path: root/0606.json

{
    "2002": {
        "0606_w02_qp_1.pdf": {
            "1": "",
            "2": "",
            "3": "",
            "4": "",
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        "0606_w02_qp_2.pdf": {
            "1": "time 2 hours instructions to candidates write your name, centre number and candidate number in the spaces provided on the answer paper/answer booklet. answer all the questions. write your answers on the separate answer paper provided. if you use more than one sheet of paper, fasten the sheets together.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. information for candidates 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 80.the use of an electronic calculator is expected, where appropriate.you are reminded of the need for clear presentation in your answers.international general certificate of secondary education cambridge international examinations additional mathematics 0606/2 paper 2 october/november session 2002 2hours additional materials: answer paper electronic calculatorgraph papermathematical tables this question paper consists of 5 printed pages and 3 blank pages. sp (nh/tc) s40047/2 \u00a9cie 2002 [turn over",
            "2": "2 0606/2/o/n/02mathematical formulae 1. algebra quadratic equation for the equation ax2+ bx+ c= 0, . binomial theorem (a+ b)n= an+ an\u20131b+ an\u20132b2 + \u2026 + an\u2013rbr+ \u2026 + bn, where nis a positive integer and = . 2. trigonometry identities sin2a+ cos2a= 1. sec2a= 1 + tan2a. cosec2a= 1 + cot2a. formulae for \u2206abc = = . a2= b2+ c2\u2013 2bccos a. \u2206= bcsin a.1 2c sin cb sin ba sin an! (n\u2013 r)!r! )n r()n r( )n 2( )n 1(xbb a c a=\u00b1\u2013\u201324 2",
            "3": "3 0606/2/o/n/02 [turn over1 write down the inverse of the matrix and use this to solve the simultaneous equations 4x+ 3y+ 7 = 0, 7x+ 6y+ 16 = 0. [4] 2 find the first three terms in the expansion, in ascending powers of x, of (2 + x)6and hence obtain the coefficient of x2in the expansion of (2 + x\u2013x2)6. [4] 3 given that k= and that p= , express in its simplest surd form (i) p, (ii) p\u2013 . [5] 4 given that /h5105= {x: \u2013 5 < x< 5}, a= {x: 8 > 2 x+ 1}, b= {x: x2> x+ 2}, find the values of x which define the set a /h20669 b. [6] 5 (a) the producer of a play requires a total cast of 5, of which 3 are actors and 2 are actresses. he auditions 5 actors and 4 actresses for the cast. find the total number of ways in which the cast canbe obtained. [3] (b) find how many different odd 4-digit numbers less than 4000 can be made from the digits 1, 2, 3, 4, 5, 6, 7 if no digit may be repeated. [3] 6 the cubic polynomial f( x) is such that the coefficient of x3is \u20131 and the roots of the equation f( x)=0 are 1, 2 and k. given that f( x) has a remainder of 8 when divided by x\u20133, find (i) the value of k, (ii) the remainder when f( x) is divided by x+3 . [6] 7 (i) differentiate xsin xwith respect to x. [2] (ii) hence evaluate \u222b0\u03c0\u20132xcos xdx. [4]1 p1+  k 1\u2013k1 3)43 76(",
            "4": "4 0606/2/o/n/028 (i) sketch the graph of y= lnx. [2] (ii) determine the equation of the straight line which would need to be drawn on the graph of y= lnx in order to obtain a graphical solution of the equation x2ex\u20132= 1. [4] 9 (a) find, in its simplest form, the product of a1 3+ b2 3and a2 3\u2013 a1 3b2 3+ b4 3. [3] (b) given that 22x+2\u00d75x\u20131= 8x\u00d752x,evaluate 10x. [4] 10 in the diagram, oa\u2192=a,ob\u2192=b,am\u2192=mb\u2192and op\u2192= 1 3ob\u2192. (i) express ap\u2192and om\u2192in terms of aand b. [3] (ii) given that oq\u2192= /h9261om\u2192, express oq\u2192in terms of /h9261, aand b. [1] (iii) given that aq\u2192= /h9262ap\u2192, express oq\u2192in terms of /h9262, aand b. [2] (iv) hence find the value of /h9261and of /h9262. [3] 11 a car moves on a straight road. as the driver passes a point aon the road with a speed of 20 ms\u20131, he notices an accident ahead at a point b. he immediately applies the brakes and the car moves with an acceleration of ams\u20132, where a=\u2013 6 and ts is the time after passing a. when t=4, the car passes the accident at b. the car then moves with a constant acceleration of 2 ms\u20132until the original speed of 20 ms\u20131is regained at a point c. find (i) the speed of the car at b, [4] (ii) the distance ab, [3] (iii) the time taken for the car to travel from bto c. [2] sketch the velocity-time graph for the journey from ato c. [2]3t 2a ob pqm ba",
            "5": "5 0606/2/o/n/0212 answer only oneof the following two alternatives. either the diagram shows a greenhouse standing on a horizontal rectangular base. the vertical semicircular ends and the curved roof are made from polythene sheeting. the radius of each semicircle is rm and the length of the greenhouse is lm. given that 120 m2of polythene sheeting is used for the greenhouse, express lin terms of rand show that the volume, vm3, of the greenhouse is given by v= 60r\u2013 . [4] given that rcan vary, find, to 2 decimal places, the value of rfor which vhas a stationary value. [3] find this value of vand determine whether it is a maximum or a minimum. [3] or the diagram shows part of the curve y=x2ln x, crossing the x-axis at qand having a minimum point at p. (i) find the value of at q. [4] (ii) show that the x-coordinate of pis . [3] (iii) find the value of at p. [3]d2y dx21 edy dxq o xy py = x2 ln x\u03c0r3 2l m r m",
            "6": "6 0606/2/o/n/02blank page",
            "7": "7 0606/2/o/n/02blank page",
            "8": "8 0606/2/o/n/02blank page"
        }
    },
    "2003": {
        "0606_s03_qp_1.pdf": {
            "1": "this document consists of 5printed pages and 3blank pages. mcs uch176 s38225/4 \u00a9 cie 2003 [turn overcambridge international examinations  international general certificate of secondary education additional mathematics 0606/01 paper 1 may/june 2003 2 hours additional materials: answer booklet/paper electronic calculator graph papermathematical tables read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen on both sides of the paper.you may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer allthe questions. write your answers on the separate answer booklet/paper provided. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of anglesin degrees, unless a different level of accuracy is specified in the question.at the end of the examination, fasten all your work securely together. 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 80.the use of an electronic calculator is expected, where appropriate.you are reminded of the need for clear presentation in your answers.",
            "2": "0606/1/m/j/032 mathema tical f ormulae 1.  algebra quadratic equation for the equation ax2+bx+c= 0, x= . binomial theorem (a+b)n=an+()an\u2013 1b+()an\u2013 2b2+ \u2026 + ()an\u2013rbr+ \u2026 + bn, where nis a positive integer and ()= . 2.  trigonometry identities sin2a+ cos2a= 1. sec2a= 1 + tan2a. cosec2a= 1 + cot2a. formulae for \u2206abc = = . a2=b2+c2\u2013 2bc cosa. \u2206=bcsina.c\u2013\u2013\u2013\u2013 sincb\u2013\u2013\u2013\u2013 sinba\u2013\u2013\u2013\u2013 sinan!\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013(n\u2013r)!r!n rn rn 2n1\u2013b\u00b1 \u221a(b2\u2013 4ac)\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u20132a 21\u2013",
            "3": "1 find the values of kfor which the line y#kx02 meets the curve y/vthinspace2#4x0x/vthinspace2. [4] 2 the area of a rectangle is . the length of one side is . find, without using a calculator, the length of the other side in the form , where aand bare integers. [4] 3 (i) find the first 3 terms in the expansion, in ascending powers of x, of (2 0x)/vthinspace5. [3] (ii)hence find the value of the constant kfor which the coefficient of xin the expansion of (k!x)(2 0x)/vthinspace5is 08. [2] 4 an ocean liner is travelling at 36 km h/vthinspace01on a bearing of 090\u00b0. at 0600 hours the liner, which is 90 km from a lifeboat and on a bearing of 315\u00b0 from the lifeboat, sends a message for assistance. the lifeboat sets off immediately and travels in a straight line at constant speed, intercepting theliner at 0730 hours. find the speed at which the lifeboat travels. [5] 5 find the distance between the points of intersection of the curve and the line y#4x!9. [6] 6 given that a# , find bsuch that 4 a /vthinspace01!b#a/vthinspace2. [6] 7 the function f is defined, for 0\u00b0 \u2264x\u2264360\u00b0, by f( x)#40cos 2x. (i)state the amplitude and period of f. [2] (ii)sketch the graph of f, stating the coordinates of the maximum points. [4] 8 the universal set /chr69and the sets o, p and s are given by /chr69#{x:xis an integer such that 3 \u2264x\u2264100}, o#{x:xis an odd number}, p#{x:xis a prime number}, s#{x:xis a perfect square}. in the venn diagram below, each of the sets o, p and sis represented by a circle. (i)copy the venn diagram and label each circle with the appropriate letter. [2] (ii)place each of the numbers 34, 35, 36 and 37 in the appropriate part of your diagram. [2] (iii)state the value of n( o\u221es) and of n( o\u2020s). [3]/chr702 0\u22123 1/chr71y/vthinspace/vthinspace/vthinspace= /vthinspace/vthinspace/vthinspace3+4 x\u221aa\u2212\u221ab(\u221a3+\u221a2)m (1+\u221a6)m/vthinspace/vthinspace2 0606/1/m/j/03 [turn over3 /chr69",
            "4": "9 solve (i)log/vthinspace42!log/vthinspace9(2x!5)#log/vthinspace864, [4] (ii)9/vthinspacey!5(3/vthinspacey010)#0. [4] the table above shows experimental values of the variables xand y. on graph paper draw the graph of xy against x/vthinspace2. [3] hence (i)express yin terms of x, [4] (ii)find the value of xfor which . [2] 11 a curve has the equation y#xe/vthinspace2x. (i)find the x-coordinate of the turning point of the curve. [4] (ii)find the value of kfor which . [3] (iii)determine whether the turning point is a maximum or a minimum. [2]d/vthinspace/vthinspace2/vthinspace/vthinspacey d/vthinspacex/vthinspace/vthinspace2/vthinspace/vthinspace/vthinspace= /vthinspace/vthinspace/vthinspaceke/vthinspace/vthinspace2x(1+x)x/vthinspace/vthinspace/vthinspace= /vthinspace/vthinspace/vthinspace45 y 0606/1/m/j/034 10x 23 45 6 y 9.2 8.8 9.4 10.4 11.6",
            "5": "12 answer only oneof the following two alternatives. either the diagram shows part of the curve y#2 sin x!4 cos x, intersecting the y-axis at aand with its maximum point at b. a line is drawn from aparallel to the x-axis and a line is drawn from b parallel to the y-axis. find the area of the shaded region. [11] or the diagram shows part of the curve , intersecting the y-axis at a. the tangent to the curve at the point p(2, 3) intersects the y-axis at b. find the area of the shaded region abp. [11]y/vthinspace/vthinspace/vthinspace= /vthinspace/vthinspace/vthinspace\u221a1+4x 0606/1/m/j/035 by ay#2 sin x ! 4 cos x ox by a ox/radicalfully#1! 4x p(2, 3)",
            "6": "blank page 0606/1/m/j/036",
            "7": "blank page 0606/1/m/j/037",
            "8": "blank page 0606/1/m/j/038"
        },
        "0606_s03_qp_2.pdf": {
            "1": "this document consists of 5printed pages and 3blank pages. mcs uch187 s46467/1 \u00a9 cie 2003 [turn overcambridge international examinations  international general certificate of secondary education additional mathematics 0606/02 paper 2 may/june 2003 2 hours additional materials: answer booklet/paper electronic calculator graph papermathematical tables read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen on both sides of the paper.you may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer allthe questions. write your answers on the separate answer booklet/paper provided. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of anglesin degrees, unless a different level of accuracy is specified in the question.at the end of the examination, fasten all your work securely together. 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 80.the use of an electronic calculator is expected, where appropriate.you are reminded of the need for clear presentation in your answers.",
            "2": "0606/2/m/j/032 mathema tical f ormulae 1.  algebra quadratic equation for the equation ax2+bx+c= 0, x= . binomial theorem (a+b)n=an+()an\u2013 1b+()an\u2013 2b2+ \u2026 + ()an\u2013rbr+ \u2026 + bn, where nis a positive integer and ()= . 2.  trigonometry identities sin2a+ cos2a= 1. sec2a= 1 + tan2a. cosec2a= 1 + cot2a. formulae for \u2206abc = = . a2=b2+c2\u2013 2bc cosa. \u2206=bcsina.c\u2013\u2013\u2013\u2013 sincb\u2013\u2013\u2013\u2013 sinba\u2013\u2013\u2013\u2013 sinan!\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013(n\u2013r)!r!n rn rn 2n1\u2013b\u00b1 \u221ab2\u2013 4ac\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u20132a 21\u2013",
