates of the local minimum point. answer(c) ( , ) [2] (d) g(x) = \u20132 x \u2013 3 on the diagram, sketch the graph of y = g( x). [2] (e) solve f( x) = g( x). answer(e) x = or x = [2] ", "12": "12 \u00a9 ucles 2014 0607/32/m/j/14 11 15 cm 15 cm 18 cm 18 cm 18 cmnot to scale the diagram shows the front of a bird box. a circular hole of radius 2.1 cm is cut out from the front. show that the area of the front is 418 cm2, correct to 3 significant figures. [6] ", "13": "13 \u00a9 ucles 2014 0607/32/m/j/14 [turn over 12 (a) ayako invests $50 000 at a rate of 3.4% per year simple interest. calculate the total amount that ayako has at the end of 6 years. answer(a) $ [3] (b) mayumi invests $48 000 at a rate of 3.25% per year compound interest. calculate the total amount that mayumi has at the end of 6 years. give your answer correct to the nearest dollar. answer(b) $ [3] 13 u soccer tennis seven children, a, b, c, d, e, f and g, are asked whether they play soccer or tennis. a, e and g play soccer. a, b and c play tennis. d and f do not play soccer or tennis. (a) complete the venn diagram. [2] (b) one of the children is chosen at random. find the probability that (i) the child plays both soccer and tennis, answer(b) (i) [1] (ii) the child does not play soccer or tennis. answer(b) (ii) [1] ", "14": "14 \u00a9 ucles 2014 0607/32/m/j/14 14 the frequency table shows the masses, in kilograms, of 30 dogs. mass ( x kg) frequency 0 < x y 10 6 10 < x y 20 8 20 < x y 30 7 30 < x y 40 6 40 < x y 50 3 (a) write down the mid-value of the interval 0 < x y 10 . answer(a) [1] (b) calculate an estimate of the mean mass of the 30 dogs. answer(b) kg [2] (c) complete the cumulative frequency table. mass ( x kg) cumulative frequency x y 10 6 x y 20 x y 30 x y 40 x y 50 30 [1] ", "15": "15 \u00a9 ucles 2014 0607/32/m/j/14 [turn over (d) use your answer to part (c) to complete the cumulative frequency curve. 30 252015 10 5 10 20 mass (kg)30 40 500xcumulative frequency [3] (e) use your graph to find (i) the median, answer(e) (i) kg [1] (ii) the lower quartile, answer(e) (ii) kg [1] (iii) the upper quartile. answer(e) (iii) kg [1] question 15 is printed on the next page. ", "16": "16 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge a ssessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/32/m/j/14 15 y x3 21 \u20131\u20132\u20133\u20134\u20135\u201360 \u2013 1 12345 \u20132 \u20133 \u20134 \u20135 (a) plot and label the points a(\u20131, \u20135) and b(3, 1). [2] (b) find the gradient of ab. answer(b) [2] (c) find the equation of the line parallel to ab passing through the point (0, 0). answer(c) [1] " }, "0607_s14_qp_33.pdf": { "1": " this document consists of 16 printed pages. ib14 06_0607_33/fp \u00a9 ucles 2014 [turn over *0284932901* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/33 paper 3 (core) may/june 2014 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96. ", "2": "2 \u00a9 ucles 2014 0607/33/m/j/14 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2014 0607/33/m/j/14 [turn over answer all the questions. 1 21 22 23 24 25 26 27 from the list above, write down (a) a square number, answer(a) [1] (b) a multiple of 7, answer(b) [1] (c) a factor of 66, answer(c) [1] (d) a cube number, answer(d) [1] (e) a prime number. answer(e) [1] 2 2 p + 3q = r (a) find r when p = 3.1 and q = 2.5 . answer(a) r = [2] (b) find p when q = \u20131 and r = 4. answer(b) p = [2] (c) rearrange 2 p + 3q = r to make q the subject. answer(c) q = [2] ", "4": "4 \u00a9 ucles 2014 0607/33/m/j/14 3 (a) 41, 37, 33, 29, 25, \u2026\u2026 find the next two terms in this sequence. answer(a) and [2] (b) find 60. give your answer correct to 1 decimal place. answer (b) [2] (c) write 0.28 as a fraction in its simplest form. answer(c) [1] (d) divide 504 in the ratio 7 : 2 . answer(d) : [2] (e) write the following numbers in order, starting with the smallest. 81 1.3 \u00d7 10\u20131 14% 0.11 answer(e) , , , [2] smallest ", "5": "5 \u00a9 ucles 2014 0607/33/m/j/14 [turn over 4 a dc nb m20\u00b0not to scale abcd is a rectangle. amn and dcn are straight lines and angle bam = 20\u00b0. find the size of (a) angle amb , answer(a) [1] (b) angle mnc , answer(b) [1] (c) angle bmn . answer(c) [1] ", "6": "6 \u00a9 ucles 2014 0607/33/m/j/14 5 jeffrey has 30 packets of raisins. the number of raisins in each packet is shown below. 39 38 41 40 38 39 37 42 38 38 39 41 41 40 39 38 37 43 38 39 40 40 39 38 41 38 42 43 39 37 (a) complete the frequency table. number of raisins frequency 37 3 38 39 40 4 41 42 43 2 [2] (b) complete the bar chart to show this information. 10 9 8765432 1 0 frequency number of raisins in a packet37 38 39 40 41 42 43 [2] ", "7": "7 \u00a9 ucles 2014 0607/33/m/j/14 [turn over (c) find (i) the range, answer(c) (i) [1] (ii) the mode, answer(c) (ii) [1] (iii) the median, answer(c) (iii) [1] (iv) the mean. answer(c) (iv) [1] (d) jeffrey opens one packet at random. find the probability that there are more than 40 raisins in this packet. answer(d) [1] ", "8": "8 \u00a9 ucles 2014 0607/33/m/j/14 6 rana gives surfing lessons. she charges $50 per hour. (a) rana works 35 hours each week. calculate how much she earns each week. answer(a) $ [1] (b) rana spends $1300 each week. find how much she has left each week. answer(b) $ [1] (c) rana gives 10% of the money she has left to charity and saves the remainder. (i) calculate the amount that rana gives to charity each week. answer(c) (i) $ [2] (ii) calculate the amount that rana saves each week. answer(c) (ii) $ [1] (d) rana has 6 weeks holiday each year. she does not earn any money during her holiday. find the amount of money that rana saves in a year (52 weeks). answer(d) $ [2] ", "9": "9 \u00a9 ucles 2014 0607/33/m/j/14 [turn over 7 max has a die with faces numbered 1 to 6. he rolls the die 120 times. the pie chart shows the results. 5 6 1 234x\u00b030\u00b0 30\u00b0 30\u00b060\u00b0not to scale (a) find the value of x. answer(a) x = [1] (b) find the number of times that max rolled a 4. answer(b) [2] (c) is the die biased? give a reason for your answer. answer(c) because [2] ", "10": "10 \u00a9 ucles 2014 0607/33/m/j/14 8 the scatter diagram shows the age, in years, and number of heart beats per minute of 20 people. (a) describe the type of correlation. answer(a) [1] (b) the mean age of the twenty people is 42 and the mean number of heart beats per minute is 80. plot this point on the scatter diagram. [1] (c) draw the line of best fit by eye. [2] (d) heidi is 28 years old. estimate heidi\u2019s number of heart beats per minute. answer(d) [1] 100 90 8070605040302010 10 20 30 40 age (years)50 60 70 800heart beats per minute", "11": "11 \u00a9 ucles 2014 0607/33/m/j/14 [turn over 9 the distance between mumbai and ahmedabad is 494 kilometres. (a) an express train takes 6.5 hours for the journey. find the average speed of the train in kilometres per hour. answer(a) km/h [1] (b) a slow train travels at an average speed of 45 kilometres per hour. find the time that this train takes to travel the 494 kilometres. give your answer correct to the nearest minute. answer(b) h min [2] 10 marcina has a box containing 20 mathematical shapes. s is the set of shapes with equal sides. a is the set of shapes with equal angles. n( s) = 8, n( a) = 7 and n( s \u2229 a) = 3. (a) complete the venn diagram. u sa [2] (b) write down the number of shapes that do not have equal sides or equal angles. answer(b) [2] (c) write down the mathematical name for a shape that could be in the set s \u2229 a. answer(c) [1] (d) shade the region a \u2229 s\u2032. [1] ", "12": "12 \u00a9 ucles 2014 0607/33/m/j/14 11 the cost of a dress is $ d. the cost of a pair of shoes is $ s. adel buys 2 dresses and 4 pairs of shoes for $1100. so, 2 d + 4s = 1100. (a) carey buys 5 dresses and 4 pairs of shoes for $1850. write this as an equation in terms of d and s. answer(a) [1] (b) solve the equations to find the cost of one dress and the cost of one pair of shoes. answer(b) dress $ pair of shoes $ [2] ", "13": "13 \u00a9 ucles 2014 0607/33/m/j/14 [turn over 12 k ljnot to scale 11 m6 m (a) find the length jk. answer(a) m [2] (b) use trigonometry to calculate angle kjl. answer(b) [2] ", "14": "14 \u00a9 ucles 2014 0607/33/m/j/14 13 18 mm 40 mm30 mm 80 mmnot to scale a gold bar is in the shape of a prism. the cross-section is a trapezium. (a) find the area of the cross-section of the gold bar. answer(a) mm2 [3] (b) find the total surface area of the gold bar. answer(b) mm2 [5] (c) find the volume of the gold bar. answer(c) mm3 [1] (d) write your answer to part (c) in cm3. answer(d) cm3 [1] (e) the gold bar is melted and made into a cylinder with radius 2 cm. calculate the height of this cylinder. answer(e) cm [2] ", "15": "15 \u00a9 ucles 2014 0607/33/m/j/14 [turn over 14 a bto r12 cm8 cmnot to scale the diagram shows a circle, centre o, radius 8 cm. chord rt is 12 cm and atb is a tangent to the circle at t. (a) use trigonometry to calculate angle rot. answer(a) [3] (b) find angle rtb. answer(b) [2] (c) calculate the length of arc rt. answer(c) cm [2] question 15 is printed on the next page. ", "16": "16 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the p ublisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge a ssessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/33/m/j/14 15 y x 4 \u20134 \u201339 0 )1 (3)f(2 \u2212+=xxx (a) on the diagram, sketch the graph of y = f(x) between x = \u20134 and x = 4. [4] (b) find the co-ordinates of the local minimum point. answer(b) ( , ) [1] (c) write down the equation of the vertical asymptote. answer(c) [1] (d) write down the range of f( x) for x < 1. answer(d) [2] (e) g(x) = 4 x + 1 on the diagram, sketch the graph of y = g( x). [2] (f) find the x co-ordinates of the points of intersection of y = f(x) and y = g( x). answer(f) x = x = [2] " }, "0607_s14_qp_41.pdf": { "1": " this document consists of 22 printed pages and 2 blank pages. ib14 06_0607_41/5rp \u00a9 ucles 2014 [turn over *7508068777* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/41 paper 4 (extended) may/june 2014 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120. ", "2": "2 \u00a9 ucles 2014 0607/41/m/j/14 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2014 0607/41/m/j/14 [turn over answer all the questions. 1 you may use these axes to help you answer this question. 0y x the transformation p is a rotation of 90 \u00b0 clockwise about the origin. the transformation q is a reflection in the line y = \u2013x. (a) find the co-ordinates of the image of the point (4, 1) under the transformation p. answer(a) ( , ) [1] (b) find the co-ordinates of the image of the point (4, 1) under the transformation q. answer(b) ( , ) [1] (c) find the co-ordinates of the image of the point ( x, y) under the transformation p followed by the transformation q. answer(c) ( , ) [2] (d) describe fully the single transformation equivalent to p followed by q. answer(d) [2] ", "4": "4 \u00a9 ucles 2014 0607/41/m/j/14 2 the points a(3, 4), b(9, 2) and c(6, 7) are shown on the diagram below. 2 4 6 8 10 12 14 1610 8 642 0y xa bc (a) write as a column vector. answer(a) \uf8f7\uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec\uf8ec \uf8ed\uf8eb [1] (b) find the gradient of the line ab. answer(b) [1] (c) find the equation of the line ab. give your answer in the form y = mx + c. answer(c) y = [2] ", "5": "5 \u00a9 ucles 2014 0607/41/m/j/14 [turn over (d) c is the midpoint of am. find the co-ordinates of m. answer(d) ( , ) [2] (e) the point n is such that abnm is a parallelogram. find the co-ordinates of n. answer(e) ( , ) [2] (f) find the length bm. answer(f) [1] ", "6": "6 \u00a9 ucles 2014 0607/41/m/j/14 3 a bc e dnot to scale in the diagram, bc is parallel to de and ba is parallel to dc. ace is a straight line. bc = 3.5 cm, de = 6.5 cm and ae = 12 cm. (a) complete the statement. triangle dec is similar to triangle [1] (b) calculate the length ac. answer(b) cm [3] ", "7": "7 \u00a9 ucles 2014 0607/41/m/j/14 [turn over (c) the area of triangle abc is 7 cm2. calculate the area of triangle cde. answer(c) cm2 [2] ", "8": "8 \u00a9 ucles 2014 0607/41/m/j/14 4 north b ac d39\u00b06.37 km 4.23 km 7.42 kmnot to scale the diagram shows four points a, b, c and d. b is due north of a and c is due east of a. ac = 4.23 km, ad = 7.42 km, bc = 6.37 km and angle cad = 39 \u00b0. (a) find the bearing of (i) d from a, answer(a) (i) [1] (ii) a from d. answer(a) (ii) [1] ", "9": "9 \u00a9 ucles 2014 0607/41/m/j/14 [turn over (b) calculate angle abc . answer(b) [2] (c) calculate cd. answer(c) km [3] (d) angle acd is obtuse. find the bearing of d from c. answer(d) [4] ", "10": "10 \u00a9 ucles 2014 0607/41/m/j/14 5 (a) solve the equation. 3log2 \u2013 2log3 + log x = 3log4 answer (a) x = [3] (b) solve the simultaneous equations. 5 x \u2013 4y = 1 4 x \u2013 5y = 8 answer(b) x = y = [4] ", "11": "11 \u00a9 ucles 2014 0607/41/m/j/14 [turn over 6 0\u20132 \u20131010 2y x (a) on the diagram, sketch the graph of y = f(x), where f( x) = |4 x2 \u2013 9| between x = \u20132 and x = 2 . [2] (b) write down the x co-ordinates where the curve meets the x-axis. answer(b) x = or x = [1] (c) the line y = 3x \u2013 2 intersects the curve y = |4x 2 \u2013 9| twice. find the y co-ordinates of the points of intersection. answer(c) y = or y = [2] (d) (i) find the value of k when the line y = k meets the curve y = |4x 2 \u2013 9| three times. answer(d) (i) [1] (ii) find the range of values of k when the line y = k meets the curve y = |4x 2 \u2013 9| four times. answe r(d)(ii) [2] ", "12": "12 \u00a9 ucles 2014 0607/41/m/j/14 7 a library allows each member to have up to 10 books on loan. the table shows the number of books currently on loan to a random sample of 75 members. number of books on loan 0 1 2 3 4, 5 or 6 7 8 or 9 10 number of members 7 4 20 14 10 8 8 4 (a) write down the mode. answer(a) [1] (b) work out the range. answer(b) [1] (c) find the median. answer(c) [1] (d) find the interquartile range. answer(d) [2] (e) calculate an estimate of the mean. answer(e) [2] (f) two members are chosen at random. find the probability that they both have at least seven books on loan. answer(f) [2] ", "13": "13 \u00a9 ucles 2014 0607/41/m/j/14 [turn over 8 the venn diagram shows the sets a, b and c. u ab c u = {25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36} a = {prime numbers} b = {square numbers} c = {multiples of 4} (a) list the elements of set a. answer(a) [1] (b) write all the elements of u in the correct parts of the venn diagram above. [3] (c) list the elements of ( a \u222a c)'. answer(c) [1] (d) find n(( a \u222a c) \u2229 b' ). answer(d) [1] ", "14": "14 \u00a9 ucles 2014 0607/41/m/j/14 9 (a) find the next term and the nth term in each of the following sequences. (i) 1, 8, 27, 64, 125, \u2026.. answer(a) (i) next term = n th term = [2] (ii) 4, 10, 18, 28, 40, \u2026.. answer(a) (ii) next term = n th term = [3] (b) use your results to part (a) , to find the next term and the nth term in the following sequence. 6, 19, 46, 93, 166, \u2026.. answer(b) next term = n th term = [3] ", "15": "15 \u00a9 ucles 2014 0607/41/m/j/14 [turn over 10 paulo bought a car on january 1st 2010. by january 1st 2011 the value of the car had reduced by 20%. by january 1st 2012 the value of the car had reduced by a further 15%. the value of the car on january 1st 2012 was $18 700. (a) find how much paulo paid for the car. answer(a) $ [3] (b) the value of the car reduces by 15% every year from 2012. find the year in which the value of the car will first be below 25% of the price paulo paid in 2010. answer(b) [3] ", "16": "16 \u00a9 ucles 2014 0607/41/m/j/14 11 not to scale the diagram shows the top of a circular cake of diameter 30 cm. the cake is cut into 16 pieces as shown in the diagram. (a) (i) the top of each of the 16 pieces of cake has the same area. find the area of one of the pieces in square centimetres. answer(a) (i) cm2 [2] (ii) write your answer to part (a)(i) in square metres. answer(a) (ii) m2 [1] (iii) show that the radius of the inner circle is 7.5 cm. [2] ", "17": "17 \u00a9 ucles 2014 0607/41/m/j/14 [turn over (b) the diagram shows the top of one of the outer pieces of cake. not to scale (i) calculate the perimeter of the top of this piece of cake. answer(b) (i) cm [3] (ii) the depth of the cake is 8 cm. calculate the total surface area of this piece of cake. answer(b) (ii) cm2 [3] ", "18": "18 \u00a9 ucles 2014 0607/41/m/j/14 12 laura is putting fencing around two flower beds. she uses 60 m of fencing. one of the flower beds is a rectangle and the other is a square. xynot to scale the length of the rectangle is five times its width, x metres. the length of a side of the square is y metres. (a) find and simplify an expression for y in terms of x. answer(a) [2] (b) the area of the rectangle is equal to the area of the square. (i) write down a quadratic equation, in terms of x, and show that it simplifies to 4x 2 \u2013 90 x + 225 = 0. [2] ", "19": "19 \u00a9 ucles 2014 0607/41/m/j/14 [turn over (ii) solve the equation 4 x2 \u2013 90 x + 225 = 0. give your answers correct to 3 significant figures. answer(b) (ii) x = or x = [3] (iii) write down the width of the rectangle, giving a reason for your choice of values of x. answer(b) (iii) x = because [1] (iv) calculate the total area of the flower beds. answer(b) (iv) m2 [2] ", "20": "20 \u00a9 ucles 2014 0607/41/m/j/14 13 laura sprays insecticide on the flowers in her flower beds. the insecticide spray is made by dissolving pellets in water. she measures the time taken, y minutes, to dissolve a pellet in water at different temperatures, x\u00b0c. her results are shown in the table. temperature, x\u00b0c 15 18 21 24 27 30 33 36 39 42 45 time, y minutes 5.1 4.9 4.5 4.0 3.2 2.8 2.4 2.1 1.8 1.6 1.1 (a) (i) complete the scatter diagram. the first four points have been plotted for you. 6 543 2 1 61 2 1 8 2 4 temperature (\u00b0c)30 36 42 480y xtime (minutes) [3] (ii) describe the type of correlation shown by the scatter diagram. answer(a) (ii) [1] ", "21": "21 \u00a9 ucles 2014 0607/41/m/j/14 [turn over (b) find (i) the mean temperature, answer(b) (i) \u00b0c [1] (ii) the mean time. answer(b) (ii) min [1] (c) (i) find the equation of the regression line in the form y = mx + c. answer(c) (i) y = [2] (ii) the value for m represents a connection between time and temperature. describe this connection. answer(c) (ii) [1] (iii) use your answer to part (c)(i) to estimate the time taken for a pellet to dissolve when the temperature is 25 \u00b0c. answer(c) (iii) min [1] ", "22": "22 \u00a9 ucles 2014 0607/41/m/j/14 14 y x4 0 \u20134\u20135 5 (a) (i) on the diagram, sketch the graph of y = f(x), where f( x) = 3 222 \u2212\u2212x xx between x = \u20135 and x = 5. [4] (ii) write down the equations of the three asymptotes of the graph. answer(a) (ii) , , [3] (iii) write down the co-ordinates of the local maximum point of the graph. answer(a) (iii) ( , ) [1] (iv) write down the co-ordinates of the local minimum point of the graph. answer(a) (iv) ( , ) [2] (b) solve the inequality 3 222 \u2212\u2212x xx > 3. answer(b) [3] ", "23": "23 \u00a9 ucles 2014 0607/41/m/j/14 blank page", "24": "24 permission to reproduce items where third -party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge asse ssment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/41/m/j/14 blank page " }, "0607_s14_qp_42.pdf": { "1": " this document consists of 19 printed pages and 1 blank page. ib14 06_0607_42/6rp \u00a9 ucles 2014 [turn over *6941565017* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/42 paper 4 (extended) may/june 2014 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120. ", "2": "2 \u00a9 ucles 2014 0607/42/m/j/14 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2014 0607/42/m/j/14 [turn over answer all the questions. 1 in one country the population of starlings reduced by 5% per year from 1980 to 2010. on 1st january 2000 the population was 8.5 million. (a) write 8.5 million in standard form. answer(a) [1] (b) calculate the population on 1st january 2010. give your answer correct to 2 significant figures. answer(b) [2] (c) calculate the population on 1st january 1980. give your answer correct to 3 significant figures. answer(c) [3] (d) calculate the percentage reduction in the population from 1st january 1980 to 1st january 2010. answer(d) % [3] (e) if the population of starlings continues to reduce at the same rate, find the year in which the population will first be below 3 500 000. answer(e) [3] ", "4": "4 \u00a9 ucles 2014 0607/42/m/j/14 2 y x20 0 \u201315\u201315 15 f(x) = 10 cos 20x\u00b0 for \u201315 y x y 15 (a) on the diagram, sketch the graph of y = f(x) . [3] (b) find the co-ordinates of the local maximum and the local minimum points. answer(b) ( , ) ( , ) ( , ) [3] (c) on the same diagram, sketch the graph of y = g( x) where g( x) = | x + 2 | for \u201315 y x y 15. [1] (d) solve f( x) = g( x) . answer(d) [2] ", "5": "5 \u00a9 ucles 2014 0607/42/m/j/14 [turn over 3 ay x8 7654321 \u20131\u201320 \u2013 1 1234567 \u20132 \u20133 \u20134 \u20135 \u20136 \u20137 (a) translate triangle a by the vector \uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec \uf8ed\uf8eb\u2212 24 . [2] (b) describe fully the single transformation that is equivalent to a translation by the vector \uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec \uf8ed\uf8eb\u2212 24 followed by a rotation of 90 \u00b0 clockwise about (\u20132, 6). answer(b) [5] ", "6": "6 \u00a9 ucles 2014 0607/42/m/j/14 4 1.3 cm 3.5 cm 2.5 cmnot to scale the diagram shows a brass object, used by builders, known as a plumb bob. the plumb bob is made up of a hemisphere, a cylinder and a cone, each of radius 1.3 cm. the height of the cylinder is 3.5 cm and the height of the cone is 2.5 cm. (a) find the total volume of the plumb bob. answer(a) cm3 [4] ", "7": "7 \u00a9 ucles 2014 0607/42/m/j/14 [turn over (b) each cubic centimetre of brass weighs 8.4 grams. calculate the total mass of the plumb bob. answer(b) g [1] (c) a mathematically similar plumb bob is also made of brass. its mass is twice the mass of the plumb bob shown in the diagram opposite. calculate the total height of the larger plumb bob. answer(c) cm [3] ", "8": "8 \u00a9 ucles 2014 0607/42/m/j/14 5 15 students each took a mathematics test and a physics test. each test was marked out of 60. these are their marks. mathematics mark 25 30 39 47 45 58 42 60 49 32 52 35 55 27 35 physics mark 15 18 25 32 35 37 29 44 28 26 38 23 40 22 32 (a) complete the scatter diagram. the first 10 points have been plotted for you. 60 504030 20 10 10 20 30 mathematics mark40 50 600physics mark [2] (b) what type of correlation is shown by the scatter diagram? answer(b) [1] ", "9": "9 \u00a9 ucles 2014 0607/42/m/j/14 [turn over (c) (i) calculate the mean of the mathematics marks. answer(c) (i) [1] (ii) calculate the mean of the physics marks. answer(c) (ii) [1] (d) find the equation of the regression line for the physics marks ( y) and the mathematics marks ( x). write your answer in the form y = mx + c. answer(d) y = [2] (e) find the value of y when x = 26. answer(e) [1] (f) draw accurately the line of regression on the scatter diagram. [2] (g) it was later decided that the physics test was too difficult. the physics teacher added 12 marks to each of the physics marks. write down the equation of the regression line for the new physics marks ( y) in terms of the mathematics marks ( x). answer(g) y = [1] ", "10": "10 \u00a9 ucles 2014 0607/42/m/j/14 6 the equation of the straight line l is 5 y + 2x + 20 = 0. (a) find the gradient of the line l. answer(a) [1] (b) find the co-ordinates of the point where the line l crosses the y-axis. answer(b) ( , ) [1] (c) find the equation of the line, perpendicular to l, which passes through the point (2, 3). give your answer in the form y = mx + c . answer(c) y = [3] ", "11": "11 \u00a9 ucles 2014 0607/42/m/j/14 [turn over 7 u b c 11 in a school, biology ( b) and chemistry ( c) are two of the optional subjects. the venn diagram represents the choices of 40 students. n( b) = 25 and n( c) = 17. 11 students study neither biology nor chemistry. (a) complete the venn diagram. [2] (b) use set notation to show the number of students who study neither biology nor chemistry. answer(b) [1] (c) one of the 40 students is chosen at random. what is the probability that this student studies both biology and chemistry? answer(c) [1] (d) two of the 40 students are chosen at random. find the probability that both students study biology but not chemistry. answer(d) [3] (e) two of the students who study biology are chosen at random. find the probability that both students also study chemistry. answer(e) [3] ", "12": "12 \u00a9 ucles 2014 0607/42/m/j/14 8 y x7 0 \u20137\u20134 7 f(x) = )1 )(3 (2 + \u2212 x xx (a) on the diagram, sketch the graph of y = f(x) for x between \u20134 and 7. [3] (b) write down the equations of the three asymptotes of the graph of y = f(x). answer(b) [3] (c) find the range of values of x for which f( x) < 4. answer(c) [3] (d) the graph of y = g( x) is the graph of y = f(x) translated by the vector \uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec \uf8ed\uf8eb 01. find g( x). answer(d) g(x) = [2] ", "13": "13 \u00a9 ucles 2014 0607/42/m/j/14 [turn over 9 the table shows a frequency distribution for 79 pieces of data. x 1 2 3 4 5 6 frequency 9 26 18 11 9 6 (a) when x is the number of children in a family, find (i) the mode, answer(a) (i) [1] (ii) the range, answer(a) (ii) [1] (iii) the median, answer(a) (iii) [1] (iv) the mean, answer(a) (iv) [2] (v) the upper quartile. answer(a) (v) [1] (b) when x is the distance, to the nearest kilometre, that the children travel to school, (i) explain why the range of the distances may not be the same as your answer to part (a)(ii) , answer(b) (i) [1] (ii) write down the modal interval. answer(b) (ii) < x y [1] ", "14": "14 \u00a9 ucles 2014 0607/42/m/j/14 10 y x 0not to scale the diagram shows a sketch of the graph of y = x2 + bx + c . the graph passes through the points (1, 2) and (\u20133, \u20136). (a) use this information to write down two equations in b and c. answer(a) [2] (b) use these equations to show that y = x 2 + 4x \u2013 3 . [3] ", "15": "15 \u00a9 ucles 2014 0607/42/m/j/14 [turn over (c) (i) solve the equation x2 + 4x \u2013 3 = 0 . give your answers correct to 2 decimal places. answer(c) (i) x = or x = [2] (ii) write down the equation of the line of symmetry of the graph of y = x2 + 4x \u2013 3 . answer(c) (ii) [1] (iii) find the minimum value of y. answer(c) (iii) [1] ", "16": "16 \u00a9 ucles 2014 0607/42/m/j/14 11 (a) ob c e da 38\u00b0 23\u00b0not to scale in the diagram, ec is a diameter of the circle centre o. abc and aed are straight lines. angle ecd = 23\u00b0 and angle bae = 38\u00b0. find (i) angle dbc , answer(a) (i) [2] (ii) angle ecb , answer(a) (ii) [2] (iii) angle doe . answer(a) (iii) [1] ", "17": "17 \u00a9 ucles 2014 0607/42/m/j/14 [turn over (b) a bc dpqr snot to scale in the diagram, qa and qb are tangents, at r and s, to the circle centre p. pc and pd are tangents, at r and s, to the circle centre q. qr = 8 cm and angle rqs = 56\u00b0. (i) calculate pr. answer(b) (i) cm [2] (ii) find angle rps. answer(b) (ii) [1] (iii) calculate the perimeter of the shaded region. answer(b) (iii) cm [4] ", "18": "18 \u00a9 ucles 2014 0607/42/m/j/14 12 a b d c12.6 cm10.1 cm 13.8 cm 19.5 cmnot to scale in the diagram angle dab = 90\u00b0. ab = 10.1 cm, db = 12.6 cm, bc = 13.8 cm and dc = 19.5 cm. (a) calculate the length ad. answer(a) cm [3] (b) calculate angle dbc . answer(b) [3] (c) calculate the total area of the quadrilateral abcd . answer(c) cm2 [4] ", "19": "19 \u00a9 ucles 2014 0607/42/m/j/14 13 gita travels from her home to work in the city. she drives her car to a car park and cycles the remaining distance. the car journey takes x minutes. the cycle journey takes 4 minutes less than the car journey. (a) write down an expression, in terms of x, for the time in hours of the cycle journey. answer(a) hours [1] (b) gita\u2019s average speed in her car is 70 km/h and her average speed on her cycle is 15 km/h. the total distance she travels is 33 km. (i) write down an equation in x and show that it simplifies to 17 x \u2013 12 = 396. [3] (ii) solve the equation to find the time taken for the car journey. answer(b) (ii) min [2] (c) find the average speed, in kilometres per hour, for the whole journey. answer(c) km/h [2] ", "20": "20 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the p ublisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge asse ssment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/42/m/j/14 blank page " }, "0607_s14_qp_43.pdf": { "1": " this document consists of 20 printed pages. ib14 06_0607_43/4rp \u00a9 ucles 2014 [turn over *9855804838* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/43 paper 4 (extended) may/june 2014 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120. ", "2": "2 \u00a9 ucles 2014 0607/43/m/j/14 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2014 0607/43/m/j/14 [turn over answer all the questions. 1 on january 1st 2014 the value of a house was $230 000. the value of the house increases at a rate of 4.5% of its value each year. (a) calculate the value of the house, in 10 years time, on january 1st 2024. give your answer correct to the nearest hundred dollars. answer(a) $ [3] (b) calculate the whole number of years, from january 1st 2014, it takes for the value of the house to exceed one million dollars. answer(b) [3] (c) calculate the percentage change in the value of the house when it increases from $230 000 to $1 000 000. answer(c) % [3] ", "4": "4 \u00a9 ucles 2014 0607/43/m/j/14 2 the five members of the schmidt family go by car on a day trip to a mountain resort in france. (a) the family leave home at 07 55. they travel 50 km at an average speed of 100 km/h and then 30 km at an average speed of 40 km/h. (i) at what time does the family arrive at the mountain resort? answer(a) (i) [3] (ii) calculate the average speed of the journey. answer(a) (ii) km/h [2] (iii) the car uses fuel at an average rate of 9.5 litres per 100 kilometres. the cost of fuel is \u20ac1.60 per litre. calculate the cost of the fuel used during the journey. answer(a) (iii) \u20ac [2] ", "5": "5 \u00a9 ucles 2014 0607/43/m/j/14 [turn over (b) the family consists of 2 adults and 3 children. they take a cable car ride and buy lunch. the tickets for the cable car cost \u20ac8.80 for each adult and \u20ac5.50 for each child. the cost of lunch for each person is \u20ac6.25 . calculate the total cost of the cable car tickets and the lunches for the family. answer(b) \u20ac [2] (c) the family also spends another \u20ac24.23 in total during the day. when the family returns home, the car uses the same amount of fuel. calculate the average cost per person of the whole day trip. answer(c) \u20ac [2] ", "6": "6 \u00a9 ucles 2014 0607/43/m/j/14 3 (a) 0123456789 1 0 1 1x write down the inequality shown by the number line. answer(a) [2] (b) y xnot to scale \u20133 \u20132 1 4 50 the diagram shows the graph of y = f(x). solve the inequality f( x) > 0. answer(b) [3] (c) solve the equation. x 2 + 4x + 2 = 0 give your answers correct to 2 decimal places. answer(c) x = or x = [3] ", "7": "7 \u00a9 ucles 2014 0607/43/m/j/14 [turn over 4 de b ac pq not to scale abcd is a rectangle, dce is a straight line and dc = ce. = p and = q. (a) find, in terms of p and q, (i) , answer(a) (i) [1] (ii) . answer(a) (ii) [1] (b) in the diagram above, a is the point (3, 3), b is the point (6, 3) and c is the point (6, 5). (i) find the co-ordinates of e. answer(b) (i) ( , ) [2] (ii) find the equation of the straight line which passes through a and e. give your answer in the form ax + by = d where a, b and d are integers. answer(b) (ii) [4] ", "8": "8 \u00a9 ucles 2014 0607/43/m/j/14 5 the table shows the test marks of 10 students in geography ( g) and science ( s). student a b c d e f g h i j geography ( g) 48 60 72 57 63 39 44 84 41 73 science ( s) 70 55 65 41 74 81 42 63 57 55 (a) find the median and the quartiles of the geography test marks. answer(a) median = lower quartile = upper quartile = [3] (b) find the mean mark for each subject. answer(b) geography science [2] (c) find the equation of the linear regression line, giving s in terms of g. answer(c) s = [2] (d) (i) use the equation in part (c) to predict the science mark when the geography mark is 54. answer(d) (i) [1] (ii) explain briefly why the answer to part (d)(i) may not be reliable. answer(d) (ii) [1] ", "9": "9 \u00a9 ucles 2014 0607/43/m/j/14 [turn over 6 y x300 0 \u2013150\u20132 5.2not to scale f( x) = 5 x4 \u2013 x5 for \u20132 y x y 5.2 (a) on the diagram, sketch the graph of y = f(x). [2] (b) find the zeros of f( x). answer(b) [2] (c) find the co-ordinates of the local maximum point. answer(c) ( , ) [1] (d) find the range of f( x). answer(d) [2] (e) the equation f( x) = k, where k is an integer, has one solution. write down a possible value of k. answer (e) [1] ", "10": "10 \u00a9 ucles 2014 0607/43/m/j/14 7 (a) five angles of an octagon are each 129 \u00b0. the other three angles are equal. calculate one of these three angles. answer(a) [3] (b) oc banot to scale a, b and c lie on a circle, centre o. the obtuse angle aob = (6 x + 2) \u00b0 and angle acb = (2 x + 19) \u00b0. find the value of x. answer(b) [3] ", "11": "11 \u00a9 ucles 2014 0607/43/m/j/14 [turn over (c) cd b ax 6 cm 5 cm3 cm not to scale ab and cd are parallel. ax = 6 cm, bx = 5 cm and cx = 3 cm. the area of triangle cxd = 5.1 cm2. calculate the area of triangle axb. answer(c) cm2 [3] ", "12": "12 \u00a9 ucles 2014 0607/43/m/j/14 8 40\u00b0r qp a bc 9 cm5 cmnot to scale the diagram shows a piece of cake. the shape is a solid prism of height 5 cm. the cross-section, abc , is a sector of a circle, centre a, with radius 9 cm. angle bac = 40 \u00b0. (a) calculate (i) the volume of the prism, answer(a) (i) cm3 [3] (ii) the total surface area of the prism. answer(a) (ii) cm2 [5] ", "13": "13 \u00a9 ucles 2014 0607/43/m/j/14 [turn over (b) the piece of cake has a mass of 160 g. it is cut from a circular cake. calculate the mass of the circular cake. give your answer in kilograms. answer(b) kg [2] 9 use graphical methods to solve these equations. use \u20132 y x y 4 in each part and sketch your graphs. (a) x 3 = 3\u2013x answer(a) [3] (b) x 2 \u2013 2x \u2013 3 = log( x + 2) answer(b) [4] ", "14": "14 \u00a9 ucles 2014 0607/43/m/j/14 10 78\u00b0 47\u00b018 km 24 km26 km c l vbnorth not to scale the diagram shows straight line distances between cherbourg ( c), barfleur ( b), valonges ( v) and les pieux ( l). (a) calculate angle bcv . show that it rounds to 63.06 \u00b0 correct to 4 significant figures. [3] (b) calculate the distance lv. answer(b) km [3] ", "15": "15 \u00a9 ucles 2014 0607/43/m/j/14 [turn over (c) (i) calculate the shortest distance from v to bc. answer(c) (i) km [2] (ii) calculate the area of triangle bcv . answer(c) (ii) km2 [2] (d) the bearing of b from c is 084\u00b0. find the bearing of (i) v from c, answer(d) (i) [1] (ii) c from v. answer(d) (ii) [1] ", "16": "16 \u00a9 ucles 2014 0607/43/m/j/14 11 (a) write as a single fraction. 23 121 \u2212+\u2212 x x answer(a) [3] (b) simplify fully, giving your answer as a single fraction. x x xx x 3 22 33 \u2212 +\u2212 answer(b) [5] ", "17": "17 \u00a9 ucles 2014 0607/43/m/j/14 [turn over 12 30 students carry out an experiment in a chemistry lesson. each student measures the time taken, t seconds, to complete a chemical reaction. the table shows the results. reaction time, t seconds 20 i t y 30 30 i t y 35 35 i t y 40 40 i t y 50 frequency 2 18 7 3 (a) calculate an estimate of the mean reaction time. answer(a) s [2] (b) on the grid, draw a histogram to show the information in the table. 4 321 10 20 30 reaction time (seconds)frequency density 40 500t [3] ", "18": "18 \u00a9 ucles 2014 0607/43/m/j/14 13 12 1 x13 2 y the diagram shows two fair dice, x and y, each with 6 faces. the numbers on x are 1, 1, 1, 1, 2 and 3. the numbers on y are 1, 1, 1, 2, 3 and 3. (a) x is rolled. write down the probability that the number on the top face is (i) odd, answer(a) (i) [1] (ii) not 1. answer(a) (ii) [1] (b) the two dice are rolled and the numbers on the top faces are noted. find the probability that (i) both numbers are 1, answer(b) (i) [2] ", "19": "19 \u00a9 ucles 2014 0607/43/m/j/14 [turn over (ii) at least one of the numbers is 1, answer(b) (ii) [3] (iii) the product of the two numbers is even. answer(b) (iii) [2] question 14 is printed on the next page. ", "20": "20 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the p ublisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge a ssessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/43/m/j/14 14 ut c b ad 12 cm7 cm3 cmnot to scale the diagram shows a prism of length 12 cm. triangle bct is a cross-section of the prism. angle bct = 90\u00b0, bc = 7 cm and ct = 3 cm. abcd is horizontal. (a) calculate the angle between the planes abtu and abcd . answer(a) [2] (b) calculate at. answer(b) cm [3] (c) calculate the angle of elevation of t from a. answer(c) [2] " }, "0607_s14_qp_51.pdf": { "1": " this document consists of 6 printed pages and 2 blank pages. ib14 06_0607_51/3rp \u00a9 ucles 2014 [turn over *6286435950* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/51 paper 5 (core) may/june 2014 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24. ", "2": "2 \u00a9 ucles 2014 0607/51/m/j/14 answer all the questions. investigation counting factors this investigation looks for a method to find how many factors a number has. 1 the five factors of 16 are: 1, 2, 4, 8, 16 write down the five factors of 16 as powers of 2. three have been written down for you. 2 0 ,21 , , , 24 2 (a) write down, in ascending order, the four factors of 27. two have been written down for you. 1 , , , 27 (b) write down the four factors of 27 as powers of 3. , , , 3 p is a prime number. (a) write down the six factors of p 5 as powers of p. two have been written down for you. p 0 , , , , , p5 (b) write down, in terms of n, the number of factors of pn. ", "3": "3 \u00a9 ucles 2014 0607/51/m/j/14 [turn over 4 (a) 2 is a prime number and 128 = 27. write down the number of factors of 128. (b) work out each factor of 128 as an ordinary number. 5 5 is a prime number. (a) write 125 as a power of 5. (b) write down the number of factors of 125. 6 (a) a number, which can be written as a power of 2, has exactly 14 factors. find this number. (b) find another number that has exactly 14 factors. ", "4": "4 \u00a9 ucles 2014 0607/51/m/j/14 7 (a) 20 is not a prime number. 20 = 22 \u00d7 51 where 2 and 5 are prime numbers. find all the factors of 20 by completing the table. powers of 5 50 51 powers of 2 20 20 \u00d7 50 = 1 \u00d7 1 = 1 20 \u00d7 51 = \u2026... \u00d7 \u2026... = \u2026... 21 21 \u00d7 50 = 2 \u00d7 1 = 2 21 \u00d7 51 = \u2026... \u00d7 \u2026... = \u2026... 22 22 \u00d7 50 = \u2026... \u00d7 \u2026... = \u2026... 22 \u00d7 51 = 4 \u00d7 5 = 20 (b) the table has 3 rows and 2 columns. describe how to find the number of factors of 20 from the number of rows and the number of columns. (c) 784 = 2 4 \u00d7 72 where 2 and 7 are prime numbers. (i) how many rows and how many columns would there be in the table for 784? rows columns (ii) work out the number of factors of 784. do not write them out. ", "5": "5 \u00a9 ucles 2014 0607/51/m/j/14 [turn over 8 (a) 1000 = 2n \u00d7 5n . find n. (b) use the method of question 7(c) to find the number of factors of 1000. (c) use the method of part (a) and part (b) to find the number of factors of 1 000 000. ", "6": "6 \u00a9 ucles 2014 0607/51/m/j/14 9 (a) 85 = 5 \u00d7 17 where 5 and 17 are prime numbers. use the method of question 7(c) to show why 85 has exactly 4 factors. (b) find all the numbers that are greater than 80 but smaller than 90 and have exactly 4 factors. this list of prime numbers is useful in answering this question. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 ", "7": "7 \u00a9 ucles 2014 0607/51/m/j/14 blank page", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge a ssessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/51/m/j/14 blank page " }, "0607_s14_qp_52.pdf": { "1": " this document consists of 7 printed pages and 1 blank page. ib14 06_0607_52/4rp \u00a9 ucles 2014 [turn over *7695187803* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/52 paper 5 (core) may/june 2014 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24. ", "2": "2 \u00a9 ucles 2014 0607/52/m/j/14 answer all the questions. investigation fractions within fractions this investigation looks at sequences of fractions. one way to form a sequence is by using fractions within fractions as shown below. 1 1then111 + 1then 111 + 1 + 11then and so on.1 111 + 1 + 1 + 11 1 the first three terms of a sequence of fractions are 1, 21, 32. these terms are calculated in the following way. 1 11 + 1 + 1121 + 1 3211 == =2 31 11 + 1 1 + 11==1 211= 1 (a) (i) fill in the box to complete the calculation of the 4th term. 3 21 5311 1 11 + 1 + 1 + 11 12 351 + 1 + 11 + 1 1== == = ", "3": "3 \u00a9 ucles 2014 0607/52/m/j/14 [turn over (ii) show that the 5th term of this sequence of fractions is 85. 11= 1 11 + 1 + 1 + 1 + 11 (iii) complete the table to show the first eight terms of this sequence of fractions. 11 21 32 53 85 2113 (iv) explain how you used a pattern to find the numerator and the denominator of the 8th term. numerator denominator ", "4": "4 \u00a9 ucles 2014 0607/52/m/j/14 (b) the numbers 1, 1, 2, 3, 5, 8, 13, 21 are the first eight numbers in a sequence. (i) work out the next five terms of this sequence. ( ii) write down the 12th term of the sequence of fractions in part (a) . 2 here is a different sequence of fractions. 2 1 + 21 + 1 + 22 1 + 21 + 2 1 + 22 2, , ,12, ... (a) calculate the 2nd and 3rd terms in this sequence of fractions. give your answers as single fractions. the 1st and 4th terms are given. 1 + 21 + 21 + 2212 12 11102= = = = 2 1 + 21 + 1 + 22 ", "5": "5 \u00a9 ucles 2014 0607/52/m/j/14 [turn over (b) find the 5th term of this sequence. give your answer as a single fraction. (c) describe the connection between the numerator of a fraction and the denominator of the previous fraction in the sequence. (d) describe the connection between the denominator of a fraction and the numerator and denominator of the previous fraction. ", "6": "6 \u00a9 ucles 2014 0607/52/m/j/14 3 here is a different sequence of fractions. the first three terms are 3, 43, 712. (a) calculate the 4th and 5th terms. give your answers as single fractions. 12 73 4 1 + 31 + 31 + 33 1 + 31 + 1 + 333 ====12 73 11 + 3 1 +3=3 431 31= ... 1 + 31 + 1 + 3331 + 3 = ... (b) explain how you can use a pattern to find the numerator and the denominator of the 5th term of this sequence. numerator denominator ", "7": "7 \u00a9 ucles 2014 0607/52/m/j/14 4 here is a sequence in terms of n. n 1 + n1 + 1 + nn 1 + n1 + n 1 + nn n, , ,1n, ... calculate the first four terms in this sequence when n = 4. give your answers as single fractions. ... , ... , ... , ... ", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge a ssessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/52/m/j/14 blank page " }, "0607_s14_qp_53.pdf": { "1": " this document consists of 7 printed pages and 1 blank page. ib14 06_0607_53/fp \u00a9 ucles 2014 [turn over *5687780575* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/53 paper 5 (core) may/june 2014 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24. ", "2": "2 \u00a9 ucles 2014 0607/53/m/j/14 answer all the questions. investigation fractions within fractions this investigation looks at sequences of fractions. one way to form a sequence is by using fractions within fractions as shown below. 1 1then111 + 1then 111 + 1 + 11then and so on.1 111 + 1 + 1 + 11 1 the first three terms of a sequence of fractions are 1, 21, 32. these terms are calculated in the following way. 1 11 + 1 + 1121 + 1 3211 == =2 31 11 + 1 1 + 11==1 211= 1 (a) (i) fill in the box to complete the calculation of the 4th term. 3 21 5311 1 11 + 1 + 1 + 11 12 351 + 1 + 11 + 1 1== == = ", "3": "3 \u00a9 ucles 2014 0607/53/m/j/14 [turn over (ii) show that the 5th term of this sequence of fractions is 85. 11= 1 11 + 1 + 1 + 1 + 11 (iii) complete the table to show the first eight terms of this sequence of fractions. 11 21 32 53 85 2113 (iv) explain how you used a pattern to find the numerator and the denominator of the 8th term. numerator denominator ", "4": "4 \u00a9 ucles 2014 0607/53/m/j/14 (b) the numbers 1, 1, 2, 3, 5, 8, 13, 21 are the first eight numbers in a sequence. (i) work out the next five terms of this sequence. ( ii) write down the 12th term of the sequence of fractions in part (a) . 2 here is a different sequence of fractions. 2 1 + 21 + 1 + 22 1 + 21 + 2 1 + 22 2, , ,12, ... (a) calculate the 2nd and 3rd terms in this sequence of fractions. give your answers as single fractions. the 1st and 4th terms are given. 1 + 21 + 21 + 2212 12 11102= = = = 2 1 + 21 + 1 + 22 ", "5": "5 \u00a9 ucles 2014 0607/53/m/j/14 [turn over (b) find the 5th term of this sequence. give your answer as a single fraction. (c) describe the connection between the numerator of a fraction and the denominator of the previous fraction in the sequence. (d) describe the connection between the denominator of a fraction and the numerator and denominator of the previous fraction. ", "6": "6 \u00a9 ucles 2014 0607/53/m/j/14 3 here is a different sequence of fractions. the first three terms are 3, 43, 712. (a) calculate the 4th and 5th terms. give your answers as single fractions. 12 73 4 1 + 31 + 31 + 33 1 + 31 + 1 + 333 ====12 73 11 + 3 1 +3=3 431 31= ... 1 + 31 + 1 + 3331 + 3 = ... (b) explain how you can use a pattern to find the numerator and the denominator of the 5th term of this sequence. numerator denominator ", "7": "7 \u00a9 ucles 2014 0607/53/m/j/14 4 here is a sequence in terms of n. n 1 + n1 + 1 + nn 1 + n1 + n 1 + nn n, , ,1n, ... calculate the first four terms in this sequence when n = 4. give your answers as single fractions. ... , ... , ... , ... ", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the p ublisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge a ssessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/53/m/j/14 blank page " }, "0607_s14_qp_61.pdf": { "1": " this document consists of 8 printed pages. ib14 06_0607_61/5rp \u00a9 ucles 2014 [turn over *5450797540* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/61 paper 6 (extended) may/june 2014 1 hour 30 minutes candidates answer on the question paper additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2014 0607/61/m/j/14 answer both parts a and b. a investigation counting factors (20 marks) you are advised to spend 45 minutes on part a. this investigation looks for a method to find how many factors a number has. 1 (a) (i) write down, in ascending order, the five factors of 16. two have been written down for you. 1 , , , , 16 (ii) write down the five factors of 16 as powers of 2. two have been written down for you. 2 0 , , , , 24 (b) write down, in ascending order, the four factors of 27 as powers of 3. , , , 2 (a) p is a prime number. (i) write down the six factors of p 5 as powers of p. one has been written down for you. p0 , , , , , (ii) write down, in terms of n, the number of factors of p n. (b) 78 125 = 5n where 5 is a prime number. find the number of factors of 78 125. do not write them out. ", "3": "3 \u00a9 ucles 2014 0607/61/m/j/14 [turn over 3 (a) 20 is not a prime number. 20 = 22 \u00d7 51 where 2 and 5 are prime numbers. find all the factors of 20 by completing the table. powers of 5 50 51 powers of 2 20 20 \u00d7 50 = 1 \u00d7 1 = 1 20 \u00d7 51 = \u2026... \u00d7 \u2026... = \u2026... 21 21 \u00d7 50 = 2 \u00d7 1 = 2 21 \u00d7 51 = \u2026... \u00d7 \u2026... = \u2026... 22 22 \u00d7 50 = \u2026... \u00d7 \u2026... = \u2026... 22 \u00d7 51 = 4 \u00d7 5 = 20 (b) the table has 3 rows and 2 columns. describe how to find the number of factors of 20 from the number of rows and the number of columns. (c) 4000 = 2 5 \u00d7 53. find the number of factors of 4000. 4 (a) (i) 1 000 000 = 2n \u00d7 5n. find n. (ii) find the number of factors of 1 000 000. (b) find n such that 10 n has 900 factors. ", "4": "4 \u00a9 ucles 2014 0607/61/m/j/14 5 x has exactly two prime factors, 3 and 7. so x can be written as 3m \u00d7 7n. find all the possible values of x that have exactly 12 factors. 6 (a) write 336 in the form p d \u00d7 qe \u00d7 rf where p, q and r are prime numbers. \u00d7 \u00d7 (b) find the number of factors of 336. 7 a number has exactly three prime factors, 2, 3 and 5. it has exactly 12 factors. find all possible numbers. ", "5": "5 \u00a9 ucles 2014 0607/61/m/j/14 [turn over b modelling tides (20 marks) you are advised to spend 45 minutes on part b. in this task you will model the height of a tide. here is the graph of y = sin x\u00b0. its period is 360. y x 30 60 90 120 150 180 210 240 270 300 330 3601 0.5 \u20130.5 \u201310 1 (a) (i) on the grid below, sketch the graph of y = sin(3 x)\u00b0. y x 30 60 90 120 150 180 210 240 270 300 330 3601 0.5 \u20130.5 \u201310 (ii) write down the period of the graph of y = sin(3 x)\u00b0. (b) write down the period of the graph of y = sin(10 x)\u00b0. (c) write down an expression, in terms of b, for the period of the graph of y = sin( bx)\u00b0. ", "6": "6 \u00a9 ucles 2014 0607/61/m/j/14 2 the graph below shows the approximate height of the tide at auckland (new zealand) during 25th april 2014. t is the time of day starting at midnight. h is the height in metres above a fixed height. 123456789 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 41.5 1 0.5 \u20130.5 \u20131 \u20131.50h t (a) write down the period of the graph. (b) explain why a model for the height of the tide on 25th april is h = 1.2 sin(30 t)\u00b0. (c) usually the height of a tide is measured as the height, h metres, above sea level. the graph below shows this for the tide at auckland on 25th april. 1234567891011121314151617181920212223244 321 0h t modify the model in part (b). h = ", "7": "7 \u00a9 ucles 2014 0607/61/m/j/14 [turn over (d) the best fishing conditions are when the height of the tide is less than one metre above sea level. (i) use your calculator with your model for h to find the two times between which there were the best fishing conditions on the morning of 25th april. give your times correct to the nearest minute. and (ii) using your answer to part (i) , write down the times between which there were the best fishing conditions on the afternoon of 25th april. and 3 here is a different model for the height of the tide, d metres, on the morning of 25th april. d = 0.022 t 3 \u2013 0.403 t2 + 1.9 t (a) compare d with h from question 2(c) by drawing their graphs on your calculator for 0 < t < 12 . comment on how the difference in height between d and h varies with time. (b) make one change to the model d that makes the graph of d very close to the graph of h for 3 < t < 9. d = question 4 and 5 are printed on the next page. ", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge a ssessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/61/m/j/14 4 the graph below shows the actual height of the tide above sea level on 25th april 2014 at auckland. 1234567891011121314151617181920212223244 321 0h t the actual period for the height of a tide is 12 hours 25 minutes. use this fact to improve your model for the height of the tide above sea level on 25th april by changing one of the numbers in your answer to question 2(c) . h = 5 the graph for 26th april can be found by translating the graph for 25th april horizontally. modify your answer to question 4 to give a model for the height of the tide above sea level at auckland on 26th april. h = " }, "0607_s14_qp_62.pdf": { "1": " this document consists of 11 printed pages and 1 blank page. ib14 06_0607_62/4rp \u00a9 ucles 2014 [turn over *6544955278* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/62 paper 6 (extended) may/june 2014 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2014 0607/62/m/j/14 answer both parts a and b. a investigation fractions within fractions (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation looks at sequences of fractions. one way to form a sequence is by using fractions within fractions as shown below. 1 1then111 + 1then 111 + 1 + 11then and so on.1 111 + 1 + 1 + 11 1 the first three terms of a sequence of fractions are 1, 21, 32. these terms are calculated in the following way. 1 11 + 1 + 1121 + 1 3211 == =2 31 11 + 1 1 + 11==1 211= 1 (a) fill in the box to complete the calculation of the 4th term. 3 21 5311 1 11 + 1 + 1 + 11 12 351 + 1 + 11 + 1 1== == = ", "3": "3 \u00a9 ucles 2014 0607/62/m/j/14 [turn over (b) show that the 5th term of this sequence of fractions is 85. 11= 1 11 + 1 + 1 + 1 + 11 (c) complete the table to show the first eight terms of this sequence of fractions. 11 21 32 53 85 2113 (d) explain how you used a pattern to find the numerator and the denominator of the 8th term. numerator denominator ", "4": "4 \u00a9 ucles 2014 0607/62/m/j/14 2 here is a different sequence of fractions. the first three terms are 2, 32, 56. (a) calculate the 4th and 5th terms. give your answers as single fractions. 6 523 1 + 21 + 21 + 22 1 + 21 + 1 + 222 ====6 52 11 + 2 1 +2=2 321 21= ... 1 + 21 + 1 + 2221 + 2 = ... (b) explain how you can use a pattern to find the numerator and the denominator of the 5th term of this sequence. numerator denominator ", "5": "5 \u00a9 ucles 2014 0607/62/m/j/14 [turn over 3 you may find this formula useful in this question. aac b bx242\u2212 \u00b1\u2212= as more terms in these sequences of fractions are calculated the difference between the terms becomes smaller and smaller. this means that the terms become nearly equal to the same number. this number is called the limit of the sequence. (a) in the sequence in question 1 all the terms after the 7th term are the same when written correct to 3 decimal places. if x is a fraction in the sequence in question 1 then the next fraction is x+11. in this case the sequence reaches its limit when xx+=11. (i) show that xx+=11 can be rearranged to give the quadratic equation x2 + x \u2212 1 = 0. (ii) solve x 2 + x \u2212 1 = 0 and write down the positive decimal solution, correct to 3 decimal places. (iii) complete the table for the sequence in question 1 . fraction 11 21 32 53 85 2113 decimal 1 0.5 0.667 0.6 0.625 0.619 ", "6": "6 \u00a9 ucles 2014 0607/62/m/j/14 (b) (i) complete the table for the sequence in question 2 . fraction 12 32 56 4342 8586 decimal 2 0.667 1.2 0.977 1.012 (ii) solve xx+=12 for x > 0. (iii) explain the connection between the decimals in part (b)(i) and your answer to part (b)(ii) . (c) the positive solution of xnx+=1 gives the limit of these sequences of fractions. (i) xnx+=1 can be rearranged to give the quadratic equation x2 + x \u2212 n = 0. solve x2 + x \u2212 n = 0 and write down the positive value of x in terms of n. (ii) find three integer values of n that make the limit a positive integer. ", "7": "7 \u00a9 ucles 2014 0607/62/m/j/14 [turn over b modelling fitness training (20 marks) you are advised to spend no more than 45 minutes on this part. viola starts her fitness training. she intends to walk, jog and run to increase her fitness. 1 (a) on day 1 she walks 1.5 km in 20 minutes. show that her average walking speed is 4.5 km/h. (b) on day 2 she increases her average walking speed to 5 km/h. how many minutes does it take her to walk the 1.5 km? (c) viola wants to increase her average walking speed by 0.5 km/h each day. if she does, on which day will she walk at an average of 6.5 km/h? 2 she now begins to jog as well as walk. on day 7 she jogs for 20 minutes at 8.1 km/h. what distance does she jog? ", "8": "8 \u00a9 ucles 2014 0607/62/m/j/14 3 from day 10 she trains for one hour. she walks at an average speed of 6.4 km/h and she jogs at an average speed of 8.1 km/h. these speeds do not change. (a) construct a formula for the total distance, d km, when she walks for x minutes and jogs for the rest of the hour. (b) show that your formula simplifies to the model 607.1 486 xd\u2212= . (c) sketch the graph of the model in part (b) on the axes below, for 0 y x y 60. 9 0distance (km) time (min)60xd ", "9": "9 \u00a9 ucles 2014 0607/62/m/j/14 [turn over (d) what distance will she travel in the hour when she walks and jogs for the same amount of time? (e) the next month viola walks for 20 minutes, jogs for 20 minutes and runs for the rest of the hour. she travels a total distance of 9 km. work out her average speed when she is running. (f) the next month viola walks for x minutes, jogs for y minutes and runs for the rest of the hour. her average speed when she is running does not change from the value found in part (e) . (i) extend your model in part (b) for the total distance, d km, to include walking for x minutes, jogging for y minutes and running for the rest of the hour. (ii) show that your model simplifies to d = 601(750 \u2013 6.1 x \u2013 4.4 y). ", "10": "10 \u00a9 ucles 2014 0607/62/m/j/14 (g) (i) rewrite the model in part (f) when viola\u2019s walking and jogging times are both n minutes. (ii) sketch the graph of the model in part (g)(i) on the axes below, for 0 y n y 30. 0distance (km) time (min)30nd (iii) what is viola doing in her training when n = 0? (iv) what is viola doing in her training when n = 30? ", "11": "11 \u00a9 ucles 2014 0607/62/m/j/14 (v) modify the models in part (b) and part (f) when viola spends h hours training. model in part (b) model in part (f) ", "12": "12 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge a ssessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/62/m/j/14 blank page " }, "0607_s14_qp_63.pdf": { "1": " this document consists of 12 printed pages. ib14 06_0607_63/2rp \u00a9 ucles 2014 [turn over *6238789273* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/63 paper 6 (extended) may/june 2014 1 hour 30 minutes candidates answer on the question paper additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2014 0607/63/m/j/14 answer both parts a and b. a investigation totals (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation looks at possible totals when you make addition sums using only two different positive integers. the integers have no common factor unless otherwise stated. example using only 3 and 4 you can make a total of 23. 23 = 3 + 3 + 3 + 3 + 3 + 4 + 4. this is written as 23 = 5 \u00d7 3 + 2 \u00d7 4. in the table below, when a total is possible, the calculation is shown. when a total is not possible, the cell is crossed out. totals using only 3 and 4 total 1 2 3 4 5 6 7 8 calculation 1 \u00d7 3 1 \u00d7 4 2 \u00d7 3 1 \u00d7 3 + 1 \u00d7 4 2 \u00d7 4 you can make all the totals bigger than 8 by adding 3 to the possible totals 6, 7, 8, \u2026 to get 9, 10, 11, \u2026 . the largest total that is not possible is 5. 1 (a) complete the tables below. one integer is always 2. totals using only 2 and 3 total 1 2 3 4 5 6 7 8 calculation 1 \u00d7 2 1 \u00d7 3 2 \u00d7 2 2 \u00d7 3 2 \u00d7 2 + 1 \u00d7 3 the largest total that is not possible is 1. ", "3": "3 \u00a9 ucles 2014 0607/63/m/j/14 [turn over totals using only 2 and 5 total 1 2 3 4 5 6 7 8 calculation 1 \u00d7 2 2 \u00d7 2 3 \u00d7 2 1 \u00d7 2 + 1 \u00d7 5 4 \u00d7 2 the largest total that is not possible is \u2026\u2026. totals using only 2 and 7 total 3 4 5 6 7 8 9 10 calculation 3 \u00d7 2 1 \u00d7 7 4 \u00d7 2 5 \u00d7 2 the largest total that is not possible is \u2026\u2026. (b) from your answers in part (a) complete the following statement. the largest total, using only 2 and y, that is not possible is \u2026\u2026\u2026\u2026 ", "4": "4 \u00a9 ucles 2014 0607/63/m/j/14 2 (a) complete the tables below. one integer is always 3. totals using only 3 and 5 total 3 4 5 6 7 8 9 10 calculation 1 \u00d7 3 1 \u00d7 5 2 \u00d7 3 3 \u00d7 3 the largest total that is not possible is 7. totals using only 3 and 7 total 8 9 10 11 12 13 14 15 calculation 1 \u00d7 3 + 1 \u00d7 7 4 \u00d7 3 2 \u00d7 7 5 \u00d7 3 the largest total that is not possible is 11. totals using only 3 and 8 total 10 11 12 13 14 15 16 calculation 4 \u00d7 3 2 \u00d7 3 + 1 \u00d7 8 5 \u00d7 3 2 \u00d7 8 the largest total that is not possible is 13. (b) 3 and 6 have a common factor of 3. explain why, using only 3 and 6, you cannot find the largest total that is not possible. ", "5": "5 \u00a9 ucles 2014 0607/63/m/j/14 [turn over 3 (a) some answers for 5 and y are shown in the table. y largest total that is not possible 5 6 19 5 7 23 5 8 27 5 9 31 find an expression, in terms of y, for the largest total that is not possible using only 5 and y. (b) some answers for 7 and y are shown in the table. y largest total that is not possible 7 2 5 7 3 11 7 4 17 7 5 23 7 6 29 find an expression, in terms of y, for the largest total that is not possible using only 7 and y. ", "6": "6 \u00a9 ucles 2014 0607/63/m/j/14 4 some answers for x and y are shown in the table. x the expression for the largest total that is not possible 2 3 2 y \u2013 3 5 7 11 10 y \u2013 11 (a) complete the table by copying the results from questions 1(b) and 3. write down an expression, in terms of y, for the largest total that is not possible when x = 13. (b) write down an expression, in terms of x and y, for the largest total that is not possible. 5 (a) using only 24 and 25, calculate the largest total that is not possible. (b) using only 24 and 25, show how it is possible to get a total of 320. ", "7": "7 \u00a9 ucles 2014 0607/63/m/j/14 [turn over 6 the example on page 2 used only 3 and 4. totals using 3 and 4 total 1 2 3 4 5 6 7 8 calculation 1 \u00d7 3 1 \u00d7 4 2 \u00d7 3 1 \u00d7 3 + 1 \u00d7 4 2 \u00d7 4 the largest total that is not possible is 5. the smallest possible total, after which all totals are possible, is 6. so 6, 7, 8, 9, \u2026 are all possible. (a) use your answer to question 4(b) to write down an expression, in terms of x and y, for the smallest possible total after which all totals are possible. (b) show that your expression in part (a) is equal to ( x \u2013 1)( y \u2013 1). (c) find all the pairs of integers so that the smallest possible total, after which all totals are possible, is 24. ", "8": "8 \u00a9 ucles 2014 0607/63/m/j/14 b modelling designing an open box (20 marks) you are advised to spend no more than 45 minutes on this part. 25 cmx cm x cm engineers use an expensive metal to make a box for a machine. the method to make a net is: \u007f take a square piece of the metal of side 25 cm \u007f cut a square, of side x cm, from each corner 1 complete the inequality for x. < x < 2 find a model for the area, a cm2, of the net by writing a in terms of x. a = ", "9": "9 \u00a9 ucles 2014 0607/63/m/j/14 [turn over 3 the engineers fold the net to make a box. the diagram shows the 8 edges of the open box that are strengthened with a seal. find a model for the length of the seal, l cm, by writing l in terms of x. write your answer in its simplest form. l = ", "10": "10 \u00a9 ucles 2014 0607/63/m/j/14 4 (a) show that a model for the volume of the box, v cm3, is v = 625 x \u2013 100 x2 + 4x3. (b) assume the measurements on the net are given accurately. give a reason why the actual volume of the box may be different to v. (c) sketch the graph of v = 625 x \u2013 100 x2 + 4x3. ov x (d) find the maximum volume of the box. ", "11": "11 \u00a9 ucles 2014 0607/63/m/j/14 [turn over 5 for the machine to work efficiently, the box must have a capacity of at least one litre. (a) complete this new inequality for x. < x < (b) because of cost, the engineers want the area, a cm2, to be less than 450 cm2. use your answer to part (a) and question 2 to show that this is not possible. (c) the engineers decide to allow an area of metal which is less than 500 cm2. complete this inequality for x. < x < question 6 is printed on the next page. ", "12": "12 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge asse ssment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/63/m/j/14 6 the cost of making the box is made up of three items. \u007f $2 per square centimetre for the area of metal ( a cm2) \u007f $1 per centimetre for the length of the seal ( l cm) \u007f $500 for the labour (a) find, in terms of x, a model for the cost, $ c. c = (b) the company wants to sell the box at a profit of 20%. write down a model for the selling price, $ s. s = (c) find the lowest selling price for a box with a capacity of one litre. $ " }, "0607_w14_qp_11.pdf": { "1": " this document consists of 10 printed pages and 2 blank pages. ib14 11_0607_11/5rp \u00a9 ucles 2014 [turn over *7769525239* cambridge international examinations international general certificate of secondary education cambridge international mathematics 0607/11 paper 1 (core) october/november 2014 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2014 0607/11/o/n/14 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2014 0607/11/o/n/14 [turn over 1 (a) write twenty thousand two hundred in figures. answer (a) [1] (b) work out. 20 \u2013 7 \u00d7 2 answer (b) [1] (c) complete the following statement. =6 7 35 [1] 2 the diagram shows a fair spinner in the shape of a regular hexagon. 55 5887 which number is the spinner most likely to land on? answer [1] ", "4": "4 \u00a9 ucles 2014 0607/11/o/n/14 3 the bar chart and the frequency table show the methods of transport used by a group of students, on one day, to travel from home to school. car02468 frequency method of transportbus walkmethod of transportfrequency car bus walk8 4 (a) use the frequency table to complete the bar chart. [1] (b) use the bar chart to complete the frequency table. [1] (c) how many students are in the group? answer (c) [1] (d) the bus fare for travelling to school is $2. find the total amount paid by the students who travelled by bus. answer (d) $ [2] ", "5": "5 \u00a9 ucles 2014 0607/11/o/n/14 [turn over 4 measure and write down the size of angle pqr. pq r answer [1] 5 a dice was rolled twelve times. these are the scores. 5 1 4 4 2 3 1 1 4 2 5 1 find (a) the range, answer (a) [1] (b) the mode, answer (b) [1] (c) the median. answer (c) [2] ", "6": "6 \u00a9 ucles 2014 0607/11/o/n/14 6 b ade cnot to scale 3 cm2 cm 6 cm in the diagram ab is parallel to de. (a) complete the following. (i) angle abc = angle [1] (ii) angle bac = angle [1] (iii) triangle abc is to triangle edc because [2] (b) ab = 6 cm, bc = 2 cm and cd = 3 cm. work out the length of de. answer (b) cm [2] ", "7": "7 \u00a9 ucles 2014 0607/11/o/n/14 [turn over 7 find the circumference of a circular pond of radius 4 m. leave your answer in terms of \u03c0. answer m [2] 8 the diagram shows the graph of y = f(x) for \u20132 y x y 2. \u20134 \u20133 \u20132 \u20131 0 1234 \u20133 \u20134\u20132\u2013112y x on the same diagram, sketch the graph of y = f(x) + 2. [2] ", "8": "8 \u00a9 ucles 2014 0607/11/o/n/14 9 an aircraft flies for 2 hours and travels a distance of 1500 km. (a) work out the speed of the aircraft. answer (a) km/h [1] (b) write your answer to part (a) in standard form. answer (b) [1] 10 (a) factorise completely. 6 pq + 2p answer (a) [2] (b) solve the following equation. 4 \u2013 2 x = 6 \u2013 5 x answer (b) x = [2] ", "9": "9 \u00a9 ucles 2014 0607/11/o/n/14 [turn over 11 some of the students in a language class have visited spain ( s), some have visited france ( f), some have visited neither country and some have visited both countries. the venn diagram below illustrates this. su f 4 64 11 (a) write down n ()\u2032\u222afs . answer (a) [1] (b) work out the total number of students. answer (b) [1] one student is chosen at random. (c) what is the probability that a student has been to france but not to spain? answer (c) [1] (d) what is the probability that a student has been to france or to spain or to both countries? answer (d) [1] ", "10": "10 \u00a9 ucles 2014 0607/11/o/n/14 12 (a) solve the simultaneous equations. 5x + 3y = 13 3x + 5y = 11 answer (a) x = y = [4] (b) the cost of buying 5 burgers and 3 drinks is $13. the cost of buying 3 burgers and 5 drinks is $11. find the cost of buying 2 burgers and 2 drinks. answer (b) $ [2] ", "11": "11 \u00a9 ucles 2014 0607/11/o/n/14 blank page", "12": "12 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge asse ssment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/11/o/n/14 blank page " }, "0607_w14_qp_12.pdf": { "1": " this document consists of 10 printed pages and 2 blank pages. ib14 11_0607_12/2rp \u00a9 ucles 2014 [turn over * 9855402138* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/12 paper 1 (core) october/november 2014 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2014 0607/12/o/n/14 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2014 0607/12/o/n/14 [turn over 1 (a) write twenty thousand two hundred in figures. answer (a) [1] (b) work out. 20 \u2013 7 \u00d7 2 answer (b) [1] (c) complete the following statement. =6 7 35 [1] 2 the diagram shows a fair spinner in the shape of a regular hexagon. 55 5887 which number is the spinner most likely to land on? answer [1] ", "4": "4 \u00a9 ucles 2014 0607/12/o/n/14 3 the bar chart and the frequency table show the methods of transport used by a group of students, on one day, to travel from home to school. car02468 frequency method of transportbus walkmethod of transportfrequency car bus walk8 4 (a) use the frequency table to complete the bar chart. [1] (b) use the bar chart to complete the frequency table. [1] (c) how many students are in the group? answer (c) [1] (d) the bus fare for travelling to school is $2. find the total amount paid by the students who travelled by bus. answer (d) $ [2] ", "5": "5 \u00a9 ucles 2014 0607/12/o/n/14 [turn over 4 measure and write down the size of angle pqr. pq r answer [1] 5 a dice was rolled twelve times. these are the scores. 5 1 4 4 2 3 1 1 4 2 5 1 find (a) the range, answer (a) [1] (b) the mode, answer (b) [1] (c) the median. answer (c) [2] ", "6": "6 \u00a9 ucles 2014 0607/12/o/n/14 6 b ade cnot to scale 3 cm2 cm 6 cm in the diagram ab is parallel to de. (a) complete the following. (i) angle abc = angle [1] (ii) angle bac = angle [1] (iii) triangle abc is to triangle edc because [2] (b) ab = 6 cm, bc = 2 cm and cd = 3 cm. work out the length of de. answer (b) cm [2] ", "7": "7 \u00a9 ucles 2014 0607/12/o/n/14 [turn over 7 find the circumference of a circular pond of radius 4 m. leave your answer in terms of \u03c0. answer m [2] 8 the diagram shows the graph of y = f(x) for \u20132 y x y 2. \u20134 \u20133 \u20132 \u20131 0 1234 \u20133 \u20134\u20132\u2013112y x on the same diagram, sketch the graph of y = f(x) + 2. [2] ", "8": "8 \u00a9 ucles 2014 0607/12/o/n/14 9 an aircraft flies for 2 hours and travels a distance of 1500 km. (a) work out the speed of the aircraft. answer (a) km/h [1] (b) write your answer to part (a) in standard form. answer (b) [1] 10 (a) factorise completely. 6 pq + 2p answer (a) [2] (b) solve the following equation. 4 \u2013 2 x = 6 \u2013 5 x answer (b) x = [2] ", "9": "9 \u00a9 ucles 2014 0607/12/o/n/14 [turn over 11 some of the students in a language class have visited spain ( s), some have visited france ( f), some have visited neither country and some have visited both countries. the venn diagram below illustrates this. su f 4 64 11 (a) write down n ()\u2032\u222afs . answer (a) [1] (b) work out the total number of students. answer (b) [1] one student is chosen at random. (c) what is the probability that a student has been to france but not to spain? answer (c) [1] (d) what is the probability that a student has been to france or to spain or to both countries? answer (d) [1] ", "10": "10 \u00a9 ucles 2014 0607/12/o/n/14 12 (a) solve the simultaneous equations. 5x + 3y = 13 3x + 5y = 11 answer (a) x = y = [4] (b) the cost of buying 5 burgers and 3 drinks is $13. the cost of buying 3 burgers and 5 drinks is $11. find the cost of buying 2 burgers and 2 drinks. answer (b) $ [2] ", "11": "11 \u00a9 ucles 2014 0607/12/o/n/14 blank page ", "12": "12 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publis her (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge asse ssment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/12/o/n/14 blank page " }, "0607_w14_qp_13.pdf": { "1": " this document consists of 10 printed pages and 2 blank pages. ib14 11_0607_13/rp \u00a9 ucles 2014 [turn over *0970045139* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/13 paper 1 (core) october/november 2014 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2014 0607/13/o/n/14 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2014 0607/13/o/n/14 [turn over 1 (a) write twenty thousand two hundred in figures. answer (a) [1] (b) work out. 20 \u2013 7 \u00d7 2 answer (b) [1] (c) complete the following statement. =6 7 35 [1] 2 the diagram shows a fair spinner in the shape of a regular hexagon. 55 5887 which number is the spinner most likely to land on? answer [1] ", "4": "4 \u00a9 ucles 2014 0607/13/o/n/14 3 the bar chart and the frequency table show the methods of transport used by a group of students, on one day, to travel from home to school. car02468 frequency method of transportbus walkmethod of transportfrequency car bus walk8 4 (a) use the frequency table to complete the bar chart. [1] (b) use the bar chart to complete the frequency table. [1] (c) how many students are in the group? answer (c) [1] (d) the bus fare for travelling to school is $2. find the total amount paid by the students who travelled by bus. answer (d) $ [2] ", "5": "5 \u00a9 ucles 2014 0607/13/o/n/14 [turn over 4 measure and write down the size of angle pqr. pq r answer [1] 5 a dice was rolled twelve times. these are the scores. 5 1 4 4 2 3 1 1 4 2 5 1 find (a) the range, answer (a) [1] (b) the mode, answer (b) [1] (c) the median. answer (c) [2] ", "6": "6 \u00a9 ucles 2014 0607/13/o/n/14 6 b ade cnot to scale 3 cm2 cm 6 cm in the diagram ab is parallel to de. (a) complete the following. (i) angle abc = angle [1] (ii) angle bac = angle [1] (iii) triangle abc is to triangle edc because [2] (b) ab = 6 cm, bc = 2 cm and cd = 3 cm. work out the length of de. answer (b) cm [2] ", "7": "7 \u00a9 ucles 2014 0607/13/o/n/14 [turn over 7 find the circumference of a circular pond of radius 4 m. leave your answer in terms of \u03c0. answer m [2] 8 the diagram shows the graph of y = f(x) for \u20132 y x y 2. \u20134 \u20133 \u20132 \u20131 0 1234 \u20133 \u20134\u20132\u2013112y x on the same diagram, sketch the graph of y = f(x) + 2. [2] ", "8": "8 \u00a9 ucles 2014 0607/13/o/n/14 9 an aircraft flies for 2 hours and travels a distance of 1500 km. (a) work out the speed of the aircraft. answer (a) km/h [1] (b) write your answer to part (a) in standard form. answer (b) [1] 10 (a) factorise completely. 6 pq + 2p answer (a) [2] (b) solve the following equation. 4 \u2013 2 x = 6 \u2013 5 x answer (b) x = [2] ", "9": "9 \u00a9 ucles 2014 0607/13/o/n/14 [turn over 11 some of the students in a language class have visited spain ( s), some have visited france ( f), some have visited neither country and some have visited both countries. the venn diagram below illustrates this. su f 4 64 11 (a) write down n ()\u2032\u222afs . answer (a) [1] (b) work out the total number of students. answer (b) [1] one student is chosen at random. (c) what is the probability that a student has been to france but not to spain? answer (c) [1] (d) what is the probability that a student has been to france or to spain or to both countries? answer (d) [1] ", "10": "10 \u00a9 ucles 2014 0607/13/o/n/14 12 (a) solve the simultaneous equations. 5x + 3y = 13 3x + 5y = 11 answer (a) x = y = [4] (b) the cost of buying 5 burgers and 3 drinks is $13. the cost of buying 3 burgers and 5 drinks is $11. find the cost of buying 2 burgers and 2 drinks. answer (b) $ [2] ", "11": "11 \u00a9 ucles 2014 0607/13/o/n/14 blank page", "12": "12 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge asse ssment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/11/o/n/14 blank page " }, "0607_w14_qp_21.pdf": { "1": " this document consists of 8 printed pages. ib14 11_0607_21/rp \u00a9 ucles 2014 [turn over *5669966743* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/21 paper 2 (extended) october/november 2014 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2014 0607/21/o/n/14 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2014 0607/21/o/n/14 [turn over answer all the questions. 1 insert brackets in these calculations so that the answers are correct. (a) 10 \u2013 4 + 3 + 2 = 5 [1] (b) 10 \u2013 5 \u00d7 7 + 2 = 45 [1] 2 h\u00b0g\u00b0not to scale the diagram shows a regular hexagon and a regular pentagon. (a) find g. answer(a) g = [3] (b) find h. answer(b) h = [2] ", "4": "4 \u00a9 ucles 2014 0607/21/o/n/14 3 find the value of (a) 50, answer(a) [1] (b) 32 8\u2212. answer(b) [2] 4 (a) 3023 is a prime number. write down the factors of 3023. answer(a) [1] (b) p and q are prime numbers. (i) write down the highest common factor (hcf) of p and q. answer(b) (i) [1] (ii) write down an expression, in terms of p and q, for the lowest common multiple (lcm) of p and q. answer(b) (ii) [1] ", "5": "5 \u00a9 ucles 2014 0607/21/o/n/14 [turn over 5 (a) solve this inequality. 3( x + 2) > 5 x \u2013 2 answer(a) [3] (b) show your answer to part (a) on this number line. \u2013 3 \u2013 2 \u2013 1 01234567x [2] 6 sanjay asks a random sample of 200 students how they travel to school. these are his results. method of travel walk cycle bus car train frequency 52 47 62 27 12 (a) find the relative frequency of a student travelling by bus. answer(a) [1] (b) the school has 1200 students. (i) explain why it is reasonable to use your answer to part (a) as the probability that a student chosen at random from the school travels by bus. answer(b) (i) [1] (ii) estimate the number of students in the school who travel by bus. answer(b) (ii) [1] ", "6": "6 \u00a9 ucles 2014 0607/21/o/n/14 7 31 students took a test which was marked out of 70. the stem and leaf diagram shows their results. 1 3 3 4 7 2 4 4 7 8 9 key 2 4 = 24 marks 3 3 3 4 6 7 8 4 0 2 5 5 8 9 9 5 3 4 6 7 8 6 2 5 5 7 (a) find the median. answer(a) [1] (b) another student took the test later. what mark did this student get if (i) the median and range do not change, answer(b) (i) [1] (ii) the median and range both increase by 1? answer(b) (ii) [1] 8 in standard form, x = a \u00d7 10 5 and y = b \u00d7 107 where a < b. in standard form, yx = c \u00d7 10d where 1 y c < 10. (a) find the value of d. answer(a) [1] (b) find c in terms of a and b. answe r(b) c = [2] ", "7": "7 \u00a9 ucles 2014 0607/21/o/n/14 [turn over 9 here are the sketches of four graphs. ya x0yb x0 yc x0yd x0 each of the graphs represents one of these equations. y = x\u00b2 + 3x y = 3 \u2013 2 x y = 3 \u2013 x\u00b2 y = 2x + 3 y = x\u00b2 y = \u2013 3x y = x\u00b2 \u2013 3 y = 3x from the equations above, write down which one represents each graph. answe r graph a y = graph b y = graph c y = graph d y = [4] questions 10 and 11 are printed on the next page. ", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the p ublisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge a ssessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/21/o/n/14 10 (a) factorise completely. 8 a2 \u2013 50 b2 answer(a) [3] (b) write as a single fraction, simplifying your answer. 53 3 22 \u2212+\u2212 x x answer(b) [3] 11 (a) find log 28 . answer(a) [1] (b) find p when log 3 + 2log 5 = log p. answer(b) p = [2] " }, "0607_w14_qp_22.pdf": { "1": " this document consists of 8 printed pages. ib14 11_0607_22/rp \u00a9 ucles 2014 [turn over *7601043393* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/22 paper 2 (extended) october/november 2014 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2014 0607/22/o/n/14 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2014 0607/22/o/n/14 [turn over answer all the questions. 1 3 2=\u2212x find the values of x. answe r [2] 2 find the nth term of this sequence. \u2013 1, 0, 3, 8, 15, \u2026... answe r [3] 3 find the value of 23 916\u2212 \uf8f7\uf8f8\uf8f6\uf8ec\uf8ed\uf8eb. answe r [2] ", "4": "4 \u00a9 ucles 2014 0607/22/o/n/14 4 b a+ = +2 123 find the values of a and b. answe r a = b = [3] 5 (a) 7 24xnot to scale find x. answer(a) x = [2] (b) y8not to scale \u03b1 sin53=\u03b1 cos54=\u03b1 tan43=\u03b1 find y. answer(b) y = [2] ", "5": "5 \u00a9 ucles 2014 0607/22/o/n/14 [turn over 6 factorise. (a) x2 \u2013 5x \u2013 24 answer(a) [2] (b) pq + p \u2013 tq \u2013 t answer(b) [2] 7 the bag contains 5 white beads and 3 black beads. two beads are taken from the bag at random, without replacement. find the probability that the two beads are different colours. answe r [3] ", "6": "6 \u00a9 ucles 2014 0607/22/o/n/14 8 y varies inversely as the square root of x. when x = 4, y = 3. find (a) y in terms of x, answer(a) y = [2] (b) y when x = 9, answer(b) [1] (c) x in terms of y. answer(c) x = [2] 9 (a) find the value of \uf8f7\uf8f8\uf8f6\uf8ec\uf8ed\uf8eb 91log3 . answer(a) [1] (b) 3loglogqp= find q in terms of p. answer(b) q = [2] ", "7": "7 \u00a9 ucles 2014 0607/22/o/n/14 [turn over 10 y xo abl mnot to scale the equation of the line l is 3x + 4y = 12. the line cuts the x-axis at a and the y-axis at b. the midpoint of ab is m. (a) find the co-ordinates of (i) a, answer (a)(i) ( , ) [1] (ii) b, answer (a)(ii) ( , ) [1] (iii) m. answer (a)(iii) ( , ) [1] (b) find the equation of the line through the origin which is perpendicular to the line l. answer(b) [3] questions 11 and 12 are printed on the next page. ", "8": "8 permission to reproduce items where third -party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge asse ssment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/22/o/n/14 11 102 3 4 5 64 321y x draw the stretch of the shaded triangle with the y-axis invariant and factor 2. [2] 12 0y x4 2not to scale the diagram shows the graph of y = ax2 + bx + c. the graph passes through (0, 0) and has a maximum point (2, 4). find the values of a, b and c. answe r a = b = c = [3] " }, "0607_w14_qp_23.pdf": { "1": " this document consists of 8 printed pages. ib14 11_0607_23/2rp \u00a9 ucles 2014 [turn over *3816987330* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/23 paper 2 (extended) october/november 2014 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2014 0607/23/o/n/14 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2014 0607/23/o/n/14 [turn over answer all the questions. 1 here are the first five terms of a sequence. 3 7 11 15 19 (a) write down the next term. answer(a) [1] (b) find the nth term of the sequence. answer(b) [2] 2 solve these equations. (a) 5x + 7 = 3 answer(a) x = [2] (b) 7(x + 3) \u2013 2( x + 4) = 10 answer(b) x = [3] ", "4": "4 \u00a9 ucles 2014 0607/23/o/n/14 3 estimate the value of this calculation. 86.113.83.61 89.8 +\u00d7 show clearly the values you use. answe r [3] 4 (a) simplify 23 25\u2212, giving your answer as a fraction. answer(a) [2] (b) simplify. (i) (x3)4 answer(b) (i) [1] (ii) 410 xx answer(b) (ii) [2] ", "5": "5 \u00a9 ucles 2014 0607/23/o/n/14 [turn over 5 in the venn diagram, show the sets a, b and c so that a \u222a b = a, b \u2229 c = \u2205 and a \u2229 c \u2260 \u2205. u [3] 6 ba d cx\u00b0 y\u00b05 cm 12 cmnot to scale ab = 5 cm, bc = 12 cm and angle abc = 90\u00b0. bcd is a straight line. find (a) tan x\u00b0, answer(a) [1] (b) cos y\u00b0. answer(b) [3] ", "6": "6 \u00a9 ucles 2014 0607/23/o/n/14 7 factorise completely. (a) 3x2 \u2013 75 y2 answer(a) [2] (b) 15ap + 10 bp \u2013 9a \u2013 6b answer(b) [2] 8 i = \uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec \uf8ed\uf8eb 01 j = \uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec \uf8ed\uf8eb 10 a = \uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec \uf8ed\uf8eb \u221264 (a) a = pi + qj find the values of p and q. answer(a) p = q = [2] (b) calculate | a |, giving your answer in the form nm where m and n are prime numbers. answer(b) [3] ", "7": "7 \u00a9 ucles 2014 0607/23/o/n/14 [turn over 9 40\u00b0bpa o cdt not to scale b, d and p are points on the circumference of a circle, centre o. tba and tdc are tangents to the circle. dp is a diameter and angle btd = 40\u00b0. find the size of angle abp. answe r [2] question 10 is printed on the next page. ", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge a ssessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/23/o/n/14 10 f(x) = 2 x + 3 g( x) = 5 \u2013 3 x (a) find g( x) when f( x) = 11. answer(a) [2] (b) find and simplify an expression for f(g( x)) . answer(b) [2] (c) find g \u20131(x). answer(c) g\u20131(x) = [2] " }, "0607_w14_qp_31.pdf": { "1": " this document consists of 16 printed pages. ib14 11_0607_31/5rp \u00a9 ucles 2014 [turn over *0878953678* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/31 paper 3 (core) october/november 2014 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96. ", "2": "2 \u00a9 ucles 2014 0607/31/o/n/14 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2014 0607/31/o/n/14 [turn over answer all the questions. 1 write down (a) a factor of 84 which is greater than 10, answer(a) [1] (b) a multiple of 12, answer(b) [1] (c) a prime number between 20 and 30, answer(c) [1] (d) the value of 80, answer(d) [1] (e) the cube root of 64, answer(e) [1] (f) an example of an obtuse angle, answer(f) [1] (g) the order of rotational symmetry of a parallelogram. answer(g) [1] ", "4": "4 \u00a9 ucles 2014 0607/31/o/n/14 2 (a) write 3648 correct to the nearest 100. answer(a) [1] (b) write 2.6351 correct to 2 decimal places. answer(b) [1] (c) write 3.0865 correct to 3 significant figures. answer(c) [1] (d) simplify. 6 a + 3b \u2013 2a \u2013 b answer(d) [2] (e) find the value of 3 p \u2013 2q when p = \u20131 and q = 2. answer(e) [2] ", "5": "5 \u00a9 ucles 2014 0607/31/o/n/14 [turn over 3 (a) work out. (i) 183 answer(a) (i) [1] (ii) (0.34 + 1.27)2 answer(a) (ii) [1] (iii) 72 \u00d7 105 answer(a) (iii) [1] (iv) 87 \u2013 41 answer(a) (iv) [1] (v) 45% of 63.8 answer(a) (v) [2] (vi) 16.2584.3 \u00d7 answer(a) (vi) [2] (b) divide 52 in the ratio 6 : 7. answer(b) , [2] (c) dragon fruit cost $1.79 each. calculate the maximum number of dragon fruit sian can buy for $20. how much change should she receive from $20? answer(c) number of dragon fruit change $ [3] ", "6": "6 \u00a9 ucles 2014 0607/31/o/n/14 4 dave has 3 cats, 2 dogs and 4 rabbits. he shows this information in a pie chart. (a) calculate the sector angle for the 3 cats. answer(a) [2] (b) construct and label the pie chart. [3] ", "7": "7 \u00a9 ucles 2014 0607/31/o/n/14 [turn over 5 (a) colin invests $600 at a rate of 2.1% per year simple interest. calculate how much interest he receives at the end of 3 years. answer(a) $ [2] (b) ryan invests $600 at a rate of 2% per year compound interest. calculate how much interest ryan receives at the end of 3 years. answer(b) $ [4] ", "8": "8 \u00a9 ucles 2014 0607/31/o/n/14 6 to make 10 cupcakes, nadia uses 250 g flour, 125 g sugar, 100 g butter and 3 eggs. (a) the ratio flour : sugar : butter = 250 : 125 : 100. write this ratio in its simplest form. answer(a) : : [2] (b) the table shows the cost of ingredients. ingredient cost ($) 500 g flour 1.20 500 g sugar 1.40 250 g butter 2.00 6 eggs 0.90 (i) find the total cost of the ingredients which nadia uses to make 10 cupcakes. answer(b) (i) $ [3] (ii) find the cost of making one cupcake. answer(b) (ii) $ [1] (iii) nadia sells the cupcakes at the school bake sale for $0.50 each. find the profit she makes on one cupcake. answer(b) (iii) $ [1] (iv) calculate the percentage profit on one cupcake. answer(b) (iv) % [2] ", "9": "9 \u00a9 ucles 2014 0607/31/o/n/14 [turn over 7 this shape is drawn on a 1cm2 grid. (a) draw the line of symmetry on this shape. [1] (b) find the area of this shape in square centimetres. answer(b) cm2 [2] (c) use pythagoras\u2019 theorem to help you calculate the perimeter of this shape. answer(c) cm [4] (d) write your answer to part (c) in metres. answer(d) m [1] ", "10": "10 \u00a9 ucles 2014 0607/31/o/n/14 8 x\u00b0 not to scale the diagram shows a regular polygon. (a) write down the mathematical name for this polygon. answer(a) [1] (b) calculate the value of x. answer(b) [3] 9 15, 11, 7, 3, \u2026 (a) write down the next two numbers in this sequence. answer(a) , [2] (b) find an expression for the nth term of this sequence. answer(b) [2] ", "11": "11 \u00a9 ucles 2014 0607/31/o/n/14 [turn over 10 y x6 54321 \u20131 \u20132\u201330 \u2013 1 123456 \u20132 \u20133 (a) plot and label the points a(\u20132, 6) and b(3, 1) and join them with a straight line. [2] (b) calculate the length of ab. answer(b) [3] (c) find the gradient of ab. answer(c) [2] (d) find the equation of the line parallel to ab passing through the point (0, 1). give your answer in the form y = mx + c. answer(d) y = [2] ", "12": "12 \u00a9 ucles 2014 0607/31/o/n/14 11 sateja tests seven candles to find the time they take to burn. the price, in dollars, and the time, in hours, are shown in the table. price ($) 1.00 1.50 2.00 2.50 5.00 7.50 10.00 time (hours) 15 23 31 42 75 135 170 (a) complete the scatter diagram. the first 4 points have been plotted for you. 200 180160140120100 80604020 123456789 1 00 price ($)time (hours) [2] ", "13": "13 \u00a9 ucles 2014 0607/31/o/n/14 [turn over (b) what type of correlation does your scatter diagram show? answer(b) [1] (c) (i) find the mean price. answer(c) (i) $ [1] (ii) find the mean time. answer(c) (ii) hours [1] (iii) plot the mean point on the scatter diagram. [1] (iv) on the diagram, draw a line of best fit by eye. [2] (d) use your line of best fit to estimate the time taken to burn a candle that costs $6.50 . answer(d) hours [1] ", "14": "14 \u00a9 ucles 2014 0607/31/o/n/14 12 \u20133 \u20131030 02xy f( x) = 2 x3 + 5x2 \u2013 2x \u2013 5 (a) on the diagram, sketch the graph of y = f(x) for \u20133 y x y 2. [2] (b) find the zeros of f( x). answer(b) x = x = x = [2] ", "15": "15 \u00a9 ucles 2014 0607/31/o/n/14 [turn over (c) find the co-ordinates of the local maximum and local minimum points. answer(c) maximum ( , ) minimum ( , ) [2] (d) write down the number of solutions to the equations (i) f(x) = 8, answer(d) (i) [1] (ii) f(x) = 2. answer(d) (ii) [1] question 13 is printed on the next page.", "16": "16 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge asse ssment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/31/o/n/14 13 ry x8 765 4 321 \u20131\u20132\u20133\u20134\u20135\u20136\u20137 \u20138\u20134 \u20132 \u20133 \u20135\u2013 1 2 3 1 04 5 7 68 the diagram shows a quadrilateral r. (a) reflect r in the line x = 3. label the image s. [2] (b) translate the image s by the vector \uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec \uf8ed\uf8eb\u2212 42. label the image t. [2] (c) rotate the image t through 180 \u00b0 about the point (3, 0). label the image u. [2] (d) the three images join r to form one shape. write down the mathematical name for this shape. answer(d) [1] " }, "0607_w14_qp_32.pdf": { "1": " this document consists of 16 printed pages. ib14 11_0607_32/fp \u00a9 ucles 2014 [turn over *2653090276* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/32 paper 3 (core) october/november 2014 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96. ", "2": "2 \u00a9 ucles 2014 0607/32/o/n/14 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2014 0607/32/o/n/14 [turn over answer all the questions. 1 write down (a) a factor of 84 which is greater than 10, answer(a) [1] (b) a multiple of 12, answer(b) [1] (c) a prime number between 20 and 30, answe r(c) [1] (d) the value of 80, answer(d) [1] (e) the cube root of 64, answer(e) [1] (f) an example of an obtuse angle, answer(f) [1] (g) the order of rotational symmetry of a parallelogram. answer(g) [1] ", "4": "4 \u00a9 ucles 2014 0607/32/o/n/14 2 (a) write 3648 correct to the nearest 100. answer(a) [1] (b) write 2.6351 correct to 2 decimal places. answer(b) [1] (c) write 3.0865 correct to 3 significant figures. answer(c) [1] (d) simplify. 6 a + 3b \u2013 2a \u2013 b answer(d) [2] (e) find the value of 3 p \u2013 2q when p = \u20131 and q = 2. answer(e) [2] ", "5": "5 \u00a9 ucles 2014 0607/32/o/n/14 [turn over 3 (a) work out. (i) 183 answer(a) (i) [1] (ii) (0.34 + 1.27)2 answer(a) (ii) [1] (iii) 72 \u00d7 105 answer(a) (iii) [1] (iv) 87 \u2013 41 answer(a) (iv) [1] (v) 45% of 63.8 answer(a) (v) [2] (vi) 16.2584.3 \u00d7 answer(a) (vi) [2] (b) divide 52 in the ratio 6 : 7. answer(b) , [2] (c) dragon fruit cost $1.79 each. calculate the maximum number of dragon fruit sian can buy for $20. how much change should she receive from $20? answer(c) number of dragon fruit change $ [3] ", "6": "6 \u00a9 ucles 2014 0607/32/o/n/14 4 dave has 3 cats, 2 dogs and 4 rabbits. he shows this information in a pie chart. (a) calculate the sector angle for the 3 cats. answer(a) [2] (b) construct and label the pie chart. [3] ", "7": "7 \u00a9 ucles 2014 0607/32/o/n/14 [turn over 5 (a) colin invests $600 at a rate of 2.1% per year simple interest. calculate how much interest he receives at the end of 3 years. answer(a) $ [2] (b) ryan invests $600 at a rate of 2% per year compound interest. calculate how much interest ryan receives at the end of 3 years. answer(b) $ [4] ", "8": "8 \u00a9 ucles 2014 0607/32/o/n/14 6 to make 10 cupcakes, nadia uses 250 g flour, 125 g sugar, 100 g butter and 3 eggs. (a) the ratio flour : sugar : butter = 250 : 125 : 100. write this ratio in its simplest form. answer(a) : : [2] (b) the table shows the cost of ingredients. ingredient cost ($) 500 g flour 1.20 500 g sugar 1.40 250 g butter 2.00 6 eggs 0.90 (i) find the total cost of the ingredients which nadia uses to make 10 cupcakes. answer(b) (i) $ [3] (ii) find the cost of making one cupcake. answe r(b)(ii) $ [1] (iii) nadia sells the cupcakes at the school bake sale for $0.50 each. find the profit she makes on one cupcake. answer(b) (iii) $ [1] (iv) calculate the percentage profit on one cupcake. answer(b) (iv) % [2] ", "9": "9 \u00a9 ucles 2014 0607/32/o/n/14 [turn over 7 this shape is drawn on a 1cm2 grid. (a) draw the line of symmetry on this shape. [1] (b) find the area of this shape in square centimetres. answer(b) cm2 [2] (c) use pythagoras\u2019 theorem to help you calculate the perimeter of this shape. answer(c) cm [4] (d) write your answer to part (c) in metres. answer(d) m [1] ", "10": "10 \u00a9 ucles 2014 0607/32/o/n/14 8 x\u00b0 not to scale the diagram shows a regular polygon. (a) write down the mathematical name for this polygon. answer(a) [1] (b) calculate the value of x. answer(b) [3] 9 15, 11, 7, 3, \u2026 (a) write down the next two numbers in this sequence. answer(a) , [2] (b) find an expression for the nth term of this sequence. answer(b) [2] ", "11": "11 \u00a9 ucles 2014 0607/32/o/n/14 [turn over 10 y x6 54321 \u20131 \u20132\u201330 \u2013 1 123456 \u20132 \u20133 (a) plot and label the points a(\u20132, 6) and b(3, 1) and join them with a straight line. [2] (b) calculate the length of ab. answer(b) [3] (c) find the gradient of ab. answer(c) [2] (d) find the equation of the line parallel to ab passing through the point (0, 1). give your answer in the form y = mx + c. answer(d) y = [2] ", "12": "12 \u00a9 ucles 2014 0607/32/o/n/14 11 sateja tests seven candles to find the time they take to burn. the price, in dollars, and the time, in hours, are shown in the table. price ($) 1.00 1.50 2.00 2.50 5.00 7.50 10.00 time (hours) 15 23 31 42 75 135 170 (a) complete the scatter diagram. the first 4 points have been plotted for you. 200 180160140120100 80604020 123456789 1 00 price ($)time (hours) [2] ", "13": "13 \u00a9 ucles 2014 0607/32/o/n/14 [turn over (b) what type of correlation does your scatter diagram show? answer(b) [1] (c) (i) find the mean price. answer(c) (i) $ [1] (ii) find the mean time. answer(c) (ii) hours [1] (iii) plot the mean point on the scatter diagram. [1] (iv) on the diagram, draw a line of best fit by eye. [2] (d) use your line of best fit to estimate the time taken to burn a candle that costs $6.50 . answer(d) hours [1] ", "14": "14 \u00a9 ucles 2014 0607/32/o/n/14 12 \u20133 \u20131030 02xy f( x) = 2 x3 + 5x2 \u2013 2x \u2013 5 (a) on the diagram, sketch the graph of y = f(x) for \u20133 y x y 2. [2] (b) find the zeros of f( x). answer(b) x = x = x = [2] ", "15": "15 \u00a9 ucles 2014 0607/32/o/n/14 [turn over (c) find the co-ordinates of the local maximum and local minimum points. answer(c) maximum ( , ) minimum ( , ) [2] (d) write down the number of solutions to the equations (i) f(x) = 8, answer(d) (i) [1] (ii) f(x) = 2. answer(d) (ii) [1] question 13 is printed on the next page. ", "16": "16 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publis her (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge asse ssment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/32/o/n/14 13 ry x8 765 4 321 \u20131\u20132\u20133\u20134\u20135\u20136\u20137 \u20138\u20134 \u20132 \u20133 \u20135\u2013 1 2 3 1 04 5 7 68 the diagram shows a quadrilateral r. (a) reflect r in the line x = 3. label the image s. [2] (b) translate the image s by the vector \uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec \uf8ed\uf8eb\u2212 42. label the image t. [2] (c) rotate the image t through 180 \u00b0 about the point (3, 0). label the image u. [2] (d) the three images join r to form one shape. write down the mathematical name for this shape. answer(d) [1] " }, "0607_w14_qp_33.pdf": { "1": " this document consists of 16 printed pages. ib14 11_0607_33/fp \u00a9 ucles 2014 [turn over *4685416834* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/33 paper 3 (core) october/november 2014 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96. ", "2": "2 \u00a9 ucles 2014 0607/33/o/n/14 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2014 0607/33/o/n/14 [turn over answer all the questions. 1 write down (a) a factor of 84 which is greater than 10, answer(a) [1] (b) a multiple of 12, answer(b) [1] (c) a prime number between 20 and 30, answe r(c) [1] (d) the value of 80, answer(d) [1] (e) the cube root of 64, answer(e) [1] (f) an example of an obtuse angle, answer(f) [1] (g) the order of rotational symmetry of a parallelogram. answer(g) [1] ", "4": "4 \u00a9 ucles 2014 0607/33/o/n/14 2 (a) write 3648 correct to the nearest 100. answer(a) [1] (b) write 2.6351 correct to 2 decimal places. answer(b) [1] (c) write 3.0865 correct to 3 significant figures. answer(c) [1] (d) simplify. 6 a + 3b \u2013 2a \u2013 b answer(d) [2] (e) find the value of 3 p \u2013 2q when p = \u20131 and q = 2. answer(e) [2] ", "5": "5 \u00a9 ucles 2014 0607/33/o/n/14 [turn over 3 (a) work out. (i) 183 answer(a) (i) [1] (ii) (0.34 + 1.27)2 answer(a) (ii) [1] (iii) 72 \u00d7 105 answer(a) (iii) [1] (iv) 87 \u2013 41 answer(a) (iv) [1] (v) 45% of 63.8 answer(a) (v) [2] (vi) 16.2584.3 \u00d7 answer(a) (vi) [2] (b) divide 52 in the ratio 6 : 7. answer(b) , [2] (c) dragon fruit cost $1.79 each. calculate the maximum number of dragon fruit sian can buy for $20. how much change should she receive from $20? answer(c) number of dragon fruit change $ [3] ", "6": "6 \u00a9 ucles 2014 0607/33/o/n/14 4 dave has 3 cats, 2 dogs and 4 rabbits. he shows this information in a pie chart. (a) calculate the sector angle for the 3 cats. answer(a) [2] (b) construct and label the pie chart. [3] ", "7": "7 \u00a9 ucles 2014 0607/33/o/n/14 [turn over 5 (a) colin invests $600 at a rate of 2.1% per year simple interest. calculate how much interest he receives at the end of 3 years. answer(a) $ [2] (b) ryan invests $600 at a rate of 2% per year compound interest. calculate how much interest ryan receives at the end of 3 years. answer(b) $ [4] ", "8": "8 \u00a9 ucles 2014 0607/33/o/n/14 6 to make 10 cupcakes, nadia uses 250 g flour, 125 g sugar, 100 g butter and 3 eggs. (a) the ratio flour : sugar : butter = 250 : 125 : 100. write this ratio in its simplest form. answer(a) : : [2] (b) the table shows the cost of ingredients. ingredient cost ($) 500 g flour 1.20 500 g sugar 1.40 250 g butter 2.00 6 eggs 0.90 (i) find the total cost of the ingredients which nadia uses to make 10 cupcakes. answer(b) (i) $ [3] (ii) find the cost of making one cupcake. answe r(b)(ii) $ [1] (iii) nadia sells the cupcakes at the school bake sale for $0.50 each. find the profit she makes on one cupcake. answer(b) (iii) $ [1] (iv) calculate the percentage profit on one cupcake. answer(b) (iv) % [2] ", "9": "9 \u00a9 ucles 2014 0607/33/o/n/14 [turn over 7 this shape is drawn on a 1cm2 grid. (a) draw the line of symmetry on this shape. [1] (b) find the area of this shape in square centimetres. answer(b) cm2 [2] (c) use pythagoras\u2019 theorem to help you calculate the perimeter of this shape. answer(c) cm [4] (d) write your answer to part (c) in metres. answer(d) m [1] ", "10": "10 \u00a9 ucles 2014 0607/33/o/n/14 8 x\u00b0 not to scale the diagram shows a regular polygon. (a) write down the mathematical name for this polygon. answer(a) [1] (b) calculate the value of x. answer(b) [3] 9 15, 11, 7, 3, \u2026 (a) write down the next two numbers in this sequence. answer(a) , [2] (b) find an expression for the nth term of this sequence. answer(b) [2] ", "11": "11 \u00a9 ucles 2014 0607/33/o/n/14 [turn over 10 y x6 54321 \u20131 \u20132\u201330 \u2013 1 123456 \u20132 \u20133 (a) plot and label the points a(\u20132, 6) and b(3, 1) and join them with a straight line. [2] (b) calculate the length of ab. answer(b) [3] (c) find the gradient of ab. answer(c) [2] (d) find the equation of the line parallel to ab passing through the point (0, 1). give your answer in the form y = mx + c. answer(d) y = [2] ", "12": "12 \u00a9 ucles 2014 0607/33/o/n/14 11 sateja tests seven candles to find the time they take to burn. the price, in dollars, and the time, in hours, are shown in the table. price ($) 1.00 1.50 2.00 2.50 5.00 7.50 10.00 time (hours) 15 23 31 42 75 135 170 (a) complete the scatter diagram. the first 4 points have been plotted for you. 200 180160140120100 80604020 123456789 1 00 price ($)time (hours) [2] ", "13": "13 \u00a9 ucles 2014 0607/33/o/n/14 [turn over (b) what type of correlation does your scatter diagram show? answer(b) [1] (c) (i) find the mean price. answer(c) (i) $ [1] (ii) find the mean time. answer(c) (ii) hours [1] (iii) plot the mean point on the scatter diagram. [1] (iv) on the diagram, draw a line of best fit by eye. [2] (d) use your line of best fit to estimate the time taken to burn a candle that costs $6.50 . answer(d) hours [1] ", "14": "14 \u00a9 ucles 2014 0607/33/o/n/14 12 \u20133 \u20131030 02xy f( x) = 2 x3 + 5x2 \u2013 2x \u2013 5 (a) on the diagram, sketch the graph of y = f(x) for \u20133 y x y 2. [2] (b) find the zeros of f( x). answer(b) x = x = x = [2] ", "15": "15 \u00a9 ucles 2014 0607/33/o/n/14 [turn over (c) find the co-ordinates of the local maximum and local minimum points. answer(c) maximum ( , ) minimum ( , ) [2] (d) write down the number of solutions to the equations (i) f(x) = 8, answer(d) (i) [1] (ii) f(x) = 2. answer(d) (ii) [1] question 13 is printed on the next page. ", "16": "16 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publis her (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge asse ssment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/33/o/n/14 13 ry x8 765 4 321 \u20131\u20132\u20133\u20134\u20135\u20136\u20137 \u20138\u20134 \u20132 \u20133 \u20135\u2013 1 2 3 1 04 5 7 68 the diagram shows a quadrilateral r. (a) reflect r in the line x = 3. label the image s. [2] (b) translate the image s by the vector \uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec \uf8ed\uf8eb\u2212 42. label the image t. [2] (c) rotate the image t through 180 \u00b0 about the point (3, 0). label the image u. [2] (d) the three images join r to form one shape. write down the mathematical name for this shape. answer(d) [1] " }, "0607_w14_qp_41.pdf": { "1": " this document consists of 20 printed pages. ib14 11_0607_41/5rp \u00a9 ucles 2014 [turn over *5562327434* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/41 paper 4 (extended) october/november 2014 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120. ", "2": "2 \u00a9 ucles 2014 0607/41/o/n/14 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2014 0607/41/o/n/14 [turn over answer all the questions. 1 y x 0 \u2013 1 123456789 1 0 \u20132 \u20133 \u2013410 9 87654321 \u20131 \u20132 the diagram shows the graph of 5 x + 8y = 40 . (a) on the grid, show accurately the region defined by these inequalities. 5x + 8y [ 40 y [ 2x + 3 x [ \u20132 [4] (b) find the minimum value of y in the region. give your answer correct to 2 decimal places. answer(b) [3] ", "4": "4 \u00a9 ucles 2014 0607/41/o/n/14 2 the table shows the scores ( y) of 10 students in a mathematics test and their number of absences ( x) from school. number of absences ( x) 6 12 0 2 20 17 35 46 35 50 score ( y) 74 61 91 71 68 40 30 63 68 60 (a) complete this scatter diagram. the first six points have been plotted for you. 100 90 8070605040302010 10 20 30 number of absences40 500y xscore [2] (b) what type of correlation is shown by the scatter diagram? answer(b) [1] (c) find the equation of the regression line. write your answer in the form y = mx + c . answer(c) y = [2] ", "5": "5 \u00a9 ucles 2014 0607/41/o/n/14 [turn over (d) a student who had 26 absences missed the test. (i) use your equation to estimate a score for that student. answer(d) (i) [1] (ii) the teacher does not have confidence in this estimate. use your diagram to explain why. answer(d) (ii) [1] 3 \u20133 \u20131422 3xy 0 (a) on the diagram, sketch the graph of y = x 3 \u2013 3x + 4 for \u20133 y x y 3. [2] (b) describe fully the symmetry of the graph. answer(b) [3] (c) find the co-ordinates of the local maximum and local minimum. answer(c) maximum ( , ) minimum ( , ) [2] (d) find the range of values of x for which y < 5. answer(d) [3] ", "6": "6 \u00a9 ucles 2014 0607/41/o/n/14 4 (a) the shapes below form a sequence. the shapes are made with 1 cm rods. shape 1 shape 2 shape 3 shape 4 (i) complete the table below. shape number 1 2 3 4 7 n number of rods 4 8 12 16 number of squares enclosed 1 3 5 7 [5] (ii) find the number of squares enclosed by shape 100. answe r(a)(ii) [1] ", "7": "7 \u00a9 ucles 2014 0607/41/o/n/14 [turn over (b) here is another sequence of shapes made with 1 cm rods. shape 1 shape 2 shape 3 shape 4 (i) find the number of rods in shape 5. answer(b) (i) [1] (ii) find an expression, in terms of n, for the number of rods in shape n. answer(b) (ii) [3] ", "8": "8 \u00a9 ucles 2014 0607/41/o/n/14 5 the diagram below shows the cylindrical tank in which dipak stores his heating oil. dcabo2.5 m0.9 mnot to scale the length of the tank is 2.5 m and its radius is 0.9 m. dipak measures the depth of the oil to be 0.2 m. the diagram below shows the cross-section of the tank and the oil. 0.2 m0.9 mo abnot to scale (a) calculate the rectangular surface area of the oil, abcd . answer(a) m2 [4] ", "9": "9 \u00a9 ucles 2014 0607/41/o/n/14 [turn over (b) calculate angle aob and show that it rounds to 77.9\u00b0 correct to 1 decimal place. [3] (c) find the number of extra litres of oil that dipak needs to fill the tank. answer(c) litres [5] ", "10": "10 \u00a9 ucles 2014 0607/41/o/n/14 6 ac b ode not to scale a b the diagram shows a parallelogram, oacb. oc is a diagonal and od = de = ec . = a and = b. (a) find these vectors in terms of a and b. write each answer in its simplest form. (i) answer(a) (i) [1] (ii) answer(a) (ii) [2] (b) show that = . [2] (c) (i) what two conclusions can you make about ad and eb? answer(c) (i) [1] (ii) what conclusion can you make about the quadrilateral aebd ? answer(c) (ii) [1] ", "11": "11 \u00a9 ucles 2014 0607/41/o/n/14 [turn over 7 in a survey, 200 people were asked whether they owned a vehicle. 130 owned a car ( c), 30 owned a motorcycle ( m) and 85 owned a bicycle ( b). 18 owned a car and a motorcycle. 17 owned a motorcycle and a bicycle. 60 owned a car and a bicycle. 8 owned a car and a motorcycle and a bicycle. (a) complete this venn diagram. u cm b.. .. 10 830200 130 85 [3] (b) find the probability that a person, chosen at random from these 200 people, (i) does not own any of the three vehicles, answer(b) (i) [1] (ii) is an element of the set b \u2229 m \u2229 c \u2032. answer(b) (ii) [1] (c) two of the 200 people are chosen at random, without replacement. calculate the probability that (i) both own a motorcycle, answer(c) (i) [2] (ii) one owns only a car and the other owns only a bicycle. answer(c) (ii) [3] ", "12": "12 \u00a9 ucles 2014 0607/41/o/n/14 8 (a) oa b cde 32\u00b0 55\u00b0not to scale a, b, c, d and e are points on the circle centre o. be is a diameter, angle bec = 32 \u00b0 and angle adc = 55 \u00b0. find (i) angle ebc , answer(a) (i) angle ebc = [1] (ii) angle abe. answer(a) (ii) angle abe = [2] ", "13": "13 \u00a9 ucles 2014 0607/41/o/n/14 [turn over (b) p xq s rnot to scale p, q, r and s are points on a circle. pr and qs intersect at x. ps = 8 cm, qr = 12 cm and px = 5 cm. (i) explain why triangle pxs is similar to triangle qxr . answer(b) (i) [2] (ii) calculate the length of qx. answer(b) (ii) cm [2] (iii) find the value of qxrpxs triangleof areatriangleof area. answer(b) (iii) [1] ", "14": "14 \u00a9 ucles 2014 0607/41/o/n/14 9 a transport company records the masses, m kg, of 160 parcels it delivers. the cumulative frequency curve shows this information. 160 140120100 80 604020 51 0 1 5 2 0 mass (kg)25 30 350cumulative frequency m (a) (i) find the median. answer(a) (i) kg [1] (ii) find the lower quartile. answer(a) (ii) kg [1] (iii) find the interquartile range. answer(a) (iii) kg [1] ", "15": "15 \u00a9 ucles 2014 0607/41/o/n/14 [turn over (b) use the cumulative frequency curve to complete the frequency table. mass ( m kg) 0 < m y 10 10 < m y 15 15 < m y 20 20 < m y 25 25 < m y 35 frequency 14 28 [3] (c) on the grid below, use the results from part (b) to draw a histogram. 10 9 87654321 51 0 1 5 2 0 mass (kg)25 30 350frequency density m [3] ", "16": "16 \u00a9 ucles 2014 0607/41/o/n/14 10 y x \u20135 \u201355 50 (a) f(x) = 10x \u2013 3. (i) on the diagram, sketch the graph of y = f(x). [2] (ii) write down the equation of the asymptote of f( x). answer(a) (ii) [1] (b) g(x) = tan 30 x\u00b0. (i) on the same diagram, sketch the graph of y = g( x). [3] (ii) write down the equations of the vertical asymptotes of g( x) for values of x between \u20135 and 5. answer(b) (ii) [2] (c) solve the equation f( x) = g( x) for values of x between \u20135 and 5. answer(c) [2] ", "17": "17 \u00a9 ucles 2014 0607/41/o/n/14 [turn over 11 janine and gitte work for the same company. (a) in 2010, the ratio janine\u2019s salary : gitte\u2019s salary was 5 : 4 . the total of their salaries was $95 400. find each of their salaries in 2010. answer (a) janine $ gitte $ [2] (b) each of their salaries was a 6% increase on their 2009 salaries. (i) write down the ratio of their salaries in 2009. answer(b) (i) : [1] (ii) find the total of their salaries in 2009. answer(b) (ii) $ [3] (c) in 2011, janine and gitte each received an increase of the same amount of money. in 2011, the ratio janine\u2019s salary : gitte\u2019s salary was 11 : 9 . find the increase they each received. answer(c) $ [3] (d) in 2012 janine\u2019s friend, alain, received a salary increase of 8%. in 2013, his salary was reduced by 8%. find the percentage change in alain\u2019s salary over the two years. say whether it is an increase or decrease. answer(d) by % [3] ", "18": "18 \u00a9 ucles 2014 0607/41/o/n/14 12 north 20\u00b0lq p sx km35 km25 km 25 kmnot to scale a ship sails from s on a bearing of 020\u00b0. there is a lighthouse at l, 35 km due north of s. the light from the lighthouse has a range of 25 km. sp = x km. (a) use the cosine rule to show that x 2 \u2013 kx + 600 = 0, where k = 65.78 correct to 2 decimal places. [3] ", "19": "19 \u00a9 ucles 2014 0607/41/o/n/14 [turn over (b) (i) solve the equation x2 \u2013 65.78 x + 600 = 0, giving your answers correct to 2 decimal places. answer(b) x = or [3] (ii) write down the distance sq. answer(b) (ii) km [1] (c) the ship is sailing at 30 km/h. use your answers to part (b) to find the length of time the light is visible from the ship. give your answer in hours and minutes correct to the nearest minute. answer(c) h min [3] question 13 is printed on the next page. ", "20": "20 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the p ublisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge a ssessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/41/o/n/14 13 f(x) = 3 x \u2013 2 g( x) = x + 3 h( x) = 2 x2 + 7x + 3 (a) find h(g(0)). answer(a) [1] (b) find f(g( x)), writing your answer in its simplest form. answer(b) [2] (c) find f \u20131(x). answer(c) [2] (d) simplify )(h)(g xx. answer(d) [3] " }, "0607_w14_qp_42.pdf": { "1": " this document consists of 20 printed pages. ib14 11_0607_42/2rp \u00a9 ucles 2014 [turn over *6674351105* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/42 paper 4 (extended) october/november 2014 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120. ", "2": "2 \u00a9 ucles 2014 0607/42/o/n/14 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2014 0607/42/o/n/14 [turn over answer all the questions. 1 (a) asha and karim share a sum of money in the ratio asha : karim = 5 : 4 . asha receives $600. show that karim receives $480. [1] (b) asha spends 20% of her $600 and invests the remaining money at a rate of 4% per year simple interest. calculate the amount asha has at the end of 3 years. answer(b) $ [4] (c) karim invests all of his $480 at a rate of 3.5% per year compound interest. (i) calculate the amount karim has at the end of 3 years. answer(c) (i) $ [3] (ii) calculate the minimum number of whole years it takes for karim\u2019s $480 to double in value. answer(c) (ii) [3] ", "4": "4 \u00a9 ucles 2014 0607/42/o/n/14 2 a train leaves beijing at 15 52 and takes 13 hours and 45 minutes to reach xian. the distance from beijing to xian is 1200 km. the cost of a ticket is 441 yuan (\u00a5). (a) calculate the cost per kilometre to travel from beijing to xian. answer(a) \u00a5 [1] (b) find the time that the train arrives in xian. answer(b) [1] (c) calculate the average speed of the train. answer(c) km/h [2] (d) one day the train is delayed and arrives in xian at 05 58. for this train, calculate the percentage increase on the scheduled journey time of 13 h 45 min. answer(d) % [4] (e) the ticket price of \u00a5 441 is a 5% increase on the previous price of a ticket. calculate the previous price of a ticket. answer(e) \u00a5 [3] ", "5": "5 \u00a9 ucles 2014 0607/42/o/n/14 [turn over 3 u tc 211 7 10 u = {30 students} t = {students who go to the theatre} c = {students who go to the cinema} (a) (i) how many students go to the theatre but do not go to the cinema? answer(a) (i) [1] (ii) find n( t \u222a c ). answer(a) (ii) [1] (iii) find n( t ' \u222a c ). answer(a) (iii) [1] (b) one of the 30 students is chosen at random. find the probability that this student (i) goes to the cinema, answer(b) (i) [1] (ii) either goes to the theatre or does not go to the cinema. answer(b) (ii) [1] (c) two of the students who go to the theatre are chosen at random. find the probability that they both also go to the cinema. answer(c) [3] ", "6": "6 \u00a9 ucles 2014 0607/42/o/n/14 4 y x \u20135 \u20132020 100 f( x) = )2 (2 \u2212xx , 2\u2260x (a) on the diagram, sketch the graph of y = f(x), for values of x between \u20135 and 10. [2] (b) find the co-ordinates of (i) the local maximum point, answer(b) (i) ( , ) [1] (ii) the local minimum point. answer(b) (ii) ( , ) [1] ", "7": "7 \u00a9 ucles 2014 0607/42/o/n/14 [turn over (c) write down the range of f( x) for x \u2208=o. answer(c) [2] (d) write down an integer value of k for which the equation f( x) = k has no solutions. answer(d) [1] (e) write down the equation of the vertical asymptote of the graph of y = f(x). answer(e) [1] (f) (i) on the same diagram, sketch the graph of y = x + 2. [1] (ii) complete the following statement. the graph of y = x + 2 is of the graph of y = f(x). [1] (g) g(x) = 1.5x + 10 (i) on the same diagram, sketch the graph of y = g( x). [2] (ii) solve the inequality g( x) < f( x). answer(g) (ii) [2] ", "8": "8 \u00a9 ucles 2014 0607/42/o/n/14 5 (a) 136\u00b0y\u00b0cd abnot to scale in the diagram, cd and ab are parallel and ab = bc . find the value of y. answer(a) y = [3] (b) (15x + 20)\u00b0 x\u00b0not to scale the diagram shows part of a regular polygon. the interior angle is (15 x + 20)\u00b0 and the exterior angle is x\u00b0. find the number of sides of this polygon. answer(b) [4] ", "9": "9 \u00a9 ucles 2014 0607/42/o/n/14 [turn over (c) d e abcnot to scale 80\u00b030\u00b0 the points a, b, c, d and e lie on the circumference of a circle. find (i) angle ace , answer(c) (i) angle ace = [1] (ii) angle aec , answer(c) (ii) angle aec = [1] (iii) angle edc . answer(c) (iii) angle edc = [1] ", "10": "10 \u00a9 ucles 2014 0607/42/o/n/14 6 (a) the time taken, t minutes, for each of 100 cars to complete the same journey is recorded. time ( t minutes) 0 < t y 10 10 < t y 15 15 < t y 20 20 < t y 40 frequency 4 38 34 24 (i) calculate an estimate of the mean. answer(a) (i) min [2] (ii) on the grid, draw a histogram to show the information given in the table. 8 7654321 10 20 time (minutes)frequency density 30 400 t [3] ", "11": "11 \u00a9 ucles 2014 0607/42/o/n/14 [turn over (b) the time taken, t minutes, for each of another 100 cars to complete the same journey is recorded. the information is shown in the diagram below. 100 90 8070605040302010 10 20 time (minutes)cumulative frequency 30 40 500t find (i) the median, answer(b) (i) min [1] (ii) the inter-quartile range, answer(b) (ii) min [2] (iii) the number of cars taking more than 35 minutes. answer(b) (iii) [2] ", "12": "12 \u00a9 ucles 2014 0607/42/o/n/14 7 (a) solve the simultaneous equations. show your working. x + 2y = 4 2 x + 5y = 11 answer(a) x = y = [3] (b) solve the equation to find x in terms of k. kx x=\u2212\u2212+ 312 72 answer(b) x = [4] ", "13": "13 \u00a9 ucles 2014 0607/42/o/n/14 [turn over (c) a library spends $120 on newspapers and $90 on magazines. newspapers cost $ x each. magazines cost $( x + 0.4) each. (i) write down, in terms of x, the number of newspapers that can be bought for $120. answer(c) (i) [1] (ii) write down, in terms of x, the number of magazines that can be bought for $90. answer(c) (ii) [1] (iii) the total number of newspapers and magazines that the library buys is 225. find the cost of a newspaper. answer(c) (iii) $ [4] ", "14": "14 \u00a9 ucles 2014 0607/42/o/n/14 8 north m gbv240 km 200 km 77\u00b068\u00b033\u00b085\u00b0 not to scale the diagram shows the straight line distances between milan ( m), venice ( v), bologna ( b) and genoa ( g). (a) calculate the distance bv. answer(a) km [3] (b) calculate the distance gb. answer(b) km [3] ", "15": "15 \u00a9 ucles 2014 0607/42/o/n/14 [turn over (c) a map of the region is drawn to a scale of 1 : 1 000 000. calculate the area, on the map, of the quadrilateral mvbg . give your answer in square centimetres. answer(c) cm2 [5] (d) the bearing of v from m is 085\u00b0. calculate the bearing of (i) g from m, answer(d) (i) [1] (ii) m from v. answer(d) (ii) [1] ", "16": "16 \u00a9 ucles 2014 0607/42/o/n/14 9 the diagram shows two containers, a cuboid and a cylinder, connected by a pipe. not to scale the cuboid measures 1.5 m by 1.5 m by 1 m. it is filled with water. the cylinder is empty. it has radius 80 cm and height 90 cm. water flows from the cuboid to the cylinder until the cylinder is full. the water flows through the pipe at a rate of 35 cm3 per second. (a) calculate the time taken to fill the cylinder. give your answer in hours and minutes, correct to the nearest minute. answer(a) h min [5] (b) calculate the amount of water remaining in the cuboid. give your answer in cm 3, correct to 2 significant figures. answer(b) cm3 [4] (c) write your answer to part (b) in standard form. answer (c) cm3 [1] ", "17": "17 \u00a9 ucles 2014 0607/42/o/n/14 [turn over 10 c d a be fnot to scale in the diagram ad = 2dc, be = 21ec and def is a straight line. = r and = t. (a) find, in terms of r and t, in their simplest forms, (i) , answer(a) (i) [1] (ii) . answer(a) (ii) [2] (b) = 31r \u2013 31t . (i) find in terms of r and/or t. answer(b) (i) [1] (ii) what does your answer show about the point f ? [1] ", "18": "18 \u00a9 ucles 2014 0607/42/o/n/14 11 (a) f(x) = 2 x + 1 find f(f(2)) . answer(a) [2] (b) y x3 21 \u20131 \u20132\u201330\u2013 1 12345 \u20132 \u20133 \u20134 \u20135 the diagram shows the graph of y = g(x) . (i) on the same diagram, sketch the graph of y = g( x + 1). [2] (ii) describe fully the single transformation that maps the graph of y = g( x) onto the graph of y = g( x + 1). [2] ", "19": "19 \u00a9 ucles 2014 0607/42/o/n/14 [turn over (c) h(x) = x3 (i) find h\u20131(x). answer(c) (i) [1] (ii) y x1 \u201310 1 \u20131 the diagram shows the graph of y = h(x) . (a) on the same diagram, sketch the graph of y = h \u20131(x). [1] (b) describe fully the single transformation that maps the graph of y = h( x) onto the graph of y = h \u20131(x). [2] question 12 is printed on the next page. ", "20": "20 permission to reproduce items where third -party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge asse ssment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/42/o/n/14 12 4 cm h cmnot to scale the two bowls are mathematically similar. the table shows some information about these bowls. bowl height (cm) surface area (cm 2) volume (cm3) large bowl 4 a 500 small bowl h 90 108 calculate (a) the height of the small bowl, h cm, answer(a) cm [3] (b) the surface area of the large bowl, a cm2. answer(b) cm2 [2] " }, "0607_w14_qp_43.pdf": { "1": " this document consists of 19 printed pages and 1 blank page. ib14 11_0607_43/3rp \u00a9 ucles 2014 [turn over *0709951729* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/43 paper 4 (extended) october/november 2014 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120. ", "2": "2 \u00a9 ucles 2014 0607/43/o/n/14 formula list for the equation ax2 + bx + c = 0 x =2_\u00b1 4 2_ bb a c a curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ==sin sin sin abc ab c a2 = b2 + c2 \u2013 2bc cos a area = 1 2bc sin a a a b cb c", "3": "3 \u00a9 ucles 2014 0607/43/o/n/14 [turn over answer all the questions. 1 (a) one year sami paid 18% of his earnings in tax. after paying tax he had $65 600. how much did sami earn before paying tax? answer(a) $ [3] (b) sami and jennie each have $5000 to invest. they both invest in accounts that give compound interest. (i) sami invests in an account that gives 4% interest in the first year, 3% interest in the second year and 2% in any year after that. calculate the value of sami\u2019s investment after 3 years. answer(b) (i) $ [3] (ii) jennie\u2019s investment gives 2.5% compound interest each year. after 5 years, how much more is the value of sami\u2019s investment than jennie\u2019s? answer(b) (ii) $ [3] ", "4": "4 \u00a9 ucles 2014 0607/43/o/n/14 2 cy xa(3, 1) b(9, \u20133)0not to scale a is the point (3, 1) and b is the point (9, \u20133). (a) c is the midpoint of ab. find the co-ordinates of c. answer(a) ( , ) [1] (b) find the equation of the line, through c, perpendicular to ab. answer(b) [4] (c) the line ab meets the y-axis at p. the line in part (b) meets the y-axis at q. find the distance pq. answer(c) [2] ", "5": "5 \u00a9 ucles 2014 0607/43/o/n/14 [turn over 3 bay x7 654321 \u20131\u20132\u20133\u201340 \u2013 1 1234567 \u20132 \u20133 \u20134 (a) describe fully the single transformation that maps triangle a onto triangle b. answer(a) [3] (b) (i) enlarge triangle a with scale factor \u20132 and centre (3, 2). label the image c. [2] (ii) describe fully the single transformation that maps triangle c onto triangle a. answer(b) (ii) [2] (c) stretch triangle b with stretch factor 2 and y-axis invariant. label the image d. [2] ", "6": "6 \u00a9 ucles 2014 0607/43/o/n/14 4 ab co5 cm 8 cmnot to scale the shaded region is formed by the arcs of two circles. one circle has centre o and radius 5 cm. the other has centre c and radius 8 cm. the points a, b and c are on the circumference of the circle, centre o. (a) calculate angle aco and show that it rounds to 36.87\u00b0 correct to 2 decimal places. [2] (b) calculate the area of the sector cab . answer(b) cm2 [2] ", "7": "7 \u00a9 ucles 2014 0607/43/o/n/14 [turn over (c) calculate the area of the sector oac . answer(c) cm2 [2] (d) calculate the area of the triangle oac . answer(d) cm2 [2] (e) using your answers to parts (b) , (c) and (d), calculate the area of the shaded region. answer(e) cm2 [2] ", "8": "8 \u00a9 ucles 2014 0607/43/o/n/14 5 015 \u201310\u20133 3y x (a) on the diagram, sketch the graph of y = f(x) where f( x) = 3 + 5 x \u2013 x3 for \u20133 y x y 3. [2] (b) find the zeros of f( x). answer(b) , , [3] (c) find the co-ordinates of the local minimum. answer(c) ( , ) [2] (d) g(x) = 4 \u2013 2 x (i) solve the equation f( x) = g( x). answer(d) (i) x = or x = or x = [3] (ii) write down the range of values of x for which f(x) > g( x). answer(d) (ii) [2] ", "9": "9 \u00a9 ucles 2014 0607/43/o/n/14 [turn over 6 here is some information about three dolls that are all mathematically similar. not to scale height 8 cm 12 cm surface area 300 cm2 800 cm2 volume 600 cm3 (a) calculate the surface area of the smallest doll. answer(a) cm2 [2] (b) calculate the volume of the largest doll. answer(b) cm3 [4] ", "10": "10 \u00a9 ucles 2014 0607/43/o/n/14 7 (a) a od p ba bnot to scale = a and = b. d is the midpoint of ab and = 32. (i) find in terms of a and b. answer(a) (i) [1] (ii) find in terms of a and b. answer(a) (ii) [1] (iii) find in terms of a and b. write your answer as simply as possible. answer(a) (iii) [2] ", "11": "11 \u00a9 ucles 2014 0607/43/o/n/14 [turn over (b) a oq ba benot to scale the triangle aob is identical to the triangle in part (a). = a and = b. e is the midpoint of and = 32ae. (i) find in terms of a and b. answer (b)(i) [1] (ii) find in terms of a and b. write your answer as simply as possible. answer(b) (ii) [2] (c) from your answers to parts (a)(iii) and (b)(ii) , what can you say about the points p and q? answer(c) [1] ", "12": "12 \u00a9 ucles 2014 0607/43/o/n/14 8 a ship sails 80 km on a bearing of 065\u00b0 from a to b. it then sails 95 km on a bearing of 210\u00b0 from b to c. it then sails back to a. the diagram below shows this journey. northnorth ab c210\u00b0 65\u00b080 km 95 kmnot to scale (a) show that angle abc = 35\u00b0. [1] (b) (i) calculate the distance the ship sails from c to a. answer(b) (i) km [3] ", "13": "13 \u00a9 ucles 2014 0607/43/o/n/14 [turn over (ii) calculate the bearing on which the ship sails from c to a. answer(b) (ii) [4] (c) the ship sails at 18 km/h from a to b. it then sails at 22 km/h from b to c and then at 15 km/h from c to a. (i) calculate the total time for the journey. give your answer in hours and minutes. answer(c) (i) hours minutes [3] (ii) find the average speed for the whole journey. answer(c) (ii) km/h [2] ", "14": "14 \u00a9 ucles 2014 0607/43/o/n/14 9 there are 9 balls in a bag. 5 of these are red, 3 are yellow and 1 is white. two balls are selected at random without replacement. (a) complete the probability tree diagram. redfirst ball second ball 5 9red yellow white yellowred yellow white whitered yellow [3] ", "15": "15 \u00a9 ucles 2014 0607/43/o/n/14 [turn over (b) find the probability that (i) both balls are yellow, answer(b) (i) [2] (ii) the two balls are different colours. answer(b) (ii) [3] (c) write down the probability that the second ball is red. answer(c) [1] ", "16": "16 \u00a9 ucles 2014 0607/43/o/n/14 10 the heights, h cm, of 100 plants in each of two different soils, a and b, were recorded. the histogram shows the heights of the plants in soil a. 3.5 3 2.5 2 1.5 1 0.5 10 20 30 40 50 height (cm)60 70 80 90 1000frequency density h (a) complete the frequency table using the information in the histogram. height (h cm) 0 < h y 20 20 < h y 40 40 < h y 50 50 < h y 60 60 < h y 70 70 < h y 100 frequency 4 16 18 [2] (b) calculate an estimate of the mean height of the plants in soil a. answer(b) cm [2] (c) complete the cumulative frequency table for the heights of the plants in soil a. height (h cm) h y 20 h y 40 h y 50 h y 60 h y 70 h y 100 cumulative frequency 4 100 [2] (d) the graph opposite shows the cumulative frequency curve for the heights of the plants in soil b. using the same grid, draw the cumulative frequency curve for the heights of the plants in soil a. ", "17": "17 \u00a9 ucles 2014 0607/43/o/n/14 [turn over 100 90 8070605040302010 10cumulative frequency 20 30 40 50 height (cm)60 70 80 90 1000hsoil b [3] (e) (i) in which soil is the median height greater? show how you decide. answer(e) (i) [1] (ii) in which soil do the heights of the plants have a greater inter-quartile range and by how much? answer(e) (ii) soil by cm [4] (f) estimate the number of plants in soil b with a height greater than 85 cm. answer(f) [2] ", "18": "18 \u00a9 ucles 2014 0607/43/o/n/14 11 010 \u20136\u20138 8y x f( x) = 42 22 \u2212xx (a) on the diagram, sketch the graph of y = f(x) between x = \u20138 and x = 8. [3] (b) find the range of f( x) when x [ 1. answer(b) [3] (c) (i) write down the equations of the three asymptotes of the graph of y = f(x). answer(c) (i) [3] (ii) write down the equations of the asymptotes of the graph of y = f(x + 3). answer(c) (ii) [2] ", "19": "19 \u00a9 ucles 2014 0607/43/o/n/14 12 fieldwall x mnot to scale a farmer makes a rectangular field. for one side of the field he uses a wall. he uses 100 m of fencing to make the other three sides. the width of the field is x metres. (a) show that the area of the field, a m2, is given by a = 100 x \u2013 2x2 . [2] (b) find the width of the field when the area is 900 m2. answer(b) m [3] (c) find the maximum area of the field. answer(c) m2 [1] (d) another farmer uses 100 m of fencing to make a circular field. find the area of this field. answer(d) m2 [4] ", "20": "20 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge a ssessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/43/o/n/14 blank page " }, "0607_w14_qp_51.pdf": { "1": " this document consists of 6 printed pages and 2 blank pages. ib14 11_0607_51/rp \u00a9 ucles 2014 [turn over *1262558721* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/51 paper 5 (core) october/november 2014 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24. ", "2": "2 \u00a9 ucles 2014 0607/51/o/n/14 answer all the questions. investigation cubes identical small cubes fit together to make larger cubes. there are no gaps between these small cubes. for each cube that is made, a cross is marked on each outside face of each small cube. the diagram shows the first three cubes that can be made. diagram 1 1 by 1 by 1diagram 2 2 by 2 by 2diagram 3 3 by 3 by 3 this investigation is about the number of crosses that can be marked on cubes. look at the 1 by 1 by 1 cube. it is made from 1 small cube. it has 6 crosses on it (3 crosses are on the faces not seen on the diagram). 1 look at the 2 by 2 by 2 cube. (a) how many small cubes is this cube made from? . (b) explain why there are only 3 crosses on each small cube. (c) find the total number of crosses on the 2 by 2 by 2 cube. . ", "3": "3 \u00a9 ucles 2014 0607/51/o/n/14 [turn over 2 look at the 3 by 3 by 3 cube. (a) how many small cubes is this cube made from? . (b) how many of these small cubes have 3 crosses on them? . (c) there are 12 small cubes with 2 crosses on them. there is 1 small cube with no crosses on it. how many small cubes have only 1 cross on them? . 3 (a) on the dotty grid below, draw a 4 by 4 by 4 cube. mark a cross on the outside face of each small cube. (b) the 4 by 4 by 4 cube is made from 64 small cubes. (i) how many of these small cubes have 3 crosses on them? . (ii) how many of these small cubes have 2 crosses on them? . ", "4": "4 \u00a9 ucles 2014 0607/51/o/n/14 4 complete this table. you may use the dotty grid on page 6 to help you. size of cube total number of small cubes number of small cubes with 0 crosses 1 cross 2 crosses 3 crosses 2 by 2 by 2 0 0 3 by 3 by 3 1 12 4 by 4 by 4 64 8 24 5 by 5 by 5 27 54 8 5 (a) to work out the number of crosses on the 3 by 3 by 3 cube, complete the following. 1 small cube with 0 crosses gives 0 crosses small cubes with 1 cross gives 6 crosses 12 small cubes with 2 crosses gives ... crosses small cubes with 3 crosses gives ... crosses total = ... crosses (b) the total number of crosses can also be worked out by the following method. complete the following. the number of crosses on one face of the 3 by 3 by 3 cube is . so the total number of crosses on all the 6 faces is . (c) find the total number of crosses on a 4 by 4 by 4 cube. . ", "5": "5 \u00a9 ucles 2014 0607/51/o/n/14 6 (a) the number of small cubes with 0 crosses forms a sequence of cube numbers. size of cube 2 by 2 by 2 3 by 3 by 3 4 by 4 by 4 5 by 5 by 5 n by n by n number of small cubes with 0 crosses 0 1 8 27 for an n by n by n cube, find an expression, in terms of n, for the number of small cubes with 0 crosses. write your answer in the table above. (b) the number of small cubes with 1 cross forms a sequence. find the nth term of this sequence. . (c) the number of small cubes with 2 crosses forms a sequence. find the nth term of this sequence. . ", "6": "6 \u00a9 ucles 2014 0607/51/o/n/14 ", "7": "7 \u00a9 ucles 2014 0607/51/o/n/14 blank page", "8": "8 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge asse ssment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/51/o/n/14 blank page " }, "0607_w14_qp_52.pdf": { "1": " this document consists of 6 printed pages and 2 blank pages. ib14 11_0607_52/fp \u00a9 ucles 2014 [turn over *9368827495* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/52 paper 5 (core) october/november 2014 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24. ", "2": "2 \u00a9 ucles 2014 0607/52/o/n/14 answer all the questions. investigation cubes identical small cubes fit together to make larger cubes. there are no gaps between these small cubes. for each cube that is made, a cross is marked on each outside face of each small cube. the diagram shows the first three cubes that can be made. diagram 1 1 by 1 by 1diagram 2 2 by 2 by 2diagram 3 3 by 3 by 3 this investigation is about the number of crosses that can be marked on cubes. look at the 1 by 1 by 1 cube. it is made from 1 small cube. it has 6 crosses on it (3 crosses are on the faces not seen on the diagram). 1 look at the 2 by 2 by 2 cube. (a) how many small cubes is this cube made from? . (b) explain why there are only 3 crosses on each small cube. (c) find the total number of crosses on the 2 by 2 by 2 cube. . ", "3": "3 \u00a9 ucles 2014 0607/52/o/n/14 [turn over 2 look at the 3 by 3 by 3 cube. (a) how many small cubes is this cube made from? . (b) how many of these small cubes have 3 crosses on them? . (c) there are 12 small cubes with 2 crosses on them. there is 1 small cube with no crosses on it. how many small cubes have only 1 cross on them? . 3 (a) on the dotty grid below, draw a 4 by 4 by 4 cube. mark a cross on the outside face of each small cube. (b) the 4 by 4 by 4 cube is made from 64 small cubes. (i) how many of these small cubes have 3 crosses on them? . (ii) how many of these small cubes have 2 crosses on them? . ", "4": "4 \u00a9 ucles 2014 0607/52/o/n/14 4 complete this table. you may use the dotty grid on page 6 to help you. size of cube total number of small cubes number of small cubes with 0 crosses 1 cross 2 crosses 3 crosses 2 by 2 by 2 0 0 3 by 3 by 3 1 12 4 by 4 by 4 64 8 24 5 by 5 by 5 27 54 8 5 (a) to work out the number of crosses on the 3 by 3 by 3 cube, complete the following. 1 small cube with 0 crosses gives 0 crosses small cubes with 1 cross gives 6 crosses 12 small cubes with 2 crosses gives ... crosses small cubes with 3 crosses gives ... crosses total = ... crosses (b) the total number of crosses can also be worked out by the following method. complete the following. the number of crosses on one face of the 3 by 3 by 3 cube is . so the total number of crosses on all the 6 faces is . (c) find the total number of crosses on a 4 by 4 by 4 cube. . ", "5": "5 \u00a9 ucles 2014 0607/52/o/n/14 [turn over 6 (a) the number of small cubes with 0 crosses forms a sequence of cube numbers. size of cube 2 by 2 by 2 3 by 3 by 3 4 by 4 by 4 5 by 5 by 5 n by n by n number of small cubes with 0 crosses 0 1 8 27 for an n by n by n cube, find an expression, in terms of n, for the number of small cubes with 0 crosses. write your answer in the table above. (b) the number of small cubes with 1 cross forms a sequence. find the nth term of this sequence. . (c) the number of small cubes with 2 crosses forms a sequence. find the nth term of this sequence. . ", "6": "6 \u00a9 ucles 2014 0607/52/o/n/14 ", "7": "7 \u00a9 ucles 2014 0607/52/o/n/14 blank page", "8": "8 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publis her (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge asse ssment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/52/o/n/14 blank page " }, "0607_w14_qp_53.pdf": { "1": " this document consists of 6 printed pages and 2 blank pages. ib14 11_0607_53/fp \u00a9 ucles 2014 [turn over *9254095 192* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/53 paper 5 (core) october/november 2014 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24. ", "2": "2 \u00a9 ucles 2014 0607/53/o/n/14 answer all the questions. investigation cubes identical small cubes fit together to make larger cubes. there are no gaps between these small cubes. for each cube that is made, a cross is marked on each outside face of each small cube. the diagram shows the first three cubes that can be made. diagram 1 1 by 1 by 1diagram 2 2 by 2 by 2diagram 3 3 by 3 by 3 this investigation is about the number of crosses that can be marked on cubes. look at the 1 by 1 by 1 cube. it is made from 1 small cube. it has 6 crosses on it (3 crosses are on the faces not seen on the diagram). 1 look at the 2 by 2 by 2 cube. (a) how many small cubes is this cube made from? . (b) explain why there are only 3 crosses on each small cube. (c) find the total number of crosses on the 2 by 2 by 2 cube. . ", "3": "3 \u00a9 ucles 2014 0607/53/o/n/14 [turn over 2 look at the 3 by 3 by 3 cube. (a) how many small cubes is this cube made from? . (b) how many of these small cubes have 3 crosses on them? . (c) there are 12 small cubes with 2 crosses on them. there is 1 small cube with no crosses on it. how many small cubes have only 1 cross on them? . 3 (a) on the dotty grid below, draw a 4 by 4 by 4 cube. mark a cross on the outside face of each small cube. (b) the 4 by 4 by 4 cube is made from 64 small cubes. (i) how many of these small cubes have 3 crosses on them? . (ii) how many of these small cubes have 2 crosses on them? . ", "4": "4 \u00a9 ucles 2014 0607/53/o/n/14 4 complete this table. you may use the dotty grid on page 6 to help you. size of cube total number of small cubes number of small cubes with 0 crosses 1 cross 2 crosses 3 crosses 2 by 2 by 2 0 0 3 by 3 by 3 1 12 4 by 4 by 4 64 8 24 5 by 5 by 5 27 54 8 5 (a) to work out the number of crosses on the 3 by 3 by 3 cube, complete the following. 1 small cube with 0 crosses gives 0 crosses small cubes with 1 cross gives 6 crosses 12 small cubes with 2 crosses gives ... crosses small cubes with 3 crosses gives ... crosses total = ... crosses (b) the total number of crosses can also be worked out by the following method. complete the following. the number of crosses on one face of the 3 by 3 by 3 cube is . so the total number of crosses on all the 6 faces is . (c) find the total number of crosses on a 4 by 4 by 4 cube. . ", "5": "5 \u00a9 ucles 2014 0607/53/o/n/14 [turn over 6 (a) the number of small cubes with 0 crosses forms a sequence of cube numbers. size of cube 2 by 2 by 2 3 by 3 by 3 4 by 4 by 4 5 by 5 by 5 n by n by n number of small cubes with 0 crosses 0 1 8 27 for an n by n by n cube, find an expression, in terms of n, for the number of small cubes with 0 crosses. write your answer in the table above. (b) the number of small cubes with 1 cross forms a sequence. find the nth term of this sequence. . (c) the number of small cubes with 2 crosses forms a sequence. find the nth term of this sequence. . ", "6": "6 \u00a9 ucles 2014 0607/53/o/n/14 ", "7": "7 \u00a9 ucles 2014 0607/53/o/n/14 blank page", "8": "8 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publis her (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge a ssessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/53/o/n/14 blank page " }, "0607_w14_qp_61.pdf": { "1": " this document consists of 11 printed pages and 1 blank page. ib14 11_0607_61/2rp \u00a9 ucles 2014 [turn over *3861217397* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/61 paper 6 (extended) october/november 2014 1 hour 30 minutes candidates answer on the question paper additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2014 0607/61/o/n/14 answer both parts a and b. a investigation cubes (20 marks) you are advised to spend no more than 45 minutes on this part. identical small cubes fit together to make larger cubes. there are no gaps between these small cubes. for each cube that is made, a cross is marked on each outside face of each small cube. the diagram shows the first three cubes that can be made. diagram 1 1 by 1 by 1diagram 2 2 by 2 by 2diagram 3 3 by 3 by 3 this investigation is about the number of crosses that can be marked on cubes. look at the 1 by 1 by 1 cube. it is made from 1 small cube. it has 6 crosses on it (3 crosses are on the faces not seen on the diagram). 1 look at the 2 by 2 by 2 cube. (a) how many small cubes is this cube made from? . (b) explain why there are only 3 crosses on each small cube. (c) find the total number of crosses on the 2 by 2 by 2 cube. . ", "3": "3 \u00a9 ucles 2014 0607/61/o/n/14 [turn over 2 look at the 3 by 3 by 3 cube. (a) how many small cubes is this cube made from? . (b) how many of these small cubes have 3 crosses on them? . (c) there are 12 small cubes with 2 crosses on them. there is 1 small cube with no crosses on it. how many small cubes have only 1 cross on them? . 3 complete this table. you may use the dotty grid on page 7 to help you. size of cube total number of small cubes number of small cubes with 0 crosses 1 cross 2 crosses 3 crosses 2 by 2 by 2 0 0 3 by 3 by 3 1 12 4 by 4 by 4 64 8 24 5 by 5 by 5 27 54 8 ", "4": "4 \u00a9 ucles 2014 0607/61/o/n/14 4 (a) to work out the number of crosses on the 3 by 3 by 3 cube, complete the following. 1 small cube with 0 crosses gives 0 crosses small cubes with 1 cross gives 6 crosses 12 small cubes with 2 crosses gives ... crosses small cubes with 3 crosses gives ... crosses total = ... crosses (b) the total number of crosses can also be worked out by the following method. complete the following. the number of crosses on one face of the 3 by 3 by 3 cube is . so the total number of crosses on all the 6 faces is . (c) find the total number of crosses on a 4 by 4 by 4 cube. . (d) find an expression, in terms of n, for the total number of crosses on an n by n by n cube. . ", "5": "5 \u00a9 ucles 2014 0607/61/o/n/14 [turn over 5 the number of small cubes with 0 crosses forms a sequence. size of cube 2 by 2 by 2 3 by 3 by 3 4 by 4 by 4 5 by 5 by 5 n by n by n number of small cubes with 0 crosses 0 1 8 27 for an n by n by n cube, find an expression, in terms of n, for the number of small cubes with 0 crosses. write your answer in the table above. 6 for an n by n by n cube, an expression for the number of small cubes with one cross is 6( n \u2013 2) 2. in an n by n by n cube, can the number of small cubes with 0 crosses equal the number of small cubes with one cross? show your working. ", "6": "6 \u00a9 ucles 2014 0607/61/o/n/14 7 for an n by n by n cube, find an expression, in terms of n, for the number of small cubes with 2 crosses. . 8 (a) in an n by n by n cube there are 64 small cubes that have 0 crosses on them. how many small cubes does it have altogether? . (b) in another n by n by n cube there are 60 small cubes that have 2 crosses on them. in this cube, how many small cubes have only 1 cross on them? . ", "7": "7 \u00a9 ucles 2014 0607/61/o/n/14 [turn over ", "8": "8 \u00a9 ucles 2014 0607/61/o/n/14 b modelling fish ponds (20 marks) you are advised to spend no more than 45 minutes on this part. volume of a cylinder of radius r, height h, is \u03c0 r2h volume of a sphere, radius r, is 3 34r\u03c0 fish ponds can be either hemispherical or cylindrical. dr dcylindrical pond hemispherical pond 1 (a) a hemispherical pond has radius r metres. when r = 3, show that the volume of the pond is 18\u03c0 m3. (b) a cylindrical pond has a radius of d metres and a depth of d metres. show that the volume of this pond is \u03c0 d 3 cubic metres. (c) the radius and the depth of the cylindrical pond in part (b) is the same as the radius of the hemispherical pond in part (a) . show that the cylindrical pond holds more water than the hemispherical pond. (d) a hemispherical pond of radius r metres has the same volume as a cylindrical pond of radius and depth d metres. show that r d 3 32= . ", "9": "9 \u00a9 ucles 2014 0607/61/o/n/14 [turn over 2 theo wants to work out how many fish he can put in a pond. a fish needs 5 litres of water for every 0.1 cm of its length. (a) the average length of 15 fish is 18 cm. find the number of cubic metres of water needed for these fish. . (b) there are f fish in the pond, with an average length of l cm. find a model for the number of cubic metres of water, w, needed. . (c) theo\u2019s pond has a volume of 20 m3. (i) use your model to find the maximum number of fish, of average length 24 cm, that can be put in this pond. . (ii) if theo\u2019s pond is hemispherical find its radius. . (iii) if theo\u2019s pond is cylindrical, and the radius and depth are the same, find its radius. . ", "10": "10 \u00a9 ucles 2014 0607/61/o/n/14 3 theo decides to have a cylindrical pond. the radius, r metres, does not have to be the same as the depth, d metres. (a) for a pond with volume 20 m3 find a model for the depth, d, in terms of r. . (b) sketch the graph of d against r for 1 y r y 5. 05rd 7 (c) what practical problem is there when the radius is less than one metre? (d) find the radius of a pond when the depth is 1 m. . ", "11": "11 \u00a9 ucles 2014 0607/61/o/n/14 4 the water level must be 30 cm below the top of the sides of the pond. (a) modify your model in question 3 (a) . . (b) explain how this affects your graph in question 3 (b) . ", "12": "12 permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge assess ment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/61/o/n/14 bank page " }, "0607_w14_qp_62.pdf": { "1": " this document consists of 11 printed pages and 1 blank page. ib14 11_0607_62/4rp \u00a9 ucles 2014 [turn over *2215383014* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/62 paper 6 (extended) october/november 2014 1 hour 30 minutes candidates answer on the question paper additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2014 0607/62/o/n/14 answer both parts a and b. a investigation taxicab geometry (20 marks) you are advised to spend no more than 45 minutes on this part. a taxicab has to travel from a to b. in taxicab geometry, to go from a to b, you must only go along gridlines and take a shortest route. a b the diagram shows two of the possible shortest routes from a to b. the taxicab distance ab is 5. 1 (a) e d c for this grid, write down the taxicab distance cd and the taxicab distance de. taxicab distance cd . taxicab distance de . ", "3": "3 \u00a9 ucles 2014 0607/62/o/n/14 [turn over (b) on the grids below, show the three possible shortest routes from c to d. remember, you must only go along gridlines. d cd cd c (c) on the grids below, show all of the possible shortest routes from d to e. draw one route on each grid. de de de de ", "4": "4 \u00a9 ucles 2014 0607/62/o/n/14 (d) (i) on the grid below, plot two points with taxicab distance equal to 5 and only one possible shortest route between them. (ii) on the answer grid below, plot two points with taxicab distance not equal to 6 and exactly six possible shortest routes between them. you may use the first grid for your working. working grid answer grid ", "5": "5 \u00a9 ucles 2014 0607/62/o/n/14 [turn over 2 the taxicab is based at t, (0, 0) on the grid. possible destinations are marked . there are 35 possible shortest routes from t to (4, 3). ty x3 2 1 102 3 435 (a) write beside each destination on the x-axis and the y-axis, the number of shortest routes from t. (b) there are three shortest routes from t to destination (1, 2). each shortest route goes through either (0, 2) or (1, 1). explain how the number of shortest routes to (0, 2) and to (1, 1) can be used to find the number of shortest routes to (1, 2). (c) write beside each destination on the grid the number of shortest routes from t. (d) there are 120 shortest routes from t to destination (7, 3). how many shortest routes are there from t to (6, 3) and what is this taxicab distance? number of shortest routes ... taxicab distance .. ", "6": "6 \u00a9 ucles 2014 0607/62/o/n/14 3 in this question, all taxicab distances are integers. (a) on the 6 by 6 grid below, plot the seven points where the taxicab distance from s is equal to the taxicab distance from t. st (b) v and w are on the same horizontal gridline. the taxicab distance vw is 9. how many points have a taxicab distance from v that is equal to the taxicab distance from w? . (c) x and y are at opposite corners of a 2 by 2 square. on each of the following grids, plot all the points where the taxicab distance from x is equal to the taxicab distance from y. (i) 2 by 2 grid xy (ii) 4 by 4 grid xy ", "7": "7 \u00a9 ucles 2014 0607/62/o/n/14 [turn over (iii) 6 by 6 grid xy (iv) x and y are on an n by n grid, when n is an even number. find an expression, in terms of n, for the number of points where the taxicab distance from x is equal to the taxicab distance from y. . ", "8": "8 \u00a9 ucles 2014 0607/62/o/n/14 b modelling throwing a ball (20 marks) you are advised to spend no more than 45 minutes on this part. when a ball is thrown the model of its path is y = ax 2 + bx + c. y is the vertical height in metres of the ball above the horizontal ground. x is the horizontal distance in metres that the ball has travelled from where it was thrown. a, b and c are constants. 1 (a) a ball is thrown from (0, 0). the model of the ball\u2019s path is y = _ 81x2 + 45x. (i) on the diagram, sketch the graph of this equation for 0 y x y 12. y x012 (ii) how far does the ball travel horizontally before hitting the ground? . (iii) what is the greatest height that the ball reaches? . (iv) a vertical fence, 2 m high, stands on the horizontal ground 6 m from where the ball was thrown. how far above this fence is the ball when it is 6 m from where it was thrown? . ", "9": "9 \u00a9 ucles 2014 0607/62/o/n/14 [turn over (v) there are two positions where a 2 m high fence could be built so that the ball just passes over the top. one position is 2 m from where the ball was thrown. find the other position. . (b) the ball is now thrown from 1.5 m above the ground. use this information to modify the model in part (a) . .. 2 a second ball is thrown from (0, 0). it passes through the points (3, 1.2) and (5, 0). (a) use these co-ordinates to write down three equations in a, b and c. .. .. .. (b) solve your equations to find values for a, b and c, and write down the equation of the path of this second ball. a = ... b = ... c = ... .. ", "10": "10 \u00a9 ucles 2014 0607/62/o/n/14 (c) a vertical fence, 2 m high, stands on the horizontal ground 2 m from where this second ball was thrown. will this second ball hit the fence? explain your answer. 3 a ball is thrown from (0, 0). it just passes over a fence, k metres from (0, 0) and hits the ground at ( x, 0). a general model of its path is ) () ( xkkxxhxy\u2212\u2212= . h is the height of the fence in metres. x is the horizontal distance, in metres, that the ball travels before hitting the ground. (a) (i) using the information in question 1(a) show that this general model gives y = _ 81x2 + 45x. (ii) explain why this general model does not give the equation of the ball\u2019s path in question 1(b) . ... . ... . ", "11": "11 \u00a9 ucles 2014 0607/62/o/n/14 (b) a ball is thrown from (0, 0). it just passes over a 2 m high fence that is 8 m from (0, 0) and hits the ground at (12, 0). (i) use the general model to find the equation of the ball\u2019s path. .. (ii) find the position where another 2 m high fence could be built so that the ball just passes over the top. . (c) a ball is thrown from (0, 0). it just passes over two 2.5 m high fences. the fences are built so that one is twice as far from (0, 0) as the other. one fence is 10 m from (0, 0). (i) find the two possible horizontal distances that the ball can travel before it hits the ground. .. (ii) find the equation for each path of this ball. .. .. (iii) what is the greatest height that the ball reaches? . ", "12": "12 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge asse ssment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/62/o/n/14 blank page " }, "0607_w14_qp_63.pdf": { "1": " this document consists of 12 printed pages. ib14 11_0607_63/5rp \u00a9 ucles 2014 [turn over *2009383695* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/63 paper 6 (extended) october/november 2014 1 hour 30 minutes candidates answer on the question paper additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2014 0607/63/o/n/14 answer both parts a and b. a investigation the end result (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation looks at some relationships between unit fractions. a unit fraction is a fraction which has a numerator of 1. 1 the difference between the unit fractions 41 and 51 is 201 2045 51 41=\u2212=\u2212 . the product of the unit fractions 41 and 51 is 201 51 41=\u00d7 . the difference and the product of the unit fractions 41 and 51 are the same. (a) (i) find the difference and the product of the unit fractions 31 and 41. difference = product = ... (ii) find the difference and the product of the unit fractions 31 and 51. difference = product = ... ", "3": "3 \u00a9 ucles 2014 0607/63/o/n/14 [turn over (iii) find another pair of unit fractions whose difference and product are the same. ... and ... (b) a and b are positive integers where a < b. write as a single algebraic fraction (i) ba11\u2212, . (ii) ba11\u00d7. . (c) a pair of unit fractions has the same difference and product. complete the following statement. when the larger fraction is n1, the smaller fraction is ... ", "4": "4 \u00a9 ucles 2014 0607/63/o/n/14 2 the sum of the unit fractions 21 and 41 is 43 86 824 41 21= =+=+ . the numbers 3 and 4 form two sides of a right-angled triangle. 3 4not to scale the hypotenuse of this triangle is 5 25 432 2= =+ . the set of integers (3, 4, 5) is called a pythagorean triple. (a) (i) find the sum of the unit fractions 51 and 71. . (ii) using your answer to part (a)(i) , find a pythagorean triple that may be formed from the sum of 51 and 71. ( ... , .. , . ) (iii) find the sum of 91 and 111. . (iv) can a pythagorean triple be formed from your answer to part (a)(iii) ? explain your answer. ... . ", "5": "5 \u00a9 ucles 2014 0607/63/o/n/14 [turn over (b) for some values of p and q, the sum of the unit fractions p1 and q1 can be used to form a pythagorean triple. (i) write as a single algebraic fraction qp1 1+. . (ii) complete the pythagorean triple in terms of p and q. ( .. , ... , pq + 2) (iii) by applying pythagoras\u2019 theorem to your answer to part (b)(ii) , show that p 2 + q2 = 2pq + 4. ", "6": "6 \u00a9 ucles 2014 0607/63/o/n/14 (iv) find the two algebraic relationships between p and q so that q p1 1+ can be used to form a pythagorean triple. . . ", "7": "7 \u00a9 ucles 2014 0607/63/o/n/14 [turn over part b starts on page 8. ", "8": "8 \u00a9 ucles 2014 0607/63/o/n/14 b modelling rescue mission (20 marks) you are advised to spend no more than 45 minutes on this part. a rescue team is going to fly to a disaster area. there must be at least 35 people in the team and they need at least 80 tonnes of equipment. the objective of this task is to find the best way to organise the rescue mission. two planes, x and y, are available to take the rescue team and their equipment. both planes must be back at the starting airport in less than 24 hours. the maximum loads, flight times and total cost for each plane are shown in the table. plane maximum number of people per flight maximum mass of equipment (tonnes) maximum return flight time (hours) cost for return flight ($ thousand) x 5 10 3 40 y 7 20 4 65 let x be the number of return flights made by plane x and y be the number of return flights made by plane y. the rescue mission is to be modelled by five inequalities. 1 (a) (i) the total mass, in tonnes, of the equipment carried by the two planes is 10 x + 20 y. explain why the mass of the equipment to be carried by the two planes can be shown by the inequality 10 x + 20 y [ 80. ... . (ii) find, in terms of x and y, an inequality to show the total number of people carried by the two planes. . (iii) find, in terms of x and y, an inequality to show the total flight time of the two planes. . ", "9": "9 \u00a9 ucles 2014 0607/63/o/n/14 [turn over (b) complete each inequality below to show (i) the greatest number of flights that plane x would be able to make, 0 y x y (ii) the greatest number of flights that plane y would be able to make. 0 y y y (c) write an expression, in terms of x and y, for the total cost of the flights, in thousands of dollars. . ", "10": "10 \u00a9 ucles 2014 0607/63/o/n/14 2 (a) on the grid, find the region satisfied by the inequalities from question 1(a) and question 1(b) . shade the unwanted region. 102 3 4 5 6 7 8 9 1010 987654321y x (b) two of the lines cross when x = 324 and y = 321. explain why these values should not be used to find the minimum cost. ", "11": "11 \u00a9 ucles 2014 0607/63/o/n/14 [turn over (c) when x = 0 and y = 5, the cost of the rescue mission is 325 thousand dollars. using your diagram, find the minimum cost of the rescue mission. write down the number of times each plane must fly. plane x . plane y .. minimum cost = ... thousand dollars 3 plane x is not available to make more than 4 return flights. how many times should each plane be used to minimise the cost? what would be the increase in cost compared to your solution in question 2 ? plane x . plane y .. increase in cost = ... thousand dollars 4 compare your solutions to question 2(c) and question 3 . which is the better solution? explain your answer. . ... . ... . ... ", "12": "12 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holder s, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. cambridge international examinations is part of the cambridge asse ssment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2014 0607/63/o/n/14 5 a third plane, z, is available to assist with the mission. this plane must also be back at the starting airport in less than 24 hours. the maximum loads, flight times and total cost for each plane are shown in the table. plane maximum number of people per flight maximum mass of equipment (tonnes) maximum return flight time (hours) cost for return flight ($ thousand) x 5 10 3 40 y 7 20 4 65 z 4 8 2 50 let x be the number of return flights made by plane x, y be the number of return flights made by plane y, and z be the number of return flights made by plane z. this rescue mission is to be modelled by six inequalities. (a) find the six inequalities and an expression for the cost in terms of x, y and z. inequalities . . . . . . cost .. (b) explain why the method of solution used in question 2 is not appropriate for this model. . ... . ... " } }, "2015": { "0607_s15_qp_11.pdf": { "1": " this document consists of 11 printed pages and 1 blank page. ib15 06_0607_11/4rp \u00a9 ucles 2015 [turn over *5433202339* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/11 paper 1 (core) may/june 2015 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2015 0607/11/m/j/15 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2015 0607/11/m/j/15 [turn over answer all the questions. 1 here is a bus timetable. bus 1 15 22 15 47 16 02 16 15 16 30a b cd ebus 2 15 40 16 05 16 20 ---- 16 42bus 3 16 09 16 34 ---- 16 54 17 09bus 4 16 38 17 04 17 22 17 50 18 11bus stop (a) find how many minutes it takes bus 4 to travel from a to e. answer(a) min [1] (b) jane arrives at b at 16 10. find how many minutes she has to wait for the next bus. answer(b) min [1] (c) desi travels from c to e. he must arrive at e by 17 00. which is the latest bus that he can catch to arrive on time? answer(c) [1] 2 find the lowest common multiple (lcm) of 2 and 5. answe r [1] ", "4": "4 \u00a9 ucles 2015 0607/11/m/j/15 3 shade three more squares so that the diagram has rotational symmetry of order 4. [2] 4 measure and write down the size of the angles marked x and y. x x = y = y [2] ", "5": "5 \u00a9 ucles 2015 0607/11/m/j/15 [turn over 5 cone parallelogram cuboid pentagon kite pyramid hexagon rhombus octagon trapezium from the list above, write down the mathematical name of each of the following shapes. (a) answer(a) (b) answer(b) (c) answer(c) (d) answer(d) (e) answer(e) [5] 6 (a) write 4 \u00d7 4 \u00d7 4 as a power of 4. answer(a) [1] (b) write down the value of 08. answer (b) [1] ", "6": "6 \u00a9 ucles 2015 0607/11/m/j/15 7 \u20132\u20132 \u20131 0 1 2 3 4 5 6 \u20131123456y xpl (a) write down the co-ordinates of p. answer(a) ( , ) [1] (b) write down the co-ordinates of the point where the line l crosses the x-axis. answer(b) ( , ) [1] ", "7": "7 \u00a9 ucles 2015 0607/11/m/j/15 [turn over 8 (a) (i) the mass of a blue whale is 180 000 kg. write 180 000 in standard form. answer(a) (i) [1] (ii) change 180 000 kg into tonnes. answer(a) (ii) tonnes [1] (b) a blue whale eats shrimps. the mass of a shrimp is 0.001kg. write 0.001 in standard form. answer(b) [1] 9 point a has co-ordinates (1, 4). point b has co-ordinates (6, 3). write ab as a column vector. you may use the grid to help you. answe r \uf8f7\uf8f7\uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec\uf8ec\uf8ec \uf8ed\uf8eb [2] ", "8": "8 \u00a9 ucles 2015 0607/11/m/j/15 10 the scatter diagram shows the marks of 10 students in a mathematics test and in a physics test. 0102030405060708090 20 40 60 physics mark80 100 90 70 50 30 10mathematics mark100 110 1200 (a) what type of correlation is shown on the scatter diagram? answer(a) [1] (b) another student scored 88 in the physics test but was absent for the mathematics test. use the line of best fit to estimate the mathematics mark for this student. answer(b) [1] ", "9": "9 \u00a9 ucles 2015 0607/11/m/j/15 [turn over 11 15 cm 5 cm2 cmy cmnot to scale the two triangles are similar. find the value of y. answe r [2] 12 (a) expand and simplify. 6 ( x \u2013 2y) + 3(2 x \u2013 y) answer(a) [2] (b) factorise fully. 5 p 2q + 10 pq2 answer(b) [3] ", "10": "10 \u00a9 ucles 2015 0607/11/m/j/15 13 solve the following simultaneous equations. 4x + y = 17 x \u2013 3y =1 answer x = y = [3] 14 a bag contains only red balls and blue balls. the probability of picking a red ball at random from the bag is 158. (a) what is the probability of picking a blue ball from the bag? answer(a) [1] (b) jane says that there must be exactly 15 balls in the bag. is she correct? give a reason for your answer. answer(b) because [1] ", "11": "11 \u00a9 ucles 2015 0607/11/m/j/15 15 the cumulative frequency diagram shows the scores of 60 students in an english test. 0102030405060 20 40 60 scorecumulative frequency 80 100 10 30 50 70 90 find (a) the median, answer(a) [1] (b) the lower quartile, answer(b) [1] (c) the interquartile range, answer(c) [1] (d) the number of students who scored more than 90. answer (d) [1] ", "12": "12 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge asse ssment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2015 0607/11/m/j/15 blank page " }, "0607_s15_qp_12.pdf": { "1": " this document consists of 11 printed pages and 1 blank page. ib15 06_0607_12/5rp \u00a9 ucles 2015 [turn over *8492677417* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/12 paper 1 (core) may/june 2015 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2015 0607/12/m/j/15 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2015 0607/12/m/j/15 [turn over answer all the questions. 1 work out . (a) 23 \u2013 6 \u00d7 3 answer(a) [1] (b) 8 \u00f7 (32 \u00f7 4) answer (b) [1] 2 write down the five factors of 16. answe r [2] 3 joe buys a magazine for $1.50 and a drink for $2.35. how much change does joe get from $5? answe r $ [2] ", "4": "4 \u00a9 ucles 2015 0607/12/m/j/15 4 (a) write down the next fraction in this sequence. 21, 51, 81, 111, 141, \u2026 answer(a) [1] (b) the nth term of a sequence is n 2 \u2013 3. find the first three terms of this sequence. answer(b) , , [2] 5 in the last ten football matches, west port fc scored the following numbers of goals. 2 5 1 1 4 7 1 3 1 4 find (a) the range, answer(a) [1] (b) the median , answer(b) [2] (c) the mean . answer(c) [2] ", "5": "5 \u00a9 ucles 2015 0607/12/m/j/15 [turn over 6 (a) 55\u00b0 p\u00b0 40\u00b0not to scale the diagram shows a triangle with one side extended. work out the size of angle p. answer(a) [2] (b) q\u00b0 130\u00b0not to scale work out the size of angle q. give a reason for your answer. answer(b) q = because [2] ", "6": "6 \u00a9 ucles 2015 0607/12/m/j/15 7 change 5.6 square centimetres into square millimetres. answe r mm2 [1] 8 write the following numbers in standard form. (a) 346 answer(a) [1] (b) 0.00216 answer (b) [1] 9 estimate the answer to the following calculation by rounding each number to 1 significant figure. show all your working. 0.47232.96 19.4+ answe r [2] ", "7": "7 \u00a9 ucles 2015 0607/12/m/j/15 [turn over 10 draw the enlargement of the pentagon, centre p, scale factor 3. p [2] 11 peter is x years old. jane is 4 years older than peter. write down an expression, in terms of x, for jane\u2019s age. answe r [1] ", "8": "8 \u00a9 ucles 2015 0607/12/m/j/15 12 make r the subject of this formula. a = 24r\u03c0 answe r r = [2] 13 solve the following simultaneous equations. 6x+ 10y =2 6 2x+ 5y =1 2 answe r x = y = [3] ", "9": "9 \u00a9 ucles 2015 0607/12/m/j/15 [turn over 14 \u20136 \u20136\u20135 \u20134 \u20133 \u20132 \u201310 123456 \u20135\u20134\u20133\u20132\u20131123456y x (a) on the grid, plot the points a(\u20133, 3) and b(5, \u20133) . [2] (b) find the gradient of the line ab. answer (b) [2] ", "10": "10 \u00a9 ucles 2015 0607/12/m/j/15 15 a biased coin is spun two times. the probability of the coin showing a head is 51 . (a) complete the tree diagram. head tailtailtailhead hea d1 5 1 51 5 [1] (b) find the probability of the coin showing a head both times. answer (b) [2] ", "11": "11 \u00a9 ucles 2015 0607/12/m/j/15 16 y xa \u201311y xb \u20131y xc \u201311 y xd 12y xe \u20131 \u20131y xf 11\u20132 1\u20132 write down the letter of the diagram that shows (a) y = \u2013x \u2013 1, answer(a) [1] (b) y = 2x + 1. answer(b) [1] ", "12": "12 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge asse ssment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2015 0607/12/m/j/15 blank page " }, "0607_s15_qp_13.pdf": { "1": " this document consists of 8 printed pages. ib15 06_0607_13/4rp \u00a9 ucles 2015 [turn over *0248860799* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/13 paper 1 (core) may/june 2015 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2015 0607/13/m/j/15 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2015 0607/13/m/j/15 [turn over answer all the questions. 1 (a) write forty five thousand in figures. answer(a) [1] (b) write in words the number 2136. answer(b) [1] 2 work out. 3 + 4 \u00d7 5 answe r [1] 3 complete the table. fraction decimal percentage 41 25% 103 0.3 0.6 60% [3] 4 write down the value of the following. (a) 81 answer(a) [1] (b) 3125 answer(b) [1] 5 change 4.1 metres into millimetres. answe r mm [1] ", "4": "4 \u00a9 ucles 2015 0607/13/m/j/15 6 name two 4-sided shapes with rotational symmetry order 2. answer and [2] 7 divide $35 in the ratio 4 : 3. answer $ and $ [2] 8 the mean of four numbers is 10. three of the numbers are 6, 15 and 12. find the other number. answe r [2] 9 work out. 107 \u2013 52 answe r [2] 10 expand the brackets. 4 x (2x \u2013 3) answe r [2] ", "5": "5 \u00a9 ucles 2015 0607/13/m/j/15 [turn over 11 solve the following simultaneous equations. 4 x + y = 13 2 x \u2013 y = 5 answer x = y = [2] 12 (a) 110\u00b0 x\u00b0not to scale find the value of x, giving a reason for your answer. answe r(a) because [2] (b) oa bc not to scale the diagram shows a circle, centre o. write down the size of angle acb . give a reason for your answer. answe r(b) = because [2] ", "6": "6 \u00a9 ucles 2015 0607/13/m/j/15 13 a fair 6-sided spinner is numbered 1, 2, 2, 2, 3 and 3. the spinner is spun once. find the probability that the spinner lands on 3. answe r [1] 14 these two rectangles are similar. 12.5 cm 5 cm 2 cmx cmnot to scale find the value of x. answe r x = [2] 15 f(x) = 3 x + 1 find (a) f(4) , answer(a) [1] (b) f \uf8f7\uf8f8\uf8f6\uf8ec\uf8ed\uf8eb\u2212 31 . answer(b) [1] ", "7": "7 \u00a9 ucles 2015 0607/13/m/j/15 [turn over 16 1 \u20131 \u20132 \u20133 \u20134 \u201352345 a b678910 xy 102 3 4 5 6 7 8 910c describe fully the single transformation that maps (a) triangle a onto triangle b, answer(a) [2] (b) triangle a onto triangle c. answer(b) [3] question 17 is printed on the next page. ", "8": "8 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge asse ssment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2015 0607/13/m/j/15 17 the cumulative frequency curve shows the heights of 100 plants. 0102030405060708090100 10 20 30 height (cm)cumulative frequency 40 50 find (a) the median, answer(a) cm [1] (b) the inter-quartile range, answer(b) cm [2] (c) the number of plants that are more than 40 cm in height. answe r(c) [2] " }, "0607_s15_qp_21.pdf": { "1": "this document consists of 8 printed pages. dc (leg/sw) 99284/5 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 1 6 4 3 4 4 6 5 9 5 * cambridge international mathematics 0607/21 paper 2 (extended) may/june 2015 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.", "2": "2 0607/21/m/j/15 \u00a9 ucles 2015formula list for the equation ax bx c02+ + = xab b ac 242!=- - curved surface area, a, of cylinder of radius r, height h. r a rh2= curved surface area, a, of cone of radius r, sloping edge l. r a rl= curved surface area, a, of sphere of radius r. r a r42= v olume, v, of pyramid, base area a, height h. v ah31= v olume, v, of cylinder of radius r, height h. rv r h2= v olume, v, of cone of radius r, height h. r v r h31 2= v olume, v, of sphere of radius r. r v r34 3= sin sin sin aa bb cc= = cos a b c bc a 22 2 2= + - sinbc a21area=a c bcb a", "3": "3 0607/21/m/j/15 \u00a9 ucles 2015 [turn overanswer all the questions. 1 (a) write 4725.6 correct to two significant figures. \t answer(a) .. [1] (b) write 0.01026 correct to three decimal places. \t answer(b) .. [1] 2 expand and simplify. (a) x x x 3 2 3 72- - - - ^ ^h h \t answer(a) . [2] (b) x y y x 5 3 2 5 - - ^ ^ h h \t answer(b) . [3]", "4": "4 0607/21/m/j/15 \u00a9 ucles 20153 find the exact value of 27 31-. \t answer\t . [2] 4 simplify x y168 221 ^ h. \t answer\t . [2] 5 (a) simplify. 27 147+ \t answer(a) . [2] (b) rationalise the denominator. 3 53 5 +- \t answer(b) . [3]", "5": "5 0607/21/m/j/15 \u00a9 ucles 2015 [turn over6 solve. log log log logx 5 25 10+ - = \t answer\t x= . [3] 7 there are 400 students at a school. 52 of the students are boys. 70% of the girls can swim. the ratio of boys that cannot swim to girls that cannot swim is 2 : 3. complete the table. boys girls total can swim cannot swim total 400 [4]", "6": "6 0607/21/m/j/15 \u00a9 ucles 20158 y\u00b0 30\u00b0x cm2 cm1 cm not to scale (a) write down the value of x. \t answer(a) x = [1] (b) find the value of y. \t answer(b) y = . [2] 9 fxx3 21=-^h (a) find f 4^h. answer(a) . [1] (b) solve fx41= ^h . answer(b) . [2] (c) find fx1-^h. \t answer(c) . [3]", "7": "7 0607/21/m/j/15 \u00a9 ucles 2015 [turn over10 not to scale nm d c b a \t abcd is a trapezium. \t ab = 2dc, dm = 2mc and an = 3nb. \t p ab= and a qd=. (a) write mc in terms of p. \t answer(a) . [2] (b) find mn in terms of p and q. \t answer(b) . [2] question 11 is printed on the next page.", "8": "8 0607/21/m/j/15 \u00a9 ucles 201511 the point a has co-ordinates \t(2, 8) and the point b has co-ordinates (6, 6). find the equation of the perpendicular bisector of the line ab. \t answer\t . [4] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_s15_qp_22.pdf": { "1": "this document consists of 8 printed pages. dc (ac/sg) 99283/6 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 1 0 4 9 5 4 7 5 2 6 * cambridge international mathematics 0607/22 paper 2 (extended) may/june 2015 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.", "2": "2 0607/22/m/j/15 \u00a9 ucles 2015formula list for the equation ax bx c02+ + = xab b ac 242!=- - curved surface area, a, of cylinder of radius r, height h. r a rh2= curved surface area, a, of cone of radius r, sloping edge l. r a rl= curved surface area, a, of sphere of radius r. r a r42= v olume, v, of pyramid, base area a, height h. v ah31= v olume, v, of cylinder of radius r, height h. rv r h2= v olume, v, of cone of radius r, height h. r v r h31 2= v olume, v, of sphere of radius r. r v r34 3= sin sin sin aa bb cc= = cos a b c bc a 22 2 2= + - sinbc a21area=a c bcb a", "3": "3 0607/22/m/j/15 \u00a9 ucles 2015 [turn overanswer all the questions. 1 (a) work out ( . )0 32. answer(a) [1] (b) find n when n 65 24= . answer(b) n = [1] 2 (a) find the value of (i) 250, answer(a) (i) [1] (ii) 10023. answer(a) (ii) [1] (b) write as a single power of 5. 5 55 3 212 # answer(b) [1] 3 find the magnitude of 46-j lkkn poo. write your answer in surd form as simply as possible. answer [3]", "4": "4 0607/22/m/j/15 \u00a9 ucles 20154 anneke, babar, c\u00e9line, and dieter each throw the same biased die. they want to find the probability of throwing a six with this die. they each throw the die a different number of times. these are their results. anneke babar c\u00e9line dieter number of throws 200 40 100 500 number of sixes 46 12 15 100 (a) complete the table below to show the relative frequencies of their results. write your answers as decimals. anneke babar c\u00e9line dieter relative frequency of throwing a six [2] (b) whose result gives the best estimate of the probability of throwing a six with the biased die? give a reason for your answer. answer(b) because ... . [1] (c) the probability of throwing a six with a different biased die is 0.41. find the expected number of sixes when this die is thrown 600 times. answer(c) [1]", "5": "5 0607/22/m/j/15 \u00a9 ucles 2015 [turn over5 a is the point (2, 8) and b is the point (6, 0). (a) find the co-ordinates of the midpoint of ab. answer(a) (... , ...) [1] (b) find the gradient of ab. answer(b) [2] 6 simplify ( )5 32+ . answer [2] 7 solve. ( ) x x2 3 4 2g+ - answer [3]", "6": "6 0607/22/m/j/15 \u00a9 ucles 20158 3 m 10 m6 m not to scale the diagram shows a shape made from a cylinder and a cone. the cylinder and cone have a common radius of 6 m. the height of the cylinder is 10 m and the height of the cone is 3 m. calculate the total volume of the shape. leave your answer as a multiple of \u03c0. answer ... m3 [3] 9 solve these simultaneous equations. x y4 3 18 - =x y5 2 11 + = answer x = y = [4]", "7": "7 0607/22/m/j/15 \u00a9 ucles 2015 [turn over10 solve the following equations. (a) log x + log 3 = log 12 answer(a) x = [1] (b) log x = 3 answer(b) x = [1] (c) 2log x \u2013 log 5 = log 20 answer(c) x = [3] 11 a, b, c and d are points on the circle, centre o. pq is a tangent to the circle at the point c. angle pcd = 55\u00b0 and angle ado = 40\u00b0. abq c po d40\u00b055\u00b0not to scale find (a) angle cod , answer(a) [2] (b) angle dac , answer(b) [1] (c) angle abc . answer(c) [1] question 12 is printed on the next page.", "8": "8 0607/22/m/j/15 \u00a9 ucles 201512 these are sketches of the graphs of six functions. y x 0a y x 0b y x0d y x 0c y x 0ey x 0f in the table below are four functions. write the correct letter in the table to match each function with its graph. function graph ( )x x 2 3 f= - ( ) ( ) x x 2 f2= - ( )x x x 4 f3= - ( )x x 5 2 f= - [4] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_s15_qp_23.pdf": { "1": "this document consists of 12 printed pages. dc (rw/sw) 99290/3 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 4 2 1 2 2 9 3 3 0 7 * cambridge international mathematics 0607/23 paper 2 (extended) may/june 2015 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.", "2": "2 0607/23/m/j/15 \u00a9 ucles 2015formula list for the equation ax bx c02+ + = xab b ac 242!=- - curved surface area, a, of cylinder of radius r, height h. r a rh2= curved surface area, a, of cone of radius r, sloping edge l. r a rl= curved surface area, a, of sphere of radius r. r a r42= v olume, v, of pyramid, base area a, height h. v ah31= v olume, v, of cylinder of radius r, height h. rv r h2= v olume, v, of cone of radius r, height h. r v r h31 2= v olume, v, of sphere of radius r. r v r34 3= sin sin sin aa bb cc= = cos a b c bc a 22 2 2= + - sinbc a21area=a c bcb a", "3": "3 0607/23/m/j/15 \u00a9 ucles 2015 [turn overanswer all the questions. 1 round these numbers to 3 significant figures. (a) 0.000 604 83 \t answer(a)\t .. [1] (b) 6 998 800 \t answer(b)\t .. [1] 2 by rounding each number to 1 significant figure, estimate the value of . .. . 1 82 10 430583 3116 # + . show your working. \t answer\t .. [2]", "4": "4 0607/23/m/j/15 \u00a9 ucles 20153 a2 3 53 2# #= b2 3 72 2 6# #= (a) find, giving each answer as the product of prime factors, (i) the highest common factor (hcf) of a and b, \t answer(a) (i)\t .. [1] (ii) b. \t answer(a) (ii)\t .. [1] (b) ap is a cube number. find the smallest integer value of p. \t answer(b)\t .. [1]", "5": "5 0607/23/m/j/15 \u00a9 ucles 2015 [turn over4 3 cm5 cm8 cm3 cm not to scale the diagram shows a rectangle, two semicircles and two right-angled triangles. (a) find the total area of the shape. give your answer in the form r a b+ . \t answer(a)\t ... cm2 [3] (b) describe fully the symmetry of the shape. answer(b) . .. [2] 5 solve. x x5 2 2 4 7 1+ -^ ^ h h \t answer\t .. [3]", "6": "6 0607/23/m/j/15 \u00a9 ucles 20156 fran\u00e7ois and george each ask a sample of students at their college how they travel to college. these are their results. walk cycle bus train cartotal number of students fran\u00e7ois 7 3 4 1 5 20 george 46 24 44 11 25 150 (a) explain why george\u2019s results will give the better estimates of the probabilities of the different types of travel. answer(a) . [1] (b) a student is selected at random. (i) use george\u2019s results to estimate the probability that the student cycles to college. \t answer(b) (i)\t .. [1] (ii) there are 3000 students at the college. use george\u2019s results to estimate the number of students who cycle to college. \t answer(b) (ii)\t .. [1] ", "7": "7 0607/23/m/j/15 \u00a9 ucles 2015 [turn over7 not to scale 0a xy the diagram shows the lines x 2=- , y x 121= + and x y3 4 20 + = . (a) use simultaneous equations to find the co-ordinates of the point a. \t answer(a)\t ( .. , .. ) [3] (b) (i) p is a point in the region such that x 21-, y x 1212+ and x y3 4 201+ . on the diagram, mark and label a possible position of p. [1] (ii) q is a point in the region such that x 22-, y x 121= + and x y3 4 201+ . on the diagram, mark and label a possible position of q. [1]", "8": "8 0607/23/m/j/15 \u00a9 ucles 20158 not to scale abc 35\u00b0d e in the diagram, a, b, c, d and e are points on the circle. ad is a diameter and angle cad 35\u00b0= . find (a) angle acd , \t answer(a)\t .. [1] (b) angle cbd , \t answer(b)\t .. [1] (c) angle aec . \t answer(c)\t .. [2]", "9": "9 0607/23/m/j/15 \u00a9 ucles 2015 [turn over9 the sets p, q and r are subsets of the universal set u. \u2022 p rk q! \u2022 q is a subset of r \u2022 q pk q= complete the venn diagram to show the sets p, q, and r. u [3]", "10": "10 0607/23/m/j/15 \u00a9 ucles 201510 (a) factorise x x 3 102- - . \t answer(a)\t .. [2] (b) make x the subject of yax3 = . \t answer(b)\t x = ... [2]", "11": "11 0607/23/m/j/15 \u00a9 ucles 2015 [turn over11 (a) find log251 5. \t answer(a)\t .. [1] (b) find x when (i) log log log x 2 6- = , \t answer(b) (i)\t .. [1] (ii) log 421 x=. \t answer(b) (ii)\t .. [1] question 12 is printed on the next page.", "12": "12 0607/23/m/j/15 \u00a9 ucles 2015permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.12 not to scaley \u20133 0 2 (0, \u201312)x the diagram shows a sketch of the graph of y ax bx c2= + +. the graph goes through the points ,3 0-^ h, ,0 12-^ h and ,2 0^ h. find the values a, b and c. \t answer\t a = . \t \t b = . \t \t c = .. [3]" }, "0607_s15_qp_31.pdf": { "1": "this document consists of 16 printed pages. dc (st/cgw) 99289/4 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 0 1 9 2 3 0 5 3 9 3 * cambridge international mathematics 0607/31 paper 3 (core) may/june 2015 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for p, use your calculator value. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.", "2": "2 0607/31/m/j/15 \u00a9 ucles 2015formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = pr2 circumference, c, of circle, radius r. c = 2pr curved surface area, a, of cylinder of radius r, height h. a = 2prh curved surface area, a, of cone of radius r, sloping edge l. a = prl curved surface area, a, of sphere of radius r. a = 4pr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v= ah31 v olume, v, of cylinder of radius r, height h. v = pr2h v olume, v, of cone of radius r, height h. v = r h31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/31/m/j/15 \u00a9 ucles 2015 [turn overanswer all the questions. 1 (a) write down three hundred thousand and fifty eight as a number. answer(a) . [1] (b) work out. 42 8 6 #- answer(b) . [1] (c) write 21 648 correct to the nearest hundred. answer(c) . [1] (d) write 0.05625 correct to 2 decimal places. answer(d) . [1] (e) find 73 of 182. answer(e) . [1] (f) the average temperature in amsterdam in february is \u22122\u00b0c. in july the average temperature is 21\u00b0c. find the difference between these two temperatures. answer(f) . \u00b0c [1] (g) write 65% as a fraction in its lowest terms. answer(g) . [2] (h) divide 133 in the ratio 4 : 3. answer(h) : .. [2] ", "4": "4 0607/31/m/j/15 \u00a9 ucles 20152 (a) simplify. x y x y 6 3 2- + + answer(a) . [2] (b) find the value of a b c 2 3+ + when , a b 3 2= = - and c4=. answer(b) . [2] (c) l x y 2 3= + find the value of x when . l 186= and . y 2 8= . answer(c) x = . [2] (d) solve the equation. x5 3 7 - = answer(d) x = .. [2] (e) complete the mapping diagram for :fx x 2 1\"-. x 0 1 2 3f(x) 1 [2]", "5": "5 0607/31/m/j/15 \u00a9 ucles 2015 [turn over3 rp s ut d\u00b0c\u00b0not to scale a\u00b026\u00b0 b\u00b0q pq and rs are parallel lines. qr is a straight line and tu is a straight line perpendicular to pq and rs. angle pqr = 26\u00b0. find the values of a, b, c and d. answer a = .. b = .. c = .. d = . [4] 4 thirty students and three teachers go by bus on a school trip to the zoo. (a) the entrance fee is $10 for each student and $15 for each teacher. find the total cost of the entrance fees. answer(a) $ . [2] (b) the bus costs $600 to hire. lunch costs $5 for each person. find the total cost of the trip including the entrance fees. answer(b) $ . [2] (c) the total cost of the trip is divided between the 30 students. calculate the cost of the trip for each student. answer(c) $ . [2]", "6": "6 0607/31/m/j/15 \u00a9 ucles 20155 a list of numbers is shown below. 5 8 6 2 8 4 5 8 (a) for the list of numbers, find (i) the mode, answer(a) (i) . [1] (ii) the median, answer(a) (ii) . [1] (iii) the lower quartile, answer(a) (iii) . [1] (iv) the range, answer(a) (iv) . [1] (v) the mean. answer(a) (v) . [1] ", "7": "7 0607/31/m/j/15 \u00a9 ucles 2015 [turn over (b) (i) using the list of numbers, complete the frequency table. number frequency 2 3 4 5 6 7 8 [1] (ii) complete the bar chart. one bar has been drawn for you. 1 2345678023 frequency number45 [2]", "8": "8 0607/31/m/j/15 \u00a9 ucles 20156 75 cm25 cm 2 cmnot to scale the diagram shows a bookshelf. it is made from a piece of wood 75 cm long, 25 cm wide and 2 cm thick. (a) find the volume of this piece of wood. answer(a) .. cm3 [2] (b) (i) find the total surface area of this piece of wood. answer(b) (i) .. cm2 [3] (ii) write your answer to part (b)(i) in square metres. answer(b) (ii) m2 [1]", "9": "9 0607/31/m/j/15 \u00a9 ucles 2015 [turn over (c) not to scale 75 cmmathse n g l i s hh i s t o r ys c i e n c ea r t jessie wants to stand 18 books on the bookshelf. \u2022 5 books are each 3 cm wide \u2022 6 books are each 4 cm wide \u2022 4 books are each 2.5 cm wide \u2022 3 books are each 7 cm wide can jessie stand all these books on the bookshelf? show all your working. [2]", "10": "10 0607/31/m/j/15 \u00a9 ucles 20157 23, 16, 9, 2, \u2026 (a) find the next two terms in this sequence. answer(a) .. , [2] (b) find an expression for the nth term of this sequence. answer(b) . [2] 8 the equation of line l is y x2 3= - . (a) find the gradient of line l. answer(a) . [2] (b) write down the gradient of a line parallel to l. answer(b) . [1] (c) find the equation of the line parallel to l that passes through the point (0, 6). answer(c) y = . [1]", "11": "11 0607/31/m/j/15 \u00a9 ucles 2015 [turn over9 a b 2u 3 64 5 1 list the elements in each of the following sets. (a) (i) a answer(a) (i) . [1] (ii) a b+ answer(a) (ii) . [1] (iii) a b, answer(a) (iii) . [1] (iv) bl answer(a) (iv) . [1] (v) a b+l answer(a) (v) . [1] (b) find n( u). answer(b) . [1]", "12": "12 0607/31/m/j/15 \u00a9 ucles 201510 123456 0 \u20133\u20132\u20131 \u20131 \u20133\u20132xy p 12345678910rq s (a) triangle q is a reflection of triangle p. on the grid, draw the line of reflection. write down the equation of this line. answer(a) . [2] (b) triangle s is a translation of triangle p. find the vector for this translation. answer(b) \u239b \u239e \u239c \u239f \u239d \u23a0 [2] (c) triangle r is a rotation of triangle p. find the centre and the angle of rotation. answer(c) centre = ...(... , ...) angle = .. [2] ", "13": "13 0607/31/m/j/15 \u00a9 ucles 2015 [turn over11 (a) campbell can text at an average speed of 100 characters per minute. find how long it takes her to text a message of 320 characters. give your answer in minutes and seconds. answer(a) min .. s [2] (b) diago texts a message of 168 characters in 1 minute 36 seconds. find the average speed at which he texts. give your answer in characters per minute. answer(b) .. characters per minute [3]", "14": "14 0607/31/m/j/15 \u00a9 ucles 201512 on the way to work herr smit drives over a bridge. the probability that the bridge is closed is 801. if the bridge is closed then the probability that herr smit is late for work is 32. if the bridge is open then the probability that he is late for work is 501. (a) complete the tree diagram. 1 80 bridge closedlate latenot late not latebridge open [3] (b) find the probability that the bridge is closed and herr smit is not late for work. answer(b) . [2] (c) in 2014, herr smit worked for 250 days. estimate the number of days that the bridge was closed and herr smit was not late for work. answer(c) . [2]", "15": "15 0607/31/m/j/15 \u00a9 ucles 2015 [turn over13 a b o46 cmnot to scale 60\u00b0 the diagram shows a sector of a circle, centre o, radius 46 cm. angle aob = 60\u00b0. (a) explain why ab = 46 cm. [2] (b) calculate the length of arc ab. answer(b) cm [2] (c) calculate the area of sector aob . answer(c) ... cm2 [2] (d) find the area of triangle aob . answer(d) .. cm2 [3] (e) use your answers to part (c) and part (d) to find the area of the shaded segment. answer(e) .. cm2 [1] question 14 is printed on the next page", "16": "16 0607/31/m/j/15 \u00a9 ucles 2015permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.14 y x38 \u20133\u201310 0 ( )fx 3 2 1( . )x0 5#= - (a) on the diagram, sketch the graph of ( )f y x= for x 10 3 g g- . [2] (b) write down the x co-ordinate of the point where the curve crosses the x-axis. answer(b) x = .. [1] (c) write down the equation of the horizontal asymptote. answer(c) . [1] (d) on the same diagram, sketch the graph of y x 2 3=- +. [2] (e) find the co-ordinates of the point where the two graphs intersect. answer(e) ( ... , . ) [2]" }, "0607_s15_qp_32.pdf": { "1": "this document consists of 16 printed pages. dc (leg/fd) 99288/5 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 8 0 2 2 0 9 9 5 2 5 * cambridge international mathematics 0607/32 paper 3 (core) may/june 2015 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.", "2": "2 0607/32/m/j/15 \u00a9 ucles 2015formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 v olume, v, of prism, cross-sectional area a, length l. v =al v olume, v, of pyramid, base area a, height h. v= ah31 v olume, v, of cylinder of radius r, height h. v = \u03c0r2h v olume, v, of cone of radius r, height h. v = r h31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/32/m/j/15 \u00a9 ucles 2015 [turn overanswer all the questions. 1 (a) write 32 652 (i) correct to the nearest 10, \t answer(a) (i) . [1] (ii) correct to the nearest 100. \t answer(a) (ii) . [1] (b) write 62.584 correct to 1 decimal place. answer(b) . [1] (c) calculate 4.84. answer(c) . [1] (d) find 2163. answer(d) . [1] (e) find the highest common factor (hcf) of 18 and 45. answer(e) . [1] (f) find the lowest common multiple (lcm) of 6 and 8. answer(f) . [1] (g) divide 442 in the ratio 8 : 9. answer(g) ... : ...[2] (h) sem buys 7 hamburgers each costing $1.20 . find how much change he receives from $10. answer(h) \t$ . [2]", "4": "4 0607/32/m/j/15 \u00a9 ucles 20152 (a) write 0.75 as a fraction. answer(a) . [1] (b) write 32 as a percentage, giving your answer correct to 4 significant figures. answer(b) . % [2] (c) write 48% as a fraction in its lowest terms. answer(c) \t . [2] (d) find 8% of 72. answer(d) . [1] (e) the price of a jacket is $96. the price is reduced by 20%. find the new price of the jacket. answer(e) \t$ . [2] (f) $800 is invested for 5 years at 3% per year simple interest. find the total interest received at the end of the 5 years. answer(f) $ . [2]", "5": "5 0607/32/m/j/15 \u00a9 ucles 2015 [turn over3 a special die has 10 faces numbered 1 to 10. when the die is rolled it is equally likely to land on any face. find the probability that the die lands on (a) an even number, \t answer(a) . [1] (b) a prime number, \t answer(b) . [1] (c) 11, \t answer(c) . [1] (d) a square number less than 5. \t answer(d) . [1]", "6": "6 0607/32/m/j/15 \u00a9 ucles 20154 jacinta asks some students in her class which colour they prefer. the results are in the table. colournumber of students brown 1 green 4 black 8 pink 12 blue 15 (a) calculate the total number of students. \t answer(a) . [1] (b) write down the most popular colour. \t answer(b) \t . [1]", "7": "7 0607/32/m/j/15 \u00a9 ucles 2015 [turn over (c) jacinta wants to draw a pie chart for these results. colournumber of studentssector angle in pie chart brown 1 green 4 black 8 pink 12 108\u00b0 blue 15 135\u00b0 (i) complete the table. [2] (ii) complete the pie chart to show this information. two sectors have been drawn for you. blue pink [2] ", "8": "8 0607/32/m/j/15 \u00a9 ucles 20155 hanra asked 30 students if they ate cereal ( c\t) or toast ( t\t) for breakfast. the information is shown in the venn diagram. uc 18 6 5t 1 write down the number of students in (a) c t+, answer(a) . [1] (b) c, answer(b) \t . [1] (c) c t, l ^ h, answer(c) . [1] (d) t c, l. answer(d) . [1]", "9": "9 0607/32/m/j/15 \u00a9 ucles 2015 [turn over6 10 cm10 cm10 cm5 cmnot to scale a trophy is in the shape of a cube of side 10 cm with a sphere of radius 5 cm on top. (a) find the surface area of the cube. \t answer(a) . cm2 [2] (b) find the surface area of the sphere. \t answer(b) . cm2 [2] (c) find the total volume of the trophy. answer(c) . cm3 [4] the trophy is made from metal that costs 4 cents per cm3. (d) find the cost of the metal used to make the trophy. give your answer in dollars. answer(d) $ . [2]", "10": "10 0607/32/m/j/15 \u00a9 ucles 20157 45\u00b0 12 cm36 cm 18 cm 31 cmb c dge fa not to scale the diagram shows a triangle abc and a trapezium cdef . \t bcgd is a straight line and angle fcd\t= 45\u00b0. ab\t= 36 cm, bc = 12 cm, cd = 31 cm and ed = 18 cm. (a) find the size of angle cfe . answer(a) \tangle cfe = . [1] (b) use trigonometry to calculate the size of angle bca . answer(b) \tangle bca = . [2] (c) use pythagoras\u2019 theorem to find the length of ac. answer(c) \tac = ... cm [2]", "11": "11 0607/32/m/j/15 \u00a9 ucles 2015 [turn over (d) use trigonometry to calculate the length of cf. answer(d) cf = ... cm [3] (e) (i) explain why ef = 13 cm. [2] (ii) find the total perimeter of the shape. answer(e) (ii)\t ... cm [1] (f) calculate the total area of the shape. answer(f) \t .. cm2 [3]", "12": "12 0607/32/m/j/15 \u00a9 ucles 20158 the table shows the number of shirts and the number of jackets owned by 12 students. shirts 3 6 2 8 8 10 6 5 9 8 4 12 jackets 5 4 2 4 6 8 5 4 6 5 4 7 (a) complete the scatter diagram. the first 6 points have been plotted for you. 012345678910 2 1 4 6 8 10 3 5 7 9 11 12 number of shirtsnumber of jackets [2] (b) write down the type of correlation shown by the scatter diagram. \t answer(b) \t . [1] (c) (i) find the mean number of shirts. \t answer(c) (i) . [1] (ii) find the mean number of jackets. \t answer(c) (ii) . [1] (iii) on the diagram, plot the mean point. [1]", "13": "13 0607/32/m/j/15 \u00a9 ucles 2015 [turn over (d) on the diagram, draw a line of best fit by eye. [2] (e) use your line of best fit to estimate the number of jackets for a student who has 7 shirts. \t answer(e) . [1]", "14": "14 0607/32/m/j/15 \u00a9 ucles 20159 \u20133 \u2013 610 x10y fx x x 6 5 32= - - ^h (a) on the diagram, sketch the graph of f y x=^h for x3 1g g- . [2] (b) write down the y\tco-ordinate of the point where the graph crosses the y-axis. answer(b) \ty = . [1] (c) write down the x\tco-ordinates of the points where the graph crosses the x-axis. answer(c) \tx\t= .. and x = ..[2] (d) find the co-ordinates of the local maximum point. \t answer(d) ( ... , ..) [1] (e) gx x 2 4= + ^h on the same diagram, sketch the graph of g y x= ^h. [2] (f) find the co-ordinates of the points of intersection of f( x) and g(x). \t answer(f) (... , ...) and (... , ...) [2]", "15": "15 0607/32/m/j/15 \u00a9 ucles 2015 [turn over10 (a) solve. (i) x5 6 4 + =- answer(a) (i) . [2] (ii) x6 3 211+ \t answer(a) (ii) . [2] (b) simplify. (i) s s3 4# \t answer(b) (i) . [1] (ii) t24^h \t answer(b) (ii) . [1] (iii) r r18 33' \t answer(b) (iii) . [2] (c) expand and simplify. \t x x4 3 3 2 1 - + + ^ ^ h h answer(c) \t . [2] (d) factorise completely. \t y y15 32- answer(d) \t . [2] question 11 is printed on the next page.", "16": "16 0607/32/m/j/15 \u00a9 ucles 2015permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.11 (a) ahmed cycles 15 kilometres in 50 minutes. find his average speed in kilometres per hour. \t answer(a) km/h [3] (b) george runs 15 kilometres at an average speed of 12 kilometres per hour. find how many minutes it takes george to run the 15 kilometres. answer(b) .. min [3]" }, "0607_s15_qp_33.pdf": { "1": "this document consists of 16 printed pages. dc (kn/cgw) 100417/4 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 7 9 4 8 3 0 2 2 3 6 * cambridge international mathematics 0607/33 paper 3 (core) may/june 2015 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.", "2": "2 0607/33/m/j/15 \u00a9 ucles 2015formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 v olume, v, of prism, cross-sectional area a, length l. v =al v olume, v, of pyramid, base area a, height h. v= ah31 v olume, v, of cylinder of radius r, height h. v = \u03c0r2h v olume, v, of cone of radius r, height h. v = r h31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/33/m/j/15 \u00a9 ucles 2015 [turn over answer all the questions. 1 12 13 14 15 16 from the list of numbers write down (a) one of the even numbers, answer(a) . [1] (b) a prime number, answer(b) . [1] (c) a multiple of 7, answer(c) . [1] (d) a factor of 84, answer(d) . [1] (e) a square number, answer(e) . [1] (f) a triangle number. answer(f) . [1]", "4": "4 0607/33/m/j/15 \u00a9 ucles 20152 (a) work out. .. . 1 831756 6 2- answer(a) . [1] (b) find 98 of 162. answer(b) . [1] (c) write 348.375 correct to (i) 1 decimal place, answer(c) (i) . [1] (ii) the nearest 10. answer(c) (ii) . [1] (d) write the following numbers in order, starting with the smallest. 31 0.3 33% .3 33 101#- answer(d) .. < .. < .. < .. [2] smallest", "5": "5 0607/33/m/j/15 \u00a9 ucles 2015 [turn over3 a shop manager buys a box of 48 tins of beans for $16.80 . (a) calculate the cost of each tin of beans. give your answer in cents. answer(a) ... cents [1] (b) the shop manager sells each tin of beans for 75 cents. (i) find the profit made on each tin of beans. answer(b) (i) ... cents [1] (ii) calculate the percentage profit. answer(b) (ii) . % [2] (c) in a special offer, the shop manager reduces the selling price of 75 cents by 20%. (i) find the new selling price of each tin of beans. answer(c) (i) ... cents [2] (ii) tirza buys 8 tins of beans at the special offer price. find how much change she receives from $5. give your answer in cents. answer(c) (ii) ... cents [2]", "6": "6 0607/33/m/j/15 \u00a9 ucles 20154 (a) the marks for a test taken by 20 students are recorded below. 56 73 42 55 63 59 65 48 77 65 73 64 52 41 78 62 73 49 55 64 complete the ordered stem-and-leaf diagram to show this information. stem leaf .. .. .. .. key: 5 \uf8ef1 = 51 [3] (b) 60 people each choose their favourite food. the pie chart shows the results. 132\u00b0150\u00b0burger pizza friespasta18\u00b060\u00b0 (i) write down the most popular choice of food. answer(b) (i) . [1] (ii) calculate the number of people who chose pizza. answer(b) (ii) . [2]", "7": "7 0607/33/m/j/15 \u00a9 ucles 2015 [turn over5 (a) solve the following equations. (i) t 28= answer(a) (i) . [1] (ii) 7.15x + 9.2 = 37.8 answer(a) (ii) . [2] (b) m = 3.4l + 2.8n (i) find the value of m when l = \u22122.1 and n = 0.6 . answer(b) (i) m = . [2] (ii) rearrange the formula to make n the subject. answer(b) (ii) n = . [2] (c) simplify. (i) n4 \u00d7 n8 answer(c) (i) . [1] (ii) yy 416 39 answer(c) (ii) . [2]", "8": "8 0607/33/m/j/15 \u00a9 ucles 20156 the shapes below are drawn on a 1 cm2 grid. shape 1 shape 5 shape 6shape 2 shape 3 shape 4 (a) complete shape 5 and shape 6 in the pattern. [2] (b) shape 1 has an area of 3 cm2. complete the sequence of areas by finding the area of each shape. answer(b) 3, .. , .. , .. , .. , .. [2] (c) find an expression, in terms of n, for the area of shape n. answer(c) .. cm2 [1]", "9": "9 0607/33/m/j/15 \u00a9 ucles 2015 [turn over7 a quiz had 7 questions each worth 1 mark. the bar chart shows the scores for 22 students. 17 6 5 4 3frequency 2 1 02 3 4 score5 6 7 (a) complete the frequency table using the bar chart above. score frequency 1 4 2 3 4 5 6 7 2 [2] (b) find (i) the mode, answer(b) (i) . [1] (ii) the range, answer(b) (ii) . [1] (iii) the median, answer(b) (iii) . [1] (iv) the mean, answer(b) (iv) . [2] (v) the interquartile range. answer(b) (v) .. [2]", "10": "10 0607/33/m/j/15 \u00a9 ucles 20158 in a class of 24 students \u2022 8 study french ( f) \u2022 6 study music ( m) \u2022 3 study both french and music. (a) complete the venn diagram. f mu [2] (b) write down the number of elements in each of the following sets. (i) f m+ l answer(b) (i) . [1] (ii) ( )f m, l answer(b) (ii) . [1]", "11": "11 0607/33/m/j/15 \u00a9 ucles 2015 [turn over9 the probability that dave goes jogging is 32. if dave goes jogging, the probability that he goes swimming is 43. if dave does not go jogging, the probability that he goes swimming is 109. (a) complete the tree diagram. jogging 2 3swimming not swimming not swimmingswimming not jogging [3] (b) find the probability that dave does not go jogging and does not go swimming. answer(b) . [2] (c) find the probability that dave goes swimming. answer(c) . [3]", "12": "12 0607/33/m/j/15 \u00a9 ucles 201510 the equation of a line is y x432 = + . (a) (i) write down the gradient of this line. answer(a) (i) . [1] (ii) write down the co-ordinates of the point where the line crosses the y-axis. answer(a) (ii) ( . , ... ) [1] (iii) find the co-ordinates of the point where the line crosses the x-axis. answer(a) (iii) ( . , ... ) [2] (b) write down the equation of the line parallel to y x432 = + that passes through the point (0, \u20133). answer(b) . [1]", "13": "13 0607/33/m/j/15 \u00a9 ucles 2015 [turn over11 a snail travels 3 metres from a to b on a bearing of 120\u00b0. it then travels 4.5 metres from b to c on a bearing of 030\u00b0. (a) show this information on the diagram. north northnot to scale ac b [2] (b) angle abc = 90\u00b0. calculate the distance ac. answer(b) metres [2] (c) use trigonometry to find the bearing of c from a. answer(c) . [3]", "14": "14 0607/33/m/j/15 \u00a9 ucles 201512 a b o8 cmnot to scale 8 cm each vertex of a regular octagon lies on the circumference of a circle, centre o, radius 8 cm. (a) calculate the circumference of the circle. answer(a) .. cm [2] (b) calculate the area of the circle. answer(b) . cm2 [2] (c) show that angle boa = 45\u00b0. [1] (d) find angle bao . answer(d) angle bao = . [2]", "15": "15 0607/33/m/j/15 \u00a9 ucles 2015 [turn over (e) find the size of each interior angle of a regular octagon. answer(e) . [1] (f) (i) use trigonometry to show that ba = 6.12 cm, correct to 3 significant figures. [2] (ii) find the area of triangle oab . answer(f) (ii) . cm2 [4] (iii) find the area of the octagon. answer(f) (iii) . cm2 [1] question 13 is printed on the next page.", "16": "16 0607/33/m/j/15 \u00a9 ucles 2015permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.13 \u20136 \u2013 1560 x15y ( ) . .x x x x 0 2 0 2 6 f3 2=- - + (a) on the diagram, sketch the graph of ( ) y x f= for x6 6g g- . [2] (b) find the co-ordinates of (i) the points where the graph crosses the x-axis, answer(b) (i) ( .. , .. ), ( .. , .. ) ( .. , .. ) [2] (ii) the local minimum point. answer(b) (ii) ( . , ... ) [2] (c) the range of f( x) for the domain ( ) x k x 6 0 0 is f g g g g - . write down the value of k. answer(c) k = . [1]" }, "0607_s15_qp_41.pdf": { "1": "this document consists of 20 printed pages. dc (kn/sw) 99287/7 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 7 2 6 0 8 7 7 3 2 5 * cambridge international mathematics 0607/41 paper 4 (extended) may/june 2015 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.", "2": "2 0607/41/m/j/15 \u00a9 ucles 2015formula list for the equation ax bx c02+ + = xab b ac 242!