            "3": "1 given that 4 x/vthinspace4012x/vthinspace30b/vthinspace2/vthinspacex/vthinspace207bx02 is exactly divisible by 2 x!b, (i)show that 3 b/vthinspace3!7b/vthinspace204#0, [2] (ii)find the possible values of b. [5] 2 the position vectors of points aand b, relative to an origin o, are 6 i03jand 15 i!9jrespectively. (i)find the unit vector parallel to {a}b. [3] the point clies on absuch that {a}c#2{c}b. (ii)find the position vector of c. [3] 3 express in the form , where aand bare integers. [6] 4 simplify . [4] 5 a function f is defined by for the domain x0. (i)evaluate f/vthinspace2(0). [3] (ii)obtain an expression for f/vthinspace01. [2] (iii)state the domain and the range of f/vthinspace01. [2] 6 find the solution set of the quadratic inequality (i) x/vthinspace208x!12p0, [3] (ii) x/vthinspace208x`0. [2] hence find the solution set of the inequality | x/vthinspace208x!6|`6. [2]f:x/vthinspace/vthinspace/vthinspace\u221a/vthinspace/vthinspace /vthinspacee/vthinspace/vthinspacex+1 416/vthinspace/vthinspacex+1+20(4/vthinspace/vthinspace2x) 2/vthinspace/vthinspacex\u22123/vthinspace/vthinspace8/vthinspace/vthinspacex+2a+b\u221a2 /chr998 /vthinspace1\u00a0/chr703\u221ax+2 \u221ax/chr71\u00a0dx 0606/2/m/j/03 [turn over3",
            "4": "7 (i) find the number of different arrangements of the letters of the word mexico. find the number of these arrangements (ii)which begin with m, (iii)which have the letter x at one end and the letter c at the other end. [5] four of the letters of the word mexico are selected at random. find the number of different combinations if (iv)there is no restriction on the letters selected, (v)the letter m must be selected. [3] 8 (a) find all the angles between 0\u00b0 and 360\u00b0 which satisfy the equation [4] (b)find all the angles between 0 and 3 radians which satisfy the equation1!3 cos /vthinspace2y#4 sin y. [4] 9 a motorcyclist travels on a straight road so that, tseconds after leaving a fixed point, his velocity, vms/vthinspace01, is given by v#12t0t/vthinspace2. on reaching his maximum speed at t#6, the motorcyclist continues at this speed for another 6 seconds and then comes to rest with a constant deceleration of 4m s/vthinspace02. (i)find the total distance travelled. [6] (ii)sketch the velocity-time graph for the whole of the motion. [2] 10 a curve has the equation . (i)find the value of kfor which . [2] (ii)find the equation of the normal to the curve at the point where the curve crosses the x-axis. [4] a point ( x,y) moves along the curve in such a way that the x-coordinate of the point is increasing at a constant rate of 0.05 units per second. (iii)find the corresponding rate of change of the y-coordinate at the instant that y#6. [3]d/vthinspacey d/vthinspacex/vthinspace/vthinspace/vthinspace= /vthinspace/vthinspace/vthinspacek (x\u22122)/vthinspace/vthinspace2y/vthinspace/vthinspace/vthinspace= /vthinspace/vthinspace/vthinspace2x+4 x\u221223(sin\u00a0x \u2212cos\u00a0x) =2(sin\u00a0x +cos\u00a0x). 0606/2/m/j/034",
            "5": "11 answer only oneof the following two alternatives. either solutions to this question by accurate drawing will not be accepted. the diagram shows a triangle abc in which ais the point (3, 2), cis the point (7, 4) and angle acb#90\u00b0. the line bdis parallel to acand dis the point ( , 11). the lines baand dcare extended to meet at e. find (i)the coordinates of b, [7] (ii)the ratio of the area of the quadrilateral abdc to the area of the triangle ebd. [3] or the diagram shows a right-angled triangle opq and a circle, centre oand radius rcm, which cuts op and oq at aand brespectively. given that ap#6 cm, pq#5 cm, qb#7 cm and angle opq#90\u00b0, find (i)the length of the arc ab, [6] (ii)the area of the shaded region. [4]13 /vthinspace1 2 /vthinspace/vthinspace/vthinspace 0606/2/m/j/035 by eoxa(3, 2)c(7, 4)d(131 2, 11) p oq r cm 6 cm ar cm7 cm b 5 cm",
            "6": "blank page 0606/2/m/j/036",
            "7": "blank page 0606/2/m/j/037",
            "8": "blank page 0606/2/m/j/038"
        },
        "0606_w03_qp_1.pdf": {
            "1": "this document consists of 6printed pages and 2blank pages. mcs uch190 s47473/1 \u00a9 cie 2003 [turn overcambridge international examinations international general certificate of secondary education additional mathematics 0606/01 paper 1 october/november 2003 2 hours additional materials: answer booklet/paper electronic calculator graph papermathematical tables read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen on both sides of the paper.you may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer allthe questions. write your answers on the separate answer booklet/paper provided. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of anglesin degrees, unless a different level of accuracy is specified in the question.at the end of the examination, fasten all your work securely together. 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 80.the use of an electronic calculator is expected, where appropriate.you are reminded of the need for clear presentation in your answers.",
            "2": "0606/1/o/n/032 mathema tical f ormulae 1.  algebra quadratic equation for the equation ax2+bx+c= 0, x= . binomial theorem (a+b)n=an+()an\u2013 1b+()an\u2013 2b2+ \u2026 + ()an\u2013rbr+ \u2026 + bn, where nis a positive integer and ()= . 2.  trigonometry identities sin2a+ cos2a= 1. sec2a= 1 + tan2a. cosec2a= 1 + cot2a. formulae for \u2206abc = = . a2=b2+c2\u2013 2bc cosa. \u2206=bcsina.c\u2013\u2013\u2013\u2013 sincb\u2013\u2013\u2013\u2013 sinba\u2013\u2013\u2013\u2013 sinan!\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013(n\u2013r)!r!n rn rn 2n1\u2013b\u00b1 \u221ab2\u2013 4ac\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u20132a 21\u2013",
            "3": "1 find the values of kfor which the line x!3y#kand the curve y/vthinspace2#2x!3do not intersect. [4] 2 without using a calculator, solve the equation . [4] 3 the expression x/vthinspace3!ax/vthinspace2!bx03, where aand bare constants, has a factor of x03 and leaves a remainder of 15 when divided by x!2. find the value of aand of b. [5] 4 a rectangular block has a square base. the length of each side of the base is and the volume of the block is . find, without using a calculator, the height of the block inthe form , where aand bare integers. [5] the diagram shows part of the curve . find the area of the shaded region bounded by the curve and the coordinate axes. [6] 6 in this question, iis a unit vector due east and jis a unit vector due north. a plane flies from pto q. the velocity, in still air, of the plane is (280 i040j)k mh /vthinspace01and there is a constant wind blowing with velocity (50 i070j)k mh/vthinspace01. find (i)the bearing of qfrom p, [4] (ii)the time of flight, to the nearest minute, given that the distance pqis 273 km. [2]y/vthinspace/vthinspace/vthinspace=/vthinspace/vthinspace/vthinspace6\u00a0sin/chr703x+\u03c0 4/chr71(a\u221a2+b\u221a3)\u00a0m(4\u221a2\u22123\u221a3)\u00a0m/vthinspace/vthinspace3(\u221a3\u2212\u221a2)\u00a0m2/vthinspace/vthinspacex\u22123 8/vthinspace/vthinspace\u2212x/vthinspace/vthinspace/vthinspace=/vthinspace/vthinspace/vthinspace32 4/vthinspace/vthinspace/vthinspace1 2/vthinspace/vthinspace/vthinspace/vthinspace/vthinspace/vthinspacex 0606/1/o/n/03 [turn over3 y#6 sin(3x !\u03c0 4)y o x5",
            "4": "7 a small manufacturing firm produces four types of product, a, b, cand d. each product requires three processes \u2013 assembly, finishing and packaging. the number of minutes required for each type of product for each process and the cost, in $ per minute, of each process are given in the followingtable. the firm receives an order for 40 of type a, 50 of type b, 50 of type cand 60 of type d. write down three matrices such that matrix multiplication will give the total cost of meeting this order. hence evaluate this total cost. [6] 8 given that ,find (i) , [3] (ii)the approximate change in yas xincreases from 1 to 1 !p, where pis small, [2] (iii)the rate of change of xat the instant when x#1, given that yis changing at the rate of 0.12 units per second at this instant. [2] 9 (a) solve, for 0\u00b0 `x`360\u00b0, the equation 4 tan /vthinspace2x!8 sec x#1. [4] (b)given that y`4, find the largest value of ysuch that 5 tan(2 y!1)#16. [4] 10 the function f is given by f: , x\u00e2/chr82. (i)state the range of f. [1] (ii)solve the equation f( x)#0, giving your answer correct to two decimal places. [2] (iii)sketch the graph of y#f(x), showing on your diagram the coordinates of the points of intersection with the axes. [2] (iv)find an expression for f/vthinspace01in terms of x. [3]x/vthinspace/vthinspace/vthinspace\u221a/vthinspace/vthinspace/vthinspace5\u22123e/vthinspace/vthinspace/vthinspace1 2/vthinspace/vthinspace/vthinspace/vthinspace/vthinspace/vthinspacexd/vthinspacey d/vthinspacexy/vthinspace/vthinspace/vthinspace=/vthinspace/vthinspace/vthinspaceln\u00a0x 2x+3 0606/1/o/n/034 number of minutescost per typeab c dminute ($) process assembly 8 6 6 5 0.60 finishing 5 4 3 2 0.20 packaging 3 3 2 2 0.50",
            "5": "11 solutions to this question by accurate drawing will not be accepted. the diagram, which is not drawn to scale, shows a parallelogram oabc where ois the origin and ais the point (2, 6). the equations of oa, oc and cbare y#3x, and y#3x015 respectively. the perpendicular from ato ocmeets oc at the point d. find (i)the coordinates of c, b and d, [8] (ii)the perimeter of the parallelogram oabc, correct to 1 decimal place. [3]y/vthinspace/vthinspace/vthinspace=/vthinspace/vthinspace/vthinspace/vthinspace1 2/vthinspace/vthinspacex 0606/1/o/n/03 [turn over5 y o xy#   x1 2y#3x 015y#3x a(2, 6) c db [question 12 is printed on the next page.]",
            "6": "12 answer only oneof the following two alternatives. either a piece of wire, 125 cm long, is bent to form the shape shown in the diagram. this shape encloses a plane region, of area acm/vthinspace2, consisting of a semi-circle of radius rcm, a rectangle of length xcm and an isosceles triangle having two equal sides of length cm. (i)express xin terms of rand hence show that . [6] given that rcan vary, (ii)calculate, to 1 decimal place, the value of rfor which ahas a maximum value. [4] or the diagram shows the cross-section of a hollow cone of height 30 cm and base radius 12 cm and a solid cylinder of radius rcm and height hcm. both stand on a horizontal surface with the cylinder inside the cone. the upper circular edge of the cylinder is in contact with the cone. (i)express hin terms of rand hence show that the volume, vcm/vthinspace3, of the cylinder is given by . [4] given that rcan vary, (ii)find the volume of the largest cylinder which can stand inside the cone and show that, in this case, the cylinder occupies of the volume of the cone. [6] [the volume, v, of a cone of height hand radius ris given by .] v/vthinspace/vthinspace/vthinspace=/vthinspace/vthinspace/vthinspace/vthinspace1 3/vthinspace/vthinspace/vthinspace/vthinspace/vthinspace/vthinspace\u03c0r/vthinspace/vthinspace2/vthinspace/vthinspaceh/vthinspace4 9/vthinspace/vthinspace/vthinspacev/vthinspace/vthinspace/vthinspace=/vthinspace/vthinspace/vthinspace\u03c0(30 r/vthinspace/vthinspace2\u2212/vthinspace5 2/vthinspace/vthinspacer/vthinspace/vthinspace3)a/vthinspace/vthinspace/vthinspace=/vthinspace/vthinspace/vthinspace125r\u2212\u03c0r/vthinspace/vthinspace2 2\u22127r/vthinspace/vthinspace2 45r 46 0606/1/o/n/03r cm  45rcm45rcmx cm 12 cm30 cm r cmh cm",
            "7": "blank page 0606/1/o/n/037",
            "8": "blank page 0606/1/o/n/038"
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    "2004": {
        "0606_s04_qp_1.pdf": {
            "1": "this document consists of 5printed pages and 3blank pages. mcs ucj106 s61381/1 \u00a9 ucles 2004 [turn overuniversity of cambridge international examinations  international general certificate of secondary education additional mathematics 0606/01 paper 1 may/june 2004 2 hours additional materials: answer booklet/paper electronic calculator graph paper (3 sheets)mathematical tables read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen on both sides of the paper.you may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer allthe questions. write your answers on the separate answer booklet/paper provided. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of anglesin degrees, unless a different level of accuracy is specified in the question.at the end of the examination, fasten all your work securely together. 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 80.the use of an electronic calculator is expected, where appropriate.you are reminded of the need for clear presentation in your answers.",
            "2": "0606/1/m/j/042 mathema tical f ormulae 1.  algebra quadratic equation for the equation ax2+bx+c= 0, x= . binomial theorem (a+b)n=an+()an\u2013 1b+()an\u2013 2b2+ \u2026 + ()an\u2013rbr+ \u2026 + bn, where nis a positive integer and ()= . 2.  trigonometry identities sin2a+ cos2a= 1. sec2a= 1 + tan2a. cosec2a= 1 + cot2a. formulae for \u2206abc = = . a2=b2+c2\u2013 2bc cosa. \u2206=bcsina.c\u2013\u2013\u2013\u2013 sincb\u2013\u2013\u2013\u2013 sinba\u2013\u2013\u2013\u2013 sinan!\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013(n\u2013r)!r!n rn rn 2n1\u2013b\u00b1 \u221ab2\u2013 4ac\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u20132a 21\u2013",
            "3": "/space5001 given that , find (i) an expression for , (ii) the x-coordinates of the stationary points. [4] /space5002 find the x-coordinates of the three points of intersection of the curve y#x/vthinspace3with the line y#5x02, expressing non-integer values in the form , where aand bare integers. [5] 3 (i) sketch on the same diagram the graphs of y#|2x!3 | and y#10x. [3] (ii) find the values of xfor which x!|2x!3|# 1. [3] /space5004 the function f is defined, for 0 \u00b0\u2264x\u2264360\u00b0, by where a, band care positive integers. given that the amplitude of f is 2 and the period of f is 120\u00b0, (i) state the value of aand of b. [2] given further that the minimum value of f is 01, (ii) state the value of c, [1] (iii) sketch the graph of f. [3] /space5005 the straight line 5y !2x#1 meets the curve xy!24#0 at the points a and b. find the length of ab, correct to one decimal place. [6] /space5006 the table below shows the daily production, in kilograms, of two types, s/vthinspace1and s/vthinspace2, of sweets from a small company, the percentages of the ingredients a, b and crequired to produce s/vthinspace1and s/vthinspace2. given that the costs, in dollars per kilogram, of a, b and care 4, 6 and 8 respectively, use matrix multiplication to calculate the total cost of daily production. [6] f(x)=a\u00a0sin\u00a0(bx )+c, a&\u221abd/vthinspacey d/vthinspacexy=3x\u22122 x/vthinspace/vthinspace2+5 0606/1/m/j/04 [turn over3 percentagedaily abc production (kg) type s/vthinspace1 60 30 10 300 type s/vthinspace2 50 40 10 240",
            "4": "/space5007 to a cyclist travelling due south on a straight horizontal road at 7 ms/vthinspace01, the wind appears to be blowing from the north-east. given that the wind has a constant speed of 12 ms/vthinspace01, find the direction from which the wind is blowing. [5] /space5008 a curve has the equation y#(ax!3) ln x, where xp0 and ais a positive constant. the normal to the curve at the point where the curve crosses the x-axis is parallel to the line 5 y!x#2. find the value of a. [7] /space5009 (a) calculate the term independent of xin the binomial expansion of . [3] (b)in the binomial expansion of (1 !kx)/vthinspacen, where n\u22653 and k is a constant, the coefficients of x/vthinspace2 and x/vthinspace3are equal. express kin terms of n. [4] the diagram shows an isosceles triangle abc in which bc#ac#20 cm, and angle bac#0.7 radians. dcis an arc of a circle, centre a. find, correct to 1 decimal place, (i) the area of the shaded region, [4] (ii) the perimeter of the shaded region. [4] the diagram shows part of a curve, passing through the points (2, 3.5) and (5, 1.4). the gradient of the curve at any point ( x, y) is , where ais a positive constant. (i) show that a#20 and obtain the equation of the curve. [5] the diagram also shows lines perpendicular to the x-axis at x#2, x#pand x#5. given that the areas of the regions aand bare equal, (ii) find the value of p. [5]\u2212/vthinspace/vthinspace/vthinspacea x/vthinspace/vthinspace3/chr70x\u22121 2x/vthinspace/vthinspace5/chr7118 0606/1/m/j/044 c bda20 cm 20 cm 0.7 rad10 y x p 5 2(2, 3.5) (5, 1.4) oab11",
            "5": "12 answer only oneof the following two alternatives. either (a)an examination paper contains 12 different questions of which 3 are on trigonometry, 4 are on algebra and 5 are on calculus. candidates are asked to answer 8 questions. calculate (i) the number of different ways in which a candidate can select 8 questions if there is no restriction, (ii) the number of these selections which contain questions on only 2 of the 3 topics,trigonometry, algebra and calculus. [4] (b)a fashion magazine runs a competition, in which 8 photographs of dresses are shown, lettereda, b, c, d, e, f, gand h. competitors are asked to submit an arrangement of 5 letters showing their choice of dresses in descending order of merit. the winner is picked at randomfrom those competitors whose arrangement of letters agrees with that chosen by a panel ofexperts. (i) calculate the number of possible arrangements of 5 letters chosen from the 8. calculate the number of these arrangements (ii) in which ais placed first, (iii) which contain a. [6] orthe table shows experimental values of the variables xand ywhich are related by the equation y#ab /vthinspacex, where aand bare constants. (i) use the data above in order to draw, on graph paper, the straight line graph of lg yagainst x, using 1 cm for 1 unit of xand 10 cm for 1 unit of lg y. [2] (ii) use your graph to estimate the value of aand of b. [5] (iii) on the same diagram, draw the straight line representing y#2/vthinspacexand hence find the value of xfor which ab/vthinspacex#2/vthinspacex. [3] 0606/1/m/j/045 x 2468 1 0 y 9.8 19.4 37.4 74.0 144.4",
            "6": "blank page 0606/1/m/j/046",
            "7": "blank page 0606/1/m/j/047",
            "8": "blank page 0606/1/m/j/048"
        },
        "0606_s04_qp_2.pdf": {
            "1": "this document consists of 5printed pages and 3blank pages. mcs ucj107 s61254/1 \u00a9 ucles 2004 [turn overuniversity of cambridge international examinations  international general certificate of secondary education additional mathematics 0606/02 paper 2 may/june 2004 2 hours additional materials: answer booklet/paper electronic calculator graph papermathematical tables read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen on both sides of the paper.you may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer allthe questions. write your answers on the separate answer booklet/paper provided. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of anglesin degrees, unless a different level of accuracy is specified in the question.at the end of the examination, fasten all your work securely together. 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 80.the use of an electronic calculator is expected, where appropriate.you are reminded of the need for clear presentation in your answers.",
            "2": "0606/2/m/j/042 mathema tical f ormulae 1.  algebra quadratic equation for the equation ax2+bx+c= 0, x= . binomial theorem (a+b)n=an+()an\u2013 1b+()an\u2013 2b2+ \u2026 + ()an\u2013rbr+ \u2026 + bn, where nis a positive integer and ()= . 2.  trigonometry identities sin2a+ cos2a= 1. sec2a= 1 + tan2a. cosec2a= 1 + cot2a. formulae for \u2206abc = = . a2=b2+c2\u2013 2bc cosa. \u2206=bcsina.c\u2013\u2013\u2013\u2013 sincb\u2013\u2013\u2013\u2013 sinba\u2013\u2013\u2013\u2013 sinan!\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013(n\u2013r)!r!n rn rn 2n1\u2013b\u00b1 \u221ab2\u2013 4ac\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u20132a 21\u2013",
            "3": "1 the position vectors of the points aand b, relative to an origin o, are i07jand 4i!kj respectively, where kis a scalar. the unit vector in the direction of {a|bis 0.6i!0.8j. find the value of k. [4] 2 given that xis measured in radians and xp10, find the smallest value of xsuch that [4] 3 given that /chr69#{students in a college}, a#{students who are over 180 cm tall}, b#{students who are vegetarian}, c#{students who are cyclists}, express in words each of the following (i) a\u221ebc#\u2205,/space500/space500(ii) /space500a\u00e4c,. [2] express in set notation the statement (iii) all students who are both vegetarians and cyclists are not over 180 cm tall. [2] 4 prove the identity (1 !sec \u03b8)(cosec \u03b80cot \u03b8)]tan \u03b8. [4] 5 the roots of the quadratic equation are cand d. without using a calculator, show that . [5] 6 (a) find the values of xfor which 2 x/vthinspace2p3x!14. [3] (b)find the values of kfor which the line y!kx#8 is a tangent to the curve x/vthinspace2!4y#20. [3] 7 functions f and g are defined for x\u00e2/chr82by f:x\u221ae/vthinspacex, g:x\u221a2x03. (i) solve the equation fg( x)#7. [2] function h is defined as gf.(ii) express h in terms of xand state its range. [2] (iii) express h /vthinspace01in terms of x. [2]1 c+1 d/vthinspace/vthinspace/vthinspace=/vthinspace/vthinspace/vthinspace\u221a5x/vthinspace/vthinspace2\u2212\u221a20x+2/vthinspace/vthinspace/vthinspace=/vthinspace/vthinspace/vthinspace0 10\u00a0cos/chr70x+1 2/chr71/vthinspace/vthinspace/vthinspace=/vthinspace/vthinspace/vthinspace3. 0606/2/m/j/04 [turn over3",
            "4": "8 solve (i)log/vthinspace3(2x!1)#2!log/vthinspace3(3x011), [4] (ii)log/vthinspace4y!log/vthinspace2y#9. [4] 9 express 6!4x0x/vthinspace2in the form a0(x!b)/vthinspace2, where aand bare integers. [2] (i) find the coordinates of the turning point of the curve y#6!4x0x/vthinspace2and determine the nature of this turning point. [3] the function f is defined by f : x\u221a6!4x0x/vthinspace2for the domain 0 \u2264x\u22645. (ii) find the range of f. [2] (iii) state, giving a reason, whether or not f has an inverse. [1] 10 solutions to this question by accurate drawing will not be accepted. in the diagram the points a, band chave coordinates ( 02, 4), (1,01) and (6, 2) respectively. the line ad is parallel to bcand angle acd#90\u00b0. (i) find the equations of adand cd. [6] (ii) find the coordinates of d. [2] (iii) show that triangle acd is isosceles. [2] 11 it is given that y#(x!1)(2x03)/vthinspace3/chr472. (i) show that can be written in the form and state the value of k. [4] hence (ii) find, in terms of p, an approximate value of ywhen x#6!p, where pis small, [3] (iii) evaluate . [3] /chr996 2x\u221a2x\u22123\u00a0d/vthinspacexkx\u221a2x\u22123d/vthinspacey d/vthinspacex 0606/2/m/j/044 d c(6, 2) b(1, \u22121)a(\u22122, 4) oy x",
            "5": "12 answer only oneof the following two alternatives. either a particle moves in a straight line so that, ts after leaving a fixed point o, its velocity, vms/vthinspace01, is given by . (i) find the acceleration of the particle when v#8. [4] (ii) calculate, to the nearest metre, the displacement of the particle from owhen t#6. [4] (iii) state the value which vapproaches as tbecomes very large. [1] (iv) sketch the velocity-time graph for the motion of the particle. [2] or (i) by considering sec \u03b8as (cos \u03b8)/vthinspace01show that . [2] (ii) the diagram shows a straight road joining two points, pand q, 10 km apart. a man is at point a, where apis perpendicular to pqand apis 2 km. the man wishes to reach qas quickly as possible and travels across country in a straight line to meet the road at point x, where angle pax#\u03b8radians. the man travels across country along axat 3 km h/vthinspace01but on reaching the road he travels at 5k mh/vthinspace01along xq. given that he takes thours to travel from ato q, show that [4] (iii) given that \u03b8can vary, show that thas a stationary value when px#1.5 km. [5] t/vthinspace/vthinspace/vthinspace=/vthinspace/vthinspace/vthinspace2\u00a0sec\u00a0\u03b8 3+2\u22122\u00a0tan\u00a0\u03b8 5/vthinspace/vthinspace/vthinspace.d d/vthinspace\u03b8\u00a0(sec \u00a0\u03b8)=sin\u00a0\u03b8 cos/vthinspace/vthinspace2\u00a0\u03b8v/vthinspace/vthinspace/vthinspace=/vthinspace/vthinspace/vthinspace10(1 \u2212e/vthinspace/vthinspace\u2212/vthinspace1 2/vthinspace/vthinspace/vthinspacet) 0606/2/m/j/045 a pxq 10 km2k m\u03b8",