=- - curved surface area, a, of cylinder of radius r, height h. r a rh2= curved surface area, a, of cone of radius r, sloping edge l. r a rl= curved surface area, a, of sphere of radius r. r a r42= v olume, v, of pyramid, base area a, height h. v ah31= v olume, v, of cylinder of radius r, height h. rv r h2= v olume, v, of cone of radius r, height h. r v r h31 2= v olume, v, of sphere of radius r. r v r34 3= sin sin sin aa bb cc= = cos a b c bc a 22 2 2= + - sinbc a21area=a c bcb a", "3": "3 0607/41/m/j/15 \u00a9 ucles 2015 [turn overanswer all the questions. 1 the table shows the marks that 80 students scored in an examination. mark 0 1 2 3 4 5 6 7 8 9 10 number of students1 5 6 8 9 10 12 8 16 3 2 (a) write down the mode. \t answer(a)\t\t [1] (b) write down the range. \t answer(b)\t\t [1] (c) find the median. \t answer(c)\t\t [1] (d) find the interquartile range. \t answer(d)\t\t [2] (e) calculate the mean. \t answer(e)\t\t [1]", "4": "4 0607/41/m/j/15 \u00a9 ucles 20152 solve the simultaneous equations. you must show all your working. 5x \u2013 2y = 11.5 4x + 3y = 0 \t answer\t\tx\t=\t\t \t y\t=\t\t [4] 3 a car of length 4.5 metres is travelling at 72 km/h. the car approaches a tunnel of length 260 metres. (a) change 72 km/h into m/s. \t answer(a)\t\t. m/s [1] (b) find the time it will take for the car to pass completely through the tunnel. give your answer in seconds. \t answer(b)\t\t.. s [2]", "5": "5 0607/41/m/j/15 \u00a9 ucles 2015 [turn over4 0 2 4 6 1 3 5 xa by \u20132 \u20134 \u20136 \u20131 \u20133 \u20135246810 13579 (a) describe fully the single transformation that maps triangle a onto triangle b. answer(a) . .. [2] (b) rotate triangle b through 90\u00b0 clockwise, centre (\u20131, 6). draw this triangle and label it c. [3] (c) describe fully the single transformation that maps triangle c onto triangle a. answer(c) .. .. [2]", "6": "6 0607/41/m/j/15 \u00a9 ucles 20155 (a) y varies inversely as the square root of x. y = 5 when x = 9. (i) find the value of y when x = 25. \t answer(a) (i) y\t=\t\t [2] (ii) find the value of x when y = 25. \t answer(a) (ii)\tx\t=\t\t [2] (iii) find x in terms of y. \t answer(a) (iii)\tx\t=\t\t [2] (b) 024 \u20134 2xy find the equation of this quadratic curve. \t answer(b)\t\t [3]", "7": "7 0607/41/m/j/15 \u00a9 ucles 2015 [turn over6 the venn diagram shows the sets a, b and c. a c bu u = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} a\t= {factors of 12} b = {factors of 6} c = {11, 12, 13, 14} (a) list the elements of sets a and b. \t answer(a)\t\ta\t= {\t... } \t b\t= {\t... } [2] (b) write all the elements of u in the correct regions of the venn diagram above. [3] (c) list the elements of (i) a b+, \t answer(c) (i)\t{\t... } [1] (ii) a c+l, \t answer(c) (ii)\t{\t... } [1] (iii) b c, l. \t answer(c) (iii)\t{\t... } [1] (d) find (i) a b c n ( ) , , l, \t answer(d) (i)\t\t [1] (ii) a b c n ( ) + + l. \t answer(d) (ii)\t\t [1]", "8": "8 0607/41/m/j/15 \u00a9 ucles 20157 squash balls have radius 1.5 cm. they are sold in boxes. each box is a cuboid. each box has length 15 cm, width 12 cm and height 3 cm. (a) show that the maximum number of balls in a box is 20. [1] (b) calculate the volume of one ball. \t answer(b)\t\t. cm3 [2] (c) calculate the total volume of 20 balls. \t answer(c)\t\t. cm3 [1] (d) write your answer to part (c) in standard form. \t answer(d)\t\t. cm3 [1] (e) calculate the percentage of the volume of the box that the 20 balls fill. \t answer(e)\t\t % [2]", "9": "9 0607/41/m/j/15 \u00a9 ucles 2015 [turn over8 oca x 26\u00b0not to scale p b a, b and c lie on a circle, centre o. ap and bp are tangents to the circle. ab intersects op at the point x and angle opb = 26\u00b0. (a) find the size of (i) angle abp, \t answer(a) (i)\t\t [1] (ii) angle oba , \t answer(a) (ii)\t\t [1] (iii) angle acb . \t answer(a) (iii)\t\t [1] (b) write down the mathematical name of quadrilateral aobp . \t answer(b)\t\t [1] (c) complete these statements. (i) triangle obp is congruent to triangle .. . [1] (ii) triangle obp is similar, but not congruent to, triangle ... . [1]", "10": "10 0607/41/m/j/15 \u00a9 ucles 20159 the table shows the amount in dollars, y, that 10 families of different size, x, spend in one week. number in family, ( x) 2 2 3 3 5 5 6 6 6 6 amount in dollars, ( y). 60 65 80 75 100 105 120 135 125 115 (a) (i) complete the scatter diagram. the first four points have been plotted for you. xy 1 05060708090100110120130140150 2 3 4 number in familyamount in dollars 5 6 7 8 [2] (ii) what type of correlation is shown by the scatter diagram? \t answer(a) (ii)\t\t [1]", "11": "11 0607/41/m/j/15 \u00a9 ucles 2015 [turn over (b) find (i) the mean family size, \t answer(b) (i)\t\t [1] (ii) the mean amount spent in one week. \t answer(b) (ii) $\t\t [1] (c) (i) find the equation of the regression line in the form y m x c= + . \t answer(c) (i)\ty\t=\t\t [2] (ii) use your answer to part (c)(i) to estimate the amount spent in one week by a family of 4. \t answer(c) (ii) $ \t [1]", "12": "12 0607/41/m/j/15 \u00a9 ucles 201510 72\u00b0 58\u00b0 dc80 mnot to scale 64 m65 m ab (a) find ac. \t answer(a)\t\t m [2]", "13": "13 0607/41/m/j/15 \u00a9 ucles 2015 [turn over (b) calculate angle cad . \t answer(b)\t\t [3] (c) calculate the area of the quadrilateral abcd . \t answer(c)\t\t... m2 [4]", "14": "14 0607/41/m/j/15 \u00a9 ucles 201511 paula invests $3000 in bank a and $3000 in bank b. (a) bank a pays compound interest at a rate of 4% each year. (i) find the total amount that paula has in bank a at the end of 3 years. \t answer(a) (i) $\t. [2] (ii) after how many complete years is the total amount that paula has in bank a greater than $4000? \t answer(a) (ii) [3] (b) bank b pays simple interest at a rate of 5% each year. (i) find the total amount that paula has in bank b at the end of 3 years. \t answer(b) (i) $ . [1] (ii) after how many complete years is the total amount that paula has in bank b greater than $4000? \t answer(b) (ii) .. [1] (c) after how many complete years will the total amount that paula has in bank a be greater than the total amount that paula has in bank b? \t answer(c)\t.. [3]", "15": "15 0607/41/m/j/15 \u00a9 ucles 2015 [turn over12 bag 1 only contains 6 blue balls and 4 red balls. bag 2 only contains 8 blue balls and 2 red balls. marco chooses a ball at random from bag 1 and puts it in bag 2. he then chooses a ball at random from bag 2 and puts it in bag 1. (a) complete the tree diagram. blue 6 10 redbluebag 2 bag 1 red blue red [2] (b) find the probability that the two balls chosen are (i) both blue, \t answer(b) (i) [2] (ii) one red and one blue. \t answer(b) (ii) [3] (c) find the probability that, after marco chooses the two balls, there are exactly 6 blue balls in bag 1. \t answer(c)\t\t [3]", "16": "16 0607/41/m/j/15 \u00a9 ucles 201513 in this question all lengths are in centimetres. 5x + 46x + 1 not to scale 2x \u2013 1 (a) write down a quadratic equation, in terms of x, and show that it simplifies to . x x7 24 16 02- - = [3] (b) factorise . x x7 24 162- - \t answer(b)\t\t [2]", "17": "17 0607/41/m/j/15 \u00a9 ucles 2015 [turn over (c) show that the area of the triangle is 84 cm2. [2] (d) the area of this rectangle is equal to the area of the triangle. find the value of y. y + 2 ynot to scale \t answer(d)\ty = [4]", "18": "18 0607/41/m/j/15 \u00a9 ucles 201514 in this question all measurements are in metres. a rectangular garden has length p and width q. the garden is divided into 3 sections as shown in the diagram. x grassflowersvegetables2 3 pp qnot to scale1 4q (a) write down an expression, in terms of p and q, for the area for flowers. \t answer(a)\t\t... .m2 [1] (b) show that x p43= . [2]", "19": "19 0607/41/m/j/15 \u00a9 ucles 2015 [turn over (c) find an expression, in terms of p and q, for the area for grass. give your answer in its simplest form. \t answer(c)\t m2 [2] (d) find the ratio area for vegetables : area for grass . \t answer(d)\t .. : .. [2] question 15 is printed on the next page.", "20": "20 0607/41/m/j/15 \u00a9 ucles 2015permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.15 the diagram shows a sketch of the graph of f y x=^h where fx x xx x 4 34 3 22 - ++ += ^h . o xy not to scale (a) (i) find the equations of the three asymptotes. answer(a) (i) .. , .. , .. [3] (ii) find the co-ordinates of the local maximum point. \t answer(a) (ii) ( .. , ..) [2] (iii) find the co-ordinates of the local minimum point. \t answer(a) (iii) ( .. , ..) [2] (b) find the values of k, when (i) fx k= ^h has no solutions, \t answer(b) (i) [2] (ii) fx k= ^h has one solution. \t answer(b) (ii) [1] (c) solve the inequality fx 02 ^h . \t answer(c)\t\t [3]" }, "0607_s15_qp_42.pdf": { "1": "this document consists of 20 printed pages. dc (nh/sw) 99286/6 \u00a9 ucles 2015 [turn over * 5 4 8 3 7 0 5 8 8 5 * cambridge international mathematics 0607/42 paper 4 (extended) may/june 2015 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/42/m/j/15 \u00a9 ucles 2015formula list for the equation ax bx c02+ + = xab b ac 242!=- - curved surface area, a, of cylinder of radius r, height h. r a rh2= curved surface area, a, of cone of radius r, sloping edge l. r a rl= curved surface area, a, of sphere of radius r. r a r42= v olume, v, of pyramid, base area a, height h. v ah31= v olume, v, of cylinder of radius r, height h. rv r h2= v olume, v, of cone of radius r, height h. r v r h31 2= v olume, v, of sphere of radius r. r v r34 3= sin sin sin aa bb cc= = cos a b c bc a 22 2 2= + - sinbc a21area=a c bcb a", "3": "3 0607/42/m/j/15 \u00a9 ucles 2015 [turn overanswer all the questions. 1 an art gallery values its paintings every five years. the value of one painting increased by 90% every five years from 1990. the value in 1995 was $76 000. (a) calculate the exact value of the painting in (i) 1990, answer(a) (i) $ .. [3] (ii) 2010. answer(a) (ii) $ .. [3] (b) the value of the painting continues to increase by 90% every five years. in which year\u2019s valuation will the value of the painting first be over $10 million? answer(b) .. [2]", "4": "4 0607/42/m/j/15 \u00a9 ucles 20152 \u20133\u20132\u201311234567 \u20134\u20133\u20132\u20131 10 2345678910xy bac (a) describe fully the single transformation that maps triangle a onto triangle b. answer(a) . .. [3] (b) complete the statement. triangle a can be mapped onto triangle c by a translation with vector j lk kkn po oo followed by a reflection in the line . .. . [2] (c) stretch triangle a with the x-axis invariant and stretch factor 2. [2]", "5": "5 0607/42/m/j/15 \u00a9 ucles 2015 [turn over3 jean-paul goes on holiday and drives 780 km. he leaves at 06 45 and arrives at 16 10. (a) find the average speed for the whole journey. answer(a) . km/h [3] (b) he travels partly on autoroutes and partly on other roads. he travels for 520 km on autoroutes at an average speed of 105 km/h. find the average speed for the part of the journey on other roads. answer(b) . km/h [3] (c) for every 100 km travelled on autoroutes, jean-paul\u2019s car uses 6 litres of fuel. for every 100 km travelled on other roads, it uses 8 litres of fuel. fuel costs 1.63 euros per litre. the total autoroute toll charges are 15.20 euros. find the total cost of the journey. answer(c) ... euros [4]", "6": "6 0607/42/m/j/15 \u00a9 ucles 20154 \u20131525 \u20132 4 0 xy x x x3 6 f3 2= - + ^h (a) on the diagram, sketch the graph of y xf=^h for x2 4g g- . [2] (b) find the co-ordinates of the local maximum point and the local minimum point. answer(b) maximum ( . , . ) minimum ( . , . ) [2] (c) find the range of values of k for which the equation x kf= ^h has 3 different solutions. answer(c) .. [2]", "7": "7 0607/42/m/j/15 \u00a9 ucles 2015 [turn over (d) describe fully the symmetry of the graph of y xf=^h. answer(d) .. .. [3] (e) the graph of y xg= ^h is the translation of the graph of y xf=^h with vector 0 2-j lkkn poo . write down and simplify xg^h. answer(e) g(x) = . [1]", "8": "8 0607/42/m/j/15 \u00a9 ucles 20155 the table shows the number of goals scored in a season, x, and the average attendance at matches in thousands, y, for ten teams in a league. team a b c d e f g h i j number of goals scored in a season ( x)86 66 75 72 66 55 71 53 47 45 average attendance in thousands ( y)76 46 41 60 36 36 45 25 20 35 (a) complete the scatter diagram. the first five points have been plotted for you. 301520253035404550556065707580y x 40 50 60 number of goals scored in a seasonaverage attendance in thousands 70 80 90 [2]", "9": "9 0607/42/m/j/15 \u00a9 ucles 2015 [turn over (b) what type of correlation is shown by the scatter diagram? answer(b) .. [1] (c) find the mean (i) number of goals scored, answer(c) (i) .. [1] (ii) average attendance. answer(c) (ii) .. thousand [1] (d) find the equation of the line of regression in the form y m x c= + . answer(d) y = . [2] (e) use your answer to part (d) to estimate the average attendance for a team that scored 80 goals in a season. answer(e) .. [1]", "10": "10 0607/42/m/j/15 \u00a9 ucles 20156 e d 180 cm120 cmnot to scale cb a the diagram shows a fence panel abcde . the vertical edges ae and bc are of length 120 cm and the horizontal base ec is of length 180 cm. d is the midpoint of ec. (a) calculate ad. answer(a) cm [2] (b) show that angle adb = 73.74\u00b0 correct to 2 decimal places. [3] (c) ab is an arc of a circle centre d. find the area of the fence panel. answer(c) ... cm2 [3]", "11": "11 0607/42/m/j/15 \u00a9 ucles 2015 [turn over (d) stefan\u2019s fence has 8 panels, each identical to abcde . he wishes to paint both sides of all the panels. each litre of paint covers an area of 6 square metres . calculate the number of litres stefan needs to paint both sides of the whole fence. answer(d) . litres [3]", "12": "12 0607/42/m/j/15 \u00a9 ucles 20157 \u2013101234567891011xy \u20132\u20133 \u20131123456789 \u20132 \u20133 \u20134 \u20135 \u20136 \u20137 \u20138 \u20139 (a) on the grid, show clearly the region defined by these inequalities. 1 xh- 2yh 2 3y xh- 3 5 30 x y g+ [7] (b) use your diagram to estimate (i) the greatest value of y in the region, answer(b) (i) .. [1] (ii) the greatest value of x + y in the region. answer(b) (ii) .. [1]", "13": "13 0607/42/m/j/15 \u00a9 ucles 2015 [turn over8 (a) give an example of (i) discrete data, answer(a) (i) . [1] (ii) continuous data. answer(a) (ii) [1] (b) the table shows the heights, h cm, of 30 students in a class. height (h cm)150 < h \ue03c 155 155 < h \ue03c 160 160 < h \ue03c 165 165 < h \ue03c 170 170 < h \ue03c 175 175 < h \ue03c 180 frequency 2 4 8 7 5 4 (i) write down the modal interval. answer(b) (i) ... < h \ue03c ... [1] (ii) write down the interval that contains the median. answer(b) (ii) .. < h \ue03c .. [1] (iii) calculate an estimate of the mean. answer(b) (iii) cm [2] (iv) explain why the answer to part (b)(iii) is an estimate and not an exact answer. answer(b) (iv) .. [1]", "14": "14 0607/42/m/j/15 \u00a9 ucles 20159 gitte has a bag containing coloured wristbands. there are 5 blue wristbands, 2 yellow wristbands and 4 pink wristbands. gitte takes a wristband at random from the bag. if it is yellow, she puts it back in the bag. if it is blue or pink she puts it on her wrist. she then takes another wristband at random from the bag. (a) complete the tree diagram. 1st wristband 2nd wristband blue blue 5 11yellow pink blue yellow yellow pink blue pink yellow pink4 112 11 [3]", "15": "15 0607/42/m/j/15 \u00a9 ucles 2015 [turn over (b) if the second wristband is yellow, gitte puts it back in the bag. if it is blue or pink she puts it on her other wrist. after choosing the second wristband, find the probability that she is wearing (i) no wristbands, answer(b) (i) .. [2] (ii) a matching pair of wristbands, answer(b) (ii) .. [3] (iii) only one wristband. answer(b) (iii) .. [3]", "16": "16 0607/42/m/j/15 \u00a9 ucles 201510 \u20132020 \u201390 360 0 xy f(x) = 2tan ( x + 30)\u00b0 (a) on the diagram, sketch the graph of y = f(x) for values of x between \u201390 and 360. [3] (b) solve the equation f( x) = 5 for values of x between \u201390 and 360. answer(b) x = .. or x = ... [2] (c) write down the equations of the two asymptotes to this graph for values of x between \u201390 and 360. answer(c) . .. [2]", "17": "17 0607/42/m/j/15 \u00a9 ucles 2015 [turn over (d) on the diagram below, sketch the graph of tan y x 2 30 \u00b0= + ^ h for values of x between \u201390 and 360. \u20132020 \u201390 360 0 xy [2]", "18": "18 0607/42/m/j/15 \u00a9 ucles 201511 35\u00b0 a dc 70 m45 m 55 mnot to scale 80 mb the diagram shows the plan of a field abcd with a path from a to c. (a) calculate (i) the obtuse angle abc , answer(a) (i) .. [4] (ii) angle cad . answer(a) (ii) .. [4] (b) waqar walks along the path ac. calculate his shortest distance from b. answer(b) .. m [2]", "19": "19 0607/42/m/j/15 \u00a9 ucles 2015 [turn over12 x x 5 2 f= - ^h , xxx4 16 41g ! =+- ^h h(x) = 5 x2 + 3x \u2013 2 (a) find f(g(1)) . answer(a) .. [2] (b) find and simplify these expressions. (i) g(f(x)) answer(b) (i) .. [2] (ii) f \u20131(x) answer(b) (ii) .. [2] (c) simplify. (i) f(x) h(x) answer(c) (i) .. [3] (ii) g(x) \u2013 x1 f^h answer(c) (ii) .. [3] question 13 is printed on the next page.", "20": "20 0607/42/m/j/15 \u00a9 ucles 2015permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.13 a d ce fnot to scale b abcd is a parallelogram. bfe and cde are straight lines. (a) explain why triangles afb and dfe are similar. answer(a) . ... .. [2] (b) bc = 10 cm, fd = 4 cm and ec = 8 cm. (i) calculate the length of ab. answer(b) (i) cm [3] (ii) find the value of area of dfe area of afb . answer(b) (ii) .. [1] (iii) find the value of area of dfe area of abcd . answer(b) (iii) .. [2]" }, "0607_s15_qp_43.pdf": { "1": "this document consists of 20 printed pages. dc (st/fd) 99285/4 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 5 6 5 0 4 7 5 9 6 2 * cambridge international mathematics 0607/43 paper 4 (extended) may/june 2015 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for p, use your calculator value. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.", "2": "2 0607/43/m/j/15 \u00a9 ucles 2015formula list for the equation ax2 + bx + c = 0 x = ab b ac 242!- - curved surface area, a, of cylinder of radius r, height h. a = 2prh curved surface area, a, of cone of radius r, sloping edge l. a = prl curved surface area, a, of sphere of radius r. a = 4pr2 v olume, v, of pyramid, base area a, height h. v= ah31 v olume, v, of cylinder of radius r, height h. v = pr2h v olume, v, of cone of radius r, height h. v = r h31 2r v olume, v, of sphere of radius r. v = r34 3r sin sin sin aa bb cc= =a c bcb a\t a2 = b2 + c2 \u2013 2bc cos a \t area = sinbc a21", "3": "3 0607/43/m/j/15 \u00a9 ucles 2015 [turn overanswer all the questions. 1 sancha flew from santiago to paris, a distance of 11 585 km. the average speed of the flight was 852.9 km/h. (a) find the length of time for the flight. give your answer in hours and minutes. answer(a) .. h min [3] (b) the journey back from paris to santiago took 14 hours 30 minutes. the plane left paris at 23 20. the local time in santiago is 6 hours behind the local time in paris. find the local time this plane arrived in santiago. answer(b) . [2] (c) find the overall average speed for the total journey from santiago to paris and back to santiago. answer(c) km/h [3]", "4": "4 0607/43/m/j/15 \u00a9 ucles 20152 45 3 2 1 \u20131 \u20132 \u20133 \u20134\u20135\u20134\u20133\u20132\u20131 1023456789a b xy (a) (i) rotate triangle a through 90\u00b0 anticlockwise about the origin. label the image c. [2] (ii) reflect triangle c in the x-axis. label the image d. [2] (iii) describe fully the single transformation that is equivalent to a rotation through 90\u00b0 anticlockwise about the origin followed by a reflection in the x-axis. answer(a) (iii) ... .. [2] (b) describe fully the single transformation that maps triangle a onto triangle b. answer(b) . .. [3]", "5": "5 0607/43/m/j/15 \u00a9 ucles 2015 [turn over3 sinitta makes necklaces. each necklace costs sinitta $56 to make. they are sold through an internet shop at a selling price of $80. (a) (i) the internet shop charges her 7% of the selling price. find the amount that sinitta receives from the shop for a necklace. answer(a) (i) $ . [2] (ii) the shop increases the charge to 12% of the selling price of $80. calculate the percentage reduction in sinitta\u2019s profit . answer(a) (ii) . % [4] (b) sinitta also makes silver rings. each ring contains 22 g of silver. in the last year the cost of silver has increased by 8% to $143.10 per 100 grams. (i) find the cost of each 100 g of silver before the increase. answer(b) (i) $ . [2] (ii) find the increase in the cost of the silver in a ring. answer(b) (ii) $ . [2]", "6": "6 0607/43/m/j/15 \u00a9 ucles 20154 p is the point (0, 4), q is the point (6, 0) and r is the point (2, 7). 0not to scaley xqr p (a) s is the point such that rs qp= . find the co-ordinates of s. answer(a) ( .. , ... ) [2] (b) calculate qp. answer(b) . [2] (c) find the equation of the line pq. answer(c) . [2]", "7": "7 0607/43/m/j/15 \u00a9 ucles 2015 [turn over (d) write down the co-ordinates of n, the midpoint of pq. answer(d) ( .. , ... ) [1] (e) find the equation of the perpendicular bisector of pq. answer(e) . [3] (f) a and b are points on the perpendicular bisector of pq such that an bn! . what is the mathematical name given to the quadrilateral p aqb ? answer(f) . [1]", "8": "8 0607/43/m/j/15 \u00a9 ucles 20155 40 cm x cm x cm30 cma d cbnot to scale the diagram shows a rectangle, with sides 40 cm and 30 cm, made from a metal sheet. a square of side x cm is cut from each of the four corners of the rectangle. the remaining shape is folded up to make a rectangular open box with abcd as the base. the height of the box is x cm. (a) show that the volume of the box is x x x 1200 140 42 3- + . [3] ", "9": "9 0607/43/m/j/15 \u00a9 ucles 2015 [turn over (b) on the diagram, sketch the graph of y x x x 1200 140 42 3= - + for x0 25g g . 025xy \u201310005000 [2] (c) solve the equation x x x 1200 140 4 20002 3- + = . answer(c) x = .. or x = .. or x = . [3] (d) which solution to part (c) is not a possible value of x when the volume of the box is 2000 cm3? give a reason for your answer. answer(d) . .. [1] (e) what is the maximum volume of the box? for this volume what is the length of the box? answer(e) maximum volume = .. cm3 length = ... cm [2] ", "10": "10 0607/43/m/j/15 \u00a9 ucles 20156 (a) (i) find an expression for the nth term of this sequence. 2, 6, 10, 14, ... answer(a) (i) . [2] (ii) use your answer to part (a)(i) to find an expression for u, the nth term of this sequence. 2 102# , 6 103# , 10 104# , 14 105# , ... answer(a) (ii) u = . [1] (b) the nth term, t, of another sequence, is given by t2 10( ) n 3 2#=-. (i) write down the first 4 terms in this sequence, giving your answers in standard form. answer(b) (i) . , . , . , . [2] (ii) using your answer to part (a)(ii) , find and simplify an expression for tu. answer(b) (ii) . [3]", "11": "11 0607/43/m/j/15 \u00a9 ucles 2015 [turn over7 north b c da 150 m 235 m55\u00b070\u00b0 120 mnot to scale the diagram shows a field abcd with a path from a to c. ac = 150 m, ad = 120 m and cd = 235 m. angle abc = 90\u00b0, angle bac = 55\u00b0 and the bearing of b from a is 070\u00b0. (a) calculate the length of ab. answer(a) . m [2] (b) calculate the bearing of d from a. answer(b) . [4] (c) calculate the area of the field abcd . answer(c) m2 [3]", "12": "12 0607/43/m/j/15 \u00a9 ucles 20158 100 light bulbs were tested. the length of life, t, in thousands of hours was recorded. the results are shown in this table. length of life ( t) in thousands of hourst4 51g t5 61g t6 71g t7 81g t8 91g t9 101g t 10 121g frequency 8 21 31 23 10 5 2 (a) calculate an estimate of the mean value of t. answer(a) . [2]", "13": "13 0607/43/m/j/15 \u00a9 ucles 2015 [turn over (b) draw a cumulative frequency curve for the length of life of the light bulbs. 40102030405060708090100 5 6 7 8 length of life / in thousands of hourscumulative frequency 9 10 11 12t [5] (c) use your graph to estimate (i) the number of light bulbs that lasted longer than 8500 hours, answer(c) (i) . [2] (ii) the interquartile range. answer(c) (ii) ... hours [2]", "14": "14 0607/43/m/j/15 \u00a9 ucles 20159 (a) a 20 cm 15 cm40 cmb d c enot to scale the diagram shows two similar triangles eab and ecd . ab = 20 cm, cd = 15 cm, ac = 40 cm and angle cab = 90\u00b0. (i) show that ec = 120 cm. [2] (ii) find ed. answer(a) (ii) ... cm [2] (iii) find db. answer(a) (iii) ... cm [2]", "15": "15 0607/43/m/j/15 \u00a9 ucles 2015 [turn over (b) 15 cm40 cm20 cm not to scale the diagram shows an open waste paper bin made from metal. the radius of the circular top is 20 cm. the radius of the circular base is 15 cm. the perpendicular height of the bin is 40 cm. using answers from part (a) , calculate (i) the volume of the waste paper bin, answer(b) (i) .. cm3 [3] (ii) the area of metal needed to make the bin. answer(b) (ii) .. cm2 [4]", "16": "16 0607/43/m/j/15 \u00a9 ucles 201510 tricia has 2 bags. in the first bag there are 6 white balls and 4 red balls. in the second bag there are 4 blue balls, 3 white balls and 2 red balls. she takes a ball at random out of the first bag. she then takes a ball at random out of the second bag. (a) complete the tree diagram to show the probability of all the possible outcomes for the two balls. first ball second ball ... ... ... ...blue bluewhitewhite whitered redred [2]", "17": "17 0607/43/m/j/15 \u00a9 ucles 2015 [turn over (b) calculate the probability that tricia\u2019s two balls are (i) both white, answer(b) (i) . [2] (ii) one white and one red, answer(b) (ii) . [3] (iii) of different colours. answer(b) (iii) . [3]", "18": "18 0607/43/m/j/15 \u00a9 ucles 201511 0 \u201312\u2013612y x 4 ( )( )( )fxxx 31 2=+- (a) on the diagram, sketch the graph of ( )f y x= for values of x between x 6=- and x4=. [3] (b) write down the equations of the asymptotes of the graph of ( )f y x= . answer(b) .. .. [2] (c) find the range of values for y when x0h. answer(c) . [2]", "19": "19 0607/43/m/j/15 \u00a9 ucles 2015 [turn over (d) 0 \u201312\u2013612y x 4 on this diagram, sketch the graph of ( )( )yxx 31 2=+-. [2] (e) solve ( )( ) xx 31 26+-=. answer(e) x = or x = .. [2] question 12 is printed on the next page.", "20": "20 0607/43/m/j/15 \u00a9 ucles 2015permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.12 ( ) f g x x x x 3 1 4 2 = - = - ^h (a) find (i) ( )g 3, answer(a) (i) . [1] (ii) ( ( )) f g 3. answer(a) (ii) . [1] (b) find and simplify expressions for (i) ( ( )) g fx, answer(b) (i) . [2] (ii) g ( )x1-, answer(b) (ii) . [2] (iii) ( ) ( ) f gx x2 3- . answer(b) (iii) . [3]" }, "0607_s15_qp_51.pdf": { "1": "this document consists of 8 printed pages. dc (nf/sg) 101336/3 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education *2977744375* cambridge international mathematics 0607/51 paper 5 (core) may/june 2015 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. y ou must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.", "2": "2 0607/51/m/j/15 \u00a9 ucles 2015answer all the questions. investigation staircases this investigation looks at the number of cubes that make different types of staircase. 1 this is an up staircase of height 3 made using 6 cubes. it is a 3-step up staircase because it has a height of 3 cubes. (a) write down the number of cubes that make an up staircase of height 2. (b) on the grid below draw an up staircase of height 4.", "3": "3 0607/51/m/j/15 \u00a9 ucles 2015 [turn over (c) complete the table for the number of cubes that make these up staircases . height number of cubes123 16456 (d) find how many cubes make an up staircase of height 10. (e) (i) what is the height of the tallest up staircase that can be made from 100 cubes? (ii) find how many cubes would be left over. ", "4": "4 0607/51/m/j/15 \u00a9 ucles 20152 this is an up and down staircase of height 3 made using 9 cubes. it is a 3-step up and down staircase because it has a height of 3 cubes. (a) find how many cubes make an up and down staircase of height 4. (b) on the grid below draw an up and down staircase of height 2.", "5": "5 0607/51/m/j/15 \u00a9 ucles 2015 [turn over (c) complete the table for the number of cubes that make these up and down staircases . height number of cubes123 19456 (d) the numbers of cubes form a sequence. write down the mathematical name of this sequence. (e) find how many cubes make an up and down staircase of height 10. (f) find an expression, in terms of n, for the number of cubes that make an up and down staircase of height n. ", "6": "6 0607/51/m/j/15 \u00a9 ucles 20153 this is a double staircase of height 3 made using 12 cubes. it is a 3-step double staircase because it has a height of 3 cubes. (a) find how many cubes make a double staircase of height 2. (b) complete the table for the number of cubes that make these double staircases . height number of cubes123 21 2456", "7": "7 0607/51/m/j/15 \u00a9 ucles 2015 [turn over (c) find how many cubes make a double staircase of height 10. (d) (i) find an expression, in terms of n, for the number of cubes that make a double staircase of height n. (ii) find the height of a double staircase made from 240 cubes. (e) write down the connection between the number of cubes that make a double staircase and the number of cubes that make an up and down staircase , when both staircases have the same height. .. . .. . question 4 is printed on the next page.", "8": "8 0607/51/m/j/15 \u00a9 ucles 2015permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to do wnload at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.4 (a) write down the connection between the number of cubes that make a double staircase and the number of cubes that make an up staircase , when both staircases have the same height. .. . .. . (b) find an expression, in terms of n, for the number of cubes that make an up staircase of height n. " }, "0607_s15_qp_52.pdf": { "1": "this document consists of 7 printed pages and 1 blank page. dc (lk/cgw) 100449/3 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education *1163799309* cambridge international mathematics 0607/52 paper 5 (core) may/june 2015 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. y ou must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.", "2": "2 0607/52/m/j/15 \u00a9 ucles 2015answer all the questions. investigation molecules this investigation looks at the structure of models of molecules. molecules called alkanes contain carbon atoms (c) and hydrogen atoms (h) arranged in a pattern. 1 these diagrams show the first three alkanes. hch hh hch hch hh hch hch hch hh (a) draw a diagram to show the next alkane which contains four carbon atoms.", "3": "3 0607/52/m/j/15 \u00a9 ucles 2015 [turn over (b) (i) complete this table to show the number of hydrogen atoms ( h) for different numbers of carbon atoms ( c). ch 14 26 3456 (ii) what is the value of h when c is 12? ... (iii) find a formula for h in terms of c. h = .. (iv) what is the value of c when h is 100? ...", "4": "4 0607/52/m/j/15 \u00a9 ucles 20152 alkanes can be made into alcohols by adding one oxygen atom (o). for example hch hch hoh (a) complete the table below for an alcohol with 3 carbon atoms. number of carbon atoms cnumber of hydrogen atoms hnumber of oxygen atoms ototal number of atoms t 1416 2619 3 (b) find a formula for t in terms of c. t = ..", "5": "5 0607/52/m/j/15 \u00a9 ucles 2015 [turn over3 chemists use small spheres and rods to make models of molecules. these diagrams show a sequence of molecules of height 1. molecule 1 molecule 2 molecule 3 (a) draw the next two molecules in this sequence. (b) complete this table for molecules of height 1. molecule mnumber of spheres snumber of rods r 110 221 332 4 5 6 (c) write down a formula for s in terms of m. s = .. (d) a molecule of height 1 has 97 spheres. how many rods does this molecule have? ...", "6": "6 0607/52/m/j/15 \u00a9 ucles 20154 these diagrams show a sequence of molecules of height 2. molecule 1 molecule 2 molecule 3 molecule 4 (a) complete this table for molecules of height 2. molecule mnumber of spheres snumber of rods r 121 244 367 4 5 6 (b) find, in terms of m, a formula for (i) s, s = .. (ii) r. r = .. (c) a molecule of height 2 has 100 spheres. how many rods does this molecule have? ...", "7": "7 0607/52/m/j/15 \u00a9 ucles 20155 (a) use your answers to questions 3(c) and 4(b) to help you complete the table for molecules of height h. height ( h)number of spheres ( s) in terms of mnumber of rods ( r) in terms of m 1 m \u2212 1 2 3 3m 5m \u2212 3 4 5 5m 9m \u2212 5 6 (b) find, in terms of m and h, a formula for (i) s, s = .. (ii) r. r = ..", "8": "8 0607/52/m/j/15 \u00a9 ucles 2015permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to do wnload at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_s15_qp_53.pdf": { "1": "this document consists of 7 printed pages and 1 blank page. dc (nh/cgw) 100444/4 \u00a9 ucles 2015 [turn over *2259231181* cambridge international mathematics 0607/53 paper 5 (core) may/june 2015 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. y ou must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/53/m/j/15 \u00a9 ucles 2015answer all the questions. investigation t-v alues a grid of any length and width 10 is numbered 1, 2, 3, \u2026 . 41 42 43 44 45 46 47 48 49 50123456789 1 0 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 the grid has a letter t placed on it, as shown. the t has a horizontal bar of length 3 and a vertical bar of length 2. the t shown is shape 1 because the number in the top left square of the t is 1. t-values are found using this method. method calculation of t-value for shape 1 square the number at the bottom of the t. 222= 484 multiply together the numbers at each end of the horizontal bar. 1 \u00d7 3 = 3 take the second answer from the first answer to find the t-value. 484 \u2013 3 = 481 the t-value for shape 1 is t1 = 481. this investigation is about finding t-values. 1 (a) complete this table. shape number nworkingt-value tn 12 22 \u2013 1 \u00d7 3 = 484 \u2013 3 t1 = 481 22 32 \u2013 2 \u00d7 4 = 529 \u2013 8 t2 = 521 3t3 = 4t4 = 5t5 =", "3": "3 0607/53/m/j/15 \u00a9 ucles 2015 [turn over (b) explain how you know that t6 = 681 without using the method in the table. .. . .. . .. . (c) when a t is placed at the end of a line, it still has a t-value. the t \u201cwraps round\u201d like this. 1 23456789 1 0 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 work out t9. t9 = ..", "4": "4 0607/53/m/j/15 \u00a9 ucles 20152 the t is now placed on this 10 by 10 grid. 41 42 43 44 45 46 47 48 49 50123456789 1 0 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 61 62 63 64 65 66 67 68 69 7051 52 53 54 55 56 57 58 59 60 81 82 83 84 85 86 87 88 89 9071 72 73 74 75 76 77 78 79 80 91 92 93 94 95 96 97 98 99 100 (a) work out the greatest t-value for a t that fits completely on this grid. ... (b) complete this statement for the numbers in the grid. in each row the numbers increase by 1 and in each column the numbers increase by .", "5": "5 0607/53/m/j/15 \u00a9 ucles 2015 [turn over (c) complete the squares in this t using expressions in terms of n. nn + 1 (d) complete this working to show that tn = 40 n + 441. the first line of working has been started for you. tn = ( n + ... )2 \u2013 n ( n + . ) (e) when tn = 2641, find the value of n. n = .. (f) explain why 840 cannot be a t-value. .. . .. .", "6": "6 0607/53/m/j/15 \u00a9 ucles 20153 the t is now placed on a new grid that is 11 squares wide. 45 46 47 48 49 50 51 52 53 54123456789 1 0 12 13 14 15 16 17 18 19 20 21 23 24 25 26 27 28 29 30 31 32 34 35 36 37 38 39 40 41 42 43 5511 22 33 44 t1, t2, t3, t4, t5, \u2026 form a sequence. (a) complete this table. shape number n12345 8 t-value tn573 661 705 (b) (i) find a formula, in terms of n, for tn . tn = .. (ii) show that your formula in part b(i) gives the correct result for t10 .", "7": "7 0607/53/m/j/15 \u00a9 ucles 20154 a different t is placed on a grid that is w squares wide. the t has a horizontal bar of length 3 and a vertical bar of length 3. 123456789 1 0 w n complete the squares in this t using expressions in terms of n and w. n", "8": "8 0607/53/m/j/15 \u00a9 ucles 2015blank page permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to do wnload at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_s15_qp_61.pdf": { "1": "this document consists of 12 printed pages. dc (ac/fd) 101335/3 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 6 7 1 4 1 0 0 3 2 9 * cambridge international mathematics 0607/61 paper 6 (extended) may/june 2015 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. y ou must show all the relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.", "2": "2 0607/61/m/j/15 \u00a9 ucles 2015answer both parts a and b. a\t investigation staircases \t(20\tmarks) you are advised to spend no more than 45 minutes on this part. this investigation looks at the number of cubes that make different types of staircase. 1\t this is an up staircase of height 3 made using 6 cubes. \t it is a 3-step up staircase because it has a height of 3 cubes. \t (a)\t write down the number of cubes that make an up staircase of height 2. ... \t (b)\t on the grid below draw an up staircase of height 4.", "3": "3 0607/61/m/j/15 \u00a9 ucles 2015 [turn\tover\t (c)\t complete the table for the number of cubes that make these up staircases. height 1 2 3 4 5 6 number of cubes1 6 \t \t (d)\t find an expression, in terms of n, for the number of cubes that make an up staircase of height n. ... \t\t \t \t (e)\t find how many cubes make an up staircase of height 10. ...", "4": "4 0607/61/m/j/15 \u00a9 ucles 20152\t this is an up and down staircase of height 3 made using 9 cubes. \t it is a 3-step up and down staircase because it has a height of 3 cubes. \t (a)\t find how many cubes make an up and down staircase of height 4. ... \t (b)\t complete the table for the number of cubes that make these up and down staircases . height 1 2 3 4 5 6 number of cubes1 9 \t (c)\t find an expression, in terms of n, for the number of cubes that make an up and down staircase of height n. ... \t (d)\t find how many cubes make an up and down staircase of height 10. ...", "5": "5 0607/61/m/j/15 \u00a9 ucles 2015 [turn\tover3\t this is a double staircase of height 3 made using 12 cubes. \t it is a 3-step double staircase because it has a height of 3 cubes. \t (a)\t complete the table for the number of cubes that make these double staircases . height 1 2 3 4 5 6 number of cubes2 12 \t (b)\t find an expression, in terms of n, for the number of cubes that make a double staircase of height n. ... \t (c)\t find how many cubes make a double staircase of height 10. ... \t (d)\t find the height of a double staircase made from 240 cubes. ...", "6": "6 0607/61/m/j/15 \u00a9 ucles 20154\t this is a sequence of multiple staircases of heights 1, 2 and 3. \t these are multiple staircases because, for each staircase, the width, the height and the depth are the same. \t (a)\t complete the table for the number of cubes that make these multiple staircases . height 1 2 3 4 5 6 number of cubes1 6 18 \t (b)\t find an expression, in terms of n, for the number of cubes that make a multiple staircase of height n. ...", "7": "7 0607/61/m/j/15 \u00a9 ucles 2015 [turn\tover5\t there are 1800 cubes available. \t use your expressions in questions \t1(d), 3(b) and 4(b) to complete the table. type of staircase maximum height using 1800 cubes number of cubes left over up up and down 42 36 double multiple", "8": "8 0607/61/m/j/15 \u00a9 ucles 2015b\t modelling boat\ttrips\t(20\tmarks) you are advised to spend no more than 45 minutes on this part. a boat travels up and down a river. the time taken for a journey depends on the speed of the boat and the speed of the water current. 1\t in this model the water is still and so the speed of the water current is zero km / h. \t the speed of the boat in still water is 15 km / h. \t (a)\t find how many minutes it will take for the boat to travel 10 km. min \t (b)\t the boat travels for 24 minutes. \t find the distance that it travels. . km", "9": "9 0607/61/m/j/15 \u00a9 ucles 2015 [turn\toverwhen a boat travels against the current it goes in exactly the opposite direction to the current. boat currentwhen a boat travels with the current it goes in exactly the same direction as the current. boat current 2\t in this model the water is not still. \t the speed of the water current is 2 km / h. \t the speed of the boat in still water is 15 km / h. \t (a)\t show that it will now take the boat approximately 46 minutes to travel 10 km against the current. \t (b)\t the boat travels for 20 minutes against the current. \t find the distance it travels. . km \t (c)\t how far will the boat travel in 46 minutes with the current? . km \t ", "10": "10 0607/61/m/j/15 \u00a9 ucles 20153\t the boat travels 20 km up the river before returning to where it started. \t the speed of the water current is 2 km / h. \t the speed of the boat in still water is v km / h. \t (a)\t (i)\t find a model for the total travelling time, t hours, for this whole journey. t = .. \t \t \t (ii)\t show that your model simplifies to tvv 440 2=-. \t \t (iii)\t sketch the graph of tvvv4400 20for2g g =-. t v200 \t \t(iv)\t the model is only appropriate for v k2. \t \t \t find the value of k and give a practical reason why k must have this value. k = .. because ...", "11": "11 0607/61/m/j/15 \u00a9 ucles 2015 [turn\tover\t (b)\t when the speed of the boat in still water is 18 km / h, find the time taken for the whole journey. . hours \t (c)\t the return journey takes the boat 3 hours. \t find the speed of the boat in still water. . km / h 4\t the boat travels 20 km up the river before returning to where it started. \t the speed of the boat in still water is v km / h. \t a whole journey takes the boat 3 hours. \t (a)\t (i)\t adjust the model in question\t3(a)(ii) for a water current of 3 km / h. t = .. \t \t (ii)\t find the speed of the boat in still water. . km / h \t (b)\t the speed of the boat in still water is now 15 km / h. \t adjust the model in question\t3(a)(ii) and find the speed of the water current. . km / h question \t5\tis\tprinted\ton\tthe\tnext\tpage.", "12": "12 0607/61/m/j/15 \u00a9 ucles 20155\t (a)\t there is a change in the boat\u2019s journey. \t explain how the journey has changed when the model in \tquestion\t3(a)(ii) becomes tvv 480 2=-\t . ... ... \t (b)\t describe fully the single transformation that maps the graph of tvv 440 2=- onto the graph \t \t of tvv 480 2=- . ... ... permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_s15_qp_62.pdf": { "1": "this document consists of 12 printed pages. dc (ac/cgw) 100447/1 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 4 0 1 6 8 6 6 9 8 7 * cambridge international mathematics 0607/62 paper 6 (extended) may/june 2015 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. y ou must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.", "2": "2 0607/62/m/j/15 \u00a9 ucles 2015answer both parts a and b. a\t investigation molecules \t(20\tmarks) you are advised to spend no more than 45 minutes on this part. this investigation looks at the number of spheres and rods that you need to make models of molecules. 1\t chemists use small spheres and rods to make models of molecules. \t these diagrams show a sequence of molecules of height 1. molecule 1 molecule 2 molecule 3 \t (a)\t draw the next two molecules in this sequence. \t (b)\t complete this table for molecules of height 1. molecule mnumber of spheres snumber of rods r 1 1 0 2 2 1 3 3 2 4 5 6 \t (c)\t write down a formula for s in terms of m. \t s = ..", "3": "3 0607/62/m/j/15 \u00a9 ucles 2015 [turn\tover2\t these diagrams show a sequence of molecules of height 2. molecule 1 molecule 2 molecule 3 molecule 4 \t (a)\t complete this table for molecules of height 2. molecule mnumber of spheres snumber of rods r 1 2 1 2 4 4 3 6 7 4 5 6 \t (b)\t find, in terms of m, a formula for \t \t (i)\t s, s = .. \t \t (ii)\t r. \t r = ..", "4": "4 0607/62/m/j/15 \u00a9 ucles 20153\t these diagrams show a sequence of molecules of height 3. molecule 1 molecule 2 molecule 3 molecule 4 \t (a)\t complete this table for molecules of height 3. molecule mnumber of spheres snumber of rods r 1 3 2 2 6 7 3 9 12 4 5 6 \t (b)\t find, in terms of m, a formula for \t \t (i)\t s, s = .. \t \t (ii)\t r. \t r = ..", "5": "5 0607/62/m/j/15 \u00a9 ucles 2015 [turn\tover4\t (a)\t use your answers to questions \t1(c), 2(b) and 3(b) to help you complete the table for molecules of height h. height ( h)number of spheres ( s) in terms of mnumber of rods ( r) in terms of m 1 m \u2212 1 2 3 4 5 5m 9m \u2212 5 6 \t (b)\t find, in terms of m and h, a formula for \t \t (i)\t s, s = .. \t \t (ii)\t r. r = ..", "6": "6 0607/62/m/j/15 \u00a9 ucles 2015\t (c)\t use your answer to part\t(b)(i)\tto find a formula for m in terms of s and h. m = .. \t (d)\t find a formula for r in terms of s and h. r = ..", "7": "7 0607/62/m/j/15 \u00a9 ucles 2015 [turn\tover5\t (a)\t a molecule has height h and width w. \t for example, molecule 4 in question\t3 has h = 3 and w = 4. \t \t use your answer to question\t4(d)\tto show that r = 2hw \u2013 h \u2212 w. \t (b)\t can a square molecule have 544 rods? ", "8": "8 0607/62/m/j/15 \u00a9 ucles 2015b\t modelling where \tis\tthe\thorizon? \t(20\tmarks) you are advised to spend no more than 45 minutes on this part. this table shows the distance to the horizon ( y kilometres) at different heights above sea level ( x metres). x 1 2 3 4 5 6 7 8 9 10 y 3.6 5.0 6.2 7.1 8.0 8.7 9.4 10.1 10.7 11.3 \t 01 1 2 3 4 5 6 height above sea level (m)distance to horizon (km) 7 8 9 10xy 23456789101112", "9": "9 0607/62/m/j/15 \u00a9 ucles 2015 [turn\tover1\t (a)\t on the grid, plot the points given in the table. \t the points (2, 5) and (5, 8) have been plotted for you. \t (b)\t the simplest way to model the data is with a straight line. \t \t (i)\t on the grid, draw the straight line passing through (2, 5) and (5, 8). \t find the equation of this line. ... \t \t (ii)\t using this model what is the distance to the horizon when at sea level? ...", "10": "10 0607/62/m/j/15 \u00a9 ucles 20152\t\tanother model for the data is y ax bx c2= + +. \t assume that, when the height is 0, the distance to the horizon is 0. \t (a)\t show that c = 0. \t (b)\t when c = 0, the model is y ax bx2= + . \t \t (i)\t use the point (2, 5) to form an equation in a and b. ... \t \t (ii)\t use the point (5, 8) to form another equation in a and b. ...", "11": "11 0607/62/m/j/15 \u00a9 ucles 2015\t (c)\t solve the equations in part\t(b) and write down your model. ... \t (d)\t sketch the graph of y against x for x0 10g g . 0 xy \t (e)\t comment on the validity of this model. ... question \t3\tis\tprinted\ton\tthe\tnext\tpage.", "12": "12 0607/62/m/j/15 \u00a9 ucles 2015permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.3\t another model for this data is y axb= . \t (a)\t use (2, 5) and (5, 8) to write down two equations in a and b. .. .. \t (b)\t show that . .1 6 2 5b= . \t (c)\t show that b = 0.5, correct to 1 decimal place. \t (d)\t find the value of a and write down your model. ... \t (e)\t compare the model in this question with the data on page 8. ... ..." }, "0607_w15_qp_11.pdf": { "1": " this document consists of 11 printed pages and 1 blank page. ib15 11_0607_11/3rp \u00a9 ucles 2015 [turn over *0120737079* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/11 paper 1 (core) october/november 2015 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2015 0607/11/o/n/15 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2015 0607/11/o/n/15 [turn over answer all the questions. 1 work out . 5 \u00d7 20 \u00f74 answe r [1] 2 (a) a shape a is drawn on a 1cm square grid. find the perimeter of shape a. answer(a) cm [1] (b) on the grid below, draw a di fferent shape which has the same area as shape a. [2] ", "4": "4 \u00a9 ucles 2015 0607/11/o/n/15 3 (a) write down the value of (\u2013 2)3. answer(a) [1] (b) simplify. \u20132 \u2013 (\u20138) 2 + 8 give your answer as a fraction in its lowest terms. answer(b) [2] 4 a farmer picks a bunch of grapes. he writes down a the colour of the grapes b the number of grapes c the weight of the grapes d which plant the grapes were picked from. (a) which one of a, b, c or d is discrete data? answer(a) [1] (b) which one of a, b, c or d is continuous data? answer(b) [1] ", "5": "5 \u00a9 ucles 2015 0607/11/o/n/15 [turn over 5 niki began a race at 10 05. she finished the race at 16 05. (a) how many hours did niki take to complete the race? answer(a) h [1] (b) the distance of the race was 42 km. work out niki\u2019s average speed. answer(b) km/h [1] 6 from this list write down the irrational number. 5 7 92 9 7 answe r [1] ", "6": "6 \u00a9 ucles 2015 0607/11/o/n/15 7 the diagram shows the graph of y = f(x). \u20134 \u20133 \u20132 \u201310 1 2 31234y x 4 5 \u20134\u20133\u20132\u20131 \u20135 \u20136 write down the equations of the two asymptotes of the graph. answer [2] ", "7": "7 \u00a9 ucles 2015 0607/11/o/n/15 [turn over 8 the total cost of a holiday was $720. the pie chart shows how this money was spent. not to scale food other items hoteltravel 120\u00b0 70\u00b080\u00b0 find the amount of money spent on (a) food, answer (a) $ [2] (b) other items. answer (b) $ [2] ", "8": "8 \u00a9 ucles 2015 0607/11/o/n/15 9 012345678 2 3 4 1 xy the diagram shows the graph of y = x 2 \u2013 4x + 8 for 0 x 4. write down the equation of the line of symmetry of this graph. answe r [1] 10 p draw the tangents from p to the circle. [1] ", "9": "9 \u00a9 ucles 2015 0607/11/o/n/15 [turn over 11 (a) simplify. (i) 3x \u2013 5 + 2 x \u2013 12 answer(a) (i) [2] (ii) 4 \u00d7 d \u00d7 2 \u00d7 d answer(a) (ii) [1] (iii) 3x \u2013 6x answer(a) (iii) [2] (b) factorise completely. 6 ab \u2013 8a 2 answer(b) [2] (c) solve the following equation. x + 8 = 15 answer(c) x = [1] (d) solve the inequality. 6 x < 4x + 11 answer(d) [2] ", "10": "10 \u00a9 ucles 2015 0607/11/o/n/15 12 data has been collected about the age (years) and the value (to the nearest $100) of the cars owned by a class of university students. age (years) 1 2 2 3 4 4 5 7 8 value ($) 8000 6400 5200 4000 3000 2100 1700 1200 800 0100020003000400050006000700080009000 1 2 3 4 5 6 age (years)value ($) 7 8 9 10 (a) complete the scatter diagram. the first five points have been plotted for you. [2] (b) what type of correlation is shown on the scatter diagram? answer(b) [1] (c) the mean age is 4 years. the mean value is $3600. draw the line of best fit on your diagram. [2] ", "11": "11 \u00a9 ucles 2015 0607/11/o/n/15 13 the base of this pyramid is a square of side 5 m. it has perpendicular height 12 m. work out the volume of the pyramid. answe r m3 [3] 14 a rectangle has sides 6 cm and 8 cm. 6 cm not to scale 8 cm work out the length of a diagonal of this rectangle. answe r cm [2] ", "12": "12 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknow ledgements booklet. this is produced for each series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge as sessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2015 0607/11/o/n/15 blank page " }, "0607_w15_qp_12.pdf": { "1": " this document consists of 11 printed pages and 1 blank page. ib15 11_0607_12/fp \u00a9 ucles 2015 [turn over *9024566157 * cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/12 paper 1 (core) october/november 2015 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2015 0607/12/o/n/15 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2015 0607/12/o/n/15 [turn over answer all the questions. 1 work out . 5 \u00d7 20 \u00f74 answe r [1] 2 (a) a shape a is drawn on a 1cm square grid. find the perimeter of shape a. answer(a) cm [1] (b) on the grid below, draw a di fferent shape which has the same area as shape a. [2] ", "4": "4 \u00a9 ucles 2015 0607/12/o/n/15 3 (a) write down the value of (\u2013 2)3. answer(a) [1] (b) simplify. \u20132 \u2013 (\u20138) 2 + 8 give your answer as a fraction in its lowest terms. answer(b) [2] 4 a farmer picks a bunch of grapes. he writes down a the colour of the grapes b the number of grapes c the weight of the grapes d which plant the grapes were picked from. (a) which one of a, b, c or d is discrete data? answer(a) [1] (b) which one of a, b, c or d is continuous data? answer(b) [1] ", "5": "5 \u00a9 ucles 2015 0607/12/o/n/15 [turn over 5 niki began a race at 10 05. she finished the race at 16 05. (a) how many hours did niki take to complete the race? answer(a) h [1] (b) the distance of the race was 42 km. work out niki\u2019s average speed. answer(b) km/h [1] 6 from this list write down the irrational number. 5 7 92 9 7 answe r [1] ", "6": "6 \u00a9 ucles 2015 0607/12/o/n/15 7 the diagram shows the graph of y = f(x). \u20134 \u20133 \u20132 \u201310 1 2 31234y x 4 5 \u20134\u20133\u20132\u20131 \u20135 \u20136 write down the equations of the two asymptotes of the graph. answer [2] ", "7": "7 \u00a9 ucles 2015 0607/12/o/n/15 [turn over 8 the total cost of a holiday was $720. the pie chart shows how this money was spent. not to scale food other items hoteltravel 120\u00b0 70\u00b080\u00b0 find the amount of money spent on (a) food, answer (a) $ [2] (b) other items. answer (b) $ [2] ", "8": "8 \u00a9 ucles 2015 0607/12/o/n/15 9 012345678 2 3 4 1 xy the diagram shows the graph of y = x 2 \u2013 4x + 8 for 0 x 4. write down the equation of the line of symmetry of this graph. answe r [1] 10 p draw the tangents from p to the circle. [1] ", "9": "9 \u00a9 ucles 2015 0607/12/o/n/15 [turn over 11 (a) simplify. (i) 3x \u2013 5 + 2 x \u2013 12 answer(a) (i) [2] (ii) 4 \u00d7 d \u00d7 2 \u00d7 d answer(a) (ii) [1] (iii) 3x \u2013 6x answer(a) (iii) [2] (b) factorise completely. 6 ab \u2013 8a 2 answer(b) [2] (c) solve the following equation. x + 8 = 15 answer(c) x = [1] (d) solve the inequality. 6 x < 4x + 11 answer(d) [2] ", "10": "10 \u00a9 ucles 2015 0607/12/o/n/15 12 data has been collected about the age (years) and the value (to the nearest $100) of the cars owned by a class of university students. age (years) 1 2 2 3 4 4 5 7 8 value ($) 8000 6400 5200 4000 3000 2100 1700 1200 800 0100020003000400050006000700080009000 1 2 3 4 5 6 age (years)value ($) 7 8 9 10 (a) complete the scatter diagram. the first five points have been plotted for you. [2] (b) what type of correlation is shown on the scatter diagram? answer(b) [1] (c) the mean age is 4 years. the mean value is $3600. draw the line of best fit on your diagram. [2] ", "11": "11 \u00a9 ucles 2015 0607/12/o/n/15 13 the base of this pyramid is a square of side 5 m. it has perpendicular height 12 m. work out the volume of the pyramid. answe r m3 [3] 14 a rectangle has sides 6 cm and 8 cm. 6 cm not to scale 8 cm work out the length of a diagonal of this rectangle. answe r cm [2] ", "12": "12 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknow ledgements booklet. this is produced for each series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge as sessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2015 0607/12/o/n/15 blank page " }, "0607_w15_qp_13.pdf": { "1": " this document consists of 11 printed pages and 1 blank page. ib15 11_0607_13/fp \u00a9 ucles 2015 [turn over *3736720442 * cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/13 paper 1 (core) october/november 2015 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2015 0607/13/o/n/15 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2015 0607/13/o/n/15 [turn over answer all the questions. 1 work out . 5 \u00d7 20 \u00f74 answe r [1] 2 (a) a shape a is drawn on a 1cm square grid. find the perimeter of shape a. answer(a) cm [1] (b) on the grid below, draw a di fferent shape which has the same area as shape a. [2] ", "4": "4 \u00a9 ucles 2015 0607/13/o/n/15 3 (a) write down the value of (\u2013 2)3. answer(a) [1] (b) simplify. \u20132 \u2013 (\u20138) 2 + 8 give your answer as a fraction in its lowest terms. answer(b) [2] 4 a farmer picks a bunch of grapes. he writes down a the colour of the grapes b the number of grapes c the weight of the grapes d which plant the grapes were picked from. (a) which one of a, b, c or d is discrete data? answer(a) [1] (b) which one of a, b, c or d is continuous data? answer(b) [1] ", "5": "5 \u00a9 ucles 2015 0607/13/o/n/15 [turn over 5 niki began a race at 10 05. she finished the race at 16 05. (a) how many hours did niki take to complete the race? answer(a) h [1] (b) the distance of the race was 42 km. work out niki\u2019s average speed. answer(b) km/h [1] 6 from this list write down the irrational number. 5 7 92 9 7 answe r [1] ", "6": "6 \u00a9 ucles 2015 0607/13/o/n/15 7 the diagram shows the graph of y = f(x). \u20134 \u20133 \u20132 \u201310 1 2 31234y x 4 5 \u20134\u20133\u20132\u20131 \u20135 \u20136 write down the equations of the two asymptotes of the graph. answer [2] ", "7": "7 \u00a9 ucles 2015 0607/13/o/n/15 [turn over 8 the total cost of a holiday was $720. the pie chart shows how this money was spent. not to scale food other items hoteltravel 120\u00b0 70\u00b080\u00b0 find the amount of money spent on (a) food, answer (a) $ [2] (b) other items. answer (b) $ [2] ", "8": "8 \u00a9 ucles 2015 0607/13/o/n/15 9 012345678 2 3 4 1 xy the diagram shows the graph of y = x 2 \u2013 4x + 8 for 0 x 4. write down the equation of the line of symmetry of this graph. answe r [1] 10 p draw the tangents from p to the circle. [1] ", "9": "9 \u00a9 ucles 2015 0607/13/o/n/15 [turn over 11 (a) simplify. (i) 3x \u2013 5 + 2 x \u2013 12 answer(a) (i) [2] (ii) 4 \u00d7 d \u00d7 2 \u00d7 d answer(a) (ii) [1] (iii) 3x \u2013 6x answer(a) (iii) [2] (b) factorise completely. 6 ab \u2013 8a 2 answer(b) [2] (c) solve the following equation. x + 8 = 15 answer(c) x = [1] (d) solve the inequality. 6 x < 4x + 11 answer(d) [2] ", "10": "10 \u00a9 ucles 2015 0607/13/o/n/15 12 data has been collected about the age (years) and the value (to the nearest $100) of the cars owned by a class of university students. age (years) 1 2 2 3 4 4 5 7 8 value ($) 8000 6400 5200 4000 3000 2100 1700 1200 800 0100020003000400050006000700080009000 1 2 3 4 5 6 age (years)value ($) 7 8 9 10 (a) complete the scatter diagram. the first five points have been plotted for you. [2] (b) what type of correlation is shown on the scatter diagram? answer(b) [1] (c) the mean age is 4 years. the mean value is $3600. draw the line of best fit on your diagram. [2] ", "11": "11 \u00a9 ucles 2015 0607/13/o/n/15 13 the base of this pyramid is a square of side 5 m. it has perpendicular height 12 m. work out the volume of the pyramid. answe r m3 [3] 14 a rectangle has sides 6 cm and 8 cm. 6 cm not to scale 8 cm work out the length of a diagonal of this rectangle. answe r cm [2] ", "12": "12 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknow ledgements booklet. this is produced for each series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge as sessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2015 0607/13/o/n/15 blank page " }, "0607_w15_qp_21.pdf": { "1": "this document consists of 8 printed pages. dc (st/sw) 103723/1 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 7 7 3 9 3 6 5 2 3 4 * cambridge international mathematics 0607/21 paper 2 (extended) october/november 2015 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.", "2": "2 0607/21/o/n/15 \u00a9 ucles 2015formula list for the equation ax bx c02+ + = xab b ac 242!=- - curved surface area, a, of cylinder of radius r, height h. r a rh2= curved surface area, a, of cone of radius r, sloping edge l. r a rl= curved surface area, a, of sphere of radius r. r a r42= v olume, v, of pyramid, base area a, height h. v ah31= v olume, v, of cylinder of radius r, height h. rv r h2= v olume, v, of cone of radius r, height h. r v r h31 2= v olume, v, of sphere of radius r. r v r34 3= sin sin sin aa bb cc= = cos a b c bc a 22 2 2= + - sinbc a21area=a c bcb a", "3": "3 0607/21/o/n/15 \u00a9 ucles 2015 [turn overanswer all the questions. 1 work out 127 1 3-. give your answer in its lowest terms. answer . [2] 2 change 12 metres per second into kilometres per hour. answer km/h [2] 3 (a) write 0.000048 in standard form. answer(a) . [1] (b) work out 2 10 6 108 7# # # ^ ^ h h , giving your answer in standard form. answer(b) . [2] 4 the price of a computer is reduced by 5%. the actual reduction is $17. find the original price of the computer. answer $ . [2]", "4": "4 0607/21/o/n/15 \u00a9 ucles 20155 simplify 75 27- . answer . [2] 6 v u at= + (a) find the value of v when u12= , a 2=- and t5=. answer(a) . [1] (b) rearrange the formula to make a the subject. answer(b) a = .. [2] 7 17 cm15 cmnot to scale a bc work out the length of ac. answer ... cm [3]", "5": "5 0607/21/o/n/15 \u00a9 ucles 2015 [turn over8 0 0 10cumulative frequency journey time (minutes)20 3020406080100120140160180200 the cumulative frequency curve shows information about the journey times to school of 200 students. (a) find the median. answer(a) .. min [1] (b) find the number of students with a journey time of more than 20 minutes. answer(b) . [2] 9 find the value of each of the following. (a) .0 23^ h answer(a) . [1] (b) 211- e o answer(b) . [1] (c) 6432 answer(c) . [1] (d) log 39 answer(d) . [1]", "6": "6 0607/21/o/n/15 \u00a9 ucles 201510 not to scale 100\u00b0 y\u00b0x\u00b0 a bcd o a, b, c and d lie on a circle, centre o. find the value of x and the value of y. answer x = .. y = . [2] 11 not to scale \u201342y x o the diagram shows the graph of y px q= + . find the value of p and the value of q. answer p = .. q = . [3]", "7": "7 0607/21/o/n/15 \u00a9 ucles 2015 [turn over12 8 7 4p q 5u the venn diagram shows the number of elements in each subset. (a) find np q, l ^ h. answer(a) . [1] (b) shade the region p q+ l. [1] 13 a is the point ,4 4-^ h and b is the point ,4 10^ h. find the equation of the perpendicular bisector of ab. answer . [4] questions 14 and 15 are printed on the next page.", "8": "8 0607/21/o/n/15 \u00a9 ucles 2015permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.14 y varies inversely as x. when x = 9, y = 3. (a) find y in terms of x. answer(a) y = . [2] (b) find the value of y when x = 81. answer(b) . [1] 15 the graph of ( )cos y a bx = c has a maximum point at (360, 3) and a minimum point at (450, \u20133). find the value of a and the value of b. answer a = .. b = . [2] " }, "0607_w15_qp_22.pdf": { "1": "this document consists of 8 printed pages. dc (rw/sw) 100759/1 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 5 1 3 8 6 2 6 4 2 7 * cambridge international mathematics 0607/22 paper 2 (extended) october/november 2015 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.", "2": "2 0607/22/o/n/15 \u00a9 ucles 2015formula list for the equation ax bx c02+ + = xab b ac 242!=- - curved surface area, a, of cylinder of radius r, height h. r a rh2= curved surface area, a, of cone of radius r, sloping edge l. r a rl= curved surface area, a, of sphere of radius r. r a r42= v olume, v, of pyramid, base area a, height h. v ah31= v olume, v, of cylinder of radius r, height h. rv r h2= v olume, v, of cone of radius r, height h. r v r h31 2= v olume, v, of sphere of radius r. r v r34 3= sin sin sin aa bb cc= = cos a b c bc a 22 2 2= + - sinbc a21area=a c bcb a", "3": "3 0607/22/o/n/15 \u00a9 ucles 2015 [turn overanswer all the questions. 1 (a) work out 16 8 2 2 4' # - + . \t answer(a)\t .. [1] (b) work out 8 10 2 104 3# # #- - ^ ^ h h , giving your answer in standard form. \t answer(b)\t .. [2] 2 solve. (a) x x x 2 3 1 4 2 11 3 - - = - ^ ^ h h \t answer(a)\t x = ... [3] (b) x4 3 11 - = \t answer(b)\t x = ... [2]", "4": "4 0607/22/o/n/15 \u00a9 ucles 20153 x varies as the square of y. when y4=, x32= . find x when y5=. \t answer\tx\t = .. [3] 4 two fair dice, each numbered 1, 2, 3, 4, 5, 6, are rolled and the total score is recorded. find the probability that the total score is (a) 12, \t answer(a)\t .. [2] (b) 13, \t answer(b)\t .. [1] (c) 7. \t answer(c)\t .. [2]", "5": "5 0607/22/o/n/15 \u00a9 ucles 2015 [turn over5 5 12a=-j lkkn poo 2 3b=-j lkkn poo (a) find 3a b- . \t answer(a)\t j lk kkn po oo [2] (b) work out a. \t answer(b)\t .. [2] 6 factorise. (a) ax by ay bx 8 2 4 - + - \t answer(a)\t .. [2] (b) x x3 5 122- - \t answer(b)\t .. [2]", "6": "6 0607/22/o/n/15 \u00a9 ucles 20157 (a) find the value of 60. \t answer(a)\t .. [1] (b) write 52- as a fraction. \t answer(b)\t .. [1] 8 108\u00b0not to scale dco ab a, b, c, and d lie on a circle, centre o. ad is parallel to oc and angle adc 108\u00b0= . find (a) angle abc , \t answer(a)\t .. [1] (b) angle aoc , \t answer(b)\t .. [1] (c) angle oca , \t answer(c)\t .. [1] (d) angle dac . \t answer(d)\t .. [1]", "7": "7 0607/22/o/n/15 \u00a9 ucles 2015 [turn over9 in triangle abc , ab 48= cm, ac 8= cm and angle abc 90\u00b0= . find (a) bc, \t answer(a)\t cm [3] (b) angle bac . \t answer(b)\t .. [2] 10 the graph of y x h k2= - + ^ h has a vertex at ,2 3-^ h. find the value of h and the value of k. \t answer\t h = \t \t k = ... [2] question 11 is printed on the next page.", "8": "8 0607/22/o/n/15 \u00a9 ucles 2015permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.11 the table shows the marks of 70 students in an examination. mark (x) frequency x0 101g 8 x 10 151g 16 x 15 201g 20 x 20 301g 12 x 30 501g 14 on the grid below, draw a histogram to show this information. 012frequency density markx345 10 20 30 40 50 [3]" }, "0607_w15_qp_23.pdf": { "1": "this document consists of 8 printed pages. dc (st/sw) 103948/3 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 4 7 9 2 8 8 9 3 6 7 * cambridge international mathematics 0607/23 paper 2 (extended) october/november 2015 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.", "2": "2 0607/23/o/n/15 \u00a9 ucles 2015formula list for the equation ax bx c02+ + = xab b ac 242!=- - curved surface area, a, of cylinder of radius r, height h. r a rh2= curved surface area, a, of cone of radius r, sloping edge l. r a rl= curved surface area, a, of sphere of radius r. r a r42= v olume, v, of pyramid, base area a, height h. v ah31= v olume, v, of cylinder of radius r, height h. rv r h2= v olume, v, of cone of radius r, height h. r v r h31 2= v olume, v, of sphere of radius r. r v r34 3= sin sin sin aa bb cc= = cos a b c bc a 22 2 2= + - sinbc a21area=a c bcb a", "3": "3 0607/23/o/n/15 \u00a9 ucles 2015 [turn overanswer all the questions. 1 find the highest common factor (hcf) of 60 and 90. \t answer [1] 2 insert one pair of brackets to make the statement correct. 5 \u2013 2 + 3 \u00d7 2 = \u2013 5 [1] 3 p = 2 3j lkkn poo q = 1 6j lkkn poo find 2 p \u2013 3q. answer [2] 4 write 0.72 as a fraction in its lowest terms. answer\t [1] 5 the mean of a list of 9 numbers is 6. when a 10th number is included in the list the mean is 5.5 . find the value of this 10th number. answer\t [2]", "4": "4 0607/23/o/n/15 \u00a9 ucles 20156 not to scalecm cm3 6 find the length of the hypotenuse of the triangle. answer .. cm [2] 7 solve the simultaneous equations. u w u w9 3 19- = + = answer u\t= .. \t\t w\t= [2] 8 the scale of a map is 1 : 250 000 . find the actual distance, in kilometres, between two cities which are 42 cm apart on the map. answer\t .. km [2]", "5": "5 0607/23/o/n/15 \u00a9 ucles 2015 [turn over9 | x | < 4 and x is an integer. find the smallest possible value of x. answer\t [1] 10 the first 4 terms of a sequence are 20, 13, 6 and \u2013 1. find (a) the next term, answer(a) [1] (b) the nth term. answer(b) [2] 11 make u the subject of the formula. v u as22 2= + answer\tu = [2] 12 factorise completely. a b ax bx 2 2- + - answer\t [2] ", "6": "6 0607/23/o/n/15 \u00a9 ucles 201513 find the exact value of (a) 33-, answer(a) [1] (b) 43 16, answer(b) [1] (c) cos 30\u00b0. \t answer(c) [1] 14 simplify x641261 ^ h. answer [2] 15 on each venn diagram, shade the region indicated. a (a /h33371 b)' (c /h33371 d) /h33370 e 'u ub c de [2]", "7": "7 0607/23/o/n/15 \u00a9 ucles 2015 [turn over16 find the equation of the straight line passing through (\u2013 2, \u2013 4) and (2, 0). answer [3] 17 rationalise the denominator. 53 2+ answer [2] 18 (a) factorise y y32-. answer(a) [1] (b) simplify yy y 93 22 --. answer(b) [2] questions 19 and 20 are printed on the next page.", "8": "8 0607/23/o/n/15 \u00a9 ucles 201519 find the value of (a) loglog 84, answer(a) [2] (b) log 84. answer(b) [1] 20 ( ) , gxxxx12 11! =-+ solve the equation ( )gx 21=-. answer\tx = [1] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_w15_qp_31.pdf": { "1": "this document consists of 16 printed pages. dc (ac/sw) 100758/4 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 0 2 5 6 8 2 0 3 3 2 * cambridge international mathematics 0607/31 paper 3 (core) october/november 2015 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.", "2": "2 0607/31/o/n/15 \u00a9 ucles 2015formula list area, a, of triangle, base b, height h. a = 21bh area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = 31ah v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = 31 rr2h v olume, v, of sphere of radius r. v = 34 rr3", "3": "3 0607/31/o/n/15 \u00a9 ucles 2015 [turn overanswer all the questions. 1 (a) complete the list of factors of 18. answer(a) 1, .. , .. , .. , .. , 18 [1] (b) work out. (i) 676 answer(b) (i) [1] (ii) 6.73 answer(b) (ii) [1] (iii) .. . 2 93635 26 1- answer(b) (iii) [2] (c) write 807.536 correct to (i) 2 decimal places, answer(c) (i) [1] (ii) 4 significant figures, answer(c) (ii) [1] (iii) the nearest 10, answer(c) (iii) [1] (iv) the nearest 100. answer(c) (iv) [1]", "4": "4 0607/31/o/n/15 \u00a9 ucles 20152 abd ecfa\u00b0 b\u00b0 c\u00b0 d \u00b0136\u00b0 not to scale 48\u00b0 abd and ecf are parallel straight lines. find the values of a, b, c and d. answer a = . b = . c = . d = . [4]", "5": "5 0607/31/o/n/15 \u00a9 ucles 2015 [turn over3 (a) tejas, wali and niamh share 100 pieces of candy in the ratio 5 : 9 : 11. find how many pieces of candy wali receives. answer(a) [2] (b) hanneke buys a gold necklace for $ 4500. she later sells it for $ 5300. calculate her percentage profit. answer(b) % [3]", "6": "6 0607/31/o/n/15 \u00a9 ucles 20154 not to scale a rectangular patio is 6 metres long and 3.2 metres wide. it is made up of 8 rows of grey tiles and white tiles as shown in the diagram. (a) calculate (i) the area of the patio, answer(a) (i) .. m2 [1] (ii) the perimeter of the patio. answer(a) (ii) ... m [1] (b) all tiles have the same width. each grey tile is twice as long as a white tile. complete this statement. a grey tile has length .. metres and width .. metres. [2] (c) find the total number of white tiles and the total number of grey tiles. answer(c) number of white tiles number of grey tiles [2] (d) each white tile costs $0.95 and each grey tile costs $1.35 . find the total cost of the tiles used to make the patio. answer(d) $ [2]", "7": "7 0607/31/o/n/15 \u00a9 ucles 2015 [turn over5 romina opens 10 packets of biscuits and counts the number of biscuits in each packet. the number of biscuits in each packet is shown below. 23 24 23 22 25 23 24 25 26 21 (a) find (i) the range, answer(a) (i) [1] (ii) the mode, answer(a) (ii) [1] (iii) the median, answer(a) (iii) [1] (iv) the mean. answer(a) (iv) [1] (b) complete the bar chart. the first bar has been drawn for you. 21012frequency34 22 23 number of biscuits24 25 26 [2]", "8": "8 0607/31/o/n/15 \u00a9 ucles 20156 each person at a school science fair receives a lunchbox. there are 50 students, 7 teachers, 9 judges and 84 parents at the science fair. (a) find the total number of people at the science fair. answer(a) [1] (b) each lunchbox contains two sandwiches. find the total number of sandwiches in all the lunchboxes. answer(b) ... [1] (c) paul\u2019s snacks make the lunchboxes. the lunchbox contains two sandwiches, one piece of fruit and one bottle of water. the cost of making each lunchbox is $4.25 . each sandwich costs $1.45 and the bottle of water costs $0.70 . find the cost of the piece of fruit. answer(c) $ [2] (d) the school pays paul\u2019s snacks $5 for each lunchbox. find how much profit paul\u2019s snacks make on each lunchbox. answer(d) $ [1]", "9": "9 0607/31/o/n/15 \u00a9 ucles 2015 [turn over7 a taxi company charges a fixed amount of $ f for each journey. it also charges $2 for each kilometre of the journey. a taxi journey is m km. (a) find an expression, in terms of f and m, for the total cost of this journey. answer(a) $ [2] (b) when f = 3 find the total cost of a journey of 6 km. answer(b) $ [2] (c) find the distance travelled when f = 3 and the total cost of the journey is $21. answer(c) . km [2]", "10": "10 0607/31/o/n/15 \u00a9 ucles 20158 u , , , , , , , , ,1 2 3 4 5 6 7 8 9 1 0 =\" , , , , , , a 1 3 5 6 7 8=\" , , , , , b 1 3 4 7 9 =\" , au b (a) write the elements of u in the correct places in the venn diagram. [2] (b) write down the elements in the set (i) a b+, answer(b) (i) [1] (ii) a b, l ^ h, answer(b) (ii) [1] (iii) a b+l. answer(b) (iii) [1]", "11": "11 0607/31/o/n/15 \u00a9 ucles 2015 [turn over (c) a number is chosen at random from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. find the probability that it is (i) an odd number, answer(c) (i) [1] (ii) a number less than 4, answer(c) (ii) [1] (iii) a triangle number. answer(c) (iii) [1] 9 these are the first five terms of a sequence. \u22122 1 6 13 22 (a) write down the next two terms in this sequence. answer(a) . , . [2] (b) find an expression for the nth term. answer(b) [3]", "12": "12 0607/31/o/n/15 \u00a9 ucles 201510 kensuke travels to school either by train or by car. the probability that he travels by train is 54. if kensuke travels by train then the probability that he is late for school is 201. if kensuke travels by car then the probability that he is late for school is 151. (a) complete the tree diagram. late not late.. .. latetrain 4 5 car not late.. [3] (b) find the probability that kensuke travels by train and is late for school. answer(b) [2] (c) find the probability that kensuke is not late for school. answer(c) [3]", "13": "13 0607/31/o/n/15 \u00a9 ucles 2015 [turn over11 \u20136\u20135\u20134\u20133\u20132\u20131012345678 \u20131 123456xpy \u20132\u20133\u20134\u20135\u20136 (a) reflect shape p in the line x1=. label the image a. [2] (b) translate shape p by the vector 32 --c m . label the image b. [2] (c) rotate shape p by 180\u00b0 about the point (0, 0). label the image c. [2]", "14": "14 0607/31/o/n/15 \u00a9 ucles 201512 \u20133\u20132\u20131012345 \u20131 12345678xy \u20132\u20133\u20134 the axes are drawn on a 1 cm2 grid. a is the point (2, 3) and b is the point (8, \u22123). (a) plot the points a and b on the grid. [2] (b) find the co-ordinates of the midpoint of ab. answer(b) ( , ) [2] (c) calculate the length of ab. give your answer correct to 2 decimal places. answer(c) .. cm [3] (d) find the gradient of ab. answer(d) [2] (e) find the equation of the straight line that passes through point a and point b. answer(e) [2]", "15": "15 0607/31/o/n/15 \u00a9 ucles 2015 [turn over13 not to scale 6 cmab oc a circle, centre o, is inscribed in a regular pentagon. each side of the pentagon has length 6 cm. (a) find angle aob . answer(a) angle aob = [1] (b) find the size of an interior angle of the regular pentagon. answer(b) [2] (c) use trigonometry to find the radius, oc, of the circle. answer(c) .. cm [2] (d) find the area of the pentagon. answer(d) cm2 [3] question 14 is printed on the next page.", "16": "16 0607/31/o/n/15 \u00a9 ucles 2015permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.14 0 \u2013525 \u2013306xy ( ) . . x x x x 0 5 9 5 10 f3 2= - - + (a) on the diagram, sketch the graph of ( ) y x f= for x5 6g g- . [2] (b) find the co-ordinates of (i) the points where the curve crosses the x-axis, answer(b) (i) ( , ), ( , ), ( , ) [2] (ii) the point where the curve crosses the y-axis, answer(b) (ii) ( , ) [1] (iii) the local minimum point. answer(b) (iii) ( , ) [2]" }, "0607_w15_qp_32.pdf": { "1": "this document consists of 16 printed pages. dc (st/sw) 117644 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 1 8 1 1 6 7 1 8 1 2 * cambridge international mathematics 0607/32 paper 3 (core) october/november 2015 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.", "2": "2 0607/32/o/n/15 \u00a9 ucles 2015formula list area, a, of triangle, base b, height h. a = 21bh area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = 31ah v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = 31 rr2h v olume, v, of sphere of radius r. v = 34 rr3", "3": "3 0607/32/o/n/15 \u00a9 ucles 2015 [turn overanswer all the questions. 1 (a) complete the list of factors of 18. answer(a) 1, .. , .. , .. , .. , 18 [1] (b) work out. (i) 676 answer(b) (i) [1] (ii) 6.73 answer(b) (ii) [1] (iii) .. . 2 93635 26 1- answer(b) (iii) [2] (c) write 807.536 correct to (i) 2 decimal places, answer(c) (i) [1] (ii) 4 significant figures, answer(c) (ii) [1] (iii) the nearest 10, answer(c) (iii) [1] (iv) the nearest 100. answer(c) (iv) [1]", "4": "4 0607/32/o/n/15 \u00a9 ucles 20152 abd ecfa\u00b0 b\u00b0 c\u00b0 d \u00b0136\u00b0 not to scale 48\u00b0 abd and ecf are parallel straight lines. find the values of a, b, c and d. answer a = . b = . c = . d = . [4]", "5": "5 0607/32/o/n/15 \u00a9 ucles 2015 [turn over3 (a) tejas, wali and niamh share 100 pieces of candy in the ratio 5 : 9 : 11. find how many pieces of candy wali receives. answer(a) [2] (b) hanneke buys a gold necklace for $ 4500. she later sells it for $ 5300. calculate her percentage profit. answer(b) % [3]", "6": "6 0607/32/o/n/15 \u00a9 ucles 20154 not to scale a rectangular patio is 6 metres long and 3.2 metres wide. it is made up of 8 rows of grey tiles and white tiles as shown in the diagram. (a) calculate (i) the area of the patio, answer(a) (i) .. m2 [1] (ii) the perimeter of the patio. answer(a) (ii) ... m [1] (b) all tiles have the same width. each grey tile is twice as long as a white tile. complete this statement. a grey tile has length .. metres and width .. metres. [2] (c) find the total number of white tiles and the total number of grey tiles. answer(c) number of white tiles number of grey tiles [2] (d) each white tile costs $0.95 and each grey tile costs $1.35 . find the total cost of the tiles used to make the patio. answer(d) $ [2]", "7": "7 0607/32/o/n/15 \u00a9 ucles 2015 [turn over5 romina opens 10 packets of biscuits and counts the number of biscuits in each packet. the number of biscuits in each packet is shown below. 23 24 23 22 25 23 24 25 26 21 (a) find (i) the range, answer(a) (i) [1] (ii) the mode, answer(a) (ii) [1] (iii) the median, answer(a) (iii) [1] (iv) the mean. answer(a) (iv) [1] (b) complete the bar chart. the first bar has been drawn for you. 21012frequency34 22 23 number of biscuits24 25 26 [2]", "8": "8 0607/32/o/n/15 \u00a9 ucles 20156 each person at a school science fair receives a lunchbox. there are 50 students, 7 teachers, 9 judges and 84 parents at the science fair. (a) find the total number of people at the science fair. answer(a) [1] (b) each lunchbox contains two sandwiches. find the total number of sandwiches in all the lunchboxes. answer(b) ... [1] (c) paul\u2019s snacks make the lunchboxes. the lunchbox contains two sandwiches, one piece of fruit and one bottle of water. the cost of making each lunchbox is $4.25 . each sandwich costs $1.45 and the bottle of water costs $0.70 . find the cost of the piece of fruit. answer(c) $ [2] (d) the school pays paul\u2019s snacks $5 for each lunchbox. find how much profit paul\u2019s snacks make on each lunchbox. answer(d) $ [1]", "9": "9 0607/32/o/n/15 \u00a9 ucles 2015 [turn over7 a taxi company charges a fixed amount of $ f for each journey. it also charges $2 for each kilometre of the journey. a taxi journey is m km. (a) find an expression, in terms of f and m, for the total cost of this journey. answer(a) $ [2] (b) when f = 3 find the total cost of a journey of 6 km. answer(b) $ [2] (c) find the distance travelled when f = 3 and the total cost of the journey is $21. answer(c) . km [2]", "10": "10 0607/32/o/n/15 \u00a9 ucles 20158 u , , , , , , , , ,1 2 3 4 5 6 7 8 9 1 0 =\" , , , , , , a 1 3 5 6 7 8=\" , , , , , b 1 3 4 7 9 =\" , au b (a) write the elements of u in the correct places in the venn diagram. [2] (b) write down the elements in the set (i) a b+, answer(b) (i) [1] (ii) a b, l ^ h, answer(b) (ii) [1] (iii) a b+l. answer(b) (iii) [1]", "11": "11 0607/32/o/n/15 \u00a9 ucles 2015 [turn over (c) a number is chosen at random from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. find the probability that it is (i) an odd number, answer(c) (i) [1] (ii) a number less than 4, answer(c) (ii) [1] (iii) a triangle number. answer(c) (iii) [1] 9 these are the first five terms of a sequence. \u22122 1 6 13 22 (a) write down the next two terms in this sequence. answer(a) . , . [2] (b) find an expression for the nth term. answer(b) [3]", "12": "12 0607/32/o/n/15 \u00a9 ucles 201510 kensuke travels to school either by train or by car. the probability that he travels by train is 54. if kensuke travels by train then the probability that he is late for school is 201. if kensuke travels by car then the probability that he is late for school is 151. (a) complete the tree diagram. late not late.. .. latetrain 4 5 car not late.. [3] (b) find the probability that kensuke travels by train and is late for school. answer(b) [2] (c) find the probability that kensuke is not late for school. answer(c) [3]", "13": "13 0607/32/o/n/15 \u00a9 ucles 2015 [turn over11 \u20136\u20135\u20134\u20133\u20132\u20131012345678 \u20131 123456xpy \u20132\u20133\u20134\u20135\u20136 (a) reflect shape p in the line x1=. label the image a. [2] (b) translate shape p by the vector 32 --c m . label the image b. [2] (c) rotate shape p by 180\u00b0 about the point (0, 0). label the image c. [2]", "14": "14 0607/32/o/n/15 \u00a9 ucles 201512 \u20133\u20132\u20131012345 \u20131 12345678xy \u20132\u20133\u20134 the axes are drawn on a 1 cm2 grid. a is the point (2, 3) and b is the point (8, \u22123). (a) plot the points a and b on the grid. [2] (b) find the co-ordinates of the midpoint of ab. answer(b) ( , ) [2] (c) calculate the length of ab. give your answer correct to 2 decimal places. answer(c) .. cm [3] (d) find the gradient of ab. answer(d) [2] (e) find the equation of the straight line that passes through point a and point b. answer(e) [2]", "15": "15 0607/32/o/n/15 \u00a9 ucles 2015 [turn over13 not to scale 6 cmab oc a circle, centre o, is inscribed in a regular pentagon. each side of the pentagon has length 6 cm. (a) find angle aob . answer(a) angle aob = [1] (b) find the size of an interior angle of the regular pentagon. answer(b) [2] (c) use trigonometry to find the radius, oc, of the circle. answer(c) .. cm [2] (d) find the area of the pentagon. answer(d) cm2 [3] question 14 is printed on the next page.", "16": "16 0607/32/o/n/15 \u00a9 ucles 2015permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.14 0 \u2013525 \u2013306xy ( ) . . x x x x 0 5 9 5 10 f3 2= - - + (a) on the diagram, sketch the graph of ( ) y x f= for x5 6g g- . [2] (b) find the co-ordinates of (i) the points where the curve crosses the x-axis, answer(b) (i) ( , ), ( , ), ( , ) [2] (ii) the point where the curve crosses the y-axis, answer(b) (ii) ( , ) [1] (iii) the local minimum point. answer(b) (iii) ( , ) [2]" }, "0607_w15_qp_33.pdf": { "1": "this document consists of 16 printed pages. dc (cw/sw) 117643 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 9 6 0 6 0 9 9 1 7 6 * cambridge international mathematics 0607/33 paper 3 (core) october/november 2015 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.", "2": "2 0607/33/o/n/15 \u00a9 ucles 2015formula list area, a, of triangle, base b, height h. a = 21bh area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = 31ah v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = 31 rr2h v olume, v, of sphere of radius r. v = 34 rr3", "3": "3 0607/33/o/n/15 \u00a9 ucles 2015 [turn overanswer all the questions. 1 (a) complete the list of factors of 18. answer(a) 1, .. , .. , .. , .. , 18 [1] (b) work out. (i) 676 answer(b) (i) [1] (ii) 6.73 answer(b) (ii) [1] (iii) .. . 2 93635 26 1- answer(b) (iii) [2] (c) write 807.536 correct to (i) 2 decimal places, answer(c) (i) [1] (ii) 4 significant figures, answer(c) (ii) [1] (iii) the nearest 10, answer(c) (iii) [1] (iv) the nearest 100. answer(c) (iv) [1]", "4": "4 0607/33/o/n/15 \u00a9 ucles 20152 abd ecfa\u00b0 b\u00b0 c\u00b0 d \u00b0136\u00b0 not to scale 48\u00b0 abd and ecf are parallel straight lines. find the values of a, b, c and d. answer a = . b = . c = . d = . [4]", "5": "5 0607/33/o/n/15 \u00a9 ucles 2015 [turn over3 (a) tejas, wali and niamh share 100 pieces of candy in the ratio 5 : 9 : 11. find how many pieces of candy wali receives. answer(a) [2] (b) hanneke buys a gold necklace for $ 4500. she later sells it for $ 5300. calculate her percentage profit. answer(b) % [3]", "6": "6 0607/33/o/n/15 \u00a9 ucles 20154 not to scale a rectangular patio is 6 metres long and 3.2 metres wide. it is made up of 8 rows of grey tiles and white tiles as shown in the diagram. (a) calculate (i) the area of the patio, answer(a) (i) .. m2 [1] (ii) the perimeter of the patio. answer(a) (ii) ... m [1] (b) all tiles have the same width. each grey tile is twice as long as a white tile. complete this statement. a grey tile has length .. metres and width .. metres. [2] (c) find the total number of white tiles and the total number of grey tiles. answer(c) number of white tiles number of grey tiles [2] (d) each white tile costs $0.95 and each grey tile costs $1.35 . find the total cost of the tiles used to make the patio. answer(d) $ [2]", "7": "7 0607/33/o/n/15 \u00a9 ucles 2015 [turn over5 romina opens 10 packets of biscuits and counts the number of biscuits in each packet. the number of biscuits in each packet is shown below. 23 24 23 22 25 23 24 25 26 21 (a) find (i) the range, answer(a) (i) [1] (ii) the mode, answer(a) (ii) [1] (iii) the median, answer(a) (iii) [1] (iv) the mean. answer(a) (iv) [1] (b) complete the bar chart. the first bar has been drawn for you. 21012frequency34 22 23 number of biscuits24 25 26 [2]", "8": "8 0607/33/o/n/15 \u00a9 ucles 20156 each person at a school science fair receives a lunchbox. there are 50 students, 7 teachers, 9 judges and 84 parents at the science fair. (a) find the total number of people at the science fair. answer(a) [1] (b) each lunchbox contains two sandwiches. find the total number of sandwiches in all the lunchboxes. answer(b) ... [1] (c) paul\u2019s snacks make the lunchboxes. the lunchbox contains two sandwiches, one piece of fruit and one bottle of water. the cost of making each lunchbox is $4.25 . each sandwich costs $1.45 and the bottle of water costs $0.70 . find the cost of the piece of fruit. answer(c) $ [2] (d) the school pays paul\u2019s snacks $5 for each lunchbox. find how much profit paul\u2019s snacks make on each lunchbox. answer(d) $ [1]", "9": "9 0607/33/o/n/15 \u00a9 ucles 2015 [turn over7 a taxi company charges a fixed amount of $ f for each journey. it also charges $2 for each kilometre of the journey. a taxi journey is m km. (a) find an expression, in terms of f and m, for the total cost of this journey. answer(a) $ [2] (b) when f = 3 find the total cost of a journey of 6 km. answer(b) $ [2] (c) find the distance travelled when f = 3 and the total cost of the journey is $21. answer(c) . km [2]", "10": "10 0607/33/o/n/15 \u00a9 ucles 20158 u , , , , , , , , ,1 2 3 4 5 6 7 8 9 1 0 =\" , , , , , , a 1 3 5 6 7 8=\" , , , , , b 1 3 4 7 9 =\" , au b (a) write the elements of u in the correct places in the venn diagram. [2] (b) write down the elements in the set (i) a b+, answer(b) (i) [1] (ii) a b, l ^ h, answer(b) (ii) [1] (iii) a b+l. answer(b) (iii) [1]", "11": "11 0607/33/o/n/15 \u00a9 ucles 2015 [turn over (c) a number is chosen at random from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. find the probability that it is (i) an odd number, answer(c) (i) [1] (ii) a number less than 4, answer(c) (ii) [1] (iii) a triangle number. answer(c) (iii) [1] 9 these are the first five terms of a sequence. \u22122 1 6 13 22 (a) write down the next two terms in this sequence. answer(a) . , . [2] (b) find an expression for the nth term. answer(b) [3]", "12": "12 0607/33/o/n/15 \u00a9 ucles 201510 kensuke travels to school either by train or by car. the probability that he travels by train is 54. if kensuke travels by train then the probability that he is late for school is 201. if kensuke travels by car then the probability that he is late for school is 151. (a) complete the tree diagram. late not late.. .. latetrain 4 5 car not late.. [3] (b) find the probability that kensuke travels by train and is late for school. answer(b) [2] (c) find the probability that kensuke is not late for school. answer(c) [3]", "13": "13 0607/33/o/n/15 \u00a9 ucles 2015 [turn over11 \u20136\u20135\u20134\u20133\u20132\u20131012345678 \u20131 123456xpy \u20132\u20133\u20134\u20135\u20136 (a) reflect shape p in the line x1=. label the image a. [2] (b) translate shape p by the vector 32 --c m . label the image b. [2] (c) rotate shape p by 180\u00b0 about the point (0, 0). label the image c. [2]", "14": "14 0607/33/o/n/15 \u00a9 ucles 201512 \u20133\u20132\u20131012345 \u20131 12345678xy \u20132\u20133\u20134 the axes are drawn on a 1 cm2 grid. a is the point (2, 3) and b is the point (8, \u22123). (a) plot the points a and b on the grid. [2] (b) find the co-ordinates of the midpoint of ab. answer(b) ( , ) [2] (c) calculate the length of ab. give your answer correct to 2 decimal places. answer(c) .. cm [3] (d) find the gradient of ab. answer(d) [2] (e) find the equation of the straight line that passes through point a and point b. answer(e) [2]", "15": "15 0607/33/o/n/15 \u00a9 ucles 2015 [turn over13 not to scale 6 cmab oc a circle, centre o, is inscribed in a regular pentagon. each side of the pentagon has length 6 cm. (a) find angle aob . answer(a) angle aob = [1] (b) find the size of an interior angle of the regular pentagon. answer(b) [2] (c) use trigonometry to find the radius, oc, of the circle. answer(c) .. cm [2] (d) find the area of the pentagon. answer(d) cm2 [3] question 14 is printed on the next page.", "16": "16 0607/33/o/n/15 \u00a9 ucles 2015permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.14 0 \u2013525 \u2013306xy ( ) . . x x x x 0 5 9 5 10 f3 2= - - + (a) on the diagram, sketch the graph of ( ) y x f= for x5 6g g- . [2] (b) find the co-ordinates of (i) the points where the curve crosses the x-axis, answer(b) (i) ( , ), ( , ), ( , ) [2] (ii) the point where the curve crosses the y-axis, answer(b) (ii) ( , ) [1] (iii) the local minimum point. answer(b) (iii) ( , ) [2]" }, "0607_w15_qp_41.pdf": { "1": "this document consists of 20 printed pages. dc (lk/cgw) 103946/2 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 1 5 4 5 7 5 4 0 2 1 * cambr idge international mathematics 0607/41 paper 4 (extended) october/ november 2015 2 hours 15 minutes candidates answer on the question paper. additional materials: geometric instruments graphics calculator read these instructi ons first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.", "2": "2 0607/41/o/n/15 \u00a9 ucles 2015formula list for the equation ax2 + bx + c = 0 x = ab b ac 242!- - curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 v olume, v, of pyramid, base area a, height h. v= ah31 v olume, v, of cylinder of radius r, height h. v = \u03c0r2h v olume, v, of cone of radius r, height h. v = 31 \u03c0r2h v olume, v, of sphere of radius r. v = 34 \u03c0r3 sin sin sin aa bb cc= =a c bcb a a2 = b2 + c2 \u2013 2bc cos a area = sinbc a21", "3": "3 0607/41/o/n/15 \u00a9 ucles 2015 [turn overanswer all the questions. 1 sunil has $80 and asha has $75. (a) write the ratio 80 : 75 in its simplest form. answer(a) . : ... [1] (b) (i) sunil spends $24. work out $24 as a percentage of $80. answer(b) (i) .. % [1] (ii) sunil invests $50 at a rate of 2% per year compound interest. calculate the interest sunil has after 20 years. answer(b) (ii) $ . [4] (c) during each month, asha spends 51 of the money that she had at the beginning of the month. (i) work out how much of the $75 asha has at the end of the 2nd month. \t answer(c) (i) $ [2] (ii) calculate the number of whole months it takes for asha to have less than $5. answer(c) (ii) . [3]", "4": "4 0607/41/o/n/15 \u00a9 ucles 20152 (a) p2 3=j lkkn poo q14 8=j lkkn poo (i) find 2 p + 3q . answer(a) (i) j lk kkn po oo [2] (ii) find q p- . \t answer(a) (ii) \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd [3] (b) the graph of y = f(x) is mapped onto the graph of y = f(x + 2) by a translation with vector u vj lkkn poo. find the value of u and the value of v. answer(b) u = .. v\t= .. [2]", "5": "5 0607/41/o/n/15 \u00a9 ucles 2015 [turn over (c) 7 d8y x6 5 4 3 2 1 \u20131 \u20132 \u20133 \u20134 \u20135 \u201360123456 \u20136\u20135\u20134\u20133\u20132\u20131te (i) draw the image of triangle t under a rotation of 90\u00b0 clockwise about the point ( , ) 1 1- - . [3] (ii) describe fully the single transformation that maps triangle t onto triangle d. ... .. [2] (iii) describe fully the single transformation that maps triangle t onto triangle e. ... .. [3]", "6": "6 0607/41/o/n/15 \u00a9 ucles 20153 y x5 \u20135\u20135 50 ( )fxx12= - , x0!\t (a) on the diagram, sketch the graph of ( )f y x=\t, for values between x 5=- and x5=. [2] (b) solve the inequality ( )fx 01 \ufffd answer(b) \t . [2]", "7": "7 0607/41/o/n/15 \u00a9 ucles 2015 [turn over (c) find ( ) fx1- . answer(c) . [3] (d) on the diagram, sketch the graph of ( ) f y x1=-\t, for values between x 5=- and x5=\t. [2] \t (e)\t describe fully the single transformation that maps the graph of ( )f y x= onto the graph of ( ) f y x1=-\t. ... .. [2]", "8": "8 0607/41/o/n/15 \u00a9 ucles 20154 (a) 9 cm3 cm 4.5 cm xb a c dnot to scale4 cm \t \t ab and cd are parallel. \t \t ad and cb intersect at x. cd = 9 cm, ab = 4 cm,\tax = 4.5 cm and bx = 3 cm. calculate the length of cx. answer(a) \t ... cm [2] (b) s py qr 4 cm 7 cm8 cm6 cm not to scale \t \t p , q, r and s lie on a circle. pr and qs intersect at y. qr = 6 cm, ps = 8 cm,\tpy = 7 cm and ys = 4 cm. calculate the length of ry. answer(b) ... cm [2]", "9": "9 0607/41/o/n/15 \u00a9 ucles 2015 [turn over (c) 12 cmnot to scale e f w cm the two shapes are mathematically similar. the area of e is 90 cm2 and the area of f is 45 cm2. find the value of w. answer(c) \tw = . [3]", "10": "10 0607/41/o/n/15 \u00a9 ucles 20155 b c da12 cm 11 cm 10 cm35\u00b0 not to scale \t calculate (a) bc, answer(a) .. cm [2] (b) angle cad , answer(b) . [3] (c) the area of the quadrilateral abcd . \t answer(c) . cm2 [3]", "11": "11 0607/41/o/n/15 \u00a9 ucles 2015 [turn over6 120 students estimate the mass, m kg, of a bag of oranges. the frequency table shows the results. mass (m kg) .m 0 5 11g .m 1 2 11g . .m 1 2 1 41g . .m 1 4 1 61g .m 1 6 21g frequency 4 36 40 32 8 (a) calculate an estimate of the mean. \t answer(a) ... kg [2] (b) complete the histogram to show the information in the table. 20 0 0.2 0.4 0.6 0.8 1.0 mass (kilograms)1.2 1.4 1.6 1.8 2.060 40 m80120 100frequency density 140160200 180 [3]", "12": "12 0607/41/o/n/15 \u00a9 ucles 20157 (a) a solid metal cuboid measures 20 cm by 8 cm by 2 cm. 1 cm3 of the metal has a mass of 7.85 g. (i) calculate the mass of the cuboid. \t answer(a) (i) . g [2] (ii) the surface of the cuboid is painted at a cost of 8 cents per cm2. calculate the cost of painting the cuboid. give your answer in dollars. answer(a) (ii) $ . [3] (b) another cuboid measures 16 cm by 6 cm by 4 cm. it is cut into cubes, each of side 2 cm. calculate the number of cubes. answer(b) . [2] \t (c) another solid metal cuboid measures 20 cm by 12 cm by 4 cm. it is melted down and made into spheres of radius 1.5 cm. calculate (i) the largest number of spheres of radius 1.5 cm that can be made, answer(c) (i) . [3]", "13": "13 0607/41/o/n/15 \u00a9 ucles 2015 [turn over (ii) the volume of metal remaining after the spheres have been made, answer(c) (ii) . cm3 [2] (iii) the radius of the sphere that can be made using all the remaining metal. answer(c) (iii) .. cm [2] (d) a plastic cone has radius r cm and perpendicular height 3 r\tcm. 1 cm3 of the plastic has a mass of 0.9 g. a wooden hemisphere has a radius of 2 r cm. 1 cm3 of the wood has a mass of 0.45 g. find the mass of the cone as a fraction of the mass of the hemisphere. give your answer in its lowest terms. answer(d) \t [4]", "14": "14 0607/41/o/n/15 \u00a9 ucles 20158 02 \u201314y x ( )fx x 32= - ( )gx xx= (a) on the diagram, sketch the graphs of ( )f y x=\tand ( )g y x=\tfor values between x0=\tand x2=. [4] (b) solve the equation x x3x 2- = for x0 2g g . answer(b) \tx\t= [1]", "15": "15 0607/41/o/n/15 \u00a9 ucles 2015 [turn over (c) solve the equation x32- = 0 for x0 2g g . answer(c) \tx\t= . [1] (d) (i) find the co-ordinates of the local minimum point on the graph of y = g(x). answer(d) (i) ( , ) [2] (ii) find the range of g( x) for the domain x 0 21g . answer(d) (ii) . [2] (e) (i) find the values of the following. g(0.1) = .. g(0.01) = .. g(0.001) = .. [3] (ii) complete the statement. starting from x = 0.1, as x gets closer and closer to 0, g(x) gets closer and closer to the value ... [1]", "16": "16 0607/41/o/n/15 \u00a9 ucles 20159 0 a11 1 b23 the diagram shows two unbiased dice, a\tand b. the numbers on die a are 0, 1, 1, 1, 2, 3. the numbers on die b are 1, 2, 2, 3, 3, 3. when a die is rolled, the number shown on the top face is recorded. (a) both dice are rolled. find the probability that (i) both dice show 3, answer(a) (i) . [2] (ii) the numbers showing on the two dice add up to 2. answer(a) (ii) . [3]", "17": "17 0607/41/o/n/15 \u00a9 ucles 2015 [turn over (b) die b is rolled until it shows 2. find the probability that this occurs when the die is rolled for the 4th time. answer(b) . [2] (c) die a is rolled until it shows 3. the probability that this occurs when the die is rolled for the nth time is 466563125 . find the value of n. answer(c) . [2]", "18": "18 0607/41/o/n/15 \u00a9 ucles 201510 f(x) = 2x + 3 g( x) = x \u2013 1 h( x) = log (x + 1) (a) find f(h(9)). \t answer(a) . [2] (b) find g(f(x)) in its simplest form. answer(b) . [2] (c) find ( ) ( ) f gx x1 1+ in terms of x. give your answer as a single fraction. answer(c) . [3]", "19": "19 0607/41/o/n/15 \u00a9 ucles 2015 [turn over (d) solve the equation. ( )hx 1=- answer(d) \tx = [2] (e) solve the equation. ( ( ))gx 52= give exact answers. answer(e) x or x = [3] question 11 is printed on the next page.", "20": "20 0607/41/o/n/15 \u00a9 ucles 201511 (a) cakes cost x cents each and drinks cost y cents each. 2 cakes and 1 drink cost $1.57 . 1 cake and 3 drinks cost $2.96 . find the total cost of 3 cakes and 2 drinks. give your answer in dollars. answer(a) \t$ . [6] (b) a child\u2019s train ticket costs $ x. an adult\u2019s train ticket costs $( x + 5). claudia buys 11 tickets. she spends $24 on children\u2019s tickets and $24 on adults\u2019 tickets. write down an equation in x and solve it to find the cost of a child\u2019s ticket. answer(b) $ . [4] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_w15_qp_42.pdf": { "1": "this document consists of 20 printed pages. dc (leg/sw) 100760/1 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 7 5 1 1 2 3 6 7 2 1 * cambridge international mathematics 0607/42 paper 4 (extended) october/november 2015 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answer in degrees should be given to one decimal place. for \u03c0, use your calculator value. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.", "2": "2 0607/42/o/n/15 \u00a9 ucles 2015formula list for the equation ax bx c02+ + = xab b ac 242!=- - curved surface area, a, of cylinder of radius r, height h. r a rh2= curved surface area, a, of cone of radius r, sloping edge l. r a rl= curved surface area, a, of sphere of radius r. r a r42= v olume, v, of pyramid, base area a, height h. v ah31= v olume, v, of cylinder of radius r, height h. rv r h2= v olume, v, of cone of radius r, height h. r v r h31 2= v olume, v, of sphere of radius r. r v r34 3= sin sin sin aa bb cc= = cos a b c bc a 22 2 2= + - sinbc a21area=a c bcb a", "3": "3 0607/42/o/n/15 \u00a9 ucles 2015 [turn overanswer all the questions. 1 (a) by writing each number correct to 1 significant figure, find an estimate for . .. ..5 13987 9 12163 1 913 2 ++ ^ h you must show your working. answer(a) . [2] (b) explain why your answer to part (a) is greater than the actual answer. answer (b) . .. [2] (c) work out. . .. ..5 13987 9 12163 1 913 2 ++ ^ h answer(c) . [1]", "4": "4 0607/42/o/n/15 \u00a9 ucles 20152 (a) solve the equations. (i) log log log logx 4 3 3 4 5 2 - = - answer (a)(i) x = . [3] (ii) sinx 4 3 1 + = for x 0 360 c cg g answer (a)(ii) .. [3] (b) make x the subject of the formula. axx1=- answer (b) x = . [3]", "5": "5 0607/42/o/n/15 \u00a9 ucles 2015 [turn over3 the table gives the marks of 10 students in a geography exam and a history exam. geography mark ( x) 12 23 36 41 57 62 78 81 89 93 history mark ( y) 32 43 41 51 52 60 68 65 76 80 (a) find (i) the mean geography mark, answer (a)(i) .. [1] (ii) the mean history mark. answer (a)(ii) .. [1] (b) (i) find the equation of the regression line for y in terms of x. answer (b)(i) y = . [2] (ii) estimate the history mark when the geography mark is 51. answer (b)(ii) .. [1]", "6": "6 0607/42/o/n/15 \u00a9 ucles 20154 the transformation p is a reflection in the x-axis. the transformation q is a rotation of 90\u00b0 clockwise about the origin. (a) write down the transformation that is (i) the inverse of p, answer(a) (i) .. .. [1] (ii) the inverse of q. answer(a) (ii) . .. [2] (b) describe fully the single transformation equivalent to p followed by q. answer (b) .. .. [2]", "7": "7 0607/42/o/n/15 \u00a9 ucles 2015 [turn over5 find the next term and the nth term in each of the following sequences. (a) 27, 20, 13, 6, \u2013 1, ... answer(a) next term = . nth term = . [3] (b) 1024, 512, 256, 128, 64, ... answer(b) next term = . nth term = . [3]", "8": "8 0607/42/o/n/15 \u00a9 ucles 20156 the marks, x, of 800 students in a mathematics exam are given in the table. mark ( x) frequency 0 < x \ue0f8 20 62 20 < x \ue0f8 30 84 30 < x \ue0f8 40 140 40 < x \ue0f8 50 160 50 < x \ue0f8 60 142 60 < x \ue0f8 80 112 80 < x \ue0f8 100 100 (a) calculate an estimate of the mean mark. answer(a) .. [2] (b) complete the cumulative frequency table. mark ( x) cumulative frequency 0 < x \ue0f8 20 62 0 < x \ue0f8 30 0 < x \ue0f8 40 0 < x \ue0f8 50 0 < x \ue0f8 60 0 < x \ue0f8 80 0 < x \ue0f8 100 800 [1]", "9": "9 0607/42/o/n/15 \u00a9 ucles 2015 [turn over (c) on the grid below, draw a cumulative frequency curve. 010203040cumulative frequency markx 5060708090100100200300400500600700800 [3] (d) use your graph in part (c) to find estimates for (i) the median mark, answer(d) (i) .. [1] (ii) the interquartile range, answer(d) (ii) .. [2] (iii) the minimum mark for a candidate to obtain a grade a, given that 15% of students gain a grade a. answer(d) (iii) .. [3]", "10": "10 0607/42/o/n/15 \u00a9 ucles 20157 \u2013415y x \u2013156 0 fxxx 2 36 11=-+^^^hhh (a) (i) on the diagram, sketch the graph of f y x=^h, for values of x between x 4=- and x6=. [2] (ii) write down the equations of the asymptotes. answer(a) (ii) . , . [2] (iii) write down the co-ordinates of the points where the graph crosses the axes. answer(a) (iii) ( ... , ... ), ( ... , ... ) [2] (b) solve the inequality. xxx 2 36 111-+ ^^ hh answer(b) . [4]", "11": "11 0607/42/o/n/15 \u00a9 ucles 2015 [turn over8 freddo lives in manchester. he drives to cambridge for a meeting. the distance from manchester to cambridge is 300 km. (a) freddo leaves manchester at 07 05 and arrives in cambridge at 10 50. calculate his average speed. answer(a) . km/h [3] (b) after the meeting freddo drives back to manchester. his average speed for this journey is 5% more than his average speed driving to cambridge. he leaves cambridge at 17 45. find the time freddo arrives in manchester. answer(b) .. [3] (c) freddo\u2019s car uses fuel at the rate of 8.1 km per litre. fuel costs \u00a31.45 per litre. find the total cost of fuel for freddo\u2019s journey from manchester to cambridge and back to manchester. answer(c) \u00a3 .. [2]", "12": "12 0607/42/o/n/15 \u00a9 ucles 20159 (a) a coat costs $100. the price is increased by 10% and then decreased by 10%. find the new price of the coat. answer(a) $ .. [2] (b) a chair costs $1000. the price is increased by 20% and then decreased by 20%. find the new price of the chair. answer(b) $ .. [2] (c) a car costs $10 000. the price is increased by x% and then decreased by x%. find an expression, in terms of x, for the new price of the car. give your answer in its simplest form. answer(c) $ .. [3]", "13": "13 0607/42/o/n/15 \u00a9 ucles 2015 [turn over10 a bag contains 3 red balls and 5 blue balls. in an experiment, three balls are chosen at random without replacement. (a) find the probability that the three balls chosen are (i) all red, answer(a) (i) .. [2] (ii) two red and one blue, answer(a) (ii) .. [3] (iii) at least one of each colour. answer(a) (iii) .. [3] (b) this experiment is to be carried out 1680 times. find the expected frequency of 3 red balls being chosen. answer(b) .. [2]", "14": "14 0607/42/o/n/15 \u00a9 ucles 201511 a is the point (2, 6) and c is the point (5, 4). the equation of the line ab is y x4 14+ = . the equation of the line bc is y x 1= - . (a) b is the point where the lines ab and bc intersect. find the co-ordinates of the point b. answer(a) ( . , .. ) [3] (b) m is the midpoint of ac. find the co-ordinates of m. answer(b) ( . , .. ) [2]", "15": "15 0607/42/o/n/15 \u00a9 ucles 2015 [turn over (c) find the equation of the line bm. answer(c) . [3] (d) the point d lies on the line bm. the co-ordinates of d are ( k, k + 9). find the value of k. answer(d) k = .. [2]", "16": "16 0607/42/o/n/15 \u00a9 ucles 201512 in the diagram, abc is a straight line and bfed is a rectangle. 120\u00b012 cm 15 cm 20 cmnot to scaleb cd efa (a) find bc. answer(a) ... cm [3] (b) show that angle dbc = 34.7\u00b0, correct to 3 significant figures . [3]", "17": "17 0607/42/o/n/15 \u00a9 ucles 2015 [turn over (c) find the perimeter of the quadrilateral acde. answer(c) ... cm [4] (d) find the area of the quadrilateral acde. answer(d) .. cm2 [3]", "18": "18 0607/42/o/n/15 \u00a9 ucles 201513 120y x \u20134050 fx210010x= - ^h (a) (i) on the diagram, sketch the graph of f y x=^h, for x0 5g g . [2] (ii) write down the x co-ordinate of the point where the graph crosses the x-axis. answer(a) (ii) .. [1] (iii) write down the range of f( x). answer(a) (iii) .. [1] (b) solve the equation. 210010 20x- = answer(b) x = . [1] (c) describe fully the single transformation that maps the graph of y2100 x= onto the graph of y210010x= - . answer(c) . [2]", "19": "19 0607/42/o/n/15 \u00a9 ucles 2015 [turn over14 a fraction p has denominator x. the numerator of the fraction is 3 less than the denominator. (a) write down fraction p in terms of x. answer(a) .. [1] (b) the numerator and the denominator of fraction p are each increased by 3 to give fraction q. write down fraction q in terms of x. answer(b) .. [1] (c) q p409- = (i) write down an equation in x and show that it simplifies to x x 3 40 02+ - =. [3] (ii) solve the equation x x 3 40 02+ - =. answer(c) (ii) x = .. or x = .. [2] (iii) write down the original fraction, p. answer(c) (iii) .. [1] question 15 is printed on the next page.", "20": "20 0607/42/o/n/15 \u00a9 ucles 2015permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.15 solve the inequalities. (a) x2 1531- answer(a) .. [3] (b) log 2 10x2 ^h answer(b) .. [2]" }, "0607_w15_qp_43.pdf": { "1": "this document consists of 16 printed pages. dc (st/sw) 103703/4 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 3 4 2 3 1 7 5 2 2 9 * cambridge international mathematics 0607/43 paper 4 (extended) october/november 2015 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.", "2": "2 0607/43/o/n/15 \u00a9 ucles 2015formula list for the equation ax bx c02+ + = xab b ac 242!=- - curved surface area, a, of cylinder of radius r, height h. r a rh2= curved surface area, a, of cone of radius r, sloping edge l. r a rl= curved surface area, a, of sphere of radius r. r a r42= v olume, v, of pyramid, base area a, height h. v ah31= v olume, v, of cylinder of radius r, height h. rv r h2= v olume, v, of cone of radius r, height h. r v r h31 2= v olume, v, of sphere of radius r. r v r34 3= sin sin sin aa bb cc= = cos a b c bc a 22 2 2= + - sinbc a21area=a c bcb a", "3": "3 0607/43/o/n/15 \u00a9 ucles 2015 [turn overanswer all the questions. 1 cd b41\u00b015 cm anot to scale 17 cm (a) calculate the length of bd. answer(a) .. cm [2] (b) calculate the area of triangle acd . answer(b) . cm2 [2] (c) use the cosine rule to find the length of ad. answer(c) .. cm [3]", "4": "4 0607/43/o/n/15 \u00a9 ucles 20152 (a) jay buys a bicycle for $220. he later sells it for $160. calculate his percentage loss. answer(a) % [3] (b) a television has a sale price of $216 after a reduction of 10%. calculate the original price of the television. answer(b) $ [3] (c) the population of a village is 2180. the population decreases by 3% each year. (i) calculate the population in 20 years time. answer(c) (i) [3] (ii) calculate the number of whole years it takes for the population to decrease from 2180 to less than 1000. answer(c) (ii) [2]", "5": "5 0607/43/o/n/15 \u00a9 ucles 2015 [turn over3 (a) the speeds, v km/h, of 120 cars passing under a bridge are measured. the table shows the results. speed (v km/h) v 30 501g v0 05 61g v0 06 71g v0 7571g v 75 901g frequency 2 25 46 41 6 (i) write down the interval that contains the lower quartile. \t answer(a) (i) [1] (ii) calculate an estimate of the mean. \t answer(a) (ii) ... km/h [2] (iii) complete the table of frequency densities. speed (v km/h) v 30 501g v0 05 61g v0 06 71g v0 7571g v 75 901g frequency density [3] (b) the table below shows the monthly rainfall and the average midday temperatures of a city. month jan feb mar apr may jun jul aug sep oct nov dec rainfall (r mm)15 20 20 35 70 90 75 70 50 30 12 8 temperature (t\t\u00b0 c)35 25 22 15 10 10 15 20 27 30 38 36 find the equation of the line of regression, giving t in terms of r. answer(b) \tt = [2]", "6": "6 0607/43/o/n/15 \u00a9 ucles 20154 (a) (i) shade in one more square so that the diagram has one line of symmetry . [1] (ii) shade in two more squares so that the diagram has rotational symmetry of order 2 and no lines of symmetry. [1] (b) c b a p qr not to scale triangle abc and triangle pqr are mathematically similar. ab : pq = 3 : 2 . \t \t (i)\t cb = 10.5 cm. calculate the length of rq. answer(b) (i) .. cm [2] (ii) the area of triangle abc is 45 cm2. calculate the area of triangle pqr . answer(b) (ii) . cm2 [2]", "7": "7 0607/43/o/n/15 \u00a9 ucles 2015 [turn over5 1 012345678910xy 2345678 u t (a) (i) describe fully the single transformation that maps triangle t onto triangle u. answer(a) (i) . . [3] (ii) describe fully the inverse of the transformation in part(a)(i) . answer(a) (ii) .. [2] (b) (i) draw the image of triangle t under a reflection in the line y = x. [2] (ii) draw the image of triangle t under a rotation of 90\u00b0 anti-clockwise about the point (6, 8). [2] (c) describe fully the single transformation equivalent to a rotation 90\u00b0 clockwise about (0, 0) followed by a reflection in the line y x=- . you may use the grid to help you. 0 xy answer(c) .. . [3]", "8": "8 0607/43/o/n/15 \u00a9 ucles 20156 the diagram shows a solid cone inside a cylinder. the base radius of the cone and the radius of the cylinder are both 10 cm. the height of both the cone and the cylinder is 30 cm. 30 cm 10 cmnot to scale (a) find the volume of the cylinder not occupied by the cone. \t answer(a) .. cm3 [3] (b) water is poured into the cylinder until it reaches a depth of 15 cm. 15 cmnot to scale (i) calculate the volume of the part of the cone that is below the water level and show that it rounds to 2749 cm3, correct to the nearest cubic centimetre. [4] (ii) calculate the amount of water that has been poured into the cylinder . give your answer in litres. answer(b) (ii) ... litres [3]", "9": "9 0607/43/o/n/15 \u00a9 ucles 2015 [turn over7 (a) kim walks 10 km at 4 km/h and then a further 6 km at 3 km/h. calculate kim\u2019s average speed. answer(a) ... km/h [3] (b) chung runs at x km/h for 45 minutes and then at ( x \u2013 2) km/h for 30 minutes. find an expression, in terms of x, for chung\u2019s average speed in km/h. give your answer in its simplest form. answer(b) ... km/h [4]", "10": "10 0607/43/o/n/15 \u00a9 ucles 20158 (a) (i) solve the inequality. ( ) ( ) x x2 3 5 31- + answer(a) (i) [3] (ii) show your answer to part(a)(i) on the number line. \u201310\u20139\u20138\u20137\u20136\u20135\u20134\u20133\u20132\u20131012345678910x [1] (b) solve the equation. ( ) ( ) x x3 1 252 2+ + + = give your answers correct to 2 decimal places. answer(b) x = ... or x = .. [6]", "11": "11 0607/43/o/n/15 \u00a9 ucles 2015 [turn over (c) solve the equations. (i) logx x 5= - answer(c) (i) x = [3] (ii) logx x 5= - \t answer(c) (ii) x = ... or x = .. [2] (d) simplify, giving your answer as a single fraction. xx x1 12 --+ answer(d) [3]", "12": "12 0607/43/o/n/15 \u00a9 ucles 20159 (a) 124\u00b025\u00b0d a bc not to scale in the quadrilateral abcd , da = ab and da is parallel to cb. angle dab = 124\u00b0 and angle bdc = 25\u00b0. calculate angle bcd . answer(a) [3] (b) nine of the angles of a 10-sided polygon are each 142\u00b0. calculate the other angle. answer(b) [3]", "13": "13 0607/43/o/n/15 \u00a9 ucles 2015 [turn over (c) d f x20\u00b0 o 25\u00b0e a bcnot to scale a, b, c and d lie on the circle, centre o. bd is a diameter and edf is a tangent at d. ac and bd intersect at x. angle bca = 25\u00b0 and angle bdc = 20\u00b0. calculate (i) angle ade , \t answer(c) (i) [2] (ii) angle dac , \t answer(c) (ii) [2] (iii) angle axd . \t answer(c) (iii) [1]", "14": "14 0607/43/o/n/15 \u00a9 ucles 201510 in this question, the weather is only considered to be either wet or dry. when the weather is dry the probability that sara will go walking is 53. when the weather is wet the probability that sara will go walking is 101. the probability of a dry day is 32. (a) complete the tree diagram. 2 3weather 3 5 .. ..walking dryyes no yes nowet [3] (b) show that the probability that sara goes walking is 3013. [2] (c) the probability that sara does not go walking when the weather is wet is 309. complete this tree diagram. 13 30weather 1 13.. ..walking yesdry wet dry wetno [3]", "15": "15 0607/43/o/n/15 \u00a9 ucles 2015 [turn over11 ( )fx x 162= - ( ) , gxxx121! =+- ( )hx 2x= (a) find h(3). \t answer(a) [1] (b) find the range of g( x) for the domain {0, 1}. answer(b) [1] (c) f(x\t\u2013 2) can be written as ( ) ( ) x a x b+ + . find the value of a and the value of b. answer(c) a = .. b = [4] (d) find the inverse of (i) g(x), \t answer(d) (i) [3] (ii) h(x). \t answer(d) (ii) [2] (e) describe fully the single transformation that maps the graph of ( )f y x=\tonto the graph of y x2 322= - . ... . [2] question 12 is printed on the next page", "16": "16 0607/43/o/n/15 \u00a9 ucles 201512 \u20136 \u20131010y x4 0 (a) on the diagram, sketch the graphs of ( )yx212=+ and y2 5x= - for values of x between x = \u2013 6 and x = 4. [4] (b) write down the equation of each asymptote of the graph of (i) yx212=+ , \t answer(b) (i) .. . [2] (ii) y2 5x= - . answer(b) (ii) [1] (c) solve the inequality. xx 2 52120 forx2 2 -+ . answer(c) [2] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_w15_qp_51.pdf": { "1": "this document consists of 7 printed pages and 1 blank page. dc (lk) 103666/3 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 8 5 1 5 2 8 4 6 1 1 * cambr idge international ma thematics 0607/51 paper 5 (core) october/ november 2015 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructi ons first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. y ou must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and to communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.", "2": "2 0607/51/o/n/15 \u00a9 ucles 2015the investigation starts on page 3.", "3": "3 0607/51/o/n/15 \u00a9 ucles 2015 [turn overanswer all the questions. investigation sums of two squares this investigation looks at the results when two square numbers are added together . 1 here is a list of the first 11 prime numbers. 2 3 5 7 11 13 17 19 23 29 31 (a) in the list there are 4 numbers that are one more than a multiple of 4. these are called pythagorean primes . the smallest one is 5 and the largest one is 29. write down the other two. 5, . , . , 29 (b) the 17th century french mathematician albert girard proved that every pythagorean prime equals the sum of two square numbers. write your answers to part (a) as the sum of two square numbers. two have been written down for you. 5 = 12 + 22 . = . + . . = . + . 29 = 22 + 52 (c) another pythagorean prime is 101. write 101 as the sum of two square numbers. 101 = . + .", "4": "4 0607/51/o/n/15 \u00a9 ucles 20152 the sum of two square numbers can equal another square number. for example, 32 + 42 = 9 + 16 = 25 = 52 we say that 3, 4, 5 is a pythagorean triple . (a) show, by calculation, that 7, 24, 25 is a pythagorean triple. (b) each row in this table is a pythagorean triple. complete the table. use patterns of numbers in the table to help you. 3 4 5 5 12 13 7 24 25 9 40 11 60 13 113", "5": "5 0607/51/o/n/15 \u00a9 ucles 2015 [turn over (c) what is the connection between the square of the smallest number and the other two numbers in each pythagorean triple in the table? ... ... (d) use your answer to part (c) and the patterns of numbers in the table to complete the following pythagorean triple. . , . , 421", "6": "6 0607/51/o/n/15 \u00a9 ucles 20153 , ,x x x 2 1 1 - + is a pythagorean triple when x is a square number. (a) (i) find the pythagorean triple when x = 16. . , . , . (ii) check that your answer to part (a)(i) is a pythagorean triple. use the method of the example in question 2 . (b) in the table, x is the square of an even number. each row is a pythagorean triple. x2 x \u2013 1 x + 1 (x = 16) (x = 36) 12 37 16 63 65 99 24 145 write your answer to part (a)(i) in the first row of this table. complete the three columns of the table. you may use patterns or the fact that , ,x x x 2 1 1 - + is a pythagorean triple to help you.", "7": "7 0607/51/o/n/15 \u00a9 ucles 2015 (c) what is the connection between the square of the smallest number and the sum of the other two numbers in each of the pythagorean triples in the table? ... ... (d) show algebraically that , ,x x x 2 1 1 - + satisfies your connection in part (c) .", "8": "8 0607/51/o/n/15 \u00a9 ucles 2015permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_w15_qp_52.pdf": { "1": "this document consists of 7 printed pages and 1 blank page. dc (nf) 118206 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 3 6 9 8 3 4 6 5 2 1 * cambr idge international ma thematics 0607/52 paper 5 (core) october/ november 2015 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructi ons first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. y ou must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and to communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.", "2": "2 0607/52/o/n/15 \u00a9 ucles 2015the investigation starts on page 3.", "3": "3 0607/52/o/n/15 \u00a9 ucles 2015 [turn overanswer all the questions. investigation sums of two squares this investigation looks at the results when two square numbers are added together . 1 here is a list of the first 11 prime numbers. 2 3 5 7 11 13 17 19 23 29 31 (a) in the list there are 4 numbers that are one more than a multiple of 4. these are called pythagorean primes . the smallest one is 5 and the largest one is 29. write down the other two. 5, . , . , 29 (b) the 17th century french mathematician albert girard proved that every pythagorean prime equals the sum of two square numbers. write your answers to part (a) as the sum of two square numbers. two have been written down for you. 5 = 12 + 22 . = . + . . = . + . 29 = 22 + 52 (c) another pythagorean prime is 101. write 101 as the sum of two square numbers. 101 = . + .", "4": "4 0607/52/o/n/15 \u00a9 ucles 20152 the sum of two square numbers can equal another square number. for example, 32 + 42 = 9 + 16 = 25 = 52 we say that 3, 4, 5 is a pythagorean triple . (a) show, by calculation, that 7, 24, 25 is a pythagorean triple. (b) each row in this table is a pythagorean triple. complete the table. use patterns of numbers in the table to help you. 3 4 5 5 12 13 7 24 25 9 40 11 60 13 113", "5": "5 0607/52/o/n/15 \u00a9 ucles 2015 [turn over (c) what is the connection between the square of the smallest number and the other two numbers in each pythagorean triple in the table? ... ... (d) use your answer to part (c) and the patterns of numbers in the table to complete the following pythagorean triple. . , . , 421", "6": "6 0607/52/o/n/15 \u00a9 ucles 20153 , ,x x x 2 1 1 - + is a pythagorean triple when x is a square number. (a) (i) find the pythagorean triple when x = 16. . , . , . (ii) check that your answer to part (a)(i) is a pythagorean triple. use the method of the example in question 2 . (b) in the table, x is the square of an even number. each row is a pythagorean triple. x2 x \u2013 1 x + 1 (x = 16) (x = 36) 12 37 16 63 65 99 24 145 write your answer to part (a)(i) in the first row of this table. complete the three columns of the table. you may use patterns or the fact that , ,x x x 2 1 1 - + is a pythagorean triple to help you.", "7": "7 0607/52/o/n/15 \u00a9 ucles 2015 (c) what is the connection between the square of the smallest number and the sum of the other two numbers in each of the pythagorean triples in the table? ... ... (d) show algebraically that , ,x x x 2 1 1 - + satisfies your connection in part (c) .", "8": "8 0607/52/o/n/15 \u00a9 ucles 2015permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_w15_qp_53.pdf": { "1": "this document consists of 7 printed pages and 1 blank page. dc (st) 118176 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 7 5 5 5 9 0 1 6 8 5 * cambr idge international ma thematics 0607/53 paper 5 (core) october/ november 2015 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructi ons first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. y ou must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and to communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.", "2": "2 0607/53/o/n/15 \u00a9 ucles 2015the investigation starts on page 3.", "3": "3 0607/53/o/n/15 \u00a9 ucles 2015 [turn overanswer all the questions. investigation sums of two squares this investigation looks at the results when two square numbers are added together . 1 here is a list of the first 11 prime numbers. 2 3 5 7 11 13 17 19 23 29 31 (a) in the list there are 4 numbers that are one more than a multiple of 4. these are called pythagorean primes . the smallest one is 5 and the largest one is 29. write down the other two. 5, . , . , 29 (b) the 17th century french mathematician albert girard proved that every pythagorean prime equals the sum of two square numbers. write your answers to part (a) as the sum of two square numbers. two have been written down for you. 5 = 12 + 22 . = . + . . = . + . 29 = 22 + 52 (c) another pythagorean prime is 101. write 101 as the sum of two square numbers. 101 = . + .", "4": "4 0607/53/o/n/15 \u00a9 ucles 20152 the sum of two square numbers can equal another square number. for example, 32 + 42 = 9 + 16 = 25 = 52 we say that 3, 4, 5 is a pythagorean triple . (a) show, by calculation, that 7, 24, 25 is a pythagorean triple. (b) each row in this table is a pythagorean triple. complete the table. use patterns of numbers in the table to help you. 3 4 5 5 12 13 7 24 25 9 40 11 60 13 113", "5": "5 0607/53/o/n/15 \u00a9 ucles 2015 [turn over (c) what is the connection between the square of the smallest number and the other two numbers in each pythagorean triple in the table? ... ... (d) use your answer to part (c) and the patterns of numbers in the table to complete the following pythagorean triple. . , . , 421", "6": "6 0607/53/o/n/15 \u00a9 ucles 20153 , ,x x x 2 1 1 - + is a pythagorean triple when x is a square number. (a) (i) find the pythagorean triple when x = 16. . , . , . (ii) check that your answer to part (a)(i) is a pythagorean triple. use the method of the example in question 2 . (b) in the table, x is the square of an even number. each row is a pythagorean triple. x2 x \u2013 1 x + 1 (x = 16) (x = 36) 12 37 16 63 65 99 24 145 write your answer to part (a)(i) in the first row of this table. complete the three columns of the table. you may use patterns or the fact that , ,x x x 2 1 1 - + is a pythagorean triple to help you.", "7": "7 0607/53/o/n/15 \u00a9 ucles 2015 (c) what is the connection between the square of the smallest number and the sum of the other two numbers in each of the pythagorean triples in the table? ... ... (d) show algebraically that , ,x x x 2 1 1 - + satisfies your connection in part (c) .", "8": "8 0607/53/o/n/15 \u00a9 ucles 2015permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_w15_qp_61.pdf": { "1": "this document consists of 12 printed pages. dc (rw/fd) 104122/3 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 0 3 7 6 2 2 7 2 5 5 * cambridge international mathematics 0607/61 paper 6 (extended) october/november 2015 1 hour 30 minutes candidates answer on the question paper additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. y ou must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.", "2": "2 0607/61/o/n/15 \u00a9 ucles 2015the investigation starts on page 3.", "3": "3 0607/61/o/n/15 \u00a9 ucles 2015 [turn overanswer both parts a and b. a investigation sums of two squares (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation looks at the results when two square numbers are added together . 1 here is a list of the first 11 prime numbers. 2 3 5 7 11 13 17 19 23 29 31 (a) in the list there are 4 numbers that are one more than a multiple of 4. these are called pythagorean primes . the smallest one is 5 and the largest one is 29. write down the other two. 5, \u2026.\u2026.\u2026 , \u2026.\u2026.\u2026 , 29 (b) the 17th century french mathematician albert girard proved that every pythagorean prime equals the sum of two square numbers. write your answers to part (a) as the sum of two square numbers. two have been written down for you. 5 = 12 + 22 \u2026.\u2026.\u2026 = \u2026.\u2026.\u2026 + \u2026.\u2026.\u2026 \u2026.\u2026.\u2026 = \u2026.\u2026.\u2026 + \u2026.\u2026.\u2026 29 = 22 + 52 (c) another pythagorean prime is 101. write 101 as the sum of two square numbers. 101 = \u2026.\u2026.\u2026 + \u2026.\u2026.\u2026", "4": "4 0607/61/o/n/15 \u00a9 ucles 20152 the sum of two square numbers can equal a square number. for example, 32 + 42 = 9 + 16 = 25 = 52 we say that 3, 4, 5 is a pythagorean triple . (a) show, by calculation, that 7, 24, 25 is a pythagorean triple. (b) each row in this table is a pythagorean triple. complete the table. use patterns of numbers in the table to help you. 3 4 5 5 12 13 7 24 25 9 40 11 60 13 113", "5": "5 0607/61/o/n/15 \u00a9 ucles 2015 [turn over (c) what is the connection between the square of the smallest number and the other two numbers in each pythagorean triple in the table? ... ... (d) use your answer to part (c) and the patterns of numbers in the table to complete the following pythagorean triples. (i) \u2026\u2026\u2026. , \u2026\u2026\u2026. , 421 (ii) 101 , \u2026\u2026\u2026. , \u2026\u2026\u2026.", "6": "6 0607/61/o/n/15 \u00a9 ucles 20153 sometimes the sum of two square numbers can equal the sum of another pair of square numbers. for example, 52 + 52 = 12 + 72 (both sums equal 50.) (a) show that (x + y)2 + (m \u2013 n)2 = (x \u2013 y)2 + (m + n)2 simplifies to xy = mn. (x + y)2 + (m \u2013 n)2 = (x \u2013 y)2 + (m + n)2 xy = mn", "7": "7 0607/61/o/n/15 \u00a9 ucles 2015 [turn over (b) x, y, m and n are different positive integers with x > y and m > n. when xy = mn = 6 one solution is x = 3, y = 2 and m = 6, n = 1. the substitution of these values into (x + y)2 + (m \u2013 n)2 = ( x \u2013 y)2 + (m + n)2 gives these equal sums of square numbers. 52 + 52 = 12 + 72 find all the possible solutions when xy = mn = 12. for each solution, write the equal sums of square numbers. (c) complete the following equal sums of square numbers. 92 + \u2026\u2026\u2026. = 52 + \u2026\u2026\u2026.", "8": "8 0607/61/o/n/15 \u00a9 ucles 2015b modelling population growth (20 marks) you are advised to spend no more than 45 minutes on this part. this modelling task compares three different models of population growth. ten fish are put into a lake to breed. the maximum number of fish that can live in the lake is 100. after ten years the number of fish stays approximately the same. the table shows the number of fish, y, in the lake at the end of x years. number of years ( x) 0 1 2 3 4 5 6 7 8 9 10 number of fish ( y) 10 18 27 41 61 78 88 93 97 99 100 this information is shown below. 0102030405060 number of fish708090100 1 2 3 4 5 number of years6 7 8 9 10xy 1 (a) why is it correct to join the points? ... ... (b) comment on the rate of increase in the number of fish when the number of fish approaches 100. ... ...", "9": "9 0607/61/o/n/15 \u00a9 ucles 2015 [turn over2 the data can be modelled using the cubic function y = ax3 + bx. (a) find an equation in a and b so that the model gives the value of y in the table when (i) x = 1, ... (ii) x = 5. ... (b) solve the simultaneous equations from part (a) and write down the model. ...", "10": "10 0607/61/o/n/15 \u00a9 ucles 20153 the data can also be modelled by the trigonometric function y = a + cosb x 18 \u00b0 ^ h. (a) find an equation in a and b so that the model gives the value of y in the table when (i) x = 0, ... (ii) x = 10. ... (b) solve the equations from part (a) and write down your model. ...", "11": "11 0607/61/o/n/15 \u00a9 ucles 2015 [turn over4 the data can also be modelled by the logistic function yk 2100 2 xx#=+. (a) the model gives the value of y in the table when x = 0. find the value of k. . (b) comment on the accuracy of the model when x = 5. ... ... question 5 is printed on the next page.", "12": "12 0607/61/o/n/15 \u00a9 ucles 2015permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.5 (a) sketch the graphs of your models in questions 2 , 3 and 4 for x0 15g g . the original data has been shown again. 0102030405060number of fish708090100 5 10 15xy number of years (b) give two reasons why the logistic model is the best. ... ... ..." }, "0607_w15_qp_62.pdf": { "1": "this document consists of 12 printed pages. dc (st/fd) 104250/3 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education * 8 7 7 2 0 7 7 2 8 1 * cambridge international mathematics 0607/62 paper 6 (extended) october/november 2015 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. y ou must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.", "2": "2 0607/62/o/n/15 \u00a9 ucles 2015answer both parts a and b. a\t investigation\t stars\t(20\tmarks) \t you are advised to spend no more than 45 minutes on this part. this investigation looks at how stars can be drawn by a robot ant. each diagram in this investigation is the path that the ant draws by repeating these two steps. \u2022 move one unit forward \u2022 turn anticlockwise through a\u00b0 where a < 180 1\t (a) a \u00b0a \u00b0 \t \t the ant repeats the two steps 7 times, going round the polygon until it reaches its starting position. \t \t the ant makes 1 complete revolution (360\u00b0) to draw this regular 7-sided polygon. \t \t show that a = 51.4, correct to 1 decimal place. \t (b)\t the ant draws a regular n-sided polygon. \t \t write down a formula for a in terms of n. ...", "3": "3 0607/62/o/n/15 \u00a9 ucles 2015 [turn\tover2\t (a) the diagrams show how the ant draws a 7-pointed star. 1st turn 5th turn2nd turn 3rd turna \u00b0 a \u00b0a \u00b0 a \u00b0 a \u00b0 6th turna \u00b0 7th turna \u00b0during the 4th turn the ant completes its first revolution. here is the completed 7-pointed star. \t \t to draw a 7-pointed star, the ant must repeat the two steps 7 times, as shown in the diagrams. \t \t in doing so, the ant makes 2 complete revolutions (720\u00b0). \t \t calculate a. ...", "4": "4 0607/62/o/n/15 \u00a9 ucles 2015\t (b) \t \t the diagram shows another 7-pointed star. \t \t to draw it, the ant repeats the two steps 7 times. \t \t (i)\t in drawing this star, how many complete revolutions does the ant make before it reaches its starting position? ... \t \t (ii)\t explain why a73360#= . ... ... \t \t (iii)\t to draw a 7-pointed star, 73360# is the largest possible value of \ta which is less than 180\u00b0. \t \t \t show that 4 complete revolutions do not give a suitable value for a.", "5": "5 0607/62/o/n/15 \u00a9 ucles 2015 [turn\tover3\t \t the diagram shows the 5-pointed star drawn using the largest possible value of a which is less than 180\u00b0. \t to draw it, the ant repeats the two steps 5 times and makes 2 complete revolutions. \t \t write down the calculation to find a. give your answer in a similar form to question\t2(b)(ii) . \t ... 4\t (a)\t complete the table for stars that are drawn using the largest possible value of a which is less than 180\u00b0. \t \t the first row gives a polygon and is shown here to help you see the pattern. number of points on the starnumber of revolutions, n, that the ant makes calculation of a a 3 131360# 120 5 2 144 773603# 154.3 9 11 163.6 \t (b)\t find a formula for a in terms of n. ... \t (c)\t find the number of points on the star when a = 172.8 . ...", "6": "6 0607/62/o/n/15 \u00a9 ucles 20155\t question \t2 shows the only two possible 7-pointed stars. \t (a)\t find the number of possible 11-pointed stars. \t \t write down the number of complete revolutions that the ant makes to draw each of these stars. ... \t (b)\t explain why the calculation of a for a 15-pointed star using 6 complete revolutions gives the calculation for the 5-pointed star. \t ... ...", "7": "7 0607/62/o/n/15 \u00a9 ucles 2015 [turn\tover\t (c)\t find all the values of a that give a 15-pointed star. ...", "8": "8 0607/62/o/n/15 \u00a9 ucles 2015b\t modelling\t \tbody\tmass\t(20\tmarks) you are advised to spend no more than 45 minutes on this part. this task looks at three different models for the approximate body mass of an adult. 1 here is a simple model to calculate the approximate body mass of an adult. measure the height in centimetres and subtract 100 to get the approximate mass in kilograms. (a)\t find the approximate body mass of an adult who is 1.8 m tall. ... (b) find the height of an adult who has an approximate body mass of 50 kg. ... (c)\t for a height, h metres, the approximate body mass is m kilograms. \t \t find the formula for m in terms of h. ... (d)\t sketch, showing appropriate scales, the graph of the approximate body mass, m. m 0 h", "9": "9 0607/62/o/n/15 \u00a9 ucles 2015 [turn\tover2\t in the 19th century, the belgian mathematician quetelet suggested a different model. \t \t in his model the approximate body mass of an adult, m kg, varies as the square of the height, h metres. \t for an adult with height 2 m the approximate body mass is 88 kg. \t (a)\t show that quetelet\u2019 s model can be written as m = 22 h2. (b)\t show that an adult with height 1.5 m has an approximate body mass of 49.5 kg. (c)\t an adult has an approximate body mass of \t77 kg. calculate the height of this adult. ... ", "10": "10 0607/62/o/n/15 \u00a9 ucles 20153\t (a)\t for some adults the simple model and quetelet\u2019 s model give the same approximate body mass. \t \t find the height of these adults. ... \t (b)\t for most adults, which model gives a larger approximate body mass? \t \t explain your answer. ... ...", "11": "11 0607/62/o/n/15 \u00a9 ucles 2015 [turn\tover4\t quetelet\u2019 s model gives an approximate body mass which is too small for taller people. \t \t a modern model uses m = khn and the following information. \t \t the approximate body mass of an adult is 78 kg for a height of 1.84 m and 50 kg for a height of 1.54 m. \t (a)\t write down two equations in terms of k and n. ... ... \t (b)\t show that 1.56 = 1.195n, correct to 3 decimal places. \t (c)\t show that n = 2.5, correct to one decimal place. (d)\t using n = 2.5, calculate the value of k, correct to the nearest integer. ... questions \t4(e)\tand\t5\tare\tprinted\ton\tthe\tnext\tpage.", "12": "12 0607/62/o/n/15 \u00a9 ucles 2015permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. (e)\t sketch the graph of the modern model . m 0h 5\t above which height does the modern model give a greater approximate body mass than the quetelet model ? ..." }, "0607_w15_qp_63.pdf": { "1": "this document consists of 12 printed pages. dc (leg/fd) 104389/2 \u00a9 ucles 2015 [turn overcambridge international examinations cambridge international general certificate of secondary education *4589965079* cambridge international mathematics 0607/63 paper 6 (extended) october/november 2015 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. y ou must show all the relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.", "2": "2 0607/63/o/n/15 \u00a9 ucles 2015answer both parts a and b. a investigation position of security cameras (20 marks) you are advised to spend no more than 45 minutes on this part. houses are built around squares. security cameras give a clear view for a distance of one side of a square in any direction. on the diagrams a cross represents a security camera. one square needs a minimum of 2 cameras to view all four sides. two squares, in a row, need a minimum of 3 cameras as shown. this investigation looks at the minimum number of security cameras for squares in different arrangements. 1 (a) (i) three squares in one row need a minimum of 4 cameras. draw 4 crosses on the diagram to show the positions of the cameras. (ii) four squares in one row need a minimum of 5 cameras. draw 5 crosses on the diagram to show the positions of the cameras. (iii) draw crosses on the diagram to show the positions of the minimum number of cameras for five squares in one row. (b) find an expression, in terms of n, for the minimum number of cameras for n squares in one row. ...", "3": "3 0607/63/o/n/15 \u00a9 ucles 2015 [turn over2 there are now three rows of squares. (a) (i) what is the minimum number of cameras needed when there is 1 square in each of three rows? draw crosses on the diagram to show the positions of these cameras. minimum = .. (ii) two squares in each of three rows need a minimum of 6 cameras. draw crosses on the diagram to show the positions of these cameras. minimum = 6 (iii) draw crosses on the diagram to show the positions of the minimum number of cameras for 3 squares in each of three rows. minimum = .. (b) find an expression, in terms of n, for the minimum number of cameras for n squares in each of three rows. ...", "4": "4 0607/63/o/n/15 \u00a9 ucles 20153 there are now five rows of squares. find the minimum number of cameras for 2 and 3 squares in each of five rows. minimum = .. minimum = ..", "5": "5 0607/63/o/n/15 \u00a9 ucles 2015 [turn over4 (a) complete the table to show the minimum number of cameras for an odd number of rows. number of squares in each row 1 square 2 squares 3 squares 4 squares 5 squares n squares one row 2345 three rows 6 five rows 6 seven rows 8 (b) find an expression for the minimum number of cameras for n squares in each of r rows, when r is an odd number. ... (c) for an odd number of rows, the minimum number of cameras is 16. find all the possible numbers of squares in each row. ...", "6": "6 0607/63/o/n/15 \u00a9 ucles 20155 now consider even numbers of rows with an even number of squares in each row. two rows, each with two squares, need a minimum of 4 cameras. two rows, each with four squares, need a minimum of 7 cameras. (a) find the minimum number of cameras for 6 and 8 squares in each of two rows. minimum = .. minimum = .. (b) find an expression for the minimum number of cameras for two rows each with n squares, when n is even. ...", "7": "7 0607/63/o/n/15 \u00a9 ucles 2015 [turn over6 (a) complete the table to show the minimum number of cameras for even numbers of rows each with an even number of squares. number of squares in each row 2 squares 4 squares 6 squares 8 squares n squares two rows 4 7 four rows 7 12 six rows 10 24 eight rows 13 40 (b) find an expression for the minimum number of cameras when the number of rows, r, and the number of squares in each row, n, are both even numbers. ...", "8": "8 0607/63/o/n/15 \u00a9 ucles 2015b modelling bacteria (20 marks) you are advised to spend no more than 45 minutes on this part. in an experiment a biologist recorded the number of bacteria in a dish at the end of each day for 5 days. the table shows the results. time in days ( x) 12345 number of bacteria ( n) 120 170 250 370 530 1 (a) on the grid below, plot the five points and join them to form a smooth curve. 0100200300400500600 12345xn (b) write down an estimate for the number of bacteria at the start of the experiment. ...", "9": "9 0607/63/o/n/15 \u00a9 ucles 2015 [turn over2 (a) which of the following models best fits the relationship between x and n? n = pqx n = px2 + q n = px + q ... (b) use the number of bacteria for day 3 and day 4 with your model to find a value for q. ... (c) find the value of p that corresponds to the value for q in part (b) . ... (d) (i) rewrite your model substituting your values for p and q. use your model to estimate the number of bacteria at the end of the seventh day. ... (ii) use your model to estimate the number of bacteria at the start of the experiment. ... (iii) compare your answer in part (ii) with your estimate in question 1(b) . .. . .. .", "10": "10 0607/63/o/n/15 \u00a9 ucles 20153 in this question log n represents log10 n. (a) complete the table of values, giving log n correct to 3 significant figures. time in days ( x) 12345 number of bacteria ( n) 120 170 250 370 530 log n (y) 2.08 (b) find the mean value of x and the mean value of y. mean value of x .. mean value of y .. (c) on the grid below, plot y against x and draw a line of best fit. 00.511.522.53 12345xy", "11": "11 0607/63/o/n/15 \u00a9 ucles 2015 [turn over (d) the equation of the line of best fit is y = mx + c. (i) estimate the value of c from your graph. ... (ii) find the value of m. ... (e) another model for the number of bacteria, n, is log n = mx + c. rewrite this model substituting your values for m and c. use this model to estimate the number of bacteria at the end of the seventh day. ... (f) use this model to estimate the number of bacteria at the start of the experiment. ... question 4 is printed on the next page.", "12": "12 0607/63/o/n/15 \u00a9 ucles 2015permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to do wnload at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.4 compare the models in question 2(d)(i) and question 3(e) . .. . .. ." } }, "2016": { "0607_s16_qp_11.pdf": { "1": " this document consists of 8 printed pages. ib16 06_0607_11/4rp \u00a9 ucles 2016 [turn over *7320481266 * cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/11 paper 1 (core) may/june 2016 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2016 0607/11/m/j/16 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2016 0607/11/m/j/16 [turn over answer all the questions. 1 shade 32 of this shape. [1] 2 draw a sector inside this circle. draw a chord inside this circle. [2] 3 write down all the factors of 21. [2] ", "4": "4 \u00a9 ucles 2016 0607/11/m/j/16 4 work out. (a) 16 + 8 \u00d7 4 [1] (b) 16 \u2013 8 \u00f7 4 [1] 5 complete the mapping diagram. 1611952 191571 [1] 6 jenny shares $40 between her two sons in the ratio 3:1. work out how much each son receives. $ and $ [2] ", "5": "5 \u00a9 ucles 2016 0607/11/m/j/16 [turn over 7 tick the shapes that have both line symmetry and rotational symmetry. rectangle kite parallelogram rhombus isosceles triangle [2] 8 the diagram shows a child\u2019s solid building block in the shape of a cuboid 2 cm by 5 cm by 10 cm. 5 cm10 cm 2 cm find the total surface area of the cuboid. cm2 [3] ", "6": "6 \u00a9 ucles 2016 0607/11/m/j/16 9 write down the next two terms in the sequence. 18, 18, 16, 12, 6, \u2026 , [2] 10 the venn diagram shows two sets a and b. u = {1, 2, 3, 4, 5, 6, 7, 8, 9} au b 4 2 6 8193 75 (a) complete the following. (i) a = { } [1] (ii) b\u2032 = { } [1] (iii) a \u2229 b = { } [1] (b) what is the mathematical name given to the numbers in set a? [1] (c) circle the statements which are correct for this venn diagram. a \u222a b = u 7 \u2209 a n(b) = 4 a \u2229 b\u2032 = {4} [2] ", "7": "7 \u00a9 ucles 2016 0607/11/m/j/16 [turn over 11 110\u00b0 not to scale 140\u00b0r\u00b0 80\u00b0 find the value of r. r = [3] 12 a car travels 100 metres in 8 seconds. find its speed in kilometres per hour. km/h [2] 13 describe the single transformation that maps y = f(x) onto y = f(x) + 3. [2] 14 an archer hits the target with probability 107 . he takes 50 shots at the target. how many times does he expect to hit the target? [1] 15 write down all the integers that satisfy the following inequality. \u20133 x < 2 [2] questions 16 and 17 are printed on the next page. ", "8": "8 permission to reproduce items where third-party owned material pr otected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknow ledgements booklet. this is produced for each series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is par t of the cambridge assessment group. cambri dge assessment is t he brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2016 0607/11/m/j/16 16 (a) factorise. (i) 3x + 6 [1] (ii) p2 + pq [1] (b) expand the brackets and simplify. x \u2013 3(2 x \u2013 7) [2] 17 solve the following simultaneous equations. 2 x + y = 8 3 x + 2y = 12 x = y = [3] " }, "0607_s16_qp_12.pdf": { "1": " this document consists of 8 printed pages. ib16 06_0607_12/3rp \u00a9 ucles 2016 [turn over *8403157003* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/12 paper 1 (core) may/june 2016 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2016 0607/12/m/j/16 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2016 0607/12/m/j/16 [turn over answer all the questions. 1 ben takes 1 hour 5 minutes to do his homework. alisa takes 20 minutes less. work out how long alisa takes. give your answer as a fraction of an hour. hour [2] 2 draw all the lines of symmetry on this shape. [1] 3 write down the mathematical name of each of these shapes. the first shape has been named for you. rectangle [ 3 ] 4 write down the value of (a) 81, [1] (b) 38. [1] ", "4": "4 \u00a9 ucles 2016 0607/12/m/j/16 5 (a) write 30% as a fraction. [1] (b) write 2018 as a percentage. % [1] (c) work out 15 % of 340 metres. m [2] 6 (a) not to scale x\u00b0 35\u00b0 find the value of x. x = [2] (b) not to scale y \u00b040\u00b0 find the value of y. y = [2] ", "5": "5 \u00a9 ucles 2016 0607/12/m/j/16 [turn over 7 work out. 53 \u00d7 72 [2] 8 (a) write 2.96 correct to 1 significant figure. [1] (b) find the approximate value of 96219 .. + 955530 .. . [2] (c) is your answer to part (b) higher or lower than the actual answer? give a reason for your answer. because [1] 9 a fair 6-sided die is numbered 1, 2, 3, 4, 5 and 6. the die is rolled once. find the probability that th e number on the top face is (a) 2, [1] (b) not 2. [1] ", "6": "6 \u00a9 ucles 2016 0607/12/m/j/16 10 (a) factorise completely. x \u2013 5x2 [1] (b) r = cb a3 2\u2212 find the value of r when a = 5, b = 2 and c = \u20135. r = [3] 11 solve the following simultaneous equations. 2 x + 5y = 15 2 x \u2013 3y = 7 x = y = [2] 12 list the integer values of n for which 3 3n < 15. [2] ", "7": "7 \u00a9 ucles 2016 0607/12/m/j/16 [turn over 13 0 123123y 445a x5b 6678 (a) find the vector ab. \uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec \uf8ed\uf8eb [2] (b) bc = \uf8f7\uf8f7 \uf8f8\uf8f6 \uf8ec\uf8ec \uf8ed\uf8eb \u2212\u2212 12 . on the grid above, plot and label the point c. [1] 14 the diagram shows the graph of y = f(x). 12y x1234 0 \u20134\u20133\u20132\u20131 34 \u20134\u20133\u20132\u20131 write down the equations of the two asymptotes of the graph. and [2] question 15 is printed on the next page. ", "8": "8 permission to reproduce items where third-party owned material pr otected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknow ledgements booklet. this is produced for each series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is par t of the cambridge assessment group. cambri dge assessment is t he brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2016 0607/12/m/j/16 15 10 20 30 40 50 80 70 6020406080100120140160180200 0cumulative frequency mark the diagram shows a cumulative frequency curve for the marks of 200 students in a test. estimate (a) the median mark, [1] (b) the interquartile range. [2] " }, "0607_s16_qp_13.pdf": { "1": " this document consists of 8 printed pages. ib16 06_0607_13/3rp \u00a9 ucles 2016 [turn over *4992578810* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/13 paper 1 (core) may/june 2016 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2016 0607/13/m/j/16 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2016 0607/13/m/j/16 [turn over answer all the questions. 1 the colour of 20 cars in a car park is recorded below. red red red blue white white blue red green green red white green red white red green red white white (a) complete the frequency table. colour of cars tally frequency red blue white green [2] (b) draw a bar chart to show this information. complete the scale on the frequency axis. green white blue redfrequency [3] 2 write these in order of size, starting with the smallest. 0.49 52 42% < < [2] smallest ", "4": "4 \u00a9 ucles 2016 0607/13/m/j/16 3 complete the diagram by shading two more squares to give a shape with rotational symmetry of order 4. [1] 4 give the mathematical name for each of these quadrilaterals. [2] 5 write the ratio 9 : 54 in the form 1 : n. 1 : [1] 6 work out the lowest common multiple (lcm) of 6 and 8. [2] ", "5": "5 \u00a9 ucles 2016 0607/13/m/j/16 [turn over 7 in a survey, the favourite lessons of a number of students were recorded. the pie chart shows the results. sportscience geographymathematics (a) find the fraction of students whose favourite lesson was geography. [2] (b) the favourite lesson of 9 students was mathematics. work out the total number of students in the survey. [2] 8 find the value of 5 x \u2013 3y when x = 4 and y = 7. [2] ", "6": "6 \u00a9 ucles 2016 0607/13/m/j/16 9 74\u00b0 58\u00b0a\u00b0 not to scale (a) find the value of a. a = [1] (b) pt so120\u00b0not to scale ps and pt are tangents to the circle centre o. angle tos = 120\u00b0. work out the size of angle tpo . angle tpo == [2] 10 estimate the value of (3.96 + 2.08 \u00d7 0.47)2 . [3] ", "7": "7 \u00a9 ucles 2016 0607/13/m/j/16 [turn over 11 a cup of coffee costs 90 cents. a cup of tea costs 85 cents. write down the total cost, in cents, of p cups of coffee and q cups of tea. cents [2] 12 the diagram shows a semicircle with diameter 18 cm. 18 cmnot to scale find the total perimeter of the semicircle. leave your answer in terms of \u03c0. cm [3] 13 a b cp q r8 cm6 cm9 cmnot to scale triangle abc and triangle pqr are similar. find the length of pr. pr = cm [2] question 14 and 15 are printed on the next page. ", "8": "8 permission to reproduce items where third-par ty owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge asse ssment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2016 0607/13/m/j/16 14 (a) complete the statement. the graph of y = f(x) is translated by the vector \uf8f7 \uf8f8\uf8f6\uf8ec \uf8ed\uf8eb \u221210 onto the graph of y = [1] (b) the function f( x) = 12 \u2013 3 x is defined for 2 x 9. write down the range of f( x). [2] 15 diagram 1 diagram 2 diagram 3 diagram 4 look at the patterns of grey and white squares. (a) complete the table to show the number of small squares in each diagram. diagram 1 2 3 4 small white squares 1 4 small grey squares 8 12 [2] (b) for diagram 8, write down the number of small white squares. [1] (c) write down a rule to find the number of small grey squares in diagram n. [2] " }, "0607_s16_qp_21.pdf": { "1": "this document consists of 11 printed pages and 1 blank page. dc (lk/ar) 115879/3 \u00a9 ucles 2016 [turn overcambridge international examinations cambridge international general certificate of secondary education * 9 9 8 9 7 3 9 1 8 6 * cambridge international mathematics 0607/21 paper 2 (extended) may/june 2016 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.", "2": "2 0607/21/m/j/16 \u00a9 ucles 2016formula list for the equation ax bx c02+ + = xab b ac 242!=- - curved surface area, a, of cylinder of radius r, height h. r a rh2= curved surface area, a, of cone of radius r, sloping edge l. r a rl= curved surface area, a, of sphere of radius r. r a r42= v olume, v, of pyramid, base area a, height h. v ah31= v olume, v, of cylinder of radius r, height h. rv r h2= v olume, v, of cone of radius r, height h. r v r h31 2= v olume, v, of sphere of radius r. r v r34 3= sin sin sin aa bb cc= = cos a b c bc a 22 2 2= + - sinbc a21area=a c bcb a", "3": "3 0607/21/m/j/16 \u00a9 ucles 2016 [turn overanswer all the questions. 1 work out. (a) .0 048 . [1] (b) 54 41- \b\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd [2] 2 (a) shade two more squares so that this shape has exactly one line of symmetry. [1] (b) shade two more triangles so that this shape has rotational symmetry of order 3. [1]", "4": "4 0607/21/m/j/16 \u00a9 ucles 20163 by rounding each number to 1 significant figure, estimate the value of this calculation. show all your working. . .. 523 99 61137 289# + . [2] 4 a2 3 75 2 3# #= b2 3 53 4# #= leaving your answer as the product of prime factors, find (a)\bb2, . [1] (b) the highest common factor (hcf) of \ba and b, . . [1] (c) the lowest common multiple (lcm) of a\band b. \b\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd [2]", "5": "5 0607/21/m/j/16 \u00a9 ucles 2016 [turn over5 luis has a large jar containing red, yellow, green and blue beads. he takes a bead at random from the jar, notes its colour and replaces it. he repeats this 200 times. the table shows his results. colour red yellow green blue number of beads26 72 64 38 relative frequency (a) complete the table to show the relative frequencies. [2] (b) (i) there are 5000 beads in the jar altogether. estimate the number of green beads in the jar. . [1] (ii) explain why this is a good estimate. ... .. [1] 6 solve. x x 2 312 -+= . [3]", "6": "6 0607/21/m/j/16 \u00a9 ucles 20167 u = {integers from 1 to 18} f = {factors of 12} m = {multiples of 3} e = {even numbers} (a) complete the venn diagram by putting the numbers 2, 3, 4, 8, 12, 15 and 18 in the correct subsets. f 1 69 10 1416 e513 71117mu [2] (b) list the members of (i) ( )e f m, , l, . [1] (ii) e m f + + l l . . [1] 8 solve. ( )x x2 3 2 3 1 2+ - . [3]", "7": "7 0607/21/m/j/16 \u00a9 ucles 2016 [turn over9 not to scale 130\u00b0 ocda b a, b, c and d are points on the circle centre o. angle bod = 130\u00b0. (a) find angle dcb . angle dcb\b=\b [1] (b) find angle bad . angle bad\b=\b [1]", "8": "8 0607/21/m/j/16 \u00a9 ucles 201610 factorise completely. (a) 12x2 \u2013 27xy . [2] (b) 4a2 + 8ab \u2013 ac \u2013 2bc \b\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd [2] 11 rationalise the denominator. 71 \b\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd [1]", "9": "9 0607/21/m/j/16 \u00a9 ucles 2016 [turn over12 q r bap write the vectors p, q and r in terms of a and b . p = \b\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd q = r = \b\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd [3]", "10": "10 0607/21/m/j/16 \u00a9 ucles 201613 3060 \u201330\u201360 901201501802102402703003302 \u20132y x\u00b0 0 the graph of y\b=\basin (x + b)\u00b0 is shown in the diagram. find the value of a and the value of b. a = b = [2]", "11": "11 0607/21/m/j/16 \u00a9 ucles 201614 o pqy xnot to scale the diagram shows a sketch of the graph of y\b=\bax2\b+\bbx\ufffd o is the point (0, 0), p\bis the point (4, 0) and \bq is the point (8, 96). find the value of a and the value of b. a = \b b\b=\b\b\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd [3]", "12": "12 0607/21/m/j/16 \u00a9 ucles 2016permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity . to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_s16_qp_22.pdf": { "1": "this document consists of 8 printed pages. dc (lk/sg) 114971/1 \u00a9 ucles 2016 [turn overcambridge international examinations cambridge international general certificate of secondary education * 5 2 9 4 0 0 2 5 2 1 * cambridge international mathematics 0607/22 paper 2 (extended) may/june 2016 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.", "2": "2 0607/22/m/j/16 \u00a9 ucles 2016formula list for the equation ax bx c02+ + = xab b ac 242!=- - curved surface area, a, of cylinder of radius r, height h. r a rh2= curved surface area, a, of cone of radius r, sloping edge l. r a rl= curved surface area, a, of sphere of radius r. r a r42= v olume, v, of pyramid, base area a, height h. v ah31= v olume, v, of cylinder of radius r, height h. rv r h2= v olume, v, of cone of radius r, height h. r v r h31 2= v olume, v, of sphere of radius r. r v r34 3= sin sin sin aa bb cc= = cos a b c bc a 22 2 2= + - sinbc a21area=a c bcb a", "3": "3 0607/22/m/j/16 \u00a9 ucles 2016 [turn overanswer all the questions. 1 work out 1 321 31+ . . [2] 2 increase 1 h 30 min by 10%. ... h ... min [2] 3 42\u00b0d c a bnot to scale in the diagram, dc is parallel to ab and ac = ab. work out angle acb . angle acb = ... [2]", "4": "4 0607/22/m/j/16 \u00a9 ucles 20164 tp1 2= rearrange the formula to write p in terms of t. p = [2] 5 a biased die, that has six faces, is numbered 1 to 6. the table shows the results when the die is rolled 60 times. number 1 2 3 4 5 6 frequency 3 12 8 16 7 14 (a) jose rolls the die. find the probability that the number shown is even. . [1] (b) jose rolls the die 1200 times. find the expected number of times that the number shown on the die is even. . [1] 6 solve the simultaneous equations. 3x \u2013 2y = 7 5x + 2y = 1 x = y = [2]", "5": "5 0607/22/m/j/16 \u00a9 ucles 2016 [turn over7 work out 5 108 10 127 ## - . give your answer in standard form. . [2] 8 solve the inequality. x x9 6 22- + . [2] 9 (a) x x xp 3 5'= find the value of p. p = [1] (b) work out. (i) 62^h . [1] (ii) 81 31- . [2]", "6": "6 0607/22/m/j/16 \u00a9 ucles 201610 the line 2 x + 3y = 36 intersects the x-axis at p and the y-axis at q. m is the midpoint of pq. find the column vector om where o is the origin. \u239b \u239e \u239c \u239f \u239d \u23a0 [4] 11 factorise completely. p q xp xq 2 2- + - . [2] 12 rationalise the denominator. 125 + . [2]", "7": "7 0607/22/m/j/16 \u00a9 ucles 2016 [turn over13 the area of a semicircle is 32\u03c0 cm2. work out the perimeter of the semicircle. give your answer in terms of \u03c0. ... cm [3] 14 00.20.40.60.81.01.21.41.61.8 x 10 20 30frequency density complete the frequency table using the information in the histogram. class interval frequency x0 201g x 20 301g [2] questions 15, 16 and 17 are printed on the next page", "8": "8 0607/22/m/j/16 \u00a9 ucles 2016permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity . to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.15 yx1\\ when x = 4, y = 3. find y in terms of x. y = [2] 16 log log log log y2 3 3 2 6 = + - find the value of y. y = [3] 17 describe fully the single transformation that maps the graph of y = cosx onto the graph of y = 3cosx. ... .. [2]" }, "0607_s16_qp_23.pdf": { "1": "this document consists of 8 printed pages. dc (nh/sw) 115871/2 \u00a9 ucles 2016 [turn over * 5 4 7 0 2 7 1 6 0 9 * cambridge international mathematics 0607/23 paper 2 (extended) may/june 2016 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/23/m/j/16 \u00a9 ucles 2016formula list for the equation ax bx c02+ + = xab b ac 242!=- - curved surface area, a, of cylinder of radius r, height h. r a rh2= curved surface area, a, of cone of radius r, sloping edge l. r a rl= curved surface area, a, of sphere of radius r. r a r42= v olume, v, of pyramid, base area a, height h. v ah31= v olume, v, of cylinder of radius r, height h. rv r h2= v olume, v, of cone of radius r, height h. r v r h31 2= v olume, v, of sphere of radius r. r v r34 3= sin sin sin aa bb cc= = cos a b c bc a 22 2 2= + - sinbc a21area=a c bcb a", "3": "3 0607/23/m/j/16 \u00a9 ucles 2016 [turn overanswer all the questions. 1 alex drives 40 km to work at a speed of 50 km/h. he leaves home at 07 45. find the time he arrives at work. \t \t .. [3] 2 alexis and bertrand share a sum of money in the ratio 3 : 5. alexis receives $36. work out how much bertrand receives. \t \t$ ... [2] 3 11 16 8 9 14 6 20 16 12 10 find the median of these ten numbers. \t \t .. [2]", "4": "4 0607/23/m/j/16 \u00a9 ucles 20164 (a) a regular polygon has 12 sides. work out the sum of the interior angles of the polygon. \t \t .. [2] (b) the interior angle of a regular polygon is 165\u00b0. find the number of sides of this polygon. \t \t .. [2] 5 the total cost of 2 kg of apples and 1.5 kg of pears is $9.70 . apples cost $2.60 per kilogram. find the cost of 1 kg of pears. \t \t$ [3]", "5": "5 0607/23/m/j/16 \u00a9 ucles 2016 [turn over6 find the next term in each of these sequences. (a) 81, 77, 72, 66, 59, ... [1] (b) 3, \u20136, 12, \u201324, 48, ... [1] (c) 16, 8, 4, 2, 1, ... [1] 7 work out, giving your answer in standard form. (a) 7.5 10 4 104 6# #+- - ^ ^ h h \t \t .. [2] (b) 7.5 10 4 104 6# # #- - ^ ^ h h \t \t .. [2]", "6": "6 0607/23/m/j/16 \u00a9 ucles 20168 expand the brackets. 7x x2 3- ^ h \t \t\t\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd [2] 9 write this list of numbers in order starting with the smallest. 32 65% 0.7 0.069 0.62 < < < < [2] smallest 10 expand the brackets and simplify. 2 3 4 3 2 3 x x- - - ^ ^ h h \t \t .. [2]", "7": "7 0607/23/m/j/16 \u00a9 ucles 2016 [turn over11 (a) simplify. 3 4 12 7 3- ^ h \t \t .. [2] (b) rationalise the denominator. 3 27 - \t \t .. [2] 12 solve the simultaneous equations. you must show all your working. 3 2 5 2 5 3x y x y+ = - - = \t \t\tx\t= ... \t \t\ty = ... [4] question 13 is printed on the next page.", "8": "8 0607/23/m/j/16 \u00a9 ucles 201613 (a) sketch the graph of 2 y x3= + . give the co-ordinates of the point where the graph crosses the y-axis. 0y x \t \t( . , . ) [2] (b) sketch the graph of 2 cos y x= for 180\u00b0 180\u00b0xg g - . give the co-ordinates of the point where the graph crosses the y-axis. 0\u2013180 180y x \t \t( . , . ) [3] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_s16_qp_31.pdf": { "1": "this document consists of 16 printed pages. dc (lk/cgw) 115323/3 \u00a9 ucles 2016 [turn overcambridge international examinations cambridge international general certificate of secondary education * 0 0 1 1 9 8 9 2 0 8 * cambridge international mathematics 0607/31 paper 3 (core) may/june 2016 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.", "2": "2 0607/31/m/j/16 \u00a9 ucles 2016formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v= ah31 v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = r h31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/31/m/j/16 \u00a9 ucles 2016 [turn overanswer all the questions. 1 (a) write 356.31 (i) correct to 1 decimal place, .. [1] (ii) correct to 2 significant figures, .. [1] (iii) correct to the nearest 100, .. [1] (iv) in standard form. .. [1] (b) (i) calculate . .168 9 612- . write down all the figures shown on your calculator, giving your answer as a decimal. .. [1] (ii) myrto estimates that the answer to part (b)(i) is 300. (a) find the difference between myrto\u2019s estimate and your answer to part (b)(i) . .. [1] (b) write this difference as a percentage of your answer to part (b)(i) . % [1]", "4": "4 0607/31/m/j/16 \u00a9 ucles 20162 (a) write 4 \u00d7 4 \u00d7 4 \u00d7 4 \u00d7 4 \u00d7 4 (i) as a power of 4, .. [1] (ii) as an integer. .. [1] (b) find the value of (i) 4 44 2+, .. [1] (ii) 4 44 0-. .. [1] (c) write 44 210 as a power of 4. .. [1] ", "5": "5 0607/31/m/j/16 \u00a9 ucles 2016 [turn over3 tingwei buys 2 kg of cheese. the cheese costs $13.50 for one kilogram. (a) work out how much tingwei pays for the 2 kg of cheese. $ . [1] (b) he uses all the cheese to make 200 cheese balls. find the mass, in grams , of one cheese ball. . g [1] (c) (i) he sells all these cheese balls at a school fair for $0.25 each. work out how much money he received. $ . [1] (ii) the profit goes to the school charity. work out how much money goes to the school charity. $ . [1] (d) the school fair makes a total profit of $460. write the profit that tingwei made as a fraction of $460. give your answer in its simplest form. .. [2] ", "6": "6 0607/31/m/j/16 \u00a9 ucles 20164 the number of strawberries in each of 20 boxes is listed below. 32 28 27 32 33 28 34 28 29 29 28 28 33 31 33 33 30 29 29 26 (a) complete the frequency table. number of strawberries26 27 28 29 30 31 32 33 34 frequency 1 1 1 [2] (b) find (i) the range, .. [1] (ii) the mode, .. [1] (iii) the median, .. [1] (iv) the mean. .. [1] (c) one of these boxes of strawberries is chosen at random. find the probability that it contains (i) exactly 33 strawberries, .. [1] (ii) fewer than 30 strawberries. .. [1]", "7": "7 0607/31/m/j/16 \u00a9 ucles 2016 [turn over5 (a) a b c d 5 221= - - (i) find the value of a when b = 2, c = 3 and d = 6. .. [2] (ii) find the value of b when a = 12, c = 1 and d = 4. .. [3] (b) find the value of 7 p \u2212 4q when p = \u22123 and q = \u20132. .. [2] (c) rearrange 2 y = 3x \u2212 9 to make x the subject. x = . [2] (d) the mass of 1 pomegranate and 2 kiwi fruit is 480 g. the mass of 1 pomegranate and 6 kiwi fruit is 840 g. find the mass of 1 pomegranate and the mass of 1 kiwi fruit. show all your working. 1 pomegranate = . g 1 kiwi fruit = . g [4]", "8": "8 0607/31/m/j/16 \u00a9 ucles 20166 30 people were asked where they were going on holiday. the results are to be shown in a pie chart. countryindia spain south africa united states australia number of people5 12 3 6 4 sector angle 60\u00b0 48\u00b0 (a) calculate the sector angle for spain. .. [2] (b) complete the pie chart. label each sector. australia india [3] ", "9": "9 0607/31/m/j/16 \u00a9 ucles 2016 [turn over7 (a) fe a cb105\u00b0 not to scale dg h afb and cgd are parallel lines. efgh is a straight line and angle afe = 105\u00b0. find (i) angle efb, angle efb = .. [1] (ii) angle cgf . angle cgf = .. [1] (b) not to scalea od c br\u00b0 s\u00b0 p\u00b070\u00b0 q\u00b0 aob and cod are diameters of a circle, centre o. the lines ad and cb are parallel and angle cab = 70\u00b0. find the values of p, q, r and s. p = q = r = s = [4]", "10": "10 0607/31/m/j/16 \u00a9 ucles 20168 not to scale2.5 km40\u00b0h c s b the diagram shows four straight cycle tracks hb, hc, bc and cs. bc = cs and hc = 2.5 km. angle hbc = 90\u00b0 and angle bhc = 40\u00b0. (a) abimela cycles from home, h, to school, s, each day along cycle track hc and cs. (i) use trigonometry to find the distance bc. .. km [2] (ii) find the distance abimela cycles to school. .. km [1] (b) one day track hc is blocked and she has to cycle along tracks hb, bc and cs. find the distance hb. .. km [2] (c) find the extra distance that abimela now has to cycle to school. .. km [1]", "11": "11 0607/31/m/j/16 \u00a9 ucles 2016 [turn over9 1 02 123456783456789y x (a) on the grid, plot the points a(2, 3) and b(5, 7). draw the line ab. [2] (b) write down the co-ordinates of the midpoint of ab. ( , ) [1] (c) find the gradient of ab. .. [2] (d) find the equation of the line parallel to ab that passes through the point (0, 4). .. [2]", "12": "12 0607/31/m/j/16 \u00a9 ucles 201610 15 cm12 cm 4 cmnot to scale the diagram shows 12 solid cylinders packed into a box. each cylinder has radius 1 cm and length 15 cm. (a) (i) find the volume of one cylinder. . cm3 [1] (ii) work out the volume of 12 cylinders. . cm3 [1] (b) the box measures 15 cm by 12 cm by 4 cm. find the volume of the box. . cm3 [1] (c) find the volume of the box not taken up by the cylinders. . cm3 [1] (d) write your answer to part (c) as a percentage of the total volume of the box. % [1]", "13": "13 0607/31/m/j/16 \u00a9 ucles 2016 [turn over11 22 \u22122 \u22124 \u2212646810y 4 6 \u22126\u22124\u221220 8 10xp the diagram shows a pentagon, p. (a) draw the image of p after a reflection in the y-axis. label this image q. [1] (b) draw the image of p after a translation by the vector 2 6-j lkkn poo . label this image r. [2] (c) draw the image of p after an enlargement, scale factor 3, centre (0, 0). label this image s. [2] (d) find the ratio length of horizontal side of s : length of horizontal side of p. : [1] (e) congruent regular similar choose a word from the list to complete the statement. p and s are \u2026\u2026\u2026\u2026\u2026..\u2026\u2026\u2026 shapes. [1]", "14": "14 0607/31/m/j/16 \u00a9 ucles 201612 the masses of 200 meerkats are recorded in the frequency table. mass ( x grams) frequency x 200 3001g 5 x 00 00 3 41g 10 x 00 00 4 51g 26 x 00 00 5 61g 34 x 00 00 6 71g 40 x 00 00 7 81g 62 x 00 00 8 91g 18 x 00 00 9 101g 5 total 200 (a) write down the modal group. x1g [1] (b) (i) show that the midpoint of the first group is 250. [1] (ii) find an estimate of the mean mass of these 200 meerkats. . g [2] (c) complete the cumulative frequency table. mass ( x grams)cumulative frequency x300g 5 x400g x500g x 006g x 007g x 008g x900g 195 x1000g 200 [2] ", "15": "15 0607/31/m/j/16 \u00a9 ucles 2016 [turn over (d) complete the cumulative frequency curve. 20 100 200 300 400 500 mass (grams)600 700 800 900 1000406080 0100120 cumulative frequency140160180200 x [3] (e) use your graph to find (i) the median, . g [1] (ii) the inter-quartile range, . g [2] (iii) the number of meerkats with a mass of more than 850 g. .. [2] question 13 is printed on the next page.", "16": "16 0607/31/m/j/16 \u00a9 ucles 2016permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.13 0 \u22123 310y x \u221210 ( )fx xx2 2= + (a) on the diagram, sketch the graph of y = f(x) from x = \u22123 to x = 3. [4] (b) write down the equation of the vertical asymptote for this graph. .. [1] (c) find the co-ordinates of the local minimum point. ( , ) [1] (d) write down the number of solutions of y = f(x) when y = 6. .. [1]" }, "0607_s16_qp_32.pdf": { "1": "this document consists of 18 printed pages and 2 blank pages. dc (lk/cgw) 115324/3 \u00a9 ucles 2016 [turn overcambridge international examinations cambridge international general certificate of secondary education * 8 2 3 4 0 5 3 6 4 6 * cambridge international mathematics 0607/32 paper 3 (core) may/june 2016 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.", "2": "2 0607/32/m/j/16 \u00a9 ucles 2016formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v =al v olume, v, of pyramid, base area a, height h. v= ah31 v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = r h31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/32/m/j/16 \u00a9 ucles 2016 [turn overanswer all the questions. 1 (a) write 9427 (i) in words, .. [1] (ii) correct to the nearest 10. .. [1] (b) here are four digits. 9 4 2 7 (i) add two of these digits to make a square number. ... + ... = ... [1] (ii) add two of these digits to make a factor of 48. ... + ... = ... [1] (iii) add two of these digits to make a prime number. ... + ... = ... [1]", "4": "4 0607/32/m/j/16 \u00a9 ucles 20162 (a) tariq does a survey of every house in his street. he records the number of children in each house. the table shows his results. number of children0 1 2 3 4 5 frequency 4 9 7 3 0 1 (i) find how many houses were in the survey altogether. .. [1] (ii) complete the bar chart to show tariq\u2019s results. 1 0 1 0 2 3 4 5 number of children23456 frequency78910 [2]", "5": "5 0607/32/m/j/16 \u00a9 ucles 2016 [turn over (b) a survey of the number of children in each house was carried out in another street. tariq draws the pie chart below to show the results. 2>20 1 (i) write down the most common number of children in a house. .. [1] (ii) explain the meaning of tariq\u2019s label >2. .. [1] (iii) measure the angle for 0 children in a house. .. [1] (iv) 15 houses in this survey had 1 child. work out the number of houses altogether in this survey. .. [2]", "6": "6 0607/32/m/j/16 \u00a9 ucles 20163 sophie\u2019s garden is a rectangle. 8 mnot to scale 10 m (a) work out the perimeter of the garden. m [1] (b) work out the area of the garden. give the units of your answer. . .. [3] (c) sophie buys 12 m3 of soil. she spreads the soil evenly over the whole of the garden. work out the depth of this soil. give your answer in centimetres. .. cm [3] (d) ben\u2019s garden is also a rectangle. it is an enlargement of sophie\u2019s garden. one side of ben\u2019s garden is 20 m. work out the two possible measurements of the other side of ben\u2019s garden. .. m and .. m [2]", "7": "7 0607/32/m/j/16 \u00a9 ucles 2016 [turn over4 the total cost of having a party in a hotel is given by this formula. total cost = cost of room hire + cost per person \u00d7 number of people the table shows the costs for two different rooms in the hotel. room name cost of room hire ($) cost per person ($) disco room 450 15 ballroom 575 11 (a) work out the total cost for a party of 62 people in the disco room. $ . [2] (b) geta has $1000 to spend on her birthday party. work out the largest number of people that can go to her party. show clearly how you decide. .. [5]", "8": "8 0607/32/m/j/16 \u00a9 ucles 20165 12345 \u20135\u20134\u20133\u20132\u201310 \u20134\u20133\u20132\u20131 123456xpqb ay (a) write down the co-ordinates of a. \t \t \t ( , ) [1] (b) write down the co-ordinates of b. \t \t \t ( , ) [1] (c) on the grid, plot the point (\u20133, \u20132). label the point c. [1] (d) write down the co-ordinates of the midpoint of ab. \t \t \t ( , ) [1] (e) reflect the line ab in the y-axis. [1] (f) describe fully the single transformation that maps ab onto pq. ... .. [2]", "9": "9 0607/32/m/j/16 \u00a9 ucles 2016 [turn over6 (a) here are the first three patterns in a sequence. pattern 1 x xpattern 2 x xpattern 3 x x x x x x x xpattern 4 (i) in the space above, draw pattern 4. [1] (ii) work out the number of crosses in pattern 15. .. [1] (b) here are the first five terms of a different sequence. 21 17 13 9 5 (i) write down the next two terms in this sequence. , [2] (ii) find an expression for the nth term of this sequence. .. [2]", "10": "10 0607/32/m/j/16 \u00a9 ucles 20167 in the diagram, acd is a straight line. 55\u00b0b d c a110\u00b0not to scale 10 cm (a) is angle bcd acute, obtuse or reflex? .. [1] (b) (i) find angle acb . angle acb = . [1] (ii) find the length of bc. give a reason for your answer. bc = cm because ... .. [3]", "11": "11 0607/32/m/j/16 \u00a9 ucles 2016 [turn over8 (a) simplify. 4a + 3a \u2013 a .. [1] (b) multiply out the brackets. x(3x2 \u2013 5) .. [2] (c) solve. 2x \u2013 10 = 8 x = . [2] (d) simplify. (i) t\t4 \u00d7 t\t3 .. [1] (ii) tt 420 25 .. [2]", "12": "12 0607/32/m/j/16 \u00a9 ucles 20169 (a) write this ratio in its simplest form. 1 hour : 24 minutes .. [2] (b) carmen works in an office. she spends time on the phone and on the computer in the ratio 5 : 7. one day carmen worked for a total of 6 hours. calculate how long carmen spent on the phone. ... hours [2] (c) carmen recorded the number of hours she worked each day for ten days. 6 7 6 521 3 121 5 6 8 7 (i) work out the range of these times. .. hours [1] (ii) work out the mean time. .. hours [1]", "13": "13 0607/32/m/j/16 \u00a9 ucles 2016 [turn over10 the length and weight of each of eight new-born babies are shown in the table below. length (cm) 51 56 50 44 49 54 48 47 weight (kg) 3.4 4.2 3.6 1.6 2.4 3.6 2.8 2.1 (a) on the grid, complete the scatter diagram to show this information. the first five points have been plotted for you. 45 3 2 40 45 50 length (cm)55 60weight (kg) 1 0 [2] (b) what type of correlation is shown in your diagram? .. [1] (c) draw a line of best fit on your scatter diagram. [1] (d) use your line of best fit to estimate the weight of a new-born baby of length 53 cm. ... kg [1]", "14": "14 0607/32/m/j/16 \u00a9 ucles 201611 (a) a car wheel has a diameter of 63 cm. calculate the circumference of this wheel and show that it is 198 cm, correct to the nearest cm. [2] (b) on a journey, this car wheel rotates 172 times in 12 seconds. calculate the average speed of the car in metres per second. . m/s [4]", "15": "15 0607/32/m/j/16 \u00a9 ucles 2016 [turn over12 each month, ravi earns $5850 plus 5% of any sales he makes. (a) one month ravi made sales of $153 000. calculate the total amount that ravi earned that month. $ ... [3] (b) the following month, ravi made sales of $172 000. calculate the percentage increase in the value of the sales he made. % [3]", "16": "16 0607/32/m/j/16 \u00a9 ucles 201613 each member of a class of students was asked which languages they could speak. they could all speak english. the only other languages were french ( f) and spanish ( s). the venn diagram below shows the results. fs12 63 8u (a) find the total number of students in the class. .. [1] (b) find the number of students in (i) f s,, .. [1] (ii) ( )f s+ l. .. [1] (c) a student is chosen at random from the class. find the probability that this student (i) speaks french, .. [1] (ii) speaks english, french and spanish, .. [1] (iii) speaks exactly two languages. .. [1]", "17": "17 0607/32/m/j/16 \u00a9 ucles 2016 [turn over14 70 cm90 cmnot to scale xy\u00b0 (a) calculate x. x = cm [3] (b) use trigonometry to calculate angle y. y = [2]", "18": "18 0607/32/m/j/16 \u00a9 ucles 201615 20 \u201310\u20132 6xy (a) on the diagram, sketch the graph of y x x4 72= - + for x2 6g g- . [2] (b) find the co-ordinates of the local minimum point. (... , ...) [1] (c) on the diagram, sketch the graph of y = 2x + 3. [2] (d) find the x co-ordinate of each of the points of intersection of y = x2 \u2013 4x + 7 and y = 2x + 3. x = ... and x = ... [2]", "19": "19 0607/32/m/j/16 \u00a9 ucles 2016blank page", "20": "20 0607/32/m/j/16 \u00a9 ucles 2016permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_s16_qp_33.pdf": { "1": "this document consists of 18 printed pages and 2 blank pages. dc (lk/cgw) 115325/4 \u00a9 ucles 2016 [turn overcambridge international examinations cambridge international general certificate of secondary education * 7 6 5 8 3 7 4 3 0 9 * cambridge international mathematics 0607/33 paper 3 (core) may/june 2016 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.", "2": "2 0607/33/m/j/16 \u00a9 ucles 2016formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v =al v olume, v, of pyramid, base area a, height h. v= ah31 v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = r h31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/33/m/j/16 \u00a9 ucles 2016 [turn overanswer all the questions. 1 1 02 123456a cb 78345678y x (a) write down the co-ordinates of c. ( ... , ... ) [1] (b) write down the mathematical name of triangle abc . .. [1] (c) measure angle acb . .. [1] (d) on the diagram, draw the line of symmetry of triangle abc . [1]", "4": "4 0607/33/m/j/16 \u00a9 ucles 20162 sophie is tiling three of the rectangular walls of a small bathroom. the diagram shows the dimensions of the three walls. 1.5 m 2.1 m 2.1 m 3 mnot to scale3 m (a) work out the total area of these three walls. give your answer in square centimetres. . cm2 [4]", "5": "5 0607/33/m/j/16 \u00a9 ucles 2016 [turn over (b) sophie chooses tiles measuring 30 cm by 30 cm to cover the three walls. (i) work out how many of these tiles she needs to cover all three walls. .. [3] (ii) the tiles can be plain or patterned. each type of tile is sold in boxes of 10. sophie decides to use 1 patterned tile for every 4 plain tiles. work out the number of boxes of each type of tile that sophie needs to buy. .. boxes of patterned tiles .. boxes of plain tiles [5] (c) the bathroom is a cuboid. work out the volume of the bathroom. m3 [2]", "6": "6 0607/33/m/j/16 \u00a9 ucles 20163 ravi has 1 green sweet, 2 red sweets, 3 orange sweets and 6 yellow sweets in a bag. (a) he picks a sweet at random from the bag. (i) which colour sweet is least likely to be picked? .. [1] (ii) which colour sweet has a 50% chance of being picked? .. [1] (iii) find the probability that he picks a red sweet. .. [1] (iv) find the probability that he picks a purple sweet. .. [1] (b) ravi eats two of the sweets from the bag. from the ten sweets remaining in the bag \u2022 the probability of picking a yellow sweet stays the same \u2022 two of the colours have equal probability of being picked. work out the number of sweets of each colour that could be in the bag now. green .. red .. orange .. yellow .. [3]", "7": "7 0607/33/m/j/16 \u00a9 ucles 2016 [turn over4 (a) an electrician charges his customers using this formula. charge = $65 \u00d7 number of hours + $30 (i) work out the charge when the job takes 4 hours. $ . [2] (ii) for another job, the electrician charges $485. work out the length of time this job takes. ... hours [2] (b) the electrician uses his van to travel to work. one journey of 8 km takes 20 minutes. calculate the average speed of this journey. km/h [2]", "8": "8 0607/33/m/j/16 \u00a9 ucles 20165 (a) 15 students go on a school trip. the age of each student in years, correct to 1 decimal place, is listed below. 13.4 14.7 13.1 15.5 15.3 15.2 14.1 14.2 16.4 14.7 15.2 15.9 13.1 15.1 16.0 (i) complete the ordered stem and leaf diagram to show this information. 16.0 has been entered for you. 13 14 15 16 0 key: ... ... represents . [3] (ii) work out the range. years [1] (iii) find the median. years [1] (b) another student is 14 years 7 months old. write this student\u2019s age in years as a decimal, correct to 1 decimal place. years [2]", "9": "9 0607/33/m/j/16 \u00a9 ucles 2016 [turn over6 here is a set of numbers. a = {1, 4, 6, 7, 8, 9, 15} (a) from this set choose (i) a factor of 12, .. [1] (ii) 81, .. [1] (iii) a multiple of 5, .. [1] (iv) 23, .. [1] (v) a prime number. .. [1] (b) here is another set of numbers. b = {2, 4, 6, 8, 10, 12, 14} complete the diagram for set a and set b. a b 1 154 12 [3]", "10": "10 0607/33/m/j/16 \u00a9 ucles 20167 (a) reflect the triangle in the line pq. p q [1] (b) rotate the triangle through 90\u00b0 clockwise about point c. c [2]", "11": "11 0607/33/m/j/16 \u00a9 ucles 2016 [turn over (c) translate the triangle by the vector 3 2j lkkn poo . [2] (d) write down as much information as you can about the single transformation that maps triangle a onto triangle b. a b .. [2]", "12": "12 0607/33/m/j/16 \u00a9 ucles 20168 (a) solve these equations. (i) x 2 = 4 x = . [1] (ii) x + 3 = \u2212 1 x = . [1] (iii) 2(6x \u2013 5) = 8 x = . [3] (b) solve these simultaneous equations. x + y = 3 x \u2013 y\u2009 = \u22127 x = ... y = ... [2]", "13": "13 0607/33/m/j/16 \u00a9 ucles 2016 [turn over9 (a) here are some test results for akbar. subjectenglish (out of 60)mathematics (out of 40)science (out of 70) mark 48 34 49 in which subject did akbar get the highest percentage? show clearly how you decide. [3] (b) last year akbar\u2019s mark in his history test was 60. this year his mark increased by 35%. work out akbar\u2019s mark in his history test this year. .. [3]", "14": "14 0607/33/m/j/16 \u00a9 ucles 201610 (a) show that (4, 5) is a point on the line y = 2x \u2013 3. [2] (b) write down the gradient of the line y = 2x \u2013 3. .. [1] (c) write down the equation of the line parallel to y = 2x \u2013 3 that passes through the point (0, 1). . [2] (d) rearrange this equation to make x the subject. y = 2x \u2013 3 x = [2]", "15": "15 0607/33/m/j/16 \u00a9 ucles 2016 [turn over11 the probability that joe is late for school on any day is 0.3 . (a) complete the tree diagram for two days. first day second day late .. not latenot latelate not latelate0.3 [2] (b) work out the probability that joe will be late for school on both days. .. [2]", "16": "16 0607/33/m/j/16 \u00a9 ucles 201612 (a) simplify. xx 2182 .. [2] (b) factorise fully. 3x2 + 6x .. [2] (c) show the inequality x3h\u2009 on the number line. 10\u20131\u20132\u20133 5x 432 [1] (d) list the integer values which satisfy the inequality x4 71g. .. [1] (e) multiply out the brackets and simplify. (x + 3)(x \u2013 2) .. [2]", "17": "17 0607/33/m/j/16 \u00a9 ucles 2016 [turn over13 the diagram shows a flagpole that is held in position by two straight wires. the wires are attached to the flagpole 11.8 m above the ground. 11.8 mnot to scale y\u00b0x 7.2 m 15.2 m (a) calculate the length of the wire, x. ... m [2] (b) use trigonometry to calculate the size of angle y. .. [2]", "18": "18 0607/33/m/j/16 \u00a9 ucles 201614 0 \u22123.5 2.525 xy \u221210 (a) on the diagram, sketch the graph of y = 2x3 + 3x2 \u2013 12x\u2009\u2009\u2009for . .x 3 5 2 5 g g- . [2] (b) write down the co-ordinates of the local maximum and the local minimum. local maximum ( . , . ) local minimum ( . , . ) [2] (c) write down the co-ordinates of the points where the curve crosses the axes. ( . , . ) ( . , . ) ( . , . ) [3]", "19": "19 0607/33/m/j/16 \u00a9 ucles 2016blank page", "20": "20 0607/33/m/j/16 \u00a9 ucles 2016permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_s16_qp_41.pdf": { "1": "this document consists of 20 printed pages. dc (kn/sg) 115864/3 \u00a9 ucles 2016 [turn overcambridge international examinations cambridge international general certificate of secondary education * 8 3 9 8 4 2 2 7 1 6 * cambridge international mathematics 0607/41 paper 4 (extended) may/june 2016 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for p, use your calculator value. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.", "2": "2 0607/41/m/j/16 \u00a9 ucles 2016formula list for the equation ax bx c02+ + = xab b ac 242!=- - curved surface area, a, of cylinder of radius r, height h. r a rh2= curved surface area, a, of cone of radius r, sloping edge l. r a rl= curved surface area, a, of sphere of radius r. r a r42= v olume, v, of pyramid, base area a, height h. v ah31= v olume, v, of cylinder of radius r, height h. rv r h2= v olume, v, of cone of radius r, height h. r v r h31 2= v olume, v, of sphere of radius r. r v r34 3= sin sin sin aa bb cc= = cos a b c bc a 22 2 2= + - sinbc a21area=a c bcb a", "3": "3 0607/41/m/j/16 \u00a9 ucles 2016 [turn overanswer all the questions. 1 (a) annelise buys a car that is one year old for $13 600. the value of this car has reduced by 15% of the value when it was new. (i) calculate the value of the car when it was new. \t $ [3] (ii) after the first year the car reduces in value by 11% each year for the next 3 years. calculate the value of the car after these 3 years. \t $ [3] (b) boris buys a car for $23 000. the value of this car reduces by 8% each year. find the number of complete years it takes for the value of the car to fall below $11 500. \t .. [3]", "4": "4 0607/41/m/j/16 \u00a9 ucles 20162 the frequency of a radio wave, f , is inversely proportional to the wavelength, l metres. a radio station broadcasts on a frequency of 93.7 and a wavelength of 3.2 m. (a) find a formula for f, in terms of l, writing any constants correct to 3 significant figures. \t f = [3] (b) chat radio broadcasts with a wavelength of 2.8 m. find the frequency of chat radio. \t . [1] (c) allsports radio broadcasts with a frequency of 0.35 . find the wavelength of allsports radio. \t .. m [2]", "5": "5 0607/41/m/j/16 \u00a9 ucles 2016 [turn over3 \u201311 02345 \u20131 12345678910 \u20132\u20133\u20134\u20135 \u20132 \u20133 \u20134 \u20135ay x (a) (i) draw the image of quadrilateral a after it has been reflected in the y-axis and then rotated through 90\u00b0 anti-clockwise about the origin. [3] (ii) describe fully the single transformation equivalent to reflection in the y-axis followed by rotation 90\u00b0 anti-clockwise about the origin. ... . [2] (b) (i) draw the image of quadrilateral a after a stretch, factor 3 with the y-axis invariant. label the image b. [2] (ii) describe fully the single transformation that maps the quadrilateral b back onto quadrilateral a. ... . [2]", "6": "6 0607/41/m/j/16 \u00a9 ucles 20164 12 cm40 cmnot to scale the diagram shows a solid trophy for a football tournament. the sphere on the top has a radius of 15 cm. the sphere rests on a cylinder with the same radius as the sphere and height 40 cm. the base is a cylinder with radius 25 cm and height 12 cm. (a) calculate the volume of the trophy. \t ... cm3 [4]", "7": "7 0607/41/m/j/16 \u00a9 ucles 2016 [turn over (b) the mass of the trophy is 15 kg. each member of the winning team receives a model of the trophy made from the same material. the model is similar to the real trophy and one-fifth of the height. (i) calculate the total height of each model trophy. \t cm [1] (ii) calculate the mass, in grams, of each model trophy. \t ... g [3]", "8": "8 0607/41/m/j/16 \u00a9 ucles 20165 in kim\u2019s game a player looks at a fixed number of objects on a tray for a length of time, t seconds. the player is then tested to find how many objects they remember. the table shows the results for 10 players. time in seconds (t)30 40 50 60 70 80 90 100 110 120 number of objects (n)8 10 15 12 16 20 18 23 19 25 (a) complete the scatter diagram. the first six points have been plotted for you. n 26 24 22 20 18 16 14 12 10 8 6 4 2 0 10 20 30 40 50 60 70 80 90 100 110 120tnumber of objects time in seconds [2] (b) what type of correlation is shown by the scatter diagram? \t . [1]", "9": "9 0607/41/m/j/16 \u00a9 ucles 2016 [turn over (c) (i) calculate the mean time. \t s [1] (ii) calculate the mean number of objects. \t . [1] (d) (i) find the equation of the regression line. give your answer in the form n m t c= + . \t n = [2] (ii) errol looks at the tray for 85 seconds. use your equation to estimate the number of objects he remembers. \t . [1]", "10": "10 0607/41/m/j/16 \u00a9 ucles 20166 (a) these are the first four terms of a sequence. 5 8 11 14 write down an expression in terms of n for the nth term, sn\t, of the sequence. \t sn = [2] (b) the nth term, tn\t, of another sequence is n n2 62-+ . write down the first four terms of this sequence. \t .. , .. , .. , .. [2] (c) the nth term of a third sequence, un\t, is given by unt 2 nn=+ . find an expression for un\t, in terms of n, giving your answer in its simplest form. \t un = [3] (d) the nth term of a fourth sequence is given by s un n+ . is 501 a term of this fourth sequence? give your reasons. because . [2]", "11": "11 0607/41/m/j/16 \u00a9 ucles 2016 [turn over7 a30 m36 mnot to scaleb c d68\u00b0 ab is a vertical tower of height 30 m. bc and bd are straight wires attached to b. a, c and d are on horizontal ground with \tc due west of d. angle bca = 68\u00b0 and bd = 36 m. (a) calculate ad. \t ad = m [3] (b) calculate ac and show that it rounds to 12.1 m, correct to 3 significant figures. [3] (c) calculate the bearing of a from d. \t\t . [3]", "12": "12 0607/41/m/j/16 \u00a9 ucles 20168 (a) 2 0 \u20134\u20133 3xy f() logx xx 1 22= + + ^ h (i) on the diagram, sketch the graph of f () y x=\tfor values of x between \u20133 and 3. [2] (ii) solve f ()x 0=. \t x = .. or x = ... [2] (iii) write down the equation of the asymptote to the graph of f () y x= . \t . [1] ", "13": "13 0607/41/m/j/16 \u00a9 ucles 2016 [turn over (b) (i) on this diagram, sketch the graph of log y x2 1= + ^ h for values of x between \u20133 and 3. 2 0 \u20134\u20133 3xy [2] (ii) describe a similarity between the graphs in part (a)(i) and part (b)(i) . ... . [1] (iii) explain the differences between the graphs in part (a)(i) and part (b)(i) . ... . [2]", "14": "14 0607/41/m/j/16 \u00a9 ucles 20169 hamish travels from perth to london by train. during the journey, the train stops in edinburgh. (a) the distance from perth to edinburgh is 65 km. the train travels at an average speed of 48.75 km/h for this part of the journey. find the time taken to travel from perth to edinburgh. give your answer in hours and minutes. \t ... h ... min [3] (b) the average speed for the whole journey from perth to london is 119.5 km/h. the distance from edinburgh to london is 632 km. find the average speed for the journey from edinburgh to london. \t km/h [5] (c) during the journey, the train travels through a tunnel of length 800 m. the train travels through this tunnel at 120 km/h. the train is 130 m long. calculate the time taken for the train to pass completely through the tunnel. give your answer in seconds. \t ... s [3]", "15": "15 0607/41/m/j/16 \u00a9 ucles 2016 [turn over10 a is the point (\u20132, \u20131) and b is the point (6, 3). (a) calculate ab. \t . [3] (b) the point p has co-ordinates ( x, y) and pa = pb. show that x y2 5+ = . [5] (c) if p is also on the line y x=, find the co-ordinates of p. \t ( , ..) [2]", "16": "16 0607/41/m/j/16 \u00a9 ucles 201611 60\u00b0 (3x \u2013 1) cm2x cm 9 cma b cnot to scale (a) use the cosine rule to show that x x7 4 80 02- - =. [4]", "17": "17 0607/41/m/j/16 \u00a9 ucles 2016 [turn over (b) (i) solve the equation x x7 4 80 02- - =. show all your working. \t x = .. or x = ... [3] (ii) find the length of ab and the length of bc. \t ab = .. cm \t bc = .. cm [2] (c) find the area of triangle abc . \t .. cm2 [2]", "18": "18 0607/41/m/j/16 \u00a9 ucles 201612 the table shows the masses in grams of 200 eggs. mass (m grams)45 1 m g\u20095050 1 m g\u20095555 1 m g\u20096060 1 m g\u20096565 1 m g\u20097070 1 m g\u20097575 1 m g\u200980 frequency 5 19 34 58 46 29 9 (a) calculate an estimate of the mean mass. \t .. g [2] (b) on the grid, complete the cumulative frequency curve for the information in the table. 200 180 160 140 120 100 80 60 40 20 0cumulative frequency mass (grams)40 45 50 55 60 65 70 75 80m [5]", "19": "19 0607/41/m/j/16 \u00a9 ucles 2016 [turn over (c) use your graph to find (i) the median mass, \t .. g [1] (ii) the interquartile range. \t .. g [2] (d) this table shows how the eggs are graded according to their mass. size small medium large very large mass (m grams) m g 53 53 1 m g 63 63 1 m g 75 m 2 75 (i) an egg is chosen at random from the 200 eggs. estimate the probability that the egg is small. \t . [1] (ii) two eggs are chosen from the 200 eggs. find the probability that both are very large. \t . [2] question 13 is printed on the next page.", "20": "20 0607/41/m/j/16 \u00a9 ucles 2016permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.13 (a) f ()x x 5 2= - (i) solve f ()x1 = 2 . \t x = [2] (ii) find and simplify f f( )x^ h. \t . [2] (iii) find f \u20131(x). \t f \u20131(x) = [2] (b) g(x) is a function with an inverse function g\u20131(x). write down the value of g(g\u20131(3)). \t . [1]" }, "0607_s16_qp_42.pdf": { "1": "this document consists of 16 printed pages. dc (lk/sg) 114972/2 \u00a9 ucles 2016 [turn over * 7 2 9 5 4 0 4 1 0 1 * cambridge international mathematics 0607/42 paper 4 (extended) may/june 2016 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/42/m/j/16 \u00a9 ucles 2016formula list for the equation ax bx c02+ + = xab b ac 242!=- - curved surface area, a, of cylinder of radius r, height h. r a rh2= curved surface area, a, of cone of radius r, sloping edge l. r a rl= curved surface area, a, of sphere of radius r. r a r42= v olume, v, of pyramid, base area a, height h. v ah31= v olume, v, of cylinder of radius r, height h. rv r h2= v olume, v, of cone of radius r, height h. r v r h31 2= v olume, v, of sphere of radius r. r v r34 3= sin sin sin aa bb cc= = cos a b c bc a 22 2 2= + - sinbc a21area=a c bcb a", "3": "3 0607/42/m/j/16 \u00a9 ucles 2016 [turn overanswer all the questions. 1 y x8 7 6 5 4 3 2 1 0 \u20131 \u20132 \u20133 \u20134 \u20135 \u20136\u20131\u20132\u20133\u20134\u20135\u20136\u20137\u20138 87654321t v u (a) translate shape t by the vector 3 4j lkkn poo. [2] (b) reflect shape t in the line y = \u2013 x. [2] (c) rotate shape t by 90\u00b0 anticlockwise about (\u20132, 1). [3] (d) describe fully the single transformation that maps (i) shape t onto shape u, ... .. [3] (ii) shape t onto shape v. ... .. [3]", "4": "4 0607/42/m/j/16 \u00a9 ucles 20162 nikhil and padma share $630 in the ratio 5 : 4. (a) show that nikhil receives $350 and that padma receives $280. [2] (b) (i) in a sale, prices are reduced by 18%. padma buys a jacket for $98.40 in this sale. calculate the original price of the jacket. $ . [3] (ii) padma decides that she does not like the jacket and sells it for $30. calculate the percentage loss made by padma. . % [3] (iii) calculate how much of the $280 padma now has. $ . [1]", "5": "5 0607/42/m/j/16 \u00a9 ucles 2016 [turn over (iv) padma invests $150 at a rate of 2% per year compound interest. calculate the total value of this investment after 10 years. give your answer correct to the nearest dollar. $ . [4] (c) on january 1st 2016, nikhil invested all of his $350 at a rate of 0.15% per month compound interest. find in which month and in which year nikhil\u2019s investment will first have a total value of at least $500. month year [5]", "6": "6 0607/42/m/j/16 \u00a9 ucles 20163 (a) the cumulative frequency curve shows information about the average speeds of 200 cars on the same journey. 20 010 20 30 40 50 60 70 80406080100120140160180200 cumulative frequency average speed (km/h) (i) find the median. km/h [1] (ii) find the inter-quartile range. km/h [2] (iii) find the number of cars with an average speed of more than 70 km/h. .. [2] (b) a bus completes a journey in 2 h 24 min at an average speed of 50 km/h. a car completes the same journey in 1 h 45 min. calculate the average speed of the car. km/h [3]", "7": "7 0607/42/m/j/16 \u00a9 ucles 2016 [turn over4 (a) the cost of a drink of water is w cents. the cost of a drink of juice is ( w + 30) cents. the total cost of 6 drinks of water and 5 drinks of juice is $4.14 . find the value of w. w = [3] (b) x cmx cm (x + 3) cm(x + 1) cmnot to scale the total area of the square and the rectangle is 10 cm2. find the perimeter of the square. give your answer correct to 2 decimal places. ... cm [5]", "8": "8 0607/42/m/j/16 \u00a9 ucles 20165 d xc banot to scale a, b, c and d lie on the circle. the chords ac and bd intersect at x. (a) show that triangles adx and bcx are similar. give a reason for each statement that you make. [2] (b) ax = 5 cm, dx = 2 cm and cx = 3 cm. calculate bx. bx = .. cm [2] (c) ad = 4.61 cm. calculate angle axd. angle axd = . [3]", "9": "9 0607/42/m/j/16 \u00a9 ucles 2016 [turn over6 y x 201.5 0 \u20131.5 ( ) ( ) f sinx x2= where x2 is in degrees. (a) on the diagram, sketch the graph of y = f(x) for x0 20g g . [2] (b) one solution of the equation f( x) = 0, for x0 20g g is x = 0. find the other two solutions. x = .. or x = .. [2] (c) find the co-ordinates of the local maximum point. ( .. , .. ) [2] (d) there is a local minimum point at (0, 0). find the co-ordinates of the other local minimum point when x0 20g g . ( .. , .. ) [2] (e) write down the range of f( x). .. [1] (f) by sketching another graph on the diagram, solve this equation. ( )sinxx 20122 = - x = [2]", "10": "10 0607/42/m/j/16 \u00a9 ucles 20167 (a) 5 cm 12 cmnot to scale the diagram shows a plastic solid made by joining a hemisphere to a cone. the radius of the hemisphere is 5 cm and the height of the cone is 12 cm. (i) calculate the volume of the solid. .. cm3 [3] (ii) one cubic centimetre of the plastic has a mass of 0.95 g. calculate the mass of the solid. give your answer in kilograms. kg [2] (iii) find the number of these solids that can be made from 1 tonne of plastic. . [2]", "11": "11 0607/42/m/j/16 \u00a9 ucles 2016 [turn over (iv) calculate the total surface area of the solid. .. cm2 [4] (b) r cm3r cmnot to scale a solid cone has radius r cm and height 3 r cm. the total surface area of the cone is 377 cm2. find the value of r. r = [5]", "12": "12 0607/42/m/j/16 \u00a9 ucles 20168 the diagram shows the graph of y = f(x) where f( x) = ( ) ( ) ( ) x x xx 2 1 2 + - - . y x0 (a) the equations of the asymptotes to the graph are , , x a x b x c = = = and y d=. find the values of a, b, c and d. a = b = c = d = [4] (b) f(x) = k has only one solution, where k is an integer and k0!. find the value of k. k = [1] (c) find the integer value of x such that ( )x 0 f1. x = [1] (d) ( )x x p g2= - on the diagram, sketch a possible graph of y = g( x) so that f( x) = g( x) has 5 solutions. [2]", "13": "13 0607/42/m/j/16 \u00a9 ucles 2016 [turn over9 p g 7 3 2u the venn diagram shows the following information. \tu = {students in a music group} p = {students who play the piano} g = {students who play the guitar} ( )np g 2 ,=l ( )np g 7 +=l ( )ng p 3 +=l . (a) n (u) = 23 find ( )np g+. . [1] (b) a student is chosen at random from the music group. find the probability that this student plays the piano but does not play the guitar. . [1] (c) two students who play the guitar are chosen at random. find the probability that they both also play the piano. . [3] (d) on the venn diagram, shade the region p g, l. [1]", "14": "14 0607/42/m/j/16 \u00a9 ucles 201610 ( )fx x x302= - - ( )gx x 362= - ( )hx x 2 7= + (a) find h(f(7)). .. [2] (b) find h \u2013 1(x). h \u2013 1(x) = . [2] (c) find g(h( x)) in its simplest factorised form. .. [3] (d) simplify ( )( ) gf xx. .. [4]", "15": "15 0607/42/m/j/16 \u00a9 ucles 2016 [turn over11 34\u00b0a b d cnot to scale 8 cm 19 cm in the diagram, adc is a straight line. (a) calculate ab. ab = .. cm [2] (b) calculate angle dbc . angle dbc = . [5] (c) calculate the area of triangle abc . .. cm2 [2] question 12 is printed on the next page.", "16": "16 0607/42/m/j/16 \u00a9 ucles 2016permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.12 (a) find the nth term of the sequence. 