            "6": "blank page 0606/2/m/j/046",
            "7": "blank page 0606/2/m/j/047",
            "8": "blank page 0606/2/m/j/048"
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        "0606_w04_qp_1.pdf": {
            "1": "this document consists of 5 printed pages and 3 blank pages. mcs ucj135 s69945/1 \u00a9ucles 2004 [turn overuniversity of cambridge international examinations  international general certificate of secondary education additional mathematics 0606/01 paper 1 october/november 2004 2hours additional materials: answer booklet/paper electronic calculator graph papermathematical tables read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen on both sides of the paper.you may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of anglesin degrees, unless a different level of accuracy is specified in the question.at the end of the examination, fasten all your work securely together. 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 80.the use of an electronic calculator is expected, where appropriate.you are reminded of the need for clear presentation in your answers.",
            "2": "\u00a9ucles 2004 0606/1/o/n/042 mathema tical f ormulae 1.  algebra quadratic equation for the equation ax2+ bx + c= 0, x= . binomial theorem (a+ b)n= an+ ()an\u2013 1b+ ()an\u2013 2b2+ \u2026 + ()an\u2013 rbr+ \u2026 + bn, where n is a positive integer and ()= . 2.  trigonometry identities sin2a+ cos2a= 1. sec2a= 1 + tan2a. cosec2a= 1 + cot2a. formulae for \u2206abc = = . a2= b2+ c2\u2013 2bc cos a. \u2206= bcsin a.c\u2013\u2013\u2013\u2013 sin cb\u2013\u2013\u2013\u2013 sin ba\u2013\u2013\u2013\u2013 sin an!\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013(n\u2013 r)! r!n rn rn 2n1\u2013b \u00b1 \u221ab2\u2013 4ac\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u20132a 21\u2013",
            "3": "/space5001 the position vectors of points a, band c, relative to an origin o, are i !9j, 5i 03jand k(i!3j) respectively, where k is a constant. given that c lies on the line ab, find the value of k. [4] /space5002 a youth club has facilities for members to play pool, darts and table-tennis. every member plays at least one of the three games. p, dand trepresent the sets of members who play pool, darts and table-tennis respectively. express each of the following in set language and illustrate each bymeans of a venn diagram. (i) the set of members who only play pool. [2] (ii) the set of members who play exactly 2 games, neither of which is darts. [2] /space5003 without using a calculator, solve, for x and y, the simultaneous equations . [5] the diagram shows a sector cod of a circle, centre o, in which angle cod #radians. the points aand blie on od and oc respectively, and ab is an arc of a circle, centre o, of radius 7 cm. given that the area of the shaded region abcd is 48 cm /vthinspace2, find the perimeter of this shaded region. [6] /space5005 given that the expansion of (a !x)(1 02x)/vthinspacenin ascending powers of xis 3 041x!bx/vthinspace2!\u2026, find the values of the constants a, n and b. [6] /space5006 the function f is defined, for 0 `x`\u03c0, by f/vthinspace (x)#5!3cos 4x. find (i) the amplitude and the period of f, [2] (ii) the coordinates of the maximum and minimum points of the curve y #f/vthinspace(x). [4] /space5007 (a) find the number of different arrangements of the 9 letters of the word singapore in whichs does not occur as the first letter. [2] (b) 3 students are selected to form a chess team from a group of 5 girls and 3 boys. find thenumber of possible teams that can be selected in which there are more girls than boys. [4]4 3)/vthinspace/vthinspacey\u22121=81 /vthinspace1 9 3/vthinspace/vthinspace4x\u00d7( 8/vthinspace/vthinspacex\u00f72/vthinspace/vthinspacey=64,  \u00a9ucles 2004 0606/1/o/n/04 [turn over3 dc b 7 cmoarad4 3/space5004",
            "4": "/space5008 the function f is defined, for x \u00e2/chr82, by (i) find f/vthinspace01in terms of x and explain what this implies about the symmetry of the graph of y#f(x). [3] the function g is defined, for x \u00e2/chr82, by (ii) find the values of x for which f(x) #g/vthinspace01(x). [3] (iii) state the value of x for which gf( x)#02. [1] /space5009 (a) solve, for 0\u00b0 \u2264x\u2264360\u00b0, the equation sin/vthinspace2x#3cos/vthinspace2x!4sinx. [4] (b)solve, for 0 `y`4, the equation cot 2y #0.25, giving your answers in radians correct  to 2 decimal places. [4] 10 a curve has the equation y #x/vthinspace3lnx, where x p0. (i) find an expression for . [2] hence (ii) calculate the value of ln xat the stationary point of the curve, [2] (iii) find the approximate increase in y as xincreases from e to e !p, where p is small, [2] (iv) find . [3] 11 the line 4y #3x!1intersects the curve xy#28x027y at the point p(1, 1) and at the point q. the perpendicular bisector of pq intersects the line y#4xat the point r. calculate the area of triangle pqr. [9]/chr99/vthinspace/vthinspace/vthinspacex/vthinspace/vthinspace2\u00a0ln\u00a0x/vthinspace/vthinspace/vthinspaced/vthinspacexd/vthinspacey d/vthinspacex g : x /vthinspace/vthinspace/vthinspace\u221a/vthinspace/vthinspace /vthinspacex\u22123 2\u00a0.  f : x /vthinspace/vthinspace/vthinspace\u221a/vthinspace/vthinspace /vthinspace3x+11 x\u22123\u00a0,\u00a0x/vthinspace/vthinspace/vthinspace=c/vthinspace/vthinspace/vthinspace3.  \u00a9ucles 2004 0606/1/o/n/044",
            "5": "12 answer only one of the following two alternatives. either (a)at the beginning of 1960, the number of animals of a certain species was estimated at 20 000. this number decreased so that, after a period of n years, the population was 20 000e/vthinspace00.05n. estimate (i) the population at the beginning of 1970, [1] (ii) the year in which the population would be expected to have first decreased to 2000. [3] (b)solve the equation 3/vthinspacex!102#8\"3/vthinspacex01. [6] or a curve has the equation . (i) show that the exact value of the y-coordinate of the stationary point of the curve is . [4] (ii) determine whether the stationary point is a maximum or a minimum. [2] (iii) calculate the area enclosed by the curve, the x-axis and the lines x #0 and x #1. [4]2\u221a3y=e/vthinspace/vthinspace/vthinspace1 2/vthinspace/vthinspace/vthinspacex+3e/vthinspace/vthinspace\u2212/vthinspace1 2/vthinspace/vthinspace/vthinspacex \u00a9ucles 2004 0606/1/o/n/045",
            "6": "blank page 0606/1/o/n/046",
            "7": "blank page 0606/1/o/n/047",
            "8": "blank page 0606/1/o/n/048 every reasonable effort has been made to trace all copyright holders. the publishers would be pleased to hear from anyone whose  rights we have unwittingly infringed. university of cambridge international examinations is part of the university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge"
        },
        "0606_w04_qp_2.pdf": {
            "1": "this document consists of 5 printed pages and 3 blank pages. (kn) s69811 \u00a9ucles 2004 [turn overuniversity of cambridge international examinations  international general certificate of secondary education additional mathematics 0606/02 paper 2 october/november 2004 2hours additional materials: answer booklet/paper electronic calculator graph papermathematical tables read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen on both sides of the paper.you may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of anglesin degrees, unless a different level of accuracy is specified in the question.at the end of the examination, fasten all your work securely together. 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 80.the use of an electronic calculator is expected, where appropriate.you are reminded of the need for clear presentation in your answers.",
            "2": "2 0606/02/o/n/04 \u00a9 ucles 2004mathematical formulae 1. algebra quadratic equation for the equation ax2+ bx + c= 0, . binomial theorem (a+ b)n= an+ an\u20131b+ an\u20132b2 + \u2026 + an\u2013rbr+ \u2026 + bn, where n is a positive integer and = . 2. trigonometry identities sin2a+ cos2a= 1. sec2a= 1 + tan2a. cosec2a= 1 + cot2a. formulae for \u2206 abc = = . a2= b2+ c2\u2013 2bc cos a. \u2206=  bcsin a.1 2c sin cb sin ba sin an! (n\u2013 r)!r!)n r()n r( )n 2( )n1(xbb a c a=\u2212\u00b1 \u221224 2",
            "3": "3 0606/02/o/n/04 [turn over1 given that a= /h20898/h20899 , find a\u20131and hence solve the simultaneous equations 2x+ 3y + 4 = 0 \u20135x+ 4y + 13 = 0. [4] 2 given that , where aand bare integers, find, without using a calculator, the value of aand of b. [4] 3 the diagram shows part of the curve   y= 3sin 2x + 4cos x. find the area of the shaded region, bounded by the curve and the coordinate axes. [5] 4 find the values of kfor which the line   y= x+ 2   meets the curve   y2+ (x+ k)2= 2. [5] 5 solve the equation   log16(3x\u2013 1) = log4(3x) + log4(0.5). [6] 6 given that   x= 3sin\u03b8\u2013 2cos\u03b8and y = 3cos\u03b8+ 2sin\u03b8, (i) find the value of the acute angle \u03b8for which x = y,[ 3] (ii) show that   x2+ y2is constant for all values of \u03b8.[ 3] 7 given that 6 x3+ 5ax \u2013 12a leaves a remainder of \u20134 when divided by x\u2013 a, find the possible values ofa. [7] 8 a motor boat travels in a straight line across a river which flows at 3 ms\u20131between straight parallel banks 200 m apart. the motor boat, which has a top speed of 6 ms\u20131in still water, travels directly from a point a on one bank to a point b, 150 m downstream of a, on the opposite bank. assuming that the motor boat is travelling at top speed, find, to the nearest second, the time it takes to travel from ato b. [7]y x o \u03c0 2ab+=+313 4323 \u20135 4 \u00a9 ucles 2004",
            "4": "4 0606/02/o/n/04 \u00a9 ucles 20049 in order that each of the equations (i) y= abx, (ii) y= axk, (iii) px+ qy = xy, where a, b, a, k, pand qare unknown constants, may be represented by a straight line, they each need to be expressed in the form   y= mx+ c, where x and yare each functions of xand/or y, and m and c are constants. copy the following table and insert in it an expression for y, x, m and c for each case. [7] 10 the function f is defined by   f: x \uf061 /h20919x2\u2013 8x + 7 /h20919 for the domain   3 /h11088x/h110888. (i) by first considering the stationary value of the function  x\uf061x2\u2013 8x + 7, show that the graph of  y= f(x) has a stationary point at x= 4 and determine the nature of this stationary point. [4] (ii) sketch the graph of y= f(x). [2] (iii) find the range of f. [2] the function g is defined by   g: x \uf061 /h20919x2\u2013 8x + 7 /h20919 for the domain   3 /h11088x/h11088k. (iv) determine the largest value of kfor which g\u20131exists. [1] 11 the diagram shows a trapezium oabc, where o is the origin. the equation of oais   y = 3x and the equation of ocis   y + 2x = 0.   the line through aperpendicular to oameets the y-axis at b and bcis parallel to ao. given that the length of oais units, calculate the coordinates of a, of b and of c. [10]250y xab cy = 3x y + 2x = 0 oyxmc y= abx y= axk px+ qy = xy",
            "5": "\u00a9 ucles 20045 0606/02/o/n/0412 answer only one of the following two alternatives. either a particle, travelling in a straight line, passes a fixed point oon the line with a speed of 0.5 ms\u20131. the acceleration, ams\u20132, of the particle, ts after passing o, is given by   a = 1.4 \u2013 0.6t. (i) show that the particle comes instantaneously to rest when t= 5. [4] (ii) find the total distance travelled by the particle between t= 0 and t = 10. [6] or each member of a set of curves has an equation of the form  y= ax + , where aand b are integers. (i) for the curve where a = 3 and b = 2, find the area bounded by the curve, the x-axis and the lines x= 2 and x = 4. [4] another curve of this set has a stationary point at (2, 3). (ii) find the value of aand of b in this case and determine the nature of the stationary point. [6]b x2",
            "6": "6 0606/02/o/n/04blank page",
            "7": "7 0606/02/o/n/04blank page",
            "8": "8 0606/02/o/n/04blank page every reasonable effort has been made to trace all copyright holders. the publishers would be pleased to hear from anyone whose rights we have unwittingly infringed. university of cambridge international examinations is part of the university of cambridge local examinations syndicate (ucles),  which is itself a department of the university of cambridge."
        }
    },
    "2005": {
        "0606_s05_qp_1.pdf": {
            "1": "this document consists of 5 printed pages and 3 blank pages. sp (nf/kn) s87030 \u00a9ucles 2005 [turn overuniversity of cambridge international examinations international general certificate of secondary education additional mathematics 0606/01 paper 1 may/june 2005 2 hours additional materials: answer booklet/paper electronic calculator graph papermathematical tables read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen on both sides of the paper.you may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of anglesin degrees, unless a different level of accuracy is specified in the question.at the end of the examination, fasten all your work securely together. 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 80.the use of an electronic calculator is expected, where appropriate.you are reminded of the need for clear presentation in your answers.",
            "2": "2 0606/01/m/j/05 \u00a9ucles 2005mathematical formulae 1. algebra quadratic equation for the equation ax2+ bx + c= 0, . binomial theorem (a+ b)n= an+ an\u20131b+ an\u20132b2 + \u2026 + an\u2013rbr+ \u2026 + bn, where n is a positive integer and = . 2. trigonometry identities sin2a+ cos2a= 1. sec2a= 1 + tan2a. cosec2a= 1 + cot2a. formulae for \u2206 abc = = . a2= b2+ c2\u2013 2bc cos a. \u2206= bcsin a.1 2c sin cb sin ba sin an! (n\u2013 r)!r!)n r()n r( )n 2( )n1(xbb a c a=\u2212\u00b1 \u221224 2",
            "3": "3 0606/01/m/j/05 \u00a9ucles 2005 [turn over1 given that   a = /h20898/h20899 ,   find (a2)\u20131. [4] 2 a student has a collection of 9 cds, of which 4 are by the beatles, 3 are by abba and 2 are by the rolling stones. she selects 4 of the cds from her collection. calculate the number of ways in whichshe can make her selection if (i) her selection must contain her favourite beatles cd, [2] (ii) her selection must contain 2 cds by one group and 2 cds by another. [3] 3 given that  \u03b8is acute and that   sin \u03b8= ,   express, without using a calculator,   in the  form   a + , where aand b are integers. [5] 4 the position vectors of points a and brelative to an origin o are  \u20133i \u2013 jand  i + 2j respectively.  the point clies on ab and is such that ac\u2192=ab\u2192. find the position vector of cand show that it is a unit vector. [6] 5 the function f is defined, for 0\u00b0 /h11088x/h11088180\u00b0, by f(x) = a + 5 cos bx, where a and b are constants. (i) given that the maximum value of f is 3, state the value of a. [1] (ii) state the amplitude of f. [1] (iii) given that the period of f is 120\u00b0, state the value of b. [1] (iv) sketch the graph of f. [3] 6 given that each of the following functions is defined for the domain   \u20132 /h11088x/h110883,   find the range of (i) f : x\uf061 2 \u2013 3x, [1] (ii) g : x\uf061/h209192 \u2013 3x /h20919, [2] (iii) h : x\uf061 2 \u2013 /h20919 3x /h20919. [2]   state which of the functions f, g and h has an inverse. [2]3\u20135bsin\u03b8\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013cos\u03b8\u2013 sin\u03b81 321 \u20131 1",
            "4": "4 0606/01/m/j/05 \u00a9ucles 20057 (a) variables l and t are related by the equation   l = l0(1 + \u03b1)twhere l0and \u03b1are constants. given that l0= 0.64 and \u03b1= 2.5 \u00d7 10\u20133, find the value of tfor which l = 0.66. [3] (b) solve the equation   1 + lg(8 \u2013 x) = lg(3x + 2). [4] 8 the table above shows experimental values of the variables xand ywhich are related by an equation of the form   y = kxn,   where k and n are constants. (i) using graph paper, draw the graph of lg yagainst lg x. [3] (ii) use your graph to estimate the value of kand of n. [4] 9 (i) determine the set of values of k for which the equation x2+ 2x + k= 3kx \u2013 1 has no real roots. [5] (ii) hence state, giving a reason, what can be deduced about the curve y= (x + 1)2and the line   y= 3x \u2013 1. [2] 10 the remainder when   2 x3+ 2x2\u2013 13x + 12   is divided by   x+ ais three times the remainder when it is divided by   x\u2013 a. (i) show that   2a3+ a2\u2013 13a + 6 = 0. [3] (ii) solve this equation completely. [5] 11 a particle travels in a straight line so that, t seconds after passing a fixed point aon the line, its acceleration, a ms\u20132, is given by   a= \u20132 \u2013 2t.   it comes to rest at a point b when t = 4. (i) find the velocity of the particle at a. [4] (ii) find the distance ab. [3] (iii) sketch the velocity-time graph for the motion from a to b. [1]x 10 100 1000 10 000 y 1900 250 31 4",
            "5": "5 0606/01/m/j/05 \u00a9ucles 200512 answer only one of the following two alternatives. either the diagram, which is not drawn to scale, shows part of the graph of   y= 8 \u2013 e2x,   crossing the y-axis at a. the tangent to the curve at acrosses the x-axis at b. find the area of the shaded region bounded by the curve, the tangent and the x-axis. [10] or a piece of wire, of length 2 m, is divided into two pieces. one piece is bent to form a square of side xm and the other is bent to form a circle of radius r m. (i) express r in terms of x and show that the total area, a m2, of the two shapes is given by a= . [4] given that x can vary, find (ii) the stationary value of a, [4] (iii) the nature of this stationary value. [2](\u03c0+ 4)x2\u2013 4x + 1\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u03c0y x oa b",
            "6": "6 0606/01/m/j/05blank page",
            "7": "7 0606/01/m/j/05blank page",
            "8": "8 0606/01/m/j/05blank 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 atthe earliest possible opportunity. university of cambridge international examinations is part of the university of cambridge local examinations syndicate (ucles),  which is itself a department of the university of cambridge."
        },
        "0606_s05_qp_2.pdf": {
            "1": "this document consists of 6 printed pages and 2 blank pages. (kn) s76935 \u00a9ucles 2005 [turn overuniversity of cambridge international examinations international general certificate of secondary education additional mathematics 0606/02 paper 2 may/june 2005 2 hours additional materials: answer booklet/paper electronic calculator graph papermathematical tables read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen on both sides of the paper.you may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of anglesin degrees, unless a different level of accuracy is specified in the question.at the end of the examination, fasten all your work securely together. 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 80.the use of an electronic calculator is expected, where appropriate.you are reminded of the need for clear presentation in your answers.",
            "2": "2 0606/02/m/j/05 \u00a9 ucles 2005mathematical formulae 1. algebra quadratic equation for the equation ax2+ bx + c= 0, . binomial theorem (a+ b)n= an+ an\u20131b+ an\u20132b2 + \u2026 + an\u2013rbr+ \u2026 + bn, where n is a positive integer and = . 2. trigonometry identities sin2a+ cos2a= 1. sec2a= 1 + tan2a. cosec2a= 1 + cot2a. formulae for \u2206 abc = = . a2= b2+ c2\u2013 2bc cos a. \u2206=  bcsin a.1 2c sin cb sin ba sin an! (n\u2013 r)!r!)n r()n r( )n 2( )n1(xbb a c a=\u2212\u00b1 \u221224 2",
            "3": "3 0606/02/m/j/05 \u00a9 ucles 2005 [turn over1 a curve has the equation   y= . (i) find an expression for   . [3] (ii) given that yis increasing at a rate of 0.2 units per second when x= \u2013 0.5, find the corresponding rate of change of x.[ 2] 2 a flower show is held over a three-day period \u2013 thursday, friday and saturday. the table below shows the entry price per day for an adult and for a child, and the number of adults and children attending oneach day. (i) write down two matrices such that their product will give the amount of entry money paid on thursday and hence calculate this product. [2] (ii) write down two matrices such that the elements of their product give the amount of entry money paid for each of friday and saturday and hence calculate this product. [2]  (iii) calculate the total amount of entry money paid over the three-day period. [1] 3 the diagram shows a square abcd of area 60 m 2. the point plies on bc and the sum of the lengths of apand bpis 12 m. given that the lengths of apand bpare xm and y m respectively, form two equations in xand y and hence find the length of bp.[ 5]ab dcpdy\u2013\u2013\u2013dx8\u2013\u2013\u2013\u2013\u20132x\u2013 1 thursday friday saturday price ($) \u2013 adult 12 10 10 price ($) \u2013 child 5 4 4 number of adults 300 180 400number of children 40 40 150",
            "4": "4 0606/02/m/j/05 \u00a9 ucles 20054 the functions f and g are defined by f : x\uf061sinx,     0 /h11088 x/h11088 , g : x\uf0612x\u2013 3,     x \u2208/h11938. solve the equation   g\u20131f(x) = g2(2.75). [5] 5(i) differentiate   xln x \u2013 x with respect to x.[ 2] (ii) the diagram shows part of the graph of   y= ln x.   use your result from part (i) to evaluate the area of the shaded region bounded by the curve, the line x= 3 and the x\u2013axis. [4]   6 a curve has the equation   y= ,   for 0 < x < \u03c0.  (i) find and show that the x-coordinate of the stationary point satisfies   2 sin x\u2013 cos x= 0. [4] (ii) find the x-coordinate of the stationary point. [2]  7 solve, for x and y, the simultaneous equations 125x= 25(5y), 7x\u00f74 9y= 1. [6]dy\u2013\u2013\u2013dxe2x\u2013\u2013\u2013\u2013sinxy x oy = ln  x 3\u03c0\u20132",
            "5": "5 0606/02/m/j/05 \u00a9 ucles 2005 [turn over8 the venn diagram above represents the sets /h5105= {homes in a certain town}, c= {homes with a computer}, d= {homes with a dishwasher}. it is given that n(c\u2229d)=  k, n(c)=  7 \u00d7n(c\u2229d), n(d)=  4 \u00d7n(c \u2229 d), and n(/h5105)=  6 \u00d7n(c\u2032 \u2229 d \u2032). (i) copy the venn diagram above and insert, in each of its four regions, the number, in terms of k, of homes represented by that region. [5] (ii) given that there are 165 000 homes which do not have both a computer and a dishwasher, calculate the number of homes in the town. [2] 9 a plane, whose speed in still air is 300 km h\u20131, flies directly from x to y. given that yis 720 km from x on a bearing of 150\u00b0 and that there is a constant wind of 120 km h\u20131blowing towards the west, find the time taken for the flight. [7] 10 (a) solve, for 0\u00b0< x< 360\u00b0, 4 tan2x+ 15 secx = 0. [4] (b) given that y> 3, find the smallest value of ysuch that tan (3y \u2013 2) = \u2013 5. [4] 11(a) (i) expand   (2 + x)5.[ 3] (ii) use your answer to part (i) to find the integers aand bfor which   (2 + )5can be expressed in the form   a+ b .[ 3 ] (b) find the coefficient of xin the expansion of   /h20898x \u2013 /h208997 .[ 3]4\u2013x33c d/h5105",
            "6": "6 0606/02/m/j/05 \u00a9 ucles 200512 answer only one of the following two alternatives.  either solutions to this question by accurate drawing will not be accepted. the diagram, which is not drawn to scale, shows a right-angled triangle abc, where a is the point  (6, 11) and b is the point (8, 8). the point d(5, 6) is the mid-point of bc. the line deis parallel to acand angle dec is a right-angle. find the area of the entire figure abdeca.[ 11]   or the diagram, which is not drawn to scale, shows a circle abcda, centre oand radius 10 cm.  the chord bdis 16 cm long. bed is an arc of a circle, centre a. (i) show that the length of abis approximately 17.9 cm. for the shaded region enclosed by the arcs bcd and bed, find (ii) its perimeter, (iii) its area. [11]bdc e o a16 cm 10 cmy x oc ed (5, 6)a (6, 11) b (8, 8)",
            "7": "7 0606/02/m/j/05blank page",
            "8": "8 0606/02/m/j/05blank page every reasonable effort has been made to trace all copyright holders where the publishers (i.e. ucles) are aware that third-party material has been reproduced. the publishers would be pleased to hear from anyone whose rights they have unwittingly infringed. university of cambridge international examinations is part of the university of cambridge local examinations syndicate (ucles),  which is itself a department of the university of cambridge."