1, 8, 27, 64, 125, \u2026 .. [1] (b) (i) find the next term in the sequence. 2, 12, 36, 80, 150, 252, \u2026 .. [2] (ii) find the nth term of the sequence. 2, 12, 36, 80, 150, 252, \u2026 .. [2]" }, "0607_s16_qp_43.pdf": { "1": "this document consists of 20 printed pages. dc (nf/sw) 115861/4 \u00a9 ucles 2016 [turn overcambridge international examinations cambridge international general certificate of secondary education * 4 0 9 5 8 6 6 3 5 7 * cambridge international mathematics 0607/43 paper 4 (extended) may/june 2016 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for p, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.", "2": "2 0607/43/m/j/16 \u00a9 ucles 2016formula list for the equation ax bx c02+ + = xab b ac 242!=- - curved surface area, a, of cylinder of radius r, height h. r a rh2= curved surface area, a, of cone of radius r, sloping edge l. r a rl= curved surface area, a, of sphere of radius r. r a r42= v olume, v, of pyramid, base area a, height h. v ah31= v olume, v, of cylinder of radius r, height h. rv r h2= v olume, v, of cone of radius r, height h. r v r h31 2= v olume, v, of sphere of radius r. r v r34 3= sin sin sin aa bb cc= = cos a b c bc a 22 2 2= + - sinbc a21area=a c bcb a", "3": "3 0607/43/m/j/16 \u00a9 ucles 2016 [turn overanswer all the questions. 1 (a) write the number 13205.17268 (i) correct to 1 decimal place, . [1] (ii) correct to 3 significant figures, \t . [1] (iii) correct to the nearest 10, \t . [1] (iv) correct to the nearest 0.001. \t . [1] (b) write the number 120 correct to the nearest 10. \t . [1] 2 (a) factorise. x x3 10 82- - . [2] (b) solve the inequality. x x3 10 8 021 - - . [2] (c) solve the equation. sin s inx x 3 10 8 02- - = for x 0 360 \u00b0 \u00b01 1 . [3]", "4": "4 0607/43/m/j/16 \u00a9 ucles 20163 y\tis directly proportional to x13+^ h. \t y = 32 when x = 3. (a) find the value of y when x = 4. y = [3] (b) find the value of x when .y 135= . \t x\t= [2] (c) find x in terms of y. \t x\t= [3]", "5": "5 0607/43/m/j/16 \u00a9 ucles 2016 [turn over4 a circle of radius r cm is inside a square, so that the circle touches the sides of the square. (a) (i) find an expression for the area of the shaded region in terms of r and r. . [2] (ii) calculate the area of the shaded region when r = 6. . cm2 [1] (b) find an expression for the perimeter of the shaded region in terms of r and r. \t . [3]", "6": "6 0607/43/m/j/16 \u00a9 ucles 20165 ab not to scale 12.4 cm30\u00b0 c the area of triangle abc\tis 34.1 cm2. \t ab = 12.4 cm and angle abc = 30\u00b0. (a) show that bc = 11 cm. [1] (b) find ac. ac = .. cm [3]", "7": "7 0607/43/m/j/16 \u00a9 ucles 2016 [turn over (c) find angle cab . angle cab = [3] (d) find the length of the perpendicular line from a\tto the line bc. ... cm [2]", "8": "8 0607/43/m/j/16 \u00a9 ucles 20166 the heights of 400 students are given in the table. height (h cm) frequency h 145 1551g 26 h 155 1601g 66 h 160 1651g 82 h 165 1701g 118 h 170 1751g 82 h 175 1901g 26 (a) calculate an estimate of the mean height of a student. \t \t\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \tcm [2] (b) (i) complete the frequency density column in this table. height (h cm) frequency frequency density h 145 1551g 26 h 155 1601g 66 h 160 1651g 82 h 165 1701g 118 h 170 1751g 82 h 175 1901g 26 [2]", "9": "9 0607/43/m/j/16 \u00a9 ucles 2016 [turn over (ii) on the grid below, draw an accurate histogram to show this information. complete the scale on the frequency density axis. 0 140 150 160 170 height (cm)hfrequency density 180 190 [4]", "10": "10 0607/43/m/j/16 \u00a9 ucles 20167 sasha bought a house on 1st january 2013. by 1st january 2014 the value of the house had increased by 10%. by 1st january 2015 the value of the house had increased by a further 5% of its value on 1st january 2014. the value of the house on 1st january 2015 was $103 950. (a) find how much sasha paid for the house in 2013. $ . [4] (b) by 1st january each year, from 2015, the value of the house increases by 5% of its value on 1st january the previous year. the value of the house on 1st january 2015 was $103 950. find the year in which the value of the house will first be greater than $200 000. . [3]", "11": "11 0607/43/m/j/16 \u00a9 ucles 2016 [turn over8 a b not to scale cxd q 6p abc\tis a triangle. ax ac32= and ad ab21=\ufffd \tax p6= and dx q=. find an expression, in terms of p and q, for\t (a) ad, \t . [2] (b) dc, . [2] (c) cb. \t . [3]", "12": "12 0607/43/m/j/16 \u00a9 ucles 20169 the transformation ab\tmeans transformation b followed by transformation a. (a) the transformation p is a rotation through 90\u00b0 clockwise about the origin. the transformation q is a rotation through 180\u00b0 about the origin. the transformation r is a rotation through 270\u00b0 clockwise about the origin. the transformation s is a reflection in the y-axis. the transformation t is a reflection in the x-axis. write down the letter of the single transformation, p, q, r, s or t, that is equivalent to each of the transformations qr, pqr , st, sq, ptp and tpp . qr = .. pqr = .. st = .. sq = .. ptp = .. tpp = .. [6]", "13": "13 0607/43/m/j/16 \u00a9 ucles 2016 [turn over (b) \u20136\u20135\u20134\u20133\u20132\u20131 123456a \u20136\u20135\u20134\u20133\u20132\u201310123456y x (i) draw the image of triangle a after a reflection in the line y = x. label this image b. [2] (ii) draw the image of triangle b after a reflection in the x-axis. label this image c. [1] (iii) describe fully the single transformation that maps triangle c onto triangle a. ... . [3]", "14": "14 0607/43/m/j/16 \u00a9 ucles 201610 a company is testing a new drug. ten patients were examined and given a score before and after taking the drug. a decrease in score represents an improvement. the results are shown in the table. patient a b c d e f g h i j score before ( x) 8 14 20 25 32 34 41 42 50 61 score after ( y) 3 4 16 15 20 27 34 28 40 49 (a) (i) complete the scatter diagram. the first four points have been plotted for you. 005101520253035404550y x score beforescore after 10 20 30 40 50 60 70 [3] (ii) what type of correlation is shown by the scatter diagram? . [1]", "15": "15 0607/43/m/j/16 \u00a9 ucles 2016 [turn over (b) find (i) the mean score before taking the drug, \t . [1] (ii) the mean score after taking the drug. \t . [1] (c) (i) find the equation of the regression line for y in terms of x. y = [2] (ii) estimate the score after taking the drug when the score before taking the drug was 30. \t . [1] (iii) a patient has a score before taking the drug of 80. explain why using the line of regression is unlikely to be reliable in predicting the score of the patient after taking the drug. ... . [1]", "16": "16 0607/43/m/j/16 \u00a9 ucles 201611 8 \u20133 f (x) = 3 +1 (x2 \u2013 4x + 3)0\u20131 5xy (a) on the diagram, sketch the graph of y = f(x) between x = \u22121 and x = 5. [4] (b) write down the equations of the three asymptotes. , , [3] (c) write down the co-ordinates of the local maximum point. ( . , . ) [1] (d) the line y = x intersects the curve y x x3 4 31 2= + - +^ h three times. find the values of the x co-ordinates of these three points of intersection. x\t= ... , x\t= ... , x\t= ... [3]", "17": "17 0607/43/m/j/16 \u00a9 ucles 2016 [turn over12 a d enot to scale c b a, b, c and d lie on a circle. \t ade and bce are straight lines that intersect at e. bd = de, angle bad =\t4x, angle bcd = 6x and angle bdc = 3x. find (a) x, \t x = [2] (b) angle cbd , angle cbd = . [2] (c) angle cde . angle cde = . [3]", "18": "18 0607/43/m/j/16 \u00a9 ucles 201613 60\u00b0 diagram 1 diagram 2 diagram 3not to scale 3 cm 60\u00b0 60\u00b03 cm 60\u00b03 cm 60\u00b0 60\u00b0 diagram 1 is a sector of a circle, radius 3 cm and sector angle 60\u00b0. diagram 2 has a right-angled triangle, with an angle of 60\u00b0, drawn on a radius of this sector. diagram 3 has a sector of a circle, with a sector angle 60\u00b0, drawn on the hypotenuse of the right-angled triangle. (a) calculate the area of (i) diagram 1, . cm2 [2] (ii) diagram 2, . cm2 [3]", "19": "19 0607/43/m/j/16 \u00a9 ucles 2016 [turn over (iii) diagram 3. . cm2 [3] (b) diagram 1, diagram 2 and diagram 3 are the first three diagrams in a pattern. there are 6 diagrams in the pattern. diagram 4 has a right-angled triangle added to diagram 3 in the same way as diagram 2. diagram 5 has a sector added to diagram 4 in the same way as diagram 3. diagram 6 has a right-angled triangle added to diagram 5 in the same way as diagram 2. find the area of diagram 6. . cm2 [4] question 14 is printed on the next page.", "20": "20 0607/43/m/j/16 \u00a9 ucles 201614 in this question, give all your answers as single fractions in terms of x and y. a bag contains x red balls and y blue balls. (a) rosario chooses a ball at random from the bag, notes its colour and replaces it in the bag. he then chooses a ball from the bag a second time, notes its colour and replaces it in the bag. find the probability, in terms of x\tand y, that the two balls chosen are (i) both red, . [2] (ii) one red and one blue. . [3] (b) magda chooses a ball at random from the bag and does not replace it. she then chooses a ball from the bag a second time. find the probability, in terms of x\tand y,\tthat the two balls chosen are (i) both red, . [3] (ii) one red and one blue. . [3] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity . to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_s16_qp_51.pdf": { "1": "this document consists of 8 printed pages. dc (nf/sg) 117229/2 \u00a9 ucles 2016 [turn over * 7 2 3 5 9 6 1 3 1 1 * cambridge international mathematics 0607/51 paper 5 (core) may/june 2016 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. y ou must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/51/m/j/16 \u00a9 ucles 2016answer all the questions. investigation\t\t dividing \trectangles this investigation looks at the connections between the rectangles made by dividing one rectangle into two smaller rectangles. in this investigation \u2022\u2022 the length of a rectangle is always longer than its width lengthlength width width \u2022\u2022 the length and width of a rectangle are always a whole number of units \u2022\u2022 the scale factor of any enlargement is greater than 1. 1\t in the diagrams below, rectangle b is an enlargement of rectangle a. \t (a)\t ba \t \t write down the scale factor of this enlargement. ..", "3": "3 0607/51/m/j/16 \u00a9 ucles 2016 [turn\tover\t (b)\t b a \t \t write down the scale factor of this enlargement. .. \t (c)\t ab 4not to scale \t \t for this pair of rectangles, the scale factor is 10. \t \t work out the length of rectangle b. .. \t (d)\t ab 3 1 5not to scale \t \t work out the length of rectangle b. ..", "4": "4 0607/51/m/j/16 \u00a9 ucles 20162\t a rectangle is cut into two smaller rectangles, a and b. a b \t when b is an enlargement of a, the original rectangle is called a scale-rectangle . a bwidth width lengthlength abwidthwidthlengthlength \t example \t a 4 by 10 rectangle is cut as shown. a b 410 2 8 4 a b2 4 48 ab2448not to scale 482length of alength of b= = and 242width of awidth of b= = \t so b is an enlargement of a with scale factor 2. \t this \tmeans\tthat\tthe\trectangle \twith\tdimensions \t4\tby\t10\tis\ta\tscale-rectangle \twith\ta\tfactor\tof\t2.", "5": "5 0607/51/m/j/16 \u00a9 ucles 2016 [turn\tover\t (a)\t a b \t \t the diagram shows a 3 by 10 rectangle. \t \t this is a scale-rectangle . \t \t show that it has a factor of 3. \t (b)\t ba \t the diagram shows a 2 by 4 rectangle. \t is this a scale-rectangle ? \t write yes or no and give reasons for your answer. \t (c)\t a b3 21m ab321m not to scale \t \t the diagram shows a scale-rectangle with a factor of 7. \t \t (i)\t find m. .. \t \t (ii)\t write down the dimensions of the scale-rectangle . by ", "6": "6 0607/51/m/j/16 \u00a9 ucles 2016\t (d)\t a b3 w75 ab3w75 not to scale \t \t the diagram shows a scale-rectangle with a factor of 5. \t \t (i)\t find w. .. \t \t (ii)\t write down the dimensions of the scale-rectangle . by 3\t a b yx z \t the diagram shows a scale-rectangle with a factor of n. \t (a)\t when x = 2 and n = 6, \t \t (i)\t work out y, .. \t \t (ii)\t find z, .. \t \t (iii)\t complete this statement with a number, z = \u00d7 x \t \t (iv)\t write down the connection between your answer to part\t(iii) and the factor, n.", "7": "7 0607/51/m/j/16 \u00a9 ucles 2016 [turn\tover\t (b)\t when x = 2 and z = 18, \t \t (i)\t find n, .. \t \t (ii)\t work out the dimensions of this scale-rectangle . by \t (c)\t use your answers to part\t(a) and part\t(b) to complete the second and third rows of the table. \t \t complete the remaining rows of the table. n x y z dimensions 2 2 4 8 4 by 10 6 2 .. by .. 2 18 .. by .. 5 7 .. by .. 1 4 16 4 by 17 5 20 .. by .. question \t4\tis\tprinted\ton\tthe\tnext\tpage.", "8": "8 0607/51/m/j/16 \u00a9 ucles 20164\t a b yx z \t the diagram shows a scale-rectangle with a factor of n. \t (a)\t work out the dimensions of this scale-rectangle in terms of n and x. by \t (b)\t show that, for any scale-rectangle , its dimensions are in the ratio width : length = n : n2 + 1. permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_s16_qp_52.pdf": { "1": "this document consists of 6 printed pages and 2 blank pages. dc (nf) 115859/2 \u00a9 ucles 2016 [turn overcambridge international examinations cambridge international general certificate of secondary education *1465512761* cambridge international mathematics 0607/52 paper 5 (core) may/june 2016 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.", "2": "2 0607/52/m/j/16 \u00a9 ucles 2016answer all the questions. investigation sums of consecutive integers this investigation looks at the results when the terms of a sequence of consecutive positive integers are added together. 1 here are four sequences of consecutive positive integers. the sequence 5, 6, 7, 8, 9, 10, 11 has 7 terms. the median (the middle term) is 8. the sequence 7, 8 has only 2 terms. the median is 7.5 . the sequence 20, 21, 22, 23, 24, 25 has 6 terms. the median is 22.5 . the sequence 20, 21, 22, , 40 has 21 terms. the median is 30. for a sequence of consecutive integers, (a) give an example to show that the number of terms is calculated using the rule last term \u2013 first term + 1 (b) describe how to calculate the median using only the first term and the last term. .. . .. .", "3": "3 0607/52/m/j/16 \u00a9 ucles 2016 [turn over2 (a) complete the table of sequences of consecutive positive integers. sequencenumber of termsmedian sum of all the terms 3, 4, 5, 6, 7, 8, 9 7 6 7, 8 2 7.520, 21, 22, , 40 21 30 6305, 6, 7 182, 3, 4, 5, 6, 7, 8, 9 8 6 4.5 27 57 (b) explain how to calculate the sum of all the terms using only the number of terms and the median. .. . (c) what is always true about the number of terms when the median is an integer? .. . (d) what is always true about the median when the number of terms is even? .. .", "4": "4 0607/52/m/j/16 \u00a9 ucles 20163 use your answer to question 2(b) to help you complete the table of sequences of two or more consecutive positive integers. sequencenumber of termsmedian sum 51 5 43 4 49 4 use your answers to question 1 and question 2(b) to help you find the sum of this sequence. 15, 16, 17, , 985. ...", "5": "5 0607/52/m/j/16 \u00a9 ucles 2016 [turn over5 sequences have 2 or more terms. find all the sequences of consecutive positive integers that have a sum of 77.", "6": "6 0607/52/m/j/16 \u00a9 ucles 20166 (a) use the factors of 16 to show why the sum of a sequence of consecutive positive integers cannot equal 16. (b) find a number larger than 20 that cannot be written as the sum of consecutive positive integers. ...", "7": "7 0607/52/m/j/16 \u00a9 ucles 2016blank page", "8": "8 0607/52/m/j/16 \u00a9 ucles 2016blank page permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to do wnload at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_s16_qp_53.pdf": { "1": "this document consists of 8 printed pages. dc (nh/sw) 115854/2 \u00a9 ucles 2016 [turn over *2800503385* cambridge international mathematics 0607/53 paper 5 (core) may/june 2016 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. y ou must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/53/m/j/16 \u00a9 ucles 2016answer all the questions. investigation areas & perimeters this investigation looks at the connection between the area and the perimeter of a rectangle. all diagrams are not to scale. the sides of all rectangles are whole numbers. 1 5 4the area of this 4 by 5 rectangle is 20. (a) 10 3 find the area of this rectangle. ... some rectangles have area 4. there are three ways to calculate their area. area 4 1 \u00d7 4 2 \u00d7 2 4 \u00d7 1", "3": "3 0607/53/m/j/16 \u00a9 ucles 2016 [turn over (b) some rectangles have area 6. there are four ways to calculate their area. complete the table below to show all four ways. the first one has been done for you. area 6 1 \u00d7 6 .. \u00d7 .. .. \u00d7 \u00d7 .. (c) some rectangles have the same area. (i) there are exactly two ways to calculate their area. complete the table when this area is a number between 6 and 15. area .. .. \u00d7 .. .. \u00d7 .. (ii) there are exactly three ways to calculate their area. complete the table when this area is a number between 6 and 15. area .. .. \u00d7 .. .. \u00d7 \u00d7 ..", "4": "4 0607/53/m/j/16 \u00a9 ucles 2016 (iii) there are more than four ways to calculate their area. complete the table when the area is a number between 6 and 15. you may not need all the lines. area .. .. \u00d7 .. .. \u00d7 \u00d7 \u00d7 \u00d7 \u00d7 \u00d7 \u00d7 ..", "5": "5 0607/53/m/j/16 \u00a9 ucles 2016 [turn over2 some rectangles have the same area. this area is between 1 and 20. (a) (i) list the areas that can be calculated in exactly two ways. ... (ii) write down the mathematical name for the numbers in your answer to part (a)(i) . ... (b) (i) list the areas that can be calculated in an odd number of ways. ... (ii) write down the mathematical name for the numbers in your answer to part (b)(i) . ... 3 some rectangles have the same area. this area is between 150 and 200. find an area that can be calculated in an odd number of ways. ...", "6": "6 0607/53/m/j/16 \u00a9 ucles 20164 5 4 the perimeter of this 4 by 5 rectangle is 18. find the perimeter of each of these rectangles. 10 3 ... 9 2 ...", "7": "7 0607/53/m/j/16 \u00a9 ucles 2016 [turn over5 the width of a rectangle is 3. its area and its perimeter have the same value. (a) find its length. ... (b) write down its perimeter. ... 6 x 4 (a) write down an expression for the area of this rectangle. ... (b) write down an expression for the perimeter of this rectangle. ... (c) the area and the perimeter have the same value. write down an equation and solve it to find x. question 7 is printed on the next page.", "8": "8 0607/53/m/j/16 \u00a9 ucles 20167 a rectangle has width 2 and length x. show that this rectangle cannot have the same value for its area as its perimeter. permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to do wnload at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_s16_qp_61.pdf": { "1": "this document consists of 12 printed pages. dc (lk/fd) 115851/4 \u00a9 ucles 2016 [turn overcambridge international examinations cambridge international general certificate of secondary education * 5 6 5 4 9 5 8 8 7 8 * cambridge international mathematics 0607/61 paper 6 (extended) may/june 2016 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. you must show all the relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together . the total number of marks for this paper is 40.", "2": "2 0607/61/m/j/16 \u00a9 ucles 2016answer both parts a and b. a investigation moving triangles (20 marks) you are advised to spend no more than 45 minutes on this part. q p ar s1 b this investigation is about finding the connection between ap and bq as p and q move. all triangles are right-angled and rs is one unit. in questions 1 , 2 and 3, p is at a. 1 rq p s b triangle pbq is an enlargement of triangle psr, with p as the centre of the enlargement. (a) write down the scale factor of the enlargement in the diagram. . (b) complete the table for enlarging triangle psr. scale factor length of ps length of pb 3 4 6 30 7 14 (c) use one word to complete this statement. psr and pbq are triangles because one is an enlargement of the other.", "3": "3 0607/61/m/j/16 \u00a9 ucles 2016 [turn over2 p s bq not to scalexr 21 (a) show that x = 10 when pb = 20. (b) find the value of x when pb = 16. .. (c) find an expression for x when pb = y. .. 3 p sr x 1q bnot to scale 4 y for this triangle, find an expression for x when pb = y. ..", "4": "4 0607/61/m/j/16 \u00a9 ucles 20164 these diagrams show p starting at a and then moving towards b. (a) p s bq r 316not to scale y in this diagram p is at a. find the value of y. .. (b) p a s bq r 216not to scale z in this diagram, p and s have moved towards b. ps is one unit less than in part (a) . find the value of z. .. (c) using your answers to part (a) and part (b) , work out the value of ap. ..", "5": "5 0607/61/m/j/16 \u00a9 ucles 2016 [turn over5 p srq bx y51 a p srq bx z41not to scale these diagrams show p starting at a and moving towards b. in the second diagram, ps has decreased by one unit. using the method of question 4 , show that ap = bq.", "6": "6 0607/61/m/j/16 \u00a9 ucles 20166 p srq bx yn1 a p srqnot to scale bx z1 these diagrams show p starting at a and moving towards b. in the second diagram, ps has decreased by one unit. show that ap = bq.", "7": "7 0607/61/m/j/16 \u00a9 ucles 2016 [turn over7 in this question, rs is no longer one unit. p starts at a and moves towards b. in the second diagram, ps has decreased by one unit. p srq bx yn p a srqnot to scale bx z (a) when rs = 2, find an expression for ap in terms of x. .. (b) when rs = m, find an expression for ap in terms of x and m. ..", "8": "8 0607/61/m/j/16 \u00a9 ucles 2016b modelling musical notes (20 marks) you are advised to spend no more than 45 minutes on this part. this task is about the connection between musical notes. a musical note is made by a sound wave which is modelled by a sine function. here is the sine wave for the note a1, where the time, t, is measured in seconds. 1 t0 \u201311 552 55 each note has a different frequency, which is measured in hertz (hz). the frequency of the note a1 is 55 hz because the sine wave repeats 55 times per second. 1 the frequency of the note a2 is two times the frequency of the note a1. on the grid below, sketch the sine wave for the note a2 for t0552g g . 1 t0 \u201311 552 55", "9": "9 0607/61/m/j/16 \u00a9 ucles 2016 [turn over2 the 12 notes in a musical scale are a, a#, b, c, c#, d, d#, e, f, f#, g, g#. the notes on a piano repeat this scale. notes in the same scale have the same subscript. (for example, a2, c#2 and f2 are all in the same scale.) the frequency, f hz, of each note on a piano is modelled by the function ( ) . fn 275 2n 12# = where n is an integer from 0 to 87. n 0 1 2 3 4 5 6 7 8 910 11 12 13 14 87 note a0a#0b0c0c#0d0d#0e0f0f#0g0g#0a1a#1b1 (a) when n = 0 the frequency of the note is 27.5 . this is the note a0. (i) work out the frequency of the note when n = 3. .. (ii) write down the note when n = 15. .. (iii) work out the frequency of the note e0. .. (b) write down all the values of n that give the note a on this piano. ... (c) which note has the highest frequency on this piano? calculate this frequency. note frequency .", "10": "10 0607/61/m/j/16 \u00a9 ucles 20163 k times the frequency of a note gives the frequency of the next note. this means that ( ) ( ) f fk n n 1 = + . find the exact value of k. .. 4 (a) on the axes below, sketch the graph of ( ) . gx 275 2x 12# = for x0 87g g . 5000 87g (x) x0 (b) find the note which has frequency closest to 1400 hz. ..", "11": "11 0607/61/m/j/16 \u00a9 ucles 2016 [turn over5 a different musical scale has 10 notes. q r s t u v w x y z the frequency of each note is modelled by the function ( )hn a 2bn#= where n is an integer from 0 to 29. when n = 0 the note is q0 and the frequency of this note is 600 hz. the frequency of the note q1 is 1200 hz. (a) write down the value of a. .. (b) find the value of b. .. (c) show that ( ) ( ) h hk n n1 = + where k is a constant to be found. question 6 is printed on the next page.", "12": "12 0607/61/m/j/16 \u00a9 ucles 2016permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity . to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.6 in musical scales the frequency of the note p1 is two times the frequency of the note p0. (a) a musical scale has 23 notes. the frequency of the first note is 75 hz. work out the frequency of the second note. .. (b) the first note in another musical scale has a frequency of 100 hz. the second note has a frequency of 108 hz. find the number of notes in this scale. .." }, "0607_s16_qp_62.pdf": { "1": "this document consists of 11 printed pages and 1 blank page. dc (leg/fd) 115846/3 \u00a9 ucles 2016 [turn overcambridge international examinations cambridge international general certificate of secondary education * 6 4 9 3 1 2 5 3 8 8 * cambridge international mathematics 0607/62 paper 6 (extended) may/june 2016 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. y ou must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.", "2": "2 0607/62/m/j/16 \u00a9 ucles 2016answer both parts a and b. a\t investigation sums\tof\tconsecutive \tintegers \t(20\tmarks) you are advised to spend no more than 45 minutes on this part. \t\t this investigation looks at the results when the terms of a sequence of consecutive positive integers are added together. 1\t the mean of 6 positive integers is 4.5 . \t calculate the sum of the 6 integers. ... 2\t (a)\t complete the table for sequences of two or more consecutive positive integers. sequencenumber of termsmean sum of all the terms 5, 6, 7, 8, 9, 10 6 10, 11, 12, .. , 40 31 25 2, 3, 4, 5, 6, 7, 8 35 4 42 49 \t (b)\t describe how to calculate the mean using only the first term and the last term of a sequence of consecutive integers. ... ...", "3": "3 0607/62/m/j/16 \u00a9 ucles 2016 [turn\tover3\t k, k + 1, k + 2, ..., k + 99 is a sequence of consecutive integers. \t (a)\t write down the number of terms in this sequence. ... \t (b)\t use the first term and the last term to find an expression for the mean in terms of k. ... \t (c)\t use your answers to part\t(a) and part\t(b) to write down an expression for the sum of all the terms of the sequence. ... 4\t use the method of question\t3 to show that the sum of the integers k, k + 1, k + 2, .., k + (n \u2013 1) is n # k n 22 1+ -.", "4": "4 0607/62/m/j/16 \u00a9 ucles 20165\t (a)\t if n is odd, explain why the value of the expression k n 22 1+ - must be an integer. ... ... \t (b)\t if n is even, explain why the value of the expression k n 22 1+ - must end in .5 . ... ... 6\t the sum of a sequence of consecutive positive integers is 84. \t (a)\t using question\t4 and question\t5, find all the possible values of n and the corresponding values for the mean. \t", "5": "5 0607/62/m/j/16 \u00a9 ucles 2016 [turn\tover\t (b)\t write down all the possible sequences of consecutive positive integers whose sum is 84. 7\t find an even number, bigger than 20, which cannot be written as the sum of consecutive integers. ...", "6": "6 0607/62/m/j/16 \u00a9 ucles 2016b\t modelling traffic \tflow\t(20\tmarks) you are advised to spend no more than 45 minutes on this part. this task looks at maximising the number of cars that can safely pass a point on a road in an hour . 1\t it takes one second to react to an emergency when driving. \t (a)\t the speed of a car is 54 km/h. \t \t calculate the number of metres that it travels in 1 second. ... \t (b)\t the speed of a car is x km/h. \t \t show that the number of metres, a, travelled in 1 second is approximately 0.278 x. 2\t the speed of a car is x km/h. \t when the driver brakes, the number of metres, b, that the car travels before stopping is kx2. \t when x = 50, b = 20. \t find an expression for b in terms of x. ...", "7": "7 0607/62/m/j/16 \u00a9 ucles 2016 [turn\tover3\t for safety, the distance between cars travelling at x km/h must be a + b. a b 4p \t the average length of a car is 4 metres. \t so the number of metres between corresponding points on a road is a + b + 4. \t (a)\t at a speed of x km/h, how many metres does a car travel in one hour? ... \t (b)\t explain why a model for the number of cars, n, safely passing point p in one hour is .nx kxx 0278 41000 2=+ + \t \t where x km/h is the speed of the cars and k has the value you found in question\t2. ... ... ...", "8": "8 0607/62/m/j/16 \u00a9 ucles 2016\t (c)\t using your value for k from question\t2, sketch the graph of n for 0 g x g 60. 0 60xn speed (km / h)number of cars per hour \t (d)\t find the maximum possible number of cars which can safely pass point p in one hour. ... \t (e)\t (i)\t find, correct to one decimal place, the speed that gives this maximum. ... \t \t (ii)\t comment on the size of this answer. ... \t (f)\t when you increase the average length of a car, what is the effect on \t \t (i)\t the maximum number of cars that can pass point p in one hour, ... \t \t (ii)\t the speed at which this maximum is possible? ...", "9": "9 0607/62/m/j/16 \u00a9 ucles 2016 [turn\tover4\t a revised model for traffic flow does not include the braking distance, b. \t this is because the car in front also travels the same braking distance. so the revised model uses k = 0. \t the model also allows 2 seconds, instead of 1 second, for the driver to react to the car in front stopping quickly. \t assume the average length of a car is 4 metres. \t (a)\t revise the model in question\t3(b). n = .. \t (b)\t sketch the graph of n for 0 g x g 60. 0 60xn speed (km / h)number of cars per hour", "10": "10 0607/62/m/j/16 \u00a9 ucles 2016\t (c)\t can 1800 cars safely pass point p in one hour? \t \t use algebra to explain your answer.", "11": "11 0607/62/m/j/16 \u00a9 ucles 20165\t there is one speed, greater than 0 km/h, at which both models give the same number of cars per hour. \t find this speed. ...", "12": "12 0607/62/m/j/16 \u00a9 ucles 2016permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank\tpage" }, "0607_s16_qp_63.pdf": { "1": "this document consists of 12 printed pages. dc (lk/sg) 115876/2 \u00a9 ucles 2016 [turn overcambridge international examinations cambridge international general certificate of secondary education * 4 3 7 2 1 8 9 1 6 3 * cambridge international mathematics 0607/63 paper 6 (extended) may/june 2016 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. you must show all the relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together . the total number of marks for this paper is 40.", "2": "2 0607/63/m/j/16 \u00a9 ucles 2016answer both parts a and b. a investigation areas and perimeters (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation looks at the connection between the perimeter and area of a rectangle. all diagrams are not to scale. 7 4 the area of this 4 by 7 rectangle is 28 and its perimeter is 22. 1 (a) 10 3 find the area and perimeter of this rectangle. area = . perimeter = .", "3": "3 0607/63/m/j/16 \u00a9 ucles 2016 [turn over (b) x 3 the area and perimeter of this rectangle have the same value. (i) find x. .. (ii) write down its perimeter. .. (c) x 7 (i) write down an expression for the area of this rectangle. .. (ii) write down an expression for the perimeter of this rectangle. .. (iii) the area and the perimeter have the same value. write down an equation and solve it to find x. ..", "4": "4 0607/63/m/j/16 \u00a9 ucles 20162 x y (a) for this rectangle, find an expression, in terms of x and y, for (i) the area, .. (ii) the perimeter. .. (b) the area and the perimeter have the same value. show that yxx 22=- .", "5": "5 0607/63/m/j/16 \u00a9 ucles 2016 [turn over3 yxx 22=- (a) find y when x12= . .. (b) find y when x1=. .. (c) sketch the graph of yxx2 2=- for values of x between 0 and 15. y x015 (d) for which values of x is the graph not valid for rectangles with area equal to perimeter? give your answer as an inequality. ..", "6": "6 0607/63/m/j/16 \u00a9 ucles 20164 x y when the area is less than the perimeter, yxx 221- . (a) explain this using your method in question 2(b) . assume that x22. (b) on your sketch in question 3(c) , mark clearly a point where yxx 221- and x22. label this point q. (c) check that the co-ordinates of your point q give a rectangle in which the area is less than the perimeter.", "7": "7 0607/63/m/j/16 \u00a9 ucles 2016 [turn over5 investigate if it is possible to find a cube where the volume is numerically equal to its total surface area.", "8": "8 0607/63/m/j/16 \u00a9 ucles 2016b modelling how much grass can the goat eat? (20 marks) you are advised to spend no more than 45 minutes on this part. a farmer owns a goat and a large field with lots of grass in it. 10 m1 the farmer ties the goat to a point in the field with a rope that is 10 m long. find the area of grass that the goat can eat. .. 2 (a) with the same 10 m rope, she ties the goat to an outside corner of a barn of length 25 m and width 15 m. 10 m 15 m 25 mnot to scale find the area of grass that the goat can eat. ..", "9": "9 0607/63/m/j/16 \u00a9 ucles 2016 [turn over (b) with a 20 m rope she ties the goat to the same corner of the barn. 20 m15 m 25 mnot to scale g explain what happens when the goat continues past point g. 3 with the original 10 m rope, she ties the goat to an outside corner of a barn of length 15 m and width 8 m. (a) draw a sketch to show the shape of the area of grass the goat can now eat. (b) show that the area of grass the goat can eat is approximately 239 m2.", "10": "10 0607/63/m/j/16 \u00a9 ucles 20164 the farmer now uses a rope that is x metres long. the barn is of length 15 m and width 8 m. (a) the goat can eat an area of grass the same shape as that in question 2(a) . (i) complete the inequality for x. . x1 1 . (ii) write down a model for the area, a m2. a = . (b) the goat can eat an area of grass in a shape of the same form as that in question 3(a) . (i) complete the inequality for x. . x1 1 . (ii) find a model for this area, a m2. a = .", "11": "11 0607/63/m/j/16 \u00a9 ucles 2016 [turn over (c) (i) when x 15 231 1 , find a model for the area of grass, a m2, that the goat can eat. a = . (ii) the goat needs to reach 700 m2 of grass. use your model to find the length of the rope. .. question 4(d) is printed on the next page.", "12": "12 0607/63/m/j/16 \u00a9 ucles 2016permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity . to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. (d) the goat needs to reach 500 m2 of grass. find the length of the rope. .." }, "0607_w16_qp_11.pdf": { "1": " this document consists of 8 printed pages. ib16 11_0607_11/2rp \u00a9 ucles 2016 [turn over *5940164292 * cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/11 paper 1 (core) october/november 2016 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the rele vant working to gain full marks and you will be given marks fo r correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2016 0607/11/o/n/16 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2016 0607/11/o/n/16 [turn over answer all the questions. 1 12y x1235 4 0 \u20134\u20133\u20132\u20131 \u20135 345 \u20134\u20133\u20132\u20131 \u20135 \u2013666 \u20136a (a) write down the co-ordinates of point a. ( , ) [1] (b) plot the point (4, \u20132) . label this point b. [1] 2 not to scale 15 cm8 cm17 cm find the perimeter of this triangle. cm [1] 3 write down all the factors of 35. [2] ", "4": "4 \u00a9 ucles 2016 0607/11/o/n/16 4 insert one pair of brackets in each of the following statements to make them correct. (a) 6 + 3 \u00d7 4 \u2013 12 = 24 [1] (b) 6 + 3 \u00d7 4 \u2013 12 = \u201318 [1] 5 work out 107 of 250. [1] 6 a recipe uses 200 g of rice for 4 people. work out how much rice this recipe uses for 10 people. g [ 2 ] 7 (a) change 7.2 kilograms into grams. g [ 1 ] (b) change 86 000 cm3 into m3. m3 [1] ", "5": "5 \u00a9 ucles 2016 0607/11/o/n/16 [turn over 8 the cost, $ c, of renting a car for n days is c = 20 + 12 n . (a) find the cost of renting a car for 5 days. $ [1] (b) the cost of renting a car was $104. find the number of days for which the car was rented. [2] 9 here are three sets a, b and c. a = {2, 5, 6, 7, 9, 16} b = {5, 6, 7, 9} c = {even integers between 1 and 10} (a) write down all the possible values for x when \u2208xa and \u2209xb. [1] (b) list the elements of .ca\u2229 [1] 10 (a) expand the brackets. \u2013 3 (x \u2013 2) [1] (b) factorise completely. 6 x \u2013 10 xy [2] ", "6": "6 \u00a9 ucles 2016 0607/11/o/n/16 11 a line is parallel to y = 3x + 1. it passes through the point (0, 7). write down the equation of this line in the form y = mx + c. y = [2] 12 12345 a b6 \u20136 \u20135 \u20134 \u20133 \u20132 \u20131 0 xy 1 2 3 4 5 6 \u20136\u20135\u20134\u20133\u20132\u20131 (a) reflect triangle a in the line x = \u20131 . [2] (b) describe the single transformation that maps triangle a onto triangle b. [3] ", "7": "7 \u00a9 ucles 2016 0607/11/o/n/16 [turn over 13 the list shows the number of ice creams sold each day by a shop for a 10 day period. 75 62 93 82 109 89 76 87 96 494 (a) write down whether this type of data is di screte or continuous. explain your answer. because [2] (b) write down which of the mean or median is th e most suitable average to use for this data. explain your answer. because [2] 14 simplify. 32xx+ [2] 15 solve the simultaneous equations. 3x + 4y = 23 6x \u2013 2y = 26 x = y = [3] question 16 is printed on the next page. ", "8": "8 permission to reproduce items where third-party owned material pr otected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknow ledgements booklet. this is produced for each series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is par t of the cambridge assessment group. cambri dge assessment is t he brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2016 0607/11/o/n/16 16 the table shows the mathematics mark, x, and the english mark, y, for each of nine students in a test. mathematics mark ( x) 95 40 30 20 70 60 80 30 25 english mark ( y) 40 70 60 80 45 40 45 75 85 (a) complete the scatter diagram. the first four points have been plotted for you. 10 20 30 40 50 80 70 60 mathematics mark0english mark xy 100 904045505560657075808590 35 [2] (b) write down the type of correlation shown on the scatter diagram. [1] (c) the mean mathematics mark is 50 and the mean english mark is 60. using this information, draw the line of best fit on your diagram. [1] " }, "0607_w16_qp_12.pdf": { "1": " this document consists of 8 printed pages. ib16 11_0607_12/5rp \u00a9 ucles 2016 [turn over *6636643373 * cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/12 paper 1 (core) october/november 2016 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2016 0607/12/o/n/16 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2016 0607/12/o/n/16 [turn over answer all the questions. 1 here is a list of numbers. 2 3 4 5 6 from this list, write down (a) the factors of 18, [1] (b) the square number, [1] (c) a prime number. [1] 2 write 0.03 as a fraction. [1] 3 a movie is 2 hours 40 minutes long. it starts at 10 40. at what time does it finish? [1] 4 work out. (a) 20 \u2013 8 \u00d7 2 [1] (b) 2 \u00d7 20 \u2013 8 [1] ", "4": "4 \u00a9 ucles 2016 0607/12/o/n/16 5 the table shows the number of books borrowe d each day from a library during one week. day monday tuesday wednesday thursday friday saturday number of books 436 297 735 626 920 1297 (a) on which day was the fewest number of books borrowed? [1] (b) find the range of the number of books borrowed. [1] 6 complete the mapping diagram. 3_26912 5172635 [1] 7 (a) write 0.08219 correct to 3 decimal places. [1] (b) write 60 952 correct to 3 significant figures. [1] 8 write down the next two numbers in this sequence. 19, 14, 9, 4, , [ 2 ] ", "5": "5 \u00a9 ucles 2016 0607/12/o/n/16 [turn over 9 not to scale 20 cm6 cm the rectangle is enlarged by a scale factor of 4. write down the size of the enlarged rectangle. length cm width cm [2] 10 north a b measure the bearing of a from b. [1] 11 write down the equation of a line parallel to y = 3x + 5. [1] 12 find the area of a circle of diameter 12 cm. give your answer in terms of \u03c0. cm2 [2] ", "6": "6 \u00a9 ucles 2016 0607/12/o/n/16 13 the area of a floor is 25 m2. jenny thinks this is the same as 2 500 cm2. is jenny correct? explain your answer. because [1] 14 the exterior angle of a regular polygon is 40\u00b0. find the number of sides of this polygon. [2] 15 b ac 30\u00b0not to scale ab is the diameter of the circle and c is a point on the circumference. work out the size of angle abc . angle abc = [2] 16 (a) simplify. (i) 30 \u00d7 6 [1] (ii) 3 31\uf8f7 \uf8f8\uf8f6\uf8ec \uf8ed\uf8eb [1] (b) find the value of n when 2n+1 = 16 . [1] ", "7": "7 \u00a9 ucles 2016 0607/12/o/n/16 [turn over 17 twenty students in a class each solve a puzzle. the time taken, t minutes, by each student to solve the puzzle is shown in the table. (a) complete the table. [1] (b) find an estimate for the mean tim e taken to solve the puzzle. min [3] 18 (a) complete the statement using one of the symbols < , = or > . 7 4 [1] (b) write down the largest integer value, x, such that (i) x \u20133, [1] (ii) 2x < 11. [1] 19 describe the single transformation that maps the graph of y = x2 onto the graph of y = x2 \u2013 2 . [2] question 20 is printed on the next page. time (minutes) number of students midpoint 0 < t 2 1 2 < t 4 6 4 < t 6 6 6 < t 8 6 8 < t 10 1 total 20 ", "8": "8 permission to reproduce items where third-party owned material pr otected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknow ledgements booklet. this is produced for each series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is par t of the cambridge assessment group. cambri dge assessment is t he brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2016 0607/12/o/n/16 20 the table shows the maximum daily temperature, x \u00b0 c, and the daily income, $ y, of an ice cream salesman. temperature ( x \u00b0 c) 25 18 30 20 25 20 22 28 15 income ($ y) 400 300 500 350 450 400 450 500 250 (a) complete the scatter diagram. the first four points have been plotted for you. 12 14 16 18 20 26 24 22 temperature ( c)150200250300350400450500550600 10income ($) xy 30 28 \u00b032100 [2] (b) write down the type of correlation shown on the scatter diagram. [1] " }, "0607_w16_qp_13.pdf": { "1": " this document consists of 8 printed pages. ib16 11_0607_13/fp \u00a9 ucles 2016 [turn over *7748862035* cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/13 paper 1 (core) october/november 2016 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2016 0607/13/o/n/16 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0r curved surface area, a, of cylinder of radius r, height h. a = 2\u03c0rh curved surface area, a, of cone of radius r, sloping edge l. a = \u03c0rl curved surface area, a, of sphere of radius r. a = 4\u03c0r2 volume, v, of prism, cross-sectional area a, length l. v =al volume, v, of pyramid, base area a, height h. v= 1 3ah volume, v, of cylinder of radius r, height h. v = \u03c0r2h volume, v, of cone of radius r, height h. v = 1 3\u03c0r2h volume, v, of sphere of radius r. v = 4 3\u03c0r3 ", "3": "3 \u00a9 ucles 2016 0607/13/o/n/16 [turn over answer all the questions. 1 here is a list of numbers. 2 3 4 5 6 from this list, write down (a) the factors of 18, [1] (b) the square number, [1] (c) a prime number. [1] 2 write 0.03 as a fraction. [1] 3 a movie is 2 hours 40 minutes long. it starts at 10 40. at what time does it finish? [1] 4 work out. (a) 20 \u2013 8 \u00d7 2 [1] (b) 2 \u00d7 20 \u2013 8 [1] ", "4": "4 \u00a9 ucles 2016 0607/13/o/n/16 5 the table shows the number of books borrowe d each day from a library during one week. day monday tuesday wednesday thursday friday saturday number of books 436 297 735 626 920 1297 (a) on which day was the fewest number of books borrowed? [1] (b) find the range of the number of books borrowed. [1] 6 complete the mapping diagram. 3_26912 5172635 [1] 7 (a) write 0.08219 correct to 3 decimal places. [1] (b) write 60 952 correct to 3 significant figures. [1] 8 write down the next two numbers in this sequence. 19, 14, 9, 4, , [ 2 ] ", "5": "5 \u00a9 ucles 2016 0607/13/o/n/16 [turn over 9 not to scale 20 cm6 cm the rectangle is enlarged by a scale factor of 4. write down the size of the enlarged rectangle. length cm width cm [2] 10 north a b measure the bearing of a from b. [1] 11 write down the equation of a line parallel to y = 3x + 5. [1] 12 find the area of a circle of diameter 12 cm. give your answer in terms of \u03c0. cm2 [2] ", "6": "6 \u00a9 ucles 2016 0607/13/o/n/16 13 the area of a floor is 25 m2. jenny thinks this is the same as 2 500 cm2. is jenny correct? explain your answer. because [1] 14 the exterior angle of a regular polygon is 40\u00b0. find the number of sides of this polygon. [2] 15 b ac 30\u00b0not to scale ab is the diameter of the circle and c is a point on the circumference. work out the size of angle abc . angle abc = [2] 16 (a) simplify. (i) 30 \u00d7 6 [1] (ii) 3 31\uf8f7 \uf8f8\uf8f6\uf8ec \uf8ed\uf8eb [1] (b) find the value of n when 2n+1 = 16 . [1] ", "7": "7 \u00a9 ucles 2016 0607/13/o/n/16 [turn over 17 twenty students in a class each solve a puzzle. the time taken, t minutes, by each student to solve the puzzle is shown in the table. (a) complete the table. [1] (b) find an estimate for the mean tim e taken to solve the puzzle. min [3] 18 (a) complete the statement using one of the symbols < , = or > . 7 4 [1] (b) write down the largest integer value, x, such that (i) x \u20133, [1] (ii) 2x < 11. [1] 19 describe the single transformation that maps the graph of y = x2 onto the graph of y = x2 \u2013 2 . [2] question 20 is printed on the next page. time (minutes) number of students midpoint 0 < t 2 1 2 < t 4 6 4 < t 6 6 6 < t 8 6 8 < t 10 1 total 20 ", "8": "8 permission to reproduce items where third-party owned material pr otected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknow ledgements booklet. this is produced for each series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is par t of the cambridge assessment group. cambri dge assessment is t he brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2016 0607/13/o/n/16 20 the table shows the maximum daily temperature, x \u00b0 c, and the daily income, $ y, of an ice cream salesman. temperature ( x \u00b0 c) 25 18 30 20 25 20 22 28 15 income ($ y) 400 300 500 350 450 400 450 500 250 (a) complete the scatter diagram. the first four points have been plotted for you. 12 14 16 18 20 26 24 22 temperature ( c)150200250300350400450500550600 10income ($) xy 30 28 \u00b032100 [2] (b) write down the type of correlation shown on the scatter diagram. [1] " }, "0607_w16_qp_21.pdf": { "1": "this document consists of 8 printed pages. dc (cw/jg) 117025/2 \u00a9 ucles 2016 [turn over * 6 3 5 0 9 3 4 6 5 0 * cambridge international mathematics 0607/21 paper 2 (extended) october/november 2016 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/21/o/n/16 \u00a9 ucles 2016formula list for the equation ax bx c02+ + = xab b ac 242!=- - curved surface area, a, of cylinder of radius r, height h. r a rh2= curved surface area, a, of cone of radius r, sloping edge l. r a rl= curved surface area, a, of sphere of radius r. r a r42= v olume, v, of pyramid, base area a, height h. v ah31= v olume, v, of cylinder of radius r, height h. rv r h2= v olume, v, of cone of radius r, height h. r v r h31 2= v olume, v, of sphere of radius r. r v r34 3= sin sin sin aa bb cc= = cos a b c bc a 22 2 2= + - sinbc a21area=a c bcb a", "3": "3 0607/21/o/n/16 \u00a9 ucles 2016 [turn overanswer all the questions. 1 sara and klaus share some money in the ratio 5 : 4 . klaus receives $48. work out how much sara receives. $ [2] 2a p n f h from the list above, write down the letter which has line symmetry only, line symmetry and rotational symmetry, rotational symmetry only. [2] 3 the list shows the quiz scores of 13 students. 11 11 11 12 12 13 14 15 15 16 16 19 19 find (a) the mode, [1] (b) the median, [1] (c) the upper quartile. [1] 4 write .4 07 1 03#- as an ordinary number. [1]", "4": "4 0607/21/o/n/16 \u00a9 ucles 20165 v = u + at (a) find v when , u a 5 1= = - and t = 1.5 . v = [2] (b) rearrange the formula to write a in terms of t, u and v. a = [2] 6 work out 98 187- , giving your answer in its lowest terms. [3] 7 the interior angle of a regular polygon is 176\u00b0. work out how many sides the polygon has. [3]", "5": "5 0607/21/o/n/16 \u00a9 ucles 2016 [turn over8 120\u00b0 100\u00b0y\u00b0 a bcd onot to scale a, b, c and d lie on the circle, centre o. work out the value of y. y = [3] 9 on each venn diagram, shade the area indicated. ( )p q+ l w v x + + l lp v w xqu u [2]", "6": "6 0607/21/o/n/16 \u00a9 ucles 201610 multiply out the brackets and simplify. ( ) ( ) 2 3 1 3 2 - + [2] 11 solve the equation. x3 1- = [2] 12 find the value of 2523-. [2] 13 x is positive and x 38 4= . find the exact value of x. x = [2]", "7": "7 0607/21/o/n/16 \u00a9 ucles 2016 [turn over14 the roots of the quadratic equation x ax b 02+ + = are 5 and - 2. find the value of a and the value of b. a = [3] b = [3] 15 y is inversely proportional to the square root of ( x - 3). when x = 7, y = 3. find y in terms of x. y = ... [2] 16 2y x \u2013245 900 the diagram shows the graph of ( ) \u00b0 sin y a bx = , for x0 90g g . find the value of a and the value of b. a = [2] b = [2] question 17 is printed on the next page", "8": "8 0607/21/o/n/16 \u00a9 ucles 201617 (a) log log k 2 3 = find the value of k. k = [1] (b) log log logp 5 2- = find the value of p. p = [1] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_w16_qp_22.pdf": { "1": "this document consists of 8 printed pages. dc (nf/jg) 117022/1 \u00a9 ucles 2016 [turn over * 1 6 8 2 9 3 5 5 7 6 * cambridge international mathematics 0607/22 paper 2 (extended) october/november 2016 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/22/o/n/16 \u00a9 ucles 2016formula list for the equation ax bx c02+ + = xab b ac 242!=- - curved surface area, a, of cylinder of radius r, height h. r a rh2= curved surface area, a, of cone of radius r, sloping edge l. r a rl= curved surface area, a, of sphere of radius r. r a r42= v olume, v, of pyramid, base area a, height h. v ah31= v olume, v, of cylinder of radius r, height h. rv r h2= v olume, v, of cone of radius r, height h. r v r h31 2= v olume, v, of sphere of radius r. r v r34 3= sin sin sin aa bb cc= = cos a b c bc a 22 2 2= + - sinbc a21area=a c bcb a", "3": "3 0607/22/o/n/16 \u00a9 ucles 2016 [turn overanswer all the questions. 1 25 26 27 28 29 30 from this list, write down a prime number. [1] 2 $84 is divided in the ratio 3 : 4. find the value of the largest share. $ [2] 3 in a sale, the price of all furniture is reduced by 30%. (a) before the sale the price of a chair was $40. find the price of this chair in the sale. $ [2] (b) in the sale, the price of a table is $140. find the price of this table before the sale. $ [3]", "4": "4 0607/22/o/n/16 \u00a9 ucles 20164 work out the following, giving each answer in standard form. (a) 6.4 10 1.6 102 3# # -- -^ ^ h h [2] (b) 6.4 10 1.6 102 3' # #- -^ ^ h h [2] 5 one day there were 720 students at a school. the table shows the type of transport the students used to get to school. type of transport walk bus car bicycle number of students 117 280 240 x (a) find the value of x. x = [1] (b) find the relative frequency of students who went to school by car. give your answer as a fraction in its lowest terms. [2]", "5": "5 0607/22/o/n/16 \u00a9 ucles 2016 [turn over6 a bag contains 10 discs. 5 discs are red, 4 are blue and 1 is green. a disc is chosen at random and not replaced. a second disc is then chosen at random. find the probability that (a) both discs are green, [1] (b) both discs are the same colour. [3] 7 expand the brackets and simplify. (a) x x x x 3 4 5 5 3 2 - - + ^ ^ h h [2] (b) x y x y 4 3 2 - +^ ^ h h [3]", "6": "6 0607/22/o/n/16 \u00a9 ucles 20168 find the value of 6431. [1] 9 find the highest common factor (hcf) of x y83 4 and x y124. [2] 10 in each of the following, rationalise the denominator and simplify your answer. (a) 36 [2] (b) 2 33 + [2]", "7": "7 0607/22/o/n/16 \u00a9 ucles 2016 [turn over11 the points a (3, 8) and b (9, 0) are shown on the diagram below. y x0ba not to scale find the equation of the perpendicular bisector of the line ab. [5] question 12 is printed on the next page.", "8": "8 0607/22/o/n/16 \u00a9 ucles 201612 y is proportional to the square of x. when x = 4, y = 8. (a) find an equation connecting y and x. [2] (b) find the values of x when y = 32. [2] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_w16_qp_23.pdf": { "1": "this document consists of 8 printed pages. dc (nh/sw) 117016/2 \u00a9 ucles 2016 [turn over * 1 4 4 1 5 4 4 9 3 8 * cambridge international mathematics 0607/23 paper 2 (extended) october/november 2016 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/23/o/n/16 \u00a9 ucles 2016formula list for the equation ax bx c02+ + = xab b ac 242!=- - curved surface area, a, of cylinder of radius r, height h. r a rh2= curved surface area, a, of cone of radius r, sloping edge l. r a rl= curved surface area, a, of sphere of radius r. r a r42= v olume, v, of pyramid, base area a, height h. v ah31= v olume, v, of cylinder of radius r, height h. rv r h2= v olume, v, of cone of radius r, height h. r v r h31 2= v olume, v, of sphere of radius r. r v r34 3= sin sin sin aa bb cc= = cos a b c bc a 22 2 2= + - sinbc a21area=a c bcb a", "3": "3 0607/23/o/n/16 \u00a9 ucles 2016 [turn overanswer all the questions. 1 here are the first four terms of a sequence. 11 8 5 2 write down the next term of the sequence. [1] 2 use the formula 2ahx y= + ^ h to find the value of a when x = 7, y = 13 and h = 6.4 . a = ... [2] 3 work out. (a) (0.2)3 [1] (b) 73 54' [2] 42x\u00b0 2x\u00b0 60\u00b0not to scalex\u00b0 x\u00b0 the diagram shows a pentagon. find the value of x. x = ... [3]", "4": "4 0607/23/o/n/16 \u00a9 ucles 20165 triangle b is the image of triangle a after a reflection. triangle c is the image of triangle b after an enlargement, scale factor 2. triangle d is the image of triangle c after a rotation. triangle e is the image of triangle d after a stretch, factor 3. complete this table. write c if the triangles are congruent. write s if the triangles are similar. write n if the triangles are neither congruent nor similar. triangles c, s or n a and b a and c b and d d and e [3] 6 the table shows the numbers of pets owned by each of 100 families. number of pets frequency 0 23 1 37 2 25 3 10 4 5 (a) write down the range. [1] (b) find the median. [1] (c) work out the mean. . [2]", "5": "5 0607/23/o/n/16 \u00a9 ucles 2016 [turn over7 solve the simultaneous equations. 4x \u2013 3y = 12 6x \u2013 y = 11 x = ... y = ... [3] 8 jakob draws a scatter diagram which shows that two quantities, x and y, are correlated. he calculates the equation of the regression line as y = 32 \u2013 1.5 x. (a) what type of correlation is there between x and y? [1] (b) the mean of the y values is 14. find the mean of the x values. [2]", "6": "6 0607/23/o/n/16 \u00a9 ucles 20169 75\u00b0 40\u00b0not to scalea b cde p a, b, c, d and e are points on a circle. ce and ad intersect at p . angle dcp = 40\u00b0 and angle cpd = 75\u00b0. find (a) angle dae , angle dae = ... [1] (b) angle abc. angle abc= ... [2] 10 (a) find log5 25. [1] (b) 2 log 3 \u2013 log 5 = log p find p. p = ... [2]", "7": "7 0607/23/o/n/16 \u00a9 ucles 2016 [turn over11 solve. 4x + 2 > 3(2 x \u2013 4) [3] 12 not to scale ap q oc ab c oabc is a parallelogram. p is the midpoint of cb. cq : qa = 5 : 3. oa = a and oc = c. find these vectors in terms of a and/or c, giving your answers in their simplest form. (a) cp [1] (b) oq [3] question 13 is printed on the next page.", "8": "8 0607/23/o/n/16 \u00a9 ucles 2016permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.13 simplify. (a) 212 [2] (b) 5 2 32-^ h [3]" }, "0607_w16_qp_31.pdf": { "1": "* 3 8 7 9 8 2 5 3 3 5 * this document consists of 16 printed pages. dc (slm/jg) 114970/2 \u00a9 ucles 2016 [turn overcambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/31 paper 3 (core) october/november 2016 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. y ou may use a pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.", "2": "2 0607/31/o/n/16 \u00a9 ucles 2016formula list area, a, of triangle, base b, height h. a = 21bh area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = 31ah v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = 31 rr2h v olume, v, of sphere of radius r. v = 34 rr3", "3": "3 0607/31/o/n/16 \u00a9 ucles 2016 [turn overanswer all the questions. 1 a bcnot to scale x cm y cm 12 cm the diagram shows three regular shapes a, b and c. (a) write down the correct mathematical name of each shape. shape a ... shape b ... shape c ... [4] (b) each shape has the same perimeter. find the value of x and the value of y. x = cm y = cm [3]", "4": "4 0607/31/o/n/16 \u00a9 ucles 20162 a conference centre has 6 rooms. one day all the rooms are used. room numbernumber of people 1 7 2 6 3 12 4 10 5 9 6 11 (a) find the total number of people in the six rooms. [1] (b) complete the bar chart for the information above. 1 2 3 4 5 60number of people room number4 2681012 [2]", "5": "5 0607/31/o/n/16 \u00a9 ucles 2016 [turn over (c) the cost of using each of the rooms for the day is $300. the cost is shared equally between the people using it. (i) calculate the total cost of using all six rooms. $ [1] (ii) for room 4, find the cost per person to use the room. $ [1] (iii) each person in room 2 has a lunch that costs $8 per person. find the total amount paid by all six people in room 2. $ [2]", "6": "6 0607/31/o/n/16 \u00a9 ucles 20163 (a) 3 9 85 21 -6 r -0.75 0.33 -18 352 from this list, write down (i) a positive integer, [1] (ii) a negative integer, [1] (iii) a square number, [1] (iv) a number between 0.5 and 1, [1] (v) an irrational number. [1] (b) write 3 as a decimal (i) correct to 4 decimal places, [1] (ii) correct to 4 significant figures. [1] ", "7": "7 0607/31/o/n/16 \u00a9 ucles 2016 [turn over (c) write 0.33 as a fraction. [1] (d) write 352 as a decimal. [1] (e) write 85 as a percentage. % [1] ", "8": "8 0607/31/o/n/16 \u00a9 ucles 20164 (a) money write down all the letters from this word that have (i) line symmetry, [2] (ii) rotational symmetry. [2] (b) a bc 15 cm 9 cm d ef 4 cm3 cmnot to scale the diagram shows two right-angled triangles. triangle abc is similar to triangle def . (i) work out the lengths ab and df. ab = .. cm df = .. cm [3] (ii) find the ratio area of triangle abc : area of triangle def . .. : .. [2] ", "9": "9 0607/31/o/n/16 \u00a9 ucles 2016 [turn over5 tutku counts the number of petals on each of 100 flowers. her results are shown in the table. number of petals frequency 15 5 16 10 17 12 18 24 19 27 20 14 21 6 22 2 find (a) the mode, [1] (b) the median, [1] (c) the interquartile range, [2] (d) the mean. [2] ", "10": "10 0607/31/o/n/16 \u00a9 ucles 20166 these are the first four terms of a sequence. 326 319 312 305 (a) find the next two terms in this sequence. . , . [2] (b) find an expression for the nth term of this sequence. [2] (c) pedro says that 249 is a term in this sequence. is he correct? show working to support your answer. [1]", "11": "11 0607/31/o/n/16 \u00a9 ucles 2016 [turn over7 (a) ab dc ea\u00b0b\u00b0 c\u00b0 d \u00b0not to scale 107\u00b042\u00b0 the diagram shows a parallelogram abcd and a straight line cde . find the values of a, b, c and d. a = ... b = ... c = ... d = ... [4] (b) bad coep\u00b062\u00b0q\u00b0 r\u00b0not to scale the diagram shows a circle, centre o, with diameter eb. the line ac is a tangent to the circle at b. d is a point on the circumference and angle abd = 62\u00b0. find the values of p, q and r. p = ... q = ... r = ... [3]", "12": "12 0607/31/o/n/16 \u00a9 ucles 20168 on any evening, the probability that elise goes to a caf\u00e9 is 52. if elise goes to a caf\u00e9, the probability that she then goes to the cinema is 31. if she does not go to a caf\u00e9, the probability that she then goes to the cinema is 74. (a) complete the tree diagram. cinema not cinema cinema not cinema..caf\u00e9 2 5 not caf\u00e9.. 1 3 [3] (b) find the probability that, on one evening, elise goes to a caf\u00e9 and goes to the cinema. [2] (c) find the probability that, on one evening, elise goes to the cinema. [3] ", "13": "13 0607/31/o/n/16 \u00a9 ucles 2016 [turn over9 sally leaves home to go to school at 07 45. she walks 100 metres to the bus stop and arrives at 07 50. (a) work out her average walking speed in km/h. ... km/h [3] (b) the bus leaves the bus stop at 07 55. it travels the 6 km to school at an average speed of 40 km/h. (i) calculate the number of minutes that the bus takes to get to school. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd min [3] (ii) work out the time that the bus gets to school. [1] (iii) sally takes 5 minutes to walk from the bus to the classroom. the lesson starts at 08 15. show that sally gets to the classroom before the lesson starts. [1]", "14": "14 0607/31/o/n/16 \u00a9 ucles 201610 (a) solve. (i) x x5 2 3 6+ = + [2] (ii) x4 10 10 1 - [2] (b) show x 22- on the number line. \u20135\u20134\u20133\u20132\u2013101234x [1] (c) simplify. (i) x x6 22 6# [2] (ii) yy 515 28 [2] (d) yassar buys 2 bottles of drink and 3 bars of chocolate for $5.25 . hassan buys 1 bottle of drink and 2 bars of chocolate for $3.05 . find the cost of 1 bottle of drink and the cost of 1 bar of chocolate. show all your working. 1 bottle of drink = $ ... 1 bar of chocolate = $ ... [4]", "15": "15 0607/31/o/n/16 \u00a9 ucles 2016 [turn over11 not to scale 12 m0.5 m 1.5 m6 m the diagram shows a rectangular garden, 6 m by 12 m. in the garden there is a circular pond with radius 1.5 m. there is a circular path of width 0.5 m around the pond. (a) the pond is 0.6 m deep. work out the volume of water in the pond when it is full. m3 [2] (b) work out the area of the path. m2 [2] (c) the rest of the garden, apart from the pond and the path, is covered by grass. work out the area covered by grass. m2 [2] question 12 is printed on the next page.", "16": "16 0607/31/o/n/16 \u00a9 ucles 2016permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.12 \u20133 \u20136y x 48 0 ( )x x x 6 f2= + - (a) (i) on the diagram, sketch the graph of ( ) y x x 3 4 f f or g g = - . [2] (ii) find the co-ordinates of the point where the graph cuts the y-axis. ( , ) [1] (iii) find the co-ordinates of the points where the graph cuts the x-axis. ( , ) and ( , ) [2] (iv) find the co-ordinates of the local maximum point. ( , ) [1] (b) ( )x x 4 g= + (i) on the diagram, sketch the graph of ( ) y x g= . [2] (ii) find the co-ordinates of the points of intersection of the graph of ( )xf and the graph of ( )xg. ( , ) and ( , ) [2]" }, "0607_w16_qp_32.pdf": { "1": "this document consists of 19 printed pages and 1 blank page. dc (lk/sg) 114937/2 \u00a9 ucles 2016 [turn overcambridge international examinations cambridge international general certificate of secondary education * 9 7 8 3 5 5 6 2 9 6 * cambridge international mathematics 0607/32 paper 3 (core) october/november 2016 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.", "2": "2 0607/32/o/n/16 \u00a9 ucles 2016formula list area, a, of triangle, base b, height h. a = 21bh area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = 31ah v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = 31 rr2h v olume, v, of sphere of radius r. v = 34 rr3", "3": "3 0607/32/o/n/16 \u00a9 ucles 2016 [turn overanswer all the questions. 1 (a) here is a child\u2019s drawing of a house and the path leading to the door. complete each label with the mathematical name of the shaded shape. ... .. ... [4] (b) here is a rectangle. (i) write down the order of rotational symmetry of the rectangle. [1] (ii) on the rectangle, draw all the lines of symmetry. [2]", "4": "4 0607/32/o/n/16 \u00a9 ucles 20162 175 students, aged 14, 15 or 16, are going on a school trip. (a) the bar chart below shows the number of males (m) and females (f) in each age group. 45 40 35 30 25 20 15 10 5 0 m f m f m f age 14 age 15 age 16number of students (i) find the number of females aged 16. [1] (ii) of the students aged 14, find how many more females than males there are. [1] (iii) find the total number of students aged 15. [2]", "5": "5 0607/32/o/n/16 \u00a9 ucles 2016 [turn over (b) the trip costs each student $25. work out the total amount the 175 students pay. give your answer correct to the nearest hundred dollars. $ ... [2] (c) 12 teachers, together with the 175 students all travel by coach. each coach holds 44 passengers. work out how many coaches will be needed. [3]", "6": "6 0607/32/o/n/16 \u00a9 ucles 20163 (a) (i) measure the size of angle p. p angle p = ... [1] (ii) what type of angle is angle p? choose from the list below. acute obtuse reflex right-angle [1] (b) 33\u00b0yz xnot to scale find the size of angle x, angle y and angle z. angle x = ... angle y = ... angle z = ... [3]", "7": "7 0607/32/o/n/16 \u00a9 ucles 2016 [turn over4 here are the first three patterns in a sequence. pattern 1 pattern 2 pattern 3 pattern 4 (a) in the space above, draw pattern 4. [1] (b) complete the table. pattern number 1 2 3 4 5 number of squares 4 7 10 [1] (c) explain how you can find the number of squares in pattern 5 without drawing it. ... . [1] (d) tom thinks the formula for the number of squares in pattern n is n + 3. sarah thinks the formula is 3 n + 1. is tom correct? is sarah correct? show clearly how you decide. [3]", "8": "8 0607/32/o/n/16 \u00a9 ucles 20165 sammy lives 641 km from school. (a) calculate the total distance that sammy will travel to school and back in 5 days. .. km [2] (b) the bus that sammy catches travels the 641 km at an average speed of 30 km/h. work out the time the bus takes to get to school. give your answer in minutes and seconds. .. minutes .. seconds [4]", "9": "9 0607/32/o/n/16 \u00a9 ucles 2016 [turn over6 (a) find the value of 6 x + 9y when x = 2 and y = 5. [2] (b) simplify. 6x + 9 \u2212 x + 4 [2] (c) factorise. 6x + 9y . [1]", "10": "10 0607/32/o/n/16 \u00a9 ucles 20167 a piece of cheese is in the shape of a prism. 10 cmnot to scale 12 cm 8 cm6 cm (a) work out the area of the shaded triangle. . cm2 [2] (b) work out the total surface area of the cheese. . cm2 [3] (c) calculate the volume of the cheese. cm3 [1]", "11": "11 0607/32/o/n/16 \u00a9 ucles 2016 [turn over8 aisha owns a shop. (a) in the shop, 5 chocolate bars cost a total of $8.95 . work out how much 9 of these chocolate bars cost. $ ... [3] (b) aisha bought cans of drink for $1.20 each. she wants to sell these cans to make a profit of 15%. work out how much she should sell each can for. $ ... [3] (c) she bought cakes for $5.50 each and sold them for $4.84 each. work out the percentage loss on each cake. % [3]", "12": "12 0607/32/o/n/16 \u00a9 ucles 20169 solve these equations. (a) x 52= x = [1] (b) 3(2x \u2013 1) = 9 x = [3] (c) 7x + 2 = 20 + 3 x x = [3]", "13": "13 0607/32/o/n/16 \u00a9 ucles 2016 [turn over10 (a) complete the table of values for y3 2x#= . x \u20132 \u20131 0 1 2 3 y 0.75 1.5 [1] (b) on the diagram, sketch the graph of y3 2x#= for x2 3g g- . 025 \u20135\u20132 3xy [2] (c) (i) on the diagram, sketch the line y = 8. [1] (ii) find the value of x where the graphs of y3 2x#= and y = 8 intersect. x = ... [1]", "14": "14 0607/32/o/n/16 \u00a9 ucles 201611 (a) steve is growing plants. here are the heights, in centimetres, of 11 plants that he grows. 27 30 10 25 41 32 27 12 20 29 17 work out the median and inter-quartile range of these heights. median = . cm inter-quartile range = . cm [3] (b) tam is growing the same type of plants. the cumulative frequency curve shows the heights of 80 plants that she grows. 80 70 60 50 40 30 20 10 0 0 5 10 15 20 25 30 35 40 45cumulative frequency height of plant (cm)", "15": "15 0607/32/o/n/16 \u00a9 ucles 2016 [turn over find the median and inter-quartile range of the heights of tam\u2019s plants. median = . cm inter-quartile range = cm [3] (c) use your answers to part (a) and part (b) to compare the heights of steve\u2019s plants and tam\u2019s plants. ... ... ... . [2]", "16": "16 0607/32/o/n/16 \u00a9 ucles 201612 marcel has a box of coloured beads. he takes a bead from the box at random, writes down its colour and returns it to the box. he repeats this 200 times. his results are shown in the table. colour red white blue number 91 42 67 (a) use the information given to complete the relative frequencies in the table below. write each value as a decimal. colour red white blue relative frequency0.455 [2] (b) give a reason why the information in part (a) gives a good estimate of the probability of taking each of the colours from the box. ... . [1] (c) there are 5000 beads in the box. calculate an estimate of the number of blue beads in the box. [2]", "17": "17 0607/32/o/n/16 \u00a9 ucles 2016 [turn over (d) marcel selects a bead from the box at random. calculate an estimate of the probability that the bead is red or white. [2] 13 this is an important formula in physics. e = mc2 (a) work out the value of e when . m 1 3 104#=- and . c3 0 108#= . give your answer in standard form. [2] (b) write .1 3 104#- as an ordinary number. [1] (c) rearrange the formula e = mc2 to make c the subject. c = ... [2]", "18": "18 0607/32/o/n/16 \u00a9 ucles 201614 the diagram shows the frame of a window made from metal rods. the shape is a rectangle with a semi-circle on top. not to scale 100 cm 80 cm work out the total length of the metal rods needed to make the window frame. .. cm [6]", "19": "19 0607/32/o/n/16 \u00a9 ucles 201615 (a) x cm 6.7 cm4.6 cmnot to scale find the value of x. x = ... [2] (b) here is another right-angled triangle. 23\u00b0y cm 10.8 cmnot to scale use trigonometry to find the value of y. y = ... [3]", "20": "20 0607/32/o/n/16 \u00a9 ucles 2016permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_w16_qp_33.pdf": { "1": "this document consists of 19 printed pages and 1 blank page. dc (rw) 126391 \u00a9 ucles 2016 [turn overcambridge international examinations cambridge international general certificate of secondary education * 8 7 3 5 3 9 2 5 5 2 * cambridge international mathematics 0607/33 paper 3 (core) october/november 2016 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.", "2": "2 0607/33/o/n/16 \u00a9 ucles 2016formula list area, a, of triangle, base b, height h. a = 21bh area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = 31ah v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = 31 rr2h v olume, v, of sphere of radius r. v = 34 rr3", "3": "3 0607/33/o/n/16 \u00a9 ucles 2016 [turn overanswer all the questions. 1 (a) here is a child\u2019s drawing of a house and the path leading to the door. complete each label with the mathematical name of the shaded shape. ... .. ... [4] (b) here is a rectangle. (i) write down the order of rotational symmetry of the rectangle. [1] (ii) on the rectangle, draw all the lines of symmetry. [2]", "4": "4 0607/33/o/n/16 \u00a9 ucles 20162 175 students, aged 14, 15 or 16, are going on a school trip. (a) the bar chart below shows the number of males (m) and females (f) in each age group. 45 40 35 30 25 20 15 10 5 0 m f m f m f age 14 age 15 age 16number of students (i) find the number of females aged 16. [1] (ii) of the students aged 14, find how many more females than males there are. [1] (iii) find the total number of students aged 15. [2]", "5": "5 0607/33/o/n/16 \u00a9 ucles 2016 [turn over (b) the trip costs each student $25. work out the total amount the 175 students pay. give your answer correct to the nearest hundred dollars. $ ... [2] (c) 12 teachers, together with the 175 students all travel by coach. each coach holds 44 passengers. work out how many coaches will be needed. [3]", "6": "6 0607/33/o/n/16 \u00a9 ucles 20163 (a) (i) measure the size of angle p. p angle p = ... [1] (ii) what type of angle is angle p? choose from the list below. acute obtuse reflex right-angle [1] (b) 33\u00b0yz xnot to scale find the size of angle x, angle y and angle z. angle x = ... angle y = ... angle z = ... [3]", "7": "7 0607/33/o/n/16 \u00a9 ucles 2016 [turn over4 here are the first three patterns in a sequence. pattern 1 pattern 2 pattern 3 pattern 4 (a) in the space above, draw pattern 4. [1] (b) complete the table. pattern number 1 2 3 4 5 number of squares 4 7 10 [1] (c) explain how you can find the number of squares in pattern 5 without drawing it. ... . [1] (d) tom thinks the formula for the number of squares in pattern n is n + 3. sarah thinks the formula is 3 n + 1. is tom correct? is sarah correct? show clearly how you decide. [3]", "8": "8 0607/33/o/n/16 \u00a9 ucles 20165 sammy lives 641 km from school. (a) calculate the total distance that sammy will travel to school and back in 5 days. .. km [2] (b) the bus that sammy catches travels the 641 km at an average speed of 30 km/h. work out the time the bus takes to get to school. give your answer in minutes and seconds. .. minutes .. seconds [4]", "9": "9 0607/33/o/n/16 \u00a9 ucles 2016 [turn over6 (a) find the value of 6 x + 9y when x = 2 and y = 5. [2] (b) simplify. 6x + 9 \u2212 x + 4 [2] (c) factorise. 6x + 9y . [1]", "10": "10 0607/33/o/n/16 \u00a9 ucles 20167 a piece of cheese is in the shape of a prism. 10 cmnot to scale 12 cm 8 cm6 cm (a) work out the area of the shaded triangle. . cm2 [2] (b) work out the total surface area of the cheese. . cm2 [3] (c) calculate the volume of the cheese. cm3 [1]", "11": "11 0607/33/o/n/16 \u00a9 ucles 2016 [turn over8 aisha owns a shop. (a) in the shop, 5 chocolate bars cost a total of $8.95 . work out how much 9 of these chocolate bars cost. $ ... [3] (b) aisha bought cans of drink for $1.20 each. she wants to sell these cans to make a profit of 15%. work out how much she should sell each can for. $ ... [3] (c) she bought cakes for $5.50 each and sold them for $4.84 each. work out the percentage loss on each cake. % [3]", "12": "12 0607/33/o/n/16 \u00a9 ucles 20169 solve these equations. (a) x 52= x = [1] (b) 3(2x \u2013 1) = 9 x = [3] (c) 7x + 2 = 20 + 3 x x = [3]", "13": "13 0607/33/o/n/16 \u00a9 ucles 2016 [turn over10 (a) complete the table of values for y3 2x#= . x \u20132 \u20131 0 1 2 3 y 0.75 1.5 [1] (b) on the diagram, sketch the graph of y3 2x#= for x2 3g g- . 025 \u20135\u20132 3xy [2] (c) (i) on the diagram, sketch the line y = 8. [1] (ii) find the value of x where the graphs of y3 2x#= and y = 8 intersect. x = ... [1]", "14": "14 0607/33/o/n/16 \u00a9 ucles 201611 (a) steve is growing plants. here are the heights, in centimetres, of 11 plants that he grows. 27 30 10 25 41 32 27 12 20 29 17 work out the median and inter-quartile range of these heights. median = . cm inter-quartile range = . cm [3] (b) tam is growing the same type of plants. the cumulative frequency curve shows the heights of 80 plants that she grows. 80 70 60 50 40 30 20 10 0 0 5 10 15 20 25 30 35 40 45cumulative frequency height of plant (cm)", "15": "15 0607/33/o/n/16 \u00a9 ucles 2016 [turn over find the median and inter-quartile range of the heights of tam\u2019s plants. median = . cm inter-quartile range = cm [3] (c) use your answers to part (a) and part (b) to compare the heights of steve\u2019s plants and tam\u2019s plants. ... ... ... . [2]", "16": "16 0607/33/o/n/16 \u00a9 ucles 201612 marcel has a box of coloured beads. he takes a bead from the box at random, writes down its colour and returns it to the box. he repeats this 200 times. his results are shown in the table. colour red white blue number 91 42 67 (a) use the information given to complete the relative frequencies in the table below. write each value as a decimal. colour red white blue relative frequency0.455 [2] (b) give a reason why the information in part (a) gives a good estimate of the probability of taking each of the colours from the box. ... . [1] (c) there are 5000 beads in the box. calculate an estimate of the number of blue beads in the box. [2]", "17": "17 0607/33/o/n/16 \u00a9 ucles 2016 [turn over (d) marcel selects a bead from the box at random. calculate an estimate of the probability that the bead is red or white. [2] 13 this is an important formula in physics. e = mc2 (a) work out the value of e when . m 1 3 104#=- and . c3 0 108#= . give your answer in standard form. [2] (b) write .1 3 104#- as an ordinary number. [1] (c) rearrange the formula e = mc2 to make c the subject. c = ... [2]", "18": "18 0607/33/o/n/16 \u00a9 ucles 201614 the diagram shows the frame of a window made from metal rods. the shape is a rectangle with a semi-circle on top. not to scale 100 cm 80 cm work out the total length of the metal rods needed to make the window frame. .. cm [6]", "19": "19 0607/33/o/n/16 \u00a9 ucles 201615 (a) x cm 6.7 cm4.6 cmnot to scale find the value of x. x = ... [2] (b) here is another right-angled triangle. 23\u00b0y cm 10.8 cmnot to scale use trigonometry to find the value of y. y = ... [3]", "20": "20 0607/33/o/n/16 \u00a9 ucles 2016permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_w16_qp_41.pdf": { "1": "this document consists of 19 printed pages and 1 blank page. dc (nf/sg) 117023/2 \u00a9 ucles 2016 [turn over * 6 6 1 6 4 7 4 6 3 4 * cambridge international mathematics 0607/41 paper 4 (extended) october/november 2016 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/41/o/n/16 \u00a9 ucles 2016formula list for the equation ax bx c02+ + = xab b ac 242!=- - curved surface area, a, of cylinder of radius r, height h. r a rh2= curved surface area, a, of cone of radius r, sloping edge l. r a rl= curved surface area, a, of sphere of radius r. r a r42= v olume, v, of pyramid, base area a, height h. v ah31= v olume, v, of cylinder of radius r, height h. rv r h2= v olume, v, of cone of radius r, height h. r v r h31 2= v olume, v, of sphere of radius r. r v r34 3= sin sin sin aa bb cc= = cos a b c bc a 22 2 2= + - sinbc a21area=a c bcb a", "3": "3 0607/41/o/n/16 \u00a9 ucles 2016 [turn overanswer all the questions. 1 toby takes a journey from johannesburg to zurich. (a) he changes 2500 rand into swiss francs (chf). 1 swiss franc = 12.43 rand. calculate the amount toby receives in swiss francs. give your answer correct to the nearest swiss franc. .. chf [2] (b) toby leaves johannesburg at 19 30 and arrives in zurich at 06 10 the next morning. local time in zurich is the same as local time in johannesburg. the distance from johannesburg to zurich is 8350 km. (i) calculate the average speed of the journey. ... km/h [3] (ii) after arriving at 06 10, toby takes a further 1 hour 55 minutes to reach his office. work out the time he arrives at his office. [1] (iii) later, toby takes a taxi from his office to a hotel. the taxi fare is made up of a fixed charge of 20 chf plus 2.40 chf per kilometre. toby paid 36.80 chf altogether. work out the distance of toby\u2019s taxi journey. .. km [3]", "4": "4 0607/41/o/n/16 \u00a9 ucles 20162 p t r q8 7910y x6 5 4 3 2 1 \u20133 \u20134\u20132\u20131 \u20135 \u20136 \u20137 \u20138 \u20139 \u201310\u20131\u20132\u20133\u20134\u20135\u20136\u20137\u20138\u20139\u201310 102345678910 (a) u3 2=- -j lkkn poo and v5 3=- -j lkkn poo (i) find u + v.j lk kkn po oo [1] (ii) draw the image of triangle t under the translation by the vector u + v. [2] (iii) calculate | u + v|. [2]", "5": "5 0607/41/o/n/16 \u00a9 ucles 2016 [turn over (b) describe fully the single transformation that maps (i) triangle t onto triangle p, ... . [2] (ii) triangle t onto triangle q, ... . [3] (iii) triangle t onto triangle r. ... . [3]", "6": "6 0607/41/o/n/16 \u00a9 ucles 20163 x 2 fsinx=^h (a) on the diagram, sketch the graph of y = f(x) for \u00b0 \u00b0x 360 360 g g - . 03 \u20130.5\u2013360\u00b0 360\u00b0y x [3] (b) find the range of f( x). [2] (c) find the value of f( x) when (i) x = 3780\u00b0, [1] (ii) x = 4050\u00b0. [1]", "7": "7 0607/41/o/n/16 \u00a9 ucles 2016 [turn over (d) (i) find the four values of x from \u2212360\u00b0 to 1080\u00b0 for which f( x) = 0.5 . , , , [2] (ii) the values in the answer to part (d)(i) form the first four terms of a sequence. find the nth term of this sequence. [2] (e) xx x 16200360g=-^^hh (i) on the diagram, sketch the graph of y = g( x) for \u00b0 \u00b0x 0 360 g g . [2] (ii) solve the equation f( x) = g( x). x = . or x = [2]", "8": "8 0607/41/o/n/16 \u00a9 ucles 20164 9 cm 9 cmnot to scale the diagrams show a solid hemisphere and a solid cone. both the hemisphere and the base of the cone have radius 9 cm. the volumes of the two shapes are equal. (a) show that the perpendicular height of the cone is 18 cm. [2] (b) (i) calculate the total surface area of the hemisphere. cm2 [2]", "9": "9 0607/41/o/n/16 \u00a9 ucles 2016 [turn over (ii) calculate the curved surface area of the cone. cm2 [3] (c) the hemisphere is made from metal. the metal is melted down and made into spheres of radius 2 cm. calculate the number of spheres that are made. [3]", "10": "10 0607/41/o/n/16 \u00a9 ucles 20165 u p q n(u) = 25 n( p) = 18 n( q) = 12 p q 3 n,=l ^ h . (a) show that p q 8 n+= ^ h . [2] (b) an element is chosen at random from u. find the probability that the element is a member of (i) p q,, [1] (ii) p q, l. [1] (c) an element is chosen at random from p. find the probability that this element is also a member of q. [1] (d) the probability of a single event is 32. describe this event in terms of p and q. . [1]", "11": "11 0607/41/o/n/16 \u00a9 ucles 2016 [turn over6 xy a b0not to scale a is the point (0, 6) and b is the point (4, 0). (a) find the equation of the perpendicular bisector of ab. [5] (b) xy a c b0not to scale the line y = 2x + 3 cuts the y-axis at c. the perpendicular bisector of ab cuts the y-axis at d. find the length cd. cd = [2]", "12": "12 0607/41/o/n/16 \u00a9 ucles 20167 p q c bx d a 20 cm10 cm9 cm not to scale the diagram shows a triangular prism with a horizontal base abcd . x is a point on the line aq. ab = 20 cm, bc = 10 cm, cq = 9 cm and angle bcq = 90\u00b0. (a) calculate angle qbc . angle qbc = [2] (b) calculate angle baq and show that it rounds to 33.9\u00b0, correct to 1 decimal place. [3]", "13": "13 0607/41/o/n/16 \u00a9 ucles 2016 [turn over (c) ax = 22 cm. calculate the length of bx. bx = .. cm [3]", "14": "14 0607/41/o/n/16 \u00a9 ucles 20168 y x0 \u20132\u20134 48 x xx13 f= + + ^h (a) on the diagram, sketch the graph of y = f(x) for values of x between \u22124 and 4. [2] (b) find the zeros of f( x). [2] (c) solve the inequality f( x) < 0. [3] (d) the asymptotes of the graph are x = a and y = x + b, where a and b are integers. find the value of a and the value of b. a = b = [2] (e) x xx1g= +^h describe fully the single transformation that maps the graph of y = f(x) onto the graph of y = g( x). ... . [2]", "15": "15 0607/41/o/n/16 \u00a9 ucles 2016 [turn over9 in one day a delivery company delivers 93 parcels. the histogram shows information about the masses, m kg, of these parcels. 20 10 0 0 1 2 3 5 mass (kilograms)frequency density 7 9 4 6 8 10m (a) complete the frequency table. mass ( m kg) m0 11g m1 21g m2 31g m3 51g m5 1 0 1g frequency [3] (b) calculate an estimate of the mean mass. ... kg [2] (c) two parcels are chosen at random. find the probability that they both have a mass greater than 1 kg. give your answer as a decimal, correct to 3 significant figures. [2]", "16": "16 0607/41/o/n/16 \u00a9 ucles 201610 (a) solve. 7x + 2 = 11 x = [2] (b) write as a single fraction, in its simplest form. x x 21 31 ++- [2] (c) simplify the following. (i) x yx y 48 3 44 2 [2] (ii) x xx 2 39 22 - -- [4]", "17": "17 0607/41/o/n/16 \u00a9 ucles 2016 [turn over11 f(x) = 3 x + 1 g(x) = logx (a) find the value of g(f(33)). [2] (b) find the value of x when g( x) = f(\u22121). x = [2] (c) find (i) f \u22121 (x), f \u20131 (x) = [2] (ii) g \u22121 (x). g \u22121 (x) = [2]", "18": "18 0607/41/o/n/16 \u00a9 ucles 201612 (a) in 2015, ahmed had a monthly salary of $1375. in 2016, his monthly salary is $1540. (i) calculate the percentage increase in ahmed\u2019s monthly salary. % [3] (ii) work out $1375 as a percentage of $1540. % [1] (iii) in 2015, ahmed\u2019s monthly salary of $1375 was 10% more than his monthly salary in 2014. calculate ahmed\u2019s monthly salary in 2014. $ . [3]", "19": "19 0607/41/o/n/16 \u00a9 ucles 2016 (b) samia invested $500 in each of two schemes. scheme a 3% per year simple interest. scheme b 2.5% per year compound interest. (i) calculate the difference between the value of scheme a and the value of scheme b after 5 years. show all your working. $ . [5] (ii) find the number of complete years it will take for the value of scheme b to be greater than the value of scheme a. [4]", "20": "20 0607/41/o/n/16 \u00a9 ucles 2016blank page permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_w16_qp_42.pdf": { "1": "this document consists of 16 printed pages. dc (leg/jg) 117020/3 \u00a9 ucles 2016 [turn overcambridge international examinations cambridge international general certificate of secondary education * 9 3 3 5 2 6 4 2 1 2 * cambridge international mathematics 0607/42 paper 4 (extended) october/november 2016 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answer in degrees should be given to one decimal place. for r, use your calculator value. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.", "2": "2 0607/42/o/n/16 \u00a9 ucles 2016formula list for the equation ax bx c02+ + = xab b ac 242!=- - curved surface area, a, of cylinder of radius r, height h. r a rh2= curved surface area, a, of cone of radius r, sloping edge l. r a rl= curved surface area, a, of sphere of radius r. r a r42= v olume, v, of pyramid, base area a, height h. v ah31= v olume, v, of cylinder of radius r, height h. rv r h2= v olume, v, of cone of radius r, height h. r v r h31 2= v olume, v, of sphere of radius r. r v r34 3= sin sin sin aa bb cc= = cos a b c bc a 22 2 2= + - sinbc a21area=a c bcb a", "3": "3 0607/42/o/n/16 \u00a9 ucles 2016 [turn overanswer all the questions. 1 the number of matches in each of 140 matchboxes are counted. the table shows the results. number of matches168 169 170 171 172 173 174 175 176 177 178 number of matchboxes7 13 16 23 22 21 14 11 8 3 2 (a) write down the modal number of matches. [1] (b) write down the range. [1] (c) find the median. [1] (d) find the inter-quartile range. [2] (e) calculate the mean. give your answer correct to one decimal place. [2]", "4": "4 0607/42/o/n/16 \u00a9 ucles 20162 roberta starts from a point a and walks 1 km north to a point b. she then walks 2 km east to a point c, then walks 3 km south to a point d and finally walks 4 km west to a point e. north a (a) find the distance ae. .. km [3] (b) find the bearing of e from a. [2] (c) find the area abcde . . km2 [2]", "5": "5 0607/42/o/n/16 \u00a9 ucles 2016 [turn over3 ten students at a school each recorded the number of hours they spent revising before an examination. the school compared the number of hours spent revising and the examination mark. number of hours spent revising ( x)3 4 8 9 10 12 13.5 17 21 24 examination mark ( y) 45 36 68 55 62 66 73 81 80 94 (a) what type of correlation is there between the number of hours spent revising and the examination mark? [1] (b) find (i) the mean number of hours spent revising, [1] (ii) the mean examination mark. [1] (c) (i) find the equation of the regression line for y in terms of x. \t y = ... [2] (ii) estimate the examination mark for a student who spent 19 hours revising. [1]", "6": "6 0607/42/o/n/16 \u00a9 ucles 20164 42\u00b0 not to scaleb p caq o \t a, b\tand c\t\tlie on a circle, centre o. \t the line qbp\tis a tangent to the circle at b. ac = bc\t= bp\tand angle qba\t=\t42\u00b0. find the value of (a) angle oab , angle oab = ... [1] (b) angle aob , angle aob = ... [2] (c) angle bca , angle bca = ... [1] (d) angle cbp , angle cbp = ... [2] (e) angle cpb . angle cpb = ... [2]", "7": "7 0607/42/o/n/16 \u00a9 ucles 2016 [turn over5 the age, h, of each of 120 passengers travelling on a train are shown in the table. age (years) frequency 0 < h \ue03c 15 12 15 < h \ue03c 20 18 20 < h \ue03c 25 13 25 < h \ue03c 35 27 35 < h \ue03c 50 22 50 < h \ue03c 90 28 (a) calculate an estimate of the mean age of a passenger. \t \t... years [2] (b) complete the frequency density column in this table. age (years) frequency frequency density 0 < h \ue03c 15 12 15 < h \ue03c 20 18 20 < h \ue03c 25 13 25 < h \ue03c 35 27 35 < h \ue03c 50 22 50 < h \ue03c 90 28 [3]", "8": "8 0607/42/o/n/16 \u00a9 ucles 20166 describe fully the single transformation that is the inverse of (a) a reflection in the line y = x, ... .. [2] (b) a rotation of 90\u00b0 clockwise, centre (2, 3), ... .. [2] (c) a translation with vector 4 3-j lkkn poo, ... .. [2] (d) an enlargement scale factor 3, centre (0, 0). ... .. [2] 7 solve the simultaneous equations. you must show all your working. x y3 4 8 + = - x y5 6 7 - = - \t x\t= ... \t y = ... [4]", "9": "9 0607/42/o/n/16 \u00a9 ucles 2016 [turn over8 (a) cosx31= for 0\u00b0 < x < 90\u00b0. find the exact value of sinx. give your answer as a surd. sinx= [3] (b) not to scale10 cm9 cm 11 cma cb (i) show that cosb31=. [2] (ii) using your answer to part (a) , show that the exact value of the area of triangle abc is 302 cm2. [3]", "10": "10 0607/42/o/n/16 \u00a9 ucles 20169 a circle of radius 5 cm is inscribed inside a square. the square has one side on the base of an equilateral triangle, abc . the other two vertices of the square touch the triangle as shown. not to scalea c b (a) work out the shaded area. . cm2 [2] (b) (i) not to scale10 cm x cm60\u00b0 find the value of x. \t x\t= ... [2]", "11": "11 0607/42/o/n/16 \u00a9 ucles 2016 [turn over (ii) work out the length of a side of the equilateral triangle abc . .. cm [2] (iii) calculate the area outside the square but inside triangle abc . . cm2 [4]", "12": "12 0607/42/o/n/16 \u00a9 ucles 201610 y x \u20136 6 \u20131010 0 fxx326= --^^hh (a) on the diagram, sketch the graph of f y x=^h for values of x\tbetween \t\u20136 and 6. [3] (b) write down the equations of the asymptotes of the graph of f y x=^h. .. and ..[2] (c) solve the equation fx x=-^h . \t \t [2] (d) solve the inequality fx x 01+^h . \t \t [3] (e) describe fully the single transformation that maps (i) yx36= - onto yx326= --^ h, ... .. [2] (ii) yx26=--^ h onto yx326= --^ h. \t... .. [2]", "13": "13 0607/42/o/n/16 \u00a9 ucles 2016 [turn over11 find the next term and the nth term in each of these sequences. (a) 1, 8, 27, 64, 125, ... next term = \t nth term = [2] (b) 3, 7, 13, 21, 31, ... next term = \t nth term = [4] (c) \u20132, 1, 14, 43, 94, ... next term = \t nth term = [4]", "14": "14 0607/42/o/n/16 \u00a9 ucles 201612 a solid hemisphere has radius 6 cm. (a) find, in terms of r, (i) the volume of the hemisphere, \t \t. cm3 [2] (ii) the total surface area of the hemisphere. \t \t. cm2 [2] (b) sixteen of these hemispheres, all with radius 6 cm, are made into one solid sphere . (i) find the radius of the sphere. \t \t.. cm [3] (ii) find the ratio surface area of the sphere : total surface area of the 16 hemispheres. give your answer in its simplest form. . : [3]", "15": "15 0607/42/o/n/16 \u00a9 ucles 2016 [turn over13 (a) log log log log p q x 3 2 6 + - = find x in terms of p and q. \t x\t\t= ... [3] (b) solve the equations. (i) 4 6x= x\t= ... [3] (ii) x x3 2 2 3 1 + - = ^ ^ h h you must show all your working. x\t= . or x\t= . [5] question 14 is printed on the next page.", "16": "16 0607/42/o/n/16 \u00a9 ucles 201614 y x \u20132 80 \u20131210 fx x 231x 3= -^h (a) on the diagram, sketch the graph of f y x=^h, for values of x between \u22122 and 8. [4] (b) write down the y co-ordinates of the local minimum points. \t y = .. and y\t=\t.. [2] (c) write down the co-ordinates of the local maximum point. ( ... , ) [2] (d) solve the equation x x 2312 1x 3- = -^ h, for all real values of x. x\t= . or x\t= . or x\t= . or x\t= . [4] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_w16_qp_43.pdf": { "1": "this document consists of 19 printed pages and 1 blank page. dc (rw/jg) 117017/3 \u00a9 ucles 2016 [turn over * 9 0 9 3 7 0 0 0 3 3 * cambridge international mathematics 0607/43 paper 4 (extended) october/november 2016 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. y ou must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/43/o/n/16 \u00a9 ucles 2016formula list for the equation ax bx c02+ + = xab b ac 242!=- - curved surface area, a, of cylinder of radius r, height h. r a rh2= curved surface area, a, of cone of radius r, sloping edge l. r a rl= curved surface area, a, of sphere of radius r. r a r42= v olume, v, of pyramid, base area a, height h. v ah31= v olume, v, of cylinder of radius r, height h. rv r h2= v olume, v, of cone of radius r, height h. r v r h31 2= v olume, v, of sphere of radius r. r v r34 3= sin sin sin aa bb cc= = cos a b c bc a 22 2 2= + - sinbc a21area=a c bcb a", "3": "3 0607/43/o/n/16 \u00a9 ucles 2016 [turn overanswer all the questions. 1 (a) work out. (i) 795073 [1] (ii) ..3 60 631 2+ [1] (b) .p 5 62 1 05# = .q 6 83 1 03# =- work out, giving your answers in standard form. (i) p2 [2] (ii) qp [2]", "4": "4 0607/43/o/n/16 \u00a9 ucles 20162 gennaro has $276 480 in his pension fund. (a) gennaro has two options. option a receive 25% of the $276 480 now plus 5.5% of the remaining 75% each year. option b receive 5.5% of the whole $276 480 each year. (i) show that the total amount gennaro will have received at the end of 10 years, if he chooses option a, is $183 168. [3] (ii) after how many whole years will the total amount received using option b become more than the total amount received under option a? [4] (b) the $276 480 is 8% more than the amount the pension fund was worth one year ago. calculate how much it was worth one year ago. $ ... [3]", "5": "5 0607/43/o/n/16 \u00a9 ucles 2016 [turn over3 y x 06 5 4 3 2 1 \u20131\u20131\u20132\u20133\u20134\u20135\u20136\u20137\u20138 \u20132 \u20133 \u20134 \u201351bd c234567a describe fully the single transformation that maps (a) triangle a onto triangle b, ... . [2] (b) triangle a onto triangle c, ... . [3] (c) triangle a onto triangle d. ... . [3]", "6": "6 0607/43/o/n/16 \u00a9 ucles 20164 not to scalev c b n ad o the diagram shows a solid, square-based pyramid vabcd . o is the centre of the base abcd and vo is perpendicular to the base. n is the midpoint of ab. ab = 6 cm and vo = 8 cm. (a) calculate (i) the volume of the pyramid, . cm3 [2] (ii) the length of vn. .. cm [2]", "7": "7 0607/43/o/n/16 \u00a9 ucles 2016 [turn over (b) the similar pyramid vpqrs is removed from the original pyramid to leave the solid below. not to scale c br qps ad the height of this solid is half the height of the pyramid vabcd . (i) find the volume of this solid. . cm3 [3] (ii) find the total surface area of this solid. . cm2 [5]", "8": "8 0607/43/o/n/16 \u00a9 ucles 20165 \u20133 \u20131025y x 30 x x x4 6 f3= - + ^h (a) on the diagram, sketch the graph of y xf=^h for x3 3g g- . [2] (b) solve the equation x x 2 3 f= +^h . x = . or x = . or x = . [3] (c) (i) find the co-ordinates of the local maximum point and the local minimum point. maximum ( , ...) minimum ( , ...) [3] (ii) find the range of values of k for which x kf=^h has only one solution. [1] (d) describe fully the symmetry of the graph of y xf=^h. ... . [3]", "9": "9 0607/43/o/n/16 \u00a9 ucles 2016 [turn over6 y x0\u00d7 b \u00d7 c \u00d7 anot to scale the diagram shows the points a (-1, -1), b (1, 3) and c (6, 3). (a) the points a, b, c and d are the vertices of a parallelogram. write down the co-ordinates of the three possible positions of d. ( , ...) ( , ...) ( , ...) [3] (b) e is a point such that c is the midpoint of the line ae. find the co-ordinates of the point e. ( , ...) [2] (c) the line l is perpendicular to the line ac and goes through a. find the equation of the line l. [4]", "10": "10 0607/43/o/n/16 \u00a9 ucles 20167 a farmer measured the milk yield of each of his 120 cows over a one-year period. the results are shown in the frequency table. milk yield (m litres)frequencymilk yield (m litres)cumulative frequency m 5000 60001g 6 m 6000g 6 m 6000 65001g 12 m 6500g m 6500 70001g 22 m 7000g m 7000 75001g 37 m 7500g m 7500 80001g 20 m 8000g m 8 00 9000 01g 17 m 9000g m 9000 10000 1g 6 m 10000g 120 (a) (i) complete the cumulative frequency table. [1] (ii) complete the cumulative frequency curve. m 500001020304050607080 cumulative frequency milk yield (litres)90100110120 6000 7000 8000 9000 10 000 [3]", "11": "11 0607/43/o/n/16 \u00a9 ucles 2016 [turn over (iii) use your graph to estimate the median. ... litres [1] (iv) use your graph to estimate the inter-quartile range. ... litres [2] (v) the farmer sells the cows with a milk yield of less than 6200 litres. use your graph to estimate the number of cows he sells. [1] (b) on the grid below, complete the histogram to represent the data in the first table. m 500000.010.020.030.040.050.060.070.08 frequency density milk yield (litres)6000 7000 8000 9000 10 000 [4]", "12": "12 0607/43/o/n/16 \u00a9 ucles 20168 a ship sails on the following course. \u2022 60 km on a bearing of 025\u00b0 from a to b \u2022 80 km on a bearing of 115\u00b0 from b to c \u2022 75 km on a bearing of 195\u00b0 from c to d the diagram shows the course. acb dnot to scalenorthnorth north 195\u00b0115\u00b0 25\u00b0 (a) show that angle abc = 90\u00b0. [1] (b) calculate angle bca . angle bca = ... [2] (c) calculate the distance ac. ac = . km [2]", "13": "13 0607/43/o/n/16 \u00a9 ucles 2016 [turn over (d) calculate the distance ad. ad = . km [4] (e) calculate the bearing of d from a. [4]", "14": "14 0607/43/o/n/16 \u00a9 ucles 20169 justine travels 760 km in her car. (a) justine\u2019s average speed for the journey is 77 km/h. calculate the time justine takes to complete the journey. give your answer in hours and minutes correct to the nearest minute. h min [3] (b) justine travels 270 km on main roads and 490 km on autoroutes. on main roads her car travels x km on each litre of fuel. on autoroutes her car travels x4+^ h km on each litre of fuel. (i) write down an expression, in terms of x, for the fuel that justine\u2019s car uses on main roads on this journey. ... litres [1] (ii) altogether justine\u2019s car uses 62 litres of fuel for the whole journey. write down an equation in x and show that it simplifies to x x31 256 540 02- - =. [3]", "15": "15 0607/43/o/n/16 \u00a9 ucles 2016 [turn over (iii) solve the equation x x31 256 540 02- - = to find the distance justine\u2019s car travels on 1 litre of fuel on autoroutes. .. km [4]", "16": "16 0607/43/o/n/16 \u00a9 ucles 201610 (a) (i) factorise. x x2 3 12- + [2] (ii) show that xx2 123+ +- can be written as xx x 22 1 1 -- - ^^ ^ hh h . [3] (b) \u20133 \u20131020y x 50 xxx x 22 1 1f-- -=^^^ ^hhh h (i) on the diagram, sketch the graph of y xf=^h for values of x between -3 and 5. [2]", "17": "17 0607/43/o/n/16 \u00a9 ucles 2016 [turn over (ii) on the same diagram, sketch the graph of y x2 1= + . [2] (iii) write down the equations of the asymptotes to the graph of y xf=^h. [2] (iv) solve x 0 f=^h . x = . or x = . [2]", "18": "18 0607/43/o/n/16 \u00a9 ucles 201611 the 50 members of an activities group either go walking or cycling. the table shows the choices of the males and females. walking cycling total male 16 29 female total 22 50 (a) complete the table. [2] (b) two of the 50 members are chosen at random. calculate the probability that they both go cycling. [2] (c) two of those who go walking are chosen at random. calculate the probability that one is a male and the other is a female. [3]", "19": "19 0607/43/o/n/16 \u00a9 ucles 201612 y is inversely proportional to the square root of x. when x = 25, y = 2. (a) find y in terms of x. y = ... [2] (b) find the value of x when y = 3. [2] (c) z = axn z is proportional to the cube of y. when x = 4, z = 500. find the value of a and the value of n. a = ... n = ... [3]", "20": "20 0607/43/o/n/16 \u00a9 ucles 2016permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_w16_qp_51.pdf": { "1": "this document consists of 7 printed pages and 1 blank page. dc (cw/sg) 117233/1 \u00a9 ucles 2016 [turn over * 8 4 5 3 9 7 5 0 6 9 * cambridge in terna tional ma thema tics 0607/51 paper 5 (core) october/ november 2016 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. y ou must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and to communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/51/o/n/16 \u00a9 ucles 2016answer all the questions. investigation\t squares \ton\tgrids this investigation looks at the number of squares drawn on square grids. all squares are drawn using gridlines. 1\t here is a 2 by 2 grid. \t explain why there are 5 squares on a 2 by 2 grid. ... ... 2\t here is a 3 by 3 grid. \t complete these statements about the numbers of different sized squares on a 3 by 3 grid. \t \t the number of 1 by 1 squares on a 3 by 3 grid is . \t \t the number of 2 by 2 squares on a 3 by 3 grid is 4 \t \t the number of 3 by 3 squares on a 3 by 3 grid is . \t \t so the total number of squares on a 3 by 3 grid is .", "3": "3 0607/51/o/n/16 \u00a9 ucles 2016 [turn\tover3\t complete these statements about the numbers of different sized squares on a 4 by 4 grid. \t you may use the grids below to help you. \t \t the number of 1 by 1 squares on a 4 by 4 grid is . \t \t the number of 2 by 2 squares on a 4 by 4 grid is . \t \t the number of 3 by 3 squares on a 4 by 4 grid is . \t \t the number of 4 by 4 squares on a 4 by 4 grid is . \t \t so the total number of squares on a 4 by 4 grid is 30", "4": "4 0607/51/o/n/16 \u00a9 ucles 20164\t (a)\t use your results from questions \t1, 2\tand\t3 to help you complete this table. size of gridnumber of\u2026.total number of squares1 by 1 squares2 by 2 squares3 by 3 squares4 by 4 squares5 by 5 squares6 by 6 squares 1 by 1 1 1 2 by 2 5 3 by 3 4 4 by 4 30 5 by 5 6 by 6 \t (b)\t what is the mathematical name for the numbers in the 1\tby\t1\tsquares column? .. \t (c)\t work out the total number of squares on an 8 by 8 grid. .. \t (d)\t here is part of a table for an n by n grid. \t \t it only has columns for 1 by 1 squares up to 6 by 6 squares. \t \t complete the table using expressions in terms of n. size of gridnumber of\u2026. 1 by 1 squares2 by 2 squares3 by 3 squares4 by 4 squares5 by 5 squares6 by 6 squares n by n (n \u2013 4)2 \t (e)\t write an expression, in terms of n, for the number of 12 by 12 squares on an n by n grid. ..", "5": "5 0607/51/o/n/16 \u00a9 ucles 2016 [turn\tover\t (f)\t (i)\t find the number of 5 by 5 squares on a 20 by 20 grid. .. \t \t (ii)\t the number of 5 by 5 squares on an n by n grid is 36. \t \t \t find the value of n. .. 5\t here is a formula for the total number of squares, t, on an n by n grid. tn n nd3 2 63 2 = + + + \t (a)\t the total number of squares on a 1 by 1 grid is 1. \t \t show that d = 0. \t (b)\t show that the formula gives the correct total number of squares on a 4 by 4 grid. \t (c)\t find the total number of squares on a 10 by 10 grid. ..", "6": "6 0607/51/o/n/16 \u00a9 ucles 20166\t (a)\t there are nine 7 by 7 squares on a 9 by 9 grid. \t \t the diagrams show a 7 by 7 square drawn in two positions on a 9 by 9 grid. \t \t in each diagram the same 2 by 2 square is shaded. \t \t consider the possible positions of the 7 by 7 square. \t \t explain how the shaded 2 by 2 square can be used to calculate the number of 7 by 7 squares on a 9 by 9 grid. ... ... ...", "7": "7 0607/51/o/n/16 \u00a9 ucles 2016\t (b)\t a square which is bigger than 9 by 9 is drawn on a square grid. \t \t it is only possible to draw 25 of these squares on the square grid. \t \t find two possible sizes for the square and the grid it is drawn on. \t \t you may use the grid below to help you. square size .. by .. on a .. by .. grid. square size .. by .. on a .. by .. grid.", "8": "8 0607/51/o/n/16 \u00a9 ucles 2016blank\tpage permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity . to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_w16_qp_52.pdf": { "1": "this document consists of 7 printed pages and 1 blank page. dc (cw/sg) 117490/2 \u00a9 ucles 2016 [turn over * 2 2 3 9 0 9 7 8 8 7 * cambridge in terna tional ma thema tics 0607/52 paper 5 (core) october/ november 2016 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. y ou must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and to communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/52/o/n/16 \u00a9 ucles 2016answer all the questions. investigation\t rectangles \twithin \trectangles this investigation looks for a method to find the number of rectangles when you draw horizontal and vertical lines inside a rectangle. one horizontal line, ab, is drawn inside a rectangle pqrs . the total number of rectangles is 3. they are pqba , pqrs and abrs .p a sq b r 1\t (a)\t another line cd is drawn inside the rectangle pqrs . \t \t the total number of rectangles is now 6.p a c sq b d r \t \t four of the 6 rectangles are pqba , pqdc , pqrs and abdc . \t \t complete the table to show the other two rectangles. pqba pqdc pqrs abdc", "3": "3 0607/52/o/n/16 \u00a9 ucles 2016 [turn\tover\t (b)\t three horizontal lines, ab, cd and ef are drawn inside the rectangle pqrs . p a c e sq b d f r complete the table to show all ten rectangles. pqba pqrs abdc abrs cdrs \t (c)\t four horizontal lines are drawn inside the rectangle. \t \t find the total number of rectangles. ...", "4": "4 0607/52/o/n/16 \u00a9 ucles 2016\t (d)\t complete the table. number of horizontal lines inside the rectangle0 1 2 3 4 5 6 7 total number of rectangles3 6 10 36 \t (e)\t the numbers in the bottom row of the table in part\t(d) form a sequence. \t \t write down the mathematical name of these numbers. ... \t (f)\t ten horizontal lines are drawn inside the rectangle. \t \t find the total number of rectangles. ...", "5": "5 0607/52/o/n/16 \u00a9 ucles 2016 [turn\tover2\t one vertical line, ab, is drawn inside rectangle pqrs . \t the total number of rectangles is 3. they are pabs , pqrs and aqrb .p a q s b r \t (a)\t two vertical lines are drawn inside a rectangle. \t \t find the total number of rectangles. ... \t (b)\t complete the table. number of vertical lines inside a rectangle0 1 2 3 4 5 6 7 total number of rectangles3 \t (c)\t what is the connection between the table in question\t1(d) and the table in question\t2(b)? ...", "6": "6 0607/52/o/n/16 \u00a9 ucles 20163\t 12 vertical lines are drawn inside a rectangle. \t show that the total number of rectangles is given by the calculation 212 3 12 22#+ + . 4\t (a)\t when n vertical lines are drawn inside a rectangle the total number of rectangles, t, is t n an b212= + +, where a and b are constants. \t \t find the value of a and the value of b. \t \t use your answers to write down the formula for t. a = .. b = .. t = ..", "7": "7 0607/52/o/n/16 \u00a9 ucles 2016\t (b)\t use your formula in part\t(a) to show that when 7 vertical lines are drawn inside a rectangle, the number of rectangles is 36. \t (c)\t calculate how many vertical lines are drawn when there are 231 rectangles. ... 5\t when 30 horizontal lines are drawn inside a rectangle, find the total number of rectangles. ...", "8": "8 0607/52/o/n/16 \u00a9 ucles 2016blank\tpage permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_w16_qp_53.pdf": { "1": "this document consists of 7 printed pages and 1 blank page. dc (rw) 126392 \u00a9 ucles 2016 [turn over * 5 2 5 7 1 0 1 9 6 7 * cambridge in terna tional ma thema tics 0607/53 paper 5 (core) october/ november 2016 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. y ou must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and to communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/53/o/n/16 \u00a9 ucles 2016answer all the questions. investigation\t rectangles \twithin \trectangles this investigation looks for a method to find the number of rectangles when you draw horizontal and vertical lines inside a rectangle. one horizontal line, ab, is drawn inside a rectangle pqrs . the total number of rectangles is 3. they are pqba , pqrs and abrs .p a sq b r 1\t (a)\t another line cd is drawn inside the rectangle pqrs . \t \t the total number of rectangles is now 6.p a c sq b d r \t \t four of the 6 rectangles are pqba , pqdc , pqrs and abdc . \t \t complete the table to show the other two rectangles. pqba pqdc pqrs abdc", "3": "3 0607/53/o/n/16 \u00a9 ucles 2016 [turn\tover\t (b)\t three horizontal lines, ab, cd and ef are drawn inside the rectangle pqrs . p a c e sq b d f r complete the table to show all ten rectangles. pqba pqrs abdc abrs cdrs \t (c)\t four horizontal lines are drawn inside the rectangle. \t \t find the total number of rectangles. ...", "4": "4 0607/53/o/n/16 \u00a9 ucles 2016\t (d)\t complete the table. number of horizontal lines inside the rectangle0 1 2 3 4 5 6 7 total number of rectangles3 6 10 36 \t (e)\t the numbers in the bottom row of the table in part\t(d) form a sequence. \t \t write down the mathematical name of these numbers. ... \t (f)\t ten horizontal lines are drawn inside the rectangle. \t \t find the total number of rectangles. ...", "5": "5 0607/53/o/n/16 \u00a9 ucles 2016 [turn\tover2\t one vertical line, ab, is drawn inside rectangle pqrs . \t the total number of rectangles is 3. they are pabs , pqrs and aqrb .p a q s b r \t (a)\t two vertical lines are drawn inside a rectangle. \t \t find the total number of rectangles. ... \t (b)\t complete the table. number of vertical lines inside a rectangle0 1 2 3 4 5 6 7 total number of rectangles3 \t (c)\t what is the connection between the table in question\t1(d) and the table in question\t2(b)? ...", "6": "6 0607/53/o/n/16 \u00a9 ucles 20163\t 12 vertical lines are drawn inside a rectangle. \t show that the total number of rectangles is given by the calculation 212 3 12 22#+ + . 4\t (a)\t when n vertical lines are drawn inside a rectangle the total number of rectangles, t, is t n an b212= + +, where a and b are constants. \t \t find the value of a and the value of b. \t \t use your answers to write down the formula for t. a = .. b = .. t = ..", "7": "7 0607/53/o/n/16 \u00a9 ucles 2016\t (b)\t use your formula in part\t(a) to show that when 7 vertical lines are drawn inside a rectangle, the number of rectangles is 36. \t (c)\t calculate how many vertical lines are drawn when there are 231 rectangles. ... 5\t when 30 horizontal lines are drawn inside a rectangle, find the total number of rectangles. ...", "8": "8 0607/53/o/n/16 \u00a9 ucles 2016blank\tpage permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_w16_qp_61.pdf": { "1": "this document consists of 12 printed pages. dc (nh/sg) 117169/4 \u00a9 ucles 2016 [turn over * 9 4 0 1 4 6 2 2 5 8 * cambridge international mathematics 0607/61 paper 6 (extended) october/november 2016 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. y ou must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/61/o/n/16 \u00a9 ucles 2016answer both parts a and b. a investigation squares on grids (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation looks at the number of squares drawn on a grid. all squares are drawn using gridlines. 1 (a) here is a 2 by 2 grid. explain why there are 5 squares on a 2 by 2 grid. ... ... (b) here is a 3 by 3 grid. complete these statements about the numbers of different sized squares on a 3 by 3 grid. the number of 1 by 1 squares on a 3 by 3 grid is . the number of 2 by 2 squares on a 3 by 3 grid is 4 the number of 3 by 3 squares on a 3 by 3 grid is . so the total number of squares on a 3 by 3 grid is .", "3": "3 0607/61/o/n/16 \u00a9 ucles 2016 [turn over (c) complete these statements about the numbers of different sized squares on a 4 by 4 grid. you may use the grids below to help you. the number of 1 by 1 squares on a 4 by 4 grid is . the number of 2 by 2 squares on a 4 by 4 grid is . the number of 3 by 3 squares on a 4 by 4 grid is . the number of 4 by 4 squares on a 4 by 4 grid is . so the total number of squares on a 4 by 4 grid is 30", "4": "4 0607/61/o/n/16 \u00a9 ucles 20162 (a) use your results from question 1 to help you complete this table. size of gridnumber of \u2026total number of squares1 by 1 squares2 by 2 squares3 by 3 squares4 by 4 squares5 by 5 squares6 by 6 squares 1 by 1 1 2 by 2 5 3 by 3 4 4 by 4 30 5 by 5 6 by 6 (b) what is the mathematical name for the numbers in the 1 by 1 squares column? .. (c) work out the total number of squares on an 8 by 8 grid. .. (d) write down an expression, in terms of n, for the number of 2 by 2 squares on an n by n grid. ..", "5": "5 0607/61/o/n/16 \u00a9 ucles 2016 [turn over3 here is a formula for the total number of squares, t, on an n by n grid. 3 2tn ncn d3 2 = + + + (a) find the values of c and d. (b) show that your formula gives a total of 385 squares on a 10 by 10 grid. (c) the total number of squares on an n by n grid is 1240. find the value of n. ..", "6": "6 0607/61/o/n/16 \u00a9 ucles 20164 here is a 1 by 2 grid. there is a total of 2 squares on a 1 by 2 grid. write an expression, in terms of n, for the total number of squares on a 1 by n grid. .. 5 here is a 2 by 3 grid. there is a total of 8 squares on a 2 by 3 grid. (a) find the total number of squares on a 2 by 4 grid. .. (b) complete this table. size of grid number of \u2026total number of squares (t\u2009)1 by 1 squares2 by 2 squares 2 by 1 2 0 2 2 by 2 2 by 3 8 2 by 4 2 by 5 2 by n", "7": "7 0607/61/o/n/16 \u00a9 ucles 2016 [turn over6 complete this table for 3 by n grids. you may use the grid below to help you. size of grid number of \u2026total number of squares (t\u2009)1 by 1 squares2 by 2 squares3 by 3 squares 3 by 1 3 0 0 3 3 by 2 6 2 0 8 3 by 3 9 1 3 by 4 12 3 by 5 15 3 by n 3n 7 the expression for t\u2009in question 6 does not work when n\u2009= 1. the expression for t for a 4 by n grid is 10 n \u2013 10. for what values of n will the expression for t for a 4 by n grid not give the correct total? ..", "8": "8 0607/61/o/n/16 \u00a9 ucles 2016b modelling measuring rod (20 marks) you are advised to spend no more than 45 minutes on this part. you may find some of these formulas useful. v olume, v, of pyramid, base area a, height h. 31v a h= v olume, v, of cylinder of radius r, height\u2009h. v r h2r= v olume, v, of cone of radius r, height h. 31v r h2r= v olume, v, of sphere of radius r. 34v r3r= a a cb bc area = 21sinab c jim has a tank for oil, shown in the picture. he uses a measuring rod to put in the top of the tank to find the amount of oil. this investigation is about how jim marks the measuring rod. here is some information about the tank. measuring rod 1770 mm 1030 mmlength 1770 mm width 1030 mm capacity 1235 litres", "9": "9 0607/61/o/n/16 \u00a9 ucles 2016 [turn overjim decides to model the volume of oil in his tank. 1 (a) select the shape that jim should use for the model. cuboid cylinder sphere cone pyramid circle .. (b) jim uses a capacity of 1200 litres and a width of 100 cm. for his model, show that the length of the tank is 153 cm, correct to the nearest centimetre. 2 (a) give a practical reason why the length of his measuring rod should be more than 100 cm. ... ... (b) this is a cross-section of the tank showing the measuring rod and some oil. not to scale oil (i) the tank contains 600 litres of oil. find how many centimetres from the bottom of the measuring rod jim should mark \u201c600 litres\u201d. .. (ii) jim now wants to mark \u201c300 litres\u201d on the measuring rod. explain why he should not mark this point halfway between the bottom of the measuring rod and the \u201c600 litres\u201d mark. ... ...", "10": "10 0607/61/o/n/16 \u00a9 ucles 20163 jim works out the distance, d\u2009cm, where \u201c300 litres\u201d should be marked on the measuring rod. o x\u00b0 b anot to scale d cm o is the centre of the cross section and oa and ob are radii. x\u00b0 is the angle between oa and ob. he uses this method. shaded area = area of sector oab \u2013 area of triangle oab (a) show that an expression for the area of triangle oab is 1250 sinx\u00b0\u2009cm2. (b) show that an expression for the area of sector oab is approximately 21.8 x\u2009cm2. (c) write down an expression, in terms of x, for the area of the shaded segment. ..", "11": "11 0607/61/o/n/16 \u00a9 ucles 2016 [turn over (d) using your result from question 1(b) rounded to the nearest centimetre and your result from question 3(c), show that a model for the volume of oil, v cm3, is approximately v = 3340x \u2013 191 000 sinx\u00b0. (e) on the axes, sketch the graph of this model. 420 000 80 000v olume (cm3)v 80 150x (f) when the tank contains exactly 300 litres of oil, use the model to find (i) the value of x, .. (ii) the value of d, the distance from the bottom of the measuring rod. .. (g) write down the distance from the bottom of the measuring rod to the \u201c900 litres\u201d mark. .. question 4 is printed on the next page.", "12": "12 0607/61/o/n/16 \u00a9 ucles 20164 jim buys oil when the tank contains 100 litres of oil. work out the distance from the bottom of the measuring rod to where \u201c100 litres\u201d should be marked. .. permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_w16_qp_62.pdf": { "1": "this document consists of 11 printed pages and 1 blank page. dc (nh/sg) 117170/2 \u00a9 ucles 2016 [turn over * 5 8 2 8 2 6 2 9 9 0 * cambridge international mathematics 0607/62 paper 6 (extended) october/november 2016 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. y ou must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/62/o/n/16 \u00a9 ucles 2016answer both parts a and b. a\t investigation\t rectangles \twithin \trectangles \t(20\tmarks) you are advised to spend no more than 45 minutes on this part. this investigation looks for a method to find the number of rectangles when you draw horizontal and vertical lines inside a rectangle. one horizontal line, ab, is drawn inside a rectangle pqrs . the total number of rectangles is 3. they are pqba, pqrs and abrs. p a sq b r 1\t (a)\t another line cd is drawn inside the rectangle pqrs . \t \t the total number of rectangles is now 6. p a c sq b d r \t \t three of the 6 rectangles are pqba , pqrs and abrs . \t \t write down the other three rectangles. ...", "3": "3 0607/62/o/n/16 \u00a9 ucles 2016 [turn\tover\t (b)\t three horizontal lines, ab, cd and ef are drawn inside the rectangle pqrs . \t \t find the total number of rectangles. p a c e sq b d f r .. \t (c)\t four horizontal lines are drawn inside the rectangle. \t \t find the total number of rectangles. ..", "4": "4 0607/62/o/n/16 \u00a9 ucles 2016\t (d)\t complete the table. number of horizontal lines inside the rectangle0 1 2 3 4 5 6 7 total number of rectangles3 6 36 \t (e)\t the numbers in the bottom row of the table in part\t(d) form a sequence. \t \t write down the mathematical name of these numbers. .. \t (f)\t ten horizontal lines are drawn inside the rectangle. \t \t find the total number of rectangles. ..", "5": "5 0607/62/o/n/16 \u00a9 ucles 2016 [turn\tover2\t one vertical line, ab, is drawn inside rectangle pqrs . \t the total number of rectangles is 3. \t they are p abs, pqrs and aqrb . pa q sb r \t complete the table. number of vertical lines inside a rectangle0 1 2 3 4 5 6 7 total number of rectangles3 3\t (a)\t n vertical lines are drawn inside a rectangle. \t \t the total number of rectangles is an2 + bn + c. \t \t find the values of a, b and c. a = . b = . c = .", "6": "6 0607/62/o/n/16 \u00a9 ucles 2016\t (b)\t using your values for a, b and c found in part\t(a), factorise an2 + bn + c. \t \t write it in the form a(n + p)(n + q). .. 4\t two horizontal lines are drawn inside rectangle pqrs to form a total of 6 rectangles. \t for each of these 6 rectangles, 3 rectangles are formed when one vertical line is also drawn inside rectangle pqrs . p q s rp q s r \t so the total number of rectangles is 18. \t (a)\t one horizontal line and one vertical line are drawn inside rectangle pqrs . \t \t find the total number of rectangles. ..", "7": "7 0607/62/o/n/16 \u00a9 ucles 2016 [turn\tover\t (b)\t three horizontal lines and two vertical lines are drawn inside a rectangle. \t \t find the total number of rectangles. .. \t (c)\t n horizontal lines and m vertical lines are drawn inside a rectangle. \t \t find an expression, in terms of n and m, for the total number of rectangles. \t \t do not simplify this expression. .. 5\t abcd is a square. \t an equal number of horizontal lines and vertical lines are drawn inside the square. \t show that the number of rectangles inside abcd could not be 762 but it could be 782.", "8": "8 0607/62/o/n/16 \u00a9 ucles 2016b\t modelling\t birthday \tmoney \t(20\tmarks) you are advised to spend no more than 45 minutes on this part. 1\t rosie\u2019s grandmother gave her $10 on her 1st birthday. \t on each birthday after that her grandmother gave her $5 more than she gave rosie on her last birthday. \t (a)\t how much did rosie receive from her grandmother on her 5th birthday? .. \t (b)\t find a model, in terms of n, for the amount in dollars, a, that rosie received from her grandmother on her nth birthday. .. \t (c)\t use your model to show that rosie received $105 from her grandmother on her 20th birthday. 2\t (a)\t find the total amount that rosie had received from her grandmother, up to and including her 5th birthday. ..", "9": "9 0607/62/o/n/16 \u00a9 ucles 2016 [turn\tover\t (b)\t a model for the total amount of money, $ t, that rosie received up to and including her nth birthday, is t = kn(n + 3). \t \t (i)\t use your answer to part\t(a) to find the value of k. .. \t \t (ii)\t show that rosie received a total of $1150 from her grandmother, up to and including her 20th birthday. \t (c)\t work out rosie\u2019s age when she first received a total of more than $4 000. .. 3\t zahari\u2019s grandfather gave him $10 on his 1st birthday. \t on each birthday after that his grandfather gave him 10% more than he gave him on his last birthday. \t how much did zahari receive from his grandfather on his 5th birthday? ..", "10": "10 0607/62/o/n/16 \u00a9 ucles 20164\t the model a = 10 \u00d7 1.1n\u20131 can be used to calculate the amount in dollars, a, that zahari received from his grandfather on his nth birthday. \t (a)\t explain why the numbers 10 and 1.1 are used in the model. ... ... ... \t (b)\t use the model to calculate how much zahari received from his grandfather on his 20th birthday. \t \t give your answer in dollars correct to the nearest cent. .. 5\t (a) 0 1 40na \t \t (i)\t on the axes, sketch the graph of the model for a that you found in question\t1(b). \t \t (ii)\t on the same axes, sketch the model a = 10 \u00d7 1.1n\u20131.", "11": "11 0607/62/o/n/16 \u00a9 ucles 2016\t (b)\t after their 1st birthdays, on which birthday did zahari first get more money than rosie? .. \t (c)\t apart from their 1st birthdays, which of these two situations, a or b, gives zahari more money than rosie on an earlier birthday? \t \t his grandfather gave him a $5 on his 1st birthday, with an increase of 15% on each birthday b $7.50 on his 1st birthday, with an increase of 12% on each birthday. \t \t give reasons for your choice. ... ... 6\t zahari\u2019s grandmother gave him $ d on his 1st birthday. \t on each birthday after that his grandmother gave him 10% more than she gave him on his last birthday. \t (a)\t change the model a = 10 \u00d7 1.1n\u20131 to show this situation. .. \t (b)\t find the value of d that will give zahari $148 on his 22nd birthday. ..", "12": "12 0607/62/o/n/16 \u00a9 ucles 2016blank\tpage permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_w16_qp_63.pdf": { "1": "this document consists of 16 printed pages. dc (nh/sg) 117171/3 \u00a9 ucles 2016 [turn over * 9 1 6 3 2 9 6 8 8 0 * cambridge international mathematics 0607/63 paper 6 (extended) october/november 2016 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. y ou may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. y ou must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/63/o/n/16 \u00a9 ucles 2016the investigation starts on page 3.", "3": "3 0607/63/o/n/16 \u00a9 ucles 2016 [turn overanswer both parts a and b. a investigation triangular grids (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation looks at geometric results using grids of equilateral triangles. 1 the area of this 2 by 3 parallelogram is 12 triangles. 3 2 (a) write down the area of this 5 by 1 parallelogram. triangles (b) find the area of this 6 by 3 parallelogram. triangles (c) find a formula for the area, a, of a parallelogram measuring s by r on a triangular grid. r s ..", "4": "4 0607/63/o/n/16 \u00a9 ucles 2016 (d) two equilateral triangles are drawn on the grid below. the area of the smaller triangle is 4. find the area of the larger triangle. .. (e) find a formula for the area, a, of an equilateral triangle with side x. .. (f) show that your formula in part (e) works. start by drawing another equilateral triangle on the grid above.", "5": "5 0607/63/o/n/16 \u00a9 ucles 2016 [turn over2 (a) each shape is made by joining dots on a triangular grid. b d c ef complete this table. shapenumber of dots inside shape ( r)number of dots on perimeter ( p)area in triangles (a) b 0 6 c 0 d 0 5 e f 0 4 2 (b) for shapes on a square grid, pick\u2019s rule is 12a rp= + -. does pick\u2019s rule work for shapes on triangular grids? use numbers from the table in part (a) to support your answer. (c) write down a formula for a in terms of p. ..", "6": "6 0607/63/o/n/16 \u00a9 ucles 2016 (d) the table below shows some values for r, p and a for shapes drawn on triangular grids. number of dots inside shape ( r)number of dots on perimeter ( p)area in triangles ( a) 0 4 2 0 6 4 0 7 5 1 4 4 1 6 6 1 8 8 1 10 10 2 4 6 2 5 7 2 8 10 2 10 12 3 8 12 3 6 10 3 10 14 3 12 16 4 11 17 4 14 20 find a formula for a in terms of r and p. .. (e) when a = 100, find a possible pair of values of r and p. ..", "7": "7 0607/63/o/n/16 \u00a9 ucles 2016 [turn over3 co-ordinates can be used on triangular grids. \u201311 1 \u20131\u20132\u20133\u20134\u20135 2345234 \u20132 \u20133 \u201340y ab cx the points a(\u20131, 3), b(2, 4) and c(4, \u20132) are shown on the grid. (a) a regular hexagon can be drawn with integer co-ordinates for vertices. this statement is not true for square grids. show, using the grid, whether the statement is true for triangular grids. \u201311 1 \u20131\u20132\u20133\u20134\u20135 2345234 \u20132 \u20133 \u201340y x the statement is .", "8": "8 0607/63/o/n/16 \u00a9 ucles 2016 (b) the point ( x, y) is rotated about (0, 0) through 180\u00b0 to the point (\u2013 x, \u2013y). this statement is true for square grids. using the grid, investigate whether the statement is true for triangular grids. \u201311 1 \u20131\u20132\u20133\u20134\u20135 2345234 \u20132 \u20133 \u201340y x the statement is . (c) the point ( x, y) is reflected in the y-axis to the point ( x, \u2013y). this statement is true for square grids. using the grid, investigate whether the statement is true for triangular grids. \u201311 1 \u20131\u20132\u20133\u20134\u20135 2345234 \u20132 \u20133 \u201340y x the statement is .", "9": "9 0607/63/o/n/16 \u00a9 ucles 2016 [turn over (d) the midpoint of the line joining the points ( x1, y1) and ( x2, y2) is 2,2x x y y1 2 1 2+ +c m. this statement is true for square grids. using the grid, investigate whether the statement is true for triangular grids. \u201311 1 \u20131\u20132\u20133\u20134\u20135 2345234 \u20132 \u20133 \u201340y x the statement is .", "10": "10 0607/63/o/n/16 \u00a9 ucles 2016b modelling wa ves (20 marks) you are advised to spend no more than 45 minutes on this part. this part is about modelling sea waves. the sketch shows part of a sea wave. wave height here are the wave heights, in metres, of a sample of 60 waves in order of size. 0.27 0.30 0.50 0.56 0.57 0.73 0.77 0.78 0.87 0.96 0.99 1.00 1.09 1.16 1.20 1.21 1.34 1.49 1.50 1.51 1.51 1.52 1.55 1.57 1.60 1.61 1.63 1.65 1.69 1.71 1.73 1.76 1.77 1.78 1.83 1.84 1.86 1.92 1.97 1.98 2.06 2.15 2.18 2.20 2.30 2.47 2.49 2.49 2.51 2.63 2.80 2.83 2.98 3.15 3.21 3.23 3.26 3.47 4.76 5.20", "11": "11 0607/63/o/n/16 \u00a9 ucles 2016 [turn over1 the mean height of the highest one-third of the waves in a sample is h. (a) for the sample of 60 waves, calculate h and show that it rounds to 2.92. (b) scientists use h to make estimates. comment on the accuracy of the following estimates. (i) the highest wave is approximately 2 h. (ii) the highest 10% of waves have a mean height of approximately 1.27 h.", "12": "12 0607/63/o/n/16 \u00a9 ucles 20162 this frequency table shows 60 wave heights. wave height (x metres)frequency ( f ) 0 < x g 0.5 2 0.5 < x g 1.0 7 1.0 < x g 1.5 9 1.5 < x g 2.0 22 2.0 < x g 2.5 8 2.5 < x g 3.0 5 3.0 < x g 3.5 5 3.5 < x g 4.0 0 4.0 < x g 4.5 0 4.5 < x g 5.0 1 5.0 < x g 5.5 1 two models for the frequency, f, are a 52 10 f1.8 x#=- -2^ h b 14 2 f x3 0.7 x# =- -2^ h (a) on the axes, sketch and label the graph of model a and the graph of model b. f x60 0 4", "13": "13 0607/63/o/n/16 \u00a9 ucles 2016 [turn over (b) for model a, find the wave height that has the maximum frequency. .. (c) for model b, find the wave height that has the maximum frequency. .. (d) which model best fits the data in the table? give two reasons for your choice. model reason 1 ... ... reason 2 ... ...", "14": "14 0607/63/o/n/16 \u00a9 ucles 20163 wave machines make waves of different heights and speeds. (a) this diagram shows the speed, s metres per second, for waves of different heights, h metres. 3.10 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.03.153.203.253.30s speed of wave (m/s) height of wave (m)h the graph of a model connecting s and h is a horizontal line. (i) without doing any calculations write down a possible model. (ii) what does your model tell you about the connection between s and h? ... ...", "15": "15 0607/63/o/n/16 \u00a9 ucles 2016 [turn over (b) another model uses the connection between water depth, d metres, and wave speed, s metres per second. here are some results from some wave machine experiments. d (metres)0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 s (metres per second)0.9 1.4 1.7 2.0 2.2 2.4 2.6 2.8 3.0 3.1 3.3 3.4 3.6 3.7 the results are plotted on this grid. 0 0 0.5 1.0 1.50.51.01.52.02.53.03.5s dspeed depth here are three possible models. s a d c= + cos s c a d= + s ad2= c+. (i) which model best fits the data? .. (ii) find suitable values for a and c in your model. a = . c = . question 3(c) is printed on the next page.", "16": "16 0607/63/o/n/16 \u00a9 ucles 2016permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. (c) these photographs, taken at different times, show a small island in the bottom right-hand corner. a wave, marked by a dotted line, travels towards the island. on both photographs 1 cm represents 100 m. each photograph shows the time in the form hour : minute : second. use your answer to part (b)(ii) to calculate the depth of the sea. .. m" } }, "2017": { "0607_s17_qp_11.pdf": { "1": " this document consists of 10 printed pages and 2 blank pages. ib17 06_0607_11/rp \u00a9 ucles 2017 [turn over \uf02a\uf039\uf034\uf030\uf035\uf032\uf036\uf034\uf030\uf035\uf035\uf02a \uf020 cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/11 paper 1 (core) may/june 2017 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2017 0607/11/m/j/17 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \uf070r2 circumference, c, of circle, radius r. c = 2\uf070r curved surface area, a, of cylinder of radius r, height h. a = 2\uf070rh curved surface area, a, of cone of radius r, sloping edge l. a = \uf070rl curved surface area, a, of sphere of radius r. a = 4\uf070r2 volume, v, of prism, cross-sectional area a, length l. v = al volume, v, of pyramid, base area a, height h. v = 1 3ah volume, v, of cylinder of radius r, height h. v = \uf070r2h volume, v, of cone of radius r, height h. v = 1 3\uf070r2h volume, v, of sphere of radius r. v = 4 3\uf070r3 ", "3": "3 \u00a9 ucles 2017 0607/11/m/j/17 [turn over answer all the questions. 1 (a) change 4.3 metres into millimetres. mm [1] (b) change 60 hours into days. days [1] 2 write down a square number between 20 and 30. [1] 3 insert brackets to make this calculation correct. 24 \u2013 12 \u00f7 3 = 4 [1] 4 find the lowest common multiple (lcm) of 6 and 15. [2] 5 draw an angle of 73\u00b0 at a. a [1] ", "4": "4 \u00a9 ucles 2017 0607/11/m/j/17 6 the diagram shows how ken\u2019s mass, in kilogram s, has increased with his age, in years. 1 2345 8 7 60 age (years) 1020304050 0mass (kg) xy 10 9 12 11 (a) write down ken\u2019s mass when he was 6 years old. kg [1] (b) write down ken\u2019s age when his mass was 30 kg. years [1] 7 a tray contains 5 pink cakes, 6 green cakes and 1 yellow cake only. hattie chooses one cake at random. complete the table. probability of choosing a pink cake probability of choosing a green cake 21 probability of choosing a yellow cake probability of choosing a blue cake [3] ", "5": "5 \u00a9 ucles 2017 0607/11/m/j/17 [turn over 8 write down the gradient of the line y = 7 \u2212 x. [1] 9 raphael is drawing a pie chart for the time, t minutes, that 90 students spe nd on the internet each day. time ( t minutes) frequency sector angle 0 < t 10 10 10 < t 30 15 30 < t 50 20 t \uf03e 50 45 180\uf0b0 (a) complete the table to show the sector angles in the pie chart. [2] (b) complete the pie chart to show this information. label each sector. t50 [2] ", "6": "6 \u00a9 ucles 2017 0607/11/m/j/17 10 1234567 8 91 0012345678910 ay x (a) write down the co-ordinates of the point a. ( , ) [1] (b) c has co-ordinates (4, 6). c is the midpoint of the line ab. find the co-ordinates of b. ( , ) [1] 11 a trader buys a carpet for $640. she sells it at a profit of 25%. calculate the selling price of the carpet. $ [3] ", "7": "7 \u00a9 ucles 2017 0607/11/m/j/17 [turn over 12 find the area of this shape. 2 cm not to scale 8 cm 8 cm4 cm cm2 [3] ", "8": "8 \u00a9 ucles 2017 0607/11/m/j/17 13 (a) shade a segment inside this circle. [1] (b) draw a radius inside this circle. [1] (c) poa b50\u00b0not to scale the diagram shows a circle, centre o. ap and bp are tangents to the circle at a and b. find angle aob . angle aob = [3] ", "9": "9 \u00a9 ucles 2017 0607/11/m/j/17 [turn over 14 \u20138 \u201310 \u201320 2210 xy p q \u20132\u20136 \u201346 48 describe fully the single transformation that maps shape p onto shape q. [3] 15 on each venn diagram, shade the region indicated. a a \u2229b a b ba \u222a b ' [2] questions 16 and 17 are printed on the next page. ", "10": "10 \u00a9 ucles 2017 0607/11/m/j/17 16 solve. 3 x \u2013 4 8 [2] 17 solve the simultaneous equations. 6x + 4y = 34 3x \u2013 y = 14 x = y = [3] ", "11": "11 \u00a9 ucles 2017 0607/11/m/j/17 blank page", "12": "12 permission to reproduce items where third-party owned material pr otected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknow ledgements booklet. this is produced for each series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is par t of the cambridge assessment group. cambri dge assessment is t he brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2017 0607/11/m/j/17 blank page " }, "0607_s17_qp_12.pdf": { "1": " this document consists of 8 printed pages. ib17 06_0607_12/2rp \u00a9 ucles 2017 [turn over \uf02a\uf034\uf037\uf035\uf038\uf037\uf038\uf036\uf039\uf037\uf035\uf02a \uf020 cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/12 paper 1 (core) may/june 2017 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2017 0607/12/m/j/17 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \uf070r2 circumference, c, of circle, radius r. c = 2\uf070r curved surface area, a, of cylinder of radius r, height h. a = 2\uf070rh curved surface area, a, of cone of radius r, sloping edge l. a = \uf070rl curved surface area, a, of sphere of radius r. a = 4\uf070r2 volume, v, of prism, cross-sectional area a, length l. v = al volume, v, of pyramid, base area a, height h. v = 1 3ah volume, v, of cylinder of radius r, height h. v = \uf070r2h volume, v, of cone of radius r, height h. v = 1 3\uf070r2h volume, v, of sphere of radius r. v = 4 3\uf070r3 ", "3": "3 \u00a9 ucles 2017 0607/12/m/j/17 [turn over answer all the questions. 1 20 25 29 32 33 40 45 from this list of numbers, write down (a) the multiple of 11, [1] (b) the prime number, [1] (c) the square number, [1] (d) the lowest common multiple (lcm) of 4 and 5. [1] 2 write 54 as a decimal. [1] 3 write 30% as a fraction in its simplest form. [2] 4 share $150 in the ratio 2 : 3. $ and $ [2] 5 write down the mathematical name for an 8-sided shape. [1] ", "4": "4 \u00a9 ucles 2017 0607/12/m/j/17 6 x\u00b0 measure the angle marked x in the diagram. [1] 7 (a) not to scale a\u00b085\u00b0 write down the size of the angle marked a and give a reason for your answer. a = because [2] (b) not to scale q\u00b0120\u00b0 100\u00b0 60\u00b0 find the size of the angle marked q. q = [2] ", "5": "5 \u00a9 ucles 2017 0607/12/m/j/17 [turn over 8 give two examples of discrete data. 1. 2. [2] 9 this sign is a company logo. 4 cm 2 cmnot to scale 2 cm2 cm 8 cm2 cm the diagram shows a rectangle with two id entical right-angled triangles removed. work out the area of the shaded region. give the units of your answer. [4] 10 the diameter of an atom is 0.000 000 03 metres. write this number in standard form. [1] ", "6": "6 \u00a9 ucles 2017 0607/12/m/j/17 11 voroda invests $200 at 3% per year simple interest. work out the total value of this investment at the end of 4 years. $ [3] 12 (a) factorise. 4 x + 10 [1] (b) expand. 4(9 a \u2013 3b) [1] 13 simplify. 109 32 x x\uf0b4 [2] ", "7": "7 \u00a9 ucles 2017 0607/12/m/j/17 [turn over 14 the point a has co-ordinates (3, 2) and \uf0f7\uf0f7 \uf0f8\uf0f6 \uf0e7\uf0e7 \uf0e8\uf0e6 \uf02d\uf03d35ab . find the co-ordinates of the point b. ( , ) [2] 15 find the gradient of the line 4 y = 3x \u2013 7. [1] 16 the point a has co-ordinates (2, 7). the point b has co-ordinates (5, 1). find the co-ordinates of the midpoint of the line ab. ( , ) [2] 17 the function f( x) = x2 is defined for \u20133 x 6. write down the range of f( x). [2] questions 18 and 19 are printed on the next page. ", "8": "8 permission to reproduce items where third-party owned material pr otected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknow ledgements booklet. this is produced for each series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is par t of the cambridge assessment group. cambri dge assessment is t he brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2017 0607/12/m/j/17 18 describe the single transformation that maps the graph of xy1\uf03d onto the graph of 31 \uf02b\uf03dxy . [2] 19 \u20136 \u20136\u20135 \u20134 \u20133 \u20132 0 123456 \u20135\u20134\u20133\u20132\u2013112456y x3p \u20131 reflect triangle p in the line y = x. [2] " }, "0607_s17_qp_13.pdf": { "1": " this document consists of 8 printed pages. ib17 06_0607_13/4rp \u00a9 ucles 2017 [turn over \uf02a\uf037\uf037\uf039\uf033\uf033\uf038\uf037\uf030\uf033\uf036\uf02a \uf020 cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/13 paper 1 (core) may/june 2017 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2017 0607/13/m/j/17 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \uf070r2 circumference, c, of circle, radius r. c = 2\uf070r curved surface area, a, of cylinder of radius r, height h. a = 2\uf070rh curved surface area, a, of cone of radius r, sloping edge l. a = \uf070rl curved surface area, a, of sphere of radius r. a = 4\uf070r2 volume, v, of prism, cross-sectional area a, length l. v = al volume, v, of pyramid, base area a, height h. v = 1 3ah volume, v, of cylinder of radius r, height h. v = \uf070r2h volume, v, of cone of radius r, height h. v = 1 3\uf070r2h volume, v, of sphere of radius r. v = 4 3\uf070r3 ", "3": "3 \u00a9 ucles 2017 0607/13/m/j/17 [turn over answer all the questions. 1 3 \uf020\uf070 9 21 36 48 from the list of numbers write down (a) a square number, [1] (b) the irrational number, [1] (c) the prime number, [1] (d) a multiple of 9. [1] 2 write down two different fractions between 41 and 21. , [2] 3 use a number to complete the statement. the diagram has lines of symmetry. [1] ", "4": "4 \u00a9 ucles 2017 0607/13/m/j/17 4 b a arc chord circumference diameter radius sector segment from the list above select the mathematical name for (a) the line ab, [1] (b) the shaded area. [1] 5 draw an angle of 164\u00b0 at a. a [1] 6 cnot to scaleb a p d abcd is a rectangle. p is the midpoint of bc. (a) write down the mathematical name of triangle apd . [1] (b) write down the mathematical name of quadrilateral apcd . [1] ", "5": "5 \u00a9 ucles 2017 0607/13/m/j/17 [turn over 7 \u20132\u201310123 \u20132\u20131456 p 5 1234xy (a) write down the co-ordinates of point p. ( , ) [1] (b) plot and label the point q (5, 1). [1] 8 a circle has diameter 12 m. find the area, leaving your answer in terms of \u03c0. m2 [1] 9 not to scale 8 cm 8 cm6 cm6 cm a square of side 2 cm is removed from the corner of a square of side 8 cm. find the area of the remaining shape. cm2 [2] ", "6": "6 \u00a9 ucles 2017 0607/13/m/j/17 10 x70\u00b0not to scale 85\u00b0 \u00b0 find the value of x. x = [2] 11 write 4.2 \u00d7 104 as an ordinary number. [1] 12 find the highest common factor (hcf) of 32 and 48. [1] 13 the mass of a lorry is 3 800 000 g. write this mass in tonnes. tonnes [1] 14 a y = 3x \u2013 2 b 3 + y = 2x c 2y = 6x \u2013 2 d 3x \u2013 2 + y = 0 a , b, c and d are the equations of four straight lines. from the list, find the two straight lines that are parallel. and [2] ", "7": "7 \u00a9 ucles 2017 0607/13/m/j/17 [turn over 15 expand the brackets and simplify. 3 (4x \u2013 1) \u2013 2 (x + 3) [2] 16 f(x) = 3 x2 + 1 find the values of x when f( x) = 49. x = and x = [2] 17 raoul invests $500 for 4 years at a rate of 3% simple interest per year. find the total interest he receives at the end of the 4 years. $ [2] 18 not to scale 5 cm4 cm10 cm x cm these two triangles are similar. find the value of x. x = [2] questions 19, 20 and 21 are printed on the next page.", "8": "8 permission to reproduce items where third-party owned material pr otected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknow ledgements booklet. this is produced for each series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is par t of the cambridge assessment group. cambri dge assessment is t he brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2017 0607/13/m/j/17 19 (a) complete the statement using one of the symbols < , = or >. \u20137 \u2013 4 [1] (b) \u20132 \u20131 01234 5 6x write the information shown on the number line as an inequality. [2] 20 \u20134\u20133\u20132\u201310 1231234 4y 5678 \u20138\u20137\u20136\u201355678 ab x describe fully the single transformation that maps triangle a onto triangle b. [3] 21 describe the single transformation that maps y = f(x) onto y = f(x + 3). [2] " }, "0607_s17_qp_21.pdf": { "1": "this document consists of 7 printed pages and 1 blank page. dc (lk/sg) 133442/3 \u00a9 ucles 2017 [turn overcambridge international examinations cambridge international general certificate of secondary education *1833319952* cambridge international mathematics 0607/21 paper 2 (extended) may/june 2017 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.", "2": "2 0607/21/m/j/17 \u00a9 ucles 2017 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/21/m/j/17 \u00a9 ucles 2017 [turn over answer all the questions. 1 work out. (.)062 . [1] 2 (a) write the fraction 6016 in its lowest terms. . [1] (b) work out. 114 115+ . [1] 3 expand. ()xx x43- . [2] 4 change cm4302 into m2. .. m2 [1] 5 write down the value of 160. . [1]", "4": "4 0607/21/m/j/17 \u00a9 ucles 2017 6 find the lowest common multiple (lcm) of 20 and 24. . [2] 7 ()fxx 23=- find the value of x when ()fx 25= . x = [2] 8 26 cm 24 cm x cmnot to scale find the value of x. x = [3]", "5": "5 0607/21/m/j/17 \u00a9 ucles 2017 [turn over 9 solve the simultaneous equations. xy43 0 += xy25-= x = y = ... [3] 10 p6 3=j lkkn poo find p , giving your answer in the form a3. . [2] 11 a is the point (3, 11) and b is the point (7, 3). find the equation of the line ab, giving your answer in the form ym xc=+ . y = [3]", "6": "6 0607/21/m/j/17 \u00a9 ucles 2017 12 solve. xx25 702-- = x = ... or x = ... [3] 13 by rationalising the denominator, simplify 612 2- . . [3] 14 a bag has 3 blue balls and 7 green balls only. one ball is chosen at random and not replaced. a second ball is then chosen at random. find the probability that both balls chosen are the same colour. give your answer in its simplest form. . [4]", "7": "7 0607/21/m/j/17 \u00a9 ucles 2017 15 expand the brackets and simplify. () () xy xy 43 25-- . [3] 16 simplify. logl og log 23 32 232-+ . [3] 17 write the list of numbers in order, starting with the smallest. \u00b0 sin60 \u00b0 cos60 \u00b0 tan60 2 ... 1 ... 1 ... 1 ... [2] smallest", "8": "8 0607/21/m/j/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_s17_qp_22.pdf": { "1": "this document consists of 8 printed pages. dc (lk/sw) 133438/1 \u00a9 ucles 2017 [turn overcambridge international examinations cambridge international general certificate of secondary education *1387440217* cambridge international mathematics 0607/22 paper 2 (extended) may/june 2017 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.", "2": "2 0607/22/m/j/17 \u00a9 ucles 2017 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/22/m/j/17 \u00a9 ucles 2017 [turn over answer all the questions. 1 (a) write 5.309 87 correct to 3 decimal places. . [1] (b) write 0.003 648 9 correct to 3 significant figures. . [1] 2 these are the number of points the storm have scored in their last 20 basketball matches. 28 33 49 37 26 54 46 48 53 34 26 17 46 41 52 48 37 30 45 53 (a) construct an ordered stem and leaf diagram to show these scores and complete the key. ... ... ... ... ... \t \t \t \t \t \t key\t...\t\u2502\t...\t= 53 [3] (b) find the median score. . [1] 3 factorise completely. xx622- . [2]", "4": "4 0607/22/m/j/17 \u00a9 ucles 2017 4 complete this statement for the parallelogram shown. this shape has . lines of symmetry and rotational symmetry of order . . [2] 5 simplify () () xx42 13 2 -- -. . [2] 6 not to scale 9 cm 6 cma c b d ad is an arc of a circle, centre c, and bcd is a straight line. cm bc 9= , cm cd 6= and angle \u00b0 cad 90= . find the total area of the shape abcd . give your answer in terms of r. . cm2 [3]", "5": "5 0607/22/m/j/17 \u00a9 ucles 2017 [turn over 7 xx32 56h+- (a) solve the inequality. . [2] (b) show your solution to part (a) on this number line. \u20136 \u20135 5 6x \u20134 4 \u20133 3 \u20132 2 \u20131 1 0 [1] 8 not to scalea d b c adc is a straight line and angle bac = angle dbc . (a) complete the following statement. triangle acb is similar to triangle ... . [1] (b) cm bc 6= and cm cd 4= . calculate the length ac. ac = . cm [2]", "6": "6 0607/22/m/j/17 \u00a9 ucles 2017 9 (a) in each diagram, shade the region indicated. a ab b cu u ab+ l ()ac b ,+ l [2] (b) use set notation to describe the shaded region. a b cu . [1] 10 expand the brackets and simplify. () () xy xy 23 34-- . [3] 11 sketch the graph of yx 2 =+ . \u20134 \u20132 224y x \u20132 \u201340 4 [3]", "7": "7 0607/22/m/j/17 \u00a9 ucles 2017 [turn over 12 not to scalea e35\u00b0 15\u00b0 cdb a, b, c, d and e are points on the circle. angle \u00b0 cad 35= and angle \u00b0 ebd 15= . find (a) angle cbd , angle cbd = [1] (b) angle cde . angle cde = [1] 13 p52 3 =+ q52 3 =- find pq22-, writing your answer in its simplest form. . [3] 14 find the value of x when logl og logx 52 8-= . x = [2] question 15 is printed on the next page.", "8": "8 0607/22/m/j/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.15 y x(3, 0) (\u20132, 0)(4, 12) not to scale0 the equation of this curve is ya xb xc2=+ +. find the values of a, b and c. a = b = c = [3]" }, "0607_s17_qp_23.pdf": { "1": "*1080381658* this document consists of 8 printed pages. dc (cw/sw) 133313/1 \u00a9 ucles 2017 [turn overcambridge international mathematics 0607/23 paper 2 (extended) may/june 2017 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/23/m/j/17 \u00a9 ucles 2017 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/23/m/j/17 \u00a9 ucles 2017 [turn over answer all the questions. 1 work out 241 . [2] 2 change 257 to a percentage. ... % [1] 3 x 5= write down the two possible values of x. x = .. or x = .. [1] 4 these are the first four terms of a sequence. 15 11 7 3 find (a) the next term, [1] (b) the nth term. [2]", "4": "4 0607/23/m/j/17 \u00a9 ucles 2017 5 expand. ()xx 332+ [2] 6 work out 810410 227 ## . give your answer in standard form. [2] 7 vu at =+ rearrange the formula to write t in terms of a, u and v. t = ... [2] 8 simplify. (a) yy8282' [2] (b) w225^ h [2]", "5": "5 0607/23/m/j/17 \u00a9 ucles 2017 [turn over 9 75\u00b0not to scalep\u00b0 q\u00b0 abcd e a, b, c, d and e lie on the circle. angle bce = 75\u02da. find the value of p and the value of q. p = q = ... [2] 10 yx 1 =+ and yx2=- find the value of x. x = ... [2]", "6": "6 0607/23/m/j/17 \u00a9 ucles 2017 11 each diagram shows the graph of y = f(x). on each diagram, sketch the function indicated. 0 y = f( x) \u2013 2 y = \u2013 f( x)y x0y x [2] 12 find the value of 1643. [1] 13 (a) simplify. () () 43 43 -+ [2] (b) rationalise the denominator. 75 [1]", "7": "7 0607/23/m/j/17 \u00a9 ucles 2017 [turn over 14 factorise. (a) pp 302-- [2] (b) () () xu vy vu -- - [2] 15 yx1 3\\ when x = 2, y = 2. find y when x = 10. y = ... [3] 16 f(x) = 6cos(6 x) find the amplitude and the period of f( x). amplitude = period = ... [2] questions 17 and 18 are printed on the next page.", "8": "8 0607/23/m/j/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.17 8 cm 5 cm60\u00b0c banot to scale find ab. ab = cm [3] 18 ()x 10 fx= find ()xf1-. ()xf1- = .. [1]" }, "0607_s17_qp_31.pdf": { "1": "this document consists of 16 printed pages. dc (nf/sw) 133436/1 \u00a9 ucles 2017 [turn overcambridge international examinations cambridge international general certificate of secondary education *9891348022* cambridge international mathematics 0607/31 paper 3 (core) may/june 2017 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.", "2": "2 0607/31/m/j/17 \u00a9 ucles 2017 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/31/m/j/17 \u00a9 ucles 2017 [turn over answer all the questions. 1 (a) what type of number is 7? give two possible mathematical words to describe it. . and . [2] (b) (i) write down a multiple of 7. .. [1] (ii) write 7% as a fraction. .. [1] (iii) work out. 7 + 72 + 73 .. [1] (c) write (i) 71 as a decimal, correct to 2 decimal places, .. [2] (ii) 7 as a decimal, correct to 3 significant figures, .. [2] (iii) 77 in standard form. .. [2]", "4": "4 0607/31/m/j/17 \u00a9 ucles 2017 2 rin asked some people how many pets they each have. the results are shown in the table. number of pets 0 1 2 3 4 5 number of people 14 45 18 11 7 5 (a) find the number of people that rin asked. .. [1] (b) find how many more people have 1 pet than have 2 pets. .. [1] (c) one of the people is chosen at random. work out the probability that this person has 1 pet. give your answer as a fraction in its simplest form. .. [2] (d) complete the bar chart. 00 1 2 3 number of petsnumber of people 4 51020304050 [2]", "5": "5 0607/31/m/j/17 \u00a9 ucles 2017 [turn over 3 the price of a game of golf at each of two golf clubs is shown below. the forest golf club each game $13.50 the valley golf club one game for $15 buy 6 games and get the 7th game free (a) (i) find how much it costs to play 7 games at the forest golf club. $ [1] (ii) find how much it costs to play 7 games at the valley golf club. $ [1] (iii) find which golf club is cheaper for 7 games, and by how much. .. is cheaper by $. [1] (b) jason is given $200 to spend playing golf at the forest golf club. find the greatest number of games he can play. show all your working. .. [3]", "6": "6 0607/31/m/j/17 \u00a9 ucles 2017 4 (a) here are three angles on a straight line. 113\u00b038\u00b0not to scale x work out the size of angle x. x = [1] (b) not to scale y (i) write down the mathematical name for this triangle. .. [1] (ii) find the size of angle y. y = [2] (iii) write down the number of lines of symmetry this triangle has. .. [1]", "7": "7 0607/31/m/j/17 \u00a9 ucles 2017 [turn over (c) not to scale 24\u00b0 z work out the size of angle z. z = [2] 5 write each of these as a single power of x. (a) x7 \u00d7 x4 .. [1] (b) xx 210 .. [1] (c) (x6)3 .. [1]", "8": "8 0607/31/m/j/17 \u00a9 ucles 2017 6 (a) here is a sequence of patterns using squares and crosses. pattern 1 pattern 2 pattern 3 pattern 4 (i) in the space above, draw pattern 4. [1] (ii) find the number of crosses in pattern 5. . [1] (b) these are the first three terms of another sequence. 1 2 4 find two different sequences that could have 1, 2 and 4 as their first three terms. in each case, write down the next three terms and the rule for continuing the sequence. 1 , 2 , 4 , . , . , . rule . 1 , 2 , 4 , . , . , . rule . [6]", "9": "9 0607/31/m/j/17 \u00a9 ucles 2017 [turn over 7 not to scale 27.5 cma b15 cm 16 cm 16 cm4 cm 6.5 cm a company sells tissues in two different boxes, a and b. each box is a cuboid. (a) find the difference between the volumes of the two boxes. .. cm3 [4] (b) the total surface area of box a is 1165 cm2. show that the total surface area of box b is approximately 80% of the total surface area of box a. [5]", "10": "10 0607/31/m/j/17 \u00a9 ucles 2017 8 (a) work out the value of 5 a \u2212 4b when a = 3 and b = 2. .. [2] (b) factorise completely. 3x2 \u2212 9x .. [2] (c) solve. (i) 4x + 5 = 13 .. [2] (ii) 3(x \u2212 4) = 15 .. [2] (d) rearrange this formula to make a the subject. f = 2a + b a = ... [2]", "11": "11 0607/31/m/j/17 \u00a9 ucles 2017 [turn over 9 \u201310 \u20132 \u20133 \u20134 \u20135\u201355 4 3 2 1 \u20134 \u20133 \u20132 \u20131 1 2 3 4 5xa by (a) describe fully the single transformation that maps triangle a onto triangle b. ... . [3] (b) on the grid, translate triangle a by the vector 4 1j lkkn poo . label the image c. [2] (c) on the grid, reflect triangle b in the line x = 1. label the image d. [2]", "12": "12 0607/31/m/j/17 \u00a9 ucles 2017 10 tariq sells cars. for each of ten days he records the number of cars sold and the number of hours of sunshine. his results are shown in the table. number of hours of sunshine6 5 2 10 11 4 8 2 5 7 number of cars sold 3 6 11 2 0 7 2 12 7 5 (a) complete the scatter diagram to show this information. the first 6 points have been plotted for you. 00123456number of cars sold789101112 1 2 3 4 5 6 number of hours of sunshine7 8 910 11 12 [2] (b) what type of correlation is shown in your diagram? .. [1]", "13": "13 0607/31/m/j/17 \u00a9 ucles 2017 [turn over (c) calculate (i) the mean number of hours of sunshine, ... hours [1] (ii) the mean number of cars sold. .. [1] (d) on the diagram, draw a line of best fit. [2] (e) use your line of best fit to estimate the number of cars sold on a day when there are 3 hours of sunshine. .. [1] (f) this table shows the number of cars tariq sold each week for one year. number of cars sold number of weeks 0 to 20 12 21 to 40 17 41 to 60 15 61 to 80 7 81 to 100 1 (i) write down the modal class of the number of cars sold. to [1] (ii) find the largest possible range and the smallest possible range of the number of cars sold. largest range .. smallest range .. [2]", "14": "14 0607/31/m/j/17 \u00a9 ucles 2017 11 (a) tammi travels 7 km at an average speed of 30 km / h. find the number of minutes this journey takes. minutes [2] (b) when the speed limit is 50 km / h, tammi travels at a speed 8% below this limit. find the speed at which tammi travels. km / h [2] (c) in a town, there are 208 roads. the speed limit on the roads is either 30 km / h or 50 km / h. the ratio number of 30 km / h roads : number of 50 km / h roads = 11 : 2. calculate the number of 30 km / h roads. .. [2]", "15": "15 0607/31/m/j/17 \u00a9 ucles 2017 [turn over 12 the diagram shows a rectangular field. 54 mnot to scaleb ax 85 m (a) find how much further it is from a to b when walking along two sides of the field rather than straight across the field. .. m [4] (b) use trigonometry to calculate angle x. x = ... [2] question 13 is printed on the next page.", "16": "16 0607/31/m/j/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.13 0xy \u20134\u201335 3 (a) on the diagram, sketch the graph of y = 2x \u2212 3 for values of x from x = \u22123 to x = 3. [2] (b) on the diagram, sketch the graph of y = x1 for values of x from x = \u22123 to x = 3. [2] (c) find the x co-ordinates of the points of intersection of y = 2x \u2212 3 and y = x1 . x = . and x = . [2]" }, "0607_s17_qp_32.pdf": { "1": "this document consists of 16 printed pages. dc (lk/sw) 133449/5 \u00a9 ucles 2017 [turn overcambridge international examinations cambridge international general certificate of secondary education *9105218512* cambridge international mathematics 0607/32 paper 3 (core) may/june 2017 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.", "2": "2 0607/32/m/j/17 \u00a9 ucles 2017 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/32/m/j/17 \u00a9 ucles 2017 [turn over answer all the questions. 1 (a) write in words the number 70 302. .. [1] (b) work out .13683. write down all the numbers on your calculator display. [1] (c) write 623.892 (i) correct to 2 decimal places, [1] (ii) correct to 3 significant figures, [1] (iii) correct to the nearest 100. [1] (d) find the value of xy85+ when x7= and y 9=- . [2] (e) solve. x 54 81 0 -= x = ... [2]", "4": "4 0607/32/m/j/17 \u00a9 ucles 2017 2 amir has 12 hens. (a) each hen lays 5 eggs every week. (i) work out the total number of eggs amir collects each week. [1] (ii) amir sells the eggs at $2.10 for 10 eggs. he sells all the eggs. work out how much money he receives. $ ... [2] (iii) cynthia buys 10 eggs and pays with a $5 note. work out how much change she receives. $ ... [1] (b) food for the hens costs $20 for a 40 kg bag. amir uses 8 kg of food each week. (i) work out how much it costs him to feed the hens each week. $ ... [2] (ii) use your answer to part (a)(ii) to work out the profit that amir makes each week. $ ... [1]", "5": "5 0607/32/m/j/17 \u00a9 ucles 2017 [turn over 3 u = {a, b, c, d, e, f, g, h} p = {a, c, e, f, g} q = {b, d, f, g} (a) write the elements of u in their correct position in the venn diagram. p qu [2] (b) write down an element of p. [1] (c) write down the elements of a proper subset of q. { . } [1] (d) write down the elements of the complement of p. { . } [1] (e) write down ()npq, l. [1] (f) using set notation, complete the statement. c p [1] (g) on the diagram below, shade the region pq+l . p qu [1]", "6": "6 0607/32/m/j/17 \u00a9 ucles 2017 4 a m db n crp the diagram shows a rectangle abcd . the points m, n, p and r are the midpoints of the sides. (a) on the diagram, label (i) an acute angle with the letter x , [1] (ii) a right angle with the letter y , [1] (iii) an obtuse angle with the letter z . [1] (b) using the letters on the diagram, write down (i) two lines that are parallel, ... and ... [1] (ii) two lines that are perpendicular, ... and ... [1] (iii) two shapes that are congruent. ... and ... [1]", "7": "7 0607/32/m/j/17 \u00a9 ucles 2017 [turn over 5 these are the first four terms of a sequence. 23 16 x 2 the difference between any two consecutive terms is the same. (a) find the value of x. x = ... [2] (b) work out the 5th term of this sequence. [1] (c) find an expression for the nth term of this sequence. [2] (d) is 187- a term in this sequence? show how you decide. [3]", "8": "8 0607/32/m/j/17 \u00a9 ucles 2017 6 (a) appointments with teachers are from 14 15 until 17 25. (i) work out the total number of minutes between 14 15 and 17 25. .. minutes [2] (ii) each appointment is for 10 minutes. find the maximum number of appointments that can be made for each teacher. [1] (iii) a teacher has only 12 appointments. work out the total number of minutes for his appointments as a percentage of the total possible number of minutes for appointments. ... % [2] (b) the table shows the number of appointments for all the teachers. teacher a b c d e f g h i j k l m number of appointments5 12 8 12 11 18 3 16 8 9 14 8 13 for these numbers of appointments, find (i) the range, [1] (ii) the mode, [1] (iii) the median. [1]", "9": "9 0607/32/m/j/17 \u00a9 ucles 2017 [turn over (c) one of the 13 teachers is chosen at random. find the probability that this teacher has (i) exactly 12 appointments, [1] (ii) more than 9 appointments. [1] 7 . 31 0552 271r -- (a) from this list write down. (i) all the integers, [2] (ii) an irrational number. [1] (b) use numbers from the list to complete the following statement. q = { } [2] (c) write 0.55 as a fraction in its simplest form. [2]", "10": "10 0607/32/m/j/17 \u00a9 ucles 2017 8 ten students of different ages record the number of lengths of a pool they can swim. age (years) 5 6 7 8 9 10 12 13 14 15 number of lengths1 3 4 10 9 7 14 15 18 20 (a) complete the scatter diagram. the first six points have been plotted for you. 00123456789101112131415161718192021 12345678 age (years)number of lengths 910111213141516 [2] (b) what type of correlation is shown in the diagram? ... [1]", "11": "11 0607/32/m/j/17 \u00a9 ucles 2017 [turn over (c) calculate (i) the mean of the ages, .. years [1] (ii) the mean of the number of lengths. [1] (d) on the scatter diagram, plot the mean point. [1] (e) on the scatter diagram, draw a line of best fit by eye. [2] (f) use your line of best fit to estimate the number of complete lengths a student of age 11 years can swim. [2]", "12": "12 0607/32/m/j/17 \u00a9 ucles 2017 9 clarissa records the number of students absent from school each day. the results for one week are shown in the bar chart. 0 monday tuesday wednesday thursday fridaynumber of absences 510152025 (a) work out the total number of absences during the five days. [1] (b) write down which day had the most students absent. [1]", "13": "13 0607/32/m/j/17 \u00a9 ucles 2017 [turn over (c) clarissa decides to draw a pie chart to show this information. (i) show, using a calculation, that the sector angle for monday is 88\u00b0. [1] (ii) complete the pie chart. label each sector clearly. monday friday 96\u00b0 88\u00b0 [3]", "14": "14 0607/32/m/j/17 \u00a9 ucles 2017 10 80 m100 mnot to scale ca b a track is in the shape of a right-angled triangle. m ab 100= and m bc 80= . (a) find the length of ac. ac= .. m [3] (b) find the total length of the track. ... m [1] (c) use trigonometry to find the size of angle abc . angle abc= ... [2] (d) margriet jogs around the track at an average speed of 9 km/h. (i) change 9 km/h to metres/minute. ... metres/minute [2] (ii) calculate the number of minutes it takes her to jog around the track 5 times. .. minutes [2]", "15": "15 0607/32/m/j/17 \u00a9 ucles 2017 [turn over 11 not to scale2 cm 10 cm 20 cm 6 cm the diagram shows a wooden spinning top in the shape of a cone with a cylinder on top. the cone has radius 6 cm and height 20 cm. the cylinder has radius 2 cm and height 10 cm. (a) find the total volume of the spinning top. cm3 [3] (b) (i) find the length of the slant height of the cone. . cm [2] (ii) the curved surface area of the cone is painted red. find the area painted red. cm2 [2] question 12 is printed on the next page.", "16": "16 0607/32/m/j/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.12 \u20131.5 2.5xy \u2013707 ()fx xxx233 232=- -+ (a) on the diagram, sketch the graph of ()fyx= for .. x 15 25 gg - . [2] (b) find the x co-ordinate of each point where the curve cuts the x-axis. x = .. and x = .. and x = .. [3] (c) find the y co-ordinate of the point where the curve cuts the y-axis. y = .. [1] (d) find the co-ordinates of the local maximum point. ( .. , .. ) [2] " }, "0607_s17_qp_33.pdf": { "1": "*1657376014* this document consists of 15 printed pages and 1 blank page. dc (lk/sg) 134125/2 \u00a9 ucles 2017 [turn overcambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/33 paper 3 (core) may/june 2017 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.", "2": "2 0607/33/m/j/17 \u00a9 ucles 2017 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v= ah31 v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/33/m/j/17 \u00a9 ucles 2017 [turn over answer all the questions. 1 (a) a bar of chocolate costs $0.80 . jenny buys 5 of these bars of chocolate. (i) how much does jenny pay for these 5 bars of chocolate? $ [1] (ii) find how much change she receives from $5. $ [1] (iii) one day there is a special offer on these bars of chocolate. buy 2 bars and get 1 extra bar free. chris wants 15 bars of chocolate. find how much he pays using the special offer. $ [2] (iv) chris shares these 15 bars between himself and his brother in the ratio 3 : 2. find how many bars his brother receives. . [2] (b) asli buys 3 slices of pizza and 1 salad for $2.10 . arend buys 2 slices of pizza and 2 salads for $2.20 . find the cost of 1 slice of pizza and the cost of 1 salad. show all your working. 1 slice of pizza = $ 1 salad = $ [4]", "4": "4 0607/33/m/j/17 \u00a9 ucles 2017 2 (a) (i) write the number three million two thousand and one in figures. . [1] (ii) work out 10 26#- . . [1] (iii) find the value of .12544 . . [1] (b) complete the list of factors of 20. 1 , .. , .. , .. , .. , 20 [2] (c) (i) calculate ..61 342# , giving your answer as a decimal. write down your full calculator display. . [1] (ii) give your answer to part (c)(i) correct to 2 decimal places. . [1] (iii) give your answer to part (c)(i) correct to 2 significant figures. . [1]", "5": "5 0607/33/m/j/17 \u00a9 ucles 2017 [turn over 3 (a) simplify. aba b 592 2 +-+ . [2] (b) rm n 62=+ (i) find r when m 3=- and n 5=. . [2] (ii) find m when r26= and n 4=. . [2] (c) solve. xx36 15 =+ . [2] (d) factorise completely. aa b 31 22- . [2] (e) simplify. xy xy 4223 2# . [2]", "6": "6 0607/33/m/j/17 \u00a9 ucles 2017 4 eight friends were asked these questions. \u2022\t how many minutes did you spend revising for the mathematics test? \u2022\t what was your test score? the results are shown in the table. number of minutes 60 75 100 150 180 220 270 300 score 62 47 58 65 62 81 90 75 (a) complete the scatter diagram. the first four points have been plotted for you. 100 90 80 70 60 50 40 30 20 10 0 0 50 100 150 number of minutes200 250 300score [2]", "7": "7 0607/33/m/j/17 \u00a9 ucles 2017 [turn over (b) find (i) the mean number of minutes spent revising, . [1] (ii) the mean mark scored on the mathematics test. . [1] (c) (i) plot the mean point on the scatter graph. [1] (ii) draw a line of best fit by eye on the scatter graph. [2] (iii) use your line of best fit to find an estimate of the mark scored on the mathematics test by a student who spent 200 minutes revising. . [1] ", "8": "8 0607/33/m/j/17 \u00a9 ucles 2017 5 30 students were asked which drink they liked best. the results are shown in the table. drink cola ice tea lemonade orange juice green tea number of students11 8 5 4 2 (a) complete the bar chart. number of students12 10 8 6 4 2 0 cola ice tea lemonade drinkorange juice green tea [2] (b) find the probability that one of these 30 students, chosen at random, likes (i) ice tea best, \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd [1] (ii) orange juice or green tea best, . [1] (iii) coffee best. . [1]", "9": "9 0607/33/m/j/17 \u00a9 ucles 2017 [turn over (c) complete the pie chart to show the results in the table. green tea cola [3] 6 the distance from breda to amsterdam is 105 km. (a) a train from breda to amsterdam takes 35 minutes to complete the journey. calculate the average speed of the train in km/h. .. km/h [2] (b) another train from breda to amsterdam travels at an average speed of 84 km/h. find the time taken for this train to travel from breda to amsterdam. give your answer in hours and minutes. hours minutes [2] ", "10": "10 0607/33/m/j/17 \u00a9 ucles 2017 7 suyeon asks each of 23 students in her class to count the number of steps in their house. the results are listed below. 23 12 16 23 18 46 32 35 15 21 16 42 41 18 34 26 41 47 23 48 23 33 37 (a) complete the ordered stem and leaf diagram to show this information. 1 2 2 3 4 key: ... ... represents . [3] (b) find (i) the mode, . [1] (ii) the median, . [1] (iii) the interquartile range, . [2] (iv) the mean. . [1] ", "11": "11 0607/33/m/j/17 \u00a9 ucles 2017 [turn over 8 (a) write 20043 as a decimal. . [1] (b) write the following fractions in order, starting with the smallest. 013 4011141 20043 5 . , . , . , . [1] smallest (c) x 5013 100= find the value of x. x = [1] (d) write 4011 as a percentage. ... % [1] (e) calculate, giving each answer as a fraction. (i) 5013 20043+ . [1] (ii) 4011 5013' . [1] (iii) 141 20043# . [1] ", "12": "12 0607/33/m/j/17 \u00a9 ucles 2017 9 these are the first four terms of a sequence. 64 81 98 115 (a) write down the next two terms in this sequence. ... , ... [2] (b) find an expression for the nth term of this sequence. . [2] 10 alperen asks 30 students if they like fish ( f ) or cheese ( c ). 19 like fish, 24 like cheese and 2 like neither fish nor cheese. (a) complete the venn diagram. u f c 2 [2] (b) write down the number of students who like fish or cheese but not both. . [1] (c) shade the region fc+ l. [1] (d) one student is chosen at random. find the probability that this student likes cheese only. . [1] ", "13": "13 0607/33/m/j/17 \u00a9 ucles 2017 [turn over 11 y x6 \u20131 \u20132 \u20133 \u20134 \u20135 \u20136\u20136 \u20135 \u20134 \u20133 \u20132 \u20131 1 2 3 4 5 65 4 3 2 1 0 on the grid, draw the image of (a) shape after a reflection in the y-axis, [1] (b) shape after a rotation of 90 \u00b0 clockwise about the origin, [2] (c) shape after a translation of 6 5- -cm . [2] ", "14": "14 0607/33/m/j/17 \u00a9 ucles 2017 12 1.5 cm 0.5 cmnot to scale tamay has 15 identical silver coins. each coin is a cylinder of radius 1.5 cm and height 0.5 cm. (a) find the total surface area of one coin. cm2 [3] (b) (i) find the total volume of all 15 coins. cm3 [2] (ii) the 15 coins are melted down to make one large cylinder of height 3 cm. calculate the radius of this cylinder. give your answer correct to 1 decimal place. . cm [3] ", "15": "15 0607/33/m/j/17 \u00a9 ucles 2017 13 020y x \u201310\u20133.5 3 ()fxx xx632=+ - (a) on the diagram, sketch the graph of ()fyx= for . x 35 3 gg- . [2] (b) write down the co-ordinates of the point where the graph crosses the y-axis. ( .. , .. ) [1] (c) write down the co-ordinates of the points where the graph crosses the x-axis. ( .. , .. ) and ( .. , .. ) and ( .. , .. ) [2] (d) write down the co-ordinates of the local minimum. ( .. , .. ) [2] (e) on the same diagram, sketch and label clearly the graph of (i) ()fyx 2 =+ , [1] (ii) ()fyx 1 =- . [1]", "16": "16 0607/33/m/j/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_s17_qp_41.pdf": { "1": "this document consists of 19 printed pages and 1 blank page. dc (rw/sw) 133483/2 \u00a9 ucles 2017 [turn over *9778586246* cambridge international mathematics 0607/41 paper 4 (extended) may/june 2017 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/41/m/j/17 \u00a9 ucles 2017 formula list for the equation ax bxc02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/41/m/j/17 \u00a9 ucles 2017 [turn over answer all the questions. 1 (a) find the next term and the nth term in each of the following sequences. (i) 4, 8, 12, 16, 20, \u2026 next term = nth term = [2] (ii) -1, -3, -5, -7, -9, \u2026 next term = nth term = [3] (iii) 3, 12, 27, 48, 75, \u2026 next term = nth term = [3] (iv) 1, 8, 27, 64, 125, \u2026 next term = nth term = [2] (b) use your answers to part (a) , to find the next term and the nth term in the following sequence. 7, 25, 61, 121, 211, \u2026 next term = nth term = [3]", "4": "4 0607/41/m/j/17 \u00a9 ucles 2017 2 (a) the heights, x cm, of some plants are shown in the table. height ( x cm) frequency x01 0 1g 7 x 10 201g 13 x 20 301g 20 x 30 401g 32 x 40 501g 28 calculate an estimate of the mean height of the plants. ... cm [2] (b) (i) complete the cumulative frequency table for the plants. height ( x cm)cumulative frequency x01 0 1g 7 x02 0 1g x03 0 1g x04 0 1g x05 0 1g [1]", "5": "5 0607/41/m/j/17 \u00a9 ucles 2017 [turn over (ii) on the grid below, draw the cumulative frequency curve. 010 20 30 40 50xcumulative frequency height (cm)20406080100 1030507090 [3] (c) use your graph in part (b)(ii) to find estimates for (i) the median height, ... cm [1] (ii) the interquartile range, ... cm [2] (iii) the range of heights of plants that are between the 45th and the 55th percentile. ... cm [3]", "6": "6 0607/41/m/j/17 \u00a9 ucles 2017 3 37\u00b030 m cd ba 26\u00b0not to scale in the diagram, bcd is a straight line. (a) find ac. ac = . m [3] (b) find bc. bc = . m [3]", "7": "7 0607/41/m/j/17 \u00a9 ucles 2017 [turn over (c) find cd. cd = . m [3] (d) find the area of triangle acd . . m2 [2]", "8": "8 0607/41/m/j/17 \u00a9 ucles 2017 4 \u20139 \u20138 \u20137 \u20136 \u20135 \u20134 \u20133 \u20132 \u2013101 2 3 4 5 6 7 8 9123456789 \u20131 \u20132 \u20133 \u20134 \u20135 \u20136 \u20137 \u20138 \u20139xy a", "9": "9 0607/41/m/j/17 \u00a9 ucles 2017 [turn over (a) translate triangle a with vector 0 4-j lkkn poo. label the image b. [2] (b) rotate triangle a through 90\u00b0 anticlockwise about (0, 0). label the image c. [2] (c) describe fully the single transformation that maps triangle c onto triangle a. ... . [2] (d) reflect triangle a in the line yx=- . label the image d. [3] (e) describe fully the single transformation that maps triangle c onto triangle d. ... . [2]", "10": "10 0607/41/m/j/17 \u00a9 ucles 2017 5 46\u00b0not to scale p d bcoa a, b, c and d lie on a circle, centre o. ap and bp are tangents to the circle. angle apb = 46\u00b0. (a) complete the statement. angle oap = 90\u00b0 because . [1] (b) find the value of (i) angle aob , angle aob = [2] (ii) angle oab , angle oab = [2]", "11": "11 0607/41/m/j/17 \u00a9 ucles 2017 [turn over (iii) angle acb , angle acb = [2] (iv) angle adb . angle adb = [2] (c) ob bisects angle abc . find angle oac . angle oac = [3]", "12": "12 0607/41/m/j/17 \u00a9 ucles 2017 6 y varies inversely as the square of x. y = 32 when x = 2. (a) find the value of y when x = 4. y = [3] (b) find the value of x when y = 512. x = [2] (c) find x in terms of y. x = [3]", "13": "13 0607/41/m/j/17 \u00a9 ucles 2017 [turn over 7 \u20134 4xy \u201310010 xx 9 f2=-^h (a) on the diagram, sketch the graph of yxf=^h, for values of x between -4 and 4. [4] (b) solve x 7 f=^h . . [2] (c) the equation xk92-= has two solutions. find the range of values of k. . [2]", "14": "14 0607/41/m/j/17 \u00a9 ucles 2017 8 the venn diagram shows the sets m, e and t. me t 48u u = {students at a school} m = {students who study mathematics} e = {students who study english} t = {students who study technology} me t 8 n++ = ^ h me t 4 n,, =l ^ h me 12 n+= ^ h , mt 14 n+= ^ h and et 20 n+= ^ h m 25 n= ^h , e 30 n= ^h , t 35 n=^h and 56 nu= ^h (a) complete the venn diagram. [3] (b) find (i) me t n+, ll ^ ^ hh, [1] (ii) mtn+ l ^ h. [1]", "15": "15 0607/41/m/j/17 \u00a9 ucles 2017 [turn over (c) one of these students is chosen at random. find the probability that this student studies english and mathematics but not technology. [2] (d) two of the 56 students are chosen at random. find the probability that they both study technology. [2] (e) a student who studies mathematics is chosen at random. find the probability that this student also studies technology but not english. [2] (f) two students who study english are chosen at random. find the probability that they both study mathematics but not technology. [3]", "16": "16 0607/41/m/j/17 \u00a9 ucles 2017 9 ab c12 cm6 cmnot to scale8 cm the diagram shows triangle abc . (a) use the cosine rule to find angle abc . angle abc = [3] (b) use the sine rule to find angle bac . angle bac = [3]", "17": "17 0607/41/m/j/17 \u00a9 ucles 2017 [turn over 10 360 270 180 90xy \u2013303 sinc os xx x 2 f=+^h for \u00b0\u00b0x 0 360 gg log xx 2 g=-^h for \u00b0\u00b0x 0 360 gg (a) on the diagram, sketch the graph of yxf=^h. [3] (b) on the same diagram, sketch the graph of yxg=^h. [2] (c) solve the equation. sinc os log xx x 22+= - [3]", "18": "18 0607/41/m/j/17 \u00a9 ucles 2017 11 vito lives in sicily. table a shows the distances, in km, between different towns. table b shows the average speed, in km/h, that vito drives his car between towns. table a (distances, in km) agrigento catania messina palermo trapani agrigento 175 275 155 170 catania 175 100 215 325 messina 275 100 225 330 palermo 155 215 225 110 trapani 170 325 330 110 table b (average speeds, in km/h) agrigento catania messina palermo trapani agrigento 90 110 75 100 catania 90 120 95 x 90+ messina 110 120 105 80 palermo 75 95 105 x 30 2+ trapani 100 x 90+ 80 x 30 2+ (a) (i) write down the distance from agrigento to messina. ... km [1] (ii) find the time taken for vito to drive from agrigento to messina. ... hours [2] (b) on another day, vito drives from agrigento to trapani. he arrives at trapani at 10 42. at what time did he leave agrigento? [3]", "19": "19 0607/41/m/j/17 \u00a9 ucles 2017 (c) one day vito drives from catania to palermo. vito\u2019s car uses fuel at the rate of 12.5 km/litre. the cost of fuel is 1.432 euros per litre. find the cost of this journey. euros [3] (d) the time for vito to drive from catania to trapani is 121 hours longer than the time for vito to drive from palermo to trapani. (i) show that xx75 1400 02-+ =. [5] (ii) find the two possible average speeds that vito drives from catania to trapani. km/h, km/h [3]", "20": "20 0607/41/m/j/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_s17_qp_42.pdf": { "1": "this document consists of 19 printed pages and 1 blank page. dc (nf/sw) 133522/2 \u00a9 ucles 2017 [turn over *0756949765* cambridge international mathematics 0607/42 paper 4 (extended) may/june 2017 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/42/m/j/17 \u00a9 ucles 2017 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/42/m/j/17 \u00a9 ucles 2017 [turn over answer all the questions. 1 in 2016, carla\u2019s salary was $23 970 per year. (a) from her salary she pays tax at a rate of 20%. she is paid monthly in equal amounts. calculate the amount carla receives each month after tax has been paid. $ [3] (b) carla\u2019s salary of $23 970 was 2% more than her salary in 2015. (i) calculate her yearly salary in 2015. $ [3] (ii) from 2016, carla\u2019s employer agrees to pay her an increase of 3% each year. calculate the year in which her salary is first greater than $30 000. [3]", "4": "4 0607/42/m/j/17 \u00a9 ucles 2017 2 (a) (i) reflection in the line y = x maps triangle a onto triangle b. describe fully the single transformation that maps triangle b onto triangle a. ... . [1] (ii) enlargement, with centre (2, 1) and scale factor 4, maps triangle c onto triangle d. describe fully the single transformation that maps triangle d onto triangle c. ... . [2] (iii) translation by the vector 3 5-j lkkn poo maps triangle e onto triangle f. describe fully the single transformation that maps triangle f onto triangle e. ... . [2] (b) \u20137 \u20136 \u20135 \u20134 \u20133 \u20132 \u2013101 2 3 4 5 6 71234 \u20131 \u20132 \u20133 \u20134xy p (i) rotate triangle p through 90\u00b0 anticlockwise about (0, 0). label the image q. [2] (ii) stretch triangle p with stretch factor 2 and the y-axis invariant. label the image r. [2]", "5": "5 0607/42/m/j/17 \u00a9 ucles 2017 [turn over 3 two judges each give a mark out of ten for each dancer in a competition. their marks for ten dancers are shown in the table. mark from judge a ( x)4.0 4.6 5.2 6.2 8.8 6.8 7.0 7.4 8.0 8.6 mark from judge b ( y)3.8 4.0 4.4 5.0 7.6 5.2 5.6 6.8 6.6 7.0 (a) complete the scatter diagram. the first four points have been plotted for you. 02 4 6 8 10 1 3 5 7 9xy mark from judge b mark from judge a246810 13579 [3] (b) what type of correlation is shown on your scatter diagram? [1] (c) (i) find the equation of the regression line, in the form y = mx + c. y = [2] (ii) judge a gives another dancer a mark of 6.4 . use your equation to estimate the mark judge b gives this dancer. [1]", "6": "6 0607/42/m/j/17 \u00a9 ucles 2017 4 p3 2=-j lkkn poo and q4 3=j lkkn poo (a) find (i) the column vector p21, j lk k kn po o o [1] (ii) the column vector q \u2212 2p, j lk k kn po o o [2] (iii) p, leaving your answer in surd form. [2] (b) ab pq=+ mark and label point b on the grid. a [2]", "7": "7 0607/42/m/j/17 \u00a9 ucles 2017 [turn over 5 nitini flies from new delhi to singapore for a holiday. (a) nitini changes 119 050 indian rupees (inr) to singapore dollars (sgd). the exchange rate is 1 sgd = 47.62 inr. find how many singapore dollars he receives. .. sgd [2] (b) the flight from new delhi to singapore takes 5 hours and 45 minutes. the distance of the flight is 4150 km. (i) the time in new delhi when the flight leaves is 21 55. the time in singapore is 221 hours ahead of the time in new delhi. find the time in singapore when the flight arrives. [2] (ii) find the average speed of the aircraft. .. km / h [3] (iii) on the return flight the average speed is 750 km / h. find the time of this flight in hours and minutes. .. h ... min [3]", "8": "8 0607/42/m/j/17 \u00a9 ucles 2017 6 (a) (i) x is proportional to v. write down an expression for x in terms of v and a constant c. x = .. [1] (ii) y is proportional to v2. write down an expression for y in terms of v and a constant k. y = .. [1] (iii) d = x + y write down an expression for d in terms of v, c and k. d = .. [1] (b) the table shows two values of v and the corresponding values of d. v d 12 750 20 2050 using your answer to part (a)(iii) , (i) show that 125 = 2 c + 24 k, [1] (ii) write down a second equation connecting c and k. [1]", "9": "9 0607/42/m/j/17 \u00a9 ucles 2017 [turn over (c) solve the simultaneous equations in part (b) to find the value of c and the value of k. c = k = [3] (d) find the value of d when v = 40. d = [2]", "10": "10 0607/42/m/j/17 \u00a9 ucles 2017 7 a ship sails 65 km on a bearing of 310\u00b0 from a to b. it then changes course and sails 40 km on a bearing of 250\u00b0 from b to c. the ship then returns to a. (a) on the diagram, sketch the path of the ship from a. on your diagram show the bearings and distances. anorth [3] (b) find angle abc . [1] (c) calculate ac and show that it rounds to 91.8 km, correct to the nearest tenth of a kilometre. [3]", "11": "11 0607/42/m/j/17 \u00a9 ucles 2017 [turn over (d) find the bearing of c from a. [4]", "12": "12 0607/42/m/j/17 \u00a9 ucles 2017 8 \u2013400 600xy 05 f(x) = 3sinx (a) sketch the graph of y = f(x) for \u00b0\u00b0x 400 600 gg - . [3] (b) find the x co-ordinates of the local maximum points of f( x) for \u00b0\u00b0x 400 600 gg - . x = .. or x = .. or x = .. [3] (c) the point (30, 3) is on the graph. the point ( a, 3) is also on the graph where \u00b0\u00b0a 600 90011 . find the two possible values of a. a = .. or a = .. [2] (d) g(x) = 3 \u2212 x 100 solve the inequality xxgf2^^hh . . [3]", "13": "13 0607/42/m/j/17 \u00a9 ucles 2017 [turn over 9 not to scale ac b(x + 2) cmx cm 60\u00b0 in the diagram ac = x cm, ab = (x + 2) cm and angle a = 60\u00b0. (a) (i) find an expression, in terms of x, for the area of triangle abc . give your answer in surd form. . cm2 [2] (ii) the area of triangle abc = 18 3 cm2. show that x2 + 2x \u2013 72 = 0. [2] (b) (i) solve the equation x2 + 2x \u2013 72 = 0. x = .. or x = .. [2] (ii) find the shortest distance between the line ab and the point c. .. cm [2]", "14": "14 0607/42/m/j/17 \u00a9 ucles 2017 10 not to scale xy 0a (2, 2)b (11, 4)c (14, 8) a is the point (2, 2), b is the point (11, 4) and c is the point (14, 8). (a) find the equation, in the form y = mx + c, of (i) the line ac, y = [3] (ii) the line through b that is perpendicular to ac. y = [3] (b) show that the point (10, 6) is on both the lines you found in part (a) . [2]", "15": "15 0607/42/m/j/17 \u00a9 ucles 2017 [turn over (c) ac is the perpendicular bisector of bd. find the co-ordinates of d. (.. , ...) [1] (d) find the exact area of the quadrilateral abcd . [4]", "16": "16 0607/42/m/j/17 \u00a9 ucles 2017 11 a farmer sorts the grapefruit he grows into sizes, according to their diameter. the diameters, d cm, of 170 grapefruit are shown in the table. size small medium large very large diameter ( d cm) d91 0 1g d 10 121g d 12 141g d 14 171g frequency 10 50 65 45 (a) calculate an estimate of the mean diameter of the grapefruit. .. cm [2] (b) on the grid, draw a histogram to represent this information. complete the scale on the frequency density axis. 10 12 14 16 18 9 8 11 13 15 17dfrequency density diameter (cm) [4]", "17": "17 0607/42/m/j/17 \u00a9 ucles 2017 [turn over (c) two of the 170 grapefruit are chosen at random. calculate the probability that (i) they are both very large, [2] (ii) one is small and the other is medium. [3]", "18": "18 0607/42/m/j/17 \u00a9 ucles 2017 12 f(x) = 4 x + 2 g( x) = 5 \u2212 2 x h( x) = x2 \u2212 3 (a) find g(\u22123). [1] (b) find f(h(2)). [2] (c) find x when f( x) = \u221210. x = [2] (d) write down the range of h( x). [1] (e) find f\u22121(x). f\u22121(x) = [2]", "19": "19 0607/42/m/j/17 \u00a9 ucles 2017 (f) k(x) = 10 \u2212 4x describe fully the single transformation that maps the graph of y = g( x) onto the graph of y = k( x). ... . [3] (g) the graph of y = h( x) is translated by the vector 2 0j lkkn poo . find the equation of the graph of the image. write your answer in the form y = ax2 + bx + c. y = [3]", "20": "20 0607/42/m/j/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_s17_qp_43.pdf": { "1": "*1497386406* this document consists of 20 printed pages. dc (cw/sw) 133314/2 \u00a9 ucles 2017 [turn overcambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/43 paper 4 (extended) may/june 2017 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.", "2": "2 0607/43/m/j/17 \u00a9 ucles 2017 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/43/m/j/17 \u00a9 ucles 2017 [turn over answer all the questions. 1 \u201310 \u201310\u20139\u20138\u20137\u20136\u20135\u20134\u20133\u20132\u2013112345678910 \u20139\u20138\u20137\u20136\u20135\u20134\u20133\u20132\u20131 1 0 2345678910y x t u (a) translate triangle t by the vector 2 7-j lkkn poo. [2] (b) (i) reflect triangle t in the x-axis. label the image p. [1] (ii) reflect triangle t in the line x 1=- . label the image q. [1] (iii) describe fully the single transformation that maps triangle p onto triangle q. ... .. [3] (c) describe fully the single transformation that maps triangle t onto triangle u. ... .. [3]", "4": "4 0607/43/m/j/17 \u00a9 ucles 2017 2 (a) 68\u00b0cda benot to scale in the diagram, abc is a triangle and ab is parallel to de. angle bca = 68\u02daand de = dc. (i) find angle bac . angle bac = ... [2] (ii) scalene equilateral isosceles right-angled choose one word from the list to complete the statement. triangle abc is ... [1] (b) calculate the interior angle of a regular 20 sided polygon. [3]", "5": "5 0607/43/m/j/17 \u00a9 ucles 2017 [turn over (c) c ab not to scalep r q in the diagram, angle a = angle p and angle b = angle q. (i) explain why angle c = angle r. .. [1] (ii) ab = 8 cm, ac = 5 cm, bc = 9 cm and pr = 3 cm. (a) complete the statement. triangle abc is to triangle pqr [1] (b) calculate qr. qr = cm [2]", "6": "6 0607/43/m/j/17 \u00a9 ucles 2017 3 (a) 12 students take part in a quiz. the table shows the number of correct answers given by each student. student a b c d e f g h i j k l number of correct answers7 6 9 5 6 4 7 8 410 9 3 find (i) the median, [1] (ii) the lower quartile, [1] (iii) the number of students with a smaller number of correct answers than the lower quartile. [1]", "7": "7 0607/43/m/j/17 \u00a9 ucles 2017 [turn over (b) the table shows the average monthly temperature and the average monthly rainfall in maseru, lesotho. month jan feb mar apr may jun jul aug sep oct nov dec temperature (t \u02dac)21 21 19 15 11 8 8 11 15 17 19 21 rainfall ( r mm) 113 102 99 59 28 12 12 14 27 62 83 88 (i) what type of correlation is there between the monthly temperature and the monthly rainfall? [1] (ii) find the range of these temperatures. .. \u02dac [1] (iii) find the mean of these temperatures. .. \u02dac [1] (iv) find the equation of the line of regression, giving r in terms of t. r = ... [2] (v) on the diagram, sketch the graph of the regression line for t82 1 gg . r t 21 80100 [2]", "8": "8 0607/43/m/j/17 \u00a9 ucles 2017 4 (a) marie has $260.50 and luk has $208.40 . (i) find, in its simplest form, the ratio marie\u2019s money : luk\u2019s money. marie\u2019s money : luk\u2019s money = : . [2] (ii) marie spends 16% of her money to buy a new coat. calculate the cost of the coat. $ ... [2] (iii) in a sale, the prices of all books are reduced by 10%. luk buys a book for $11.25 . calculate the original price of the book. $ ... [3] (iv) marie invests $200 at a rate of 2% per year simple interest. calculate the total value of this investment at the end of 25 years. $ ... [3]", "9": "9 0607/43/m/j/17 \u00a9 ucles 2017 [turn over (v) luk invests $190 at a rate of 2% per year compound interest. calculate the value of this investment at the end of 25 years. $ ... [3] (b) fredrik invests $120 at a rate of 5.7% per year compound interest. calculate the number of complete years it will take until the value of this investment is first greater than $300. [3]", "10": "10 0607/43/m/j/17 \u00a9 ucles 2017 5 8 cm 16 cmnot to scale the diagram shows a solid sphere of radius 4 cm inside a hollow cone of radius 8 cm and height 16 cm. the sphere touches the interior of the cone. (a) calculate the volume of the cone that is not occupied by the sphere. cm3 [3] (b) calculate the curved surface area of the cone. cm2 [3]", "11": "11 0607/43/m/j/17 \u00a9 ucles 2017 [turn over (c) 8 cm 16 cm vo4 cmnot to scale the centre, o, of the sphere is directly above the vertex, v, of the cone. calculate the length ov. ov = cm [4]", "12": "12 0607/43/m/j/17 \u00a9 ucles 2017 6 y x 1006 f(x) = log xx5- (a) on the diagram, sketch the graph of y = f(x) for x01 0 1g . [2] (b) find the co-ordinates of the local minimum point. ( ... , ... ) [2] (c) find the range of f( x) for the domain x15gg . [2] (d) solve the equation f( x) = 2. x = or x = [2] (e) solve the inequality f( x) 1 2. [1] (f) (i) find f(0.001), f(0.000 01) and f(0.000 000 1). f(0.001) = , f(0.000 01) = , f(0.000 000 1) = [1] (ii) complete the statement. the y-axis is to the graph of y = f(x). [1]", "13": "13 0607/43/m/j/17 \u00a9 ucles 2017 [turn over 7 35\u00b0b cda 9 cm8 cm 6 cmnot to scale (a) calculate ab. ab = cm [3] (b) calculate angle bcd . angle bcd = ... [3]", "14": "14 0607/43/m/j/17 \u00a9 ucles 2017 8 ()xx 1 f2=+ ()xx 32 g=+ () , xxx111 h ! =+- (a) find ()3f-. [1] (b) find the value of g(h(1)). [2] (c) simplify f(g( x)) + f( x). [3] (d) find ()xh1-. ()xh1- = ... [3]", "15": "15 0607/43/m/j/17 \u00a9 ucles 2017 [turn over (e) solve. (i) g(x) = 1 x = ... [2] (ii) ()x 1 g1=- x = ... [1]", "16": "16 0607/43/m/j/17 \u00a9 ucles 2017 9 in a survey, 40 students are asked if they like football, f, and if they like baseball, b. 22 like football, 19 like baseball and 6 do not like either football or baseball. (a) complete the venn diagram to show this information. u f 6.. .. ..b [2] (b) how many of these students (i) like both football and baseball, [1] (ii) either like football or do not like baseball? [1] (c) find ()fbn+ l. [1] (d) two of these students are chosen at random. find the probability that they both like football. [2]", "17": "17 0607/43/m/j/17 \u00a9 ucles 2017 [turn over (e) (i) one of the 19 students who like baseball is chosen at random. find the probability that this student also likes football. [1] (ii) two of the 19 students who like baseball are chosen at random. find the probability that one likes football and one does not like football. [3] (f) another n students take part in the survey. they all like both baseball and football. a student is then chosen at random from the (40 + n) students. the probability that a student likes both football and baseball is 165. find the value of n. n = ... [3] (g) u f b on the venn diagram, shade the region fb,ll . [1]", "18": "18 0607/43/m/j/17 \u00a9 ucles 2017 10 (a) the time, t hours, taken by each of 200 cars to complete a journey of 200 km is recorded. the results are shown in the table. time ( t hours) 2.5 1 t g 3 3 1 t g 3.25 3.25 1 t g 3.75 frequency 60 100 40 (i) calculate an estimate of the mean. h [2] (ii) on the grid, draw the histogram to show the information in the table. 2.5050100150200250 frequency density time (hours)300350400450 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8t [3]", "19": "19 0607/43/m/j/17 \u00a9 ucles 2017 [turn over (b) one car completes the 200 km journey at an average speed of x km/h. another car completes the 200 km journey at an average speed of ( x + 10) km/h. the difference between the times taken by the two cars is 20 minutes . (i) show that xx10 6000 02+- =. [4] (ii) find the time taken for the slower journey. give your answer in hours and minutes correct to the nearest minute. h min [4] question 11 is printed on the next page.", "20": "20 0607/43/m/j/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.11 anm abb onot to scale in the diagram, oa a= and ob b=. m is the midpoint of ab and n is the midpoint of am. (a) find each of these vectors in terms of a and b. give each vector in its simplest form. (i) ab ab = ... [1] (ii) an an = ... [1] (iii) on on = ... [2] (b) o is the point (0, 0). oa8 0=j lkkn poo and ob2 6=j lkkn poo. find the co-ordinates of n. ( ... , ... ) [3]" }, "0607_s17_qp_51.pdf": { "1": "*6611381144* this document consists of 8 printed pages. dc (al/ar) 136864/1 \u00a9 ucles 2017 [turn overcambridge international mathematics 0607/51 paper 5 (core) may/june 2017 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/51/m/j/17 \u00a9 ucles 2017 answer all the questions. investigation virus this investigation looks at the way a virus spreads in plants in a field. 1 in a field there are a large number of plants in a straight line. the diagram shows the plants near the middle of the field. on day 1, one of the plants is infected with a virus (v). v on day 2, that plant is dead (d) and the virus infects the plants next to it. dv v this continues from day to day so this is the pattern on day 3. ddv vd the diagram shows that the virus infects two more plants on day 3. so the total number of plants that are infected or dead is five. (a) draw the pattern for day 4. (b) complete this table. day ( n)total number of plants that are infected or dead ( t) 1 1 2 3 3 5 4 5", "3": "3 0607/51/m/j/17 \u00a9 ucles 2017 [turn over (c) what is the name of the numbers in the t column in part (b) ? .. (d) find the total number of plants that are infected or dead on day 9. .. (e) find a formula for t in terms of n. .. (f) on which day are there a total of 97 plants that are infected or dead? ..", "4": "4 0607/51/m/j/17 \u00a9 ucles 2017 2 in another field there are a large number of plants in equally spaced rows and columns. the diagram shows the plants near the middle of the field. one of the plants is infected with the virus (v). v on day 2, that plant is dead (d) and the virus infects the plants next to it. these plants form a cross. dv vv v on day 3, the virus spreads along the arms of the cross. ddv vddv dv this continues from day to day. (a) draw the pattern for day 4.", "5": "5 0607/51/m/j/17 \u00a9 ucles 2017 [turn over (b) complete this table. day ( n)total number of plants that are infected or dead ( t) 1 1 2 5 3 9 4 5 (c) find a formula for t in terms of n. .. 3 in another field, one of the plants is infected with a different virus (z). this virus affects all the plants next to it. z on day 2 that plant is dead (d) and the plants next to it are infected. dz zz z on day 3 there are 5 dead plants and 8 infected plants. ddz zddz dz z z zz", "6": "6 0607/51/m/j/17 \u00a9 ucles 2017 (a) draw the pattern for day 4. (b) complete this table to show the number of infected plants each day. day ( n) number of infected plants ( p) 1 1 2 4 3 8 4 5 you may use this grid to help you.", "7": "7 0607/51/m/j/17 \u00a9 ucles 2017 [turn over (c) work out a formula for the number of infected plants ( p) in terms of the day ( n) for n2h. .. (d) complete this table to show the total number of infected or dead plants each day. day ( n)total number of infected or dead plants ( t) 1 1 2 5 3 13 4 5 (e) the formula for t in terms of n is tn bn c 22=+ +. find the value of b and the value of c. b = \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd c = \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd question 3(f) is printed on the next page.", "8": "8 0607/51/m/j/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. (f) show that your formula works when n = 6." }, "0607_s17_qp_52.pdf": { "1": "*6940747871* this document consists of 7 printed pages and 1 blank page. dc (st) 133977/1 \u00a9 ucles 2017 [turn overcambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/52 paper 5 (core) may/june 2017 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.", "2": "2 0607/52/m/j/17 \u00a9 ucles 2017 answer all the questions. investigation number stems this investigation is about finding numbers that have the same number stem . the possible number stems are the nine integers from 1 to 9. here is how to calculate the number stem of a number. step 1 add the digits of the number to get a total. step 2 if the total is 9 or less, stop. otherwise, add the digits of the total. step 3 repeat step 2. examples number 124 number 893 step 1 1 + 2 + 4 = 7 step 1 8 + 9 + 3 = 20 step 2 stop step 2 2 + 0 = 2 number stem i s 7. step 3 stop number stem is 2. 1 (a) complete the tables to show the number stems for these multiples of 3, 12, 21 and 30. multiple of 3 3 6 9 12 15 18 21 24 27 30 number stem 3 6 9 3 9 3 6 9 3 multiple of 12 12 24 36 48 60 72 84 96 108 120 number stem 3 6 9 9 9 3 multiple of 21 21 42 63 84 105 126 147 168 189 210 number stem 3 9 3 6 9 3 multiple of 30 30 60 90 120 150 180 210 240 270 300 number stem 3 9 3 6 9 3", "3": "3 0607/52/m/j/17 \u00a9 ucles 2017 [turn over (b) complete this statement. the numbers in the table that have a number stem of 9 are all . of 9. (c) complete this table. 3 \u00f7 9 = 0 remainder 3 12 \u00f7 9 = 1 remainder 3 21 \u00f7 . = 2 remainder 3 . \u00f7 9 = 3 remainder 3 39 \u00f7 9 = . remainder (d) complete the statement. a number that has a . of 3 when divided by 9 has a number stem of .", "4": "4 0607/52/m/j/17 \u00a9 ucles 2017 (e) the only one-digit number with a number stem of 3 is 3. this sequence shows the first four numbers greater than 3 with a number stem of 3. 12, 21, 30, 39, ... (i) write down the rule for continuing this sequence. ... (ii) find the nth term of this sequence. ... (iii) find the 87th number greater than 3 that has a number stem of 3. ... ", "5": "5 0607/52/m/j/17 \u00a9 ucles 2017 [turn over 2 (a) complete the tables to show the number stems for different multiples of 2 and 11. multiple of 2 2 4 6 8 10 12 14 16 18 20 22 24 number stem 2 4 6 8 2 4 6 multiple of 11 11 22 33 44 55 66 77 88 99 number stem 2 4 6 8 2 4 6 (b) the sequence shows the first three numbers greater than 2 with a number stem of 2. 11, 20, 29, ... (i) write down the next two numbers of the sequence. , (ii) find the nth term of this sequence. ... (iii) show that 1352 is the 150th number greater than 2 that has a number stem of 2.", "6": "6 0607/52/m/j/17 \u00a9 ucles 2017 3 (a) write down the first four numbers greater than 8 with a number stem of 8. . , . , . , . (b) find the nth term of this sequence. ... (c) using your answer to part (b) , find the number closest to 10 000 that has a number stem of 8. ...", "7": "7 0607/52/m/j/17 \u00a9 ucles 2017 4 the integer k is a number stem . (a) write down, in terms of k, expressions for the first four numbers greater than k with a number stem of k. .. , .. , ... , ... (b) write down, in terms of n and k, the nth term for the sequence of numbers greater than k with a number stem of k. ...", "8": "8 0607/52/m/j/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_s17_qp_53.pdf": { "1": "this document consists of 12 printed pages. dc (st/ar) 134779/2 \u00a9 ucles 2017 [turn over *6057766904* cambridge international mathematics 0607/53 paper 5 (core) may/june 2017 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/53/m/j/17 \u00a9 ucles 2017 answer all the questions. investigation regular stars this investigation is about the construction of regular stars and their properties. here are some regular stars. 1 you can make regular stars by extending the sides of regular polygons. for example, this regular polygon makes a regular star with 10 sides and 5 points. (a) use a straight edge to draw the regular stars made from these regular polygons.", "3": "3 0607/53/m/j/17 \u00a9 ucles 2017 [turn over (b) draw the starting polygon inside this regular star. (c) (i) complete this table. number of sides ( p) of the starting polygonnumber of sides ( s) of the star 5 10 6 7 8 9 (ii) write down a formula for s in terms of p. ... ", "4": "4 0607/53/m/j/17 \u00a9 ucles 2017 (d) this is a point angle. the sum of the 5 point angles in this regular star is 180\u00b0. (i) complete the table. regular star number of pointssum of star\u2019s point angles 5 6 7 8 9180\u00b0 360\u00b0 540\u00b0 720\u00b0 (ii) is it possible for a regular star, made from a regular polygon, to have the sum of its point angles equal to 1450\u00b0? explain how you decide. ... ...", "5": "5 0607/53/m/j/17 \u00a9 ucles 2017 [turn over (e) (i) the regular pentagon making a regular star is shown in bold. the sum of the interior angles of a pentagon is 540\u00b0. use this information to calculate the value of p. p\u00b0not to scale ... (ii) this diagram shows part of a different regular star. it also shows, in bold, part of the regular polygon that makes it. not to scalea\u00b0 b\u00b0 find an equation connecting a and b. write your answer in its simplest form. ...", "6": "6 0607/53/m/j/17 \u00a9 ucles 2017 2 you can also make stars by placing two congruent regular polygons on top of each other and rotating one of the polygons about their common centre. for example and and ", "7": "7 0607/53/m/j/17 \u00a9 ucles 2017 [turn over (a) complete this table. number of sides ( p) of the starting polygonnumber of points of the starnumber of sides ( s) of the star 3 4 5 10 20 6 (b) write down an equation connecting p and s. ...", "8": "8 0607/53/m/j/17 \u00a9 ucles 2017 3 you can also make regular stars by joining dots that are equally spaced round a circle. here is a star made by joining every second dot round a circle with 5 equally spaced dots. this 3-point star is made by connecting every second dot round a circle with 6 equally spaced dots. regular polygons are also regular stars and their vertices are the points of the star. (a) draw the stars made by connecting every second dot round these circles. 