        },
        "0606_w05_qp_1.pdf": {
            "1": "university of cambridge international examinations international general certificate of secondary education additional mathematics 0606/01 paper 1 october/november 2005 2 hours additional materials: answer booklet/paper electronic calculator graph paper (2 sheets)mathematical tables read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen on both sides of the paper.you may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of anglesin degrees, unless a different level of accuracy is specified in the question.at the end of the examination, fasten all your work securely together. 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 80.the use of an electronic calculator is expected, where appropriate.you are reminded of the need for clear presentation in your answers. this document consists of 6 printed pages and 2 blank pages. sp (nf/kn) s96217/1 \u00a9 ucles 2005 [turn over",
            "2": "2 0606/01/o/n/05 \u00a9 ucles 2005mathematical formulae 1. algebra quadratic equation for the equation ax2+ bx + c= 0, . binomial theorem (a+ b)n= an+ an\u20131b+ an\u20132b2 + \u2026 + an\u2013rbr+ \u2026 + bn, where n is a positive integer and = . 2. trigonometry identities sin2a+ cos2a= 1. sec2a= 1 + tan2a. cosec2a= 1 + cot2a. formulae for \u2206 abc = = . a2= b2+ c2\u2013 2bc cos a. \u2206= bcsin a.1 2c sin cb sin ba sin an! (n\u2013 r)!r!)n r()n r( )n 2( )n1(xbb a c a=\u2212\u00b1 \u221224 2",
            "3": "3 0606/01/o/n/05 \u00a9 ucles 2005 [turn over1 find the set of values of xfor which   (x \u2013 6)2> x. [3] 2 (a) (i) (ii) for each of the venn diagrams above, express the shaded region in set notation. [2] (b) (i) copy the venn diagram above and shade the region that represents  a\u2229b\u2229c'. [1] (ii) copy the venn diagram above and shade the region that represents  a'\u2229(b\u222ac). [1] 3 find the values of the constant cfor which the line   2y = x+ c is a tangent to the curve   y= 2x + . [4] 4 a cuboid has a square base of side   (2 \u2013 ) m   and a volume of   (2 \u2013 3) m3. find the height of the cuboid in the form   (a + b ) m,   where a and b are integers. [4] 5 the diagram, which is not drawn to scale, shows a horizontal rectangular surface. one corner of the surface is taken as the origin o andiand j are unit vectors along the edges of the surface. a fly, f, starts at the point with position vector  ( i+ 12j) cm  and crawls across the surface with a velocity of (3i+ 2j) cm s\u20131.  at the instant that the fly starts crawling, a spider, s, at the point with position vector (85i + 5j) cm,  sets off across the surface with a velocity of  (\u20135 i+ kj) cm s\u20131,  where k is a constant. given that the spider catches the fly, calculate the value of k. [6]j i o33 36\u2013xab c/h5105ab/h5105ab/h5105",
            "4": "4 0606/01/o/n/05 \u00a9 ucles 20056 a particle starts from rest at a fixed point o and moves in a straight line towards a point a. the  velocity,  v ms\u20131, of the particle, t seconds after leaving o, is given by   v = 6 \u2013 6e\u20133t.   given that the particle reaches a when t = ln 2, find (i) the acceleration of the particle at a, [3] (ii) the distance oa. [4] 7 (a) solve   log7(17y + 15) = 2 + log7(2y\u2013 3). [4] (b) evaluate   logp8 \u00d7log16p. [3] 8 a curve has the equation   y= (x+ 2) . (i) show that   = , where kis a constant, and state the value of k. [4] (ii) hence evaluate   /h2084825dx. [4] 9 (a) find all the angles between 0\u00b0 and 360\u00b0 which satisfy the equation 3cos x= 8tan x. [5] (b) given that 4 /h11088 y/h110886, find the value of yfor which 2cos/h20898/h20899 + = 0. [3] 32y\u2013\u20133x\u22121xx\u22121kx dy\u2013\u2013\u2013dxx\u22121",
            "5": "5 0606/01/o/n/05 \u00a9 ucles 2005 [turn over10 solutions to this question by accurate drawing will not be accepted. the diagram, which is not drawn to scale, shows a quadrilateral abcd in which a is (0, 10), b is (2, 16) and cis (8, 14). (i) show that triangle abc is isosceles. [2] the point d lies on the x-axis and is such that ad= cd. find (ii) the coordinates of d, [4] (iii) the ratio of the area of triangle abc to the area of triangle acd. [3] 11 a function f is defined by   f : x\uf061/h209192x\u2013 3/h20919\u2013 4,   for \u20132 /h11088x/h110883. (i) sketch the graph of y= f(x). [2] (ii) state the range of f. [2] (iii) solve the equation f(x) = \u20132. [3] a function g is defined by   g: x\uf061/h209192x\u2013 3/h20919\u2013 4,   for \u20132 /h11088x/h11088k. (iv) state the largest value of k for which g has an inverse. [1] (v) given that g has an inverse, express g in the form   g: x\uf061ax+ b,   where a and b are constants. [2]y xb (2, 16) c (8, 14) da (0, 10) o",
            "6": "6 0606/01/o/n/05 \u00a9 ucles 200512 answer only one of the following two alternatives. either variables xand y are related by the equation   yxn= a,   where aand n are constants. the table below shows measured values of x and y. (i) on graph paper plot lg yagainst lg x, using a scale of 2 cm to represent 0.1 on the lg xaxis and 1 cm to represent 0.1 on the lg yaxis. draw a straight line graph to represent the equation   yxn= a. [3] (ii) use your graph to estimate the value of aand of n. [4] (iii) on the same diagram, draw the line representing the equation   y = x2and hence find the value of x for which   xn+ 2= a. [3] or the diagram shows a semicircle, centre o, of radius 8 cm. the radius oc makes an angle of 1.2 radians with the radius ob. the arc cd of a circle has centre a and the point d lies on ob. find the area of (i) sector cob, [2] (ii) sector cad, [5] (iii) the shaded region. [3]abc od8 cm 8 cm1.2 radx 1.5 2 2.5 3 3.5 y 7.3 3.5 2.0 1.3 0.9",
            "7": "7 0606/01/o/n/05blank page",
            "8": "8 0606/01/o/n/05blank 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, thepublisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge."
        },
        "0606_w05_qp_2.pdf": {
            "1": "university of cambridge international examinations international general certificate of secondary education additional mathematics 0606/02 paper 2 october/november 2005 2 hours additional materials: answer booklet/paper electronic calculator graph papermathematical tables read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen on both sides of the paper.you may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of anglesin degrees, unless a different level of accuracy is specified in the question.at the end of the examination, fasten all your work securely together. 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 80.the use of an electronic calculator is expected, where appropriate.you are reminded of the need for clear presentation in your answers. this document consists of 5 printed pages and 3 blank pages. sp (nf/kn) s93693 \u00a9 ucles 2005 [turn over",
            "2": "2 0606/02/o/n/05 \u00a9 ucles 2005mathematical formulae 1. algebra quadratic equation for the equation ax2+ bx + c= 0, . binomial theorem (a+ b)n= an+ an\u20131b+ an\u20132b2 + \u2026 + an\u2013rbr+ \u2026 + bn, where n is a positive integer and = . 2. trigonometry identities sin2a+ cos2a= 1. sec2a= 1 + tan2a. cosec2a= 1 + cot2a. formulae for \u2206 abc = = . a2= b2+ c2\u2013 2bc cos a. \u2206= bcsin a.1 2c sin cb sin ba sin an! (n\u2013 r)!r!)n r()n r( )n 2( )n1(xbb a c a=\u2212\u00b1 \u221224 2",
            "3": "3 0606/02/o/n/05 \u00a9 ucles 2005 [turn over1 variables v and t are related by the equation v= 1000e\u2013kt, where k is a constant. given that v= 500 when t = 21, find (i) the value of k, [2]  (ii) the value of v when t = 30. [2] 2 the line   x + y= 10   meets the curve   y2= 2x + 4   at the points a and b. find the coordinates of the  mid-point of ab. [5] 3 (i) given that   y = 1 + ln (2 x\u2013 3),   obtain an expression for  . [2] (ii) hence find, in terms of p, the approximate value of ywhen  x = 2 + p,  where p is small. [3] 4 the function f is given by   f : x\uf0612 + 5 sin 3x  for 0\u00b0 /h11088x/h11088180\u00b0. (i) state the amplitude and period of f. [2]  (ii) sketch the graph of y= f(x). [3] 5 the binomial expansion of (1 + px)n, where n > 0, in ascending powers of xis 1 \u2013 12x + 28p2x2+ qx3+ ... . find the value of n, of p and of q. [6] 6 it is given that   a = /h20898/h20899 and that   a +a\u20131= ki,  where p and kare constants and i is the identity matrix. evaluate p and k. [6]31 5pdy\u2013\u2013\u2013dx",
            "4": "4 0606/02/o/n/05 \u00a9 ucles 20057 in the diagram  op\u2192 = p,  oq\u2192 = q,  pm\u2192 = pq\u2192  and  on\u2192 = oq\u2192. (i) given that ox\u2192 = mom\u2192, express ox\u2192 in terms of m, p and q. [2] (ii) given that px\u2192 = npn\u2192, express ox\u2192 in terms of n, p and q. [3] (iii) hence evaluate m and n. [2] 8 (a) find the value of each of the integers pand q for which   /h20898/h20899\u2013 = 2p\u00d75q. [2] (b) (i) express the equation   4x\u2013 2x+ 1= 3   as a quadratic equation in 2x. [2]   (ii) hence find the value of x, correct to 2 decimal places. [3] 9 the function   f(x) = x3\u2013 6x2+ ax+ b,   where a and bare constants, is exactly divisible by  x\u2013 3  and leaves a remainder of \u201355 when divided by  x+ 2. (i) find the value of aand of b. [4] (ii) solve the equation f(x) = 0. [4] 10 a curve is such that   = 6x \u2013 2.   the gradient of the curve at the point (2, \u20139) is 3. (i) express y in terms of x. [5] (ii) show that the gradient of the curve is never less than \u2013 . [3] 11 (a) each day a newsagent sells copies of 10 different newspapers, one of which is the times . a customer buys 3 different newspapers. calculate the number of ways the customer can select his newspapers (i) if there is no restriction, [1] (ii) if 1 of the 3 newspapers is the times . [1] (b) calculate the number of different 5-digit numbers which can be formed using the digits 0,1,2,3,4 without repetition and assuming that a number cannot begin with 0. [2] how many of these 5-digit numbers are even? [4]16\u2013\u20133d2y\u2013\u2013\u2013\u2013 dx23\u20132 25\u2013\u2013162\u201351\u20133p m q onxp q",
            "5": "5 0606/02/o/n/05 \u00a9 ucles 200512 answer only one of the following two alternatives. either the diagram, which is not drawn to scale, shows part of the curve   y= x2\u2013 10x + 24   cutting the x-axis at q(4, 0). the tangent to the curve at the point pon the curve meets the coordinate axes at s(0, 15) and at  t(3.75, 0). (i) find the coordinates of p. [4]  the normal to the curve at p meets the x-axis at r. (ii) find the coordinates of r. [2] (iii) calculate the area of the shaded region bounded by the x-axis, the line pr and the curve pq. [5] or a curve has the equation   y= 2cos x\u2013 cos 2x,   where 0 < x /h11088 . (i) obtain expressions for   and . [4] (ii) given that  sin 2x may be expressed as  2sin xcosx,  find the x-coordinate of the stationary point of the curve and determine the nature of this stationary point. [4] (iii) evaluate   \u222bydx. [3]d2y\u2013\u2013\u2013\u2013 dx2dy\u2013\u2013\u2013dx\u03c0\u20132s (0, 15) q (4, 0)p rot (3.75, 0)xy y = x2 \u2013 10x + 24 \u03c0/2 \u03c0/3",
            "6": "6 0606/02/o/n/05blank page",
            "7": "7 0606/02/o/n/05blank page",
            "8": "8 0606/02/o/n/05blank 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, thepublisher will be pleased to make amends at the earliest possible opportunity. university of cambridge international examinations is part of the university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge."
        }
    },
    "2006": {
        "0606_s06_qp_1.pdf": {
            "1": "this document consists of 5 printed pages and 3 blank pages. spa (nf/kn) t04535 \u00a9 ucles 2006 [turn overuniversity of cambridge international examinations international general certificate of secondary education additional mathematics 0606/01 paper 1 may/june 2006 2 hours additional materials: answer booklet/paper electronic calculator graph papermathematical tables read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen on both sides of the paper.you may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of anglesin degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.you are reminded of the need for clear presentation in your answers. 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 80.at the end of the examination, fasten all your work securely together.",
            "2": "2 0606/01/m/j/06 \u00a9 ucles 2006mathematical formulae 1. algebra quadratic equation for the equation ax2+ bx + c= 0, . binomial theorem (a+ b)n= an+ an\u20131b+ an\u20132b2 + \u2026 + an\u2013rbr+ \u2026 + bn, where n is a positive integer and = . 2. trigonometry identities sin2a+ cos2a= 1. sec2a= 1 + tan2a. cosec2a= 1 + cot2a. formulae for \u2206 abc = = . a2= b2+ c2\u2013 2bc cos a. \u2206= bcsin a.1 2c sin cb sin ba sin an! (n\u2013 r)!r!)n r()n r( )n 2( )n1(xbb a c a=\u2212\u00b1 \u221224 2",
            "3": "3 0606/01/m/j/06 \u00a9 ucles 2006 [turn over1 a curve has the equation   y= (x\u2013 1)(2x \u2013 3)8.   find the gradient of the curve at the point where x= 2. [4] 2 the line   y + 4x = 23   intersects the curve   xy+ x= 20   at two points, aand b.  find the equation of the perpendicular bisector of the line ab. [6] 3 a plane flies due north from ato b, a distance of 1000 km, in a time of 2 hours. during this time a steady wind, with a speed of 150 km h\u20131, is blowing from the south-east. find  (i) the speed of the plane in still air, [4] (ii) the direction in which the plane must be headed. [2] 4 the diagram shows part of the curve  y= f(x),  where   f(x) = p \u2013 exand p is a constant.   the curve crosses the y-axis at (0, 2).   (i) find the value of p. [2] (ii) find the coordinates of the point where the curve crosses the x-axis. [2] (iii) copy the diagram above and on it sketch the graph of  y= f\u20131(x). [2] 5 the matrices a and b are given by   a= /h20898/h20899, b= /h20898/h20899.   find matrices p and q such that (i) p = b2\u2013 2a, [3] (ii) q = b(a\u20131). [4] 6 the cubic polynomial f(x) is such that the coefficient of x3is 1 and the roots of f(x) = 0 are  \u20132, 1 + and 1 \u2013 . (i) express f(x) as a cubic polynomial in xwith integer coefficients. [3] (ii) find the remainder when f(x) is divided by   x\u2013 3. [2] (iii) solve the equation  f(\u2013 x) = 0. [2]3 30\u2013 1 43\u20132 \u20131 6212 12y x o",
            "4": "4 0606/01/m/j/06 \u00a9 ucles 20067 a particle moves in a straight line, so that, t s after leaving a fixed point o, its velocity, v ms\u20131, is given by v= pt2+ qt+ 4, where pand qare constants. when t = 1 the acceleration of the particle is 8 m s\u20132. when t = 2 the displacement of the particle from o is 22 m. find the value of pand of q. [7] 8 (i) given that   y = ,   show that   = . [5] (ii) the diagram shows part of the curve   y= .   using the result given in part (i), find the   area of the shaded region bounded by the curve, the x-axis and the lines x = and x= .   [3] 9 (a) given that u = log4x, find, in simplest form in terms of u, (i) x, (ii) log4/h20898/h20899 , (iii) logx8. [5] (b) solve the equation   (log3y)2+ log3(y2) = 8. [4] 10 the function f is defined, for 0\u00b0 /h11088x/h11088180\u00b0, by  f(x) = 3cos 4x \u2013 1. (i) solve the equation f(x) = 0. [3]   (ii) state the amplitude of f. [1] (iii) state the period of f. [1] (iv) state the maximum and minimum values of f. [2] (v) sketch the graph of y= f(x). [3]16\u2013\u2013x5\u03c0\u2013\u2013 \u201343\u03c0\u2013\u2013 \u201342\u2013\u2013\u2013\u2013\u2013\u2013\u20131 \u2013 sin xy x oy = 2\u2013\u2013\u2013\u2013\u2013\u20131 \u2013 sinx 3\u03c0\u2013\u2013\u201345\u03c0\u2013\u2013\u201341\u2013\u2013\u2013\u2013\u2013\u2013\u20131 \u2013 sin xdy\u2013\u2013dx1 + sin x\u2013\u2013\u2013\u2013\u2013\u2013\u2013cosx",
            "5": "5 0606/01/m/j/06 \u00a9 ucles 200611 answer only one of the following two alternatives. either the table below shows values of the variables xand ywhich are related by the equation y= , where a and b are constants. (i) using graph paper, plot yagainst xy and draw a straight line graph. [3] (ii) use your graph to estimate the value of aand of b. [4] an alternative method for obtaining a straight line graph for the equation   y= is to plot x on the vertical axis and on the horizontal axis. (iii) without drawing a second graph, use your values of aand bto estimate the gradient and the intercept on the vertical axis of the graph of xplotted against . [3] or the diagram, which is not drawn to scale, shows a quadrilateral abcd in which a is (6, \u20133), b is (0, 6) and angle bad is 90\u00b0. the equation of the line bcis   5y = 3x + 30   and c lies on the line   y= x.   the line cd is parallel to the y-axis. (i) find the coordinates of cand of d. [6] (ii) show that triangle bad is isosceles and find its area. [4]y x obc d a(6, \u20133)(0, 6)y = x 5y = 3x + 301\u2013y1\u2013\u2013ya\u2013\u2013 \u2013\u2013\u2013x + ba\u2013\u2013 \u2013\u2013\u2013x + b x 0.1 0.4 1.0 2.0 3.0 y 8.0 6.0 4.0 2.6 1.9",
            "6": "6 0606/01/m/j/06blank page",
            "7": "7 0606/01/m/j/06blank page",
            "8": "8 0606/01/m/j/06blank 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 atthe earliest possible opportunity. university of cambridge international examinations is part of the university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge."