7 dots 8 dots 9 dots 10 dots", "9": "9 0607/53/m/j/17 \u00a9 ucles 2017 [turn over complete this table. number of equally spaced dotsnumber of points of the star 5 5 6 3 7 8 9 10 11 12 (b) there are 370 equally spaced dots round a circle. every second dot is joined. find the number of points of the star. ...", "10": "10 0607/53/m/j/17 \u00a9 ucles 2017 4 in question 3 you made stars by joining every second dot round a circle. you can also make stars by joining every third dot. starting from 1, dots are numbered clockwise. this gives a way to code the star. 1 4 7 2 5 8 3 6 1 1 2 3 4 5678 (a) here is the code for a star. 1 4 2 5 3 1 (i) draw this star on the diagram below. 1 2 3 45 (ii) write down a different code for the star you have drawn. ...", "11": "11 0607/53/m/j/17 \u00a9 ucles 2017 [turn over (b) here are some more stars and their codes. 1 2 3 4 56781 2 3 4 5678 1 2 3 4 56781 2 3 4 5 6 7 8 11 2 3 4 56781 2 3 4 5678 1 2 3 4 56781 3 5 7 11 2 3 4 56781 2 3 4 5678 1 2 3 4 5678 1 4 7 2 5 8 3 6 1 (i) write down the connection between the code and the number of points of the star. ... ... (ii) write down the connection between the code and the number of dots round the circle. ... ... questions 4(c) and 4(d) are printed on the next page.", "12": "12 0607/53/m/j/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. (c) make a sketch showing the numbered dots and the regular star with this code. 1 4 7 1 (d) find three codes, each starting with 1, which make a star with 10 points. you may use these circles to help you. ... ... ..." }, "0607_s17_qp_61.pdf": { "1": "this document consists of 12 printed pages. dc (kn/sw) 136671/3 \u00a9 ucles 2017 [turn overcambridge international examinations cambridge international general certificate of secondary education *6802550875* cambridge international mathematics 0607/61 paper 6 (extended) may/june 2017 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. you must show all the relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.", "2": "2 0607/61/m/j/17 \u00a9 ucles 2017 answer all the questions. a investigation virus (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation looks at the way a virus spreads in plants in a field. 1 in a field there are a large number of plants in a straight line. the diagram shows the plants near the middle of the field. on day 1, one of the plants is infected with a virus (v). v on day 2, that plant is dead (d) and the virus infects the plants next to it. dv v this continues from day to day so this is the pattern on day 3. ddv vd the diagram shows that the virus infects two more plants on day 3. so the total number of plants that are infected or dead is five. (a) complete this table. day ( n)total number of plants that are infected or dead ( t) 1 1 2 3 3 5 4 5", "3": "3 0607/61/m/j/17 \u00a9 ucles 2017 [turn over (b) find a formula for t in terms of n. ... (c) on which day are there a total of 97 plants that are infected or dead? ... 2 in another field there are a large number of plants in equally spaced rows and columns. the diagram shows the plants near the middle of the field. on day 1, one of the plants is infected with a virus (v). the virus infects all the plants next to it. v on day 2 that plant is dead (d) and the plants next to it are infected. dv vv v on day 3 there are 5 dead plants and 8 infected plants. ddv vddv dv v v vv", "4": "4 0607/61/m/j/17 \u00a9 ucles 2017 (a) draw the pattern for day 4. (b) complete this table to show the number of infected plants each day. day ( n) number of infected plants ( p) 1 1 2 4 3 8 4 5 you may use this grid to help you.", "5": "5 0607/61/m/j/17 \u00a9 ucles 2017 [turn over (c) work out a formula for the number of infected plants ( p) in terms of the day ( n) for n2h. ... (d) complete this table to show the total number of infected or dead plants each day. day ( n)total number of infected or dead plants ( t) 1 1 2 5 3 13 4 5 (e) find a formula for t in terms of n. ...", "6": "6 0607/61/m/j/17 \u00a9 ucles 2017 (f) show that your formula works when n = 6. (g) on which day are exactly 221 plants infected or dead? ...", "7": "7 0607/61/m/j/17 \u00a9 ucles 2017 [turn over 3 in another field on day 1 eight plants, in the arrangement below, are infected. vvvvv vvv on day 2 these plants are dead and the plants next to them are infected. (a) show that the number of plants that are infected on day n, where n2h, is n43+. (b) find an expression for the total number of plants that are infected or dead on day n, where n2h. ...", "8": "8 0607/61/m/j/17 \u00a9 ucles 2017 b modelling scout\u2019s pace (20 marks) you are advised to spend no more than 45 minutes on this part. this task investigates a way of travelling long distances on foot using a mixture of walking and jogging. 1 explain why multiplying by 601000 changes km/h into metres per minute. ... ... 2 (a) a scout walks at 5 km/h. show that 5 km/h is approximately 83.3 metres per minute. (b) when walking at 5 km/h, the scout takes 120 paces in one minute. how many metres does the scout walk in 30 paces? ... (c) when jogging at 10 km/h, the scout takes 150 paces in one minute. how many metres does the scout jog in 30 paces? ...", "9": "9 0607/61/m/j/17 \u00a9 ucles 2017 [turn over 3 scout\u2019 s pace means to walk for 30 paces then to jog for 30 paces and to keep repeating this. (a) show that the scout takes 27 seconds to walk 30 paces then to jog 30 paces. (b) find the average speed, in m/s, of the scout when using scout\u2019 s pace . ... (c) change your answer in part (b) into km/h. ...", "10": "10 0607/61/m/j/17 \u00a9 ucles 2017 4 to find a model for average speed using scout\u2019 s pace assume that, at different speeds, the scout always takes \u2022 120 paces per minute when walking and \u2022 150 paces per minute when jogging. the scout walks at x km/h and jogs at y km/h. (a) show that an expression for the distance travelled by the scout when walking 30 paces is x 625 metres. (b) the distance travelled by the scout when jogging 30 paces is y 310 metres. show that a model for the average speed, s km/h, using scout\u2019 s pace is sxy 954=+.", "11": "11 0607/61/m/j/17 \u00a9 ucles 2017 [turn over (c) find the average speed using scout\u2019 s pace when the jogging speed, y km/h, is twice the walking speed, x km/h. give your answer, in terms of x, in its simplest form. ... (d) find y in terms of x when the average speed is 1.5 x km/h. ... (e) the average speed is 7 km/h. the jogging speed is 10 km/h. find the walking speed. ... question 5 is printed on the next page.", "12": "12 0607/61/m/j/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.5 the scout now walks at 150 paces per minute and jogs at 180 paces per minute. change the model in question 4(b) for the average speed using scout\u2019 s pace . give your answer in its simplest form. ..." }, "0607_s17_qp_62.pdf": { "1": "*3006023635* this document consists of 12 printed pages. dc (lk/sg) 133976/4 \u00a9 ucles 2017 [turn overcambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/62 paper 6 (extended) may/june 2017 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.", "2": "2 0607/62/m/j/17 \u00a9 ucles 2017 answer both parts a and b. a investigation number stems (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation is about finding numbers that have the same number stem . the possible number stems are the nine integers from 1 to 9. here is how to calculate the number stem of a number. step 1 add the digits of the number to get a total. step 2 if the total is 9 or less, stop. otherwise, add the digits of the total. step 3 repeat step 2. examples number 124 number 893 step 1 1 + 2 + 4 = 7 step 1 8 + 9 + 3 = 20 step 2 stop step 2 2 + 0 = 2 number stem is 7. step 3 stop number stem is 2. 1 (a) complete the tables to show the number stems for these multiples of 3 and 12. multiple of 3 3 6 9 12 15 18 21 24 27 30 number stem 3 6 9 3 9 3 6 9 3 multiple of 12 12 24 36 48 60 72 84 96 108 120 number stem 3 6 9 (b) (i) complete the sequence to show the first four numbers greater than 3 that have a number stem of 3. 12, 21, 30, . (ii) find the nth term of the sequence in part (b)(i) . \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "3": "3 0607/62/m/j/17 \u00a9 ucles 2017 [turn over (iii) find the 87th number greater than 3 that has a number stem of 3. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (c) (i) complete this table. number number stem calculation answer 3 3 3 \u00f7 9 0 remainder 3 19 1 19 \u00f7 9 2 remainder 1 22...22 \u00f7...2 remainder 4 35...35 \u00f7 9remainder ...7...\u00f7 9remainder (ii) a number, that is not a multiple of 9, is divided by 9. what is the connection between its number stem and the remainder? ... (iii) using your answer to part (c)(ii) write down the remainder when 104 020 100 is divided by 9. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "4": "4 0607/62/m/j/17 \u00a9 ucles 2017 2 the sequence shows the first three numbers greater than 2 with a number stem of 2. 11, 20, 29, \u2026 (a) write down the next two numbers of the sequence. .. , .. (b) find the nth term of this sequence. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (c) using your answer to part (b) , find the largest number less than 10 000 that has a number stem of 2. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd 3 the integer k is a number stem . (a) write down, in terms of k, the first four numbers greater than k with a number stem of k. .. , ... , ... , ... (b) write down, in terms of n and k, the nth term for the sequence of numbers greater than k with a number stem of k. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "5": "5 0607/62/m/j/17 \u00a9 ucles 2017 [turn over 4 (a) complete this table. calculation answer 7 \u00f712 0 remainder 7 15 \u00f712 1 remainder .. 23 \u00f712..remainder.. (b) an integer, that is not a multiple of 12, has remainder f when it is divided by 12. find, in terms of n and f, the nth term for the sequence of numbers greater than f with a remainder of f. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (c) show that f + 10 cannot be a term of the sequence of numbers greater than f with a remainder of f.", "6": "6 0607/62/m/j/17 \u00a9 ucles 2017 b modelling elev ators (20 marks) you are advised to spend no more than 45 minutes on this part. this task is about the mass an elevator carries and the time it takes to move between floors. easyup is a company that makes elevators. for each type of elevator, the company uses two mathematical models. model 1 the company models the masses of the passengers using the elevator. model 2 the company models the time it takes the elevator to move between floors. 1 the easyup -5 elevator carries a maximum of 5 passengers. (a) for model 1, the company estimates that \u2022\t102 of the passengers have a mass of 50 kg \u2022\t104 of the passengers have a mass of 70 kg \u2022\t104 of the passengers have a mass of 85 kg. from the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 \u2022\t 0 and 1 give a mass of 50 kg \u2022\t 2, 3, 4 and 5 give a mass of 70 kg \u2022\t 6, 7, 8 and 9 give a mass of 85 kg.", "7": "7 0607/62/m/j/17 \u00a9 ucles 2017 [turn over (i) numbers are chosen at random from 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. each number models the mass of a passenger. the 5 passengers are a, b, c, d and e. here is a random number table, arranged in groups of 5 numbers. 1 6 8 5 2 4 7 9 1 1 6 9 8 7 4 9 1 4 6 8 4 2 1 9 0 8 2 8 8 0 8 9 4 7 6 7 4 1 6 5 1 0 4 7 6 6 0 0 4 5 use the last four rows of the random number table to complete the table of trials below. the first six trials have been completed for you. mass of passenger (kg)total mass (kg)a b c d e trial 1 50 85 85 70 70 360 trial 2 70 85 85 50 50 340 trial 3 85 85 85 85 70 410 trial 4 85 50 70 85 85 375 trial 5 70 70 50 85 50 325 trial 6 85 70 85 85 50 375 trial 7 85 85 trial 8 trial 9 trial 10 (ii) the easyup -5 elevator carries a maximum total mass of 400 kg. use the results of trials 1 to 10 to work out the relative frequency that the total mass will be more than 400 kg. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "8": "8 0607/62/m/j/17 \u00a9 ucles 2017 (b) for model 2, the diagram below is a distance-time graph for the easyup -5 elevator. the graph modelling the movement is y = f(t), where f( t) is the number of floors above or below the ground floor (floor 0) at time t seconds. y t 5 10 15 204 3 2 1 0 \u20131 \u20132ground floor (i) the graph shows the elevator starting one floor below the ground floor. at which floor does it stop? \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (ii) between which two floors does the elevator have the greatest average speed? ... and ... (iii) find the average time it takes the elevator to move from one floor to the next. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "9": "9 0607/62/m/j/17 \u00a9 ucles 2017 [turn over 2 the easyup -3 elevator carries a maximum of 3 passengers. the maximum total mass is 240 kg. (a) for model 1, the company now uses different proportions of passengers for each mass, as shown in the table. a number is chosen from 0, 1, 2, 3, 4, 5, 6 and 7 to give the mass. for example, the numbers 1, 2, 3, 4 and 5 each give the mass 70 kg. (i) complete the table below. proportion of passengers85 82 amount of numbers 5 numbers 0 1, 2, 3, 4, 5 mass of passenger (kg) 50 70 85 (ii) random numbers model the masses of the 3 passengers, a, b and c. here is a random number table, arranged in groups of four numbers. three random numbers are needed for each trial. the numbers 8 and 9 are not used. cross out the numbers 8 and 9 in the table. when four numbers remain in a row, cross out the last number. 8 2 1 5 1 6 3 3 6 7 0 5 0 9 1 5 2 0 8 6 1 0 1 1 3 4 8 2 9 0 4 3 use the last four rows of the random number table to complete the table of trials below. the first four trials have been completed for you. mass of passenger (kg) total mass (kg) a b c trial 1 70 70 70 210 trial 2 70 85 70 225 trial 3 85 85 50 220 trial 4 50 70 70 190 trial 5 trial 6 trial 7 trial 8", "10": "10 0607/62/m/j/17 \u00a9 ucles 2017 (b) for model 2, the diagram below is a distance-time graph for the easyup -3 elevator. the graph modelling the movement is y = h(t), where h( t) is the number of floors above or below the ground floor (floor 0) at time t seconds. 15 20 10 51 0 \u20131y tground floor (i) the graph shows that the easyup -3 elevator starts to move from floor 1. find the average time it takes the elevator to move from one floor to the next. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (ii) ()hc os tk t = . find the value of the integer k. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd 3 the mass carried by an elevator is x kilograms. easyup say that an elevator is well designed when \u2022\t the probability that x is less than the maximum total mass is greater than 0.95 and \u2022\t it takes at most 5 seconds on average to move between floors. explain whether (a) the easyup -5 elevator is well designed, ... ... (b) the easyup -3 elevator is well designed. ... ...", "11": "11 0607/62/m/j/17 \u00a9 ucles 2017 [turn over 4 write down two ways to improve model 1 in question 1(a) . ... ... ... ... 5 the easyup -n elevator carries a maximum of n passengers. the maximum total mass is 80 n kilograms. (a) for model 1, the company uses different proportions of passengers for each mass, as shown in the table. a number is chosen at random from m integers to give the mass. (i) complete the table. proportion of passengers m2 mm3- amount of numbers mass of passenger (kg) 50 70 85 (ii) explain why m 4h. ... .. question 5(b) and question 5(c) are printed on the next page.", "12": "12 0607/62/m/j/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. (b) for model 2, the distance-time graph for the easyup -7 elevator is modelled by ()h yt 2=- . (i) use your answer to question 2 (b)(ii) to write down the equation of this distance-time graph. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (ii) on the grid below, sketch the graph of ()h yt 2=- , for t01 0 gg . 10 5012 \u20131 \u20132y t (c) the mass carried by an elevator is x kilograms. the probability that x is less than the maximum mass is 0.99 . use this information and your graph in part (b)(ii) to explain why the easyup -7 elevator is well designed. ... ..." }, "0607_s17_qp_63.pdf": { "1": "this document consists of 16 printed pages. dc (nh/ar) 134782/2 \u00a9 ucles 2017 [turn overcambridge international examinations cambridge international general certificate of secondary education *7141363470* cambridge international mathematics 0607/63 paper 6 (extended) may/june 2017 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. you must show all the relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.", "2": "2 0607/63/m/j/17 \u00a9 ucles 2017 answer both parts a and b. a investigation regular stars (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation is about the construction of regular stars and their properties. here are some regular stars. 1 you can make regular stars by extending the sides of regular polygons. for example, this regular polygon makes a regular star with 10 sides and 5 points. (a) use a straight edge to draw the regular stars made from these regular polygons.", "3": "3 0607/63/m/j/17 \u00a9 ucles 2017 [turn over (b) (i) complete this table. number of sides ( p) of the starting polygonnumber of sides ( s) of the star 5 10 6 7 8 9 (ii) write down a formula for s in terms of p. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "4": "4 0607/63/m/j/17 \u00a9 ucles 2017 (c) this is a point angle. the sum of the 5 point angles in this regular star is 180\u00b0. (i) complete the table. regular star number of pointssum of star\u2019s point angles 5 6 7 8 9180\u00b0 360\u00b0 540\u00b0 720\u00b0 (ii) is it possible for a regular star, made from a regular polygon, to have the sum of its point angles equal to 1450\u00b0? explain how you decide. ... ...", "5": "5 0607/63/m/j/17 \u00a9 ucles 2017 [turn over (d) (i) the regular pentagon making a regular star is shown in bold. the sum of the interior angles of a pentagon is 540\u00b0. use this information to calculate the value of p. p\u00b0not to scale ... (ii) this diagram shows part of a different regular star. it also shows, in bold, part of the regular polygon that makes it. not to scalea\u00b0 b\u00b0 find an equation connecting a and b. write your answer in its simplest form. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "6": "6 0607/63/m/j/17 \u00a9 ucles 2017 2 you can also make regular stars by joining dots that are equally spaced round a circle. here is a star made by joining every second dot round a circle with 5 equally spaced dots. the 3-point star below is made by connecting every second dot round a circle with 6 equally spaced dots. regular polygons are also regular stars and their vertices are the points of the star. (a) draw the stars made by connecting every second dot round these circles. 7 dots 8 dots 9 dots 10 dots", "7": "7 0607/63/m/j/17 \u00a9 ucles 2017 [turn over complete this table. number of equally spaced dotsnumber of points on the star 5 5 6 3 7 8 9 10 11 (b) write down two conclusions you can make from the results in your table. 1 ... 2 ...", "8": "8 0607/63/m/j/17 \u00a9 ucles 2017 3 in question 2 you made stars by joining every second dot round a circle. you can also make stars by joining every third dot. 1 starting from 1, dots are numbered clockwise. this gives a code for this star. 4 7 10 11 2 3 4 5 6 789101112 (a) on the circle below draw the star with this code. 1 3 5 7 9 11 11 2 3 4 5 6 789101112 (b) to make stars you join every nth dot round a circle with 12 dots. when n = 2 not all the dots are used. when n = 3 not all the dots are used. when n g 6, find two other values of n and the codes for stars that do not use all the dots. there are some 12-dot circles below if you need them. n = ... with code 1 ... n = ... with code 1 ... 1 2 3 4 5 6 7891011121 2 3 4 5 6 789101112", "9": "9 0607/63/m/j/17 \u00a9 ucles 2017 [turn over (c) (i) to make stars you join every nth dot round a circle with 20 dots. for n g 10, not all the dots are used when n = 2 or 4 or 5 or 10. when d is the number of dots round a circle and nd 2g, what is true about n when not all the dots are used? ... ... ... ... (ii) when d is a prime number greater than 2, find an expression, in terms of d, for the number of different stars that can be drawn. ... ...", "10": "10 0607/63/m/j/17 \u00a9 ucles 2017 (d) here are the last four numbers in the code for a star. ... 98 106 114 1 (i) find the number of dots round the circle \ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (ii) find the number of points on the star. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "11": "11 0607/63/m/j/17 \u00a9 ucles 2017 [turn over the modelling task starts on page 12.", "12": "12 0607/63/m/j/17 \u00a9 ucles 2017 b modelling reliability (20 marks) you are advised to spend no more than 45 minutes on this part. this task is about modelling the reliability of usb memory sticks. a factory makes three types of usb memory stick, usb1, usb2 and usb3. the factory tests the reliability of a sample by saving and deleting data 10 000 times a day. the percentage of sticks that still work at the end of each week is recorded. this gives a measure of reliability \ufffd 1 this bar chart shows the percentage, w, of three types of usb stick that were still working at the end of each week, t\ufffd percentage of usb sticks still working number of weeksusb1 usb2 usb3100 90 80 70 60 50 40 30 20 10 01 2 3tw (a) what percentage of the usb2 sticks were still working after two weeks? \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (b) which type of usb stick had the greatest percentage failure from the end of week 1 to the end of week 2? write down this percentage. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "13": "13 0607/63/m/j/17 \u00a9 ucles 2017 [turn over (c) the results for the usb3 sticks are modelled by this equation. w = 100 \u2013 15 t explain why this is not a good model for usb3 sticks that have been tested for 7 or more weeks. ... ... (d) the results for the usb1 sticks fit this model. w = t2 \u20137t + 100 (i) sketch the graph for this model on the axes below for t g 5. percentage of usb1 sticks still working number of weeks100 80 tw 0 5 (ii) explain why this model is not suitable for usb1 sticks that have been tested for more than three weeks. ... ... (e) a model for the usb2 sticks is w = kt + 100, where k is a constant. find the value of k. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd ", "14": "14 0607/63/m/j/17 \u00a9 ucles 2017 2 the factory\u2019s engineers want to estimate the percentage of usb1 memory sticks that still work after a year of testing. they use the mean time between failures (mtbf) to measure the reliability. mtbftotal numbe roffailure stotaltesting time= example 15 400 memory sticks are each tested for 10 weeks. during this time 1100 failed. mtbf = 110015400 10# = 140 weeks a model for the percentage, w, of memory sticks still working after time t weeks is w 100 3mt # =-ak, where m is the mtbf in weeks. (a) a sample of memory sticks has mtbf = 10 weeks. (i) sketch a graph of w against t for t g 30. percentage of memory sticks still working number of weekstw 00 (ii) after how many weeks are only half the sticks still working? \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "15": "15 0607/63/m/j/17 \u00a9 ucles 2017 [turn over (b) a sample of ten usb1 sticks is tested for 8 weeks. during this time 4 failed. use the model for w to calculate the percentage of usb1 sticks still working after one year (52 weeks). \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (c) use the model to estimate the probability of a memory stick still working for as long as its mtbf. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (d) another factory says that 99% of their memory sticks still work after 52 weeks. find the mtbf. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd question 3 is printed on the next page.", "16": "16 0607/63/m/j/17 \u00a9 ucles 2017 3 one engineer suggests a simpler model. she says test 100 memory sticks for 1 week. the probability that x fail is x 100. (a) explain why her model for the percentage of memory sticks still working after t weeks is wx100 1100t # =- a k ... ... ... (b) one memory stick out of the 100 failed in the first week. (i) use her model to find the percentage of memory sticks still working after 5 weeks. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (ii) compare her model with the model in question 2 . permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_w17_qp_11.pdf": { "1": " this document consists of 8 printed pages. ib17 11_0607_11/3rp \u00a9 ucles 2017 [turn over \uf02a\uf035\uf031\uf032\uf031\uf039\uf031\uf031\uf033\uf034\uf035 \uf02a\uf020 cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/11 paper 1 (core) october/november 2017 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2017 0607/11/o/n/17 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \uf070r2 circumference, c, of circle, radius r. c = 2\uf070r curved surface area, a, of cylinder of radius r, height h. a = 2\uf070rh curved surface area, a, of cone of radius r, sloping edge l. a = \uf070rl curved surface area, a, of sphere of radius r. a = 4\uf070r2 volume, v, of prism, cross-sectional area a, length l. v = al volume, v, of pyramid, base area a, height h. v = 1 3ah volume, v, of cylinder of radius r, height h. v = \uf070r2h volume, v, of cone of radius r, height h. v = 1 3\uf070r2h volume, v, of sphere of radius r. v = 4 3\uf070r3 ", "3": "3 \u00a9 ucles 2017 0607/11/o/n/17 [turn over answer all the questions. 1 2 4 8 16 32 48 64 from the list of numbers write down (a) the square of 4, [1] (b) the square root of 64, [1] (c) the cube of 2, [1] (d) the lowest common multiple (lcm) of 16 and 32. [1] 2 work out. (a) (7 \u2013 3) \u00d7 5 [1] (b) 9 \u2013 4 \u00d7 2 [1] 3 (a) write down the next term in the following sequence. 7, 11, 15, 19, 23, \u2026 [1] (b) write down the rule for continuing the following sequence. 3, 8, 13, 18, 23, \u2026 [1] ", "4": "4 \u00a9 ucles 2017 0607/11/o/n/17 4 work out 30 \uf0b4 4\u20132. give your answer as a fraction. [2] 5 a b c e d (a) write down the letters of two congruent shapes. and [1] (b) write down the letters of two shapes which are similar but not congruent. and [1] 6 draw all the lines of symmetry on this regular hexagon. [2] ", "5": "5 \u00a9 ucles 2017 0607/11/o/n/17 [turn over 7 when f( x) = x6, find (a) f(2), [1] (b) f(\u20132), [1] (c) f\uf0f7\uf0f8\uf0f6\uf0e7\uf0e8\uf0e6 21. [1] 8 what type of correlation is shown in each scatter diagram? [2] 9 u = {1, 2, 3, 4, 5, 6} a = {2, 4, 6} b = {2, 3, 5, 6} c = {2, 4} complete the following. (a) ba\uf0c7 = { } [1] (b) b\u2032 = { } [1] (c) c b\uf0c8 = { } [1] (d) n( c b\uf0c8 ) = [1] ", "6": "6 \u00a9 ucles 2017 0607/11/o/n/17 10 find the smallest integer value, x, such that (a) x > \u20133, [1] (b) 2x > 16. [1] 11 (a) find the value of 6 x + 7y when x = 3 and y = \u20135. [2] (b) write down an expression, in terms of x and y, for the total cost of x apples at 70 cents each and y pears at 50 cents each. cents [2] (c) a line has equation 3 x + 4y = 12. write the equation of this line in the form y = mx + c. y = [2] 12 20 mx mnot to scale50\u00b0 sin 50\u00b0 = 0.766 cos 50\u00b0 = 0.643 tan 50\u00b0 = 1.192 use the information given to work out the value of x. x = [2] ", "7": "7 \u00a9 ucles 2017 0607/11/o/n/17 [turn over 13 \u20133\u20132 01231234 45 \u20133\u20132\u2013156 \u20135\u20134y x \u20131 write down the equations of the two asymptotes of the graph. [2] 14 \u20133\u20132 01231234 45 \u20133\u20132\u2013156 \u20136\u20135\u20134\u20136\u20135\u20134 6y x \u20131 on the grid, enlarge the shaded triangle with scale factor 2, centre (3, 4). [2] question 15 is printed on the next page. ", "8": "8 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknow ledgements booklet. this is produced for each series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge as sessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2017 0607/11/o/n/17 15 (a) not to scale oc b a the diagram shows a circle centre o. write down the mathematical word that describes the line (i) oa, [1] (ii) bc. [1] (b) not to scale ba c o ab is a diameter of a circle centre o. write down the size of angle acb . angle acb = [1] " }, "0607_w17_qp_12.pdf": { "1": " this document consists of 8 printed pages. ib17 11_0607_12/rp \u00a9 ucles 2017 [turn over \uf02a\uf030\uf031\uf035\uf038\uf038\uf032\uf033\uf032\uf038\uf039 \uf02a\uf020 cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/12 paper 1 (core) october/november 2017 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2017 0607/12/o/n/17 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \uf070r2 circumference, c, of circle, radius r. c = 2\uf070r curved surface area, a, of cylinder of radius r, height h. a = 2\uf070rh curved surface area, a, of cone of radius r, sloping edge l. a = \uf070rl curved surface area, a, of sphere of radius r. a = 4\uf070r2 volume, v, of prism, cross-sectional area a, length l. v = al volume, v, of pyramid, base area a, height h. v = 1 3ah volume, v, of cylinder of radius r, height h. v = \uf070r2h volume, v, of cone of radius r, height h. v = 1 3\uf070r2h volume, v, of sphere of radius r. v = 4 3\uf070r3 ", "3": "3 \u00a9 ucles 2017 0607/12/o/n/17 [turn over answer all the questions. 1 write 42 652 correct to the nearest hundred. [1] 2 0 1234567812345678y xa (a) write down the co-ordinates of the point a. ( , ) [1] (b) on the grid, plot the point (7, 5). label it b. [1] 3 complete the second column in the table using the words discrete or continuous. data collected in a survey type of data number of students the mass of students number of pets that students own the time it takes to get to school [2] ", "4": "4 \u00a9 ucles 2017 0607/12/o/n/17 4 class 1number of students 0481216202428 boys key: girls class 2 class 3 the bar chart shows the numbers of students in each of three classes. work out the difference in the total number of boys and the total number of girls. [2] 5 (a) draw all the lines of symmetry on the regular pentagon. [2] (b) shade four squares on the grid to give the diagram 4 lines of symmetry. [1]", "5": "5 \u00a9 ucles 2017 0607/12/o/n/17 [turn over 6 the mass, x grams, of each of 130 tomatoes is recorded. this information is shown in the frequency table below. mass ( x grams) 0 < x 35 35 < x 50 50 < x 65 65 < x 80 80 < x 100 frequency 25 27 30 28 20 complete the cumulative frequency table. mass ( x grams) 0 < x 35 0 < x 50 0 < x 65 0 < x 80 0 < x 100 cumulative frequency 130 [2] 7 this table shows the ages, in years, of 50 students in a school. age (years) 11 12 13 14 15 16 number of boys 4 3 6 2 5 4 number of girls 2 5 3 6 4 6 (a) how many girls are less than 14 years old? [1] (b) what percentage of the students are at least 15 years old? % [2] (c) one of the 50 students is chosen at random. what is the probability that this student is less than 13 years old? give your answer as a fraction in its simplest form. [2] ", "6": "6 \u00a9 ucles 2017 0607/12/o/n/17 8 x\u00b0158 \u00b0172 \u00b0not to scale find the value of x. x = [1] 9 30 cm 20 cm 40 cmnot to scale find the volume of the cuboid. cm3 [2] 10 not to scale x\u00b0 the diagram shows a regular pentagon. find the size of the exterior angle, x. [2] ", "7": "7 \u00a9 ucles 2017 0607/12/o/n/17 [turn over 11 2hba\uf0b4\uf03d find the value of b when a = 21 and h = 6. b = [2] 12 (a) write down the value of 80. [1] (b) simplify 6 p3 \u00d7 3p6. [2] 13 write 88 as a product of prime factors. [2] 14 a radio originally cost $75. it is sold for $84. work out the percentage profit. % [3] questions 15, 16 and 17 are printed on the next page. ", "8": "8 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknow ledgements booklet. this is produced for each series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge as sessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2017 0607/12/o/n/17 15 work out (8 \u00d7 10\u20133) \u00d7 (7 \u00d7 109). give your answer in standard form. [2] 16 find the image of the point (2, 3) after a reflection in the line x = 1. you may use the grid to help you. xy 2 4 \u20132 \u201344 2 \u20132 \u201340 ( , ) [3] 17 p is the point (5, 7) and \uf0f7 \uf0f8\uf0f6\uf0e7 \uf0e8\uf0e6\uf03d\uf02d23pq . (a) find the co-ordinates of q. ( , ) [1] (b) describe fully the single transformation that maps q onto p. [2] " }, "0607_w17_qp_13.pdf": { "1": " this document consists of 8 printed pages. ib17 11_0607_13/fp \u00a9 ucles 2017 [turn over \uf02a\uf038\uf031\uf032\uf033\uf039\uf031\uf033\uf030\uf030\uf037 \uf02a\uf020 cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/13 paper 1 (core) october/november 2017 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2017 0607/13/o/n/17 [turn over formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \uf070r2 circumference, c, of circle, radius r. c = 2\uf070r curved surface area, a, of cylinder of radius r, height h. a = 2\uf070rh curved surface area, a, of cone of radius r, sloping edge l. a = \uf070rl curved surface area, a, of sphere of radius r. a = 4\uf070r2 volume, v, of prism, cross-sectional area a, length l. v = al volume, v, of pyramid, base area a, height h. v = 1 3ah volume, v, of cylinder of radius r, height h. v = \uf070r2h volume, v, of cone of radius r, height h. v = 1 3\uf070r2h volume, v, of sphere of radius r. v = 4 3\uf070r3 ", "3": "3 \u00a9 ucles 2017 0607/13/o/n/17 [turn over answer all the questions. 1 write 42 652 correct to the nearest hundred. [1] 2 0 1234567812345678y xa (a) write down the co-ordinates of the point a. ( , ) [1] (b) on the grid, plot the point (7, 5). label it b. [1] 3 complete the second column in the table using the words discrete or continuous. data collected in a survey type of data number of students the mass of students number of pets that students own the time it takes to get to school [2] ", "4": "4 \u00a9 ucles 2017 0607/13/o/n/17 [turn over 4 class 1number of students 0481216202428 boys key: girls class 2 class 3 the bar chart shows the numbers of students in each of three classes. work out the difference in the total number of boys and the total number of girls. [2] 5 (a) draw all the lines of symmetry on the regular pentagon. [2] (b) shade four squares on the grid to give the diagram 4 lines of symmetry. [1]", "5": "5 \u00a9 ucles 2017 0607/13/o/n/17 [turn over 6 the mass, x grams, of each of 130 tomatoes is recorded. this information is shown in the frequency table below. mass ( x grams) 0 < x 35 35 < x 50 50 < x 65 65 < x 80 80 < x 100 frequency 25 27 30 28 20 complete the cumulative frequency table. mass ( x grams) 0 < x 35 0 < x 50 0 < x 65 0 < x 80 0 < x 100 cumulative frequency 130 [2] 7 this table shows the ages, in years, of 50 students in a school. age (years) 11 12 13 14 15 16 number of boys 4 3 6 2 5 4 number of girls 2 5 3 6 4 6 (a) how many girls are less than 14 years old? [1] (b) what percentage of the students are at least 15 years old? % [2] (c) one of the 50 students is chosen at random. what is the probability that this student is less than 13 years old? give your answer as a fraction in its simplest form. [2] ", "6": "6 \u00a9 ucles 2017 0607/13/o/n/17 [turn over 8 x\u00b0158 \u00b0172 \u00b0not to scale find the value of x. x = [1] 9 30 cm 20 cm 40 cmnot to scale find the volume of the cuboid. cm3 [2] 10 not to scale x\u00b0 the diagram shows a regular pentagon. find the size of the exterior angle, x. [2] ", "7": "7 \u00a9 ucles 2017 0607/13/o/n/17 [turn over 11 2hba\uf0b4\uf03d find the value of b when a = 21 and h = 6. b = [2] 12 (a) write down the value of 80. [1] (b) simplify 6 p3 \u00d7 3p6. [2] 13 write 88 as a product of prime factors. [2] 14 a radio originally cost $75. it is sold for $84. work out the percentage profit. % [3] questions 15, 16 and 17 are printed on the next page. ", "8": "8 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknow ledgements booklet. this is produced for each series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge as sessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2017 0607/13/o/n/17 15 work out (8 \u00d7 10\u20133) \u00d7 (7 \u00d7 109). give your answer in standard form. [2] 16 find the image of the point (2, 3) after a reflection in the line x = 1. you may use the grid to help you. xy 2 4 \u20132 \u201344 2 \u20132 \u201340 ( , ) [3] 17 p is the point (5, 7) and \uf0f7 \uf0f8\uf0f6\uf0e7 \uf0e8\uf0e6\uf03d\uf02d23pq . (a) find the co-ordinates of q. ( , ) [1] (b) describe fully the single transformation that maps q onto p. [2] " }, "0607_w17_qp_21.pdf": { "1": "*1855009495* this document consists of 8 printed pages. dc (lk/cgw) 134060/1 \u00a9 ucles 2017 [turn overcambridge international mathematics 0607/21 paper 2 (extended) october/november 2017 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/21/o/n/17 \u00a9 ucles 2017 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/21/o/n/17 \u00a9 ucles 2017 [turn over answer all the questions. 1 by rounding each number correct to 1 significant figure, estimate the value of .. ..18964128 000509 000298# +. [3] 2 written as the product of their prime factors, 7056 23 742 2##= and 8232 23 733##= . giving your answers as the product of prime factors, find (a) the highest common factor (hcf) of 7056 and 8232, [1] (b) the lowest common multiple (lcm) of 7056 and 8232, [1] (c) 7056 . [1] 3 show the inequality x141g - on this number line. \u20135 \u20134 \u20133 \u20132 \u20131 0 1 2 3 4 5x [2]", "4": "4 0607/21/o/n/17 \u00a9 ucles 2017 4 work out 83 61-, giving your answer as a fraction in its lowest terms. [2] 5 solve the simultaneous equations. x \u2013 3y = 4 5x \u2013 6y = \u20137 x = y = [3] 6 a is the point (3, 6) and b is the point (, )510- . (a) work out the co-ordinates of the midpoint of ab. ( ... , ... ) [2] (b) find the length of ab, giving your answer in the form a5. [3] 7 work out, giving your answer in standard form. (. )( .) 63 10 56 1045## + [2]", "5": "5 0607/21/o/n/17 \u00a9 ucles 2017 [turn over 8 shade the region indicated in each of these venn diagrams. (a) a b cuaa bb cuu ab+ll [1] (b) ()ab c ,+ [1] (c) ab c ++ l [1]", "6": "6 0607/21/o/n/17 \u00a9 ucles 2017 9 140\u00b0not to scale 25\u00b0a bd co a, b, c and d are points on a circle centre o. find (a) angle acd , angle acd = \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd [2] (b) angle bad . angle bad = ... [2]", "7": "7 0607/21/o/n/17 \u00a9 ucles 2017 [turn over 10 y is inversely proportional to the square root of x. when x = 9, y = 12. find y when x = 100. [3] 11 (a) factorise xx31 02-- . [2] (b) using your answer to part (a) , solve xx31 0022 -- \ufffd [2] questions 12 and 13 are printed on the next page.", "8": "8 0607/21/o/n/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.12 rationalise the denominator and simplify. 3142 2+ [3] 13 expand the brackets and simplify. () () ab ab 35 23 -- [3]" }, "0607_w17_qp_22.pdf": { "1": "*4505123050* this document consists of 8 printed pages. dc (st/cgw) 134057/1 \u00a9 ucles 2017 [turn overcambridge international mathematics 0607/22 paper 2 (extended) october/november 2017 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/22/o/n/17 \u00a9 ucles 2017 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area =a c bcb a", "3": "3 0607/22/o/n/17 \u00a9 ucles 2017 [turn over answer all the questions. 1 100\u00b0not to scale140\u00b0e d a bxc w\u00b0 the diagram shows two parallel lines with two straight lines crossing. find the value of w. w = ... [2] 2 the volume of a cube is 27 cm3. find the total surface area. . cm2 [2]", "4": "4 0607/22/o/n/17 \u00a9 ucles 2017 3 find the highest common factor (hcf) of 30, 48 and 66. [1] 4 f(x) = 2x - 3 find the range of f( x) for the domain {0, 1, 2}. {. } [1] 5 a cb 10 cm \u221a 91 cmnot to scale work out the length of ab. ab = .. cm [3]", "5": "5 0607/22/o/n/17 \u00a9 ucles 2017 [turn over 6 y = 2x2 - 1 rearrange the formula to write x in terms of y. x = [3] 7 (a) change 20 m/s into km/h. ... km/h [2] (b) a train travels at 20 m/s for 45 minutes. work out the distance travelled. give your answer in kilometres. .. km [2] 8 work out (. )( .) 32 10 23 1021 20## + , giving your answer in standard form. . [2] 9 find the value of (0.1)2. . [1]", "6": "6 0607/22/o/n/17 \u00a9 ucles 2017 10 9x\u00b0 6x\u00b0 ba 130\u00b0not to scalec ed abcd is a cyclic quadrilateral. dc is extended to e. angle bce = 130\u00b0, angle abc = 6x\u00b0 and angle adc = 9x\u00b0. find the value of (a) angle bad , angle bad =\t [1] (b) angle abc . angle abc = [2] 11 simplify. (a) xx 412 412 [2] (b) ()x161641 [2]", "7": "7 0607/22/o/n/17 \u00a9 ucles 2017 [turn over 12 y is proportional to x1. when x = 4, y = 2. find y when x = 64. y = [3] 13 (a) simplify 18 72+ . [2] (b) rationalise the denominator. 51 2+ [2] 14 simplify. xxx 122 -- [3] questions 15 and 16 are printed on the next page.", "8": "8 0607/22/o/n/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.15 (a) logk = 2log3 - 5log2 find the value of k. k =\t [2] (b) log2 p = -1 find the value of p. p =\t [1] 16 i is an acute angle and tan3i= . write down the value of i. i= [1]" }, "0607_w17_qp_23.pdf": { "1": "*4493042720* this document consists of 8 printed pages. dc (st/cgw) 134059/2 \u00a9 ucles 2017 [turn overcambridge international mathematics 0607/23 paper 2 (extended) october/november 2017 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/23/o/n/17 \u00a9 ucles 2017 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/23/o/n/17 \u00a9 ucles 2017 [turn over answer all the questions. 1 27 39 49 51 53 55 58 from this list write down the prime number. [1] 2 a is the point (1, 3) and b is the point (4, 9). find ab. ab = j lk kkn po oo [2] 3 36\u00b0 not to scale c ba x\u00b0 ab = ac. find the value of x. x = ... [2]", "4": "4 0607/23/o/n/17 \u00a9 ucles 2017 4 $144 is shared in the ratio 1 : 7. find the value of the smaller share. $ ... [2] 5 ciara buys 6 red pens and 4 blue pens for a total cost of $3.90 . blue pens cost $0.45 each. find the cost of one red pen. $ ... [3] 6 write each number in standard form. (a) 58 000 [1] (b) 0.008 09 . [1] ", "5": "5 0607/23/o/n/17 \u00a9 ucles 2017 [turn over 7 the interior angle of a regular polygon is 160\u00b0. find the number of sides of this polygon. [3] 8 solve the equation. x459015 -= x = ... [3] 9 the mean of two numbers is 46. the difference between the two numbers is 12. find the two numbers. . and . [2]", "6": "6 0607/23/o/n/17 \u00a9 ucles 2017 10 solve the equation. xx52 402-- = x = or x = [3] 11 rationalise the denominator and simplify your answer. 832 [2] 12 the volume of a sphere is r332 cm3. find the radius of the sphere. .. cm [2]", "7": "7 0607/23/o/n/17 \u00a9 ucles 2017 [turn over 13 a is the point (1, 8) and b is the point (5, 0). find the equation of the perpendicular bisector of ab in the form ym xc=+ . y = ... [4] 14 rearrange the formula to make x the subject. axx 253=- x = [3] questions 15 and 16 are printed on the next page.", "8": "8 0607/23/o/n/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.15 factorise completely. xy5 12522- [3] 16 the probability that it rains today is 0.3 . if it rains today, the probability that it will rain tomorrow is 0.4 . if it does not rain today, the probability that it will rain tomorrow is 0.15 . find the probability that it will rain tomorrow. [3]" }, "0607_w17_qp_31.pdf": { "1": "this document consists of 15 printed pages and 1 blank page. dc (lk/cgw) 133482/3 \u00a9 ucles 2017 [turn over *4610588250* cambridge international mathematics 0607/31 paper 3 (core) october/november 2017 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/31/o/n/17 \u00a9 ucles 2017 formula list area, a, of triangle, base b, height h. a = 21bh area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = 31ah v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = 31 rr2h v olume, v, of sphere of radius r. v = 34 rr3", "3": "3 0607/31/o/n/17 \u00a9 ucles 2017 [turn over answer all the questions. 1 (a) bijul and samar work in a restaurant on saturdays. (i) one saturday bijul sells 280 hamburgers at $1.50 each and 330 bags of fries at $1.10 each. calculate the total amount of money bijul receives. $ [2] (ii) samar is paid $12 per hour. work out how much she is paid for working 8 hours. $ [1] (iii) bijul is paid $15 per hour. work out samar\u2019s pay per hour as a percentage of bijul\u2019s pay per hour. % [1] (b) bijul has $15 to spend on cards. cards cost $1.20 per packet. find the greatest number of packets bijul can buy and how much change she receives. packets of cards and $ ... change [3] (c) samar invests $600 at a rate of 4% simple interest per year. calculate how much interest she will receive at the end of 5 years. $ [2]", "4": "4 0607/31/o/n/17 \u00a9 ucles 2017 2 (a) (i) the mean number of sweets in 9 bags is 35. show that the total number of sweets in all 9 bags is 315. [1] (ii) another bag has 45 sweets. find the mean number of sweets in all 10 bags. . [2] (b) ad, ben and gal share 72 sweets. they share the sweets in the ratio ad : ben : gal = 5 : 4 : 3. work out the number of sweets that ben receives. . [2]", "5": "5 0607/31/o/n/17 \u00a9 ucles 2017 [turn over 3 (a) write 3562.845 (i) correct to 2 decimal places, . [1] (ii) correct to 3 significant figures, . [1] (iii) correct to the nearest hundred. . [1] (b) work out 14284 632-. write your answer correct to the nearest whole number. . [2] (c) find the value of .15625. . [1] (d) write 38% as a fraction in its simplest form. . [2] (e) complete the list of factors of 63. 1, , , , , 63 [2] (f) write the following in order of size, starting with the smallest. 53 55% 0.59 0.52 1 1 1 [2] smallest", "6": "6 0607/31/o/n/17 \u00a9 ucles 2017 4 lucy plays a game with the cards below. \u20132.7 11 3 5 68 927 5.8 \u20135 \u2013 7 9 (a) from these numbers, write down (i) a positive integer, . [1] (ii) a square number, . [1] (iii) a prime number. . [1] (b) the 10 cards are turned over to hide the numbers and one card is chosen at random. find the probability that the number is (i) negative, . [1] (ii) even, . [1] (iii) less than 1. . [1]", "7": "7 0607/31/o/n/17 \u00a9 ucles 2017 [turn over 5 24 students each recorded the number of hours of voluntary service they completed during one year. the results are shown in the table. number of hours30 40 50 60 70 80 number of students9 5 4 1 2 3 (a) for the number of hours completed, find (i) the range, .. hours [1] (ii) the mode. .. hours [1] (b) find the mean number of hours completed by a student. .. hours [2] (c) complete the bar chart. 30012345number of students number of hours6 40 50 60 70 80789 [2]", "8": "8 0607/31/o/n/17 \u00a9 ucles 2017 6 here is a pattern of shapes. pattern 1 pattern 2 pattern 3 pattern 4 (a) in the space above, draw pattern 4. [1] (b) complete the table. pattern number 1 2 3 4 5 number of dots 1 3 [2] (c) find an expression for the number of dots in pattern n. . [2] (d) use your expression in part (c) to find the number of dots in pattern 18. . [2]", "9": "9 0607/31/o/n/17 \u00a9 ucles 2017 [turn over 7 a c f edg103\u00b0 s\u00b042\u00b0not to scale 30\u00b0p\u00b0r\u00b0 t\u00b0q\u00b0b abc , gd and fe are parallel lines. agf and cde are also parallel lines. find the values of p, q, r, s and t. p = q = r = s = t = [5]", "10": "10 0607/31/o/n/17 \u00a9 ucles 2017 8 400 students each took a mathematics test. the results are shown in the table below. mark ( x) frequency x 10 201g 10 x00231g 30 x00341g 40 x00451g 60 x00561g 120 x00671g 60 x00781g 30 x00891g 30 x0091 0 1g 20 (a) complete the cumulative frequency table for this data. mark ( x) cumulative frequency x g 20 10 x g 30 40 x g 40 x g 50 x g 60 x g 70 x g 80 350 x g 90 380 x g 100 400 [2]", "11": "11 0607/31/o/n/17 \u00a9 ucles 2017 [turn over (b) complete the cumulative frequency curve. 0100200 10 20 0 30 40 50 mark ( x)60 70 80 90 100300400 cumulative frequency [2] (c) use your curve to find (i) the median mark, . [1] (ii) the inter-quartile range, . [2] (iii) the number of students with a mark greater than 75. . [2]", "12": "12 0607/31/o/n/17 \u00a9 ucles 2017 9 80 m 80 mnot to scale 220 m a path is made up of three straight lines and the arc of a semicircle. (a) write down the length of the diameter of the semicircle. m [1] (b) find the length of the arc of the semicircle. m [2] (c) find the total length of the path. m [1] (d) kumi walks at an average speed of 4.5 km/h. work out the time it takes him to walk the whole length of the path. ... minutes [2] (e) calculate the total area enclosed by the path. ... m2 [3]", "13": "13 0607/31/o/n/17 \u00a9 ucles 2017 [turn over 10 daisuke is given the following directions. \u2022 start at a. \u2022 face north and then turn clockwise through 150\u00b0. \u2022 walk 225 metres in a straight line to point b. \u2022 face north and then turn 60\u00b0 clockwise. \u2022 walk 270 metres in a straight line to point c. (a) draw a sketch to show this information. on the sketch, label b and c and mark the angles and distances. north a [4] (b) angle abc is a right angle. use pythagoras\u2019 theorem to calculate the distance ac. ac ... m [2] (c) use trigonometry to help you work out the bearing of c from a. . [3]", "14": "14 0607/31/o/n/17 \u00a9 ucles 2017 11 (a) solve. xx35 3 += - x = [2] (b) expand the brackets and simplify. () () xx13-+ . [2] (c) factorise completely. xy xy323- . [2] (d) (i) aa ap 41 2#= find the value of p. p = [1] (ii) bbbq 412= find the value of q. q = [1] (e) simplify. yy 32 53- . [2]", "15": "15 0607/31/o/n/17 \u00a9 ucles 2017 12 \u20132.5 2.5xy \u20131015 0 () . fxx x 31 592=- - (a) on the diagram, sketch the graph of ()fyx= for .. x 25 25 gg- . [2] (b) find the co-ordinates of the points where the graph cuts (i) the x-axis, ( , ) and ( , ) [2] (ii) the y-axis. ( , ) [1] (c) find the co-ordinates of the local minimum point. ( , ) [2] (d) find the x co-ordinates of the two points of intersection of the graph of ()fyx= and the line y5=. x = .. and x = .. [2]", "16": "16 0607/31/o/n/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_w17_qp_32.pdf": { "1": "this document consists of 16 printed pages. dc (nh/ar) 133481/2 \u00a9 ucles 2017 [turn over *5164933141* cambridge international mathematics 0607/32 paper 3 (core) october/november 2017 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/32/o/n/17 \u00a9 ucles 2017 formula list area, a, of triangle, base b, height h. a = 21bh area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = 31ah v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = 31 rr2h v olume, v, of sphere of radius r. v = 34 rr3", "3": "3 0607/32/o/n/17 \u00a9 ucles 2017 [turn over answer all the questions. 1 (a) write a mathematical word in each box to describe the three lines and the shaded area. x [4] (b) measure angle x. x = [1] 2 complete the table for the three sequences. rule sequence \u22124 27, 23, .., .., .. . 64, 32, 16, 8, 4 \u00d7 3 then +1 2, 7, .., .., .. [4]", "4": "4 0607/32/o/n/17 \u00a9 ucles 2017 3 (a) here are some scores in a mathematics test. 15 7 10 12 20 19 16 11 9 14 (i) work out the range of these scores. . [1] (ii) work out the mean score. . [1] (b) a group of students were asked if they preferred lessons in mathematics or science. complete the table. science mathematics total boys 18 girls 15 total 25 48 [3]", "5": "5 0607/32/o/n/17 \u00a9 ucles 2017 [turn over (c) the results for 30 students in an english exam are shown in the table. pass merit distinction 5 18 7 complete the pie chart to show this information. you must show all your working. [5]", "6": "6 0607/32/o/n/17 \u00a9 ucles 2017 4 (a) write in figures the number seven thousand and sixty one. . [1] (b) write down (i) a multiple of 9, . [1] (ii) an even number between 21 and 29. . [1] (c) find the value of (i) 625, . [1] (ii) 113, . [1] (iii) 5 7292-3. . [1] (d) insert one pair of brackets to make this calculation correct. 3\u2003 \u00d7\u2003 6\u2003 +\u2003 5\u2003 \u2212\u2003 4\u2003 =\u2003 29 [1] (e) work out. ... 61 38252 + write your answer correct to two decimal places. . [2] (f) write 0.031 626 (i) correct to three significant figures, . [1] (ii) in standard form. . [1]", "7": "7 0607/32/o/n/17 \u00a9 ucles 2017 [turn over 5 (a) a train takes 1 hour 30 minutes to travel from cambridge to london. (i) the train leaves cambridge at 07 25. find the time that this train arrives in london. . [1] (ii) the distance from cambridge to london is 105 km. work out the average speed of this train. km/h [2] (b) there are 104 trains travelling from cambridge to london each day. (i) 3% of these trains arrive late in london. work out how many of the trains arrive late in london. . [2] (ii) trains from cambridge are either express trains or local trains. the ratio express trains : local trains = 5 : 3. how many of the 104 trains are local trains? . [2]", "8": "8 0607/32/o/n/17 \u00a9 ucles 2017 6 the number 7 is drawn on a rectangular piece of paper. 8 cm not to scale4 cm 16 cm 4 cm4 cm 10 cm (a) work out the area of the rectangular piece of paper. .. cm2 [2] (b) work out the total area of the shaded number 7. .. cm2 [4]", "9": "9 0607/32/o/n/17 \u00a9 ucles 2017 [turn over (c) what fraction of the area of the rectangular piece of paper is the area of the shaded number 7? give your answer as a fraction in its simplest form. . [2] (d) write down the mathematical name for each of the two quadrilaterals that make up the shaded number 7. and ... [2] 7 solve these equations to find the value of x, the value of y and the value of z. x + x + x = 42 x + y + y = 32 x + y + z = 22 x = y = z = [4]", "10": "10 0607/32/o/n/17 \u00a9 ucles 2017 8 not to scale25 cm 24 cm7 cm74\u00b0 x (a) (i) work out the perimeter of the triangle. ... cm [1] (ii) write your answer to part (a)(i) in metres. . m [1] (b) work out the size of angle x. x = [1] (c) the triangle is enlarged by scale factor 3. find the lengths of the sides and the sizes of the angles in the enlarged triangle. sides .. cm .. cm .. cm angles .. \u00b0 .. \u00b0 .. \u00b0 [3] (d) complete this statement with a mathematical word. the enlarged triangle is .. to the original triangle. [1]", "11": "11 0607/32/o/n/17 \u00a9 ucles 2017 [turn over 9 in a class of students, 11 like classical music ( c ), 15 like pop music ( p), 8 like both and 6 like neither. (a) complete the venn diagram to show this information. cp u [2] (b) find the total number of students in the class. . [1] (c) one student is chosen at random. find the probability that this student likes both classical music and pop music. . [1]", "12": "12 0607/32/o/n/17 \u00a9 ucles 2017 10 a cycle track has two straight sections, each 78 m long. each of the two semi-circular ends has diameter 30 m. not to scale 30 m 78 m work out the perimeter of the cycle track. . m [3] 11 (a) factorise. 5x \u2013 15 . [1] (b) solve. 4(3x \u2013 2) = 28 . [3]", "13": "13 0607/32/o/n/17 \u00a9 ucles 2017 [turn over (c) simplify. a ab 4 23 22 #b . [2] (d) on the number line, show the inequality x g 3. \u20135 \u20134 \u20133 \u20132 \u20131 0 1 2 3 4 5x [1] (e) solve. 7x > 3x + 6 . [2] (f) solve these simultaneous equations. x + y = 5 x \u2013 y = 7 x = y = [2]", "14": "14 0607/32/o/n/17 \u00a9 ucles 2017 12 find the highest common factor (hcf) and the lowest common multiple (lcm) of 54 and 72. highest common factor lowest common multiple [4] 13 sandy is playing a game with a fair dice numbered 1 to 6. to win the game she needs a 6 on each of the next two throws. (a) complete the tree diagram. first throw second throw not a 6not a 6 not a 61 666 6 .. . . . [2] (b) work out the probability that sandy does not win the game. . [3]", "15": "15 0607/32/o/n/17 \u00a9 ucles 2017 [turn over 14 the line ab is drawn on a 1 cm2 grid. 6 5 4 3 2 1 0\u20133 \u20132 \u20131 3 2 1xy ab (a) write down the co-ordinates of the midpoint of ab. (... , ...) [1] (b) use pythagoras\u2019 theorem to work out the length of ab. ab = .. cm [2] (c) work out the gradient of ab. . [2] (d) write down the equation of ab in the form y = mx + c. y = ... [2] question 15 is printed on the next page.", "16": "16 0607/32/o/n/17 \u00a9 ucles 2017 15 25 \u2013250\u20131 3xy (a) on the diagram, sketch the graph of y = 8x2\u2003\u221218x\u2003\u2212\u20035\u2003for\u2003\u22121\u2003g x g 3. [2] (b) solve the equation 8 x2\u2003\u221218x\u2003\u2212\u20035\u2003=\u20030. x = . or x = . [2] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_w17_qp_33.pdf": { "1": "this document consists of 16 printed pages. dc (leg) 154696 \u00a9 ucles 2017 [turn over *4647667183* cambridge international mathematics 0607/33 paper 3 (core) october/november 2017 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/33/o/n/17 \u00a9 ucles 2017 formula list area, a, of triangle, base b, height h. a = 21bh area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = 31ah v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = 31 rr2h v olume, v, of sphere of radius r. v = 34 rr3", "3": "3 0607/33/o/n/17 \u00a9 ucles 2017 [turn over answer all the questions. 1 (a) write a mathematical word in each box to describe the three lines and the shaded area. x [4] (b) measure angle x. x = [1] 2 complete the table for the three sequences. rule sequence \u22124 27, 23, .., .., .. . 64, 32, 16, 8, 4 \u00d7 3 then +1 2, 7, .., .., .. [4]", "4": "4 0607/33/o/n/17 \u00a9 ucles 2017 3 (a) here are some scores in a mathematics test. 15 7 10 12 20 19 16 11 9 14 (i) work out the range of these scores. . [1] (ii) work out the mean score. . [1] (b) a group of students were asked if they preferred lessons in mathematics or science. complete the table. science mathematics total boys 18 girls 15 total 25 48 [3]", "5": "5 0607/33/o/n/17 \u00a9 ucles 2017 [turn over (c) the results for 30 students in an english exam are shown in the table. pass merit distinction 5 18 7 complete the pie chart to show this information. you must show all your working. [5]", "6": "6 0607/33/o/n/17 \u00a9 ucles 2017 4 (a) write in figures the number seven thousand and sixty one. . [1] (b) write down (i) a multiple of 9, . [1] (ii) an even number between 21 and 29. . [1] (c) find the value of (i) 625, . [1] (ii) 113, . [1] (iii) 5 7292-3. . [1] (d) insert one pair of brackets to make this calculation correct. 3\u2003 \u00d7\u2003 6\u2003 +\u2003 5\u2003 \u2212\u2003 4\u2003 =\u2003 29 [1] (e) work out. ... 61 38252 + write your answer correct to two decimal places. . [2] (f) write 0.031 626 (i) correct to three significant figures, . [1] (ii) in standard form. . [1]", "7": "7 0607/33/o/n/17 \u00a9 ucles 2017 [turn over 5 (a) a train takes 1 hour 30 minutes to travel from cambridge to london. (i) the train leaves cambridge at 07 25. find the time that this train arrives in london. . [1] (ii) the distance from cambridge to london is 105 km. work out the average speed of this train. km/h [2] (b) there are 104 trains travelling from cambridge to london each day. (i) 3% of these trains arrive late in london. work out how many of the trains arrive late in london. . [2] (ii) trains from cambridge are either express trains or local trains. the ratio express trains : local trains = 5 : 3. how many of the 104 trains are local trains? . [2]", "8": "8 0607/33/o/n/17 \u00a9 ucles 2017 6 the number 7 is drawn on a rectangular piece of paper. 8 cm not to scale4 cm 16 cm 4 cm4 cm 10 cm (a) work out the area of the rectangular piece of paper. .. cm2 [2] (b) work out the total area of the shaded number 7. .. cm2 [4]", "9": "9 0607/33/o/n/17 \u00a9 ucles 2017 [turn over (c) what fraction of the area of the rectangular piece of paper is the area of the shaded number 7? give your answer as a fraction in its simplest form. . [2] (d) write down the mathematical name for each of the two quadrilaterals that make up the shaded number 7. and ... [2] 7 solve these equations to find the value of x, the value of y and the value of z. x + x + x = 42 x + y + y = 32 x + y + z = 22 x = y = z = [4]", "10": "10 0607/33/o/n/17 \u00a9 ucles 2017 8 not to scale25 cm 24 cm7 cm74\u00b0 x (a) (i) work out the perimeter of the triangle. ... cm [1] (ii) write your answer to part (a)(i) in metres. . m [1] (b) work out the size of angle x. x = [1] (c) the triangle is enlarged by scale factor 3. find the lengths of the sides and the sizes of the angles in the enlarged triangle. sides .. cm .. cm .. cm angles .. \u00b0 .. \u00b0 .. \u00b0 [3] (d) complete this statement with a mathematical word. the enlarged triangle is .. to the original triangle. [1]", "11": "11 0607/33/o/n/17 \u00a9 ucles 2017 [turn over 9 in a class of students, 11 like classical music ( c ), 15 like pop music ( p), 8 like both and 6 like neither. (a) complete the venn diagram to show this information. cp u [2] (b) find the total number of students in the class. . [1] (c) one student is chosen at random. find the probability that this student likes both classical music and pop music. . [1]", "12": "12 0607/33/o/n/17 \u00a9 ucles 2017 10 a cycle track has two straight sections, each 78 m long. each of the two semi-circular ends has diameter 30 m. not to scale 30 m 78 m work out the perimeter of the cycle track. . m [3] 11 (a) factorise. 5x \u2013 15 . [1] (b) solve. 4(3x \u2013 2) = 28 . [3]", "13": "13 0607/33/o/n/17 \u00a9 ucles 2017 [turn over (c) simplify. a ab 4 23 22 #b . [2] (d) on the number line, show the inequality x g 3. \u20135 \u20134 \u20133 \u20132 \u20131 0 1 2 3 4 5x [1] (e) solve. 7x > 3x + 6 . [2] (f) solve these simultaneous equations. x + y = 5 x \u2013 y = 7 x = y = [2]", "14": "14 0607/33/o/n/17 \u00a9 ucles 2017 12 find the highest common factor (hcf) and the lowest common multiple (lcm) of 54 and 72. highest common factor lowest common multiple [4] 13 sandy is playing a game with a fair dice numbered 1 to 6. to win the game she needs a 6 on each of the next two throws. (a) complete the tree diagram. first throw second throw not a 6not a 6 not a 61 666 6 .. . . . [2] (b) work out the probability that sandy does not win the game. . [3]", "15": "15 0607/33/o/n/17 \u00a9 ucles 2017 [turn over 14 the line ab is drawn on a 1 cm2 grid. 6 5 4 3 2 1 0\u20133 \u20132 \u20131 3 2 1xy ab (a) write down the co-ordinates of the midpoint of ab. (... , ...) [1] (b) use pythagoras\u2019 theorem to work out the length of ab. ab = .. cm [2] (c) work out the gradient of ab. . [2] (d) write down the equation of ab in the form y = mx + c. y = ... [2] question 15 is printed on the next page.", "16": "16 0607/33/o/n/17 \u00a9 ucles 2017 15 25 \u2013250\u20131 3xy (a) on the diagram, sketch the graph of y = 8x2\u2003\u221218x\u2003\u2212\u20035\u2003for\u2003\u22121\u2003g x g 3. [2] (b) solve the equation 8 x2\u2003\u221218x\u2003\u2212\u20035\u2003=\u20030. x = . or x = . [2] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_w17_qp_41.pdf": { "1": "*7234083009* this document consists of 19 printed pages and 1 blank page. dc (nf/sw) 134061/2 \u00a9 ucles 2017 [turn overcambridge international mathematics 0607/41 paper 4 (extended) october/november 2017 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/41/o/n/17 \u00a9 ucles 2017 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/41/o/n/17 \u00a9 ucles 2017 [turn over answer all the questions. 1 these are 12 of stefan\u2019s recent homework scores. 10 16 18 11 18 15 8 18 13 9 12 11 (a) find (i) the mode, [1] (ii) the range, [1] (iii) the median, [1] (iv) the mean, [1] (v) the interquartile range. [2] (b) the teacher wants to compare stefan\u2019s scores with those of another student in the class. explain why the mode is not the best value to use to represent stefan\u2019s scores. ... . [1]", "4": "4 0607/41/o/n/17 \u00a9 ucles 2017 2 two banks pay interest in the following ways. bank a simple interest at a rate of 2.5% per year for the first year and then compound interest at a rate of 1.5% per year for each year after that. bank b simple interest at 1.6% per year. (a) cherie invested $3000 in bank a on 1st january 2016. find how much the investment will be worth on 1st january 2019. $ [3] (b) dieter invested $3000 in bank b on 1st january 2016. find how much the investment will be worth on 1st january 2019. $ [3] (c) show that cherie\u2019s investment will be the first to be worth $3500. [4]", "5": "5 0607/41/o/n/17 \u00a9 ucles 2017 [turn over 3 (a) the nth term of a sequence is n2 + 3n. find the first four terms of this sequence. , , , [2] (b) these are the first four terms of another sequence. 5 7 9 11 (i) write down the next two terms. . , [1] (ii) find the nth term of this sequence. [2] (c) using the sequences in part (a) and part (b) , or otherwise, find the nth term of this sequence. 14, 24, 36, 50, \u2026 write your answer as simply as possible. [2]", "6": "6 0607/41/o/n/17 \u00a9 ucles 2017 4 the table shows the distance that each of 12 students lives from school and the time they each take to get to school. distance (x km)0.8 1.1 1.2 1.6 1.8 2.4 2.8 3.1 3.5 4.2 4.7 5.1 time (t minutes)15 18 15 24 23 35 37 35 45 48 52 63 (a) complete the scatter diagram. the first six points have been plotted for you. 1 0 2 3 4 5 6xt time (minutes) distance (km)10 0203040506070 [2] (b) what type of correlation is shown by the scatter diagram? [1]", "7": "7 0607/41/o/n/17 \u00a9 ucles 2017 [turn over (c) (i) find the equation of the regression line in the form t = mx + c. t = ... [2] (ii) use your answer to part (c)(i) to estimate the time taken to get to school for a student who lives 2.2 km from school. . min [1] (iii) why would it not be sensible to use your answer to part (c)(i) to estimate the time taken to get to school for a student who lives 10 km from school? ... . [1]", "8": "8 0607/41/o/n/17 \u00a9 ucles 2017 5 the diagram shows a paper cup. not to scale the curved surface of the cup is made from a sector of a circle with a smaller sector cut from it, as shown below. not to scale 45\u00b032.5 cm 22.5 cm the small sector has radius 22.5 cm and the large sector has radius 32.5 cm. the sectors have the same centre and both have sector angle 45\u00b0. (a) show that the radius of the base of the cup is 2.81 cm, correct to 2 decimal places. [3]", "9": "9 0607/41/o/n/17 \u00a9 ucles 2017 [turn over (b) find the total area of the paper that makes the cup, including the circular base. cm2 [5] (c) a mathematically similar cup holds 8 times as much liquid as this cup. find the total area of the paper that makes the larger cup. cm2 [2]", "10": "10 0607/41/o/n/17 \u00a9 ucles 2017 6 \u20134 \u20133 \u20132 \u2013101 2 3 4 5 6 7 8 9101234567891011121314 \u20131 \u20132 \u20133 \u20134xy acb (a) describe fully the single transformation that maps triangle a onto triangle b. ... . [2] (b) on the grid, draw the image of triangle a after a stretch with scale factor 3 and invariant line the x-axis. [2] (c) triangle a can be mapped onto triangle c by a rotation followed by a reflection. complete the following to fully describe the two transformations. rotation reflection . [3]", "11": "11 0607/41/o/n/17 \u00a9 ucles 2017 [turn over 7 javier starts a journey at 22 50. (a) for the first part of the journey he drives for 2 hours 45 minutes at 70 km/h. find the distance he travels. .. km [3] (b) javier then stops for 30 minutes. he then drives the remaining 180 km of his journey at 85 km/h. (i) find his average speed for the whole journey. ... km/h [4] (ii) find the time he arrives at his destination. [2]", "12": "12 0607/41/o/n/17 \u00a9 ucles 2017 8 abc and acd are two triangular fields. not to scalenorth 60 m 55\u00b0 63\u00b076\u00b030\u00b0 a dcb (a) find the bearing of b from c. [3] (b) calculate ac and show that it rounds to 104.6 m, correct to 1 decimal place. [3]", "13": "13 0607/41/o/n/17 \u00a9 ucles 2017 [turn over (c) calculate the total area of the two fields. .. m2 [6] (d) maria walks in a straight line from d towards a. she stops when she is at her closest point to c. calculate her distance from c. m [2]", "14": "14 0607/41/o/n/17 \u00a9 ucles 2017 9 two bags each contain white balls and black balls only. bag a bag b bag a contains 3 white balls and 5 black balls. bag b contains 6 white balls and 3 black balls. a ball is picked at random from the 8 balls in bag a. \u2022 if it is white, the ball is not replaced and a second ball is picked at random from bag a. \u2022 if it is black, a second ball is picked at random from the 9 balls in bag b. (a) complete the tree diagram. white blackwhite1st ball 2nd ball blackwhite black [3]", "15": "15 0607/41/o/n/17 \u00a9 ucles 2017 [turn over (b) find the probability that (i) both balls are white, [2] (ii) exactly one of the two balls is black. [3]", "16": "16 0607/41/o/n/17 \u00a9 ucles 2017 10 (a) make y the subject of 3 x + y = 8. y = ... [1] (b) the line 3 x + y = 8 intersects the curve x2 + y2 = 25 at two points. (i) use substitution to show that 10 x2 \u2212 48 x + 39 = 0. [3] (ii) solve the equation 10 x2 \u2212 48 x + 39 = 0 and find the co-ordinates of the two points of intersection. show all your working. ( , ...) ( , ...) [5]", "17": "17 0607/41/o/n/17 \u00a9 ucles 2017 [turn over 11 x 6 \u20136 \u20136012y xxxxx 2323f2 =+-+^^^hhh (a) on the diagram, sketch the graph of y = f(x) for values of x between \u22126 and 6. [3] (b) find the co-ordinates of the local minimum. ( . , ..) [2] (c) find the equations of the two asymptotes that are parallel to the y-axis. . and .. [2] (d) g(x) = 3 x + 2 solve. (i) f(x) = g( x) [3] (ii) xxfg2^^hh . [3]", "18": "18 0607/41/o/n/17 \u00a9 ucles 2017 12 f(x) = 5 \u2212 3 x g(x) = 2 x + 3 (a) solve f( x) = 11. x = ... [2] (b) find f \u22121(x). f \u22121(x) = ... [2] (c) solve f( x) \u00d7 g( x) = 0. [2] (d) simplify. (i) g\u22121(g(x)) [1] (ii) f(f(x)) + g( x) [3] (iii) xx24 fg+^^hh [3]", "19": "19 0607/41/o/n/17 \u00a9 ucles 2017 13 not to scale a bq c o cap oabc is a parallelogram and opq is a straight line. p divides ac in the ratio 1 : 2. p divides oq in the ratio 1 : 2. oa a= and oc c=. (a) find these vectors in terms of a and/or c. give each answer in its simplest form. (i) ac [1] (ii) op [2] (iii) cq [2] (b) use your answer to part(a)(iii) to complete the statement. the points c, b and q are .. [1]", "20": "20 0607/41/o/n/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_w17_qp_42.pdf": { "1": "*5752784072* this document consists of 16 printed pages. dc (lk/ar) 133963/2 \u00a9 ucles 2017 [turn overcambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/42 paper 4 (extended) october/november 2017 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.", "2": "2 0607/42/o/n/17 \u00a9 ucles 2017 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/42/o/n/17 \u00a9 ucles 2017 [turn over answer all the questions. 1 (a) these are the first four terms of a sequence. 27 20 13 6 (i) write down the next two terms. ... , . [2] (ii) find the nth term. [2] (b) these are the first four terms of another sequence. 8 16 32 64 (i) write down the next two terms. ... , . [2] (ii) find the nth term. [2]", "4": "4 0607/42/o/n/17 \u00a9 ucles 2017 2 in a sale, a shop reduces all of its prices by 15%. (a) jake buys a jacket which had an original price of $65. (i) calculate how much jake pays for the jacket. $ ... [2] (ii) after paying for the jacket, jake has $24.75 left. work out $24.75 as a fraction of the total amount of money jake had before he bought the jacket. give your answer in its lowest terms. [2] (b) in the sale, amy pays $80.75 for a coat. calculate the original price of the coat. $ ... [3] (c) one day the shop reduces its sale prices by 10%. calculate the overall percentage reduction of the original prices. ... % [2]", "5": "5 0607/42/o/n/17 \u00a9 ucles 2017 [turn over 3 q py x \u20138 \u20137 \u20136 \u20135 \u20134 \u20133 \u20132 \u20131 \u20138\u20137\u20136\u20135\u20134\u20133\u20132\u201311 2 3 4 5 6123456 0 (a) (i) reflect shape p in the line y1=. label the image a. [2] (ii) rotate shape p through 90\u00b0 clockwise about (, )11- . label the image b. [2] (iii) describe fully the single transformation that maps shape a onto shape b. .. .. [2] (b) describe fully the single transformation that maps shape p onto shape q. .. .. [3] (c) stretch shape p with the x-axis invariant and factor 2. [2]", "6": "6 0607/42/o/n/17 \u00a9 ucles 2017 4 y x \u20133 0 \u2013545 ()()fxxxx 22=-- (a) on the diagram, sketch the graph of ()fyx= for values of x from \u20133 to 4. [3] (b) find the two values of x for which f( x) does not exist. ... , . [2] (c) when k0!, write down the number of solutions to the equation ()fxk=. [1] (d) ()gx 21x=+- (i) on the diagram, sketch the graph of ()gyx= for x24gg- . [2] (ii) write down the equation of the asymptote to the graph of ()gyx= . [1] (e) solve the equation () () g f x x= . x = . or x = . [2]", "7": "7 0607/42/o/n/17 \u00a9 ucles 2017 [turn over 5 (a) carlos owns a vintage car. each year the value of the car increases by 4% of its value at the start of the year. at the start of 2012 the value of the car was $17 500. calculate the value of the car at the start of 2018. give your answer correct to the nearest $100. $ ... [4] (b) alex invests $200 at a rate of r % per year compound interest. after 12 years, alex has a total amount of $239.12 . find the value of r. r = ... [3]", "8": "8 0607/42/o/n/17 \u00a9 ucles 2017 6 (a) a factory tests the lifetime, t hours, of each of 200 batteries. the table shows the results. lifetime ( t hours) t 20 301g t00341g t00451g t00561g t00671g t00781g frequency 9 17 39 97 29 9 (i) write down the modal interval. [1] (ii) complete the cumulative frequency curve. tcumulative frequency lifetime (hours)200 180 160 140 120 100 80 8060 6040 4020 200 30 50 70 [4] (iii) use your curve to find (a) the median, . hours [1] (b) the number of batteries with a lifetime greater than 65 hours. [2]", "9": "9 0607/42/o/n/17 \u00a9 ucles 2017 [turn over (b) this table shows the lifetimes of the same batteries but the time intervals are different. lifetime ( t hours) t00241g t00451g t055 51g t 55 601g t 60 081g frequency 26 39 55 42 38 (i) calculate an estimate of the mean. . hours [2] (ii) complete the table to show the frequency densities. lifetime ( t hours) t00241g t00451g t055 51g t 55 601g t 60 081g frequency 26 39 55 42 38 frequency density 3.9 [2] (iii) complete the histogram. 12 80 60 40 200 30 50 70t11 10 9 8 7 6 5 4 3 2 1frequency density lifetime (hours) [3] ", "10": "10 0607/42/o/n/17 \u00a9 ucles 2017 7 (a) ali walks for 1 hour at x km/h and then for 2 hours at x41+fp km/h. he walks a total distance of 8 km. write an equation and solve it to find the value of x. x = ... [3] (b) not to scale x x x2x(x \u2013 2) (x \u2013 2) the volume of the cube is equal to the volume of the cuboid. (i) show that xxx88 032-+ =. [3]", "11": "11 0607/42/o/n/17 \u00a9 ucles 2017 [turn over (ii) y x 0 \u2013407.540 on the diagram, sketch the graph of yxxx8832=- + for . x07 5 gg . [2] (iii) find the volume of the cuboid. [2]", "12": "12 0607/42/o/n/17 \u00a9 ucles 2017 8 a fair 6-sided die is numbered 0, 1, 1, 2, 3, 3. (a) the die is rolled and the number it shows is recorded. find the probability that the number is (i) 3, [1] (ii) not 3, [1] (iii) an odd number. [1] (b) the die is rolled twice. find the probability that (i) both numbers are 0, [2] (ii) one number is 2 and the other is 3. [3] (c) the die is rolled three times and the three numbers shown are added. find the probability that the total is not 0. [2]", "13": "13 0607/42/o/n/17 \u00a9 ucles 2017 [turn over 9 (a) (i) find the equation of the line that passes through the points (1, 2) and (3, 12). give your answer in the form ym xc=+ . y = ... [3] (ii) find the equation of the line that passes through the point (0, 2) and is perpendicular to the line in part (a)(i) . [2] . (b) (i) solve the equation xx34 402+- =. you must show all your working. x = or x = [3] (ii) solve the inequality xx34 4021 +- . ... [2] (c) the graph of ya xb xc2=+ + has its vertex at the point (1, 5) and intersects the y-axis at (0, 1). find the values of a, b and c. a = ... b = ... c = ... [3]", "14": "14 0607/42/o/n/17 \u00a9 ucles 2017 10 not to scalea bcdnorth 90 m 120 m 115 m35\u00b0 65\u00b0 the diagram shows a school playing field, abcd , which is on horizontal ground, with d due east of a. (a) find the bearing of (i) c from a, [1] (ii) a from c. [2] (b) calculate the length of cd. cd = .. m [3]", "15": "15 0607/42/o/n/17 \u00a9 ucles 2017 [turn over (c) calculate angle bac . angle bac = ... [3] (d) (i) calculate the area of the school playing field. .. m2 [4] (ii) in the school office there is a plan of the school playing field. it is drawn to a scale of 1 : 500. calculate the area of the school playing field on the plan. give your answer in cm2. cm2 [3] question 11 is printed on the next page.", "16": "16 0607/42/o/n/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.11 ()fxx 21=+ ()gxx 12=+ ()hl og xx= (a) (i) find the value of f(4.5). [1] (ii) find the value of h(f(4.5)). [1] (b) find ()fx1-. ()fx1=- ... [2] (c) find g(f( x)) in the form ax bx c2++ . [3] (d) ()pxx 12=- find the single transformation that maps the graph of y = g(x) onto the graph of y = p(x). .. [2] (e) solve the equation ()hx 10001=-. x = ... [1]" }, "0607_w17_qp_43.pdf": { "1": "*2134418509* this document consists of 19 printed pages and 1 blank page. dc (st/cgw) 133973/4 \u00a9 ucles 2017 [turn overcambridge international mathematics 0607/43 paper 4 (extended) october/november 2017 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/43/o/n/17 \u00a9 ucles 2017 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/43/o/n/17 \u00a9 ucles 2017 [turn over answer all the questions. 1 () () ,( )( ) fg h xx xxxx x 321022=- == =+ y (a) find (i) f(4), [1] (ii) gf(4). [1] (b) find g(g(5)). [2] (c) solve f(h( x)) = 10. x = . or x = . [3] (d) find g(h(f( x))) in terms of x. [2]", "4": "4 0607/43/o/n/17 \u00a9 ucles 2017 2 alan, brendan and cieran work as gardeners. (a) the total amount of money they earn is shared in the ratio of the time each person works. one day alan works for 2 hours 40 minutes, brendan works for 5.5 hours and cieran works for 200 minutes. they earn, in total, $379.50 . by changing all the times into minutes, find the amount of money each person earns. alan $ ... brendan $ ... cieran $ ... [5] (b) (i) alan needs to buy some gardening tools. in shop a, the price of the tools is $70.20 . in shop b, the price of the tools is 5% less than in shop a. find the price of the tools in shop b. $ [2] (ii) the price of $70.20 is 8% higher than it was last year. find the price last year. $ [3]", "5": "5 0607/43/o/n/17 \u00a9 ucles 2017 [turn over (c) (i) brendan invests $450 for 5 years at a rate of 3.5% per year simple interest. show that the total value of this investment after 5 years is $528.75 . [2] (ii) cieran invests $450 for 5 years at a rate of x % compound interest. the value of cieran\u2019s investment after 5 years is $530.60 . find the value of x. x = [3]", "6": "6 0607/43/o/n/17 \u00a9 ucles 2017 3 pepe wants to find out if there is a correlation between the hours of sunshine, x hours, and the rainfall, y cm, in phuket. pepe recorded the following results. month jan feb mar apr may jun jul aug sep oct nov dec daily sunshine (x hours)8 9.2 7.9 9.4 8 7.4 7.9 8 7.3 7.4 7.5 8 monthly rainfall (y cm)4 3 4 15 20 24 30 26 40 28 20 6 (a) (i) complete the scatter diagram. the first eight points have been plotted for you. xy 0510152025303540 monthly rainfall (cm) daily sunshine (hours)45 8 7 10 9 [2] (ii) what type of correlation is shown by the scatter diagram? [1]", "7": "7 0607/43/o/n/17 \u00a9 ucles 2017 [turn over (b) (i) find the mean number of hours of sunshine. hours [1] (ii) find the mean rainfall. cm [1] (c) (i) find the equation of the regression line for y in terms of x. y = [2] (ii) estimate the rainfall when the number of hours of sunshine is 7.7 . cm [1] ", "8": "8 0607/43/o/n/17 \u00a9 ucles 2017 4 the masses of 120 peaches are recorded in the table. mass ( m grams) frequency 0 1 m g 120 12 120 1 m g 150 27 150 1 m g 180 33 180 1 m g 210 15 210 1 m g 250 28 250 1 m g 300 5 (a) calculate an estimate of the mean mass of a peach. give your answer correct to the nearest gram. g [3] (b) two peaches are chosen at random. find the probability that they both have a mass of more than 210 g. give your answer as a fraction in its simplest form. [3]", "9": "9 0607/43/o/n/17 \u00a9 ucles 2017 [turn over (c) (i) complete the frequency density column in this table. mass ( m grams) frequencyfrequency density 0 1 m g 120 12 120 1 m g 150 27 150 1 m g 180 33 180 1 m g 210 15 210 1 m g 250 28 250 1 m g 300 5 0.1 [2] (ii) on the grid, draw an accurate histogram to show this information. frequency density mass (grams)00 300m 250 200 150 100 50 [4]", "10": "10 0607/43/o/n/17 \u00a9 ucles 2017 5 a d fnot to scale e b c abc is a triangle and bcfd is a parallelogram. ad ab31= and aaec31= . ab p6= and ac q6= . (a) find an expression, in terms of p and/or q, for (i) bc, [1] (ii) de, [2] (iii) fc, [1]", "11": "11 0607/43/o/n/17 \u00a9 ucles 2017 [turn over (iv) be. [2] (b) the area of triangle ade is 24 units2. (i) find the area of triangle abc . units2 [2] (ii) find the area of triangle efc . units2 [3]", "12": "12 0607/43/o/n/17 \u00a9 ucles 2017 6 b c a d8 cm \u221a72 cmnot to scale pv \u221a72 cm the diagram shows a pyramid with a square base abcd of side 72 cm. the diagonals of the base, ac and bd, meet at p. the vertex, v, is vertically above p and vp = 8 cm. (a) find the volume of the pyramid. give the units of your answer. .. [3] (b) find the length ac. ac = cm [2]", "13": "13 0607/43/o/n/17 \u00a9 ucles 2017 [turn over (c) find the length dv. dv = cm [3] (d) find angle vdp . angle vdp = [2] (e) x is the midpoint of the side cd. (i) find the length vx. vx = cm [3] (ii) find angle vxp. angle vxp = [2] (f) the pyramid is cut parallel to abcd to form a smaller pyramid vefgh . the volume of vefgh is 24 cm3. find the vertical height of this pyramid. cm [3]", "14": "14 0607/43/o/n/17 \u00a9 ucles 2017 7 30 cm 10 cm the diagram shows a hollow metal hemisphere. the outside diameter of the hemisphere is 30 cm and the inside diameter is 10 cm. (a) find the volume of metal used to make the hemisphere. cm3 [3] (b) find the total surface area of the hemisphere. cm2 [5]", "15": "15 0607/43/o/n/17 \u00a9 ucles 2017 [turn over 8 you may use the grid to help you in answering this question. the transformation p is a rotation through 90\u00b0 anti-clockwise about the origin. the transformation q is a reflection in the line yx=- . (a) find the image of the point (5, 1) under the transformation p. ( , ...) [2] (b) find the image of the point (5, 1) under the transformation q. ( , ...) [2] (c) describe fully the single transformation equivalent to the transformation p followed by the transformation q. ... .. [2]", "16": "16 0607/43/o/n/17 \u00a9 ucles 2017 9 12y x 0 4 \u20132 ()fxx x 102=+ - for x04gg (a) (i) on the diagram, sketch the graph of ()fyx= . [2] (ii) write down the co-ordinates of the points where the graph crosses the axes. ( , ...) or ( , ...) [2] (iii) solve ()fx 1=. x = [1]", "17": "17 0607/43/o/n/17 \u00a9 ucles 2017 [turn over (b) ()gl og xx x 102=- (i) on the same diagram, sketch the graph of ()gyx= , for x041g. [2] (ii) write down the co-ordinates of the minimum point of g (x). ( , ...) [2] (iii) solve the equation. f (x) = g (x) [2] (iv) solve the equation. f (x - 1) = g (x - 1) [2]", "18": "18 0607/43/o/n/17 \u00a9 ucles 2017 10 (a) solve the equation xx41 232=- . give your answers correct to 2 decimal places. you must show all your working. x = . or x = . [4] (b) solve the inequality xx41 2322- . [2] (c) solve the inequality xx45 12 32g+- . [4] ", "19": "19 0607/43/o/n/17 \u00a9 ucles 2017 11 (a) solve the simultaneous equations. you must show all your working. xy xy32 11 45 10-= -= x = y = [4] (b) use your answers to part (a) to solve the simultaneous equations. ab ab32 45 022 2-= -= a = b = [2] (c) (i) use your answers to part (a) to find the exact answers to these simultaneous equations. 3102 10 11 10 10 1 45 0pq pq## ##-= -= p = q = [3] (ii) find the value of pq+. [1]", "20": "20 0607/43/o/n/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_w17_qp_51.pdf": { "1": "this document consists of 6 printed pages and 2 blank pages. dc (kn/sg) 134793/2 \u00a9 ucles 2017 [turn over *9465699284* cambridge international mathematics 0607/51 paper 5 (core) october/november 2017 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and to communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/51/o/n/17 \u00a9 ucles 2017 answer all the questions. investigation equable shapes in this investigation, lengths are given in centimetres. the area of a shape is a square centimetres and its perimeter is p centimetres. this task investigates the dimensions of equable shapes. the shape is equable if a = p. all the diagrams in this investigation are not to scale. 1 (a) 3.6 4.5 this rectangle is equable. write down the calculations to show that a = 16.2 and p = 16.2 . ... ... (b) all the rectangles in this table are equable. complete the table. length ( x) width ( y) area ( a) perimeter ( p) 4.5 3.6 16.2 16.2 7 2.8 10 25 12 28.8 2.2 48.4", "3": "3 0607/51/o/n/17 \u00a9 ucles 2017 [turn over (c) for the rectangle in part (a) , the value of ( x \u2013 2)( y \u2013 2) is (4.5 \u2013 2)(3.6 \u2013 2) = 2.5 # 1.6 = 4. the rectangles in the table are equable. use your answers to part (b) to complete the first two columns of the table. calculate the value of ( x \u2013 2)( y \u2013 2) for each rectangle. length ( x) width ( y) (x \u2013 2)( y \u2013 2) 4.5 3.6 2.5 # 1.6 = 4 7 2.8 10 12 2.2 42 2.1 (d) use what you notice about the value of ( x \u2013 2)( y \u2013 2) in part (c) to find all the equable rectangles that have integer lengths and widths. ...", "4": "4 0607/51/o/n/17 \u00a9 ucles 2017 2 the area, a, of a triangle is 21 # base # height. (a) 6.5 7.29.7 this right-angled triangle is equable. write down the calculations to show that a = 23.4 and p = 23.4 . ... ... (b) x 20x + 16 (i) write down, in its simplest form, an expression, in terms of x, for the perimeter of this triangle. ... (ii) write down, in its simplest form, an expression, in terms of x, for the area of this triangle. ... (iii) this triangle is equable. using your answers to part (i) and part (ii) find x. write down the length of each side. ...", "5": "5 0607/51/o/n/17 \u00a9 ucles 2017 [turn over (c) x yz in the diagram, x, y and z are the lengths of the sides of a right-angled triangle. all the right-angled triangles in the table below are equable. use this fact and your answer to part (b)(iii) to complete the table. x y z area ( a) perimeter ( p) 6.5 7.2 9.7 23.4 23.4 20 14 14.8 33.6 5.6 9", "6": "6 0607/51/o/n/17 \u00a9 ucles 2017 (d) for the triangle in part (a) , the value of (x \u2013 4)( y \u2013 4) is (6.5 \u2013 4)(7.2 \u2013 4) = 2.5 # 3.2 = 8. the triangles in the table are equable. use your answers to part (c) to complete the first column of this table. calculate the value of ( x \u2013 4)( y \u2013 4) for each triangle. x y (x \u2013 4)( y \u2013 4) 6.5 7.2 2.5 # 3.2 = 8 4.4 24 20 14 5.6 9 (e) use what you notice about the value of ( x \u2013 4)( y \u2013 4) in part (d) to find all the equable right-angled triangles that have integer bases and heights. find the lengths of the three sides for each triangle. ...", "7": "7 0607/51/o/n/17 \u00a9 ucles 2017 blank page", "8": "8 0607/51/o/n/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_w17_qp_52.pdf": { "1": "this document consists of 8 printed pages. dc (st/fc) 134792/2 \u00a9 ucles 2017 [turn over *2616309764* cambridge international mathematics 0607/52 paper 5 (core) october/november 2017 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and to communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/52/o/n/17 \u00a9 ucles 2017 answer all the questions. investigation number walls this investigation looks at what happens when you place numbers on a number wall . you make a number wall like this. \u2022 integers are put on the bottom row of bricks. \u2022 the number on a brick is the sum of the numbers on the two bricks below. examples total = 1 45 total = \u20135 72 total = 1 23 58 3 1 (a) complete this number wall . total = 1 3 2 (b) in part (a) , the number 3 is on the middle brick of the bottom row. in the example, the number 3 is on the end brick of the bottom row. explain why putting the number 3 on the middle brick of the bottom row increases the total. ... ...", "3": "3 0607/52/o/n/17 \u00a9 ucles 2017 [turn over 2 (a) complete this number wall . total = 1 2 3 4 (b) put the numbers 1, 2, 3 and 4 on the bottom row and complete this number wall so that the total is bigger than the total in part (a) . total = (c) complete this number wall . you may use negative numbers. total = 31 10 4 7 4", "4": "4 0607/52/o/n/17 \u00a9 ucles 2017 3 this number wall is 3 bricks high. (a) complete each brick using expressions in terms of a, b and c. write each expression in its simplest form. b c a (b) use the expression for the total you found in part (a) to find the value of b. b 77 4 ...", "5": "5 0607/52/o/n/17 \u00a9 ucles 2017 [turn over 4 (a) this number wall is 4 bricks high. complete each brick using expressions in terms of a, b, c and d. write each expression in its simplest form. b aa + b d c (b) in another wall that is 4 bricks high, the total is 34 and the values of a, b, c and d are all the same. use the expression for the total you found in part (a) to show that the value of a cannot be an integer.", "6": "6 0607/52/o/n/17 \u00a9 ucles 2017 (c) in this number wall that is 5 bricks high, only integers greater than 0 are used. find one set of possible values for a, b, c, d and e. b a d e c43 14 9 6 a = b = c = d = e = 5 in 1653 a french mathematician, blaise pascal, wrote about a triangle of numbers similar to the one shown below. it is made in the same way as number walls but \u2022 the number on a brick is the sum of the numbers on the two bricks above and \u2022 the number on the first and last brick in each row is always 1. 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1row 1 row 2 row 3 row 4 row 5 row 6 6 15 20 15 6 1", "7": "7 0607/52/o/n/17 \u00a9 ucles 2017 [turn over (a) the wall in question 4(a) is 4 bricks high. show clearly how your expression for the total in question 4(a) connects to the numbers in one row of this triangle. write down which row this is. row ... (b) a wall that is 5 bricks high has a, b, c, d and e, in that order, along the bottom row. write down an expression in terms of a, b, c, d and e for the total. .. (c) use your expression from part (b) to check that the set of values you found for a, b, c, d and e in question 4(c) gives a total of 43. question 5(d) is printed on the next page.", "8": "8 0607/52/o/n/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. (d) a wall that is 5 bricks high has the number 2017 on each brick of the bottom row. find the total. ..." }, "0607_w17_qp_53.pdf": { "1": "this document consists of 8 printed pages. dc (leg) 154695 \u00a9 ucles 2017 [turn over *8826971234* cambridge international mathematics 0607/53 paper 5 (core) october/november 2017 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and to communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/53/o/n/17 \u00a9 ucles 2017 answer all the questions. investigation number walls this investigation looks at what happens when you place numbers on a number wall . you make a number wall like this. \u2022 integers are put on the bottom row of bricks. \u2022 the number on a brick is the sum of the numbers on the two bricks below. examples total = 1 45 total = \u20135 72 total = 1 23 58 3 1 (a) complete this number wall . total = 1 3 2 (b) in part (a) , the number 3 is on the middle brick of the bottom row. in the example, the number 3 is on the end brick of the bottom row. explain why putting the number 3 on the middle brick of the bottom row increases the total. ... ...", "3": "3 0607/53/o/n/17 \u00a9 ucles 2017 [turn over 2 (a) complete this number wall . total = 1 2 3 4 (b) put the numbers 1, 2, 3 and 4 on the bottom row and complete this number wall so that the total is bigger than the total in part (a) . total = (c) complete this number wall . you may use negative numbers. total = 31 10 4 7 4", "4": "4 0607/53/o/n/17 \u00a9 ucles 2017 3 this number wall is 3 bricks high. (a) complete each brick using expressions in terms of a, b and c. write each expression in its simplest form. b c a (b) use the expression for the total you found in part (a) to find the value of b. b 77 4 ...", "5": "5 0607/53/o/n/17 \u00a9 ucles 2017 [turn over 4 (a) this number wall is 4 bricks high. complete each brick using expressions in terms of a, b, c and d. write each expression in its simplest form. b aa + b d c (b) in another wall that is 4 bricks high, the total is 34 and the values of a, b, c and d are all the same. use the expression for the total you found in part (a) to show that the value of a cannot be an integer.", "6": "6 0607/53/o/n/17 \u00a9 ucles 2017 (c) in this number wall that is 5 bricks high, only integers greater than 0 are used. find one set of possible values for a, b, c, d and e. b a d e c43 14 9 6 a = b = c = d = e = 5 in 1653 a french mathematician, blaise pascal, wrote about a triangle of numbers similar to the one shown below. it is made in the same way as number walls but \u2022 the number on a brick is the sum of the numbers on the two bricks above and \u2022 the number on the first and last brick in each row is always 1. 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1row 1 row 2 row 3 row 4 row 5 row 6 6 15 20 15 6 1", "7": "7 0607/53/o/n/17 \u00a9 ucles 2017 [turn over (a) the wall in question 4(a) is 4 bricks high. show clearly how your expression for the total in question 4(a) connects to the numbers in one row of this triangle. write down which row this is. row ... (b) a wall that is 5 bricks high has a, b, c, d and e, in that order, along the bottom row. write down an expression in terms of a, b, c, d and e for the total. .. (c) use your expression from part (b) to check that the set of values you found for a, b, c, d and e in question 4(c) gives a total of 43. question 5(d) is printed on the next page.", "8": "8 0607/53/o/n/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. (d) a wall that is 5 bricks high has the number 2017 on each brick of the bottom row. find the total. ..." }, "0607_w17_qp_61.pdf": { "1": "*3088304286* this document consists of 10 printed pages and 2 blank pages. dc (st/sw) 134794/2 \u00a9 ucles 2017 [turn overcambridge international mathematics 0607/61 paper 6 (extended) october/november 2017 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/61/o/n/17 \u00a9 ucles 2017 answer both parts a and b. a investigation equable shapes (20 marks) you are advised to spend no more than 45 minutes on this part. in this investigation lengths are given in centimetres. the area of a shape is a square centimetres and its perimeter is p centimetres. this task investigates the dimensions of equable shapes. the shape is equable if a = p. all the diagrams in this investigation are not to scale. 1 3.6 4.5 this rectangle is equable. show by calculation that a = p. ... ... 2 y 10 (a) write down an expression, in terms of y, for the area of this rectangle. ... (b) write down an expression, in terms of y, for the perimeter of this rectangle. ... (c) this rectangle is equable. using your answers to part (a) and part (b) write an equation in terms of y. solve this equation. ...", "3": "3 0607/61/o/n/17 \u00a9 ucles 2017 [turn over 3 y x this rectangle is equable. (a) write down the equation a = p in terms of x and y. (b) show that ( x - 2)(y - 2) = 4 is equivalent to your equation in part (a) . (c) use part (b) to find all the equable rectangles that have integer lengths and widths. ...", "4": "4 0607/61/o/n/17 \u00a9 ucles 2017 4 this isosceles triangle has base 6 and height 7.2 . its area is 21\u00d7 base \u00d7 height = 3 \u00d7 7.2 = 21.6 . show that it is equable. 3 37.2 5 this isosceles triangle has base 2 a and height h. a ah (a) find, in terms of a and h, an expression for a and an expression for p. when a = p, show that ah aa h 2222-= + .", "5": "5 0607/61/o/n/17 \u00a9 ucles 2017 [turn over (b) (i) by squaring both sides of the equation in part (a) show that a2h \u2013 4a2 = 4h. (ii) write a2 in terms of h. ... (iii) for which values of h, the height of an equable isosceles triangle, is your formula for a2 valid? ... (c) an equable isosceles triangle has a height of 4.5 . find its perimeter. ...", "6": "6 0607/61/o/n/17 \u00a9 ucles 2017 b modelling carbon dioxide measurements (20 marks) you are advised to spend no more than 45 minutes on this part. this task models data from mauna loa on the island of hawaii. since 1958, scientists at mauna loa have been measuring the amount of carbon dioxide in the atmosphere. the units of measurement are parts per million by volume (ppm). the scientists use a sine wave to model the graph of the amount of carbon dioxide in the atmosphere. here is the graph of y = sin x\u00b0. its period is 360. \u20131\u20130.53000.51 60 90 120 150 180 210 240 270 300 330 360xy 1 (a) \u20131\u20130.53000.51 60 90 120 150 180 210 240 270 300 330 360xy (i) on the grid, sketch the graph of y = sin(2 x)\u00b0 for x0 360 gg . (ii) write down the period of y = sin(2 x)\u00b0. ... (b) write down the period of y = sin(6 x)\u00b0. ... (c) find the value of k when the period of y = sin(kx)\u00b0 is 40. ...", "7": "7 0607/61/o/n/17 \u00a9 ucles 2017 [turn over 2 the graph below models the change in the amount of carbon dioxide at mauna loa in one year. x is the number of months since the start of the year. x = 0 is the beginning of january and x = 12 is the end of december. y is the amount of carbon dioxide above a given level. \u20132 \u201341024 2 3 4 5 6 7 8 9 10 11 12xy the equation of the graph is y = a sin(bx)\u00b0. (a) write down the period of the graph and find b. period = ... b = ... (b) write down the value of a and the equation of the graph. ... ", "8": "8 0607/61/o/n/17 \u00a9 ucles 2017 3 the table shows the amount of carbon dioxide at the beginning of each year. yearnumber of months since the beginning of 2012 ( x)amount of carbon dioxide in ppm ( y) 2012 0 393 2013 12 395 2014 24 397 2015 36 399 2016 48 401 2017 60 403 (a) on the grid, plot these points. 390 0 12 24 36 48 60xy 395400405 (b) find the equation for y in terms of x that fits the data. ...", "9": "9 0607/61/o/n/17 \u00a9 ucles 2017 [turn over 4 the expressions for y in question 2 and question 3 combine together to give the complete model. use one of the operations, addition, subtraction, multiplication or division, to write down the complete model. 5 the graph shows the complete model for the amount of carbon dioxide between the beginning of 2012 and the beginning of 2017. label the points marked on the axes. x number of months since the beginning of 2012amount of carbon dioxide (ppm)y", "10": "10 0607/61/o/n/17 \u00a9 ucles 2017 6 answer this question using your model from question 4 . (a) find the highest amount of carbon dioxide in the atmosphere between the beginning of january 2012 and the beginning of january 2017. give your answer correct to 1 decimal place. ... (b) find the amount of carbon dioxide at the end of may 2015. give your answer correct to 1 decimal place. ... 7 assume that the graph in question 5 continues in the same way. find when the amount of carbon dioxide first reaches 410 ppm. write down the year and the month. year ... month ... 8 explain why this model may not be appropriate for finding the amount of carbon dioxide in the atmosphere in the year 2050. ... ...", "11": "11 0607/61/o/n/17 \u00a9 ucles 2017 blank page", "12": "12 0607/61/o/n/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_w17_qp_62.pdf": { "1": "*4364429874* this document consists of 14 printed pages and 2 blank pages. dc (nf/fc) 134786/2 \u00a9 ucles 2017 [turn overcambridge international mathematics 0607/62 paper 6 (extended) october/november 2017 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and to communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/62/o/n/17 \u00a9 ucles 2017 answer both parts a and b. a investigation number walls (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation looks at what happens when you place numbers on a number wall . you make a number wall like this. \u2022 integers are put on the bottom row of bricks. \u2022 the number on a brick is the sum of the numbers on the two bricks below. examples total = 5 1 4total = 2 \u20135 7 total = 8 3 1 2 35 1 (a) complete this number wall . total = 1 3 2 (b) in part (a) , the number 3 is on the middle brick of the bottom row. in the example, the number 3 is on the end brick of the bottom row. explain why putting the number 3 on the middle brick of the bottom row increases the total. ... ...", "3": "3 0607/62/o/n/17 \u00a9 ucles 2017 [turn over 2 (a) complete this number wall . total = 1 2 3 4 (b) put the numbers 1, 2, 3 and 4 on the bottom row and complete this number wall so that the total is bigger than the total in part (a) . total = (c) complete this number wall . you may use negative numbers. total = 31 4 7 410", "4": "4 0607/62/o/n/17 \u00a9 ucles 2017 3 (a) this number wall is 4 bricks high. complete each brick using expressions in terms of a, b, c and d. write each expression in its simplest form. a + b a b c d (b) in another wall that is 4 bricks high, the total is 34 and the values of a, b, c and d are all the same. use the expression for the total you found in part (a) to show that the value of a cannot be an integer.", "5": "5 0607/62/o/n/17 \u00a9 ucles 2017 [turn over (c) in this number wall that is 5 bricks high, only integers greater than 0 are used. find both sets of possible values for a, b, c, d and e. a b43 9 14 6 c d e set 1 a = b = c = d = e = set 2 a = b = c = d = e = ", "6": "6 0607/62/o/n/17 \u00a9 ucles 2017 4 in 1653 a french mathematician, blaise pascal, wrote about a triangle of numbers similar to the one shown below. it is made in the same way as number walls but \u2022 the number on a brick is the sum of the numbers on the two bricks above and \u2022 the number on the first and last brick in each row is always 1. 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1row 1 row 2 row 3 row 4 row 5 row 6 6 15 20 15 6 1 (a) the wall in question 3(a) is 4 bricks high. show clearly how your expression for the total in question 3(a) connects to the numbers in one row of this triangle. write down which row this is. row . (b) a wall that is 5 bricks high has a, b, c, d and e, in that order, along the bottom row. write down an expression in terms of a, b, c, d and e for the total. . (c) use your expression from part (b) to check that one of the sets of values you found for a, b, c, d and e in question 3(c) gives a total of 43.", "7": "7 0607/62/o/n/17 \u00a9 ucles 2017 [turn over 5 (a) each brick in the bottom row of a number wall has the letter a written on it. complete this table. height of wall (h bricks high)total 1 a 2 2a 3 4 h (b) a wall that is 6 bricks high has the same integer written on each brick on the bottom row. the total is 96. find the integer that has been used. .. (c) a wall has the number 5 written on each brick on the bottom row. the total is 20 971 520. find the height of the wall. ..", "8": "8 0607/62/o/n/17 \u00a9 ucles 2017 6 the bricks on the bottom row of a wall are numbered consecutively using positive integers. for example, 7, 8, 9, \u2026 the total for the wall is 80. find all the possible heights of the wall. ..", "9": "9 0607/62/o/n/17 \u00a9 ucles 2017 [turn over b modelling ranges (20 marks) you are advised to spend no more than 45 minutes on this part. this task looks at the horizontal distance a ball, fired from a toy cannon on horizontal ground, travels before it hits the ground. the horizontal distance that the ball travels is called the range. the angle the barrel of the toy cannon makes with horizontal ground is called the angle of elevation. angle of elevationthe barrel the range depends on the angle of elevation. this diagram shows the path of a ball and its range for three different angles of elevation. range range range", "10": "10 0607/62/o/n/17 \u00a9 ucles 2017 1 paul has a toy cannon which fires a ball at a speed of v m/s. he uses a model to calculate the range for the same speed but for different angles of elevation. angle of elevation ( x degrees) 0 10 20 30 40 50 60 70 80 90 range ( r metres) 0 3.5 6.6 8.8 10.0 10.0 8.8 6.6 3.5 0 (a) on the grid, plot these points and draw a graph to show this information. 001234567891011r x 10 20 30 40 50 angle of elevation (degrees)range (metres) 60 70 80 90 (b) paul wants the range to be 8 m. use the graph to find the angles of elevation he could use. .. (c) paul wants the range to be the maximum. use the graph to find the angle of elevation he should use. ..", "11": "11 0607/62/o/n/17 \u00a9 ucles 2017 [turn over (d) a model for the range is r = a sin(2 x)\u00b0. find the value of a and write down the model. .. (e) use your model to find r when x = 100. explain your result. ... ... ... 2 paul now fires 8 balls from his cannon. each ball has the same mass and is fired at the same speed of v m/s. he records the angle of elevation and range for each ball. angle of elevation ( x degrees) 10 20 30 40 50 60 70 80 range ( r metres) 3.4 5.9 8.3 9.1 9.1 8.0 5.8 3.2 (a) paul did not use an angle of elevation of 90 \u00b0. give a reason why. ... (b) use the information in the table to draw a graph using the axes on the previous page. (c) how can you tell that the model in question 1 is a good model for these results? ... ...", "12": "12 0607/62/o/n/17 \u00a9 ucles 2017 3 paul now fires balls from his cannon, each with a speed of 20 m/s. (a) another model for the range is .sin rvx9812\u00b02 = ^h. on the axes below, sketch a graph of the expected ranges using this model. 00range (metres) angle of elevation (degrees)80xr (b) paul records the actual range when he fires the balls. angle of elevation ( x degrees). 10 20 30 40 50 60 70 80 range ( r metres). 12.0 21.8 29.2 30.7 30.2 26.3 19.5 10.6 on the same axes, sketch the graph for these ranges. comment on the suitability of using the model to predict the range. ... ...", "13": "13 0607/62/o/n/17 \u00a9 ucles 2017 [turn over 4 paul changes the speed with which each ball is fired. he records each speed and the maximum range, r metres. speed ( v m/s) 1 5 10 15 20 25 maximum range ( r metres) 0.10 2.49 9.62 19.85 31.03 43.26 (a) on the axes below, sketch the graph of r against v. 00maximum range (metres) speed (m/s)25vr (b) paul improves his model in question 3(a) to estimate the maximum range, and to take account of air resistance. the new model is .rvv 9812 981kv 22#=- where k is a constant. when v = 15 m/s, find the value of k, correct to 2 decimal places. ..", "14": "14 0607/62/o/n/17 \u00a9 ucles 2017 (c) comment on the suitability of the model as speed increases. ... ... ...", "15": "15 0607/62/o/n/17 \u00a9 ucles 2017 blank page", "16": "16 0607/62/o/n/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_w17_qp_63.pdf": { "1": "this document consists of 12 printed pages. dc (kn/sg) 137085/3 \u00a9 ucles 2017 [turn over *8729490689* cambridge international mathematics 0607/63 paper 6 (extended) october/november 2017 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a and b. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and to communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/63/o/n/17 \u00a9 ucles 2017 answer both parts a and b. a investigation chequered flags (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation is about the number of coloured squares on a chequered flag. a chequered flag has two or more colours making a pattern of squares. there is always a black square in the top left corner. the size of a flag is m by n, where m is the number of rows and n is the number of columns. 1 (a) the flag above is a 4 by 5, black and white chequered flag. write down the number of black squares and the number of white squares. black . white . (b) (i) complete both tables. size of flag 2 by 1 2 by 2 2 by 3 2 by 4 2 by 5 2 by n black 1 2 white 1 2 size of flag 4 by 1 4 by 2 4 by 3 4 by 4 4 by 5 4 by n black 2 white 2", "3": "3 0607/63/o/n/17 \u00a9 ucles 2017 [turn over (ii) find two expressions, in terms of n, for the number of black squares and the number of white squares on a 6 by n flag. black . white . (c) how many different sizes of black and white chequered flags are there with 12 black squares and 12 white squares? .. (d) m is an even number. for the flags in this question find an expression, in terms of m and n, for the number of black squares on an m by n chequered flag. ..", "4": "4 0607/63/o/n/17 \u00a9 ucles 2017 2 this is a 3 by 5, black and white chequered flag. (a) write down the number of black squares and the number of white squares. black . white . (b) is your expression in question 1(d) correct for this flag? write down the restrictions on m and n for your expression in question 1(d) . ... (c) complete both tables. size of flag 3 by 1 3 by 2 3 by 3 3 by 4 3 by 5 black white size of flag 5 by 1 5 by 2 5 by 3 5 by 4 5 by 5 black white (d) m and n are both odd numbers. using your answer to question 1(d) , find an expression, in terms of m and n, for the number of black squares and the number of white squares. black . white .", "5": "5 0607/63/o/n/17 \u00a9 ucles 2017 [turn over 3 this is a 4 by 6, black, white and grey three-coloured chequered flag. (a) for this flag, write down the number of squares of each colour. black . white . grey . (b) (i) complete both tables. size of flag 3 by 1 3 by 2 3 by 3 3 by 4 3 by 5 3 by n black white grey size of flag 6 by 1 6 by 2 6 by 3 6 by 4 6 by 5 6 by n black white grey (ii) for the flags in this question, find an expression, in terms of m and n, for the number of black squares on an m by n three-coloured chequered flag. .. (iii) is your expression in part (ii) correct for a flag with 2 rows? write down the restriction on n for your expression in part (ii) . ...", "6": "6 0607/63/o/n/17 \u00a9 ucles 2017 4 the number of black squares on a flag with six colours is mn 6. (a) show that this is not true for a 16 by 14 flag with six colours. (b) a six-coloured chequered flag has 3 black squares. find all the possible sizes of the flag. 5 the expression pmn gives the number of each coloured square on an m by n flag with p colours. what is true about m, n and p? ...", "7": "7 0607/63/o/n/17 \u00a9 ucles 2017 [turn over b modelling areas of polygons (20 marks) you are advised to spend no more than 45 minutes on this part. this task looks at the relationship between the number of sides and the area of an enclosure. a farmer has a 24 metre length of fencing to make an enclosure. 1 (a) he makes a rectangular enclosure as shown in this diagram. 11 m 1 m area = 11 m2not to scale complete this table to show all the possible rectangular enclosures he can make with 24 m of fencing. the sides of the enclosure are always a whole number of metres. 1 by 11 and 11 by 1 are the same rectangle. width (m) length (m) area (m2) 1 11 11 2 10 20 (b) what is the mathematical name of the rectangle that gives the maximum area of the enclosure? ..", "8": "8 0607/63/o/n/17 \u00a9 ucles 2017 2 the farmer makes an enclosure that is an equilateral triangle with a perimeter of 24 m. the perpendicular distance from a corner to the opposite side of the enclosure is h metres. hnot to scale show that the area of this triangle is 27.7 m2, correct to 1 decimal place. 3 (a) the farmer makes an enclosure that is a regular pentagon with a perimeter of 24 m. a\u00b0not to scale (i) show that a = 72.", "9": "9 0607/63/o/n/17 \u00a9 ucles 2017 [turn over (ii) the regular pentagon can be divided into 5 isosceles triangles. the perpendicular distance from the centre of the pentagon to a side is h metres. use trigonometry to find the value of h. a\u00b0 h 24 5mnot to scale .. (iii) use your value of h to find the area of the isosceles triangle. .. (iv) show that the area of the pentagon is 40 m2, correct to the nearest square metre.", "10": "10 0607/63/o/n/17 \u00a9 ucles 2017 (b) the farmer makes an enclosure in the shape of a regular hexagon with a perimeter of 24 m. use the method in part (a) to find the area of this hexagon. .. 4 the farmer makes an enclosure that is an n-sided regular polygon with a perimeter of 24 m. here is an isosceles triangle from this polygon. a\u00b0 h 24 nmnot to scale (a) (i) use this triangle and the method from question 3 , to show that a model for calculating the area ( a m2) of a regular n-sided polygon with perimeter 24 m is \u00b0tana nn180144=j lkkn poo . show all your working.", "11": "11 0607/63/o/n/17 \u00a9 ucles 2017 [turn over (ii) write down a condition for n. ... (b) use the model to show that the area of a regular octagon with a perimeter of 24 m is 43.5 m2, correct to 1 decimal place. (c) sketch the graph of \u00b0tana nn180144=j lkkn poo for n35 0 gg on the grid below. a 50 0 3 50n (d) the farmer wants to use the 24 m of fencing to make a regular polygon with an area of 44.0 m2, correct to the nearest 0.1 m2. find the number of sides of this polygon. .. questions 4(e), 4(f) and 4(g) are printed on the next page.", "12": "12 0607/63/o/n/17 \u00a9 ucles 2017 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. (e) use your graph to write down an estimate of the greatest possible area of a polygon with a perimeter of 24 m. .. (f) (i) when n is very large, the shape of the polygon is approximately a . (ii) calculate the exact value of the greatest possible area of a shape with a perimeter of 24 m. .. (g) change the model in question 4(a) to find the area of any regular polygon with a perimeter of p. .." } }, "2018": { "0607_s18_qp_11.pdf": { "1": " this document consists of 8 printed pages. ib18 06_0607_11/2rp \u00a9 ucles 2018 [turn over \uf02a\uf030\uf032\uf031\uf030\uf034\uf034\uf032\uf032\uf038\uf033\uf02a \uf020 cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/11 paper 1 (core) may/june 2018 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2018 0607/11/m/j/18 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \uf070r2 circumference, c, of circle, radius r. c = 2\uf070r curved surface area, a, of cylinder of radius r, height h. a = 2\uf070rh curved surface area, a, of cone of radius r, sloping edge l. a = \uf070rl curved surface area, a, of sphere of radius r. a = 4\uf070r2 volume, v, of prism, cross-sectional area a, length l. v = al volume, v, of pyramid, base area a, height h. v = 1 3ah volume, v, of cylinder of radius r, height h. v = \uf070r2h volume, v, of cone of radius r, height h. v = 1 3\uf070r2h volume, v, of sphere of radius r. v = 4 3\uf070r3 ", "3": "3 \u00a9 ucles 2018 0607/11/m/j/18 [turn over answer all the questions. 1 3 6 12 15 18 36 from the list of numbers write down (a) a common factor of 9 and 18, [1] (b) a common multiple of 6 and 12. [1] 2 work out 103 of 120. [1] 3 write down the value of 364 . [1] 4 write down a prime number between 20 and 30. [1] 5 insert one pair of brackets to make this calculation correct. 5 + 10 \u00d7 3 \u2013 1 = 25 [1] 6 write down the number of lines of symmetry of this sector. [1] ", "4": "4 \u00a9 ucles 2018 0607/11/m/j/18 7 the table shows the number of students in each year group at a school. boys girls total year 1 59 65 124 year 2 64 72 136 year 3 70 67 137 year 4 63 65 128 year 5 58 67 125 total 314 336 650 write down (a) the number of boys in year 4, [1] (b) the total number of students in year 2, [1] (c) the year group in which there are more boys than girls. [1] 8 adele is collecting data about the people who live in paris. (a) write down a type of discrete data that adele could collect. [1] (b) write down a type of continuous data that adele could collect. [1] 9 the diagram shows a circle, centre o, and a straight line ab. write down the mathematical name of the line ab. [1] b ao", "5": "5 \u00a9 ucles 2018 0607/11/m/j/18 [turn over 10 write down the letters for all the shapes that are congruent. [1] 11 use one of the symbols >, < or = to make the following statement correct. 257 51 [1] 12 simplify. 5 e \u2013 4f \u2013 e + 3f [2] 13 the table shows the favourite football team of each of 30 students. favourite team chelsea liverpool middlesbrough preston west ham number of students 5 6 12 4 3 paula draws a pie chart to show this information. work out the sector angle for liverpool. [2] ab c d e f g", "6": "6 \u00a9 ucles 2018 0607/11/m/j/18 14 \u20136 \u20136\u20135\u20134\u20133\u20132\u201310 123456 \u20135\u20134\u20133\u20132\u2013112456y x3a the diagram shows a point a and the line y = 23x + 3. (a) write down the co-ordinates of point a. ( , )[ 1 ] (b) plot and label the point b (\u20131, \u20133). [1] (c) draw the line x = 4. [1] (d) write down the co-ordinates of the point where the line y = 23x + 3 crosses the x-axis. ( , )[ 1 ] (e) write down the gradient of the line y = 23x + 3. [1] ", "7": "7 \u00a9 ucles 2018 0607/11/m/j/18 [turn over 15 (a) reflect triangle p in the y-axis. label the image q. [1] (b) rotate triangle p through 90\u00b0 clockwise about the origin. label the image r. [2] (c) describe fully the single transformation that maps triangle q onto triangle r. [2] 16 write down the elements in a \uf0c7b\uf0a2. { } [2] 17 omar runs at an average speed of 12 km/h. find the time he will take to run 18 km. hours [2] questions 18, 19 and 20 are printed on the next page. ab 4 98 1624 123 15 21\u20134\u20133\u20132\u201310 1231234 4 \u20134\u20133\u20132\u20131p xy", "8": "8 permission to reproduce items where third-party owned material pr otected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related informati on to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknow ledgements booklet. this is produced for ea ch series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge as sessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2018 0607/11/m/j/18 18 f(x) = x5 work out f(36). [1] 19 (a) solve the equation. 5 x = 35 x = [1] (b) solve the equation. 5( y \u2013 7 ) = 10 y = [2] 20 solve the simultaneous equations. x \u2013 2y = 1 3x + y = 10 x = y = [3] " }, "0607_s18_qp_12.pdf": { "1": " this document consists of 8 printed pages. ib18 06_0607_12/rp \u00a9 ucles 2018 [turn over \uf02a\uf030\uf033\uf035\uf034\uf030\uf039\uf038\uf037\uf032\uf033\uf02a \uf020 cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/12 paper 1 (core) may/june 2018 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2018 0607/12/m/j/18 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \uf070r2 circumference, c, of circle, radius r. c = 2\uf070r curved surface area, a, of cylinder of radius r, height h. a = 2\uf070rh curved surface area, a, of cone of radius r, sloping edge l. a = \uf070rl curved surface area, a, of sphere of radius r. a = 4\uf070r2 volume, v, of prism, cross-sectional area a, length l. v = al volume, v, of pyramid, base area a, height h. v = 1 3ah volume, v, of cylinder of radius r, height h. v = \uf070r2h volume, v, of cone of radius r, height h. v = 1 3\uf070r2h volume, v, of sphere of radius r. v = 4 3\uf070r3 ", "3": "3 \u00a9 ucles 2018 0607/12/m/j/18 [turn over answer all the questions. 1 work out. 6 + 24 \u00f7 3 [1] 2 by rounding each number to one significant figure, estimate the value of 3.17 \u00d7 4.8 . [2] 3 work out 32 of 21. [1] 4 find 20% of 200. [1] 5 write down a square number between 12 and 18. [1] 6 (a) write 2 \u00d7 2 \u00d7 2 as a power of 2. [1] (b) work out 32. [1] ", "4": "4 \u00a9 ucles 2018 0607/12/m/j/18 7 the diagram shows a triangle on a 1 cm2 grid. find the area of the triangle. cm2 [1] 8 9 cmnot to scale the length of this rectangle is 9 cm. the perimeter of this rectangle is 30 cm. work out the width of this rectangle. cm [2] 9 1 kg of bananas and 2 kg of pears cost $5.95 in total. pears cost $1.80 per kilogram. work out the cost of 1 kg of bananas. $ [2] ", "5": "5 \u00a9 ucles 2018 0607/12/m/j/18 [turn over 10 find the lowest common multiple (lcm) of 12 and 16. [2] 11 (a) write down the co-ordinates of point a. ( , )[ 1 ] (b) plot the point (\u20133, 1). label this point b. [1] 12 find the values of x and y. x = y = [2] y x \u2013 4 \u2013 444 3 2 1 \u20133 \u20132 \u20131 1 2 3 \u20133\u20132\u201310a not to scale x\u00b080\u00b0 y\u00b070\u00b0", "6": "6 \u00a9 ucles 2018 0607/12/m/j/18 13 the point p has co-ordinates (2, 12) and the point q has co-ordinates (10, 8). find the co-ordinates of the midpoint of pq. ( , )[ 2 ] 14 the list shows the mark for each of ten students in an examination. 7 9 5 5 8 2 6 4 4 9 (a) find the median. [2] (b) find the mean. [2] 15 a = {2, 3, 4, 5, 6, 7} b = {2, 3, 5, 8} (a) write down n( a). [1] (b) write down the elements of a \uf0c8 b. { } [1] 16 the equations of some straight lines are shown below. x = 4 y = 3x \u2013 3 y = 4x \u2013 3 y = 4x + 7 y = 4 y = \u20133 x \u2013 3 write down the equations of th e two lines that are parallel. and [1] ", "7": "7 \u00a9 ucles 2018 0607/12/m/j/18 [turn over 17 y x \u2013 4 \u2013 444 3 2 1 \u20133 \u20132 \u20131 1 2 3 \u20133\u20132\u201310a on the grid, draw the image of triangle a after a reflection in the line y = 1. [2] 18 describe the single transformation that maps y = f(x) onto y = f(x) \u2013 2. [2] 19 f(x) = x2 + 3 find the range of f( x) when the domain is {\u20132, 0, 2, 3}. { } [2] questions 20, 21 and 22 are printed on the next page. ", "8": "8 permission to reproduce items where third-party owned material pr otected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknow ledgements booklet. this is produced for each series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge as sessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2018 0607/12/m/j/18 20 simplify fully. efe 352\uf0b4 [2] 21 write down all integer values of x that satisfy \u20133 < x 1 . [2] 22 solve the simultaneous equations. \u00a0 5 x \u2013 y = 7 4 x \u2013 y = 5 x = y = [2] " }, "0607_s18_qp_13.pdf": { "1": " this document consists of 8 printed pages. ib18 06_0607_13/4rp \u00a9 ucles 2018 [turn over \uf02a\uf030\uf032\uf035\uf033\uf032\uf036\uf035\uf033\uf036\uf030 \uf02a\uf020 cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/13 paper 1 (core) may/june 2018 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2018 0607/13/m/j/18 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \uf070r2 circumference, c, of circle, radius r. c = 2\uf070r curved surface area, a, of cylinder of radius r, height h. a = 2\uf070rh curved surface area, a, of cone of radius r, sloping edge l. a = \uf070rl curved surface area, a, of sphere of radius r. a = 4\uf070r2 volume, v, of prism, cross-sectional area a, length l. v = al volume, v, of pyramid, base area a, height h. v = 1 3ah volume, v, of cylinder of radius r, height h. v = \uf070r2h volume, v, of cone of radius r, height h. v = 1 3\uf070r2h volume, v, of sphere of radius r. v = 4 3\uf070r3 ", "3": "3 \u00a9 ucles 2018 0607/13/m/j/18 [turn over answer all the questions. 1 write 0.37 as a percentage. %[ 1 ] 2 write down the next square number after 36. [1] 3 change 5 years into months. months [1] 4 change 260 centimetres into metres. metres [1] 5 the distance-time graph shows sammy\u2019s journey from geneva to berne and back to geneva. (a) how far from geneva was sammy at 11 00? km [1] (b) sammy stays for 121 hours in berne. he then returns to geneva. (i) how long did the journey from berne to geneva take? hours [1] (ii) find the average speed of this journey. km / h[ 1 ] 10 00 time4080120160 distance (km) 09 00 11 0012 00 13 00 14 00 15 0016 00berne geneva 0", "4": "4 \u00a9 ucles 2018 0607/13/m/j/18 6 on the grid, shade two squares to give the diagram rotational symmetry of order 4. [1] 7 a polygon has 8 sides. write down the mathematical name for this shape. [1] 8 complete the statement. an angle that is more than 90\u00b0 but is less than 180 \uf0b0 is called [1] 9 the diagram shows a line l drawn on a grid. (a) on the grid, draw the line x = 3. [1] (b) write down the co-ordinates where the line l and the line x = 3 intersect. ( , )[ 1 ] 10 find the distance between the points (\u20133, 4) and (5 , 4). [1] \u20132\u201310123123 4 \u20133\u20132\u2013154 \u20133 \u20134 \u20135 \u20134xly", "5": "5 \u00a9 ucles 2018 0607/13/m/j/18 [turn over 11 complete the mapping diagram. \uf0f7\uf0f7\uf0f7\uf0f7\uf0f7\uf0f7\uf0f7\uf0f7\uf0f7\uf0f7 \uf0f8\uf0f6 \uf0e7\uf0e7\uf0e7\uf0e7\uf0e7\uf0e7\uf0e7\uf0e7\uf0e7\uf0e7 \uf0e8\uf0e6 1411631 \uf0f7\uf0f7\uf0f7\uf0f7\uf0f7\uf0f7\uf0f7\uf0f7\uf0f7\uf0f7 \uf0f8\uf0f6 \uf0e7\uf0e7\uf0e7\uf0e7\uf0e7\uf0e7\uf0e7\uf0e7\uf0e7\uf0e7 \uf0e8\uf0e6 . ..161186 [1] 12 write down the next term of this sequence. 5, 9, 13, 17, \u2026 [1] 13 find an expression for the nth term of this sequence. 4, 7, 10, 13, 16, \u2026 [2] 14 the pie chart represents 60 students. work out how many of the students are boys. [2] 120\u00b0boys girls", "6": "6 \u00a9 ucles 2018 0607/13/m/j/18 15 the diagram shows an isosceles triangle. find the value of x. x = [2] 16 (a) measure the angle marked x. x = [1] (b) write down the bearing of q from p. [1] 17 find the highest common factor (hcf) of 54 and 72. [1] 18 work out (3 \u00d7 106) \u00d7 (4 \u00d7 104) . write your answer in standard form. [2] north x\u00b0 pqnot to scale148x\u00b0not to scale \u00b0", "7": "7 \u00a9 ucles 2018 0607/13/m/j/18 [turn over 19 describe fully the single transformation that maps shape a onto shape b. [3] 20 a is the point (4, 9) and b is the point (1, 3). find \uf0be\uf0ae\uf0be ab. \uf0be\uf0ae\uf0be ab = \uf0f7\uf0f7\uf0f7 \uf0f8\uf0f6 \uf0e7\uf0e7\uf0e7 \uf0e8\uf0e6 [2] 21 a bag contains red, blue and green beads only. there are 40 beads in the bag. one bead is chosen at random. the probability that the bead is red is 81. the probability that the bead is blue is 85. (a) find the probability that the bead is green. [2] (b) work out the number of blue beads in the bag. [1] questions 22 and 23 are printed on the next page. y x 44 3 2 1 \u20131 1 2 3 \u20133\u20132\u201310a b", "8": "8 permission to reproduce items where third-party owned material pr otected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknow ledgements booklet. this is produced for each series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge as sessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2018 0607/13/m/j/18 22 write down an expression, in terms of x and y, for the total cost of x pens at 25 cents each and y pens at 45 cents each. cents [2] 23 solve the simultaneous equations. 3x + 2y = 21 4x \u2013 5y = 5 x = y = [4] " }, "0607_s18_qp_21.pdf": { "1": "this document consists of 8 printed pages. dc (nh/sw) 153513/1 \u00a9 ucles 2018 [turn over *4065397237* cambridge international mathematics 0607/21 paper 2 (extended) may/june 2018 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/21/m/j/18 \u00a9 ucles 2018 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/21/m/j/18 \u00a9 ucles 2018 [turn over answer all the questions. 1 (a) work out 57 28#-+ . [1] (b) find .00013. [1] 2 (a) find, by measuring, the size of this reflex angle. [1] (b) 80\u00b0not to scale x\u00b0 work out the value of x. x = [1] (c) find the size of one exterior angle of a regular 18-sided polygon. [2]", "4": "4 0607/21/m/j/18 \u00a9 ucles 2018 3 solve these simultaneous equations. xy xy37 25-= -= x = y = [2] 4 (a) write 0.68 as a fraction in its lowest terms. [1] (b) work out 73 98' . [2] 5 these are the first five terms of a sequence. 1 0 1 4 9 find the nth term of this sequence. [2]", "5": "5 0607/21/m/j/18 \u00a9 ucles 2018 [turn over 6 (a) expand and simplify. () () pq pq 27-+ [2] (b) factorise. ta at 22-- + [2] 7 not to scale 140\u00b0o x\u00b0 y\u00b0 o is the centre of the circle. find the value of x and the value of y. x = y = [2]", "6": "6 0607/21/m/j/18 \u00a9 ucles 2018 8 y varies inversely as x2. when x = 3, y = 4. find y in terms of x. y = [2] 9 (a) find the value of 2732. [1] (b) simplify hh18 318 3' . [2] 10 vu as222=- find s in terms of a, u and v. s = [2] 11 in each venn diagram, shade the region indicated. uu ap bq r (a /h33371 b)'(p /h33371 q)/h33370 r [2]", "7": "7 0607/21/m/j/18 \u00a9 ucles 2018 [turn over 12 (a) simplify fully. 700 [1] (b) rationalise the denominator. 721 - [2] 13 simplify fully. ttt 93 22 -- [3] 14 (a) write down the value of log39. [1] (b) logl og logx 22 11+= . find the value of x. x = [2] question 15 is printed on the next page.", "8": "8 0607/21/m/j/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.15 not to scale8 cm ob a the length of the arc ab34cmr= . the area of the sector oab is kcm2r . find the value of k. k = [3]" }, "0607_s18_qp_22.pdf": { "1": "*3757916466* this document consists of 8 printed pages. dc (nf/sw) 153514/1 \u00a9 ucles 2018 [turn overcambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/22 paper 2 (extended) may/june 2018 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.", "2": "2 0607/22/m/j/18 \u00a9 ucles 2018 formula list for the equation ax bxc02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/22/m/j/18 \u00a9 ucles 2018 [turn over answer all the questions. 1 a quadrilateral has exactly one pair of parallel sides. write down the mathematical name for this quadrilateral. [1] 2 76\u00b0not to scale b a41\u00b0x\u00b0 ab is a straight line. find the value of x. x = [1] 3 a bag contains 2 blue balls, 3 red balls and 5 green balls only. one ball is chosen at random. find the probability that this ball is red. [1] 4 write down a prime number between 60 and 70. [1]", "4": "4 0607/22/m/j/18 \u00a9 ucles 2018 5 solve. xx79 51 7 += + x = [2] 6 write 36 as a product of prime factors. [2] 7 solve. x37 11+ [2] 8 point a has co-ordinates (2, 12). point b has co-ordinates (4, 2). find the co-ordinates of the midpoint of ab. ( ... , ...) [2]", "5": "5 0607/22/m/j/18 \u00a9 ucles 2018 [turn over 9 work out. 452132- [3] 10 0020406080100 10 20xcumulative frequency 30 40 50 use the cumulative frequency curve to estimate the inter-quartile range. [2]", "6": "6 0607/22/m/j/18 \u00a9 ucles 2018 11 here are the first four terms of a sequence. 13 9 5 1 (a) write down the next term. [1] (b) find an expression, in terms of n, for the nth term. [2] 12 simplify. 75 12 27 -+ [2] 13 shade the given sets in each of these diagrams. u (a' /h33371 b')' a' /h33370 ba bu a b [2]", "7": "7 0607/22/m/j/18 \u00a9 ucles 2018 [turn over 14 point a has co-ordinates (2, 3). point b has co-ordinates (4, 11). find the equation of the line ab. give your answer in the form ym xc=+ . y = [3] 15 expand the brackets and simplify. xy xy 35 53--`` jj [3] 16 a factory makes soft centre chocolates and hard centre chocolates only. the probability that a chocolate chosen at random has a hard centre is 0.6 . three chocolates are chosen at random. find the probability they are all soft centre chocolates. [3] questions 17 and 18 are printed on the next page.", "8": "8 0607/22/m/j/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.17 factorise. xx yy 44 322-- [3] 18 write as a single fraction in its simplest form. nn nn 11 11 -+-+- [4]" }, "0607_s18_qp_23.pdf": { "1": "*4854375045* this document consists of 8 printed pages. dc (lk/sw) 153515/1 \u00a9 ucles 2018 [turn overcambridge international mathematics 0607/23 paper 2 (extended) may/june 2018 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/23/m/j/18 \u00a9 ucles 2018 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/23/m/j/18 \u00a9 ucles 2018 [turn over answer all the questions. 1 \u20135\u20134\u20133\u20132\u201310 12345xy \u20135\u20134\u20133\u20132\u2013112345 ml (a) write down the equation of line l. [1] (b) write down the co-ordinates of the point of intersection of line l and line m. ( , ) [1] (c) find the gradient of line m. [2] 2 find the highest common factor (hcf) of 96 and 60. [1] 3 expand and simplify () () xy yx 52 33 42 +- - . [2]", "4": "4 0607/23/m/j/18 \u00a9 ucles 2018 4 write down the value of 170. [1] 5 vufuf=- find v when u = 30 and f = 10. v = ... [2] 6 (a) find a fraction, n, that satisfies this inequality. n75 7611 n = ... [1] (b) write down an irrational number, m, that satisfies this inequality. m4711 m = ... [1] 7 q is the point (3, 7) and pq6 3=-eo . (a) find the co-ordinates of p. ( , ) [2] (b) find pq. give your answer in its simplest surd form. [3]", "5": "5 0607/23/m/j/18 \u00a9 ucles 2018 [turn over 8 work out (5.6 \u00d7 10\u20137) \u2013 (7.8 \u00d7 10\u20138). give your answer in standard form. [2] 9 kim has a piece of rope 18 metres long. he cuts the rope into two pieces. the lengths of the pieces are in the ratio 1 : 5. calculate the length of each piece. ... m ... m [2] 10 solve xx32 15 h-+ . [2]", "6": "6 0607/23/m/j/18 \u00a9 ucles 2018 11 jamil has a biased 6-sided die. he rolls it 350 times. the results are shown in the table. number on die 1 2 3 4 5 6 frequency 20 50 72 68 56 84 (a) find the relative frequency of getting a 2 with jamil\u2019s die. [1] (b) explain why your answer to part (a) is a good estimate of the probability of getting a 2. ... [1] (c) estimate the number of times jamil will get a 2 if he rolls the die 1400 times. [1] 12 (a) on the grid, sketch the graph of \u00b0sin yx= for x0 360 gg . 360 0y x [2] (b) the point ( a, 0.5) is on the graph of \u00b0sin yx= . find the two possible values of a. a = or a = [2]", "7": "7 0607/23/m/j/18 \u00a9 ucles 2018 [turn over 13 the masses, m kg, of some watermelons are measured. the results are shown in the table. mass ( m kg) m81 0 1g m 1 10 1 1g m 1 11 2 1g m 1 12 4 1g m 1 14 8 1g frequency p 26 38 24 17 part of the histogram to show this information is shown below. 8010203040 10 12 mass (kg)mfrequency density 14 16 18 (a) complete the histogram. [2] (b) find the value of p. p = ... [1] questions 14 and 15 are printed on the next page.", "8": "8 0607/23/m/j/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.14 rearrange this formula to make x the subject. ybxcax=+ x = ... [3] 15 (a) solve logl og logx 32 25-= . x = ... [3] (b) solve log431 y=. y = ... [1]" }, "0607_s18_qp_31.pdf": { "1": "*6847148825* this document consists of 15 printed pages and 1 blank page. dc (st/sw) 153516/2 \u00a9 ucles 2018 [turn overcambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/31 paper 3 (core) may/june 2018 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.", "2": "2 0607/31/m/j/18 \u00a9 ucles 2018 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/31/m/j/18 \u00a9 ucles 2018 [turn over answer all the questions. 1 (a) work out. (i) ..1642 38- [1] (ii) ..52 34 1#- [1] (b) (i) work out .142 . [1] (ii) write 64% as a fraction in its lowest terms. [2] (c) write the following in order of size, starting with the smallest. 95 0.55 55.5% ... 1 ... 1 ... [1] smallest (d) (i) write 2076 in words. .. [1] (ii) write two million, five hundred and fifty thousand and two as a number. [1]", "4": "4 0607/31/m/j/18 \u00a9 ucles 2018 2 (a) a pack of 200 cards is 80 mm thick. find the thickness of 1 card. . mm [1] (b) write 358.297 (i) correct to 1 decimal place, [1] (ii) correct to 3 significant figures, [1] (iii) correct to the nearest 10. [1] (c) work out 59% of $348. $ [2] (d) divide 630 in the ratio 8 : 13. . : . [2] ", "5": "5 0607/31/m/j/18 \u00a9 ucles 2018 [turn over 3 food number of calories 1 bread roll 78 1 bagel 69 1 tomato 3 1 slice of chicken 60 1 slice of cheese 69 1 lettuce leaf 1 1 apple 53 (a) for lunch, clint has 1 bread roll, 1 lettuce leaf, 1 tomato, 2 slices of chicken and 1 apple. work out the total number of calories in clint\u2019s lunch. [2] (b) work out your answer to part (a) as a percentage of 2500. % [1] (c) a bagel costs $0.65 . find the greatest number of these bagels that clint can buy with $10. how much change does he receive? . bagels change = $ [3]", "6": "6 0607/31/m/j/18 \u00a9 ucles 2018 4 (a) find the lowest common multiple (lcm) of 7 and 8. [2] (b) find the highest common factor (hcf) of 18 and 48. [2] (c) jovana invested some money at a rate of 3% per year simple interest. at the end of 4 years the interest is $78. work out the amount that she invested. $ [3] (d) isabelle invests $800 at a rate of 3.2% per year compound interest. work out the value of the investment at the end of 2 years. $ [3] (e) change 8 kilometres per hour to metres per minute. .. metres per minute [2] ", "7": "7 0607/31/m/j/18 \u00a9 ucles 2018 [turn over 5 merel counts the number of three-letter words on every page of a book. her results are shown in the table. number of three-letter words on a page 5 7 8 12 13 16 number of pages (frequency) 10 16 15 13 9 6 (a) find the total number of pages in the book. [1] (b) write down the mode. [1] (c) find the median. [1] (d) find the mean. [2] (e) use the information in the table to complete the bar chart. 5 7 8 12 13 160246810121416 number of three-letter words on a pagenumber of pages [2] ", "8": "8 0607/31/m/j/18 \u00a9 ucles 2018 6 p mo nr 48\u00b0not to scales p, r and s lie on a circle, centre o. mpn is a tangent to the circle at p and angle rpn = 48\u00b0. (a) find the size of (i) angle opr , angle opr = [1] (ii) angle orp , angle orp = [1] (iii) angle por , angle por = [1] (iv) angle sor, angle sor = [1] (v) angle srp, angle srp = [1] (vi) angle osr. angle osr = [2] ", "9": "9 0607/31/m/j/18 \u00a9 ucles 2018 [turn over (b) op = 3 cm. find (i) the circumference of the circle, . cm [2] (ii) the length of the minor arc sr, . cm [2] (iii) the area of the circle, cm2 [2] (iv) the area of the minor sector sor. cm2 [2] ", "10": "10 0607/31/m/j/18 \u00a9 ucles 2018 7 (a) complete the mathematical name of each of these angles. ... angle ... angle ... angle [3] (b) not to scale110\u00b0 160\u00b0x\u00b0 95\u00b0110\u00b0135\u00b0 the diagram shows a hexagon. find the value of x. x = [3] ", "11": "11 0607/31/m/j/18 \u00a9 ucles 2018 [turn over 8 (a) on any day, the probability that the sun will shine is 0.64 . if the sun is shining, the probability that mees goes to the beach is 0.82 . if the sun is not shining, the probability that mees goes to the beach is 0.15 . (i) complete the tree diagram. sun is shining sun is not shining ..0.64 ...goes to the beach does not go to the beach goes to the beach does not go to the beach [3] (ii) find the probability that the sun is shining and mees does not go to the beach. [2] (b) on any day in june, the probability that it does not rain is 0.7 . there are 30 days in june. find the number of days that it is expected to rain in june. [2] ", "12": "12 0607/31/m/j/18 \u00a9 ucles 2018 9 a scientist measures the temperature at seven different heights above sea level. the table shows her results. height above sea level (h metres)0 500 1000 1500 2500 3000 5000 temperature ( t \u00b0c) 15 11 8.5 5 -1 -5 -17 (a) complete the scatter diagram. the first three points have been plotted for you. 0 \u20132 \u20134 \u20136 \u20138 \u201310 \u201312 \u201314 \u201316 \u2013181000 2000 3000 4000 5000ht 246810121416 [2] ", "13": "13 0607/31/m/j/18 \u00a9 ucles 2018 [turn over (b) what type of correlation is shown in the scatter diagram? [1] (c) find (i) the mean height, m [1] (ii) the mean temperature. ... \u00b0c [1] (d) (i) plot the mean point on the scatter diagram. [1] (ii) on the scatter diagram, draw a line of best fit. [2] (iii) use your line of best fit to estimate the temperature at a height of 4000 m. ... \u00b0c [1] ", "14": "14 0607/31/m/j/18 \u00a9 ucles 2018 10 (a) (i) solve. x23 151- [2] (ii) show your answer to part (a)(i) on this number line. 10 9 8 7 6 5 4 3 2 1 0 \u20131 \u20132x [1] (b) solve. xx35 43+= - x = [2] (c) expand the brackets and simplify. () () xx21 3 -+ [2] (d) simplify fully. (i) rr23# [1] (ii) rr 28 [1] ", "15": "15 0607/31/m/j/18 \u00a9 ucles 2018 11 \u20131010 0 6xy () xx x 21 21 0 f2=- +- (a) on the diagram, sketch the graph of () yxf= for x06gg . [2] (b) find the co-ordinates of the points where the graph crosses the x-axis. ( , ) and ( , ) [2] (c) find the co-ordinates of the local maximum. ( , ) [1] (d) (i) on the same diagram, draw the line yx 2=- . [2] (ii) solve. xx x 21 21 022-+ -= - x = . or x = . [2]", "16": "16 0607/31/m/j/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_s18_qp_32.pdf": { "1": "*4080524437* this document consists of 16 printed pages. dc (st/sw) 153517/2 \u00a9 ucles 2018 [turn overcambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/32 paper 3 (core) may/june 2018 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.", "2": "2 0607/32/m/j/18 \u00a9 ucles 2018 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/32/m/j/18 \u00a9 ucles 2018 [turn over answer all the questions. 1 (a) complete the statement. 6 weeks = ... days [1] (b) write in figures the number fifteen thousand and twenty seven. [1] (c) write (i) 144.1 correct to the nearest 10, [1] (ii) 5.5349 correct to 2 decimal places, [1] (iii) 50 617 correct to 2 significant figures. [1] (d) write 0.7 (i) as a fraction, [1] (ii) as a percentage. % [1] (e) find the value of 0.73. [1]", "4": "4 0607/32/m/j/18 \u00a9 ucles 2018 2 tam recorded the number of hours of homework he did each night for 25 nights. his results, in hours, are shown below. 4 1 4 3 2 3 4 2 1 1 3 2 1 2 1 1 3 5 4 1 3 3 1 3 4 (a) complete the frequency table. number of hours number of nights 1 2 3 4 5 [2] (b) which number of hours is the mode? .. hours [1] (c) draw a bar chart to show this information. 0 1 2 3 number of hoursnumber of nights 4 512345678910 [2]", "5": "5 0607/32/m/j/18 \u00a9 ucles 2018 [turn over (d) on one of the nights, tam did mathematics homework, english homework and history homework. the pie chart shows the time he spent on each subject. 80\u00b0 130\u00b0mathematicsnot to scale historyenglish (i) work out the fraction of the total time he spent on mathematics homework. give your answer in its simplest form. [2] (ii) tam spent 3 hours altogether on his homework that night. work out the time, in minutes, tam spent on english homework. . min [3]", "6": "6 0607/32/m/j/18 \u00a9 ucles 2018 3 \u201311234 1 2 3 4 5 6 7 \u20132 \u20133 \u201310 \u20132 \u20133xy p\u00b0t r (a) write down the co-ordinates of (i) t, ( , ) [1] (ii) r. ( , ) [1] (b) on the grid, draw the line of symmetry of the quadrilateral. [1] (c) measure the size of angle p. [1]", "7": "7 0607/32/m/j/18 \u00a9 ucles 2018 [turn over 4 in each part, give the mathematical name for the shape described. (a) a quadrilateral with each pair of opposite sides parallel. [1] (b) a triangle with exactly two sides equal in length. [1] (c) a polygon with 6 sides. [1] (d) a quadrilateral with all sides of equal length but not all angles equal. [1] (e) a solid shape with six faces. four of the faces are identical rectangles and the other two faces are identical squares. [1]", "8": "8 0607/32/m/j/18 \u00a9 ucles 2018 5 (a) a box contains 40 orange counters and 32 blue counters only. (i) write the ratio orange counters : blue counters in its simplest form. : [2] (ii) some of the orange counters are removed. the ratio orange counters : blue counters is now 1 : 2. work out how many orange counters have been removed. [2] (b) another box contains 6 white counters, 3 black counters and 2 red counters only. (i) one of the 11 counters is chosen from the box at random. write down the colour of the counter that is least likely to be chosen. [1] (ii) one of the 11 counters is chosen from the box at random. work out the probability that this counter is white. [1] (iii) one white counter is removed from the box of 11 counters. a counter is now chosen from the box at random. work out the probability that this counter is white. [1]", "9": "9 0607/32/m/j/18 \u00a9 ucles 2018 [turn over (c) a different box contains 180 counters. the counters are either yellow or green in the ratio yellow counters : green counters = 5 : 1. work out the number of counters of each colour. yellow ... green ... [2] 6 john and asif take part in a 30 km cycle race. (a) john starts his race at 10 15. he takes 121 hours to complete the race. (i) at what time does john complete the race? [1] (ii) work out john\u2019s average speed, in km/h, for the 30 km race. ... km/h [1] (b) asif completes the 30 km race at a speed of 16 km/h. work out the time, in hours and minutes, asif takes to complete the race. h min [3]", "10": "10 0607/32/m/j/18 \u00a9 ucles 2018 7 (a) find the missing terms in each of these sequences. (i) , 9, 17, 25, [2] (ii) , 8, 16, , 64 [2] (iii) 35, 25, 16, 8, , [2] (iv) , x24-, x39-, x41 4- , [2] (b) the nth term of another sequence is nn2+. find the first three terms of this sequence. ... , ... , ... [2] (c) find the nth term of this sequence. 1, 5, 9, 13, ... [2]", "11": "11 0607/32/m/j/18 \u00a9 ucles 2018 [turn over 8 (a) (i) rearrange this formula to make d the subject. cdr= d = ... [1] (ii) a circle has a circumference of 2 metres. work out the diameter of this circle. give your answer in centimetres, correct to the nearest whole number. .. cm [3] (b) a cd is a ring with inner radius 0.8 cm and outer radius 6 cm. 0.8 cm6 cmnot to scale find the area of the cd, shown shaded. cm2 [4]", "12": "12 0607/32/m/j/18 \u00a9 ucles 2018 9 (a) factorise completely. x12 16+ [2] (b) multiply out the brackets. ()xx23 5- [2] (c) solve. ()x82 34 8 += x = ... [3]", "13": "13 0607/32/m/j/18 \u00a9 ucles 2018 [turn over 10 a square has side 8 cm. a small square is drawn inside this larger square so that the corners of the small square touch the sides of the larger square. not to scale1 cm 1 cm1 cm 1 cm8 cm (a) (i) calculate the area of the shaded triangle. . cm2 [2] (ii) using your answer to part (a)(i) , calculate the area of the small square. . cm2 [2] (b) calculate the perimeter of the small square. .. cm [3]", "14": "14 0607/32/m/j/18 \u00a9 ucles 2018 11 the cumulative frequency curve shows the heights, in cm, of 200 girls. 120020406080100120140160180200 130 140 150 160 height (cm)cumulative frequency 170 180 190 (a) find the median height. .. cm [1] (b) work out the inter-quartile range of the heights. .. cm [2] (c) find the number of girls with a height of 160 cm or less. [1]", "15": "15 0607/32/m/j/18 \u00a9 ucles 2018 [turn over 12 (a) not to scale x\u00b0 3.5 m5 m the diagram shows a ladder, 5 m long, leaning against a vertical wall. the bottom of the ladder is on horizontal ground, 3.5 m from the wall. use trigonometry to find the value of x. x = ... [2] (b) a different ladder leans against the same wall. this ladder makes an angle of 49\u00b0 with the ground and touches the wall 4 m above the ground. use trigonometry to find the length of this ladder. include a labelled sketch in your working. m [4] questions 13 and 14 are printed on the next page.", "16": "16 0607/32/m/j/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.13 a painting is valued at $2400. the value of the painting increases by 5% each year. find the value of the painting at the end of 3 years. $ ... [4] 14 a curve has equation yx x62=+ -. (a) find the co-ordinates of the points where this curve crosses (i) the y-axis, ( , ) [1] (ii) the x-axis. ( , ) and ( , ) [2] (b) find the co-ordinates of the local minimum. ( , ) [2] (c) find the equation of the line of symmetry of the curve. [2]" }, "0607_s18_qp_33.pdf": { "1": "*3410304642* this document consists of 16 printed pages. dc (st/ct) 153518/2 \u00a9 ucles 2018 [turn overcambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/33 paper 3 (core) may/june 2018 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.", "2": "2 0607/33/m/j/18 \u00a9 ucles 2018 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/33/m/j/18 \u00a9 ucles 2018 [turn over answer all the questions. 1 (a) work out. ..36 25 1#+ . [1] (b) find. (i) 81 . [1] (ii) 812 . [1] (c) change 41 to a decimal. . [1] (d) write 56.3942 (i) correct to 2 decimal places, . [1] (ii) correct to 3 significant figures, . [1] (iii) correct to the nearest 10. . [1] (e) calculate the interest received when (i) $600 is invested for 3 years at a rate of 2% per year simple interest, $ [2] (ii) $600 is invested for 3 years at a rate of 2% per year compound interest. $ [3] ", "4": "4 0607/33/m/j/18 \u00a9 ucles 2018 2 here is a list of numbers. 9 12 35 41 56 (a) from the list of numbers above, write down (i) an even number, . [1] (ii) a prime number. . [1] (b) charee picks one of the five numbers from the list above at random. find the probability that this number is (i) an odd number, . [1] (ii) a multiple of 4, . [1] (iii) a factor of 18. . [1] ", "5": "5 0607/33/m/j/18 \u00a9 ucles 2018 [turn over 3 (a) three brothers, al, bob and cole, go to the cinema. their mother gives them $60 to share in the ratio of their ages. al : bob : cole = 15 : 16 : 17 al receives $18.75 . show that cole receives $21.25 . [2] (b) cinema tickets cost $14 each. al, bob and cole each buy a cinema ticket. find how much money al has left. $ [1] (c) popcorn (large box) $3.50 popcorn (medium box) $2.50 popcorn (small box) $1.50 water $2.00 cola $2.50 after paying for his cinema ticket, bob wants to buy a large box of popcorn and a cola. does he have enough money from his share of the $60? show how you decide. [3] ", "6": "6 0607/33/m/j/18 \u00a9 ucles 2018 4 here are the ages, in years, of 21 teachers. 26 31 28 64 42 35 58 60 32 49 53 38 29 47 26 48 33 24 63 32 51 (a) complete an ordered stem-and-leaf diagram, including the key, for these ages. key .. | .. represents .. [3] (b) for these ages, find (i) the range, . [1] (ii) the median, . [1] (iii) the upper quartile, . [1] (iv) the inter-quartile range. . [1] ", "7": "7 0607/33/m/j/18 \u00a9 ucles 2018 [turn over 5 4 3 2 1 \u20131\u20131 1 2 3 4 5 \u20132 \u20133 \u20134 \u20135 \u20132 \u20133 \u201340xy ab (a) write down the co-ordinates of point a and point b. a ( , ) b ( , ) [2] (b) find the co-ordinates of the midpoint of ab. ( , ) [1] (c) find the gradient of ab. . [2] (d) find the equation of the line ab. give your answer in the form ym xc+= . y = [2] ", "8": "8 0607/33/m/j/18 \u00a9 ucles 2018 6 (a) a triangle, a rectangle and a semicircle are joined to form this shape. b 11 cm 12 cm 9 cmc ea dnot to scale cd is the diameter of the semicircle. (i) show that the length of be is 15 cm. [2] (ii) find the perimeter of the shape abcde . .. cm [3] (iii) find the total area of the shape abcde . . cm2 [4] ", "9": "9 0607/33/m/j/18 \u00a9 ucles 2018 [turn over (b) the diagram shows two similar triangles, abc and dec . not to scalet cm 9.6 cm6.3 cm85\u00b0 39\u00b0 3.2 cm r cm 2.4 cmca b e d ab is parallel to ed. (i) find the value of r and the value of t. r = t = [3] (ii) find angle acb . angle acb = [1] (iii) find angle cde . angle cde = [1] ", "10": "10 0607/33/m/j/18 \u00a9 ucles 2018 7 eight people were asked their age and the number of attempts they took to pass their driving test. the results are shown in the table. age (years) 17 18 19 20 22 25 30 45 number of attempts 1 2 3 3 6 5 4 8 (a) complete the scatter diagram. the first 4 points have been plotted for you. 01 5 10 15 20 25 30 35 40 452345678 number of attempts age (years) [2] (b) find (i) the mean age, . [1] (ii) the mean number of attempts. . [1] ", "11": "11 0607/33/m/j/18 \u00a9 ucles 2018 [turn over (c) (i) on the scatter diagram, plot the mean point. [1] (ii) on the scatter diagram, draw a line of best fit. [2] (iii) use your line of best fit to estimate the number of attempts a 40 year old person might take to pass their driving test. . [1] ", "12": "12 0607/33/m/j/18 \u00a9 ucles 2018 8 (a) here are six venn diagrams. a diagram 1b\u222a a diagram 2b\u222a a diagram 3b\u222a a diagram 4b\u222a a diagram 5b\u222a a diagram 6b\u222a complete the table. shaded areavenn diagram number ab, 3 ab+ al ab+ l [3] ", "13": "13 0607/33/m/j/18 \u00a9 ucles 2018 [turn over (b) (i) 20 students are asked if they study history ( h) or geography ( g). 10 study history, 12 study geography and 3 study both history and geography. complete the venn diagram. \u222a h g [3] (ii) write down the number of students who do not study history or geography. . [1] ", "14": "14 0607/33/m/j/18 \u00a9 ucles 2018 9 the diagram shows a bridge for a model train set. the bridge is a cuboid with two identical tunnels. each tunnel is a cuboid. 38 cmnot to scale 2 cm 2 cm8 cm 2 cm7 cm12 cm (a) find the shaded area. . cm2 [4] (b) find the volume of the bridge. . cm3 [2] ", "15": "15 0607/33/m/j/18 \u00a9 ucles 2018 [turn over 10 (a) solve. x38 2+= x = [2] (b) (i) solve. x 32 3g- . [2] (ii) show your answer to part (b)(i) on the number line. x \u20136 \u20135 \u20134 \u20133 \u20132 \u20131 0 1 2 3 4 5 6 [1] (c) simplify. ab ab 32 3 ++ - . [2] (d) expand the brackets and simplify. () () xx31 24-+ . [2] (e) factorise completely. xy xy323 2- . [2] (f) pa b 322=+ (i) find the value of p when a2= and b 1=- . p = [2] (ii) rearrange the formula to make a the subject. a = [2] question 11 is printed on the next page.", "16": "16 0607/33/m/j/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.11 xy 50 10 \u2013200 () () () xx x 25 8 f=- - (a) on the diagram, sketch the graph of () yxf= for x01 0 gg . [2] (b) find the co-ordinates of the point where the graph crosses the y-axis. ( , ) [1] (c) write down the x co-ordinate of each point where the graph crosses the x-axis. x = and x = [2] (d) find the co-ordinates of the local minimum. ( , ) [2] (e) () . x 14 10 gx=- find the x co-ordinate of each point of intersection of () yxf= and () yxg= . x = and x = [2] " }, "0607_s18_qp_41.pdf": { "1": "this document consists of 19 printed pages and 1 blank page. dc (sc/cgw) 153519/3 \u00a9 ucles 2018 [turn over *7051052947* cambridge international mathematics 0607/41 paper 4 (extended) may/june 2018 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/41/m/j/18 \u00a9 ucles 2018 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/41/m/j/18 \u00a9 ucles 2018 [turn over answer all the questions. 1 \u22122 2810 6 4 279 5 3 1a t b 4 6 8 1 3 5 7 109xy \u22124 \u22126 0\u22121 \u22123 \u22125 (a) describe fully the single transformation that maps (i) triangle t onto triangle a, . . [2] (ii) triangle t onto triangle b. . . [2] (b) enlarge triangle t with centre (5, 0) and scale factor 2. [2] (c) stretch triangle t with the y-axis invariant and factor 2. [2]", "4": "4 0607/41/m/j/18 \u00a9 ucles 2018 2 conrad, delia and eli share $8000 in the ratio conrad : delia : eli = 5 : 7 : 8 . (a) show that eli receives $3200. [2] (b) conrad buys a toy for $65. he sells it for $55. calculate the percentage loss. . % [3] (c) delia invests $2500 at a rate of 2.5% per year simple interest. calculate the interest delia has at the end of 8 years. $ [2] (d) eli invests $2400 at a rate of 2.4% per year compound interest. calculate the interest eli has at the end of 8 years. $ [3] (e) conrad buys a coat in a sale. the sale price is $79.80 after a reduction of 5%. calculate the original price of the coat. $ [3]", "5": "5 0607/41/m/j/18 \u00a9 ucles 2018 [turn over 3 (a) show that the point (3, -1) lies on the line yx27=- . [1] (b) find the co-ordinates of the points where the line yx84=+ crosses (i) the x-axis, ( , ) [1] (ii) the y-axis. ( , ) [1] (c) find the equation of the straight line that passes through the points (1, 2) and (4, 11). give your answer in the form ym xc=+ . y = [3]", "6": "6 0607/41/m/j/18 \u00a9 ucles 2018 4 (a) the list shows the temperature, in degrees celsius, at noon in paris on each of 14 days. 19 18 21 21 23 21 22 20 24 25 22 21 19 17 (i) construct an ordered stem and leaf diagram to show this information, including the key. key ... ... = [3] (ii) find the median and the lower quartile. median = lower quartile = [2] (iii) find the angle on a pie chart that represents the number of days the temperature was less than 20 \u00b0c. .. [2] (b) 200 students estimated the capacity, x litres, of a container. the results are shown in the cumulative frequency curve. 200 x150 100 50 0 0 1 2 3 capacity (litres)4 5cumulative frequency", "7": "7 0607/41/m/j/18 \u00a9 ucles 2018 [turn over find (i) the median, litres [1] (ii) the inter-quartile range, litres [2] (iii) the number of students who estimated more than 3.5 litres. . [2] (c) 200 students estimated the area, y m2, of a field. the table shows the results. area ( y m2) y 100 2001g y 200 2501g y 250 4001g frequency 25 100 75 (i) calculate an estimate of the mean. m2 [2] (ii) complete the histogram to show the information in the table. 2 y1.5 1 0.5 0100 200 area (m2)300 400frequency density [4]", "8": "8 0607/41/m/j/18 \u00a9 ucles 2018 5 2 xy 1 0 180 360 540 \u22121 \u22122 () \u00b0sin xxf= ()\u00b0logsinxx1g=j lkkn poo (a) (i) on the diagram, sketch the graph of () yxf= for x0 540 gg . [2] (ii) write down the range of ()xf for x0 540 gg . . [1] (b) (i) on the same diagram, sketch the graph of () yxg= for values of x between 0 and 540. [2] (ii) give a reason why there are no values of ()xg for x 180 360 gg . . [1] (iii) write down the co-ordinates of the minimum points on the graph of () yxg= . ( , ) and ( , ) [2] (iv) write down the equations of the four asymptotes to the graph of () yxg= . , , , [2]", "9": "9 0607/41/m/j/18 \u00a9 ucles 2018 [turn over (c) (i) () () kkfg= and k09 0 gg . find the value of k. k = [1] (ii) solve the inequality () () xxfg2 for values of x between 0 and 540. . [2] (iii) j is an integer. the equation ()xjf= has no solutions. the equation ()xjg= has no solutions. write down a possible value of j. j = [1]", "10": "10 0607/41/m/j/18 \u00a9 ucles 2018 6 (a) 12 cm 40 cmnot to scale (i) the rectangle can be made into a hollow cylinder with height 40 cm. (a) show that the radius of this cylinder is 1.910 cm, correct to 3 decimal places. [2] (b) calculate the volume of this cylinder. .. cm3 [2] (ii) the rectangle can also be made into a hollow cylinder with height 12 cm. calculate the difference between the volumes of this cylinder and the cylinder in part (i) . give your answer correct to the nearest 10 cm3. .. cm3 [4]", "11": "11 0607/41/m/j/18 \u00a9 ucles 2018 [turn over (b) a model of a car is mathematically similar to the actual car. the volume of the model is 75 cubic centimetres and the volume of the actual car is 4.8 cubic metres . the scale is model : actual = 1 : n . find the value of n. n = [4]", "12": "12 0607/41/m/j/18 \u00a9 ucles 2018 7 1 cent 1 cent 5 cents 10 cents 10 cents 10 cents the diagram shows coins of values 1 cent, 5 cents and 10 cents. two of these coins are chosen at random. find the probability that (a) each coin has a value of less than 10 cents, . [2] (b) the total value of the two coins is 11 cents, . [3] (c) the total value of the two coins is more than 2 cents. . [2]", "13": "13 0607/41/m/j/18 \u00a9 ucles 2018 [turn over 8 every year the value of xavier\u2019s car decreases by 10%. the value is now $12 960. (a) calculate the value of the car 2 years ago. $ [2] (b) calculate the number of complete years it will take for the value to decrease from $12 960 to less than $6480. . [3]", "14": "14 0607/41/m/j/18 \u00a9 ucles 2018 9 not to scalee a b cd13 cm 15 cm50\u00b0 70\u00b0 in the diagram, abc is a straight line, ae = be = 13 cm and bc = 15 cm. angle eab = 70\u00b0, angle ebd = 90\u00b0 and angle bed = 50\u00b0. calculate (a) the length of the perpendicular line from e to ab, ... cm [2] (b) the length bd, bd = .. cm [2]", "15": "15 0607/41/m/j/18 \u00a9 ucles 2018 [turn over (c) the length cd, cd = .. cm [4] (d) the area of the quadrilateral acde . .. cm2 [3]", "16": "16 0607/41/m/j/18 \u00a9 ucles 2018 10 (a) sam walks for 30 minutes at 4 km/h and then runs 5 km in 25 minutes. calculate his average speed. give your answer in km/h. km/h [3] (b) (i) tami walks for 10 minutes at x km/h and then runs y kilometres in z minutes. find her average speed in terms of x, y and z. give your answer in km/h, in its simplest form. km/h [3] (ii) when tami walks for 10 minutes at 3 km/h and then runs for 20 minutes, her average speed is 11 km/h. find the distance tami runs. ... km [2]", "17": "17 0607/41/m/j/18 \u00a9 ucles 2018 [turn over (c) urs walks for t minutes at 3 km/h and then runs for ()t10+ minutes at 7 km/h. (i) show that his average speed is tt 553 5 ++ km/h. [3] (ii) when the average speed is 521 km/h, find the value of t. t = [2]", "18": "18 0607/41/m/j/18 \u00a9 ucles 2018 11 ()x 10 fx= ()xx 21 g=- (a) find the value of g(3). . [1] (b) find the range of f (x) for the domain { -1, 0, 1, 2}. { ... } [2] (c) find x when ()x 12 g= . x = [2] (d) the graph of () yxg= is translated by the vector 2 3eo onto the graph of h( x). find h( x). give your answer in its simplest form. h(x) = [3]", "19": "19 0607/41/m/j/18 \u00a9 ucles 2018 (e) find ()xf1-. ()xf1=- [2] (f) (()) tan x 1 g= and \u00b0\u00b0x 0 180 gg . find the two values of x. x = or x = [3]", "20": "20 0607/41/m/j/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_s18_qp_42.pdf": { "1": "this document consists of 20 printed pages. dc (sc/cgw) 153520/3 \u00a9 ucles 2018 [turn overcambridge international examinations cambridge international general certificate of secondary education *6395456361* cambridge international mathematics 0607/42 paper 4 (extended) may/june 2018 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.", "2": "2 0607/42/m/j/18 \u00a9 ucles 2018 formula list for the equation ax bxc02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area =a c bcb a", "3": "3 0607/42/m/j/18 \u00a9 ucles 2018 [turn over answer all the questions. 1 (a) work out. .315402 23 [1] (b) write 130.47 correct to (i) one decimal place, [1] (ii) one significant figure. [1] (c) work out 23% of $76.80 . $ [2] (d) $4200 is shared in the ratio 3 : 4 : 6 : 8 . find the difference between the largest share and the smallest share. $ [3] (e) write down an irrational number less than 10. [1] (f) work out ..7311 01 56 1021## +-- . give your answer in standard form. [2]", "4": "4 0607/42/m/j/18 \u00a9 ucles 2018 2 5 \u22125\u22125 0 5y x ()()fxxx 192=-- (a) on the diagram, sketch the graph of () yxf= , for values of x between -5 and 5. [3] (b) write down the equations of the three asymptotes. ..., ..., ... [3] (c) the line yx= intersects the curve ()yxx192=-- three times. find the values of the x co-ordinates of the points of intersection. x = . or x = . or x = . [3]", "5": "5 0607/42/m/j/18 \u00a9 ucles 2018 [turn over 3 (a) y varies directly as the square root of x. y = 32 when x = 16. (i) find y in terms of x. y = [2] (ii) find the value of y when x = 4. y = [1] (iii) find x in terms of y. x = [2] (b) p varies inversely as q2+. p = 3 when q = 2. find the value of p when q = 4. p = [3]", "6": "6 0607/42/m/j/18 \u00a9 ucles 2018 4 (a) the mass, x grams, of each of 100 oranges is found. the results are shown in the table. mass ( x grams) frequency x0 1001g 4 x 100 1401g 14 x 140 1801g 22 x 180 2501g 35 x 250 3001g 25 (i) calculate an estimate of the mean mass of the oranges. . g [2] (ii) two of these oranges are chosen at random. calculate the probability that they both have a mass of 140 g or less. [2] (iii) the oranges with a mass of 140 g or less are removed. from the remaining oranges, two are chosen at random. calculate the probability that one orange has a mass of 250 g or less and the other has a mass of more than 250 g. [3]", "7": "7 0607/42/m/j/18 \u00a9 ucles 2018 [turn over (b) (i) complete the frequency density column in this table. mass ( x grams) frequency frequency density x0 1001g 4 x 100 1401g 14 x 140 1801g 22 x 180 2501g 35 x 250 3001g 25 [2] (ii) on the grid, draw a histogram to show this information. 50 100 00 150 mass (grams)frequency density 200x 250 300 [4]", "8": "8 0607/42/m/j/18 \u00a9 ucles 2018 5 p r ba not to scale cd qs 12 m30 m16 m 24 m 40 m18 m in the diagram, abcd is a rectangle. (a) find ps. ps = m [2] (b) find angle brs. angle brs = [2] (c) find the perimeter of pqrs . m [3]", "9": "9 0607/42/m/j/18 \u00a9 ucles 2018 [turn over (d) find the shaded area. ... m2 [3] (e) explain why triangle asp is similar to triangle bsr. . . [2]", "10": "10 0607/42/m/j/18 \u00a9 ucles 2018 6 \u22122 2810 6 4 2a \u22122 \u22124 \u22126 \u22128 \u2212104 6 8xy \u22124 \u22126 0 \u22128", "11": "11 0607/42/m/j/18 \u00a9 ucles 2018 [turn over (a) translate triangle a with vector 7 3- -eo . label the image b. [2] (b) rotate triangle a through 90\u00b0 anti-clockwise about ( -1, 2). label the image c. [2] (c) describe fully the single transformation that maps triangle c onto triangle b. . . [3] (d) enlarge triangle a scale factor -2 with centre (3, 1). label the image d. [2] (e) describe fully the single transformation that maps triangle d onto triangle a. . . [2]", "12": "12 0607/42/m/j/18 \u00a9 ucles 2018 7 in this question, all lengths are measured in millimetres. 44 55 28a 5555 a small plastic cup, a, is shown in this diagram. 44 55 28a 5555 these plastic cups are stacked as shown in the diagram. (a) find the height of a stack of 8 of these cups. . mm [2] (b) find the number of these cups in a stack that has a total height of 105 mm. [2] (c) a similar cup, b, has base diameter 42 mm. find the height of this cup. . mm [2]", "13": "13 0607/42/m/j/18 \u00a9 ucles 2018 [turn over (d) 2r + 2a h 2r the formula for the volume of a similar cup is r()vhr ara 33322 =++. (i) for cup a, show that a = 8 mm. [2] (ii) find the volume of cup a. mm3 [2] (iii) find the volume of cup b. mm3 [3] (iv) rearrange r()vhr ara 33322 =++ to make h the subject. h = [2] ", "14": "14 0607/42/m/j/18 \u00a9 ucles 2018 8 b a c 120\u00b0not to scale 36\u00b0 o d e f a, b, c and d lie on a circle, centre o. def is a tangent to the circle at d. aocf and bce are straight lines. (a) complete the statement. angle ode = 90\u00b0 because . . [1] (b) find the value of (i) angle aod , angle aod = [2] (ii) angle odc , angle odc = [2]", "15": "15 0607/42/m/j/18 \u00a9 ucles 2018 [turn over (iii) angle abc , angle abc = [1] (iv) angle cfd , angle cfd = [1] (v) angle cab . angle cab =\t [1]", "16": "16 0607/42/m/j/18 \u00a9 ucles 2018 9 ab c8.2 cmnot to scale9.1 cm 11 cm (a) show that angle . bac 470\u00b0 = , correct to 1 decimal place. [3] (b) use the sine rule to find angle abc . angle abc =\t [3]", "17": "17 0607/42/m/j/18 \u00a9 ucles 2018 [turn over (c) find the area of triangle abc . . cm2 [2] (d) find the length of the perpendicular from b to ac. .. cm [2]", "18": "18 0607/42/m/j/18 \u00a9 ucles 2018 10 wasim sprays different amounts of fertiliser on some seedlings. he measures the amount, x millilitres, sprayed on each seedling. a week later he measures the height, y centimetres, of each seedling. his results are shown in the table. amount of fertiliser ( x ml)1 3 5 7 10 14 18 25 30 35 40 height ( y cm) 15.1 15.6 16.5 16.6 17 19.8 21 25.1 28.8 28.6 29.1 (a) (i) complete the scatter diagram. the first four points have been plotted for you. 30y x28 26 24 22 20 18 16 14 0 10 20 30 amount of fertiliser (ml)40height (cm) [3]", "19": "19 0607/42/m/j/18 \u00a9 ucles 2018 [turn over (ii) what type of correlation is shown by the scatter diagram? [1] (b) find (i) the mean amount of fertiliser, ... ml [1] (ii) the mean height. .. cm [1] (c) (i) find the equation of the regression line in the form ym xc=+ . y = [2] (ii) use your answer to part (c)(i) to estimate the height of a seedling when the amount of fertiliser is 20 ml. .. cm [1] (iii) write down the units of m in the equation of the regression line, ym xc=+ . [1] question 11 is printed on the next page.", "20": "20 0607/42/m/j/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.11 ()xx 27 f=- ()xxg= ()xx1h= , x0=y (a) (i) find f (3). [1] (ii) solve ()x 1 f=. x = [2] (b) find ()xf1-. ()xf1- = [2] (c) (i) find (())xfg in terms of x. [1] (ii) solve (())x 5 fg =. x = [3] (d) (i) find ((()))x hgf in terms of x. [2] (ii) find an inequality in terms of x for which ((()))x hgf exists. [2]" }, "0607_s18_qp_43.pdf": { "1": "*6501475003* this document consists of 20 printed pages. dc (leg/sg) 153521/3 \u00a9 ucles 2018 [turn overcambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/43 paper 4 (extended) may/june 2018 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.", "2": "2 0607/43/m/j/18 \u00a9 ucles 2018 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/43/m/j/18 \u00a9 ucles 2018 [turn over answer all the questions. 1 gunter keeps chickens. he records the number of eggs he collects each day for 31 days. these are the results. number of eggs10 11 12 13 14 15 16 17 18 19 20 number of days5 3 2 3 2 3 2 4 4 1 2 (a) write down the range of the numbers of eggs. [1] (b) find the inter-quartile range. [2] (c) write down the mode. [1] (d) find the median. [1] (e) find the mean. [2] (f) explain why the mode is not the best measure of average to represent these results. .. [1]", "4": "4 0607/43/m/j/18 \u00a9 ucles 2018 2 flavia makes china cats. they each cost $22.60 to make. (a) flavia sells some of them to ari. she makes a profit of 35% on each cat. calculate the price ari pays for each cat. $ ... [2] (b) ari sells each cat for $43. calculate ari\u2019s percentage profit. % [3] (c) jean buys 92 of flavia\u2019s cats. this is 15% more than the number ari bought. calculate the number of cats that ari bought. [3] (d) jean bought the cats for $32 each. he sells some of the cats for $45 each. for the rest of the cats he reduces the price by 5% each day. find the number of reductions he has made when the price first falls below $32. [3]", "5": "5 0607/43/m/j/18 \u00a9 ucles 2018 [turn over 3 \u20137\u20136\u20135\u20134\u20133\u20132\u2013112345678910 \u20133 \u20132 \u20131 1 0 2 3 4 5 6 7 8 910y xa b (a) draw the image of triangle a after a translation by the vector 3 7-cm . [2] (b) draw the image of triangle b after a stretch, factor 3 and the x-axis invariant. [2] (c) describe fully the single transformation that maps triangle a onto triangle b. .. .. [3]", "6": "6 0607/43/m/j/18 \u00a9 ucles 2018 4 hamid records the population density, p persons/km2, in ten regions of the city in which he lives. he also records the distance, d km, of each region from the city centre. the results are shown in the table. region a b c d e f g h i j distance ( d km) 0.8 1.7 3.1 4.1 3.5 2.8 4.6 3.7 1.9 5.1 population density (p persons/km2)5600 4800 3600 4500 2800 3300 1100 2300 3900 800 (a) complete the scatter diagram. the first four points have been plotted for you. 6000 5000 4000 3000 2000 1000 0 0 1 2 3 distance (km)population density (persons/km2) 4 5 6p d [3] (b) (i) what type of correlation is shown in your scatter diagram? [1] (ii) which region fits this model of correlation least well? region ... [1]", "7": "7 0607/43/m/j/18 \u00a9 ucles 2018 [turn over (c) (i) calculate the equation of the regression line in the form p = md + c. p = ... [2] (ii) use this equation to estimate the population density of a region 2.4 km from the city centre. .. persons/km2 [1] (iii) why would it not be sensible to use this equation to estimate the population density of a region 6.3 km from the city centre? .. [1]", "8": "8 0607/43/m/j/18 \u00a9 ucles 2018 5 \u20136 \u20131010 6 0y x f(x) = xxxx 625 22 +--+ ^ ^ hh (a) on the diagram, sketch the graph of y = f(x) for values of x between -6 and 6. [3] (b) find the co-ordinates of the local maximum. ( ... , ... ) [2] (c) find the equations of the three asymptotes to the graph of y = f(x) . , , [3] (d) the equation f( x) = k has no solutions. find the range of values of k. [2]", "9": "9 0607/43/m/j/18 \u00a9 ucles 2018 [turn over (e) g(x) = x1+ (i) solve f( x) = g(x). x = .. or x = .. [2] (ii) solve the inequality f( x) 2 g(x). [2] ", "10": "10 0607/43/m/j/18 \u00a9 ucles 2018 6 oy x65\u00b0125\u00b0north north not to scale 80 km 140 km a cb a ship sails 80 km on a bearing of 065\u00b0 from a to b. it then sails 140 km on a bearing of 125\u00b0 from b to c. (a) find ab as a column vector with the components in kilometres. fp [4]", "11": "11 0607/43/m/j/18 \u00a9 ucles 2018 [turn over (b) find ac as a column vector with the components in kilometres. fp [5] (c) the ship sails directly back from c to a. using your answer to part (b) , calculate (i) the distance the ship sails from c to a, . km [2] (ii) the bearing of a from c. [3]", "12": "12 0607/43/m/j/18 \u00a9 ucles 2018 7 d a e b cf105\u00b0 0.6 m0.8 m 1.2 mnot to scale abcdef is a solid triangular prism. (a) calculate the volume of the prism. ... m3 [3] (b) calculate the total surface area of the prism. ... m2 [5]", "13": "13 0607/43/m/j/18 \u00a9 ucles 2018 [turn over (c) abcdef is made of metal and has a mass of 2170 kg. it is melted down and made into prisms similar to abcdef . each of these prisms has a mass of 2.17 kg. calculate the total surface area of each of these smaller prisms. ... m2 [3]", "14": "14 0607/43/m/j/18 \u00a9 ucles 2018 8 rashid takes a language examination that has three tests. the probability that rashid passes the listening and reading test is 0.9 . the probability that rashid passes the speaking test is 0.8 . the probability that rashid passes the writing test is 0.7 . (a) complete the tree diagram to show the probabilities of passing (p) and failing (f) each part. listening speaking writing and reading p p pf f fp f. .0.8 0.9 .. . .p f. . p f. . p f. . [3]", "15": "15 0607/43/m/j/18 \u00a9 ucles 2018 [turn over (b) to pass the whole examination rashid has to pass all three tests. calculate the probability that he passes the whole examination. [2] (c) if rashid only fails one test, he can take that test again. calculate the probability that rashid needs to take one test again. [4]", "16": "16 0607/43/m/j/18 \u00a9 ucles 2018 9 pattern 1 pattern 2 pattern 3 pattern 4 (a) complete the table for the sequence of patterns above. pattern number 1 2 3 4 5 6 number of grey tiles 1 1 9 9 number of white tiles 0 4 4 16 total number of tiles 1 5 13 [3] (b) find the number of each colour of tiles in (i) pattern 15, grey ... white ... [2] (ii) pattern 20. grey ... white ... [2]", "17": "17 0607/43/m/j/18 \u00a9 ucles 2018 [turn over (c) find an expression, in terms of n, for the total number of tiles in pattern n. [2]", "18": "18 0607/43/m/j/18 \u00a9 ucles 2018 10 isabel drives from geneva to rome, a distance of 930 km. her average speed is x km/h. (a) write down an expression, in terms of x, for the time, in hours, the journey takes. h [1] (b) she returns from rome to geneva along the same route at an average speed of ( x + 5) km/h. the journey takes 21 hour less than the journey from geneva to rome. (i) write down an equation, in terms of x, and show that it simplifies to x2 + 5x \u2013 9300 = 0. [3] (ii) solve this equation. give your answers correct to 1 decimal place. x = ... or x = ... [3] (iii) find the time taken for the journey from rome to geneva in hours and minutes. ... h ... min [2]", "19": "19 0607/43/m/j/18 \u00a9 ucles 2018 [turn over 11 not to scale xbb dy ca a, b, c and d are points on the circle. abx, cdx , ayd and byc are straight lines. (a) (i) explain why triangle adx is similar to triangle cbx. .. .. .. [2] (ii) use part (a)(i) to show that xa # xb = xc # xd [1] (b) xb = 6 cm, dc = 5 cm and xd = 7 cm. calculate the length ab. . cm [2] (c) find the value of these fractions. (i) area of triangle adx area of triangle cbx [1] (ii) area of triangle ayb area of triangle cyd [1] question 12 is printed on the next page.", "20": "20 0607/43/m/j/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.12 f(x) = 2x + 1 g(x) = 4 \u2013 3 x h(x) = 2x \u2013 1 (a) find h( -2). [1] (b) find g-1(x). g-1(x) = ... [2] (c) find g(f(3)). [2] (d) find and simplify g(g( x)). [2] (e) find h-1(7). ... [2] (f) write as a single fraction in its simplest form. fgxx11+^^hh [3]" }, "0607_s18_qp_51.pdf": { "1": "*9594950325* this document consists of 7 printed pages and 1 blank page. dc (ks) 153522/2 \u00a9 ucles 2018 [turn overcambridge international mathematics 0607/51 paper 5 (core) may/june 2018 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/51/m/j/18 \u00a9 ucles 2018 answer all the questions. investigation largest products this investigation looks at finding the largest product when two or more positive integers have a given sum. for the positive integers 2 and 5 \u2022 the sum 2 + 5 is 7 \u2022 the product 2 \u00d7 5 is 10. 1 (a) complete this table for all the different pairs of positive integers that have a sum of 8. integers sum product 1 8 2 8 3 8 4 4 8 16 write down the calculation that gives the largest product. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (b) complete this table for all the different pairs of positive integers that have a sum of 10. note that 3 and 7 is the same pair as 7 and 3. integers sum product 10 10 3 7 10 21 10 10 write down the calculation that gives the largest product. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "3": "3 0607/51/m/j/18 \u00a9 ucles 2018 [turn over (c) find the largest product of two positive integers that have a sum of 6. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (d) use your answers to part (a) , part (b) and part (c) to help you complete the table. sum 6 8 10 12 14 largest product 49 (e) (i) the sum of two positive integers is s. s is an even number. find an expression, in terms of s, for the largest product of the two integers. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (ii) the sum of two positive integers is 62. find the largest product of the two integers. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (f) the sum of two positive integers is s. s is an even number. the largest product of the two integers is 576. find the value of s. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "4": "4 0607/51/m/j/18 \u00a9 ucles 2018 2 (a) complete this table for all the different pairs of positive integers that have a sum of 9. note that 2 and 7 is the same pair as 7 and 2. integers sum product 9 9 9 9 write down the calculation that gives the largest product. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (b) find the largest product of two positive integers that have a sum of 7. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd ", "5": "5 0607/51/m/j/18 \u00a9 ucles 2018 [turn over (c) use your answers to part (a) and part (b) to help you complete the table. sum 7 9 11 13 101 largest product 30 (d) the sum of two positive integers is s. s is an odd number. (i) explain why the largest product of the two integers is always even. ... ... (ii) find an expression, in terms of s, for the largest product of the two integers. do not simplify your answer. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "6": "6 0607/51/m/j/18 \u00a9 ucles 2018 3 (a) three positive integers have a sum of 6. complete the table for all the different sets of positive integers that have a sum of 6. writing the positive integers in a different order does not give a different set. integers sum product 6 6 6 write down the calculation that gives the largest product. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (b) look at how you found the largest product in part (a) and in question 1(a) . four positive integers have a sum of 40. show that the largest product of these four integers is 10 000.", "7": "7 0607/51/m/j/18 \u00a9 ucles 2018 (c) complete the table. sum 6 40 15 24 number of positive integers in the sum3 4 5 6 largest product 10 000 (d) n integers have a sum of 40, where n is a factor of 40. find the value of the largest product of the n integers. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "8": "8 0607/51/m/j/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_s18_qp_52.pdf": { "1": "*5174399737* this document consists of 7 printed pages and 1 blank page. dc (ce/sw) 153512/2 \u00a9 ucles 2018 [turn overcambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/52 paper 5 (core) may/june 2018 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.", "2": "2 0607/52/m/j/18 \u00a9 ucles 2018 answer all the questions. investigation tile patterns this investigation looks at the number of grey tiles and the number of white tiles in a sequence of square patterns. all the tiles are the same size and each is a square. the grey tiles and white tiles make borders around a single grey tile. the single grey tile is the first grey border. the first white border is 8 white tiles surrounding the grey tile. the second grey border is 16 grey tiles surrounding the 8 white tiles. 1 (a) on this grid, complete the diagram to show the second white border. ", "3": "3 0607/52/m/j/18 \u00a9 ucles 2018 [turn over (b) on this grid, complete the diagram to show the third grey border. 2 this question looks at the patterns that finish with a white border. pattern finishes withnumber of white tiles in bordertotal number of white tiles in pattern 1st white border 8 8 2nd white border 32 3rd white border 72 4th white border 128 (a) complete the table.", "4": "4 0607/52/m/j/18 \u00a9 ucles 2018 (b) the values in the last column are the first four terms of a sequence. (i) write each term as a multiple of 8. 8 = 8 # 32 = 8 # 72 = 8 # 128 = 8 # (ii) the numbers that are multiplied by 8 also form a sequence. write down the name for this sequence of numbers. ... (iii) write down an expression, in terms of n, for the total number of white tiles in the pattern that finishes with the nth white border. ... (c) here is the pattern that finishes with the first white border. there are 3 white tiles along one side. (i) complete the table. pattern finishes withnumber of white tiles along one side 1st white border 3 2nd white border 3rd white border 4th white border", "5": "5 0607/52/m/j/18 \u00a9 ucles 2018 [turn over (ii) the numbers of white tiles along one side form a sequence. find an expression, in terms of n, for the number of white tiles along one side of the pattern that finishes with the nth white border. ... (iii) use your answer to part(c)(ii) to write down an expression, in terms of n, for the total number of all tiles in the pattern that finishes with the nth white border. ... (d) use your answers to part (c)(iii) and part (b)(iii) to show that an expression for the total number of grey tiles in the pattern that finishes with the nth white border is 8n2 \u2013 8n + 1.", "6": "6 0607/52/m/j/18 \u00a9 ucles 2018 3 a workman uses the method of question 2 to cover a square floor completely with tiles. the first tile is grey and the final border is white. (a) the square floor measures 5.7 m by 5.7 m. each tile measures 30 cm by 30 cm. (i) work out the number of tiles along one side of the floor. ... (ii) use your result from question 2(c)(ii) to show that this is the 5th white border. (iii) work out the number of white tiles and the number of grey tiles that the workman needs to cover the floor completely. number of white tiles = ... number of grey tiles = ... (iv) tiles are sold in packs of 20 white tiles and packs of 20 grey tiles. find the number of packs of white tiles and the number of packs of grey tiles that the workman needs. number of packs of white tiles = ... number of packs of grey tiles = ...", "7": "7 0607/52/m/j/18 \u00a9 ucles 2018 (b) the workman tiles a different square floor. he uses the same method of tiling, starting with a grey tile. he buys enough packs of 20 grey tiles and packs of 20 white tiles to cover the floor completely. explain why the workman will have some grey tiles left over, whatever the size of the square floor. ... ... ... ...", "8": "8 0607/52/m/j/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_s18_qp_53.pdf": { "1": "this document consists of 7 printed pages and 1 blank page. dc (leg/sg) 153610/1 \u00a9 ucles 2018 [turn over *5213851942* cambridge international mathematics 0607/53 paper 5 (core) may/june 2018 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/53/m/j/18 \u00a9 ucles 2018 answer all the questions. investigation estimating r this investigation is about using relative frequency to estimate the value of r. area of rectangle = length # width. area, a, of circle radius r is a= rr2. lee draws circles on rectangular pieces of paper. he drops grains of rice at random onto the pieces of paper. he counts the number of grains of rice inside each circle. 1 lee draws a circle of radius 5 cm on a rectangular piece of paper measuring 40 cm by 20 cm. 5 cm40 cm 20 cmnot to scale (a) (i) find the area of the rectangle. ... (ii) the probability, p, that a grain of rice lands inside the circle is p = area of circle area of rectangle. the area of the circle is 25 # r. show that p is approximately 0.098 for this piece of paper. (b) lee drops 10 grains of rice at random onto the piece of paper. the diagram shows the result. not to scale key: represents one grain of rice.", "3": "3 0607/53/m/j/18 \u00a9 ucles 2018 [turn over (i) how many of the grains of rice are inside the circle? ... (ii) the relative frequency that a grain of rice is inside the circle = number of grains of rice inside the circle total number of grains of rice dropped. find the relative frequency that a grain of rice is inside the circle. ... (c) lee drops 10 more grains of rice at random onto the piece of paper. not to scale show that the relative frequency that a grain of rice is inside the circle is 0.15 . (d) the relative frequency that a grain of rice is inside the circle gives an estimate for the probability, p. the area of the circle is 25 # r. use area of circle area of rectangle = 0.15 to show that an estimate for r is 4.8 .", "4": "4 0607/53/m/j/18 \u00a9 ucles 2018 2 lee draws a circle of radius 10 cm on a rectangular piece of paper measuring 30 cm by 20 cm. not to scale 10 cm30 cm 20 cm (a) complete this statement with a number. area of circle = . # r (b) lee drops 10 grains of rice at random onto the piece of paper. diagram a shows the result. not to scalea lee removes the 10 grains of rice and drops another 10 grains of rice at random onto the piece of paper. diagram b shows the result. not to scaleb", "5": "5 0607/53/m/j/18 \u00a9 ucles 2018 [turn over (i) complete the table. a bcombined results for all 20 grains of rice number of grains of rice inside circle relative frequency 10 20 (ii) use the formula area of circle area of rectangle = relative frequency to estimate r using the combined results for all 20 grains of rice. r = ", "6": "6 0607/53/m/j/18 \u00a9 ucles 2018 3 lee draws two circles on a different rectangular piece of paper. the circles touch the edges of the piece of paper and touch each other. x cm 8 cm 16 cm (a) (i) find the value of x. ... (ii) complete this statement with a number. total area of the two circles = # r (b) lee drops 50 grains of rice at random onto the piece of paper. he removes the 50 grains of rice and drops another 50 grains of rice at random onto the piece of paper. the table shows his results. first 50 second 50combined results for all 100 grains of rice number of grains of rice inside circle36 43 relative frequency complete the table. (c) use the formula total area of circles area of rectangle = relative frequency to estimate r. r = (d) give one reason why the estimate for r in question 3(c) is more accurate than the estimate for r in question 2(b)(ii) . ...", "7": "7 0607/53/m/j/18 \u00a9 ucles 2018 4 lee draws one circle of radius r cm on a different piece of paper. the circle touches all four edges of the paper. r cm (a) lee drops 500 grains of rice at random onto the piece of paper. he removes the 500 grains of rice and drops another 500 grains of rice at random onto the piece of paper. the combined number of grains of rice inside the circle is 785. use the formula area of circle area of rectangle = relative frequency to estimate r. r = (b) complete this sentence with a single number. to estimate the value of r when the circle touches all four edges of the paper, multiply the relative frequency by .. (c) lee drops n grains of rice at random onto the piece of paper. he removes the n grains of rice and drops another n grains of rice at random onto the piece of paper. the combined number of grains of rice inside the circle is k. show that nk2 is an estimate for r. ", "8": "8 0607/53/m/j/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_s18_qp_61.pdf": { "1": "*5572385172* this document consists of 12 printed pages. dc (lk/sg) 153611/3 \u00a9 ucles 2018 [turn overcambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/61 paper 6 (extended) may/june 2018 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a (questions 1 to 4) and b (questions 5 to 9). you must show all the relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.", "2": "2 0607/61/m/j/18 \u00a9 ucles 2018 answer both parts a and b. a investigation (questions 1 to 4) largest products (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation looks at finding the largest product when two or more positive integers have a given sum. for the positive integers 2 and 5 \u2022 the sum 2 + 5 is 7 \u2022 the product 2 \u00d7 5 is 10. 1 (a) (i) complete the table for all the different pairs of positive integers that have a sum of 8. integers sum product 1 8 2 8 3 5 8 4 8 16 write down the calculation that gives the largest product. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (ii) find the largest product of two positive integers that have a sum of 20. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd write down the calculation that gives this product. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "3": "3 0607/61/m/j/18 \u00a9 ucles 2018 [turn over (b) (i) complete this table for all the different pairs of positive integers that have a sum of 9. note that 2 and 7 is the same pair as 7 and 2. integers sum product 1 9 9 9 9 write down the calculation that gives the largest product. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (ii) find the largest product for two positive integers that have a sum of 21. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd write down the two positive integers that give this product. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd ", "4": "4 0607/61/m/j/18 \u00a9 ucles 2018 2 tom wants to find the set of positive integers that have a sum of 19 and give the largest product. he uses the ideas from question 1 and the following method. \u2022 write 19 in the top box of the diagram. \u2022 write the two positive integers that give the largest product in the two boxes on the next row. \u2022 complete the remaining boxes in the same way. (a) complete the diagram. 19 9 2 2 2 3 2 3 2 3 the largest product using tom\u2019s method is 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 2 \u00d7 3 \u00d7 2 \u00d7 3 = 25 \u00d7 33 = 864. (b) explain why tom does not replace the 2s and the 3s to make another row in the diagram. ... ...", "5": "5 0607/61/m/j/18 \u00a9 ucles 2018 [turn over (c) complete the diagram and find the largest product that tom\u2019s method gives for positive integers that have a sum of 22. 22 \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "6": "6 0607/61/m/j/18 \u00a9 ucles 2018 3 in any set of positive integers, the replacement of a set of three 2s with a set of two 3s will not change the sum. (a) explain why this is correct. ... (b) explain why this replacement will always increase the product of a set of positive integers. ... ... (c) here is tom\u2019s result from question 2(a) . 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 2 \u00d7 3 \u00d7 2 \u00d7 3 = 25 \u00d7 33 = 864 (i) use the replacement to calculate the largest product of a set of positive integers that have a sum of 19. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (ii) write your answer to part (i) as a product of powers of 2 and 3. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "7": "7 0607/61/m/j/18 \u00a9 ucles 2018 [turn over 4 (a) the sum of a set of positive integers is n. after replacing each set of three 2s in tom\u2019s method with two 3s, the largest product will be 2x \u00d7 3y. (i) find, in terms of x and y, a formula for the sum n. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (ii) explain why x can only be 0, 1 or 2. ... ... (b) use part (a) to find the largest product of a set of positive integers that have a sum of (i) 60, \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (ii) 62. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (c) 6 377 292 is the largest product of a set of positive integers that have a sum of n. find the value of n. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "8": "8 0607/61/m/j/18 \u00a9 ucles 2018 b modelling (questions 5 to 9) counting prime numbers (20 marks) you are advised to spend no more than 45 minutes on this part. prime numbers have only two factors: 1 and the number itself. in this task you will use models for the number of primes in a given range. the function p( x) gives the number of primes that are less than x. for example, p(10) = 4 because there are exactly four primes that are less than 10. these four primes are 2, 3, 5 and 7. 5 (a) show that p(20) = 8. (b) p(40) = 12. find p(50). \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (c) p(100) = 25. find p(90). \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "9": "9 0607/61/m/j/18 \u00a9 ucles 2018 [turn over 6 use your answers to question 5 to complete the table. x 10 20 40 50 90 100 140 200 p(x) 4 8 12 25 34 46 on the grid plot this information. the first three points have been plotted for you. 50 40 30 20 10 00 20 40 60 80 100 120 140 160 180 200xp(x)", "10": "10 0607/61/m/j/18 \u00a9 ucles 2018 7 a model, l( x), for the number of primes less than x, is a straight line that passes through the points (40, 12) and (140, 34). (a) find the equation of the line. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (b) use your model to estimate the number of primes that are less than 1000. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd 8 a quadratic model, q( x), for the number of primes that are less than x, is q(x) = kx \u2013 0.001 x2 . (a) the model estimates that there are 34 primes that are less than 140. find the value of k, giving your answer correct to 1 decimal place. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (b) the model is quite accurate for the number of primes when x 1 200. why is the model unsuitable for the number of primes when x 2 200? ... ...", "11": "11 0607/61/m/j/18 \u00a9 ucles 2018 [turn over 9 a very good model for the number of primes less than x, where x is less than 1000, is ()()nlogxxx 210= . (a) use the model to find how many primes there are that are (i) less than 400, \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (ii) less than 800. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (b) use your answers to part (a) to complete the table. x0 2001g x 200 4001g x 400 0061g x 600 0081g number of primes44 31 question 9(c) and 9(d) are printed on the next page.", "12": "12 0607/61/m/j/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. (c) the model is still a good model for x1000h . (i) a number is chosen at random from the numbers 1 to 10 000. use the model to estimate the probability that it is prime. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (ii) a number is chosen at random from numbers in the range 1 to x. find, in its simplest form, a model for the probability that it is prime. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (d) use the model ()()logxxx 2n 10= to estimate the 100th prime. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd" }, "0607_s18_qp_62.pdf": { "1": "*4366897499* this document consists of 14 printed pages and 2 blank pages. dc (nf/ct) 153612/2 \u00a9 ucles 2018 [turn overcambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/62 paper 6 (extended) may/june 2018 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a (questions 1 to 3) and b (questions 4 to 6). you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.", "2": "2 0607/62/m/j/18 \u00a9 ucles 2018 answer both parts a and b. a investigation (questions 1 to 3) tile patterns (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation looks at the number of grey tiles and the number of white tiles in a sequence of square patterns. all the tiles are the same size and each is a square. the grey tiles and white tiles make borders around a single grey tile. the single grey tile is the first grey border. the first white border is 8 white tiles surrounding the grey tile. the second grey border is 16 grey tiles surrounding the 8 white tiles. 1 (a) on this grid, complete the diagram to show the second white border. ", "3": "3 0607/62/m/j/18 \u00a9 ucles 2018 [turn over (b) on this grid, complete the diagram to show the third grey border. 2 this question looks at the patterns that finish with a white border. pattern finishes withnumber of white tiles in bordertotal number of white tiles in pattern 1st white border 8 8 2nd white border 32 3rd white border 40 4th white border 128 5th white border 72 200 (a) complete the table.", "4": "4 0607/62/m/j/18 \u00a9 ucles 2018 (b) the values in the last column, for the total number of white tiles in these patterns, form a sequence. find an expression, in terms of n, for the total number of white tiles in the pattern that finishes with the nth white border. .. (c) there are 3 white tiles along one side of the pattern that finishes with the first white border. (i) complete the table. pattern finishes withnumber of white tiles along one side 1st white border 3 2nd white border 3rd white border nth white border (ii) use your answer to part (c)(i) to write down an expression, in terms of n, for the total number of all tiles in the pattern that finishes with the nth white border. ..", "5": "5 0607/62/m/j/18 \u00a9 ucles 2018 [turn over (d) use your answers in part (b) and part (c) to show that an expression for the total number of grey tiles in the pattern that finishes with the nth white border is nn88 12-+ . 3 (a) michel uses the tiling method of question 2 to cover a square floor. the first tile is grey and the final border is white. the square floor measures 5.7 m by 5.7 m. each tile measures 30 cm by 30 cm. work out the number of white tiles and the number of grey tiles michel needs to cover the floor completely. number of white tiles = . number of grey tiles = .", "6": "6 0607/62/m/j/18 \u00a9 ucles 2018 (b) jasmine has 500 white tiles and 500 grey tiles. each tile measures 30 cm by 30 cm. she uses the same method of tiling, but she can finish with a grey border or a white border. find the side length of the biggest square floor that she can cover completely. find how many tiles of each colour will not be used in this case. side length of biggest square floor = . number of white tiles not used = . number of grey tiles not used = .", "7": "7 0607/62/m/j/18 \u00a9 ucles 2018 [turn over b modelling (questions 4 to 6) going with the flow (20 marks) you are advised to spend no more than 45 minutes on this part. in this task you will look at models for how the speed of water in a river changes with its height above the river bed. the river is 2 metres deep. an engineer measures the speed of water at different heights above the river bed. the water flows parallel to the river bed. the speed of the water at height x metres above the river bed is v cm/s. 2 mx mv cm/ssurface water river bednot to scale the table shows the data that the engineer collects. height above river bed (x metres)speed of water (v cm/s) 0.2 15.1 0.4 17.5 0.6 18.9 0.8 20.0 1.0 21.0 1.2 21.7 1.4 22.2 1.6 23.0 1.8 23.5 2.0 24.0 the data is plotted on the grid on the next page.", "8": "8 0607/62/m/j/18 \u00a9 ucles 2018 speed of water (cm/s) height above river bed (m)14 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.015161718192021222324v x", "9": "9 0607/62/m/j/18 \u00a9 ucles 2018 [turn over 4 (a) the engineer models the data using va xb x122=+ + where a and b are constants. (i) use the values of v when x = 1 and when x = 2 to write down two equations, each in terms of a and b. ... ... (ii) solve your equations to find the value of a and the value of b. write your values in the model below. v = x2 + x + 12 (b) the table shows the values that this model gives. x 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 v14.3 16.3 18.1 19.7 21.0 22.1 22.9 23.5 23.9 24.0 (i) plot these values and draw the graph of the model on the grid on page 8. (ii) give the range of values of x for which this model overestimates the speed of the water. ..", "10": "10 0607/62/m/j/18 \u00a9 ucles 2018 5 in this question, all logarithms are base 10. the engineer decides to test another model for how v changes with x. this model is vkx 2m =bl where k and m are constants. (a) using x = 2.0 and v = 24.0 find the value of k for this model. k = \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (b) (i) take logarithms of both sides of this model to complete the equation below. log v = . logx 2bl + .", "11": "11 0607/62/m/j/18 \u00a9 ucles 2018 [turn over (ii) the graph shows the data values of log v plotted against logx 2bl and a line of best fit. \u20131 \u20130.9 \u20130.8 \u20130.7 \u20130.6 \u20130.5 \u20130.4 \u20130.3 \u20130.2 \u20130.11.181.201.221.241.261.281.301.321.341.361.38 0log v logx 2bl use the graph to calculate the value of m for the model, and write down the model. m = .. v = .x 2bl. (c) use this model to find the height above the river bed where the water is moving at 12 cm/s. ..", "12": "12 0607/62/m/j/18 \u00a9 ucles 2018 6 a factory releases some dirt into the river. the dirt moves parallel to the river bed at the same speed as the water. at the same instant that the factory releases the dirt, the engineer lowers a metal grid into the river. the metal grid is 20 m from the factory. the metal grid does not affect the speed of the water but will stop the dirt. 2 mx m20 m dirtv cm/s u cm/ssurfacemetal grid river bednot to scale (a) the metal grid moves vertically downwards at speed u centimetres per second. show that the number of seconds it takes the bottom of the metal grid to move from the surface to a height x metres above the river bed is ux 100 2-` j . (b) the dirt moves along the river towards the grid at the speed given by the model in question 5(b)(ii) . find an expression, in terms of x, for the time it takes the dirt to move 20 m along the river. ..", "13": "13 0607/62/m/j/18 \u00a9 ucles 2018 [turn over (c) use part (a) and your answer to part (b) to show that the metal grid stops the dirt at height x if . uxx1222.02 h -` bjl. question 6(d) is printed on the next page.", "14": "14 0607/62/m/j/18 \u00a9 ucles 2018 (d) (i) on the axes below, sketch the graph of . uxx1222.02 =- ` bjl for x02gg . 02u x (ii) find the smallest value of u that stops all the dirt. ..", "15": "15 0607/62/m/j/18 \u00a9 ucles 2018 blank page", "16": "16 0607/62/m/j/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_s18_qp_63.pdf": { "1": "*5499642845* this document consists of 14 printed pages and 2 blank pages. dc (sc/cgw) 153613/2 \u00a9 ucles 2018 [turn overcambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/63 paper 6 (extended) may/june 2018 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a (questions 1 to 4) and b (questions 5 to 9). you must show all the relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.", "2": "2 0607/63/m/j/18 \u00a9 ucles 2018 answer both parts a and b. a investigation (questions 1 to 4) estimating r (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation is about using relative frequency to estimate the value of r. area, a, of circle radius r is a = rr2. 1 lee draws circles on rectangular pieces of paper. he drops grains of rice at random onto the pieces of paper. he counts the number of grains of rice inside each circle. (a) lee draws a circle of radius 5 cm on a rectangular piece of paper measuring 40 cm by 20 cm. 5 cm 20 cm40 cm not to scale the probability, p, that a grain of rice lands inside the circle is p = area of circle area of paper . (i) show that p is approximately 0.098 for this piece of paper. (ii) lee drops 10 grains of rice at random onto the piece of paper. the diagram shows the result. not to scale key: represents one grain of rice.", "3": "3 0607/63/m/j/18 \u00a9 ucles 2018 [turn over the relative frequency that a grain of rice is inside the circle = number of grains of rice inside the circle total number of grains of rice dropped . find the relative frequency that a grain of rice is inside the circle. ... (iii) lee drops 10 more grains of rice at random onto the piece of paper. not to scale show that the relative frequency that a grain of rice is inside the circle is 0.15 . (iv) the relative frequency that a grain of rice is inside the circle gives an estimate for the probability, p. the area of the circle is r25#. use area of circle area of paper = 0.15 to show that an estimate for r is 4.8 .", "4": "4 0607/63/m/j/18 \u00a9 ucles 2018 (b) lee draws a circle of radius 10 cm on a rectangular piece of paper measuring 30 cm by 20 cm. not to scale 10 cm30 cm 20 cm (i) complete this statement with a number. area of circle = # r (ii) lee drops 10 grains of rice at random onto the piece of paper. diagram a shows the result. not to scalea lee removes the 10 grains of rice and drops another 10 grains of rice at random onto the piece of paper. diagram b shows the result. not to scaleb", "5": "5 0607/63/m/j/18 \u00a9 ucles 2018 [turn over complete the table. a bcombined results for all 20 grains of rice number of grains of rice inside circle relative frequency2010 (iii) use the formula area of circle area of paper = relative frequency to estimate r using the combined results for all 20 grains of rice. r = ...", "6": "6 0607/63/m/j/18 \u00a9 ucles 2018 2 (a) lee draws a circle of radius 12 cm on a different piece of paper. the circle touches all four edges of the paper. 12 cm lee drops 50 grains of rice at random onto the piece of paper. he removes the 50 grains of rice and drops another 50 grains of rice at random onto the piece of paper. the combined number of grains of rice inside the circle is 78. use the formula area of circle area of paper = relative frequency to estimate r. r = ... (b) lee draws a circle of radius r cm on a different piece of paper. the circle touches all four edges of the paper. r cm show that, for any value of r, estimate for r = k # relative frequency, where k is an integer. find the value of k. k = ...", "7": "7 0607/63/m/j/18 \u00a9 ucles 2018 [turn over 3 lee draws a circle on a piece of paper in the shape of a regular hexagon of side length x cm. the circle touches all six edges of the paper. x cmnot to scale \u2014 x cm2\u221a3 lee drops grains of rice at random onto the piece of paper. he counts the number of grains of rice inside the circle and finds the relative frequency. (a) find an estimate for the value of r when x = 30 and the relative frequency that the grain of rice is inside the circle is 0.905 . use the formula area of circle area of paper = relative frequency . ...", "8": "8 0607/63/m/j/18 \u00a9 ucles 2018 (b) show that, for any value of x, estimate for r = k # relative frequency, where k is an exact constant. find the value of k. k = ...", "9": "9 0607/63/m/j/18 \u00a9 ucles 2018 [turn over 4 lee draws a circle on a piece of paper in the shape of a regular polygon with n sides. the circle touches all n edges of the paper. he drops grains of rice at random onto the piece of paper. he counts the number of grains of rice inside the circle and finds the relative frequency. estimate for r = k # relative frequency explain clearly why the constant k gives an approximation for r, as the value of n increases.", "10": "10 0607/63/m/j/18 \u00a9 ucles 2018 b modelling (questions 5 to 9) shoe business (20 marks) you are advised to spend no more than 45 minutes on this part. this task is about the profit made by making and selling shoes. a company makes and sells two styles of shoe, x and y. the objective of the task is for the company to maximise the amount of profit it makes each day. the number of shoes made each day is modelled using inequalities. each day the company \u2022 makes x pairs of shoes of style x and y pairs of shoes of style y \u2022 makes at most 150 pairs of shoes. 5 (a) (i) write down, in terms of x and y, an inequality to show how many pairs of shoes can be made each day. ... two machines are used to make each pair of shoes. machine a is used for at least 3 hours each day. machine b is used for at least 4 hours each day. the table shows some information about making each style of shoe. style x style y maximum number of pairs of shoes made each day 80 100 time taken by machine a for each pair of shoes 5 min 2 min time taken by machine b for each pair of shoes 4 min 5 min cost of making one pair of shoes $20 $15 selling price of one pair of shoes $100 $70 (ii) explain why x08 0 gg and y0 100 gg . ... ... (iii) an inequality for the total time each day, in minutes, that machine a is used is xy52 180h+ . find, in terms of x and y, an inequality for the total time each day, in minutes, that machine b is used. ... (b) the company sells all the pairs of shoes it makes each day. find an expression , in terms of x and y, for the total profit made each day. ...", "11": "11 0607/63/m/j/18 \u00a9 ucles 2018 [turn over 6 (a) three lines x80= , y100= and xy52 180 += have been drawn on the grid. draw two more lines to find the region defined by the five inequalities from question 5(a) . shade the unwanted region. 0020406080100 20 40 60 80 100 120 10 30 50 70 90 110 140 130 1501030507090120140 110130150y x (b) show that the greatest profit each day is $10 250. write down the number of pairs of shoes of each style to make this profit. style x style y ", "12": "12 0607/63/m/j/18 \u00a9 ucles 2018 7 the table shows the amount of material for each style. style x style y material for one pair of shoes 0.5 m20.4 m2 there is a shortage of material and 50 m2 is used each day to make all the shoes. (a) draw a line on the grid in question 6 to show this information. (b) work out the decrease in the greatest profit because of the shortage. ...", "13": "13 0607/63/m/j/18 \u00a9 ucles 2018 [turn over 8 the company is considering making bags. research shows that a model for the profit each day, $ p, from the sale of b bags is . pb b3056 52=- - . (a) on the axes below, sketch the graph of . pb b3056 52=- - for b03 5 gg . p b0 35 (b) find the minimum number of bags the company needs to sell each day in order to make a positive profit. ... (c) the greatest number of bags the company can make each day is 80. find the profit that the company will make each day when it sells all 80 bags. ...", "14": "14 0607/63/m/j/18 \u00a9 ucles 2018 9 the company decides to make 80 bags each day. for every 2 bags that it makes, it has to decrease the number of pairs of style x shoes by one. the shortage of material for making shoes is the same as in question 7 . there is no shortage of material for making bags. (a) find the greatest number of pairs of shoes of style y that the company can make. ... (b) show that the company\u2019s profit each day has increased.", "15": "15 0607/63/m/j/18 \u00a9 ucles 2018 blank page", "16": "16 0607/63/m/j/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_w18_qp_11.pdf": { "1": " this document consists of 8 printed pages. ib18 11_0607_11/2rp \u00a9 ucles 2018 [turn over \uf02a\uf038\uf039\uf035\uf034\uf032\uf032\uf038\uf030\uf039\uf032\uf02a \uf020 cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/11 paper 1 (core) october/november 2018 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2018 0607/11/o/n/18 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \uf070r2 circumference, c, of circle, radius r. c = 2\uf070r curved surface area, a, of cylinder of radius r, height h. a = 2\uf070rh curved surface area, a, of cone of radius r, sloping edge l. a = \uf070rl curved surface area, a, of sphere of radius r. a = 4\uf070r2 volume, v, of prism, cross-sectional area a, length l. v = al volume, v, of pyramid, base area a, height h. v = 1 3ah volume, v, of cylinder of radius r, height h. v = \uf070r2h volume, v, of cone of radius r, height h. v = 1 3\uf070r2h volume, v, of sphere of radius r. v = 4 3\uf070r3 ", "3": "3 \u00a9 ucles 2018 0607/11/o/n/18 [turn over answer all the questions. 1 write the number ten thousand and eleven in figures. [1] 2 find 10% of 200. [1] 3 6 8 10 12 14 16 from the list of numbers write down (a) a cube number, [1] (b) a triangle number. [1] 4 work out. \u20135 \u00d7 \u2013 4 \u2013 2 [1] 5 write down the mathematical name for the angle shown. [1] ", "4": "4 \u00a9 ucles 2018 0607/11/o/n/18 6 o is the centre of the circle. on the diagram, draw a diameter. [1] 7 40\u00b0x\u00b0not to scale ab ab is a straight line. find the value of x. x = [1] 8 change 3 kg into grams. g [1] 9 complete the statement. the diagram has rotational symmetry of order [1] o", "5": "5 \u00a9 ucles 2018 0607/11/o/n/18 [turn over 10 divide 42 in the ratio 2 : 5. and [2] 11 y x \u2013 4 43 2 1 \u20133 \u20132 \u20131 3 0 2 1 a \u20132 \u20133\u20131 on the grid, draw the image of shape a after a reflection in the y-axis. [1] 12 g c ci is ec xander spins this unbiased spinner a nd records the letters it lands on. write down the letter he is most likely to record. [1] ", "6": "6 \u00a9 ucles 2018 0607/11/o/n/18 13 in a sale, the price of a washing machine is reduced by 25%. the original price is $400. work out the sale price. $ [2] 14 write down the lowest common multiple (lcm) of 10 and 12. $ [2] 15 complete the mapping diagram. \uf0f7\uf0f7\uf0f7\uf0f7\uf0f7\uf0f7\uf0f7\uf0f7\uf0f7\uf0f7 \uf0f8\uf0f6 \uf0e7\uf0e7\uf0e7\uf0e7\uf0e7\uf0e7\uf0e7\uf0e7\uf0e7\uf0e7 \uf0e8\uf0e6 604227156 \uf0f7\uf0f7\uf0f7\uf0f7\uf0f7\uf0f7\uf0f7\uf0f7\uf0f7\uf0f7 \uf0f8\uf0f6 \uf0e7\uf0e7\uf0e7\uf0e7\uf0e7\uf0e7\uf0e7\uf0e7\uf0e7\uf0e7 \uf0e8\uf0e6 . ..14952 [1] 16 the volume of a cone can be estimated using the following formula. volume = height \u00d7 (base radius) 2 use this formula to find the volume of a cone with base radius 6 cm and height 5 cm. cm3[2] 17 asha takes 20 minutes to walk to school. she walks at 4.5 km / h. work out how far asha walks. km [2] ", "7": "7 \u00a9 ucles 2018 0607/11/o/n/18 [turn over 18 the exterior angle of a regular polygon is 20\u00b0. find the number of sides of this polygon. [2] 19 the time taken, in minutes, by each of 12 st udents to walk to school is shown below. 22 10 23 11 20 24 21 15 29 24 6 11 (a) work out the range. min [1] (b) find the median. min [2] (c) find the lower quartile. min [1] 20 40 students were asked if they liked tea or coffee. 10 liked tea only. 16 liked coffee only. 8 did not like tea or coffee. use this information to complete the venn diagram. coffeeu tea 8 [2] questions 21, 22, 23 and 24 are printed on the next page. ", "8": "8 permission to reproduce items where third-party owned material pr otected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknow ledgements booklet. this is produced for each series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge as sessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2018 0607/11/o/n/18 21 a is the point (6, 4) and b is the point (3, 9). write down \uf0be\uf0ae\uf0be ab. \uf0be\uf0ae\uf0be ab = \uf0f7\uf0f7\uf0f7 \uf0f8\uf0f6 \uf0e7\uf0e7\uf0e7 \uf0e8\uf0e6 [2] 22 write down all the integer values of x that satisfy \u20132 < x 2. [2] 23 factorise completely. 4 x2 + 6x [2] 24 solve the simultaneous equations. 5 x + y = 8 3 x + 2y = 9 x = y = [3] " }, "0607_w18_qp_12.pdf": { "1": " this document consists of 8 printed pages. ib18 11_0607_12/2rp \u00a9 ucles 2018 [turn over \uf02a\uf031\uf030\uf034\uf039\uf032\uf035\uf033\uf037\uf035\uf030\uf02a \uf020 cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/12 paper 1 (core) october/november 2018 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2018 0607/12/o/n/18 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \uf070r2 circumference, c, of circle, radius r. c = 2\uf070r curved surface area, a, of cylinder of radius r, height h. a = 2\uf070rh curved surface area, a, of cone of radius r, sloping edge l. a = \uf070rl curved surface area, a, of sphere of radius r. a = 4\uf070r2 volume, v, of prism, cross-sectional area a, length l. v = al volume, v, of pyramid, base area a, height h. v = 1 3ah volume, v, of cylinder of radius r, height h. v = \uf070r2h volume, v, of cone of radius r, height h. v = 1 3\uf070r2h volume, v, of sphere of radius r. v = 4 3\uf070r3 ", "3": "3 \u00a9 ucles 2018 0607/12/o/n/18 [turn over answer all the questions. 1 write the number 51 025 in words. [1] 2 write down two factors of 12. , [1] 3 work out. 7 + 14 \u00f7 7 \u2013 3 [1] 4 work out 5% of 100. [1] 5 paulo and his sister share 35 sweets in the ratio 4 : 3. paulo keeps the larger share. how many sweets does paulo keep? [2] 6 find the value of x. x = [2] 44\u00b0not to scale x\u00b0", "4": "4 \u00a9 ucles 2018 0607/12/o/n/18 7 continuous cumulative discrete random wendi is collecting data on apples. which of the words in the box above describes the following type of data. (a) the number of apples on a tree. [1] (b) the weight of an apple. [1] 8 here are the test scores of five students. 13 16 14 19 13 (a) write down the mode. [1] (b) work out the range. [1] (c) work out the mean. [2] 9 a biased die is rolled 200 times and the number on the top face is recorded. the results are shown in the table. number on the top face 1 2 3 4 5 6 frequency 21 26 19 84 27 23 (a) write down the relative frequency of rolling a 2. [1] (b) the die is rolled 1000 times. work out an estimate of the number of times the top face shows 4. [2] ", "5": "5 \u00a9 ucles 2018 0607/12/o/n/18 [turn over 10 complete the statement. a quadrilateral with exactly one pa ir of parallel sides is called a . [1] 11 the volume of this cuboid is 6000 cm3. the length of the cuboid is 30 cm and the width of the cuboid is 10 cm. find h, the height of the cuboid. cm [2] 12 alex starts from point a and walks on a bearing of 030 \uf0b0 to point b. he then walks east to point c. find the bearing of (a) b from c, [1] (b) a from b. [2] h 10 cm 30 cmnot to scale not to scale abc 30\u00b0north north", "6": "6 \u00a9 ucles 2018 0607/12/o/n/18 13 find the highest common factor (hcf) of 12 and 30. [1] 14 write 134.6 in standard form. [1] 15 the nth term of a sequence is n2 \u2013 3. write down the first three terms. , , [2] 16 factorise. x 2 \u2013 5x [1] 17 a line has equation 6 2 3\uf03d\uf02by x . write the equation of this line in the form c mxy\uf02b\uf03d . y = [2] ", "7": "7 \u00a9 ucles 2018 0607/12/o/n/18 [turn over 18 u = {x | x is an integer and 1 x < 5} a\uf0a2 = {2, 4} (a) write down the elements of the universal set. { } [1] (b) write down the elements of the set a. { } [1] 19 y x \u2013 444 3 2 1 \u20133 \u20132 \u20131 1 2 3 \u20132\u201310 \u2013 5 \u2013 65 6 75 8 \u20133 \u2013 4 \u20135 the diagram shows the graph of y = f(x). write down the equations of the two asymptotes. [2] 20 complete the statement. the graph of y = g( x) is translated by the vector \uf0f7 \uf0f8\uf0f6\uf0e7 \uf0e8\uf0e6 02 onto the graph of y = [1] questions 21 and 22 are printed on the next page. ", "8": "8 permission to reproduce items where third-party owned material pr otected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknow ledgements booklet. this is produced for each series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge as sessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2018 0607/12/o/n/18 21 write down the value of (a) sin x\u00b0, [1] (b) tan y\u00b0. [1] 22 16 cmo 10 cmnot to scale x the diagram shows a chord of length 16 cm inside a circle centre o, radius 10 cm. work out the length x. cm [3] 13 mm 12 mm5 mmx ynot to scale" }, "0607_w18_qp_13.pdf": { "1": " this document consists of 8 printed pages. ib18 11_0607_13/rp \u00a9 ucles 2018 [turn over \uf02a\uf031\uf036\uf033\uf033\uf031\uf039\uf032\uf036\uf038\uf039\uf02a \uf020 cambridge international examinations cambridge international general certificate of secondary education cambridge international mathematics 0607/13 paper 1 (core) october/november 2018 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2018 0607/13/o/n/18 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \uf070r2 circumference, c, of circle, radius r. c = 2\uf070r curved surface area, a, of cylinder of radius r, height h. a = 2\uf070rh curved surface area, a, of cone of radius r, sloping edge l. a = \uf070rl curved surface area, a, of sphere of radius r. a = 4\uf070r2 volume, v, of prism, cross-sectional area a, length l. v = al volume, v, of pyramid, base area a, height h. v = 1 3ah volume, v, of cylinder of radius r, height h. v = \uf070r2h volume, v, of cone of radius r, height h. v = 1 3\uf070r2h volume, v, of sphere of radius r. v = 4 3\uf070r3 ", "3": "3 \u00a9 ucles 2018 0607/13/o/n/18 [turn over answer all the questions. 1 write the number 51 025 in words. [1] 2 write down two factors of 12. , [1] 3 work out. 7 + 14 \u00f7 7 \u2013 3 [1] 4 work out 5% of 100. [1] 5 paulo and his sister share 35 sweets in the ratio 4 : 3. paulo keeps the larger share. how many sweets does paulo keep? [2] 6 find the value of x. x = [2] 44\u00b0not to scale x\u00b0", "4": "4 \u00a9 ucles 2018 0607/13/o/n/18 7 continuous cumulative discrete random wendi is collecting data on apples. which of the words in the box above describes the following type of data. (a) the number of apples on a tree. [1] (b) the weight of an apple. [1] 8 here are the test scores of five students. 13 16 14 19 13 (a) write down the mode. [1] (b) work out the range. [1] (c) work out the mean. [2] 9 a biased die is rolled 200 times and the number on the top face is recorded. the results are shown in the table. number on the top face 1 2 3 4 5 6 frequency 21 26 19 84 27 23 (a) write down the relative frequency of rolling a 2. [1] (b) the die is rolled 1000 times. work out an estimate of the number of times the top face shows 4. [2] ", "5": "5 \u00a9 ucles 2018 0607/13/o/n/18 [turn over 10 complete the statement. a quadrilateral with exactly one pa ir of parallel sides is called a . [1] 11 the volume of this cuboid is 6000 cm3. the length of the cuboid is 30 cm and the width of the cuboid is 10 cm. find h, the height of the cuboid. cm [2] 12 alex starts from point a and walks on a bearing of 030 \uf0b0 to point b. he then walks east to point c. find the bearing of (a) b from c, [1] (b) a from b. [2] h 10 cm 30 cmnot to scale not to scale abc 30\u00b0north north", "6": "6 \u00a9 ucles 2018 0607/13/o/n/18 13 find the highest common factor (hcf) of 12 and 30. [1] 14 write 134.6 in standard form. [1] 15 the nth term of a sequence is n2 \uf02d 3. write down the first three terms. , , [2] 16 factorise. x2 \u2013 5x [1] 17 a line has equation 6 2 3\uf03d\uf02by x . write the equation of this line in the form c mx y\uf02b\uf03d . y = [2] ", "7": "7 \u00a9 ucles 2018 0607/13/o/n/18 [turn over 18 u = {x | x is an integer and 1 x < 5} a\uf0a2 = {2, 4} (a) write down the elements of the universal set. { } [1] (b) write down the elements of the set a. { } [1] 19 the diagram shows the graph of y = f(x). write down the equations of the two asymptotes. [2] 20 complete the statement. the graph of y = g( x) is translated by the vector \uf0f7 \uf0f8\uf0f6\uf0e7 \uf0e8\uf0e6 02 onto the graph of y = [1] questions 21 and 22 are printed on the next page. y x \u2013 444 3 2 1 \u20133 \u20132 \u20131 1 2 3 \u20132\u201310 \u2013 5 \u2013 65 6 75 8 \u20133 \u2013 4 \u20135", "8": "8 permission to reproduce items where third-party owned material pr otected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge international examinations copyright acknow ledgements booklet. this is produced for each series of examinations and is freely a vailable to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge as sessment group. cambridge assessment is the brand name of unive rsity of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge. \u00a9 ucles 2018 0607/13/o/n/18 21 write down the value of (a) sin x\u00b0, [1] (b) tan y\u00b0. [1] 22 16 cmo 10 cmnot to scale x the diagram shows a chord of length 16 cm inside a circle centre o, radius 10 cm. work out the length x. cm [3] 13 mm 12 mm5 mmx ynot to scale" }, "0607_w18_qp_21.pdf": { "1": "*0297609332* this document consists of 7 printed pages and 1 blank page. dc (sc/sg) 155515/3 \u00a9 ucles 2018 [turn overcambridge international mathematics 0607/21 paper 2 (extended) october/november 2018 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/21/o/n/18 \u00a9 ucles 2018 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/21/o/n/18 \u00a9 ucles 2018 [turn over answer all the questions. 1 work out. 75#-- [1] 2 156\u00b0x\u00b0 132\u00b0not to scale find the value of x. x = [1] 3 a bag contains 8 blue balls, 3 red balls and 4 green balls only. one ball is chosen at random. find the probability that this ball is red. give your answer as a fraction in its simplest form. [2] 4 write 3-2 as a fraction. [1] 5 solve. x65 19-= x = [2]", "4": "4 0607/21/o/n/18 \u00a9 ucles 2018 6 find the lowest common multiple (lcm) of 12 and 15. [2] 7 find the size of one exterior angle of a regular octagon. [2] 8 the point a has co-ordinates (1, 9). the point b has co-ordinates (4, 5). find the length of ab. [2] 9 simplify. ()xy543 2 [2]", "5": "5 0607/21/o/n/18 \u00a9 ucles 2018 [turn over 10 list the integer values of x for which x 42 61g- . [2] 11 simplify. 32 72 50 -+ [2] 12 find the next term and an expression for the nth term of the following sequence. -9, -3, 7, 21, 39, \u2026 next term = nth term = [3] 13 the bearing of point b from point a is 234\u00b0. work out the bearing of point a from point b. [2]", "6": "6 0607/21/o/n/18 \u00a9 ucles 2018 14 solve the simultaneous equations. xy xy32 4 23 7+= -= x = y = [4] 15 factorise. xx47 22-- [2] 16 a bag contains 4 red balls and 5 blue balls only. two balls are chosen at random without replacement. find the probability that the two balls chosen are different colours. [3]", "7": "7 0607/21/o/n/18 \u00a9 ucles 2018 17 rationalise the denominator, giving your answer in its simplest form. 5353 -+ [3] 18 the surface area of a sphere with radius r is equal to the curved surface area of a cone with radius r and height h. show that hr k= , where k is a constant. [4]", "8": "8 0607/21/o/n/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_w18_qp_22.pdf": { "1": "*9162960159* this document consists of 8 printed pages. dc (sc/ct) 155517/2 \u00a9 ucles 2018 [turn overcambridge international mathematics 0607/22 paper 2 (extended) october/november 2018 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/22/o/n/18 \u00a9 ucles 2018 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area =a c bcb a", "3": "3 0607/22/o/n/18 \u00a9 ucles 2018 [turn over answer all the questions. 1 (a) write 49 059 300 correct to 3 significant figures. [1] (b) write your answer to part (a) in standard form. [1] 2 find 383 3. [2] 3 shade two small squares so that the shape has exactly one line of symmetry. [1] 4 53p=-eo (a) find the column vector 3 p. fp [1] (b) find p, giving your answer in surd form. [2]", "4": "4 0607/22/o/n/18 \u00a9 ucles 2018 5 ()xx 27 f=- for all real x. (a) find ()2f. [1] (b) write down the range of ()xf. [1] 6 the line with equation xy23 6 += is drawn on the grid. 01 1 \u20131 \u20132 \u20133 \u20134 2 3 4 5 6 7 8 \u20131 \u20132 \u20133 \u2013423456y x on the grid, show clearly the single region defined by these three inequalities. xy23 6g+ x 3h- y 1g- [3] 7 factorise. (a) x64 12- [1] (b) yy262-- [2]", "5": "5 0607/22/o/n/18 \u00a9 ucles 2018 [turn over 8 (a) 22 2p 37'= find the value of p. [1] (b) 22q 5= find the value of q. [1] 9 an archer shoots 150 arrows at a target with sections coloured gold, red, blue, black and white. the table shows her results. colour gold red blue black white frequency 30 60 36 15 9 complete the compound bar chart to show these results as percentages. 0 10 20 30 40 50 60 70 80 90 100 percentagegold red [3] 10 solve. () xx49 32 1 g+- [3]", "6": "6 0607/22/o/n/18 \u00a9 ucles 2018 11 the diagram shows nine sketch graphs. a oy xb oy xc oy x d oy xe oy xf oy x g oy xh oy xi oy x write the letter of the graph which shows each of these functions. ()xx 23 f=- graph ()xx 3 f2=- graph ()xx 3 f3=- graph () ()xx 3 f2=- graph [4]", "7": "7 0607/22/o/n/18 \u00a9 ucles 2018 [turn over 12 oa d cq pb not to scale 40\u00b0 20\u00b0 a, b, c and d are points on the circle centre o. pq is a tangent to the circle at c. find these angles. (a) angle dac angle dac = ... [2] (b) angle abc angle abc = ... [1] (c) angle acq angle acq = ... [2] question 13, 14 and 15 are printed on the next page.", "8": "8 0607/22/o/n/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.13 simplify. ()52 32+ [3] 14 (a) find the value of n when logl og logl ogn 532+- = . [1] (b) find () log3. 314. [1] 15 () \u00b0 sin xx 32 f= (a) write down the amplitude of the graph of ()xf. [1] (b) the graph of () yx f= goes through the points (75, 1.5) and ( a, 1.5) . find a possible value of a, greater than 75. [1]" }, "0607_w18_qp_23.pdf": { "1": "this document consists of 8 printed pages. dc (nh/ct) 155516/1 \u00a9 ucles 2018 [turn over *6850365055* cambridge international mathematics 0607/23 paper 2 (extended) october/november 2018 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/23/o/n/18 \u00a9 ucles 2018 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area =a c bcb a", "3": "3 0607/23/o/n/18 \u00a9 ucles 2018 [turn over answer all the questions. 1 ym xc=+ (a) find y when m = 21, x = -2 and c = 4. y = [2] (b) rearrange the formula to write m in terms of x, y and c. m = [2] 2 solve. t 62 12 -= - t = [2] 3 x 4 3 2 \u20136 \u20135 \u20134 \u20133 \u20132 \u20131 1 0 write down the inequality shown above. . [1] 4 danny stands to watch a train go past. the train has a length of 120 m and takes 3 seconds to pass. find the speed of the train (a) in m/s, .. m/s [1] (b) in km/h. km/h [2]", "4": "4 0607/23/o/n/18 \u00a9 ucles 2018 5 work out 65 1615' . give your answer in its lowest terms. . [2] 6 (a) simplify 98 . . [1] (b) rationalise the denominator. 351 - . [2] 7 solve the simultaneous equations. tu tu35 32 1-= - += t = u = [2]", "5": "5 0607/23/o/n/18 \u00a9 ucles 2018 [turn over 8 simplify. (a) vv12 312 3# . [2] (b) x100100 23 ` j . [2] 9 for the diagram, write down (a) the number of lines of symmetry, . [1] (b) the order of rotational symmetry. . [1] 10 the volume of a sphere is r36 cubic centimetres. find the radius of the sphere. ... cm [2]", "6": "6 0607/23/o/n/18 \u00a9 ucles 2018 11 (a) t, u and v lie on a circle, centre o. pq is a tangent to the circle at t. tu is a diameter. find the value of x and the value of y.not to scale u vt pq o 42\u00b0x\u00b0 y\u00b0 x = y = [2] (b) abcd is a cyclic quadrilateral. find the value of p and the value of q.d abc not to scale 85\u00b044\u00b0q\u00b0 p\u00b0 p = q = [2] 12 sin21i=- and \u00b0\u00b00 360 ggi . find the two values of i. i = .. or i = . [2]", "7": "7 0607/23/o/n/18 \u00a9 ucles 2018 [turn over 13 find the equation of the straight line perpendicular to the line y = 2x + 1 that passes through the point (2, 5). give your answer in the form y = mx + c. y = [3] 14 not to scale the two solids are mathematically similar. the larger solid has a volume of 64 cm3. the smaller solid has a volume of 8 cm3 and a height of 5 cm. work out the height of the larger solid. ... cm [3] question 15 is printed on the next page.", "8": "8 0607/23/o/n/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.15 write as a single fraction in its simplest form. xx17 235 --+ . [3]" }, "0607_w18_qp_31.pdf": { "1": "this document consists of 16 printed pages. dc (leg/cgw) 153614/2 \u00a9 ucles 2018 [turn overcambridge international examinations cambridge international general certificate of secondary education *6607853333* cambridge international mathematics 0607/31 paper 3 (core) october/november 2018 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, highlighters, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.", "2": "2 0607/31/o/n/18 \u00a9 ucles 2018 formula list area, a, of triangle, base b, height h. a = 21bh area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = 31ah v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = 31 rr2h v olume, v, of sphere of radius r. v = 34 rr3", "3": "3 0607/31/o/n/18 \u00a9 ucles 2018 [turn over answer all the questions. 1 (a) (i) write 88% as a decimal. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd [1] (ii) write 0.3 as a fraction. [1] (iii) shade 60% of this diagram. [1] (b) find the value of (i) 63, [1] (ii) .64, giving your answer correct to 1 decimal place, [2] (iii) ..2128 8489 + . [1] (c) complete the list of factors of 12. 1 , . , . , . , . , 12 [1]", "4": "4 0607/31/o/n/18 \u00a9 ucles 2018 2 one day, pat and terry walk to school. (a) it takes pat 10 minutes 7 seconds to walk to school. it takes terry 14 minutes 49 seconds to walk to school. (i) who takes the least time and by how much? takes the least time by minutes seconds [1] (ii) when pat left home, her watch showed this time. hours minutes seconds 7 58 45 what time did the watch show when pat arrived at school? hours minutes seconds [2] (b) pat lives 0.78 km from school. terry lives 87 km from school. work out who lives closer to school and by how much. give your answer in metres. ... lives closer by . metres [2]", "5": "5 0607/31/o/n/18 \u00a9 ucles 2018 [turn over (c) one day pat takes 1180 steps on her way to school. the next day she takes 15% more steps. work out how many more steps she takes. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd [1] (d) on a different day pat takes 1240 steps on her way to school and terry takes 1400 steps. write the ratio 1240 : 1400 in its simplest form. : ... [2] ", "6": "6 0607/31/o/n/18 \u00a9 ucles 2018 3 here is a rectangle drawn on a 1 cm2 grid. (a) work out the perimeter and the area of the rectangle. perimeter = \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd cm2 [2] area = ... cm2 [2] (b) a square has the same area as the rectangle. work out the length of one side of the square. . cm [2] (c) h bnot to scale work out a value for b and a value for h so that this triangle has the same area as the rectangle. b = \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd cm [3] h = cm [3]", "7": "7 0607/31/o/n/18 \u00a9 ucles 2018 [turn over 4 (a) here are the first four terms of a sequence. 1 4 7 10 (i) write down the next two terms of this sequence. ... , ... [1] (ii) write down the rule to find the next term. ... [1] (b) here are the first four terms of another sequence. 80 40 20 10 write down the next four terms of this sequence. ... , ... , ... , ... [2] (c) here are the first five terms of a different sequence. 1 3 5 7 9 (i) find the nth term. ... [2] (ii) explain why multiplying together any two terms in this sequence gives an answer that is also a term in the sequence. ... [1]", "8": "8 0607/31/o/n/18 \u00a9 ucles 2018 5 \u20132\u20131 1 2 3 4 5 6 7 8 9 \u20133\u20132\u20131012345y xab c (a) write down the co-ordinates of (i) point b, ( , ) [1] (ii) point a. ( , ) [1] (b) abcd is a kite. (i) on the grid, plot the point d and complete the kite. [1] (ii) write down the co-ordinates of point d. ( , ) [1] (c) on the grid, draw the line of symmetry of the kite. [1] (d) the equation of the line bc is 2 y + x = 10. (i) rearrange 2 y + x = 10 to make y the subject. y = ... [2] (ii) write down the gradient of the line bc. ... [1] (e) the equation of the line ab is y = x + 2. write down the equation of the line parallel to ab, passing through the point (0, \u22124). ... [2]", "9": "9 0607/31/o/n/18 \u00a9 ucles 2018 [turn over 6 (a) (i) work out the value of 9 y + 12 when y = 5. ... [1] (ii) factorise 9 y + 12. ... [1] (b) solve these equations. (i) x 2 = 8 x = .. [1] (ii) 3x \u2013 5 = 7 x = .. [2] (c) multiply out the brackets and simplify. (x + 3)( x + 2) ... [2] (d) write down the value of x0. ... [1] (e) simplify fully. (i) tt53# ... [1] (ii) (p4)2 ... [1] (iii) yy 618 39 ... [2]", "10": "10 0607/31/o/n/18 \u00a9 ucles 2018 7 the table shows how the value of a car changes as it gets older. age (years) 1 1.5 2 3 4 4.5 5 6 value ($) 9000 8000 5000 4500 3000 2500 2000 2000 (a) complete the scatter diagram. the first four points have been plotted for you. 00200040006000800010 000 1 2 3 4 age (years)value ($) 5 6 [2] (b) what type of correlation is shown in your scatter diagram? ... [1] (c) (i) find the mean age and the mean value. mean age = years [2] mean value = $ \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd [2] (ii) on the scatter diagram, draw a line of best fit. [2] (d) use your line of best fit to estimate the value of the car when it was 2.5 years old. $ ... [1]", "11": "11 0607/31/o/n/18 \u00a9 ucles 2018 [turn over 8 (a) in the diagram, bcd is a straight line and ce = cd. 110\u00b0not to scale 80\u00b0125\u00b0 x\u00b0y\u00b0d e ab c work out the value of (i) x, x = .. [2] (ii) y. y = .. [2] (b) on a map, two towns are 8.5 cm apart. the scale of the map is 1 centimetre represents 5 kilometres. work out the actual distance between the two towns. .. km [1] (c) north 70\u00b0y xnorth not to scale the bearing of y from x is 070\u00b0. work out the bearing of x from y. ... [2]", "12": "12 0607/31/o/n/18 \u00a9 ucles 2018 9 a bag contains black counters, white counters and red counters only. tam takes a counter, at random, from the bag. he records the colour of the counter and then replaces the counter in the bag. he does this 500 times. the table below shows his results. colour of counter black white red number of times 163 128 209 (a) complete the relative frequency table below. give each of your answers as a decimal. colour of counter black white red relative frequency [2] (b) tam chooses another counter from the bag at random. work out an estimate of the probability that it is either black or white. ... [2] (c) there is a total of 24 counters in the bag. work out an estimate of the number of red counters. ... [2]", "13": "13 0607/31/o/n/18 \u00a9 ucles 2018 [turn over 10 (a) work out . . 84 10 15 1038## #-` `j j, giving your answer (i) in standard form, ... [1] (ii) as an ordinary number. ... [1] (b) the sun is a sphere of radius 696 000 km. (i) write 696 000 in standard form. ... [1] (ii) work out the surface area of the sun. write your answer in standard form correct to 2 significant figures. . km2 [3]", "14": "14 0607/31/o/n/18 \u00a9 ucles 2018 11 nur recorded the distance, d cm, that 100 people each sit from their computer screen. the table shows her results. distance from screen ( d cm) frequency d00341g 4 d00451g 50 d00561g 27 d00671g 16 d00781g 3 (a) write down the modal class. ... d1g ... [1] (b) work out an estimate of the mean distance. .. cm [2] (c) draw a bar chart to show this data. 3002040 50 70 distance from screen (cm)frequency 40 60 80103050 d [2]", "15": "15 0607/31/o/n/18 \u00a9 ucles 2018 [turn over 12 27 cmx cm 51 cmnot to scale 34 cm the diagram shows two rectangular computer screens. the screens are mathematically similar. (a) find the value of x. x = .. [2] (b) 27 cm 34 cmnot to scale y cm p\u00b0 for the smaller computer screen, work out (i) the value of y, y = .. [2] (ii) the value of p. p = .. [2] question 13 is printed on the next page.", "16": "16 0607/31/o/n/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.13 here is a sketch of the graph y = xx 34 ++ for values of x between \u22126 and 2. \u20134\u20136x \u2013444 \u20136 20y (a) (i) on the sketch, draw the asymptotes for this graph. [1] (ii) find the equation of each asymptote you have drawn. ... [2] ... [2] (b) solve the equation xx 34 ++ = 3. x = .. [1] (c) describe fully the single transformation that maps the graph of y = xx 34 ++ onto the graph of y = xx 34 ++ \u2013 1. [2]" }, "0607_w18_qp_32.pdf": { "1": "*8503854593* this document consists of 16 printed pages. dc (st/sg) 153615/2 \u00a9 ucles 2018 [turn overcambridge international mathematics 0607/32 paper 3 (core) october/november 2018 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/32/o/n/18 \u00a9 ucles 2018 formula list area, a, of triangle, base b, height h. a = 21bh area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = 31ah v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = 31 rr2h v olume, v, of sphere of radius r. v = 34 rr3", "3": "3 0607/32/o/n/18 \u00a9 ucles 2018 [turn over answer all the questions. 1 (a) here is a list of numbers. 8 10 14 17 20 25 from this list, write down (i) an odd number, . [1] (ii) a multiple of 7, . [1] (iii) a square number. . [1] (b) here are the first four numbers in a sequence. 8 11 14 17 write down the next two terms in this sequence. ... , ... [2] (c) write 3658 correct to the nearest 100. . [1] (d) write 68.437 (i) correct to 2 decimal places, . [1] (ii) correct to 3 significant figures. . [1] (e) sm n3 2=+ find the value of s when m = 4.8 and n = 1.6 . s = [2] (f) change 2.3 kilometres into metres. . m [1]", "4": "4 0607/32/o/n/18 \u00a9 ucles 2018 2 a school shop sells the following. cost (cents) pencil 12 sharpener 25 eraser 10 ruler 30 (a) gigue buys 3 pencils and 1 sharpener. work out how much he spends. ... cents [2] (b) the cost of a ruler is increased by 20%. work out the new cost of a ruler. ... cents [2] (c) in a sale, the cost of a sharpener is reduced to 19 cents. work out the percentage reduction. . % [2] ", "5": "5 0607/32/o/n/18 \u00a9 ucles 2018 [turn over 3 some students were asked to choose their favourite colour of candy. all their choices are shown in the table. favourite colour red blue yellow green orange number of students 6 5 2 2 3 (a) find the number of students that were asked. . [1] (b) one of these students is chosen at random. find the probability that their favourite colour of candy is blue. . [1] (c) complete the bar chart. red blue yellow favourite colourgreen orange01234567 number of students [2] ", "6": "6 0607/32/o/n/18 \u00a9 ucles 2018 4 there are 36 cars altogether in a car park. there are 11 black cars, 10 red cars and the rest of the cars are blue. (a) work out the number of blue cars. . [1] (b) write down the fraction of cars in the car park that are black. . [1] (c) the information is to be shown in a pie chart. work out the sector angle for red cars. . [2] ", "7": "7 0607/32/o/n/18 \u00a9 ucles 2018 [turn over 5 (a) vrind from the letters above, write down all the letters that have (i) line symmetry, . [2] (ii) rotational symmetry, . [2] (iii) both line symmetry and rotational symmetry, . [1] (iv) neither line symmetry nor rotational symmetry. . [1] (b) on a poster, the letter i is a rectangle of width 2 cm and height 11 cm. (i) work out the perimeter of the letter i. ... cm [1] (ii) work out the area of the letter i. . cm2 [1] ", "8": "8 0607/32/o/n/18 \u00a9 ucles 2018 6 a bag contains 15 marshmallows. 8 of these are white and 7 are pink. terry picks a marshmallow at random from the bag and eats it. he then picks a second marshmallow at random from the bag and eats it. (a) complete the probability tree diagram. ... ...white pink... ...white pink... ...white pinkfirst marshmallow second marshmallow [3] (b) find the probability that both marshmallows were white. . [2] ", "9": "9 0607/32/o/n/18 \u00a9 ucles 2018 [turn over 7 a bcy x \u20136 \u20135 \u20134 \u20133 \u20132 \u20131 \u20136\u20135\u20134\u20133\u20132\u201311 2 3 4 5 6123456 0 (a) describe fully the single transformation that maps triangle a onto triangle b. .. .. [2] (b) describe fully the single transformation that maps triangle a onto triangle c. .. .. [2] (c) on the grid, draw the image of triangle a after a rotation of 180\u00b0 about the origin. label this image d. [2] (d) describe fully the single transformation that maps triangle c onto triangle d. .. .. [2] ", "10": "10 0607/32/o/n/18 \u00a9 ucles 2018 8 250 m 100 mnot to scale the diagram shows a rectangle joined to a semicircle. there is a path along the perimeter of this shape. (a) show that the length of the path is 757 m, correct to the nearest metre. [3] (b) maggie runs around the path at a speed of 220 metres per minute. work out how long it takes maggie to run around the path. give your answer in minutes. .. min [1] (c) jack takes 10 minutes to walk around the path. work out his average speed in km/h. km/h [3] (d) work out the total area enclosed by the path. m2 [3] (e) the area inside the path is covered with grass. grass cost $0.29 for one square metre. work out the total cost for the grass. $ . [1] ", "11": "11 0607/32/o/n/18 \u00a9 ucles 2018 [turn over 9 the diagram shows a 1cm2 grid. y x 1 2 3 4 5 6123456 07 8 9 10789 (a) on the grid, plot the points r(2, 2), s(8, 2) and t(8, 8). join these points to form a right-angled triangle. [2] (b) find (i) the length of rs, ... cm [1] (ii) the area of the triangle, .. cm2 [1] (iii) the gradient of rt. . [2] (c) find the co-ordinates of the midpoint of rt. ( ... , ... ) [1] (d) write down the equation of the line st. . [1] ", "12": "12 0607/32/o/n/18 \u00a9 ucles 2018 10 (a) a cob e d f15\u00b0 10\u00b0not to scale the diagram shows a circle, centre o. ab and cd are parallel chords and the line edf is a tangent to the circle at d. angle odc = 10\u00b0 and angle ocb = 15\u00b0. find the size of (i) angle ode , angle ode = [1] (ii) angle cdf , angle cdf = ... [1] (iii) angle cod , angle cod = ... [2] (iv) angle cba . angle cba = ... [1] ", "13": "13 0607/32/o/n/18 \u00a9 ucles 2018 [turn over (b) x + 15\u00b0x + 10\u00b0 x + 20\u00b0not to scale x\u00b0x + 25\u00b0 the diagram shows a pentagon. find the value of x. x = ... [3] ", "14": "14 0607/32/o/n/18 \u00a9 ucles 2018 11 the venn diagram shows the number of students in a class wearing a t-shirt, t, or a cardigan, c. t 8 3 7c .u (a) there are 20 students in total in the class. complete the venn diagram. [1] (b) find the probability that one of these students, chosen at random, wears (i) both a t-shirt and a cardigan, . [1] (ii) a t-shirt but not a cardigan. . [1] (c) find n( t ). . [1] (d) on the venn diagram, shade ct+ l. [1] 12 (a) tr s 5=- find the value of t when r = 3 and s = 4. t = [2] (b) simplify fully. (i) aba b 362-+- . [2] (ii) xx 510 . [1]", "15": "15 0607/32/o/n/18 \u00a9 ucles 2018 [turn over (c) solve. (i) x 25= x = [1] (ii) x72 51+= x = [2] (d) expand the brackets and simplify. () () xx42 22 1 +++ [2] (e) write down the inequality shown by this number line. \u20134 \u20133 \u20132 \u20131 0 1 2 3 4 5 6 7x . [1] (f) solve these simultaneous equations. you must show all your working. xy 9 2-= xy31 6 += x = y = [2] question 13 is printed on the next page.", "16": "16 0607/32/o/n/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.13 \u20132 4xy \u20131210 0not to scale the diagram shows the graph of () yxf= where ()xx x 25 6 f2=- ++ for x24gg- . (a) use your calculator to find the zeros of ()xf. ... and .. [2] (b) use your calculator to find the co-ordinates of the local maximum. ( ... , ... ) [2] (c) write down the equation of the line of symmetry. . [1] " }, "0607_w18_qp_33.pdf": { "1": "*2440412193* this document consists of 16 printed pages. dc (jc) 171353 \u00a9 ucles 2018 [turn overcambridge international mathematics 0607/33 paper 3 (core) october/november 2018 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/33/o/n/18 \u00a9 ucles 2018 formula list area, a, of triangle, base b, height h. a = 21bh area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = 31ah v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = 31 rr2h v olume, v, of sphere of radius r. v = 34 rr3", "3": "3 0607/33/o/n/18 \u00a9 ucles 2018 [turn over answer all the questions. 1 (a) here is a list of numbers. 8 10 14 17 20 25 from this list, write down (i) an odd number, . [1] (ii) a multiple of 7, . [1] (iii) a square number. . [1] (b) here are the first four numbers in a sequence. 8 11 14 17 write down the next two terms in this sequence. ... , ... [2] (c) write 3658 correct to the nearest 100. . [1] (d) write 68.437 (i) correct to 2 decimal places, . [1] (ii) correct to 3 significant figures. . [1] (e) sm n3 2=+ find the value of s when m = 4.8 and n = 1.6 . s = [2] (f) change 2.3 kilometres into metres. . m [1]", "4": "4 0607/33/o/n/18 \u00a9 ucles 2018 2 a school shop sells the following. cost (cents) pencil 12 sharpener 25 eraser 10 ruler 30 (a) gigue buys 3 pencils and 1 sharpener. work out how much he spends. ... cents [2] (b) the cost of a ruler is increased by 20%. work out the new cost of a ruler. ... cents [2] (c) in a sale, the cost of a sharpener is reduced to 19 cents. work out the percentage reduction. . % [2] ", "5": "5 0607/33/o/n/18 \u00a9 ucles 2018 [turn over 3 some students were asked to choose their favourite colour of candy. all their choices are shown in the table. favourite colour red blue yellow green orange number of students 6 5 2 2 3 (a) find the number of students that were asked. . [1] (b) one of these students is chosen at random. find the probability that their favourite colour of candy is blue. . [1] (c) complete the bar chart. red blue yellow favourite colourgreen orange01234567 number of students [2] ", "6": "6 0607/33/o/n/18 \u00a9 ucles 2018 4 there are 36 cars altogether in a car park. there are 11 black cars, 10 red cars and the rest of the cars are blue. (a) work out the number of blue cars. . [1] (b) write down the fraction of cars in the car park that are black. . [1] (c) the information is to be shown in a pie chart. work out the sector angle for red cars. . [2] ", "7": "7 0607/33/o/n/18 \u00a9 ucles 2018 [turn over 5 (a) vrind from the letters above, write down all the letters that have (i) line symmetry, . [2] (ii) rotational symmetry, . [2] (iii) both line symmetry and rotational symmetry, . [1] (iv) neither line symmetry nor rotational symmetry. . [1] (b) on a poster, the letter i is a rectangle of width 2 cm and height 11 cm. (i) work out the perimeter of the letter i. ... cm [1] (ii) work out the area of the letter i. . cm2 [1] ", "8": "8 0607/33/o/n/18 \u00a9 ucles 2018 6 a bag contains 15 marshmallows. 8 of these are white and 7 are pink. terry picks a marshmallow at random from the bag and eats it. he then picks a second marshmallow at random from the bag and eats it. (a) complete the probability tree diagram. ... ...white pink... ...white pink... ...white pinkfirst marshmallow second marshmallow [3] (b) find the probability that both marshmallows were white. . [2] ", "9": "9 0607/33/o/n/18 \u00a9 ucles 2018 [turn over 7 a bcy x \u20136 \u20135 \u20134 \u20133 \u20132 \u20131 \u20136\u20135\u20134\u20133\u20132\u201311 2 3 4 5 6123456 0 (a) describe fully the single transformation that maps triangle a onto triangle b. .. .. [2] (b) describe fully the single transformation that maps triangle a onto triangle c. .. .. [2] (c) on the grid, draw the image of triangle a after a rotation of 180\u00b0 about the origin. label this image d. [2] (d) describe fully the single transformation that maps triangle c onto triangle d. .. .. [2] ", "10": "10 0607/33/o/n/18 \u00a9 ucles 2018 8 250 m 100 mnot to scale the diagram shows a rectangle joined to a semicircle. there is a path along the perimeter of this shape. (a) show that the length of the path is 757 m, correct to the nearest metre. [3] (b) maggie runs around the path at a speed of 220 metres per minute. work out how long it takes maggie to run around the path. give your answer in minutes. .. min [1] (c) jack takes 10 minutes to walk around the path. work out his average speed in km/h. km/h [3] (d) work out the total area enclosed by the path. m2 [3] (e) the area inside the path is covered with grass. grass cost $0.29 for one square metre. work out the total cost for the grass. $ . [1] ", "11": "11 0607/33/o/n/18 \u00a9 ucles 2018 [turn over 9 the diagram shows a 1cm2 grid. y x 1 2 3 4 5 6123456 07 8 9 10789 (a) on the grid, plot the points r(2, 2), s(8, 2) and t(8, 8). join these points to form a right-angled triangle. [2] (b) find (i) the length of rs, ... cm [1] (ii) the area of the triangle, .. cm2 [1] (iii) the gradient of rt. . [2] (c) find the co-ordinates of the midpoint of rt. ( ... , ... ) [1] (d) write down the equation of the line st. . [1] ", "12": "12 0607/33/o/n/18 \u00a9 ucles 2018 10 (a) a cob e d f15\u00b0 10\u00b0not to scale the diagram shows a circle, centre o. ab and cd are parallel chords and the line edf is a tangent to the circle at d. angle odc = 10\u00b0 and angle ocb = 15\u00b0. find the size of (i) angle ode , angle ode = [1] (ii) angle cdf , angle cdf = ... [1] (iii) angle cod , angle cod = ... [2] (iv) angle cba . angle cba = ... [1] ", "13": "13 0607/33/o/n/18 \u00a9 ucles 2018 [turn over (b) x + 15\u00b0x + 10\u00b0 x + 20\u00b0not to scale x\u00b0x + 25\u00b0 the diagram shows a pentagon. find the value of x. x = ... [3] ", "14": "14 0607/33/o/n/18 \u00a9 ucles 2018 11 the venn diagram shows the number of students in a class wearing a t-shirt, t, or a cardigan, c. t 8 3 7c .u (a) there are 20 students in total in the class. complete the venn diagram. [1] (b) find the probability that one of these students, chosen at random, wears (i) both a t-shirt and a cardigan, . [1] (ii) a t-shirt but not a cardigan. . [1] (c) find n( t ). . [1] (d) on the venn diagram, shade ct+ l. [1] 12 (a) tr s 5=- find the value of t when r = 3 and s = 4. t = [2] (b) simplify fully. (i) aba b 362-+- . [2] (ii) xx 510 . [1]", "15": "15 0607/33/o/n/18 \u00a9 ucles 2018 [turn over (c) solve. (i) x 25= x = [1] (ii) x72 51+= x = [2] (d) expand the brackets and simplify. () () xx42 22 1 +++ [2] (e) write down the inequality shown by this number line. \u20134 \u20133 \u20132 \u20131 0 1 2 3 4 5 6 7x . [1] (f) solve these simultaneous equations. you must show all your working. xy 9 2-= xy31 6 += x = y = [2] question 13 is printed on the next page.", "16": "16 0607/33/o/n/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.13 \u20132 4xy \u20131210 0not to scale the diagram shows the graph of () yxf= where ()xx x 25 6 f2=- ++ for x24gg- . (a) use your calculator to find the zeros of ()xf. ... and .. [2] (b) use your calculator to find the co-ordinates of the local maximum. ( ... , ... ) [2] (c) write down the equation of the line of symmetry. . [1] " }, "0607_w18_qp_41.pdf": { "1": "*8575909565* this document consists of 16 printed pages. dc (nf/ct) 156327/3 \u00a9 ucles 2018 [turn overcambridge international mathematics 0607/41 paper 4 (extended) october/november 2018 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/41/o/n/18 \u00a9 ucles 2018 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area =a c bcb a", "3": "3 0607/41/o/n/18 \u00a9 ucles 2018 [turn over answer all the questions. 1 (a) solve the following equations. (i) x 12 4 -= x = [1] (ii) xx94 68 -= + x = [2] (iii) x1259+= x = [2] (b) (i) solve xx65 102-+ =. x = or x = [3] (ii) use your answer to part (b)(i) to solve sins in xx 65 102-+ = for \u00b0\u00b0x 09 0 gg . x = ... or x = [3]", "4": "4 0607/41/o/n/18 \u00a9 ucles 2018 2 the table shows the marks for 75 students in a test. mark 0 1 2 3 4 5, 6 or 7 8 number of students 6 18 16 8 15 5 7 (a) write down the mode. [1] (b) find the range. [1] (c) find the median. [1] (d) find the inter-quartile range. [2] (e) calculate an estimate of the mean. [2] (f) give a reason why your answer to part (e) is an estimate. . . [1] (g) two of these students are chosen at random. find the probability that the highest mark of these students is 2. [3]", "5": "5 0607/41/o/n/18 \u00a9 ucles 2018 [turn over 3 04 \u20134\u201390 90y x () ()sinx x 12 21 0 f\u00b0=- - (a) on the diagram sketch the graph of () yxf= , for x 90 90 gg- . [3] (b) write down the co-ordinates of the x-intercepts. ( , ) ( , ) [2] (c) write down the co-ordinates of the local maximum. ( , ) [1] (d) the graph of yx 60=- intersects the graph of ()sin yx12 21 0\u00b0=- - three times. find the value of the x co-ordinate at each point of intersection. x = .. or x = .. or x = .. [3]", "6": "6 0607/41/o/n/18 \u00a9 ucles 2018 4 o cd ba not to scaley x abcd is a rectangle. the equation of the line ab is xy43 24 += . (a) find the co-ordinates of (i) point a, ( , ) [1] (ii) point b, ( , ) [1] (iii) the midpoint of ab. ( , ) [2]", "7": "7 0607/41/o/n/18 \u00a9 ucles 2018 [turn over (b) rearrange the equation xy43 24 += to make y the subject. y = [2] (c) find the equation of the line bc. give your answer in the form ym xc=+ . y = [3] (d) find the co-ordinates of (i) point c, ( , ) [1] (ii) point d. ( , ) [3]", "8": "8 0607/41/o/n/18 \u00a9 ucles 2018 5 the number of fish in a lake decreases by 4% each year. in january 2018 there are 30 000 fish in the lake. (a) calculate the number of fish in the lake in (i) january 2019, [2] (ii) january 2029, [3] (iii) january 2017. [3] (b) find the last year in which there were at least 50 000 fish in the lake. [4]", "9": "9 0607/41/o/n/18 \u00a9 ucles 2018 [turn over (c) philip runs a fishing business and he works 50 weeks every year. in 2018, he catches 800 kg of fish in each of these weeks. he sells all the fish he catches at a price of $3.50 for each kilogram. (i) calculate the total amount he receives in 2018. $ [3] (ii) for each of the 50 weeks, philip\u2019s business costs $2240 to run. calculate his profit as a percentage of $2240. % [3] (d) in 2019, philip\u2019s business costs 8% more to run than in 2018. the selling price of fish decreases by 10%. find the amount of fish, in kilograms, philip will need to catch each week to keep the percentage profit found in part (c)(ii) the same. ... kg [4]", "10": "10 0607/41/o/n/18 \u00a9 ucles 2018 6 y x 01 \u20131 \u20132 \u20133 \u20134 \u20135 \u20136 \u20137 \u20138 \u201391 \u20131 \u20132 \u20133 \u20134 \u20135 \u20136 \u20137 \u20138 \u2013923456789 2 3 4 5 6 7 8 9a (a) reflect triangle a in the line x 2=- . label the image b. [2] (b) rotate triangle a through 180\u00b0 about ( -2, -1). label the image c. [2] (c) describe fully the single transformation that maps triangle c onto triangle b. . . [2] (d) enlarge triangle a with centre of enlargement (1, 2) and scale factor 2. label the image d. [2]", "11": "11 0607/41/o/n/18 \u00a9 ucles 2018 [turn over 7 (a) find an expression for the nth term for each of these sequences. (i) 80, 77, 74, 71, \u2026 [2] (ii) 128, 64, 32, 16, \u2026 [2] (b) the nth term of a sequence is n 12-. find the first four terms of this sequence. , , , [2] (c) the nth term of a sequence is n3- . find the first four terms of this sequence. , , , [2] (d) the nth term of a sequence is nn 412++ . (i) find the first three terms of this sequence. , , [2] (ii) show that when n = 41 the number in this sequence is not prime. [1]", "12": "12 0607/41/o/n/18 \u00a9 ucles 2018 8 not to scales ba o d t c a, b, c and d lie on a circle, centre o. st is a tangent to the circle at a. odt is a straight line that bisects angle aoc . (a) complete the statement. angle oat = because ... . [2] (b) dt = oc find angle abc . angle abc = [4]", "13": "13 0607/41/o/n/18 \u00a9 ucles 2018 [turn over 9 050 \u201350\u20133 5y x ()x xxx34 1 f32=- -+ for x35gg- . (a) on the diagram, sketch the graph of () yxf= . [2] (b) write down the co-ordinates of the local minimum. (. , .) [2] (c) find the range of values of k so that ()xkf= has only one solution. ... [2] (d) () xx x 36 4 g2=- - for x35gg- . the graph of () yxf= intersects the graph of () yxg= twice. solve () () xxfg2 . [2]", "14": "14 0607/41/o/n/18 \u00a9 ucles 2018 10 not to scalea xb dc o oac is a triangle with ab : bc = 1 : 2 and od : dc = 1 : 2. the lines ob and ad intersect at x. oa a6= and oc c6= . (a) find an expression, in terms of a and/or c, for (i) ac, ac = [1] (ii) bc, bc = [1] (iii) bd, giving your answer in its simplest form. bd = [2]", "15": "15 0607/41/o/n/18 \u00a9 ucles 2018 [turn over (b) use your answer to part (a)(iii) to explain why oa and bd are parallel. . [1] (c) explain why triangle oax and triangle bdx are similar. . . [2] (d) find an expression, in terms of a and c, for (i) ad, ad = [2] (ii) xd, giving your answer in its simplest form. xd = ... [2] (e) find the ratio area axo : area bxd . : [2] question 11 is printed on the next page.", "16": "16 0607/41/o/n/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.11 not to scale ab c8.6 cm 9.3 cm the area of triangle abc = 23.5 cm2. (a) show that angle bac =\u00a036.0\u00b0, correct to 1 decimal place. [2] (b) use the cosine rule to find bc. bc = ... cm [3] (c) all the angles in triangle abc are acute. use the sine rule to find the largest angle in the triangle abc . [3]" }, "0607_w18_qp_42.pdf": { "1": "this document consists of 18 printed pages and 2 blank pages. dc (nh/cgw) 156329/3 \u00a9 ucles 2018 [turn over *3130754688* cambridge international mathematics 0607/42 paper 4 (extended) october/november 2018 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/42/o/n/18 \u00a9 ucles 2018 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/42/o/n/18 \u00a9 ucles 2018 [turn over answer all the questions. 1 adila has $10 000. (a) she uses some of the money to buy a car. the salesman reduces the price from $3800 to $3610. calculate the percentage reduction. % [3] (b) adila invests the remaining $6390 at a rate of 3% per year compound interest. (i) find the value of the investment at the end of 5 years. $ [3] (ii) find the least number of complete years after which the value of the investment is more than $9000. [4]", "4": "4 0607/42/o/n/18 \u00a9 ucles 2018 2 here are 12 numbers. 15 9 6 14 6 8 12 21 11 19 6 12 (a) for these numbers find (i) the range, [1] (ii) the mode, [1] (iii) the median, [1] (iv) the mean, [1] (v) the inter-quartile range. [2] (b) dee chooses a number at random from these numbers. find the probability that it is a prime number. [1]", "5": "5 0607/42/o/n/18 \u00a9 ucles 2018 [turn over 3 \u20132 \u20133 \u20134 \u20135 \u20136 \u20131 1 10 2 3 4 5 6 7 8 9 \u20133 \u20134 \u20135\u20132\u201310123457 6 ab xy (a) translate triangle a by the vector 5 3-eo . [2] (b) describe fully the single transformation that maps triangle a onto triangle b. .. .. [3] (c) describe fully the single transformation that is equivalent to a reflection in y = -x followed by a reflection in the y-axis. you may use the grid below to help you. .. .. [3]", "6": "6 0607/42/o/n/18 \u00a9 ucles 2018 4 (a) y varies directly as the square of ( x + 2). when x = 3, y = 100. (i) find an equation connecting x and y. [2] (ii) find the value of y when x = 18. [1] (iii) find the values of x when y = 25. [2] (b) z varies inversely as w. when w = a, z = 18. find the value of z when w = a 9. [2]", "7": "7 0607/42/o/n/18 \u00a9 ucles 2018 [turn over 5 30 \u2013200 \u20134 4xy ()xx x12 6 f3=- + (a) on the diagram, sketch the graph of () yxf= for x44gg- . [2] (b) find the positive zeros of f( x). [2] (c) find the co-ordinates of (i) the local maximum, ( , ) [1] (ii) the local minimum. ( , ) [1] (d) describe fully the symmetry of the graph of y = f(x). .. .. [3]", "8": "8 0607/42/o/n/18 \u00a9 ucles 2018 6 10 cmnot to scale the diagram shows a regular pentagon, of side 10 cm, with its vertices lying on a circle. (a) show that the radius of the circle is 8.51 cm, correct to 3 significant figures. [4] (b) calculate (i) the perimeter of the shaded segment, .. cm [3] (ii) the area of the shaded segment. . cm2 [3]", "9": "9 0607/42/o/n/18 \u00a9 ucles 2018 [turn over 7 the length of the jinghu high speed railway from beijing to shanghai is 1318 km. (a) a train travels at an average speed of 252 km/h. this train leaves beijing at 12 49. the local time in beijing is the same as the local time in shanghai. find the time, correct to the nearest minute, that this train arrives in shanghai. [4] (b) on the journey this train passes over a bridge of length 6772 m at 252 km/h. the train is 401 m long. (i) change 252 kilometres per hour to metres per second. . m/s [2] (ii) calculate the time, in seconds, for the train to completely cross the bridge. . s [2]", "10": "10 0607/42/o/n/18 \u00a9 ucles 2018 8 the 150 members of a sports club were asked if they played cricket ( c), hockey ( h) or tennis ( t). some members play none of the three sports. the venn diagram shows the numbers of members who play the three sports. c th 12 8 13 1524 2735u (a) calculate the number of members who play none of the three sports. [1] (b) two of the 150 members are picked at random. calculate the probability that (i) they both play hockey and tennis but not cricket, [2] (ii) they are both members of the set ()ch t ,+ l. [3]", "11": "11 0607/42/o/n/18 \u00a9 ucles 2018 [turn over (c) three of the members who play tennis are chosen at random. calculate the probability that none of them play cricket. [3]", "12": "12 0607/42/o/n/18 \u00a9 ucles 2018 9 120 students each took two mathematics examinations, paper 1 and paper 2. the marks for paper 1 are shown below. mark ( m) frequency 10 1 m g 20 2 20 1 m g 30 4 30 1 m g 40 6 40 1 m g 50 12 50 1 m g 60 22 60 1 m g 70 34 70 1 m g 80 28 80 1 m g 90 12 (a) complete the cumulative frequency diagram to show the results. the first section has been drawn for you. 02040 20 0 40 mark60 806080100 cumulative frequency120 m [4]", "13": "13 0607/42/o/n/18 \u00a9 ucles 2018 [turn over (b) use your cumulative frequency diagram to estimate (i) the median mark, [1] (ii) the inter-quartile range, [2] (iii) the number of students with a mark greater than 84. [2] (c) the table below shows some information about paper 2. lowest mark 4 highest mark 80 median 44 lower quartile 32 inter-quartile range 24 on the grid opposite, draw the cumulative frequency diagram for paper 2. [3]", "14": "14 0607/42/o/n/18 \u00a9 ucles 2018 10 north 120 mnorth not to scale b a in the diagram, point b is due east of point a. (a) point c is on a bearing of 060\u00b0 from a and a bearing of 325\u00b0 from b. calculate the distance bc. bc = m [4] (b) point d is south of ab. d is 80 m from a and 90 m from b. calculate the bearing of d from b. [4]", "15": "15 0607/42/o/n/18 \u00a9 ucles 2018 [turn over 11 not to scale 8 m 1.8 m the diagram shows a polythene structure in which a farmer grows vegetables. the structure consists of a prism with a quarter of a sphere at one end. the cross-section of the prism is a semicircle. the semicircle has a radius of 1.8 m and the length of the prism is 8 m. (a) calculate the volume of the structure. ... m3 [3] (b) the curved surface of the prism and the two ends of the structure are made of polythene. calculate the area of the polythene. ... m2 [4]", "16": "16 0607/42/o/n/18 \u00a9 ucles 2018 12 15 \u2013100 \u20136 6y x ()()()xxx 223f=+- (a) on the diagram, sketch the graph of y = f(x) for values of x between -6 and 6. [3] (b) write down the equations of the asymptotes of y = f(x). [2] (c) g(x) = 5 - 2x (i) solve f( x) = g(x). x = or x = [2] (ii) find g(f( x)). give your answer as a single fraction in its simplest form. [3]", "17": "17 0607/42/o/n/18 \u00a9 ucles 2018 [turn over 13 a a bbopnot to scale the point p divides ab in the ratio 3 : 2. oa a= and ob b=. (a) write each of these vectors in terms of a and/or b, giving each answer in its simplest form. (i) ab ab = [1] (ii) op op = [2] (b) the point q is such that oq op35= . (i) write bq, in terms of a and/or b, in its simplest form. bq = [2] (ii) use your answer to part (b)(i) to explain why oa and bq are parallel. .. [1]", "18": "18 0607/42/o/n/18 \u00a9 ucles 2018 14 a is the point (1, 9) and b is the point (7, 1). (a) find the length of ab. [3] (b) find the co-ordinates of the midpoint of ab. ( , ) [2] (c) b is the reflection of a in the line l. find the equation of the line l. [4]", "19": "19 0607/42/o/n/18 \u00a9 ucles 2018 blank page", "20": "20 0607/42/o/n/18 \u00a9 ucles 2018 blank page permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_w18_qp_43.pdf": { "1": "*3837763901* this document consists of 16 printed pages. dc (sc/cgw) 156335/2 \u00a9 ucles 2018 [turn overcambridge international mathematics 0607/43 paper 4 (extended) october/november 2018 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/43/o/n/18 \u00a9 ucles 2018 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/43/o/n/18 \u00a9 ucles 2018 [turn over answer all the questions. 1 (a) in a school there are 225 girls and 190 boys. (i) work out the number of boys as a fraction of the total number of students. give your answer in its lowest terms. [2] (ii) write the ratio number of girls : number of boys in its simplest form. [2] (b) in a mathematics class there are 15 boys. the ratio number of girls : number of boys = 6 : 5. find the number of girls in this class. [2] (c) in a science class of 33 students there are 15 boys. (i) find the number of boys as a percentage of the number of students in the class. % [1] (ii) 20% of these boys did not complete an experiment. work out the number of boys who did not complete the experiment. [2] (d) this year the number of students studying mathematics is 390. this is an increase of 4% on the number of students who studied mathematics last year. work out the number of students who studied mathematics last year. [3]", "4": "4 0607/43/o/n/18 \u00a9 ucles 2018 2 \u20132 \u20133 \u20134 \u20135 \u20131 1 10 2 3 4 5 0 6 7 8 9123457 6810 9 tpy x (a) describe fully the single transformation that maps triangle t onto triangle p. . . [3] (b) reflect triangle t in the y-axis. [1] (c) translate triangle t by the vector 5 6eo. [2] (d) stretch triangle t, stretch factor 3 and x-axis invariant. [2]", "5": "5 0607/43/o/n/18 \u00a9 ucles 2018 [turn over 3 (a) p2 1=-eo 3 2q=eo find (i) qp-, fp [1] (ii) 2p, fp [1] (iii) 2p. [2] (b) a is the point (0, 2) and b is the point (2, 7). (i) write ab as a column vector. fp [2] (ii) 2 bc ab= find the co-ordinates of c. ( , ) [2]", "6": "6 0607/43/o/n/18 \u00a9 ucles 2018 4 (a) 4 \u201340 \u20133 3xy ()xxx21f=+ , x0=y (i) on the diagram, sketch the graph of () yx f= for values of x between -3 and 3. [3] (ii) find the co-ordinates of the local minimum point. ( , ) [2] (iii) find the range of f()x for x02. [1] (iv) write down the equations of the two asymptotes to the graph of () yx f= . [2]", "7": "7 0607/43/o/n/18 \u00a9 ucles 2018 [turn over (b) 5 \u201330 \u20132 3xy (i) on the diagram, sketch the graph of (a) y23x=- for x23gg- , [2] (b) log yx 6= for x02. [2] (ii) solve the inequality logx 62 3x2-. [2]", "8": "8 0607/43/o/n/18 \u00a9 ucles 2018 5 the table shows the scores of 10 students in a mathematics test and in a physics test. student a b c d e f g h i j mathematics ( x) 4 6 6 8 9 9 9 10 10 10 physics ( y) 5 5 6 9 9 8 7 9 10 7 (a) find the median and the upper quartile of the physics scores. median = upper quartile = [2] (b) write down the type of correlation between the mathematics scores and the physics scores. [1] (c) find the equation of the line of regression in the form ym xc=+ . y = [2] 6 23 cm11 cm 50\u00b0x cmnot to scale calculate (a) the area of the triangle, . cm2 [2] (b) the value of x. x = [3]", "9": "9 0607/43/o/n/18 \u00a9 ucles 2018 [turn over 7 (a) the population of a small town is decreasing at a rate of 5% every 10 years. the population is now 26 010. calculate the population in 20 years time. give your answer correct to the nearest 100. [3] (b) the population was previously increasing at a rate of 2% each year. the population is now 26 010. (i) calculate the population 2 years ago. [2] (ii) find the number of complete years since the population was last less than 20 000. [4]", "10": "10 0607/43/o/n/18 \u00a9 ucles 2018 8 6 \u201350 \u20131 5xy ()xx x 14 f2=+ - (a) on the diagram, sketch the graph of () yx f= for x15gg- . [2] (b) write down the equation of the line of symmetry of the graph of () yx f= . [1] (c) (i) find the zeros of ()xf. [2] (ii) solve the inequality ()x 0 f2. [1] (d) solve the equation ()x 10 f+= . x = or x = [2] (e) ()xx 5 g=- on the diagram, sketch the graph of () yx g= for x15gg- . [2] (f) on the diagram, shade the region where () yx fg and () yx gg . [1]", "11": "11 0607/43/o/n/18 \u00a9 ucles 2018 [turn over 9 when helena goes for a walk, she walks d kilometres. the probability that d021g is 51 and the probability that d241g is 41. (a) find the probability that d42. [2] (b) if it rains, helena never goes for a walk. if it does not rain, helena always goes for a walk. on any day, the probability that it rains is 31. (i) complete the tree diagram showing the probabilities of the two events. rain distance ( d km) rain 0 < d g 2 2 < d g 4 d > 4not rain.. ..1 3 1 5 1 4 [1] (ii) find the probability that, on any day, helena walks more than 2 km. [3] (iii) find the expected number of days that helena walks more than 2 km, during a period of 90 days. [1]", "12": "12 0607/43/o/n/18 \u00a9 ucles 2018 10 p c d a b8 cm6 cmnot to scale 7 cm the diagram shows a pyramid of height 7 cm on a rectangular base 8 cm by 6 cm. the point p is directly above the centre of the base. (a) calculate the angle between the triangle pbc and the base abcd . [2] (b) calculate the angle between pb and the base abcd . [3] (c) calculate pc. pc = .. cm [2]", "13": "13 0607/43/o/n/18 \u00a9 ucles 2018 [turn over (d) calculate angle pcb . angle pcb = [2] (e) x is a point on the line pc so that angle bxc = 60\u00b0. calculate bx. bx = .. cm [3] 11 the mass, m grams, of each of 200 potatoes is measured. the histogram shows the results. 2 1.5 1frequency density 0.5 0 0 50 100 150 mass (grams)m 200 250 300 (a) complete the frequency table. mass ( m grams) m0 1001g m 100 1501g m 150 2001g m 200 3001g frequency 20 [2] (b) calculate an estimate of the mean. . g [2]", "14": "14 0607/43/o/n/18 \u00a9 ucles 2018 12 (a) (x + 1) cm (3x + 2) cmnot to scale the perimeter of the rectangle is 44 cm. find the value of x. x = [3] (b) y cm( y \u22121) cm not to scale the area of the rectangle is 272 cm2. find the value of y. y = [3]", "15": "15 0607/43/o/n/18 \u00a9 ucles 2018 [turn over (c) w cmarea = 7 cm2area = 5 cm2 w cmv cm( v + 1) cmnot to scale the two rectangles have the same length, w cm. find the value of v. v = [3] (d) 2p cm 3p cmarea = 9 cm2area = 10 cm2not to scale the perimeter of the larger rectangle is 2 cm more than the perimeter of the smaller rectangle. find the value of p. p = [4] question 13 is printed on the next page.", "16": "16 0607/43/o/n/18 \u00a9 ucles 2018 13 ()xx 1 f=- ()xx 32 g=- ()xx 4 h2=- ()xx 32 k2=+ (a) find ()0h. [1] (b) find, giving your answer in its simplest form. (i) (( ))x gf [2] (ii) () () () xx x gf k #+ [3] (c) find ()x f1-. ()x f1- = [1] (d) find x when (i) ()x 2 g=, x = [2] (ii) ()x 3 h=. x = [3] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_w18_qp_51.pdf": { "1": "*0726134080* this document consists of 8 printed pages. dc (rw/cgw) 153616/1 \u00a9 ucles 2018 [turn overcambridge international mathematics 0607/51 paper 5 (core) october/november 2018 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and to communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/51/o/n/18 \u00a9 ucles 2018 answer all the questions. investigation dots in rectangles this investigation looks at the number of dots inside rectangles drawn on square dotty paper. 1 rectangles with a height of 1 unit have no dots inside. height 1 width 1height 1 width 2height 1 width 3height 1 width 4 (a) (i) these rectangles all have a height of 2 units. height 2 width 1height 2 width 2height 2 width 3height 2 width 4 complete the table. height of rectangle (h)width of rectangle (w)number of dots inside rectangle (d) 2 1 2 2 2 3 2 4 (ii) find an expression, in terms of w, for the number of dots, d, inside rectangles of height 2. ...", "3": "3 0607/51/o/n/18 \u00a9 ucles 2018 [turn over (b) complete the tables below. you may use the square dotty paper on this page to help you. height of rectangle (h)width of rectangle (w)number of dots inside rectangle (d) 3 1 3 2 3 3 3 4 3 w 2(w - 1) height of rectangle (h)width of rectangle (w)number of dots inside rectangle (d) 4 1 4 2 4 3 4 4 4 w", "4": "4 0607/51/o/n/18 \u00a9 ucles 2018 (c) (i) find a formula, in terms of h and w, for the number of dots, d, inside a rectangle of height h and width w. d = ... (ii) use your formula in part (i) to show that there are 30 dots inside a rectangle of height 6 and width 7. (iii) there are 33 dots inside a rectangle. find the height and the width of this rectangle. ... 2 (a) squares are formed when h = w. change your formula in question 1(c)(i) to find the number of dots, d, inside a square of side s. ... (b) find the number of dots inside a square of side 10. ...", "5": "5 0607/51/o/n/18 \u00a9 ucles 2018 [turn over 3 the rectangles below are drawn at an angle of 45\u00b0 to the horizontal. they are called diagonal rectangles. the diagonal lines between the dots give the height and the width of the diagonal rectangles. width 3width 2width 1 height 1 height 1 height 1 height 2 width 1", "6": "6 0607/51/o/n/18 \u00a9 ucles 2018 (a) complete the tables below. height of diagonal rectangle (h)width of diagonal rectangle (w)number of dots inside diagonal rectangle (d) 1 1 1 1 2 2 1 3 3 1 4 height of diagonal rectangle (h)width of diagonal rectangle (w)number of dots inside diagonal rectangle (d) 2 1 2 2 2 2 3 2 4 2 w 3w - 1 height of diagonal rectangle (h)width of diagonal rectangle (w)number of dots inside diagonal rectangle (d) 3 1 3 2 3 3 3 4", "7": "7 0607/51/o/n/18 \u00a9 ucles 2018 [turn over (b) use your results from part (a) and any patterns you notice to complete the following table with expressions, in terms of the width w, for the number of dots inside diagonal rectangles. height of diagonal rectangle (h)number of dots inside diagonal rectangle (d) 1 2 3w - 1 3 4 5 9w - 4 (c) (i) find a formula, in terms of h and w, for the number of dots, d, inside a diagonal rectangle. ... (ii) use your formula in part (i) to find the number of dots inside the diagonal rectangle of height 10 and width 3. ... question 4 is printed on the next page.", "8": "8 0607/51/o/n/18 \u00a9 ucles 2018 4 (a) diagonal squares are formed when h = w. change your formula in question 3(c)(i) to find the number of dots, d, inside a diagonal square of side s. ... (b) there are 181 dots in a diagonal square. find the length of one side. ... permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge." }, "0607_w18_qp_52.pdf": { "1": "*3136995946* this document consists of 7 printed pages and 1 blank page. dc (lk/cgw) 153617/1 \u00a9 ucles 2018 [turn overcambridge international mathematics 0607/52 paper 5 (core) october/november 2018 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and to communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/52/o/n/18 \u00a9 ucles 2018 answer all the questions. investigation right spirals this investigation is about the lengths of spirals drawn on a square grid. a robot starts from 0 and moves 1 unit to corner 1. it then turns right and moves 1 unit to corner 2. it then turns right and moves 2 units to corner 3. it then turns right and moves 2 units to corner 4. it then turns right and moves 3 units to corner 5. this forms a spiral, shown on the grid below. 5 4 32 1 010 the robot continues to turn and move in the same way. 1 (a) continue the spiral to corner 10. (b) the length of the spiral from 0 to corner 4 is 6 units. find the length of the spiral from 0 to corner 10. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "3": "3 0607/52/o/n/18 \u00a9 ucles 2018 [turn over (c) use your spiral to complete this table. corner numberlengths added length from 0 1 1 1 2 1 + 1 2 3 1 + 1 + 2 4 4 6 5 6 1 + 1 + 2 + 2 + 3 + 3 12 7 1 + 1 + 2 + 2 + 3 + 3 + 4 16 8 1 + 1 + 2 + 2 + 3 + 3 + 4 + 4 9 10 1 + 1 + 2 + 2 + 3 + 3 + 4 + 4 + 5 + 5", "4": "4 0607/52/o/n/18 \u00a9 ucles 2018 2 this table shows the first five terms of a sequence. n 1 2 3 4 5 6 7 term of the sequence1 3 6 10 15 (a) for this sequence, fill in the next two terms. (b) write down the mathematical name for this sequence of numbers. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (c) the nth term for this sequence is ()nn 21+. show that this is correct when n = 5. 3 this table shows the length, l, of the spiral from 0 to an even numbered corner, k. (a) use your table from question 1(c) to help you complete this table. klength (l) 2 2 4 6 6 12 8 10 12 14 56 16", "5": "5 0607/52/o/n/18 \u00a9 ucles 2018 [turn over (b) complete this table using your answers to question 2(a) and question 3(a) . nterm of the sequenceklength (l) 1 1 2 2 2 3 4 6 3 6 6 12 4 10 8 5 15 10 6 12 (i) complete this formula for n in terms of k. n = \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (ii) write down the connection between the length, l, and the term of the sequence. ... (iii) use part (i) , part(ii) and question 2(c) to show that the formula for the length, l, of the spiral from 0 to an even numbered corner, k, is lkk 221 =+ eo . (iv) show that the formula from part(iii) is correct for corner 6. (v) show that the formula from part (iii) is not correct when k is an odd number .", "6": "6 0607/52/o/n/18 \u00a9 ucles 2018 4 (a) write down the length of the spiral (i) from corner 5 to corner 6 , \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (ii) from corner 6 to corner 7. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (b) when k is an even number, find an expression, in terms of k, for the length of the spiral (i) from corner ( k \u2013 1) to corner k, \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (ii) from corner k to corner ( k + 1). \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "7": "7 0607/52/o/n/18 \u00a9 ucles 2018 5 (a) using question 3(b)(iii) and question 4 (b)(i) , show that the length of the spiral from 0 to corner 7 is 16 units. (b) find the length of the spiral from 0 to corner 91. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "8": "8 0607/52/o/n/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_w18_qp_53.pdf": { "1": "*5524846572* this document consists of 7 printed pages and 1 blank page. dc (jc) 171350 \u00a9 ucles 2018 [turn overcambridge international mathematics 0607/53 paper 5 (core) october/november 2018 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and to communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/53/o/n/18 \u00a9 ucles 2018 answer all the questions. investigation right spirals this investigation is about the lengths of spirals drawn on a square grid. a robot starts from 0 and moves 1 unit to corner 1. it then turns right and moves 1 unit to corner 2. it then turns right and moves 2 units to corner 3. it then turns right and moves 2 units to corner 4. it then turns right and moves 3 units to corner 5. this forms a spiral, shown on the grid below. 5 4 32 1 010 the robot continues to turn and move in the same way. 1 (a) continue the spiral to corner 10. (b) the length of the spiral from 0 to corner 4 is 6 units. find the length of the spiral from 0 to corner 10. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "3": "3 0607/53/o/n/18 \u00a9 ucles 2018 [turn over (c) use your spiral to complete this table. corner numberlengths added length from 0 1 1 1 2 1 + 1 2 3 1 + 1 + 2 4 4 6 5 6 1 + 1 + 2 + 2 + 3 + 3 12 7 1 + 1 + 2 + 2 + 3 + 3 + 4 16 8 1 + 1 + 2 + 2 + 3 + 3 + 4 + 4 9 10 1 + 1 + 2 + 2 + 3 + 3 + 4 + 4 + 5 + 5", "4": "4 0607/53/o/n/18 \u00a9 ucles 2018 2 this table shows the first five terms of a sequence. n 1 2 3 4 5 6 7 term of the sequence1 3 6 10 15 (a) for this sequence, fill in the next two terms. (b) write down the mathematical name for this sequence of numbers. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (c) the nth term for this sequence is ()nn 21+. show that this is correct when n = 5. 3 this table shows the length, l, of the spiral from 0 to an even numbered corner, k. (a) use your table from question 1(c) to help you complete this table. klength (l) 2 2 4 6 6 12 8 10 12 14 56 16", "5": "5 0607/53/o/n/18 \u00a9 ucles 2018 [turn over (b) complete this table using your answers to question 2(a) and question 3(a) . nterm of the sequenceklength (l) 1 1 2 2 2 3 4 6 3 6 6 12 4 10 8 5 15 10 6 12 (i) complete this formula for n in terms of k. n = \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (ii) write down the connection between the length, l, and the term of the sequence. ... (iii) use part (i) , part(ii) and question 2(c) to show that the formula for the length, l, of the spiral from 0 to an even numbered corner, k, is lkk 221 =+ eo . (iv) show that the formula from part(iii) is correct for corner 6. (v) show that the formula from part (iii) is not correct when k is an odd number .", "6": "6 0607/53/o/n/18 \u00a9 ucles 2018 4 (a) write down the length of the spiral (i) from corner 5 to corner 6 , \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (ii) from corner 6 to corner 7. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (b) when k is an even number, find an expression, in terms of k, for the length of the spiral (i) from corner ( k \u2013 1) to corner k, \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (ii) from corner k to corner ( k + 1). \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "7": "7 0607/53/o/n/18 \u00a9 ucles 2018 5 (a) using question 3(b)(iii) and question 4 (b)(i) , show that the length of the spiral from 0 to corner 7 is 16 units. (b) find the length of the spiral from 0 to corner 91. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "8": "8 0607/53/o/n/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_w18_qp_61.pdf": { "1": "this document consists of 15 printed pages and 1 blank page. dc (nh/ct) 153618/3 \u00a9 ucles 2018 [turn over *6949648158* cambridge international mathematics 0607/61 paper 6 (extended) october/november 2018 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a (questions 1 to 4) and part b (questions 5 to 7). you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/61/o/n/18 \u00a9 ucles 2018 answer both parts a and b. a investigation (questions 1 to 4) dots in rectangles (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation looks at the number of dots inside rectangles drawn on square dotty paper. 1 rectangles are drawn at an angle to the horizontal. they are called diagonal rectangles. the rectangles below are drawn at an angle of 45\u00b0 to the horizontal. two sides of each rectangle have a gradient of 1. these are diagonal rectangles with gradient 1. length 3length 2length 1 width 1 width 1 width 1width 2 length 1", "3": "3 0607/61/o/n/18 \u00a9 ucles 2018 [turn over (a) complete the tables below. width (w )length (l)number of dots inside a diagonal rectangle with gradient 1 (d) 1 1 1 1 2 2 1 3 1 4 1 5 width (w )length (l)number of dots inside a diagonal rectangle with gradient 1 (d ) 2 1 2 2 2 2 3 2 4 2 5 width (w )length (l)number of dots inside a diagonal rectangle with gradient 1 (d ) 3 1 3 3 2 3 3 3 4 3 5", "4": "4 0607/61/o/n/18 \u00a9 ucles 2018 (b) use your results from part (a) and any patterns you notice to complete the table. width (w )number of dots inside a diagonal rectangle with gradient 1 (d ) 1 2 3l \u2212 1 3 4 5 9l \u2212 4 (c) a formula, in terms of w and l, for the number of dots, d, inside a diagonal rectangle with gradient 1, is d = (aw + b)l - (w + c) . find the values of a, b and c. a = ... b = ... c = ... 2 the diagram below shows three diagonal rectangles, each of width 1 and gradient 21.", "5": "5 0607/61/o/n/18 \u00a9 ucles 2018 [turn over (a) complete the tables below. you may use the square dotty paper to help you. width (w )length (l)number of dots inside a diagonal rectangle with gradient 21 (d ) 1 1 4 1 2 8 1 3 12 1 4 1 5 width (w )length (l)number of dots inside a diagonal rectangle with gradient 21 (d ) 2 1 8 2 2 17 2 3 2 4 2 5", "6": "6 0607/61/o/n/18 \u00a9 ucles 2018 width (w )length (l)number of dots inside a diagonal rectangle with gradient 21 (d ) 3 1 12 3 2 3 3 40 3 4 3 5", "7": "7 0607/61/o/n/18 \u00a9 ucles 2018 [turn over (b) use your results from part (a) and any patterns you notice to complete the table. width (w)number of dots inside a diagonal rectangle with gradient 21 (d ) 1 2 3 4 19l \u2212 3 5 24l \u2212 4 (c) find a formula, in terms of w and l, for the number of dots, d, inside a diagonal rectangle with gradient 21. ...", "8": "8 0607/61/o/n/18 \u00a9 ucles 2018 3 the diagram below shows three diagonal rectangles, each of width 1 and gradient 1 3.", "9": "9 0607/61/o/n/18 \u00a9 ucles 2018 [turn over (a) complete the table. you may use the square dotty paper below to help you. width (w )number of dots inside a diagonal rectangle with gradient 1 3(d ) 1 2 19l \u2212 1 3 4 5 49l \u2212 4 (b) find a formula, in terms of w and l, for the number of dots, d, inside a diagonal rectangle with gradient 1 3. ...", "10": "10 0607/61/o/n/18 \u00a9 ucles 2018 4 (a) complete the following table, using your answers to question 1(c) , question 2(c) and question 3(b) and any patterns you notice. gradientnumber of dots inside a diagonal rectangle (d ) 1 1 2 1 3 1 4(17w \u2013 1)l \u2013 (w \u2013 1) 1 5 (b) use your answers to part (a) to find a formula, in terms of w, l and n, for the number of dots, d, inside a diagonal rectangle with a gradient of n1. ... (c) there are 4833 dots inside a 4 by 12 diagonal rectangle. find the gradient of this rectangle. ...", "11": "11 0607/61/o/n/18 \u00a9 ucles 2018 [turn over b modelling (questions 5 to 7) ladders (20 marks) you are advised to spend no more than 45 minutes on this part. this task looks at the safe positions for placing a ladder against a wall. a ladder is x metres long. it leans against a vertical wall. the bottom of the ladder is 1.5 m from the base of the wall. the ladder touches the wall y metres above the ground. not to scale xy 1.5 5 (a) show that . yx 2252=- . (b) (i) sketch the graph of . yx 2252=- on the axes below. \u20136 0 66y x (ii) only one part of the graph fits this practical situation. give a reason why the other part does not. ... ...", "12": "12 0607/61/o/n/18 \u00a9 ucles 2018 6 safety rules for ladders say that the angle between the bottom of the ladder and the ground must be more than 76\u00b0. not to scale x z (a) to use a ladder safely, show that a model for its position is . zx02421 . (b) to use a ladder safely the angle between the bottom of the ladder and the ground must be less than 82\u00b0. find a second inequality connecting z and x. ...", "13": "13 0607/61/o/n/18 \u00a9 ucles 2018 [turn over (c) on the axes, shade the region defined by the inequalities in part (a) and part (b) . z x 0 0 1 2 3 4 5 612 (d) a ladder is 3 m long. to use this ladder safely, a 1 z 1 b. use your graph in part (c) to find the value of a and the value of b. 1 z 1 ", "14": "14 0607/61/o/n/18 \u00a9 ucles 2018 7 ladders can be extended to increase their original length. a ladder is extended by 0.9 times its original length. the bottom of this ladder is 1.5 m from the base of the wall. 1.5yx + 0.9 x (a) find a formula for y in terms of x. ... (b) (i) when the ladder is extended it reaches higher up the wall. this increase in height, y, is c metres. using the model in question 5(a) , show that a model for c is .. . cx x 3612 25 22522=- -- .", "15": "15 0607/61/o/n/18 \u00a9 ucles 2018 (ii) on the axes below, sketch the graph of c for 0 1 x 1 6. c 6x 0 (c) this part is about the smallest increase in height that the ladder reaches up the wall. (i) find this smallest increase in height. ... (ii) write down the original length of the ladder. ... (iii) show how you can decide whether the extended ladder is safe.", "16": "16 0607/61/o/n/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_w18_qp_62.pdf": { "1": "*1289084149* this document consists of 14 printed pages and 2 blank pages. dc (nf/cgw) 153619/2 \u00a9 ucles 2018 [turn overcambridge international mathematics 0607/62 paper 6 (extended) october/november 2018 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a (questions 1 to 4) and b (questions 5 to 8). you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and to communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/62/o/n/18 \u00a9 ucles 2018 answer both parts a and b. a investigation (questions 1 to 4) right spirals (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation is about the lengths of spirals drawn on a square co-ordinate grid. a robot starts from (0, 0) and moves 1 unit to corner 1. it then turns right and moves 1 unit to corner 2. it then turns right and moves 2 units to corner 3. it then turns right and moves 2 units to corner 4. it then turns right and moves 3 units to corner 5. this forms a spiral, shown on the grid below. 406 4 2 \u22122 \u22124 \u22126\u22126 \u22124 \u22122 2 4 6xy 5 2 1 3 the robot continues to turn and move in the same way.", "3": "3 0607/62/o/n/18 \u00a9 ucles 2018 [turn over 1 (a) by continuing the spiral, show that corner 10 is at (3, 3). (b) the length of the spiral from (0, 0) to corner 4 is 6 units. find the length of the spiral from (0, 0) to corner 10. ... (c) use your spiral to complete this table. corner numberlengths added length from (0, 0) 1 1 1 2 1 + 1 2 3 1 + 1 + 2 4 4 6 5 6 1 + 1 + 2 + 2 + 3 + 3 12 7 1 + 1 + 2 + 2 + 3 + 3 + 4 16 8 20 9 10 1 + 1 + 2 + 2 + 3 + 3 + 4 + 4 + 5 + 5", "4": "4 0607/62/o/n/18 \u00a9 ucles 2018 2 the table shows the length, l, of the spiral from (0, 0) to corner k, where k is an even number. term number (n)klength (l) 1 2 2 2 4 6 3 6 12 4 8 20 n k nn 1+` j (a) find a formula for n in terms of k. .. (b) use part (a) to show that the formula for the length, l, of the spiral from (0, 0) to corner k is lkk42 =+ ` j. (c) show that the formula gives the correct length of the spiral from (0, 0) to corner 14.", "5": "5 0607/62/o/n/18 \u00a9 ucles 2018 [turn over 3 (a) when k is an even number, find an expression, in terms of k, for the length of the spiral (i) from corner k - 1 to corner k, .. (ii) from corner k to corner k + 1. .. (b) (i) using question 2(b) , find a formula, in terms of k, for the length, l, of the spiral from (0, 0) to corner k + 1. .. (ii) use your formula to show that the length of the spiral from (0, 0) to corner 7 is 16.", "6": "6 0607/62/o/n/18 \u00a9 ucles 2018 4 a corner on the spiral has co-ordinates ( x, y). horizontal lengths of the spiral are added to give the total horizontal length, h. x co-ordinate (x)horizontal lengthstotal horizontal length (h) 1 1 1 2 1 + 2 + 3 6 3 1 + 2 + 3 + 4 + 5 15 4 1 + 2 + 3 + 4 + 5 + 6 + 7 28 5 (a) complete the table. (b) find a formula, in terms of x, for the total horizontal length, h, of the spiral from (0, 0) to the corner with co-ordinates ( x, y). .. (c) write down a formula, in terms of y, for the total vertical length, v, of the spiral from (0, 0) to the corner with co-ordinates ( x, y). ..", "7": "7 0607/62/o/n/18 \u00a9 ucles 2018 [turn over (d) k is an even number. (i) use your answers to part (b) and part (c) to show that a formula for the length, l, of the spiral from (0, 0) to corner k with co-ordinates ( x, y) is lx x22 1 =- ` j. (ii) the spiral has length 1560 from (0, 0) to the corner with co-ordinates ( x, y). use the formula in part (i) to find the value of x. ..", "8": "8 0607/62/o/n/18 \u00a9 ucles 2018 b modelling (questions 5 to 8) open boxes (20 marks) you are advised to spend no more than 45 minutes on this part. this task looks at maximum volumes when open boxes are made using regular shaped pieces of metal. jenny makes open triangular-based boxes from a piece of metal in the shape of an equilateral triangle. ao 30\u00b0 30 cmnot to scale she cuts equal sized pieces from each corner of the equilateral triangle. each cut is at right angles to the side of the shape. 30\u00b0 30 cmcut = heightnot to scale the sides are folded up to form the vertical sides of an open triangular box. height", "9": "9 0607/62/o/n/18 \u00a9 ucles 2018 [turn over 5 (a) the length of one side of the metal equilateral triangle is 30 cm. use trigonometry to show that oa is 17.32 cm, correct to 4 significant figures. (b) here is an enlargement of one corner cut from the metal triangle. 30\u00b02 cm2 cmnot to scale r cm (i) jenny makes a cut of 2 cm at right angles to the side of the equilateral triangle. show that r = 4.", "10": "10 0607/62/o/n/18 \u00a9 ucles 2018 (ii) 30\u00b0 30 cmnot to scale ao using oa = 17.32 cm and r = 4, find the area of the shaded triangle. you should use this formula. area = sinbc a21 b a ca bc .. (iii) jenny cuts the corner shown in part (b) from each corner of the equilateral triangle. she folds the sides up to make an open box. show that the volume of the box is approximately 461 cm3.", "11": "11 0607/62/o/n/18 \u00a9 ucles 2018 [turn over 6 jenny wants a model for the volume, v cm3, of the open box made from an equilateral triangle of side 30 cm. she makes a cut of length x cm at right angles to the side of the equilateral triangle. 30\u00b0x cmr cm 30\u00b0 30 cmnot to scale o 30\u00b0 (a) (i) find an expression for r, in terms of x. .. (ii) find an expression, in terms of x, for the area of the shaded isosceles triangle. .. (iii) the height of the open box is x cm. explain why the model for the volume, v cm3, of the open box is sincos sinvxx1203015 30 23\u00b0\u00b0 \u00b02 =- eo . ... ... ...", "12": "12 0607/62/o/n/18 \u00a9 ucles 2018 (iv) sketch the graph of v against x on the axes below. v x 00550 9v olume (cm3) height (cm) (b) for what values of x is the model valid? .. (c) find the possible heights of the open box when v = 400. ..", "13": "13 0607/62/o/n/18 \u00a9 ucles 2018 [turn over 7 the equilateral triangle now has side e cm. (a) give a reason why the model in question 6(a)(iii) becomes sincos sinvxex12023 0 30 23\u00b0\u00b0 \u00b02 =- eo . ... ... (b) use this model to find the height that gives the greatest volume when e = 60. ..", "14": "14 0607/62/o/n/18 \u00a9 ucles 2018 8 jenny makes an open square-based box from a square piece of metal of side e cm. (a) change the model in question 7(a) so that it gives the volume of this box. .. (b) the model in part (a) simplifies to vx ex22=-` j. find the relationship between e and x which gives the maximum volume of the box. ..", "15": "15 0607/62/o/n/18 \u00a9 ucles 2018 blank page", "16": "16 0607/62/o/n/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" }, "0607_w18_qp_63.pdf": { "1": "*7757861635* this document consists of 15 printed pages and 1 blank page. dc (ce/sw) 153620/4 \u00a9 ucles 2018 [turn overcambridge international mathematics 0607/63 paper 6 (extended) october/november 2018 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a (questions 1 to 3) and b (questions 4 to 6). you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and to communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.cambridge international examinations cambridge international general certificate of secondary education", "2": "2 0607/63/o/n/18 \u00a9 ucles 2018 answer both parts a and b. a investigation (questions 1 to 3) nearest neighbours (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation is about pairs of dots on rectangular grids. when two dots are next to each other, they are called nearest neighbours . here are four equally spaced dots in a row. the dots marked with crosses are nearest neighbours. there are 3 pairs of nearest neighbours. 1 (a) complete this table showing the number of pairs of nearest neighbours. number of dots in row number of pairs of nearest neighbours 2 1 3 4 3 5 6 n", "3": "3 0607/63/o/n/18 \u00a9 ucles 2018 [turn over (b) with four dots in a row there are a total of 6 different arrangements of two crosses. in 3 of these arrangements the crosses mark dots that are nearest neighbours. complete this table. number of dots in rownumber of pairs of nearest neighbourstotal number of different arrangements of two crosses 2 1 1 3 4 3 6 5 6 15 n (c) (i) multiply the number of dots in a row by the number of pairs of nearest neighbours. write down a connection between your answer and the total number of different arrangements of two crosses. ... ... (ii) in a row of n dots, write down an expression, in terms of n, for the total number of different arrangements of two crosses. ...", "4": "4 0607/63/o/n/18 \u00a9 ucles 2018 2 as well as pairs of nearest neighbours there are also pairs of 2nd nearest neighbours, 3rd nearest neighbours, 4th nearest neighbours and so on. here are some examples. nearest neighbours 2nd nearest neighbours 3rd nearest neighbours (a) complete this table. number of dots in rownumber of pairs of nearest neighbours 2nd nearest neighbours 3rd nearest neighbours 2 1 3 4 3 5 6 n (b) find an expression for the number of pairs of kth nearest neighbours in a row of n dots. ... ", "5": "5 0607/63/o/n/18 \u00a9 ucles 2018 [turn over (c) (i) you can find the total number of different arrangements of two crosses by adding the number of pairs of nearest neighbours, 2nd nearest neighbours, 3rd nearest neighbours and so on. use this method to find the total number of different arrangements of two crosses in a row of 11 dots. ... (ii) use your expression in question 1(c)(ii) to show that your answer in question 2(c)(i) is correct.", "6": "6 0607/63/o/n/18 \u00a9 ucles 2018 3 here is a 2 by 5 rectangle of dots. it has 2 rows of 5 dots. a b the distance between the dots in each column is a and the distance between each row is b. (a) when a = b, here are two pairs of crosses which are nearest neighbours. there are a total of 13 pairs of nearest neighbours for a 2 by 5 rectangle of dots. for a 2 by w rectangle of dots, where w h 2, find an expression for the number of pairs of nearest neighbours. ... ", "7": "7 0607/63/o/n/18 \u00a9 ucles 2018 [turn over (b) when a ! b, the pairs of nearest neighbours are the dots that are closest to each other. nearest neighboursnot nearest neighbours for a 2 by w rectangle of dots, where w h 2, find an expression for the number of pairs of nearest neighbours, (i) when a 2 b, ... (ii) when a 1 b. ... ", "8": "8 0607/63/o/n/18 \u00a9 ucles 2018 (c) here are two rectangles of dots. a a3 by 5 rectangle of dots 6 by 4 rectangle of dotsb b (i) for an h by w rectangle of dots, here are some expressions for the number of pairs of nearest neighbours, t. in all cases a 2 b and w h 2. hnumber of pairs of nearest neighbours ( t\u200a\u200a) 3 2w 4 3w 5 4w 6 5w find the formula for t in terms of h and w. ... (ii) for a 2 b, there are 1000 pairs of nearest neighbours in a 101 by w rectangle of dots. find the value of w. ... ", "9": "9 0607/63/o/n/18 \u00a9 ucles 2018 [turn over (d) for an h by w rectangle of dots, find an expression for t when a = b and w h 2. ... ", "10": "10 0607/63/o/n/18 \u00a9 ucles 2018 the modelling starts on page 11.", "11": "11 0607/63/o/n/18 \u00a9 ucles 2018 [turn over b modelling (questions 4 to 6) long jump (20 marks) you are advised to spend no more than 45 minutes on this part. this task is about modelling long jumping. athletes run along a track and then jump as far as they can in one leap. the horizontal distance jumped is called their long jump distance. run-up take-off flight through the air landing at take-off, athletes jump up giving them a vertical speed. their horizontal speed carries them forward in their flight through the air. the vertical speed and the horizontal speed give the take-off speed. 4 here is a formula connecting the vertical speed, v m/s, and the maximum height, j metres, jumped by the athlete. v2 = 20j an athlete has a vertical speed of 3.5 m/s. find the maximum height jumped by this athlete. ... ", "12": "12 0607/63/o/n/18 \u00a9 ucles 2018 5 this scatter diagram shows the horizontal speed and the long jump distance for each of 13 athletes in a recent world championship. 6.56.577.588.59 7 7.5 8 8.5 9 9.5 horizontal speed (m / s)long jump distance (metres)d r the mean horizontal speed, r, is 8.5 m/s. the mean long jump distance, d, is 7.9 m. (a) (i) on the scatter diagram plot the mean point and draw, by eye, a line of best fit. (ii) use your line of best fit to work out the equation that models the relationship between horizontal speed and long jump distance. ... ", "13": "13 0607/63/o/n/18 \u00a9 ucles 2018 [turn over (iii) an athlete has a horizontal speed of 6.6 m/s. this gives a long jump distance of 4.45 m. compare this long jump distance with the distance given by your equation in part (ii) . ... ... (b) long jump distance ( d\u200a\u200a) and horizontal speed ( r) can also be modelled by the following quadratic equation. d = -0.46r\u200a2 + 8.7r \u2013 32.8 (i) the athlete in part (a)(iii) had a horizontal speed of 6.6 m/s and a long jump distance of 4.45 m. which model gives a better approximation for this athlete\u2019s long jump distance, the model you used in part (a)(iii) or this quadratic model? ... ... (ii) sketch the graph of d = -0.46r\u200a2 + 8.7 r \u2013 32.8 for 5 g r g 12. d r 12 5 (iii) write down an inequality, in terms of r, for which the model is valid. ... ", "14": "14 0607/63/o/n/18 \u00a9 ucles 2018 6 when athletes jump they take-off at an angle a to the horizontal. the vertical speed and the horizontal speed give the take-off speed, t\u2009\u200am/s. dat a model for the long jump distance, d metres, is d = sincos ta a 52 . (a) sketch the graph of y = sin a cos a for 0\u00b0 g a g 90\u00b0. 0\u00b0 90\u00b0ay (b) show that when sin a cos a has its maximum value the greatest jump distance is d = t 102 . (c) an experienced long jumper has a take-off speed of 9.6 m/s. this gives a long jump distance of 7.89 m. compare this long jump distance with the distance given by the formula in part (b) . ... ...", "15": "15 0607/63/o/n/18 \u00a9 ucles 2018 (d) take-off speed ( t m/s), horizontal speed ( h m/s) and vertical speed ( v m/s) are related by the right -angled triangle below. t hav (i) use trigonometry to show that sincosdta a 52 = can be written as dvh 5= . (ii) an athlete has a take-off speed of 10 m/s. this gives a greatest height of 1.25 m. find the horizontal speed, h m/s, and the angle a. you may need to use the formula in question 4 . ...", "16": "16 0607/63/o/n/18 \u00a9 ucles 2018 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge international examinations copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. cambridge international examinations is part of the cambridge assessment group. cambridge assessment is the brand name of university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge.blank page" } }, "2019": { "0607_s19_qp_11.pdf": { "1": " this document consists of 11 printed pages and 1 blank page. ib19 06_0607_11/2rp \u00a9 ucles 2019 [turn over \uf02a\uf039\uf032\uf039\uf033\uf037\uf034\uf031\uf032\uf036\uf037\uf02a\uf020 cambridge assessment international education cambridge international general certificate of secondary education cambridge international mathematics 0607/11 paper 1 (core) may/june 2019 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2019 0607/11/m/j/19 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \uf070r2 circumference, c, of circle, radius r. c = 2\uf070r curved surface area, a, of cylinder of radius r, height h. a = 2\uf070rh curved surface area, a, of cone of radius r, sloping edge l. a = \uf070rl curved surface area, a, of sphere of radius r. a = 4\uf070r2 volume, v, of prism, cross-sectional area a, length l. v = al volume, v, of pyramid, base area a, height h. v = 1 3ah volume, v, of cylinder of radius r, height h. v = \uf070r2h volume, v, of cone of radius r, height h. v = 1 3\uf070r2h volume, v, of sphere of radius r. v = 4 3\uf070r3 ", "3": "3 \u00a9 ucles 2019 0607/11/m/j/19 [turn over answer all the questions. 1 write 36 247 correct to the nearest thousand. [1] 2 write down three multiples of 12. , , [1] 3 cb a o d the diagram shows a circle centre o and three lines, oa, ab and cd. write down the line that is (a) a chord, [1] (b) a tangent. [1] ", "4": "4 \u00a9 ucles 2019 0607/11/m/j/19 4 the cost, in dollars, of a taxi journey is 2 \u00d7 (number of kilometres travelled) + 10. find the cost of a taxi journey of 30 kilometres. $ [2] 5 change 2.4 metres into millimetres. mm [1] 6 (a) x\u00b0120\u00b0not to scale find the value of x. x = [1] (b) y\u00b0 110\u00b0not to scale 70\u00b050\u00b0 find the value of y. y = [1] ", "5": "5 \u00a9 ucles 2019 0607/11/m/j/19 [turn over 7 1234567 write down all the integers that satisfy the inequality shown on this number line. [1] 8 (a) work out 83 of 16. [1] (b) write 201 as a percentage. % [1] (c) write 81 as a decimal. [1] 9 8 cm 6 cm 3 cm2 cmnot to scale work out the area of this shape. cm 2 [3] ", "6": "6 \u00a9 ucles 2019 0607/11/m/j/19 10 huda is drawing a pie chart for the times, in mi nutes, that 60 students take to travel to school. time ( t minutes) frequency angle (degrees) t \u2264 10 5 30 10 \uf03c t \u2264 15 15 15 \uf03c t \u2264 20 10 t \uf03e 20 30 (a) complete the table to show the sector angles in the pie chart. [2] (b) complete the pie chart to show this information. t10 [2] ", "7": "7 \u00a9 ucles 2019 0607/11/m/j/19 [turn over 11 \u20132\u201310123123 4 \u20133\u20132\u2013145 \u20133 \u2013 467 a bxy a is the point (\u20133, 6) and b is the point (3, \u20132). find the co-ordinates of the midpoint of ab. ( , ) [2] 12 solve 2 x < 8. [1] 13 27 = 128 find the value of 28. [1] ", "8": "8 \u00a9 ucles 2019 0607/11/m/j/19 14 write down the type of correlation shown in each of these scatter diagrams. [2] 15 f(x) = x2 + 1 work out the values of x when f( x) = 26. x = or x = [2] 16 300\u00b0abnot to scalenorth the bearing of b from a is 300\u00b0. find the bearing of a from b. [2] ", "9": "9 \u00a9 ucles 2019 0607/11/m/j/19 [turn over 17 036 3b a 12 3 4512457 xy (a) write down the equation of line a. [1] (b) find the equation of line b. [2] 18 solve the simultaneous equations. x + y = 3 x \u2013 4y = 13 x = y = [2] ", "10": "10 \u00a9 ucles 2019 0607/11/m/j/19 19 (a) on the venn diagram shade the region represented by a\uf0a2. a [1] (b) x y b g s tya e the venn diagram shows two sets x and y. u = {a, b, e, g, s, t, y} a letter is chosen at random. write down the probability that it is in set y but not in set x. [1] ", "11": "11 \u00a9 ucles 2019 0607/11/m/j/19 20 a is the point (\u20133, 4) and b is the point (2, 2). find the vector ab. \uf0e6\uf0f6 \uf0e7\uf0f7 \uf0e8\uf0f8 [2] 21 the graph of y = f(x) is translated by the vector \uf0f7 \uf0f8\uf0f6\uf0e7 \uf0e8\uf0e6\uf02d 02. write down the equation of the new graph. y = [1] ", "12": "12 permission to reproduce items where third-party owned material pr otected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the camb ridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which it self is a department of the university of cambridge. \u00a9 ucles 2019 0607/11/m/j/19 blank page " }, "0607_s19_qp_12.pdf": { "1": " this document consists of 11 printed pages and 1 blank page. ib19 06_0607_12/3rp \u00a9 ucles 2019 [turn over \uf02a\uf036\uf034\uf033\uf038\uf031\uf038\uf030\uf035\uf039\uf030\uf02a \uf020 cambridge assessment international education cambridge international general certificate of secondary education cambridge international mathematics 0607/12 paper 1 (core) may/june 2019 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2019 0607/12/m/j/19 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \uf070r2 circumference, c, of circle, radius r. c = 2\uf070r curved surface area, a, of cylinder of radius r, height h. a = 2\uf070rh curved surface area, a, of cone of radius r, sloping edge l. a = \uf070rl curved surface area, a, of sphere of radius r. a = 4\uf070r2 volume, v, of prism, cross-sectional area a, length l. v = al volume, v, of pyramid, base area a, height h. v = 1 3ah volume, v, of cylinder of radius r, height h. v = \uf070r2h volume, v, of cone of radius r, height h. v = 1 3\uf070r2h volume, v, of sphere of radius r. v = 4 3\uf070r3 ", "3": "3 \u00a9 ucles 2019 0607/12/m/j/19 [turn over answer all the questions. 1 write 123.456 correct to the nearest 10. [1] 2 work out how many days there are in 5 weeks. days [1] 3 find 10% of 300. [1] 4 draw all the lines of symmetry on the diagram. [2] ", "4": "4 \u00a9 ucles 2019 0607/12/m/j/19 5 \u20132\u201310123123 x4 \u20133\u20132\u20131545 \u20133 \u2013 4 \u20135 \u20135\u2013 4y on the grid, plot and label the points a (\u2013 4, 3) and b (5, \u20132). [2] 6 complete the statement. an angle that is more than 180 \uf0b0 but is less than 360 \uf0b0 is called [1] 7 12 cm12 cm3 cm 3 cmnot to scale a square of side 3 cm is removed from the corner of a square of side 12 cm. find the area of the remaining shape. cm 2 [2] ", "5": "5 \u00a9 ucles 2019 0607/12/m/j/19 [turn over 8 p = r + 5t find the value of p when r = 7 and t = 6. p = [2] 9 north a b the diagram shows two towns, a and b, on a map. measure the bearing of b from a. [1] 10 complete the mapping diagram. 1 23 52 8 18 98 x f(x) [2] ", "6": "6 \u00a9 ucles 2019 0607/12/m/j/19 11 x ay o x by o x cy ox dy o the diagrams a, b, c and d each show the graph of a straight line. write down the letter of the diagram which shows the line (a) x = 3, [1] (b) y = 2x \u2013 1. [1] ", "7": "7 \u00a9 ucles 2019 0607/12/m/j/19 [turn over 12 a circle has radius 3.5 cm. find the circumference of the circle. leave your answer in terms of \u03c0. cm [2] 13 xy 0\u22121 \u22122 \u22123 \u22124 \u22125 \u22126 \u22127 \u22128 1 2 3423 145 \u22121 \u22122 \u22123\u22124 \u22125 the diagram shows the graph of a function that has two asymptotes. the equation of one asymptote is y = 0. on the diagram, draw the other asymptote. [1] ", "8": "8 \u00a9 ucles 2019 0607/12/m/j/19 14 factorise 4 p \u2013 14. [1] 15 f(x) = 31x2 find f(\u20136). [1] 16 10 m x mnot to scale 40\u00b0 sin 40\u00b0 cos 40\u00b0 tan 40\u00b0 0.643 0.766 0.839 use the information to work out the value of x. x = [2] ", "9": "9 \u00a9 ucles 2019 0607/12/m/j/19 [turn over 17 the marks of 200 students in a mathematic s test are recorded in the table below. mark ( x) 0 < x \u2264 20 20 < x \u2264 30 30 < x \u2264 40 40 < x \u2264 50 50 < x \u2264 60 60 < x \u2264 80 80 < x \u2264 100 frequency 15 21 35 40 36 28 25 complete the following cumulative frequency table. mark ( x) x \u2264 20 x \u2264 30 x \u2264 40 x \u2264 50 x \u2264 60 x \u2264 80 x \u2264 100 cumulative frequency 2 0 0 [2] 18 a bag contains 5 red balls and 3 green balls. two balls are chosen at random. complete the diagram. red greenred greenredgreen73 7585 first ball second ball [2] ", "10": "10 \u00a9 ucles 2019 0607/12/m/j/19 19 solve the simultaneous equations. 5x + 2y = 1 2x + 3y = 7 x = y = [4] 20 the interior angle of a regular polygon is 160 \uf0b0. find the number of sides of the polygon. [3] ", "11": "11 \u00a9 ucles 2019 0607/12/m/j/19 21 u = {x | 3 \u2264 x \u2264 10, where x is an integer} a = {x | x is a multiple of 3 or 5} b = {x | 3x + 2 < 20} (a) list the members of set b. { } [2] (b) complete the venn diagram. ab 10 7 [2] (c) list the members of a \uf0c7 b. { } [1] ", "12": "12 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge assessment international education copyri ght acknowledgements booklet. this is produc ed for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the ca mbridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which it self is a department of the university of cambridge. \u00a9 ucles 2019 0607/12/m/j/19 blank page " }, "0607_s19_qp_13.pdf": { "1": " this document consists of 10 printed pages and 2 blank pages. ib19 06_0607_13/5rp \u00a9 ucles 2019 [turn over \uf02a\uf031\uf034\uf035\uf035\uf038\uf036\uf031\uf032\uf038\uf034\uf02a \uf020 cambridge assessment international education cambridge international general certificate of secondary education cambridge international mathematics 0607/13 paper 1 (core) may/june 2019 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2019 0607/13/m/j/19 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \uf070r2 circumference, c, of circle, radius r. c = 2\uf070r curved surface area, a, of cylinder of radius r, height h. a = 2\uf070rh curved surface area, a, of cone of radius r, sloping edge l. a = \uf070rl curved surface area, a, of sphere of radius r. a = 4\uf070r2 volume, v, of prism, cross-sectional area a, length l. v = al volume, v, of pyramid, base area a, height h. v = 1 3ah volume, v, of cylinder of radius r, height h. v = \uf070r2h volume, v, of cone of radius r, height h. v = 1 3\uf070r2h volume, v, of sphere of radius r. v = 4 3\uf070r3 ", "3": "3 \u00a9 ucles 2019 0607/13/m/j/19 [turn over answer all the questions. 1 ola gives her grandson $3 each month. work out how much her grandson receives in 1 year. $ [1] 2 0 123123y 4 5xa write down the co-ordinates of point a. ( , ) [1] 3 15 17 21 25 36 38 from the list of numbers write down (a) the prime number, [1] (b) a square number. [1] ", "4": "4 \u00a9 ucles 2019 0607/13/m/j/19 4 abcd is a quadrilateral. d c banot to scale write down the mathematical name (a) for this quadrilateral, [1] (b) for triangle abd . [1] 5 to use his mobile phone, paul is charged 12 cents for each minute plus $20 monthly line rental. one month paul used his mobile phone for 30 minutes. find the total charge for this month. $ [2] 6 complete the statement. the diagram has rotational symmetry of order [1] ", "5": "5 \u00a9 ucles 2019 0607/13/m/j/19 [turn over 7 write down which of the following data is discrete. a the weight of a child. b the number of eggs in a basket. c the time it takes to bake a cake. [1] 8 complete the mapping diagram. 1 23 44 7 10 22x f(x) [2] 9 use one of the following symbols >, < or = to make each statement correct. 1 20 \u00f7 (5 \u2013 3) 2 + 3 \uf0b4 3 11 [2] ", "6": "6 \u00a9 ucles 2019 0607/13/m/j/19 10 200 people were asked to choose their favourite type of restaurant. the results are shown in the pie chart. italian 37%indian 16% chinese 22% mexicannot to scale (a) find the sector angle for mexican restaurants. [2] (b) how many of the 200 people chose chinese restaurants? [2] 11 not to scale 50\u00b0a bnorth north find the bearing of point b from point a. [2] ", "7": "7 \u00a9 ucles 2019 0607/13/m/j/19 [turn over 12 solve 15 2x\uf03d. x = [1] 13 change 12 310 cm2 into m2. m 2 [1] 14 adil and serena share a prize in the ratio adil : serena = 3 : 7. adil receives $60. work out how much serena receives. $ [2] 15 james buys a bottle of cola for 40 cents. he then sells it for 50 cents. work out his percentage profit. % [2] ", "8": "8 \u00a9 ucles 2019 0607/13/m/j/19 16 a circle has radius 5 cm. find the area of the circle giving your answer in terms of \u03c0. cm 2 [1] 17 find the equation of the line that is parallel to the y-axis and passes through the point (3, 0). [2] 18 here are the first five terms in a sequence. \u20131 5 11 17 23 find the nth term. [2] 19 not to scale20 cm x cm 47\u00b0 put a ring around the correct expression for the distance x. 20 tan 47\uf0b0 20 sin 47 \uf0b0 20 cos 47 \uf0b0 [1] ", "9": "9 \u00a9 ucles 2019 0607/13/m/j/19 [turn over 20 yan and ahmed play two games. the probability that yan wins a game is 41. yan wins ahmed winsyanwins ahme d winsyan wins ahme d wins41 41 41 4343 43first game second game work out the probability that yan wins exactly one game. [2] 21 solve the simultaneous equations. 3x + y = 4 2x \uf02d y = 6 x = y = [2] ", "10": "10 \u00a9 ucles 2019 0607/13/m/j/19 22 160 height (cm)165 170 180 1755101520253035404550 0cumulative frequency 185 the diagram shows a cumulative frequency curve for the heights of 50 students. estimate (a) the median height, cm [1] (b) the inter-quartile range. cm [2] 23 the graph of y = x3 is translated by the vector \uf0f7 \uf0f8\uf0f6\uf0e7 \uf0e8\uf0e6 \uf02d30. write down the equation of the new graph. y = [1] ", "11": "11 \u00a9 ucles 2019 0607/13/m/j/19 blank page ", "12": "12 permission to reproduce items where third-party owned material pr otected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the camb ridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which it self is a department of the university of cambridge. \u00a9 ucles 2019 0607/13/m/j/19 blank page " }, "0607_s19_qp_21.pdf": { "1": "this document consists of 8 printed pages. dc (nh/sw) 164749/2 \u00a9 ucles 2019 [turn overcambridge assessment international education cambridge international general certificate of secondary education *8407547624* cambridge international mathematics 0607/21 paper 2 (extended) may/june 2019 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.", "2": "2 0607/21/m/j/19 \u00a9 ucles 2019 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/21/m/j/19 \u00a9 ucles 2019 [turn over answer all the questions. 1 work out. (a) (0.3)2 [1] (b) 94 61- [2] 2 divide 360 in the ratio 7 : 2. . , . [2] 3 not to scale 64\u00b0 33\u00b0 55\u00b0f b d cea abc is a triangle. fed and bcd are straight lines. work out angle edc . angle edc = [2]", "4": "4 0607/21/m/j/19 \u00a9 ucles 2019 4 expand and simplify. 4(3x + y) - 3(x - 2y) [2] 5 sacha drove 425 km from home at an average speed of 100 km/h. (a) calculate the time for the journey giving your answer in hours and minutes. ... h ... min [2] (b) the return journey took 3 hours and 55 minutes. she started at 21 56. at what time did she arrive home? [2] 6 (a) write down the integer solutions to this inequality. x 22 81g- [2] (b) solve xx 22 51 4 2++ . [2]", "5": "5 0607/21/m/j/19 \u00a9 ucles 2019 [turn over 7 work out (5.2 # 1018) - (2.4 # 1017). give your answer in standard form. [2] 8 a map is drawn to a scale of 1 cm to 5 km. (a) on the map, the distance between two towns is 4.8 cm. find the actual distance between the towns. ... km [1] (b) an island has an area of 75 km2. find the area of the island on the map. .. cm2 [2] 9 factorise completely. 2x2 - 18 [2]", "6": "6 0607/21/m/j/19 \u00a9 ucles 2019 10 u = {integers from 1 to 12} a = {1, 2, 4, 5, 12} b = {2, 3, 4, 6, 10} c = {1, 2, 8, 9, 10} (a) complete the venn diagram. u a cb [2] (b) find (( ) ab c n+, )l. [1] 11 the point a has co-ordinates (3, 8). the point b has co-ordinates (7, 0). (a) find the co-ordinates of the midpoint of ab. ( ... , ) [1] (b) find the equation of the perpendicular bisector of ab. write your answer in the form y = mx + c. y = [3]", "7": "7 0607/21/m/j/19 \u00a9 ucles 2019 [turn over 12 not to scale r cm60\u00b0 12 cm the sector and the circle have the same area. the angle of the sector is 60\u00b0. the radius of the sector is 12 cm and the radius of the circle is r cm. work out the value of r. give your answer as a surd in its simplest form. r = [3] 13 rearrange this formula to make b the subject. ()aabh2=+ b = [3] question 14 is printed on the next page.", "8": "8 0607/21/m/j/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.14 (a) find the value of log525. [1] (b) simplify logl og 63 23- . [2]" }, "0607_s19_qp_22.pdf": { "1": "this document consists of 8 printed pages. dc (sc/sw) 164744/2 \u00a9 ucles 2019 [turn overcambridge assessment international education cambridge international general certificate of secondary education *2002671041* cambridge international mathematics 0607/22 paper 2 (extended) may/june 2019 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.", "2": "2 0607/22/m/j/19 \u00a9 ucles 2019 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area =a c bcb a", "3": "3 0607/22/m/j/19 \u00a9 ucles 2019 [turn over answer all the questions. 1 not to scale 65\u00b0x\u00b0y\u00b0 find the value of x and the value of y. x = y = [2] 2 a regular polygon has 40 sides. find the size of one exterior angle. [2] 3 a is the point (1, 5) and b is the point (6, 2). find the column vector ab. fp [2] 4 t = 3p2 (a) find the value of t when p = 4. t = [1] (b) re-arrange the formula to write p in terms of t. p = \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd [2]", "4": "4 0607/22/m/j/19 \u00a9 ucles 2019 5 00200400600800 100300500700 10 20 height (cm)cumulative frequency 30 40 50 the cumulative frequency curve shows some information about the heights of 800 plants. find (a) the median, ... cm [1] (b) the upper quartile. ... cm [1] 6 work out 54121' . [2] 7 a car travels 85 km in 50 minutes. find the average speed of the car, giving your answer in km/h. km/h [2]", "5": "5 0607/22/m/j/19 \u00a9 ucles 2019 [turn over 8 solve the simultaneous equations. a + b = 16 2a - b = 17 a = b = [2] 9 find the equation of the line parallel to the line y = 3 - x that passes through the point (0, 7). [2] 10 work out the value of 27131- eo . [1] 11 .pq 5u n(u) = 25 n(p) = 10 n(q) = 17 ()pqn, l = 5 complete the venn diagram. [2] 12 factorise completely. ab - a - b + 1 [2]", "6": "6 0607/22/m/j/19 \u00a9 ucles 2019 13 work out 1.1 # 1030 + 1.1 # 1029 , giving your answer in standard form. [2] 14 find the highest common factor (hcf) of 8 p4q8 and 4 p3q10. [2] 15 not to scale 25\u00b0a\u00b0 b\u00b0 80\u00b0 the diagram shows a cyclic quadrilateral. find the value of a and the value of b. a = b = [2]", "7": "7 0607/22/m/j/19 \u00a9 ucles 2019 [turn over 16 rationalise the denominator. 51 1- [2] 17 y is inversely proportional to x4+. when x = 5, y = 12. find y in terms of x. y \u0003= [2] 18 simplify. xy xy 392 +- [3] question 19 is printed on the next page.", "8": "8 0607/22/m/j/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.19 (a) logl og x 23 4 = find the value of x. x = [2] (b) logl og logl og xu vp +- = find p in terms of x, u and v. p = [1]" }, "0607_s19_qp_23.pdf": { "1": "this document consists of 8 printed pages. dc (lk/sw) 164745/2 \u00a9 ucles 2019 [turn overcambridge assessment international education cambridge international general certificate of secondary education *0139225842* cambridge international mathematics 0607/23 paper 2 (extended) may/june 2019 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.", "2": "2 0607/23/m/j/19 \u00a9 ucles 2019 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/23/m/j/19 \u00a9 ucles 2019 [turn over answer all the questions. 1 work out. ()23- [1] 2 ()fxx 13=- find the value of ()f1-. [1] 3 not to scale 71\u00b0132\u00b0 x\u00b0 find the value of x. x = [2] 4 expand the brackets and simplify. () () xx23 13 12 -+ - [2]", "4": "4 0607/23/m/j/19 \u00a9 ucles 2019 5 a quadrilateral has \u2022 two pairs of parallel sides \u2022 all sides the same length \u2022 no right angles. write down the mathematical name of this quadrilateral. [1] 6 16 10 11 15 10 12 14 13 17 10 15 find the median of these eleven numbers. [1] 7 work out. 552132# [3]", "5": "5 0607/23/m/j/19 \u00a9 ucles 2019 [turn over 8 work out the following. give each answer in standard form. (a) () () 1102 1012## +- [2] (b) () () 1102 1012## '- [2] 9 a bag contains 2 blue balls, 3 red balls and 5 green balls only. john takes a ball out of the bag at random. he records the colour and puts the ball back in the bag. flavia takes a ball out of the bag at random and records the colour. find the probability that both balls are red. [2] 10 a6 8=eo b2 8=-eo (a) find ab3-. fp [2] (b) work out a. [2]", "6": "6 0607/23/m/j/19 \u00a9 ucles 2019 11 a travel agent has the following exchange rates. \u00a31 = $1.25 \u00a31 = \u20ac1.20 (a) change \u00a3200 into dollars ($). $ [1] (b) change $100 into euros (\u20ac). \u20ac [2] 12 the point a has co-ordinates (1, 3) and the point b has co-ordinates (4, 1). b is the midpoint of the line ac. find the co-ordinates of the point c. ( ... , ... ) [2] 13 make a the subject of su ta t21 2=+ . a = . [3] 14 factorise completely. ac bc ad bd 698 12 -- + [2]", "7": "7 0607/23/m/j/19 \u00a9 ucles 2019 [turn over 15 erica walks 13 km in 2 hours. she then runs at a speed of 12 km/h for 45 minutes. find her average speed in km/h for the whole journey. ... km/h [3] 16 not to scale x\u00b0y\u00b0 oad c b the diagram shows a circle, centre o. aob is a straight line. bcd is a tangent to the circle at c. find y in terms of x. y = [3] question 17 is printed on the next page.", "8": "8 0607/23/m/j/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.17 the table shows the heights, x cm, of some students at a school. height ( x cm) frequency x 150 1601g 8 x 160 1651g 20 x 165 1701g 24 on the grid below, draw a histogram to show this information. 024 135 150 160 height (cm)frequency density 170 x [3]" }, "0607_s19_qp_31.pdf": { "1": "this document consists of 18 printed pages and 2 blank pages. dc (lk/fc) 168251/2 \u00a9 ucles 2019 [turn over *7314200078* cambridge international mathematics 0607/31 paper 3 (core) may/june 2019 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.cambridge assessment international education cambridge international general certificate of secondary education", "2": "2 0607/31/m/j/19 \u00a9 ucles 2019 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/31/m/j/19 \u00a9 ucles 2019 [turn over answer all the questions. 1 (a) write in words the number 6015. [1] (b) find the value of (i) 43, ... [1] (ii) () 31 623 9 #+ , ... [1] (iii) 352#, ... [1] (iv) 40 102#- . ... [1] (c) find (i) 81, ... [1] (ii) a prime number between 20 and 30, ... [1] (iii) 60 as a product of prime factors. ... [2]", "4": "4 0607/31/m/j/19 \u00a9 ucles 2019 2 this shape is drawn on a 1 cm2 grid. (a) (i) work out the area and the perimeter of the shape. give the units of each answer. area = . . perimeter = . . [4] (ii) the shape is enlarged by a scale factor of 3. find the perimeter of the enlarged shape. give your answer in metres. ... m [3] (b) write down the order of rotational symmetry of the shape. ... [1] (c) on the diagram, draw all the lines of symmetry. [2]", "5": "5 0607/31/m/j/19 \u00a9 ucles 2019 [turn over (d) work out the sum of all the interior angles of the shape. ... [3] (e) \u20132 \u20133\u20132\u2013112345 \u20131 0 1a bxy 4 5 6 2 3 write down the co-ordinates of point a and point b. a ( . , . ) b ( . , . ) [2]", "6": "6 0607/31/m/j/19 \u00a9 ucles 2019 3 (a) a packet of cereal costs $2.80 . work out the largest number of these packets that can be bought with $20. how much change would you get? .. packets and $ .. change [3] (b) a packet originally contained 450 g of cereal. the mass of cereal in the packet is increased by 15%. work out how much extra cereal is added to the packet. g [2] (c) 51 out of 300 people said they would buy the heavier packet of cereal. work out 51 as a percentage of 300. ... % [1]", "7": "7 0607/31/m/j/19 \u00a9 ucles 2019 [turn over 4 this formula can be used to change a temperature in degrees celsius, c, to a temperature in degrees fahrenheit, f. fc23 0 =+ (a) find the value of f when (i) c 0=, ... [1] (ii) c 120= . ... [1] (b) find the value of c when f350= . ... [2] (c) find the value of c when fc=. ... [2] (d) rearrange the formula to make c the subject. fc23 0 =+ c = .. [2]", "8": "8 0607/31/m/j/19 \u00a9 ucles 2019 5 henri records the number of people in each car passing through his village. the results are shown in the table. number of people number of cars 1 35 2 25 3 20 4 10 5 10 (a) complete the bar chart to show this information. 01 2 3 4 number of peoplenumber of cars 5510152025303540 [2]", "9": "9 0607/31/m/j/19 \u00a9 ucles 2019 [turn over (b) find the total number of cars that henri recorded. ... [1] (c) using the results in the table, work out (i) the mode, ... [1] (ii) the median, ... [1] (iii) the mean. ... [2] (d) one of the cars is chosen at random. work out the probability that it contains (i) 4 people, ... [1] (ii) 1 or 2 people. give your answer as a fraction in its simplest form. ... [2]", "10": "10 0607/31/m/j/19 \u00a9 ucles 2019 6 (a) these are the first four terms of a sequence. 11 18 25 32 (i) write down the rule for continuing this sequence. [1] (ii) find an expression for the nth term of this sequence. ... [2] (b) here are the first four terms of another sequence. 23 18 13 8 find the next two terms of this sequence. . , [2]", "11": "11 0607/31/m/j/19 \u00a9 ucles 2019 [turn over 7 (a) on the grid, draw the image of the shape after a translation by vector 4 2-eo . [2] (b) on the grid, draw the image of the shape after a rotation of 90\u00b0 anticlockwise about the point o. o [2]", "12": "12 0607/31/m/j/19 \u00a9 ucles 2019 8 (a) simplify. aaa423+- ... [1] (b) solve. (i) x 17 4-= x = .. [1] (ii) x 54= x = .. [1] (iii) x23 14 4 +=` j x = .. [3] (c) factorise fully. x12 30- ... [2]", "13": "13 0607/31/m/j/19 \u00a9 ucles 2019 [turn over (d) simplify fully. (i) xxx 743# ... [2] (ii) yy 315 26 ... [2]", "14": "14 0607/31/m/j/19 \u00a9 ucles 2019 9 crystal carries out a survey of cars, vans and lorries that drive past her house. (a) she sees a total of 500 of these types of vehicle. the ratio cars : vans : lorries = 14 : 4 : 7. work out how many of each type of vehicle she sees. cars .. vans .. lorries .. [3] (b) one car travels 2.5 km in 5 minutes. work out the speed of this car in kilometres per hour. .. km/h [2] (c) crystal measures the speed of each of the 500 vehicles. her results are shown in the table. speed ( s km/h) frequency s01 0 1g 0 s 10 021g 20 s 20 031g 230 s 30 041g 170 s 40 051g 60 s 50 061g 20", "15": "15 0607/31/m/j/19 \u00a9 ucles 2019 [turn over (i) complete the cumulative frequency table. speed ( s km/h)cumulative frequency s10g 0 s20g s30g s40g s50g s60g 500 [1] (ii) on the grid, draw a cumulative frequency curve for this information. 0 10 0 20 30 40 speed (km/h)cumulative frequency 50 60s100200300400500 [3] (iii) use your cumulative frequency curve to estimate the number of cars travelling faster than 35 km/h. ... [2]", "16": "16 0607/31/m/j/19 \u00a9 ucles 2019 10 7 cm h cmnot to scale a cylinder has radius 7 cm and height h cm. (a) show that the area of the circular end of the cylinder is 154 cm2, correct to the nearest whole number. [2] (b) the volume of the cylinder is 2 litres. work out the value of h. h = .. [2] (c) a cube has side length x cm. it has the same volume as the cylinder. find the value of x. x = .. [3]", "17": "17 0607/31/m/j/19 \u00a9 ucles 2019 [turn over 11 a vertical post, 1.75 m tall, stands on horizontal ground. one day, the post casts a shadow of length 3.28 m. x m 1.75 mnot to scale 3.28 my\u00b0sun (a) find the value of x. x = .. [2] (b) find the value of y, the angle of elevation of the sun. y = .. [2]", "18": "18 0607/31/m/j/19 \u00a9 ucles 2019 12 xy \u201330\u2013320 5 the diagram shows the graph of yx 2=+ for x35gg- . (a) find the co-ordinates of the y-intercept. ( , ) [1] (b) on the diagram, sketch the graph of yx x12=- - for x35gg- . [2] (c) solve this equation. xx x122-- =+ x = . or x = . [2]", "19": "19 0607/31/m/j/19 \u00a9 ucles 2019 blank page", "20": "20 0607/31/m/j/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_s19_qp_32.pdf": { "1": "this document consists of 16 printed pages. dc (sc/tp) 168252/2 \u00a9 ucles 2019 [turn over *9252898331* cambridge international mathematics 0607/32 paper 3 (core) may/june 2019 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.cambridge assessment international education cambridge international general certificate of secondary education", "2": "2 0607/32/m/j/19 \u00a9 ucles 2019 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/32/m/j/19 \u00a9 ucles 2019 [turn over answer all the questions. 1 (a) write in words the number 27 003. [1] (b) write 0.37 as a fraction. [1] (c) write down a square number between 30 and 50. [1] (d) complete the list of factors of 12. .. , 2 , .. , .. , 6 , .. [2] (e) work out ..26 072- . [1] 2 mr and mrs tan and their three children go on a boat trip. (a) one adult fare costs $15 and one child fare costs $8. (i) find the total cost of their fares. $ [2] (ii) find how much change they receive from $100. $ [1] (b) the boat sails 6 km in 90 minutes. work out the speed of the boat in km/h. km/h [3]", "4": "4 0607/32/m/j/19 \u00a9 ucles 2019 3 (a) the bar chart shows the number of pieces of different types of fruit in a basket. oranges apples grapes bananas cherries02468101214 number of pieces of fruit (i) find the total number of pieces of fruit in the basket. [1] (ii) find how many more cherries there are than oranges. [1] (iii) one piece of fruit is chosen at random from the basket. find the probability that it is a banana. [1] (iv) find the percentage of pieces of fruit in the basket that are apples. . % [2]", "5": "5 0607/32/m/j/19 \u00a9 ucles 2019 [turn over (b) 15 18 21 32 11 8 34 17 21 6 45 from this list of eleven numbers, find (i) the mode, [1] (ii) the range, [1] (iii) the median, [1] (iv) the mean, [1] (v) the lower quartile, [1] (vi) the inter-quartile range. [1]", "6": "6 0607/32/m/j/19 \u00a9 ucles 2019 4 (a) write down the correct mathematical name for each shape. [4]", "7": "7 0607/32/m/j/19 \u00a9 ucles 2019 [turn over (b) 52\u00b0 88\u00b0not to scalea de fc b abc is parallel to def , db is parallel to ec and be is parallel to cf. angle abd = 52\u00b0 and angle deb = 88\u00b0. find the size of (i) angle bde , angle bde = [1] (ii) angle dbe , angle dbe = [1] (iii) angle cfe , angle cfe = [1] (iv) angle cbe , angle cbe = [1] (v) angle bec . angle bec = [1]", "8": "8 0607/32/m/j/19 \u00a9 ucles 2019 5 (a) siobhan makes a rabbit run in the shape of a right-angled triangle. she uses x metres of the garden fence for one side of the run. the other two sides are made from 36 metres of wire mesh, as shown in the diagram. x m 20 m16 mnot to scalefence (i) work out the value of x. x =\u2009 [3] (ii) find the area of garden used for the run. m2 [1] (b) siobhan\u2019s friend makes a rabbit run in the shape of a square. she uses y metres of the garden fence for one side of the run. the other three sides are made from 36 metres of wire mesh. y m not to scalefence (i) work out the value of y. y =\u2009 [1] (ii) find the area of garden used for the square run. m2 [1]", "9": "9 0607/32/m/j/19 \u00a9 ucles 2019 [turn over 6 \u201322468101214 \u2013 4 \u2013 6 \u20138 \u201310 \u201312 \u2013146 4 8 10 12 2 \u20132 \u2013 4 \u2013 6 0y x the diagram shows the graph of () yx f= . (a) write down the zeros of () yx f= . x = . or x = . [1] (b) on the diagram, draw the line of symmetry of () yx f= . [1] (c) write down the co-ordinates of the y-intercept. ( . , . ) [1] (d) on the diagram (i) sketch the image of the graph of () yx f= after reflection in the x-axis, [1] (ii) sketch the graph of () yx 2 f=+ , [1] (iii) sketch the graph of () yx 3 f=+ . [1]", "10": "10 0607/32/m/j/19 \u00a9 ucles 2019 7 (a) joska and sem go to the cinema to see a film. the film starts at 15 45 and lasts for 1 hour 53 minutes. work out the time that the film ends. [1] (b) not to scale 6 cm6 cm10 cm the cinema shop sells popcorn in small boxes and large boxes. each box is a cuboid and the cuboids are mathematically similar. the small box has dimensions 6 cm by 6 cm by 10 cm. the ratio of dimensions small box : large box = 2 : 3. work out the dimensions of a large box. cm by cm by cm [2] (c) find the volume of a small box and the volume of a large box. small box =\u2009 .. cm3 large box =\u2009 .. cm3 [2] (d) a small box of popcorn costs $2.50 and a large box of popcorn costs $4.00 . find which box of popcorn is the better value. show all your working. [2] (e) write your answers to part (c) as a ratio in its simplest form. volume of small box : volume of large box =\u2009 : [1]", "11": "11 0607/32/m/j/19 \u00a9 ucles 2019 [turn over 8 (a) show x 22- on the number line. \u2013 4 \u20135 \u20133 \u20132 \u20131 0 1 2x [1] (b) solve. (i) x 35= x =\u2009 [1] (ii) x11 91 3 -= x =\u2009 [2] (c) expand and simplify. () () xx27 3- + [2] (d) factorise completely. xy y 262- [2] (e) simplify fully. xx4753# [2]", "12": "12 0607/32/m/j/19 \u00a9 ucles 2019 9 the mass of each of eight cars, in kg, and the time taken, in seconds, each takes to reach a speed of 100 km/h is recorded. mass (kg) 1200 1290 1320 1410 1430 1490 1580 1650 time (seconds) 11.4 10.3 10.9 6.1 7.0 4.4 4.2 3.9 (a) complete the scatter diagram. the first four points have been plotted for you. 1100012345678911 1012 1200 1300 mass (kg)time (seconds) 1400 1500 1600 1700 [2] (b) write down the type of correlation shown in the scatter diagram. [1]", "13": "13 0607/32/m/j/19 \u00a9 ucles 2019 [turn over (c) (i) find the mean mass. kg [1] (ii) find the mean time. ... seconds [1] (iii) on the scatter diagram, draw a line of best fit. [2] (d) use your line of best fit to find an estimate of the time taken to reach 100 km/h for a car that has a mass of 1550 kg. ... seconds [1] 10 some students are asked if they travel to school by tram ( t) or bicycle ( b) or both. 17 travel by tram, 14 travel by bicycle and 6 travel by both tram and bicycle. (a) show this information on the venn diagram. t b u [2] (b) the total number of students asked is 30. work out the number of students who do not travel to school by tram or bicycle or both. [1] (c) one of the 30 students is chosen at random. find the probability that this student travels to school by bicycle and not by tram. [1] (d) on the venn diagram, shade the region ()tb, l. [1]", "14": "14 0607/32/m/j/19 \u00a9 ucles 2019 11 the shape, , is shown on the diagram. \u2013 4 \u20133 \u20132 \u20131 1 0 2 3 4 5 6 7 86 5 4 39 8 7 6 2 1 \u20131 \u20132 \u20133 \u2013 4y x on the diagram, draw the image of after (a) a rotation of 180\u00b0 about the origin, [2] (b) a translation by the vector 1 3-eo , [2] (c) an enlargement, scale factor 2, with centre (0, 0). [2]", "15": "15 0607/32/m/j/19 \u00a9 ucles 2019 [turn over 12 here is a sequence of patterns. pattern 1 pattern 2 pattern 3 pattern 4 (a) in the space above, draw pattern 4. [1] (b) complete the table. pattern number 1 2 3 4 5 number of dots 2 [2] (c) write down the rule for continuing the sequence of numbers of dots. [1] (d) find an expression for the nth term of the sequence of numbers of dots. [2] (e) zoe thinks that 134 is a term in this sequence. is she correct? show how you decide. because ... [2] question 13 is printed on the next page.", "16": "16 0607/32/m/j/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.13 5 \u201355 \u20135y x 0 ()xx2f= (a) on the diagram, sketch the graph of () yx f= for values of x between 5- and 5. [2] (b) write down the equation of the vertical asymptote. [1] (c) on the same diagram, sketch the graph of yx 2= for x55gg- . [2] (d) find the values of x when xx2 2= . x = . or x = . [2]" }, "0607_s19_qp_33.pdf": { "1": "this document consists of 18 printed pages and 2 blank pages. dc (leg/sg) 168253/4 \u00a9 ucles 2019 [turn over *7816467950* cambridge international mathematics 0607/33 paper 3 (core) may/june 2019 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.cambridge assessment international education cambridge international general certificate of secondary education", "2": "2 0607/33/m/j/19 \u00a9 ucles 2019 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/33/m/j/19 \u00a9 ucles 2019 [turn over answer all the questions. 1 (a) 7 8 9 10 11 12 13 from this list of numbers, write down (i) an even number, [1] (ii) a multiple of 5, [1] (iii) a factor of 27. [1] (b) write (i) 33% as a decimal, [1] (ii) 43 as a decimal, [1] (iii) 20% as a fraction, [1] (iv) 0.9 as a percentage. . % [1] (c) write 6.666 correct to 1 decimal place. [1] (d) work out 40. give your answer correct to 2 significant figures. [2]", "4": "4 0607/33/m/j/19 \u00a9 ucles 2019 2 (a) x y measure angle x and angle y. x = y = [2] (b) a cd be fgnot to scale in the first diagram, two lines intersect. in the second diagram, three lines meet at a point. (i) complete each statement using one letter from either diagram. angle . is acute. angle . is reflex. [2] (ii) complete each statement with a number. e = .\u00b0 d + a = .\u00b0 e + f + g = .\u00b0 [3]", "5": "5 0607/33/m/j/19 \u00a9 ucles 2019 [turn over 3 (a) item item cost ($)number of itemscost ($) bread 2.35 3 milk 3.00 4 eggs 2.82 1 cheese 22.04 1 total cost ($) (i) complete the shopping bill. [2] (ii) work out how much change there will be from $50. $ [1] (b) a jar of coffee usually costs $7.50 . this cost is reduced by 4%. by how much is the cost reduced? $ [1] (c) water can be bought in a pack of 6 bottles or a pack of 10 bottles. in both packs, the bottles are the same size. pack of 6 bottles costs $1.38 pack of 10 bottles costs $2.20 work out which pack is the better value. show all your working. pack of bottles is the better value [3]", "6": "6 0607/33/m/j/19 \u00a9 ucles 2019 4 (a) y x \u2013 5 \u2013 4 \u2013 3 \u2013 2 \u2013 1 1 2 3 4 5 0 \u2013 112345 \u2013 2 \u2013 3 \u2013 4 \u2013 5r pq (i) on the grid, draw the reflection of rectangle r in the y-axis. [1] (ii) triangle p is a reflection of triangle q. on the grid, draw the line of reflection. [1]", "7": "7 0607/33/m/j/19 \u00a9 ucles 2019 [turn over (b) y x \u2013 5 \u2013 4 \u2013 3 \u2013 2 \u2013 1 1 2 3 4 5 0 \u2013 112345 \u2013 2 \u2013 3 \u2013 4 \u2013 5a cb (i) describe fully the single transformation that maps shape a onto shape b. ... [3] (ii) describe fully the single transformation that maps shape a onto shape c. ... [2]", "8": "8 0607/33/m/j/19 \u00a9 ucles 2019 5 (a) ten people each invest money in a bank. the amount each person invests and their age is shown in the table. age (years) 28 40 30 66 71 70 62 56 75 22 amount ($ thousands)2.5 4.5 3.5 6 8 7 7.5 6 9 3 (i) complete the scatter diagram. the first five points have been plotted for you. age (years)amount ($ thousands) 20012345678910 30 40 50 60 70 80 [2] (ii) work out the mean age and the mean amount. mean age years mean amount $ thousands [2] (iii) using your answers to part (ii) , draw a line of best fit on the scatter diagram. [2] (iv) use your line of best fit to estimate how much someone aged 60 might invest. $ thousands [1]", "9": "9 0607/33/m/j/19 \u00a9 ucles 2019 [turn over (b) 100 other people were asked how much they had invested in the bank. the table below shows this information. amount ($ x) number of people x0 10001g 29 x 000 1000 21g 26 x 000 000 23 1g 19 x 000 000 34 1g 14 x 000 000 45 1g 12 (i) write down the modal group. . x1g [1] (ii) work out an estimate of the mean. $ [3]", "10": "10 0607/33/m/j/19 \u00a9 ucles 2019 6 (a) simplify fully. (i) pp62- [1] (ii) kg kg 75 3 ++ - [2] (b) solve. xx42 10 =+ x = [2] (c) multiply out the brackets. x39 4-^ h [1] (d) al w#= 22pl w =+ work out the value of a and the value of p when l = 7 and w = 5. a = p = [3]", "11": "11 0607/33/m/j/19 \u00a9 ucles 2019 [turn over (e) write down the value of x0 . [1] (f) simplify. (i) tt54# [1] (ii) pp 27 [1] (g) write down all the integer values of n that satisfy this inequality. ln51g [1]", "12": "12 0607/33/m/j/19 \u00a9 ucles 2019 7 some students are each asked how many cats and how many rabbits they have as pets. each of the students has no other pets. the results are shown in the table. example: the shaded square shows 1 student has 2 rabbits and 4 cats. number of cats 0 1 2 3 4 number of rabbits0 4 3 1 2 0 1 1 1 0 1 1 2 3 2 2 2 1 3 2 1 0 2 0 4 2 2 0 0 0 (a) find the total number of students asked. [1] (b) work out the number of students with (i) exactly 3 cats, [1] (ii) exactly 4 pets, [1] (iii) fewer than 3 pets, [1] (iv) the same number of cats as rabbits. [1]", "13": "13 0607/33/m/j/19 \u00a9 ucles 2019 [turn over 8 (a) 20 cm 16 cmx cm12 cmc a bnot to scale (i) work out the perimeter of triangle abc . ... cm [1] (ii) work out the area of triangle abc . .. cm2 [1] (iii) using your answer to part (ii) , find the value of x. x = [2] (b) these two triangles are mathematically similar. 12 cm18 cm 16 cm y cm20 cmnot to scale find the value of y. y = [2]", "14": "14 0607/33/m/j/19 \u00a9 ucles 2019 9 u ,, ,, ,,, ,, 12 34 567 8910 =\" , ,, , s 2357=\" , ,,,, t 1357 9 =\" , (a) write down (i) ns^h, [1] (ii) st+, \" .. , [1] (iii) st,, \" .. , [1] (iv) sl. \" .. , [1] (b) (i) a number is chosen at random from s. work out the probability that it is 3. [1] (ii) 60 students each choose a number at random from s. find the expected number of times that 3 is chosen. [1]", "15": "15 0607/33/m/j/19 \u00a9 ucles 2019 [turn over 10 35 cm 95 cmnot to scale a container is made from a cylinder and a hemisphere. the cylinder has radius 35 cm and height 95 cm and the hemisphere has radius 35 cm. the container is full of water. calculate the total volume of water in the container. give your answer in litres. litres [4]", "16": "16 0607/33/m/j/19 \u00a9 ucles 2019 11 the line ab is drawn on a 1 cm2 grid. 01 1 2 32345678910 xaby (a) write down the co-ordinates of the midpoint of the line ab. ( . , . ) [1] (b) find the gradient of the line ab. [2] (c) use pythagoras\u2019 theorem to work out the length of ab. ab = ... cm [3]", "17": "17 0607/33/m/j/19 \u00a9 ucles 2019 [turn over 12 (a) (i) the mass of the earth\u2019s atmosphere is 5.15 \u00d7 1018 kg. when 5.15 \u00d7 1018 is written as an ordinary number, how many zeros are there in the number? [1] (ii) 0.000 055% of the earth\u2019s atmosphere is hydrogen. write 0.000 055 in standard form. [1] (b) (i) the international space station travels round the earth at a height of 450 km. write 450 km in centimetres. give your answer in standard form. ... cm [2] (ii) the international space station travels at a speed of 8 km/s. work out the distance it travels in 1 day. ... km [2]", "18": "18 0607/33/m/j/19 \u00a9 ucles 2019 13 10y x \u2013100 \u20131 6 (a) (i) on the diagram, sketch the graph of yx x 52=- for x16gg- . [2] (ii) find the co-ordinates of the local maximum. ( . , . ) [2] (b) on the diagram, sketch the graph of yx 3=+ for x16gg- . [2] (c) solve this equation. xx x 532-= + x =... or x = ... [2]", "19": "19 0607/33/m/j/19 \u00a9 ucles 2019 blank page", "20": "20 0607/33/m/j/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_s19_qp_41.pdf": { "1": "cambridge assessment international education cambridge international general certificate of secondary education *4886478967* this document consists of 19 printed pages and 1 blank page. dc (rw/sw) 164748/3 \u00a9 ucles 2019 [turn overcambridge international mathematics 0607/41 paper 4 (extended) may/june 2019 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.", "2": "2 0607/41/m/j/19 \u00a9 ucles 2019 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/41/m/j/19 \u00a9 ucles 2019 [turn over answer all the questions. 1 in a sale, a shop reduces all its prices by 15%. (a) calculate the sale price of a television originally costing $630. $ ... [2] (b) the price of a fridge in the sale is $952. calculate the original price. $ ... [3] (c) after one week the shop reduces the price of the television in part (a) by a further 5% each week until it is sold. calculate the number of weeks from the start of the sale until the television reaches half the original price. [4]", "4": "4 0607/41/m/j/19 \u00a9 ucles 2019 2 a bc11 10 9 8 7 6 5 4 3 2 1 0 \u2013 1 \u2013 2 \u2013 3 \u2013 4 \u2013 5123456789101112y x (a) describe fully the single transformation that maps triangle a onto triangle b. [2] (b) translate triangle a by the vector 6 3-eo . [2] (c) triangle a can be mapped onto triangle c by a rotation followed by an enlargement. (i) use trigonometry to calculate the angle of rotation. [3] (ii) the scale factor of the enlargement is a where a is an integer. find the value of a. a = ... [3]", "5": "5 0607/41/m/j/19 \u00a9 ucles 2019 [turn over 3 1 3 5 9 15 45 the list shows the six factors of 45. this is a method for finding how many factors a number has. \u2022 write the number as the product of its prime factors in index form. \u2022 add one to each of the powers and multiply these numbers together. for example, 45 3521#= () () 21 11 32 6 ##++ == so 45 has 6 factors. (a) 24 2331#= by listing all the factors of 24, show that the method works for 24. [3] (b) use the method to find how many factors 360 has. [4]", "6": "6 0607/41/m/j/19 \u00a9 ucles 2019 4 rani planted some seeds in her garden. after two months she measured the heights, h cm, of each of 120 plants. the results are shown in the table. height ( h cm) h01 0 1g h 10 201g h 20 251g h 25 301g h 30 351g h 35 401g h 40 501g frequency 0 16 28 32 24 14 6 (a) calculate an estimate of the mean height. ... cm [2] (b) draw a cumulative frequency curve for this information. 0020406080100120 10 20 height (cm)cumulative frequency 30 40 50 h [5]", "7": "7 0607/41/m/j/19 \u00a9 ucles 2019 [turn over (c) use your cumulative frequency curve to estimate (i) the median height, ... cm [1] (ii) the interquartile range, ... cm [2] (iii) the number of plants with a height of more than 37 cm. [2] (d) (i) complete this table of frequency densities for the 120 plants. height (h cm)h01 0 1g h 10 201g h 20 251g h 25 301g h 30 351g h 35 401g h 40 501g frequency density0 1.6 [2] (ii) draw a histogram to show this information. 00246 1357 10 20 height (cm)frequency density 30 40 50 h [3]", "8": "8 0607/41/m/j/19 \u00a9 ucles 2019 5 jian asks 60 people what their favourite type of television programme is. these are the results. type of programme number of people factual 15 sport 18 drama 12 game show 10 other 5 (a) jian draws a pie chart to show these results. calculate the sector angle for drama. [2] (b) jian chooses one of the 60 people at random. write down the probability that the person says factual. [1] (c) jian chooses two of the 60 people at random. (i) find the probability that one of them says drama and the other says game show. [3] (ii) find the probability that at least one person says sport. [3]", "9": "9 0607/41/m/j/19 \u00a9 ucles 2019 [turn over 6 y is inversely proportional to x. when x9=, y6=. (a) (i) find an equation connecting x and y. [2] (ii) calculate y when x30= . [1] (iii) calculate x when y15= . [2] (b) for the three variables x, y and z, z is also proportional to ()y5+. when x9=, z33= . find an equation connecting x and z. [2]", "10": "10 0607/41/m/j/19 \u00a9 ucles 2019 7 the vectors a and b are shown on the grids. a b (a) on the grid below, draw and label the following three vectors. 2b ab2+ ab2- [3]", "11": "11 0607/41/m/j/19 \u00a9 ucles 2019 [turn over (b) vectors p, q, and r are drawn on this grid. write each of the vectors in terms of a and/or b. p q r p = ... q = ... r = ... [3]", "12": "12 0607/41/m/j/19 \u00a9 ucles 2019 8 not to scale 6 cm13 cm 9 cm 11 cmda cb abcd is a quadrilateral. (a) show that bd = 9.22 cm, correct to 3 significant figures. [3] (b) calculate angle abd . angle abd = ... [3] (c) calculate the total area of the quadrilateral abcd . .. cm2 [3]", "13": "13 0607/41/m/j/19 \u00a9 ucles 2019 [turn over (d) calculate the length of the diagonal ac. ac = .. cm [3]", "14": "14 0607/41/m/j/19 \u00a9 ucles 2019 9 in this question all lengths are in centimetres. not to scale 15 20x x x x xx the diagram shows a picture frame with three pictures. the frame and the pictures are rectangles. each picture measures 20 cm by 15 cm. the width of the borders between each picture and between each picture and the frame are all x cm. the total area of the frame is 2208 cm2. (a) show that xx48 5 654 02+- =. [3] (b) solve the equation xx48 5 654 02+- =. you must show all your working. x = or x = ... [3]", "15": "15 0607/41/m/j/19 \u00a9 ucles 2019 [turn over (c) find the dimensions of the picture frame. length .. cm height .. cm [2]", "16": "16 0607/41/m/j/19 \u00a9 ucles 2019 10 (a) ()xx 52 f=- ()xx 32 g=+ (i) find ()3 f- . [1] (ii) find (( ))4 fg . [2] (iii) solve () ()x x2f g= . x= ... [3] (iv) find ()x f1- . ()x f1=- ... [2] (v) find and simplify (( ))x gf . [2]", "17": "17 0607/41/m/j/19 \u00a9 ucles 2019 [turn over (vi) write as a single fraction in its simplest form. () () xx32 fg+ [3] (b) the function ()xh has an inverse function ()xj. write down, in its simplest form, (( ))x jh . [1]", "18": "18 0607/41/m/j/19 \u00a9 ucles 2019 11 y x7 \u20132 0 \u201366 ()() ()()xxxx 142f=--+ (a) on the diagram, sketch the graph of () yx f= for values of x between -2 and 7. [3] (b) write down the co-ordinates of the local maximum. ( , ) [2] (c) write down the equation of each of the three asymptotes. .. , .. , .. [3] (d) ()xx 5 g=- (i) solve the equation () () xxfg= . x = . or x = . or x = . [3] (ii) solve the inequality () () xxfg2 . [3]", "19": "19 0607/41/m/j/19 \u00a9 ucles 2019 12 here is a sequence of patterns made using identical regular hexagons. pattern 1 pattern 2 pattern 3 pattern 4 pattern number 1 2 3 4 5 6 number of white hexagons1 1 13 13 number of grey hexagons0 6 6 24 total number of hexagons1 7 19 37 61 (a) complete the table for pattern 5 and pattern 6. [5] (b) the nth term of the sequence for the total number of hexagons is np nq 32++ . find the value of p and the value of q. p = ... q = ... [2]", "20": "20 0607/41/m/j/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_s19_qp_42.pdf": { "1": "cambridge assessment international education cambridge international general certificate of secondary education *0217364842* this document consists of 19 printed pages and 1 blank page. dc (nf/sw) 164743/3 \u00a9 ucles 2019 [turn overcambridge international mathematics 0607/42 paper 4 (extended) may/june 2019 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.", "2": "2 0607/42/m/j/19 \u00a9 ucles 2019 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/42/m/j/19 \u00a9 ucles 2019 [turn over answer all the questions. 1 louis and maria share $50 in the ratio 11 : 14. (a) show that louis receives $22. [1] (b) louis and maria each spend $6 from their share of the $50. find the new ratio louis\u2019 money : maria\u2019s money. : ... [2] (c) louis spends 3217 of his remaining money to buy a bus ticket. calculate the cost of the bus ticket. $ [1] (d) in a sale, a bookshop reduces the price of each book by 10%. maria buys two of these books. (i) the first book maria buys has an original price of $6. calculate how much maria pays for this book. $ [2] (ii) maria pays $3.69 for her second book. calculate the original price of this book. $ [3]", "4": "4 0607/42/m/j/19 \u00a9 ucles 2019 2 03 5y x (a) on the diagram, sketch the graph of logyxx1=+bl for x051g. [2] (b) write down the equations of the asymptotes to the graph of logyxx1=+bl . [2] (c) solve the equation . logxx105+= bl . x = [1] (d) on the same diagram, sketch the graph of yx 2= for x051g. [1] (e) solve the equation logxxx1 2+= bl . x = [1] (f) on your diagram, shade the region where . y05g , yx 2h and log yxx1h+bl . [1]", "5": "5 0607/42/m/j/19 \u00a9 ucles 2019 [turn over 3 jono walks to school when the weather is fine. when the weather is not fine, jono takes the bus. if jono walks to school, the probability that he is late is 0.2 . if jono takes the bus, the probability that he is late is 0.05 . on any day, the probability that the weather is fine is 0.7 . (a) complete the tree diagram. 0.7fine not finelate not late ..0.2 .. late not late [3] (b) (i) find the probability that, on any day, jono is late. [3] (ii) jono attends school on 200 days. find the expected number of days that jono is late. [1]", "6": "6 0607/42/m/j/19 \u00a9 ucles 2019 4 not to scale l cm3 cm the diagram shows a solid made from a cylinder and two hemispheres. the radius of the cylinder and each hemisphere is 3 cm. the total volume of the solid is 144 r cm3. (a) the length of the cylinder is l cm. find the value of l. l = [3] (b) the solid is made of steel. 1 cm3 of steel has a mass of 7.8 g. calculate the mass of the solid. give your answer in kilograms. kg [2]", "7": "7 0607/42/m/j/19 \u00a9 ucles 2019 [turn over (c) the solid is melted down and made into 20 cubes each of side length 2.8 cm. calculate the volume of steel not used for the cubes as a percentage of the 144 r cm3. . % [3] (d) a solid that is mathematically similar to the original solid has a volume of 18 r cm3. find the radius of the new cylinder. ... cm [3]", "8": "8 0607/42/m/j/19 \u00a9 ucles 2019 5 (a) karl invests $200 at a rate of 1.5% per year simple interest. calculate the value of karl\u2019s investment at the end of 8 years. $ [3] (b) lena invests $200 at a rate of 1.4% per year compound interest. calculate the value of lena\u2019s investment at the end of 8 years. $ [3] (c) the rates of interest remain the same as in part (a) and part (b) . find how many more complete years it will take for the value of lena\u2019s investment to be greater than the value of karl\u2019s investment. [2]", "9": "9 0607/42/m/j/19 \u00a9 ucles 2019 [turn over 6 \u2013 10 \u2013 2 \u2013 3 \u2013 4 \u2013 5 \u2013 6\u2013 556 4 3 2 1 \u2013 6 \u2013 4 \u2013 3 \u2013 2 \u2013 1 1 2 3 4 5 6y x pq (a) reflect shape p in the y-axis. [1] (b) translate shape p by the vector 6 3-eo . [2] (c) describe fully the single transformation that maps shape p onto shape q. [3] (d) stretch shape p with stretch factor 2 and the x-axis invariant. [2]", "10": "10 0607/42/m/j/19 \u00a9 ucles 2019 7 a stone is thrown vertically upwards from ground level. its height, h metres above ground level, after t seconds, is given by . ht t 20 492=- . (a) find the height of the stone after 1 second. . m [1] (b) (i) on the diagram, sketch the graph of . ht t 20 492=- for . t04 5 gg . 025 \u2013104.5h t [2] (ii) complete the statement. the maximum height reached by the stone is ... m when t = .. s. [2] (iii) find the length of time the stone is in the air before it hits the ground. .. s [1] (iv) find the length of time the stone is more than 18 m above ground level. .. s [3]", "11": "11 0607/42/m/j/19 \u00a9 ucles 2019 [turn over 8 find the nth term of each sequence. (a) 7, 14, 21, 28, ... [1] (b) 10, 7, 4, 1, ... [2] (c) 8, 16, 32, 64, ... [2] (d) 2, 6, 12, 20, ... [2]", "12": "12 0607/42/m/j/19 \u00a9 ucles 2019 9 240 students take part in a charity run. the table shows information about the times, t minutes, taken to complete the run. time ( t minutes) t 20 401g t 40 501g t 50 551g t 55 751g number of students 20 70 120 30 (a) write down the time interval that contains the median. t1g . [1] (b) calculate an estimate of the mean. .. min [2] (c) complete the histogram to show the information in the table. 200510152025 30 40 time (minutes)frequency density 50 60 70 80 t [4]", "13": "13 0607/42/m/j/19 \u00a9 ucles 2019 [turn over (d) (i) one of the 240 students is chosen at random. find the probability that this student took more than 55 minutes to complete the run. [1] (ii) two students are chosen at random from the 240 students. calculate the probability that they both took more than 50 minutes. [2] (iii) two students are chosen at random from the 240 students. complete the statement. the probability that they both had times in the interval .. t1g .. is 1912161. [2]", "14": "14 0607/42/m/j/19 \u00a9 ucles 2019 10 (a) amy buys 3 pencils and 1 ruler and pays 67 cents. ben buys 2 pencils and 3 rulers and pays 96 cents. find the cost of 1 pencil and the cost of 1 ruler. you must show all your working. pencil ... cents ruler ... cents [5] (b) in this part, all measurements are in centimetres. not to scale x + 1x \u2013 4x x 453+ the area of the triangle is the same as the area of the rectangle. (i) show that xx31 04 802-- =. [4]", "15": "15 0607/42/m/j/19 \u00a9 ucles 2019 [turn over (ii) factorise xx31 04 82-- . [2] (iii) find the area of the triangle. . cm2 [2]", "16": "16 0607/42/m/j/19 \u00a9 ucles 2019 11 not to scalenorth d c b60\u00b030\u00b0 102 m 110 m a the diagram shows two fields on horizontal ground. a is due south of d and c is due east of d. (a) calculate dc. dc = . m [3] (b) calculate ab. ab = . m [3]", "17": "17 0607/42/m/j/19 \u00a9 ucles 2019 [turn over (c) calculate the total area of the fields. ... m2 [3] (d) calculate the bearing of a from b. [4]", "18": "18 0607/42/m/j/19 \u00a9 ucles 2019 12 xx 10 f=-`j xx 1 g2=+`j xx1h=`j log xxj3=`j (a) find g(3). [1] (b) find f(h(2)). [2] (c) find g(f( x)) in the form ax bx c2++ . [3] (d) for some functions, p-1(x) = p(x). write down which two functions, f( x), g(x), h(x) or j( x), have this property. .. and .. [2] (e) write x x1h f-` `j j as a single fraction in its simplest form. [3]", "19": "19 0607/42/m/j/19 \u00a9 ucles 2019 (f) (i) find j(243). [1] (ii) find x when j( x) = 1.5 . x = [1] (iii) find j-1(x). j \u2013 1(x) = [2]", "20": "20 0607/42/m/j/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_s19_qp_43.pdf": { "1": "this document consists of 19 printed pages and 1 blank page. dc (nh/tp) 164746/3 \u00a9 ucles 2019 [turn overcambridge assessment international education cambridge international general certificate of secondary education *8580548649* cambridge international mathematics 0607/43 paper 4 (extended) may/june 2019 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for \u03c0, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.", "2": "2 0607/43/m/j/19 \u00a9 ucles 2019 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/43/m/j/19 \u00a9 ucles 2019 [turn over answer all the questions. 1 (a) not to scale 7 cm3 cmh cm the diagram shows a cuboid. the volume of this cuboid is 52.5 cm3. find the value of h. h = [2] (b) not to scale the diagram shows a pyramid. the area of the base is 500 m2. the height of the pyramid is 27 m. find the volume of this pyramid. ... m3 [2]", "4": "4 0607/43/m/j/19 \u00a9 ucles 2019 2 the table shows the marks of 10 students in a physics examination and a chemistry examination. physics mark ( x) 17 29 34 46 57 66 73 84 92 96 chemistry mark ( y) 26 42 41 56 52 61 76 65 73 80 (a) find (i) the mean physics mark, [1] (ii) the mean chemistry mark. [1] (b) find the equation of the regression line for y in terms of x. y = [2] (c) use your regression line to estimate the chemistry mark when (i) the physics mark is 60, [1] (ii) the physics mark is 5. [1] (d) which physics mark, 60 or 5, is likely to give the most reliable chemistry mark? give a reason for your answer. [1]", "5": "5 0607/43/m/j/19 \u00a9 ucles 2019 [turn over 3 there are 120 students at a school. there are 30 students in each class. the number of boys and the number of girls in each class is shown in the table. class 1 class 2 class 3 class 4 boys 16 19 12 13 girls 14 11 18 17 (a) a student is chosen at random from the 120 students. calculate the probability that the student chosen is (i) a boy from class 2, [1] (ii) not from class 3. [1] (b) a boy is chosen at random. calculate the probability that he is from class 4. [2] (c) three students from class 1 are chosen at random. calculate the probability 3 girls are chosen. [3]", "6": "6 0607/43/m/j/19 \u00a9 ucles 2019 4 y x \u201366 0 \u2013270 270 (a) on the diagram, sketch the graph of y = f(x) where ()cosxx1f= for values of x between -270 and 270 . [3] (b) write down the range of f( x). [2] (c) (i) on the same diagram, sketch the graph of y = g(x) where ()()xxx 2720g=+ for values of x between -270 and 270 . [2] (ii) find the values of the x co-ordinates of the points of intersection of the two graphs. x = or x = or x = [3] (iii) find the equation of each asymptote of the graph of y = g(x). [2]", "7": "7 0607/43/m/j/19 \u00a9 ucles 2019 [turn over 5 the venn diagram shows the sets a, b and c. u a cb u = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13} a = {prime numbers} b = {factors of 12} c = {multiples of 3} (a) list the elements of set a. [1] (b) write all the elements of u in the correct parts of the venn diagram above. [3] (c) list the elements of () ' ab, . [1] (d) find (( )' ) bc a n,+ . [1]", "8": "8 0607/43/m/j/19 \u00a9 ucles 2019 6 you may use this grid to help you answer this question. y x 0 the transformation p is a reflection in the line y = x. the transformation q is a rotation of 180\u00b0 about the origin. the transformation r is a stretch, scale factor 2 with x-axis invariant. the transformation s is a stretch, scale factor 2 with y-axis invariant.", "9": "9 0607/43/m/j/19 \u00a9 ucles 2019 [turn over (a) (i) find the co-ordinates of the image of the point (5, 1) under the transformation p. ( , ...) [1] (ii) find the co-ordinates of the image of the point ( x, y) under the transformation p followed by the transformation q. ( , ...) [2] (iii) describe fully the single transformation equivalent to p followed by q. [2] (b) describe fully the single transformation equivalent to r followed by s. [3] (c) describe fully the single transformation equivalent to the inverse of r. [2]", "10": "10 0607/43/m/j/19 \u00a9 ucles 2019 7 (a) sergio invests $2000 at a rate of 3% per year compound interest. (i) find the value of his investment at the end of 5 years. $ [3] (ii) after how many complete years is the value of his investment greater than $4000? [3] (b) anna invests $2000 at a rate of 0.24% per month compound interest. find the value of her investment at the end of 5 years. $ [3] (c) calculate the monthly compound interest rate that is equal to a compound interest rate of 3% per year. . % [3]", "11": "11 0607/43/m/j/19 \u00a9 ucles 2019 [turn over 8 y x \u201366 0 \u20133 3 (a) on the diagram, sketch the graph of y = f(x), where ()xx 4 f2-= for values of x between -3 and 3. [3] (b) write down the equation of the line of symmetry of the graph. [1] (c) write down the zeroes of f( x). and [1] (d) (i) find the value of k when y = k meets the curve yx 42=- three times. k = [1] (ii) find the range of values of k when y = k meets the curve yx 42=- four times. [2]", "12": "12 0607/43/m/j/19 \u00a9 ucles 2019 9 (a) solve the following equations. (i) x1355= x = [1] (ii) xx35 72 5 += + x = [2] (iii) xx81 122=- x = or x = [4] (b) solve the following inequalities. (i) x 62 10h- [2] (ii) x2132- [3]", "13": "13 0607/43/m/j/19 \u00a9 ucles 2019 [turn over (c) solve the simultaneous equations. you must show all your working. xy35 3 += - xy52 26 -= x = y = [4] (d) solve the equation. logl og log x42 13 += x = [3]", "14": "14 0607/43/m/j/19 \u00a9 ucles 2019 10 the points a (1, 2) and b (7, 5) are shown on the diagram below. x 16y 12 0not to scale b a (a) write ab as a column vector. fp [1] (b) calculate the length of the line ab. [2] (c) the point c has co-ordinates (10, k). ab = bc and k 2 0. show that k = 11. [3]", "15": "15 0607/43/m/j/19 \u00a9 ucles 2019 [turn over (d) find the equation of the line that is perpendicular to ac that passes through the midpoint of ac. give your answer in the form y = mx + c. y = [4] (e) the points a, b, c and d form a rhombus. find the co-ordinates of d. ( , ...) [3]", "16": "16 0607/43/m/j/19 \u00a9 ucles 2019 11 not to scale af b c d6.2 m 5.5 m 41\u00b0 the diagram shows four points a, b, c and d on horizontal ground. there is a vertical flagpole, fb, held in place by straight wires af, cf and df. bcd is a straight line, ab = 5.5 m, bc = 6.2 m and angle fa b = 41\u00b0. (a) show that fb = 4.781 m, correct to 3 decimal places. [2] (b) calculate angle fcb . angle fcb = [2]", "17": "17 0607/43/m/j/19 \u00a9 ucles 2019 [turn over (c) angle cdf = 18\u00b0. show that cd = 8.514, correct to 3 decimal places. [3] (d) angle abc = 78\u00b0. find ad. ad = . m [3] (e) find the area of triangle abd . ... m2 [2]", "18": "18 0607/43/m/j/19 \u00a9 ucles 2019 12 (a) y varies directly as the square root of ( x + 1). y = 8 when x = 24. (i) find the value of y when x = 15. y = [3] (ii) find the value of x when y = 16. x = [2]", "19": "19 0607/43/m/j/19 \u00a9 ucles 2019 (b) find the next term in each of the following sequences. (i) 18, 13, 8, 3, \u20132, \u2026 [1] (ii) 3, 6, 11, 18, 27, \u2026 [1] (iii) \u20131000, 100, \u201310, 1, \u2026 [1] (iv) 0, 0, 0, 6, 24, 60, \u2026 [2]", "20": "20 0607/43/m/j/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_s19_qp_51.pdf": { "1": "this document consists of 7 printed pages and 1 blank page. dc (leg) 170700/2 \u00a9 ucles 2019 [turn over *0078478114* cambridge international mathematics 0607/51 paper 5 (core) may/june 2019 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.cambridge assessment international education cambridge international general certificate of secondary education", "2": "2 0607/51/m/j/19 \u00a9 ucles 2019 answer all the questions. investigation games in a competition this investigation looks at games played in a competition. in a competition every team must play each of the other teams once. example there are three teams, a, b and c in the competition. three different games are played. these are: a against b a against c b against c these are written as: ab ac bc note that ab is the same as ba. 1 (a) (i) there are now four teams a, b, c and d in the competition. write down the 6 different games played by these four teams. ... (ii) there are now five teams a, b, c, d and e in the competition. write down all the different games played by these five teams. ...", "3": "3 0607/51/m/j/19 \u00a9 ucles 2019 [turn over (b) complete the table. use your answer to part (a)(ii) to help you. number of teams ( n) 2 3 4 5 6 7 number of games ( g) 1 3 6 (c) (i) the numbers of games in the second row of the table form a sequence. write down the mathematical name for this sequence. .. (ii) write down the rule to find further terms in this sequence. ... ...", "4": "4 0607/51/m/j/19 \u00a9 ucles 2019 (d) when there are n teams in the competition the number of games played is g, where gn kn212=+ . find the value of k. .. (e) using your value of k, show that the formula in part (d) is correct for 8 teams. (f) find the number of games played when there are 20 teams in the competition. ..", "5": "5 0607/51/m/j/19 \u00a9 ucles 2019 [turn over 2 there are now 8 teams in the competition, a, b, c, d, e, f, g and h. every team plays one game each week. note that ab is the same as ba. (a) complete the table to show the games for the first three weeks. there are many ways of doing this. you only need to show one way. game 1 game 2 game 3 game 4 week 1 ab dg ch week 2 ac week 3 (b) write down the total number of weeks it will take to play all the games. ..", "6": "6 0607/51/m/j/19 \u00a9 ucles 2019 (c) points are awarded to each of the 8 teams in the competition every time they play one of their 7 games. a team gets \u2022 3 points for a win \u2022 1 point for a draw (when the score for each team is the same) \u2022 0 points for a loss. a team plays all 7 games. (i) find the highest number of points that this team can get. .. (ii) write down the smallest number of points that this team can get. .. (iii) the team wins two games, loses two games and draws the rest. calculate the number of points that this team gets. ..", "7": "7 0607/51/m/j/19 \u00a9 ucles 2019 (iv) can this team finish the competition with 20 points? show how you decide. (v) find all the different ways that this team could score 9 points. one way is 1 win and 6 draws.", "8": "8 0607/51/m/j/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_s19_qp_52.pdf": { "1": "this document consists of 8 printed pages. dc (rw) 170701/3 \u00a9 ucles 2019 [turn over *7566243408* cambridge international mathematics 0607/52 paper 5 (core) may/june 2019 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.cambridge assessment international education cambridge international general certificate of secondary education", "2": "2 0607/52/m/j/19 \u00a9 ucles 2019 answer all the questions. square roots within square roots this investigation looks at sequences of terms with square roots. you can form a sequence by using square roots within square roots. 6, 66+ , 66 6 ++ , 66 66 ++ + , \u2026 you can calculate the first four terms of this sequence as follows. 6 = 2.4494\u2026 66+ = . 62 4494f + = .84494f = 2.9068\u2026 66 6 ++ = . 62 9068f + = .89068f = 2.9844\u2026 66 66 ++ + = . 62 9844f + = .89844f = 2.9974\u2026 1 (a) complete each part of the calculation below to work out the next term of the sequence, writing each decimal as far as the 4th decimal place. 66 66 6 ++ ++ = 6+ = = . (b) as the sequence continues, the terms get closer and closer to an integer. this integer is the integer limit of the sequence. write down the integer limit of this sequence. ...", "3": "3 0607/52/m/j/19 \u00a9 ucles 2019 [turn over 2 here is a similar sequence of square roots. 30, 30 30+ , 30 30 30 ++ , 30 30 30 30 ++ + , \u2026 (a) calculate the first three terms, writing each decimal as far as the 4th decimal place. . , . , . (b) write down the integer limit of this sequence. ...", "4": "4 0607/52/m/j/19 \u00a9 ucles 2019 3 (a) complete this table for sequences similar to those in question 1(a) and question 2. 1st term integer limit 2 6 12 4 20 30 42 7 (b) (i) use part (a) to find the first term of the sequence that has an integer limit of 8. ... (ii) calculate the 2nd term of the sequence in part (i), writing the decimal as far as the 4th decimal place. ...", "5": "5 0607/52/m/j/19 \u00a9 ucles 2019 [turn over 4 the general sequence is k, kk+ , kk k ++ , kk kk ++ + , \u2026 the integer limit of the sequence is the integer n. for such sequences, () kn na=- , where a is a constant. (a) use the last row of the table in question 3(a) to find the value of a. ... (b) use () kn na=- to show that 90, 90 90+ , 90 90 90 ++ , 90 90 90 90 ++ + , \u2026 has an integer limit of n 10= . (c) find the first three terms, in square root form , of the sequence that has an integer limit of n 26= . , , ", "6": "6 0607/52/m/j/19 \u00a9 ucles 2019 5 here is the general form of another sequence of square roots with integer limit n. k, kk2+ , kk k 22++ , kk kk 22 2 ++ + , \u2026 for such sequences, () kn na=- , where a is a constant. when k24= the integer limit of the sequence is n 6=. (a) find the value of the constant a. ... (b) (i) find the value of k when the integer limit is n 5=. ... (ii) write down the 3rd term of the sequence in part (i) in square root form. ... (iii) calculate the 3rd term, writing the decimal as far as the 4th decimal place. ...", "7": "7 0607/52/m/j/19 \u00a9 ucles 2019 [turn over 6 here is the general form of another sequence of square roots with integer limit n. k, kk5+ , kk k 55++ , kk kk 55 5 ++ + , \u2026 for this sequence, () kn na=- , where a is a constant. the sequence 14, 14 514 + , 14 5145 14 ++ , 14 5145 14 514 ++ + , \u2026 has an integer limit of n 7=. find the value of the constant a. ... question 7 is printed on the next page.", "8": "8 0607/52/m/j/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.7 here is the general sequence with integer limit n. k, kx k+ , kx kx k ++ , kx kx kx k ++ + , \u2026 for all such sequences, () kn na=- , where a is a constant that depends on the value of x. (a) (i) use question 4, question 5 and question 6 to complete the table. x a question 4 1 question 5 question 6 5 (ii) write down an expression for k in terms of n and x. ... (b) find the integer limit, n, of this sequence. 7, 76 7+ , 76 76 7 ++ , 76 76 76 7 ++ + , \u2026 ..." }, "0607_s19_qp_53.pdf": { "1": "this document consists of 10 printed pages and 2 blank pages. dc (ks/cgw) 170702/2 \u00a9 ucles 2019 [turn over *6234282358*cambridge assessment international education cambridge international general certificate of secondary education cambridge international mathematics 0607/53 paper 5 (core) may/june 2019 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.", "2": "2 0607/53/m/j/19 \u00a9 ucles 2019 answer all the questions. investigation jumping frogs this investigation looks at the number of different ways that a frog can jump between stones in a line. the stones are always 1 unit apart. the frog always jumps \u2022 from left to right \u2022 from the first stone to the last stone. the diagram shows a frog sitting on a stone in a pond. first stone last stone this frog has a jump length of 1 unit . this is enough to move from one stone to the next stone. there is only 1 way to jump between two stones. first stone last stone there is only 1 way to jump between three stones. when there are more than three stones in a line, there is always only 1 way for this frog to jump from the first stone to the last stone.", "3": "3 0607/53/m/j/19 \u00a9 ucles 2019 [turn over 1 a different frog has a maximum jump length of 2 units . there is still only 1 way to jump between two stones. there are now 2 ways to jump between three stones. (a) complete the diagrams below to show the 3 ways that this frog can jump between four stones. ", "4": "4 0607/53/m/j/19 \u00a9 ucles 2019 (b) complete the diagrams below to show the 5 ways that this frog can jump between five stones. ", "5": "5 0607/53/m/j/19 \u00a9 ucles 2019 [turn over (c) the table shows the number of ways to jump between stones when the maximum jump length is 2 units. number of stones number of ways 2 1 3 2 4 3 5 5 6 8 7 13 the numbers in the last column of the table form a sequence. (i) write down the addition rule to find further terms in this sequence. ... ... (ii) use your rule to show that the number of ways for this frog to jump between 8 stones is 21.", "6": "6 0607/53/m/j/19 \u00a9 ucles 2019 2 another frog has a maximum jump length of 3 units . there is only 1 way for this frog to jump between two stones. there are 2 ways to jump between three stones. (a) there are 4 ways to jump between four stones. these are the same 3 ways as in question 1(a) and 1 new way. draw the new way on the diagram below. (b) there are 7 ways to jump between five stones. these are the same 5 ways as in question 1(b) and 2 new ways. draw the 2 new ways on the diagrams below.", "7": "7 0607/53/m/j/19 \u00a9 ucles 2019 [turn over (c) the table shows the number of ways to jump between stones when the maximum jump length is 3 units. number of stones number of ways 2 1 3 2 4 4 5 7 6 13 7 24 the numbers in the last column of the table form a sequence. (i) write down the rule to find further terms in this sequence. ... ... (ii) use your rule to find the number of ways for this frog to jump between 8 stones.", "8": "8 0607/53/m/j/19 \u00a9 ucles 2019 3 the table shows the number of ways to jump between 2 to 8 stones when the maximum jump length is 1 to 6 units. number of stonesmaximum jump length 1 unit 2 units 3 units 4 units 5 units 6 units 2 1 1 1 1 1 1 3 1 2 2 2 2 2 4 1 3 4 4 4 4 5 1 5 7 8 8 8 6 1 8 13 15 16 16 7 1 13 24 29 31 32 8 1 21 (a) complete the table. (b) the numbers in the column for maximum jump length of 4 units form a sequence. write down the rule for finding further terms in this sequence. ... ... (c) the numbers in the column for the maximum jump length of 5 units also form a sequence. write down the rule for finding further terms in this sequence. ... ...", "9": "9 0607/53/m/j/19 \u00a9 ucles 2019 [turn over 4 this is the same table as in question 3 , with some numbers missing. some of the numbers have been written as powers of 2. number of stonesmaximum jump length 1 unit 2 units 3 units 4 units 5 units 6 units 2 20 3 1 2121212121 4 1 3 5 1 5 7 6 1 8 13 15 7 1 13 24 29 31 8 1 21 (a) copy your values from the table in question 3 into the row for 8 stones. complete the table by writing in the remaining values as powers of 2. (b) use patterns from your table to write down, as a power of 2, the number of ways of jumping between 30 stones when the maximum jump length is 29 units. ... (c) find the number of ways of jumping between 30 stones when the maximum jump length is 28 units. ...", "10": "10 0607/53/m/j/19 \u00a9 ucles 2019 (d) from the table, the largest number of ways of jumping between 3 stones is 21. write down, as a power of 2, the largest number of ways of jumping between (i) 5 stones, ... (ii) 20 stones, ... (iii) x stones. ... (e) (i) find the smallest jump length that gives your answer in part (d)(i) . ... (ii) find an expression in terms of x for the smallest jump length that gives your answer in part (d)(iii) . ...", "11": "11 0607/53/m/j/19 \u00a9 ucles 2019 blank page", "12": "12 0607/53/m/j/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page " }, "0607_s19_qp_61.pdf": { "1": "this document consists of 12 printed pages. dc (rw/cb) 170703/3 \u00a9 ucles 2019 [turn over *1654377826* cambridge international mathematics 0607/61 paper 6 (extended) may/june 2019 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a (questions 1 to 5) and b (questions 6 to 8). you must show all the relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.cambridge assessment international education cambridge international general certificate of secondary education", "2": "2 0607/61/m/j/19 \u00a9 ucles 2019 answer both parts a and b. a investigation (questions 1 to 5) games in a competition (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation looks at the numbers of games played in two kinds of competition. 1 in a knock\u2011out competition each team plays a game against one of the other teams. the teams that win these games play in the second round. the teams that win in the second round play in the third round and so on. (a) (i) there are two teams in the last round, called the final. the round before the final is called the semi\u2011finals. the round before the semi \u2011finals is called the quarter\u2011finals. write down the number of teams in the quarter\u2011finals. ... (ii) there are 32 teams in a competition. find the number of rounds. ... (iii) there are 7 rounds in a competition. find the number of teams. ...", "3": "3 0607/61/m/j/19 \u00a9 ucles 2019 [turn over (b) use your answers to question 1(a) to help you complete the table. number of rounds ( r) 1 2 3 4 5 6 7 8 number of teams ( t) 2 256 (c) (i) find a formula for t, the number of teams, in terms of r, the number of rounds. ... (ii) use your formula to calculate the number of teams in a competition with 15 rounds. ...", "4": "4 0607/61/m/j/19 \u00a9 ucles 2019 2 the number of teams in a knock\u2011out competition should be a number in the sequence in question 1. the number 11 is not in the sequence. when there are 11 teams, a first round is played to reduce the number of teams to 8. in this first round, only 6 teams play, giving 3 winners. the remaining 5 teams go through to the second round without playing. (a) there are 25 teams in a knock\u2011out competition. (i) find the number of rounds. ... (ii) find the total number of games. ... (b) find the total number of games when there are 36 teams. ... (c) what is the connection between the number of teams and the number of games? ...", "5": "5 0607/61/m/j/19 \u00a9 ucles 2019 [turn over 3 in a league competition every team must play each of the other teams once. example there are three teams, a, b and c in the competition. three different games are played. these are: a against b a against c b against c these are written as: ab ac bc (a) complete this table. number of teams ( n) 2 3 4 5 6 7 8 number of games ( g) 1 3 28 (b) when there are n teams in the competition the number of games played is g, where ga nb n2=+ . find the value of a and the value of b. write down the formula for g in terms of n. ... (c) show that your formula in part (b) gives the correct result for 8 teams.", "6": "6 0607/61/m/j/19 \u00a9 ucles 2019 4 there are now 8 teams in this competition, a, b, c, d, e, f, g and h. every team plays one game each week. note that ab is the same as ba. complete the table to show the games for the first three weeks. there are many ways of doing this. you only need to show one way. game 1 game 2 game 3 game 4 week 1 ab dg ch week 2 ac week 3", "7": "7 0607/61/m/j/19 \u00a9 ucles 2019 [turn over 5 there are more than two teams in each competition. (a) it is possible to have the same number of games in both a knock\u2011out competition and a league competition. find a possible number of games and the number of teams in each competition. number of games .. number of teams in knock\u2011out .. number of teams in league .. (b) it is possible to have half the number of games in a knock\u2011out competition as in a league competition. there is the same number of teams in each competition. find the number of teams and the number of games in each competition. number of teams .. number of games in knock\u2011out .. number of games in league ..", "8": "8 0607/61/m/j/19 \u00a9 ucles 2019b modelling (questions 6 to 8) throwing stones (20 marks) you are advised to spend no more than 45 minutes on this part. this part looks at modelling the path of a stone thrown from a vertical cliff onto horizontal ground. not to scale cliff groundh a stone is thrown horizontally from the top of the cliff at height h metres above the horizontal ground. the model of its height, h metres, at time, t seconds, is . hh t492=- . 6 (a) charlie stands on the top of the cliff. he throws a stone horizontally at a height of 122.5 m above the horizontal ground. write down the model for the height of his stone. ... (b) sketch the model in part (a) on the axes below, for t05gg . 5 0 th", "9": "9 0607/61/m/j/19 \u00a9 ucles 2019 [turn over (c) write down the number of seconds that the stone takes to hit the ground. ... (d) not to scalex a stone is thrown horizontally, with speed v, from the top of the cliff. at time t seconds the stone is x metres from the cliff. a model for the horizontal distance is xv t=. (i) write down the units of v. ... (ii) when charlie throws his stone, v20= . find the value of x when this stone hits the ground. ... (e) (i) when v20= , use the models in part (a) and part (d) to show that . hx400 49000 492=- .", "10": "10 0607/61/m/j/19 \u00a9 ucles 2019 (ii) sketch the graph of . hx400 49000 492=- , for x0 100 gg . 100 0xh 7 belinda stands on a ledge on the cliff. she throws a stone horizontally, with . v 283= . a model of the height of her stone is .. hx6125 498002 =- . (a) write down the height from which belinda throws her stone. ... (b) on the axes in question 6(e)(ii) , sketch the graph of .. hx6125 498002 =- , for x0 100 gg . (c) using the model in question 6(d) , calculate the time belinda\u2019s stone takes to hit the ground. ...", "11": "11 0607/61/m/j/19 \u00a9 ucles 2019 [turn over 8 jayden is standing next to charlie and mackenzie is standing next to belinda. jayden throws a stone horizontally towards a point which is 50 m horizontally from the base of the cliff. (a) the model of the height of jayden\u2019s stone is .. hkx122 54 9162 =- eo . jayden\u2019s stone hits the point. find the value of k. ... (b) find the horizontal distance from the cliff to where jayden\u2019s stone crosses the path of belinda\u2019s stone. ... questions 8(c) and 8(d) are printed on the next page.", "12": "12 0607/61/m/j/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge. (c) belinda\u2019s stone does not hit the point. use the model for the height of belinda\u2019s stone in question 7, to calculate how far down the cliff she should move so that when she throws her stone it hits the point. ... (d) mackenzie throws a stone horizontally and hits the point. find the speed with which mackenzie throws this stone. ..." }, "0607_s19_qp_62.pdf": { "1": "this document consists of 12 printed pages. dc (leg/cb) 170704/3 \u00a9 ucles 2019 [turn over *6707905996* cambridge international mathematics 0607/62 paper 6 (extended) may/june 2019 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a (questions 1 to 6) and b (questions 7 to 9). you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.cambridge assessment international education cambridge international general certificate of secondary education", "2": "2 0607/62/m/j/19 \u00a9 ucles 2019 answer both parts a and b. a investigation (questions 1 to 6) square roots within square roots (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation looks at sequences of terms with square roots. you can form a sequence by using square roots within square roots. 6 , 66+ , 66 6 ++ , 66 66 ++ + , ... you can calculate the first four terms of this sequence as follows. 6 = 2.4494.\u2026. 66+ = . ... 62 4494+ = . ... 84494 = 2.9068.\u2026. 66 6 ++ = . ... 62 9068+ = . ... 89068 = 2.9844.\u2026. 66 66 ++ + = . ... 62 9844+ = . ... 89844 = 2.9974\u2026.. 1 (a) calculate the next term of the sequence, writing the decimal as far as the 4th decimal place. .. (b) as the sequence continues, the terms get closer and closer to an integer. this integer is the integer limit of the sequence. write down the integer limit of this sequence. ..", "3": "3 0607/62/m/j/19 \u00a9 ucles 2019 [turn over 2 here is a similar sequence of square roots. 30 , 30 30+ , 30 30 30 ++ , 30 30 30 30 ++ + , ... (a) calculate the first three terms, writing each decimal as far as the 4th decimal place. . , . , . (b) write down the integer limit of this sequence. ..", "4": "4 0607/62/m/j/19 \u00a9 ucles 2019 3 (a) complete this table for similar sequences. first term integer limit 2 6 12 20 30 42 7 (b) (i) use part (a) to find the first term of the sequence that has an integer limit of 8. .. (ii) calculate the 4th term of the sequence in part (b)(i) . give your answer correct to 4 decimal places. ..", "5": "5 0607/62/m/j/19 \u00a9 ucles 2019 [turn over 4 the general sequence is k , kk+ , kk k ++ , kk kk ++ + , ... so, when x is one of the terms, the next term is kx+ . the sequence reaches its limit, x, when one term equals the next term. that is, when xk x =+ . (a) make k the subject of the equation xk x =+ . .. (b) use part (a) to check that the sequence below has a limit, x, equal to 7. 42 , 42 42+ , 42 42 42 ++ , 42 42 42 42 ++ + , ... 5 you will find the following information useful in this question. for the equation ax bx c02++ =, xabb ac 242!=-- the limit of 3 , 33+ , 33 3 ++ , 33 33 ++ + , ... is not an integer. find the exact value of this limit. ..", "6": "6 0607/62/m/j/19 \u00a9 ucles 2019 6 here is another type of sequence. 5 , 51 3+ , 51 35++ , 51 35 13 ++ + , 51 35 13 5 ++ ++ , ... (a) the limit of this sequence is an integer, x. by calculating some terms of this sequence, find x. .. (b) the general form of this sequence is a , ab+ , aba++ , ab ab ++ + , ... where a and b are positive integers and ab!. the sequence has a limit, x, when xa bx =+ + . show that this equation can be written as xa bx2-= + .", "7": "7 0607/62/m/j/19 \u00a9 ucles 2019 [turn over (c) (i) use your answer to part (a) to show that the equation xa bx2+ -= is correct for this sequence. 5 , 51 3+ , 51 35++ , 51 35 13 ++ + , 51 35 13 5 ++ ++ , ... (ii) there are other pairs of positive integers, a and b, where ab!, such that the sequence a , ab+ , aba++ , ab ab ++ + , ... has the same limit as in part (a) . find all these pairs of positive integers.", "8": "8 0607/62/m/j/19 \u00a9 ucles 2019b modelling (questions 7 to 9) making cones (20 marks) you are advised to spend no more than 45 minutes on this part. you may find some of these formulas useful. circumference, c, of a circle of radius r. cr 2r= v olume, v, of cone of radius r, height h. vr h31 2r= curved surface area, a, of cone of radius r, sloping edge l. ar lr= this task looks at modelling the volume of a cone, which is made from a circular disc. in this part lengths are given in centimetres and angles in degrees. raj makes a cone from a circular disc of radius 18. he cuts out part of the circular disc, leaving the shaded sector with sector angle x. he joins the two radii of 18 together. the cone that he makes has base radius r and height h. 18 18not to scale18 x rh 7 (a) show that the arc length of the shaded sector is x 10r. (b) this arc length forms the circumference of the base of the cone. find r in terms of x. ..", "9": "9 0607/62/m/j/19 \u00a9 ucles 2019 [turn over (c) show that hx3244002 =- . (d) (i) show that a model for the volume, v, of this cone, is . vxx00026 32440022 =- . (ii) use part (i) to find the volume of the cone if raj uses a semicircle of radius 18. ..", "10": "10 0607/62/m/j/19 \u00a9 ucles 2019 (e) sketch the graph of the model for 0 < x < 360. 0 360v x (f) for the cone with maximum volume, find (i) the angle, x, .. (ii) the maximum volume, v, .. (iii) the curved surface area. ..", "11": "11 0607/62/m/j/19 \u00a9 ucles 2019 [turn over8 raj decides that he can make two cones from his circular disc. 18not to scale 18 xy one comes from the sector with sector angle x. the other comes from the remaining sector with sector angle y. (a) write down a formula for y in terms of x. .. (b) the total volume of the two cones is .. vxxyy00026 32440000026 3244002222 =- +- . use your answer to part (a) to write down, in terms of x, a model for the total volume of the two cones. ... (c) sketch the graph of this model. 025002700v x (d) find the two angles, x, that give the maximum total volume for the two cones. . and . question 9 is printed on the next page.", "12": "12 0607/62/m/j/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.9 instead of the circular disc of radius 18, raj now uses a disc of radius 36 to make one cone with the maximum volume. find (a) the volume of this cone, .. (b) the angle that gives this volume. .." }, "0607_s19_qp_63.pdf": { "1": "*7096774549* this document consists of 16 printed pages. dc (nh/cgw) 170705/2 \u00a9 ucles 2019 [turn overcambridge international mathematics 0607/63 paper 6 (extended) may/june 2019 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a (questions 1 to 3) and b (questions 4 to 6). you must show all the relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.cambridge assessment international education cambridge international general certificate of secondary education", "2": "2 0607/63/m/j/19 \u00a9 ucles 2019 the investigation starts on page 3.", "3": "3 0607/63/m/j/19 \u00a9 ucles 2019 [turn over answer both parts a and b. a investigation (questions 1 to 3) jumping frogs (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation looks at the number of different ways that a frog can jump between stones in a line. the stones are always 1 unit apart. the frog always jumps \u2022 from left to right \u2022 from the first stone to the last stone. the diagram shows a frog sitting on a stone in a pond. first stone last stone this frog has a jump length of 1 unit . this is enough to move from one stone to the next stone. there is only 1 way to jump between two stones. there is only 1 way to jump between three stones. first stone last stone when there are more than three stones in a line, there is always only 1 way for this frog to jump from the first stone to the last stone. 1 a different frog has a maximum jump length of 2 units . there is still only 1 way to jump between two stones. there are now 2 ways to jump between three stones.", "4": "4 0607/63/m/j/19 \u00a9 ucles 2019 (a) complete the diagrams below to show the 3 ways that this frog can jump between four stones. (b) complete the diagrams below to show the 5 ways that this frog can jump between five stones.", "5": "5 0607/63/m/j/19 \u00a9 ucles 2019 [turn over (c) the table shows the number of ways to jump between stones when the maximum jump length is 2 units. number of stones number of ways 2 1 3 2 4 3 5 5 6 8 7 13 8 9 the numbers in the last column of the table form a sequence. (i) complete the table. (ii) write down the rule to find further terms in this sequence. ... ...", "6": "6 0607/63/m/j/19 \u00a9 ucles 2019 2 another frog has a maximum jump length of 3 units . there is only 1 way for this frog to jump between two stones. there are 2 ways to jump between three stones. (a) there are 4 ways to jump between four stones. these are the same 3 ways as in question 1(a) and 1 new way. draw the new way on the diagram below. (b) there are the same 5 ways as in question 1(b) to jump between five stones and some new ways. draw diagrams to show the new ways below.", "7": "7 0607/63/m/j/19 \u00a9 ucles 2019 [turn over (c) the table shows the number of ways to jump between stones when the maximum jump length is 3 units. number of stones number of ways 2 1 3 2 4 4 5 6 13 7 24 8 9 the numbers in the last column of the table form a sequence. (i) use your answer to part (b) to help you complete the table. (ii) write down the rule to find further terms in this sequence. ... ...", "8": "8 0607/63/m/j/19 \u00a9 ucles 2019 3 the table shows the number of ways to jump between 2 to 9 stones when the maximum jump length is 1 to 8 units. number of stonesmaximum jump length 1 unit 2 units 3 units 4 units 5 units 6 units 7 units 8 units 2 1 1 1 1 1 1 1 1 3 1 2 2 2 2 2 2 2 4 1 3 4 4 4 4 4 4 5 1 5 8 8 8 8 8 6 1 8 13 15 16 16 16 16 7 1 13 24 29 31 32 32 32 8 1 56 61 63 64 64 9 1 120 125 127 128 (a) complete the table. (b) the numbers in the column for maximum jump length of 4 units form a sequence. write down the rule for finding further terms in this sequence. ... ...", "9": "9 0607/63/m/j/19 \u00a9 ucles 2019 [turn over (c) the terms of the sequence for a maximum jump length of 8 units are 1, 2, 4, 8, 16, 32, 64, 128 (i) find an expression, in terms of x, for the number of ways of jumping between x stones, where . x 29gg (ii) show that this expression does not give the number of ways for . x 10= (d) complete the two rules for finding the number of ways of jumping between x stones when the maximum jump length is m units. rule 1 for x2gg the number of ways = rule 2 for x > the number of ways is found by ... (e) a frog sits on the first of 20 equally spaced stones. the frog has a maximum jump length of 18 units. find the number of ways the frog can jump between the 20 stones. ", "10": "10 0607/63/m/j/19 \u00a9 ucles 2019 b modelling (questions 4 to 6) play tents (20 marks) you are advised to spend no more than 45 minutes on this part. this task is about maximising the volume of a tent for a given area of material. a company makes play tents for children. they make them in the shape of cuboids or square-based pyramids. the top and sides of the tents are made from material. no material is used for the base. cuboid tent pyramid tent h m x mx m4 the cuboid tent has a square base of side x metres and height h metres.cuboid tent pyramid tent h m x mx m (a) write down the volume, v, of the cuboid in terms of h and x. (b) show that the total area, am2, of material for the cuboid tent is . ax hx42=+", "11": "11 0607/63/m/j/19 \u00a9 ucles 2019 [turn over (c) the company uses 8m2 of material to make each cuboid tent. use this information and part (a) and part (b) to show that a model for the volume is ()vxx 482 =-. (d) (i) on the axes below, sketch the graph of the model ()vxx 482 =-. v 0 3 x (ii) find the maximum volume of a cuboid tent made from 8m2 of material. (e) customers want to buy tents with a height of at least 1 metre. (i) using your answer to part (a) , sketch, on the axes above, the graph of v against x when h = 1. (ii) find the volume of a cuboid tent made from 8m2 of material with a height of 1 metre. ", "12": "12 0607/63/m/j/19 \u00a9 ucles 2019 5 the pyramid tent also has a square base of side x metres and a height of h metres. the distance between the top of the pyramid and the midpoint of each edge of the base is y metres. h m y m x m the triangle below shows one of the faces of the pyramid. x my m (a) find a model, in terms of x and y, for the total area, s, of the four triangular faces of the pyramid. give your answer in its simplest form. ", "13": "13 0607/63/m/j/19 \u00a9 ucles 2019 [turn over (b) find an expression for y2 in terms of h and x. (c) use part (a) and part (b) to show that hxsx 4 4222 =- cm .", "14": "14 0607/63/m/j/19 \u00a9 ucles 2019 (d) the company uses 8m2 of material to make each tent. v olume of a pyramid 31#= base area # height (i) show that a model for the volume of the pyramid tent is vx xx 316 42 22 =- cm . (ii) on the axes below, sketch the graph of vx xx 316 42 22 =- cm . v 0 3 x", "15": "15 0607/63/m/j/19 \u00a9 ucles 2019 [turn over (iii) write down the maximum volume of a pyramid tent that uses 8m2 of material. (iv) customers want to buy tents with a height of at least 1 metre. sketch, on the axes on page 14, the graph of v against x when . h 1= (v) find the maximum volume of a pyramid tent made from 8m2 of material with a height of at least 1 metre. question 6 is printed on the next page.", "16": "16 0607/63/m/j/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.6 the company decides that the cuboid tent and the pyramid tent should have the same volume. which type of tent will customers want to buy? give a reason for your answer. type of tent .. because .. ..." }, "0607_w19_qp_11.pdf": { "1": " this document consists of 11 printed pages and 1 blank page. ib19 11_0607_11/3rp \u00a9 ucles 2019 [turn over \uf02a\uf035\uf030\uf039\uf035\uf034\uf036\uf031\uf037\uf038\uf030\uf02a \uf020 cambridge assessment international education cambridge international general certificate of secondary education cambridge international mathematics 0607/11 paper 1 (core) october/november 2019 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2019 0607/11/o/n/19 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \uf070r2 circumference, c, of circle, radius r. c = 2\uf070r curved surface area, a, of cylinder of radius r, height h. a = 2\uf070rh curved surface area, a, of cone of radius r, sloping edge l. a = \uf070rl curved surface area, a, of sphere of radius r. a = 4\uf070r2 volume, v, of prism, cross-sectional area a, length l. v = al volume, v, of pyramid, base area a, height h. v = 1 3ah volume, v, of cylinder of radius r, height h. v = \uf070r2h volume, v, of cone of radius r, height h. v = 1 3\uf070r2h volume, v, of sphere of radius r. v = 4 3\uf070r3 ", "3": "3 \u00a9 ucles 2019 0607/11/o/n/19 [turn over answer all the questions. 1 write down the square root of 36. [1] 2 9 11 15 22 27 33 from the list of numbers write down (a) the triangle number, [1] (b) the even number. [1] 3 work out 74 of 42. [1] 4 insert one pair of brackets to make this statement correct. 3 \u2212 2 \u00d7 5 + 1 = 6 [1] 5 x measure angle x. [1] ", "4": "4 \u00a9 ucles 2019 0607/11/o/n/19 6 ab d c complete the statements. diagram shows perpendicular lines. diagram shows a reflex angle. [2] 7 find the perimeter of this rectangle. cm [1] 4 cm 12 cmnot to scale", "5": "5 \u00a9 ucles 2019 0607/11/o/n/19 [turn over 8 (a) complete the diagram above so that the dotted line is a line of symmetry. [1] (b) a 1y x0 2 3b 2 \u201313 1 \u20131\u20132 \u2013 4 \u20133 4 (i) on the grid, plot and label the point c(3, 1). join the points to form triangle abc . [1] (ii) a shape is made from two congruent triangles abc and abd . the shape has rotational symmetry of order 2 and no lines of symmetry. on the grid draw triangle abd . [1] ", "6": "6 \u00a9 ucles 2019 0607/11/o/n/19 9 look at this train timetable. bunley 08 35 09 00 09 05 09 35 10 05 10 35 11 00 11 35 alton 08 51 09 51 10 51 11 51 sidcot 09 19 09 44 09 30 10 19 11 19 11 44 12 19 bilham 09 59 10 59 11 59 12 59 tim spa 10 22 10 56 11 30 12 22 12 36 13 22 trickway 10 35 11 11 12 35 12 49 13 35 wester 11 25 12 14 13 30 14 04 (a) a train goes from bunley to tim spa without stopping. write down the time this train leaves bunley. [1] (b) find which train takes the longest time to travel from bunley to wester. [2] 10 not to scale x\u00b045\u00b0115\u00b0d a bc the diagram shows a triangle abc and a straight line bd. find the size of angle x. x = [2] ", "7": "7 \u00a9 ucles 2019 0607/11/o/n/19 [turn over 11 change 45 g into kilograms. kg [1] 12 simplify. 4 m + m \uf02d 3m [1] 13 a = {x \uf07c x is a factor of 30 and x 10} list the elements of set a. { } [2] 14 these are the marks of 11 students in a mathematics test. 23 43 17 8 21 23 41 6 15 11 34 draw an ordered stem and leaf diagram for these marks. key \u01c0 represents [3] ", "8": "8 \u00a9 ucles 2019 0607/11/o/n/19 15 a cyclist travels 120 km in 6 hours. calculate his average speed. km / h [1] 16 43 = 64 find the value of 4 4. [1] 17 factorise 2 x 2 + 5x. [1] 18 put a ring around the correct expression for the distance x. 30 tan 37\uf0b0 30 sin 53 \uf0b0 30 cos 53 \uf0b0 30 cos 37 \uf0b0 [1] not to scale 30 cmx cm 53\u00b0 37\u00b0", "9": "9 \u00a9 ucles 2019 0607/11/o/n/19 [turn over 19 not to scale 7 cm30 cm the diagram shows a pyramid with vertical height 30 cm. the horizontal base of the pyramid is a square with side 7 cm. work out the volume of the pyramid. cm 3 [3] 20 the bearing of town x from town y is 045\u00b0. find the bearing of town y from town x. [2] 21 f(x) = (x + 2)( x \u2013 1) work out f(5). [1] ", "10": "10 \u00a9 ucles 2019 0607/11/o/n/19 22 y x\u2013 444 3 2 1 \u20133 \u20132 3 \u20133\u20132\u201310 12a cs \u2013 555 \u2013 4 \u2013 5\u2013 4\u20133\u20132\u20131\u20131 (a) on the grid, draw the image of shape a after an enlargement by scale factor 2 about centre c. [2] (b) shape s is the image of a shape after a translation by the vector \uf0f7 \uf0f8\uf0f6\uf0e7 \uf0e8\uf0e6 32. on the grid, draw the original shape. [2] ", "11": "11 \u00a9 ucles 2019 0607/11/o/n/19 23 the cumulative frequency table shows the marks, x, of 100 students in a science test. mark ( x) cumulative frequency 0 < x \u2264 20 18 0 < x \u2264 40 54 0 < x \u2264 60 78 0 < x \u2264 80 100 on the grid, draw a cumulative frequenc y curve to show this information. x mark20 40 80 6020406080100 0cumulative frequency [2] ", "12": "12 permission to reproduce items where third-party owned material pr otected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the camb ridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which it self is a department of the university of cambridge. \u00a9 ucles 2019 0607/11/o/n/19 blank page " }, "0607_w19_qp_12.pdf": { "1": " this document consists of 11 printed pages and 1 blank page. ib19 11_0607_12/fp \u00a9 ucles 2019 [turn over \uf02a\uf031\uf038\uf033\uf036\uf036\uf037\uf035\uf035\uf039\uf033\uf02a \uf020 cambridge assessment international education cambridge international general certificate of secondary education cambridge international mathematics 0607/12 paper 1 (core) october/november 2019 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2019 0607/12/o/n/19 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \uf070r2 circumference, c, of circle, radius r. c = 2\uf070r curved surface area, a, of cylinder of radius r, height h. a = 2\uf070rh curved surface area, a, of cone of radius r, sloping edge l. a = \uf070rl curved surface area, a, of sphere of radius r. a = 4\uf070r2 volume, v, of prism, cross-sectional area a, length l. v = al volume, v, of pyramid, base area a, height h. v = 1 3ah volume, v, of cylinder of radius r, height h. v = \uf070r2h volume, v, of cone of radius r, height h. v = 1 3\uf070r2h volume, v, of sphere of radius r. v = 4 3\uf070r3 ", "3": "3 \u00a9 ucles 2019 0607/12/o/n/19 [turn over answer all the questions. 1 write down the square root of 36. [1] 2 9 11 15 22 27 33 from the list of numbers write down (a) the triangle number, [1] (b) the even number. [1] 3 work out 74 of 42. [1] 4 insert one pair of brackets to make this statement correct. 3 \u2212 2 \u00d7 5 + 1 = 6 [1] 5 x measure angle x. [1] ", "4": "4 \u00a9 ucles 2019 0607/12/o/n/19 6 ab d c complete the statements. diagram shows perpendicular lines. diagram shows a reflex angle. [2] 7 find the perimeter of this rectangle. cm [1] 4 cm 12 cmnot to scale", "5": "5 \u00a9 ucles 2019 0607/12/o/n/19 [turn over 8 (a) complete the diagram above so that the dotted line is a line of symmetry. [1] (b) a 1y x0 2 3b 2 \u201313 1 \u20131\u20132 \u2013 4 \u20133 4 (i) on the grid, plot and label the point c(3, 1). join the points to form triangle abc . [1] (ii) a shape is made from two congruent triangles abc and abd . the shape has rotational symmetry of order 2 and no lines of symmetry. on the grid draw triangle abd . [1] ", "6": "6 \u00a9 ucles 2019 0607/12/o/n/19 9 look at this train timetable. bunley 08 35 09 00 09 05 09 35 10 05 10 35 11 00 11 35 alton 08 51 09 51 10 51 11 51 sidcot 09 19 09 44 09 30 10 19 11 19 11 44 12 19 bilham 09 59 10 59 11 59 12 59 tim spa 10 22 10 56 11 30 12 22 12 36 13 22 trickway 10 35 11 11 12 35 12 49 13 35 wester 11 25 12 14 13 30 14 04 (a) a train goes from bunley to tim spa without stopping. write down the time this train leaves bunley. [1] (b) find which train takes the longest time to travel from bunley to wester. [2] 10 not to scale x\u00b045\u00b0115\u00b0d a bc the diagram shows a triangle abc and a straight line bd. find the size of angle x. x = [2] ", "7": "7 \u00a9 ucles 2019 0607/12/o/n/19 [turn over 11 change 45 g into kilograms. kg [1] 12 simplify. 4 m + m \uf02d 3m [1] 13 a = {x \uf07c x is a factor of 30 and x 10} list the elements of set a. { } [2] 14 these are the marks of 11 students in a mathematics test. 23 43 17 8 21 23 41 6 15 11 34 draw an ordered stem and leaf diagram for these marks. draw an ordered stem and leaf diagram for these marks. key \u01c0 represents [3] ", "8": "8 \u00a9 ucles 2019 0607/12/o/n/19 15 a cyclist travels 120 km in 6 hours. calculate his average speed. km / h [1] 16 43 = 64 find the value of 44. [1] 17 factorise 2 x 2 + 5x. [1] 18 put a ring around the correct expression for the distance x. 30 tan 37\uf0b0 30 sin 53 \uf0b0 30 cos 53 \uf0b0 30 cos 37 \uf0b0 [1] not to scale 30 cmx cm 53\u00b0 37\u00b0", "9": "9 \u00a9 ucles 2019 0607/12/o/n/19 [turn over 19 not to scale 7 cm30 cm the diagram shows a pyramid with vertical height 30 cm. the horizontal base of the pyramid is a square with side 7 cm. work out the volume of the pyramid. cm 3 [3] 20 the bearing of town x from town y is 045\u00b0. find the bearing of town y from town x. [2] 21 f(x) = (x + 2)( x \u2013 1) work out f(5). [1] ", "10": "10 \u00a9 ucles 2019 0607/12/o/n/19 22 y x\u2013 444 3 2 1 \u20133 \u20132 3 \u20133\u20132\u201310 12a cs \u2013 555 \u2013 4 \u2013 5\u2013 4\u20133\u20132\u20131\u20131 (a) on the grid, draw the image of shape a after an enlargement by scale factor 2 about centre c. [2] (b) shape s is the image of a shape after a translation by the vector \uf0f7 \uf0f8\uf0f6\uf0e7 \uf0e8\uf0e6 32. on the grid, draw the original shape. [2] ", "11": "11 \u00a9 ucles 2019 0607/12/o/n/19 23 the cumulative frequency table shows the marks, x, of 100 students in a science test. mark ( x) cumulative frequency 0 < x \u2264 20 18 0 < x \u2264 40 54 0 < x \u2264 60 78 0 < x \u2264 80 100 on the grid, draw a cumulative frequenc y curve to show this information. x mark20 40 80 6020406080100 0cumulative frequency [2] ", "12": "12 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge assessment international education copyright acknowledgements booklet. this is produc ed for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the ca mbridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which it self is a department of the university of cambridge. \u00a9 ucles 2019 0607/12/o/n/19 blank page " }, "0607_w19_qp_13.pdf": { "1": " this document consists of 11 printed pages and 1 blank page. ib19 11_0607_13/fp \u00a9 ucles 2019 [turn over \uf02a\uf030\uf033\uf035\uf033\uf036\uf034\uf036\uf030\uf037\uf035\uf02a cambridge assessment international education cambridge international general certificate of secondary education cambridge international mathematics 0607/13 paper 1 (core) october/november 2019 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain fu ll marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40. ", "2": "2 \u00a9 ucles 2019 0607/13/o/n/19 formula list area, a, of triangle, base b, height h. a = 1 2bh area, a, of circle, radius r. a = \uf070r2 circumference, c, of circle, radius r. c = 2\uf070r curved surface area, a, of cylinder of radius r, height h. a = 2\uf070rh curved surface area, a, of cone of radius r, sloping edge l. a = \uf070rl curved surface area, a, of sphere of radius r. a = 4\uf070r2 volume, v, of prism, cross-sectional area a, length l. v = al volume, v, of pyramid, base area a, height h. v = 1 3ah volume, v, of cylinder of radius r, height h. v = \uf070r2h volume, v, of cone of radius r, height h. v = 1 3\uf070r2h volume, v, of sphere of radius r. v = 4 3\uf070r3 ", "3": "3 \u00a9 ucles 2019 0607/13/o/n/19 [turn over answer all the questions. 1 write down the square root of 36. [1] 2 9 11 15 22 27 33 from the list of numbers write down (a) the triangle number, [1] (b) the even number. [1] 3 work out 74 of 42. [1] 4 insert one pair of brackets to make this statement correct. 3 \u2212 2 \u00d7 5 + 1 = 6 [1] 5 x measure angle x. [1] ", "4": "4 \u00a9 ucles 2019 0607/13/o/n/19 6 ab d c complete the statements. diagram shows perpendicular lines. diagram shows a reflex angle. [2] 7 find the perimeter of this rectangle. cm [1] 4 cm 12 cmnot to scale", "5": "5 \u00a9 ucles 2019 0607/13/o/n/19 [turn over 8 (a) complete the diagram above so that the dotted line is a line of symmetry. [1] (b) a 1y x0 2 3b 2 \u201313 1 \u20131\u20132 \u2013 4 \u20133 4 (i) on the grid, plot and label the point c(3, 1). join the points to form triangle abc . [1] (ii) a shape is made from two congruent triangles abc and abd . the shape has rotational symmetry of order 2 and no lines of symmetry. on the grid draw triangle abd . [1] ", "6": "6 \u00a9 ucles 2019 0607/13/o/n/19 9 look at this train timetable. bunley 08 35 09 00 09 05 09 35 10 05 10 35 11 00 11 35 alton 08 51 09 51 10 51 11 51 sidcot 09 19 09 44 09 30 10 19 11 19 11 44 12 19 bilham 09 59 10 59 11 59 12 59 tim spa 10 22 10 56 11 30 12 22 12 36 13 22 trickway 10 35 11 11 12 35 12 49 13 35 wester 11 25 12 14 13 30 14 04 (a) a train goes from bunley to tim spa without stopping. write down the time this train leaves bunley. [1] (b) find which train takes the longest time to travel from bunley to wester. [2] 10 not to scale x\u00b045\u00b0115\u00b0d a bc the diagram shows a triangle abc and a straight line bd. find the size of angle x. x = [2] ", "7": "7 \u00a9 ucles 2019 0607/13/o/n/19 [turn over 11 change 45 g into kilograms. kg [1] 12 simplify. 4 m + m \uf02d 3m [1] 13 a = {x \uf07c x is a factor of 30 and x 10} list the elements of set a. { } [2] 14 these are the marks of 11 students in a mathematics test. 23 43 17 8 21 23 41 6 15 11 34 draw an ordered stem and leaf diagram for these marks. key \u01c0 represents [3] ", "8": "8 \u00a9 ucles 2019 0607/13/o/n/19 15 a cyclist travels 120 km in 6 hours. calculate his average speed. km / h [1] 16 43 = 64 find the value of 4 4. [1] 17 factorise 2 x 2 + 5x. [1] 18 put a ring around the correct expression for the distance x. 30 tan 37\uf0b0 30 sin 53 \uf0b0 30 cos 53 \uf0b0 30 cos 37 \uf0b0 [1] not to scale 30 cmx cm 53\u00b0 37\u00b0", "9": "9 \u00a9 ucles 2019 0607/13/o/n/19 [turn over 19 not to scale 7 cm30 cm the diagram shows a pyramid with vertical height 30 cm. the horizontal base of the pyramid is a square with side 7 cm. work out the volume of the pyramid. cm 3 [3] 20 the bearing of town x from town y is 045\u00b0. find the bearing of town y from town x. [2] 21 f(x) = (x + 2)( x \u2013 1) work out f(5). [1] ", "10": "10 \u00a9 ucles 2019 0607/13/o/n/19 22 y x\u2013 444 3 2 1 \u20133 \u20132 3 \u20133\u20132\u201310 12a cs \u2013 555 \u2013 4 \u2013 5\u2013 4\u20133\u20132\u20131\u20131 (a) on the grid, draw the image of shape a after an enlargement by scale factor 2 about centre c. [2] (b) shape s is the image of a shape after a translation by the vector \uf0f7 \uf0f8\uf0f6\uf0e7 \uf0e8\uf0e6 32. on the grid, draw the original shape. [2] ", "11": "11 \u00a9 ucles 2019 0607/13/o/n/19 23 the cumulative frequency table shows the marks, x, of 100 students in a science test. mark ( x) cumulative frequency 0 < x \u2264 20 18 0 < x \u2264 40 54 0 < x \u2264 60 78 0 < x \u2264 80 100 on the grid, draw a cumulative frequenc y curve to show this information. x mark20 40 80 6020406080100 0cumulative frequency [2] ", "12": "12 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared w here possible. every reasonable effort has been made by the publisher (ucles) to trac e copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of ans wer-related information to candidates, all copyright acknowledgements are reproduced onl ine in the cambridge assessment international education copyright acknowledgements booklet. this is produc ed for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the ca mbridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which it self is a department of the university of cambridge. \u00a9 ucles 2019 0607/13/o/n/19 blank page " }, "0607_w19_qp_21.pdf": { "1": "this document consists of 8 printed pages. dc (rw/fc) 170393/2 \u00a9 ucles 2019 [turn over *1751561870* cambridge international mathematics 0607/21 paper 2 (extended) october/november 2019 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.cambridge assessment international education cambridge international general certificate of secondary education", "2": "2 0607/21/o/n/19 \u00a9 ucles 2019 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/21/o/n/19 \u00a9 ucles 2019 [turn over answer all the questions. 1 work out 15 142#+ . ... [1] 2 here is a list of numbers. 21 23 29 33 39 63 91 92 from the list, write down (a) a factor of 46, ... [1] (b) a prime number. ... [1] 3 list the integer values of x such that x311g - . ... [2] 4 at a railway station, the probability that any train departs on time is 87. the number of trains in one day is 72. work out the expected number of trains that depart on time. ... [1] 5 work out 43421' . give your answer as a fraction in its lowest terms. ... [2]", "4": "4 0607/21/o/n/19 \u00a9 ucles 2019 6 9, 27, 81, 243, \u2026 find the nth term of this sequence. ... [2] 7 not to scale 3 cm 7 cm the diagram shows a hemisphere joined to a cone. the hemisphere has a radius of 3 cm. the cone has a radius of 3 cm and a height of 7 cm. the total volume of the shape is kr cm3. find the value of k. k= .. [3] 8 find the value of 834 . ... [1]", "5": "5 0607/21/o/n/19 \u00a9 ucles 2019 [turn over 9 p12 5=-fp find (a) 2p, fp [1] (b) p. ... [2] 10 solve. ww48 502-- = w= .. or w= .. [3] 11 y varies inversely as x. when x16= , y9=. find y in terms of x. y= .. [2]", "6": "6 0607/21/o/n/19 \u00a9 ucles 2019 12 (a) dc b ax\u00b0100\u00b0not to scale the points a, b, c and d lie on the circle. find the value of x. x= .. [1] (b) o cba y\u00b0 36\u00b0not to scale the points a, b and c lie on the circle, centre o. find the value of y. y= .. [1]", "7": "7 0607/21/o/n/19 \u00a9 ucles 2019 [turn over 13 (a) simplify 20 125+ . ... [2] (b) rationalise the denominator and simplify your answer. 718 1- ... [2] 14 make l the subject of the formula r tgl2= . l= .. [3] 15 simplify ()t27 31 . ... [1] questions 16 and 17 are printed on the next page.", "8": "8 0607/21/o/n/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.16 a is the point (0, 8) and b is the point (6, 0). the line l passes through b and is perpendicular to ab. find the equation of l. ... [4] 17 simplify aab ac bc 422 2--+ -. ... [4]" }, "0607_w19_qp_22.pdf": { "1": "this document consists of 8 printed pages. dc (sc/sg) 170550/2 \u00a9 ucles 2019 [turn over *6177834697* cambridge international mathematics 0607/22 paper 2 (extended) october/november 2019 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.cambridge assessment international education cambridge international general certificate of secondary education", "2": "2 0607/22/o/n/19 \u00a9 ucles 2019 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/22/o/n/19 \u00a9 ucles 2019 [turn over answer all the questions. 1 8 27 49 51 53 55 99 from this list write down the square number. [1] 2 change 3.2 metres into millimetres. .. mm [1] 3 write each number in standard form. (a) 28 010 [1] (b) 0.100 209 [1] 4 each interior angle of a regular polygon is 170\u00b0. find the number of sides of this polygon. [3]", "4": "4 0607/22/o/n/19 \u00a9 ucles 2019 5 xian walks 8 km in 121 hours. she then runs 10 km in 45 minutes. find her average speed in km/h for the whole journey. km/h [3] 6 28\u00b0 x\u00b0a b cnot to scale ab = ac find the value of x. x = ... [2]", "5": "5 0607/22/o/n/19 \u00a9 ucles 2019 [turn over 7 the lengths of the sides of a right-angled triangle are 6 cm, 8 cm and 10 cm. find the tangent of the smallest angle. [1] 8 magda buys 6 apples and 4 oranges for a total cost of $4.18 . oranges cost $0.52 each. find the cost of one apple. $ ... [3] 9 the mean of five numbers is 16. when two extra numbers are included the mean of the seven numbers is 20. find the mean of the two extra numbers. [2]", "6": "6 0607/22/o/n/19 \u00a9 ucles 2019 10 the point a has co-ordinates (, ) 15- and the point b has co-ordinates (, )91. find the equation of the perpendicular bisector of ab in the form ym xc=+ . y = ... [5] 11 factorise completely. x81 82- [2]", "7": "7 0607/22/o/n/19 \u00a9 ucles 2019 [turn over 12 (a) simplify. 300 27- [2] (b) rationalise the denominator and simplify your answer. 3214 - [3] 13 solve the equation. logl og log x 34 42 -= x = ... [3] questions 14 and 15 are printed on the next page.", "8": "8 0607/22/o/n/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.14 rearrange the formula to make x the subject. yxx135=-- x = ... [4] 15 an archer fires three arrows at a target. the probability that the archer hits the target with each arrow is 53. find the probability that the archer hits the target exactly twice. [3]" }, "0607_w19_qp_23.pdf": { "1": "this document consists of 8 printed pages. dc (sc/sg) 170551/3 \u00a9 ucles 2019 [turn over *4755091919* cambridge international mathematics 0607/23 paper 2 (extended) october/november 2019 45 minutes candidates answer on the question paper. additional materials: geometrical instruments read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. calculators must not be used in this paper. all answers should be given in their simplest form. you must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 40.cambridge assessment international education cambridge international general certificate of secondary education", "2": "2 0607/23/o/n/19 \u00a9 ucles 2019 formula list for the equation ax bxc02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/23/o/n/19 \u00a9 ucles 2019 [turn over answer all the questions. 1 work out. (a) ()42- [1] (b) (.)032 [1] 2 (a) write down a prime number between 80 and 90. [1] (b) write down a triangle number between 30 and 50. [1] 3 (a) shade two squares so that this shape has exactly one line of symmetry. [1] (b) shade two squares so that this shape has rotational symmetry of order 2. [1]", "4": "4 0607/23/o/n/19 \u00a9 ucles 2019 4 a cat eats 132 tins of food each day. how many tins are needed for one week? [2] 5 factorise. (a) x12- [1] (b) xa xaxy ay 36 222-- + [2] 6 triangle abc is isosceles and angle a = 40\u00b0. find the three possible values for angle b. .. , .. , .. [2] 7 the mean of 10 numbers is 15. when an 11th number is included, the mean is 16. find the 11th number. [2]", "5": "5 0607/23/o/n/19 \u00a9 ucles 2019 [turn over 8 200 students record the method they use most to travel to school. the results are shown in the table. method of travel bus car walk cycle number of students 40 98 37 25 (a) find, as a fraction, the relative frequency of a student travelling to school by bus. [1] (b) give a reason why it is reasonable to use your answer to part (a) to estimate the probability that a student travels to school by bus. [1] (c) the school has 1800 students. estimate the number of students who travel to school by bus. [1] 9 (a) solve xx32 762-+ . [2] (b) show your solution to part (a) on this number line. 5 4 3 2 1 0 \u20131 \u20132 \u20133 \u20134 \u20135x [1]", "6": "6 0607/23/o/n/19 \u00a9 ucles 2019 10 rearrange this formula to make a the subject. yaa 132=-- [3] 11 expand and simplify. ()32 72+ [3] 12 the equation of the line l is yx32=- . (a) find the co-ordinates of the point a, where the line l crosses the y-axis. (. , .) [1] (b) find the co-ordinates of the point b, where the line l crosses the x-axis. (. , .) [1] (c) the line m passes through the point a and is perpendicular to the line l. find the equation of the line m. [2]", "7": "7 0607/23/o/n/19 \u00a9 ucles 2019 [turn over 13 a dpb cqnot to scale abcd is a parallelogram. ap = pq = qc. show that triangles bqc and dpa are congruent. statement reason [3] 14 o p (2, \u20133)y xnot to scale the diagram shows a sketch of the graph yx bxc2=+ +. the minimum point is at (, ) p23-. find the value of b and the value of c. b = ... c = ... [3] question 15 is printed on the next page.", "8": "8 0607/23/o/n/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.15 the table shows the height, h cm, of some plants. height ( h cm) h01 0 1g h 10 401g h 40 601g frequency p q 44 (a) complete the histogram to show this information. 0 10 20 30 40 50 600123456 frequency density height (cm)h [1] (b) find the value of p and the value of q. p = ... q = ... [2]" }, "0607_w19_qp_31.pdf": { "1": "this document consists of 15 printed pages and 1 blank page. dc (nf/fc) 168254/3 \u00a9 ucles 2019 [turn over *2501179758*cambridge assessment international education cambridge international general certificate of secondary education cambridge international mathematics 0607/31 paper 3 (core) october/november 2019 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.", "2": "2 0607/31/o/n/19 \u00a9 ucles 2019 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/31/o/n/19 \u00a9 ucles 2019 [turn over answer all the questions. 1 (a) write 52 as a decimal. [1] (b) write 169 as a percentage. . % [1] (c) work out .. . 6852 3417 9# - . [2] (d) write down a factor of 17. [1] (e) write 4928 in its simplest form. [1] (f) write down the next two terms in this sequence. 81, 74, 67, 60, \u2026 , [2] (g) $380 is invested at a rate of 3% per year simple interest. work out the interest at the end of 4 years. $ ... [2] (h) cupcakes cost $1.30 each. find the largest number of these cupcakes that can be bought with $10. [2]", "4": "4 0607/31/o/n/19 \u00a9 ucles 2019 2 benji has 15 bags of potatoes. the number of potatoes in each bag is shown below. 38 36 42 36 36 41 40 38 37 39 39 40 37 38 36 (a) complete the frequency table. number of potatoes 36 37 38 39 40 41 42 frequency 4 [2] (b) for the number of potatoes, find (i) the range, [1] (ii) the mode, [1] (iii) the median, [1] (iv) the mean. [1] (c) complete the bar chart. frequency number of potatoes36012345 37 38 39 40 41 42 [2]", "5": "5 0607/31/o/n/19 \u00a9 ucles 2019 [turn over 3 (a) write sixty thousand and twenty in figures. [1] (b) complete the mapping diagram for the function ()xx 34 f=- . x 0 .f (x) 1 . 2 . 3 . [2] (c) write down a prime number between 35 and 45. [1] (d) a 158 75= find the value of a. a= ... [1] (e) write 6789 correct to the nearest 10. [1] (f) write 189.436 correct to 2 decimal places. [1] (g) write 3462 (i) correct to 3 significant figures, [1] (ii) in standard form. [1]", "6": "6 0607/31/o/n/19 \u00a9 ucles 2019 4 01ab 23456y x1 2 3 4 5 6 the diagram shows two points, a and b, plotted on a 1 cm2 grid. (a) write down the co-ordinates of point a and the co-ordinates of point b. a ( ... , ... ) b ( ... , ... ) [2] (b) calculate the length of ab. ... cm [2] (c) find the co-ordinates of the midpoint of ab. ( ... , ... ) [1] (d) find the gradient of ab. [2] (e) write down the equation of the line parallel to ab passing through (0, 3). y= ... [2]", "7": "7 0607/31/o/n/19 \u00a9 ucles 2019 [turn over 5 two cylindrical candles are mathematically similar. the small candle has radius 2 cm and height 5 cm. the large candle has radius 7 cm. not to scale 5 cm2 cm7 cm (a) find the height of the large candle. ... cm [2] (b) the small candle burns for 4 hours and the large candle burns for 60 hours. write the ratio 4 : 60 in its simplest form. . : [1] (c) the price of the large candle is $28. in a sale, this price is reduced by 15%. find the sale price. $ [2]", "8": "8 0607/31/o/n/19 \u00a9 ucles 2019 6 (a) for each diagram, draw all the lines of symmetry. not to scale [3] (b) not to scale simi makes a flower using some mathematical shapes. the centre is a circle with radius 2 cm. each of the five petals is an isosceles triangle with base 2.3 cm and perpendicular height 4 cm. the stem is a rectangle with length 6 cm and width 1 cm. find the total area shaded. . cm2 [4]", "9": "9 0607/31/o/n/19 \u00a9 ucles 2019 [turn over 7 the table shows the age, in months, and length, in centimetres, of seven babies. age (months)0 2 4 5 9 10 12 length (cm)50 58 63 64 71 73 76 (a) complete the scatter diagram to show this information. the first three points have been plotted for you. 04050607080 2 4 6 age (months)length (cm) 8 10 12 [2] (b) find. (i) the mean age, ... months [1] (ii) the mean length. ... cm [1] (c) on the scatter diagram, draw a line of best fit. [2] (d) use your line of best fit to find an estimate for the length of a baby aged 7 months. ... cm [1]", "10": "10 0607/31/o/n/19 \u00a9 ucles 2019 8 (a) 40\u00b0 36 mq p anot to scale 1.8 m the diagram shows a vertical tower, pq, standing on horizontal ground. matthijs stands at point a. he is 1.8 m tall. the base of the tower, p, is 36 m from point a. find the height of the tower. . m [3]", "11": "11 0607/31/o/n/19 \u00a9 ucles 2019 [turn over (b) b 4 cmnot to scale 4 cm co a 38\u00b0 ab and ac are tangents to a circle with centre, o, and radius 4 cm. angle \u00b0 bac 38= . (i) write down the size of angle oba . angle oba= ... [1] (ii) find the size of angle boc . angle boc= ... [1] (c) use trigonometry to find the length of oa. oa= .. cm [3]", "12": "12 0607/31/o/n/19 \u00a9 ucles 2019 9 20 people were asked if they liked banana milk shake, b, or chocolate milk shake, c. b 4 3 9c .u (a) complete the venn diagram. [1] (b) write down ()bcn+. [1] (c) one of these 20 people is chosen at random. find the probability that this person likes (i) banana milk shake, [1] (ii) chocolate milk shake but not banana milk shake. [1] (d) on the venn diagram, shade cb+l. [1]", "13": "13 0607/31/o/n/19 \u00a9 ucles 2019 [turn over 10 y 20 \u2013250 \u20132 5x ()xxxx 52 8 f32=- ++ (a) on the diagram, sketch the graph of () yx f= for x25gg- . [3] (b) write down the co-ordinates of the point where the curve crosses the y-axis. ( ... , ... ) [1] (c) write down the co-ordinates of the three points where the curve crosses the x-axis. ( .. , .. ), ( .. , .. ), ( .. , .. ) [2] (d) find the co-ordinates of the local maximum. ( ... , ... ) [2] (e) find the number of times that the line y9= crosses the curve () yx f= . [1]", "14": "14 0607/31/o/n/19 \u00a9 ucles 2019 11 (a) solve. (i) y36= y= ... [1] (ii) y65 13-= y= ... [2] (iii) y362- [2] (b) expand and simplify. () () yy57 34-- ... [2] (c) pt26=- (i) find the value of p when t8=. p= ... [1] (ii) rearrange the formula to make t the subject. t= [2] (d) simplify. yy 32 5+ . [2]", "15": "15 0607/31/o/n/19 \u00a9 ucles 2019 12 angie goes to school on 5 days each week. on a school day, the probability that angie gets up before 7 am is 109 . on a non-school day, the probability that angie gets up before 7 am is 201 . (a) complete the tree diagram. school day non-school day..5 7gets up before 7 am does not get up before 7 am .. gets up before 7 am does not get up before 7 am .. [3] (b) one day of the week is chosen at random. find the probability that the day is a non-school day and that angie gets up before 7 am. [2]", "16": "16 0607/31/o/n/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_w19_qp_32.pdf": { "1": "this document consists of 15 printed pages and 1 blank page. dc (kn) 187896 \u00a9 ucles 2019 [turn over *9667552344*cambridge assessment international education cambridge international general certificate of secondary education cambridge international mathematics 0607/32 paper 3 (core) october/november 2019 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.", "2": "2 0607/32/o/n/19 \u00a9 ucles 2019 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/32/o/n/19 \u00a9 ucles 2019 [turn over answer all the questions. 1 (a) write 52 as a decimal. [1] (b) write 169 as a percentage. . % [1] (c) work out .. . 6852 3417 9# - . [2] (d) write down a factor of 17. [1] (e) write 4928 in its simplest form. [1] (f) write down the next two terms in this sequence. 81, 74, 67, 60, \u2026 , [2] (g) $380 is invested at a rate of 3% per year simple interest. work out the interest at the end of 4 years. $ ... [2] (h) cupcakes cost $1.30 each. find the largest number of these cupcakes that can be bought with $10. [2]", "4": "4 0607/32/o/n/19 \u00a9 ucles 2019 2 benji has 15 bags of potatoes. the number of potatoes in each bag is shown below. 38 36 42 36 36 41 40 38 37 39 39 40 37 38 36 (a) complete the frequency table. number of potatoes 36 37 38 39 40 41 42 frequency 4 [2] (b) for the number of potatoes, find (i) the range, [1] (ii) the mode, [1] (iii) the median, [1] (iv) the mean. [1] (c) complete the bar chart. frequency number of potatoes36012345 37 38 39 40 41 42 [2]", "5": "5 0607/32/o/n/19 \u00a9 ucles 2019 [turn over 3 (a) write sixty thousand and twenty in figures. [1] (b) complete the mapping diagram for the function ()xx 34 f=- . x 0 .f (x) 1 . 2 . 3 . [2] (c) write down a prime number between 35 and 45. [1] (d) a 158 75= find the value of a. a= ... [1] (e) write 6789 correct to the nearest 10. [1] (f) write 189.436 correct to 2 decimal places. [1] (g) write 3462 (i) correct to 3 significant figures, [1] (ii) in standard form. [1]", "6": "6 0607/32/o/n/19 \u00a9 ucles 2019 4 01ab 23456y x1 2 3 4 5 6 the diagram shows two points, a and b, plotted on a 1 cm2 grid. (a) write down the co-ordinates of point a and the co-ordinates of point b. a ( ... , ... ) b ( ... , ... ) [2] (b) calculate the length of ab. ... cm [2] (c) find the co-ordinates of the midpoint of ab. ( ... , ... ) [1] (d) find the gradient of ab. [2] (e) write down the equation of the line parallel to ab passing through (0, 3). y= ... [2]", "7": "7 0607/32/o/n/19 \u00a9 ucles 2019 [turn over 5 two cylindrical candles are mathematically similar. the small candle has radius 2 cm and height 5 cm. the large candle has radius 7 cm. not to scale 5 cm2 cm7 cm (a) find the height of the large candle. ... cm [2] (b) the small candle burns for 4 hours and the large candle burns for 60 hours. write the ratio 4 : 60 in its simplest form. . : [1] (c) the price of the large candle is $28. in a sale, this price is reduced by 15%. find the sale price. $ [2]", "8": "8 0607/32/o/n/19 \u00a9 ucles 2019 6 (a) for each diagram, draw all the lines of symmetry. not to scale [3] (b) not to scale simi makes a flower using some mathematical shapes. the centre is a circle with radius 2 cm. each of the five petals is an isosceles triangle with base 2.3 cm and perpendicular height 4 cm. the stem is a rectangle with length 6 cm and width 1 cm. find the total area shaded. . cm2 [4]", "9": "9 0607/32/o/n/19 \u00a9 ucles 2019 [turn over 7 the table shows the age, in months, and length, in centimetres, of seven babies. age (months)0 2 4 5 9 10 12 length (cm)50 58 63 64 71 73 76 (a) complete the scatter diagram to show this information. the first three points have been plotted for you. 04050607080 2 4 6 age (months)length (cm) 8 10 12 [2] (b) find. (i) the mean age, ... months [1] (ii) the mean length. ... cm [1] (c) on the scatter diagram, draw a line of best fit. [2] (d) use your line of best fit to find an estimate for the length of a baby aged 7 months. ... cm [1]", "10": "10 0607/32/o/n/19 \u00a9 ucles 2019 8 (a) 40\u00b0 36 mq p anot to scale 1.8 m the diagram shows a vertical tower, pq, standing on horizontal ground. matthijs stands at point a. he is 1.8 m tall. the base of the tower, p, is 36 m from point a. find the height of the tower. . m [3]", "11": "11 0607/32/o/n/19 \u00a9 ucles 2019 [turn over (b) b 4 cmnot to scale 4 cm co a 38\u00b0 ab and ac are tangents to a circle with centre, o, and radius 4 cm. angle \u00b0 bac 38= . (i) write down the size of angle oba . angle oba= ... [1] (ii) find the size of angle boc . angle boc= ... [1] (c) use trigonometry to find the length of oa. oa= .. cm [3]", "12": "12 0607/32/o/n/19 \u00a9 ucles 2019 9 20 people were asked if they liked banana milk shake, b, or chocolate milk shake, c. b 4 3 9c .u (a) complete the venn diagram. [1] (b) write down ()bcn+. [1] (c) one of these 20 people is chosen at random. find the probability that this person likes (i) banana milk shake, [1] (ii) chocolate milk shake but not banana milk shake. [1] (d) on the venn diagram, shade cb+l. [1]", "13": "13 0607/32/o/n/19 \u00a9 ucles 2019 [turn over 10 y 20 \u2013250 \u20132 5x ()xxxx 52 8 f32=- ++ (a) on the diagram, sketch the graph of () yx f= for x25gg- . [3] (b) write down the co-ordinates of the point where the curve crosses the y-axis. ( ... , ... ) [1] (c) write down the co-ordinates of the three points where the curve crosses the x-axis. ( .. , .. ), ( .. , .. ), ( .. , .. ) [2] (d) find the co-ordinates of the local maximum. ( ... , ... ) [2] (e) find the number of times that the line y9= crosses the curve () yx f= . [1]", "14": "14 0607/32/o/n/19 \u00a9 ucles 2019 11 (a) solve. (i) y36= y= ... [1] (ii) y65 13-= y= ... [2] (iii) y362- [2] (b) expand and simplify. () () yy57 34-- ... [2] (c) pt26=- (i) find the value of p when t8=. p= ... [1] (ii) rearrange the formula to make t the subject. t= [2] (d) simplify. yy 32 5+ . [2]", "15": "15 0607/32/o/n/19 \u00a9 ucles 2019 12 angie goes to school on 5 days each week. on a school day, the probability that angie gets up before 7 am is 109 . on a non-school day, the probability that angie gets up before 7 am is 201 . (a) complete the tree diagram. school day non-school day..5 7gets up before 7 am does not get up before 7 am .. gets up before 7 am does not get up before 7 am .. [3] (b) one day of the week is chosen at random. find the probability that the day is a non-school day and that angie gets up before 7 am. [2]", "16": "16 0607/32/o/n/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_w19_qp_33.pdf": { "1": "this document consists of 15 printed pages and 1 blank page. dc (kn) 187895 \u00a9 ucles 2019 [turn over *0883234879*cambridge assessment international education cambridge international general certificate of secondary education cambridge international mathematics 0607/33 paper 3 (core) october/november 2019 1 hour 45 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 96.", "2": "2 0607/33/o/n/19 \u00a9 ucles 2019 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = rr2 circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = 4rr2 v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rr2h v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/33/o/n/19 \u00a9 ucles 2019 [turn over answer all the questions. 1 (a) write 52 as a decimal. [1] (b) write 169 as a percentage. . % [1] (c) work out .. . 6852 3417 9# - . [2] (d) write down a factor of 17. [1] (e) write 4928 in its simplest form. [1] (f) write down the next two terms in this sequence. 81, 74, 67, 60, \u2026 , [2] (g) $380 is invested at a rate of 3% per year simple interest. work out the interest at the end of 4 years. $ ... [2] (h) cupcakes cost $1.30 each. find the largest number of these cupcakes that can be bought with $10. [2]", "4": "4 0607/33/o/n/19 \u00a9 ucles 2019 2 benji has 15 bags of potatoes. the number of potatoes in each bag is shown below. 38 36 42 36 36 41 40 38 37 39 39 40 37 38 36 (a) complete the frequency table. number of potatoes 36 37 38 39 40 41 42 frequency 4 [2] (b) for the number of potatoes, find (i) the range, [1] (ii) the mode, [1] (iii) the median, [1] (iv) the mean. [1] (c) complete the bar chart. frequency number of potatoes36012345 37 38 39 40 41 42 [2]", "5": "5 0607/33/o/n/19 \u00a9 ucles 2019 [turn over 3 (a) write sixty thousand and twenty in figures. [1] (b) complete the mapping diagram for the function ()xx 34 f=- . x 0 .f (x) 1 . 2 . 3 . [2] (c) write down a prime number between 35 and 45. [1] (d) a 158 75= find the value of a. a= ... [1] (e) write 6789 correct to the nearest 10. [1] (f) write 189.436 correct to 2 decimal places. [1] (g) write 3462 (i) correct to 3 significant figures, [1] (ii) in standard form. [1]", "6": "6 0607/33/o/n/19 \u00a9 ucles 2019 4 01ab 23456y x1 2 3 4 5 6 the diagram shows two points, a and b, plotted on a 1 cm2 grid. (a) write down the co-ordinates of point a and the co-ordinates of point b. a ( ... , ... ) b ( ... , ... ) [2] (b) calculate the length of ab. ... cm [2] (c) find the co-ordinates of the midpoint of ab. ( ... , ... ) [1] (d) find the gradient of ab. [2] (e) write down the equation of the line parallel to ab passing through (0, 3). y= ... [2]", "7": "7 0607/33/o/n/19 \u00a9 ucles 2019 [turn over 5 two cylindrical candles are mathematically similar. the small candle has radius 2 cm and height 5 cm. the large candle has radius 7 cm. not to scale 5 cm2 cm7 cm (a) find the height of the large candle. ... cm [2] (b) the small candle burns for 4 hours and the large candle burns for 60 hours. write the ratio 4 : 60 in its simplest form. . : [1] (c) the price of the large candle is $28. in a sale, this price is reduced by 15%. find the sale price. $ [2]", "8": "8 0607/33/o/n/19 \u00a9 ucles 2019 6 (a) for each diagram, draw all the lines of symmetry. not to scale [3] (b) not to scale simi makes a flower using some mathematical shapes. the centre is a circle with radius 2 cm. each of the five petals is an isosceles triangle with base 2.3 cm and perpendicular height 4 cm. the stem is a rectangle with length 6 cm and width 1 cm. find the total area shaded. . cm2 [4]", "9": "9 0607/33/o/n/19 \u00a9 ucles 2019 [turn over 7 the table shows the age, in months, and length, in centimetres, of seven babies. age (months)0 2 4 5 9 10 12 length (cm)50 58 63 64 71 73 76 (a) complete the scatter diagram to show this information. the first three points have been plotted for you. 04050607080 2 4 6 age (months)length (cm) 8 10 12 [2] (b) find. (i) the mean age, ... months [1] (ii) the mean length. ... cm [1] (c) on the scatter diagram, draw a line of best fit. [2] (d) use your line of best fit to find an estimate for the length of a baby aged 7 months. ... cm [1]", "10": "10 0607/33/o/n/19 \u00a9 ucles 2019 8 (a) 40\u00b0 36 mq p anot to scale 1.8 m the diagram shows a vertical tower, pq, standing on horizontal ground. matthijs stands at point a. he is 1.8 m tall. the base of the tower, p, is 36 m from point a. find the height of the tower. . m [3]", "11": "11 0607/33/o/n/19 \u00a9 ucles 2019 [turn over (b) b 4 cmnot to scale 4 cm co a 38\u00b0 ab and ac are tangents to a circle with centre, o, and radius 4 cm. angle \u00b0 bac 38= . (i) write down the size of angle oba . angle oba= ... [1] (ii) find the size of angle boc . angle boc= ... [1] (c) use trigonometry to find the length of oa. oa= .. cm [3]", "12": "12 0607/33/o/n/19 \u00a9 ucles 2019 9 20 people were asked if they liked banana milk shake, b, or chocolate milk shake, c. b 4 3 9c .u (a) complete the venn diagram. [1] (b) write down ()bcn+. [1] (c) one of these 20 people is chosen at random. find the probability that this person likes (i) banana milk shake, [1] (ii) chocolate milk shake but not banana milk shake. [1] (d) on the venn diagram, shade cb+l. [1]", "13": "13 0607/33/o/n/19 \u00a9 ucles 2019 [turn over 10 y 20 \u2013250 \u20132 5x ()xxxx 52 8 f32=- ++ (a) on the diagram, sketch the graph of () yx f= for x25gg- . [3] (b) write down the co-ordinates of the point where the curve crosses the y-axis. ( ... , ... ) [1] (c) write down the co-ordinates of the three points where the curve crosses the x-axis. ( .. , .. ), ( .. , .. ), ( .. , .. ) [2] (d) find the co-ordinates of the local maximum. ( ... , ... ) [2] (e) find the number of times that the line y9= crosses the curve () yx f= . [1]", "14": "14 0607/33/o/n/19 \u00a9 ucles 2019 11 (a) solve. (i) y36= y= ... [1] (ii) y65 13-= y= ... [2] (iii) y362- [2] (b) expand and simplify. () () yy57 34-- ... [2] (c) pt26=- (i) find the value of p when t8=. p= ... [1] (ii) rearrange the formula to make t the subject. t= [2] (d) simplify. yy 32 5+ . [2]", "15": "15 0607/33/o/n/19 \u00a9 ucles 2019 12 angie goes to school on 5 days each week. on a school day, the probability that angie gets up before 7 am is 109 . on a non-school day, the probability that angie gets up before 7 am is 201 . (a) complete the tree diagram. school day non-school day..5 7gets up before 7 am does not get up before 7 am .. gets up before 7 am does not get up before 7 am .. [3] (b) one day of the week is chosen at random. find the probability that the day is a non-school day and that angie gets up before 7 am. [2]", "16": "16 0607/33/o/n/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_w19_qp_41.pdf": { "1": "this document consists of 18 printed pages and 2 blank pages. dc (sc/fc) 170547/2 \u00a9 ucles 2019 [turn over *2803584907* cambridge international mathematics 0607/41 paper 4 (extended) october/november 2019 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.cambridge assessment international education cambridge international general certificate of secondary education", "2": "2 0607/41/o/n/19 \u00a9 ucles 2019 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area =a c bcb a", "3": "3 0607/41/o/n/19 \u00a9 ucles 2019 [turn over answer all the questions. 1 12 students are each given a spelling test. here is a list of the scores. 9 5 10 9 11 7 7 6 6 7 8 11 find (a) the range, [1] (b) the mode, [1] (c) the median, [1] (d) the upper quartile, [1] (e) the inter-quartile range, [1] (f) the mean. [1]", "4": "4 0607/41/o/n/19 \u00a9 ucles 2019 2 (a) increase 4.5 kg by 16%. kg [2] (b) find the percentage profit when the cost price of a book is $8.50 and the selling price is $11.05 . . % [3] (c) the price of a loaf of bread increases by $0.06 . this is a 5% increase. find the original price of this loaf of bread. $ [2]", "5": "5 0607/41/o/n/19 \u00a9 ucles 2019 [turn over 3 \u20132\u20133 3 0 xy 4 ()(), xxx111 f3! =- (a) on the diagram, sketch the graph of () yx f= for values of x between 3- and 3. [3] (b) write down the range of f( x) for x30gg- . [2] (c) on the same diagram, sketch the graph of yx2= for x22gg- . [1] (d) (i) solve the equation xx11 32 -= . x = ... [1] (ii) the equation xx11 32 -= can be written in the form xx 10uw-+ =. find the value of u and the value of w. u = ... w = ... [2]", "6": "6 0607/41/o/n/19 \u00a9 ucles 2019 4 \u20132\u20131 \u20133012345678910y x1 2 3 4 5 6 7 8 9 10a c t b (a) describe fully the single transformation that maps triangle t onto (i) triangle a, [2] (ii) triangle b, [3] (iii) triangle c. [3] (b) stretch triangle t by a factor of 2 with the y\u2013axis invariant. [2]", "7": "7 0607/41/o/n/19 \u00a9 ucles 2019 [turn over 5 each year the value of a motor bike decreases by 10% of its value at the start of the year. at the start of 2019, the value of the motor bike was $2025. (a) find the value at the end of 4 years. give your answer correct to the nearest dollar. $ [4] (b) find the value at the start of 2017. $ [2] (c) find the number of complete years it takes for the value of $2025 to decrease to a value less than $500. [4]", "8": "8 0607/41/o/n/19 \u00a9 ucles 2019 6 the diagram shows a six-sided die and a coin. the numbers on the faces of the die are 1, 1, 1, 2, 2, 3. when the die is rolled it is equally likely for any of the six faces to be on the top. when the coin is spun it is equally likely to land showing heads or tails. (a) abi rolls the die. write down the probability that it shows the number 3 on the top. [1] (b) beatrice rolls the die and spins the coin. (i) find the probability that the die shows the number 2 on the top and the coin shows heads. [2] (ii) find the probability that the die shows the number 2 on the top or the coin shows heads or both. [2] (c) carl spins the coin 3 times. find the probability that the coin shows heads at least once. [2]", "9": "9 0607/41/o/n/19 \u00a9 ucles 2019 [turn over (d) drew rolls the die 3 times and records the numbers on the top. find the probability that the die shows each of the numbers, 1, 2 and 3, once. [3] (e) eva spins the coin n times. the probability that the coin shows tails each time is 641. find the value of n. n = ... [1] (f) frank rolls the die twice and records the two numbers. the probability of these two numbers occurring is 31. find these two numbers. ... and ... [2]", "10": "10 0607/41/o/n/19 \u00a9 ucles 2019 7 north 18 kma dcb 10 km 21 km12 km150\u00b0north not to scale the diagram shows four villages a, b, c and d and five straight roads connecting them. b is 10 km due east of a. c is 12 km from b on a bearing of 150\u00b0. d is 21 km from c and 18 km from a. (a) calculate the distance ac and show that your answer rounds to 19.08 km, correct to 2 decimal places. [4] (b) using the sine rule, calculate angle acb and show that your answer rounds to 27.0\u00b0, correct to 1 decimal place. [3]", "11": "11 0607/41/o/n/19 \u00a9 ucles 2019 [turn over (c) calculate the bearing of d from c. [4] (d) a straight path, bp, connects b to the closest point, p, on ac. calculate the length of this path. ... km [2] (e) the area within triangle abc is grassland. calculate the area of this grassland. .. km2 [2]", "12": "12 0607/41/o/n/19 \u00a9 ucles 2019 8 (a) 200 people took part in a charity walk. they each recorded how far, d metres, they walked in one hour. the table shows the results. distance ( d metres) d 1000 20001g d 2000 25001g d 2500 30001g d 3000 40001g number of people 40 60 80 20 0050 100cumulative frequency distance (metres)150200 1000 2000 3000 4000d (i) complete the cumulative frequency curve. [3] (ii) use your curve to find the inter-quartile range. . m [2] (iii) use your curve to estimate the number of people who walked further than 3500 m. [2]", "13": "13 0607/41/o/n/19 \u00a9 ucles 2019 [turn over (b) 2000 people took part in a \u201cno food for 6 hours\u201d day. they each recorded the reduction in their mass, m grams, at the end of the day. the histogram shows their results. 005 10 frequency density mass (grams)15 100 200 300 400 50 150 250 350m (i) complete the frequency table. reduction in mass (m grams)m05 0 1g m 50 1001g m 100 2001g m 200 4001g number of people 500 [2] (ii) calculate an estimate of the mean. .. g [2]", "14": "14 0607/41/o/n/19 \u00a9 ucles 2019 9 (a) lionel runs 10.6 km in 94 minutes. calculate his average speed in km/h. km/h [2] (b) monika walks 2 km at a speed of 4 km/h and then 3 km at a speed of 3 km/h. calculate monika\u2019s overall average speed. km/h [3] (c) a train is travelling at v metres per second. find an expression, in terms of v, for the speed of the train in kilometres per hour. give your answer in its simplest form. km/h [2]", "15": "15 0607/41/o/n/19 \u00a9 ucles 2019 [turn over (d) (i) a car travels 50 km at x km/h and then 80 km at ()x10+ km/h. find an expression, in terms of x, for the total time taken, t hours. give your answer as a single fraction, in its simplest form. t = . h [3] (ii) when t2=, show that xx55 250 02-- =. [2] (iii) when t2=, find the value of x. x = ... [3]", "16": "16 0607/41/o/n/19 \u00a9 ucles 2019 10 ()xx 23 f=+ ()xx1g=, x0! ()x 2 hx= () log xxj3= (a) find (i) () ,2 f- [1] (ii) .21geo [1] (b) find (( )).1 gf [2] (c) find x when () . x81h= x = ... [1] (d) find ()81j . [1] (e) find (( ))x ff in its simplest form. [2]", "17": "17 0607/41/o/n/19 \u00a9 ucles 2019 [turn over (f) find () () () xx x 1 ff f # ++ in its simplest form. [3] (g) find ().x j1- ()x j1=- ... [2]", "18": "18 0607/41/o/n/19 \u00a9 ucles 2019 11 \u20134180 0 xy 4 () (\u00b0 ) sin xx 33 f= (a) on the diagram, sketch the graph of () yx f= for . x 0 180 gg [2] (b) write down the amplitude and the period of () .xf amplitude = ... period = ... [2] (c) solve the inequality () . x 15 f1- for . x 0 180 gg [2] (d) () (\u00b0) sin xx 3 g= (i) on the same diagram, sketch the graph of () yx g= for . x 0 180 gg [1] (ii) on the diagram, shade the regions where () (). xxfgh [1] (iii) describe fully the single transformation that maps the graph of () yx g= onto the graph of () . yx f= [3]", "19": "19 0607/41/o/n/19 \u00a9 ucles 2019 blank page", "20": "20 0607/41/o/n/19 \u00a9 ucles 2019 blank page permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge." }, "0607_w19_qp_42.pdf": { "1": "this document consists of 20 printed pages. dc (sc/fc) 170548/2 \u00a9 ucles 2019 [turn over *9839689253* cambridge international mathematics 0607/42 paper 4 (extended) october/november 2019 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.cambridge assessment international education cambridge international general certificate of secondary education", "2": "2 0607/42/o/n/19 \u00a9 ucles 2019 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/42/o/n/19 \u00a9 ucles 2019 [turn over answer all the questions. 1 a \u2013 6 \u20135 \u2013 4 \u20133 \u20132 \u20131 0 1 2 3 4 5 6 \u2013 6\u20135\u2013 4\u20133\u20132\u20131123456y x (a) reflect triangle a in the x-axis. label the image b. [1] (b) translate triangle a by the vector 0 3-eo . label the image c. [1] (c) describe fully the single transformation that maps triangle b onto triangle c. [2] (d) rotate triangle a through 90\u00b0 anti-clockwise, about the origin. label the image d. [2] (e) describe fully the single transformation that maps triangle b onto triangle d. [2]", "4": "4 0607/42/o/n/19 \u00a9 ucles 2019 2 ()xx21f=-, x2! ()xx 2 g=+ ()xxh2= (a) find ().6f [1] (b) solve () . x 2 f=- x = ... [2] (c) find (( )).x hg [1] (d) solve (( )) () . xx 2 hg h=+ x = ... [4] (e) find ().x f1- ()x f1=- ... [3]", "5": "5 0607/42/o/n/19 \u00a9 ucles 2019 [turn over (f) 9y x\u20133 0 3 \u20133 (i) on the diagram, sketch the graph of () yx f= and the graph of () yx h= for values of x between 3- and 3. [3] (ii) write down the equation of the line of symmetry of (). yx h= [1] (iii) solve () (). xxfh2 [2]", "6": "6 0607/42/o/n/19 \u00a9 ucles 2019 3 alana and bill share some money in the ratio 5 : 4. alana\u2019s share is $160. (a) show that bill\u2019s share is $128. [1] (b) alana spends $ x. the ratio of alana\u2019s money : bill\u2019s money is now 4 : 5. find the value of x. x = ... [3] (c) a shop has a sale. bill buys a jacket in the sale for $32. (i) write $32 as a percentage of $128. . % [1] (ii) the original price of the jacket was reduced by 20% to $32. work out the original price. $ [3]", "7": "7 0607/42/o/n/19 \u00a9 ucles 2019 [turn over 4 (a) solve the following equations. (i) x23 11 -=- x = ... [2] (ii) x364=- x = ... [2] (iii) xx61 31 72 += - x = ... [2] (b) solve the simultaneous equations. you must show all your working. xy xy53 19 35 21+= - += - x = ... y = ... [4]", "8": "8 0607/42/o/n/19 \u00a9 ucles 2019 5 ca bd o xnot to scale 20\u00b025\u00b025\u00b0 a, b, c and d lie on a circle, centre o. ax is a tangent to the circle at a and bx is a tangent to the circle at b. angle \u00b0 oab 20= and angle \u00b0. dax 25= (a) find the value of (i) angle aob , angle aob = ... [2] (ii) angle acb , angle acb = ... [1] (iii) angle adb , angle adb = ... [1]", "9": "9 0607/42/o/n/19 \u00a9 ucles 2019 [turn over (iv) angle bad , angle bad = ... [1] (v) angle dba , angle dba = ... [1] (vi) angle axb. angle axb = ... [1] (b) what type of quadrilateral is acbd ? [1]", "10": "10 0607/42/o/n/19 \u00a9 ucles 2019 6 spinner a is numbered 1, 2, 3, 4. spinner b is numbered 1, 2, 3, 4, 5, 6. each spinner is equally likely to land on any of its numbers. the two spinners are each spun once and the number that each spinner lands on is recorded. find the probability that (a) the number on spinner a is greater than 4, [1] (b) the number on spinner b is not a 3, [1] (c) the number on spinner a is the same as the number on spinner b, [2] (d) one number is odd and one number is even, [3] (e) the sum of the numbers is 6. [2]", "11": "11 0607/42/o/n/19 \u00a9 ucles 2019 [turn over 7 (a) (i) factorise xx21 162-- . [2] (ii) using your answer to part (i), solve . xx21 16 021 -- [2] (b) solve the equation . xx35 02-- = give your answers correct to 2 decimal places. you must show all your working. x = or x = [3]", "12": "12 0607/42/o/n/19 \u00a9 ucles 2019 8 there are 100 students in a year group. each student studies at least one of the languages, french ( f), italian ( i) and spanish ( s). x students study all 3 languages. y students study french only. 18 students study italian only. 4 students study french and italian but not spanish. 12 students study french and spanish but not italian. 2 students study italian and spanish but not french. 74 students study only one language. (a) show this information on the venn diagram. f i sxu [2]", "13": "13 0607/42/o/n/19 \u00a9 ucles 2019 [turn over (b) twice as many students study french as italian. find the number of students who study (i) all 3 subjects, x = ... [2] (ii) french only, y = ... [2] (iii) spanish only. [1]", "14": "14 0607/42/o/n/19 \u00a9 ucles 2019 9 26 cm 24 cm 18 cm 14 cmr cm r cmh cmnot to scale the diagram shows three solids, a prism, a sphere and a cone. the radius of the sphere is equal to the base radius of the cone. the volume of each solid is the same. (a) show that the volume of the prism is 7392 cm3. [3]", "15": "15 0607/42/o/n/19 \u00a9 ucles 2019 [turn over (b) a similar prism has a volume of 924 cm3. the length of the original prism is 24 cm. find the length of this similar prism. ... cm [3] (c) find the value of r. r = ... [2] (d) find the value of h. h = ... [2] (e) when exact values of h and r are used, . hr 4= find, in terms of r, an exact expression for the curved surface area of the cone. give your answer in its simplest form. [3]", "16": "16 0607/42/o/n/19 \u00a9 ucles 2019 10 the mass of each of 80 apples is shown in the table. mass ( m grams) frequency m0 1001g 6 m 100 1201g 22 m 120 1401g 31 m 140 1601g 13 m 160 2501g 8 (a) calculate an estimate of the mean mass of an apple. .. g [2] (b) find the interval which contains the upper quartile. m1g [1] (c) two of these apples are chosen at random. find the probability that they both have a mass of 120 g or less. give your answer as a fraction in its simplest form. [3]", "17": "17 0607/42/o/n/19 \u00a9 ucles 2019 [turn over (d) (i) complete the frequency density column in this table. mass ( m grams) frequency frequency density m0 1001g 6 m 100 1201g 22 m 120 1401g 31 m 140 1601g 13 m 160 2501g 8 [2] (ii) on the grid, draw a histogram to show this information. 0 50 100 150 20000.20.40.60.81.01.21.41.61.82.0 250 mass (grams)mfrequency density [3]", "18": "18 0607/42/o/n/19 \u00a9 ucles 2019 11 b a dc8 cm 64 \u00b0 9 cm6.5 cmnot to scale the diagram shows a quadrilateral abcd . ab = 8 cm, ad = 9 cm, cd = 6.5 cm and angle bad = 64\u00b0. (a) calculate bd and show that your answer rounds to 9.05 cm, correct to 2 decimal places. [2] (b) the area of the quadrilateral abcd is 57.3 cm2. (i) calculate angle bdc and show that your answer rounds to 58\u00b0, correct to the nearest degree. [4]", "19": "19 0607/42/o/n/19 \u00a9 ucles 2019 [turn over (ii) calculate angle bcd . angle bcd = ... [5] question 12 is printed on the next page.", "20": "20 0607/42/o/n/19 \u00a9 ucles 2019 12 \u20133 \u201344y x3 0 (a) on the diagram, sketch the graph of (), yx f= where ()() ()xxx x111f=-+ for values of x between 3- and 3. [4] (b) write down the equations of the asymptotes. , , , [3] (c) write down the co-ordinates of the local maximum. ( , ) [2] (d) the line yx21=+ intersects the curve () yx f= twice. find the value of the x co-ordinate of each point of intersection. x = . or x = . [2] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge." }, "0607_w19_qp_43.pdf": { "1": "this document consists of 20 printed pages. dc (sc/fc) 170549/3 \u00a9 ucles 2019 [turn over *5937878046* cambridge international mathematics 0607/43 paper 4 (extended) october/november 2019 2 hours 15 minutes candidates answer on the question paper. additional materials: geometrical instruments graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. answers in degrees should be given to one decimal place. for r, use your calculator value. you must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. the number of marks is given in brackets [ ] at the end of each question or part question. the total number of marks for this paper is 120.cambridge assessment international education cambridge international general certificate of secondary education", "2": "2 0607/43/o/n/19 \u00a9 ucles 2019 formula list for the equation ax bxc02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. rar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/43/o/n/19 \u00a9 ucles 2019 [turn over answer all the questions. 1 (a) aisha invests $12 000 at a compound interest rate of 3.5% per year. calculate the value of her investment at the end of 4 years. $ [3] (b) 2 years ago, byron invested $ p at a compound interest rate of 3% per year. the value of his investment is now $10 078.55 . calculate the value of p. p = ... [3] (c) 5 years ago cheng invested $ q at a simple interest rate of 4% per year. the value of his investment is now $20 400. calculate the value of q. q = ... [3]", "4": "4 0607/43/o/n/19 \u00a9 ucles 2019 2 the table shows the number of goals scored in 100 matches. number of goals0 1 2 3 4 5 6 7 frequency 17 23 20 18 11 6 4 1 find (a) the mode, [1] (b) the range, [1] (c) the median, [1] (d) the inter-quartile range, [2] (e) the mean. [2]", "5": "5 0607/43/o/n/19 \u00a9 ucles 2019 [turn over 3 15 \u20131.5 \u2013150y 3x ()xx x 253 f32=- + for .x 15 3 gg- (a) on the diagram, sketch the graph of (). yxf= [2] (b) find the zeros of f( x). ... [3] (c) find the co-ordinates of the local maximum. (. , .) [1] (d) find the co-ordinates of the local minimum. (. , .) [2] (e) the equation xx k 25332-+ = has three solutions. find the range of values of k. [2]", "6": "6 0607/43/o/n/19 \u00a9 ucles 2019 4 the table shows the mathematics mark and the physics mark for each of 10 students in an examination. mathematics mark ( m)14 28 38 41 60 66 76 82 90 98 physics mark ( p)8 28 66 43 67 56 51 74 85 88 (a) complete the scatter diagram. the first five points have been plotted for you. 00102030405060708090100 10 20 30 40 50 mathematics markphysics mark 60 70 80 90 100mp [2] (b) write down the type of correlation shown by the scatter diagram. [1] (c) find the equation of the regression line. write the answer in the form pa mb=+ . p = ... [2]", "7": "7 0607/43/o/n/19 \u00a9 ucles 2019 [turn over (d) a student was absent for the physics examination but gained 56 marks in the mathematics examination. use your answer to part (c) to estimate a physics mark for this student. [1] (e) the school decided that the physics examination was too difficult and added 5 marks to each of the physics marks. write down the new equation of the regression line. [1]", "8": "8 0607/43/o/n/19 \u00a9 ucles 2019 5 \u20137 \u20137\u2013 6\u20135\u2013 4\u20133\u20132\u201311234567 \u2013 6\u2013 5\u2013 4\u20133 \u20132 \u201310 1 2 3 4 5 6 7xy c ba (a) reflect triangle a in the line . y1= [2] (b) rotate triangle b through 90\u00b0 clockwise about (1, 0). [3] (c) describe fully the single transformation that maps triangle a onto triangle b. [3] (d) describe fully the single transformation that maps triangle b onto triangle c. [3]", "9": "9 0607/43/o/n/19 \u00a9 ucles 2019 [turn over 6 (a) p is the point (3, 5) and q is the point (, ). 72- q is the midpoint of pr. find the co-ordinates of the point r. (. , .) [2] (b) a o bcnot to scale a b a oa= and .b ob= c divides ab in the ratio 4 : 3. find these vectors, in terms of a and b, in their simplest form. (i) ab ab= ... [1] (ii) oc oc= ... [3]", "10": "10 0607/43/o/n/19 \u00a9 ucles 2019 7 not to scale 4 cm6 cm the diagram shows a child\u2019s toy made of a cone joined to a hemisphere. the cone and the hemisphere each have a radius of 4 cm. the perpendicular height of the cone is 6 cm. (a) (i) find the volume of the hemisphere. .. cm3 [2] (ii) find the volume of the cone. .. cm3 [2] (iii) each cubic centimetre of the hemisphere has a mass of 7.85 g. each cubic centimetre of the cone has a mass of 0.65 g. find the total mass of the toy. .. g [2]", "11": "11 0607/43/o/n/19 \u00a9 ucles 2019 [turn over (b) find the total surface area of the toy. .. cm2 [5] (c) the height of the cone on a similar toy is 9 cm. find the total surface area of this toy. .. cm2 [2]", "12": "12 0607/43/o/n/19 \u00a9 ucles 2019 8 a dance club has 90 members. here is some information about types of dancing members like. 50 like ballroom ( b) 37 like latin ( l) 47 like modern ( m) 18 like ballroom and latin 15 like ballroom and modern 22 like latin and modern 8 like ballroom, latin and modern (a) complete the venn diagram. b l m10 8u [2] (b) write down the number of members who do not like any of these three types of dancing. [1] (c) two of the 90 members are chosen at random. find the probability that they both like ballroom and latin but not modern. [2]", "13": "13 0607/43/o/n/19 \u00a9 ucles 2019 [turn over (d) two of the members who like ballroom are chosen. find the probability that one of these members likes latin but not modern and the other likes modern but not latin. [3]", "14": "14 0607/43/o/n/19 \u00a9 ucles 2019 9 a 58\u00b0 14 cm 12 cmnot to scale b n co a, b and c are points on the circle, centre o. on is perpendicular to bc. ab = 14 cm, ac = 12 cm and angle bac = 58\u00b0. (a) show that bc = 12.73 cm, correct to 2 decimal places. [3] (b) explain why angle bon = 58\u00b0. [1] (c) calculate ob, the radius of the circle. ob = .. cm [3]", "15": "15 0607/43/o/n/19 \u00a9 ucles 2019 [turn over (d) calculate the area of the shaded segment. .. cm2 [3]", "16": "16 0607/43/o/n/19 \u00a9 ucles 2019 10 all lengths in this question are in metres and all areas are in square metres. not to scale2x + 3 the length of this rectangle is ()x23+ and the area is 840. (a) write down an expression, in terms of x, for the width of the rectangle. [1] (b) the perimeter of the rectangle is 118. show that . xx25 3 336 02-+ = [3] (c) solve the equation . xx25 3 336 02-+ = show all your working. x = or [3]", "17": "17 0607/43/o/n/19 \u00a9 ucles 2019 [turn over (d) find the length and the width of the rectangle. length = m width = m [2]", "18": "18 0607/43/o/n/19 \u00a9 ucles 2019 11 (a) simplify. (i) aaa 354# [2] (ii) ()log5x 5 [1] (iii) ()log3x 9 [1] (b) solve. logl og logx 31 02 5 -= x = ... [2]", "19": "19 0607/43/o/n/19 \u00a9 ucles 2019 [turn over 12 8 \u20138 \u201380y 8x ()() ()xxxx 2332f=+-+ (a) on the diagram, sketch the graph of ()yxf= for values of x between 8- and 8. [3] (b) write down the equations of the asymptotes. , , [3] (c) ()xx 2 g=- (i) on the diagram, sketch the graph of () yxg= for . x68gg- [1] (ii) solve () (). xxfg= x = or x = or x = [3] (iii) solve () (). xxfg2 [3] question 13 is printed on the next page.", "20": "20 0607/43/o/n/19 \u00a9 ucles 2019 13 ()xx 25 f=+ ()xx 12 g=- (a) find ()4g-. [1] (b) find ()7 f1--. [2] (c) find (())3gf . [2] (d) find and simplify (())xfg . [2] (e) find and simplify ()xg1-. ()xg1=- ... [2] (f) write as a single fraction, simplifying your answer. ()x23 f+ [2] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge." }, "0607_w19_qp_51.pdf": { "1": "this document consists of 7 printed pages and 1 blank page. dc (lk) 170791/3 \u00a9 ucles 2019 [turn over *0326659552* cambridge international mathematics 0607/51 paper 5 (core) october/november 2019 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and to communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.cambridge assessment international education cambridge international general certificate of secondary education", "2": "2 0607/51/o/n/19 \u00a9 ucles 2019 answer all the questions. investigation decimal forms this investigation looks at the patterns when changing a fraction to its decimal form. examples ..320666 06 f == o this is a repeating decimal. .43075= this is a terminating decimal. the fraction 85 has a numerator of 5 and a denominator of 8. 1 this question is about terminating decimals. (a) (i) complete these equivalent fractions. 21 105= 51 102= 207 100= 251 100= 5003 1000= (ii) the denominators of the equivalent fractions in part (i) are 10, 100 and 1000. the smallest prime number is 2. put a prime number in each box to complete these statements. 10= =2#5 100=10#10 =2#5# # 1000 =10#10#10=2#5# # # # (iii) complete the table. fraction21 51 207 251 5003 decimal 0.5 0.2 (iv) write down a different fraction with a numerator of 1 and a denominator between 30 and 99 which can be written as a terminating decimal. ", "3": "3 0607/51/o/n/19 \u00a9 ucles 2019 [turn over (b) (i) put a prime number in each box to complete these statements. 20 = 2 # 2 # 5 25 = 5 # 5 50 = 2 # # 5 100 = # # 5 # 5 500 = 2 # 2 # # # (ii) use your answers to part (i) to help you complete the table. fraction decimalnumber of decimal placesdenominator written as a product of primes using powerslarger power 2010.05 2 252# 2 2570.28 2 52 2 0590.18 2 019 100.19 2 200130.065 3 2532# 3 01 5010.022 17 50000.0034 2534# 4 (iii) a fraction has a numerator of 1 and a denominator of 2514 7#. write down the number of decimal places in the decimal form of this fraction. (iv) the denominator of a fraction that can be written as a terminating decimal only has one or two possible prime factors. write down these prime factors. ... and ...", "4": "4 0607/51/o/n/19 \u00a9 ucles 2019 2 this question is about repeating decimals. the number of digits in the repeating pattern is called the repeat length . example ..1310076923 076923 076923 0076923 f == oo acbbbb this is a repeating decimal with a repeat length of 6. (a) (i) complete these equivalent fractions. 31 9= 111 99= 371 999= 1111 999= 411 99999= 71 999999= (ii) complete the table. fraction1 3 111 371 1 111 411 71 decimal .03o .009oo .0027oo .0142857o o repeat length1 2 3 5 6 (iii) use your answers to part (i) and part (ii) to help you complete the table. fraction decimal repeat length denominator of equivalent fraction 1 3.03o 1 9 =10 11- 111.009oo 2 99 =10 12- 371.0027oo 999 = 1 1113 999 = 4115 99 999 = 71.142 857 0o o 6 999 999 = (iv) give an example of a fraction with a numerator of 1 which can be written as a repeating decimal with a repeat length of 9. ", "5": "5 0607/51/o/n/19 \u00a9 ucles 2019 [turn over (v) a repeating decimal has a repeat length of k. write down an expression, in terms of k, for the denominator of this fraction. (b) (i) 4071 11371 111 371 ## == 4071 is changed to its decimal form. show that this has a repeat length that is equal to the lowest common multiple (lcm) of the repeat lengths of the decimal forms of 111 and 371. (ii) show how the lowest common multiple (lcm) of the repeat lengths of 71 and 371 gives the repeat length of 2591.", "6": "6 0607/51/o/n/19 \u00a9 ucles 2019 3 some decimals have non-repeating decimal parts followed by repeating decimal parts. example ..0650 65555 f =o in this decimal, the 6 does not repeat but the 5 does. (a) show that adding the decimal forms of 51 and 1 3 gives a decimal of this type. (b) complete the table. fraction decimalnumber of non- repeating decimal placesrepeat lengthdenominator written as a product of primes using powers 61.016o 1 1 23# 121.0083o 2 1 757 24113 600317.05283o 25 332## 13201.0000 75oo 3 2 253# 113 ## 10175050001.0491410319oo 3 6 25 11373## #", "7": "7 0607/51/o/n/19 \u00a9 ucles 2019 (c) a fraction of the form cd 251 ab## # where a and b are positive integers and c and d are different primes is changed to its decimal form. using your answers to question 1(b) and question 2(b) , explain how to find the number of non-repeating decimal places and the repeat length. ... ... ... ...", "8": "8 0607/51/o/n/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_w19_qp_52.pdf": { "1": "this document consists of 7 printed pages and 1 blank page. dc (pq) 188054 \u00a9 ucles 2019 [turn over *8610850208* cambridge international mathematics 0607/52 paper 5 (core) october/november 2019 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and to communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.cambridge assessment international education cambridge international general certificate of secondary education", "2": "2 0607/52/o/n/19 \u00a9 ucles 2019 answer all the questions. investigation decimal forms this investigation looks at the patterns when changing a fraction to its decimal form. examples ..320666 06 f == o this is a repeating decimal. .43075= this is a terminating decimal. the fraction 85 has a numerator of 5 and a denominator of 8. 1 this question is about terminating decimals. (a) (i) complete these equivalent fractions. 21 105= 51 102= 207 100= 251 100= 5003 1000= (ii) the denominators of the equivalent fractions in part (i) are 10, 100 and 1000. the smallest prime number is 2. put a prime number in each box to complete these statements. 10= =2#5 100=10#10 =2#5# # 1000 =10#10#10=2#5# # # # (iii) complete the table. fraction21 51 207 251 5003 decimal 0.5 0.2 (iv) write down a different fraction with a numerator of 1 and a denominator between 30 and 99 which can be written as a terminating decimal. ", "3": "3 0607/52/o/n/19 \u00a9 ucles 2019 [turn over (b) (i) put a prime number in each box to complete these statements. 20 = 2 # 2 # 5 25 = 5 # 5 50 = 2 # # 5 100 = # # 5 # 5 500 = 2 # 2 # # # (ii) use your answers to part (i) to help you complete the table. fraction decimalnumber of decimal placesdenominator written as a product of primes using powerslarger power 2010.05 2 252# 2 2570.28 2 52 2 0590.18 2 019 100.19 2 200130.065 3 2532# 3 01 5010.022 17 50000.0034 2534# 4 (iii) a fraction has a numerator of 1 and a denominator of 2514 7#. write down the number of decimal places in the decimal form of this fraction. (iv) the denominator of a fraction that can be written as a terminating decimal only has one or two possible prime factors. write down these prime factors. ... and ...", "4": "4 0607/52/o/n/19 \u00a9 ucles 2019 2 this question is about repeating decimals. the number of digits in the repeating pattern is called the repeat length . example ..1310076923 076923 076923 0076923 f == oo acbbbb this is a repeating decimal with a repeat length of 6. (a) (i) complete these equivalent fractions. 31 9= 111 99= 371 999= 1111 999= 411 99999= 71 999999= (ii) complete the table. fraction1 3 111 371 1 111 411 71 decimal .03o .009oo .0027oo .0142857o o repeat length1 2 3 5 6 (iii) use your answers to part (i) and part (ii) to help you complete the table. fraction decimal repeat length denominator of equivalent fraction 1 3.03o 1 9 =10 11- 111.009oo 2 99 =10 12- 371.0027oo 999 = 1 1113 999 = 4115 99 999 = 71.142 857 0o o 6 999 999 = (iv) give an example of a fraction with a numerator of 1 which can be written as a repeating decimal with a repeat length of 9. ", "5": "5 0607/52/o/n/19 \u00a9 ucles 2019 [turn over (v) a repeating decimal has a repeat length of k. write down an expression, in terms of k, for the denominator of this fraction. (b) (i) 4071 11371 111 371 ## == 4071 is changed to its decimal form. show that this has a repeat length that is equal to the lowest common multiple (lcm) of the repeat lengths of the decimal forms of 111 and 371. (ii) show how the lowest common multiple (lcm) of the repeat lengths of 71 and 371 gives the repeat length of 2591.", "6": "6 0607/52/o/n/19 \u00a9 ucles 2019 3 some decimals have non-repeating decimal parts followed by repeating decimal parts. example ..0650 65555 f =o in this decimal, the 6 does not repeat but the 5 does. (a) show that adding the decimal forms of 51 and 1 3 gives a decimal of this type. (b) complete the table. fraction decimalnumber of non- repeating decimal placesrepeat lengthdenominator written as a product of primes using powers 61.016o 1 1 23# 121.0083o 2 1 757 24113 600317.05283o 25 332## 13201.0000 75oo 3 2 253# 113 ## 10175050001.0491410319oo 3 6 25 11373## #", "7": "7 0607/52/o/n/19 \u00a9 ucles 2019 (c) a fraction of the form cd 251 ab## # where a and b are positive integers and c and d are different primes is changed to its decimal form. using your answers to question 1(b) and question 2(b) , explain how to find the number of non-repeating decimal places and the repeat length. ... ... ... ...", "8": "8 0607/52/o/n/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_w19_qp_53.pdf": { "1": "this document consists of 7 printed pages and 1 blank page. dc (pq) 188053 \u00a9 ucles 2019 [turn over *1478426571* cambridge international mathematics 0607/53 paper 5 (core) october/november 2019 1 hour candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer all the questions. you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and to communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 24.cambridge assessment international education cambridge international general certificate of secondary education", "2": "2 0607/53/o/n/19 \u00a9 ucles 2019 answer all the questions. investigation decimal forms this investigation looks at the patterns when changing a fraction to its decimal form. examples ..320666 06 f == o this is a repeating decimal. .43075= this is a terminating decimal. the fraction 85 has a numerator of 5 and a denominator of 8. 1 this question is about terminating decimals. (a) (i) complete these equivalent fractions. 21 105= 51 102= 207 100= 251 100= 5003 1000= (ii) the denominators of the equivalent fractions in part (i) are 10, 100 and 1000. the smallest prime number is 2. put a prime number in each box to complete these statements. 10= =2#5 100=10#10 =2#5# # 1000 =10#10#10=2#5# # # # (iii) complete the table. fraction21 51 207 251 5003 decimal 0.5 0.2 (iv) write down a different fraction with a numerator of 1 and a denominator between 30 and 99 which can be written as a terminating decimal. ", "3": "3 0607/53/o/n/19 \u00a9 ucles 2019 [turn over (b) (i) put a prime number in each box to complete these statements. 20 = 2 # 2 # 5 25 = 5 # 5 50 = 2 # # 5 100 = # # 5 # 5 500 = 2 # 2 # # # (ii) use your answers to part (i) to help you complete the table. fraction decimalnumber of decimal placesdenominator written as a product of primes using powerslarger power 2010.05 2 252# 2 2570.28 2 52 2 0590.18 2 019 100.19 2 200130.065 3 2532# 3 01 5010.022 17 50000.0034 2534# 4 (iii) a fraction has a numerator of 1 and a denominator of 2514 7#. write down the number of decimal places in the decimal form of this fraction. (iv) the denominator of a fraction that can be written as a terminating decimal only has one or two possible prime factors. write down these prime factors. ... and ...", "4": "4 0607/53/o/n/19 \u00a9 ucles 2019 2 this question is about repeating decimals. the number of digits in the repeating pattern is called the repeat length . example ..1310076923 076923 076923 0076923 f == oo acbbbb this is a repeating decimal with a repeat length of 6. (a) (i) complete these equivalent fractions. 31 9= 111 99= 371 999= 1111 999= 411 99999= 71 999999= (ii) complete the table. fraction1 3 111 371 1 111 411 71 decimal .03o .009oo .0027oo .0142857o o repeat length1 2 3 5 6 (iii) use your answers to part (i) and part (ii) to help you complete the table. fraction decimal repeat length denominator of equivalent fraction 1 3.03o 1 9 =10 11- 111.009oo 2 99 =10 12- 371.0027oo 999 = 1 1113 999 = 4115 99 999 = 71.142 857 0o o 6 999 999 = (iv) give an example of a fraction with a numerator of 1 which can be written as a repeating decimal with a repeat length of 9. ", "5": "5 0607/53/o/n/19 \u00a9 ucles 2019 [turn over (v) a repeating decimal has a repeat length of k. write down an expression, in terms of k, for the denominator of this fraction. (b) (i) 4071 11371 111 371 ## == 4071 is changed to its decimal form. show that this has a repeat length that is equal to the lowest common multiple (lcm) of the repeat lengths of the decimal forms of 111 and 371. (ii) show how the lowest common multiple (lcm) of the repeat lengths of 71 and 371 gives the repeat length of 2591.", "6": "6 0607/53/o/n/19 \u00a9 ucles 2019 3 some decimals have non-repeating decimal parts followed by repeating decimal parts. example ..0650 65555 f =o in this decimal, the 6 does not repeat but the 5 does. (a) show that adding the decimal forms of 51 and 1 3 gives a decimal of this type. (b) complete the table. fraction decimalnumber of non- repeating decimal placesrepeat lengthdenominator written as a product of primes using powers 61.016o 1 1 23# 121.0083o 2 1 757 24113 600317.05283o 25 332## 13201.0000 75oo 3 2 253# 113 ## 10175050001.0491410319oo 3 6 25 11373## #", "7": "7 0607/53/o/n/19 \u00a9 ucles 2019 (c) a fraction of the form cd 251 ab## # where a and b are positive integers and c and d are different primes is changed to its decimal form. using your answers to question 1(b) and question 2(b) , explain how to find the number of non-repeating decimal places and the repeat length. ... ... ... ...", "8": "8 0607/53/o/n/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_w19_qp_61.pdf": { "1": "this document consists of 12 printed pages. dc (sc/cgw) 170792/1 \u00a9 ucles 2019 [turn over *1952650704* cambridge international mathematics 0607/61 paper 6 (extended) october/november 2019 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a (questions 1 to 3) and b (questions 4 to 5). you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.cambridge assessment international education cambridge international general certificate of secondary education", "2": "2 0607/61/o/n/19 \u00a9 ucles 2019 answer both parts a and b. a investigation (questions 1 to 3) decimal forms (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation looks at the patterns when changing a fraction to its decimal form. examples ..320666 06 f == o this is a repeating decimal. .43075= this is a terminating decimal. the fraction 85 has a numerator of 5 and a denominator of 8. 1 this question is about terminating decimals. (a) (i) complete the table. fraction21 51 207 251 5003 equivalent fraction 10 10 100 100 1000 decimal 0.5 0.2 (ii) what is always true about the denominators of equivalent fractions when the decimal form is a terminating decimal? ... ... (b) (i) write each number as a product of its prime factors. the first two have been completed for you. 20 = 2 # 2 # 5 25 = 5 # 5 50 = 100 = 500 =", "3": "3 0607/61/o/n/19 \u00a9 ucles 2019 [turn over (ii) use your answers to part (i) to help you complete the table. fraction decimalnumber of decimal placesdenominator written as a product of primes using powerslarger power 2010.05 2 252# 2 2570.28 2 52 2 5090.18 2 100190.19 2 200130.065 3 2532# 3 500110.022 5000170.0034 2534# 4 (iii) a fraction with denominator 25pq#, where q is greater than p, is changed to its decimal form. write down the number of decimal places in the decimal form of this fraction. ", "4": "4 0607/61/o/n/19 \u00a9 ucles 2019 2 this question is about repeating decimals. the number of digits in the repeating pattern is called the repeat length . example ..1310076923 076923 076923 0076923 f == oo acbbbb this is a repeating decimal with a repeat length of 6. (a) (i) complete the table. fraction31 111 371 1111 411 71 equivalent fraction 93 999 999 99999 999999 denominator of equivalent fraction10 11- 10 12- 10 13- decimal .03o .009oo .0027oo .0142857o o repeat length 1 2 5 6 (ii) a repeating decimal has a repeat length of k. write down an expression, in terms of k, for the denominator of this fraction. ", "5": "5 0607/61/o/n/19 \u00a9 ucles 2019 [turn over (b) (i) 4071 11371 111 371 ## == 4071 is changed to its decimal form. show that this has a repeat length that is equal to the lowest common multiple (lcm) of the repeat lengths of the decimal forms of 111 and 371. (ii) show how the lowest common multiple (lcm) of the repeat lengths of 71 and 371 gives the repeat length of 2591. (iii) m and n are different prime numbers. the decimal form of m1 has a repeat length of 6. the decimal form of n1 has a repeat length of 9. find the repeat length of the decimal form of mn1 #. ", "6": "6 0607/61/o/n/19 \u00a9 ucles 2019 3 some decimals have non-repeating decimal parts followed by repeating decimal parts. example ..0650 65555 f =o in this decimal, the 6 does not repeat but the 5 does. (a) show that adding the decimal forms of 51 and 31 gives a decimal of this type. (b) complete the table. fraction decimalnumber of non- repeating decimal placesrepeat lengthdenominator written as a product of primes using powers 61.016o 1 1 2 # 3 121.0083o 2 1 757 24113 600317.05283o 23 # 52 # 3 13201.0000 75oo 3 2 23 # 5 # 11 # 3 10175050001.0491410319oo 3 6 2 # 53 # 11 # 37", "7": "7 0607/61/o/n/19 \u00a9 ucles 2019 [turn over (c) a fraction is of the form cd 251 ab## #. in the fraction a and b are positive integers and c and d are different prime numbers less than 90. the decimal form of this fraction has 5 non-repeating decimal places and a repeat length of 30. using question 1(b) and question 2(a)(i) , find a possible value for each of a, b, c and d. a = b = c = d = (d) m and n are different prime numbers. the decimal form of the fraction m1 has a repeat length of q. the decimal form of the fraction n1 has a repeat length of 3 q. the decimal form of the fraction w1 has \u2022 k non-repeating decimal places and \u2022 a repeat length of 3 q. find a possible expression for w, in terms of k, m and n. ", "8": "8 0607/61/o/n/19 \u00a9 ucles 2019 b modelling (questions 4 to 5) flowering times (20 marks) you are advised to spend no more than 45 minutes on this part. this task is about when plants flower. the number of hours of darkness affects when plants flower. in this investigation, the number of hours of darkness + the number of hours of daylight = 24. 4 (a) the graph shows the approximate number of hours of daylight in normandy, france for 2017. on the x-axis, 0 is 1st january 2017, 12 is 1st january 2018 and 24 is 1st january 2019. 1 1 3 5 7 9 11 13 15 17 19 21 23 4 2 0 6 8 10 12 14 16 18 20 f a j a o d f a j a o m m j j s n j m monthm j s n jd22 2403 25 47 6810 912 11number of hours14 131517y x16 (i) the pattern for the number of hours of daylight remains the same each year. complete the graph to show the approximate number of hours of daylight for 2018. (ii) on the same grid, draw the graph to show the number of hours of darkness for the two years. (iii) describe fully the single transformation that maps the graph of the number of hours of daylight onto the graph of the number of hours of darkness. ... (b) pierre grows oats in normandy, france. oat plants flower when there are less than 12 hours of darkness. find the earliest month when an oat plant flowers. ", "9": "9 0607/61/o/n/19 \u00a9 ucles 2019 [turn over (c) pierre models the number of hours of daylight , p, using \u00b0 .sin px 12 39 30 23120=+ - feo p where x has the following value at the start of each month. month jan feb mar apr may jun jul aug sep oct nov dec x 0 1 2 3 4 5 6 7 8 9 10 11 (i) using pierre\u2019s model, find the maximum number of hours of daylight and the month in which it occurs. maximum hours of daylight ... month ... (ii) pierre thinks that his oat plants flower at their best when the number of hours of darkness is at its minimum. find the minimum number of hours of darkness . (iii) using pierre\u2019s model, write down a model for the number of hours of darkness , q. .. (d) on 20th march, the number of hours of darkness is the same as the number of hours of daylight. there are 31 days in march. show that pierre\u2019s model finds this date accurately.", "10": "10 0607/61/o/n/19 \u00a9 ucles 2019 5 alexa grows soybeans in queensland, australia. in australia, there are more hours of darkness in june than there are in january. alexa records the number of hours of darkness for 360 days, from 1st january to 26th december. she finds this information. hours of darknessmaximum 13.8 minimum 10.2 alexa models the number of hours of darkness, y, by drawing the graph of \u00b0 cos ya bt=- where t is the day of the year. (a) (i) write suitable calculations to show that a12= and . b 18= . (ii) on the axes, sketch the graph of the model .\u00b0cos yt 12 18 =- for t0 360gg . 0360y t", "11": "11 0607/61/o/n/19 \u00a9 ucles 2019 [turn over (b) soybeans flower when there are more than 12 hours of darkness. the flowers grow at the fastest rate when there are 13.6 or more hours of darkness. (i) find the number of days when the flowers are growing at their fastest rate. (ii) the table shows the value of t on the first day of each month. month jan feb mar apr may jun jul aug sep oct nov dec t 1 32 60 91 121 152 182 213 244 274 305 335 on average, alexa\u2019s soybeans flower 53 days after she plants them. she wants to plant them so that, when they begin to flower, the flowers grow at the fastest rate. use alexa\u2019s model to show that the latest date she should plant her soybeans is 3rd june. question 5(c) is printed on the next page.", "12": "12 0607/61/o/n/19 \u00a9 ucles 2019 (c) (i) alexa uses her model, .\u00b0cos yt 12 18 =- , to find the first date when the number of hours of darkness is the same as the number of hours of daylight. find this date. (ii) the actual date when the number of hours of darkness was the same as the number of hours of daylight was 20th march. alexa decides to change her model so that it finds this date accurately. she does this by a translation of the graph of her model. find the new model. permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge." }, "0607_w19_qp_62.pdf": { "1": "*0258908058* this document consists of 15 printed pages and 1 blank page. dc (nh/sw) 170793/2 \u00a9 ucles 2019 [turn overcambridge international mathematics 0607/62 paper 6 (extended) october/november 2019 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a (questions 1 to 6) and b (questions 7 to 11). you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and to communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.cambridge assessment international education cambridge international general certificate of secondary education", "2": "2 0607/62/o/n/19 \u00a9 ucles 2019 answer both parts a and b. a investigation (questions 1 to 6) crossing points (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation is about how many times lines cross when you join two rows of dots. dots are arranged along two parallel lines, a and b. straight lines join each dot on a to each dot on b. a crossing point is where exactly two straight lines cross. example when there are 2 dots on a and 4 dots on b there are 6 crossing points. a 2 dots b 4 dots you must complete all diagrams accurately using a ruler and a sharp pencil. 1 when there is 1 dot on a and 1 dot on b, there is no crossing point. a b (a) each of these diagrams has 1 dot on a. complete the diagrams by joining the dot on a to each dot on b. a ba b (b) the number of dots on b is b. the number of crossing points is p. complete this statement. when there is 1 dot on a and b dots on b, then the value of p is .. .", "3": "3 0607/62/o/n/19 \u00a9 ucles 2019 [turn over 2 there are now 2 dots on a. (a) complete the diagrams for 1 dot on b and 3 dots on b, and use your results to complete the table. a ba ba b a b a b number of dots on b (b)number of crossing points (p) 1 2 1 3 4 6 5 10 (b) find a formula for p in terms of b when there are 2 dots on a. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "4": "4 0607/62/o/n/19 \u00a9 ucles 2019 3 there are now 3 dots on a. (a) complete each diagram and use your results to complete the table. the first diagram has been completed for you. a ba b a b a b number of dots on b (b)number of crossing points (p) 1 2 3 9 4 5 30 (b) find a formula for p in terms of b when there are 3 dots on a. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "5": "5 0607/62/o/n/19 \u00a9 ucles 2019 [turn over 4 there are now 4 dots on a. this table shows the number of crossing points. number of dots on b (b)number of crossing points (p) 1 0 2 6 3 18 4 36 5 60 find a formula for p in terms of b when there are 4 dots on a. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "6": "6 0607/62/o/n/19 \u00a9 ucles 2019 5 use your answers to question 2(b) , question 3(b) and question 4 to help you complete the table when there are b dots on b. number of dots on anumber of crossing points ( p)factorised form for number of crossing points ( p) 1 0 0 2 bb222-()bb 2- 3 bb222-()bb 2- 4 bb222-()bb 2- 5 bb210 210 2-()bb 210 1- a bb222-() () aa bb 22#--", "7": "7 0607/62/o/n/19 \u00a9 ucles 2019 [turn over 6 (a) there are now a dots on a. when the number of dots on b is the same as the number of dots on a, show that your factorised form from question 5 becomes ()aa 4122-. (b) (i) show that the expression in part (a) does not give the correct number of crossing points for the dots in this diagram. a b (ii) give a reason why this happens. ... ...", "8": "8 0607/62/o/n/19 \u00a9 ucles 2019 (c) equal numbers of dots are marked on a and b so that the expression in part (a) will give the correct number of crossing points. (i) explain why there cannot be 50 crossing points. ... ... (ii) there are 29 241 crossing points. find the number of dots on a. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "9": "9 0607/62/o/n/19 \u00a9 ucles 2019 [turn over the modelling task starts on the next page.", "10": "10 0607/62/o/n/19 \u00a9 ucles 2019 b modelling (questions 7 to 11) v alue of a car (20 marks) you are advised to spend no more than 45 minutes on this part. this task is about how the value of a car changes with time. the value of any car changes continuously. 7 anna says that this is a model for the value of a car as it gets older. at the end of each year, the value of the car will be half of its value at the start of the year. eddie pays $16 000 for a new car. (a) use anna\u2019s model to complete the table. age of car ( x years) 0 1 2 3 4 5 6 value ( v dollars) 16 000 8000", "11": "11 0607/62/o/n/19 \u00a9 ucles 2019 [turn over (b) use these values to draw a graph of v against x. 00200040006000800010 00012 00014 00016 000 1 2 3 age of car (years)value of car (dollars) 4 5 6v x (c) complete this model for v in terms of x. v = 16 000 \u00d7 \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (d) using anna\u2019s model, find the value of eddie\u2019s car when it is 10 years old. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "12": "12 0607/62/o/n/19 \u00a9 ucles 2019 8 john\u2019 s cars model the value of a car in this way. each year, the value of the car decreases by a percentage of its value when it was new. the table shows the value of the car as a percentage of its value when it is new. age of car ( x years) 0 1 2 3 4 5 6 percentage of value when new ( p)100 72 58 48 44 42 40 (a) on the grid, plot the values of p against x. 00102030405060708090100 1 2 3 age of car (years)percentage 4 5 6p x (b) show which of the two models gives a higher value for eddie\u2019s car when it is 5 years old.", "13": "13 0607/62/o/n/19 \u00a9 ucles 2019 [turn over 9 eddie models the percentage values used by john\u2019 s cars . .. log px x 5621 56 0 for102 =- . (a) on the axes, sketch the graph of this model. age of car (years)100 0 0 10percentagep x (b) how well does this model fit the percentages used by john\u2019 s cars for cars that are less than 3 years old? ...", "14": "14 0607/62/o/n/19 \u00a9 ucles 2019 10 lia makes a different model ()pax1100=+. (a) the table in question 8 shows that p = 72 when x = 1. these values fit lia\u2019s model. find the value of a, correct to 1 decimal place. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (b) on the axes in question 9 , sketch the graph of this model. (c) how well does lia\u2019s model fit the percentages used by john\u2019 s cars ? ... ...", "15": "15 0607/62/o/n/19 \u00a9 ucles 2019 11 (a) use lia\u2019s model to write a model for the value, $ v, of a car that costs $ c when it is new. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (b) use this model to find the age of eddie\u2019s car when its value is $6500. give your answer in years and months, correct to the nearest month. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd", "16": "16 0607/62/o/n/19 \u00a9 ucles 2019 blank page permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge." }, "0607_w19_qp_63.pdf": { "1": "this document consists of 12 printed pages. dc (ce/fc) 170794/3 \u00a9 ucles 2019 [turn over *4821203557* cambridge international mathematics 0607/63 paper 6 (extended) october/november 2019 1 hour 30 minutes candidates answer on the question paper. additional materials: graphics calculator read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen. do not use staples, paper clips, glue or correction fluid. you may use an hb pencil for any diagrams or graphs. do not write in any barcodes. answer both parts a (questions 1 to 6) and b (questions 7 to 9). you must show all relevant working to gain full marks for correct methods, including sketches. in this paper you will also be assessed on your ability to provide full reasons and to communicate your mathematics clearly and precisely. at the end of the examination, fasten all your work securely together. the total number of marks for this paper is 40.cambridge assessment international education cambridge international general certificate of secondary education", "2": "2 0607/63/o/n/19 \u00a9 ucles 2019 the investigation starts on the next page.", "3": "3 0607/63/o/n/19 \u00a9 ucles 2019 [turn over answer both parts a and b. a investigation (questions 1 to 6) remainders (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation is about the remainder when one positive integer is divided by another. example 83 80'=, with a remainder of 8. this can be written as []83 88 r' =. 1 find (a) []13 5 r', (b) []51 3 r' . 2 show that []4000 19 10 r ' = . 3 x is a factor of 20. show that [] x 20 0 r'=. 4 for a positive integer, n, write down the largest and smallest values of []n100 r' . largest ... smallest ...", "4": "4 0607/63/o/n/19 \u00a9 ucles 2019 5 (a) complete this table of values of []abr'. b 1 2 3 4 5 6 a1 0 1 1 1 1 1 2 0 3 0 4 0 5 0 6 0 (b) [] [] 10 10 10 99 rr''+= [] [] 11 11 11 77 rr''+= these examples suggest that [] [] xx x yy rr''+= . use values from the table to show one example that this is not always true. (c) the remainder when a positive integer, n, is divided by 100 is []n100 r' . explain why dividing []n100 r' by 100 gives the same remainder. ... ...", "5": "5 0607/63/o/n/19 \u00a9 ucles 2019 [turn over 6 in this question x, y and z are positive integers. (a) when []xz a r'= and []yz b r'=, then [] [] xyza bz rr''= . (i) check that this is true when x = 2, y = 8 and z = 5. (ii) using algebra, show that [] [] xz az rr22''= . (iii) use the result in part(a)(ii) to show that []76 71 r2'=.", "6": "6 0607/63/o/n/19 \u00a9 ucles 2019 (b) from part (a) [] [] xyza bz rr''= and [] [] xz az rr22''= . (i) use patterns to help you complete the table. []7919 13 r ' = 2 [] [] 7919 13 21 3 rr22'' = []41 3 r' = 4= [] [] 7919 13 13 4 rr2 4'' = [] 13 16r' = 3= [] [] 7919 13 13 3 rr82'' = []139r' = 9= []r = (ii) 79197is over 20 digits long. the following example shows how to calculate []7919 13 r7' . 7919 7919 7919 791974 21## = [] [( )] 7919 13 34 21 3 rr7'' ## = []24 13 r' = 11= find []7919 13 r11' . ", "7": "7 0607/63/o/n/19 \u00a9 ucles 2019 [turn over (iii) is 13 a factor of 79199? show how you decide. (c) work out whether 7 is a factor of 7919 564+.", "8": "8 0607/63/o/n/19 \u00a9 ucles 2019 b modelling (questions 7 to 9) orbiting satellites (20 marks) you are advised to spend no more than 45 minutes on this part. this investigation is about satellites orbiting the earth at a height, h kilometres, above the ground. h 7 the scatter diagram shows the heights and the orbit times, t minutes, for 9 satellites making circular orbits around the earth. 2009095100105 time (minutes) height (km)110115t h300 400 500 600 700 800 900 1000 1100 1200 1300 1400 (a) (i) the mean of these satellite heights is 770 km and the mean orbit time is 100 minutes. plot this point. (ii) draw a line of best fit. (iii) use your line of best fit to find a straight line model (model a) connecting t and h. give your answer in the form . tm hc=+", "9": "9 0607/63/o/n/19 \u00a9 ucles 2019 [turn over (b) another model (model b) connecting t and h is .( ) th1659 10 637043## =+-. the satellite norad 40730 has a circular orbit. it takes 728.9 minutes to orbit the earth at a height of 20 450 km. find which of the two models gives an orbit time closer to the actual orbit time. (c) communication satellites need an orbit time of 1440 minutes. use model b to find the height which gives an orbit time of 1440 minutes.", "10": "10 0607/63/o/n/19 \u00a9 ucles 2019 8 some satellites do not have circular orbits. 114 027 km7079 kmnot to scale the height of satellite norad 25989 is between 7079 km and 114 027 km. it has an orbit time of 2872 minutes. use h as the mean of these two heights to calculate the orbit time using model b. .( ) th1659 10 637043## =+- how does this time compare with the actual orbit time?", "11": "11 0607/63/o/n/19 \u00a9 ucles 2019 [turn over 9 some satellites eventually fall back to the earth. a model for the descent time of a satellite, d days, with an initial height, h kilometres, is dh 510. 24 964#=-` j . (a) sketch the graph of this model for h 400 600 gg . d h40003000 600 (b) the first satellite, sputnik 1 , had an initial height of 577 km and a descent time of 92 days. compare this descent time with the descent time given by the model. question 9(c) is printed on the next page.", "12": "12 0607/63/o/n/19 \u00a9 ucles 2019 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge. (c) radiation from the sun affects the descent time, d days. this radiation, s, is measured in solar flux units (sfu). the table shows the descent times, in days, for different values of h and s. radiation ( s sfu) 20 40 60 80 100 120 140 160 initial height (h km)500 553 350 233 163 118 88 68 53 475 298 195 134 96 71 54 43 34 450 158 107 76 56 43 33 27 22 425 82 58 42 32 25 20 16 14 400 42 31 23 18 15 12 10 9 (i) write down the descent time of a satellite with an initial height of 450 km when the radiation is 100 sfu. (ii) what does the table show about the effect of radiation on the descent time of a satellite? ... ... (iii) a satellite has an initial height of 500 km. d = ks1.1 d = k \u2013 s d = ks0.9 d = ks\u20131 where k is a constant. which one of these equations is the best model connecting descent time and radiation? give a reason for your answer. ... ..." } }, "2020": { "0607_s20_qp_11.pdf": { "1": "*2851231485*cambridge igcse\u2122 dc (kn/sw) 188562/1 \u00a9 ucles 2020 [turn overthis document has 12 pages. blank pages are indicated.cambridge international mathematics 0607/11 paper 1 (core) may/june 2020 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/11/m/j/20 \u00a9 ucles 2020 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/11/m/j/20 \u00a9 ucles 2020 [turn over answer all the questions. 1 write 73% as a fraction. . [1] 2 write down all the factors of 11. . [1] 3 30\u00b0x\u00b0not to scale ba ab is a straight line. find the value of x. x = [1] 4 (a) not to scale write down the mathematical name of this polygon. . [1] (b) not to scale write down the mathematical name of this polygon. . [1]", "4": "4 0607/11/m/j/20 \u00a9 ucles 2020 5 not to scale oa b o is the centre of the circle. write down the mathematical name of the line ab. . [1] 6 the diagram shows the favourite subject of each student in a class. 0 english french history subjectnumber of students mathematics science246810 write down the number of students whose favourite subject is (a) french, . [1] (b) mathematics. . [1] 7 work out. 30 57 1 #-+ . [1]", "5": "5 0607/11/m/j/20 \u00a9 ucles 2020 [turn over 8 not to scale 9 cm 9 cm this shape is made from an equilateral triangle and a square. find the perimeter of this shape. cm [2] 9 on the 1 cm2 grid, draw a triangle with an area of 6 cm2. [1] 10 draw all the lines of symmetry on this regular pentagon. [2]", "6": "6 0607/11/m/j/20 \u00a9 ucles 2020 11 x\u00b0 find, by measuring, the angle marked x. . [1] 12 change 4 m 25 cm into millimetres. .. mm [1] 13 simplify the ratio 10 : 15 . ... : ... [1] 14 work out 25. . [1] 15 solve the equation. x41 6 += x = . [2]", "7": "7 0607/11/m/j/20 \u00a9 ucles 2020 [turn over 16 find the coordinates of the mid-point of the line joining the point (0, 0) to the point (\u22122, 4). ( ... , ..) [2] 17 write down the integers that satisfy the inequality n 3711 . . [1] 18 the diagram shows the graph of () yx f= . \u2013 4\u2013 3\u2013 2\u2013 101234567 \u2013 5\u2013 4\u2013 3\u2013 2\u2013 1 1 2 3 4 5y x draw the horizontal asymptote for the graph of () yx f= . [1]", "8": "8 0607/11/m/j/20 \u00a9 ucles 2020 19 apples are stored in boxes. there are 100 apples in a box. two boxes are chosen at random and the apples are sorted into good and bad. (a) complete the table of results. good bad total box 1 12 100 box 2 95 100 total 183 200 [2] (b) one of these 200 apples is chosen at random. write down the probability that this apple is good. . [1] 20 8 cmnot to scale 6 cmx cm work out the value of x. x = . [2]", "9": "9 0607/11/m/j/20 \u00a9 ucles 2020 [turn over 21 the scatter diagram shows a correlation between x and y. y x 5510152025303540 010 15 20 25 30 (a) write down the type of correlation shown in the scatter diagram. . [1] (b) the mean point is (14, 18). (i) draw the line of best fit. [2] (ii) use your line of best fit to estimate the value of x when y25= . x = . [1] 22 a sphere has a radius of 3 cm. find the surface area of the sphere. give your answer in terms of r. .. cm2 [2]", "10": "10 0607/11/m/j/20 \u00a9 ucles 2020 23 16 cm 8 cm6 cmnot to scalex cm these triangles are similar. find the value of x. x = . [1] 24 describe fully the single transformation that maps yx2= onto yx 42=+ . . [2] 25 solve the simultaneous equations. xy31 3 += xy21 0 += x = . y = . [2]", "11": "11 0607/11/m/j/20 \u00a9 ucles 2020 blank page", "12": "12 0607/11/m/j/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_s20_qp_12.pdf": { "1": "*6276546679* dc (pq/sw) 188561/2 \u00a9 ucles 2020 [turn overthis document has 12 pages. blank pages are indicated.cambridge international mathematics 0607/12 paper 1 (core) may/june 2020 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ].cambridge igcse\u2122", "2": "2 0607/12/m/j/20 \u00a9 ucles 2020 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/12/m/j/20 \u00a9 ucles 2020 [turn over answer all the questions. 1 (a) write the number 30 000 010 in words. . [1] (b) write the number thirty thousand and one hundred in figures. . [1] 2 work out. 16 52-+ . [1] 3 \u2013 4\u2013 3\u2013 2\u2013 10 \u2013 4\u2013 3\u2013 2\u2013 1 1234y x1234 on the grid, plot the point (3, 2). [1] 4 cm cm2 cm3 m m2 m3 km km2 km3 from the list, write down the best unit to use to measure the floor area of a school. . [1]", "4": "4 0607/12/m/j/20 \u00a9 ucles 2020 5 complete the statement with ,1 = or 2. 200 80 [1] 6 (a) these are the first four terms of a sequence. 2 5 8 11 write down the next term in this sequence. . [1] (b) these are the first five terms of another sequence 0.1 1 10 100 1000 write down the rule for continuing this sequence. . [1] 7 write 0.16 as a fraction in its simplest form. . [2] 8 change 6.3 kilograms into grams. .. g [1]", "5": "5 0607/12/m/j/20 \u00a9 ucles 2020 [turn over 9 12 cm5 cm13 cmnot to scale work out the perimeter of this triangle. cm [1] 10 work out ..01 03# . . [1] 11 this table shows the distances, in kilometres, between four cities in the usa. boston 1580 chicago 4800 3243 los angeles 2414 2218 4394 miami (a) write down the distance between boston and miami. km [1] (b) write down the name of the nearest city to chicago. . [1] 12 the probability that a light bulb is faulty is 5%. find the probability that a light bulb is not faulty. . [1]", "6": "6 0607/12/m/j/20 \u00a9 ucles 2020 13 \u2013 4\u2013 3\u2013 2\u2013 10 \u2013 4\u2013 3\u2013 2\u2013 1 1234y x1234 on the grid, draw the line x2=. [1] 14 not to scale y\u00b0x\u00b0 the diagram shows two straight lines. complete the statement. the value of x is equal to the value of y because they are . angles. [1] 15 not to scaley\u00b0 50\u00b0 60\u00b0 find the value of y. y= . [1]", "7": "7 0607/12/m/j/20 \u00a9 ucles 2020 [turn over 16 carlo drives 150 km in 2 hours. work out his average speed. km/h [1] 17 solve xx 16 24 5 -= -. x= . [2] 18 y xab \u2013 2\u2013 10 \u2013 4 \u2013 5 \u2013 6 \u2013 3\u2013 2\u2013 1 1 2 3 4 5 61234567 describe fully the single transformation that maps shape a onto shape b. . . [2]", "8": "8 0607/12/m/j/20 \u00a9 ucles 2020 19 work out the size of one exterior angle of a regular hexagon. . [2] 20 u p 2 5 4 89 673 q write down (a) the set pl, { ... } [1] (b) the set pq,, { ... } [1] (c) ()nq. . [1]", "9": "9 0607/12/m/j/20 \u00a9 ucles 2020 [turn over 21 a is the point ( 3-, 8) and b is the point (5, 2). find the coordinates of the mid-point of ab. (.. , ..) [2] 22 find the gradient of the line with equation yx84=- . . [1] 23 the height of a triangle is 8 cm and its area is 40 cm2. find the length of the base. ... cm [2] 24 a b cnot to scale 12 cm the diagram shows a right-angled triangle abc with ac 12= cm. . sinc 06= . cosc 08= . tanc 075 = find the length of ab. ... cm [2]", "10": "10 0607/12/m/j/20 \u00a9 ucles 2020 25 this cumulative frequency diagram shows the mass, in kilograms, of each of 120 animals. 20406080100120 020 40 60 80 mass (kg)cumulative frequency 100 120 140 use the diagram to find (a) the median, kg [1] (b) the inter-quartile range. kg [2]", "11": "11 0607/12/m/j/20 \u00a9 ucles 2020 26 y x \u2013 10 \u2013 4\u2013 3\u2013 2\u2013 1 1 2 3 41234567 f(x) g(x) the diagram shows the graphs of () yx f= and () yx g= . the graph of () yx g= is a translation of the graph of () yx f= . write down the function ()xg in terms of ()xf. ()xg= . [1]", "12": "12 0607/12/m/j/20 \u00a9 ucles 2020 blank page permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge." }, "0607_s20_qp_21.pdf": { "1": "cambridge igcse\u2122dc (jc/jg) 182612/1 \u00a9 ucles 2020 [turn overthis document has 8 pages. blank pages are indicated. *3103934013* cambridge international mathematics 0607/21 paper 2 (extended) may/june 2020 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/21/m/j/20 \u00a9 ucles 2020 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/21/m/j/20 \u00a9 ucles 2020 [turn over answer all the questions. 1 a cuboid has a square base of side 10 cm and a volume of 1200 cm3. work out the height of the cuboid. ... cm [2] 2 p13=-eo q21=-eo (a) find qp+. fp [1] (b) a is the point (2, 7). the point a is translated to the point b by the vector qp+. find the coordinates of b. ( , ) [2] 3 work out 43221' . give your answer as a fraction in its lowest terms. [3]", "4": "4 0607/21/m/j/20 \u00a9 ucles 2020 4 a truck of length 10 m passes a gate of length 2 m. the speed of the truck is 8 m/s. find the time the truck takes to completely pass the gate. .. s [2] 5 find the volume of a cone with radius 3 cm and perpendicular height 8 cm. give your answer in terms of r. . cm3 [2] 6 14 cmx cm30\u00b0 not to scale work out the value of x. x = [3] 7 simplify. (a) ww 315 315 [2] (b) y125632 ` j [2]", "5": "5 0607/21/m/j/20 \u00a9 ucles 2020 [turn over 8 rr ar hr232=+ rearrange the formula to write h in terms of r, r and a. h = [2] 9 not to scale acb x\u00b070\u00b0 t a, b and c are points on a circle. ta is a tangent to the circle at a. ca = cb and angle bat = 70\u00b0. work out the value of x. x = [2] 10 when jack sells a computer for $264 he makes a profit of 20%. work out the price jack paid for the computer. $ [2]", "6": "6 0607/21/m/j/20 \u00a9 ucles 2020 11 y is inversely proportional to x. when x9=, y2=. find y in terms of x. y = [2] 12 logl og log yx w 32 =- find y in terms of x and w. y = [3] 13 rationalise the denominator. 729 - [2]", "7": "7 0607/21/m/j/20 \u00a9 ucles 2020 [turn over 14 y x 0(4, 2) in the diagram, the graph passes through the point (4, 2). write down the equation of the graph. [2] 15 simplify. pt ap ata 36 23 -- +- [3] question 16 is printed on the next page.", "8": "8 0607/21/m/j/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.16 write as a single fraction in its simplest form. x x312 -- [3]" }, "0607_s20_qp_22.pdf": { "1": "*6568146797* dc (nf/cb) 182613/2 \u00a9 ucles 2020 [turn overthis document has 8 pages. blank pages are indicated.cambridge international mathematics 0607/22 paper 2 (extended) may/june 2020 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ].cambridge igcse\u2122", "2": "2 0607/22/m/j/20 \u00a9 ucles 2020 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/22/m/j/20 \u00a9 ucles 2020 [turn over answer all the questions. 1 31 37 39 49 51 53 77 87 from this list write down all the prime numbers. . [2] 2 work out 15% of 600. . [2] 3 work out. (a) . . 006012# . [1] (b) .023 . [1] (c) .. 00804 . [1] 4 a bag contains red balls, blue balls and green balls only. there are twice as many blue balls as green balls. there are twice as many red balls as blue balls. there are 16 blue balls in the bag. find the total number of balls in the bag. . [2]", "4": "4 0607/22/m/j/20 \u00a9 ucles 2020 5 dippi buys 5 burgers and 4 bags of chips for a total cost of $8.10 . burgers cost $1.10 each. find the cost of one bag of chips. $ ... [3] 6 2x\u00b03x\u00b04x\u00b0not to scale a b ab is a straight line. find the value of x. x = . [2] 7 work out the following, giving each answer in standard form. (a) (. )( ) 43 10 31 044## #- . [2] (b) () () 61 03 1023## +-- . [2]", "5": "5 0607/22/m/j/20 \u00a9 ucles 2020 [turn over 8 solve the simultaneous equations. xy32 1 += - xy72 6 -= x = . y = . [3] 9 the interior angle of a regular polygon is 150\u00b0. find the number of sides of this polygon. . [3] 10 rearrange the formula to make x the subject. ()yx 42+= x = . [2]", "6": "6 0607/22/m/j/20 \u00a9 ucles 2020 11 footballrunning tennis45\u00b0 60\u00b0 swimming the pie chart shows the favourite sports of all the students at a school. 180 students chose running as their favourite sport. work out (a) the total number of students at the school, . [1] (b) the number of students that chose football as their favourite sport. . [2] 12 factorise. xx23 52-- . [2]", "7": "7 0607/22/m/j/20 \u00a9 ucles 2020 [turn over 13 solve. () () xx43 02 -+ . [2] 14 a is the point (1, 7) and b is the point (4, 13). find the equation of the perpendicular bisector of ab in the form ym xc=+ . y = . [5] question 15 is printed on the next page.", "8": "8 0607/22/m/j/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.15 not to scale x11 7 find the value of x. x = . [2]" }, "0607_s20_qp_23.pdf": { "1": "cambridge igcse\u2122this document has 8 pages. blank pages are indicated. dc (jc/jg) 182614/1 \u00a9 ucles 2020 [turn over *2152689991* cambridge international mathematics 0607/23 paper 2 (extended) may/june 2020 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/23/m/j/20 \u00a9 ucles 2020 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/23/m/j/20 \u00a9 ucles 2020 [turn over answer all the questions. 1 (a) write 0.047 996 correct to 4 decimal places. .. [1] (b) write 60 449 correct to 3 significant figures. .. [1] 2 work out 1 441 65- . give your answer as a mixed number in its simplest form. [3] 3 simplify. aaa 325# [2] 4 (a) write down the mathematical name of the quadrilateral that has rotational symmetry of order 2 but no lines of symmetry. [1] (b) write down the mathematical name of the quadrilateral that has exactly one line of symmetry. [1]", "4": "4 0607/23/m/j/20 \u00a9 ucles 2020 5 solve. () xx 92 56g-+ [3] 6 a biased four-sided spinner is spun 150 times. the number of times that the spinner lands on each number is shown in the table. number on spinner 1 2 3 4 frequency 34 63 27 26 (a) write down the relative frequency of the spinner landing on 2. [1] (b) explain why it is reasonable to use your answer to part (a) as the probability of this spinner landing on 2. [1] (c) the spinner is spun 3000 times. find the expected number of times that the spinner lands on 2. [2] 7 divide 96 cm in the ratio 5 : 3. cm , ... cm [2]", "5": "5 0607/23/m/j/20 \u00a9 ucles 2020 [turn over 8 a is the point , ()24- and b is the point ,()71. find the length of ab giving your answer in its simplest surd form. .. [4] 9 not to scale56\u00b0 98\u00b0 57\u00b0 dc qb p a a, b, c and d are points on the circle. pbq is a straight line. (a) find angle dcb , giving a reason for your answer. angle dcb = ... because .. [2] (b) is pbq a tangent to the circle? give a reason for your answer. ... because . [1]", "6": "6 0607/23/m/j/20 \u00a9 ucles 2020 10 solve the simultaneous equations. xy yx23 5 39+= =+ x = y = [3] 11 the table shows some trigonometric ratios, each correct to 3 decimal places. sine cosine tangent 40\u00b0 0.643 0.766 0.839 70\u00b0 0.940 0.342 2.747 use this information to find (a) sin110\u00b0, [1] (b) tan320\u00b0. [1]", "7": "7 0607/23/m/j/20 \u00a9 ucles 2020 [turn over 12 factorise completely. (a) xy xy 4622- [2] (b) x912- [1] 13 solve. (a) log9 2x= x = [1] (b) logl og log x 24 9 -= x = [2] 14 y varies inversely as the square root of x. when x25= , y6=. find y in terms of x. y = . [2] question 15 is printed on the next page.", "8": "8 0607/23/m/j/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.15 (a) on the venn diagram, shade the set ab c ++ l. a cbu [1] (b) use set notation to describe the shaded region. p rqu [1]" }, "0607_s20_qp_31.pdf": { "1": "cambridge igcse\u2122this document has 16 pages. blank pages are indicated. dc (ce/fc) 183470/2 \u00a9 ucles 2020 [turn over *8470777360* cambridge international mathematics 0607/31 paper 3 (core) may/june 2020 1 hour 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 96. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/31/m/j/20 \u00a9 ucles 2020 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/31/m/j/20 \u00a9 ucles 2020 [turn over answer all the questions. 1 24 people take part in a cookie-eating competition. the number of cookies eaten by each person in two minutes is recorded. 11 12 13 8 12 8 12 10 9 11 8 13 11 10 12 9 9 10 10 9 10 9 9 12 (a) complete the frequency table. number of cookies 8 9 10 11 12 13 frequency 3 [2] (b) find (i) the mode, .. [1] (ii) the range, .. [1] (iii) the median, .. [1] (iv) the mean, .. [1] (v) the interquartile range. .. [2] (c) complete the bar chart. 01 8 9 10 number of cookiesfrequency 11 12 13234567 [2]", "4": "4 0607/31/m/j/20 \u00a9 ucles 2020 2 (a) 1 2 3 4 5 6 7 8 9 10 from this list of numbers, write down (i) a square number, .. [1] (ii) a triangle number, .. [1] (iii) a prime number, .. [1] (iv) a factor of 13, .. [1] (v) a multiple of 6. .. [1] (b) work out 65% of 34. .. [2] (c) write 9876.543 (i) correct to 2 decimal places, .. [1] (ii) correct to 4 significant figures, .. [1] (iii) correct to the nearest hundred. .. [1] (d) write your answer to part (c)(iii) in standard form. .. [1]", "5": "5 0607/31/m/j/20 \u00a9 ucles 2020 [turn over (e) work out. give each answer as a fraction in its simplest form. (i) 52 31+ .. [1] (ii) 85 41- .. [1] (iii) 3103 65# .. [1]", "6": "6 0607/31/m/j/20 \u00a9 ucles 2020 3 (a) write down the rule for continuing each sequence. (i) 86, 78, 70, 62, \u2026 . [1] (ii) 4, 12, 36, 108, \u2026 . [1] (iii) 80, 40, 20, 10, \u2026 . [1] (b) the nth term of a sequence is n212+. work out the first two terms of this sequence. , ... [2] (c) these are the first four terms of another sequence. 8 19 30 41 (i) find the next two terms of this sequence. , ... [2] (ii) find the nth term of this sequence. .. [2] (iii) use your expression from part (ii) to find the 30th term. .. [1]", "7": "7 0607/31/m/j/20 \u00a9 ucles 2020 [turn over 4 23 cm 18 cma b not to scale c d52\u00b0 e 18 cm abcd is a rectangle and edc is a straight line. de = bc = 18 cm, ab = 23 cm and angle bca = 52\u00b0. find (a) angle bac , angle bac = . [1] (b) angle aed , angle aed = . [1] (c) angle eac , angle eac = . [2] (d) ae, ae = cm [2] (e) the total perimeter of the shape abce . .. cm [1]", "8": "8 0607/31/m/j/20 \u00a9 ucles 2020 5 (a) cinzia goes to the zoo with her mother. cinzia is 12 years old. the entrance fee is $25 for each adult and $14 for each child under the age of 16 years. work out the total entrance fee for cinzia and her mother and how much change they receive from $50. total entrance fee $ . change $ . [2] (b) cinzia and her mother arrive at the zoo at 11 35 and leave at 15 45. find the time, in hours and minutes, that they are at the zoo. . h min [1] (c) cinzia sees this notice. monkeys 500 metres cinzia can walk at 5 km/h. find how many minutes it takes cinzia to walk to the monkeys. min [3]", "9": "9 0607/31/m/j/20 \u00a9 ucles 2020 [turn over 6 50 cm 24 cm 4 mnot to scale the diagram shows a cylindrical pipe. the external radius is 50 cm and the internal radius is 24 cm. (a) find the shaded area. ... cm2 [3] (b) the pipe is 4 metres long. (i) change 4 metres into centimetres. . cm [1] (ii) find the volume of the pipe. ... cm3 [1] (c) work out the area of the outside curved surface of the pipe. ... cm2 [2]", "10": "10 0607/31/m/j/20 \u00a9 ucles 2020 7 (a) solve. (i) xx46 81 4 =-+ x = . [2] (ii) ()x23 11 += x = . [2] (b) cm n 23=+ (i) find c when m = 1.8 and n = 1.3 . c = . [2] (ii) find m when c = 8.4 and n = 0.6 . m = . [2] (iii) rearrange the formula to make n the subject. n = . [2]", "11": "11 0607/31/m/j/20 \u00a9 ucles 2020 [turn over 8 a boat sails 300 m on a bearing of 060\u00b0 from a to b. it then changes course and sails 220 m on a bearing of 150\u00b0 from b to c. the boat then returns directly to a. (a) on the diagram, sketch the path of the boat. show the distances and bearings that you have been given. not to scalenorth a [4] (b) angle abc = 90\u00b0. (i) calculate angle bac . angle bac = . [2] (ii) find the bearing of c from a. .. [1]", "12": "12 0607/31/m/j/20 \u00a9 ucles 2020 9 8 \u20131 0 3.5xy \u2013 4 the diagram shows the graph of yx x 25 32=- ++ for . x13 5 gg- . (a) use your calculator to find (i) the coordinates of the point of intersection of the graph with the y-axis, ( ... , ...) [1] (ii) the coordinates of the points of intersection of the graph with the x-axis, \b (\u200a\u200a... \b\u200a\u200a,\b...) \band\b(\u200a\u200a... \b\u200a\u200a,\b...) \b[2] (iii) the coordinates of the local maximum. ( ... , ...) [2] (b) on the diagram, sketch the graph of yx21=+ . [2] (c) find the coordinates of the points of intersection of yx x 25 32=- ++ and yx21=+ . \b (\u200a\u200a... \b\u200a\u200a,\b...) \band\b(\u200a\u200a... \b\u200a\u200a,\b...) \b[2]", "13": "13 0607/31/m/j/20 \u00a9 ucles 2020 [turn over 10 bac 12345678910 xy \u201310 \u20139\u20138\u20137\u2013 6\u20135\u2013 4\u20133\u20132 \u201310\u20139\u20138\u20137\u2013 6\u20135\u2013 4\u20133\u20132\u2013112345678910 0\u20131 (a) reflect shape a in the y-axis. [1] (b) describe fully the single transformation that maps shape a onto shape b. [3] (c) describe fully the single transformation that maps shape a onto shape c. [2] (d) enlarge shape a with centre (0, 0) and scale factor 2-. [2]", "14": "14 0607/31/m/j/20 \u00a9 ucles 2020 11 (a) in a class of 24 students \u2022 10 students wear glasses ( g\u200a) \u2022 12 students have black hair ( b\u200a) \u2022 5 students do not wear glasses and do not have black hair. (i) complete the venn diagram. gu b ... [2] (ii) describe in words the set gb+ . students who .. [1] (iii) one of the 24 students is chosen at random. write down the probability that this student wears glasses but does not have black hair. ... [1] (iv) on the venn diagram below, shade the region gb+l . gu b [1]", "15": "15 0607/31/m/j/20 \u00a9 ucles 2020 (b) another class has 20 students. in this class \u2022 5 students wear glasses and have black hair \u2022 8 students wear glasses and do not have black hair \u2022 all the students either wear glasses or have black hair or both. (i) complete the venn diagram. g ... .u b [2] (ii) write down the number of students in this class who have black hair. .. [1]", "16": "16 0607/31/m/j/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_s20_qp_32.pdf": { "1": "cambridge igcse\u2122this document has 20 pages. blank pages are indicated. dc (st/ct) 183469/2 \u00a9 ucles 2020 [turn over *1383446504* cambridge international mathematics 0607/32 paper 3 (core) may/june 2020 1 hour 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 96. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/32/m/j/20 \u00a9 ucles 2020 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/32/m/j/20 \u00a9 ucles 2020 [turn over answer all the questions. 1 (a) write down a multiple of 7. .. [1] (b) here are the factors of 99. 1 3 9 11 33 99 write down the factors that are prime. .. [2] (c) write down all of the factors of 20. .. [2] (d) write 54 as a product of its prime factors. .. [2] (e) for an activity, students are split into groups. the students can be split exactly either into groups of 15 or into groups of 21. work out the smallest number of students taking part in the activity. .. [2]", "4": "4 0607/32/m/j/20 \u00a9 ucles 2020 2 (a) the temperature, in \u00b0c, in each of five cities is listed in the table. city temperature (\u00b0c) amsterdam \u2007 \u22124 dublin 5 oslo \u221211 venice 6 warsaw 9 (i) write down which city is the coldest. .. [1] (ii) work out the difference in temperature between amsterdam and warsaw. .. \u00b0c [1] (iii) work out the difference in temperature between amsterdam and oslo. .. \u00b0c [1] (b) chris climbs from kathmandu to the top of mount everest. he uses this formula to find the temperature, t \u00b0c, at different heights, h metres, above sea level. . th 0008 30 # =- + (i) the top of mount everest is 8850 m above sea level. show that the temperature at the top of mount everest is -40.8 \u00b0c. [1]", "5": "5 0607/32/m/j/20 \u00a9 ucles 2020 [turn over (ii) kathmandu is 1400 m above sea level. work out the temperature in kathmandu. .. \u00b0c [1] (iii) the\u2007temperature \u2007at\u2007everest\u2007base\u2007camp\u2007is\u2007\u221212.4\u2007\u00b0c. work out the height of everest base camp above sea level. .. m [2] (iv) rearrange this formula to make h the subject. . th 0008 30 # =- + h = . [2]", "6": "6 0607/32/m/j/20 \u00a9 ucles 2020 3 (a) y x \u2013 3 \u2013 4 \u2013 5\u2013 2\u2013 1\u2013 1 1 2 3 4 5 \u2013 2 \u2013 3 \u2013 4 \u2013 512345 0ca b the diagram shows a hexagon drawn on a 1cm2 grid. (i) write down the coordinates of (a) point a, ( ... , ...) [1] (b) point b, ( ... , ...) [1] (c) point c. ( ... , ...) [1] (ii) on the grid, draw the reflection of the hexagon in the x-axis. [2]", "7": "7 0607/32/m/j/20 \u00a9 ucles 2020 [turn over (b) (i) write down the order of rotational symmetry of this shape. .. [1] (ii) on the shape above, draw all the lines of symmetry. [2] 4 (a) use the correct mathematical word to complete each sentence. (i) the distance around the edge of a circle is the .. . [1] (ii) a straight line which touches the edge of a circle once only is a . . [1] (iii) a straight line from the edge of a circle to its centre is a .. . [1] (b) 6 cm18 cmnot to scale this shape is a rectangle joined to two semicircles. work out the total area of this shape. give the units of your answer. ... .. [5]", "8": "8 0607/32/m/j/20 \u00a9 ucles 2020 5 (a) the bar chart shows the numbers of girls and boys in a village school and their ages. key girls boys number of students 02 12 13 14 age (years)15 16468101214161820222426 (i) there are 19 boys aged 16 in the school. complete the bar chart. [1] (ii) for students aged 13, work out how many more boys than girls there are. .. [1] (iii) find the total number of students aged 12. .. [1] (iv) find the total number of girls in the school. .. [1] (v) which age has the largest total number of students? .. [1]", "9": "9 0607/32/m/j/20 \u00a9 ucles 2020 [turn over (b) in a country there are 11.5 million children. the probability that one of these children has measles is 0.2 . work out the expected number of these children that have measles. .. million [2] (c) in a town, the probability that a student aged 17 has passed their driving test is 0.7 . two students aged 17 are chosen at random from the town. (i) complete the tree diagram. has passed has not passedhas not passed has passedhas passed has not passed0.7 ... . .first student second student [2] (ii) work out the probability that both students have not passed their driving test. .. [2]", "10": "10 0607/32/m/j/20 \u00a9 ucles 2020 6 (a) write each of these ratios in its simplest form. (i) 6 : 30 : ... [1] (ii) 75 cents : 2 dollars : ... [2] (b) (i) one year, amir earns $85 000. he pays 51 of this in tax. work out how much amir pays in tax. $ . [1] (ii) the next year, the $85 000 that amir earns is increased by 3%. work out how much amir now earns. $ . [2]", "11": "11 0607/32/m/j/20 \u00a9 ucles 2020 [turn over (iii) another year, amir receives a bonus of $8400. he decides to use this bonus for savings and for pleasure in the ratio savings : pleasure = 1 : 5. work out how much of the bonus amir uses for savings and how much he uses for pleasure. savings $ . pleasure $ . [2]", "12": "12 0607/32/m/j/20 \u00a9 ucles 2020 7 the table shows the height and the shoe size of each of eight children. height (cm) 57 79 102 100 92 81 109 60 shoe size 21 23 25.5 24 25 24 27.5 22 (a) complete the scatter diagram. the first four points have been plotted for you. 20 1550 60 70 80 height (cm)90 100 1102530 shoe size [2] (b) what type of correlation is shown in the scatter diagram? .. [1] (c) (i) work out the mean height and the mean shoe size. mean height = ... cm mean shoe size = ... [2] (ii) on the scatter diagram, draw a line of best fit. [2] (d) use your line of best fit to estimate the shoe size of a child with height 70 cm. .. [1]", "13": "13 0607/32/m/j/20 \u00a9 ucles 2020 [turn over 8 (a) (i) 7 \u00d7 7 \u00d7 7 \u00d7 7 \u00d7 7 \u00d7 7 = 7n write down the value of n. n = . [1] (ii) write down the value of 70. .. [1] (b) simplify fully. (i) x 72 43# .. [2] (ii) xx 72' .. [3]", "14": "14 0607/32/m/j/20 \u00a9 ucles 2020 9 (a) y x \u2013 3 \u2013 4 \u2013 5\u2013 2\u2013 1\u2013 1 1 2 3 4 5 \u2013 2 \u2013 3 \u2013 4 \u2013 512345 0 rotate the triangle by 90\u00b0 clockwise about (0, 0). [2] (b) 12 cm 8.4 cm 5 cm x cmnot to scale these two triangles are mathematically similar. work out the value of x. x = . [2]", "15": "15 0607/32/m/j/20 \u00a9 ucles 2020 [turn over (c) y x \u2013 3 \u2013 4 \u2013 5\u2013 2\u2013 1\u2013 1 1 2 3 4 5 \u2013 2 \u2013 3 \u2013 4 \u2013 512345 0b a describe fully the single transformation that maps triangle a onto triangle b. ... ... [3]", "16": "16 0607/32/m/j/20 \u00a9 ucles 2020 10 (a) solve. (i) x 36= x = . [1] (ii) x25 4h- .. [2] (b) solve the simultaneous equations. you must show all your working. xy31 3 += xy21 2 -= x = . y = . [2] (c) multiply out the brackets and simplify. () () xx14+- .. [2]", "17": "17 0607/32/m/j/20 \u00a9 ucles 2020 [turn over 11 y x30 \u2013 20\u2013 5 5 0 (a) (i) on the diagram, sketch the graph of yx x282=+ - for x55gg- . [2] (ii) find the coordinates of the local minimum. ( ... , ...) [1] (b) on the diagram, sketch the graph of yx32=- for x55gg- . [2] (c) find the x-coordinate of each point of intersection of yx x282=+ - and yx32=- . x = and x = [2]", "18": "18 0607/32/m/j/20 \u00a9 ucles 2020 12 (a) north ab scale: 1 cm to 10 km a boat sails from a to b. (i) measure the bearing of b from a. .. [1] (ii) work out the actual distance from a to b. km [2]", "19": "19 0607/32/m/j/20 \u00a9 ucles 2020 (b) x\u00b0y m 8 m 2 m 4.5 mnot to scale the boat has two triangular sails. (i) find the value of x. x = . [2] (ii) find the value of y. y = . [2]", "20": "20 0607/32/m/j/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_s20_qp_41.pdf": { "1": "cambridge igcse\u2122this document has 20 pages. blank pages are indicated. *2566649839* dc (st/jg) 182696/2 \u00a9 ucles 2020 [turn overcambridge international mathematics 0607/41 paper 4 (extended) may/june 2020 2 hours 15 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 120. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/41/m/j/20 \u00a9 ucles 2020 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/41/m/j/20 \u00a9 ucles 2020 [turn over answer all the questions. 1 2 3 15 4 3 2 1 4 5x0 \u2013 4\u2013 3\u2013 2\u2013 1 \u2013 1 \u2013 2 \u2013 3\u2013 5y \u2013 4 pt q \u2013 5 \u2013 6 (a) (i) reflect shape t in the y-axis. [1] (ii) translate shape t by the vector 5 3-eo . [2] (iii) enlarge shape t by scale factor 2, centre (2, 0). [2] (b) describe fully the single transformation that maps shape t onto (i) shape p, . . [3] (ii) shape q. . . [3]", "4": "4 0607/41/m/j/20 \u00a9 ucles 2020 2 (a) these are tom\u2019s ten homework marks. 8 7 10 8 9 5 8 10 6 8 find (i) the range, .. [1] (ii) the mean, .. [1] (iii) the median, .. [1] (iv) the upper quartile. .. [1] (b) the mass, m kg, of each of 120 parcels is recorded. the cumulative frequency curve shows the results. 120 100 80 60 40 20 m 0 0 1 1.5 2.5 3.5 0.5 2 3 4 mass (kg)cumulative frequency", "5": "5 0607/41/m/j/20 \u00a9 ucles 2020 [turn over (i) find the median. . kg [1] (ii) find the lower quartile. . kg [1] (iii) find the interquartile range. . kg [1] (iv) find the number of parcels with a mass of more than 3 kg. .. [2] (v) (a) use the cumulative frequency curve to complete the frequency table. mass ( m kg) m 011g . m 1 151g . m 15 21g m 231g m 341g frequency 30 30 [3] (b) use the frequency table to calculate an estimate of the mean. . kg [2]", "6": "6 0607/41/m/j/20 \u00a9 ucles 2020 3 y xnot to scale od ac b abcd is a parallelogram. a is the point (3, 1), b is the point (10, 2) and d is the point (2, 3). (a) find the coordinates of c. (.. , ..) [2] (b) calculate the length of ab. give your answer as a surd in its simplest form. ab = . [3] (c) the diagonals of the parallelogram meet at x. find the coordinates of x. (.. , ..) [2]", "7": "7 0607/41/m/j/20 \u00a9 ucles 2020 [turn over (d) the straight line ba is extended to meet the y-axis at p and the x-axis at q. find the coordinates of p and the coordinates of q. p (.. , ..) q (.. , ..) [5]", "8": "8 0607/41/m/j/20 \u00a9 ucles 2020 4 find the n th term of each sequence. (a) 16, 25, 36, 49, 64, ... .. [2] (b) 3, 10, 29, 66, 127, ... .. [2] (c) 64, 32, 16, 8, 4, ... .. [2]", "9": "9 0607/41/m/j/20 \u00a9 ucles 2020 [turn over 5 (a) expand the brackets and simplify. (i) () () pp 52 33 2 -- + .. [2] (ii) () () gh gh 72 31 1 -+ .. [3] (b) factorise completely. (i) xy xy 2423 32- .. [2] (ii) tu49 922- .. [2] (iii) dd622+- .. [2]", "10": "10 0607/41/m/j/20 \u00a9 ucles 2020 6 (a) y 01.5 5x (i) on the diagram, sketch the graph of log yx= for x 051g . [2] (ii) solve the equations. (a) . logx 02= x = or x = [2] (b) logxx14=- x = or x = [4]", "11": "11 0607/41/m/j/20 \u00a9 ucles 2020 [turn over (b) 01.5 5xy \u2013 5\u2013 5 (i) on the diagram, sketch the graph of log yx= for values of x between 5- and 5. [2] (ii) solve the equation . logx 02= . x = or x = [2] (c) write down the range of values of x for which the graph of log yx= is the same as the graph of log yx= . .. [1]", "12": "12 0607/41/m/j/20 \u00a9 ucles 2020 7 (a) louis invests $500 at a rate of 2.5% per year simple interest. calculate the total amount of interest at the end of 8 years. $ . [2] (b) martha invests $500 at a rate of 2.4% per year compound interest. calculate the total amount of interest at the end of 8 years. $ . [4] (c) naomi invests an amount of money at a rate of 2.1% per year compound interest. find the number of complete years it takes for the value of naomi\u2019s investment to double. .. [4]", "13": "13 0607/41/m/j/20 \u00a9 ucles 2020 [turn over (d) oscar invests an amount of money at a rate of r % per year compound interest. at the end of 31 years the value of oscar\u2019s investment is 2.5 times greater than the original amount of money. find the value of r. r = . [3]", "14": "14 0607/41/m/j/20 \u00a9 ucles 2020 8 (a) when the weather is fine, the probability that sara goes to the park is 0.9 . when the weather is not fine, the probability that sara goes to the park is 0.2 . on any day, the probability that the weather is fine is 0.7 . (i) complete the tree diagram. 0.7weather park fine not finesara goes sara does not go sara goes sara does not go .. [3] (ii) find the probability that, on any day, sara goes to the park. .. [3]", "15": "15 0607/41/m/j/20 \u00a9 ucles 2020 [turn over (b) 30 students are asked if they like mathematics ( m) and if they like english ( e). the venn diagram shows the number of students in each subset. u m e 17 5 17 (i) find ()men, l. .. [1] (ii) two students are chosen at random. find the probability that they both like mathematics but not english. .. [3]", "16": "16 0607/41/m/j/20 \u00a9 ucles 2020 9 06 4.5xy \u2013 6\u2013 0.5 ()x xxx 68 f32=- + for .. x 05 45 gg- (a) on the diagram, sketch the graph of () yx f= . [2] (b) solve the inequality ()x 0 f1. .. [3] (c) find the positive value of k when ()xkf= has two different solutions. k = . [2]", "17": "17 0607/41/m/j/20 \u00a9 ucles 2020 [turn over 10 ()xx 23 f=+ ()x 5 gx= (a) find (( ))3 fg . .. [2] (b) find ()x f1-. ()x f1- = . [2] (c) find x when ()x25 51g= . x = . [2] (d) find ()x g1-. ()x g1- = . [2]", "18": "18 0607/41/m/j/20 \u00a9 ucles 2020 11 (a) a b12 cm11 cmnot to scalec 60\u00b0 calculate the shortest distance from b to ac. . cm [7]", "19": "19 0607/41/m/j/20 \u00a9 ucles 2020 (b) r qpv m 8 cm6 cmnot to scale sh cm the diagram shows a pyramid on a rectangular base pqrs . the diagonals of the base meet at m and v is vertically above m. pq = 8 cm, qr = 6 cm and vm = h cm. the volume of the pyramid is 112 cm3. (i) show that h = 7. [2] (ii) calculate the length of vr. vr = cm [3] (iii) k is the mid-point of ps and l is the mid-point of qr. calculate angle kvl. angle kvl = . [3]", "20": "20 0607/41/m/j/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_s20_qp_42.pdf": { "1": "cambridge igcse\u2122this document has 20 pages. blank pages are indicated. dc (st/ct) 182697/2 \u00a9 ucles 2020 [turn over *2221820169* cambridge international mathematics 0607/42 paper 4 (extended) may/june 2020 2 hours 15 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 120. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/42/m/j/20 \u00a9 ucles 2020 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/42/m/j/20 \u00a9 ucles 2020 [turn over answer all the questions. 1 a class of 40 students complete a science test. the table shows the marks of the 40 students. mark 0 1 2 3 4 5 6 7 8 9 10 number of students 1 1 2 5 5 5 6 3 9 2 1 (a) write down the mode. .. [1] (b) work out the range. .. [1] (c) find the median. .. [1] (d) find the interquartile range. . [2] (e) calculate the mean. . [2] (f) two of the students are chosen at random. find the probability that the difference in their marks is 8. . [3]", "4": "4 0607/42/m/j/20 \u00a9 ucles 2020 2 (a) y x \u2013 6\u2013 5\u2013 4\u2013 3\u2013 2\u2013 1 1 0 2 3 4 5 6678910 5 4 3 2 1 \u2013 1 \u2013 2 \u2013 3 \u2013 4 \u2013 5 \u2013 6a bc (i) describe fully the single transformation that maps triangle a onto triangle b. . . [2] (ii) describe fully the single transformation that maps triangle a onto triangle c. . . [3]", "5": "5 0607/42/m/j/20 \u00a9 ucles 2020 [turn over (b) you may use the grid to help you in answering this question. the transformation p is a rotation of 90\u00b0 clockwise about the origin. the transformation q is a reflection in the line yx=- . (i) find the image of the point ,()52- under the transformation p. ( , ) [1] (ii) find the image of the point ,()52- under the transformation q. ( , ) [1] (iii) describe fully the single transformation equivalent to p followed by q. . . [2] (iv) describe fully the single transformation equivalent to q followed by p. . . [2]", "6": "6 0607/42/m/j/20 \u00a9 ucles 2020 3 petra is a singer. she wants to estimate how much to spend on advertising. the table shows the amount spent on advertising, $ x, and the number of tickets sold, y, for 10 performances. amount spent ($ x) 80 60 50 120 90 40 100 110 70 150 number of tickets sold ( y)100 90 60 150 100 75 120 120 100 150 (a) (i) complete the scatter diagram. the first six points have been plotted for you. 0050100 number of tickets sold150 20 40 60 80 amount spent (dollars)100 120 140 160y x [2] (ii) what type of correlation is shown by the scatter diagram? .. [1]", "7": "7 0607/42/m/j/20 \u00a9 ucles 2020 [turn over (b) find the mean amount of money spent on advertising. $ . [1] (c) (i) find the equation of the regression line for y in terms of x. y = . [2] (ii) use your regression line to estimate the number of tickets sold when petra spends $130 on advertising. .. [1] (iii) explain why petra should not rely on this regression line to estimate the number of tickets she will sell if she spends $500 on advertising. . . [1]", "8": "8 0607/42/m/j/20 \u00a9 ucles 2020 4 a piece of metal is in the shape of a cuboid. the cuboid has length 18 cm, width 12 cm and height 12 cm. a cylinder is removed from the cuboid. the cylinder has length 18 cm and radius 4 cm. not to scale18 cm 12 cm 4 cm 12 cm (a) (i) find the volume of the metal remaining after the cylinder has been removed. ... cm3 [3] (ii) write your answer to part (i) in standard form. ... cm3 [1]", "9": "9 0607/42/m/j/20 \u00a9 ucles 2020 [turn over (b) find the total surface area of the metal remaining after the cylinder has been removed. ... cm2 [4] (c) the cylinder removed is melted and formed into 16 identical spheres. (i) calculate the volume of one sphere. ... cm3 [1] (ii) calculate the radius of one sphere. . cm [2]", "10": "10 0607/42/m/j/20 \u00a9 ucles 2020 5 fifty students, 25 boys and 25 girls, were asked which sport they prefer. the results are shown in the table. athletics football swimming tennis boy 4 9 2 10 girl 3 3 12 7 (a) a student is selected at random. calculate the probability that the student chosen is (i) a girl who prefers swimming, .. [1] (ii) a boy who does not prefer football, .. [1] (iii) a student who prefers athletics. .. [1] (b) two of the girls are chosen at random. calculate the probability they both prefer tennis. .. [2]", "11": "11 0607/42/m/j/20 \u00a9 ucles 2020 [turn over (c) two of the students who prefer athletics are chosen at random. calculate the probability that one is a boy and one is a girl. .. [3] (d) three of the 50 students are chosen at random. calculate the probability that one is a boy and two are girls and they all prefer swimming. .. [4]", "12": "12 0607/42/m/j/20 \u00a9 ucles 2020 6 herman bought a motorbike on 1 january 2014. by 1 january 2015 the value of the motorbike had reduced by 16%. by 1 january 2016 the value of the motorbike had reduced by 12% of the value on 1 january 2015. the value of the motorbike on 1 january 2016 was $7392. (a) find how much herman paid for the motorbike. $ . [3] (b) from 2016, the value of the motorbike reduced by 8% each year. calculate the number of complete years it will take for the value of the motorbike to decrease from $7392 to $5000. .. [4]", "13": "13 0607/42/m/j/20 \u00a9 ucles 2020 [turn over 7 y x9 \u2013 3\u2013 6 2 0 (a) ()xx221f=++ (i) on the diagram, sketch the graph of () yx f= for values of x between 6- and 2. [2] (ii) write down the coordinates of the points where the graph crosses the axes. (... , ...) and (... , ...) [2] (iii) write down the equations of the asymptotes of the graph. ... , ... [2] (b) () () xx 4 g2=+ on the diagram, sketch the graph of () yx g= for x61gg-- . [2] (c) solve the equation. () () xxfg= [3] (d) solve the inequality. () () xxfgh [2]", "14": "14 0607/42/m/j/20 \u00a9 ucles 2020 8 northnorth a c db 48\u00b0 6.42 km6.13 km5.37 kmnot to scale the diagram shows four points a, b, c and d on horizontal ground. b is due north of c and c is due east of a. (a) find the bearing of (i) d from a, .. [1] (ii) a from d. .. [1] (b) calculate angle abc . angle abc = . [2]", "15": "15 0607/42/m/j/20 \u00a9 ucles 2020 [turn over (c) calculate the area of quadrilateral abcd . .. mk2 [3] (d) calculate cd. cd = ... km [3] (e) angle acd is acute. find the bearing of d from c. .. [4]", "16": "16 0607/42/m/j/20 \u00a9 ucles 2020 9 ()xx 43 f=- () , xxx111 g ! =- ()xxh2= (a) find (i) ()2f, .. [1] (ii) (( ))4 fg . .. [2] (b) find (( ))1 gg- . .. [2] (c) solve. (( ))x 9 hf = x = or x = [3] (d) find (( ))x 1 f2- in terms of x. give your answer in the form () () kaxb cx d ++ where a, b, c, d and k are integers. .. [3]", "17": "17 0607/42/m/j/20 \u00a9 ucles 2020 [turn over 10 50\u00b0 20\u00b0d c b a 12 mnot to scale the diagram shows a vertical pole cd. abc is a straight line on level ground. find dc. dc = . m [6]", "18": "18 0607/42/m/j/20 \u00a9 ucles 2020 11 (a) solve the equations. (i) x 52 1 += x = . [2] (ii) x6101 -= x = . [2] (iii) () ) ( xx 31 22 47 -= -- x = . [3] (b) (i) solve xx67 32=- . give your answers correct to 3 decimal places. you must show all your working. x = or x = [4]", "19": "19 0607/42/m/j/20 \u00a9 ucles 2020 (ii) solve yy67 342=- . give your answers correct to 3 decimal places. y = or y = [2] (c) solve logl ogx 51 2 += . x = . [4]", "20": "20 0607/42/m/j/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_s20_qp_43.pdf": { "1": "cambridge igcse\u2122this document has 20 pages. blank pages are indicated. dc (st/jg) 182698/2 \u00a9 ucles 2020 [turn over *9976719342* cambridge international mathematics 0607/43 paper 4 (extended) may/june 2020 2 hours 15 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 120. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/43/m/j/20 \u00a9 ucles 2020 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/43/m/j/20 \u00a9 ucles 2020 [turn over answer all the questions. 1 for each sequence, write down the next two terms and find an expression for the nth term. (a) 15, 11, 7, 3, 1-, ... next two terms ... , ... nth term . [3] (b) 1, 2, 4, 8, 16, ... next two terms ... , ... nth term . [3] (c) 4, 10, 18, 28, 40, ... next two terms ... , ... nth term . [3]", "4": "4 0607/43/m/j/20 \u00a9 ucles 2020 2 10 students take a language examination. the examination consists of two parts, a speaking test and a writing test. both tests are marked out of 100. the marks for the students in each of the tests is shown in the table. speaking mark ( x) 86 62 53 34 76 95 30 70 88 72 writing mark ( y) 73 48 44 12 62 66 26 44 90 75 (a) complete the scatter diagram to show these results. the first five points have been plotted for you. 100 80 60 40 20 0 20 10 40 50 30 60 70 80 90 100xy 01030507090 speaking markwriting mark [2] (b) what type of correlation is shown in your scatter diagram? .. [1]", "5": "5 0607/43/m/j/20 \u00a9 ucles 2020 [turn over (c) (i) calculate the equation of the regression line in the form ym xc=+ . y = . [2] (ii) use this equation to estimate a mark in the writing test for a student who scored 48 in the speaking test. .. [1]", "6": "6 0607/43/m/j/20 \u00a9 ucles 2020 3 (a) riaz invests $5000 at a rate of 2.5% per year simple interest. (i) calculate the value of the investment at the end of 4 years. $ . [3] (ii) calculate the number of complete years it will take for the value of the investment to be $6500. .. [2] (b) yasmin invests $5000 at a rate of 2% per year compound interest. (i) calculate the value of yasmin\u2019s investment at the end of 4 years. $ . [3] (ii) calculate the number of complete years it will take for the value of yasmin\u2019s investment to first be worth more than $6500. .. [4]", "7": "7 0607/43/m/j/20 \u00a9 ucles 2020 [turn over 4 030 5xy \u2013 40\u2013 3 ()x xxx 43 18 f32=- -+ (a) on the diagram, sketch the graph of () yx f= for x35gg- . [2] (b) solve the equation ()x 10 f= . x = . , or x = . , or x = . [3] (c) write down the coordinates of (i) the local maximum, ( , ) [2] (ii) the local minimum. ( , ) [1] (d) ()xkf= has only 1 solution. find the ranges of values of k . .. [2]", "8": "8 0607/43/m/j/20 \u00a9 ucles 2020 5 (a) (i) a reflection in the line y3= maps triangle a onto triangle b. describe fully the single transformation that maps triangle b onto triangle a. . . [1] (ii) a translation using the vector 5 4-eo maps triangle c onto triangle d. describe fully the single transformation that maps triangle d onto triangle c. . . [2] (iii) an enlargement, centre (, ) 21-, scale factor 3, maps triangle g onto triangle h. describe fully the single transformation that maps triangle h onto triangle g. . . [2]", "9": "9 0607/43/m/j/20 \u00a9 ucles 2020 [turn over (b) xy 1 2 3 4 5123456 d a 0 \u2013 2 \u2013 3 \u2013 4 \u2013 5 \u2013 6 \u2013 7 \u2013 8 \u2013 9 \u2013 10 \u2013 11 \u2013 1 \u2013 1 \u2013 2 \u2013 3 \u2013 4 (i) rotate triangle a through 90\u00b0 anticlockwise, centre ( -1, 0). label the image b. [2] (ii) enlarge triangle a with scale factor 21- , centre (1, 3). label the image c. [2] (iii) describe fully the single transformation that maps triangle a onto triangle d. . . [3]", "10": "10 0607/43/m/j/20 \u00a9 ucles 2020 6 the cumulative frequency graph shows the heights, in centimetres, of 120 plants in location a. 120 100 80 60cumulative frequency 40 20 0 10 20 40 60 80 10001030507090110 30 50 70 90 height (cm) (a) use the graph to estimate (i) the median, . cm [1] (ii) the interquartile range, . cm [2] (iii) the number of plants over 80 cm in height. .. [2]", "11": "11 0607/43/m/j/20 \u00a9 ucles 2020 [turn over (b) the table gives some information about 120 similar plants in location b. minimum height (cm)lower quartile (cm)median (cm)interquartile range (cm)range (cm) 10 34 50 28 90 (i) on the grid opposite, draw the cumulative frequency curve for the heights of the plants in location b. [3] (ii) use the curves to estimate how many more plants had heights of over 70 cm in location a than in location b. .. [2] (iii) the heights of the plants in location a are more consistent than the heights of the plants in location b. by comparing the shapes of the curves, explain how you know this is true. . . [1]", "12": "12 0607/43/m/j/20 \u00a9 ucles 2020 7 the diagram shows a radio in the shape of a prism. this diagram shows the base of the radio. ae d i hgf c b abc is an equilateral triangle. the circles have their centres at a, b and c and each has a radius of 5 cm. de, fg and hi are tangents to the circles. (a) show that ab = 8.66 cm, correct to 3 significant figures. [3]", "13": "13 0607/43/m/j/20 \u00a9 ucles 2020 [turn over (b) calculate the area of the base of the radio. .. cm2 [4] (c) the height of the radio is 12 cm. calculate the volume of the radio. .. cm3 [1]", "14": "14 0607/43/m/j/20 \u00a9 ucles 2020 8 the number of people living in each house in a street of 100 houses is recorded. the results are shown in the table. number of people frequency 1 5 2 16 3 28 4 32 5 17 6 2 (a) find (i) the range, .. [1] (ii) the median, .. [1] (iii) the mean. .. [2]", "15": "15 0607/43/m/j/20 \u00a9 ucles 2020 [turn over (b) two of the houses are selected at random. find the probability that (i) both had exactly one person living in them, .. [2] (ii) one had exactly 2 people living in it and the other had exactly 3 people living in it, .. [3] (iii) at least one house had fewer than 5 people living in it. .. [2]", "16": "16 0607/43/m/j/20 \u00a9 ucles 2020 9 o xy a bnot to scale c a is the point ( -2, 6), b is the point (3, 2) and c is the point (3, -4). (a) write down the equation of bc. .. [1] (b) find the coordinates of the point m, the mid-point of ac. ( , ) [1] (c) the quadrilateral abcd has rotational symmetry of order 2 about the point m. find the coordinates of the point d. ( , ) [2] (d) find the equation of the perpendicular bisector of ac. .. [4]", "17": "17 0607/43/m/j/20 \u00a9 ucles 2020 [turn over 10 in this question, all lengths are in centimetres. x4x24+ x45+x21+ 30\u00b0not to scale the areas of the two triangles are equal. (a) show that xx81 85 02+- =. [5] (b) solve xx81 85 02+- =. you must show all your working. x = or x = [3] (c) find the area of each of the triangles. .. cm2 [2]", "18": "18 0607/43/m/j/20 \u00a9 ucles 2020 11 80 km 120 kmnot to scalenorth northa b c110\u00b0 the diagram shows the positions of three ports, a, b and c. (a) calculate bc. bc = ... km [3] (b) use the sine rule to calculate angle abc . angle abc = . [3]", "19": "19 0607/43/m/j/20 \u00a9 ucles 2020 [turn over (c) the bearing of c from a is 130\u00b0. find the bearing of b from c. .. [2] (d) a ship leaves b at 13 50 and sails in a straight line towards c. its constant speed is 37 km/h. find the time when it is at its closest point to a. give your answer correct to the nearest minute. .. [5] question 12 is printed on the next page.", "20": "20 0607/43/m/j/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.12 () x x 23 f=+ ()xx 53 g=- (a) find ()4f. .. [1] (b) solve () () xx 5 fg-= . x = . [2] (c) find ()x g1-. ()x g1- = . [2] (d) find and simplify (( ))x fg . .. [2] (e) simplify () () xx23 fg+ . .. [3]" }, "0607_s20_qp_51.pdf": { "1": "cambridge igcse\u2122dc (lk) 187931/2 \u00a9 ucles 2020 [turn overthis document has 8 pages. blank pages are indicated.cambridge international mathematics 0607/51 paper 5 investigation (core) may/june 2020 1 hour 10 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 36. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *1848014657*", "2": "2 0607/51/m/j/20 \u00a9 ucles 2020 answer all the questions. combining triangle numbers this investigation looks at results when adding or subtracting triangle numbers. here is a table of the first 21 triangle numbers, t1 to t21. t1t2t3t4t5t6t7t8t9t10t11t12t13t14t15t16t17t18t19t20t21 1 3 610 15 21 28 36 45 55 66 78 91105 120 136 153 171 190 210 231 1 find the next two triangle numbers. t22 = t23 = [4] 2 (a) complete the table. t11 t2 - t12 t3 - t2 t4 - t3 t5 - t4 t6 - t56 ttnn 1-- [2] (b) (i) tt 100nn 1-=-. write down the value of n. . [1] (ii) write down the difference between the 50th and the 49th triangle numbers. . [1]", "3": "3 0607/51/m/j/20 \u00a9 ucles 2020 [turn over 3 complete the table for adding two consecutive triangle numbers. t11 t2 + t14 t3 + t29 t4 + t3 t5 + t4 t6 + t5 ttnn 1+- [2] 4 (a) use the last row of the table in question 2(a) to complete the equation ttnn 1-=- ... use the last row of the table in question 3 to complete the equation ttnn 1+=- ... by adding these two equations together show that tnn 2 n2 =+. [1] (b) find t1000 . . [2]", "4": "4 0607/51/m/j/20 \u00a9 ucles 2020 5 (a) the table shows the difference of the squares of two consecutive triangle numbers. complete the table. (t1)21 (t2)2 - (t1)2 8 (t3)2 - (t2)2 (t4)2 - (t3)2 (t5)2 - (t4)2 125 (t6)2 - (t5)2 216 (tn)2 - (tn-1)2 [3] (b) calculate the difference between the squares of the 50th and the 49th triangle numbers. . [2] 6 the sum of two different triangle numbers sometimes equals another triangle number. when this happens, we have a triangle triple . example \u2022 start with the triangle number t 63=. \u2022 from the table in question 2(a) tt 665-= . so tt t65 3-= . \u2022 rearrange the equation tt t35 6+= . \u2022 the triangle triple is then (3, 5, 6). the three different numbers must be written in order of increasing size. (a) start with triangle number t 155= and complete the method of the example to find another triangle triple. t15 - = so - = t5 t5 + = the triangle triple is ( 5, , ) [4]", "5": "5 0607/51/m/j/20 \u00a9 ucles 2020 [turn over (b) in the table, each row is a triangle triple. use your answer to part (a) and any patterns you notice to complete the table. triangle triple 3 5 6 4 9 10 5 6 7 [5] (c) use the list of triangle numbers on page 2 to check the triangle triple beginning with 6. [1]", "6": "6 0607/51/m/j/20 \u00a9 ucles 2020 7 (a) the triangle numbers t1 and t3 are not consecutive. they are two apart. complete the table for subtracting triangle numbers that are two apart. t3 - t15 t4 - t2 t5 - t3 t6 - t4 t7 - t513 ttnn 2-- [4] (b) use the triangle number t 459= to find a triangle triple where \u2022 the smallest number is 9 \u2022 the difference between the other two numbers is 2. hints: use the last row of the table in part (a) . use a method similar to that in the example in question 6 . ( 9 , ... , ... ) [4]", "7": "7 0607/51/m/j/20 \u00a9 ucles 2020 blank page", "8": "8 0607/51/m/j/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_s20_qp_52.pdf": { "1": "cambridge igcse\u2122dc (lk/sw) 187930/2 \u00a9 ucles 2020 [turn overthis document has 8 pages. blank pages are indicated.cambridge international mathematics 0607/52 paper 5 investigation (core) may/june 2020 1 hour 10 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 36. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *9477420618*", "2": "2 0607/52/m/j/20 \u00a9 ucles 2020 answer all the questions. investigation dotty polygons this investigation is about the number of dots in shapes that are regular polygons. for any dotty polygon \u2022 p is the number of sides \u2022 n is the number of dots on one side \u2022 there are the same number of dots on each side. example this is a dotty triangle. in this dotty triangle, p3= and n4=. 1 (a) look at the numbers of dots in each row of the example. complete this sum for the total number of dots in the dotty triangle. 1 + 2 + 3 + = [2] (b) for a dotty triangle where n10= , complete this sum and find the total number of dots. 1 + 2 + 3 + + + + + + + = [2] (c) show that nn 222 + gives the correct number of dots when n10= . [2]", "3": "3 0607/52/m/j/20 \u00a9 ucles 2020 [turn over 2 the diagram shows the first four dotty triangles. the number of dots added each time is d. n = 1 n = 2 n = 3 n = 4 d = 1 d = 2 d = 3 d = 4 so, for dotty triangles, dn=. this diagram shows the first three dotty squares. n = 1 n = 2 n = 3 n = 4 d = 1 d = 3 d = 5 d = 7 (a) draw the dotty square for n4= in the space above. [1] (b) (i) write down the total number of dots in each of the first four dotty squares. ... , ... , ... , ... [1] (ii) write down an expression, in terms of n, for the total number of dots in the nth dotty square. . [1] (c) for dotty squares, find a formula for d in terms of n. . [3]", "4": "4 0607/52/m/j/20 \u00a9 ucles 2020 (d) a formula for d, in terms of p (the number of sides) and n is ()dn p p 3 2 =- + - . by substituting appropriate values for p, show that this formula gives (i) the formula for dotty triangles, [2] (ii) your formula for dotty squares. [2]", "5": "5 0607/52/m/j/20 \u00a9 ucles 2020 [turn over 3 (a) for dotty pentagons, show that the formula in question 2(d) becomes dn32=- . [1] (b) this diagram shows the first three dotty pentagons. d = 1 d = 4 d = 7 total = 1 total = 5 total = 12 dotty pentagons grow along the grey lines. this diagram shows how to form the first three dotty pentagons. (i) use dn32=- to find the number of dots that you add to the 3rd dotty pentagon to make the 4th dotty pentagon. . [2] (ii) complete the diagram to show the 4th and 5th dotty pentagons. [2]", "6": "6 0607/52/m/j/20 \u00a9 ucles 2020 (iii) complete the final statement. 1st pentagon + 4 dots = 2nd pentagon 2nd pentagon + 7 dots = 3rd pentagon h\t \t \t h\t h th pentagon + 52 dots = th pentagon [2] 4 (a) this table shows the total number of dots in some dotty polygons. use question 2 , question 3 and any patterns you notice to help you complete this table. position of dotty polygon in its sequence polygon p 1st 2nd 3rd 4th 5th nth triangle 3 1 3 6 10 nn 222 + square 4 1 4 9 pentagon 5 1 5 12 hexagon 6 1 6 [8]", "7": "7 0607/52/m/j/20 \u00a9 ucles 2020 (b) the number of dots in a =\t the number of dots in a dotty pentagon \u00d7 3 dotty triangle (i) give two examples from the table that show this statement is true. [2] (ii) the number of dots in the 4th = the number of dots in the kth dotty pentagon \u00d7 3 dotty triangle find the value of k. . [3]", "8": "8 0607/52/m/j/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_s20_qp_61.pdf": { "1": "cambridge igcse\u2122dc (lk/sg) 187928/1 \u00a9 ucles 2020 [turn overthis document has 12 pages. blank pages are indicated.cambridge international mathematics 0607/61 paper 6 investigation and modelling (extended) may/june 2020 1 hour 40 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer both part a (questions 1 to 8) and part b (questions 9 to 12). \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 60. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *7457115179*", "2": "2 0607/61/m/j/20 \u00a9 ucles 2020 answer both parts a and b. a investigation (questions 1 to 8) combining triangle numbers (30 marks) you are advised to spend no more than 50 minutes on this part. this investigation looks at results when adding, subtracting and multiplying triangle numbers. here is a table of the first 5 triangle numbers, t1 to t5. t1t2t3t4t5 1 3 610 15 1 find the next triangle number. . [2] 2 complete the table for subtracting consecutive triangle numbers. t1 1 t2 - t12 t3 - t2 t4 - t3 t5 - t45 t6 - t5 tn-2 - tn-3 tn-1 - tn-2 tn - tn-1 [2]", "3": "3 0607/61/m/j/20 \u00a9 ucles 2020 [turn over 3 complete the table for adding two consecutive triangle numbers. t1 1 t2 + t1 4 t3 + t2 9 t4 + t3 t5 + t4 t6 + t5 tn + tn-1 [2] 4 use the last row of the table in question 2 to complete equation 1. ttnn 1-=- use the last row of the table in question 3 to complete equation 2. ttnn 1= +- (a) by adding equations 1 and 2 together show that tnn 2 n2 =+. [1] (b) (i) by multiplying equations 1 and 2 together, find a result about the squares of consecutive triangle numbers. [2] (ii) give a numerical example of this result. [2]", "4": "4 0607/61/m/j/20 \u00a9 ucles 2020 5 the sum of two different triangle numbers sometimes equals another triangle number. when this happens, we have a triangle triple . example \u2022 start with the triangle number t 63= \u2022 from the table in question 2 tt 665-= so tt t65 3-= \u2022 rearrange the equation tt t35 6+= \u2022 the triangle triple is then (3, 5, 6) the three different numbers must be written in order of increasing size. (a) start with triangle number t 155= and complete the method of the example to find another triangle triple. t15 - = so - = t5 t5 + = the triangle triple is ( 5, , ) [3] (b) in the table, each row is a triangle triple. use part (a) and any patterns you notice to complete the table. triangle triple 3 5 6 4 5 6 7 [3]", "5": "5 0607/61/m/j/20 \u00a9 ucles 2020 [turn over 6 (a) when you add the last two rows in the table in question 2 , you get an expression for ttnn 2--. this is the difference between triangle numbers that are two apart. give this expression in its simplest form. . [1] (b) (i) find n when tt 15nn 2-=-. . [1] (ii) t 155= use your answer to part (i) to find a triangle triple where \u2022 the smallest number is 5 \u2022 the difference between the other two numbers is 2. ( 5, , ) [2]", "6": "6 0607/61/m/j/20 \u00a9 ucles 2020 7 (a) by adding rows in the table in question 2 , show that tt n33nn 3-= --. this is the difference between triangle numbers that are three apart. [1] (b) t 10514= use part (a) to find a triangle triple where \u2022 the smallest number is 14 \u2022 the difference between the other two numbers is 3. ( 14, , ) [3]", "7": "7 0607/61/m/j/20 \u00a9 ucles 2020 [turn over 8 find all the triangle triples where the smallest number is 14. [5]", "8": "8 0607/61/m/j/20 \u00a9 ucles 2020 b modelling (questions 9 to 12) speed of planets (30 marks) you are advised to spend no more than 50 minutes on this part. this task looks at models for the distance of a planet from the sun and the time it takes to travel once round the sun. the task uses these models to find a model for the speed of a planet. astronomers use astronomical units, au, to measure distance in space. 1 au = the distance from the sun to the earth. 9 in the 18th century, the german astronomer bode numbered the planets venus to neptune from 0 to 7. the table shows his numbers and the distance from the sun to each planet. bode\u2019s number, nplanetdistance from sun, r aubode\u2019s estimates (au) mercury 0.39 0 venus 0.72 0.7 1 earth 1.00 2 mars 1.52 3 unknown 4 jupiter 5.20 5 saturn 9.55 6 uranus 19.22 19.6 7 neptune 30.11 bode estimated the distance from the sun to venus as 0.7 au. after that, for each planet, he used the following rule to estimate the distance of the next planet in the table. double the estimate for the distance and subtract 0.4 (a) complete the table for bode\u2019s estimates. [3] (b) bode\u2019s rule gives a good model for the planets venus to uranus. work out bode\u2019s estimate for neptune. is it a good estimate? . [2]", "9": "9 0607/61/m/j/20 \u00a9 ucles 2020 [turn over (c) find an estimate for mercury using bode\u2019s rule. . [2] 10 bode\u2019s rule requires doubling each time. so a possible model for the distance of a planet from the sun, r au, is abr 2n#=+ where n is bode\u2019s number and a and b are constants that transform the graph of r2n= . (a) write down the two types of transformation used. , [2] (b) using the information for earth and jupiter on page 8, write two equations in a and b. . . [2] (c) show how solving these simultaneous equations gives .. r 03 20 4n#=+ . [2]", "10": "10 0607/61/m/j/20 \u00a9 ucles 2020 11 the table shows the time, t years, it takes a planet to go once round the sun. the table includes the \u2018dwarf planet\u2019 ceres which bode\u2019s rule predicts. planet r (au) t (years) mercury 0.39 0.24 venus 0.72 0.62 earth 1.00 1.00 mars 1.52 1.88 ceres 2.77 4.60 jupiter 5.20 11.86 saturn 9.55 29.46 uranus 19.22 84.01 neptune 30.11 164.80 a possible model for t is tk rp#= where k and p are constants. (a) (i) use the information in the table for earth to find k. . [2] (ii) using the result from part (i) and the information in the table for jupiter, find p correct to 1 decimal place. . [3] (b) write down the model for t in terms of r. is this a good model for the time that it takes mercury to go once round the sun? show how you decide. [2]", "11": "11 0607/61/m/j/20 \u00a9 ucles 2020 [turn over 12 (a) assume that planets travel in a circle with the sun at the centre. use your model in question 11(b) and .. r 03 20 4n#=+ to show that a model for the average speed of a planet is r ..s03 20 42 n#=+, where n is bode\u2019s number and s is measured in au/year. [3] (b) sketch the graph of s for n05gg . 00 5ns [2] questions 12(c) and 12(d) are printed on the next page.", "12": "12 0607/61/m/j/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge. (c) the graph in part (b) is approximately a straight line. find a linear model for s, in terms of n, by finding the equation of this straight line. write the numbers in your model correct to 1 decimal place. . [3] (d) bode\u2019s number for neptune is 7. show that your model does not give a sensible answer for the speed of neptune. [2]" }, "0607_s20_qp_62.pdf": { "1": "cambridge igcse\u2122dc (lk/sg) 187927/2 \u00a9 ucles 2020 [turn overthis document has 12 pages. blank pages are indicated.cambridge international mathematics 0607/62 paper 6 investigation and modelling (extended) may/june 2020 1 hour 40 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer both part a (questions 1 to 6) and part b (questions 7 to 10). \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 60. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *8487829357*", "2": "2 0607/62/m/j/20 \u00a9 ucles 2020 answer both parts a and b. a investigation (questions 1 to 6) dotty polygons (30 marks) you are advised to spend no more than 50 minutes on this part. this investigation is about the number of dots in shapes that are regular polygons. for any polygon \u2022 p is the number of sides \u2022 n is the number of dots on one side \u2022 there are the same number of dots on each side. 1 this is a dotty triangle. in this dotty triangle, p = 3 and n = 4. (a) look at the numbers of dots in each row of the triangle. complete this sum for the total number of dots in the triangle. 1 + 2 + 3 + . = . [1] (b) show that nn 222 + gives the correct number of dots when n = 10. [3]", "3": "3 0607/62/m/j/20 \u00a9 ucles 2020 [turn over 2 the diagram shows the first four dotty triangles. the number of dots added each time is d. n = 1 n = 2 n = 3 n = 4 d = 1 d = 2 d = 3 d = 4 so, for dotty triangles, d = n. this diagram shows the first four dotty squares. n = 1 n = 2 n = 3 n = 4 d = 1 d = 3 d = 5 d = 7 (a) find an expression, in terms of n, for the total number of dots in the nth dotty square. . [1] (b) for dotty squares, find a formula for d in terms of n. . [2]", "4": "4 0607/62/m/j/20 \u00a9 ucles 2020 3 (a) a formula for d, in terms of p (the number of sides) and n is ()dp np23 =- + - . for dotty pentagons, show that the formula becomes dn32=- . [1] (b) this diagram shows the first three dotty pentagons. d = 1 d = 4 d = 7 total = 1 total = 5 total = 12 dotty pentagons grow along the grey lines. this diagram shows how to form the first three dotty pentagons. complete the diagram to show the 4th and 5th dotty pentagons. [2]", "5": "5 0607/62/m/j/20 \u00a9 ucles 2020 [turn over 4 (a) this table shows the total number of dots in some dotty polygons. use question 2 , question 3 and any patterns you notice to help you complete this table. position of dotty polygon in its sequence polygon p 1st 2nd 3rd 4th 5th nth triangle 3 1 3 6 10 nn 222 + square 4 1 4 9 16 pentagon 5 1 5 12 hexagon 6 1 6 [8] (b) complete this expression, in terms of n, for the total number of dots in any dotty pentagon. n 232 [3]", "6": "6 0607/62/m/j/20 \u00a9 ucles 2020 5 (a) use question 4 and any patterns you notice to help you complete this table. polygon ptotal number of dots (n) triangle 3 nn 222 + square 4 pentagon 5 hexagon 6 ... n- [2] (b) find, in terms of n and p, an expression for the total number of dots in any dotty polygon. . [3]", "7": "7 0607/62/m/j/20 \u00a9 ucles 2020 [turn over 6 when p = 50, the total number of dots in the nth dotty polygon + 865=the total number of dots in the (n + 1)th dotty polygon. find the value of n. . [4]", "8": "8 0607/62/m/j/20 \u00a9 ucles 2020 b modelling (questions 7 to 10) stopping a car (30 marks) you are advised to spend no more than 50 minutes on this part. this task is about the distance a car travels as it stops. 7 (a) show that a speed of 130 km/h is approximately 36 m/s. [2] (b) a car travels at 130 km/h. a model for the distance travelled, d metres, in time t seconds, is dt36= . write a similar model for a car travelling at 80 km/h. . [2]", "9": "9 0607/62/m/j/20 \u00a9 ucles 2020 [turn over (c) on the diagram, sketch both models for t03gg . d t3 00 time (seconds)distance (metres) [3] (d) on your sketch, shade the region showing the distances travelled at speeds from 80 km/h to 130 km/h for t03gg . [1] 8 when a driver looks at a mobile phone they do not look at the road. on average, they look at their mobile phone for 2 seconds. for speeds between 80 km/h and 130 km/h, find the range of distances that the car travels in these 2 seconds. g distance g [3]", "10": "10 0607/62/m/j/20 \u00a9 ucles 2020 9 a car continues to travel after the brakes are applied. the distance travelled is the braking distance , b metres. a model for b is bfv 202 = where v is the speed of the car in metres per second f is a measure of grip the tyre has on the road. (a) when the road is dry the value of f is 0.7 . write, and simplify, the model for b when the road is dry. . [2] (b) when the road is icy the value of f is 0.3 . write, and simplify, the model for b when the road is icy. . [2] (c) on the diagram, sketch both models for v02 0 gg . b v20 00 speed (m/s)braking distance (metres) [3]", "11": "11 0607/62/m/j/20 \u00a9 ucles 2020 [turn over (d) a car travels at 60 km/h. (i) on the diagram in part (c) , sketch a vertical line at 60 km/h. [2] (ii) find how much greater the braking distance is when the road is icy than when the road is dry. . [3] question 10 is printed on the next page.", "12": "12 0607/62/m/j/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.10 glen is driving his car when an emergency happens. he usually takes 0.7 seconds to react before braking. because he is looking at his mobile phone he takes an extra 2 seconds to react. the weather is wet and the measure of grip the tyre has on the road is 0.5 . glen is driving at x km/h. (a) show that x km/h is approximately 0.28 x m/s. [2] (b) the total stopping distance is the distance the car travels from when the emergency happens to when the car stops. use question 8 and question 9 to find, in terms of x, a model for glen\u2019s total stopping distance in metres. give your answer as simply as possible. . [5]" }, "0607_s20_qp_63.pdf": { "1": "cambridge igcse\u2122dc (lk/sg) 187926/2 \u00a9 ucles 2020 [turn overthis document has 12 pages. blank pages are indicated.cambridge international mathematics 0607/63 paper 6 investigation and modelling (extended) may/june 2020 1 hour 40 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer both part a (questions 1 to 6) and part b (questions 7 to 11). \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 60. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *4683457078*", "2": "2 0607/63/m/j/20 \u00a9 ucles 2020 answer both parts a and b. a investigation (questions 1 to 6) digital roots (30 marks) you are advised to spend no more than 50 minutes on this part. this investigation is about the digital roots of positive integers. to find the digital root of a positive integer, add its digits and, if necessary, the digits of the resulting number and so on until a single digit remains. examples the digital root of 7: = 7 the digital root of 23: 2 + 3 = 5 the digital root of 78: 7 + 8 = 15 1 + 5 = 6 the digital root of 199: 1 + 9 + 9 = 19 1 + 9 = 10 1 + 0 = 1 1 (a) find the digital root of 2067. . [2] (b) the digital root of 295 is 7. this can be written as d(295) = 7. find d(173). . [1] (c) find a 3-digit number with a digital root of 4. . [1]", "3": "3 0607/63/m/j/20 \u00a9 ucles 2020 [turn over 2 (a) write down the maximum value of a digital root. . [1] (b) find a number, greater than 9500, which will give this maximum value for its digital root. . [2] 3 (a) use some values of x to find the relationship between d( x) and d( x + 9). .. [3] (b) find the relationship between d( x) and d( x + 9n) where n is a positive integer. [2]", "4": "4 0607/63/m/j/20 \u00a9 ucles 2020 4 (a) complete this table. x y d(x)d(y) d(x # y) d(d( x) # d(y)) 63 101 9 2d(63 # 101) = d(6363) = d(18) = 9d(9 # 2) = d(18) = 9 315 76 9 4d(315 # 76) = d(23940) = d(...) = ...d(9 # 4) = d(36) = 9 253 42 1 6d(1 # 6) = d(6) = 6 [3] (b) write down an algebraic relationship between d( x \u00d7 y) and d(d( x) \u00d7 d( y)). .. [1] (c) d(x2) = (d(x))2 is this statement correct? show how you decide. .. because [2]", "5": "5 0607/63/m/j/20 \u00a9 ucles 2020 [turn over 5 the diagram shows some values of d( x3) plotted against values of x from 1 to 10. 00123456789 5 10 xd(x3) (a) complete the diagram. [2] (b) find the nth term of the sequence of values of x for which d( x3) = 8 . . [2] (c) use digital roots to decide whether 1 000 030 300 106 031 030 301 is a cube number. give a reason for your answer. [2]", "6": "6 0607/63/m/j/20 \u00a9 ucles 2020 6 (a) pn is the nth prime number. the diagram shows the value of d( pn) for the 5th to the 50th prime number. 00 5 10 15 20 25 30 35 40 45 50123456789 d(pn) n (i) complete the diagram for the first four prime numbers. [1] (ii) is it possible to use the diagram to predict d( p51)? give a reason for your answer. . [1]", "7": "7 0607/63/m/j/20 \u00a9 ucles 2020 [turn over (b) this diagram shows the frequency of the digital roots for the first 1200 prime numbers. 1 2 3 4 5 digital rootfrequency 050100150200 6 7 8 9 (i) write down two observations from the diagram about the digital roots of these prime numbers. 1 .. 2 .. [2] (ii) 4 \u2026 27 is a 4-digit number which is not a prime number. use the diagram to find a possible missing digit. . [2]", "8": "8 0607/63/m/j/20 \u00a9 ucles 2020 b modelling (questions 7 to 11) earthquakes (30 marks) you are advised to spend no more than 50 minutes on this part. the task is about the strength and frequency of earthquakes and the probability of their occurrence. the strength of an earthquake is measured in magnitudes. an increase in magnitude of 1 increases the energy released by the earthquake by a factor of 32. example a magnitude 4.7 earthquake releases 32 times as much energy as a magnitude 3.7 earthquake. 7 (a) write down the magnitude of an earthquake that releases 32 times the energy of a magnitude 2.5 earthquake. . [1] (b) a magnitude 6 earthquake releases 30 000 units of energy. calculate the number of units of energy a magnitude 7 earthquake releases. . [2]", "9": "9 0607/63/m/j/20 \u00a9 ucles 2020 [turn over 8 a model for the energy, e, that an earthquake releases is e = g # h1.5m where g and h are constants and m is the magnitude of the earthquake. (a) an earthquake of magnitude 6 releases 30 000 units of energy. write an equation involving g and h. . [1] (b) an earthquake of magnitude 8 releases 30 000 000 units of energy, correct to 1 significant figure. write an equation involving g and h. . [1] (c) use part (a) and part (b) to find (i) the value of h, . [3] (ii) the value of g. . [2] (d) the magnitude of an earthquake is 6.2 . calculate the number of units of energy that it releases. . [2]", "10": "10 0607/63/m/j/20 \u00a9 ucles 2020 9 this table shows information about the number of earthquakes in northern chile between april 2008 and april 2018. minimum magnitude (m)number of earthquakes (n) 3.5 2028 4.0 1912 4.5 784 5.0 230 5.5 57 6.0 14 6.5 3 7.0 0 there were a total of 2028 earthquakes with . m 35h . there were a total of 2028 - 1912 = 116 earthquakes with a magnitude in the range .. m 35 401g . (a) find the number of earthquakes in the range . m 56 51g . . [2] (b) a model for this data is nmk= , where k is a constant and n is the number of earthquakes with minimum magnitude m. is this a suitable model? show how you decide. [2]", "11": "11 0607/63/m/j/20 \u00a9 ucles 2020 [turn over 10 another model for these earthquakes is . log cm n 715 =+ where c is a constant. (a) complete the table for log n, correct to 1 decimal place. m n logn 3.5 2028 3.3 4.0 1912 3.3 4.5 784 2.9 5.0 230 2.4 5.5 57 6.0 14 6.5 3 [2] (b) complete this scatter diagram of log n against m. the first four points have been plotted for you. 4 3.5 3 2.5 2 1.5 1 0.5 0 3 3.5 4 4.5 5 5.5 6 6.5 7logn m [1] (c) (i) the mean point is (5, 2.2). on the diagram, draw a line of best fit. [1] (ii) use your line of best fit to find the value of c. . [2] question 11 is printed on the next page.", "12": "12 0607/63/m/j/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.11 a model for the number of earthquakes, n, in san francisco between 1950 and 2018 is n = 10 (6.6-0.91 m), where m is the minimum magnitude. (a) there were 1013 earthquakes with a minimum magnitude of 4 during this time. find the difference between this actual number and the number that the model predicts. . [2] (b) use the model to estimate the total number of earthquakes of any magnitude. . [2] (c) (i) on the diagram, sketch the graph of n for .. m 35 70 gg . 0 3.5 7n m [3] (ii) what effect would another earthquake of magnitude 7.0 in this period have on the graph? . [1]" }, "0607_w20_qp_11.pdf": { "1": "dc (nf/sg) 188559/3 \u00a9 ucles 2020 [turn overthis document has 12 pages. blank pages are indicated.cambridge international mathematics 0607/11 paper 1 (core) october/november 2020 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *4821146894*cambridge igcse\u2122", "2": "2 0607/11/o/n/20 \u00a9 ucles 2020 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/11/o/n/20 \u00a9 ucles 2020 [turn over answer all the questions. 1 work out. 15 32'+ .. [1] 2 change 400 centimetres into metres. ... m [1] 3 complete the mapping diagram. x 3 4 5 65 6 .. 8f(x) [1] 4 a bd cnot to scale (a) write down the mathematical name for this quadrilateral. .. [1] (b) write down the mathematical name for the angle at b. .. [1] 5 write down the mathematical name for the perimeter of a circle. .. [1]", "4": "4 0607/11/o/n/20 \u00a9 ucles 2020 6 ajay is facing east. he turns 90 \u00b0 clockwise. write down the direction he is now facing. .. [1] 7 \u2013 4\u2013 3\u2013 2\u2013 1 102 3 4y x4 3 2 1 \u2013 1 \u2013 2 \u2013 3 \u2013 4 on the grid, plot the point (2, 3). [1] 8 some students were each asked to name their favourite subject. the bar chart shows the results. mathematics science english40 35 30 25 20 15 10 5 0girls boysnumber of students (a) work out how many more boys than girls named english as their favourite subject. .. [1] (b) work out how many students named mathematics as their favourite subject. .. [1]", "5": "5 0607/11/o/n/20 \u00a9 ucles 2020 [turn over 9 imran records data about cars. put a tick (\u2713) in each row to show whether the data is discrete or continuous. data discrete continuous number of seats kilometres per litre age in complete years maximum speed [2] 10 the list shows the mark for each of eleven students in an examination. 17 23 12 36 14 28 20 19 15 32 29 (a) find the range. .. [1] (b) find the median. .. [2] (c) find the upper quartile. .. [1] 11 write 526.316 correct to 2 significant figures. \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd [1]", "6": "6 0607/11/o/n/20 \u00a9 ucles 2020 12 a is the point (3, 2) and b is the point (3, 4). find the length of ab. .. [1] 13 01 123456782c d34 xy find the coordinates of the mid-point of the line cd. ( ... , ...) [1] 14 y x l2 \u2013 2 \u2013 224 0 \u2013 4\u2013 4 4 write down the equation of the line l. .. [1] 15 show the inequality n491g on the number line. 2 3 4 5 6 7 8 9 10n [2]", "7": "7 0607/11/o/n/20 \u00a9 ucles 2020 [turn over 16 solve . x42 0= x = . [1] 17 (a) \u2013 1 1 2 3 4 5 6xy \u2013 11 023456 \u2013 2 \u2013 3 \u2013 4 \u2013 5 \u2013 6\u2013 2 \u2013 3 \u2013 4 \u2013 5 \u2013 6 reflect the triangle in the line . x 1=- [2] (b) \u2013 1 1 2xy \u2013 1012 \u2013 2 \u2013 3\u2013 2 33 \u2013 3 rotate the triangle through 90\u00b0 anti-clockwise about the origin. [2]", "8": "8 0607/11/o/n/20 \u00a9 ucles 2020 18 these diagrams show three different types of correlation. oa ob oc (a) write down the letter of the diagram which shows negative correlation. .. [1] (b) the number of bottles of water sold in a shop increases as the temperature rises. which diagram, a, b or c, shows this correlation? .. [1] 19 5 m 1 m2 m15 m 2 m12 m 3 mnot to scale work out the shaded area. . m2 [3]", "9": "9 0607/11/o/n/20 \u00a9 ucles 2020 [turn over 20 (a) xiong spins a fair 5-sided spinner, numbered 1, 2, 3, 4, 5, two times. complete the tree diagram. 514 not 44 not 4 4 not 4 .. .. ..score on first spin score on second spin [2] (b) ed bac this fair 5-sided spinner is spun 200 times. work out the expected number of times it lands on c. .. [2]", "10": "10 0607/11/o/n/20 \u00a9 ucles 2020 21 a b c 8 cmnot to scale in the right -angled triangle abc , bc = 8 cm. . sinc 06= . cosc 08= . tanc 075 = find the length of ab\ufffd . cm [2] 22 find the lowest common multiple (lcm) of 10 and 12. .. [2]", "11": "11 0607/11/o/n/20 \u00a9 ucles 2020 blank page", "12": "12 0607/11/o/n/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_w20_qp_12.pdf": { "1": "cambridge igcse\u2122cambridge international mathematics 0607/12 paper 1 (core) october/november 2020 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ]. this document has 12 pages. blank pages are indicated. dc (lk/cb) 188558/2 \u00a9 ucles 2020 [turn over *3852725810*", "2": "2 0607/12/o/n/20 \u00a9 ucles 2020 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/12/o/n/20 \u00a9 ucles 2020 [turn over answer all the questions. 1 work out. 35-+ .. [1] 2 27 32 35 36 39 42 from the list, write down the square number. .. [1] 3 (a) y x0123456 123456 on the grid, plot the point (5, 3). [1] (b) y l x012345 12345 write down the coordinates of any point on the straight line, l. ( ... , ... ) [1]", "4": "4 0607/12/o/n/20 \u00a9 ucles 2020 4 the diagram shows a shape on a cm12 grid. estimate the area of this shape. .. cm2 [1] 5 write 103 as a decimal. .. [1] 6 work out 13 1 of 77. .. [1] 7 insert brackets to make this calculation correct. 3 \u00d7 2 + 4 = 18 [1]", "5": "5 0607/12/o/n/20 \u00a9 ucles 2020 [turn over 8 01020304050 number of visitors walk bike carsaturday sunday bus60708090 the bar chart shows some information about the way visitors travel to a museum. (a) 20 visitors walked on saturday and 30 visitors walked on sunday. complete the bar chart. [1] (b) find how many more visitors arrived by bus than by car on saturday. .. [1] 9 the probability that joanna is late for school is 0.15 . find the probability that joanna is not late for school. .. [1]", "6": "6 0607/12/o/n/20 \u00a9 ucles 2020 10 pattern 1 pattern 2 pattern 3 there are 3 rods in pattern 1. write down the number of rods in pattern 5. .. [1] 11 (a) 30\u00b0 40\u00b0105\u00b0not to scale b a explain why line ab cannot be a straight line. . [1] (b) 30\u00b0 c\u00b0not to scale complete the statement. c = because [2]", "7": "7 0607/12/o/n/20 \u00a9 ucles 2020 [turn over 12 by writing each number correct to 1 significant figure, find an estimate of (. .) . 6983 04 7992# + . .. [2] 13 \u2013 5\u2013 4\u2013 3\u2013 2\u2013 1 0 1 2 3 4 5n complete the statement using ,,, or 12gh= . this number line shows the inequality -2 ... n ... 4. [2] 14 not to scale10 cm 3 cm3 cm the diagram shows a square-based pyramid of base length 3 cm and vertical height 10 cm. calculate the volume of this pyramid. .. cm3 [3]", "8": "8 0607/12/o/n/20 \u00a9 ucles 2020 15 (a) y x123456789101112 0123456789 13 on the grid, translate the triangle by the vector 4 2-eo . [2] (b) \u2013 1 12345678 \u2013 2 \u2013 3 \u2013 4 \u2013 5 \u2013 6 \u2013 7 \u2013 8\u2013 1 \u2013 2 \u2013 3 \u2013 4 \u2013 5 \u2013 6 \u2013 77 6 5 4 3 2 1 0y x on the grid, enlarge the shape by scale factor 3 about the point (4, 2). [2]", "9": "9 0607/12/o/n/20 \u00a9 ucles 2020 [turn over 16 north p q measure the bearing of p from q. .. [1] 17 y x the scatter diagram shows 11 crosses. 10 of the crosses represent data. the point marked y x is the mean point. on the grid, draw a line of best fit. [2] 18 make x the subject of the formula. ya x5 += x = . [2]", "10": "10 0607/12/o/n/20 \u00a9 ucles 2020 19 find the highest common factor (hcf) of 15 and 21. .. [1] 20 y cm50 cm x\u00b0not to scale sinx135= cosx1312= tanx125= find the value of y. y = . [2]", "11": "11 0607/12/o/n/20 \u00a9 ucles 2020 [turn over 21 the diagram shows the graph of ()fx y= . y x0 2 \u2013 2 \u2013 22 here are four more graphs, a, b, c and d. y xy x y xy x0 2 \u2013 2 \u2013 22 0 2a b c d\u2013 2 \u2013 22 0 2 \u2013 2 \u2013 22 0 2 \u2013 2 \u2013 22 write down the letter of the graph which shows (a) ()f yx 2 =+ , . [1] (b) ()f yx 2 =+ . . [1] question 22 is printed on the next page.", "12": "12 0607/12/o/n/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.22 y x1 2 3 4 5 0123456 ab 7 (a) write down the equation of line a. .. [1] (b) find the equation of line b. .. [3]" }, "0607_w20_qp_13.pdf": { "1": "cambridge igcse\u2122cambridge international mathematics 0607/13 paper 1 (core) october/november 2020 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ]. this document has 12 pages. blank pages are indicated. dc (mb) 202083 \u00a9 ucles 2020 [turn over *1734374453*", "2": "2 0607/13/o/n/20 \u00a9 ucles 2020 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/13/o/n/20 \u00a9 ucles 2020 [turn over answer all the questions. 1 work out. 35-+ .. [1] 2 27 32 35 36 39 42 from the list, write down the square number. .. [1] 3 (a) y x0123456 123456 on the grid, plot the point (5, 3). [1] (b) y l x012345 12345 write down the coordinates of any point on the straight line, l. ( ... , ... ) [1]", "4": "4 0607/13/o/n/20 \u00a9 ucles 2020 4 the diagram shows a shape on a cm12 grid. estimate the area of this shape. .. cm2 [1] 5 write 103 as a decimal. .. [1] 6 work out 13 1 of 77. .. [1] 7 insert brackets to make this calculation correct. 3 \u00d7 2 + 4 = 18 [1]", "5": "5 0607/13/o/n/20 \u00a9 ucles 2020 [turn over 8 01020304050 number of visitors walk bike carsaturday sunday bus60708090 the bar chart shows some information about the way visitors travel to a museum. (a) 20 visitors walked on saturday and 30 visitors walked on sunday. complete the bar chart. [1] (b) find how many more visitors arrived by bus than by car on saturday. .. [1] 9 the probability that joanna is late for school is 0.15 . find the probability that joanna is not late for school. .. [1]", "6": "6 0607/13/o/n/20 \u00a9 ucles 2020 10 pattern 1 pattern 2 pattern 3 there are 3 rods in pattern 1. write down the number of rods in pattern 5. .. [1] 11 (a) 30\u00b0 40\u00b0105\u00b0not to scale b a explain why line ab cannot be a straight line. . [1] (b) 30\u00b0 c\u00b0not to scale complete the statement. c = because [2]", "7": "7 0607/13/o/n/20 \u00a9 ucles 2020 [turn over 12 by writing each number correct to 1 significant figure, find an estimate of (. .) . 6983 04 7992# + . .. [2] 13 \u2013 5\u2013 4\u2013 3\u2013 2\u2013 1 0 1 2 3 4 5n complete the statement using ,,, or 12gh= . this number line shows the inequality -2 ... n ... 4. [2] 14 not to scale10 cm 3 cm3 cm the diagram shows a square-based pyramid of base length 3 cm and vertical height 10 cm. calculate the volume of this pyramid. .. cm3 [3]", "8": "8 0607/13/o/n/20 \u00a9 ucles 2020 15 (a) y x123456789101112 0123456789 13 on the grid, translate the triangle by the vector 4 2-eo . [2] (b) \u2013 1 12345678 \u2013 2 \u2013 3 \u2013 4 \u2013 5 \u2013 6 \u2013 7 \u2013 8\u2013 1 \u2013 2 \u2013 3 \u2013 4 \u2013 5 \u2013 6 \u2013 77 6 5 4 3 2 1 0y x on the grid, enlarge the shape by scale factor 3 about the point (4, 2). [2]", "9": "9 0607/13/o/n/20 \u00a9 ucles 2020 [turn over 16 north p q measure the bearing of p from q. .. [1] 17 y x the scatter diagram shows 11 crosses. 10 of the crosses represent data. the point marked y x is the mean point. on the grid, draw a line of best fit. [2] 18 make x the subject of the formula. ya x5 += x = . [2]", "10": "10 0607/13/o/n/20 \u00a9 ucles 2020 19 find the highest common factor (hcf) of 15 and 21. .. [1] 20 y cm50 cm x\u00b0not to scale sinx135= cosx1312= tanx125= find the value of y. y = . [2]", "11": "11 0607/13/o/n/20 \u00a9 ucles 2020 [turn over 21 the diagram shows the graph of ()fx y= . y x0 2 \u2013 2 \u2013 22 here are four more graphs, a, b, c and d. y xy x y xy x0 2 \u2013 2 \u2013 22 0 2a b c d\u2013 2 \u2013 22 0 2 \u2013 2 \u2013 22 0 2 \u2013 2 \u2013 22 write down the letter of the graph which shows (a) ()f yx 2 =+ , . [1] (b) ()f yx 2 =+ . . [1] question 22 is printed on the next page.", "12": "12 0607/13/o/n/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.22 y x1 2 3 4 5 0123456 ab 7 (a) write down the equation of line a. .. [1] (b) find the equation of line b. .. [3]" }, "0607_w20_qp_21.pdf": { "1": "cambridge igcse\u2122*8147553465* dc (pq) 187921/1 \u00a9 ucles 2020 [turn overthis document has 8 pages. blank pages are indicated.cambridge international mathematics 0607/21 paper 2 (extended) october/november 2020 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/21/o/n/20 \u00a9 ucles 2020 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/21/o/n/20 \u00a9 ucles 2020 [turn over answer all the questions. 1 work out. 12 34# +- . [1] 2 work out. 48 8'-- . [1] 3 simplify fully. x x 125 154# . [2] 4 solve. () x 31 49 -- = x= . [3] 5 divide 120 in the ratio 3 : 5. ... , ... [2]", "4": "4 0607/21/o/n/20 \u00a9 ucles 2020 6 the mean of 5 numbers is 12. the mean of 3 of these numbers is 8. find the mean of the other two numbers. . [3] 7 y varies inversely as x. when x3=, y16= . find x when y6=. x= . [3] 8 4 3a=- -eo 2 1b=-eo (a) find 3ab- . fp [2] (b) find the magnitude of 4 3- -eo . . [2]", "5": "5 0607/21/o/n/20 \u00a9 ucles 2020 [turn over 9 a shop has a sale and all prices are reduced by 20%. (a) the original price of a shirt is $16. find the sale price of the shirt. $ . [2] (b) the sale price of a dress is $40. find the original price of the dress. $ . [2] 10 factorise. (a) x81 4+ . [1] (b) ax bx 8623- . [2] (c) ax ay bx by 698 12 +- - . [2]", "6": "6 0607/21/o/n/20 \u00a9 ucles 2020 11 work out 423-. . [2] 12 the table shows the marks of 80 students in an examination. mark ( x) frequency x 01 0 1g 8 x 10 151g 16 x 15 201g 25 x 20 301g 17 x 30 501g 14 (a) on the grid, draw a cumulative frequency curve to show this information. 001020304050607080 10 20 30 markcumulative frequency 40 50x [4] (b) use your graph to estimate the median mark of the students. . [1]", "7": "7 0607/21/o/n/20 \u00a9 ucles 2020 13 a is the point (1, 7) and b is the point (4, 1). find the equation of the perpendicular bisector of ab in the form ym xc=+ . y= . [5]", "8": "8 0607/21/o/n/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_w20_qp_22.pdf": { "1": "cambridge igcse\u2122*4440708064* dc (pq/sw) 187920/1 \u00a9 ucles 2020 [turn overthis document has 8 pages. blank pages are indicated.cambridge international mathematics 0607/22 paper 2 (extended) october/november 2020 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/22/o/n/20 \u00a9 ucles 2020 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/22/o/n/20 \u00a9 ucles 2020 [turn over answer all the questions. 1 a quadrilateral has rotational symmetry of order two, two lines of symmetry and its angles are not right angles. what is the special name of this quadrilateral? . [1] 2 work out the exact value of 972. . [2] 3 these are the first four terms in a sequence. 27 19 11 3 (a) write down the next term. . [1] (b) find an expression, in terms of n, for the nth term of the sequence. . [2] 4 work out 6432-`j . . [2] 5 vu at =+ find v when u5=, a 3=- and t4=. v= ... [2]", "4": "4 0607/22/o/n/20 \u00a9 ucles 2020 6 not to scale8 cm 6 cm the four vertices of the rectangle each lie on the circle. find the shaded area. give your answer, in terms of r, in its simplest form. .. cm2 [4] 7 5 numbers have a mean of 12. when a 6th number is included the mean is 9. work out the 6th number. . [2]", "5": "5 0607/22/o/n/20 \u00a9 ucles 2020 [turn over 8 written as the product of its prime factors, 540 23523##= . (a) write 360 as a product of its prime factors. . [2] (b) find the highest common factor (hcf) of 540 and 360. . [1] (c) 540n is a cube number. find the smallest possible value of n. . [1] 9 pierre records the colour of each of 200 cars passing his home. the table shows the results. colour silver black red green blue other frequency 23 68 35 20 32 22 (a) write down the relative frequency of a silver car. . [1] (b) explain why it is reasonable to use the answer to part (a) as the probability that the next car which passes will be silver. . [1] (c) over the whole day 1200 vehicles pass pierre\u2019s home. estimate the number of these cars that are silver. . [1]", "6": "6 0607/22/o/n/20 \u00a9 ucles 2020 10 factorise (a) xx 62-- , . [2] (b) ax bx by ay 324 6 +- - . . [2] 11 (a) in each venn diagram, shade the given set. u a bu a b ab, ()ab+ l [2] (b) in this venn diagram, the number of elements in each of the subsets is shown. u p 12 47 6 11 853 rq find. (i) (( )) pq r n,+ . [1] (ii) (( ))' pq r n,+ . [1]", "7": "7 0607/22/o/n/20 \u00a9 ucles 2020 [turn over 12 a b p c qdnot to scale 110\u00b030\u00b0 the points a, b, c and d lie on a circle. pcq is a tangent to the circle at c. angle abc 110\u00b0= and angle \u00b0 bac 30= . find (a) angle adc , angle adc= . [1] (b) angle acp , angle acp= . [1] (c) angle pcb . angle pcb= [1] 13 (a) find log91 3eo. . [1] (b) solve logl og log x25 15 += . . [2] question 14 is printed on the next page.", "8": "8 0607/22/o/n/20 \u00a9 ucles 2020 14 a rectangular piece of paper has sides of length a cm and b cm. the paper is cut in half. ba not to scale the ratio of the length of the longer side to the length of the shorter side in both pieces of paper is the same. find a in terms of b. a= . [3] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge." }, "0607_w20_qp_23.pdf": { "1": "cambridge igcse\u2122*8904149492* dc (pq/sw) 187919/1 \u00a9 ucles 2020 [turn overthis document has 8 pages. blank pages are indicated.cambridge international mathematics 0607/23 paper 2 (extended) october/november 2020 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/23/o/n/20 \u00a9 ucles 2020 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/23/o/n/20 \u00a9 ucles 2020 [turn over answer all the questions. 1 work out (. )023. . [1] 2 solve the equation. x27 3 -=- x= . [2] 3 work out 65 1615' . give your answer as a fraction in its lowest terms. . [2] 4 find the integer values of x when x131g- . . [2] 5 solve the simultaneous equations. pq23 7 -= pq32+= p= . q= . [2]", "4": "4 0607/23/o/n/20 \u00a9 ucles 2020 6 find the area of the sector. give your answer, in terms of r, in its simplest form. not to scale 8 cm45\u00b08 cm .. cm2 [2] 7 find, as a fraction, the value of siny. not to scale 5 cm 12 cmy siny= . [3] 8 find the value of (a) 213- bl , . [1] (b) log 1255. . [1]", "5": "5 0607/23/o/n/20 \u00a9 ucles 2020 [turn over 9 simplify xx4545# . .. [2] 10 () jm kh22=+ rearrange the formula to make h the subject. h= . [3] 11 not to scalex cm8 cm 60\u00b0 10 cm find the value of x2. x2= [3]", "6": "6 0607/23/o/n/20 \u00a9 ucles 2020 12 not to scale56\u00b0 y\u00b0 ba c in the diagram, a, b and c are points on parallel lines. ac bc= . work out the value of y. y= . [3] 13 pq 23 32 62-= + `j find the value of p and the value of q. p= . q= . [3]", "7": "7 0607/23/o/n/20 \u00a9 ucles 2020 [turn over 14 y varies inversely as x32-`j . when x1=, y4=. find y in terms of x. y= . [2] 15 logl og log x23 52 =- find the value of x. x= . [2] 16 a is acute and tan xa=. find, in terms of x, (a) ()tan 180 a-, ()tan 180 a-= . [1] (b) ()tan09a-. ()tan90a-= [1] question 17 is printed on the next page.", "8": "8 0607/23/o/n/20 \u00a9 ucles 2020 17 simplify. xxy ax ay xy36 2 232-- + - . [4] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge." }, "0607_w20_qp_31.pdf": { "1": "cambridge igcse\u2122this document has 20 pages. blank pages are indicated. dc (st/ct) 183466/2 \u00a9 ucles 2020 [turn over *4792580888* cambridge international mathematics 0607/31 paper 3 (core) october/november 2020 1 hour 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 96. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/31/o/n/20 \u00a9 ucles 2020 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/31/o/n/20 \u00a9 ucles 2020 [turn over answer all the questions. 1 (a) write down the fraction of the shape that is shaded. .. [1] (b) shade 30% of this shape. [1] (c) write as a decimal. (i) 60% .. [1] (ii) 43 .. [1] (d) work out. (i) 63 .. [1] (ii) .. . 59 33 23'+ give your answer correct to 2 decimal places. .. [2]", "4": "4 0607/31/o/n/20 \u00a9 ucles 2020 2 (a) (i) write down the mathematical name of this shape. .. [1] (ii) write down the number of lines of symmetry of the shape. .. [1] (iii) write down the order of rotational symmetry of the shape. .. [1] (iv) on the shape, draw one line to divide it into two congruent triangles. [1]", "5": "5 0607/31/o/n/20 \u00a9 ucles 2020 [turn over (b) xy \u2013 3\u2013 2\u2013 1\u2013 1 1 2 3 \u2013 2 \u2013 3123 0a b c (i) write down the coordinates of (a) point a, ( ... , ...) [1] (b) point b, ( ... , ...) [1] (c) point c. ( ... , ...) [1] (ii) the shape is drawn on a 1cm2 grid. find the area of the shape. ... cm2 [2]", "6": "6 0607/31/o/n/20 \u00a9 ucles 2020 3 (a) sonny\u2019s old car is for sale at $5500. paula pays him 32 of this price. work out how much paula pays. give your answer correct to the nearest dollar. $ . [2] (b) sonny buys a new car in a sale. the original price of the car is $18 000. in the sale, this price is reduced by 12%. work out the sale price of the car. $ . [2] (c) sonny does some research about his new car. (i) the car has a mass of 1.4 tonnes. work out the total mass of 8 of these cars. t [1] (ii) it took 421 years to develop the design of the car. change 421 years into months. .. months [1] (iii) the car can travel 2 km in 1 minute 24 seconds. change 1 minute 24 seconds into seconds. . seconds [1]", "7": "7 0607/31/o/n/20 \u00a9 ucles 2020 [turn over 4 (a) here are the first three patterns in a sequence of dots. pattern 1 pattern 2 pattern 3 pattern 4 (i) in the space above, draw pattern 4. [1] (ii) complete the table. pattern number 1 2 3 4 number of dots 4 [1] (iii) write down the rule for continuing the sequence of dots. .. [1] (iv) find the number of dots in pattern 9. .. [1] (b) the nth term of another sequence is nn 22-. find the first three terms of this sequence. ... , ... , ... [2] (c) these are the first five terms of a different sequence. 3 7 11 15 19 find the nth term of this sequence. .. [2]", "8": "8 0607/31/o/n/20 \u00a9 ucles 2020 5 (a) (i) not to scale52\u00b0 y\u00b0 work out the value of y. y = . [1] (ii) for any right-angled triangle, explain why none of the angles can be obtuse. . . [1] (b) a\u00b0 c\u00b0b\u00b065\u00b080\u00b0 not to scaleb e c ad in the diagram, ace is a straight line. find the value of a, the value of b and the value of c. a = . b = . c = . [3]", "9": "9 0607/31/o/n/20 \u00a9 ucles 2020 [turn over (c) work out the size of one exterior angle of a regular hexagon. .. [2] 6 this word formula can be used to work out the total number of points scored by a hockey team during one season. total number of points = 3 \u00d7 number of games won plus 1 \u00d7 number of games drawn (a) one team had won 17 games and drawn 7 games. work out the total number of points scored by this team. .. [2] (b) another team scored a total of 44 points. this team had drawn 5 games. work out how many games this team had won. .. [2] (c) a different team scored a total of 36 points. this team had won and drawn exactly the same number of games. work out how many games this team had won. .. [2]", "10": "10 0607/31/o/n/20 \u00a9 ucles 2020 7 (a) the diagram shows the path of a boat that sails from a to b to c. the scale of the diagram is 1 cm represents 20 km. north a cb scale: 1 cm to 20 km (i) find the actual distance from a to b. km [2] (ii) the boat travels from a to b in 4 hours. work out the speed of the boat in kilometres per hour. . km/h [2] (iii) measure the bearing of c from b. .. [1]", "11": "11 0607/31/o/n/20 \u00a9 ucles 2020 [turn over (b) 7 cm 25 cmx cmnot to scale find the value of x. x = . [3]", "12": "12 0607/31/o/n/20 \u00a9 ucles 2020 8 (a) solve. (i) x38+= x = . [1] (ii) ()x32 51 2 -= x = . [3] (b) multiply out and simplify. () () xx74+- .. [2] (c) simplify. yxy 20 4# .. [2]", "13": "13 0607/31/o/n/20 \u00a9 ucles 2020 [turn over 9 040 \u2013 10\u2013 6 4y x (a) (i) on the diagram, sketch the graph of yx x432=+ + for x64gg- . [2] (ii) write down the coordinates of the local minimum. ( ... , ...) [1] (b) on the diagram, sketch the graph of yx x21 52=- -+ for x64gg- . [2] (c) find the x-coordinate of each point of intersection of yx x432=+ + and yx x21 52=- +- . x = and x = [2]", "14": "14 0607/31/o/n/20 \u00a9 ucles 2020 10 (a) 6 cm 2 cm 10 cmnot to scale a toilet roll is a cylinder with radius 6 cm and height 10 cm. it has a hollow cylindrical centre of radius 2 cm. work out the volume of paper in the toilet roll. ... cm3 [3] (b) there are 325 million people in the usa. on average, each person uses 23.6 toilet rolls during one year. calculate the total number of toilet rolls used in the usa in one year. give your answer in standard form. .. [2]", "15": "15 0607/31/o/n/20 \u00a9 ucles 2020 [turn over (c) not to scale8 cm 12 cm 10 cm toilet paper can also be bought in a box. the box is a cuboid. (i) work out the volume of the box. ... cm3 [2] (ii) the box is completely filled with individual sheets of toilet paper, one sheet on top of another. one sheet of toilet paper measures 12 cm by 10 cm and is .16 10 cm2#- thick. the box is 8 cm deep. work out the largest number of sheets of toilet paper that can be placed in the box. .. [2]", "16": "16 0607/31/o/n/20 \u00a9 ucles 2020 11 the time taken, t seconds, for the first points to be scored in each of 100 basketball games is shown in the table. time ( t seconds) frequency 0 1 t g 20 1 20 1 t g 40 4 40 1 t g 60 22 60 1 t g 80 26 80 1 t g 100 31 100 1 t g 120 16 (a) write down the time interval that is the mode. 1 t g ... [1] (b) one of these games is chosen at random. work out the probability that the first points in this game were scored in the first 60 seconds. .. [2] (c) work out an estimate of the mean time. s [2]", "17": "17 0607/31/o/n/20 \u00a9 ucles 2020 [turn over (d) (i) complete the cumulative frequency table. time ( t seconds) cumulative frequency t g 20 1 t g 40 t g 60 t g 80 t g 100 84 t g 120 100 [2] (ii) complete the cumulative frequency curve. 100 80 60 40 20 0 20 40 60 time (seconds)80 100 120t 01030507090 10 30 50 70 90 110cumulative frequency [3] (iii) use your curve to find the median time. s [1]", "18": "18 0607/31/o/n/20 \u00a9 ucles 2020 12 u = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} a = {2, 3, 4, 5} (a) write down. (i) n(a) .. [1] (ii) al { } [1] (b) use a mathematical symbol to complete each of the following. (i) 2 a [1] (ii) {3, 4} a [1] (c) b = {7, 8, 9, 10} (i) list the elements of ab,. .. [1] (ii) find ab+. .. [1] (d) u = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} a = {2, 3, 4, 5} b = {7, 8, 9, 10} draw a venn diagram to show this information. u [3]", "19": "19 0607/31/o/n/20 \u00a9 ucles 2020 blank page", "20": "20 0607/31/o/n/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_w20_qp_32.pdf": { "1": "cambridge igcse\u2122this document has 16 pages. blank pages are indicated. dc (st/jg) 183467/1 \u00a9 ucles 2020 [turn over *9705632668* cambridge international mathematics 0607/32 paper 3 (core) october/november 2020 1 hour 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 96. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/32/o/n/20 \u00a9 ucles 2020 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/32/o/n/20 \u00a9 ucles 2020 [turn over answer all the questions. 1 ben was born on 25th march, 1936. (a) write the number 1936 in words. [1] (b) work out how old ben is on the 25th march, 2020. .. [1] (c) work out the year of ben\u2019s 99th birthday. .. [1] (d) find 1936 . .. [1] (e) write down 1936 (i) correct to the nearest 10, .. [1] (ii) correct to 2 significant figures, .. [1] (iii) in standard form. .. [1] (f) write down a multiple of 1936. .. [1]", "4": "4 0607/32/o/n/20 \u00a9 ucles 2020 2 the number of seconds that it took each of 15 students to run 200 metres is shown below. 32 35 29 41 41 39 51 57 45 62 42 53 38 43 60 (a) work out the mean. s [1] (b) complete the stem-and-leaf diagram to show this information. key | represents [3] (c) find (i) the range, s [1] (ii) the mode, s [1] (iii) the median, s [1] (iv) the interquartile range. s [2]", "5": "5 0607/32/o/n/20 \u00a9 ucles 2020 [turn over 3 a supermarket sells saving stamps for $0.10 each. these stamps are stuck onto pages in a special stamp book. (a) each page of the stamp book has 35 stamps. work out how much is paid for the stamps to fill one page. $ . [1] (b) it costs $49 to fill the book with stamps. find the number of pages in the book. .. [2] (c) each full book of stamps can be used in the supermarket to pay for food costing $52. (i) work out how much is saved by paying for food with a full book of stamps. $ . [1] (ii) work out the answer to part (i) as a percentage of $49. .. % [2] (d) fred buys fruit and coffee for $49. the ratio cost of fruit : cost of coffee = 3 : 4. find the cost of the coffee. $ . [2]", "6": "6 0607/32/o/n/20 \u00a9 ucles 2020 4 (a) petra has a birthday party. the party starts at 19 30 and ends at 23 45. (i) find how long the party lasts. . hours . minutes [1] (ii) the cost of hiring a band for the party is a total of $150. the cost of hiring a hall is $50 per hour. petra hires the hall for 6 hours. find the total cost of hiring the hall and the band. $ . [2] (b) petra received $650 for her birthday. (i) she invests half of this in a bank at a rate of 3.1% per year compound interest. work out the value of her investment at the end of 3 years. $ . [3] (ii) petra invests the other half of her birthday money in a different bank at a rate of 3.5% per year simple interest. work out the value of this investment at the end of 3 years. $ . [3]", "7": "7 0607/32/o/n/20 \u00a9 ucles 2020 [turn over 5 not to scalea db o e c31\u00b0 the diagram shows a circle, centre o. the straight line abc touches the circle at b. doec is a straight line, d and e lie on the circumference and angle obd = 31\u00b0. (a) using the letters in the diagram, write down (i) the diameter, .. [1] (ii) a radius, .. [1] (iii) a chord, .. [1] (iv) the tangent. .. [1] (b) find (i) angle obc , angle obc = . [1] (ii) angle abd , angle abd = . [1] (iii) angle bod , angle bod = . [2] (iv) angle bco . angle bco = . [2]", "8": "8 0607/32/o/n/20 \u00a9 ucles 2020 6 (a) the diagram shows a shape drawn on a 1cm2 grid. x cm (i) use pythagoras\u2019 theorem to calculate the value of x. x = . [2] (ii) work out the perimeter of the shape. . cm [1] (b) shade one small square so that the diagram has line symmetry. [1]", "9": "9 0607/32/o/n/20 \u00a9 ucles 2020 [turn over (c) shade one small square so that the diagram has rotational symmetry of order 2. [1] (d) a d e fb cnot to scale 7.5 cm 3 cm 2 cm x cm abc and def are similar triangles. find the value of x. x = . [2]", "10": "10 0607/32/o/n/20 \u00a9 ucles 2020 7 one day, mr amir made a note of the number of employees who were on time for work and the number who were late for work. he asked each employee if they ate breakfast or not. the information is shown in the table. number who ate breakfastnumber who did not eat breakfasttotal number who were on time for work12 a 17 number who were late for work 2 c b total 14 6 20 (a) work out the value of each of a, b and c. a = . b = . c = . [3] (b) an employee is chosen at random. find the probability that this employee (i) was on time, .. [1] (ii) did not eat breakfast, .. [1] (iii) ate breakfast and was late for work. .. [1]", "11": "11 0607/32/o/n/20 \u00a9 ucles 2020 [turn over 8 u = {f, r, a, c, t, i, o, n} x = {r, a, t, i, o} y = {f, a, c, t} (a) write down the elements in xy+. .. [1] (b) complete the venn diagram. x yu [2] (c) find ()xyn, l. .. [1] (d) on the venn diagram below, shade the region xy,l. x yu [1]", "12": "12 0607/32/o/n/20 \u00a9 ucles 2020 9 (a) () x x 21 f2=- (i) find f(4). .. [1] (ii) find x when f( x) = 17. x = or x = [3] (b) solve. (i) x71 41 4 -= x = . [2] (ii) xx53 37 -= + x = . [2] (c) expand. ()xx34- .. [2]", "13": "13 0607/32/o/n/20 \u00a9 ucles 2020 [turn over (d) simplify fully. rr 618 28 .. [2] (e) (i) 33 3m 61 8#= find the value of m. m = . [1] (ii) 888n 32= find the value of n. n = . [1] (f) solve the simultaneous equations. you must show all your working. xy24 22 += xy23 15 -= x = . y = . [2]", "14": "14 0607/32/o/n/20 \u00a9 ucles 2020 10 12xy 015 \u2013 1\u2013 1 (a) (i) on the diagram, sketch the graph of .() y81 42x#=+- for x11 2 gg- . [2] (ii) find the coordinates of the point where the graph crosses the y-axis. ( ... , ...) [1] (iii) write down the equation of the horizontal asymptote. .. [1] (b) on the same diagram, sketch the graph of yx 3 =+ . [2] (c) find the coordinates of the point of intersection of the graphs of .() y81 42x#=+- and yx 3 =+ . ( ... , ...) [2]", "15": "15 0607/32/o/n/20 \u00a9 ucles 2020 11 a c dbey x 02 4 6 8 10 12 14 16 18 20 22 \u2013 2 \u2013 2 2 4 6 8 10 12 14 16 \u2013 4 \u2013 6\u2013 4 \u2013 6 \u2013 8 describe fully the single transformation that maps (a) shape a onto shape b, [3] (b) shape a onto shape c, [2] (c) shape a onto shape d, [2] (d) shape a onto shape e. [3]", "16": "16 0607/32/o/n/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_w20_qp_33.pdf": { "1": "cambridge igcse\u2122this document has 16 pages. blank pages are indicated. dc (mb) 207017 \u00a9 ucles 2020 [turn over *7326248900* cambridge international mathematics 0607/33 paper 3 (core) october/november 2020 1 hour 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 96. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/33/o/n/20 \u00a9 ucles 2020 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/33/o/n/20 \u00a9 ucles 2020 [turn over answer all the questions. 1 ben was born on 25th march, 1936. (a) write the number 1936 in words. [1] (b) work out how old ben is on the 25th march, 2020. .. [1] (c) work out the year of ben\u2019s 99th birthday. .. [1] (d) find 1936 . .. [1] (e) write down 1936 (i) correct to the nearest 10, .. [1] (ii) correct to 2 significant figures, .. [1] (iii) in standard form. .. [1] (f) write down a multiple of 1936. .. [1]", "4": "4 0607/33/o/n/20 \u00a9 ucles 2020 2 the number of seconds that it took each of 15 students to run 200 metres is shown below. 32 35 29 41 41 39 51 57 45 62 42 53 38 43 60 (a) work out the mean. s [1] (b) complete the stem-and-leaf diagram to show this information. key | represents [3] (c) find (i) the range, s [1] (ii) the mode, s [1] (iii) the median, s [1] (iv) the interquartile range. s [2]", "5": "5 0607/33/o/n/20 \u00a9 ucles 2020 [turn over 3 a supermarket sells saving stamps for $0.10 each. these stamps are stuck onto pages in a special stamp book. (a) each page of the stamp book has 35 stamps. work out how much is paid for the stamps to fill one page. $ . [1] (b) it costs $49 to fill the book with stamps. find the number of pages in the book. .. [2] (c) each full book of stamps can be used in the supermarket to pay for food costing $52. (i) work out how much is saved by paying for food with a full book of stamps. $ . [1] (ii) work out the answer to part (i) as a percentage of $49. .. % [2] (d) fred buys fruit and coffee for $49. the ratio cost of fruit : cost of coffee = 3 : 4. find the cost of the coffee. $ . [2]", "6": "6 0607/33/o/n/20 \u00a9 ucles 2020 4 (a) petra has a birthday party. the party starts at 19 30 and ends at 23 45. (i) find how long the party lasts. . hours . minutes [1] (ii) the cost of hiring a band for the party is a total of $150. the cost of hiring a hall is $50 per hour. petra hires the hall for 6 hours. find the total cost of hiring the hall and the band. $ . [2] (b) petra received $650 for her birthday. (i) she invests half of this in a bank at a rate of 3.1% per year compound interest. work out the value of her investment at the end of 3 years. $ . [3] (ii) petra invests the other half of her birthday money in a different bank at a rate of 3.5% per year simple interest. work out the value of this investment at the end of 3 years. $ . [3]", "7": "7 0607/33/o/n/20 \u00a9 ucles 2020 [turn over 5 not to scalea db o e c31\u00b0 the diagram shows a circle, centre o. the straight line abc touches the circle at b. doec is a straight line, d and e lie on the circumference and angle obd = 31\u00b0. (a) using the letters in the diagram, write down (i) the diameter, .. [1] (ii) a radius, .. [1] (iii) a chord, .. [1] (iv) the tangent. .. [1] (b) find (i) angle obc , angle obc = . [1] (ii) angle abd , angle abd = . [1] (iii) angle bod , angle bod = . [2] (iv) angle bco . angle bco = . [2]", "8": "8 0607/33/o/n/20 \u00a9 ucles 2020 6 (a) the diagram shows a shape drawn on a 1cm2 grid. x cm (i) use pythagoras\u2019 theorem to calculate the value of x. x = . [2] (ii) work out the perimeter of the shape. . cm [1] (b) shade one small square so that the diagram has line symmetry. [1]", "9": "9 0607/33/o/n/20 \u00a9 ucles 2020 [turn over (c) shade one small square so that the diagram has rotational symmetry of order 2. [1] (d) a d e fb cnot to scale 7.5 cm 3 cm 2 cm x cm abc and def are similar triangles. find the value of x. x = . [2]", "10": "10 0607/33/o/n/20 \u00a9 ucles 2020 7 one day, mr amir made a note of the number of employees who were on time for work and the number who were late for work. he asked each employee if they ate breakfast or not. the information is shown in the table. number who ate breakfastnumber who did not eat breakfasttotal number who were on time for work12 a 17 number who were late for work 2 c b total 14 6 20 (a) work out the value of each of a, b and c. a = . b = . c = . [3] (b) an employee is chosen at random. find the probability that this employee (i) was on time, .. [1] (ii) did not eat breakfast, .. [1] (iii) ate breakfast and was late for work. .. [1]", "11": "11 0607/33/o/n/20 \u00a9 ucles 2020 [turn over 8 u = {f, r, a, c, t, i, o, n} x = {r, a, t, i, o} y = {f, a, c, t} (a) write down the elements in xy+. .. [1] (b) complete the venn diagram. x yu [2] (c) find ()xyn, l. .. [1] (d) on the venn diagram below, shade the region xy,l. x yu [1]", "12": "12 0607/33/o/n/20 \u00a9 ucles 2020 9 (a) () x x 21 f2=- (i) find f(4). .. [1] (ii) find x when f( x) = 17. x = or x = [3] (b) solve. (i) x71 41 4 -= x = . [2] (ii) xx53 37 -= + x = . [2] (c) expand. ()xx34- .. [2]", "13": "13 0607/33/o/n/20 \u00a9 ucles 2020 [turn over (d) simplify fully. rr 618 28 .. [2] (e) (i) 33 3m 61 8#= find the value of m. m = . [1] (ii) 888n 32= find the value of n. n = . [1] (f) solve the simultaneous equations. you must show all your working. xy24 22 += xy23 15 -= x = . y = . [2]", "14": "14 0607/33/o/n/20 \u00a9 ucles 2020 10 12xy 015 \u2013 1\u2013 1 (a) (i) on the diagram, sketch the graph of .() y 81 42x#=+- for x11 2 gg- . [2] (ii) find the coordinates of the point where the graph crosses the y-axis. ( ... , ...) [1] (iii) write down the equation of the horizontal asymptote. .. [1] (b) on the same diagram, sketch the graph of yx 3 =+ . [2] (c) find the coordinates of the point of intersection of the graphs of .() y 81 42x#=+- and yx 3 =+ . ( ... , ...) [2]", "15": "15 0607/33/o/n/20 \u00a9 ucles 2020 11 a c dbey x 02 4 6 8 10 12 14 16 18 20 22 \u2013 2 \u2013 2 2 4 6 8 10 12 14 16 \u2013 4 \u2013 6\u2013 4 \u2013 6 \u2013 8 describe fully the single transformation that maps (a) shape a onto shape b, [3] (b) shape a onto shape c, [2] (c) shape a onto shape d, [2] (d) shape a onto shape e. [3]", "16": "16 0607/33/o/n/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_w20_qp_41.pdf": { "1": "this document has 20 pages. blank pages are indicated. dc (rw/sw) 187925/3 \u00a9 ucles 2020 [turn over *8780959871* cambridge international mathematics 0607/41 paper 4 (extended) october/november 2020 2 hours 15 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 120. \u25cf the number of marks for each question or part question is shown in brackets [ ].cambridge igcse\u2122", "2": "2 0607/41/o/n/20 \u00a9 ucles 2020 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/41/o/n/20 \u00a9 ucles 2020 [turn over answer all the questions. 1 ten students at a school each study chemistry and physics. their marks in an examination in each subject are recorded. chemistry mark ( x) 27 36 48 52 53 62 75 80 86 93 physics mark ( y) 45 68 36 55 62 73 66 81 94 80 (a) what type of correlation is there between the chemistry mark and the physics mark? . [1] (b) find (i) the mean chemistry mark, . [1] (ii) the mean physics mark. . [1] (c) (i) find the equation of the regression line for y in terms of x. y= . [2] (ii) another student scored 40 in the chemistry examination but was absent for the physics examination. estimate a physics mark for this student. . [1]", "4": "4 0607/41/o/n/20 \u00a9 ucles 2020 2 (a) write the number 25.0467 (i) correct to 1 decimal place, . [1] (ii) correct to 3 significant figures, . [1] (iii) correct to the nearest 10, . [1] (iv) correct to the nearest 0.001, . [1] (v) in standard form. . [1] (b) change (i) 20 cm into metres, .. m [1] (ii) 20m2 into square centimetres, .. cm2 [1] (iii) 18 km/h into metres per second. m/s [2]", "5": "5 0607/41/o/n/20 \u00a9 ucles 2020 [turn over 3 (a) solve the simultaneous equations. you must show all your working. xy xy25 12 73 1+= - -= - x= . y= . [4] (b) solve () () xx41 23 5 -+ =- . you must show all your working. x= ... or x= ... [5]", "6": "6 0607/41/o/n/20 \u00a9 ucles 2020 4 (a) \u2013 112345678 0 \u2013 2 \u2013 3 \u2013 4 \u2013 5 \u2013 6 \u2013 7 \u2013 8\u2013 8\u2013 7\u2013 6\u2013 5\u2013 4\u2013 3\u2013 2\u2013 1 1 2 3 4 5 6 7 8y xc ab (i) describe fully the single transformation that maps triangle a onto triangle b. . . [3] (ii) describe fully the single transformation that maps triangle a onto triangle c. . . [3] (iii) on the grid, draw the stretch of triangle a, scale factor 2, y-axis invariant. [2]", "7": "7 0607/41/o/n/20 \u00a9 ucles 2020 [turn over (b) describe fully the single transformation that is the inverse of (i) a reflection in y2=, . . [1] (ii) a translation with vector 5 2-eo . . . [2]", "8": "8 0607/41/o/n/20 \u00a9 ucles 2020 5 47\u00b0 65\u00b0 ot b dcnot to scale ax a, b, c and d lie on a circle, centre o. ad cd= and xbt is a tangent to the circle at b. tcd is a straight line. angle \u00b0 xba 47= and angle \u00b0 tbc 65= . find the value of (a) angle obx , angle obx= . [1] (b) angle aob , angle aob= . [2] (c) angle cao , angle cao= . [2]", "9": "9 0607/41/o/n/20 \u00a9 ucles 2020 [turn over (d) angle cda , angle cda= . [2] (e) angle dac , angle dac= . [2] (f) angle ctb. angle ctb= . [2]", "10": "10 0607/41/o/n/20 \u00a9 ucles 2020 6 find the next term and the nth term in each of these sequences. (a) 125, 64, 27, 8, 1, \u2026 next term . nth term . [3] (b) 6, 12, 20, 30, 42, \u2026 next term . nth term . [4]", "11": "11 0607/41/o/n/20 \u00a9 ucles 2020 [turn over 7 0y x \u2013 1.5 \u2013 55 1.5 ()xxx1f3=- (a) on the diagram, sketch the graph of () yx f= , for values of x between .15- and 1.5 . [3] (b) write down the equation of the asymptote of the graph. . [1] (c) solve the equation ()x 2 f= for values of x between .15- and 0. x= ... or x= ... [2] (d) solve the inequality ()xx 2 f2g+ for values of x between .15- and 1.5 . . [3]", "12": "12 0607/41/o/n/20 \u00a9 ucles 2020 8 12 cm 8 cm 20 cmnot to scale dab ce f abcdef is a triangular prism. abcd is a rectangle. find (a) ac, ac= . cm [2] (b) ed, ed= . cm [2]", "13": "13 0607/41/o/n/20 \u00a9 ucles 2020 [turn over (c) angle ead , angle ead= . [2] (d) angle fa c. angle fac= . [2]", "14": "14 0607/41/o/n/20 \u00a9 ucles 2020 9 16 cm12 cm5 cm not to scale 24 cm the diagram shows a solid made from a cuboid and a solid hemisphere. the cuboid measures 12 cm by 16 cm by 24 cm. the hemisphere has radius 5 cm. (a) find (i) the volume of the solid, .. cm3 [3] (ii) the volume of a similar solid where the radius of the hemisphere is 3 cm. .. cm3 [2]", "15": "15 0607/41/o/n/20 \u00a9 ucles 2020 [turn over (b) find (i) the total surface area of the original solid, .. cm2 [3] (ii) the total surface area of a similar solid where the radius of the hemisphere is 6 cm. .. cm2 [2]", "16": "16 0607/41/o/n/20 \u00a9 ucles 2020 10 not to scale46\u00b0b a cd 8.1 cm 9.6 cm15\u00b078\u00b0 abc and adc are triangles. ad= 8.1 cm and cd= 9.6 cm. angle \u00b0 abc 46= , angle \u00b0 adc 78= and angle \u00b0 bad 15= . (a) find ac. ac= . cm [3] (b) show that angle \u00b0 dac 57= , correct to the nearest degree. [3]", "17": "17 0607/41/o/n/20 \u00a9 ucles 2020 [turn over (c) find bc. bc= . cm [3] (d) find the area of quadrilateral abcd . .. cm2 [4]", "18": "18 0607/41/o/n/20 \u00a9 ucles 2020 11 a bag contains 4 red balls, 5 black balls and 3 white balls only. (a) in an experiment, one ball is chosen at random. (i) find the probability that the ball chosen is not black. . [1] (ii) this experiment is carried out 1440 times. find the expected number of times the ball chosen is not black. . [1] (b) in a different experiment, one ball is chosen at random, the colour is noted, and the ball is replaced in the bag. another ball is then chosen at random and the colour is noted. find the probability that the balls chosen are (i) both white, . [2] (ii) both the same colour, . [3]", "19": "19 0607/41/o/n/20 \u00a9 ucles 2020 [turn over (iii) different colours. . [1] (c) in another experiment, three balls are chosen at random without replacement. (i) find the probability that the first ball is not black, the second ball is black and the third ball is white. . [3] (ii) find the probability that exactly two of the balls are red. . [4] question 12 is printed on the next page.", "20": "20 0607/41/o/n/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.12 solve the equations. (a) x622 -=- x= . [3] (b) () () xx 32 45 12 8 ++ =- + x= . [3] (c) logl og logl og x 32 32 62 += + x= . [3] (d) 21 0x= x= . [3]" }, "0607_w20_qp_42.pdf": { "1": "this document has 20 pages. blank pages are indicated. dc (rw/sw) 187924/1 \u00a9 ucles 2020 [turn over *3591527429* cambridge international mathematics 0607/42 paper 4 (extended) october/november 2020 2 hours 15 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 120. \u25cf the number of marks for each question or part question is shown in brackets [ ].cambridge igcse\u2122", "2": "2 0607/42/o/n/20 \u00a9 ucles 2020 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/42/o/n/20 \u00a9 ucles 2020 [turn over answer all the questions. 1 asif buys a one-year old car. he pays $19 975 which is 15% less than its price when it was new. (a) calculate the price when it was new. $ . [2] (b) option 1 pay 10% of the $19 975 and then pay $345 per month for 5 years. option 2 borrow $19 975 and pay this back at the end of 5 years at a rate of 2.5% per year compound interest. asif can pay for the car using option 1 or option 2. (i) using option 1, find how much asif would pay in total for the car. $ . [3] (ii) by how much is option 2 cheaper than option 1? $ . [4]", "4": "4 0607/42/o/n/20 \u00a9 ucles 2020 2 \u2013 112345 0 \u2013 2 \u2013 3 \u2013 4 \u2013 5\u2013 5\u2013 4\u2013 3\u2013 2\u2013 1 1 2 3 4 5 6 7y xe a b (a) describe fully the single transformation that maps triangle a onto triangle b. . . [2] (b) reflect triangle a in the line yx=- . label the image c. [2] (c) rotate triangle a through 90\u00b0 clockwise about centre (1, 1-). label the image d. [2] (d) describe fully the single transformation that maps triangle c onto triangle d. . . [2] (e) describe fully the single transformation that maps triangle a onto triangle e. . . [3]", "5": "5 0607/42/o/n/20 \u00a9 ucles 2020 [turn over 3 the table shows the engine capacity, x litres, and the fuel consumption, y kilometres per litre, for each of nine cars. engine capacity (x litres)1 1.3 1.5 1.8 2 2.5 3 3.5 4 fuel consumption (y km/l)16.6 15.6 13.8 14.4 13.2 11.0 11.5 9.2 7.4 (a) complete the scatter diagram. the first five points have been plotted for you. 6 1 1.5 2 2.5 engine capacity (litres)fuel consumption (km / l) 3 3.5 4789101112131415161718y x [2] (b) what type of correlation is shown in your scatter diagram? . [1] (c) find the equation of the regression line for y in terms of x. y= . [2] (d) use your answer to part (c) to estimate the fuel consumption for a car with engine capacity 2.8 litres. .. km/l [1]", "6": "6 0607/42/o/n/20 \u00a9 ucles 2020 4 0y x \u2013 3 \u2013 1015 3 ()fxx x533=- + for x33gg- (a) on the diagram, sketch the graph of ()f yx= . [2] (b) find the coordinates of the local minimum point. ( .. , .. ) [2] (c) describe fully the symmetry of the diagram. . . [3] (d) ()gxx 21=- (i) solve () () fgxx= for x33gg- . .. , .. , .. [3] (ii) use your answers to part(i) to solve () () fgxx2 . ... [2]", "7": "7 0607/42/o/n/20 \u00a9 ucles 2020 [turn over 5 naomi flies non-stop from london, england, to perth, australia. the flight takes 16 hours 45 minutes. the distance is 14 498 km. (a) find the average speed of the plane in km/h. . km/h [2] (b) the plane leaves london at 13 15. the time in perth is 8 hours ahead of the time in london. find the time in perth when the plane lands. . [3] (c) the cost, in pounds (\u00a3), of the flight is \u00a3827.75 . the exchange rate is 1 australian dollar = \u00a30.55 . calculate the cost of the flight in australian dollars. . australian dollars [2]", "8": "8 0607/42/o/n/20 \u00a9 ucles 2020 6 75\u00b0 ab cnot to scale d44 m 74 m62 mnorth 95 m the diagram shows a field abcd with a straight path from a to c. the bearing of b from a is 075\u00b0 and angle \u00b0 adc 90= . (a) show that angle .\u00b0 bac 316= , correct to 1 decimal place. [3]", "9": "9 0607/42/o/n/20 \u00a9 ucles 2020 [turn over (b) find the bearing of d from a. . [3] (c) find the shortest distance from b to ac. .. m [2] (d) find the total area of the field abcd . m2 [3]", "10": "10 0607/42/o/n/20 \u00a9 ucles 2020 7 a obnot to scaley x a is the point (3, 2) and b is the point (9, 5). (a) find the length ab. ab= . [3] (b) find the equation of the line ab. give your answer in the form ym xc=+ . y= . [3] (c) c is the point (8, 2). find the equation of the line perpendicular to ab which passes through c. give your answer in the form ym xc=+ . y= . [3]", "11": "11 0607/42/o/n/20 \u00a9 ucles 2020 [turn over (d) find the coordinates of the point where the line in part (c) intersects ab. ( .. , .. ) [2] (e) d is the reflection of c in the line ab. (i) find the coordinates of d. ( .. , .. ) [2] (ii) what is the special name of quadrilateral acbd ? . [1] (f) find the area of the quadrilateral acbd . . [3]", "12": "12 0607/42/o/n/20 \u00a9 ucles 2020 8 bag a bag b bag a contains 5 black balls and 2 white balls. bag b contains 4 black balls and 5 white balls. (a) gustav picks one ball at random from bag a and replaces it. write down the probability that the ball gustav picks is black. . [1] (b) sharia picks one ball at random from bag a, notes its colour, and places it in bag b. she then picks a ball at random from bag b. find the probability that (i) both balls are white, . [2] (ii) one ball is black and the other ball is white. . [3]", "13": "13 0607/42/o/n/20 \u00a9 ucles 2020 [turn over (c) the balls are returned to their original bags. jean picks a ball at random from bag a. he then replaces the ball. he continues to do this until he gets a white ball. find the probability that the first time he gets a white ball is on the 5th pick. . [2] (d) the balls are returned to their original bags. leanne picks a ball at random from bag b. she continues to do this without replacement until she gets a white ball. the probability that she picks the first white ball on her nth attempt is 1265. find the value of n. . [3]", "14": "14 0607/42/o/n/20 \u00a9 ucles 2020 9 the cumulative frequency curve shows the marks of 120 students in an examination. 0 0 20 40 60 markscumulative frequency 80 100 10 30 50 70 90102030405060708090100110120 (a) use the graph to estimate (i) the median, . [1] (ii) the interquartile range. . [2] (b) the top 15% of the students gained a grade a in the examination. estimate the minimum mark for a grade a. . [3]", "15": "15 0607/42/o/n/20 \u00a9 ucles 2020 [turn over 10 y is inversely proportional to the square root of x. when x25= , y4=. (a) find y in terms of x. y= . [2] (b) find y when . x 025= . y= . [1] (c) find x when y5=. x= . [2] (d) z is proportional to y2+. when x4=, z84= . find z in terms of x. z= . [3]", "16": "16 0607/42/o/n/20 \u00a9 ucles 2020 11 ()fxx 53=- ()gxx 27=+ (a) solve () () xxfg= . . [2] (b) find and simplify (( )) gfx. . [2] (c) (i) find () () fgxx22+ simplifying your answer. . [2] (ii) find (( )( )) fgxx2+ giving your answer in the form ax bx c2++ . . [3]", "17": "17 0607/42/o/n/20 \u00a9 ucles 2020 [turn over (d) find ()fx1-. ()fx1=- . [2] (e) write as a single fraction in its simplest form. () () fgxx23- . [3]", "18": "18 0607/42/o/n/20 \u00a9 ucles 2020 12 (a) the vector a3 2=eo and the vector b2 1=-eo . on the grid, draw and label these vectors. (i) 2a [1] (ii) b- [1] (iii) 2ab- [2]", "19": "19 0607/42/o/n/20 \u00a9 ucles 2020 (b) pq2 31 410 7+-=-ee e oo o by solving a pair of simultaneous equations, find the value of p and the value of q. show all your working. p= . q= . [4]", "20": "20 0607/42/o/n/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_w20_qp_43.pdf": { "1": "cambridge igcse\u2122cambridge international mathematics 0607/43 paper 4 (extended) october/november 2020 2 hours 15 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 120. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *6223443111* this document has 20 pages. blank pages are indicated. dc (lk/cb) 187911/3 \u00a9 ucles 2020 [turn over", "2": "2 0607/43/o/n/20 \u00a9 ucles 2020 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/43/o/n/20 \u00a9 ucles 2020 [turn over answer all the questions. 1 adam and brenda share $560 in the ratio adam : brenda = 4 : 3. (a) show that adam receives $320. [1] (b) adam spends 15% of his $320 on some software. calculate how much adam spends on this software. $ [2] (c) in a sale, brenda buys a computer for $179.40 . this is 8% less than the original price. calculate the original price of the computer. $ [2] (d) adam spends a further $29.60 on a train ticket. adam and brenda then work out how much money each of them has left. show that adam has 4 times as much left as brenda. [3]", "4": "4 0607/43/o/n/20 \u00a9 ucles 2020 2 (a) find the size of one interior angle of a regular polygon with 45 sides. . [3] (b) a tb c dnot to scale75\u00b035\u00b0 in the diagram, a, b, c and d lie on the circle. ta is a tangent to the circle at a. angle tad = 75\u02da and angle dac = 35\u02da. find (i) angle acd , angle acd = [1] (ii) angle abc . angle abc = [2]", "5": "5 0607/43/o/n/20 \u00a9 ucles 2020 [turn over (c) a bc e dnot to scale in the diagram, de is parallel to bc. (i) complete the statement. triangle ade is .. to triangle abc . [1] (ii) ae = 6 cm, ec = 3 cm and db = 2 cm. calculate the length of ad. ad = ... cm [3] (iii) the area of triangle ade is 9 cm2. calculate the area of triangle abc . . cm2 [2]", "6": "6 0607/43/o/n/20 \u00a9 ucles 2020 3 (a) eva records her science homework marks during the school year. the table shows the results. homework mark 5 6 7 8 9 10 frequency 2 7 11 13 5 2 find (i) the range, . [1] (ii) the mode, . [1] (iii) the median, . [1] (iv) the lower quartile, . [1] (v) the mean. . [2] (b) frank compares the science marks, x, with the mathematics marks, y, of ten students. the table shows the results. science mark ( x) 14 18 15 20 17 17 18 15 18 15 mathematics mark ( y)13 19 16 19 17 14 17 15 15 12 (i) complete the scatter diagram. the first six points have been plotted for you. y x101011121314151617181920 1112131415 science markmathematics mark 1617181920 [2]", "7": "7 0607/43/o/n/20 \u00a9 ucles 2020 [turn over (ii) what type of correlation is shown on the scatter diagram? . [1] (iii) find the equation of the line of regression, giving y in terms of x. y = [2] (iv) another student\u2019s science mark is 16. use your answer to part (b)(iii) to find an expected mathematics mark for this student. . [1] (c) georgio records the time, t minutes, he takes to complete each of 40 pieces of mathematics homework. the table shows his results. time ( t minutes) t 01 01g t 10 151g t 0 15 21g t 20 041g frequency 9 20 6 5 calculate an estimate of the mean. .. min [2]", "8": "8 0607/43/o/n/20 \u00a9 ucles 2020 4 the venn diagram shows the number of students who like sweets ( s) and the number of students who like nuts ( n). us n 7 27 13 3 (a) (i) find the number of students who like nuts. . [1] (ii) find the number of students who like sweets or nuts but not both. . [1] (b) (i) find n( u). . [1] (ii) find n ()sn,. . [1] (iii) find n ()sn,l . . [1] (c) one of these students is chosen at random. find the probability that this student likes nuts but not sweets. . [1] (d) two of these students are chosen at random. find the probability that they both like sweets and nuts. . [2]", "9": "9 0607/43/o/n/20 \u00a9 ucles 2020 [turn over (e) two students who like sweets are chosen at random. find the probability that they both also like nuts. . [3]", "10": "10 0607/43/o/n/20 \u00a9 ucles 2020 5 (a) carla invests $600 at a rate of 1.8% per year compound interest. calculate the value of carla\u2019s investment at the end of 7 years. $ [3] (b) dominic wants to invest his money so that it will double its value in 17 years. find the lowest possible rate of compound interest per year that will give dominic this result. give your answer correct to 1 decimal place. % [4]", "11": "11 0607/43/o/n/20 \u00a9 ucles 2020 [turn over (c) each year, the population of a village is decreasing at a rate of 4% of its value at the beginning of that year. the population is now 2120. find the number of complete years since the population was last greater than 2700. . [4]", "12": "12 0607/43/o/n/20 \u00a9 ucles 2020 6 not to scale11 cm 3 cm the diagram shows a solid made from a cylinder and two hemispheres. the cylinder has radius 3 cm and length 11 cm. each hemisphere has radius 3 cm. (a) find the volume of the solid. give your answer in terms of r. ... cm3 [3] (b) the solid is melted down and all the metal is used to make a cylinder of length 15 cm. (i) use your answer to part (a) to find the radius of this cylinder. cm [2]", "13": "13 0607/43/o/n/20 \u00a9 ucles 2020 [turn over (ii) a rectangular tank contains water. the base of the tank measures 20 cm by 10 cm. the cylinder is placed in the tank so that it is completely covered by water. no water overflows the tank. calculate the increase in the depth of the water in the tank. ... cm [2]", "14": "14 0607/43/o/n/20 \u00a9 ucles 2020 7 (a) (i) factorise ab22-. . [1] (ii) not to scalea a bb the diagram shows two squares. the difference between the areas of the squares is .cm 7412. the difference between the lengths of the sides of the squares is 1.3 cm. find the area of the larger square. . cm2 [5]", "15": "15 0607/43/o/n/20 \u00a9 ucles 2020 [turn over (b) (i) factorise xx52 42-- . . [2] (ii) not to scale (x + 1) cm(2x + 1) cm(x + 13) cm(x + 4) cmba the area of rectangle a is cm152 greater than the area of rectangle b. find the area of rectangle a. . cm2 [8]", "16": "16 0607/43/o/n/20 \u00a9 ucles 2020 8 (a) 04 \u2013 2 2y x (i) on the diagram, sketch the graph of . y 15x=- for x22gg- . [2] (ii) solve the inequality ..05 15 1xgg-. . [3] (iii) solve the equation . x 15x 2=- for x22gg- . . [3] (iv) on your diagram shade the regions where . x 15x 21- for x22gg- . [1] (b) oy x the diagram shows a sketch of the graph of yxaxb2=+-+. the asymptotes of the graph are x2= and y 2=- . the graph passes through the point (0, 2). find the value of a and the value of b. a = b = . [3]", "17": "17 0607/43/o/n/20 \u00a9 ucles 2020 [turn over (c) om x = a x = by = ky x f(x) is a function such that \u2022 the asymptotes of the graph are xa=, xb= and yk= \u2022 when xa1, the gradient of the graph is positive \u2022 when xb2, the gradient of the graph is negative \u2022 m is the only local maximum point \u2022 the graph does not cross any asymptote. on the diagram sketch the graph of ()f yx= . [3]", "18": "18 0607/43/o/n/20 \u00a9 ucles 2020 9 pq1 32 1=-=-ee oo a is the point (3, 4). (a) find pq-. fp [1] (b) a is translated onto h by the vector p. find the coordinates of h. ( . , . ) [1] (c) j is translated onto a by the vector q. find the coordinates of j. ( . , . ) [1] (d) find the coordinates of the mid-point of hj. ( . , . ) [1] (e) find the length of hj. hj = [3] (f) a line l, parallel to the vector q, has gradient 21-. find the equation of the line perpendicular to the line l that passes through the point a. . [3]", "19": "19 0607/43/o/n/20 \u00a9 ucles 2020 [turn over 10 (a) y xtv 0 \u2013 11 \u2013 22 \u2013 33 \u2013 44 \u2013 55 \u2013 66 \u2013 1 \u2013 2 \u2013 3 \u2013 4 \u2013 5 \u2013 61 2 3 4 5 6 (i) describe fully the single transformation that maps shape t onto shape v. . . [3] (ii) reflect shape t in the line y 2=- . [2] (iii) stretch shape t by a factor of 2 with the x-axis invariant. [2] (b) () () f log xx= () () g log xx3= describe fully the single transformation that maps the graph of ()f yx= onto the graph of ()g yx= . . . [3] question 11 is printed on the next page.", "20": "20 0607/43/o/n/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.11 ()fxx3= ()gx 3x= (a) find () () gf22- . . [2] (b) find x when ()gx91=. . [1] (c) write ()fxx1- in terms of x. give your answer as a single fraction. . [2] (d) find () fx1-. () fx1=- [1]" }, "0607_w20_qp_51.pdf": { "1": "cambridge igcse\u2122dc (kn/sg) 189358/2 \u00a9 ucles 2020 [turn overthis document has 8 pages. blank pages are indicated. *7460435561* cambridge international mathematics 0607/51 paper 5 investigation (core) october/november 2020 1 hour 10 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 36. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/51/o/n/20 \u00a9 ucles 2020 answer all the questions. investigation piling squares this investigation looks at different ways of piling squares. all the squares are the same size. 1 squares are piled in a pattern, like this: 1 square on the bottom row total = 1 square 2 squares on the bottom row total = 3 squares 3 squares on the bottom row total = 6 squares (a) on the dotty paper, complete the next two diagrams in this sequence. [2]", "3": "3 0607/51/o/n/20 \u00a9 ucles 2020 [turn over (b) (i) complete the table. number of squares on the bottom row ( s)1 2 3 4 5 6 total number of squares ( t)1 3 6 [3] (ii) when the number of squares on the bottom row is 3 the total number of squares is 6. use this information to explain how to calculate the total number of squares when there are 4 squares on the bottom row. . [1] (c) (i) write down the number of extra squares needed to change a pattern with 9 squares on the bottom row to one with 10 squares on the bottom row. . [1] (ii) calculate the total number of squares when there are 10 squares on the bottom row. . [2]", "4": "4 0607/51/o/n/20 \u00a9 ucles 2020 (d) (i) a formula for finding the total number of squares, t, in terms of the number of squares on the bottom row, s, is tk ss21 2=+ , where k is a constant. use the results in part (b)(i) to find the value of k. . [2] (ii) a pattern has 12 squares on the bottom row. show that your formula in part (i) gives the correct total number of squares. [3]", "5": "5 0607/51/o/n/20 \u00a9 ucles 2020 [turn over 2 black squares and white squares are now piled on top of each other like this: 1 square on the bottom row height = 2 squares total = 2 squares 2 squares on the bottom row height = 3 squares total = 6 squares 3 squares on the bottom row height = 4 squares total = 12 squares (a) on the dotty paper, complete the next diagram in the sequence. [1] (b) (i) complete the table. number of squares on the bottom row ( s)1 2 3 4 5 6 height ( h) 2 3 4 [1] (ii) write down a formula for the height, h, in terms of the number of squares on the bottom row, s. . [1]", "6": "6 0607/51/o/n/20 \u00a9 ucles 2020 (c) (i) complete the table. number of squares on the bottom row ( s)1 2 3 4 5 6 total number of squares ( t)2 6 12 [3] (ii) find a formula for the total number of squares, t, in terms of the number of squares on the bottom row, s. . [4] (iii) find the total number of squares in a pattern with 15 squares on the bottom row. . [2] (d) write down a formula to calculate the number of black squares, n, in a pattern with s squares on the bottom row. . [1]", "7": "7 0607/51/o/n/20 \u00a9 ucles 2020 (e) calculate the number of white squares, the number of black squares and the total number of squares in a pattern with 50 squares on the bottom row. number of white squares = number of black squares = total number of squares = [3] (f) (i) a pattern of black squares and white squares has 561 black squares. find the number of squares in the bottom row. . [3] (ii) is it possible to have a pattern of black squares and white squares with a total of 480 squares? give a reason for your answer. ... because ... . [3]", "8": "8 0607/51/o/n/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_w20_qp_52.pdf": { "1": "cambridge igcse\u2122dc (kn/sg) 189357/1 \u00a9 ucles 2020 [turn overthis document has 8 pages. blank pages are indicated. *3375474850* cambridge international mathematics 0607/52 paper 5 investigation (core) october/november 2020 1 hour 10 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 36. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/52/o/n/20 \u00a9 ucles 2020 answer all the questions. investigation area of right-angled triangles this investigation looks at finding the area of a right-angled triangle using its perimeter. in this investigation all lengths are in centimetres. wnot to scale bh w is the hypotenuse of the triangle, b is the base of the triangle, h is the height of the triangle. perimeter, p, of this triangle. bhwp=+ + area, a, of this triangle. ab h21= 1 (a) this right-angled triangle is drawn on a 1 cm2 grid. (i) measure and write down the length of the hypotenuse. ... [1] (ii) show that the perimeter is 12. [1] (iii) find the area of the triangle. . [1]", "3": "3 0607/52/o/n/20 \u00a9 ucles 2020 [turn over (b) 10 86not to scale (i) find the perimeter of this triangle. . [2] (ii) find the area of this triangle. . [2] ", "4": "4 0607/52/o/n/20 \u00a9 ucles 2020 (c) wnot to scale bh complete the table for right-angled triangles with sides b, h and w. b h w perimeter, p area, a 12 5 13 30 30 84 13 85 24 25 56 84 60 11 132 [5]", "5": "5 0607/52/o/n/20 \u00a9 ucles 2020 [turn over 2 (a) not to scale26 2410 this triangle has perimeter p = 60. show that the calculation 260 26026 #- bl gives the correct area for this triangle. [3] (b) not to scale50 48 this triangle has perimeter p = 112. show that the calculation 2112 211250 # - bl gives the correct area for this triangle. [3]", "6": "6 0607/52/o/n/20 \u00a9 ucles 2020 3 (a) complete the table. b h w p a calculation 24 10 26 60 120260 26026 #- bl =120 12 9 15 36 542236 3615 #- bl = 54 48 50 11222112 11250 # - bl = 15 8 17 60 = 60 21 29 70 210 = 12 37 210 = [8] (b) write an expression for the area of a right-angled triangle in terms of p and w. . [1]", "7": "7 0607/52/o/n/20 \u00a9 ucles 2020 [turn over (c) wnot to scale bh pythagoras\u2019 theorem wb h22 2=+ not to scale 5633 use your expression from part (b) to find the area of this triangle. . [4] question 4 is printed on the next page.", "8": "8 0607/52/o/n/20 \u00a9 ucles 2020 4 (a) w bhnot to scale this is a rhombus. use question 3(b) to write down an expression for the area of this rhombus in terms of p and w. . [1] (b) use your expression from part (a) to find the area of this rhombus when w = 41 and b = 40. . [4] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge." }, "0607_w20_qp_53.pdf": { "1": "cambridge igcse\u2122dc (mb) 207018 \u00a9 ucles 2020 [turn overthis document has 8 pages. blank pages are indicated. *1893755370* cambridge international mathematics 0607/53 paper 5 investigation (core) october/november 2020 1 hour 10 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 36. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/53/o/n/20 \u00a9 ucles 2020 answer all the questions. investigation area of right-angled triangles this investigation looks at finding the area of a right-angled triangle using its perimeter. in this investigation all lengths are in centimetres. wnot to scale bh w is the hypotenuse of the triangle, b is the base of the triangle, h is the height of the triangle. perimeter, p, of this triangle. bhwp=+ + area, a, of this triangle. ab h21= 1 (a) this right-angled triangle is drawn on a 1 cm2 grid. (i) measure and write down the length of the hypotenuse. ... [1] (ii) show that the perimeter is 12. [1] (iii) find the area of the triangle. . [1]", "3": "3 0607/53/o/n/20 \u00a9 ucles 2020 [turn over (b) 10 86not to scale (i) find the perimeter of this triangle. . [2] (ii) find the area of this triangle. . [2] ", "4": "4 0607/53/o/n/20 \u00a9 ucles 2020 (c) wnot to scale bh complete the table for right-angled triangles with sides b, h and w. b h w perimeter, p area, a 12 5 13 30 30 84 13 85 24 25 56 84 60 11 132 [5]", "5": "5 0607/53/o/n/20 \u00a9 ucles 2020 [turn over 2 (a) not to scale26 2410 this triangle has perimeter p = 60. show that the calculation 260 26026 #- bl gives the correct area for this triangle. [3] (b) not to scale50 48 this triangle has perimeter p = 112. show that the calculation 2112 211250 # - bl gives the correct area for this triangle. [3]", "6": "6 0607/53/o/n/20 \u00a9 ucles 2020 3 (a) complete the table. b h w p a calculation 24 10 26 60 120260 26026 #- bl =120 12 9 15 36 542236 3615 #- bl = 54 48 50 11222112 11250 # - bl = 15 8 17 60 = 60 21 29 70 210 = 12 37 210 = [8] (b) write an expression for the area of a right-angled triangle in terms of p and w. . [1]", "7": "7 0607/53/o/n/20 \u00a9 ucles 2020 [turn over (c) wnot to scale bh pythagoras\u2019 theorem wb h22 2=+ not to scale 5633 use your expression from part (b) to find the area of this triangle. . [4] question 4 is printed on the next page.", "8": "8 0607/53/o/n/20 \u00a9 ucles 2020 4 (a) w bhnot to scale this is a rhombus. use question 3(b) to write down an expression for the area of this rhombus in terms of p and w. . [1] (b) use your expression from part (a) to find the area of this rhombus when w = 41 and b = 40. . [4] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge." }, "0607_w20_qp_61.pdf": { "1": "cambridge igcse\u2122cambridge international mathematics 0607/61 paper 6 investigation and modelling (extended) october/november 2020 1 hour 40 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer both part a (questions 1 and 2) and part b (questions 3 to 6). \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 60. \u25cf the number of marks for each question or part question is shown in brackets [ ]. dc (lk/cb) 189361/3 \u00a9 ucles 2020 [turn overthis document has 12 pages. blank pages are indicated. *9969408613*", "2": "2 0607/61/o/n/20 \u00a9 ucles 2020 answer both parts a and b. a investigation (questions 1 and 2) piling squares (30 marks) you are advised to spend no more than 50 minutes on this part. this investigation looks at different ways of piling squares. all the squares are the same size. 1 squares are piled in a pattern, like this: 1 square on the bottom row 2 squares on the bottom row 3 squares on the bottom row total = 1 square total = 3 squares total = 6 squares (a) on the dotty paper, complete the next diagram in the sequence. [1]", "3": "3 0607/61/o/n/20 \u00a9 ucles 2020 [turn over (b) (i) complete the table. number of squares on the bottom row ( s)1 2 3 4 5 6 7 total number of squares ( t)1 3 6 [2] (ii) a formula for finding the total number of squares is xs ys t2=+ . find the value of x and the value of y. x = y = [3] (iii) show that the formula in part (ii) gives the correct total for a pattern of squares with 8 squares on the bottom row. [3]", "4": "4 0607/61/o/n/20 \u00a9 ucles 2020 2 black squares and white squares are now piled on top of each other. every row starts with a white square, followed by a black square, followed by a white square and so on. 1 square on the bottom row 2 squares on the bottom row 3 squares on the bottom row 1 white square 2 white squares 4 white squares 0 black squares 1 black square 2 black squares total = 1 square total = 3 squares total = 6 squares (a) on the dotty paper, complete the next diagram in the sequence. [1] (b) complete the table. number of squares on the bottom row ( s)1 2 3 4 5 6 7 number of black squares ( b)0 1 2 9 number of white squares ( w)1 2 4 12 total number of squares ( t )1 3 6 21 [3]", "5": "5 0607/61/o/n/20 \u00a9 ucles 2020 [turn over (c) (i) complete the two tables for black squares. some of the information is in the table in part (b) . odd number of squares on the bottom row ( s)1 3 5 7 9 number of black squares ( b)0 2 20 even number of squares on the bottom row ( s)2 4 6 8 10 number of black squares ( b)1 9 16 [1] (ii) a formula for finding the number of black squares, b, when the number of squares on the bottom row, s, is an odd number is bx sy2=+ . find the value of x and the value of y. x = y = [3] (iii) find a formula for the number of black squares, b, when the number of squares on the bottom row, s, is an even number. . [2]", "6": "6 0607/61/o/n/20 \u00a9 ucles 2020 (d) (i) complete the two tables for white squares. some of the information is in the table in part (b) . odd number of squares on the bottom row ( s)1 3 5 7 9 number of white squares ( w)1 4 25 even number of squares on the bottom row ( s)2 4 6 8 10 number of white squares ( w)2 12 20 [1] (ii) a formula for finding the number of white squares, w, when the number of squares on the bottom row, s, is an odd number is wx sy s41 2=+ +. find the value of x and the value of y. x = y = [3]", "7": "7 0607/61/o/n/20 \u00a9 ucles 2020 [turn over (iii) find a formula for the number of white squares, w, when the number of squares on the bottom row, s, is an even number. . [3] (e) a pattern has a total of 253 squares. calculate the number of squares on the bottom row, the total number of white squares and the total number of black squares. number of squares on the bottom row . total number of white squares .. total number of black squares .. [4]", "8": "8 0607/61/o/n/20 \u00a9 ucles 2020 b modelling (questions 3 to 6) a bouncing ball (30 marks) you are advised to spend no more than 50 minutes on this part. this task looks at modelling the bounce of a ball. a ball drops vertically onto a hard floor. each time the ball bounces it rises vertically upwards until its speed becomes zero. at this point the ball drops vertically to bounce on the hard floor again. 3 a ball drops from a height of 10 metres. each time it bounces it rises to a maximum height which is half the height that it previously dropped. not to scale10 m 5 m 2.5 m 1st bounce 2nd bounce 3rd bounce (a) calculate the maximum height of the ball after 4 bounces. . [2] (b) (i) calculate the first maximum height that is less than 10 cm. . [2] (ii) write down how many bounces the ball has made when its first maximum height is less than 10 cm. . [1]", "9": "9 0607/61/o/n/20 \u00a9 ucles 2020 [turn over (c) a model for the maximum height, h metres, which the ball rises after n bounces, is hp qn#= . for example, when n1=, h5=. find the value of p and the value of q. p = q = [3] 4 a ball drops from a height of 35 metres. after 4 bounces it reaches a maximum height of 0.056 metres. each time it bounces it rises to a maximum height which is a fraction of the height that it previously dropped. calculate the value of this fraction. . [3]", "10": "10 0607/61/o/n/20 \u00a9 ucles 2020 5 a model for the total distance, d metres, which a ball travels vertically, is dpqq 11=-+eo , where p is the height from which the ball is dropped and q is the fraction of the previous maximum height. (a) (i) when q0=, find d and explain what happens to the ball. d = and . . [1] (ii) when q1=, explain what happens to the ball. . . [1] (b) calculate the total distance that the ball in question 3 travels vertically. . [3] (c) a ball drops from a height of 40 metres. the ball travels a total distance of 200 metres. each time it bounces it rises to a maximum height which is a fraction of the height that it previously dropped. calculate the value of this fraction. . [3]", "11": "11 0607/61/o/n/20 \u00a9 ucles 2020 [turn over 6 a ball drops from a height of 10 metres. each time it bounces it rises to a maximum height which is half the height that it previously dropped. time is measured in seconds. (a) a model for the time taken until the nth bounce, tn, is tqqq 710 112 nn =-+-fp , where q is the fraction of the previous maximum height. (i) show that t710 1= . [1] (ii) show that the time taken until the 10th bounce is 8.0 seconds, correct to 2 significant figures. [2] (b) a model for t, the total time that the ball bounces, is tqq 710 11=-+fp . calculate the total time that the ball bounces. . [2] questions 6(c) and 6(d) are printed on the next page.", "12": "12 0607/61/o/n/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge. (c) sketch the graph of the model for t in part (b) , for q011g . 00time (seconds) fraction of the previous maximum heightt q1 [4] (d) the time taken until the first bounce, t1, is also modelled by .tp 982 1= , where p is the initial height that the ball drops. (i) find the value of t1 when the ball is dropped from a height of 22.5 m. . [1] (ii) change the model for the total time t, in part (b) , for the ball when it is dropped from a height of 22.5 m. . [1]" }, "0607_w20_qp_62.pdf": { "1": "cambridge igcse\u2122cambridge international mathematics 0607/62 paper 6 investigation and modelling (extended) october/november 2020 1 hour 40 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer both part a (questions 1 to 4) and part b (questions 5 to 9). \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 60. \u25cf the number of marks for each question or part question is shown in brackets [ ]. dc (lk/cb) 189360/2 \u00a9 ucles 2020 [turn overthis document has 16 pages. blank pages are indicated. *5876549733*", "2": "2 0607/62/o/n/20 \u00a9 ucles 2020 answer both parts a and b. a investigation (questions 1 to 4) area of right-angled triangles (30 marks) you are advised to spend no more than 50 minutes on this part. this investigation looks at finding the area of a right-angled triangle using its perimeter. in this investigation all lengths are in centimetres. h bw w is the hypotenuse of the triangle, b is the base of the triangle, h is the height of the triangle. perimeter, p, of this triangle. bhwp=+ + area, a, of this triangle. ab h21= 1 (a) 3 4not to scale5 (i) find the perimeter of this triangle. . [1] (ii) find the area of this triangle. . [1]", "3": "3 0607/62/o/n/20 \u00a9 ucles 2020 [turn over (b) h bwnot to scale complete the table for right-angled triangles with sides b, h and w. b h w perimeter, p area, a 12 5 13 30 30 84 13 85 24 25 56 84 60 11 132 [3]", "4": "4 0607/62/o/n/20 \u00a9 ucles 2020 2 (a) 10 24not to scale26 this triangle has perimeter p60= . show that the calculation 260 26026 #- bl gives the correct area for this triangle. [3] (b) 48not to scale50 this triangle has perimeter p112= . show that the calculation 2112 211250 # - bl gives the correct area for this triangle. [3]", "5": "5 0607/62/o/n/20 \u00a9 ucles 2020 [turn over 3 (a) complete the table. b h w p a calculation 24 10 26 60 120260 26026 #- bl = 120 12 9 15 36 542236 3615 #- bl = 54 48 50 11222112 11250 # - bl = 15 8 17 60 = 60 21 29 70 210 = 12 37 210 = [4] (b) write an expression for the area of a right-angled triangle in terms of p and w. . [1]", "6": "6 0607/62/o/n/20 \u00a9 ucles 2020 (c) h bw pythagoras\u2019 theorem wb h22 2=+ 56not to scale33 use your expression from part (b) to find the area of this triangle. . [4]", "7": "7 0607/62/o/n/20 \u00a9 ucles 2020 [turn over (d) 3k 4knot to scale5k show that your expression from part (b) works for right-angled triangles with sides 3 k, 4k and 5 k. [2]", "8": "8 0607/62/o/n/20 \u00a9 ucles 2020 4 (a) an isosceles right-angled triangle has sides x, x and 10. (i) use question 3(b) to find an expression for the area of this triangle. give your answer in its simplest form. . [2] (ii) use your answer to part (i) and the formula for the area of a triangle, to find the exact value of x. . [2]", "9": "9 0607/62/o/n/20 \u00a9 ucles 2020 [turn over (b) h bwnot to scale (i) by writing ub h=+ and using your expression from question 3(b) , find an expression, in terms of u and w, for the area of any right-angled triangle. [3] (ii) use pythagoras\u2019 theorem to show that your expression from part (i) gives bh21 for all right- angled triangles. [1]", "10": "10 0607/62/o/n/20 \u00a9 ucles 2020 b modelling (questions 5 to 9) hot air balloon flight (30 marks) you are advised to spend no more than 50 minutes on this part. this task is about the flight of a hot air balloon. a balloon travels in the direction of the wind. the pilot can make the balloon rise or descend. a journey is in four parts. part 1 lift-off. the balloon leaves the ground and rises. part 2 the flight. part 3 the balloon descends quickly. part 4 the balloon descends slowly and lands. 5 this journey is at sunrise. for part 1, a model for the height of the balloon above the ground ( h metres), t minutes after lift-off, is () \u00b0 cos ht 480 12 0 =- `j for t09gg . (a) on the diagram, sketch the graph of h for t09gg . 00h t960 3 6 time (minutes)height (metres) 9 [2]", "11": "11 0607/62/o/n/20 \u00a9 ucles 2020 [turn over (b) find the height of the balloon 3 minutes after lift-off. . [1] (c) find the increase in height between 3 minutes and 6 minutes after lift-off. . [2] (d) find the average speed at which the balloon is rising between 3 minutes and 6 minutes after lift -off. give your answer in metres per second. . [3] (e) part 1 is complete 9 minutes after lift-off. use the model for h in terms of t to show that the height of the balloon at this time is 960 m. [1]", "12": "12 0607/62/o/n/20 \u00a9 ucles 2020 6 for part 2, the table shows the height of the balloon above the ground ( l metres), t minutes after lift -off. time (t minutes)9 10 11 12 13 14 15 16 17 18 19 20 height (l metres)960 959 960 960 960 959 960 987 1014 1041 1068 1095 (a) on the grid, complete the scatter diagram for these results. the first seven points have been plotted for you. 9900l t1000 95010501100 10 11 12 13 14 15 16 time (minutes)height (metres) 17 18 20 19 [2]", "13": "13 0607/62/o/n/20 \u00a9 ucles 2020 [turn over (b) between 15 minutes and 25 minutes after lift-off, the balloon rises at the same rate. it then travels at a constant height for 10 minutes. complete the list of linear functions to model l for part 2. (i) for t 91 51g l = ... (ii) for t 15 251g l = ... (iii) for .. t1g .. l = ... [5]", "14": "14 0607/62/o/n/20 \u00a9 ucles 2020 7 for part 3, the balloon descends at a constant speed of 2.5 m/s until it is 180 m above the ground. find how many minutes it takes the balloon to travel from lift-off to the end of part 3 of the journey. . [4] 8 for part 4, a model for the height above the ground ( d metres), t minutes after lift-off, is .dt4012545060 =--. (a) find how many minutes after lift-off the balloon lands. . [3]", "15": "15 0607/62/o/n/20 \u00a9 ucles 2020 [turn over (b) find the average speed of the balloon during part 4 of the journey. give your answer in metres per minute. . [2] question 9 is printed on the next page.", "16": "16 0607/62/o/n/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.9 another journey is at sunset. (a) the balloon completes part 1 of the journey in 7.5 minutes. at the end of part 1, the height of the balloon above the ground is 960 m. a model for part 1 is ()\u00b0 cos hk t 480 1 =- `j for . t 07 5 gg . find the value of k. . [2] (b) in part 2, the first 6 minutes of the journey are at a constant height of 960 m. then, the balloon rises 2 times as fast as in question 6(b)(ii) . change the model in question 6(b)(ii) so that it models this part of the journey. . [3]" }, "0607_w20_qp_63.pdf": { "1": "cambridge igcse\u2122cambridge international mathematics 0607/63 paper 6 investigation and modelling (extended) october/november 2020 1 hour 40 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer both part a (questions 1 to 4) and part b (questions 5 to 8). \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 60. \u25cf the number of marks for each question or part question is shown in brackets [ ]. dc (lk/cb) 189359/1 \u00a9 ucles 2020 [turn overthis document has 20 pages. blank pages are indicated. *8140996719*", "2": "2 0607/63/o/n/20 \u00a9 ucles 2020 answer both parts a and b. a investigation (questions 1 to 4) areas of polygons inside and outside a circle (30 marks) you are advised to spend no more than 50 minutes on this part. this investigation looks at the areas of polygons drawn inside and outside a circle of radius 10 cm. an inscribed polygon is a polygon in which all the vertices lie on a circle. this is an inscribed square. a circumscribed polygon is a polygon in which each side is a tangent to a circle. this is a circumscribed square. you may find some of these formulas useful. area, a, of circle, radius r ar2r= area, a, of triangle, base b, height h ab h21= in a right-angled triangle, hypotenus eopposit esini= , coshypotenus eadjacenti= , opposit etanadjacen ti= .", "3": "3 0607/63/o/n/20 \u00a9 ucles 2020 [turn over 1 (a) not to scale10 cmo a square circumscribes a circle, centre o, radius 10 cm. work out the area of the square. . [1]", "4": "4 0607/63/o/n/20 \u00a9 ucles 2020 (b) not to scale10 cmo a square is inscribed in a circle, centre o, radius 10 cm. work out the area of the square. . [2] (c) show that the area of a circle, radius 10 cm, is cm 1002r . [1] (d) area of inscribed square 1 area of circle 1 area of circumscribed square use this statement to complete the inequality below. . 1 r 1 . [1]", "5": "5 0607/63/o/n/20 \u00a9 ucles 2020 [turn over 2 (a) not to scale10 cmo a regular hexagon is inscribed in a circle, centre o, radius 10 cm. find the area of the hexagon. . [3]", "6": "6 0607/63/o/n/20 \u00a9 ucles 2020 (b) (i) not to scale 10 cm an equilateral triangle has height 10 cm. find the area of the triangle. . [3] (ii) not to scaleo 10 cm a regular hexagon circumscribes a circle, centre o, radius 10 cm. using your answer to part (i) , find the area of the hexagon. . [2]", "7": "7 0607/63/o/n/20 \u00a9 ucles 2020 [turn over (c) (i) use question 1(c) , question 2(a) and question 2(b)(ii) to complete the inequality. . 1 r 1 . [1] (ii) give a geometric reason why the range in the inequality in question 2(c)(i) is smaller than the range in the inequality in question 1(d) . . . [1]", "8": "8 0607/63/o/n/20 \u00a9 ucles 2020 3 (a) not to scaleo 10 cm a regular 12-sided polygon is inscribed in a circle, centre o, radius 10 cm. find the area of this polygon. . [2]", "9": "9 0607/63/o/n/20 \u00a9 ucles 2020 [turn over (b) not to scaleo 10 cm a regular 12-sided polygon circumscribes a circle, centre o, radius 10 cm. find the area of this polygon. . [3] (c) use the answers to part (a) and part (b) to complete the inequality. . 1 r 1 . [1]", "10": "10 0607/63/o/n/20 \u00a9 ucles 2020 4 (a) (i) show that a formula for the area, cma2, of a regular polygon with n sides inscribed in a circle, radius 10 cm, is sin ann50360\u00b0 = bl . [2] (ii) show that a formula for the area, cmb2, of a regular polygon with n sides that circumscribes a circle, radius 10 cm, is tan bnn100180\u00b0 = bl . [2]", "11": "11 0607/63/o/n/20 \u00a9 ucles 2020 [turn over (b) (i) work out the area of a regular polygon with 100 sides that is inscribed in a circle, radius 10 cm. give your answer correct to 4 significant figures. . [2] (ii) work out the area of a regular polygon with 100 sides that circumscribes a circle, radius 10 cm. give your answer correct to 4 significant figures. . [2] (c) use your answers to part (b) to explain how you can find the value of r correct to 3 significant figures. . . [1]", "12": "12 0607/63/o/n/20 \u00a9 ucles 2020 b modelling (questions 5 to 8) modelling containers (30 marks) you are advised to spend no more than 50 minutes on this part. olivia wants to design a closed container with a volume of cm 10003 and minimum surface area. 5 olivia uses a square-based cuboid to model the container. not to scaleh cm x cm x cm (a) (i) write down a formula for the volume of the cuboid, cmv3, in terms of x and h. . [1] (ii) find a formula for the surface area, cms2, of the cuboid, in terms of x and h. give your answer in its simplest form. . [2] (b) (i) v1000= . write h in terms of x. . [1] (ii) show that sxx24000 2=+ . [1]", "13": "13 0607/63/o/n/20 \u00a9 ucles 2020 [turn over (iii) work out the value of s when x25= . . [1] (c) sketch the graph of sxx24000 2=+ for x 02 5 1g . 00s x25 [3] (d) (i) find the minimum surface area of the cuboid. . [1] (ii) describe the container that gives the minimum surface area for olivia\u2019s model. . . [2]", "14": "14 0607/63/o/n/20 \u00a9 ucles 2020 6 v olume, v, of a cylinder of radius r, height h vr h2r= curved surface area, a, of a cylinder of radius r, height h rh a2r= olivia now uses a cylinder to model the container. not to scale h cmr cm the total surface area of this model is cmt2. (a) v1000= . show that trr22000 2r=+ . [3] (b) (i) find the minimum surface area of the cylinder. . [2]", "15": "15 0607/63/o/n/20 \u00a9 ucles 2020 [turn over (ii) find the dimensions of the cylinder with the minimum surface area. r = h = [2]", "16": "16 0607/63/o/n/20 \u00a9 ucles 2020 7 v olume, v, of a pyramid, base area a, height h vh a31= olivia now uses a square-based pyramid to model the container. not to scale x cmo cd a beh cm the pyramid, oabcd , has a square base of side x cm and height h cm. the vertex of the pyramid, o, is directly above the centre of the square base. e is the mid-point of bc. (a) find an expression for oe in terms of h and x. . [2]", "17": "17 0607/63/o/n/20 \u00a9 ucles 2020 [turn over (b) the total surface area of this model is cmp2. v1000= . show that pxxx36000000 26 =++ . [4]", "18": "18 0607/63/o/n/20 \u00a9 ucles 2020 (c) (i) find the minimum surface area of the pyramid. . [2] (ii) find the dimensions of the pyramid with the minimum surface area. x = h = [2]", "19": "19 0607/63/o/n/20 \u00a9 ucles 2020 8 olivia recommends the container with the smallest surface area to a company. give a geometric reason why the company might not accept olivia\u2019s recommendation. olivia recommends the geometric reason ... . [1]", "20": "20 0607/63/o/n/20 \u00a9 ucles 2020 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" } }, "2021": { "0607_m21_qp_12.pdf": { "1": "this document has 8 pages. dc (rw/cb) 207184/2 \u00a9 ucles 2021 [turn over *9192120993* cambridge international mathematics 0607/12 paper 1 (core) february/march 2021 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ].cambridge igcse\u2122", "2": "2 0607/12/f/m/21 \u00a9 ucles 2021 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/12/f/m/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 write the number seven million twenty thousand in figures. . [1] 2 write 48% as a decimal. . [1] 3 in paris, the average temperature (\u00b0c) and the average rainfall (mm) for each month are shown. month average temperature (\u00b0c) average rainfall (mm) january 5 56 february 6 46 march 9 36 april 11 43 may 15 56 june 16 51 july 20 56 august 20 61 september 16 51 october 12 50 november 7 50 december 5 51 (a) write down the average temperature in paris for july. . \u00b0c [1] (b) write down the month with the highest average rainfall. . [1] 4 a polygon has 6 sides. write down the mathematical name of this polygon. . [1] 5 write 45.1665 correct to 2 decimal places. . [1]", "4": "4 0607/12/f/m/21 \u00a9 ucles 2021 6 the scale shows the probability of events x, y and z. x y z0 1 (a) complete the following statement. event is impossible. [1] (b) event e is less likely than event y . on the scale, draw an arrow to show the probability of event e. [1] 7 work out 41 of 200. . [1] 8 complete the mapping diagram. 3x f(x) 5 7 .. 116 10 14 18 22 [1] 9 how many seconds are there in 30 minutes? seconds [1] 10 insert one pair of brackets to make this statement correct. 1 + 2 # 3 + 1 = 9 [1]", "5": "5 0607/12/f/m/21 \u00a9 ucles 2021 [turn over 11 find the value of xy72- when x2= and y5=. . [2] 12 write the ratio 6 : 9 in its simplest form. ... :\u200a ... [1] 13 these are the first six terms of a sequence. x 2 9 16 23 y (a) find the value of x and the value of y. x= . y= . [2] (b) explain why 42 is not in this sequence. . . [1] 14 david buys 12 pens for $2.40 . work out the cost of 18 pens. $ . [2] 15 carla walks 6 km in 90 minutes. find her average speed in km/h. . km/h [2]", "6": "6 0607/12/f/m/21 \u00a9 ucles 2021 16 aliscoreenglish mathematics science 50100150200250 ben mia suzi0 four students take tests in english, mathematics and science. the compound bar chart shows the scores for three students. (a) work out mia\u2019s score for english. . [1] (b) suzi scored 75 in each test. complete the compound bar chart to show suzi\u2019s scores. [1] (c) write down the name of the student with the highest mathematics score. . [1] 17 factorise fully. yy14 352- . [2] 18 find the value of () () 31 05 1042## # , giving your answer in standard form. . [2]", "7": "7 0607/12/f/m/21 \u00a9 ucles 2021 [turn over 19 a spinner has four sections. each section is a different colour. it is spun 400 times and the colour it lands on is recorded in the table. colour red green blue white frequency 81 126 119 74 (a) write down an estimate for the probability of the spinner landing on green. . [1] (b) the spinner is spun 2000 times. estimate the number of times the spinner lands on red. . [2] 20 not to scale4x\u00b03x\u00b0 3x\u00b02x\u00b0 work out the value of x. x= . [2] 21 solve .x 20 622+ . [2] questions 22, 23 and 24 are printed on the next page.", "8": "8 0607/12/f/m/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.22 the line yk x5 =+ is parallel to the line yx265 0 -+ =. find the value of k. k= . [1] 23 solve the simultaneous equations. ab ab52 28 62 36-+ =- -= a= . b= . [2] 24 xy 0 2 11 \u2013 12 \u2013 234 \u2013 2\u2013 1 \u2013 3 \u2013 4 the diagram shows the graph of ()f yx= . on the same diagram, sketch the graph of ()f yx 1 =+ . [1]" }, "0607_m21_qp_22.pdf": { "1": "this document has 8 pages. cambridge igcse\u2122cambridge international mathematics 0607/22 paper 2 (extended) february/march 2021 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ]. dc (lk/sw) 207825/1 \u00a9 ucles 2021 [turn over *4045934305*", "2": "2 0607/22/f/m/21 \u00a9 ucles 2021 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area =a c bcb a", "3": "3 0607/22/f/m/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 these are the test results for 14 students. 27 19 22 25 18 23 24 17 16 25 17 27 23 26 (a) construct an ordered stem-and-leaf diagram to show this information, including a key. key: | = [3] (b) find the median. . [1] 2 point a (7, 5) is translated to point b (2, 2). find the vector that represents this translation. fp [2] 3 find the highest common factor (hcf) of 84 and 72. . [1] 4 solve. x27+= . [1]", "4": "4 0607/22/f/m/21 \u00a9 ucles 2021 5 point a has coordinates ( -3, 2). point b has coordinates (5, -4). (a) find the mid-point of ab. ( , . ) [2] (b) find the length of ab. . [3] 6 find the value of p when 24 2p 67'= . p = [3]", "5": "5 0607/22/f/m/21 \u00a9 ucles 2021 [turn over 7 iraj travels to school either by bus or on a bicycle. the probability that he goes by bus is 0.3 . he can have lunch at home or at school. the probability that he has lunch at school is 0.6 . (a) complete the tree diagram. bicyclebus homeschool 0.3 .0.6 . . homeschool . [2] (b) find the probability that iraj travels on a bicycle to school and goes home for lunch. . [2] 8 expand and simplify. () () ab ba 42 53 63 +- - . [2]", "6": "6 0607/22/f/m/21 \u00a9 ucles 2021 9 (a) a e dnot to scale76\u00b0 cb a, b, c, and d are points on a circle. cde is a straight line. find angle abc . angle abc = [1] (b) rq o s tp not to scale 40\u00b025\u00b0 p, q, r, s and t are points on the circle centre o. toq is a straight line. (i) find angle str. angle str = [1] (ii) find angle qor. angle qor = [1] ", "7": "7 0607/22/f/m/21 \u00a9 ucles 2021 [turn over 10 aisha picks three number cards from a pack. the mean of the three numbers is 61 3. she picks another card from the pack. the mean of the four numbers is 621. work out the number on the fourth card. . [3] 11 find the next term and an expression for the nth term of this sequence. 35, 29, 19, 5, \u2026 next term = nth term = [3] 12 rearrange this formula to make x the subject. yxax 3=- x = [3] questions 13 and 14 are printed on the next page.", "8": "8 0607/22/f/m/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.13 rationalise the denominator and simplify. 52 1+ . [3] 14 write as a single fraction in its simplest form. aa aa 43 21 +-- . [3]" }, "0607_m21_qp_32.pdf": { "1": "this document has 16 pages. any blank pages are indicated. cambridge igcse\u2122 dc (ce/cgw) 199834/2 \u00a9 ucles 2021 [turn overcambridge international mathematics 0607/32 paper 3 (core) february/march 2021 1 hour 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 96. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *5485313677*", "2": "2 0607/32/f/m/21 \u00a9 ucles 2021 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/32/f/m/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 (a) 6 13 21 25 27 38 39 41 43 49 from the list above, write down (i) an even number, .. [1] (ii) a factor of 50, .. [1] (iii) a multiple of 7, .. [1] (iv) a triangle number, .. [1] (v) a cube number, .. [1] (vi) a prime number. .. [1] (b) find 4213. give your answer correct to 4 significant figures. .. [2] (c) work out 274941 #. give your answer correct to 5 decimal places. .. [2] ", "4": "4 0607/32/f/m/21 \u00a9 ucles 2021 2 here is the price list in a restaurant. you can choose a 1-course meal or a 2-course meal or a 3-course meal. 1-course meal $28 2-course meal $35 3-course meal $42 coffee or tea $3 anna and alexa eat a meal in this restaurant. anna has a 3-course meal and a cup of coffee. alexa has a 2-course meal and two cups of tea. (a) work out how much this costs altogether. $ .. [2] (b) they pay a service charge of 15% of this cost. (i) work out the total cost including the service charge. $ .. [2] (ii) they each pay half of the total cost including the service charge. work out how much they each pay. $ .. [1]", "5": "5 0607/32/f/m/21 \u00a9 ucles 2021 [turn over 3 a b d ce6 cm 10 cm 100\u00b0x\u00b0not to scale abcd is a rectangle. ad = 6 cm, ae = 10 cm and angle aeb = 100\u00b0. (a) write down the size of one interior angle of a rectangle. .. [1] (b) use trigonometry to show that the value of x is 37, correct to the nearest whole number. [2] (c) find the size of (i) angle dae , angle dae = . [1] (ii) angle abe, angle abe = . [2] (iii) angle ebc . angle ebc = . [1]", "6": "6 0607/32/f/m/21 \u00a9 ucles 2021 4 hikaru throws a die 40 times. the results are shown in the bar chart. 246 frequency number on die810 1 03579 1 2 3 4 5 6 (a) write down the mode. .. [1] (b) find how many more times she throws 2 than 1. .. [1] (c) calculate the mean. .. [2] (d) hikaru represents her results in a pie chart. work out the sector angle for throwing a 3. .. [2] ", "7": "7 0607/32/f/m/21 \u00a9 ucles 2021 [turn over 5 the diagram shows a 1 cm2 grid. 0y x2468 1357 1 3 5 7 9 2 4 6 8 (a) on the grid, plot and label the points a (3, 5), b (6, 5), c (8, 1) and d (1, 1). join the points to form a quadrilateral. [2] (b) write down the mathematical name for quadrilateral abcd . .. [1] (c) write down the coordinates of the mid-point of bc. ( ... , ...) [1] (d) work out the gradient of da. .. [2] (e) use pythagoras\u2019 theorem to work out the length of bc. . cm [2] (f) work out the perimeter of abcd . . cm [2]", "8": "8 0607/32/f/m/21 \u00a9 ucles 2021 6 piotr works at a pottery making solid spheres. (a) each sphere has a radius of 2 cm. (i) calculate the volume of one sphere. ... cm3 [2] (ii) calculate the surface area of one sphere. ... cm2 [2] (b) a sphere costs $4.50 to make. the selling price of a sphere is $25. (i) work out the profit made when a sphere is sold. $ .. [1] (ii) in a sale, the selling price of a sphere is reduced by 16%. work out the sale price of a sphere. $ .. [2]", "9": "9 0607/32/f/m/21 \u00a9 ucles 2021 [turn over 7 (a) solve. (i) x63+= - x = . [1] (ii) ()x52 16-= x = . [2] (b) show the inequality x2h on the number line. 4 2 0 3 1 \u2013 1 5x \u2013 2 [1] (c) simplify. rr r 32+- .. [1] (d) aa ann 16#= find the value of n. n = . [1] (e) write as a single fraction in its simplest form. (i) mm 7 23+ .. [2] (ii) m m 43 98# .. [2] ", "10": "10 0607/32/f/m/21 \u00a9 ucles 2021 8 11 males were asked to score how pleased they were to receive socks as a present. for each male, their score from 0 to 10 and their age in years are shown in the table. age (years) 10 15 20 25 30 35 45 50 60 70 80 score 1 2 3 7 5.5 6.5 5 7.5 10 9.5 9 (a) complete the scatter diagram. the first 6 points have been plotted for you. 024score6 13579 810 10 30 50 70 20 0 40 60 80 age (years) [2] (b) what type of correlation is shown in the scatter diagram? .. [1] ", "11": "11 0607/32/f/m/21 \u00a9 ucles 2021 [turn over (c) find (i) the mean age, . years [1] (ii) the mean score. .. [1] (d) on the scatter diagram, draw a line of best fit. [2] (e) use your line of best fit to find a score for a male aged 55 years. .. [1] ", "12": "12 0607/32/f/m/21 \u00a9 ucles 2021 9 (a) u = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} a = {2, 4, 6, 8, 10} b = {1, 2, 5, 10} (i) complete each statement. ab+= {...} n(b) = ... 5g ... [3] (ii) write each element in the correct region of the venn diagram. a bu [2] (b) on the venn diagram, shade the region ()pq, l . p qu [1]", "13": "13 0607/32/f/m/21 \u00a9 ucles 2021 [turn over 10 a birthday cake is in the shape of a cylinder of radius 11 cm and height 10 cm. (a) calculate the volume of the cake. give the units of your answer. . ... [3] (b) the top of the cake and the curved surface area of the cake are covered in icing. calculate the area of the cake that is covered in icing. ... cm2 [3] (c) the top of the cake is divided into 12 equal sectors. work out the arc length of one sector. give your answer correct to the nearest centimetre. . cm [3]", "14": "14 0607/32/f/m/21 \u00a9 ucles 2021 11 a b d c0y x 9 8 7 6 5 4 3 2 1 \u2013 1 \u2013 2 \u2013 3 \u2013 4123456789 \u2013 5 \u2013 6\u2013 4\u2013 3\u2013 2\u2013 1 (a) describe fully the single transformation that maps shape a onto shape b. . . [2] (b) describe fully the single transformation that maps shape a onto shape c. . . [3] (c) describe fully the single transformation that maps shape a onto shape d. . . [2] (d) draw the enlargement of shape a with scale factor 2 and centre (0, 0). [2]", "15": "15 0607/32/f/m/21 \u00a9 ucles 2021 12 0y x\u2013 3 3 \u2013 58 (a) on the diagram, sketch the graph of . y 05x= for x33gg- . [2] (b) write down the equation of the horizontal asymptote. .. [1] (c) on the same diagram, sketch the graph of yx 42=- + for x33gg- . [2] (d) find the zeros of the graph of yx 42=- +. .. and . [2] (e) find the x-coordinate of each point where the graphs of . y 05x= and yx 42=- + intersect. x = .. and x = .. [2]", "16": "16 0607/32/f/m/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_m21_qp_42.pdf": { "1": "this document has 20 pages. any blank pages are indicated. cambridge igcse\u2122 dc (ce/ct) 207877/2 \u00a9 ucles 2021 [turn over *0796500410* cambridge international mathematics 0607/42 paper 4 (extended) february/march 2021 2 hours 15 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 120. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/42/f/m/21 \u00a9 ucles 2021 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area =a c bcb a", "3": "3 0607/42/f/m/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 (a) \u2013 8\u2013 6\u2013 4 \u2013 10 \u2013 20 2 4 6 8 1010 8 6 4 2 \u2013 2 \u2013 4 \u2013 6aay x (i) rotate triangle a through 90\u00b0 anticlockwise about (0, 0). label the image b. [2] (ii) reflect triangle a in the y-axis. label the image c. [1] (iii) describe fully the single transformation that maps triangle b onto triangle c. . . [2] (b) de de 0 2 4 6 8 10 12246y x describe fully the single transformation that maps trapezium d onto trapezium e. . . [3]", "4": "4 0607/42/f/m/21 \u00a9 ucles 2021 2 (a) write 260 512 correct to 3 significant figures. . [1] (b) write 0.000 000 576 in standard form. . [1] (c) calculate 27 63 1. 20 3#- . give your answer correct to 1 decimal place. . [2] (d) (i) work out 37% of $820. $ [2] (ii) work out $36 as a percentage of $150. . % [1] (e) an amount of money is shared between alan, bjorn and carlo in the ratio 3 : 7 : 5. carlo receives $695. (i) find the total amount of money shared. $ [3] (ii) carlo invests 40% of his $695 at a rate of 1.2% per year compound interest. calculate the value of his investment at the end of 5 years. $ [3]", "5": "5 0607/42/f/m/21 \u00a9 ucles 2021 [turn over (f) dana invests $2100 for 12 years at a rate of x% per year compound interest. at the end of the 12 years, the value of her investment is $2663.31 . calculate the value of x. x = [3]", "6": "6 0607/42/f/m/21 \u00a9 ucles 2021 3 (a) (i) write down the coordinates of the point where the line yx 23=- + crosses the y-axis. (.. , ..) [1] (ii) write down the gradient of the line yx 23=- +. . [1] (b) the line xy 6 += crosses the line x 2=- at point a. find the y-coordinate of a. . [1] (c) find the equation of the straight line that passes through the points (3, -1) and (12, 5). . [3] (d) the line l passes through the point (3, 4). line l is perpendicular to the line yx25 6 =+ . find the equation of line l. . [4]", "7": "7 0607/42/f/m/21 \u00a9 ucles 2021 [turn over (e) \u2013 2 \u2013 1 1 0 2 3 4 5 6 767 5 4 3 2 1 \u2013 1 \u2013 2y x (i) on the grid, draw the lines , yx y 43=+ = and yx 1 =- . [3] (ii) by shading the unwanted regions, find and label the region r that satisfies these three inequalities. y4g xy 3h+ yx 1h- [1] ", "8": "8 0607/42/f/m/21 \u00a9 ucles 2021 4 (a) the mass, m grams, of each of 50 apples is found. the results are shown in the table. mass ( m grams) frequency 70 1 m g 90 2 90 1 m g 110 7 110 1 m g 130 14 130 1 m g 150 10 150 1 m g 170 12 170 1 m g 190 5 (i) write down the modal class. .. 1 \u200am \u200ag .. [1] (ii) calculate an estimate of the mean. .. g [2] (b) the mass, x grams, of each of 120 different apples is found. the results are shown in table 1. (i) complete the cumulative frequency column in table 2. mass ( x grams) frequency 70 1 x g 90 8 90 1 x g 110 8 110 1 x g 120 22 120 1 x g 130 39 130 1 x g 140 27 140 1 x g 150 9 150 1 x g 170 7 mass ( x grams) cumulative frequency x g 90 8 x g 110 x g 120 x g 130 x g 140 x g 150 x g 170 table 1 table 2 [2]", "9": "9 0607/42/f/m/21 \u00a9 ucles 2021 [turn over (ii) on the grid, draw the cumulative frequency curve to show the results in table 2. 120 100 80 60 40 20 70 90 110 130 150 1700 80 100 120 140 160 180cumulative frequency mass (grams) [3] (iii) use your cumulative frequency curve to estimate (a) the median, .. g [1] (b) the interquartile range. .. g [2]", "10": "10 0607/42/f/m/21 \u00a9 ucles 2021 5 (a) ab c49 mm91 mmnot to scale calculate the length of ac. ac = . mm [2] (b) o ab 16 cm305\u00b0not to scale the diagram shows a circle with centre o and radius 16 cm. calculate the length of the major arc ab. cm [2] (c) not to scale 12 cm the diagram shows a prism with length 12 cm. the cross-section of the prism is a quarter of a circle. the radius of the circle is 6 cm. calculate the volume of the prism. .. cm3 [2]", "11": "11 0607/42/f/m/21 \u00a9 ucles 2021 [turn over (d) not to scale bc a ed(2x + 4) cm (x + 1) cm (x \u2013 3) cm shape abcde is made by joining rectangle abde and triangle bcd . the perpendicular height of triangle bcd is (2 x + 4) cm. the total area of abcde is 11 cm2. (i) show that xx23 20 02-- =. [3] (ii) factorise xx23 202-- . . [2] (iii) use your answer to part (ii) to solve the equation xx23 20 02-- =. x = ... or x = .. [1] (iv) find the perpendicular height of triangle bcd . cm [1]", "12": "12 0607/42/f/m/21 \u00a9 ucles 2021 6 (a) y is inversely proportional to the square of x. (i) when x = 2, y = 8. find y in terms of x. y = [2] (ii) find the value of y when x = 4. y = [1] (iii) find the value of x when y = 128. x = [2] (b) r is directly proportional to the cube of ( p + 1) . when p = 1, r = 16. find the value of r when p = 4. r = [3]", "13": "13 0607/42/f/m/21 \u00a9 ucles 2021 [turn over 7 \u2013 4 313 \u2013 3y x 0 ()xx21g=- , x2! (a) on the diagram, sketch the graph of y = g(x) for values of x between - 4 and 3. [3] (b) write down the equations of the asymptotes of the graph of y = g(x). . . [2] (c) () () xx 3 1 h2=-+ solve the inequality () () xxgh2 . . [4]", "14": "14 0607/42/f/m/21 \u00a9 ucles 2021 8 northnorth 142\u00b017 km 4 kmb c anot to scale rani sails in a boat race around a triangular course. she sails from a to b to c and then directly back to a. b is due north of c. (a) find the bearing rani sails on from c to a. . [1] (b) show that ab = 20.3 km, correct to 1 decimal place. [3]", "15": "15 0607/42/f/m/21 \u00a9 ucles 2021 [turn over (c) calculate the bearing of b from a. . [3] (d) rani starts the race at 08 57 and returns to a at 12 33. calculate the average speed of her boat in km/h. km/h [3]", "16": "16 0607/42/f/m/21 \u00a9 ucles 2021 9 (a) the venn diagram shows information about 115 people who play musical instruments. f = {people who play the flute} d = {people who play the drums} fu d 8x3 x2+ x41+ (i) calculate the number of people who play both the flute and the drums. . [3] (ii) on the venn diagram, shade fd+l . [1] (iii) briony plays both the flute and the drums. use set notation to complete the statement. briony ()fd+ [1]", "17": "17 0607/42/f/m/21 \u00a9 ucles 2021 [turn over (b) briony has 6 red socks, 4 green socks and 8 white socks. (i) she picks a sock at random. find the probability that the sock is green. . [1] (ii) briony replaces the sock. she now picks two socks at random, without replacement. calculate the probability that the two socks are different colours. . [4]", "18": "18 0607/42/f/m/21 \u00a9 ucles 2021 10 b a rhc not to scale cone a has radius r and perpendicular height h. cone b is mathematically similar to cone a. solid c is formed by removing cone a from cone b. the ratio height of cone a : height of cone b = 2 : 3. (a) find the ratio volume of cone a : volume of solid c. ... : ... [3] ", "19": "19 0607/42/f/m/21 \u00a9 ucles 2021 [turn over (b) cone a has radius 4 cm and height 10 cm. calculate the total surface area of solid c. .. cm2 [8] question 11 is printed on the next page.", "20": "20 0607/42/f/m/21 \u00a9 ucles 2021 11 ()xx 31 f=+ ()xx 5 g2=- ()x 3 hx= (a) find g(3). . [1] (b) find f(h(2)). . [2] (c) find the value of r when f( r) = r. r = [2] (d) solve g(f( x)) = 20. x = ... or x = .. [3] (e) find ()x h1-. ()x h1=- [2] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge." }, "0607_m21_qp_52.pdf": { "1": "this document has 12 pages. any blank pages are indicated. cambridge igcse\u2122 dc (ce) 207878/1 \u00a9 ucles 2021 [turn overcambridge international mathematics 0607/52 paper 5 investigation (core) february/march 2021 1 hour 10 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 36. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *5297052325*", "2": "2 0607/52/f/m/21 \u00a9 ucles 2021 consecutive numbers (36 marks) this task is about what happens when consecutive numbers are changed from positive to negative and added. consecutive numbers are sequences of integers which increase by 1 from term to term. examples 0, 1, 2, 3, 4 or 5, 6, 7 or 46, 47, 48, 49, 50, 51 or 3, 4, 5, ..., 120. in this investigation use this method throughout. \u2022 add the positive consecutive numbers. \u2022 find all the possible additions and totals when you make one of the numbers negative. \u2022 find all the possible additions and totals when you make two of the numbers negative. \u2022 continue in this way until all the numbers are negative. 1 1, 2 is a sequence of two consecutive numbers. (a) (i) complete the table using the method with 1 and 2 to find all the possible totals. addition total all positive 1 + 2 = 3 one negative -1 + 2 = ... 1 + \t-2 = ... all negative -1 + \t-2 = \t-3 [1] (ii) using the consecutive numbers 1 and 2 the highest total is 3 and the lowest total is -3. you cannot make all the integers between the highest total and the lowest total using the method. write down all the integers between 3 and -3 that cannot be made using 1 and 2. remember: 0 is an integer. . [1]", "3": "3 0607/52/f/m/21 \u00a9 ucles 2021 [turn over (b) (i) complete the table using the method with the consecutive numbers 2 and 3. addition total all positive 2 + 3 = 5 one negative\t-2 + ... = 1 2 + ... = ... all negative \t-2 + \t-3 = ... [2] (ii) using the table in part (i) , complete these statements. the highest total is 5 and the lowest total is ... . the number of integers between the highest total and the lowest total that cannot be made is ... . [2] (c) (i) complete the table using the method with two consecutive numbers. addition total all positive ... + ... = 15 one negative... + ... = ... ... + ... = ... all negative ... + ... = \t-15 [2] (ii) find the number of integers between 15 and -15 that cannot be made using these consecutive numbers. . [1]", "4": "4 0607/52/f/m/21 \u00a9 ucles 2021 2 a and a + 1 are two consecutive numbers. (a) find expressions for the four totals that can be made using a and a + 1. give each expression in its simplest form. ... , ... , ... , ... [3] (b) an expression for the number of integers between the highest total and the lowest total that cannot be made using a and a + 1 is 4 a - 1. show that this gives the correct number when a = 10. [4]", "5": "5 0607/52/f/m/21 \u00a9 ucles 2021 [turn over 3 (a) there are now three consecutive numbers. (i) complete the table using the method with the consecutive numbers 3, 4 and 5. addition total all positive 3 + 4 + 5 = 12 one negative\t-3 + 4 + 5 = 6 ... + \t-4 + ... = 4 ... + ... + ... = 2 two negative\t-3 + \t-4 + = \t-2 \t-3 + ... + \t-5 = ... ... + ... + ... = ... all negative \t-3 + \t-4 + \t-5 = \t-12 [2] (ii) find the number of integers that cannot be made between 12 and -12. . [2]", "6": "6 0607/52/f/m/21 \u00a9 ucles 2021 (b) there are now four consecutive numbers. complete the table using the method and the consecutive numbers 3, 4, 5 and 6. addition total all positive 3 + 4 + 5 + 6 = 18 one negative\t-3 + 4 + 5 + 6 = 12 ... +\t-4 + 5 + 6 = 10 3 + 4 +\t-5 + 6 = 8 ... + ... + ... + ... = ... two negative\t-3 +\t-4 + 5 + 6 = ... \t-3 + 4 + ... + 6 = 2 \t-3 + 4 + 5 +\t-6 = 0 3 +\t-4 + ... + 6 = 0 3 +\t-4 + ... +\t-6 = ... 3 + 4 +\t-5 +\t-6 =\t-4 three negative\t-3 +\t-4 + ... + ... = ... \t-3 +\t-4 + ... + ... =\t-8 \t-3 + 4 +\t-5 + ... =\t-10 3 + ... + ... + ... =\t-12 all negative \t-3 +\t-4 +\t-5 +\t-6 =\t-18 [3]", "7": "7 0607/52/f/m/21 \u00a9 ucles 2021 [turn over turn over for question 4", "8": "8 0607/52/f/m/21 \u00a9 ucles 2021 4 (a) there are 16 additions in the table on page 6 . complete the table below. use question 1 and question 3 to help you. number of consecutive numbersnumber of additions 2 = 3 = 23 4 16 = 24 5 32 = n [2] (b) complete this table. use question 2(a) to help you. number of consecutive numbersconsecutive numbersexpression for the highest total in terms of a 2 a, a + 1 3 3a + 3 4 5 a, a + 1, a + 2, a + 3, a + 4 n ... + ()nn 21- [5]", "9": "9 0607/52/f/m/21 \u00a9 ucles 2021 [turn over (c) anna uses this method to work out the number of integers that cannot be made. \u2022 use question 4(b) to find the highest total. \u2022 find the number of integers from the highest total to the lowest total. \u2022 use question 4(a) to find the number of additions. \u2022 subtract the number of additions from the number of integers. example there are three consecutive numbers. the first number is 4. the highest total is 3 a + 3 = 3 # 4 + 3 = 15. the number of integers from 15 to -15 is 31. the number of additions is 23. the number of integers that cannot be made is 31 - 23 = 23. (i) there are two consecutive numbers. use anna\u2019s method to find the number of integers that cannot be made when the first number is 9. . [3]", "10": "10 0607/52/f/m/21 \u00a9 ucles 2021 (ii) anna uses her method to find the number of integers that cannot be made with the three consecutive numbers 1, 2 and 3. her method gives the answer 5. explain why her method gives the wrong answer. . [3]", "11": "11 0607/52/f/m/21 \u00a9 ucles 2021 blank page", "12": "12 0607/52/f/m/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_m21_qp_62.pdf": { "1": "this document has 16 pages. any blank pages are indicated. cambridge igcse\u2122 dc (ce/sw) 207879/1 \u00a9 ucles 2021 [turn over *6407495703* cambridge international mathematics 0607/62 paper 6 investigation and modelling (extended) february/march 2021 1 hour 40 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer both part a (questions 1 to 5) and part b (questions 6 to 10). \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 60. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/62/f/m/21 \u00a9 ucles 2021 answer both parts a and b. a investigation (questions 1 to 5) enclosed cuboids (30 marks) you are advised to spend no more than 50 minutes on this part. this task is about the number of white cubes needed to enclose a grey cuboid with integer sides. 1 the diagram shows: \u2022 a grey cube with each edge 1 centimetre long (a 1 cm cube) \u2022 a view showing how the grey cube is enclosed in a layer of 1 cm white cubes \u2022 the resulting cube. first cube second cube not to scale (a) the enclosing layer of white cubes is 1 cm thick. this makes the second cube with each edge 3 cm long. find the number of white cubes. . [1] (b) the second cube is enclosed in a layer of 1 cm white cubes to make the third cube. there are now 2 layers enclosing the grey cube. each layer is 1 cm thick. (i) write down the length of one edge of the third cube. . [1] (ii) find the number of white cubes in the third cube. . [2]", "3": "3 0607/62/f/m/21 \u00a9 ucles 2021 [turn over (c) for any cube made in this way, write down the relationship between the total number of 1 cm cubes and the number of white cubes. . [1] (d) for any cube made in this way, n = the number of enclosing layers l = the length of the outer edge in centimetres w = the number of white cubes. for the first cube, n = 0 and l = 1. for the second cube, n = 1 and l = 3. complete this table for a grey cube of edge length 1 cm. number of enclosing layers0 1 2 3 4 n l 1 3 w 0 728 [5]", "4": "4 0607/62/f/m/21 \u00a9 ucles 2021 2 a grey cube has edge length 2 cm. this cube will be enclosed in layers of 1 cm white cubes. the diagram shows some of the white cubes in the first layer. not to scale (a) this calculation gives the number of white cubes when there is one enclosing layer. 43 - 23 explain why this calculation works. . . . [2] (b) complete this table for a grey cube of edge length 2 cm. number of enclosing layers0 1 2 3 4 n l 2 10 w 0 56 992 [4]", "5": "5 0607/62/f/m/21 \u00a9 ucles 2021 [turn over 3 (a) complete this table for a grey cube of edge length 3 cm. number of enclosing layers0 1 2 3 4 n l 3 w 0 98 316 702 1304 [2] (b) a grey cube has edge length e cm. write your expressions for w from questions 1(d) , 2(b) and 3(a) in this table. complete the table. edge length of grey cubew 1 2 3 e [2]", "6": "6 0607/62/f/m/21 \u00a9 ucles 2021 4 not to scale3 cm 2 cm 5 cm this grey cuboid has edge lengths of 2 cm, 3 cm and 5 cm. (a) find the number of white cubes when there is one enclosing layer. . [3] (b) a grey cuboid has edge lengths of a cm, b cm and c cm. the cuboid has n enclosing layers. find the formula for the number of white cubes, w. [2]", "7": "7 0607/62/f/m/21 \u00a9 ucles 2021 [turn over 5 a grey cuboid has edge lengths of k cm, k cm and 2 k cm. the grey cuboid has 8 enclosing layers of 1 cm white cubes. the largest face of the resulting cuboid has 546 white cubes. find the value of k. . [5]", "8": "8 0607/62/f/m/21 \u00a9 ucles 2021 b modelling (questions 6 to 10) enclosures for cats (30 marks ) you are advised to spend no more than 50 minutes on this part. v olume, v, of cylinder of radius r, height h. vr h2r= v olume, v, of cone of radius r, height h. vr h31 2r= v olume, v, of sphere of radius r. vr34 3r= this task looks at modelling the floor area and volume of enclosures for cats. dorothy has two cats and is going to build an enclosure for them. she considers three designs. 6 design 1 is a cone and design 2 is a hemisphere. the cone and the hemisphere have the same diameter, d. d dhhemisphere cone (a) (i) show that the volume of the cone is dh 122r. [1]", "9": "9 0607/62/f/m/21 \u00a9 ucles 2021 [turn over (ii) find the volume of the hemisphere. write your answer in its simplest form, in terms of r and d. . [2] (b) write h in terms of d when the volume of the cone is equal to the volume of the hemisphere. . [1] (c) (i) find the volume of the cone when hd 2=. write your answer in its simplest form, in terms of r and d. . [2] (ii) which is smaller, the volume of the cone in part (c)(i) or the volume of the hemisphere? show how you decide. . [1]", "10": "10 0607/62/f/m/21 \u00a9 ucles 2021 information about cat enclosures minimum floor sleep area per cat 0.5 m2 minimum floor exercise area per cat 2.8 m2 minimum extra floor area per cat 1 m2 highest point above floor must be 2 m or more 7 (a) show that the total minimum floor area for two cats is 8.6 m2. [1] (b) calculate the diameter that gives this minimum floor area for both the cone and the hemisphere. . [2] (c) explain why a hemisphere with this minimum floor area is not a suitable enclosure. . . [1]", "11": "11 0607/62/f/m/21 \u00a9 ucles 2021 [turn over 8 dorothy decides on a volume of 10 m3 for the enclosure for the two cats. (a) use question 6(a)(i) to find a model for h, in terms of r and d, for the cone enclosure. . [2] (b) sketch your model for h for d 01 2 1g . 0 diameterheight12 12dh [2] (c) find the total floor area of the enclosure when the height of the cone is 2 m. . [3]", "12": "12 0607/62/f/m/21 \u00a9 ucles 2021 9 design 3 is a half-cylinder. it has diameter d and length w. half-cylinder dw (a) use the information on page 10 to write down the smallest value of d. . [1] (b) show that the volume of the half-cylinder is dw 82r. [2] (c) (i) show that a model for w for a half-cylinder enclosure that has a volume of 10 m3 is wd80 2r= . [1]", "13": "13 0607/62/f/m/21 \u00a9 ucles 2021 (ii) sketch the model for w for d 01 2 1g . lengthw 0 diameter12 12d [1] (d) (i) the total floor area is 8.6 m2. write down a model for w in terms of d. . [1] (ii) on the axes above sketch your model from part (d)(i) . [2] (e) find the height of the half-cylinder enclosure that fits both models. . [3] 10 write down which enclosure of volume 10 m3, cone or half-cylinder, you think dorothy should choose for her two cats. explain your choice. . . [1]", "14": "14 0607/62/f/m/21 \u00a9 ucles 2021 blank page", "15": "15 0607/62/f/m/21 \u00a9 ucles 2021 blank page", "16": "16 0607/62/f/m/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_s21_qp_11.pdf": { "1": "this document has 8 pages. cambridge igcse\u2122 dc (ce/cb) 207179/1 \u00a9 ucles 2021 [turn overcambridge international mathematics 0607/11 paper 1 (core) may/june 2021 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *1117266921*", "2": "2 0607/11/m/j/21 \u00a9 ucles 2021 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/11/m/j/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 write 25% as a fraction. .. [1] 2 write down two multiples of 12. .. [1] 3 e fd boc a complete the statement using letters from the diagram. line . is a tangent to the circle, centre o. [1] 4 change 1500 centilitres into litres. . litres [1] 5 work out. 10 44'- .. [1] 6 21 22 23 24 25 26 27 from the list of numbers, write down (a) the cube number, .. [1] (b) the triangle number. .. [1]", "4": "4 0607/11/m/j/21 \u00a9 ucles 2021 7 00100200300400 5 10 15 20 time (minutes)distance (metres)library 25 30 35 40 45home the travel graph shows suba\u2019s bicycle journey from her home to the library and back. (a) write down the distance from suba\u2019s home to the library. .. m [1] (b) write down the number of minutes suba was in the library. ... min [1] 8 these are the test results of 12 students. 17 21 9 11 24 21 8 15 12 6 10 21 (a) find the median. .. [2] (b) write down the mode. .. [1] (c) find the range. .. [1] 9 p = {prime number less than 10} write down the members of set p. .. [2]", "5": "5 0607/11/m/j/21 \u00a9 ucles 2021 [turn over 10 work out 60% of 35. .. [2] 11 simplify. w # w # w .. [1] 12 what type of correlation is shown on the scatter diagram? .. [1] 13 q p 0123456 x3 4 5 2 6 1y describe fully the single transformation that maps shape p onto shape q. . . [3]", "6": "6 0607/11/m/j/21 \u00a9 ucles 2021 14 shade the region indicated below each venn diagram. a b c du u ab, cd+ [2] 15 012345 x3 4 5 2 \u2013 2 6 7 1 \u2013 1y the diagram shows the graph of a function with one asymptote. on the diagram, draw the asymptote. [1] 16 solve the inequality x21 0g . .. [1] 17 find the highest common factor (hcf) of 70 and 80. .. [1] 18 a train travels 250 metres in 5 seconds. work out its average speed in kilometres per hour. .. km/h [3]", "7": "7 0607/11/m/j/21 \u00a9 ucles 2021 [turn over 19 simplify. x y12 25# .. [2] 20 ()fxx 23=- for x52 1 gg- find the range of ()fx. .. [2] 21 not to scale a dbe gcf 12 cm10 cm5 cm rectangles abcd and aefg are mathematically similar. work out ef. ef = . cm [2] questions 22 and 23 are printed on the next page.", "8": "8 0607/11/m/j/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.22 a is the point (, )31- and b is the point (1, 3). find the gradient of the line ab. .. [2] 23 not to scale 6 cmo120\u00b0 the diagram shows a sector of a circle centre o, radius 6 cm. find the area of the sector. leave your answer in terms of r. cm2 [2]" }, "0607_s21_qp_12.pdf": { "1": "this document has 8 pages. cambridge igcse\u2122 dc (lk/cb) 207180/2 \u00a9 ucles 2021 [turn overcambridge international mathematics 0607/12 paper 1 (core) may/june 2021 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *8198260037*", "2": "2 0607/12/m/j/21 \u00a9 ucles 2021 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/12/m/j/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 write 3262.7 correct to the nearest 100. . [1] 2 write down the value of 62. . [1] 3 on the diagram, draw the line of symmetry. [1] 4 ..023222 21 - from the list of numbers, write down the integer. . [1] 5 write the missing number in the box. 16 20=5 [1] 6 42\u00b0y\u00b0not to scale the diagram shows two straight lines. write down the value of y. y = [1]", "4": "4 0607/12/m/j/21 \u00a9 ucles 2021 7 work out. 17 32#- . [1] 8 the list shows the ages of six people. 8 10 76 8 10 8 (a) write down the mode. . [1] (b) find the range. . [1] (c) find the median. . [1] (d) find the mean. . [2] 9 f = ma find f when m = 25 and a = 3. f = . [1] 10 () () () fxx x 23 1 =- - work out ()f7. . [2] 11 write the ratio 18 : 24 in its simplest form. ... : ... [1]", "5": "5 0607/12/m/j/21 \u00a9 ucles 2021 [turn over 12 a = {1, 2, 3, 4, 5} b = {2, 3} complete the following statements using set notation. b a 5 a [2] 13 a bus travels at an average speed of 70 km/h. find the distance it travels in 4 hours. ... km [1] 14 priya invests $4500 for 3 years at a rate of 2% per year simple interest. work out the value of priya\u2019s investment at the end of 3 years. $ [3] 15 solve the equation. 5(x + 3) = 30 x = [2]", "6": "6 0607/12/ m / j /21 \u00a9 ucles 202116 not to scale 6 m18 m 10 m patiograss 5 m the diagram shows the rectangular garden of a house. work out the area of the grass. m2 [2] 17 change 46 square centimetres into square millimetres. . mm2 [1] 18 xy 0 34 211 \u2013 1 \u2013 23 \u2013 34 \u2013 4\u2013 2\u2013 1 \u2013 3 \u2013 4 b2a describe fully the single transformation that maps shape a onto shape b. . . [3]", "7": "7 0607/12/m/j/21 \u00a9 ucles 2021 [turn over 19 these are the first five numbers in a sequence. 1 3 9 27 81 (a) find the next number in this sequence. . [1] (b) explain how you found your answer to part (a) . . [1] 20 150 students are asked whether they study mathematics ( m ) or english ( e ). 10 study neither subject, 15 study both subjects and 50 study mathematics only. (a) complete the venn diagram to show all 150 students. m eu [2] (b) one of the 150 students is selected at random. find the probability that this student studies english. give your answer as a fraction in its simplest form. . [2] questions 21 and 22 are printed on the next page.", "8": "8 0607/12/m/j/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.21 work out. 810 41017 6## write your answer in standard form. . [2] 22 solve the simultaneous equations. xy xy6 16+= -= x = . y = . [2]" }, "0607_s21_qp_13.pdf": { "1": "this document has 8 pages. cambridge igcse\u2122 dc (lk/cb) 207181/2 \u00a9 ucles 2021 [turn overcambridge international mathematics 0607/13 paper 1 (core) may/june 2021 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *6805643091*", "2": "2 0607/13/m/j/21 \u00a9 ucles 2021 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/13/m/j/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 write 104 as a decimal. . [1] 2 complete the statement. two straight lines which meet at 90\u00b0 are called . lines. [1] 3 2 876543 1 xander spins this unbiased 8-sided spinner. find the probability that the spinner lands on an even number. give your answer as a decimal. . [2] 4 total mass of hay = mass of one bale \u00d7 number of bales work out the total mass of hay when there are 10 bales and the mass of each bale is 21 kg. kg [1] 5 10 11 12 14 15 16 from the list of numbers, write down (a) the square number, . [1] (b) the prime number. . [1]", "4": "4 0607/13/m/j/21 \u00a9 ucles 2021 6 on the diagram, draw all the lines of symmetry. [2] 7 find 75% of 200. . [1] 8 change 341 hours into minutes. minutes [1] 9 insert one pair of brackets to make this statement correct. 10 \u00f7 2 + 2 + 1 = 2 [1] 10 the coordinates of two points are (1, 5) and (5, 5). work out the distance between the two points. . [1] 11 rosa wants to collect information about cars. (a) write down an example of discrete data that she could collect. . [1] (b) write down an example of continuous data that she could collect. . [1]", "5": "5 0607/13/m/j/21 \u00a9 ucles 2021 [turn over 12 not to scale 125\u00b0c\u00b0 find the value of c. give a reason for your answer. c = . because .. [2] 13 write down the largest integer value of x so that x 241-. . [1] 14 find the total surface area of a cube of side 2 cm. .. cm2 [2] 15 a shark swims 200 metres in 40 seconds. find its average speed. ... m/s [1] 16 factorise. ab c 15 39-+ . [1]", "6": "6 0607/13/m/j/21 \u00a9 ucles 2021 17 megan asked some people if they prefer to read emails on their phone or on their laptop. the results are shown in the table. phone laptop 10 1 age g 30 9 1 30 1 age g 50 6 4 50 1 age g 70 3 7 one of these people is chosen at random. find the probability that they prefer to read emails on their phone. . [2] 18 not to scale 60\u00b0(x + 10)\u00b0 x\u00b0 find the value of x. x = [3] 19 solve the inequality. x131+ . [1] 20 a bag contains 20 almonds. the mean mass of an almond in the bag is 4 grams. work out the total mass of the almonds in the bag. ... grams [1]", "7": "7 0607/13/m/j/21 \u00a9 ucles 2021 [turn over 21 u = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} a = {1, 4, 5, 6, 9} b = {2, 4, 7, 10} (a) complete the venn diagram by writing each element in the correct region. a bu [2] (b) find a + b. a + b = { ... } [1] (c) find n( a , b ). . [1] 22 (a) write each number in standard form. (i) 8500 . [1] (ii) 0.02 . [1] (b) find the value of . 8500 002 # . write your answer in standard form. . [2] questions 23 and 24 are printed on the next page.", "8": "8 0607/13/m/j/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.23 ()fxx 3 =- the domain of f( x) is x19gg . find the range of f( x). . [2] 24 xy 0 1123456789 23456 explain why the gradient of this line is 2-. . . [1] " }, "0607_s21_qp_21.pdf": { "1": "this document has 8 pages. cambridge igcse\u2122 dc (lk/cgw) 199660/2 \u00a9 ucles 2021 [turn over *6765421013* cambridge international mathematics 0607/21 paper 2 (extended) may/june 2021 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/21/m/j/21 \u00a9 ucles 2021 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/21/m/j/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 work out. (a) . 30 018- . [1] (b) .0042 . [1] (c) .. 02008 . [1] 2 (a) write 5249.6 correct to two significant figures. . [1] (b) write .00030626 correct to three decimal places. . [1] 3 a car travels 300 metres in 20 seconds. find the average speed of the car in (a) metres per second, ... m/s [1] (b) kilometres per hour. km/h [2]", "4": "4 0607/21/m/j/21 \u00a9 ucles 2021 4 solve. (a) () x 24 52 0 -- = x = . [2] (b) x25 9 -= x = ... or x = ... [2] 5 find the value of (a) 640, . [1] (b) 6431 . . [1] 6 a regular polygon has 30 sides. find the size of one exterior angle. . [2]", "5": "5 0607/21/m/j/21 \u00a9 ucles 2021 [turn over 7 factorise. (a) ab ya yb x x1223 8 -+ - . [2] (b) xx56 82-- . [2] 8 (a) work out 12 554 1 ---ee oo . fp [2] (b) work out the magnitude of 3 4-eo . . [2]", "6": "6 0607/21/m/j/21 \u00a9 ucles 2021 9 rearrange this equation to make x the subject. xa xb 23 5 -= x = . [3] 10 (a) solve. sinx21= for \u00b0\u00b0x 09 0 gg x = . [1] (b) solve. sinx21=- for \u00b0\u00b0x 0 360 gg x = . [2]", "7": "7 0607/21/m/j/21 \u00a9 ucles 2021 [turn over 11 o ba not to scaley x the points a (2, 8) and b (, ) 62- are shown on the diagram. find the equation of the perpendicular bisector of the line ab. give your answer in the form ym xc=+ . y = . [5] question 12 is printed on the next page.", "8": "8 0607/21/m/j/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.12 a bag contains 12 discs. 7 discs are red and 5 discs are green. a disc is picked at random and not replaced. a second disc is then picked at random. find the probability that (a) both discs are green, . [2] (b) at least one disc is green. . [3]" }, "0607_s21_qp_22.pdf": { "1": "this document has 8 pages. cambridge igcse\u2122 dc (lk/cgw) 199662/1 \u00a9 ucles 2021 [turn over *2585309447* cambridge international mathematics 0607/22 paper 2 (extended) may/june 2021 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/22/m/j/21 \u00a9 ucles 2021 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area =a c bcb a", "3": "3 0607/22/m/j/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 work out .. 000436 . . [1] 2 these are the masses, in kilograms, of 16 newborn babies. 2.5 3.2 3.8 3.2 1.9 3.4 1.7 4.1 3.0 2.8 4.0 2.7 3.9 2.7 4.1 3.7 complete the ordered stem-and-leaf diagram for the masses. 1 2 3 4 key: 3 | 2 = 3.2 [2] 3 work out 221341' . give your answer as a fraction in its simplest form. . [3] 4 insert two pairs of brackets to make this statement correct. 3 # 7 - 3 + 4 # 2 = 32 [1]", "4": "4 0607/22/m/j/21 \u00a9 ucles 2021 5 a b c df e 115\u00b0 40\u00b0not to scale abcd is a straight line and be is parallel to cf. find angle ecf . angle ecf = . [2] 6 (a) factorise ab22- . . [1] (b) work out ..5374 6322- . . [2] 7 solve xx23 51 2 1+- . . [2] 8 expand and simplify () () 23 54 3 -+ . . [2]", "5": "5 0607/22/m/j/21 \u00a9 ucles 2021 [turn over 9 ba 84\u00b0not to scale the diagram shows part of polygon a and part of polygon b. a is a regular polygon with n sides. b is a regular hexagon. find the value of n. n = . [3] 10 c4107#= . d 58 106# = work out, giving your answers in standard form, (a) c2 , . [2] (b) cd- . . [2]", "6": "6 0607/22/m/j/21 \u00a9 ucles 2021 11 yx32=+ rearrange the formula to make x the subject. x = . [3] 12 x\u00b0not to scale 6 cm the area of this sector is cm52r . find the value of x. x = . [3]", "7": "7 0607/22/m/j/21 \u00a9 ucles 2021 [turn over 13 the heights, h cm, of 100 plants are measured. the table shows the results. height, h cm frequency h 04 0 1g 15 h 40 081g 40 h 80 1201g 45 calculate an estimate for the mean height of the plants. cm [3] 14 not to scale 30\u00b0 12 cmk3cm find the value of k. k = . [3] questions 15 and 16 are printed on the next page.", "8": "8 0607/22/m/j/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.15 11 10 9 8 7 6 5 4 3 2 1 \u2013 3\u2013 2\u2013 1\u2013 3\u2013 2\u2013 1 1 0 234567891011 xy the diagram shows the line xy 8 += . on the diagram, show clearly the region defined by these inequalities. xy 8g+ x2h y3g [2] 16 simplify xxxy xy 233 22 --- . . [3]" }, "0607_s21_qp_23.pdf": { "1": "this document has 8 pages. cambridge igcse\u2122 dc (ce/fc) 199661/1 \u00a9 ucles 2021 [turn overcambridge international mathematics 0607/23 paper 2 (extended) may/june 2021 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *6179368984*", "2": "2 0607/23/m/j/21 \u00a9 ucles 2021 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/23/m/j/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 write 84% as a fraction in its lowest terms. .. [1] 2 work out (. ) 10 82- . .. [1] 3 find the value of xx2- when x = -3. .. [1] 4 a quadrilateral has all sides equal and exactly two lines of symmetry. write down the mathematical name of this quadrilateral. .. [1] 5 60\u00b050\u00b0x\u00b0not to scale find the value of x. x = . [1]", "4": "4 0607/23/m/j/21 \u00a9 ucles 2021 6 on the venn diagram, shade ab,. a bu [1] 7 find the size of one interior angle of a regular polygon with 20 sides. .. [3] 8 find the value of 44-+ . .. [1] 9 a van has length 9 m. it takes 1 second for the van to completely pass a gate of length 1 m. find the speed of the van. give your answer in km/h. km/h [2]", "5": "5 0607/23/m/j/21 \u00a9 ucles 2021 [turn over 10 the faces of a die are numbered 1, 1, 2, 3, 3 and 4. when it is rolled it is equally likely to show any face. the die is rolled twice. find the probability that it shows an odd number both times. .. [2] 11 here are the first five terms of a sequence. 41 1 4 16 64 (a) find the next term. .. [1] (b) find the nth term. .. [2] 12 factorise. ac ac 1+- - .. [2]", "6": "6 0607/23/m/j/21 \u00a9 ucles 2021 13 a b c10 cm8 cm 9 cmp q r6 cmnot to scale the diagram shows two similar triangles, abc and pqr . (a) find the length of pr. pr = cm [2] (b) the triangles are the cross-sections of mathematically similar prisms. the volume of the larger prism is 500 cm3. find the volume of the smaller prism. ... cm3 [2] 14 () ap x13=+ rearrange the formula to write x in terms of a and p. x = . [3]", "7": "7 0607/23/m/j/21 \u00a9 ucles 2021 [turn over 15 a tbq70\u00b070\u00b0rsnot to scale points q, r, s and t lie on the circle. ab is a tangent to the circle at t. angle rtb = 70\u02da. find angle rqt . angle rqt = . [2] 16 p varies inversely as the square root of q. when q = 9, p = 12. find p when q = 16. p = . [3] 17 simplify by rationalising the denominator. 22 13 - .. [2] questions 18, 19 and 20 are printed on the next page.", "8": "8 0607/23/m/j/21 \u00a9 ucles 2021 18 xy not to scale 4 0 2 the diagram shows the graph of ya xb=+ , where a 02. find the value of a and the value of b. a = . b = . [2] 19 write as a single fraction in its simplest form. x232-- .. [2] 20 logl og log px y 23 =- find p in terms of x and y. p = . [3] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge." }, "0607_s21_qp_31.pdf": { "1": "this document has 16 pages. cambridge igcse\u2122 dc (ce/cgw) 199831/2 \u00a9 ucles 2021 [turn overcambridge international mathematics 0607/31 paper 3 (core) may/june 2021 1 hour 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 96. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *8639188823*", "2": "2 0607/31/m/j/21 \u00a9 ucles 2021 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/31/m/j/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 (a) work out. (i) 36 .. [1] (ii) 73 .. [1] (b) (i) 4 # 4 # 4 # 4 # 4 # 4 = 4n write down the value of n. n = . [1] (ii) write down the value of 40. .. [1] (c) work out. 21 71 2+ give your answer correct to 3 decimal places. .. [2] (d) (i) write 0.000 082 in standard form. .. [1] (ii) work out. (. )( .) 73 10 18 1094## #- give your answer in standard form. .. [2]", "4": "4 0607/31/m/j/21 \u00a9 ucles 2021 2 0 x2345 \u2013 3\u2013 2 \u2013 5\u2013 4\u2013 1\u2013 1 \u2013 2 \u2013 3 \u2013 4 \u2013 5 3 4 5 2 1y a b 1 c points a, b and c are plotted on a 1 cm2 grid. (a) write down the coordinates of (i) point b, ( ... , ...) [1] (ii) point a. ( ... , ...) [1] (b) on the grid, plot the point ( -3, -1) and label it d. [1] (c) join a, b, c and d to form a quadrilateral. write down the mathematical name of quadrilateral abcd . .. [1]", "5": "5 0607/31/m/j/21 \u00a9 ucles 2021 [turn over (d) work out the area of quadrilateral abcd . ... cm2 [2] (e) on the grid, draw the reflection of quadrilateral abcd in the x-axis. [2]", "6": "6 0607/31/m/j/21 \u00a9 ucles 2021 3 ralf records the number of people in each car entering the school car park. the results are shown in the table. number of people in the car number of cars 1 8 2 13 3 6 4 3 5 2 (a) work out the total number of cars that ralf records. .. [1] (b) work out the total number of people in these cars. .. [2] (c) on the grid, draw and label a bar chart to show the information in the table. number of people in the carnumber of cars [4]", "7": "7 0607/31/m/j/21 \u00a9 ucles 2021 [turn over 4 (a) ana is 28 years 3 months old. change 28 years 3 months into months. .. months [2] (b) ana has three children. the ages of the children are 7 years 11 months 5 years 4 months 2 years 6 months. for these three ages, work out (i) the range, years months [1] (ii) the mean. years months [3] (c) jon has a watch that records the number of calories he uses when he goes for a walk. he uses 0.05 calories for each step he takes. he takes 1250 steps for every kilometre he walks. one day he uses 300 calories on a walk. work out how far he has walked. km [2]", "8": "8 0607/31/m/j/21 \u00a9 ucles 2021 5 (a) complete this sequence of patterns by drawing pattern 1 and pattern 5. pattern 1 pattern 2 pattern 3 pattern 4 pattern 5 x x x x x x x x x x x x x x x x x x [2] (b) these are the first four terms of a sequence. 4 7 10 13 for this sequence, write down (i) the next term, .. [1] (ii) the rule for continuing the sequence. ... [1] (c) the nth term of another sequence is 3 n2. work out the first two terms of this sequence. . \u200aand\u200a . [2] (d) these are the first five terms of a different sequence. 7 15 23 31 39 find the nth term of this sequence. .. [2]", "9": "9 0607/31/m/j/21 \u00a9 ucles 2021 [turn over 6 (a) simplify. yy y 34+- .. [1] (b) solve. (i) x62 0 += x = . [1] (ii) x 48= x = . [1] (iii) ()x23 14 -= x = . [2] (c) on the number line, show the inequality x4h. 0 1 2 3 4 5 6x [1] (d) factorise. 5x + 20 .. [1] (e) multiply out the brackets and simplify. () () xx65 3 +- .. [2]", "10": "10 0607/31/m/j/21 \u00a9 ucles 2021 7 (a) 48\u00b084\u00b0not to scale cab what type of triangle is abc\u200a ? show how you decide. [2] (b) work out the size of one exterior angle of a regular pentagon. .. [2]", "11": "11 0607/31/m/j/21 \u00a9 ucles 2021 [turn over (c) 126\u00b0 x\u00b057\u00b034\u00b0 not to scale a d ec b in the diagram, ade is a straight line. (i) find the value of x. x = . [2] (ii) show that abcd is not a trapezium. [2]", "12": "12 0607/31/m/j/21 \u00a9 ucles 2021 8 here are three unbiased spinners made from regular polygons. 1 46 453 5 62 31 54 6 1 spinner b spinner c spinner a6 63 5 56 12 (a) (i) for spinner a work out the probability of getting 6. .. [1] (ii) spinner a is spun twice. work out the probability of getting 6 each time. .. [2] (b) show that, of the three spinners, spinner c has the greatest probability of getting 6 on one spin. [4]", "13": "13 0607/31/m/j/21 \u00a9 ucles 2021 [turn over 9 (a) amir has car insurance, home insurance and health insurance. in one year he spends a total of $5775 on insurance in the ratio car : home : health = 2 : 3 : 6. work out how much he spends on each type of insurance. car $ .. home $ .. health $ .. [3] (b) a company offers samal health insurance for $850 when it is not bought online. the company offers a 15% reduction when this insurance is bought online. work out how much this insurance will cost samal if she buys it online. $ .. [2] (c) terry\u2019s car insurance increases from $900 to $1100. work out the percentage increase. .. % [3]", "14": "14 0607/31/m/j/21 \u00a9 ucles 2021 10 (a) the line with equation y = mx + 1 passes through the point (3, 19). work out the value of m. m = . [3] (b) 0b8 anot to scaley x \u2013 4 in the diagram, the line meets the x-axis at a (-4, 0) and the y-axis at b (0, 8). (i) find the coordinates of the mid-point of ab. ( ... , ...) [2] (ii) find the equation of the line ab. .. [3]", "15": "15 0607/31/m/j/21 \u00a9 ucles 2021 [turn over 11 in this question, all lengths are in metres. 2.5 2 23not to scalex\u00b0h the diagram shows a shed in the shape of a prism. (a) use pythagoras\u2019 theorem to show that h = 1.5 . [2] (b) use trigonometry to find the value of x. x = . [2] (c) (i) the end of the shed is shaded. calculate this area. . m2 [2] (ii) work out the volume of the shed. give the units of your answer. .. .. [2] question 12 is printed on the next page.", "16": "16 0607/31/m/j/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.12 0y x\u2013 3 2 \u2013 1025 (a) (i) on the diagram, sketch the graph of yx x332=+ for x32gg- . [2] (ii) find the coordinates of the local minimum. ( ... , ...) [1] (iii) find the coordinates of the local maximum. ( ... , ...) [1] (b) on the diagram, sketch the graph of yx352=- for x32gg- . [2] (c) find the coordinates of the point of intersection of the graphs of yx x332=+ and yx352=- . ( ... , ...) [2]" }, "0607_s21_qp_32.pdf": { "1": "this document has 16 pages. cambridge igcse\u2122 dc (ce/cgw) 199830/3 \u00a9 ucles 2021 [turn overcambridge international mathematics 0607/32 paper 3 (core) may/june 2021 1 hour 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 96. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *2714541401*", "2": "2 0607/32/m/j/21 \u00a9 ucles 2021 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/32/m/j/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 (a) ruri buys these items. 1 bag of lettuce $1.20 1 cucumber $0.90 1 box of 8 tomatoes $1.60 1 bag of 3 peppers $1.50 1 bag of 6 avocados $3.00 (i) work out the total cost of the items. $ . [1] (ii) ruri makes a salad. the items she uses are shown in the table. complete the table. item cost ($) 1 bag of lettuce 21 a cucumber 0.45 4 tomatoes 1 pepper 1 avocado total [3] (b) roses cost $1.50 each. ruri has $10.00 to spend. (i) work out the greatest number of roses she can buy. .. roses [1] (ii) work out how much money she has left. $ .. [1]", "4": "4 0607/32/m/j/21 \u00a9 ucles 2021 2 there are 200 shirts in the school shop. lotem counts the number of shirts of each size. size s m l xl xxl frequency 36 64 48 32 20 (a) complete the bar chart to show this information. 02040 frequency60 10305070 s m l xl xxl size of shirt [2] (b) which size is the mode? .. [1] (c) work out how many more shirts are size s than size xl. .. [1] (d) complete the relative frequency table. write each value as a decimal. size s m l xl xxl relative frequency [2] (e) find the probability that a shirt, chosen at random, is not size l. .. [1]", "5": "5 0607/32/m/j/21 \u00a9 ucles 2021 [turn over 3 (a) write the number 30 062 in words. . [1] (b) write down all the factors of 50. ... [2] (c) write 61, 17% and 0.16 in order of size, starting with the smallest. , , [1] smallest (d) find the value of 62. give your answer correct to 3 decimal places. .. [2] (e) work out ... 8464 93+ . give your answer correct to 2 significant figures. .. [2] (f) these are the first four terms of a sequence. 60 53 46 39 (i) find the next two terms of this sequence. , [2] (ii) find the nth term of this sequence. .. [2]", "6": "6 0607/32/m/j/21 \u00a9 ucles 2021 4 0x23456 \u2013 3\u2013 2 \u2013 5 \u2013 6\u2013 4\u2013 1\u2013 1 \u2013 2 \u2013 3 \u2013 4 \u2013 5 \u2013 6 \u2013 7 \u2013 8 345 2 78 6 1y 1 (a) on the grid, plot the points a (2, 1), b (6, 1) and c (6, -3). [2] (b) abcd is a square. (i) on the grid, plot point d and draw the square. [1] (ii) write down the coordinates of point d. ( ... , ...) [1] (c) write down the coordinates of the mid-point of bc. ( ... , ...) [1] (d) write down the equation of the line ab. .. [1] (e) reflect square abcd in the y-axis. [1] (f) translate square abcd by the vector 1- 5bl . [2] ", "7": "7 0607/32/m/j/21 \u00a9 ucles 2021 [turn over 5 10 cm2.5 cm20 cm not to scale the diagram shows a sign made from card. the card is in the shape of a rectangle with a circle cut from it. (a) work out the perimeter of the rectangle. . cm [1] (b) some of these signs are cut from a sheet of card measuring 1.8 metres by 1.6 metres. work out the maximum number of these signs that can be cut from this sheet of card. .. [3] (c) the radius of the circle is 2.5 cm. work out the shaded area. ... cm2 [3] (d) the rectangle is enlarged by scale factor 3. work out the length and width of the enlarged rectangle. \b ...\b\u200acm\b\u200aand\b...\b\u200acm\b[2]", "8": "8 0607/32/m/j/21 \u00a9 ucles 2021 6 (a) y x6 5 4 3 2 1 \u2013 1 \u2013 2 \u2013 3\u2013 4 \u2013 3 \u2013 2 \u2013 1 1 0 2 3 4 5 6 the diagram shows the graph of y = f(x). on the same diagram, sketch the graph of (i) y = f(x) + 2, [1] (ii) y = f(x + 3). [1] (b) 6 \u2013 30 3 \u2013 1y x (i) on the diagram, sketch the graph of yx x 242=- for x13gg- . [2] (ii) find the coordinates of the local minimum. ( ... , ...) [1]", "9": "9 0607/32/m/j/21 \u00a9 ucles 2021 [turn over 7 an unbiased blue die has a cross on 2 faces and a circle on the other 4 faces. an unbiased red die has a cross on 1 face and a circle on the other 5 faces. (a) micha rolls the blue die. find the probability that he rolls (i) a circle, .. [1] (ii) a tick. .. [1] (b) derk rolls both dice. (i) find the probability that he rolls a cross on the blue die and a cross on the red die. .. [2] (ii) derk rolls the two dice 360 times. find the expected number of times he rolls a cross on the blue die and a cross on the red die. .. [1]", "10": "10 0607/32/m/j/21 \u00a9 ucles 2021 8 (a) a b not to scale d cm 53\u00b0z\u00b0 y\u00b0x\u00b0 the diagram shows a rectangle, abcd . m is the mid-point of ab and angle bmc = 53\u00b0. find the value of each of x, y and z. x = . y = . z = . [3] (b) the diagram shows another rectangle pqrs . p q not to scale s r complete each statement using one word from this list. similar congruent acute obtuse right reflex alternate corresponding the angle qps is .. the angle qrp is .. triangle pqr is .. to triangle psr. angle qpr is equal to angle prs because they are .. angles. [4]", "11": "11 0607/32/m/j/21 \u00a9 ucles 2021 [turn over 9 (a) 3 kmnot to scale4 kmnorth ab x\u00b0 c the diagram shows the positions of three houses, a, b and c. b is 4 km due east of a. c is 3 km due south of b. (i) use trigonometry to calculate the value of x. x = . [2] (ii) find the bearing of a from c. .. [1] (b) inez walks from home to hindy\u2019s house. the distance is 7 km. inez walks at a speed of 4 km/h. (i) work out how long this takes. give your answer in hours and minutes. . hours . minutes [2] (ii) inez leaves home at 13 20. work out the time that she arrives at hindy\u2019s house. .. [1]", "12": "12 0607/32/m/j/21 \u00a9 ucles 2021 10 (a) solve. xx47 89 += - x = . [2] (b) expand and simplify. () () xy xy 23 2 +-- .. [2] (c) factorise fully. pq pq 3623- .. [2] (d) 22 2nn 21 2# = find the value of n. n = . [1] (e) 555t64= find the value of t. t = . [1]", "13": "13 0607/32/m/j/21 \u00a9 ucles 2021 [turn over (f) write as a single fraction in its simplest form. (i) aa 2 52+ .. [2] (ii) tt 923# .. [2] (iii) mm 53 42 ' .. [2]", "14": "14 0607/32/m/j/21 \u00a9 ucles 2021 11 the cumulative frequency curve shows the time, in minutes, that 200 customers waited to be served in a restaurant. 02040cumulative frequency 6080100120140160180200 0 1 2 3 4 time (minutes)5 6", "15": "15 0607/32/m/j/21 \u00a9 ucles 2021 [turn over (a) use the curve to find (i) the median, . minutes [1] (ii) the lower quartile, . minutes [1] (iii) the interquartile range. . minutes [1] (b) (i) complete the frequency table. time ( t minutes) frequency t 011g t 121g t 231g t 341g t 451g t 561g 10 [2] (ii) write down the modal class. .. 1 \u200at\b\b\u200ag .. [1] (iii) work out an estimate of the mean. . minutes [2] question 12 is printed on the next page.", "16": "16 0607/32/m/j/21 \u00a9 ucles 2021 12 not to scale 0.2 cm13 cm h cm5 cm 6 cm a trophy is in the shape of a solid cone on top of a solid cylinder. the cone has radius 5 cm and slant height 13 cm. the cylinder has radius 6 cm and height 0.2 cm. (a) work out the volume of the cylinder. ... cm3 [2] (b) use pythagoras\u2019 theorem to show that the vertical height, h cm, of the cone is 12 cm. [2] (c) work out the volume of the cone. ... cm3 [2] (d) work out the curved surface area of the cone. ... cm2 [2] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge." }, "0607_s21_qp_33.pdf": { "1": "this document has 16 pages. any blank pages are indicated. cambridge igcse\u2122 dc (ce/cgw) 199829/2 \u00a9 ucles 2021 [turn overcambridge international mathematics 0607/33 paper 3 (core) may/june 2021 1 hour 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 96. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *8701230420*", "2": "2 0607/33/m/j/21 \u00a9 ucles 2021 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/33/m/j/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 (a) (i) write in words 78 616. . [1] (ii) write 78 616 correct to the nearest thousand. .. [1] (iii) write 78 616 correct to 3 significant figures. .. [1] (b) work out. (i) 4253 532451 474 -+ .. [1] (ii) 7293 .. [1] (iii) ..2431 6522+ give your answer correct to 2 decimal places. .. [2] (c) (i) write down all the factors of 12. ... [2] (ii) find the highest common factor (hcf) and the lowest common multiple (lcm) of 12 and 18. hcf . lcm . [3]", "4": "4 0607/33/m/j/21 \u00a9 ucles 2021 2 owen carried out a survey of the weather in 2020. he randomly chose some days from each month and recorded the type of weather for each day. the results are shown in the table. type of weather tally frequency cloud iiii ii rain iiii iii sun iiii iiii iiii iii snow ii fog iiii (a) complete the frequency column of the table. [1] (b) work out the total number of days owen chose in his survey. .. [1] (c) write down the most common type of weather in owen\u2019s survey. .. [1] (d) on the grid, draw a bar chart to show the information in the table. cloud024681012141618 rain sun type of weatherfrequency snow fog20 [2]", "5": "5 0607/33/m/j/21 \u00a9 ucles 2021 [turn over (e) one of these days is chosen at random. work out the probability that the type of weather on this day is sun. .. [1] (f) use the information in the table to estimate how many days in one year (365 days) will have rain. .. [2] (g) owen makes a pie chart using the information in the table. work out the sector angle for cloud. .. [2]", "6": "6 0607/33/m/j/21 \u00a9 ucles 2021 3 (a) these are the first four terms of a sequence. 800 400 200 100 for this sequence, write down (i) the next two terms, , [2] (ii) the rule for continuing the sequence. ... [1] (b) these are the first six terms of a different sequence. -5 -3 \u2003\u2003\u2212 1 \u2003\u20031 \u2003\u20033 \u2003\u20035 find the nth term of this sequence. .. [2] (c) the nth term of another sequence is 6 n + 5. (i) work out the first three terms of this sequence. , , [2] (ii) rearrange the formula p = 6n + 5 to make n the subject. n = . [2]", "7": "7 0607/33/m/j/21 \u00a9 ucles 2021 [turn over 4 (a) a packet of breakfast cereal costs $2.80 . (i) work out the greatest number of these packets that can be bought with $20. .. [2] (ii) work out how much of the $20 is left. $ .. [1] (b) the breakfast cereal contains only grain, fruit and nuts. the ratio, by mass, is grain : fruit : nuts = 16 : 7 : 2. work out the mass of each ingredient in a box containing 500 g of cereal. grain ... g fruit ... g nuts ... g [3] (c) a box of the cereal normally contains 500 g. in a special offer, the mass of cereal in a box is increased by 12%. work out the total mass of cereal in a special offer box. ... g [2]", "8": "8 0607/33/m/j/21 \u00a9 ucles 2021 5 (a) 40\u00b0not to scaleb ac dy\u00b0 x\u00b0 abc is an isosceles triangle and acd is a straight line. (i) find the value of x and the value of y. x = . y = . [2] (ii) find the size of the reflex angle at b. .. [1] (b) not to scale z\u00b0155\u00b0 find the value of z. z = . [3]", "9": "9 0607/33/m/j/21 \u00a9 ucles 2021 [turn over 6 an examination consists of two papers, paper 1 and paper 2. the scores for each of nine candidates are shown below. paper 1 75 73 68 60 60 55 47 33 15 paper 2 29 34 26 31 25 19 20 17 6 (a) complete the scatter diagram. the first five points have been plotted for you. 01020 paper 23040 0 10 20 30 40 paper 150 60 70 80 [2] (b) what type of correlation is shown in the scatter diagram? .. [1] (c) (i) work out the mean of the paper 1 scores and the mean of the paper 2 scores. mean paper 1 = . mean paper 2 = . [2] (ii) on the scatter diagram, draw a line of best fit. [2] (d) sajid scored 22 on paper 2. use your line of best fit to estimate his score on paper 1. .. [1]", "10": "10 0607/33/m/j/21 \u00a9 ucles 2021 7 (a) simplify. 2x + 3y + 4x - y .. [2] (b) solve. 4x - 3 = 9 x = . [2] (c) multiply out the brackets. ()xx x 32 52- .. [2] (d) write as a single fraction in its simplest form. (i) yy 83 522 ' .. [2] (ii) xx 74 3+ .. [2]", "11": "11 0607/33/m/j/21 \u00a9 ucles 2021 [turn over 8 \u2013 6\u2013 4\u2013 226 048 2 3 ab 4 5 1y x (a) work out the coordinates of the mid-point of line ab. ( ... , ...) [2] (b) find the equation of line ab. .. [3] (c) (i) on the grid, draw the line y = 2. [1] (ii) write down the coordinates of the point where the line y = 2 crosses line ab. ( ... , ...) [1]", "12": "12 0607/33/m/j/21 \u00a9 ucles 2021 9 18 m 24 m31 mnot to scale43 m y m the diagram shows a rectangle with a triangular corner cut off. (a) work out the area of the shaded shape. give the units of your answer. .. .. [5] (b) use pythagoras\u2019 theorem to work out the value of y. y = . [2] (c) work out the perimeter of the shaded shape. .. m [3]", "13": "13 0607/33/m/j/21 \u00a9 ucles 2021 [turn over 10 0 x2c a b34567 \u2013 3\u2013 2 \u2013 5\u2013 4\u2013 1\u2013 1 \u2013 2 \u2013 3 \u2013 4 3 4 5 2 7 8 9 6 1y 1 (a) describe fully the single transformation which maps triangle a onto triangle b. ... ... [2] (b) describe fully the single transformation which maps triangle a onto triangle c. ... ... [3] (c) reflect triangle a in the line x = 3. label the image x. [2] (d) rotate triangle a by 90\u00b0 clockwise about (0, 0). label the image y. [2]", "14": "14 0607/33/m/j/21 \u00a9 ucles 2021 11 10 \u2013 10 2 \u2013 3y x (a) (i) on the diagram, sketch the graph of yx x212=+ + for x32gg- . [2] (ii) find the coordinates of the local minimum. ( ... , ...) [1] (b) on the diagram, sketch the graph of y2x= for x32gg- . [2] (c) find the x-coordinate of each point of intersection of yx x212=+ + and y2x= . .. and . [2]", "15": "15 0607/33/m/j/21 \u00a9 ucles 2021 blank page", "16": "16 0607/33/m/j/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_s21_qp_41.pdf": { "1": "this document has 20 pages. any blank pages are indicated. cambridge igcse\u2122 dc (ce/sg) 199667/4 \u00a9 ucles 2021 [turn overcambridge international mathematics 0607/41 paper 4 (extended) may/june 2021 2 hours 15 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 120. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *6664245211*", "2": "2 0607/41/m/j/21 \u00a9 ucles 2021 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l = curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area =a c bcb a", "3": "3 0607/41/m/j/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 a stadium sells tickets at 10 different prices for a sporting event. the table shows the number of tickets sold at each price. ticket price ($ x) 22 23 35 40 53 55 58 61 69 73 number of tickets sold ( y)8600 9100 7000 7600 5200 6000 4800 4500 2600 3000 (a) what type of correlation is shown by the data? . [1] (b) find the mean of the 10 ticket prices. $ [1] (c) (i) find the equation of the regression line for y in terms of x. y = [2] (ii) the stadium decides to sell some tickets at a price of $45. use your answer to part (i) to estimate the number of tickets it will sell at this price. . [1]", "4": "4 0607/41/m/j/21 \u00a9 ucles 2021 2 a \u2013 9\u2013 8\u2013 7\u2013 6\u2013 5\u2013 4\u2013 3\u2013 2\u2013 1 \u2013 1 \u2013 2 \u2013 3 \u2013 4 \u2013 5 \u2013 61123456789 2 3 4 5 6 7 8 9 0 xy (a) translate triangle a with vector 53 --bl . label the image b. [2] (b) describe fully the single transformation that maps triangle b onto triangle a. . . [2] (c) rotate triangle a through 90\u00b0 clockwise about (0, 0). label the image c. [2] (d) reflect triangle a in the line yx=. label the image d. [2] (e) describe fully the single transformation that maps triangle c onto triangle d. . . [2]", "5": "5 0607/41/m/j/21 \u00a9 ucles 2021 [turn over 3 find the next term and the nth term in each of the following sequences. (a) 13, 18, 23, 28, 33, \u2026 next term = nth term = [3] (b) \u20139, \u20136, \u20131, 6, 15, \u2026 next term = nth term = [3] (c) 1089, 2178, 3267, 4356, 5445, \u2026 next term = nth term = [2] (d) 2, \u20134, 8, \u201316, 32, \u2026 next term = nth term = [3]", "6": "6 0607/41/m/j/21 \u00a9 ucles 2021 4 the marks, x, of 300 students in a chemistry test are shown in the table. mark ( x) frequency x 01 0 1g 41 x 10 021g 32 x 00231g 44 x 00341g 50 x 00461g 65 x 00681g 48 x 0081 0 1g 20 (a) calculate an estimate of the mean mark. . [2] (b) complete the cumulative frequency table. mark ( x)cumulative frequency x10g 41 x 02g x 03g x 04g x 06g x 08g x100g 300 [1]", "7": "7 0607/41/m/j/21 \u00a9 ucles 2021 [turn over (c) on the grid, draw a cumulative frequency curve. 0050100150200250300 10 20 30 40 50 markcumulative frequency 60 70 80 90 100 [3] (d) use your curve in part (c) to find an estimate for (i) the median mark, . [1] (ii) the interquartile range. . [2] (e) 35% of the students pass the test. use your curve in part (c) to find an estimate of the minimum mark needed to pass. . [2]", "8": "8 0607/41/m/j/21 \u00a9 ucles 2021 5 ()xx 21 f=- ()xx 3 g =- ()xxh2= (a) find (i) ()2 f-, . [1] (ii) (( ))2 hg- . . [2] (b) solve ()x 7 f=. x = [2] (c) find (( ))x fg . . [1] (d) solve () () () xx x20 fg h # += . x = [3] (e) find ()x g1-. ()x g1- = [2]", "9": "9 0607/41/m/j/21 \u00a9 ucles 2021 [turn over (f) y x 0 \u2013 2\u2013 3 310 (i) on the diagram, sketch the graph of () yx h= for values of x between 3- and 3. [2] (ii) write down the equation of the line of symmetry of the graph of () yx h= . . [1] (iii) on the diagram, sketch the graph of () yx g= for values of x between 3- and 3. [1] (iv) solve () () xxgh2 . [2]", "10": "10 0607/41/m/j/21 \u00a9 ucles 2021 6 piero invests $5000 in bank a and $5000 in bank b. (a) bank a pays simple interest at a rate of 6.5% each year. (i) find the total amount piero has in bank a at the end of 4 years. $ [3] (ii) find the number of complete years it takes for the total amount that piero has in bank a to be greater than $10 000. . [3] (b) bank b pays compound interest at a rate of 4% each year. (i) find the total amount piero has in bank b at the end of 4 years. $ [2]", "11": "11 0607/41/m/j/21 \u00a9 ucles 2021 [turn over (ii) find the number of complete years it takes for the total amount that piero has in bank b to be greater than $10 000. . [4] (c) by sketching suitable graphs, find the number of complete years it takes for the total amount that piero has in bank b to be greater than the total amount in bank a. . [4]", "12": "12 0607/41/m/j/21 \u00a9 ucles 2021 7 (a) solve the simultaneous equations. you must show all your working. xy xy72 8 23 13+= -= x = y = [4] (b) solve. (i) x34 19 -= - x = [2] (ii) xx 15 57 3 -= - x = [2] (iii) ()x1284+=- x = [2] (c) logl og logl og px q 38 2 -- = find x in terms of p and q. x = [3]", "13": "13 0607/41/m/j/21 \u00a9 ucles 2021 [turn over 8 spinner a is numbered 2, 3, 4, 5, 6, 7. spinner b is numbered 2, 3, 4, 5. each spinner is equally likely to stop on any of its numbers. the two spinners are each spun once and the number that each spinner stops on is recorded. find the probability that (a) spinner a stops on a number less than 4, . [1] (b) spinner b stops on 6, . [1] (c) spinner a and spinner b both stop on the same number, . [2] (d) one number is prime and one number is not prime, . [3] (e) the sum of the numbers is a multiple of 3. . [2]", "14": "14 0607/41/m/j/21 \u00a9 ucles 2021 9 f d cba enot to scale 20 cm 12 cm the diagram shows rectangle abcd and two right-angled isosceles triangles, abf and bce . (a) find the perimeter of the quadrilateral cdfe . ... cm [3]", "15": "15 0607/41/m/j/21 \u00a9 ucles 2021 [turn over (b) (i) find the area of the quadrilateral cdfe . .. cm2 [3] (ii) quadrilateral q is similar to quadrilateral cdfe . the area of quadrilateral q is 158 cm2. find the length of the shortest side of quadrilateral q. cm [2] (c) calculate angle afe. angle afe = [2]", "16": "16 0607/41/m/j/21 \u00a9 ucles 2021 10 142\u00b042\u00b0a co p d bnot to scale a, d, b and c lie on a circle, centre o. ap is a tangent to the circle at a and bp is a tangent to the circle at b. angle aob = 142\u00b0 and angle dap = 42\u00b0. (a) find the value of (i) angle abd , angle abd = [1] (ii) angle acb , angle acb = [1] (iii) angle adb , angle adb = [1] (iv) angle bad , angle bad = [1] (v) angle apb. angle apb = [1]", "17": "17 0607/41/m/j/21 \u00a9 ucles 2021 [turn over (b) the radius of the circle is 11 cm. find the area of triangle abd . .. cm2 [5]", "18": "18 0607/41/m/j/21 \u00a9 ucles 2021 11 (a) using a suitable sketch, solve 51 0x= . 12 \u2013 1\u2013 1 3 0 xy x = \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd [3]", "19": "19 0607/41/m/j/21 \u00a9 ucles 2021 (b) solve. xxx61235-=++ you must show all your working. x = or x = [5]", "20": "20 0607/41/m/j/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_s21_qp_42.pdf": { "1": "this document has 24 pages. any blank pages are indicated. cambridge igcse\u2122 dc (ce/sg) 199668/3 \u00a9 ucles 2021 [turn overcambridge international mathematics 0607/42 paper 4 (extended) may/june 2021 2 hours 15 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 120. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *8706246210*", "2": "2 0607/42/m/j/21 \u00a9 ucles 2021 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/42/m/j/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 ernst makes chairs. (a) the total cost of making a chair is $250. total cost = cost of materials + $26 for each hour worked ernst works for 621 hours to make a chair. calculate the cost of the materials as a percentage of the total cost of $250. . % [3] (b) ernst sells the chairs to a shop. the shop makes 24% profit when they sell a chair for $396.80 . calculate the amount the shop pays ernst for a chair. $ . [2] (c) in a sale the shop reduces the price, $396.80, of each chair by 3% each day until it is sold. find the number of days until the price first goes below $200. . [4]", "4": "4 0607/42/m/j/21 \u00a9 ucles 2021 2 (a) ab 123456789 \u2013 3\u2013 2\u2013 1\u2013 1 \u2013 2 \u2013 3 3 4 5xy 2 1 0 (i) rotate triangle a 90\u00b0 anticlockwise about ( -1, 2). [2] (ii) describe fully the single transformation that maps triangle a onto triangle b. . . [3]", "5": "5 0607/42/m/j/21 \u00a9 ucles 2021 [turn over (b) describe fully the single transformation that is equivalent to reflection in x = 3 followed by reflection in x = 7. you may use the grid below to help you. . . [2]", "6": "6 0607/42/m/j/21 \u00a9 ucles 2021 3 the table shows the masses of 30 sheep. mass, m kg m 08 0 61g m 0081 0 1g m 0010 121g m 120 104 1g frequency 8 3 12 7 (a) write down the modal group. . [1] (b) write down the class which contains the lower quartile. . [1] (c) maria says that the range of masses is 80 kg. explain why she is incorrect. . . [1] (d) draw an accurate pie chart to show this information. [4]", "7": "7 0607/42/m/j/21 \u00a9 ucles 2021 [turn over 4 15 \u2013 150 5 \u2013 5y x ()xx 10 f2=- (a) on the diagram, sketch the graph of y = f(x) for x55gg- . [2] (b) solve the equation f( x) = 6. [2] (c) solve ()x 6 f2. [3] (d) find the values of k for which f( x) = k has exactly two solutions. [2]", "8": "8 0607/42/m/j/21 \u00a9 ucles 2021 5 35\u00b0p bc a20 m10 mnot to scale a, b and c are points on horizontal ground. bp is a vertical pole. bc = 20 m and bp = 10 m. angle pa b = 35\u00b0. (a) show that pc = 22.36 m correct to 2 decimal places. [2] (b) show that ab = 14.28 m correct to 2 decimal places. [2]", "9": "9 0607/42/m/j/21 \u00a9 ucles 2021 [turn over (c) calculate ap. ap = m [2] (d) angle abc = 125\u00b0. calculate ac. ac = m [3] (e) calculate angle apc . angle apc = [3]", "10": "10 0607/42/m/j/21 \u00a9 ucles 2021 6 the cumulative frequency curve shows the times, in minutes, for runner a in 160 races of 10 000 m. 30020406080100 cumulative frequency120140160 30.5 31 31.5 time (minutes)32 32.5 33", "11": "11 0607/42/m/j/21 \u00a9 ucles 2021 [turn over (a) use the curve to estimate (i) the median time for runner a, .. min [1] (ii) the interquartile range for runner a, .. min [2] (iii) the 80th percentile for runner a. .. min [2] (b) in the same 160 races, runner b has a median time of 31.7 minutes and an interquartile range of 1 minute. one of the runners is to be selected for a team. (i) give one reason why it may be better to select runner b. . [1] (ii) give one reason why it may be better to select runner a. . [1]", "12": "12 0607/42/m/j/21 \u00a9 ucles 2021 7 roisin drives 250 km. she drives the first 200 km at an average speed of x km/h. (a) write down an expression for the time, in hours, it takes to drive the 200 km. .. h [1] (b) for the remainder of the journey, roisin is in heavy traffic and her average speed is 40 km/h less than for the first 200 km. the total time for the journey is 321 hours. show that xx7 780 16000 02-+ =. [4] (c) solve the equation xx7 780 16000 02-+ = to find the time taken to travel the first 200 km. give your answer in hours and minutes correct to the nearest minute. ... h ... min [5]", "13": "13 0607/42/m/j/21 \u00a9 ucles 2021 [turn over 8 (a) y is inversely proportional to the square root of x. when x = 25, y = 0.05 . (i) show that yx41= . [2] (ii) find y when x = 9. . [1] (iii) find x in terms of y. x = [2] (iv) find x when y21=. . [1] (b) b is inversely proportional to a3. when a = p, b = 24. find b when a = 2p. . [2]", "14": "14 0607/42/m/j/21 \u00a9 ucles 2021 9 not to scale5 cm 12 cm the diagram shows a cup in the shape of a cone. (a) calculate the curved surface area of the cup. .. cm2 [3]", "15": "15 0607/42/m/j/21 \u00a9 ucles 2021 [turn over (b) the cup is filled with water. a metal sphere of radius r\u2009\u200acm\u2009is\u2009lowered\u2009into\u2009the\u2009cup. the top of the sphere is level with the surface of the water. not to scale r cm (i) use similar triangles to show that r = 3.33 cm correct to 3 significant figures. [3] (ii) calculate the volume of the water in the cup. .. cm3 [3]", "16": "16 0607/42/m/j/21 \u00a9 ucles 2021 10 hua travels to school by bus or she cycles or she walks. if it rains, the probability that she travels by bus is 0.7 and the probability that she cycles is 0.25 . if it does not rain, the probability that she cycles is 0.55 and the probability that she walks is 0.25 . on any day, the probability that it rains is 0.6 . (a) complete the tree diagram to show the probabilities of the three methods of travel. rainbus cycle walk not rainbus cycle walk0.7 0.6 0.55 [2] (b) calculate the probability that, on any day, (i) hua walks to school, . [3] (ii) hua does not cycle. . [3]", "17": "17 0607/42/m/j/21 \u00a9 ucles 2021 [turn over (c) last week it rained every day of the 5 school days. calculate the probability that hua travelled by bus on exactly 4 of the 5 days. . [3]", "18": "18 0607/42/m/j/21 \u00a9 ucles 2021 11 y xp oa (\u2013 2, 4) b (8, \u2013 1)not to scale a is the point ( -2, 4) and b is the point (8, -1). p divides ab in the ratio 3 : 2. (a) show that the coordinates of p are (4, 1). ( .. , .. ) [2] (b) the line l is perpendicular to ab and passes through p. find the equation of line l. . [4]", "19": "19 0607/42/m/j/21 \u00a9 ucles 2021 [turn over (c) the point c has coordinates (6, 5). show that point c lies on line l. [1] (d) (i) find the distance ab. give your answer in surd form. . [2] (ii) calculate the area of triangle abc . . [3]", "20": "20 0607/42/m/j/21 \u00a9 ucles 2021 12 ()xx 23 f=- ()xx 235g=- (a) find f(4). . [1] (b) solve g( x) = 4. . [3] (c) find ()x f1-. ()x f1- = [2] (d) find (( ))x gf . write your answer as a single fraction in its simplest form. . [2]", "21": "21 0607/42/m/j/21 \u00a9 ucles 2021 [turn over (e) find f( x) - g(x). write your answer as a single fraction in its simplest form. . [3]", "22": "22 0607/42/m/j/21 \u00a9 ucles 2021 13 y x55 \u2013 5\u2013 5 0 ()() ()xxxx 133f2 =-++ (a) on the diagram, sketch the graph of y = f(x) for values of x between -5 and 5. [3] (b) find the equations of the asymptotes parallel to the y-axis. [2] (c) solve f( x) = 2x + 3. [3]", "23": "23 0607/42/m/j/21 \u00a9 ucles 2021 blank page", "24": "24 0607/42/m/j/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_s21_qp_43.pdf": { "1": "this document has 20 pages. any blank pages are indicated. cambridge igcse\u2122 dc (ce/sg) 199669/2 \u00a9 ucles 2021 [turn overcambridge international mathematics 0607/43 paper 4 (extended) may/june 2021 2 hours 15 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 120. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *3271308107*", "2": "2 0607/43/m/j/21 \u00a9 ucles 2021 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area =a c bcb a", "3": "3 0607/43/m/j/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 y x5 0 5 \u2013 5\u2013 5 ()xxx4f=- (a) on the diagram, sketch the graph of y = f(x) for values of x between -5 and 5. [2] (b) find the zeros of f( x). x = or x = [2] (c) solve the equation f( x) = 2. x = or x = [2] (d) g(x) = f(x + 2) (i) on the same diagram, sketch the graph of y = g(x) for values of x between -5 and 5. [2] (ii) describe fully the single transformation that maps the graph of y = f(x) onto the graph of y = g(x). . . [2]", "4": "4 0607/43/m/j/21 \u00a9 ucles 2021 2 (a) increase $55 by 250%. $ [2] (b) (i) beatrice invests $500 at a rate of 1.5% per year simple interest. find the amount beatrice has at the end of 12 years. $ [3] (ii) dan invests $500 at a rate of 1.5% per year compound interest. find the difference between dan\u2019s amount and beatrice\u2019s amount at the end of 12 years. $ [3] (c) eva invests an amount of money at a rate of 2.1% per year compound interest. find the number of complete years it takes for eva\u2019s investment to double in value. . [4]", "5": "5 0607/43/m/j/21 \u00a9 ucles 2021 [turn over (d) each year the value of fred\u2019s car reduces by 15% of its value at the start of that year. the value of the car is now $5158.65 . find the value of fred\u2019s car 3 years ago. $ [3]", "6": "6 0607/43/m/j/21 \u00a9 ucles 2021 3 xy bc ad onot to scale abcd is a rectangle. a is the point ( -2, -1) and b is the point (5, 0). (a) find the equation of bc. . [4] (b) c is the point ( p, 14). find the value of p. p = [2]", "7": "7 0607/43/m/j/21 \u00a9 ucles 2021 [turn over (c) find the coordinates of point d. ( .. , .. ) [2] (d) find the area of rectangle abcd . . [4]", "8": "8 0607/43/m/j/21 \u00a9 ucles 2021 4 12 cm 20 cm 5 cmnot to scale the diagram shows a solid made by joining a cone and a hemisphere to a cylinder. the radius of each of the three shapes is 5 cm. the height of the cylinder is 20 cm and the height of the cone is 12 cm. (a) calculate the total surface area of the solid. .. cm2 [5]", "9": "9 0607/43/m/j/21 \u00a9 ucles 2021 [turn over (b) the total volume of the solid is 32050cm3r. it is melted down and made into spheres of radius 1.2 cm. (i) find the greatest number of spheres that can be made. . [3] (ii) work out the percentage of the 32050cm3r that remains after the spheres have been made. . % [3]", "10": "10 0607/43/m/j/21 \u00a9 ucles 2021 5 (a) there are 200 students in a school. the table shows information about their heights, h cm. height, h cm h 150 1651g h 1165 70 1g h 10 15 771g h 1175 80 1g h 10 1 89 0 1g h 109 2001g frequency 7 17 43 64 49 20 calculate an estimate of the mean height. cm [2] (b) a biased die in the shape of a cube is numbered 0, 1, 1, 2, 3 and 3. it is rolled 100 times. the table shows the results. score 0 1 2 3 frequency x y 30 45 the mean score is 2.13 . find the value of x and the value of y. x = y = . [3]", "11": "11 0607/43/m/j/21 \u00a9 ucles 2021 [turn over 6 (a) ten students compare their test marks in physics ( x) and chemistry ( y). the table shows the results. student a b c d e f g h i j physics ( x) 50 48 31 80 65 85 27 30 45 53 chemistry ( y) 55 56 30 83 63 90 30 32 45 55 (i) write down the type of correlation between the physics and chemistry marks. . [1] (ii) find the equation of the line of regression, giving y in terms of x. y = [2] (iii) student k scores 70 in the physics test. use your answer to part (a)(ii) to estimate this student\u2019s mark in chemistry. . [1] (b) the stem-and-leaf diagram shows information about the speeds of cars passing a school. 4 2 2 3 4 5 8 5 1 3 3 4 4 5 7 9 6 0 0 1 1 2 5 key : 4 | 5 = 45 km/h find (i) the range, . km/h [1] (ii) the median, . km/h [1] (iii) the lower quartile. . km/h [1]", "12": "12 0607/43/m/j/21 \u00a9 ucles 2021 7 in this question all lengths are in centimetres. (a) 8x\u00b0 () \u00b0 x5+b c anot to scale in triangle abc , ac = bc, angle abc = () \u00b0 x5+ and angle \u00b0x acb 8= . find the value of x. x = [3] (b) not to scale()p2- ()p1+ the diagram shows a rectangle with sides of length ()p1+ and ()p2-. the area of the rectangle is 90 cm2 . find the value of p. p = [4]", "13": "13 0607/43/m/j/21 \u00a9 ucles 2021 [turn over (c) 30\u00b0not to scale()y4-()y1- the diagram shows a right-angled triangle. find the value of y. y = [3] (d) not to scale()w 1+ ()w23+13 the diagram shows a right-angled triangle with sides of length ()w 1+, ()w23+ and 13. work out the area of the triangle. .. cm2 [6]", "14": "14 0607/43/m/j/21 \u00a9 ucles 2021 8 c bd a 16 cm18 cm 13 cm7 cm not to scale (a) calculate angle bca and show that it rounds to 59.57\u00b0, correct to 2 decimal places. [3] (b) find the area of quadrilateral abcd . .. cm2 [3]", "15": "15 0607/43/m/j/21 \u00a9 ucles 2021 [turn over (c) find the shortest distance from a to bc. cm [2] (d) d is due north of b. find the bearing of b from c. . [6]", "16": "16 0607/43/m/j/21 \u00a9 ucles 2021 9 10 02.5y x () , xx x 0 fx2 = (a) on the diagram, sketch the graph of y = f(x) for . x 02 5 1g . [2] (b) find the coordinates of the local minimum point. ( .. , .. ) [2] (c) (i) find x when f( x) = 3x. . [3] (ii) solve ()xx 3 fh . [2]", "17": "17 0607/43/m/j/21 \u00a9 ucles 2021 [turn over 10 (a) kris can go to school by bus or by taxi. on any day the probability that kris goes by bus is 0.9 . when kris goes by bus, the probability that she is late for school is 0.06 . when she goes by taxi, the probability that she is late for school is 0.01 . (i) find the probability that, on any day, kris is late for school. . [3] (ii) find the probability that, on any day, kris is not late for school. . [1] (iii) in one year, kris attends school on 200 days. find the number of days kris is expected not to be late. . [1] (b) alex also goes to school by bus or by taxi. the probability that alex goes by bus is 0.8 . the probability that alex goes by bus and is late is 0.12 . find the probability that alex is late when he goes by bus. . [2]", "18": "18 0607/43/m/j/21 \u00a9 ucles 2021 11 (a) f(x) = 3x + 2 g(x) = x2 h(x) = 2x (i) find f(2). . [1] (ii) find f(g(3)). . [2] (iii) find the value of (( )) (( ))3 3hg gh. . [3] (iv) find ()x f1-. ()x f1=- [2] (v) find ()x h1-. ()x h1=- [2]", "19": "19 0607/43/m/j/21 \u00a9 ucles 2021 (b) (i) find the value of logl og 8139 31- bl. . [2] (ii) log25b 32= find the value of b. b = [2]", "20": "20 0607/43/m/j/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_s21_qp_51.pdf": { "1": "this document has 8 pages. cambridge igcse\u2122cambridge international mathematics 0607/51 paper 5 investigation (core) may/june 2021 1 hour 10 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 36. \u25cf the number of marks for each question or part question is shown in brackets [ ]. dc (lk/sw) 207496/1 \u00a9 ucles 2021 [turn over *9038285806*", "2": "2 0607/51/m/j/21 \u00a9 ucles 2021 answer all the questions. investigation rolling square this investigation looks at the path of a point on a square as it rolls along the x-axis. a square of side 1 cm rolls along the x-axis. one roll is a turn of 90\u00b0 clockwise about its bottom right corner. 0.511.5 0.5 1 1.5diagram 1 starting position 2 2.5 3y x 0 00.511.5 0.5 1 1.5diagram 2 after one roll 2 2.5 3y xposition 1 centre of rotationposition 1 position 2 centre of rotation diagram 1 shows the square in position 1. one side of the square is bold to help show the rotation. the centre of the square is (0.5, 0.5). diagram 2 shows the square rolled 90\u00b0 clockwise about (1, 0) to position 2. 1 to get to position 3 the square rolls 90\u00b0 clockwise about (2, 0). to get to position 4 the square then rolls 90\u00b0 clockwise about (3, 0). (a) on the diagram below, draw the square in position 4, position 5 and position 6. 012 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15y x [2] (b) complete this table to show the x-coordinate of the centre of the square in each position. you may use the diagram to help you. position ( n) 1 2 3 4 5 6 n x-coordinate 0.5 1.5 2.5 [2]", "3": "3 0607/51/m/j/21 \u00a9 ucles 2021 [turn over (c) find the x-coordinate of the centre of the square in position 92. . [2] (d) 012 1 2 3 4 5 6 7y x (i) the square rolls from position 1 to position n. the centre has moved a distance equal to the circumference of 1 circle. the radius, r, of the circle is half the diagonal of the square. (a) write down the number of rolls needed. . [1] (b) write down the value of n. . [1] (ii) circumference, c, of circle, radius r. c = 2rr yr xhypotenuse, r, of a right-angled triangle with sides r, x and y. rx y22 2=+ (a) show that the radius of the circle is 0.707 cm, correct to 3 decimal places. [2] (b) find the length of the arc that the centre of the square moves along from position 1 to position 2. . [2]", "4": "4 0607/51/m/j/21 \u00a9 ucles 2021 2 the side of the square is now 2 cm. 0123 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15y x the square rolls along the x-axis in the same way as in question 1 . (a) complete the table of x-coordinates of the centre of the square in different positions. position ( n) 1 2 3 4 5 6 n x-coordinate 1 3 [3] (b) find the coordinates of the centre of the square in position 35. ( .. , .. ) [3] 3 (a) the side of the square is now 3 cm. complete the table of x-coordinates of the centre of the square in different positions. you may use the diagram below to help you. position ( n) 1 2 3 4 5 6 n x-coordinate 1.5 0123 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15y x [3]", "5": "5 0607/51/m/j/21 \u00a9 ucles 2021 [turn over (b) the side of the square is now 4 cm. complete the table of x-coordinates of the centre of the square in different positions. position ( n) 1 2 3 4 5 6 n x-coordinate 2 [2] 4 write your expressions from questions 1(b) , 2(a) and 3 in the table below. complete the table using any patterns you notice. side of square (w cm)x-coordinate in position n 1 2 3 4 5 w [4]", "6": "6 0607/51/m/j/21 \u00a9 ucles 2021 5 a square of side w cm rolls from position 1 to position 120. at position 120, the x-coordinate of the centre of the square is 2151. find the value of w. . [3]", "7": "7 0607/51/m/j/21 \u00a9 ucles 2021 [turn over 6 a square of side a cm is in position 1. the coordinates of the centre of the square are (11, k ). (a) find the value of k and the value of a. k = a = [2] (b) find the coordinates of the top right corner of the square. ( .. , .. ) [1] (c) write down the y-coordinate of the centre of the square in position 400. . [1] question 7 is printed on the next page.", "8": "8 0607/51/m/j/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.7 a square rolls along the x-axis. for the top left corner give a reason why total distance moved in 2 rolls = total distance moved in 3 rolls. you may use this grid. . . [2]" }, "0607_s21_qp_52.pdf": { "1": "this document has 12 pages. any blank pages are indicated. dc (rw/fc) 207546/2 \u00a9 ucles 2021 [turn over *6553228563* cambridge international mathematics 0607/52 paper 5 investigation (core) may/june 2021 1 hour 10 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 36. \u25cf the number of marks for each question or part question is shown in brackets [ ].cambridge igcse\u2122", "2": "2 0607/52/m/j/21 \u00a9 ucles 2021 answer all the questions. investigation nearest neighbours this investigation looks at the distances from the origin (0, 0) to the centres of squares and hexagons that form a pattern. the diagram shows a pattern of congruent squares. a dot marks the centre of each square. the coordinates of some of the centres are (0, 0), ( 3-, 2-) and (3, 1). y x 1 2 3 4123 \u20133\u20132\u20131\u20134 \u20133 \u20132 \u20131 0", "3": "3 0607/52/m/j/21 \u00a9 ucles 2021 [turn over 1 (a) complete this table, using a tick in each row, to show whether a point is \u2022 at the centre of a square \u2022 inside a square, but not at its centre \u2022 on the side of two squares \u2022 where four squares meet. the first three have been done for you. pointat the centre of a squareinside a square, not at its centreon the side of two squareswhere four squares meet (0, 0) \uf0fc (1-, 0.5) \uf0fc (0.5, 0.5) \uf0fc (1.5, 1.5) (0, 1.5) (0.25, 0) (100.5, 99.5) [4] (b) give a reason for your answer for (100.5, 99.5). . . [1]", "4": "4 0607/52/m/j/21 \u00a9 ucles 2021 2 each dot on the grid marks the centre of a square. y x 1 2 3123 \u20133\u20132\u20131\u20133 \u20132 \u20131 0 the nearest dots to (0, 0) are ( 1-, 0), (0, 1), (1, 0) and (0, 1-). these four dots are the 1st nearest neighbours . the 2nd nearest neighbours to (0, 0) are (1, 1), (1, 1-), ( 1-, 1-) and ( 1-, 1). all nearest neighbours have integer coordinates.", "5": "5 0607/52/m/j/21 \u00a9 ucles 2021 [turn over (a) one of the 3rd nearest neighbours to (0, 0) is (2, 0). find the other 3rd nearest neighbours and write down their coordinates. . [3] (b) find the coordinates of all the 4th nearest neighbours to (0, 0). . . [3]", "6": "6 0607/52/m/j/21 \u00a9 ucles 2021 3 you can find the distance, d, from (0, 0) to the point ( a, b) using pythagoras\u2019 theorem. da b22 2=+ (a) show that the distance of a 4th nearest neighbour from (0, 0) is 5. [2] (b) here are four points and their coordinates. a(20, 5) b(7, 24) c(7-, 24) d(0, 25) which of these points are a distance of 25 units from (0, 0)? . [3]", "7": "7 0607/52/m/j/21 \u00a9 ucles 2021 [turn over (c) there are more than 10 nearest neighbours to (0, 0) with d5=. four of them are (0, 5), (5, 0), ( 5-, 0) and (0, 5-). on the grid, mark with a cross all the nearest neighbours to (0, 0) with d5=. y x 1 2 3 4 512345 \u20133 \u20134 \u20135\u20132\u20131\u20133 \u20134 \u20135 \u20132 \u20131 0 [4]", "8": "8 0607/52/m/j/21 \u00a9 ucles 2021 4 here is a pattern of congruent regular hexagons. each dot marks the centre of a hexagon. the triangle shown is an equilateral triangle. (a) (i) explain why the triangle shown is an equilateral triangle. . [1] the dots at the centre of the hexagons have coordinates as shown on the grid below. y x01234 1 2 3 4 5 6 7(7, 0)(5, 4) (ii) a line is made by joining the points (3, 0) and (4, 1). work out the size of the acute angle between this line and the x\u2011axis. . [2]", "9": "9 0607/52/m/j/21 \u00a9 ucles 2021 [turn over (b) the point at the centre of each hexagon has six 1st nearest neighbours. (i) complete this list of the 1st nearest neighbours to the point (1, 1). (0, 1), (0, 2), (1, 2), ... [2] (ii) find, in terms of a and b, the coordinates of the six 1st nearest neighbours to the point ( a, b). . . [3]", "10": "10 0607/52/m/j/21 \u00a9 ucles 2021 (c) a student suggests that an estimate of d, the distance from (0, 0) to the point ( a, b), is d aba b22=+ + . the distance between any point and its 1st nearest neighbours on this grid is 1 cm. y x0234 \u20131 \u20133 \u2013 4 \u2013 5\u20132\u20131 \u20132 \u20133 \u20134 1 2 3 4 51 does the student\u2019s formula give a good estimate for the distance from (0, 0) to (4, 3-)? show how you decide. [5]", "11": "11 0607/52/m/j/21 \u00a9 ucles 2021 5 the circles show the 1st, 2nd, 3rd, and 4th nearest neighbours to the point x. x (a) complete this table. nearest neighbour 1st 2nd 3rd 4th 5th 6th 7th 8th number of nearest neighbours 6 12 6 [2] (b) a computer calculates that there is a total of 9 points for a certain nearest neighbour distance. explain why the computer is probably wrong. . [1]", "12": "12 0607/52/m/j/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_s21_qp_53.pdf": { "1": "this document has 8 pages. dc (rw/fc) 207547/2 \u00a9 ucles 2021 [turn over *9976971165* cambridge international mathematics 0607/53 paper 5 investigation (core) may/june 2021 1 hour 10 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 36. \u25cf the number of marks for each question or part question is shown in brackets [ ].cambridge igcse\u2122", "2": "2 0607/53/m/j/21 \u00a9 ucles 2021 answer all the questions. investigation paths around squares and rectangles this investigation looks at paths around different squares and rectangles. in this investigation \u2022 all lengths are in metres \u2022 all tiles are squares of side 1 metre. the path around a square of side 1 needs 8 square tiles. this is the path around a square of side 2. 1 (a) on this grid, draw the path around the square of side 3. [1]", "3": "3 0607/53/m/j/21 \u00a9 ucles 2021 [turn over (b) on this grid, draw the path around a square of side 4. [1] (c) this table shows the number of tiles in the paths around squares of different sizes. complete the table. side of square number of tiles in path 1 8 2 3 4 [1] (d) work out the number of tiles that make the path around a square of side 6. . [2]", "4": "4 0607/53/m/j/21 \u00a9 ucles 2021 (e) explain why the path around a square cannot have exactly 50 tiles. . [1] (f) find an expression, in terms of n, for the number of tiles in the path around a square of side n. . [2] (g) work out the number of tiles in the path around a square of side 88. . [2] (h) the path around a square has 400 tiles. work out the area of the square. . [3]", "5": "5 0607/53/m/j/21 \u00a9 ucles 2021 [turn over 2 this is the path around a rectangle of width 1 and length 2. (a) on the grid, draw a diagram to show the path around the given rectangles. rectangle width 1 and length 3 rectangle width 1 and length 4 [2] (b) complete the table to show the number of tiles in the paths around rectangles of width 1 with different lengths. length of rectangle ( l) number of tiles in path 2 3 4 5 [2] (c) find an expression, in terms of l, for the number of tiles in the path around a rectangle of width 1 and length l. . [3]", "6": "6 0607/53/m/j/21 \u00a9 ucles 2021 3 (a) (i) complete the table to show the number of tiles in the paths around rectangles of width 2 with different lengths. you may use the grid to help you. length of rectangle ( l) number of tiles in path 1 2 3 4 [3] (ii) find an expression, in terms of l, for the number of tiles in the path around a rectangle of width 2 and length l. . [2]", "7": "7 0607/53/m/j/21 \u00a9 ucles 2021 [turn over (b) find an expression, in terms of l, for the number of tiles in the path around a rectangle of width 3 and length l. . [2] (c) complete the table. use your expressions from questions 2(c) , 3(a)(ii) and 3(b). width of rectangle ( w)number of tiles in path around a rectangle of length l 1 2 3 4 [2] (d) find an expression, in terms of l and w, for the number of tiles in the path around a rectangle of length l and width w. . [2] (e) use your answer to part (d) to write an expression for the number of tiles in the path around a rectangle of length n and width n. give your answer in its simplest form. . [2] question 4 is printed on the next page.", "8": "8 0607/53/m/j/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.4 the path around a rectangle has 20 tiles. complete the table to show all the possible lengths and widths of the rectangle. you may not need all the rows. you may use the grid to help you. length of rectangle ( l) width of rectangle ( w) [3]" }, "0607_s21_qp_61.pdf": { "1": "this document has 16 pages. any blank pages are indicated. cambridge igcse\u2122 dc (ce/jg) 207497/3 \u00a9 ucles 2021 [turn overcambridge international mathematics 0607/61 paper 6 investigation and modelling (extended) may/june 2021 1 hour 40 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer both part a (questions 1 to 6) and part b (questions 7 to 10). \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 60. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *7326343854*", "2": "2 0607/61/m/j/21 \u00a9 ucles 2021 answer both parts a and b. a investigation (questions 1 to 6) rolling square (30 marks) you are advised to spend no more than 50 minutes on this part. this investigation looks at the path of a point on a square as it rolls along the x-axis. a square of side 1 cm rolls along the x-axis. one roll is a turn of 90\u00b0 clockwise about its bottom right corner. 0.511.5 0.5 1 1.5diagram 1 starting position 2 2.5 3y x 0 00.511.5 0.5 1 1.5diagram 2 after one roll 2 2.5 3y xposition 1 centre of rotationposition 1 position 2 centre of rotation diagram 1 shows the square in position 1. one side of the square is bold to help show the rotation. the centre of the square is (0.5, 0.5). diagram 2 shows the square rolled 90\u00b0 clockwise about (1, 0) to position 2. 1 to get to position 3 the square rolls 90\u00b0 clockwise about (2, 0). to get to position 4 the square then rolls 90\u00b0 clockwise about (3, 0). (a) on the diagram below, draw the square in position 4, position 5 and position 6. 012 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15y x [1]", "3": "3 0607/61/m/j/21 \u00a9 ucles 2021 [turn over (b) complete this table to show the x-coordinate of the centre of the square in each position. you may use the diagram on page 2 to help you. position ( n) 1 2 3 4 5 6 n x-coordinate 0.5 1.5 2.5 [2] (c) find the x-coordinate of the centre of the square in position 92. . [2] 2 the side of the square is now 2 cm. 123 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15y x 0 the square rolls along the x-axis in the same way as in question 1 . (a) complete the table of x-coordinates of the centre of the square in different positions. position ( n) 1 2 3 4 5 6 n x-coordinate 1 3 [3] (b) find the coordinates of the centre of the square in position 35. (.. , ..) [1]", "4": "4 0607/61/m/j/21 \u00a9 ucles 2021 3 the side of the square is now 3 cm. complete the table of x-coordinates of the centre of the square in different positions. you may use the diagram below to help you. position ( n) 1 2 3 4 5 6 n x-coordinate 1.5 123 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15y x 0 [3] 4 write your expressions from questions 1(b) , 2(a) and 3 in the table below. complete the table using any patterns you notice. you may use the grid on page 5 to help you. side of square (w cm)x-coordinate in position n 1 2 3 4 5 w", "5": "5 0607/61/m/j/21 \u00a9 ucles 2021 [turn over 123456 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15y x 0 [5] 5 a square of side w cm rolls from position 1 to position 120. at position 120, the x-coordinate of the centre of the square is 2151. find the value of w. . [3]", "6": "6 0607/61/m/j/21 \u00a9 ucles 2021 6 a square of side 2 cm rolls along the x-axis. a 123 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15y xposition 1 position 2 0 (a) the table shows the x-coordinate of the point a for each position. complete the table. position 1 2 3 4 5 6 7 8 9 10 11 12 13 x-coordinate 0 4 6 8 12 14 20 22 24 [1] (b) in the row of x-coordinates there are four sequences. for positions 4, 8, 12, ... the expression for the position is 4 a, where a is a positive integer. complete the table. a 1 2 3 4 5 a position (4 a) 4 8 12 16 20 4a x-coordinate 14 22 8a - .. position (4 a \u2013 1) 3 7 11 15 19 4a \u2013 1 x-coordinate 6... position (4 a \u2013 2) 2 6 10 14 18 4a \u2013 2 x-coordinate 4 12 20... position (4 a \u2013 3) 1 4a \u2013 3 x-coordinate 0... [5]", "7": "7 0607/61/m/j/21 \u00a9 ucles 2021 [turn over (c) the 2 cm square rolls to position 523. use part (b) to help you find the coordinates of point a. (.. , ..) [4]", "8": "8 0607/61/m/j/21 \u00a9 ucles 2021 b modelling (questions 7 to 10) wind turbines (30 marks) you are advised to spend no more than 50 minutes on this part. this task looks at the use of wind turbines to generate electricity. area, a, of circle, radius r. a = \u03c0r2 circumference, c, of circle, radius r. c = 2\u03c0 r 7 this is the front view and the side view of a wind turbine. blade length height of towerarea covered by blade side view wind turbines with longer blades generate more electrical power than wind turbines with shorter blades. power is measured in kilowatts (kw). a wind turbine has blades that are 27 m long and a tower of height 80 m. (a) find the greatest and least height above the ground for the tip of a blade as it turns. greatest height least height [2]", "9": "9 0607/61/m/j/21 \u00a9 ucles 2021 [turn over (b) an international soccer pitch is a rectangle measuring 70 m by 105 m. (i) find the area covered by the blades of this wind turbine. write your answer as a percentage of the area of the international soccer pitch. . [3] (ii) new wind turbines have blades that are 107 m long. find the area covered by these blades as a percentage of the area of the international soccer pitch. . [2]", "10": "10 0607/61/m/j/21 \u00a9 ucles 2021 8 the amount of power generated depends on wind speed as well as the area covered. this table shows the power (in kw) for blades of different lengths at a fixed wind speed. blade length ( b metres) 27 33 40 44 48 54 64 72 80 power ( p kw) 225 300 500 600 750 1000 1500 2000 2500 (a) plot the last three points on this graph. the first six points have been plotted for you. 0500 01000150020002500 10 20 30 40 50power (kw) blade length (m)60 70 80p b [1]", "11": "11 0607/61/m/j/21 \u00a9 ucles 2021 [turn over (b) a model for the power, p kw, is p = cb2, where b is the length of the blade in metres and c is a constant. use the information to find a value for c and write down the model. . [2] (c) another wind turbine generates 1200 kw. use your model to find the length of its blade. . [2]", "12": "12 0607/61/m/j/21 \u00a9 ucles 2021 9 (a) a blade rotates through 30\u00b0 every second. (i) find the time it takes to complete a full turn and the number of complete turns it makes in a minute. time = number of turns = [3] (ii) different parts of the blade travel through air at different speeds. 27 m show that the speed of the tip of this blade, with length 27 m, is 14.1 m/s, correct to 3 significant figures. [3]", "13": "13 0607/61/m/j/21 \u00a9 ucles 2021 [turn over (b) the blade with length 27 m now rotates through 40\u00b0 every second. find the new speed of the blade tip in m/s. . [2] (c) a blade turns through t degrees every second. the length of the blade is l metres. write a model for the speed, s m/s, of the blade tip in terms of \u03c0, t and l. give your answer in its simplest form. . [2] (d) the maximum speed for a blade tip is 72 m/s. find the maximum speed of rotation, in degrees per second, for a blade with length 107 m. . [3]", "14": "14 0607/61/m/j/21 \u00a9 ucles 2021 10 wind enters a turbine at a speed of u m/s. the wind leaves the turbine at a reduced speed of v m/s. u v x is the fraction that v is of u, so xuv=. a model for the efficiency, e, of the wind turbine is () ()exx 2112 =-+ . (a) what can you say about the wind speeds v and u if the efficiency, e, is zero? . [1]", "15": "15 0607/61/m/j/21 \u00a9 ucles 2021 (b) sketch the graph of the model for e for x01gg . 0e x11 [2] (c) find the value of x that gives maximum efficiency. . [1] (d) find the greatest value for e. give your answer as a percentage. . [1]", "16": "16 0607/61/m/j/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_s21_qp_62.pdf": { "1": "this document has 16 pages. any blank pages are indicated. cambridge igcse\u2122cambridge international mathematics 0607/62 paper 6 investigation and modelling (extended) may/june 2021 1 hour 40 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer both part a (questions 1 to 5) and part b (questions 6 to 9). \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 60. \u25cf the number of marks for each question or part question is shown in brackets [ ]. dc (lk/cb) 207548/3 \u00a9 ucles 2021 [turn over *0358135902*", "2": "2 0607/62/m/j/21 \u00a9 ucles 2021 answer both parts a and b. a investigation (questions 1 to 5) nearest neighbours (30 marks) you are advised to spend no more than 50 minutes on this part. this investigation is about the distances between points on square and triangular grids. all points have integer coordinates. xy 0 11 \u2013 1\u2013 1 2 \u2013 2 \u2013 3 \u2013 4 3 42 \u2013 23 \u2013 34 \u2013 4 the point (0, 0) has 4 points closest to it. each point has a circle around it. the points have coordinates ( -1, 0), (0, 1), (1, 0) and (0, -1). they are called the 1st nearest neighbours to (0, 0). 1 the points which are next closest to (0, 0) are its 2nd nearest neighbours . one of these points has coordinates (1, 1). find the coordinates of the other 2nd nearest neighbours. . [2] 2 the distance from (0, 0) to its 1st nearest neighbour is 1. show that the distance from (0, 0) to (1, 1), a 2nd nearest neighbour, is 2. [2]", "3": "3 0607/62/m/j/21 \u00a9 ucles 2021 [turn over 3 the table shows information about the nth nearest neighbours to (0, 0) for values of n from 1 to 11. d is the distance from (0, 0) to a nearest neighbour. n 1 2 3 4 5 6 7 8 9 10 11 d 21 2 4 5 8 9 10 13 16 17 18 d 1 2 8 3 10 13 4 17 18 number of nth nearest neighbours4 4 4 8 8 4 8 4 (a) complete the table. [2] (b) is d 2 directly proportional to n? show how you decide. [2] (c) the 12th nearest neighbours to (0, 0) are at a distance h, where h 2 = 20. find the coordinates of all these nearest neighbours. . . [3]", "4": "4 0607/62/m/j/21 \u00a9 ucles 2021 4 here is a rectangular pattern of points on a square grid. xy 0 11 \u2013 1 \u2013 122 \u2013 2 \u2013 233 \u2013 3 \u2013 344 \u2013 4 \u2013 455 \u2013 5 \u2013 56 \u2013 6 7 \u2013 7 8 \u2013 8 nearest neighbour distances can be found for these points. the two 1st nearest neighbours to (0, 0) have circles around them. the four 2nd nearest neighbours to (0, 0) have squares around them. the four 3rd nearest neighbours to (0, 0) have triangles around them. complete this table. nearest neighbour 1st 2nd 3rd 4th 5th 6th 7th d 21 4 5 9 13 16 number of nearest neighbours 2 4 4 2 4 4 [3]", "5": "5 0607/62/m/j/21 \u00a9 ucles 2021 [turn over 5 this is a grid of points made from equilateral triangles of side 1. these points have coordinates as shown on the grid below. xy 0 \u2013 1 \u2013 11234 1 2 3 4 \u2013 2 \u2013 2\u2013 3 \u2013 3 \u2013 4(\u2013 2, 3) (2, 3) the circles show the 1st and 2nd nearest neighbours to (0, 0). the six 1st nearest neighbours to (0, 0) have coordinates (0, 1), (1, 0), (1, -1), (0, -1), (-1, 0) and (-1, 1). (a) points are not always integer distances from (0, 0). (i) complete this table to show when a point is an integer distance from (0, 0). point (1, 0) (-1, 1) (-1, 2) (2, -2) (2, 2) (0, -3) integer distance 3 not integer distance [2] (ii) the point ( a, 4) is an integer distance from (0, 0). write down two possible values for a. . [2]", "6": "6 0607/62/m/j/21 \u00a9 ucles 2021 (b) to calculate a distance on a triangular grid, the geometry of triangles is needed. a b cacbsins in sin aa bb cc== cos ab cb ca222 2=+ - this grid of points is made from equilateral triangles of side length 1. a triangle is drawn on the grid. the triangle\u2019s vertices are at (0, 0), (1, 0) and (1, 2). it has sides of length 1, 2 and d, the distance of (1, 2) from (0, 0). xy 4 33 2d2 11 \u2013 1 \u2013 1\u2013 2 \u2013 2\u2013 3 \u2013 3\u2013 4 0 (i) explain why the largest angle in the triangle is 120\u00b0. . [1]", "7": "7 0607/62/m/j/21 \u00a9 ucles 2021 [turn over (ii) calculate the distance of (1, 2) from (0, 0). . [2] (c) a point on a triangular grid has coordinates ( a, b), where a and b are positive integers. show that its distance, d, from (0, 0) is given by d aba b22=+ + . [2] (d) use the formula in part (c) to calculate the distance of a 6th nearest neighbour from (0, 0). give your answer as a square root. xy o . [3]", "8": "8 0607/62/m/j/21 \u00a9 ucles 2021 (e) use the formula d aba b22=+ + to show that it is not possible for a nearest neighbour to be a distance of 14 from (0, 0) on a triangular grid. [4]", "9": "9 0607/62/m/j/21 \u00a9 ucles 2021 [turn over the modelling task starts on the next page.", "10": "10 0607/62/m/j/21 \u00a9 ucles 2021 b modelling (questions 6 to 9) high river flow (30 marks) you are advised to spend no more than 50 minutes on this part. this task looks at estimating the probability of high river flows. planners need to estimate the probability of extreme events such as high river flow. to do this they use the return period, r years. this is an estimate of the number of years before they expect another high river flow. a model for r is rhn1=+ where n is the number of years for which there are river flow results, h is the number of times that high river flow occurs during the n years. the probability of high river flow occurring in any year is r1. example on 3 occasions during a period of 65 years, a river flow was greater than 4000 cubic metres per second (m3/s). so, the return period for a water flow greater than 4000 m3/s is r365 1 366 22years.=+= = this is not very likely in a year, but very likely in the lifetime of a bridge designed to last for 100 years. the probability of a river flow greater than 4000 m3/s in any year is 221. 6 these are the maximum flows, in m3/s, each year for a small river. 30 119 13 30 9 64 19 83 71 64 37 61 55 33 131 91 78 59 32 29 121 7 56 65 (a) calculate the return period, r, for a flow greater than 100 m3/s. . [2] (b) use your answer to part (a) to find the probability of a flow greater than 100 m3/s the next year. . [1]", "11": "11 0607/62/m/j/21 \u00a9 ucles 2021 [turn over 7 (a) the probability of an event occurring in one year is p. (i) write an expression, in terms of p, for the probability of the event not occurring in one year. . [1] (ii) find an expression, in terms of p, for the probability of the event not occurring for 10 consecutive years. . [1] (iii) explain why the probability of the event occurring at least once in 10 consecutive years is ()p 1110-- . . [1] (b) a model for the probability, y, of a flow greater than 130 m3/s occurring in the river in question 6 at least once in x years is (. ) y 11 004x=- - . (i) sketch the graph of (. ) y 11 004x=- - for x05 2 gg . xy 0 0 25 [3] (ii) find the number of years that pass before the probability of a flow greater than 130 m3/s first becomes greater than 50%. . [2]", "12": "12 0607/62/m/j/21 \u00a9 ucles 2021 8 the table shows the probabilities of various river flows in a year at waverly on the missouri river in the usa. flow in thousands of m3/s (f) probability of flow f2 (p) 2 0.99 4 0.85 6 0.56 8 0.26 10 0.11 12 0.04 14 0.02 16 0.02 18 0.02 20 0.02 22 0.01 (a) a possible model for the above data is pf k1=- where k is a constant. use figures from the table to decide whether or not this is a reasonable model. . [2] (b) another model is pcf= where c is a constant. use figures from the table to decide whether or not this is a reasonable model. . [2]", "13": "13 0607/62/m/j/21 \u00a9 ucles 2021 [turn over (c) another model for the data is .. . pf f 00048 1619 13281 02=+ - for f22 2 gg . the dashed line on the diagram shows the graph of this model. (i) plot the values from the table on the previous page onto the grid. the first 7 points have been done for you. fp 05 10 15 20 25 00.10.20.30.40.50.60.70.80.91 \u2013 0.1 [1] (ii) give the ranges of values of f for which .. . pf f 00048 1619 13281 02=+ - is a good model and not a good model. a good model .. not a good model [2]", "14": "14 0607/62/m/j/21 \u00a9 ucles 2021 9 engineers use this formula to model the probability of high river flows. bfa - p3=feo p where p is the probability of an event greater than f and a and b are both constants. (a) show that p31= when bf=. [2] (b) give a reason why 8 is the best integer estimate for b when p31=. use part (a) and values from the table for the missouri river on page 12 in your answer. . [1] (c) (i) on the axes below, sketch three graphs of bfa - p3=feo p for f02 5 gg . use b8= and \u2022 a = 0.5, \u2022 a = 1, \u2022 a = 2.5 . the graph with b8= and a10= is sketched for you. fp 025 [4]", "15": "15 0607/62/m/j/21 \u00a9 ucles 2021 (ii) find the coordinates of the points of intersection of the curves. . [2] (iii) describe the effect on the graph when a increases and the flow is between 6000 m3/s and 8000 m3/s. . [1] (iv) which value of a gives the best model for the missouri river data on page 12? give a reason for your answer. a = because ... . [2]", "16": "16 0607/62/m/j/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_s21_qp_63.pdf": { "1": "this document has 12 pages. cambridge igcse\u2122cambridge international mathematics 0607/63 paper 6 investigation and modelling (extended) may/june 2021 1 hour 40 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer both part a (questions 1 to 3) and part b (questions 4 to 7). \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 60. \u25cf the number of marks for each question or part question is shown in brackets [ ]. dc (lk/cb) 207549/3 \u00a9 ucles 2021 [turn over *3872696403*", "2": "2 0607/63/m/j/21 \u00a9 ucles 2021 answer both parts a and b. a investigation (questions 1 to 3) paths around shapes (30 marks) you are advised to spend no more than 50 minutes on this part. this investigation looks at paths around different shapes. in this investigation \u2022 all lengths are in metres \u2022 all tiles are squares of side 1 metre. the path around a square of side 1 needs 8 square tiles. this is the path around a square of side 2. 1 (a) on the grid, draw the path around the square of side 3. [1] ", "3": "3 0607/63/m/j/21 \u00a9 ucles 2021 [turn over (b) this table shows the number of tiles in the paths around squares of different sizes. complete the table. side of square number of tiles in path 1 8 2 3 4 [2] (c) explain why the path around a square cannot have exactly 50 tiles. . [1] (d) find an expression, in terms of n, for the number of tiles in the path around a square of side n. . [2] (e) work out the number of tiles in the path around a square of side 88. . [2] (f) the path around a square has 400 tiles. work out the area of the square. . [3]", "4": "4 0607/63/m/j/21 \u00a9 ucles 2021 2 this is the path around a rectangle of width 1 and length 2. (a) (i) complete the table to show the number of tiles in the paths around rectangles of width 1 with different lengths. length of rectangle ( l) number of tiles in path 2 10 3 4 5 [1] (ii) complete the expression for the number of tiles in the path around a rectangle of width 1 and length l. 2l + [1]", "5": "5 0607/63/m/j/21 \u00a9 ucles 2021 [turn over (b) write your expression from question 2(a)(ii) in the table. complete the table to show expressions for the number of tiles in the paths around rectangles of different widths and lengths. width of rectangle ( w)number of tiles in path around a rectangle of length l 1 2 3 4 [3] (c) find an expression, in terms of l and w, for the number of tiles in the path around a rectangle of length l and width w. . [2] (d) the path around a rectangle has 20 tiles. find all the possible dimensions of the rectangle. . [3]", "6": "6 0607/63/m/j/21 \u00a9 ucles 2021 3 area, a, of circle, radius r. a = rr2 this question looks at the area of a path around a circle. (a) the shaded circle has radius 2. there is a path of width 1 around the shaded circle. show that the area of the path is 5 r. [2] (b) show that the area of a path of width 1 around a circle of radius 3 is 7 r. [2]", "7": "7 0607/63/m/j/21 \u00a9 ucles 2021 [turn over (c) complete the table to show the areas of paths of width 1 around circles of different sizes. radius of shaded circle area of path 1 2 5r 3 7r 4 [2] (d) find an expression for the area of a path of width w around a circle of radius r. give your answer in its simplest form in terms of r, r and w. . [3]", "8": "8 0607/63/m/j/21 \u00a9 ucles 2021 b modelling (questions 4 to 7) playground swing (30 marks) you are advised to spend no more than 50 minutes on this part. this task looks at the height of the seat of a playground swing as it moves. 4 (a) this is the graph of \u00b0 cos yx= for x0 360 gg . its period is 360. 901 0 \u2013 1180 270 360y x (i) on the same grid, sketch the graph of () \u00b0 cos yx 2 = for x0 360 gg . [2] (ii) write down the period of the graph of () \u00b0 cos yx 2 = . . [1] (b) show that the period of the graph of () \u00b0 cos yx 15 = is 24. [1] (c) write down an expression, in terms of k, for the period of the graph of () \u00b0 cos yx k = . . [1]", "9": "9 0607/63/m/j/21 \u00a9 ucles 2021 [turn over 5 the graph models the height of the seat of a swing from its highest point, down to its lowest point, and back to its highest point again. t is the time in seconds. h is the height in metres from a fixed point. h t 0.5 1 1.5 200.3 \u2013 0.3 the equation of the model is () \u00b0 cos ha bt = . (a) write down the period of the graph and find the value of b. period = b = [2] (b) find the value of a and use this to write down the equation of the model. ... [1]", "10": "10 0607/63/m/j/21 \u00a9 ucles 2021 (c) h is the height in metres of the seat above the ground. this graph models h. h t 1 2 00.20.40.60.81 use your answer to part (b) to write down the model for h. ... [2] (d) find the two times when the swing is 0.8 m above the ground for t02gg . . and . [3]", "11": "11 0607/63/m/j/21 \u00a9 ucles 2021 [turn over 6 another model for the height of the seat above the ground is .( .) () \u00b0. cos dt 04 07 200 06t=+ where d is the height in metres and t is the time in seconds. (a) find the height of the seat above the ground when t = 0. . [1] (b) sketch the graph of this model for t05gg . d t 0 5 [3] (c) find the total time that the seat is at least 75 cm above the ground. . [3] (d) what does the model suggest about the height of the seat as t gets larger? . . [2] question 7 is printed on the next page.", "12": "12 0607/63/m/j/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.7 a different model for the height of the seat above the ground is () da tt bt 1124=- + + where d is the height in metres and t is the time in seconds. (a) given that d = 0.4 when t = 1, find the value of b. . [2] (b) given that d = 1 when t = 2, find the value of a. . [2] (c) write down the model for d and use it to find the height of the seat when t = 0.5 . . [2] (d) is this a reasonable model? show how you decide. . . [2]" }, "0607_w21_qp_11.pdf": { "1": "this document has 8 pages. dc (rw/cb) 207176/3 \u00a9 ucles 2021 [turn over *5387189052* cambridge international mathematics 0607/11 paper 1 (core) october/november 2021 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ].cambridge igcse\u2122", "2": "2 0607/11/o/n/21 \u00a9 ucles 2021 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/11/o/n/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 write the missing numbers in the boxes. 1 20 5=10= % = [2] 2 0123456 xp 345 2 6 1y write down the coordinates of p. ( .. , .. ) [1] 3 the diagram shows a circle with centre o. draw a chord in this circle. o [1] 4 complete the statement. 45 ml is cm3. [1]", "4": "4 0607/11/o/n/21 \u00a9 ucles 2021 5 ab 4 cm12 cm not to scale 2 cm6 cm complete the statement. rectangle b is an enlargement of rectangle a with scale factor [1] 6 in a sale, the price of a dress is reduced from $20 to $15. work out the percentage reduction. .. % [2] 7 north b c measure the bearing of c from b. . [1]", "5": "5 0607/11/o/n/21 \u00a9 ucles 2021 [turn over 8 a cuboid has a volume of 140 cm3. the width of the cuboid is 7 cm and the height is 2 cm. find the length of this cuboid. cm [2] 9 this table shows the ages of 20 cars. age (years) frequency 1 2 2 7 3 4 4 3 5 4 (a) work out the range. years [1] (b) work out the mean age of the cars. years [3] 10 x631g-- write down all the integer values of x. . [1] 11 a circle has radius 8.5 cm. find the circumference of the circle. leave your answer in terms of r. cm [2]", "6": "6 0607/11/o/n/21 \u00a9 ucles 2021 12 u = {x | x is an integer and x11 0 gg } a = {x | x is a square number} (a) list the elements of set a. . [1] (b) write down ()nal. . [1] 13 the scatter diagram shows the number of ice creams sold each day and the temperature on that day. number of ice creams sold temperature (\u00b0c)1004080120 15 20 25 (a) what type of correlation is shown in the scatter diagram? . [1] (b) describe what the scatter diagram shows about the number of ice creams sold each day and the temperature on that day. . . [1] 14 a football club had the following results from their last 10 games. outcome of match win draw lose frequency 2 5 3 use this data to estimate the probability that they will not lose their next match. . [2]", "7": "7 0607/11/o/n/21 \u00a9 ucles 2021 [turn over 15 expand. ()kk 62- . [2] 16 a car travels 20 km at an average speed of 30 km/h. it then travels 30 km at an average speed of 60 km/h. calculate the total number of minutes this 50 km journey takes. minutes [3] 17 not to scale 30\u00b0a\u00b0 a\u00b0 a\u00b0 find the value of a. a= . [3] 18 work out () () 31 05 1046## # . write your answer in standard form. . [2] questions 19, 20 and 21 are printed on the next page.", "8": "8 0607/11/o/n/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.19 0123456 x789 ef 345 2 6789101112 1y describe fully the single transformation that maps shape e onto shape f. . . [3] 20 write down the equation of the line with gradient 3 that passes through (0, 1-). . [2] 21 find the value of x when 55 5x 34#= . x= . [1]" }, "0607_w21_qp_12.pdf": { "1": "this document has 8 pages. cambridge igcse\u2122 dc (lk/cb) 207177/2 \u00a9 ucles 2021 [turn overcambridge international mathematics 0607/12 paper 1 (core) october/november 2021 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *4723519693*", "2": "2 0607/12/o/n/21 \u00a9 ucles 2021 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/12/o/n/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 write 3468 correct to the nearest ten. . [1] 2 x complete the statement. angle x is an ... angle. [1] 3 write 10059 as a percentage. . % [1] 4 work out. ()29 23 5 ##-- . [2] 5 not to scale p (\u2013 2, 1) q (3, 1) o xy work out the distance pq. . [1] 6 find the cube root of 64. . [1]", "4": "4 0607/12/o/n/21 \u00a9 ucles 2021 7 mario invests $400 for 2 years at a rate of 5% per year simple interest. work out the interest that mario receives. $ [2] 8 find the total surface area of a cube of side 3 cm. .. cm2 [2] 9 find the distance a train travels in 2 hours when its average speed is 120 km/h. ... km [1] 10 an apartment costs $500 per month to rent. calculate the cost to rent the apartment for 1 year 3 months. $ [2] 11 north landsea q pnorth measure the bearing of town q from town p. . [1]", "5": "5 0607/12/o/n/21 \u00a9 ucles 2021 [turn over 12 xy point x is translated to point y. write down the vector for this translation. fp [1] 13 simplify. vv3' . [1] 14 write down a number, greater than 1, that is both a square number and a triangle number. . [1] 15 microchips are checked for defects. out of 10 000 microchips made on a particular machine, 500 were found to be defective. find the probability that a microchip from this machine is defective. give your answer as a decimal. . [2] 16 ()fxx 5= work out the value of x when ()fx 10= . x = . [1]", "6": "6 0607/12/o/n/21 \u00a9 ucles 2021 17 solve the equation. ()x23 20 += x = [2] 18 ..540972035 7 r from the list of numbers write down (a) the integer, . [1] (b) the irrational number. . [1] 19 the table shows the number of televisions in each of 20 homes. number of televisions 0 1 2 3 4 frequency 2 8 7 2 1 (a) write down the mode. . [1] (b) find the mean. . [3] 20 find the lowest common multiple (lcm) of 24 and 60. . [2]", "7": "7 0607/12/o/n/21 \u00a9 ucles 2021 [turn over 21 simplify fully. y6 2 2'y . [2] 22 a bag contains 13 red beads and 7 blue beads. two beads are taken out of the bag at random. complete the tree diagram. bead 1 bead 2 red blue ..red blue .. ..red blue2013 [2] questions 23 and 24 are printed on the next page.", "8": "8 0607/12/o/n/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.23 a class has 30 students. 5 students play both football and cricket. 15 students play football and 13 students play cricket. use this information to complete the venn diagram. football cricket 10 5 .. ..u [2] 24 not to scale170\u00b0 the diagram shows one interior angle of a regular polygon. find the number of sides of the polygon. . [3]" }, "0607_w21_qp_21.pdf": { "1": "this document has 12 pages. any blank pages are indicated. cambridge igcse\u2122cambridge international mathematics 0607/21 paper 2 (extended) october/november 2021 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *7847885517* dc (cj/sg) 214441/3 \u00a9 ucles 2021 [turn over", "2": "2 0607/21/o/n/21 \u00a9 ucles 2021 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/21/o/n/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 (a) write 4 347 849 correct to the nearest ten thousand. . [1] (b) write 0.004 024 3 correct to 2 significant figures. . [1] 2 90 91 92 93 94 95 96 97 98 99 from this list, write down (a) a prime number, . [1] (b) a common multiple of 4 and 6. . [1] 3 draw all the lines of symmetry on each of these shapes. [2]", "4": "4 0607/21/o/n/21 \u00a9 ucles 2021 4 the table shows the percentage of students in each of three classes who study physics, chemistry and biology. physics (p) chemistry (c) biology (b) class h 34 28 38 class j 24 18 58 class k 46 32 22 complete the compound bar chart to show this information. class h class j class k0102030405060708090100 percentage pcb [3]", "5": "5 0607/21/o/n/21 \u00a9 ucles 2021 [turn over 5 solve. () () xx24 13 21 -= + x= [3] 6 (a) write 0.000 058 6 in standard form. . [1] (b) () () k 21 08 10 10ab n' ## #= where k11 01g . (i) find the value of k. k= [1] (ii) write an expression for n in terms of a and b. n= . . [1]", "6": "6 0607/21/o/n/21 \u00a9 ucles 2021 7 mia carries out a survey in a school to find out what students will do when they leave school. these are her results. university job training travelling total frequency 112 43 27 18 200 (a) find the relative frequency of university. . [1] (b) there are 1600 students in this school. (i) explain why the result in part (a) is a reasonable estimate of the probability that a student from this school will go to university. . [1] (ii) calculate an estimate for the number of students in this school who will go travelling. . [2] 8 solve the simultaneous equations. x5+=xy32 12 -= y7 x= y= [3]", "7": "7 0607/21/o/n/21 \u00a9 ucles 2021 [turn over 9 y varies inversely as the square of ()x2+. when ,. xy 40 5 == . find y in terms of x. y= [2] 10 30\u00b0not to scale6 cm the diagram shows a sector of a circle with radius 6 cm and sector angle 30\u00b0. the area of the shaded segment is r() cm ab2- . find the value of a and the value of b. a= b= [3]", "8": "8 0607/21/o/n/21 \u00a9 ucles 2021 11 in this question all lengths are in centimetres. xnot to scale53+32 find the value of x2. give your answer in the form ab 3+ where a and b are integers. x2= [4]", "9": "9 0607/21/o/n/21 \u00a9 ucles 2021 [turn over 12 not to scaley x o gca db fe the diagram shows the lines , yx yx2113 =+ = and xy34 12 += . these lines divide the space into 7 regions, a, b, c, d, e, f, and g. write down the letter of the region which is defined by (a) , yx yx2113 gg+ and xy34 12g+ , region [1] (b) , yx yx2113 hh+ and xy34 12g+ . region [1] ", "10": "10 0607/21/o/n/21 \u00a9 ucles 2021 13 not to scaley x 0\u2013 2 3 \u2013 12 the equation of the curve is ya xb x122=+ -. find the value of a and the value of b. a= b= [3]", "11": "11 0607/21/o/n/21 \u00a9 ucles 2021 14 solve. (a) logx43= x= [1] (b) logl og log x 23 25 0 -= x= [3]", "12": "12 0607/21/o/n/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_w21_qp_22.pdf": { "1": "this document has 12 pages. any blank pages are indicated. cambridge igcse\u2122 *0529762483* dc (ce/fc) 212406/1 \u00a9 ucles 2021 [turn overcambridge international mathematics 0607/22 paper 2 (extended) october/november 2021 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/22/o/n/21 \u00a9 ucles 2021 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/22/o/n/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 work out. 37 25#++ . [1] 2 complete the statement. a parallelogram has rotational symmetry of order . and . lines of symmetry. [2] 3 (a) a number is greater than 1. the number is also both a square number and a cube number. write down a possible value of this number. . [1] (b) write down a prime number between 90 and 100. . [1] 4 \u2013 4\u2013 3 4x\u2013 2 \u2013 1 0 1 2 3 write down the inequality shown on the number line. . [1]", "4": "4 0607/22/o/n/21 \u00a9 ucles 2021 5 work out. 43 98' . [2] 6 x 21 write down all the integer values of x. . [1] 7 the bearing of p from q is 110\u00b0. find the bearing of q from p. . [2]", "5": "5 0607/22/o/n/21 \u00a9 ucles 2021 [turn over 8 on the diagram, sketch the graph of yx1=. xy o [2] 9 o40\u00b0 r cmnot to scale the diagram shows an arc of a circle, centre o, radius r cm. the length of the arc is krr\u200acm. find the value of k. give your answer as a fraction in its simplest form. k = [2]", "6": "6 0607/22/o/n/21 \u00a9 ucles 2021 10 (a) shade the region ()pq, l. p qu [1] (b) the venn diagram shows the number of elements in each region. 78 9 10t ru find n ()rt+ l. . [1] (c) use set notation to describe the shaded region. a bu . [1]", "7": "7 0607/22/o/n/21 \u00a9 ucles 2021 [turn over 11 yw 22 = rearrange the formula to make w the subject. w = [1] 12 work out the value of 3252. . [1]", "8": "8 0607/22/o/n/21 \u00a9 ucles 2021 13 77\u00b040\u00b0a t bnot to scalex\u00b0 ab is a tangent to the circle at t. find the value of x. x = [2] 14 simplify. 125 80+ . [2]", "9": "9 0607/22/o/n/21 \u00a9 ucles 2021 [turn over 15 solve. xx 38 21 -=+ x = [3] 16 factorise. xx yy 36 24+- - . [2] 17 32 7xx 2=+ find the value of x. x = [2]", "10": "10 0607/22/o/n/21 \u00a9 ucles 2021 18 simplify. www 25 39 22 +-- . [4] 19 logl og logl ogt 48 18 22 4 +- = find the value of t. t = [3]", "11": "11 0607/22/o/n/21 \u00a9 ucles 2021 20 tanxk= \u00b0\u00b0x 09 0 11 find, in terms of k, (a) (\u00b0 ) tan x 180-, . [1] (b) (\u00b0 ) tan x 90-. . [1]", "12": "12 0607/22/o/n/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_w21_qp_23.pdf": { "1": "this document has 8 pages. any blank pages are indicated. cambridge igcse\u2122 dc (ce) 214442/1 \u00a9 ucles 2021 [turn over *0296149060* cambridge international mathematics 0607/23 paper 2 (extended) october/november 2021 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/23/o/n/21 \u00a9 ucles 2021 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/23/o/n/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 work out. (a) () () () 23 4 -+ -- - . [1] (b) () () () 234##--- . [1] 2 91 93 95 97 99 from this list write down a prime number. . [1] 3 $126 is divided into 3 shares in the ratio 1 : 2 : 4 . find the value of the largest share. $ . [2] 4 solve. (a) x 52 0 -= x = [1] (b) xx 12 25 3 -+ =- x = [2]", "4": "4 0607/23/o/n/21 \u00a9 ucles 2021 5 there are 640 students in a school. the table shows the favourite colour of each of the students. favourite colour blue green red yellow number of students 120 2x 280 x (a) find the value of x. x = [2] (b) find the relative frequency of students whose favourite colour is red. give your answer as a fraction in its lowest terms. . [2] 6 (a) simplify. 75 27- . [2] (b) rationalise the denominator and simplify your answer. 5510 - . [3]", "5": "5 0607/23/o/n/21 \u00a9 ucles 2021 [turn over 7 a is the point (3, 7) and b is the point (, ) 91-. calculate the length ab. ab = [3] 8 (a) a regular polygon has 12 sides. work out the sum of the interior angles of the polygon. . [2] (b) the interior angle of a regular polygon is x\u00b0. find an expression, in terms of x, for the number of sides of this polygon. . [2]", "6": "6 0607/23/o/n/21 \u00a9 ucles 2021 9 expand the brackets and simplify. () () xx xx 52 33 32 -- - . [2] 10 solve the simultaneous equations. you must show all your working. xy xy43 10 34 5+= - -= x = y = [4] 11 ()xx251f=- , . x 25! (a) find ()2f. . [1] (b) solve ()x 5 f=. . [2]", "7": "7 0607/23/o/n/21 \u00a9 ucles 2021 12 xx xx bx cax 2323 2323 2 +---+=- find the values of a, b and c. a = b = c = . [4] 13 a bag contains 12 discs. there are 2 red discs, 4 blue discs, 5 green discs and 1 yellow disc. a disc is chosen at random and not replaced. a second disc is then chosen at random. find the probability that both discs are the same colour. . [3]", "8": "8 0607/23/o/n/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_w21_qp_31.pdf": { "1": "this document has 20 pages. any blank pages are indicated. cambridge igcse\u2122 dc (ce/cgw) 199833/2 \u00a9 ucles 2021 [turn overcambridge international mathematics 0607/31 paper 3 (core) october/november 2021 1 hour 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 96. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *2440459145*", "2": "2 0607/31/o/n/21 \u00a9 ucles 2021 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/31/o/n/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 (a) write sixty thousand and three in figures. .. [1] (b) work out 729. .. [1] (c) work out. ... 3214 73689 + .. [1] (d) write down all the factors of 10. ... [2] (e) write 965.384 correct to (i) 1 decimal place, .. [1] (ii) 3 significant figures, .. [1] (iii) the nearest ten. .. [1]", "4": "4 0607/31/o/n/21 \u00a9 ucles 2021 2 (a) these are the first four terms of a sequence. 23 27 31 35 (i) write down the next two terms of this sequence. , [2] (ii) write down the rule for continuing this sequence. . [1] (b) here is a list of numbers. -2 3 0.24 9 31- write down one of the numbers from the list to complete each statement. you must use a different number in each statement. .. is a natural number ( n). .. is an integer ( z). .. is a rational number ( q). [3]", "5": "5 0607/31/o/n/21 \u00a9 ucles 2021 [turn over 3 (a) kate works part-time in a supermarket. she is paid $14 per hour. one month, kate works 64 hours. work out how much she is paid that month. $ .. [1] (b) kate invests $560 at a rate of 1.6% per year simple interest. calculate the total interest she receives at the end of 8 years. $ .. [2] (c) ruth invests $800 at a rate of 2.1% per year compound interest. work out the value of her investment at the end of 4 years. $ .. [3]", "6": "6 0607/31/o/n/21 \u00a9 ucles 2021 4 (a) decorations $5 for a packet of 3 decorations $9 for a packet of 6 decorations (i) paul buys 5 packets of 3 decorations and 2 packets of 6 decorations. (a) work out the total number of decorations he buys. .. [1] (b) work out the total amount he pays for these decorations. $ .. [2] (ii) vasek buys 15 decorations. work out the least amount that he pays for 15 decorations. $ .. [2]", "7": "7 0607/31/o/n/21 \u00a9 ucles 2021 [turn over (b) vasek buys 12 praline balls. (i) one praline ball costs $0.83 . work out the cost of the 12 praline balls. $ .. [1] (ii) vasek pays with $10. work out how much change he receives. $ .. [1] (iii) vasek shares the 12 praline balls with his friend, paul, in the ratio vasek : paul = 2 : 1. work out how many praline balls they each receive. vasek . paul . [2]", "8": "8 0607/31/o/n/21 \u00a9 ucles 2021 5 (a) a taxi company charges a fixed amount of $3 and then $1.50 for each kilometre travelled. (i) write a formula for the cost, $ c, for travelling n kilometres. .. [2] (ii) menno travels 15 kilometres in a taxi from this company. work out the cost of menno\u2019s taxi journey. $ .. [2] (iii) weston pays $37.50 for a taxi journey with this company. work out how many kilometres the taxi travels. km [2]", "9": "9 0607/31/o/n/21 \u00a9 ucles 2021 [turn over (b) the table shows the number of customers for some taxi companies on monday. there is a total of 875 customers on monday. taxi company a b c d e number of customers 200 150 225 125 175 (i) complete the bar chart to show this information. 50 0100150 number of customers taxi company200250 a b c e d [2] (ii) write down the company that had the most customers. .. [1] (iii) one of the 875 customers is chosen at random. find the probability that this customer used company e. .. [1]", "10": "10 0607/31/o/n/21 \u00a9 ucles 2021 6 33\u00b0 46\u00b0x\u00b0 y\u00b0 m\u00b0t\u00b0 z\u00b0not to scalea b d e c abcd is a trapezium with angle adb = 33\u00b0 and angle bcd = 46\u00b0. ab is parallel to dc and ad = ab. dce is a straight line. (a) write down the mathematical name for triangle abd . .. [1] (b) find the value of each of x, y, z, m and t. x = . y = . z = . m = . t = . [5]", "11": "11 0607/31/o/n/21 \u00a9 ucles 2021 [turn over 7 a bag contains 30 pieces of fruit. there are 16 grapes and 14 cherries. fumi takes one piece of fruit at random from the bag and eats it. (a) find the probability that she takes a grape. .. [1] (b) fumi takes a second piece of fruit at random from the bag. (i) complete the tree diagram. second piece of fruit first piece of fruit grape cherry grape cherry grape cherry [3] (ii) work out the probability that fumi takes 2 cherries. .. [2]", "12": "12 0607/31/o/n/21 \u00a9 ucles 2021 8 (a) solve. (i) x 73= x = . [1] (ii) x37 8 += - x = . [2] (b) mqp23=+ find the value of m when p = 2.13 and q = 1.46 . m = . [2] (c) simplify. ab ab 34 2 -+ + .. [2] (d) simplify fully. abab 23 .. [2] (e) write as a single fraction in its simplest form. pp 54 83 # .. [2]", "13": "13 0607/31/o/n/21 \u00a9 ucles 2021 [turn over 9 15 cm2 cmnot to scale 3 cm a solid metal disc is in the shape of a cylinder with a smaller cylinder removed from the centre. the radius of the larger cylinder is 15 cm and the radius of the smaller cylinder is 3 cm. the height of the disc is 2 cm. (a) find the shaded area. ... cm2 [3] (b) find the volume of the disc. ... cm3 [1] (c) a solid cube has the same volume as the disc. find the length of one side of this cube. .. cm [2]", "14": "14 0607/31/o/n/21 \u00a9 ucles 2021 10 not to scale x\u00b0 o d cba e m the diagram shows a regular pentagon, abcde , inscribed in a circle, centre o. (a) show that x = 72\u00b0. [1] (b) show that angle oab = 54\u00b0. [1]", "15": "15 0607/31/o/n/21 \u00a9 ucles 2021 [turn over (c) the circle has radius 6 cm. m is the mid-point of bc. (i) use trigonometry to calculate om. . cm [2] (ii) calculate bc. .. cm [3] (iii) calculate the area of the pentagon. ... cm2 [2] ", "16": "16 0607/31/o/n/21 \u00a9 ucles 2021 11 a farmer finds the mass, in kilograms, of each of 100 chickens. the results are shown in the table. mass ( w kg) frequency 1 1 w g 1.5 8 1.5 1 w g 2 15 2 1 w g 2.5 32 2.5 1 w g 3 23 3 1 w g 3.5 16 3.5 1 w g 4 6 (a) write down the modal class. ... 1 w g ... [1] (b) complete the cumulative frequency table for this data. mass ( w kg) cumulative frequency w g 1.5 w g 2 w g 2.5 w g 3 w g 3.5 w g 4 100 [2]", "17": "17 0607/31/o/n/21 \u00a9 ucles 2021 [turn over (c) on the grid, draw a cumulative frequency curve. 00102030405060708090100 1 2 3w 4 mass (kg)cumulative frequency [3] (d) use your curve to find an estimate for (i) the median, . kg [1] (ii) the interquartile range, . kg [2] (iii) the number of chickens with a mass greater than 3.25 kg. .. [2]", "18": "18 0607/31/o/n/21 \u00a9 ucles 2021 12 0y x\u2013 2 2 \u2013 88 (a) on the diagram, sketch the graph of yx3= for x22gg- . [2] (b) write down the coordinates of the point where the graph crosses the y-axis. ( ... , ...) [1] (c) on the same diagram, sketch the graph of yx2= for x22gg- . [2] (d) find the x-coordinate of the points of intersection of yx3= and yx2= . , , [3]", "19": "19 0607/31/o/n/21 \u00a9 ucles 2021 blank page", "20": "20 0607/31/o/n/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_w21_qp_32.pdf": { "1": "this document has 16 pages. cambridge igcse\u2122 dc (ce/cgw) 199832/1 \u00a9 ucles 2021 [turn overcambridge international mathematics 0607/32 paper 3 (core) october/november 2021 1 hour 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 96. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *6240978390*", "2": "2 0607/32/o/n/21 \u00a9 ucles 2021 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/32/o/n/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 (a) these are the first three patterns of a sequence made using lines. pattern 1 pattern 2 pattern 4 pattern 5pattern 3 (i) in the space above, draw pattern 4 and pattern 5. [2] (ii) complete the table. pattern number 1 2 3 4 5 6 number of lines 3 5 [2] (iii) write down the rule for continuing the sequence of lines. ... [1] (b) these are the first four terms of a different sequence. 23 17 11 5 write down the next two terms of this sequence. , [2] (c) the nth term of another sequence is nn 52+. find the first three terms of this sequence. , , [2]", "4": "4 0607/32/o/n/21 \u00a9 ucles 2021 2 (a) wilfred went to a shop to buy plants for his garden. complete the bill. item cost ($) 8 shrubs at $9.95 each ... 12 bushes at $... each 207.00 ... plants at $1.60 each 25.60 total $ ... [4] (b) the shop bought 960 tomato plants. (i) in the first week they sold 800 of the tomato plants. write 960800 as a fraction in its simplest form. .. [1] (ii) in the second week, 5% of the remaining 160 plants died and 53 of the remaining 160 plants were sold. work out how many tomato plants are left at the end of the second week. .. [3]", "5": "5 0607/32/o/n/21 \u00a9 ucles 2021 [turn over (c) olga and zak each buy some plants. these plants are all the same price. olga pays $67.95 for 15 plants. zak buys 12 plants. work out how much zak pays for his plants. $ .. [2]", "6": "6 0607/32/o/n/21 \u00a9 ucles 2021 3 (a) 0 x234 a b c \u2013 3\u2013 2\u2013 13 4 5 2 7 6 1y 1 (i) write down the coordinates of (a) point a, ( ... , ...) [1] (b) point b, ( ... , ...) [1] (c) point c. ( ... , ...) [1] (ii) write down the coordinates of the mid-point of ac. ( ... , ...) [1] (iii) write down the equation of the line ab. .. [1]", "7": "7 0607/32/o/n/21 \u00a9 ucles 2021 [turn over (b) 110\u00b0not to scale x\u00b0z\u00b0 y\u00b0 r s tp q in the diagram, pq is parallel to ts and qs = sr. tsr is a straight line. (i) write down the mathematical name of quadrilateral pqrt . .. [1] (ii) find the value of x. x = . [1] (iii) find the value of y. y = . [2] (iv) find the value of z. z = . [1]", "8": "8 0607/32/o/n/21 \u00a9 ucles 2021 4 (a) simplify. pp p 57 4 -+ .. [1] (b) solve. x41 9 -= x = . [2] (c) factorise fully. xx y 15 9+ .. [2] (d) complete this statement with either 2 or 1 . show clearly how you decide. 112 ... 53 [1] (e) write down the inequality shown on the number line. 5 3 1 4 2 0 6x .. [1]", "9": "9 0607/32/o/n/21 \u00a9 ucles 2021 [turn over 5 the results of 24 matches played by a football team are recorded below. they can win (w), lose (l) or draw (d). w l w l d w l l l w w l l d l l w l l d w l l w (a) complete the table. result frequency pie chart angle w d l total 24 360\u00b0 [6] (b) draw a pie chart to show this information. [3] (c) one of these matches is chosen at random. find the probability that the result is a win. .. [1]", "10": "10 0607/32/o/n/21 \u00a9 ucles 2021 6 not to scale 6 cm w\u00b0 c da b 7 cm 5 cm (a) work out the area of quadrilateral abcd . give the units of your answer. .. .. [3] (b) work out the perimeter of quadrilateral abcd . . cm [3] (c) use trigonometry to work out the value of w. w = . [2]", "11": "11 0607/32/o/n/21 \u00a9 ucles 2021 [turn over 7 an aircraft flies 40 000 km around the earth. (a) write 40 000 in words. . [1] (b) change 40 000 km to metres. give your answer in standard form. .. m [2] (c) the flight takes 67 hours. (i) change 67 hours to seconds. give your answer correct to 2 significant figures. s [3] (ii) calculate the average speed of the aircraft. give your answer in metres per second. m/s [1]", "12": "12 0607/32/o/n/21 \u00a9 ucles 2021 8 5 cm this shape is made by joining four identical semi-circles to the sides of a square. (a) work out the perimeter of the shape. . cm [2] (b) write down the order of rotational symmetry of the shape. .. [1] (c) on the diagram, draw all the lines of symmetry. [2]", "13": "13 0607/32/o/n/21 \u00a9 ucles 2021 [turn over 9 0 x234567 ba \u2013 3\u2013 2\u2013 1 \u2013 6 \u2013 7\u2013 5\u2013 43 4 5 2 7 6 1y 1 shape a is mapped onto shape b by a single transformation. describe fully three different types of transformation that will map shape a onto shape b. 1 .. . 2 .. . 3 .. . [7]", "14": "14 0607/32/o/n/21 \u00a9 ucles 2021 10 tilda recorded the time, in minutes, that each of 100 cars was parked in a hospital car park. her results are shown in the frequency table. time ( t minutes) frequency time ( t minutes) cumulative frequency 0 1 t g 20 0 t g 20 20 1 t g 40 12 t g 40 40 1 t g 60 18 t g 60 60 1 t g 80 16 t g 80 80 1 t g 100 38 t g 100 100 1 t g 120 16 t g 120 100 (a) complete the cumulative frequency table. [2] (b) on the grid, draw a cumulative frequency curve to show the information. 02040cumulative frequency60 1030507090 80100 10 30 50 70 90 20 0 40 60 120t 110 80 100 time (minutes) [3]", "15": "15 0607/32/o/n/21 \u00a9 ucles 2021 [turn over (c) use your cumulative frequency curve to find an estimate of (i) the median, ... min [1] (ii) the interquartile range. ... min [2] (d) tilda thinks that approximately three quarters of the cars were parked in the car park for between 50 and 110 minutes. is tilda correct? use information from the curve to justify your answer. [4] question 11 is printed on the next page.", "16": "16 0607/32/o/n/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.11 0y x\u2013 3 3 \u2013 310 (a) (i) on the diagram, sketch the graph of yx72=- for x33gg- . [2] (ii) find the coordinates of the local maximum. ( ... , ...) [1] (b) (i) on the diagram, sketch the graph of yx6 2= for values of x from -3 to 3. [2] (ii) write down the equation of each asymptote of yx6 2= . .. and . [2] (c) find the x-coordinate of each point of intersection of yx72=- and yx6 2= . . [4]" }, "0607_w21_qp_41.pdf": { "1": "dc (nf/sg) 215048/2 \u00a9 ucles 2021 [turn overthis document has 20 pages. *4055595395* cambridge international mathematics 0607/41 paper 4 (extended) october/november 2021 2 hours 15 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 120. \u25cf the number of marks for each question or part question is shown in brackets [ ].cambridge igcse\u2122", "2": "2 0607/41/o/n/21 \u00a9 ucles 2021 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/41/o/n/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 amir, bibi and caitlyn are each given $1500 to invest. (a) amir invests his $1500 in an account which pays compound interest. the interest rate is 3% per year for 5 years, after which it is 2% per year. find the value of amir\u2019s investment at the end of 11 years. $ . [3] (b) bibi invests her $1500 in an account which pays r % per year simple interest. at the end of 11 years, the investment is worth $1962. calculate the value of r. r= [3] (c) caitlyn invests her $1500 in an account which pays t % per year compound interest. at the end of 11 years, the investment is worth $1968.13 . calculate the value of t. t= [3]", "4": "4 0607/41/o/n/21 \u00a9 ucles 2021 2 (a) in part (a) enlargements and stretches have scale factors greater than 1. (i) a transformation maps triangle a onto triangle b. triangle a is congruent to triangle b. tick all the possible transformations it could be. transformation tick (\u2713) rotation reflection translation enlargement stretch [1] (ii) a transformation maps triangle c onto triangle d. the angles of triangle c are the same as the corresponding angles of triangle d. tick all the possible transformations it could be. transformation tick (\u2713) rotation reflection translation enlargement stretch [1] (iii) a transformation maps triangle e onto triangle f. triangle f has a larger area than triangle e. tick all the possible transformations it could be. transformation tick (\u2713) rotation reflection translation enlargement stretch [1]", "5": "5 0607/41/o/n/21 \u00a9 ucles 2021 [turn over (b) y x1 0 \u2013 1 \u2013 2 \u2013 3 \u2013 4 2 3 4 5 6 7 8 \u2013 1 \u2013 2 \u20133 \u2013 4 \u2013 5123456 q p (i) describe fully the single transformation that maps triangle p onto triangle q. . . [3] (ii) stretch triangle p with the x-axis invariant and scale factor 2. [2]", "6": "6 0607/41/o/n/21 \u00a9 ucles 2021 3 the table shows the number of days, d, since planting and the heights, h cm, of some plants. number of days ( d) 20 20 42 76 90 24 86 98 10 56 height ( h cm) 34 66 80 76 100 50 86 94 40 54 (a) complete the scatter diagram. the first five points have been plotted for you. h d 10 0020 30 40 50 number of days60 70 80 90 100102030405060708090100 height (cm) [2] (b) what type of correlation is shown in the scatter diagram? . [1] (c) find the equation of the regression line for h in terms of d. h= [2]", "7": "7 0607/41/o/n/21 \u00a9 ucles 2021 [turn over (d) use your regression line to estimate the height of a plant that was planted 28 days ago. cm [1] (e) a plant was planted 140 days ago. explain why you should not use the equation of the regression line to estimate the height of this plant. . [1]", "8": "8 0607/41/o/n/21 \u00a9 ucles 2021 4 the table shows a set of data. x frequency 5 16 6 18 7 25 8 11 9 6 10 4 total 80 (a) when x represents the number of emails essa receives each day, find (i) the median, . [1] (ii) the range, . [1] (iii) the upper quartile, . [1] (iv) the mean. . [2] (b) when x represents the height of a seedling, correct to the nearest centimetre, explain why you cannot work out the range of the heights. . . [1]", "9": "9 0607/41/o/n/21 \u00a9 ucles 2021 [turn over 5 y x7 \u2013 7\u2013 7 7 0 ()() ()()xxxx 1223f2 =+-+ for x77gg- (a) on the diagram, sketch the graph of () . yx f= [3] (b) write down the equation of each asymptote parallel to the y-axis. . [2] (c) write down the coordinates of the local minimum. ( ... , ..) [2] (d) find the range of values of x for which the gradient of ()xf is negative. . [3] (e) solve () . xxf=- x= [1]", "10": "10 0607/41/o/n/21 \u00a9 ucles 2021 6 the masses of 300 apples are shown in the table. mass (m grams)m 02 5 1g m 25 501g m 05571g m 75 1001g m 100 1251g m 125 1501g frequency 4 26 60 88 106 16 (a) draw a cumulative frequency curve to show these results. m10 0020 30 40 50 mass (grams)60 70 80 90 100 110 120 130 140 15050100150200250300 cumulative frequency [4] (b) use your curve to find the interquartile range. . [2] (c) apples with a mass below 80 g are used to make drinks. find the percentage of the 300 apples that are used to make drinks. .. % [2]", "11": "11 0607/41/o/n/21 \u00a9 ucles 2021 [turn over 7 (a) the nth term of a sequence is () ().nn n 612 1 ++ find the first three terms of this sequence. . , . , . [2] (b) for each of the following sequences: \u2022 find the next two terms \u2022 find an expression for the nth term. (i) 11 8 5 2 next two terms ... , .. nth term [3] (ii) 2- 2- 0 4 10 18 next two terms ... , .. nth term [3] (iii) 3 5 9 17 33 next two terms ... , .. nth term [3]", "12": "12 0607/41/o/n/21 \u00a9 ucles 2021 8 not to scalee b af c d4 cm 6 cm 11 cm the diagram shows a right-angled triangular prism. abcd , adfe and bcfe are rectangles. ,cm ad 11= cm dc 6= and the height cm cf 4= . (a) calculate the volume of the prism. .. cm3 [2] (b) calculate the total surface area of the prism. .. cm2 [4] (c) calculate the length af. af= ... cm [3]", "13": "13 0607/41/o/n/21 \u00a9 ucles 2021 [turn over (d) calculate angle fa c. angle fac= [2] (e) the volume of a mathematically similar prism is ..cm 44553 calculate the total surface area of this similar prism. .. cm2 [3]", "14": "14 0607/41/o/n/21 \u00a9 ucles 2021 9 not to scale \u2013 4 0 44 \u2013 4 ab xy the equation of the circle is . xy 1622+= the equation of the straight line is . yx 31=+ the line crosses the circle at the points a and b. (a) use substitution to show that the x-coordinates of the points a and b satisfy the equation . xx10 61 502+- = [3] (b) solve the equation xx10 61 502+- = to find the coordinates of the points a and b. show your working and give your answers correct to 2 decimal places. a ( .. , ...) b ( .. , ...) [4]", "15": "15 0607/41/o/n/21 \u00a9 ucles 2021 [turn over 10 ()xx 32 f=- () () xx 3 g2=- (a) find (( )).1 fg . [2] (b) solve () . x 25 g= x= ... or x= ... [2] (c) find ().4 f1- . [2] (d) write down (( )).x ff1- . [1]", "16": "16 0607/41/o/n/21 \u00a9 ucles 2021 11 not to scalenorth cb a108 km 217 km159 km a, b and c are three ports. (a) show that angle .\u00b0 abc 107 2 = correct to 1 decimal place. [3] (b) the bearing of b from a is \u00b0.305 (i) using the sine rule, show that angle .\u00b0 bac 444= correct to 1 decimal place. [3] (ii) find the bearing of c from a. . [1]", "17": "17 0607/41/o/n/21 \u00a9 ucles 2021 [turn over (c) a ship leaves a at 22 50 and sails at a constant speed of 24 km/h towards c. calculate the time, correct to the nearest minute, when the ship is nearest to b. . [5]", "18": "18 0607/41/o/n/21 \u00a9 ucles 2021 12 (a) (i) for each venn diagram, shade the given set. ab,la bu a bu ab+ l [2] (ii) use set language to describe the shaded set. a bu . [1] (b) 40 people are asked which of 3 television programmes, p, q and r, they watch. the results are shown in the venn diagram. p rqu 7 4 5 86 45 1", "19": "19 0607/41/o/n/21 \u00a9 ucles 2021 [turn over (i) two of the 40 people are chosen at random. find the probability that they both watch exactly 2 of the 3 programmes. . [2] (ii) two of the people who watch programme p are chosen at random. find the probability that one of them watches both other programmes and one watches just one of the other programmes. . [3] (iii) three of the 40 people are chosen at random. find the probability that two of them watch only programme q and one of them watches only programme r. . [3] question 13 is printed on the next page.", "20": "20 0607/41/o/n/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.13 (a) rearrange yex fax b=++ to make x the subject. x= [4] (b) () () \u00b0 xx 32 fs in= (i) write down the amplitude and the period of () .xf amplitude = period = [2] (ii) the graph of () yx f= is stretched with the x-axis invariant and scale factor 3 to give the graph of (). yx g= find ().xg ()xg= [1] (iii) the graph of () yx f= is translated through 90 0-eo to give the graph of (). yx h= find ()xh, giving your answer in its simplest form. ()xh= [2]" }, "0607_w21_qp_42.pdf": { "1": "this document has 20 pages. any blank pages are indicated. cambridge igcse\u2122 dc (lk/fc) 212427/1 \u00a9 ucles 2021 [turn overcambridge international mathematics 0607/42 paper 4 (extended) october/november 2021 2 hours 15 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 120. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *1059670861*", "2": "2 0607/42/o/n/21 \u00a9 ucles 2021 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/42/o/n/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 (a) stella and tomas share $200 in the ratio 11 : 14. (i) show that stella receives $88. [1] (ii) stella invests her $88 at a rate of 1.5% per year simple interest. calculate the amount of interest stella has at the end of 6 years. $ [2] (b) urs buys some clothes in a sale. (i) he buys a jacket for $22. the original price of the jacket was $25. calculate the percentage reduction in the price of the jacket. . % [3] (ii) urs buys a shirt for $13.50 . this is the price after a reduction of 10% of the original price. calculate the original price of the shirt. $ [2]", "4": "4 0607/42/o/n/21 \u00a9 ucles 2021 2 ()fs in xx= for \u00b0\u00b0x 0 360gg () () gs in xx2= for \u00b0\u00b0x 0 360gg 90 180 270 360 - 11 0y x (a) on the diagram, sketch the graph of ()f yx= . [2] (b) write down the coordinates of the local minimum point on the graph of ()f yx= . ( .. , .. ) [1] (c) write down the period and amplitude of the graph of ()f yx= . period = amplitude = [2] (d) on the same diagram, sketch the graph of ()g yx= . [2] (e) write down the range of (i) ()fx, . [1] (ii) ()gx. . [1] (f) on the diagram, shade the regions where () sins in xx2h . [1] ", "5": "5 0607/42/o/n/21 \u00a9 ucles 2021 [turn over 3 (a) the number of members in a social media group increases exponentially at a rate of 5% per month. at the start of the first month there are 882 members. (i) calculate the number of members at the end of 10 months. give your answer correct to the nearest integer. . [3] (ii) calculate the number of complete months from the start until the group has 2000 members. . [4] (b) the mass of a radioactive substance decreases exponentially at a rate of r % per month. at the end of 10 months, its mass has decreased from 500 g to 242 g. find the value of r. r = [3]", "6": "6 0607/42/o/n/21 \u00a9 ucles 2021 4 the mass of each of 200 potatoes is measured. the cumulative frequency curve shows the results. 100020406080100120140160180200 120 140 160 180 200 mass (g)cumulative frequency", "7": "7 0607/42/o/n/21 \u00a9 ucles 2021 [turn over (a) (i) write down the mass of the heaviest potato. .. g [1] (ii) find the median. .. g [1] (iii) find the interquartile range. .. g [2] (iv) find the number of potatoes with a mass greater than 170 g. . [2] (b) this frequency table also shows information about the masses of the 200 potatoes. mass ( m g) m 100 1401g m 10 14 461g m 1146 62 1g m 11 0 62 9 1g frequency 50 10 90 50 calculate an estimate of the mean mass. .. g [2]", "8": "8 0607/42/o/n/21 \u00a9 ucles 2021 5 (a) p t - 10 - 10- 8- 6- 4- 2246810 - 8 - 6 - 4 - 2 0 2 4 6xy (i) reflect shape t in the y-axis. [1] (ii) translate shape t by the vector 10 5-eo . [2] (iii) rotate shape t through 90\u00b0 clockwise about the point (2, 0). [2] (iv) enlarge shape t with scale factor -2 and centre (0, 0). [2] (v) describe fully the single transformation that maps shape t onto shape p. . . [3]", "9": "9 0607/42/o/n/21 \u00a9 ucles 2021 [turn over (b) ()f x x2= (i) the graph of ()f yx= is mapped onto the graph of ()g yx= by a translation with vector 0 2eo. find ()gx in terms of x. ()gx= [1] (ii) the graph of ()f yx= is mapped onto the graph of ()h yx= by a stretch with factor 2 and the x-axis invariant. find ()hx in terms of x. ()hx= [1]", "10": "10 0607/42/o/n/21 \u00a9 ucles 2021 6 (a) (i) work out 3 521 2-- -eeoo . fp [2] (ii) a is the point (3, 5) and c is the point (4, 3). find the column vector that maps the point a onto the point c. fp [2] (iii) d is the point (1, 3) and the vector from d to e is 3 2eo. find the coordinates of e. ( .. , .. ) [1] (iv) find the magnitude of the vector 3 4- -eo . . [2]", "11": "11 0607/42/o/n/21 \u00a9 ucles 2021 [turn over (b) (i) p is the point (\u20131, 6) and q is the point (3, 4). find the equation of the perpendicular bisector of the line pq. . [5] (ii) find the coordinates of the point where the perpendicular bisector in part(b)(i) crosses the x-axis. ( .. , .. ) [2]", "12": "12 0607/42/o/n/21 \u00a9 ucles 2021 7 (a) the cost of a newspaper is $ p. the cost of a magazine is $ m. the total cost of 3 newspapers and 5 magazines is $13.30 . the total cost of 1 newspaper and 7 magazines is $15.90 . find the value of p and the value of m. p = m = [5]", "13": "13 0607/42/o/n/21 \u00a9 ucles 2021 [turn over (b) xx1+ not to scalex21\u2013 x21\u2013 the area of the rectangle is equal to the area of the square. find the value of x. x = [7]", "14": "14 0607/42/o/n/21 \u00a9 ucles 2021 8 (a) ()f x x 32=- ()g x x 51=- () , hxxx111! =+- (i) find (a) f(3), . [1] (b) h(f(3)). . [1] (ii) find f(g( x)) in its simplest form. . [2] (iii) solve () () fgxx= . x = [2] (iv) find ()gx1-. ()gx1=- [2]", "15": "15 0607/42/o/n/21 \u00a9 ucles 2021 [turn over (v) simplify () () hhxx21++ . give your answer as a single fraction, in terms of x, in its simplest form. . [4] (b) ()jx 5x= (i) find the value of x when ()jx551= . x = . [1] (ii) find ()jx1-. ()jx1=- [2]", "16": "16 0607/42/o/n/21 \u00a9 ucles 2021 9 (a) complete the table for each sequence. sequence 1st term 2nd term 3rd term 4th term 5th term nth term a 7 5 3 1 b 16 25 36 49 c211 2 4 [9] (b) yx1? and zy3? . when x36= , y2= and z24= . find z in terms of x. z= [4]", "17": "17 0607/42/o/n/21 \u00a9 ucles 2021 [turn over 10 fast trains and slow trains travel from city a to city b. 40% of the trains from city a to city b are fast trains. the probability that a fast train arrives in city b on time is 0.9 . the probability that a slow train arrives in city b on time is 0.95 . manuela goes to the station in city a and takes the next train to city b. (a) complete the tree diagram. train fast slow0.4arrives on time not on time. .. . .on time not on time [3] (b) find the probability that manuela arrives in city b on time. . [3]", "18": "18 0607/42/o/n/21 \u00a9 ucles 2021 11 5 cm 8 cm 20 cmaq p c bd 100\u00b0not to scale the diagram shows a solid triangular prism of length 20 cm. the cross-section of the prism is triangle bcp and three faces are rectangles. bc = 8 cm, cp = 5 cm and angle adq = angle bcp = 100\u00b0. (a) calculate the total surface area of the prism. . cm2 [7]", "19": "19 0607/42/o/n/21 \u00a9 ucles 2021 (b) (i) on the diagram of the prism, draw two straight lines and mark angle pa c. [1] (ii) angle apc = 73.45\u00b0. calculate angle pa c. angle pa c = [4]", "20": "20 0607/42/o/n/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_w21_qp_43.pdf": { "1": "this document has 20 pages. any blank pages are indicated. dc (rw/cgw) 215049/3 \u00a9 ucles 2021 [turn over *0410226176* cambridge international mathematics 0607/43 paper 4 (extended) october/november 2021 2 hours 15 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 120. \u25cf the number of marks for each question or part question is shown in brackets [ ].cambridge igcse\u2122", "2": "2 0607/43/o/n/21 \u00a9 ucles 2021 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/43/o/n/21 \u00a9 ucles 2021 [turn over answer all the questions. 1 the table shows the marks scored by 180 students in an examination. mark 0 1 2 3 4 5 6 7 8 9 10 number of students3 7 16 11 7 32 20 26 28 19 11 (a) (i) write down the mode. . [1] (ii) write down the range. . [1] (iii) find the median. . [1] (iv) find the interquartile range. . [2] (v) calculate the mean. . [2] (b) a different group of 140 students take the same examination. the marks of the two groups are combined and the mean mark of the 320 students is 6.5 . find the mean mark of the 140 students. . [2]", "4": "4 0607/43/o/n/21 \u00a9 ucles 2021 2 you may use this grid to help you answer this question. y o x transformation p is a rotation of 180\u00b0 about the origin. transformation q is a reflection in the line yx=. (a) find the coordinates of the image of the point (5, 2) under transformation p. ( .. , .. ) [1] (b) find the coordinates of the image of the point (5, 2) under transformation q. ( .. , .. ) [1] (c) find the coordinates of the image of the point ( x, y) under transformation p followed by transformation q. ( .. , .. ) [2] (d) describe fully the single transformation that is equivalent to transformation q followed by transformation p. . . [2]", "5": "5 0607/43/o/n/21 \u00a9 ucles 2021 [turn over 3 anna flies by plane from manchester (uk) to goa (india). the plane flies a distance of 7650 km. (a) the flight takes 8.5 hours. (i) calculate the average speed of the plane. . km/h [1] (ii) the plane leaves manchester at 20 45. the local time in goa is 5 hours 30 minutes ahead of the local time in manchester. find the local time in goa when the plane lands. . [2] (b) the exchange rate is 1 pound (\u00a3) = 90 indian rupees (inr). (i) the cost of the flight is \u00a3299. calculate the cost of the flight in indian rupees. inr . [1] (ii) anna returns to manchester with 4014 indian rupees. she changes this money into pounds. calculate this amount in pounds. \u00a3 . [1]", "6": "6 0607/43/o/n/21 \u00a9 ucles 2021 4 oay xnot to scale b the points a (2, 5) and b (10, 1) are shown on the diagram. (a) find the gradient of the line ab. . [2] (b) find the equation of the line ab. give your answer in the form ym cx=+ . y= . [2]", "7": "7 0607/43/o/n/21 \u00a9 ucles 2021 [turn over (c) the point c has coordinates (6, k) where k02. the line ca is perpendicular to the line ab and ac ab= . find k. k= . [3] (d) the point d is such that abdc is a square. find the coordinates of d. ( .. , .. ) [2] (e) find the area of triangle bcd . . [3]", "8": "8 0607/43/o/n/21 \u00a9 ucles 2021 5 (a) alana and beau share $200 in the ratio x : y. an expression for the amount of money alana receives is xyx200 +. (i) write down an expression for the amount of money beau receives. . [1] (ii) alana and beau are each given an extra $50. the ratio of the total amount of money that each person now has is 3 : 1. find the value of yx. yx= . [5]", "9": "9 0607/43/o/n/21 \u00a9 ucles 2021 [turn over (b) (i) on 1 january each year bruno invests $1000 in bank a. bank a pays simple interest at a rate of 4% per year. show that the total value of bruno\u2019s investment in bank a at the end of 4 years is $4400. [3] (ii) on 1 january each year bruno also invests $1000 in bank b. bank b pays compound interest at a rate of 3.5% per year. find the total value of bruno\u2019s investment in bank b at the end of 4 years. $ . [3]", "10": "10 0607/43/o/n/21 \u00a9 ucles 2021 6 the venn diagram shows the sets p, f and m. p f mu u= {integer values of x x21 2 ;g g } p= {prime numbers} f= {factors of 12} m= {multiples of 3} (a) list the elements of set p and the elements of set f. p= f= [2] (b) write each element of u in the correct region of the venn diagram. [2] (c) list the elements of (i) fm,, . [1] (ii) pm+l , . [1] (iii) ()pfm,, l. . [1] (d) find (( )) npf m ++ l . . [1]", "11": "11 0607/43/o/n/21 \u00a9 ucles 2021 [turn over 7 y varies inversely as the square of x. y5= when x3=. (a) (i) find y in terms of x. y= . [2] (ii) find the value of x when y20= . x= . [2] (b) z varies directly as the square root of y. z12= when y9=. use your answer to part (a)(i) to find z in terms of x. z= . [3]", "12": "12 0607/43/o/n/21 \u00a9 ucles 2021 8 \u2013 2 0 25y x \u2013 5 ()fxx x 33=- for x22gg- (a) on the diagram, sketch the graph of ()f yx= . [2] (b) find the coordinates of the local maximum. ( .. , .. ) [1] (c) write down the x-coordinates of the points where the curve meets the x-axis. x= .. , x= .. , x= .. [2] (d) (i) describe fully the single transformation that maps ()f yx= onto ()f yx 1 =+ . . . [2] (ii) solve () () ffxx 1 =+ for x22gg- . . [2] (iii) solve () () ffxx 1 h+ for x22gg- . . [2]", "13": "13 0607/43/o/n/21 \u00a9 ucles 2021 [turn over 9 a bcpnot to scale dx\u00b0 o a, b and c lie on a circle, centre o. ap and bp are tangents to the circle. ab intersects op at d and angle \u00b0 oxab=. (a) write down the size of angle obp . angle obp= . [1] (b) find, in terms of x, (i) angle aod , angle aod= . [1] (ii) angle acb , angle acb= . [1] (iii) angle apb. angle apb= . [1] (c) write down the mathematical name of quadrilateral aobp . . [1] (d) write down (i) two triangles that are congruent, . [1] (ii) two triangles that are similar but not congruent. . [1]", "14": "14 0607/43/o/n/21 \u00a9 ucles 2021 10 16 cm 12 cm4 cmnot to scale the diagram shows a solid made from a cylinder, a hemisphere and a cone, each with radius 4 cm. the cylinder has length 16 cm. the slant height of the cone is 12 cm. (a) find the volume of the solid. .. cm3 [5]", "15": "15 0607/43/o/n/21 \u00a9 ucles 2021 [turn over (b) show that the total surface area of the solid is r208 cm2. [4] (c) a mathematically similar solid has a total surface area of r468 cm2. find the radius of the cylinder in this solid. cm [3]", "16": "16 0607/43/o/n/21 \u00a9 ucles 2021 11 b c da120 m45 m not to scale48\u00b0 28\u00b0 54 m angles acb and acd are obtuse. (a) show that ac = 95.9 m correct to the nearest 0.1 metre. [3]", "17": "17 0607/43/o/n/21 \u00a9 ucles 2021 [turn over (b) find angle acd . angle acd= . [4] (c) the area of triangle abd is 5137 m2. calculate the area of triangle bcd . m2 [4]", "18": "18 0607/43/o/n/21 \u00a9 ucles 2021 12 (a) solve. (i) x952=- x= . [3] (ii) x4632- . [3] (b) (i) solve the equation, giving your answers correct to 3 significant figures. xx25 102+=- x= ... or x= ... [3] (ii) use your answers to part (b)(i) to solve () () tant an yy 25 102+= - for y 0 180 \u00b0\u00b0gg . y= ... or y= ... [2]", "19": "19 0607/43/o/n/21 \u00a9 ucles 2021 13 two bags each contain only blue balls and red balls. bag 1 contains 7 blue balls and 3 red balls. bag 2 contains 3 blue balls and 7 red balls. maria chooses a ball at random from bag 1 and puts it into bag 2. (a) find the probability that the ball chosen is blue. . [1] (b) maria now chooses a ball at random from bag 2 and puts it into bag 1. (i) find the probability that both balls chosen are red. . [2] (ii) find the probability that one of the balls chosen is red and the other is blue. . [3] (iii) find the probability that there are now exactly 7 blue balls in bag 1. . [3]", "20": "20 0607/43/o/n/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_w21_qp_51.pdf": { "1": "this document has 8 pages. any blank pages are indicated. cambridge igcse\u2122 dc (pq) 212407/1 \u00a9 ucles 2021 [turn over *1364711255* cambridge international mathematics 0607/51 paper 5 investigation (core) october/november 2021 1 hour 10 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 36. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/51/o/n/21 \u00a9 ucles 2021 answer all the questions. adding square numbers this investigation looks at adding two or more square numbers to make another square number. in this investigation all numbers are positive integers. 1 complete the list of the first six square numbers. 112= 22= ... 392= 42= ... 52= ... 63 62= [1] 2 (a) work out (i) 92, . [1] (ii) 402. . [1] (b) show that 94 04 122 2+= . [2] 3 when ab c22 2+= then ( a, b, c) is a 3-square set . a, b and c are positive integers. example in question 2(b) , a9=, b40= and c41= . 94 04 122 2+= , so (9, 40, 41) is a 3-square set. when ab c22 2+= then ca b22=+ . use this formula and any patterns you notice to complete the table on the next page for 3-square sets.", "3": "3 0607/51/o/n/21 \u00a9 ucles 2021 [turn over a b c 3 4 5 5 12 13 7 24 25 9 40 41 11 60 13 84 85 112 113 144 19 181 21 221 25 312 313 [6] 4 when abc d22 22++ = then ( a, b, c, d) is a 4-square set . it is possible to make a 4-square set using two rows in the table. example from the table row two 51 21 322 2+= row six 13 84 8522 2+= replace 132 in the second equation with 51 222+ from the first equation: . 51 28 48 5222 2++ = so (5, 12, 84, 85) is a 4-square set. use the same method with rows from the table to find two more 4-square sets. (. , . , . , .) and (. , . , . , .) [3]", "4": "4 0607/51/o/n/21 \u00a9 ucles 2021 5 (a) show that (6, 12, 12, 18) is a 4-square set. [2] (b) k is any positive integer greater than 1. if (ka, kb, kc, kd) is a 4-square set, then ka kb kc kd22 22++ = `` `` jj jj . show that ( a, b, c, d) must also be a 4-square set. [2]", "5": "5 0607/51/o/n/21 \u00a9 ucles 2021 [turn over (c) the numbers in the 4-square set (6, 12, 12, 18) have common factors. (i) find a common factor of 6, 12, 12 and 18 that is greater than 1. . [1] (ii) use (6, 12, 12, 18) and part (b) to find a 4-square set where a, b, c and d do not have a common factor greater than 1. (. , . , . , .) [2]", "6": "6 0607/51/o/n/21 \u00a9 ucles 2021 6 here is another method for finding a 4-square set ( a, b, c, d). choose two positive integers a and b with a less than b. then cab 2122 =+- and abd2122 =++ make the 4-square set ( a, b, c, d). (a) use this to find a 4-square set when (i) a2= and b3=, (2, 3, . , .) [3] (ii) a2= and d 34= . (2, . , . , 43) [3] (b) (i) use your answers to part (a) and any patterns you notice to complete the table for 4-square sets that start with 2. a b c d 2 3 2 5 14 15 2 7 26 27 2 43 2 [3] (ii) write down an equation connecting c and d. . [1]", "7": "7 0607/51/o/n/21 \u00a9 ucles 2021 (c) when a and b are both even then cab 2122 =+- and abd2122 =++ do not give a 4-square set. give an example to show this. [2] (d) when a and b are both odd there are no 4-square sets. in a 4-square set, d23= . (i) show that ab 4522+= . [1] (ii) find a 4-square set when d23= . (. , . , . , 23) [2]", "8": "8 0607/51/o/n/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.blank page" }, "0607_w21_qp_52.pdf": { "1": "this document has 8 pages. cambridge igcse\u2122 dc (kn/sg) 215050/2 \u00a9 ucles 2021 [turn over *2561531814* cambridge international mathematics 0607/52 paper 5 investigation (core) october/november 2021 1 hour 10 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 36. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/52/o/n/21 \u00a9 ucles 2021 this square dotty paper may be used for your diagrams.", "3": "3 0607/52/o/n/21 \u00a9 ucles 2021 [turn over answer all the questions. investigation connecting dots this investigation looks at the number of ways of connecting dots using straight lines. this diagram shows 1 dot. there is 1 row and 1 column. this is a 1 by 1 diagram. there are no connections to other dots. this diagram shows 4 dots. there are 2 rows and 2 columns. this is a 2 by 2 diagram. there are 6 ways to join 2 dots. these are: \u2022 2 vertical connectors (solid lines) \u2022 2 horizontal connectors (solid lines) \u2022 1 up diagonal connector (dashed line) \u2022 1 down diagonal connector (dashed line). 1 (a) this is a 3 by 3 diagram. the diagram shows: \u2022 6 horizontal connectors \u2022 4 up diagonal connectors. each connector joins 2 dots. complete the diagram by drawing the 6 vertical connectors and the 4 down diagonal connectors that join 2 dots. [2]", "4": "4 0607/52/o/n/21 \u00a9 ucles 2021 (b) this is a 4 by 4 diagram. on this 4 by 4 diagram, (i) draw the horizontal connectors and the vertical connectors that join 2 dots, [1] (ii) draw the up diagonal connectors and the down diagonal connectors that join 2 dots. [1] (c) complete the table for the numbers of connectors that join 2 dots. use part (b) and any patterns you notice. you may use the square dotty paper on page 2 for diagrams. numbers of connectors that join 2 dots horizontal vertical up diagonal down diagonal total size of diagram (n by n)1 by 1 0 0 0 0 0 2 by 2 2 2 1 1 6 3 by 3 6 6 4 4 20 4 by 4 5 by 5 20 16 6 by 6 110 [5]", "5": "5 0607/52/o/n/21 \u00a9 ucles 2021 [turn over (d) in an n by n diagram there are n rows and n columns. (i) find an expression, in terms of n, for the number of up diagonal connectors that join 2 dots on an n by n diagram. . [2] (ii) find an expression, in terms of n, for the number of horizontal connectors that join 2 dots on an n by n diagram. . [3] (e) use your answers to part (d) to find the total number of connectors that join 2 dots on a 15 by 15 diagram. . [3]", "6": "6 0607/52/o/n/21 \u00a9 ucles 2021 2 this is a 3 by 3 diagram. there are 8 ways to join 3 dots . these are: \u2022 3 vertical connectors \u2022 3 horizontal connectors \u2022 1 up diagonal connector \u2022 1 down diagonal connector. (a) this is a 4 by 4 diagram. find the number of horizontal, vertical, up diagonal and down diagonal connectors that join 3 dots. two horizontal connectors have been drawn for you. horizontal vertical up diagonal down diagonal [2]", "7": "7 0607/52/o/n/21 \u00a9 ucles 2021 [turn over (b) complete the table for the numbers of connectors that join 3 dots. use your answers to part (a) and any patterns you notice. you may use the square dotty paper on page 2 for diagrams. numbers of connectors that join 3 dots horizontal vertical up diagonal down diagonal total size of diagram (n by n)2 by 2 0 0 0 0 0 3 by 3 3 3 1 1 8 4 by 4 5 by 5 15 6 by 6 80 [4] (c) (i) this is an expression for the number of up diagonal connectors that join 3 dots on an n by n diagram. ()n22- work out the number of up diagonal connectors that join 3 dots on a 20 by 20 diagram. . [1] (ii) this is an expression for the number of horizontal connectors that join 3 dots on an n by n diagram. na n2+ find the value of a and write down the expression. . [3] question 3 is printed on the next page.", "8": "8 0607/52/o/n/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.3 (a) complete the table for the numbers of connectors that join 4 dots. numbers of connectors that join 4 dots horizontal vertical up diagonal down diagonal total size of diagram (n by n)3 by 3 0 0 0 0 0 4 by 4 10 5 by 5 10 6 by 6 18 18 9 9 54 [2] (b) (i) write down an expression, in terms of n, for the number of up diagonal connectors that join 4 dots on an n by n diagram. . [1] (ii) find an expression, in terms of n, for the number of horizontal connectors that join 4 dots on an n by n diagram. . [2] (c) show that the total number of connectors that join 4 dots on an n by n diagram is nn41 81 82-+ . [2] (d) find the size of the diagram which has a total of 180 connectors that join 4 dots. . [2]" }, "0607_w21_qp_61.pdf": { "1": "this document has 12 pages. cambridge igcse\u2122 dc (lk/sg) 212584/2 \u00a9 ucles 2021 [turn overcambridge international mathematics 0607/61 paper 6 investigation and modelling (extended) october/november 2021 1 hour 40 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer both part a (questions 1 to 7) and part b (questions 8 to 12). \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 60. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *1328839610*", "2": "2 0607/61/o/n/21 \u00a9 ucles 2021 answer both parts a and b. a investigation (questions 1 to 7) pythagorean sets of four (30 marks) you are advised to spend no more than 50 minutes on this part. this investigation looks at finding the integer lengths of the sides of a cuboid that has an integer length for its diagonal. 1 s r q p 356not to scale the diagram shows a cuboid with sides of length 3, 5 and 6. (a) using pythagoras\u2019 theorem in triangle pqr gives pr 3522 2=+ . find the value of pr2. . [1] (b) using pythagoras\u2019 theorem in triangle prs gives ps pr 622 2=+ . find the value of ps2. . [2]", "3": "3 0607/61/o/n/21 \u00a9 ucles 2021 [turn over 2 s r q p abc dnot to scale the diagram shows a cuboid with sides of integer length a, b and c. its diagonal, ps, has integer length d. (a) use pythagoras\u2019 theorem in triangle pqr to write down an expression for pr2 in terms of a and b. . [1] (b) use your answer to part (a) , and pythagoras\u2019 theorem in triangle prs, to show that da bc22 22=+ +. [1] 3 a cuboid has sides of length a, b and c, where a, b and c are integers and abcgg . if the length of the diagonal, d, is also an integer then ( a, b, c, d) is a pythagorean set of four . use da bc22 22=+ + to show that a cuboid with sides of length 4, 17 and 28 gives a pythagorean set of four. complete the pythagorean set of four. (4, 17, 28, . ) [3]", "4": "4 0607/61/o/n/21 \u00a9 ucles 2021 4 (a) in a pythagorean set of four ( a, b, c, d ) da bc22 2 2=+ + . when da c=+ , show that acb 22 = . [2] (b) explain why b must be even. . . . [2]", "5": "5 0607/61/o/n/21 \u00a9 ucles 2021 [turn over 5 here is a method for finding pythagorean sets of four using question 4 : \u2022 choose any even integer for b. \u2022 calculate ac using question 4(a) . \u2022 find all the possible pairs of integers for a and c, where ac1. use this method to find all the pythagorean sets of four when you choose b8=. . [7]", "6": "6 0607/61/o/n/21 \u00a9 ucles 2021 6 (a) which one of these two sets is a pythagorean set of four? (18, 24, 72, 78) or (18, 24, 72, 84)? show how you decide. (18, 24, 72, . ) [2] (b) (ka, kb, kc, kd ) is a pythagorean set of four, where k is a positive integer greater than 1. use algebra to show that ( a, b, c, d ) must also be a pythagorean set of four. [2] (c) (a, b, c, d ) is a basic pythagorean set of four if the numbers a, b, c and d have no common factor greater than 1. find the basic pythagorean set of four for your answer to part (a) . . [2]", "7": "7 0607/61/o/n/21 \u00a9 ucles 2021 [turn over 7 the method in question 5 to find pythagorean sets of four is: \u2022 choose any even integer for b. \u2022 calculate ac using question 4(a) . \u2022 find all the possible pairs of integers for a and c, where ac1. use this method to find two basic pythagorean sets of four where the smallest integer, a, is 2. (... , ... , ... , ...) and (... , ... , ... , ...) [5]", "8": "8 0607/61/o/n/21 \u00a9 ucles 2021 b modelling (questions 8 to 12) reflecting a laser beam (30 marks) you are advised to spend no more than 50 minutes on this part. this task looks at models for the height of the image of a reflected laser beam on a vertical wall. in this task all the measurements are in metres. the diagram shows, by a dashed line, the side view of the path of a laser beam. the laser beam \u2022 starts at source l \u2022 travels to a point r on horizontal ground ab \u2022 reflects at the point r so that angle lra = angle nrb \u2022 travels to n, its image, on a vertical wall. wall l a r bn h 4 ground 6 15not to scale the height of l above the horizontal ground is la 4=. the height of n above the horizontal ground is h nb=. ar 6= and rb 15= . 8 complete the statements to show that h10= . triangle lra is similar to triangle nrb . h 415= ... #== 10 h .. ... [2]", "9": "9 0607/61/o/n/21 \u00a9 ucles 2021 [turn over 9 the laser source, l, can move towards or away from the wall. it now moves x metres to the right so that ar becomes x6- metres. the point r does not move. the other given measurements remain the same. when the laser beam reflects at r, triangle lra and triangle nrb will always be similar. l a r bn h 4 15not to scale ()x6- (a) use the method in question 8 to find a model for h in terms of x. . [2] (b) sketch the graph of h against x for x 6611- . h x\u2013 6 0 6 [2] (c) (i) write down the equation of the vertical asymptote. . [2] (ii) give a reason why there is a vertical asymptote. refer to the path of the laser beam. . . [1]", "10": "10 0607/61/o/n/21 \u00a9 ucles 2021 10 the laser source, l, now stays fixed. at the start ar 6= and rb 15= . the point r then moves x metres towards b along the ground. the dashed line shows the path of the laser beam. l a r bh x4 6 (a) show that hxx 660 4=+- . [2] (b) sketch the graph of hxx 660 4=+- for x 61 5 1g - . h x\u2013 6 0 15 [3] (c) when the point r has moved x metres towards b, the height, h, is 6. find the value of x. . [2]not to scale", "11": "11 0607/61/o/n/21 \u00a9 ucles 2021 [turn over 11 l a r b x4 6h10y at the start, when ar 6=, the height of the image is 10. after the point r moves x metres, the height of the image is hxx 660 4=+- . y is the change in the height of the image, so yh10=- . (a) show that a model for y is yxx 614=+ . [3] (b) (i) when the point r moves one metre to the left, away from b, x 1=- . use the model in part (a) to find the change in height of the image. . [2] (ii) the point r moves an additional one metre to the left, away from b. (a) write down the value of x. . [1] (b) find the additional change in height. . [3] question 12 is printed on the next page.not to scale", "12": "12 0607/61/o/n/21 \u00a9 ucles 2021 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge.12 l a r bn 4 ah b (a) find h in terms of a and b. . [2] (b) the point r moves x metres to the right, towards b, along the horizontal ground. y is the change in h. find a model for y in terms of a, b and x. do not simplify your answer. . [3]not to scale" }, "0607_w21_qp_62.pdf": { "1": "this document has 12 pages. cambridge igcse\u2122 *0093871881* dc (pq/cgw) 215051/4 \u00a9 ucles 2021 [turn overcambridge international mathematics 0607/62 paper 6 investigation and modelling (extended) october/november 2021 1 hour 40 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer both part a (questions 1 to 4) and part b (questions 5 to 7). \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 60. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/62/o/n/21 \u00a9 ucles 2021 answer both parts a and b. a investigation (questions 1 to 4) connecting dots (30 marks) you are advised to spend no more than 50 minutes on this part. this investigation looks at the number of ways of connecting dots using straight lines. this diagram shows 1 dot. there is 1 row and 1 column. this is a 1 by 1 diagram. there are no connections to other dots. this diagram shows 4 dots. there are 2 rows and 2 columns. this is a 2 by 2 diagram. there are 6 ways to join 2 dots. these are: \u2022 2 vertical connectors (solid lines) \u2022 2 horizontal connectors (solid lines) \u2022 1 up diagonal connector (dashed line) \u2022 1 down diagonal connector (dashed line). 1 (a) this is a 3 by 3 diagram. the diagram shows: \u2022 6 horizontal connectors \u2022 4 up diagonal connectors. each connector joins 2 dots. write down the number of vertical connectors and the number of down diagonal connectors that join 2 dots. vertical down diagonal [2]", "3": "3 0607/62/o/n/21 \u00a9 ucles 2021 [turn over (b) complete the table for the numbers of connectors that join 2 dots. use part (a) and any patterns you notice. you may use the square dotty paper on page 12 for diagrams. numbers of connectors that join 2 dots horizontal verticalup diagonaldown diagonaltotal size of diagram (n by n)1 by 1 0 0 0 0 0 2 by 2 2 2 1 1 6 3 by 3 6 4 4 by 4 9 5 by 5 20 6 by 6 110 [3] (c) in an n by n diagram there are n rows and n columns. (i) find an expression, in terms of n, for the number of up diagonal connectors that join 2 dots on an n by n diagram. . [2] (ii) find an expression, in terms of n, for the number of horizontal connectors that join 2 dots on an n by n diagram. . [3] (iii) use your answers in part (i) and part (ii) to find an expression for the total number of connectors that join 2 dots. do not simplify your expression. . [1]", "4": "4 0607/62/o/n/21 \u00a9 ucles 2021 2 this is a 3 by 3 diagram. there are 8 ways to join 3 dots together. these are: \u2022 3 vertical connectors \u2022 3 horizontal connectors \u2022 1 up diagonal connector \u2022 1 down diagonal connector. (a) this is a 4 by 4 diagram. find the number of horizontal, vertical, up diagonal and down diagonal connectors that join 3 dots. two horizontal connectors have been drawn for you. horizontal vertical up diagonal down diagonal [2]", "5": "5 0607/62/o/n/21 \u00a9 ucles 2021 [turn over (b) complete the table for the numbers of connectors that join 3 dots. use your answers to part (a) and any patterns you notice. you may use the square dotty paper on page 12 for diagrams. numbers of connectors that join 3 dots horizontal verticalup diagonaldown diagonaltotal size of diagram (n by n)2 by 2 0 0 0 0 0 3 by 3 3 3 1 1 8 4 by 4 5 by 5 15 6 by 6 80 [2] (c) (i) this is an expression for the number of up diagonal connectors that join 3 dots on an n by n diagram. ()n22- work out the number of up diagonal connectors that join 3 dots on a 20 by 20 diagram. . [1] (ii) this is an expression for the number of horizontal connectors that join 3 dots on an n by n diagram. na n2+ find the value of a and write down the expression. . [3] (d) find an expression, in terms of n, for the total number of connectors that join 3 dots on an n by n diagram. do not simplify your expression. . [1]", "6": "6 0607/62/o/n/21 \u00a9 ucles 2021 3 (a) complete the table for the numbers of connectors that join 4 dots. numbers of connectors that join 4 dots horizontal verticalup diagonaldown diagonaltotal size of diagram (n by n)3 by 3 0 0 0 0 0 4 by 4 10 5 by 5 10 6 by 6 54 n by n [4] (b) find an expression, in terms of n, for the total number of connectors that join 4 dots on an n by n diagram. do not simplify your answer. . [1] 4 (a) this is an expression for the total number of connectors that join m dots on an n by n diagram. () () nn kn k 222-+ - what is the relationship between k and m? . [1] ", "7": "7 0607/62/o/n/21 \u00a9 ucles 2021 [turn over (b) (i) use part (a) to show that when n5= and m 2= there is a total of 72 connectors. [1] (ii) find all the possible values for n and m that give a total of 72 connectors. . [3] ", "8": "8 0607/62/o/n/21 \u00a9 ucles 2021 b modelling (questions 5 to 7) breeding deer (30 marks) you are advised to spend no more than 50 minutes on this part. this task looks at modelling the population of a herd of deer. in this herd there are equal numbers of males and females. each adult female deer gives birth to a male and a female fawn (baby deer) every year. at the start of the first year a farmer has 20 adult deer. there are 10 males and 10 females. at the end of each year all the deer are adult. 5 (a) (i) at the end of the first year the farmer sends 20% of the 20 deer to other farmers. he sends an equal number of male and female deer. show that at the start of the second year he has 36 deer in his herd. [2] (ii) pn = the number of deer in the herd at the start of year n. pn1=+ the number of deer in the herd at the start of year n1+. at the end of each year the farmer sends 20% of pn to other farmers. he always sends an equal number of male and female deer. show that . pp 18nn1=+. [2] (b) (i) when the farmer finds pn1+ he rounds the value to the nearest even integer . the table shows the number of deer in the herd, pn, at the start of year n. use part (a)(ii) to complete the table. year ( n) 1 2 3 4 5 6 7 8 number in herd ()pn20 36 116 374 [4]", "9": "9 0607/62/o/n/21 \u00a9 ucles 2021 [turn over (ii) use your answers to part (b)(i) to plot the four missing points. 200 0 10400600800100012001400 2 3 4 yearnumber in herd 5 6 7 8p n [2] (c) the farmer models the data using pa bn1=-. use the first two years in the table in part (b)(i) to find the value of a and the value of b and write down the model. . [3]", "10": "10 0607/62/o/n/21 \u00a9 ucles 2021 6 the farmer now models the data in the table on page 8 using () () pa nb nc 112=- +- +. (a) (i) use the first year in the table in question 5(b)(i) to show that c20= . [1] (ii) use year 2 and year 4 in the table in question 5(b)(i) to write down a pair of simultaneous equations in terms of a and b. . . [2] (b) (i) solve your simultaneous equations from part (a)(ii) and write down the model. ... [4] (ii) sketch your model on the grid in question 5(b)(ii) for n18gg . [2] (c) is this a suitable model for the number of deer in the herd? give one reason for your answer. . . [1]", "11": "11 0607/62/o/n/21 \u00a9 ucles 2021 [turn over 7 the farmer now models the data in the table on page 8 using () pa n1b=- . (a) use the data for year 2 and year 4 in the table in question 5(b)(i) to (i) find a, . [2] (ii) find b and write down the model. . [3] (b) give two reasons why the model in part (a) is not suitable for the number of deer in the herd. 1 .. . 2 .. . [2] ", "12": "12 0607/62/o/n/21 \u00a9 ucles 2021 this square dotty paper may be used for your diagrams in the investigation. permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge." }, "0607_w21_qp_63.pdf": { "1": "this document has 12 pages. cambridge igcse\u2122 *4427926590* dc (ks/sg) 212585/1 \u00a9 ucles 2021 [turn overcambridge international mathematics 0607/63 paper 6 investigation and modelling (extended) october/november 2021 1 hour 40 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer both part a (questions 1 to 3) and part b (questions 4 to 6). \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 60. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/63/o/n/21 \u00a9 ucles 2021 answer both parts a and b. a investigation (questions 1 to 3) girard\u2019s sums (30 marks) you are advised to spend no more than 50 minutes on this part. albert girard, a 17th century french mathematician, investigated numbers, n, that can be written as the sum of two squares, ab22+. this task is about these numbers. for this task, a and b are integers where a0h and b0h. 1 (a) complete the table. a a2b b2na b22=+ n4' 2 4 6 36 40 10 remainder 0 18 10 106 remainder 0 28 16 256 remainder 0 4 64 20 remainder 0 144 196 85 remainder 0 20 400 884 221 remainder 0 0 0 900 225 remainder 0 [5] (b) (i) when a2= and b4= then nk 4= , so n is a multiple of 4. find the value of k. . [2]", "3": "3 0607/63/o/n/21 \u00a9 ucles 2021 [turn over (ii) the values of a and b in the table are all even numbers. when am2= and bn2= then nk 4= . find an expression for k in terms of m and n. . [3] (c) not all multiples of 4 can be written as the sum of two square numbers. show that there are no values of a and b that give k11= . [2]", "4": "4 0607/63/o/n/21 \u00a9 ucles 2021 2 (a) complete the table. a a2b b2na b22=+ n4' 7 49 5 25 74 18 remainder 2 21 19 802 200 remainder 2 17 289 914 remainder 2 49 170 remainder 2 1 1 remainder [4] (b) when a is an odd number, an21=- . (i) use algebra to explain why, when a is an odd number, a 42' has a remainder of 1. . [3] (ii) explain why, for the values in the table in part (a) , n is always k42+. . . [2]", "5": "5 0607/63/o/n/21 \u00a9 ucles 2021 [turn over (c) when a and b are both odd, , nk 42=+ so n is a multiple of 4 plus 2. not all multiples of 4 plus 2 can be written as the sum of two square numbers. find all the values of k from 1 to 9 where na b22=+ . . [3]", "6": "6 0607/63/o/n/21 \u00a9 ucles 2021 3 the values of n that can be written as the sum of two square numbers are of the form , kr4+ where the remainder r is a constant. (a) explain why r can be 0, 1 or 2 but cannot be 3. [3] (b) na b22=+ find all the values of n, where , n 10 30 11 that are of the form k41+. . [3]", "7": "7 0607/63/o/n/21 \u00a9 ucles 2021 [turn over the modelling task starts on page 8.", "8": "8 0607/63/o/n/21 \u00a9 ucles 2021 b modelling (questions 4 to 6) production boundaries (30 marks) you are advised to spend no more than 50 minutes on this part. this task is about the number of computer tablets and mobile phones a company makes and sells. the company owns two factories, a and b. factory a makes a-tablets and a-phones. factory b makes b-tablets and b-phones. a production boundary is a curve or line. points on the curve or line are the maximum numbers of the two items a factory can make when all resources are used. it is the boundary of the region which shows all the combinations of the two items a factory can make. 4 factory a makes t a-tablets and p a-phones each day. the manager of factory a uses the model pt900010002 =- where , t 0h as the production boundary for the output of a-tablets and a-phones. (a) on the axes below, sketch this model. 10 000p t40000number of a-phones number of a-tablets [2] (b) when factory a makes 9000 a-phones it cannot make any a-tablets. write down the maximum number of a-tablets it can make when it does not make any a-phones. . [1] (c) on monday, factory a makes 1000 a-tablets. on tuesday, factory a makes 1500 a-tablets. find the decrease in the maximum number of a-phones it can make from monday to tuesday. . [3]", "9": "9 0607/63/o/n/21 \u00a9 ucles 2021 [turn over (d) (i) on wednesday, factory a makes 5000 a-phones. use your graph from part (a) to explain why it is not possible for it to make 2500 a-tablets on wednesday. . . [1] (ii) on the graph in part (a) shade the region that represents the numbers of a-phones and a-tablets that factory a can make. [1] (e) the company sells all the a-phones and a-tablets that factory a makes each day. the company makes $160 profit for each a-tablet and $100 profit for each a-phone it sells. the greatest possible daily profit at factory a is $964 000. (i) write down a linear equation for this profit in terms of p and t. give your answer in the form pm tc=+ . . [2] (ii) find the number of a-tablets and a-phones that factory a should sell in order to make a profit of $964 000. t = p = [3]", "10": "10 0607/63/o/n/21 \u00a9 ucles 2021 5 factory b makes t b-tablets and p b-phones. the table shows the maximum numbers of b-phones that factory b can make each day for some numbers of b-tablets. number of b-tablets tnumber of b-phones p 1000 8000 2000 6000 3000 4000 4000 2000 as the number of b-tablets increases, the number of b-phones decreases at a constant rate. (a) (i) draw the production boundary for factory b on the axes below. p t 0 [2] (ii) find the equation which models this production boundary, giving p as a function of t. ... [2]", "11": "11 0607/63/o/n/21 \u00a9 ucles 2021 [turn over (iii) factory b makes at least 1000 b-tablets but no more than 4000 b-tablets each day. write down the domain of the model in part (a)(ii) . . [1] (b) the company sells all the b-tablets and b-phones factory b makes each day. the company makes $200 profit for each b-tablet and $190 profit for each b-phone it sells. each day, the manager of factory b expects to make the greatest possible profit. (i) find the greatest possible profit each day. . [3] (ii) one day factory b has to make 2500 b-tablets. on this day the profit is 73.3% of the greatest possible profit. work out the number of b-phones factory b makes on this day. . [4] question 6 is printed on the next page.", "12": "12 0607/63/o/n/21 \u00a9 ucles 2021 6 the company puts new machinery to make phones in factory a and factory b. factory a can now make double the number of a-phones. factory b can now make 10% more b-phones. all other conditions remain the same. (a) complete the following models for the production boundaries at each factory after the changes. use the models in question 4 and question 5(a) . factory a: p = . for t0h factory b: . pt 22 11000 =- + for .. g t g .. [2] (b) after the changes, the greatest possible profit made each day by factory a is $1 830 000. find the total greatest possible profit made each day by the company. . [3] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of the cambridge assessment group. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which itself is a department of the university of cambridge." } }, "2022": { "0607_m22_qp_12.pdf": { "1": "this document has 8 pages. [turn overdc (rw/ct) 220234/1 \u00a9 ucles 2022 *8690008957* cambridge international mathematics 0607/12 paper 1 (core) february/march 2022 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ].cambridge igcse\u2122", "2": "2 0607/12/f/m/22 \u00a9 ucles 2022 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/12/f/m/22 \u00a9 ucles 2022 [turn over answer all the questions. 1 write 21 as a percentage. .. % [1] 2 a b write down the mathematical name for (a) angle a, . [1] (b) angle b. . [1] 3 write down the second triangle number. . [1] 4 complete the mapping diagram. 3 5 8 12 205 . 15 23 39x f(x) [1]", "4": "4 0607/12/f/m/22 \u00a9 ucles 2022 5 01 \u2013 12345 1 2 3 4 5 6y x (a) plot the point (3, 4). [1] (b) write down the coordinates of one of the points where the curve crosses the x-axis. ( .. , .. ) [1] 6 work out. ()23 4 #+ . [1] 7 work out. 843 2+ . [2] 8 \u2013 2 \u2013 1 0 1 2 3 4n complete the statement. this number line shows the inequality n 11- 3. [1]", "5": "5 0607/12/f/m/22 \u00a9 ucles 2022 [turn over 9 these are the scores of 10 students in a mathematics test. 29 17 9 11 11 24 9 31 11 19 (a) find the mode. . [1] (b) work out the median. . [2] 10 work out 20% of 45. . [1] 11 {ax x = is a positive integer less than 10 and x is a multiple of 4} list the elements of set a. . [1] 12 sam and his brother share $42 in the ratio 2 : 5. sam has the larger share. find the amount sam has. $ . [2]", "6": "6 0607/12/f/m/22 \u00a9 ucles 2022 13 sara pays $1 per day for her mobile phone. in one week she can make 100 minutes of free calls. all other calls are charged at 50 cents per minute. work out the total amount sara pays in one week when she makes 120 minutes of calls. $ . [3] 14 (a) alys rolls a fair six-sided die. find the probability that alys rolls a 2. . [1] (b) elora has a six-sided die. she thinks that her die is biased. she rolls it 100 times to test it. (i) complete the table. number on die 1 2 3 4 5 6 frequency 5 15 18 16 16 relative frequency 0.05 0.15 [2] (ii) write down the number elora is most likely to get when she rolls her die. . [1] 15 factorise completely. xy x 24 8+ . [2]", "7": "7 0607/12/f/m/22 \u00a9 ucles 2022 [turn over 16 simplify. xx2# . [1] 17 write down the highest common factor (hcf) of 5 and 7. . [1] 18 a is the point (3, 8) and b is the point (5, 2-). find the coordinates of the mid -point of ab. ( .. , .. ) [2] 19 write down the two rational numbers from this list. 32 3 2 r . [1] 20 a bag contains 5 silver coins and 2 gold coins. gill takes a coin at random from the bag and then replaces it. she does this a second time. find the probability that both coins are gold. . [2] questions 21, 22 and 23 are printed on the next page.", "8": "8 0607/12/f/m/22 \u00a9 ucles 2022 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge.21 rnot to scale the area of the circle is rcm162. find the radius, r, of the circle. cm [2] 22 in triangle abc , cm ab ac x == . bc is 4 cm longer than ab. find an expression, in terms of x, for the perimeter of this triangle. give your answer in its simplest form. . [2] 23 work out () () 41 03 1035## #--. give your answer in standard form. . [2]" }, "0607_m22_qp_22.pdf": { "1": "this document has 8 pages. [turn overcambridge igcse\u2122 dc (ce/jg) 219195/1 \u00a9 ucles 2022 *4718159596* cambridge international mathematics 0607/22 paper 2 (extended) february/march 2022 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/22/f/m/22 \u00a9 ucles 2022 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/22/f/m/22 \u00a9 ucles 2022 [turn over answer all the questions. 1 write down a cube number between 10 and 100. . [1] 2 work out (. )014. . [1] 3 alex goes to sleep at 20 40 and wakes up the next morning at 06 10. work out the length of time, in hours and minutes, that alex is asleep. h ... min [1] 4 (a) work out 22 33 5--eeoo . fp [2] (b) f is the point (5, 7). the vector that maps f onto the point g is 1 3-eo . find the coordinates of g. (.. , ..) [1] 5 work out 43 61-, giving your answer as a fraction in its lowest terms. . [2]", "4": "4 0607/22/f/m/22 \u00a9 ucles 2022 6 divide $140 in the ratio 2 : 1 : 4. $ , $ , $ [2] 7 the volume of a hemisphere with radius 3 cm is cmk3r . find the value of k. k = [2] 8 write 42- as a fraction. . [1] 9 a train is travelling at a speed of 30 m/s. the length of the train is 70 m. the train passes through a station of length 170 m. find the time the train takes to pass completely through the station. ... s [2]", "5": "5 0607/22/f/m/22 \u00a9 ucles 2022 [turn over 10 (a) not to scale ac b6 cm 7 cm 8 cmpr q5 cm triangle pqr is similar to triangle abc . work out the length of pr. pr = ... cm [2] (b) two mathematically similar containers have capacities of 27 litres and 8 litres. the surface area of the smaller container is cm 16002. work out the surface area of the larger container. .. cm2 [3] 11 factorise. xyx y 1+- - . [2]", "6": "6 0607/22/f/m/22 \u00a9 ucles 2022 12 (a) 0y xpq 24 135 1 3 2 describe fully the single transformation that maps triangle p onto triangle q. . . [3] (b) 0y xt24 13 1 3 5 7 2 4 6 8 stretch triangle t by a factor of 2 with invariant line x = 1. [2] 13 rationalise the denominator. 32 . [1]", "7": "7 0607/22/f/m/22 \u00a9 ucles 2022 [turn over 14 in this calculation, the three numbers are written in standard form. () () . n 41 01 03 21 0pp t 2# ## #=+ n, p and t are integers. (a) find the value of n. n = [1] (b) find t in terms of p. t = [1] 15 simplify. xx 164 2-- . [2] 16 the solutions to the equation xg xh 02++ = are 211 7- and 11 7 2+. find the value of g and the value of h. g = h = [3] questions 17 and 18 are printed on the next page.", "8": "8 0607/22/f/m/22 \u00a9 ucles 2022 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge.17 write as a single fraction, giving your answer in its simplest form. x213-+ . [2] 18 find the value of logl og log 58 22 +- . . [3]" }, "0607_m22_qp_32.pdf": { "1": "this document has 20 pages. [turn overdc (rw/cgw) 214153/1 \u00a9 ucles 2022 *1944007077* cambridge international mathematics 0607/32 paper 3 (core) february/march 2022 1 hour 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 96. \u25cf the number of marks for each question or part question is shown in brackets [ ].cambridge igcse\u2122", "2": "2 0607/32/f/m/22 \u00a9 ucles 2022 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/32/f/m/22 \u00a9 ucles 2022 [turn over answer all the questions. 1 (a) simon swims 25 metres. change 25 metres to centimetres. cm [1] (b) aroon swims four lengths of a 50 -metre pool. here is the time, in seconds, for each length. 44.8 45.3 44.5 44.4 work out the total time. give your answer in minutes and seconds. ... minutes ... seconds [2] (c) tam swims 200 metres in a total time of 3.2 minutes. calculate her average speed in metres per second. ... m/s [3]", "4": "4 0607/32/f/m/22 \u00a9 ucles 2022 2 (a) these are the first three patterns in a sequence. pattern 1 pattern 2 pattern 3 pattern 4 pattern 5 (i) in the space above, draw pattern 4 and pattern 5. [2] (ii) complete the table for the number of squares in each pattern. pattern number 1 2 3 4 5 8 number of squares 5 [3] (b) these are the first four terms of another sequence. 5 9 13 17 for this sequence, (i) write down the rule for continuing the sequence, . [1] (ii) find the nth term. . [2]", "5": "5 0607/32/f/m/22 \u00a9 ucles 2022 [turn over (c) the nth term, t, of a different sequence is given by this formula. tn 52=- (i) work out the value of t when n4=. t= . [1] (ii) rearrange the formula to make n the subject. n= . [2]", "6": "6 0607/32/f/m/22 \u00a9 ucles 2022 3 students in a college carry out a science experiment. (a) at the start of the experiment, the temperature of a gas was -\u200a42\u2009\u00b0c. during\u2009the\u2009experiment, \u2009the\u2009temperature \u2009of\u2009the\u2009gas\u2009rises\u2009to\u200928\u2009\u00b0c. (i) work out how much the temperature of the gas rises during the experiment. . \u2009\u00b0c\u2009[1] (ii) work out the temperature that is half -way between -\u200a42\u2009\u00b0c\u2009and\u200928\u2009\u00b0c. . \u2009\u00b0c\u2009[1] (b) the experiment began at 07 50 and ended at 15 25. work out the length of time the experiment lasted. give your answer in hours and minutes. h ... min [1] (c) when the results were posted online, there were 1279 views in the first day. write 1279 correct to the nearest 10. . [1] (d) by the end of the week, there had been 15 503 views. (i) write 15 503 in words. . [1] (ii) write 15 503 in standard form, correct to two significant figures. . [2]", "7": "7 0607/32/f/m/22 \u00a9 ucles 2022 [turn over (e) in the college, 53 students study science. 32 study physics ( p). 24 study chemistry ( c). 18 study both physics and chemistry. complete the venn diagram. p c.. .. u [3]", "8": "8 0607/32/f/m/22 \u00a9 ucles 2022 4 50 students were asked the number of magazines they bought in a week. the results are shown in the table. number of magazines 0 1 2 3 4 number of students 18 8 14 7 3 (a) work out how many more students bought 2 magazines than bought 1 magazine. . [1] (b) write down the most common number of magazines bought. . [1] (c) one of the students is chosen at random. find the probability that this student bought 3 or 4 magazines. give your answer as a fraction in its simplest form. . [2] (d) work out the mean number of magazines bought. . [2]", "9": "9 0607/32/f/m/22 \u00a9 ucles 2022 [turn over (e) on the grid, draw a bar chart to show the information in the table. 00 number of magazinesnumber of students 2468101214161820 1 2 3 4 [2]", "10": "10 0607/32/f/m/22 \u00a9 ucles 2022 5 in the diagram, all lengths are in centimetres and all angles are right angles. 4 7 5 67 7not to scale312 (a) work out the area of the shaded shape. give the units of your answer. ... [4] (b) work out the perimeter of the shaded shape. cm [3]", "11": "11 0607/32/f/m/22 \u00a9 ucles 2022 [turn over 6 in a school there are 960 students. 540 of the students are girls. (a) write the ratio girls : boys in its simplest form. . \u2009\u2009\u2009:\u200a\u2009\u2009\u2009. \u2009[3] (b) two thirds of the 540 girls and 45% of the boys travel to school by bus. work out how many more girls than boys travel to school by bus. . [3]", "12": "12 0607/32/f/m/22 \u00a9 ucles 2022 7 (a) x\u00b0 26\u00b0not to scale find the value of x. x= . [1] (b) not to scale 50\u00b0155\u00b0p\u00b0 r\u00b0q\u00b0 b a xy z the diagram shows a triangle xyz and a straight line ab. ab is parallel to xz. find the value of p, the value of q and the value of r. p= . q= . r= . [3]", "13": "13 0607/32/f/m/22 \u00a9 ucles 2022 [turn over (c) 106\u00b0 42\u00b075\u00b0not to scaley\u00b0 find the value of y. y= . [1] (d) d ce\u00b0 b pa qnot to scale abcd is part of a regular octagon. pbcq is part of a regular hexagon. find the value of e. e= . [4]", "14": "14 0607/32/f/m/22 \u00a9 ucles 2022 8 in a competition, each diver is given a score out of 10 by each of two judges. the table shows the scores for eight divers. judge 1 2.3 7.3 7.9 4.4 8.5 7.7 1.8 8.1 judge 2 2.4 7.7 7.9 4.7 8.8 7.9 2.4 7.8 (a) complete the scatter diagram. the first four points have been plotted for you. 00 1 2 3 4 5 6 7 8 9 10judge 2 score judge 1 score12345678910 [2] (b) what type of correlation is shown in the scatter diagram? . [1]", "15": "15 0607/32/f/m/22 \u00a9 ucles 2022 [turn over (c) calculate the mean of the scores given by each judge. judge 1 . judge 2 . [2] (d) on the scatter diagram, draw a line of best fit. [2] (e) judge 1 gives another diver a score of 5.6 . use your line of best fit to estimate the score given to this diver by judge 2. . [1]", "16": "16 0607/32/f/m/22 \u00a9 ucles 2022 9 ac by x 0 5 4 3 2 1 \u2013 1 \u2013 2 \u2013 3 \u2013 4 \u2013 512345 \u2013 5\u2013 4\u2013 3\u2013 2\u2013 1 the diagram shows three triangles a, b and c. (a) describe fully the single transformation that maps triangle a onto triangle b. . . [2] (b) describe fully the single transformation that maps triangle a onto triangle c. . . [2] (c) rotate triangle a\u2009through\u2009180\u00b0\u2009about\u2009(0,\u20090). label the image p. [2] (d) enlarge triangle a, scale factor 2, centre (1, 4). label the image q. [2]", "17": "17 0607/32/f/m/22 \u00a9 ucles 2022 [turn over 10 (a) solve. (i) x71 1 += x= . [1] (ii) ()x43 21 0 -= x= . [3] (iii) x 519+= x= . [2] (b) multiply out the brackets and simplify. () () xx68+- . [2]", "18": "18 0607/32/f/m/22 \u00a9 ucles 2022 11 x\u00b0a c75 cm25 cm not to scale25 cm 75 cmod b 96 cmh cm the diagram shows a table standing on a horizontal floor. the table top is horizontal and is supported by two legs aob and cod . (a) use trigonometry to find the value of x. x= . [3] (b) use similar triangles to find db. db= cm [2]", "19": "19 0607/32/f/m/22 \u00a9 ucles 2022 [turn over (c) use pythagoras\u2019 theorem to find the height, h cm, of o above the floor. cm [3] question 12 is printed on the next page.", "20": "20 0607/32/f/m/22 \u00a9 ucles 2022 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge.12 0 a by x\u2013 6 4 \u2013 1020 the diagram shows the graph of () () yx x42 =+ - for x64gg- . a and b are two of the points where the graph crosses the axes. (a) find the coordinates of (i) point a, ( .. , .. ) [1] (ii) point b, ( .. , .. ) [1] (iii) the local minimum. ( .. , .. ) [1] (b) on the diagram, sketch the graph of yx1=- for x64gg- . [2] (c) find the x-coordinate of each point of intersection of () () yx x42 =+ - and yx1=- . x= . and . [2]" }, "0607_m22_qp_42.pdf": { "1": "this document has 20 pages. any blank pages are indicated. [turn overcambridge igcse\u2122 dc (ce/ct) 301839/2 \u00a9 ucles 2022 *0931684579* cambridge international mathematics 0607/42 paper 4 (extended) february/march 2022 2 hours 15 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 120. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/42/f/m/22 \u00a9 ucles 2022 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area =a c bcb a", "3": "3 0607/42/f/m/22 \u00a9 ucles 2022 [turn over answer all the questions. 1 (a) find the gradient and y-intercept of the line with equation xy34 24 += . gradient = y-intercept = [3] (b) y xlnot to scale 0(4, 3)(8, 5) the diagram shows line l and the coordinates of two points on the line. (i) show that the equation of line l is yx22-= . [3] (ii) find the equation of the line parallel to l that passes through the point (0, 7). give your answer in the form ym xc=+ . y = [2]", "4": "4 0607/42/f/m/22 \u00a9 ucles 2022 2 (a) find 12 kg as a percentage of 80 kg. .. % [1] (b) find 19% of $250. $ [2] (c) xavier invests $500 at a rate of 1.5% per year simple interest. at the end of y years, the value of xavier\u2019s investment is $612.50 . find the value of y. y = [3]", "5": "5 0607/42/f/m/22 \u00a9 ucles 2022 [turn over (d) each year the value of a car decreases by 12% of its value at the beginning of that year. the original value of the car is $20 000. (i) calculate the value of the car at the end of 3 years. give your answer correct to the nearest dollar. $ [3] (ii) find the number of complete years for the value of $20 000 to decrease until it is first below $1000. . [4] (e) each year the value of another car decreases by r\u200a\u200a% of its value at the beginning of that year. at the end of 10 years, the value has decreased from $12 000 to $4673. find the value of r. r = [3]", "6": "6 0607/42/f/m/22 \u00a9 ucles 2022 3 (a) the table shows the coursework grades for 20 students. grade 3 4 5 6 7 frequency 1 3 6 2 8 find (i) the mode, . [1] (ii) the range, . [1] (iii) the median, . [1] (iv) the lower quartile. . [1] (b) the table shows some information about the heights, h cm, of 100 bushes. height ( h cm) h 100 1101g h 10 11 151g h 11 0 15 3 1g frequency 18 37 45 calculate an estimate of the mean height. cm [2] (c) the table shows some information about the times, t minutes, taken by some students to read a magazine. time ( t minutes) t 01 01g t 10 021g t 20 031g t 30 041g frequency 3 11 n 19 when using mid-interval values, an estimate of the mean value of t is 25.4 . find the value of n. n = [4]", "7": "7 0607/42/f/m/22 \u00a9 ucles 2022 [turn over 4 (a) not to scalea\u00b0 b\u00b0 65\u00b0 30\u00b0 c\u00b0 the diagram shows two straight lines crossing two parallel lines. find the values of a, b and c. a = b = c = [3] (b) not to scalek ael bcd 30\u00b020\u00b020\u00b0 70\u00b0 w\u00b0 x\u00b0 z\u00b0v\u00b0u\u00b0y\u00b0 a, b, c, d and e are points on the circle. kl is a tangent to the circle at e. ac = ad. find the values of u, v, w, x, y and z. u = x = v = y = w = z = [6]", "8": "8 0607/42/f/m/22 \u00a9 ucles 2022 5 (a) (i) expand and simplify x232+`j . .. [2] (ii) the equation xx41 25 02++ = can be written as xk232+=`j . find the value of k. k = [1] (iii) use your answer to part(ii) to solve the equation xx41 25 02++ =. x = ... or x = .. [2]", "9": "9 0607/42/f/m/22 \u00a9 ucles 2022 [turn over (b) x varies inversely as the square root of ( w \u2013 1). when w = 10, x = 2. (i) find x in terms of w. x = [2] (ii) find x when w = 3.25 . x = [1] (iii) find w in terms of x. w = [3]", "10": "10 0607/42/f/m/22 \u00a9 ucles 2022 6 in this question all lengths are in centimetres. not to scale x51+x1 2\u2013 x 13\u20137 the area of the larger rectangle is cm842 greater than the area of the smaller rectangle. (a) show that xx52 88 02+- =. [4] (b) factorise xx52 882+- . . [2] (c) find the area of the smaller rectangle. . cm2 [2]", "11": "11 0607/42/f/m/22 \u00a9 ucles 2022 [turn over 7 \u2013 4 412 \u2013 12y x 0 ()xx 4 f2=- for x44gg- (a) on the diagram, sketch the graph of () yx f= . [2] (b) write down the zeros of f( x). . [2] (c) write down the coordinates of the local maximum. (.. , ..) [1] (d) the equation xk42-= has 4 solutions and k is an integer. write down a possible value of k. k = [1] (e) (i) on the diagram, sketch the graph of yx2= . [1] (ii) solve the equation xx422-= . . [2] (iii) on the diagram, shade the regions where , yy x 02hg and yx 42g- . [2]", "12": "12 0607/42/f/m/22 \u00a9 ucles 2022 8 ()fxx 21=+ ()gxx 32=- () () hl og xx 1 =+ (a) find the value of (i) f(12), . [1] (ii) g(f(12)). . [1] (b) find the value of x when () () fgxx= . x = [2] (c) find f(g( x)), giving your answer in its simplest form. . [2] (d) find ()gx1-. ()gx1- = [2]", "13": "13 0607/42/f/m/22 \u00a9 ucles 2022 [turn over (e) find x when () (. ) hfx 05= . x = [2] (f) find ()hx1-. ()hx1- = [2]", "14": "14 0607/42/f/m/22 \u00a9 ucles 2022 9 (a) not to scale4 cmx cm 40\u00b0 calculate the value of x. x = [3] (b) not to scale ac b8 cm 9 cm 10 cm (i) calculate angle abc . angle abc = [3] (ii) t is the point on ab that is the shortest distance from c. calculate bt. bt = ... cm [3]", "15": "15 0607/42/f/m/22 \u00a9 ucles 2022 [turn over (c) another triangle pqr has qr = 12 cm, pr = 7 cm and angle pqr = 35\u00b0. calculate the difference between the two possible values of angle qpr . . [5]", "16": "16 0607/42/f/m/22 \u00a9 ucles 2022 10 when zena wears a sweatshirt, the probability that she goes for a walk is 107. when zena does not wear a sweatshirt, the probability that she goes for a walk is 109. on any day, the probability that she wears a sweatshirt is 51. (a) complete the tree diagram. yeswears a sweatshirt goes for a walk noyes no yes no51 .. [3] (b) (i) find the probability that on one day zena does not wear a sweatshirt and she goes for a walk. . [2] (ii) find the probability that on one day zena goes for a walk. . [2]", "17": "17 0607/42/f/m/22 \u00a9 ucles 2022 [turn over (c) in the tree diagram below, the value of j is the answer to part (b)(i) and the value of k is the answer to part (b)(ii) . yeswears a sweatshirt goes for a walk noyesno yesno .. j k (i) find the probability that zena does not wear a sweatshirt when she goes for a walk. . [2] (ii) complete the tree diagram above. [3]", "18": "18 0607/42/f/m/22 \u00a9 ucles 2022 11 (a) r y\u00b02r not to scale the diagram shows a sector of a circle with radius r and angle y\u00b0. the length of the arc of the sector is 2 r. calculate the value of y. y = [3]", "19": "19 0607/42/f/m/22 \u00a9 ucles 2022 (b) 8 cmnot to scale x\u00b0 the diagram shows a sector of a circle with radius 8 cm and angle x\u00b0. the area of the shaded segment is cma2. (i) show that sin axx45832r=- . [2] (ii) find the value of a when x = 90. . [1] (iii) by sketching the graph of sin axx45832r=- , find the value of x when a = 5.5 . a x20 90 0 x = [3]", "20": "20 0607/42/f/m/22 \u00a9 ucles 2022 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge.blank page" }, "0607_m22_qp_52.pdf": { "1": "this document has 12 pages. any blank pages are indicated. [turn overdc (rw/jg) 303239/2 \u00a9 ucles 2022 *2730862341* cambridge international mathematics 0607/52 paper 5 investigation (core) february/march 2022 1 hour 10 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 36. \u25cf the number of marks for each question or part question is shown in brackets [ ].cambridge igcse\u2122", "2": "2 0607/52/f/m/22 \u00a9 ucles 2022 answer all the questions. investigation dot patterns this investigation looks at patterns in sequences of dots, and of dots and crosses. 1 this is a sequence of dot patterns. pattern 2 pattern 1 pattern 3 (a) draw pattern 4. [1] (b) complete the table. pattern number, n 1 2 3 4 5 6 number of dots 2 3 4 [1] (c) how many dots are in pattern 9? . [1] (d) write down an expression, in terms of n, for the number of dots in pattern n. . [1] (e) find the number of the pattern that has 26 dots. . [2]", "3": "3 0607/52/f/m/22 \u00a9 ucles 2022 [turn over 2 this is another sequence of dot patterns. pattern 2 pattern 1 pattern 3 (a) complete the table. you may use the grid below to help you. pattern number, n 1 2 3 4 5 6 number of dots 21 [3] (b) find an expression, in terms of n, for the number of dots in pattern n. . [2] (c) work out the number of dots in pattern 40. . [2]", "4": "4 0607/52/f/m/22 \u00a9 ucles 2022 3 (a) oliver draws this sequence of patterns called centred squares . pattern 3 pattern 2 pattern 1 (i) pattern 3 is drawn on the grid. complete the diagram to show pattern 4. [1]", "5": "5 0607/52/f/m/22 \u00a9 ucles 2022 [turn over (ii) complete the table. pattern number, n 1 2 3 4 5 number of dots 1 5 13 [2] (iii) work out the number of dots in pattern 6. . [2]", "6": "6 0607/52/f/m/22 \u00a9 ucles 2022 (b) oliver draws the patterns of centred squares using dots and crosses. pattern 3 pattern 4 pattern 2 pattern 1 (i) pattern 4 is drawn on the grid. complete the diagram to show pattern 5. [1]", "7": "7 0607/52/f/m/22 \u00a9 ucles 2022 [turn over (ii) complete the table. pattern number, n number of dots number of crossestotal number of dots and crosses 1 1 0 1 2 1 4 5 3 9 4 13 4 16 5 6 [3] (iii) complete the table. pattern number, n number of dots number of crossestotal number of dots and crosses 1 112= 002= 10 122+= 2 112= 422= 21 522+= 3 932= 422= 32 1322+= 4 16= 5 6 [2] (iv) complete the formula for the total number of dots and crosses, t, in pattern n. t= . [2]", "8": "8 0607/52/f/m/22 \u00a9 ucles 2022 4 sophia draws the patterns of centred squares using dots and crosses in a different way. pattern 3 pattern 4 pattern 2 pattern 1 (a) complete the table. pattern number, n number of dots number of crossestotal number of dots and crosses 1 1 0 1 2 5 0 5 3 9 4 13 4 13 25 5 [2]", "9": "9 0607/52/f/m/22 \u00a9 ucles 2022 (b) complete the table. pattern number, nnumber of dotsnumber of crossestotal number of dots and crosses 1 1 04 0#= 14 01#+= 2 5 04 0#= 54 05#+= 3 9 44 1#= 4191 3 #+= 4 13 () 12 41 2 #=+ ) ( 13 41 22 5 #++ = 5 ()41 2 #=+ + + = 6 [3] (c) (i) in sophia\u2019s patterns, pattern k has 112 crosses . find the value of k. k= . [3] (ii) work out the total number of dots and crosses in pattern k. . [2]", "10": "10 0607/52/f/m/22 \u00a9 ucles 2022 blank page", "11": "11 0607/52/f/m/22 \u00a9 ucles 2022 blank page", "12": "12 0607/52/f/m/22 \u00a9 ucles 2022 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge.blank page" }, "0607_m22_qp_62.pdf": { "1": "this document has 20 pages. any blank pages are indicated. [turn overcambridge igcse\u2122 dc (lk/jg) 301931/3 \u00a9 ucles 2022 *5982622981* cambridge international mathematics 0607/62 paper 6 investigation and modelling (extended) february/march 2022 1 hour 40 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer both part a (questions 1 to 3) and part b (questions 4 to 8). \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 60. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/62/f/m/22 \u00a9 ucles 2022 answer both parts a and b. a investigation (questions 1 to 3) sequences of centred polygons (30 marks) you are advised to spend no more than 50 minutes on this part. this investigation looks at sequences of centred polygons . the first pattern in each sequence is a single dot. the sequence continues by adding polygons of increasing size around the central dot. 1 (a) oliver draws this sequence of dot patterns called centred squares . pattern 3 pattern 2 pattern 1 (i) pattern 3 is drawn on the grid. complete the diagram to show pattern 4. [1]", "3": "3 0607/62/f/m/22 \u00a9 ucles 2022 [turn over (ii) complete the table. pattern number, n 1 2 3 4 5 number of dots 1 5 13 [2] (iii) work out the number of dots in pattern 7. . [2]", "4": "4 0607/62/f/m/22 \u00a9 ucles 2022 (b) oliver draws the dot patterns of centred squares using dots and crosses. pattern 3 pattern 4 pattern 2 pattern 1 (i) pattern 4 is drawn on the grid. complete the diagram to show pattern 5. [1] (ii) complete the table. pattern number, n number of dots number of crossestotal number of dots and crosses 1 1 0 1 2 1 4 5 3 9 4 13 4 16 5 6 [2]", "5": "5 0607/62/f/m/22 \u00a9 ucles 2022 [turn over (iii) complete the table. pattern number, n number of dots number of crossestotal number of dots and crosses 1 112= 002= 10 122+= 2 112= 422= 21 522+= 3 932= 422= 32 1322+= 4 16= 5 6 [2] (iv) complete the formula for the total number of dots and crosses, t, in pattern n. t = [2] (v) show that the formula for t is nn22 12-+ . [1] (vi) work out the total number of dots and crosses in pattern 15. . [2]", "6": "6 0607/62/f/m/22 \u00a9 ucles 2022 2 this is the sequence of centred triangles. pattern 3 pattern 2 pattern 1 (a) complete the table. pattern number, n 1 2 3 4 5 number of dots, t 1 4 10 [3] (b) the formula for the number of dots, t, in pattern n is ta nb nc2=+ + . (i) give a reason why a is 23. . [1] (ii) find the value of b and the value of c. b = c = [4]", "7": "7 0607/62/f/m/22 \u00a9 ucles 2022 [turn over (c) there are 571 dots in pattern k. find the value of k. k = ... [4]", "8": "8 0607/62/f/m/22 \u00a9 ucles 2022 3 the formula for the number of dots, t, in the sequence of centred hexagons is tn n 33 12=- +. the number of dots in the nth centred hexagon is 6 more than the number of dots in the nth centred square. find the value of n and the number of dots in the centred hexagon. n = number of dots in the centred hexagon : [3]", "9": "9 0607/62/f/m/22 \u00a9 ucles 2022 [turn over b modelling (questions 4 to 8) daylight hours (30 marks) you are advised to spend no more than 50 minutes on this part. this task looks at modelling the number of daylight hours throughout the year. the number of daylight hours is the length of time between sunrise and sunset. 4 sophia looks at the number of daylight hours in london, england. she knows the shortest number of daylight hours, shortest day , is on 21 december. she knows the longest number of daylight hours, longest day , is on 21 june. she collects data for the sunrise and sunset times on the 21st day of every month. she works out the length of daylight in hours and minutes and converts it to a time in hours correct to 1 decimal place. her results are in this table. daylight hours in london month day sunrise sunsetdaylight in hours and minutesdaylight in hours december 21 08 03 15 53 7 h 50 min 7.8 january 21 07 52 16 30 8 h 38 min 8.6 february 21 07 02 17 26 10 h 24 min 10.4 march 21 06 00 18 15 12 h 15 min 12.3 april 21 05 51 20 07 14 h 16 min 14.3 may 21 05 00 20 54 15 h 54 min 15.9 june 21 04 43 21 21 16 h 38 min 16.6 july 21 05 08 21 04 15 h 56 min 15.9 august 21 05 55 20 10 14 h 15 min 14.3 september 21 06 45 19 00 12 h 15 min 12.3 october 21 07 35 17 54 november 21 07 28 16 03 8 h 35 min 8.6 december 21 08 03 15 53 7 h 50 min 7.8 (a) complete the row for october. [2]", "10": "10 0607/62/f/m/22 \u00a9 ucles 2022 (b) sophia puts her results from the table on this graph. 12 10 8 6 4 2 0 2 4 6 8 10013579111317 15 141618 1 3 5 7 9 11 12hours months after 21 decemberdaylight hours in london (i) plot the value for daylight hours on 21 october. [1]", "11": "11 0607/62/f/m/22 \u00a9 ucles 2022 [turn over (ii) write down the number of daylight hours on the shortest day and on the longest day in london. shortest day longest day [1] (iii) show that the length of time halfway between the number of daylight hours on the shortest day and the number of daylight hours on the longest day is 12.2 hours. [1]", "12": "12 0607/62/f/m/22 \u00a9 ucles 2022 5 sophia changes the order of her table. \u2022 she starts with 21 march. \u2022 she works out daylight hours above and below 12.2 . daylight hours in london month day sunrise sunsetdaylight in hours and minutesdaylight in hours, hdaylight in hours above 12.2 , h march 21 06 00 18 15 12 h 15 min 12.3 0.1 april 21 05 51 20 07 14 h 16 min 14.3 2.1 may 21 05 00 20 54 15 h 54 min 15.9 3.7 june 21 04 43 21 21 16 h 38 min 16.6 4.4 july 21 05 08 21 04 15 h 56 min 15.9 3.7 august 21 05 55 20 10 14 h 15 min 14.3 2.1 september 21 06 45 19 00 12 h 15 min 12.3 0.1 october 21 07 35 17 54 november 21 07 28 16 03 8 h 35 min 8.6 \u0336 3.6 december 21 08 03 15 53 7 h 50 min 7.8 \u0336 4.4 january 21 07 52 16 30 8 h 38 min 8.6 \u0336 3.6 february 21 07 02 17 26 10 h 24 min 10.4 \u0336 1.8 march 21 06 00 18 15 12 h 15 min 12.3 0.1 (a) complete the row for october. [1]", "13": "13 0607/62/f/m/22 \u00a9 ucles 2022 [turn over (b) sophia puts her results from the table into this graph. 0h x 9 8 10 11 12 7 6 5 4 3 2 112345 \u2013 5 months after 21 march\u2013 4\u2013 3\u2013 2\u2013 1number of hours above 12.2 0 sophia models the number of daylight hours in london using the points on her graph. she decides on this model. . ()sin hx 44 30 = h is the number of daylight hours above 12.2 and x is the number of months after 21 march. give a reason why sophia uses (i) the number 4.4, . . [1] (ii) the number 30. . . [1]", "14": "14 0607/62/f/m/22 \u00a9 ucles 2022 (c) sophia changes her model. h is the number of daylight hours and x is the number of months after 21 march. complete the model for h. h = [1] (d) (i) use the model in part (c) to calculate the number of daylight hours on 21 april and 21 january. april january [4] (ii) sophia thinks that the calculated values for april and january show that her model is a good one. is she correct? give a reason for your answer. . . [1] (iii) what assumption has sophia made about the months for her model? . [1]", "15": "15 0607/62/f/m/22 \u00a9 ucles 2022 [turn over 6 this table shows sunrise and sunset times for tokyo in japan on the 21st day of every month. sunrise and sunset times in tokyo month day sunrise sunset march 21 05 43 17 53 april 21 05 00 18 19 may 21 04 32 18 44 june 21 04 25 19 00 july 21 04 40 18 53 august 21 05 04 18 23 september 21 05 28 17 39 october 21 05 52 16 58 november 21 06 22 16 30 december 21 06 47 16 32 january 21 06 48 16 56 february 21 06 22 17 27 march 21 05 43 17 53 the shortest day is 21 december and the longest day is 21 june. find a model for the number of daylight hours, h, in tokyo. write your model in the form )(sin ha xcb =+ , where x is the number of months after 21 march and a, b and c are numbers to be found. h = ... [6]", "16": "16 0607/62/f/m/22 \u00a9 ucles 2022 7 this is a model of the number of daylight hours in cairo in egypt. . ()sin hx 23 01 22 =+ h is the number of daylight hours and x is the number of months after 21 march. (a) use the model to estimate the number of daylight hours on the shortest day in cairo. . [2] (b) what is the date of the shortest day in cairo according to the model? . [1]", "17": "17 0607/62/f/m/22 \u00a9 ucles 2022 8 this is a model of the number of daylight hours in melbourne in australia. .( ). sinx h 24 30 180 122 =+ + h is the number of daylight hours and x is the number of months after 21 march. (a) on the axes below sketch the models for the number of daylight hours: \u2022 in cairo \u2022 in melbourne. months after 21 marchh x 12 0daylight hours15 9 [3] (b) make a statement about the number of daylight hours in melbourne on the shortest day in cairo. . [1] (c) find the dates when the number of daylight hours in cairo is the same as it is in melbourne. . [2]", "18": "18 0607/62/f/m/22 \u00a9 ucles 2022 blank page", "19": "19 0607/62/f/m/22 \u00a9 ucles 2022 blank page", "20": "20 0607/62/f/m/22 \u00a9 ucles 2022 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge.blank page" }, "0607_s22_qp_11.pdf": { "1": "this document has 8 pages. [turn overcambridge igcse\u2122cambridge international mathematics 0607/11 paper 1 (core) may/june 2022 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *7826623390* dc (cj/cb) 302845/2 \u00a9 ucles 2022", "2": "2 0607/11/m/j/22 \u00a9 ucles 2022 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/11/m/j/22 \u00a9 ucles 2022 [turn over answer all the questions. 1 write down the mathematical name for this shape. . [1] 2 change 21 days into weeks. ... weeks [1] 3 in a shop, there are 3 red roses, 5 white roses and 4 yellow roses. milo chooses a rose at random. which colour of rose is he most likely to choose? . [1] 4 a carton contains 1 litre of juice. the juice is poured into glasses. a full glass holds 300 ml of juice. complete the statement. there are . full glasses and . ml of juice left. [2] 5 write down the value of 121. . [1]", "4": "4 0607/11/m/j/22 \u00a9 ucles 2022 6 find 53 of 30. . [1] 7 boys girls total swimming 13 30 football 26 2 28 running 3 7 cycling 8 12 total 46 34 80 the table shows the favourite sports of 80 students. complete the table. [2] 8 measure angle x. x\u00b0 x= [1] 9 complete this statement. 251 100== % [1]", "5": "5 0607/11/m/j/22 \u00a9 ucles 2022 [turn over 10 complete the mapping diagram. 12 16 20 . 407 9 11 15 21x f(x) [1] 11 three packets of sweets cost 60 cents. work out the cost of four packets of these sweets. cents [1] 12 work out. () () 57 14#-- . [2] 13 work out. 73 95# give your answer as a fraction in its lowest terms. . [2]", "6": "6 0607/11/m/j/22 \u00a9 ucles 2022 14 the value of a car is $3000. at the end of one year the value of the car has reduced by 25%. work out the value of the car at the end of one year. $ [2] 15 \u20132\u201310 1234812y 4 \u201312\u20138\u2013456 8716 x this is the graph of yx x62=- . (a) on the grid, draw the line of symmetry. [1] (b) write down the equation of this line of symmetry. . [1] 16 factorise fully. xy x 84- . [2] 17 the probability that a bus is not late is always 0.9 . heather uses the bus 20 times. work out how many times the bus is expected to arrive late. . [2]", "7": "7 0607/11/m/j/22 \u00a9 ucles 2022 [turn over 18 x\u00b0 3x\u00b020\u00b0 not to scale work out the value of x. . [2] 19 write the ratio 360 : 200 : 120 in its simplest form. : : [2] 20 solve the simultaneous equations. xy xy52 30 34 32+= += x= y= [3] questions 21, 22 and 23 are printed on the next page.", "8": "8 0607/11/m/j/22 \u00a9 ucles 2022 21 write as a single fraction. x y 23-. . [2] 22 there are 112 books on a bookshelf. 84 are paperback books ( p). 59 are fiction books ( f). 37 of the paperback books are fiction books. (a) complete the venn diagram. pu f [2] (b) find n () . pf, l . [1] (c) what type of books are represented by ()pf, l? . [1] 23 99 9k 53' =-- (a) find the value of k. k= [1] (b) using your answer to part (a) , write 9k as a fraction. . [1] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge." }, "0607_s22_qp_12.pdf": { "1": "this document has 8 pages. [turn overcambridge igcse\u2122 dc (pq/sg) 220235/1 \u00a9 ucles 2022cambridge international mathematics 0607/12 paper 1 (core) may/june 2022 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *4299481670*", "2": "2 0607/12/m/j/22 \u00a9 ucles 2022 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/12/m/j/22 \u00a9 ucles 2022 [turn over answer all the questions. 1 change 121 years into months. . months [1] 2 write 10010 as a percentage. . % [1] 3 suzy hires a car for 5 days. it cost $35 for the first day and $20 for each extra day. work out the total amount suzy pays. $ [2] 4 change 57 kilograms into grams. .. g [1] 5 these are the scores of 7 students in a spelling test. 12 8 9 7 13 10 11 (a) work out the range. . [1] (b) work out the mean. . [2]", "4": "4 0607/12/m/j/22 \u00a9 ucles 2022 6 a drawer contains 40 socks. 15 socks are black, 5 socks are grey and 20 socks are white. samir chooses one sock from the drawer at random. (a) write down the colour of sock he is most likely to choose. . [1] (b) find the probability that the sock is not black. . [1] 7 work out. ()52-- . [1] 8 120 people were asked what type of car they own. the results are shown in the pie chart. petrol dieselelectrichybrid work out how many people own an electric car. . [2]", "5": "5 0607/12/m/j/22 \u00a9 ucles 2022 [turn over 9 a rectangle measures 10 cm by 30 cm. it is enlarged by a scale factor of 3. work out the size of the new rectangle. ... cm by ... cm [2] 10 work out the value of 26. . [1] 11 find the coordinates of the mid-point of the line joining the points (0, 0) and (4, 6). (... , ...) [1] 12 a circle has circumference 16r cm. find the radius of this circle. cm [2] 13 ()xx 3 f2=+ work out ()5f. . [1]", "6": "6 0607/12/m/j/22 \u00a9 ucles 2022 14 0 56 4xy 321 \u20133\u20132\u20131 \u20131 \u20132 \u20133 \u2013 4 \u20135\u2013 4 \u20135456 3 2 1 reflect the shape in the line y1=. [2] 15 find the lowest common multiple (lcm) of 12 and 30. . [2] 16 a= {square numbers less than 20} b= {multiples of 4 less than 20} list the elements of ab+ and ab,. ab+= ab,= . [3]", "7": "7 0607/12/m/j/22 \u00a9 ucles 2022 [turn over 17 a bag contains 5 red balls and 3 blue balls. magda takes one ball at random out of the bag, notes the colour, and replaces it. she then takes another ball at random out of the bag and notes the colour. complete the tree diagram. second ball first ball red blue5 8red blue... ... .. ...red blue [2] 18 simplify. ab acb 62' . [2] 19 a c bnot to scale c is the centre of a circle. ab is a tangent to the circle at b. write down the value of angle abc . angle abc= [1] questions 20, 21, 22 and 23 are printed on the next page.", "8": "8 0607/12/m/j/22 \u00a9 ucles 2022 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge.20 a young goat is weighed. the mass of the goat is 5 kg. the next time it is weighed, its mass is 7 kg. work out the percentage increase in the mass of the goat. . % [2] 21 expand and simplify. () () xx22 13 3 -+ - . [2] 22 write 0.002 74 in standard form. . [1] 23 solve the simultaneous equations. ab26 22 += ab79 -+ = a= b= [3]" }, "0607_s22_qp_13.pdf": { "1": "this document has 8 pages. [turn overdc (rw/ct) 220236/1 \u00a9 ucles 2022 *3093229846* cambridge international mathematics 0607/13 paper 1 (core) may/june 2022 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ].cambridge igcse\u2122", "2": "2 0607/13/m/j/22 \u00a9 ucles 2022 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/13/m/j/22 \u00a9 ucles 2022 [turn over answer all the questions. 1 write 41 as a percentage. .. % [1] 26 31 3 1 2 3 the diagram shows a fair 6-sided spinner which can land on the numbers 1, 2 or 3. write down the number on which the spinner is least likely to land. . [1] 3 change 4 centilitres into millilitres. . ml [1] 4 write 26 830 correct to the nearest hundred. . [1] 5 canoe hire costs $30 per day. a canoe is hired for 7 days. work out the total cost. $ . [1] 6 the table shows some data collected in a probability experiment. put a tick ( \u2713) in each row to show whether the data is discrete or continuous. data discrete continuous score on die number of rolls of die time taken to roll die [1]", "4": "4 0607/13/m/j/22 \u00a9 ucles 2022 7 a is the point (3, 2) and b is the point (3, 8). work out the length of ab. . units [1] 8 fill in the two missing terms of the sequence. 4-, , 2, 5, 8, , \u2026 [2] 9 d bec a not to scale y 60\u00b0x\u00b0 lines ab and cd are straight lines that intersect at right angles at x. find the value of y. y= . [2] 10 simplify. ab ba 34 2 ++- . [2]", "5": "5 0607/13/m/j/22 \u00a9 ucles 2022 [turn over 11 a cuboid has a volume of cm3003. the length of the cuboid is 25 cm and the width is 4 cm. find its height. cm [2] 12 insert two pairs of brackets to make this statement correct. 3 + 2 # 5 = 5 # 4 + 6 ' 2 = 25 [2] 13 in a sale a shop reduces its prices by 10%. paula buys a coat which had an original price of $50. work out how much paula pays for the coat. $ . [2] 14 work out the size of one exterior angle of a 12-sided regular polygon. . [2]", "6": "6 0607/13/m/j/22 \u00a9 ucles 2022 15 the table shows the number of spots on each of 30 ladybirds. number of spots 0 2 7 10 13 frequency 5 2 11 9 3 work out the mean number of spots. . [3] 16 what type of correlation is shown on the scatter diagram? . [1] 17 ab \u201310 \u20132 5 6 4xy 3 2 1 \u20131456 3 2 1 describe fully the single transformation that maps triangle a onto triangle b. . . [2]", "7": "7 0607/13/m/j/22 \u00a9 ucles 2022 [turn over 18 find the highest common factor (hcf) of 15 and 65. . [1] 19 a machine produces rivets. for every 50 rivets the machine produces, 1 rivet is defective. (a) a rivet is chosen at random. find the probability that this rivet is defective. . [1] (b) in a batch of 10 000 rivets, find the expected number of defective rivets. . [2] 20 xmaths science 21 3 9u the number of students in a class studying maths and science are shown in the venn diagram. (a) write down how many students study both subjects. . [1] (b) find how many students study only one of these subjects. . [1] (c) there are 50 students altogether. x students do not study either maths or science. find the value of x. x= . [2] questions 21, 22 and 23 are printed on the next page.", "8": "8 0607/13/m/j/22 \u00a9 ucles 2022 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge.21 the width of a fibre is 0.000 019 m. write the width in standard form. .. m [1] 22 10 cm 6 cm 4 cm cb f g da e hnot to scale rectangles abcd and efgh are mathematically similar. work out eh. eh= cm [2] 23 solve. x10 751+ . [2]" }, "0607_s22_qp_21.pdf": { "1": "this document has 8 pages. [turn overcambridge igcse\u2122 dc (pq/sw) 215443/1 \u00a9 ucles 2022 *1539934785* cambridge international mathematics 0607/21 paper 2 (extended) may/june 2022 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/21/m/j/22 \u00a9 ucles 2022 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/21/m/j/22 \u00a9 ucles 2022 [turn over answer all the questions. 1 on the number line, show the inequality x231g- . \u2013 4 \u2013 3 \u2013 2 \u2013 1 0 1 2 3 4x [2] 2 work out 6 24#-eo . fp [1] 3 21 24 25 27 29 39 48 from the list of numbers, write down (a) the prime number, . [1] (b) the cube number. . [1] 4 factorise xx23-. . [1] 5 (a) write 7.297 84 correct to 3 significant figures. . [1] (b) write 0.000 003 06 in standard form. . [1] 6 solve. (a) x42 8= x= [1] (b) ()a36 24 -= a= [2]", "4": "4 0607/21/m/j/22 \u00a9 ucles 2022 7 karen has 3 blue hats, 5 red hats and 2 white hats. she also has 4 blue scarves, 3 red scarves and 1 white scarf. (a) karen takes a hat at random and replaces it. find the probability that it is white. . [1] (b) karen takes a hat and a scarf at random. find the probability that both the hat and the scarf are blue. . [2] 8 find the value of 4921. . [1] 9 write 90 as the product of its prime factors. . [2] 10 find the magnitude of the vector 2 6eo. give your answer in simplest surd form. . [2]", "5": "5 0607/21/m/j/22 \u00a9 ucles 2022 [turn over 11 (a) shade pq,. p qu [1] (b) describe the shaded area using set notation. r su . [1] (c) the venn diagram shows the number of elements in each subset. a b 53 6 2 7 1 4 2cu find (( )) bc a n++l . . [1]", "6": "6 0607/21/m/j/22 \u00a9 ucles 2022 12 (a) 32\u00b0ab cnot to scale d a, b, c, and d are points on a circle. angle \u00b0 dac 32= . . bc dc= find angle bcd . angle bcd= [2] (b) not to scaledb ac42\u00b0o e a, b and c are points on the circle centre o. ecd is a tangent to the circle at c. angle \u00b0 ace 42= . find angle aoc . angle aoc= [2]", "7": "7 0607/21/m/j/22 \u00a9 ucles 2022 [turn over 13 (a) simplify fully. 75 48 12 -+ . [2] (b) rationalise the denominator, giving your answer in its simplest form. 31 5+ . [2] 14 () xx cx d 1422-+ =+ find the value of c and the value of d. c = d = [3] questions 15 and 16 are printed on the next page.", "8": "8 0607/21/m/j/22 \u00a9 ucles 2022 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge.15 (a) factorise fully. xx67 32-- . [2] (b) solve. xx67 3021 -- . [3] 16 solve. logl og logp 23 2-= p= . [2]" }, "0607_s22_qp_22.pdf": { "1": "this document has 8 pages. [turn overcambridge igcse\u2122 dc (kn/sg) 214829/1 \u00a9 ucles 2022 *5358682218* cambridge international mathematics 0607/22 paper 2 (extended) may/june 2022 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/22/m/j/22 \u00a9 ucles 2022 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area =a c bcb a", "3": "3 0607/22/m/j/22 \u00a9 ucles 2022 [turn over answer all the questions. 1 work out. (. ) 0032 . [1] 2 (a) write the fraction 4015 in its lowest terms. . [1] (b) work out. 32 92+ . [2] 3 solve the equation. x11 4 -= - x= [1] 4 change cm6003 into m3. m3 [1] 5 work out 6431 . . [1]", "4": "4 0607/22/m/j/22 \u00a9 ucles 2022 6 63\u00b0 75\u00b0not to scalea b ced ab is parallel to cd. find angle acd . angle acd = [1] 7 kendra jogs 7 km in 45 minutes. she then runs at 12 km/h for 30 minutes. find her average speed in km/h for the whole journey. . km/h [3] 8 the mean of eight numbers is 25. when two extra numbers are included the mean of the ten numbers is 24. find the mean of the two extra numbers. . [2]", "5": "5 0607/22/m/j/22 \u00a9 ucles 2022 [turn over 9 solve the simultaneous equations. xy xy52 12 35+= - -= - x = y = [3] 10 a is the point (\u20131, 13) and b is the point (3, 1). find the equation of the line ab, giving your answer in the form ym xc=+ . y = [3] 11 solve. xx65 602-- = x = ... or x = ... [3]", "6": "6 0607/22/m/j/22 \u00a9 ucles 2022 12 the lengths of the sides of a triangle are 3 cm, 4 cm and 5 cm. find the sine of the smallest angle. . [1] 13 john goes to a shop that sells newspapers and magazines only. (a) complete the table of probabilities of john buying something at the shop. buys a newspaper does not buy a newspaper total buys a magazine 0.40 does not buy a magazine 0.25 total 0.55 1.00 [2] (b) find the probability that john buys a magazine but not a newspaper. . [1] 14 ()xx 23 f=+ find the values of x when ()x 15 f= . . [2]", "7": "7 0607/22/m/j/22 \u00a9 ucles 2022 [turn over 15 a bag has 5 black counters, 4 white counters and 1 red counter. one counter is chosen at random and is replaced. a second counter is then chosen at random. find the probability that the two counters chosen are different colours. . [4] 16 solve. logl og logl og x19 8232=+ -+ x = [3] question 17 is printed on the next page.", "8": "8 0607/22/m/j/22 \u00a9 ucles 2022 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge.17 (a) expand the brackets and simplify. ab ab +- `` jj . [2] (b) rationalise the denominator. 71 6+ . [1] (c) work out the value of 911111 87 76 65 54 8 ++++ +++++ . . [2]" }, "0607_s22_qp_23.pdf": { "1": "this document has 8 pages. [turn overcambridge igcse\u2122 dc (ce/fc) 303202/2 \u00a9 ucles 2022 *7852959116* cambridge international mathematics 0607/23 paper 2 (extended) may/june 2022 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf calculators must not be used in this paper. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods even if your answer is incorrect. \u25cf all answers should be given in their simplest form. information \u25cf the total mark for this paper is 40. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/23/m/j/22 \u00a9 ucles 2022 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/23/m/j/22 \u00a9 ucles 2022 [turn over answer all the questions. 1 work out. (a) ..03 02# . [1] (b) . 12 04' . [1] 2 this is a list of 8 numbers. 11 7 8 13 7 14 15 5 (a) find the median. . [2] (b) an extra number is added to the list. the mean of the nine numbers is 1 more than the mean of the eight numbers. find the ninth number. . [3] 3 show this inequality on the number line. x 341g - x\u20136 \u20135 \u2013 4 \u20133 \u20132 \u20131 0 1 2 3 4 5 6 [2]", "4": "4 0607/23/m/j/22 \u00a9 ucles 2022 4 (a) express 175 as the product of its prime factors. . [2] (b) kurt has two timers. one is set to ring every 175 minutes. the other is set to ring every 70 minutes. both timers ring together at 09 15. find the time when the timers next ring together. . [3] 5 expand. ()x32 1- . [1] 6 find the exterior angle of a regular polygon with 15 sides. . [2]", "5": "5 0607/23/m/j/22 \u00a9 ucles 2022 [turn over 7 eggs are graded into four sizes: extra large, large, medium and small. a farmer records the sizes of a sample of 100 eggs that she collects. the results are shown in the table. size extra large large medium small number of eggs 28 36 24 12 (a) find the relative frequency for large eggs. . [1] (b) in one month, the farmer collects 2500 eggs. calculate an estimate for the number of these eggs that are small. . [2] 8 factorise fully. cx dx cx d 222-- + . [2]", "6": "6 0607/23/m/j/22 \u00a9 ucles 2022 9 not to scalee f c b ad abcd is a parallelogram. eda and efb are straight lines. (a) show that triangles edf and bcf are similar. [2] (b) bc = 4 cm, de = 5 cm and fb = 3 cm. find ef. ef = ... cm [2]", "7": "7 0607/23/m/j/22 \u00a9 ucles 2022 [turn over 10 a is the point ( -5, 7) and c is the point (1, -2). (a) b is the mid-point of ac. find the coordinates of b. (... , ...) [2] (b) the line cd is perpendicular to the line ac. find the equation of line cd. . [4] 11 y is inversely proportional to ()x22+ . when x = 3, y = 2. (a) find y in terms of x. y = [2] (b) find the positive value of x when y = 0.5 . x = [2] question 12 is printed on the next page.", "8": "8 0607/23/m/j/22 \u00a9 ucles 2022 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge.12 a4 10=-eo b4 2=-eo find the magnitude of the vector a - b. give your answer in its simplest surd form. . [4]" }, "0607_s22_qp_31.pdf": { "1": "this document has 16 pages. [turn overcambridge igcse\u2122cambridge international mathematics 0607/31 paper 3 (core) may/june 2022 1 hour 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 96. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *4089846623* dc (cj/sg) 304968/2 \u00a9 ucles 2022", "2": "2 0607/31/m/j/22 \u00a9 ucles 2022 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/31// m/j/22 \u00a9 ucles 2022 [turn over answer all the questions. 1 (a) write the number 20 202 in words. . [1] (b) work out. ... 1756272 48+ . [1] (c) write down all the factors of 42. ... [2] (d) write down a prime number between 15 and 20. . [1] (e) write 7832.948 (i) correct to 2 decimal places, . [1] (ii) correct to 4 significant figures, . [1] (iii) correct to the nearest 100. . [1] (f) insert the symbols (),, ,# +- so that the following statement is correct. 5 3 4 1 = 9 [1] (g) jeffrey invests $550 for 3 years at a rate of 3.2% per year simple interest. work out the interest he receives. $ [2]", "4": "4 0607/31/m/j/22 \u00a9 ucles 2022 2 wim measures the amount of rain, in mm, each day for 31 days. the bar chart shows his results. amount of rain (mm)number of days 0012345678910 1 2 3 4 5 (a) write down the mode. .. mm [1] (b) write down the number of days that had no rain. . [1] (c) work out the mean amount of rain per day. .. mm [2] (d) wim picks one of these days at random. find the probability that, on that day, the amount of rain was 3 mm or more. . [1]", "5": "5 0607/31// m/j/22 \u00a9 ucles 2022 [turn over 3 4.2 cma ob e c dnot to scale the diagram shows a circle, centre o, radius 4.2 cm. a, b and c are points on the circle. the line de touches the circle at c. (a) write down the mathematical name for each of these straight lines. ac is a .. de is a .. ab is a .. [3] (b) work out (i) the circumference of the circle, cm [2] (ii) the area of the circle. .. cm2 [2] (c) angle aob = 110\u00b0. calculate the area of sector aob . .. cm2 [2]", "6": "6 0607/31/m/j/22 \u00a9 ucles 2022 4 10 9 8 7 6 5 4 3 2 1 0 \u2013 1 \u2013 2\u2013 1 1 2 3 4 5 6 7 \u2013 2 \u2013 3xy a c the diagram shows point a and point c plotted on a 1 cm2 grid. (a) plot point (, ) b57 and point (, ) d 17- and draw the quadrilateral abcd . [2] (b) (i) find the length of ac. ac= ... cm [1] (ii) use pythagoras\u2019 theorem to find the length of ab. ab= ... cm [2] (c) write down the mathematical name for quadrilateral abcd . . [1] (d) reflect quadrilateral abcd in the line y4=. [2]", "7": "7 0607/31// m/j/22 \u00a9 ucles 2022 [turn over 5 (a) solve. (i) x69 6= x= [1] (ii) x76 13 -= - x= [2] (b) simplify. (i) rr r 52-- . [1] (ii) a bab 4 372--+ . [2] (c) tm n 42=+ find (i) the value of t when . m 18= and . n 03=- , t= [2] (ii) the value of n when t26= and . m 34= . n= [2]", "8": "8 0607/31/m/j/22 \u00a9 ucles 2022 6 30 members of a sports club were asked what their favourite game was. they could choose from tennis (t), squash (s) or badminton (b). these are the results. b t s s t s b b t s s s s t t t s s b t b t s s t t b s s t (a) complete the frequency table. game frequency tennis (t) squash (s) badminton (b) [2] (b) find how many more members chose tennis than badminton. . [1] (c) one of the 30 members is chosen at random. write down the probability that this member chose squash. . [1]", "9": "9 0607/31// m/j/22 \u00a9 ucles 2022 [turn over (d) shadana begins to draw a pie chart to show the results. (i) show that the sector angle for tennis is 132\u00b0. [2] (ii) complete the pie chart for shadana. [3]", "10": "10 0607/31/m/j/22 \u00a9 ucles 2022 7 gheza wants to know if the number of weeks that a song is number one in the charts is related to the length of the song, in minutes. the table shows the results for one year. number of weeks at number one 3 2 1 5 4 11 7 4 3 3 9 length of song (minutes) 3.5 3.9 4.2 3.1 3.2 2.5 2.9 3.0 3.4 3.7 2.9 (a) complete the scatter diagram. the first 6 points have been plotted for you. 012345 0 1 2 3 4 5 6 number of weeks at number one7 8 9 10 11length of song (minutes) [2] (b) what type of correlation is shown in the diagram? . [1]", "11": "11 0607/31// m/j/22 \u00a9 ucles 2022 [turn over (c) find (i) the mean number of weeks at number one, . [1] (ii) the mean length of a song. .. min [1] (d) on the scatter diagram, draw a line of best fit. [2]", "12": "12 0607/31/m/j/22 \u00a9 ucles 2022 8 (a) the nth term of a sequence is n232+. write down the first three terms of this sequence. , , [2] (b) these are the first four terms of a different sequence. 5 3- 11- 19- (i) find the next two terms of the sequence. , ... [2] (ii) find the nth term of the sequence. . [2] (iii) sanjay says that 101- is a term of the sequence. show that he is not correct. [2]", "13": "13 0607/31// m/j/22 \u00a9 ucles 2022 [turn over 9 cb a7 6 5 4 3 2 1 0 \u2013 1 \u2013 2 \u2013 3 \u2013 4\u2013 1 1 2 3 4 5 6 7 \u2013 2 \u2013 3 \u2013 4xy (a) describe fully the single transformation that maps shape a onto shape b. . [3] (b) describe fully the single transformation that maps shape a onto shape c. . [2] (c) rotate shape a 90\u00b0 clockwise about (0, 0). [2]", "14": "14 0607/31/m/j/22 \u00a9 ucles 2022 10 not to scale16 0 \u2013 123 \u2013 4xy the diagram shows a sketch of the graph of .. yx xx 05 0652 232=+ -+ for x43gg- . (a) find the coordinates of the point where the graph crosses the y-axis. ( ... , ... ) [1] (b) find the coordinates of the point where the graph crosses the x-axis. ( ... , ... ) [1] (c) find the coordinates of the local maximum. ( ... , ... ) [2] (d) find the coordinates of the local minimum. ( ... , ... ) [2] (e) on the diagram, sketch the graph of y8=. [1] (f) solve this equation. ..xx x 05 0652 2832+- += . x= [1] ", "15": "15 0607/31// m/j/22 \u00a9 ucles 2022 [turn over 11 x\u00b0y\u00b0a bo14 cm not to scale the diagram shows a regular hexagon with centre andc m oo ao b14 == . (a) work out the size of angle x and the size of angle y. x= y= [2] (b) write down the length of ab. ab= ... cm [1] (c) work out the area of triangle aob . .. cm2 [3] the regular hexagon is the cross-section of a prism. the length of the prism is 5 cm. (d) work out the volume of the prism. .. cm3 [2] question 12 is printed on the next page.", "16": "16 0607/31/m/j/22 \u00a9 ucles 2022 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge.12 ruben\u2019s house is 1.3 km from the supermarket. (a) he walks to the supermarket at a speed of 5 km / h. work out how long it takes him. give your answer in minutes and seconds. min s [3] (b) on another day, ruben cycles to the supermarket in a time of 5 minutes 12 seconds. (i) show that 12 seconds = 0.2 minutes. [1] (ii) work out ruben\u2019s average speed when cycling to the supermarket. give your answer in km / h. ... km / h [2]" }, "0607_s22_qp_32.pdf": { "1": " [turn overdc (nf/sw) 214443/2 \u00a9 ucles 2022this document has 16 pages. *5214594003* cambridge international mathematics 0607/32 paper 3 (core) may/june 2022 1 hour 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 96. \u25cf the number of marks for each question or part question is shown in brackets [ ].cambridge igcse\u2122", "2": "2 0607/32/m/j/22 \u00a9 ucles 2022 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/32/m/j/22 \u00a9 ucles 2022 [turn over answer all the questions. 1 (a) 21 22 23 24 25 26 27 28 29 from this list of numbers, write down (i) an even number, . [1] (ii) a multiple of 6, . [1] (iii) a factor of 100, . [1] (iv) a prime number. . [1] (b) find the value of (i) , 841 . [1] (ii) .63 . [1] (c) work out. ... 521325 3551+ give your answer correct to 2 decimal places. . [2]", "4": "4 0607/32/m/j/22 \u00a9 ucles 2022 2 2 0y x 24 135 4 1 3 5 6a db c quadrilateral abcd is drawn on a 1 cm square grid. (a) write down the mathematical name of quadrilateral abcd . . [1] (b) write down the coordinates of point b. ( . , ..) [1] (c) work out the area and the perimeter of quadrilateral abcd . area ... cm2 perimeter ... cm [2] (d) on the diagram, draw the lines of symmetry of quadrilateral abcd . [2]", "5": "5 0607/32/m/j/22 \u00a9 ucles 2022 [turn over 3 (a) these are the first four terms of a sequence. 4 8 12 16 (i) write down the next two terms of this sequence. . , . [1] (ii) write down the rule for continuing this sequence. . [1] (iii) find the nth term of this sequence. . [1] (b) look at the patterns of numbers in this table. row 1 20 19 3922-= row 2 13 19 8722-= row 3 3 18 17 522-= row 4 13 17 6322-= row 5 row 8 (i) complete row 5 of the table. [1] (ii) complete row 8 of the table. [2] (iii) find the nth term of this sequence. 39 37 35 33 . [2]", "6": "6 0607/32/m/j/22 \u00a9 ucles 2022 4 108\u00b0not to scaley\u00b0 x\u00b0q b c pa in the diagram, aqb and pbc are straight lines and . pq pb= (a) what type of triangle is bpq ? . [1] (b) find the value of x. x= [3] (c) find the value of y. y= [1] (d) ab and bc are two sides of a regular polygon. work out the number of sides of this polygon. . [2]", "7": "7 0607/32/m/j/22 \u00a9 ucles 2022 [turn over 5 (a) the table shows the melting point, in \u00b0c, of some metals. metal melting point (\u00b0c) zinc 420 gold 1063 silver 893 copper 1084 aluminium 660 (i) write these five temperatures in order of size starting with the smallest. . , . , . , . , . [1] smallest (ii) write 1063 correct to the nearest 10. . [1] (iii) write 1084 in words. . [1] (b) brass can be made by combining copper and zinc in this ratio. copper : zinc = 13 : 7 work out the mass of copper and the mass of zinc used to make 60 kg of brass. copper .. kg zinc .. kg [2]", "8": "8 0607/32/m/j/22 \u00a9 ucles 2022 6 (a) (i) a train travels from amsterdam to brussels in 2 hours 15 minutes. it leaves amsterdam at 11 10. work out the time the train arrives in brussels. . [1] (ii) on its return journey, the train leaves brussels at 14 50. it arrives in amsterdam at 17 15. work out the length of time this journey took. give your answer in hours and minutes. ... h ... min [1] (b) one day, the adult train fare from amsterdam to brussels is 75 euros. (i) the fare for a child is 53 of the adult fare. work out the child fare for the journey. euros [1] (ii) on another day the adult fare of 75 euros is increased by 12%. work out the adult fare on this day. euros [2] (c) the train from amsterdam to brussels travels 180 km in 2 hours 15 minutes. work out the average speed of the train in kilometres per hour. km / h [2]", "9": "9 0607/32/m/j/22 \u00a9 ucles 2022 [turn over 7 the graph shows the cost, y dollars, of printing x cards. 0010203040 10 20 30 number of cardscost ($) 40 50y x (a) (i) find the cost of printing 45 cards. $ [1] (ii) find the largest number of cards that can be printed for $28. . [1] (b) (i) find the equation of the line in the form . ym xc=+ y= [3] (ii) any number of cards can be printed. steffi needs 100 cards. use your equation from part (b)(i) to find how much these will cost. $ [2]", "10": "10 0607/32/m/j/22 \u00a9 ucles 2022 8 y x20 \u2013 5\u2013 4 0 3 (a) on the diagram, sketch the graph of yx x32=+ for . x 43gg- [2] (b) on the diagram, sketch the graph of yx26=+ for . x 43gg- [2] (c) find the coordinates of each point of intersection of yx x32=+ and . yx 26=+ ( . , . ) and ( . , . ) [2] 9 (a) complete each of these statements using 1 or 2 . 11 . 7 11- . 7- [1] (b) simplify. (i) xx x 35++ . [1] (ii) ptpt62 43 -- + . [2]", "11": "11 0607/32/m/j/22 \u00a9 ucles 2022 [turn over (c) factorise fully. xx y 12 3+ . [2] (d) solve. (i) x 55= x= [1] (ii) xx73 35 += + x= [2] (e) yx62= (i) find the value of y when x = 5. y= [1] (ii) find the value of x when y = 294. x= [2] (iii) rearrange the formula y = 6x2 to make x the subject. x= [2]", "12": "12 0607/32/m/j/22 \u00a9 ucles 2022 10 a garage sells used cars. the table shows the selling price, in $, and the distance travelled, in km, of eight used cars. all cars are of the same make and model. distance travelled (km)8000 15 000 25 000 22 000 34 000 2000 40 000 46 000 selling price ($) 7300 5000 3900 5500 4000 6000 2000 2300 (a) complete the scatter diagram. the first four points have been plotted for you. 002000400060008000 1000300050007000 10 000 20 000 30 000 distance travelled (km)selling price ($) 40 000 50 000 [2] (b) what type of correlation is shown in the scatter diagram? [1] (c) the mean distance travelled is 24 000 km and the mean selling price is $4500. on the scatter diagram, draw a line of best fit. [2] (d) another used car of this make and model had travelled a distance of 30 000 km. use your line of best fit to estimate the selling price of this car. $ [1]", "13": "13 0607/32/m/j/22 \u00a9 ucles 2022 [turn over 11 b ad ec68\u00b0 54 mm 35 mm45 mmnot to scale the diagram shows three right-angled triangles abc , bcd and cde . , ac 54mm= , cd 45mm= ce 35mm= and angle \u00b0. bac 68= (a) use trigonometry to show that , bc 134mm = correct to the nearest mm. [2] (b) use trigonometry to find angle bcd . angle bcd= [2] (c) use pythagoras\u2019 theorem to find de. de= .. mm [2]", "14": "14 0607/32/m/j/22 \u00a9 ucles 2022 12 the table shows the frequency distribution for the masses, in kg, of 100 students. mass ( m kg) m 30 401g m 00451g m 00561g m 00671g m 00781g m 00891g frequency 16 23 28 18 11 4 (a) complete the cumulative frequency table. mass ( m kg) m 40g m 05g m 06g m 07g m 08g m 09g cumulative frequency [2] (b) on the grid below, draw the cumulative frequency curve for this data. 30020406080 10305070100 90 50 70 90 mass (m kg)cumulative frequency 40 60 80 [3]", "15": "15 0607/32/m/j/22 \u00a9 ucles 2022 [turn over (c) use your cumulative frequency curve to find an estimate of (i) the median, . kg [1] (ii) the interquartile range. kg [2] (d) use your cumulative frequency curve to find an estimate for the number of students with a mass of less than 68 kg. . [1] question 13 is printed on the next page.", "16": "16 0607/32/m/j/22 \u00a9 ucles 2022 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge.13 (a) a cube has edges of length 3 cm. not to scale 3 cm (i) find the volume of the cube. ... cm3 [2] (ii) find the total surface area of the cube. ... cm2 [2] (b) not to scale15 cm 20 cm 30 cm some cubes, each with edges of length 3 cm, are placed in a box. the box is a cuboid with dimensions 30 cm by 20 cm by 15 cm. work out the greatest number of these cubes that can be placed in the box. . [3]" }, "0607_s22_qp_33.pdf": { "1": "this document has 20 pages. any blank pages are indicated. [turn overcambridge igcse\u2122 *3445827789* dc (ce/sg) 303913/2 \u00a9 ucles 2022cambridge international mathematics 0607/33 paper 3 (core) may/june 2022 1 hour 45 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 96. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/33/m/j/22 \u00a9 ucles 2022 formula list area, a, of triangle, base b, height h. a = bh21 area, a, of circle, radius r. a = r2r circumference, c, of circle, radius r. c = 2rr curved surface area, a, of cylinder of radius r, height h. a = 2rrh curved surface area, a, of cone of radius r, sloping edge l. a = rrl curved surface area, a, of sphere of radius r. a = r42r v olume, v, of prism, cross-sectional area a, length l. v = al v olume, v, of pyramid, base area a, height h. v = ah31 v olume, v, of cylinder of radius r, height h. v = rh2r v olume, v, of cone of radius r, height h. v = rh31 2r v olume, v, of sphere of radius r. v = r34 3r", "3": "3 0607/33/m/j/22 \u00a9 ucles 2022 [turn over answer all the questions. 1 (a) write sixteen thousand and twenty-four in numbers. . [1] (b) write 852 as a decimal. . [1] (c) write down the square number between 10 and 20. . [1] (d) work out ... 26 5832 + . give your answer correct to 5 significant figures. . [2] (e) find the value of .4234. give your answer correct to 1 decimal place. . [2] (f) kelly buys candy bars that cost $0.72 each. he buys the greatest number of candy bars he can with $8. (i) work out the number of candy bars that he buys. . [2] (ii) work out how much change he receives. $ [1]", "4": "4 0607/33/m/j/22 \u00a9 ucles 2022 2 the table shows the type of doughnut and the number of doughnuts sold in a shop on one day. type sugar raisin cream jam iced number 2000 2500 1500 1250 750 (a) find the total number of doughnuts sold. . [1] (b) write down the most popular type of doughnut. . [1] (c) work out how many more jam doughnuts were sold than iced doughnuts. . [1] (d) work out the fraction of the doughnuts sold that were jam doughnuts. give your answer as a fraction in its simplest form. . [2] (e) write the ratio 1500 : 1250 : 750 in its simplest form. ... : .. : .. [2]", "5": "5 0607/33/m/j/22 \u00a9 ucles 2022 [turn over (f) on the grid below, complete the bar chart to show the information in the table. 050010001500200025003000 number of doughnuts sold sugar raisin cream type of doughnutjam iced [2] (g) sugar doughnuts cost $1.25 each. raisin doughnuts cost $1.50 each. work out the total cost of 5 sugar doughnuts and 3 raisin doughnuts. $ [2]", "6": "6 0607/33/m/j/22 \u00a9 ucles 2022 3 (a) this shape is drawn on a 1 cm2 grid. work out the perimeter and the area of the shape. give the units of each answer. perimeter ... ... area ... ... [3] (b) add one more square to the shape above so that the shape has rotational symmetry of order 2. [1]", "7": "7 0607/33/m/j/22 \u00a9 ucles 2022 [turn over (c) (i) add one more square to the shape above so that the shape has line symmetry. [1] (ii) on your shape, draw the line of symmetry. [1]", "8": "8 0607/33/m/j/22 \u00a9 ucles 2022 4 \u2013 4\u2013 3\u2013 2\u2013 1123456 0 \u2013 1 1 2 3 4 5 6 7 \u2013 2 \u2013 3 \u2013 4 \u2013 5 \u2013 6 \u2013 7y x ca b d the diagram shows quadrilateral abcd drawn on a 1 cm2 grid. (a) write down the coordinates of points a, b and c. a (...\u200a\u200a,\u200a\u200a...) b (...\u200a\u200a,\u200a\u200a...) c (...\u200a\u200a,\u200a\u200a...) [3] (b) write down the mathematical name of (i) quadrilateral abcd , . [1] (ii) triangle bcd . . [1]", "9": "9 0607/33/m/j/22 \u00a9 ucles 2022 [turn over (c) use pythagoras\u2019 theorem to calculate the length of ad. ad = ... cm [2] (d) use trigonometry to calculate angle dcb . angle dcb = [2] (e) reflect quadrilateral abcd in the y-axis. [1]", "10": "10 0607/33/m/j/22 \u00a9 ucles 2022 5 to hire a van, a company charges $2.50 for each kilometre travelled plus a fixed charge of $800. (a) the total cost is t dollars when the distance travelled is k kilometres. write an equation for t in terms of k. . [2] (b) kiera hires a van and travels 324 kilometres. find the total amount she has to pay. $ [2] (c) misty hires a van and pays $1045. find how many kilometres she travels. ... km [2]", "11": "11 0607/33/m/j/22 \u00a9 ucles 2022 [turn over 6 the cumulative frequency curve shows the heights, in cm, of 100 adult emperor penguins. 0 100 105 110 115 height (cm)120 125 130102030405060708090100 cumulative frequency use the curve to estimate (a) the median, cm [1] (b) the lower quartile, cm [1] (c) the interquartile range, cm [1] (d) the number of emperor penguins that have a height of 120 cm or more. . [2]", "12": "12 0607/33/m/j/22 \u00a9 ucles 2022 7 greta joins a gym for one year. (a) she can pay her membership every week, every month or in one payment for the whole year. payment type cost weekly $5.95 monthly $25.00 yearly $297.75 work out which payment type is the cheapest. show all your working. . [3] (b) on the cycle machine, greta cycles a distance of 3.2 km in 10 minutes. work out her average speed in km/h. . km/h [2] (c) on the treadmill, greta walks at 6.3 km/h. (i) work out the distance she walks in 27 minutes. give your answer in kilometres. ... km [2] (ii) change 6.3 km/h to m/min. .. m/min [2]", "13": "13 0607/33/m/j/22 \u00a9 ucles 2022 [turn over 8 c5 cm b136\u00b0not to scale da o the diagram shows a circle, centre o, radius 5 cm. angle aob = 136\u00b0 and cbd is a tangent to the circle at b. (a) find the size of (i) angle obc , angle obc = [1] (ii) angle oab , angle oab = [2] (iii) angle abd . angle abd = [1] (b) show that the area of the minor sector aob is 29.7 cm2, correct to 1 decimal place. [2] (c) work out the length of the minor arc ab. cm [2]", "14": "14 0607/33/m/j/22 \u00a9 ucles 2022 9 (a) solve. (i) x64 2= x = [1] (ii) x42 2-= x = [2] (b) factorise completely. bb71 42- . [2] (c) expand. ()a42 5- . [2] (d) solve the simultaneous equations. show all your working. ab ab52 12 61 1-= += a = b = [3]", "15": "15 0607/33/m/j/22 \u00a9 ucles 2022 [turn over (e) find the value of x in each of the following. (i) aaax 26 = x = [1] (ii) aa ax 31 5#= x = [1] (f) write as a single fraction in its simplest form. (i) xx 3 52+ . [2] (ii) mn mn 5 1522 ' . [3]", "16": "16 0607/33/m/j/22 \u00a9 ucles 2022 10 y x10 \u2013 10\u2013 2 2 0 (a) on the diagram, sketch the graph of yxx1 3=+ for values of x between 2- and 2. [2] (b) write down the equation of the vertical asymptote. . [1] (c) find the coordinates of the local minimum. (...\u200a\u200a,\u200a\u200a...) [2] (d) on the same diagram, sketch the graph of yx5= for x22gg- . [2] (e) solve the equation xxx153+= for values of x between 2- and 2. . and . [2] ", "17": "17 0607/33/m/j/22 \u00a9 ucles 2022 11 the probability that it snows on any day in february is 106. if it snows, the probability that maud goes for a walk is 52. if it does not snow, the probability that maud goes for a walk is 75. (a) complete the tree diagram to show this information. .. .. .. snowsgoes for a walk does not go for a walk goes for a walk does not go for a walkdoes not snow106 [3] (b) one day in february is chosen at random. find the probability that it snows and maud does not go for a walk. . [2]", "18": "18 0607/33/m/j/22 \u00a9 ucles 2022 blank page", "19": "19 0607/33/m/j/22 \u00a9 ucles 2022 blank page", "20": "20 0607/33/m/j/22 \u00a9 ucles 2022 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge.blank page" }, "0607_s22_qp_41.pdf": { "1": "this document has 20 pages. any blank pages are indicated. [turn overcambridge igcse\u2122cambridge international mathematics 0607/41 paper 4 (extended) may/june 2022 2 hours 15 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 120. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *6483893081* dc (cj/cb) 215444/1 \u00a9 ucles 2022", "2": "2 0607/41/m/j/22 \u00a9 ucles 2022 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/41/m/j/22 \u00a9 ucles 2022 [turn over answer all the questions. 1 \u2013 4 \u2013 3 \u2013 2 \u2013 1 \u2013 1 \u2013 2 \u2013 31 023 1 2 3 4y x t p (a) translate triangle t by the vector 2 2-eo . [2] (b) reflect triangle t in the line . y 05= . [2] (c) describe fully the single transformation that maps triangle p onto triangle t. . . [3] (d) enlarge triangle p with scale factor 2-, centre (, ) 31-. [2]", "4": "4 0607/41/m/j/22 \u00a9 ucles 2022 2 (a) the cumulative frequency curve shows the marks for 300 students in a history test. 050100150200250300 0 10 20 30 40 50 history markcumulative frequency (i) find an estimate for the median. . [1] (ii) estimate the number of students with a mark of more than 20. . [2] (iii) 70% of the students pass the test. find the pass mark. . [2]", "5": "5 0607/41/m/j/22 \u00a9 ucles 2022 [turn over (b) the table shows the marks for 100 students in a geography test. mark m m 10 201g m 00231g m 00341g m 00451g frequency 2 28 57 13 calculate an estimate of the mean. . [2] (c) the table shows the marks for 9 students in chemistry and in physics. chemistry mark ( x)33 28 39 40 22 25 38 43 36 physics mark ( y)45 32 26 49 18 36 29 40 35 (i) find the equation of the regression line for y in terms of x. y= [2] (ii) what type of correlation is seen in this data? . [1] (iii) use your answer to part (c)(i) to estimate the physics mark for a student with a mark of 30 in chemistry. . [1]", "6": "6 0607/41/m/j/22 \u00a9 ucles 2022 3 y x\u2013 3 \u2013 55 0 1 ()fxxx241 2=+ - (a) on the diagram, sketch the graph of ()f yx= for values of x between 3- and 1. [3] (b) write down the equation of the asymptote of the graph. . [1] (c) find the coordinates of the local maximum. (... , ...) [1] (d) g()xx x53=- for x31gg- . solve () g() fxxg . . [4]", "7": "7 0607/41/m/j/22 \u00a9 ucles 2022 [turn over 4 (a) $216 is shared in the ratio 5 : 1. work out the larger share. $ [2] (b) luis shares some money between ali, betty and clare in the ratio 3 : 4 : 6. ali receives $171. find the total amount of money luis shared. $ [2] (c) farima invests $1400 in a savings account paying simple interest at a rate of 2.5% per year. calculate the total amount in the account at the end of 3 years. $ [3] (d) emir invests $3000 at a rate of 2% per year compound interest. (i) calculate the value of emir\u2019s investment at the end of 4 years. $ . [2] (ii) find the number of complete years until emir\u2019s investment is first worth more than $4000. . [4]", "8": "8 0607/41/m/j/22 \u00a9 ucles 2022 5 a sequence of patterns is made using grey tiles and white tiles. pattern 1 pattern 2 pattern 3 (a) complete the table. pattern number 1 2 3 4 n number of grey tiles 6 10 number of white tiles 0 2 [6] (b) find and simplify an expression for the total number of tiles in pattern n. . [1] (c) pattern k has a total of 600 tiles. find the number of grey tiles in pattern k. . [4]", "9": "9 0607/41/m/j/22 \u00a9 ucles 2022 [turn over (d) the tiles in a pattern are put in a bag. the probability of taking a grey tile from the bag at random is 125. a tile is taken from the bag at random and replaced. this is repeated 3 times. find the probability that all 3 tiles are white. . [2] (e) all the grey tiles from pattern 4 are put in a bag. two tiles are taken from the bag at random without replacement. find the probability that one tile came from a corner of the pattern and the other did not. . [3]", "10": "10 0607/41/m/j/22 \u00a9 ucles 2022 6 (a) obc a30\u00b05 cmnot to scale the diagram shows a circle, centre o, with radius 5 cm. ba and bc are tangents to the circle at a and c. angle abc \u00b030= . calculate the area of the shaded minor segment. . cm2 [4]", "11": "11 0607/41/m/j/22 \u00a9 ucles 2022 [turn over (b) not to scaleoo de d e40\u00b0 12 cmheight the circle, centre o, has radius 12 cm. angle \u00b0 doe 40= . the minor sector doe is removed. the major sector is formed into a cone by joining od to oe. calculate the height of the cone. cm [5]", "12": "12 0607/41/m/j/22 \u00a9 ucles 2022 7 abbi makes wooden boards in three sizes, small, medium and large. they are all cuboids. the medium board has height 2 cm, width 23 cm and length 50 cm. (a) calculate the volume of the medium board. . cm3 [2] (b) the small board is mathematically similar to the large board. the small board has a volume of .cm 28753and a height of 1.15 cm. the large board has a volume of cm 184003. (i) find the height of the large board. cm [3] (ii) is the medium board mathematically similar to the large board? explain how you decide. ... because ... . [3]", "13": "13 0607/41/m/j/22 \u00a9 ucles 2022 [turn over 8 (a) a is the point (, ) 11 7- and b is the point (, ) 81 3- . find the length of ab. . [3] (b) p is the point (, ) 25- and q is the point (, ) 611. line l is perpendicular to pq and crosses pq at point r. the ratio pr : rq = 3 : 1. find the equation of line l. . [6]", "14": "14 0607/41/m/j/22 \u00a9 ucles 2022 9 (a) () () () fg h xx xx x 23 24 3x=+ =- = (i) find f(5). . [1] (ii) find and simplify g(f( x)). . [2] (iii) find ()gx1-. ()gx1=- [2] (iv) solve ()hx 48= . . [2]", "15": "15 0607/41/m/j/22 \u00a9 ucles 2022 [turn over (b) (i) the diagram shows a sketch of the graph of ()j yx= . y x\u2013 10 \u2013 5 5 10 \u2013 55 010 \u2013 10j(x) on the same diagram, sketch the graph of ()j yx 2 =+ . [1] (ii) the diagram shows the graphs of () () ka nd m yx yx == . y x\u2013 5 3 \u2013 55 0k(x) m(x)10 \u2013 10 write ()kx in terms of ()mx. ()kx= [1]", "16": "16 0607/41/m/j/22 \u00a9 ucles 2022 10 (a) simplify fully. xy yx 34 122 ' . [2] (b) write as a single fraction in its simplest form. xx 31 23 --- . [3] (c) the nth term of a sequence is an bn 52+- . the second term of this sequence is 3- and the third term is 4. find the value of a and the value of b. you must show all your working. a= b= [6]", "17": "17 0607/41/m/j/22 \u00a9 ucles 2022 [turn over 11 2.1 m 0.9 m110\u00b0 110\u00b0not to scale the diagram shows the symmetrical cross-section of a ditch containing water. the angle between the base and each side of the ditch is 110\u00b0. the width of the base is 0.9 m and the depth of the water is 2.1 m. the ditch is 100 m long. (a) calculate the volume of water in the ditch. . m3 [4] (b) on a different day, the ditch contains m3003of water. water is pumped out of the ditch at a rate of 4.2 litres per second. calculate the time taken to empty the ditch completely. give your answer in hours and minutes, correct to the nearest minute. ... h ... min [4]", "18": "18 0607/41/m/j/22 \u00a9 ucles 2022 12 22 m16 m9 m80\u00b0 115\u00b0b cdanot to scale (a) calculate the area of triangle bcd . m2 [2] (b) calculate angle adb . angle adb = [6]", "19": "19 0607/41/m/j/22 \u00a9 ucles 2022 blank page", "20": "20 0607/41/m/j/22 \u00a9 ucles 2022 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge.blank page" }, "0607_s22_qp_42.pdf": { "1": "this document has 20 pages. [turn overcambridge igcse\u2122 dc (ks/sg) 214830/2 \u00a9 ucles 2022cambridge international mathematics 0607/42 paper 4 (extended) may/june 2022 2 hours 15 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 120. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *0643142836*", "2": "2 0607/42/m/j/22 \u00a9 ucles 2022 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/42/m/j/22 \u00a9 ucles 2022 [turn over answer all the questions. 1 \u2013 9\u2013 8\u2013 7\u2013 6\u2013 5\u2013 4\u2013 3\u2013 2\u2013 1 1 0 2 3 4 5 6 7 8 9x \u2013 112345678 \u2013 2 \u2013 3 \u2013 4 \u2013 5 \u2013 6 \u2013 7 \u2013 8y a b (a) describe fully the single transformation that maps triangle a onto triangle b. . . [2] (b) rotate triangle b through 90\u00b0 clockwise with centre of rotation (1, 0). draw this triangle and label it c. [2] (c) describe fully the single transformation that maps triangle c onto triangle a. . . [2]", "4": "4 0607/42/m/j/22 \u00a9 ucles 2022 2 the number of hours, x, spent revising and the mark scored, y, in an examination for each of 10 students are shown in the table. time, x hours 1 3 4.5 4 6 4 5.5 6 12 8 mark, y 15 18 28 24 28 30 38 40 43 48 (a) (i) complete the scatter diagram. the first four points have been plotted for you. 0 0 1 2 3 4 5 6 time (hours)7 8 9 10 11 121020304050 mark xy [2] (ii) write down the type of correlation shown by the scatter diagram. . [1] (b) find the mean mark. . [1]", "5": "5 0607/42/m/j/22 \u00a9 ucles 2022 [turn over (c) (i) find the equation of the regression line for y in terms of x. give your answer in the form . ym xc=+ y = [2] (ii) the value for m represents a connection between time and mark. write down the units of m. ... [1] (d) use your answer to part (c)(i) to estimate (i) the mark scored for a student who revised for 10 hours, . [1] (ii) the number of hours spent revising for a student to score a mark of 36. . [1]", "6": "6 0607/42/m/j/22 \u00a9 ucles 2022 3 () \u00b0 x30-x\u00b0a q p b cdonot to scale a, b, c and d lie on a circle centre o. pqa is a tangent to the circle. qbc and pbod are straight lines. angle bqa = x\u00b0 and angle oda = ()x30- \u00b0. find, in terms of x, expressions for each of the following angles. give each answer in its simplest form. (a) angle boa angle boa = [1] (b) angle qbo angle qbo = [3] (c) angle cdb angle cdb = [3] ", "7": "7 0607/42/m/j/22 \u00a9 ucles 2022 [turn over 4 \u2013 4 \u2013 4404y x (a) on the diagram, sketch the graph of f() yx= , where f()xx 42=- for values of x between 4- and 4. [3] (b) write down the x-coordinates of the points where the graph meets the x-axis. x = . and x = [1] (c) on the diagram, sketch the graph of g() yx= , where () . gxx 0252= for values of x between 4- and 4. [2] (d) write down the equation of the line of symmetry of the graph of g() yx= . . [1] (e) find the value of the x-coordinate of each point of intersection of the two graphs. x = . and x = [2] (f) on your diagram shade the region defined by f()g (). xxh [1]", "8": "8 0607/42/m/j/22 \u00a9 ucles 2022 5 (a) alenia, bob and cara share some money in the ratio 5 : 3 : 4 . alenia\u2019s share is $1240. (i) show that bob\u2019s share is $744. [1] (ii) cara spends $ x from her share. the ratio of bob\u2019s money : cara\u2019s money is now 4 : 3 . find the value of x. x = [3] (b) a shop has a sale and all prices are reduced by 20%. (i) bob buys a coat. the original price of the coat was $92. work out the sale price of the coat. $ [2] (ii) cara buys a jacket in the sale for $132. work out the original price of the jacket. $ [2]", "9": "9 0607/42/m/j/22 \u00a9 ucles 2022 [turn over (c) on 1 january 2022 alenia buys a scooter for $1240. on 1 january 2023 the value of the scooter is reduced by 18%. on 1 january 2024 the value of the scooter is reduced by 12% of its 1 january 2023 value. (i) calculate the value of the scooter on 1 january 2024. $ [3] (ii) after 1 january 2024, the value of the scooter is reduced by 12% each year. find the year in which the value of the scooter on 1 january will first be below $310. . [4]", "10": "10 0607/42/m/j/22 \u00a9 ucles 2022 6 the lifetimes, x hours, of 80 electric light bulbs are shown in the table. lifetime ( x hours) frequency x 850 8701g 4 x 8870 90 1g 6 x 890 9001g 12 x 900 9201g 18 x 920 9401g 16 x 940 9501g 20 x 950 10001g 4 (a) calculate an estimate of the mean lifetime. .. h [2] (b) complete the cumulative frequency table. lifetime ( x hours) cumulative frequency x870g 4 x890g x900g x920g x940g x 509g x1000g 80 [1]", "11": "11 0607/42/m/j/22 \u00a9 ucles 2022 [turn over (c) on the grid below, draw a cumulative frequency curve. 850 860 870 880 890 900 910 920 930 lifetime (hours)940 950 960 970 980 990 1000x 01020304050607080 cumulative frequency [3] (d) use your graph in part (c) to find an estimate for (i) the median lifetime, .. h [1] (ii) the interquartile range. .. h [2] (e) find the percentage of bulbs that have a lifetime of more than 900 hours. . % [2]", "12": "12 0607/42/m/j/22 \u00a9 ucles 2022 7 north 535 m 420 m 750 m28\u00b0b c danot to scale the diagram shows four points a, b, c and d. b is due north of c and c is due east of a. ac = 420 m, ad = 750 m, bc = 535 m and angle cad = 28\u00b0. (a) find the bearing of (i) d from a, . [1] (ii) a from d. . [1] (b) calculate ab. ab = m [2]", "13": "13 0607/42/m/j/22 \u00a9 ucles 2022 [turn over (c) calculate cd. cd = m [3] (d) calculate the area of quadrilateral abcd . ... m2 [3] (e) angle acd is obtuse. find the bearing of d from c. . [4]", "14": "14 0607/42/m/j/22 \u00a9 ucles 2022 8 the venn diagram shows the sets a, b and c. a b cu u = {integers from 10 to 20, including 10 and 20} a = {prime numbers} b = {multiples of 3} c = {multiples of 4} (a) list the elements of set a. . [1] (b) write all the elements of u in the correct parts of the venn diagram. [2] (c) list the elements of ()ab, l. ... [1] (d) find n(() ) ab c ,+ l. . [1]", "15": "15 0607/42/m/j/22 \u00a9 ucles 2022 [turn over 9 find the next term and the nth term in each of the following sequences. (a) 100, 91, 82, 73, 64, ... next term = nth term = [3] (b) 64, -32, 16, -8, 4, ... next term = nth term = [3] (c) \u20131, 8, 21, 38, 59, ... next term = nth term = [3]", "16": "16 0607/42/m/j/22 \u00a9 ucles 2022 10 (a) ()pxy 53=+ work out the value of p when x 18=- and y28= . p = [3] (b) simplify fully. xy x 25 34# . [2] (c) factorise fully. (i) ab bc 15 25- . [2] (ii) xy xy 61 625 33- . [2] (iii) cd dc 63 92-- + . [2]", "17": "17 0607/42/m/j/22 \u00a9 ucles 2022 [turn over (d) make x the subject of the formula. axax3122=-+ x = [4] (e) solve the inequality. xx 2312+- . [3]", "18": "18 0607/42/m/j/22 \u00a9 ucles 2022 11 (a) a pyramid has a square base with sides of length 9 cm and vertical height h cm. find an expression, in terms of h, for the volume of the pyramid. . cm3 [1] (b) 10 cm a cm 9 cmh cma c e dbnot to scale ade is an isosceles triangle. bc is parallel to de, bc = a cm and de = 9 cm. the vertical height of triangle ade is h cm and the vertical height of triangle abc is 10 cm. show that ah90= [1] (c) a square-based pyramid with base of side 9 cm and vertical height h cm contains some water. when the pyramid is placed on level ground the surface of the water is 10 cm below the vertex of the pyramid (see diagram 1). when the pyramid stands vertically on its vertex, the surface of the water is 1 cm below the base of the pyramid (see diagram 2). 10 cm 1 cm 9 cm diagram 19 cm diagram 2h cm h cma cmb cm", "19": "19 0607/42/m/j/22 \u00a9 ucles 2022 [turn over (i) use diagram 1 to find an expression, in terms of a and h, for the volume of the water. . cm3 [1] (ii) use diagram 2 to find an expression, in terms of b and h, for the volume of the water. . cm3 [1] (iii) show that () hh 1000 133-= - . [3] (iv) the equation () hh 1000 133-= - simplifies to hh 333 02-- =. use a graphical method to find the value of h. h = [2] question 12 is printed on the next page.", "20": "20 0607/42/m/j/22 \u00a9 ucles 2022 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge.12 a bag contains 7 red balls, 4 blue balls and 1 green ball. in an experiment, three balls are chosen at random without replacement. (a) find the probability that the three balls chosen are (i) all green, . [1] (ii) all red, . [2] (iii) two red and one blue. . [3] (b) this experiment is to be carried out 2640 times. use your answer from part (a)(ii) to find the expected frequency of 3 red balls being chosen. . [1]" }, "0607_s22_qp_43.pdf": { "1": "this document has 20 pages. any blank pages are indicated. [turn overdc (rw/jg) 303207/1 \u00a9 ucles 2022 *1152731180* cambridge international mathematics 0607/43 paper 4 (extended) may/june 2022 2 hours 15 minutes you must answer on the question paper. you will need: geometrical instruments instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly and you will be given marks for correct methods, including sketches, even if your answer is incorrect. \u25cf give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. \u25cf for r, use your calculator value. information \u25cf the total mark for this paper is 120. \u25cf the number of marks for each question or part question is shown in brackets [ ].cambridge igcse\u2122", "2": "2 0607/43/m/j/22 \u00a9 ucles 2022 formula list for the equation ax bx c02++ = xabb ac 242!=-- curved surface area, a, of cylinder of radius r, height h. r ar h2= curved surface area, a, of cone of radius r, sloping edge l. r ar l= curved surface area, a, of sphere of radius r. r ar42= v olume, v, of pyramid, base area a, height h. va h31= v olume, v, of cylinder of radius r, height h. rvr h2= v olume, v, of cone of radius r, height h. r vr h31 2= v olume, v, of sphere of radius r. r vr34 3= sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21area=a c bcb a", "3": "3 0607/43/m/j/22 \u00a9 ucles 2022 [turn over answer all the questions. 1 (a) anneka invests $2500 in an account paying compound interest at a rate of 1.6% per year. find the amount in the account at the end of 3 years. $ . [2] (b) bashir invests $2500 in an account paying simple interest at a rate of r% per year. at the end of 5 years the amount in the account is $2718.75 . calculate the value of r. r= . [3] (c) chanda invests $2500 in an account paying compound interest at a rate of 1.55% per year. find the number of complete years until chanda\u2019s investment is first worth more than $4000. . [4]", "4": "4 0607/43/m/j/22 \u00a9 ucles 2022 2 the heights, h cm, of 100 seedlings are shown in the table. h cm frequency .. h 45 551g 9 .. h 55 651g 18 .. h 65 751g 27 .. h 75 851g 19 .. h 85 951g 16 .. h 95 105 1g 11 total 100 (a) calculate an estimate for the mean. cm [2] (b) write down the modal group. .. h1g .. [1]", "5": "5 0607/43/m/j/22 \u00a9 ucles 2022 [turn over (c) (i) draw a cumulative frequency curve for the heights of the seedlings. 4020406080 10305070100 90 5 6 7 8 9 10 11 h height (cm)cumulative frequency [4] (ii) use your curve to estimate the median. cm [1] (iii) use your curve to estimate the interquartile range. cm [2] (iv) find an estimate of the percentage of the seedlings that were more than 8 cm in height. .. % [2]", "6": "6 0607/43/m/j/22 \u00a9 ucles 2022 3 y x \u2013112345678910 \u20132 \u20133 \u2013 412345678910 0\u20131\u20132\u20133\u2013 4 \u20135\u2013 6a cbd the diagram shows triangles a, b, c and d and the line with equation xy 9+= . (a) enlarge triangle a with centre (4, 3) and scale factor 3. [2] (b) describe fully the single transformation that maps triangle a onto (i) triangle b, . . [2] (ii) triangle c. . . [3] (c) triangle a can be mapped onto triangle d by a rotation of 90\u00b0 clockwise about a point on the line xy 9+= followed by a reflection. find one possible centre of rotation and the equation of the corresponding mirror line. centre ( ... , ... ) equation of mirror line . [2]", "7": "7 0607/43/m/j/22 \u00a9 ucles 2022 [turn over 4 (a) solve x43 7-= . x= . [2] (b) yzx31=+ find the value of y when . x 43= and z 2=- . y= . [2] (c) solve the simultaneous equations. you must show all your working. xy xy43 14 35 25-= += x= . y= . [4] (d) simplify yxx yx 524 104 222 '+-. . [4]", "8": "8 0607/43/m/j/22 \u00a9 ucles 2022 5 0y x\u2013 3 3 \u2013 1020 ()fxx x533=- + for x33gg- (a) on the diagram, sketch the graph of ()f yx= . [2] (b) find the coordinates of the local maximum. ( .. , .. ) [2] (c) describe fully the symmetry of the graph of ()f yx= . . . [3] (d) find the zeros of the graph of ()f yx= . [3]", "9": "9 0607/43/m/j/22 \u00a9 ucles 2022 [turn over (e) ()gxx x222=- + for x33gg- (i) on the same diagram, sketch the graph of ()g yx= . [2] (ii) use your graphs to solve xx x31 032-- += . [3]", "10": "10 0607/43/m/j/22 \u00a9 ucles 2022 6 12 cm 12 cmnot to scalev b do ca vabc is a pyramid with a triangular base. all the edges have length 12 cm. o is vertically below v. d is the mid\u2011point of ac and bo bd32= . (a) show that .c m bo 6928= , correct to 3 decimal places. [4] (b) calculate the volume of the pyramid. .. cm3 [4]", "11": "11 0607/43/m/j/22 \u00a9 ucles 2022 [turn over 7 (a) shade the region indicated below each of these venn diagrams. a bu u p q ()ab, l () () pq pq +, + ll [2] (b) bag a bag b bag a contains 4 white balls and 3 black balls. bag b contains 4 white balls and 5 black balls. a ball is taken at random from bag a. if the ball is white, it is replaced in bag a. if the ball is black, it is put in bag b. a ball is then taken at random from bag b. find the probability that (i) the ball taken from bag a is white, . [1] (ii) both balls are black, . [2] (iii) the balls are different colours. . [3]", "12": "12 0607/43/m/j/22 \u00a9 ucles 2022 8 north 55\u00b0cb anorth not to scale 120\u00b0 65 km the diagram shows the route of a ship between three ports, a, b and c. the bearing of b from a is 055\u00b0 and the bearing of c from b is 120\u00b0. km bc 65= . the ship takes 7 hours to sail from a to b. it sails at a speed of 20 km/h. (a) find the distance ab. km [1] (b) show that angle \u00b0 abc 115= . [1] (c) (i) calculate the distance ca. km [3]", "13": "13 0607/43/m/j/22 \u00a9 ucles 2022 [turn over (ii) calculate the bearing of a from c. . [4] (d) the ship takes 3.6 hours to sail from b to c. it then sails from c to a at a speed of 21.5 km/h. find the average speed for the complete journey from a to b to c and back to a. . km/h [3]", "14": "14 0607/43/m/j/22 \u00a9 ucles 2022 9 ()fxx 23=- () () gxx 12=+ ()hl og xx= (a) find. (i) ()f4- . [1] (ii) (( )) fg 3 . [2] (iii) ()f41- . [2] (iv) ()h21- . [2] (b) solve (( ))fx 51=-. x= . [3]", "15": "15 0607/43/m/j/22 \u00a9 ucles 2022 [turn over (c) find (( )) gfx. write your answer in the form ax bx c2++ . . [3] (d) (( )) hf yx= find x in terms of y. x= . [3]", "16": "16 0607/43/m/j/22 \u00a9 ucles 2022 10 (a) gcba e dnot to scale o f54\u00b0 62\u00b0 a, b, c, d and e are points on the circle centre o. fbg is a tangent to the circle at b. angle \u00b0 abf 62= and angle \u00b0 bed 54= . find (i) angle aeb, angle aeb= . [1] (ii) angle bad , angle bad= . [1] (iii) angle ead , angle ead= . [1] (iv) angle bcd , angle bcd= . [1] (v) angle fbd . angle fbd= . [1]", "17": "17 0607/43/m/j/22 \u00a9 ucles 2022 [turn over (b) a p bo6 cm 120\u00b0not to scale pa and pb are tangents to the circle centre o. the radius of the circle is 6 cm and angle \u00b0 aob 120= . the shaded area r () cm ab32=- . find the value of a and the value of b. a= . b= . [5]", "18": "18 0607/43/m/j/22 \u00a9 ucles 2022 11 a tank has a capacity of 400 litres. water from tap a flows at x litres per minute. water from tap b flows at 2 litres per minute less than the water from tap a. (a) write down an expression in terms of x for the time, in minutes, for tap a to fill the tank. . [1] (b) tap b takes 10 minutes longer to fill the tank than tap a. write down an equation in terms of x and show that it simplifies to xx28 002-- =. [4] (c) solve xx28 002-- = and find the time it takes to fill the tank when both taps are turned on. give your answer in minutes and seconds, correct to the nearest second. .. minutes .. seconds [4]", "19": "19 0607/43/m/j/22 \u00a9 ucles 2022 blank page", "20": "20 0607/43/m/j/22 \u00a9 ucles 2022 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge.blank page" }, "0607_s22_qp_51.pdf": { "1": "this document has 8 pages. [turn overcambridge igcse\u2122 *1306263972* dc (pq) 303072/2 \u00a9 ucles 2022cambridge international mathematics 0607/51 paper 5 investigation (core) may/june 2022 1 hour 10 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 36. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/51/m/j/22 \u00a9 ucles 2022 answer all the questions. investigation storage bins this investigation looks at different methods to store items in storage bins. amara wants to use the smallest number of storage bins possible. each bin can hold a maximum total mass. 1 amara uses this method. method 1 put each item in the first bin that can hold its mass. example these are the masses, in kg, of four items. 6 7 4 2 the maximum total mass that each bin can hold is 10 kg. the tables show how amara puts these items into bins. amara puts the first item in bin 1. bin mass of items in bin unused mass in bin 1 6 4 2 3 4 kg of storage is unused in this bin. the second item will not go in bin 1 bin mass of items in bin unused mass in bin 1 6 4 2 7 3 3 because it is more than 4 kg. amara puts the second item in bin 2. the third item is 4 kg. bin mass of items in bin unused mass in bin 1 6, 4 4 0 2 7, 2 3 1 3 amara puts this in bin 1. bin 1 is now full. the fourth item will go in bin 2. bin 3 is not used. amara needs two bins which can hold a total of 20 kg. 1 kg out of the total of 20 kg of storage is unused. ", "3": "3 0607/51/m/j/22 \u00a9 ucles 2022 [turn over (a) these are the masses, in kg, of ten items. 38 6 21 50 32 7 15 9 27 25 the maximum total mass that each bin can hold is 60 kg. amara uses method 1 to put these ten items into bins. the table shows how she puts the first 6 items into bins. bin mass of items in bin unused mass in bin 1 38, 6, 7 22 16 9 2 21, 32 39 7 3 50 10 4 5 (i) complete amara\u2019s table to show that she needs 5 bins. [4] (ii) work out the total unused mass in the 5 bins. . [2] (b) these are the masses, in kg, of six items. 8 16 13 10 5 3 the maximum total mass that each bin can hold is 20 kg. bin mass of items in bin unused mass in bin 1 8 12 2 3 4 5 use method 1 to complete the table for all six items. the first item has been put in for you. you may not need all the bins. [2]", "4": "4 0607/51/m/j/22 \u00a9 ucles 2022 2 amara wants to see if she can use fewer bins. she puts her items in order of mass before she puts them in bins. she uses this method. method 2 put the masses in order, largest first. then use method 1 . these are the masses, in kg, of the ten items from question 1(a) . 38 6 21 50 32 7 15 9 27 25 (a) write these ten masses in order, largest first. . , . , . , . , . , . , . , . , . , . [1] (b) the maximum total mass that each bin can hold is 60 kg. complete the table using method 2. bin mass of items in bin unused mass in bin 1 2 3 4 5 [3] (c) work out the difference in the total unused mass when using method 1 and method 2. use your answers from question 1(a)(ii) and question 2(b) . . [2]", "5": "5 0607/51/m/j/22 \u00a9 ucles 2022 [turn over 3 a best solution uses the smallest possible number of bins. (a) (i) a set of items with a total mass of 270 kg is put into 4 bins. the maximum total mass that each bin can hold is 80 kg. show that this is a best solution. [2] (ii) show that the solution in question 1(b) is a best solution. [2] (b) amara knows that for a particular set of items a best solution is 6 bins. the maximum total mass that each bin can hold is 5 kg. the total mass of the items is 27.5 kg. work out the amount of unused storage for a best solution for these items. . [2]", "6": "6 0607/51/m/j/22 \u00a9 ucles 2022 4 amara tries another way to improve method 1. method 3 look for items that combine to make as many full bins as possible and place these first. for the remaining items, use method 2 . (a) these are the masses, in kg, of eight items. 21 10 30 19 13 7 28 4 the maximum total mass that each bin can hold is 40 kg. does method 3 give a best solution for these items? show how you decide. bin mass of items in bin unused mass in bin 1 2 3 4 5 [6]", "7": "7 0607/51/m/j/22 \u00a9 ucles 2022 [turn over (b) amara puts nine items into bins using method 3. the maximum total mass that each bin can hold is 40 kg. bin mass of items in bin unused mass in bin 1 18, 22 0 2 32, 5, 3 0 3 32 8 4 19, 15 21 6 5 12 28 amara only wants to use 4 bins. she removes the last item she packed and divides it into two smaller items with the same total mass. she puts each of these two items into a bin that can hold its mass. work out how much the percentage of unused storage changes when amara uses 4 bins instead of 5 bins. . [5] question 5 is printed on the next page.", "8": "8 0607/51/m/j/22 \u00a9 ucles 2022 5 these are the masses, in kg, of eight items. 31 10 39 20 29 47 50 12 the maximum total mass that each bin can hold is 60 kg . each bin amara uses costs $13.50 . use method 2 or method 3 to put these items into bins to give a best solution. find the cost of this solution. bin mass of items in bin unused mass in bin 1 2 3 4 5 $ [5] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge." }, "0607_s22_qp_52.pdf": { "1": "this document has 8 pages. [turn overcambridge igcse\u2122cambridge international mathematics 0607/52 paper 5 investigation (core) may/june 2022 1 hour 10 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 36. \u25cf the number of marks for each question or part question is shown in brackets [ ]. *7390739188* dc (lk/sg) 219350/1 \u00a9 ucles 2022", "2": "2 0607/52/m/j/22 \u00a9 ucles 2022 answer all the questions. investigation opposite corners this investigation is about the difference between the products of the numbers in the opposite corners of a square window on a grid. to calculate the opposite difference for any window: \u2022 multiply the numbers in the opposite corners \u2022 subtract the smaller answer from the larger answer. 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 consecutive even numbers fill a grid of width 10 as shown. the grid continues downwards. a 2 by 2 window moves on the grid. example this is the first window. 2 4 22 24 2248 8 #= 2244 8 #= 88 48 40 -= the opposite difference is 40.", "3": "3 0607/52/m/j/22 \u00a9 ucles 2022 [turn over 1 (a) use the grid to complete each window and find the opposite difference. 14 34 36 34 # .. = .. 14 # 36 = .. .. - .. = .. opposite difference = 66 8668 . 150 152 . [4] (b) what do you notice about the opposite difference for each of these windows on this grid? . [1]", "4": "4 0607/52/m/j/22 \u00a9 ucles 2022 2 a 3 by 3 window moves on the same grid. (a) complete the corner squares in the first window. 2 6 [1] (b) complete the opposite difference calculations for this window. .. # 6 = .. 2 # .. = .. .. - .. = .. [2] (c) complete the corner squares for each window and find the opposite difference. 444 . 5410 . 174 . [4]", "5": "5 0607/52/m/j/22 \u00a9 ucles 2022 [turn over 3 a 4 by 4 window moves on the grid on page 2. (a) complete the corner squares in the first window. 2 8 [2] (b) complete the opposite difference calculations for this window. .. # 8 = .. 2 # .. = .. .. - .. = .. [2] (c) complete the corner squares for each window and find the opposite difference. 64 . 20 . [3]", "6": "6 0607/52/m/j/22 \u00a9 ucles 2022 4 (a) copy the opposite differences that you have found and complete the table. size of window opposite difference 2 by 2 ()212- = 1 3 by 3 () 132- = 4 4 by 4 () 142- = 9 5 by 5 w by w 40( ) [4] (b) find the greatest possible opposite difference for a square window on the grid on page 2. . [3] (c) can a square window on this grid have an opposite difference of 1400? show how you decide. [2]", "7": "7 0607/52/m/j/22 \u00a9 ucles 2022 [turn over 5 another grid of consecutive even numbers has width 5. the diagram shows the start of the grid. 2 4 6 8 10 12 the diagram shows a 2 by 2 window on the grid. n is the first number in the window. n2+ n (a) complete the window using expressions in terms of n. [2] (b) use your expressions to show that the opposite difference for a 2 by 2 window is 20. [3] question 6 is printed on the next page.", "8": "8 0607/52/m/j/22 \u00a9 ucles 2022 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge.6 a square window moves on the grid of width 5 with squares numbered 2, 4, 6, \u2026 . the opposite difference for this window is 180. find the size of the window. . [3]" }, "0607_s22_qp_53.pdf": { "1": "this document has 12 pages. any blank pages are indicated. [turn overdc (rw/sg) 219276/1 \u00a9 ucles 2022 *3595570361* cambridge international mathematics 0607/53 paper 5 investigation (core) may/june 2022 1 hour 10 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer all questions. \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 36. \u25cf the number of marks for each question or part question is shown in brackets [ ].cambridge igcse\u2122", "2": "2 0607/53/m/j/22 \u00a9 ucles 2022 answer all the questions. investigation circles and regions this is an investigation into the number of regions formed by drawing lines on a circle. 1 radii the diagrams show the number of regions inside a circle when 1 radius and 2 radii are drawn. the regions inside the circle are numbered. 1 1 radius1 2 2 radii (a) (i) draw radii on the circles below and number the regions. 5 radii 4 radii 3 radii [3] (ii) complete the table. number of radiinumber of regions 1 1 2 2 3 4 5 6 [1] (b) write a formula, in terms of n, for the number of regions, r, when there are n radii. . [1]", "3": "3 0607/53/m/j/22 \u00a9 ucles 2022 [turn over 2 diameters the diagrams show the number of regions inside a circle when 1 diameter and 2 diameters are drawn. 1 diameter1 2 2 diameters1 2 3 4 (a) complete the table for 3, 4 and 5 diameters. you may use the empty circle to help you. number of diametersnumber of regions 1 2 2 4 3 4 5 [3] (b) write a formula, in terms of n, for the number of regions, r, when there are n diameters. . [2]", "4": "4 0607/53/m/j/22 \u00a9 ucles 2022 3 chords in this investigation: \u2022 each chord must cut every other chord \u2022 only two chords may intersect at any point. the diagrams show the number of regions inside a circle when 1 chord, 2 chords and 3 chords are drawn. 3 chords 2 chords 1 chord1 1 23 44 75 6312 2 (a) count the number of regions in the circle when 4 chords are drawn. . [1]", "5": "5 0607/53/m/j/22 \u00a9 ucles 2022 [turn over (b) complete this table. you may use the empty circle to help you. number of chordsnumber of regions 1 2 2 4 3 7 4 5 6 22 [2] (c) this is a formula for the number of regions, r, when there are n intersecting chords. rn bn2112=+ + find the value of b. . [3]", "6": "6 0607/53/m/j/22 \u00a9 ucles 2022 4 tangents a region can be inside or outside the circle when the lines are tangents. these two diagrams both show a circle with 2 tangents and the regions numbered. the maximum number of regions for a circle with 2 tangents is 6. 24 51 3213 54 6 (a) give a reason why the first diagram does not have the maximum number of regions with 2 tangents. . . [1] (b) (i) use this diagram to find the maximum number of regions when there are 3 tangents. . [1]", "7": "7 0607/53/m/j/22 \u00a9 ucles 2022 [turn over (ii) draw a fourth tangent on the diagram below to find the maximum number of regions. . [2] (c) use your answers to part (b) to complete the table. number of tangentsmaximum number of regions 1 3 2 6 3 4 5 [2] (d) this is a formula for the maximum number of regions, r, when there are n tangents. rn bn2112=+ + find the value of b. . [3]", "8": "8 0607/53/m/j/22 \u00a9 ucles 2022 5 secants a secant is a straight line that intersects a circle at two points and extends outside the circle. in this investigation: \u2022 each secant must cut every other secant \u2022 only 2 secants may intersect at any point \u2022 secants must not intersect on the circumference of the circle. secant the diagrams show the number of regions when 1 secant and 2 secants are drawn. 1 secant2 4 31 2 secants2 5 4 763 81 (a) draw a third secant on the diagram below to find the number of regions when there are 3 secants. complete the table. number of secantsnumber of regions 1 4 2 8 3 4 19 5 26 [2]", "9": "9 0607/53/m/j/22 \u00a9 ucles 2022 [turn over (b) this is a formula for the number of regions, r, when there are n secants. rn bn c212=+ + find the value of b and the value of c. b= . c= . [5]", "10": "10 0607/53/m/j/22 \u00a9 ucles 2022 6 there are two circles. the first circle has chords drawn on it. the second circle has tangents drawn on it. the number of chords on the first circle is the same as the number of tangents on the second circle. each circle has the maximum number of regions. one circle has 60 more regions than the other. (a) find the number of straight lines on each diagram. . [2] (b) find the larger number of regions. . [2]", "11": "11 0607/53/m/j/22 \u00a9 ucles 2022 blank page", "12": "12 0607/53/m/j/22 \u00a9 ucles 2022 blank page permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge." }, "0607_s22_qp_61.pdf": { "1": "this document has 16 pages. any blank pages are indicated. [turn overcambridge igcse\u2122cambridge international mathematics 0607/61 paper 6 investigation and modelling (extended) may/june 2022 1 hour 40 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer both part a (questions 1 to 4) and part b (questions 5 to 7). \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 60. \u25cf the number of marks for each question or part question is shown in brackets [ ]. dc (lk/sg) 303084/2 \u00a9 ucles 2022 *0074308036*", "2": "2 0607/61/m/j/22 \u00a9 ucles 2022 answer both parts a and b. a investigation (questions 1 to 4) storage bins (30 marks) you are advised to spend no more than 50 minutes on this part. this investigation looks at different methods to store items in storage bins. amara wants to use the smallest number of storage bins possible. each bin can hold a maximum total mass. 1 amara uses this method. method 1 put each item in the first bin that can hold its mass. example these are the masses, in kg, of four items. 6 7 4 2 the maximum total mass that each bin can hold is 10 kg. the tables show how amara puts these items into bins. amara puts the first item in bin 1. 4 kg of storage is unused in this bin. bin mass of items in bin unused mass in bin 16 4 2 3 the second item will not go in bin 1 because it is more than 4 kg. amara puts the second item in bin 2.bin mass of items in bin unused mass in bin 16 4 27 3 3 the third item is 4 kg. amara puts this in bin 1. bin 1 is now full. the fourth item will go in bin 2. bin 3 is not used.bin mass of items in bin unused mass in bin 16, 4 4 0 27, 2 3 1 3 amara needs two bins which can hold a total of 20 kg. 1 kg out of the total of 20 kg of storage is unused.", "3": "3 0607/61/m/j/22 \u00a9 ucles 2022 [turn over (a) these are the masses, in kg, of ten items. 38 6 21 50 32 7 15 9 27 25 the maximum total mass that each bin can hold is 60 kg. amara uses method 1 to put these ten items into bins. the table shows how she puts the first 6 items into bins. bin mass of items in bin unused mass in bin 1 38, 6, 7 22 16 9 2 21, 32 39 7 3 50 10 4 5 complete amara\u2019s table to show that she needs 5 bins. [4] (b) these are the masses, in kg, of six items. 8 16 13 10 5 3 the maximum total mass that each bin can hold is 20 kg. bin mass of items in bin unused mass in bin 1 8 12 2 3 4 5 use method 1 to complete the table for all six items. the first item has been put in for you. you may not need all the bins. [2]", "4": "4 0607/61/m/j/22 \u00a9 ucles 2022 2 amara wants to see if she can use fewer bins. she puts her items in order of mass before she puts them in bins. she uses this method. method 2 put the mas ses in order, largest first. then use method 1 . these are the masses, in kg, of the ten items from question 1(a) . 38 6 21 50 32 7 15 9 27 25 (a) write these ten masses in order, largest first. . , . , . , . , . , . , . , . , . , . [1] (b) the maximum total mass that each bin can hold is 60 kg. complete the table using method 2. bin mass of items in bin unused mass in bin 1 2 3 4 5 [2]", "5": "5 0607/61/m/j/22 \u00a9 ucles 2022 [turn over (c) find and compare the percentage of unused storage for these ten items when using method 1 and method 2. use your answers from question 1(a) and question 2(b) . [4] (d) a best solution uses the smallest possible number of bins. a set of items with a total mass of 270 kg is put into 4 bins. the maximum total mass that each bin can hold is 80 kg. show that this is a best solution. [2]", "6": "6 0607/61/m/j/22 \u00a9 ucles 2022 (e) amara tries another way to improve method 1. method 3 look for items that combine to make as many full bins as possible and place these first. for the remaining items, use method 2 . these are the masses, in kg, of eight items. 21 10 30 19 13 7 28 4 the maximum total mass that each bin can hold is 40 kg. does method 3 give a best solution for these items? show how you decide. bin mass of items in bin unused mass in bin 1 2 3 4 5 [4]", "7": "7 0607/61/m/j/22 \u00a9 ucles 2022 [turn over 3 amara has six items. the mass, in kg, of each item is an integer. these are the masses of her six items. 9 4 7 15 x y the maximum total mass that each bin can hold is 20 kg. amara finds that method 1 needs fewer bins than method 2. find the value of x and the value of y. x = y = [4]", "8": "8 0607/61/m/j/22 \u00a9 ucles 2022 4 amara now also uses the dimensions of each bin and of each item to find the maximum number of items that will go into a bin. each item is a cuboid and is the same height as the bin. amara looks at the rectangular top of each bin to work out the maximum number of items that will go into it. storage bin view of top of storage bin not to scale a bin is now full either because it contains the maximum total mass or because it contains the maximum number of items that will go into it. she uses this method. method 4 work out the maximum number of items for each bin using dimensions. then use method 2 . (a) the rectangular top of amara\u2019s bin measures 90 cm by 90 cm. the rectangular top of each item measures 60 cm by 30 cm. find the maximum number of items that will go into a bin using these dimensions. ... [2]", "9": "9 0607/61/m/j/22 \u00a9 ucles 2022 [turn over (b) these are the masses, in kg, of eleven items with tops measuring 60 cm by 30 cm. 41 33 22 18 16 14 8 7 6 5 4 the maximum total mass that each bin can hold is 90 kg. the top of each bin measures 90 cm by 90 cm. each bin costs $13.50 . use method 4 to put these items into bins. show that this is a best solution and find the cost of this solution. bin mass of items in bin unused mass in binnumber of items 1 2 3 4 5 $ [5] ", "10": "10 0607/61/m/j/22 \u00a9 ucles 2022 b modelling (questions 5 to 7) half-lives (30 marks) you are advised to spend no more than 50 minutes on this part. some chemicals decay naturally. this means that their mass reduces. this task is about the decreasing mass of these chemicals. the half-life is the time it takes for the mass of a chemical to become half of its mass. lee uses different models to look at some of these chemicals. 5 (a) the half-life of chemical a is 100 minutes. lee has 400 grams of this chemical. lee uses this model for the mass, in grams, of chemical a which remains at time t minutes. ()at 40021t 100= bl at the end of 1 half-life, t = 100 and half of the mass of chemical a, 200 g, remains. at the end of 2 half-lives, t = 200 and 100 g of chemical a remains. (i) find the mass, in grams, of chemical a which remains at the end of 4 half-lives. . [2] (ii) on the axes below, sketch the graph of ()a yt= for t0 600gg . ty 0 600time (minutes)mass (grams) [2] (iii) find the decrease in mass from t = 50 to t = 100. . [2]", "11": "11 0607/61/m/j/22 \u00a9 ucles 2022 [turn over (iv) find the number of half-lives when the mass remaining is 10 grams. give your answer correct to 2 decimal places. . [3] (b) the half-life of chemical b is 30 minutes. lee has 200 grams of this chemical. (i) change the model from part (a) to find the mass, in grams, of chemical b which remains at time t minutes. ()bt21#ff kk = eo [1] (ii) find the fraction of the mass of chemical b which remains at the end of 300 minutes. . [2] (c) the quarter-life is the time it takes for the mass of a chemical to become a quarter of its mass. at the end of 1 quarter-life , one quarter of the mass remains. the quarter-life of chemical c is 48 minutes. lee has 240 grams of this chemical. he changes the model from part (a) so that it finds the mass, in grams, of chemical c which remains at time t minutes. his model is valid for 6 quarter-lives. complete lee\u2019s model. ()ct= for tgg [3]", "12": "12 0607/61/m/j/22 \u00a9 ucles 2022 6 lee now uses this model in his calculations for the mass of a chemical which remains at time t minutes. ()nnt 3kt 0#= where k is a constant (a) (i) explain why n0 is the mass of the chemical lee starts with. . [1] (ii) write an expression in terms of n0 for the mass remaining at the end of 1 half-life. . [1] (iii) lee thinks 321 kh= , for any starting mass n0 and any half-life h minutes. show that lee is correct. [1] (b) the half-life of chemical d is 10 minutes. (i) use logarithms to show that the value of k for chemical d is .0063- , correct to 3 decimal places. [2]", "13": "13 0607/61/m/j/22 \u00a9 ucles 2022 [turn over (ii) lee has 40 grams of chemical d. use n( t) to find the time it takes for the mass of chemical d to become 10% of its mass. . [4]", "14": "14 0607/61/m/j/22 \u00a9 ucles 2022 7 lee has 60 grams of chemical e. this decreases by 11 grams in 1.6 minutes. (a) use ()nnt 3kt 0#= , where k is a constant, to find the half-life of chemical e in minutes. . [5] (b) change the model from question 5(a) to find the mass, in grams, of chemical e which remains at time t minutes and use it to check your answer to question 7(a) . [1]", "15": "15 0607/61/m/j/22 \u00a9 ucles 2022 blank page", "16": "16 0607/61/m/j/22 \u00a9 ucles 2022 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge.blank page" }, "0607_s22_qp_62.pdf": { "1": "this document has 16 pages. any blank pages are indicated. [turn overcambridge igcse\u2122cambridge international mathematics 0607/62 paper 6 investigation and modelling (extended) may/june 2022 1 hour 40 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer both part a (questions 1 to 6) and part b (questions 7 to 9). \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 60. \u25cf the number of marks for each question or part question is shown in brackets [ ]. dc (lk/ct) 303199/3 \u00a9 ucles 2022 *7289158168*", "2": "2 0607/62/m/j/22 \u00a9 ucles 2022 answer both parts a and b. a investigation (questions 1 to 6) opposite corners (30 marks) you are advised to spend no more than 50 minutes on this part. this investigation is about the difference between the products of the numbers in the opposite corners of a square window on a grid. to calculate the opposite difference for any window: \u2022 multiply the numbers in the opposite corners \u2022 subtract the smaller answer from the larger answer. 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 consecutive even numbers fill a grid of width 10 as shown. the grid continues downwards. a 2 by 2 window moves on the grid. example this is the first window. 2 4 22 24 2248 8 2244 8# #= = 88 48 40 -= the opposite difference is 40.", "3": "3 0607/62/m/j/22 \u00a9 ucles 2022 [turn over 1 use the grid to complete each window and find the opposite difference. 14 34 36 34 # .. = .. 14 # 36 = .. .. - .. = .. opposite difference = ... 66 68 86 . 150 152 . [3]", "4": "4 0607/62/m/j/22 \u00a9 ucles 2022 2 a 3 by 3 window moves on the same grid. (a) complete the corner squares in the first window. 2 6 [1] (b) complete the opposite difference calculations for this window. .. # 6 = .. 2 # .. = .. .. - .. = .. [1] (c) complete the corner squares for each window and find the opposite difference. 4 44 . 10 54 . 174 . [3]", "5": "5 0607/62/m/j/22 \u00a9 ucles 2022 [turn over 3 (a) copy the opposite differences that you have found and complete the table. size of window opposite difference 2 by 2 ()212- = 1 3 by 3 () 132- = 4 4 by 4 () 142- = 9 5 by 5 w by w 40( ) you may use this grid, which continues downwards, to help you. 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 [4] (b) find the greatest possible opposite difference for a window on this grid. . [2]", "6": "6 0607/62/m/j/22 \u00a9 ucles 2022 4 another grid of consecutive even numbers has width 7 units. the diagram shows the start of the grid. 2 4 6 8 10 12 14 16 the diagram shows a 2 by 2 window on the grid. n is the first number in the window. n n + 2 (a) complete the window using expressions in terms of n. [2] (b) use part (a) to show that the opposite difference for a 2 by 2 window is 28. [2]", "7": "7 0607/62/m/j/22 \u00a9 ucles 2022 [turn over 5 a 2 by 2 window moves on a grid of width g, with squares numbered 2, 4, 6, \u2026 . use algebra to find an expression for the opposite difference on this grid. give your answer in its simplest form. you may use this diagram to help you. . [4]", "8": "8 0607/62/m/j/22 \u00a9 ucles 2022 6 (a) a square window of side x1+ moves on a grid of width g, with squares numbered 2, 4, 6, \u2026 . n is the first number in the window. nx + 1 x + 1 show that an expression for the opposite difference using this window is gx42, where x can be any positive integer. [4]", "9": "9 0607/62/m/j/22 \u00a9 ucles 2022 [turn over (b) a square window moves on a grid numbered 2, 4, 6, \u2026 . the opposite difference is 144. use your answer to part (a) to find all the ways this is possible. [4]", "10": "10 0607/62/m/j/22 \u00a9 ucles 2022 b modelling (questions 7 to 9) crickets and temperature (30 marks) you are advised to spend no more than 50 minutes on this part. this task looks at the connection between the temperature and the number of times a cricket, a small insect, makes a chirping sound. amos dolbear (1837 to 1910) was an american scientist who suggested a relationship between the temperature and the number of times a snowy tree cricket makes a chirp. he measured the air temperature and counted the number of chirps that a cricket makes in a given time. the table shows his data. temperature, t \u00b0cnumber of chirps in 60 seconds, n 14 83 16 88 17 102 19 106 21 129 22 138 23 157 25 180 27 208 7 (a) calculate the mean temperature and the mean number of chirps. temperature number of chirps [2] (b) plot the data on the grid on page 11. the first five points have been plotted for you.", "11": "11 0607/62/m/j/22 \u00a9 ucles 2022 [turn over tn 7010 15 20 25 308090100110120130140150160170180190200210220 number of chirps in 60 seconds temperature, \u00b0c [2] (c) a model for the number of chirps, n, is the regression line for n in terms of t. find this model. . [2] (d) draw the graph of the model on the axes. [2] (e) a snowy tree cricket chirps 170 times in 60 seconds. use your model to find the temperature. . [2] ", "12": "12 0607/62/m/j/22 \u00a9 ucles 2022 (f) amos dolbear originally counted the number of chirps in 13 seconds and measured the temperature in degrees fahrenheit, f. to change the temperature from t \u00b0c to f, use . ft 18 32 =+ . (i) complete the table to change the data to the form amos dolbear used. all the data in the table is correct to the nearest integer. temperature number of chirps t \u00b0c f in 60 seconds in 13 seconds 14 57 83 18 16 61 88 19 17 63 102 22 19 106 21 129 22 138 23 73 157 34 25 77 180 39 27 81 208 45 [4] (ii) amos dolbear suggested a simple model to find the temperature, f, from the number of chirps. add 40 to the number of chirps in 13 seconds to find the temperature, f. is this a suitable model for the data? give a reason for your answer. . . [1]", "13": "13 0607/62/m/j/22 \u00a9 ucles 2022 [turn over 8 this is another model for the data on page 10. . nt atb 052=+ + where a and b are constants (a) use the information in the table on page 10 for temperatures of 16 \u00b0c and 27 \u00b0c to find the value of a and the value of b, each correct to the nearest integer. write down the model. a = b = . nt 052= [5] (b) sketch the graph of the model on the axes on page 11. [2] (c) explain how suitable the model is for the data on page 10. . . [1]", "14": "14 0607/62/m/j/22 \u00a9 ucles 2022 9 the number of chirps per second, a, made by a type of african cricket is counted. these crickets do not chirp at higher or lower temperatures. the graph shows the results and a linear model. ta 1.517 17.5 18 18.5 19 19.5 20 20.5 21 21.5 2222.533.54 number of chirps per second temperature, \u00b0c (a) (i) use the points (17.5, 2.35) and (21, 3.5) to find a linear model for a in terms of t. . [4]", "15": "15 0607/62/m/j/22 \u00a9 ucles 2022 (ii) a is the number of chirps per second . n is the number of chirps per minute . use your model for a to write a linear model for n. . [1] (b) write two statements comparing the chirping of the snowy tree cricket and this african cricket. statement 1 . . . statement 2 . . . [2]", "16": "16 0607/62/m/j/22 \u00a9 ucles 2022 permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge.blank page" }, "0607_s22_qp_63.pdf": { "1": "this document has 16 pages. [turn overcambridge igcse\u2122 dc (cj/sg) 305621/3 \u00a9 ucles 2022 *1882827971* cambridge international mathematics 0607/63 paper 6 investigation and modelling (extended) may/june 2022 1 hour 40 minutes you must answer on the question paper. no additional materials are needed. instructions \u25cf answer both part a (questions 1 to 7) and part b (questions 8 to 11). \u25cf use a black or dark blue pen. you may use an hb pencil for any diagrams or graphs. \u25cf write your name, centre number and candidate number in the boxes at the top of the page. \u25cf write your answer to each question in the space provided. \u25cf do not use an erasable pen or correction fluid. \u25cf do not write on any bar codes. \u25cf you should use a graphic display calculator where appropriate. \u25cf you may use tracing paper. \u25cf you must show all necessary working clearly, including sketches, to gain full marks for correct methods. \u25cf in this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. information \u25cf the total mark for this paper is 60. \u25cf the number of marks for each question or part question is shown in brackets [ ].", "2": "2 0607/63/m/j/22 \u00a9 ucles 2022 answer both parts a and b. a investigation (questions 1 to 7) circles and regions (30 marks) you are advised to spend no more than 50 minutes on this part. this is an investigation into the number of regions formed by drawing lines on a circle. 1 radii the diagrams show the number of regions inside a circle when 1 radius and 2 radii are drawn. the regions inside the circle are numbered. 1 1 radius1 2 2 radii (a) complete the table. number of radiinumber of regions 1 1 2 2 3 4 5 6 [1] (b) write a formula, in terms of n, for the number of regions, r, when there are n radii. . [1]", "3": "3 0607/63/m/j/22 \u00a9 ucles 2022 [turn over 2 diameters the diagrams show the number of regions inside a circle when 1 diameter and 2 diameters are drawn. 1 diameter1 2 2 diameters1 2 3 4 (a) complete the table for 3, 4 and 5 diameters. you may use the empty circle to help you. number of diametersnumber of regions 1 2 2 4 3 4 5 [2] (b) write a formula, in terms of n, for the number of regions, r, when there are n diameters. . [1]", "4": "4 0607/63/m/j/22 \u00a9 ucles 2022 3 chords in this investigation: \u2022 each chord must cut every other chord \u2022 only two chords may intersect at any point. the diagrams show the number of regions inside a circle when 1 chord, 2 chords and 3 chords are drawn. 3 chords 2 chords 1 chord1 1 23 44 75 6312 2 (a) count the number of regions in the circle when 4 chords are drawn. . [1]", "5": "5 0607/63/m/j/22 \u00a9 ucles 2022 [turn over (b) complete this table. you may use the empty circle to help you. number of chordsnumber of regions 1 2 2 4 3 7 4 5 6 22 [1] (c) find a formula, in terms of n, for the number of regions, r, when there are n intersecting chords. . [4]", "6": "6 0607/63/m/j/22 \u00a9 ucles 2022 4 tangents a region can be inside or outside the circle when the lines are tangents. these two diagrams both show a circle with 2 tangents and the regions numbered. the maximum number of regions for a circle with 2 tangents is 6. 32 41 5213 54 6 (a) give a reason why the first diagram does not have the maximum number of regions with 2 tangents. . . [1] (b) use this diagram to find the maximum number of regions when there are 3 tangents. . [1] ", "7": "7 0607/63/m/j/22 \u00a9 ucles 2022 [turn over (c) draw a fourth tangent on the diagram below to find the maximum number of regions. complete the table. number of tangentsmaximum number of regions 1 3 2 6 3 4 5 21 [2] (d) this is a formula for the maximum number of regions, r, when there are n tangents. rn bn2112=+ + find the value of b. . [2]", "8": "8 0607/63/m/j/22 \u00a9 ucles 2022 5 secants a secant is a straight line that intersects a circle at two points and extends outside the circle. in this investigation: \u2022 each secant must cut every other secant \u2022 only 2 secants may intersect at any point \u2022 secants must not intersect on the circumference of the circle. secant the diagram shows the number of regions with 2 secants drawn on a circle. 2 68 7 543 1 (a) find the number of regions when there are 3 secants. complete the table. number of secantsnumber of regions 1 4 2 8 3 4 19 5 26 [2]", "9": "9 0607/63/m/j/22 \u00a9 ucles 2022 [turn over (b) this is a formula for the number of regions, r, when there are n secants. rn bn c212=+ + find the value of b and the value of c. b= c= [4]", "10": "10 0607/63/m/j/22 \u00a9 ucles 2022 6 tangents are drawn on a circle to give the maximum number of regions. there are 1225 regions. find the number of tangents. . [3] 7 there are two circles. the first circle has chords drawn on it. the second circle has secants drawn on it. the number of chords on the first circle is the same as the number of secants on the second circle. each circle has the maximum number of regions. one circle has 60 more regions than the other. (a) find the number of straight lines on each diagram. . [2] (b) find the larger number of regions. . [2]", "11": "11 0607/63/m/j/22 \u00a9 ucles 2022 [turn over b modelling (questions 8 to 11) airport runway (30 marks) you are advised to spend no more than 50 minutes on this part. this task looks at the factors that affect the decision to build a second runway at an airport. the factors are: \u2022 the number of seconds a plane waits over the airport before it can start to land \u2022 the number of seconds it then takes to land. a plane cannot begin to land until the runway is free but must wait over the airport. as soon as the runway is free the plane begins to land. the number of seconds between one plane and the next plane arriving over the airport is called the inter-arrival time . the number of seconds from when a plane begins to land and when it stops is called the landing time . 8 this table shows the data for the first 5 planes arriving at the airport for the 1080 seconds after 8 am on day 1. for example: plane b arrives 120 seconds after plane a. plane a has not ended its landing. plane b starts its landing 180 seconds after 8 am, as soon as plane a has ended its landing. planeinter-arrival time (seconds)arrival over airport (seconds after 8 am)start of landing (seconds after 8 am)landing time (seconds)end of landing (seconds after 8 am)seconds waiting to land a 30 30 150 180 0 b 120 150 180 110 290 30 c 360 510 510 100 610 0 d 25 535 610 280 75 e 60 44 934 (a) complete the table. [5] (b) a plane uses the runway for the whole of its landing time. calculate the total time that the runway was not used during these 1080 seconds. . [2]", "12": "12 0607/63/m/j/22 \u00a9 ucles 2022 9 to decide if a second runway should be built, more data is needed. the table shows the data for 180 planes. all values are given correct to the nearest integer. (a) complete the table. inter-arrival time (t seconds)number of planespercentage of planesinter-arrival time (t seconds)cumulative percentage of planes ( p) 0 t1g 60 42 23 tg 60 23 60 t1g 120 34 19 tg 120 42 120 t1g 180 29 tg 180 180 t1g 240 23 tg 240 71 240 t1g 300 16 tg 300 80 300 t1g 360 11 6 tg 360 86 360 t1g 420 11 6 tg 420 420 t1g 480 7 4 tg 480 480 t1g 540 4 2 tg 540 540 t1g 600 2 1 tg 600 99 600 t1g 660 0 0 tg 660 99 660 t1g 720 0 0 tg 720 99 720 t1g 780 1 1 tg 780 100 780 t1g 840 0 0 tg 840 100 840 t1g 900 0 0 tg 900 100 [3]", "13": "13 0607/63/m/j/22 \u00a9 ucles 2022 [turn over (b) on the grid below, complete the cumulative percentage curve. p t 0020406080100 100 200 300 400 500 time (seconds)600 700 800 900 1000cumulative percentage [2] (c) use the graph to estimate the inter-arrival time for a cumulative percentage of 50. . [1]", "14": "14 0607/63/m/j/22 \u00a9 ucles 2022 10 this is a model for the cumulative percentage, p, in terms of the inter-arrival time, t. () pk ta1 3 =- where a and k are constants (a) use the points (60, 23) and (360, 86) to write down two equations in terms of a and k. ... ... [1] (b) show that .aa52360360=-- , where 52.3 is correct to 1 decimal place. [2] (c) solve the equation in part (b) to show that a54= , correct to the nearest integer. [3]", "15": "15 0607/63/m/j/22 \u00a9 ucles 2022 [turn over (d) find the value of k, correct to the nearest integer, and complete the model. .( . ) pt31=- [2] (e) use the model to find the inter-arrival time for a cumulative percentage of 50. . [3] (f) sketch the model on the axes in question 9(b) . [2] (g) comment on the validity of this model. . . [1] question 11 is printed on the next page.", "16": "16 0607/63/m/j/22 \u00a9 ucles 2022 11 (a) use the model to find the percentage of planes that arrived over the airport within 120 seconds of the previous plane. . [1] (b) the table shows information about landing times for the 180 planes. all values are given correct to the nearest integer. landing time (t seconds)number of planespercentage of planeslanding time (t seconds)cumulative percentage of planes ( p) 0 t1g 60 2 1 tg 60 1 60 t1g 120 7 4 tg 120 5 120 t1g 180 11 6 tg 180 11 180 t1g 240 15 8 tg 240 19 240 t1g 300 20 11 tg 300 30 300 t1g 360 34 19 tg 360 49 360 t1g 420 42 23 tg 420 72 420 t1g 480 30 17 tg 480 89 480 t1g 540 18 10 tg 540 99 540 t1g 600 1 1 tg 600 100 find the percentage of planes where the landing time is more than 120 seconds. . [1] (c) based on your answers to part (a) and part (b) , should a second runway be built at the airport? give a reason for your answer. . . [1] permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. every reasonable effort has been made by the publisher (ucles) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. to avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the cambridge assessment international education copyright acknowledgements booklet. this is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. cambridge assessment international education is part of cambridge assessment. cambridge assessment is the brand name of the university of cambridge local examinations syndicate (ucles), which is a department of the university of cambridge." } }, "Other Resources": {}, "Specimen Papers": {} }