        },
        "0606_s06_qp_2.pdf": {
            "1": "this document consists of 6 printed pages and 2 blank pages. spa (nf/kn) t04646 \u00a9 ucles 2006 [turn overuniversity of cambridge international examinations international general certificate of secondary education additional mathematics 0606/02 paper 2 may/june 2006 2 hours additional materials: answer booklet/paper electronic calculator mathematical tables read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen on both sides of the paper.you may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of anglesin degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.you are reminded of the need for clear presentation in your answers. 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 80.at the end of the examination, fasten all your work securely together.",
            "2": "2 0606/02/m/j/06 \u00a9 ucles 2006mathematical formulae 1. algebra quadratic equation for the equation ax2+ bx + c= 0, . binomial theorem (a+ b)n= an+ an\u20131b+ an\u20132b2 + \u2026 + an\u2013rbr+ \u2026 + bn, where n is a positive integer and = . 2. trigonometry identities sin2a+ cos2a= 1. sec2a= 1 + tan2a. cosec2a= 1 + cot2a. formulae for \u2206 abc = = . a2= b2+ c2\u2013 2bc cos a. \u2206= bcsin a.1 2c sin cb sin ba sin an! (n\u2013 r)!r!)n r()n r( )n 2( )n1(xbb a c a=\u2212\u00b1 \u221224 2",
            "3": "3 0606/02/m/j/06 \u00a9 ucles 2006 [turn over1 variables xand yare connected by the equation   y= (3x \u2013 1) ln x.   given that xis increasing at the rate of 3 units per second, find the rate of increase of ywhen x = 1. [4] 2 the table shows the number of games played and the results of five teams in a football league. played won drawn lost parrots 8530 quails 7412 robins 8404 swallows 7214 terns 8116 a win earns 3 points, a draw 1 point and a loss 0 points. write down two matrices which on multiplication display in their product the total number of points earned by each team and hencecalculate these totals. [4] 3 the points a and bare such that the unit vector in the direction of ab\u2192is   0.28i + pj,   where p is a positive constant. (i) find the value of p. [2]   the position vectors of aand b, relative to an origin o, are   qi \u2013 7j and   12i + 17j respectively. (ii) find the value of the constant q. [3] 4 (a) differentiate   e tanxwith respect to x. [2]  (b) evaluate /h208480e1\u20132xdx. [4]   5 the diagram shows a right-angled triangle abc in which the length of acis ( + )cm. the area of triangle abc is (1 + )cm2. (i) find the length of abin the form (a + b )cm, where a and b are integers. [3] (ii) express (bc)2in the form (c + d )cm2, where c and d are integers. [3] 155 3155 3b ac1\u20132",
            "4": "4 0606/02/m/j/06 \u00a9 ucles 20066 (a) the venn diagram above represents the universal set /h5105of all teachers in a college. the sets c, b and prepresent teachers who teach chemistry, biology and physics respectively.  sketch the diagram twice.  (i) on the first diagram shade the region which represents those teachers who teach  physics and chemistry but not biology. [1] (ii) on the second diagram shade the region which represents those teachers who teach either biology or chemistry or both, but not physics. [1] (b) in a group of 20 language teachers, fis the set of teachers who teach french and s is the set of teachers who teach spanish. given that n( f) = 16 and n(s) = 10, state the maximum and minimum possible values of (i) n(f\u2229 s), (ii) n(f\u222a s). [4]  7 (a) 7 boys are to be seated in a row. calculate the number of different ways in which this can be done if 2 particular boys, andrew and brian, have exactly 3 of the other boys between them. [4] (b) a box contains sweets of 6 different flavours. there are at least 2 sweets of each flavour. a girlselects 3 sweets from the box. given that these 3 sweets are not all of the same flavour, calculatethe number of different ways she can select her 3 sweets. [3] 8 (i) in the binomial expansion of    /h20898x + /h208998 , where k is a positive constant, the term independent of x is 252. evaluate k. [4] (ii) using your value of k, find the coefficient of x4in the expansion of   /h208981\u2013  /h20899/h20898x + /h208998 . [3]k\u2013\u2013 x3x4\u2013\u20134k\u2013\u2013 x3c b p/h5105",
            "5": "5 0606/02/m/j/06 \u00a9 ucles 2006 [turn over9 a cuboid has a total surface area of 120 cm2.  its base measures x cm by 2x cm and its height is h cm. (i) obtain an expression for hin terms of x. [2] given that the volume of the cuboid is vcm3, (ii) show that   v = 40x \u2013 . [1] given that x can vary, (iii) show that v has a stationary value when   h= . [4] 10 (a) given that   a = sec x + cosec x and   b = sec x \u2013 cosec x,   show that  a2+ b2\u22612sec2xcosec2x. [4] (b) find, correct to 2 decimal places, the values of ybetween 0 and 6 radians which satisfy the equation  2cot y = 3sin y. [5] 11 the diagram shows a sector oacb of a circle, centre o, in which angle aob = 2.5 radians. the line ac is parallel to ob. (i) show that angle aoc = (5 \u2013 \u03c0) radians. [3] given that the radius of the circle is 12 cm, find (ii) the area of the shaded region, [3] (iii) the perimeter of the shaded region. [3]2.5 rad o bc a4x\u2013\u201334x3\u2013\u2013\u20133",
            "6": "6 0606/02/m/j/06 \u00a9 ucles 200612 answer only one of the following two alternatives. either (i) express   2x2\u2013 8x + 3   in the form   a(x+ b)2+ c,   where a, b and c are integers. [2] a function f is defined by   f : x\uf0612x2\u2013 8x + 3,   x \u2208/h11938. (ii) find the coordinates of the stationary point on the graph of y= f (x). [2] (iii) find the value of f2(0). [2] a function g is defined by   g : x\uf0612x2\u2013 8x + 3,   x \u2208/h11938,   where x /h11088n.  (iv) state the greatest value of n for which g has an inverse. [1] (v) using the result obtained in part (i), find an expression for g\u20131. [3] or the equation of a curve is   y= 10 \u2013 x2+ 6x. (i) find the set of values of xfor which y /h1109115. [3] (ii) express y in the form   a \u2013 (x+ b)2,   where a andbare integers. [2] (iii) hence, or otherwise, find the coordinates of the stationary point on the curve. [2] functions f and g are defined, for x\u2208/h11938, by f : x\uf061 10 \u2013 x2+ 6x, g : x\uf0612x\u2013 k, where k is a constant. (iv) find the value of kfor which the equation   gf ( x) = 0   has two equal roots. [3]",
            "7": "7 0606/02/m/j/06blank page",
            "8": "8 0606/02/m/j/06blank 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 atthe earliest possible opportunity. university of cambridge international examinations is part of the university of cambridge local examinations syndicate (ucles), which is itself a department of the university of cambridge."
        },
        "0606_w06_qp_1.pdf": {
            "1": "university of cambridge international examinations international general certificate of secondary education additional mathematics  0606/01 paper 1 october/november 2006 2 hours additional materials: answer paper  electronic calculator graph paper (1 sheet) mathematical tables read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen on both sides of the paper.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. 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 80.at the end of the examination, fasten all your work securely together. this document consists of 6 printed pages and 2 blank pages. sp (slm) t26709/1 \u00a9 ucles 2006 [turn over",
            "2": "2 0606/01/o/n/06 \u00a9 ucles 2006mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!. 2. trigonometry identities  sin2 a + cos2 a = 1.  sec2 a = 1 + tan2 a.  cosec2 a = 1 + cot2 a. formulae for \u2206 abc a sin a = b sin b = c sin c . a2 = b2 + c2 \u2013 2bc cos a. \u2206 = 1  2 bc sin a .",
            "3": "3 0606/01/o/n/06 \u00a9 ucles 2006 [turn over1 express each of the following statements in appropriate set notation.  (i) x is not an element of set a.  (ii) the number of elements not in set b is 16.  (iii) sets c and d have no common element.  [3] 2 \u20131 \u20133\u2013201y 60\u00b0 120\u00b0 90\u00b0 30\u00b0 x  the diagram shows part of the graph of   y = asin(bx) + c.   state the value of  (i) a,  (ii) b,  (iii) c.  [3] 3 the equation of a curve is   y = 8 (3x \u2013 4)2 .  (i) find the gradient of the curve where x = 2. [3]  (ii) find the approximate change in y when x increases from 2 to 2 + p, where p is small. [2] 4 the vector \u2192op has a magnitude of 10 units and is parallel to the vector  3 i \u2212 4j. the vector \u2192oq has a  magnitude of 15 units and is parallel to the vector 4 i + 3j.  (i) express  \u2192op  and  \u2192oq  in terms of i and j. [3]  (ii) given that the magnitude of  \u2192pq  is  \u03bb13,  find the value of \u03bb . [3]",
            "4": "4 0606/01/o/n/06 \u00a9 ucles 20065 a large airline has a fleet of aircraft consisting of 5 aircraft of type a, 8 of type b, 4 of type c and  10 of type d. the aircraft have 3 classes of seat known as economy, business and first. the table  below shows the number of these seats in each of the 4 types of aircraft. class of seat type of aircrafteconomy business first a 300 60 40 b 150 50 20 c 120 40 0 d 100 0 0  (i) write down two matrices whose product shows the total number of seats in each class.  (ii) evaluate this product of matrices.  on a particular day, each aircraft made one flight. 5% of the economy seats were empty, 10% of the  business seats were empty and 20% of the first seats were empty.  (iii) write down a matrix whose product with the matrix found in part (ii) will give the total number of  empty seats on that day.  (iv) evaluate this total.  [6] 6 given that the coefficient of  x2  in the expansion of  ( k + x)(2 \u2013 x 2)6  is 84, find the value of the  constant k.  [6] 7 the function f is defined for the domain  \u20133 /h11088 x /h11088 3  by f(x) = 9(x \u2013 1 3)2 \u2013 11.  (i) find the range of f. [3]  (ii) state the coordinates and nature of the turning point of   (a) the curve y = f(x),   (b) the curve y =  /h20919 f(x) /h20919.  [4]",
            "5": "5 0606/01/o/n/06 \u00a9 ucles 2006 [turn over8 (a) solve the equation   lg( x + 12) = 1 + lg(2 \u2013 x). [3]  (b) given that  log2 p = a,  log8 q = b  and  p q = 2c,  express c in terms of a and b. [4] 9 a curve has the equation   y = 2x \u2013 4 x + 3 .  (i) obtain an expression for dydx and hence explain why the curve has no turning points. [3]  the curve intersects the x-axis at the point p. the tangent to the curve at p meets the y-axis at the  point q.  (ii) find the area of the triangle poq, where o is the origin. [5] 10 the cubic polynomial f( x) is such that the coefficient of  x 3  is 1 and the roots of f( x) = 0 are 1, k and k2.  it is given that f( x) has a remainder of 7 when divided by  x \u2013 2.  (i) show that   k3 \u2013 2k2 \u2013 2k \u2013 3 = 0. [3]  (ii) hence find a value for k and show that there are no other real values of k which satisfy this  equation. [5] 11 (a) solve, for  0\u00b0 /h11088 x /h11088 360\u00b0,  the equation     2cot x = 1 + tan x. [5]  (b) given that y is measured in radians, find the two smallest positive values of y such that     6sin(2y + 1) + 5 = 0. [5]",
            "6": "6 0606/01/o/n/06 \u00a9 ucles 200612 answer only one of the following two alternatives.  either y xb ao cy = 4  \u2013 e\u20132 x  the diagram shows part of the curve   y = 4 \u2013 e\u20132x   which crosses the axes at a and at b.  (i) find the coordinates of a and of b. [2]  the normal to the curve at b meets the x-axis at c.  (ii) find the coordinates of c. [4]  (iii) show that the area of the shaded region is approximately 10.3 square units. [5]  or  the variables x and y are related by the equation  y = 10\u2013abx, where a and b are constants. the table  below shows values of x and y. x   15 20 25 30 35 40 y0.15 0.38 0.95 2.32 5.90 14.80  (i) draw a straight line graph of lg y against x, using a scale of 2 cm to represent 5 units on the x-axis  and 2 cm to represent 0.5 units on the lg y  - axis. [2]  (ii) use your graph to estimate the value of a and of b. [4]  (iii) estimate the value of x when y = 10. [2]  (iv) on the same diagram, draw the line representing   y5 = 10\u2013x   and hence find the value of x    for which   10a \u2013 x 5 = bx. [3]",
            "7": "7 0606/01/o/n/06blank page",
            "8": "8 0606/01/o/n/06blank 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. university of cambridge international examinations is part of the university of cambridge local examinations syndicate (ucles), which is itself a department  of the university of cambridge."
        },
        "0606_w06_qp_2.pdf": {
            "1": "university of cambridge international examinations international general certificate of secondary education additional mathematics 0606/02 paper 2 october/november 2006 2 hours additional materials: answer paper  electronic calculator mathematical tables read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen on both sides of the paper.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. 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 80.at the end of the examination, fasten all your work securely together. this document consists of 5 printed pages and 3 blank pages. sp (slm) t26710/1 \u00a9 ucles 2006 [turn over",
            "2": "2 0606/02/o/n/06 \u00a9 ucles 2006mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  . 2. trigonometry identities sin2 a + cos2 a = 1. sec2 a = 1 + tan2 a. cosec2 a = 1 + cot2 a. formulae for \u2206 abc a sin a = b sin b = c sin c  . a2 = b2 + c2 \u2013 2bc cos a. \u2206 = 12 bc sin a.",
            "3": "3 0606/02/o/n/06 \u00a9 ucles 2006 [turn over1 the functions f and g are defined for x /h20678 /h11938 by     f : x  /h21739 x3,     g : x  /h21739 x + 2.  express each of the following as a composite function, using only f, g, f \u20131 and/or g\u20131 :  (i) x /h21739 x3 + 2, [1]  (ii) x /h21739 x3 \u2013 2, [1]  (iii) x /h21739 (x + 2)1 3. [1] 2 prove the identity  cos x cot x + sin x /h11013 cosec x . [4] 3 evaluate      \u222b0\u03c0\u20136sin(2x + \u03c0\u20136 )dx.  [4] 4 90  m2 ms\u20131 ab   the diagram shows a river 90 m wide, flowing at 2 ms\u20131 between parallel banks. a ferry travels in a  straight line from a point a to a point b directly opposite a. given that the ferry takes exactly one  minute to cross the river, find  (i) the speed of the ferry in still water, [3]  (ii) the angle to the bank at which the ferry must be steered. [2] 5  the straight line   2 x + y  =  14   intersects the curve   2 x2 \u2013 y2  =  2 xy \u2013 6   at the points a and b. show  that the length of ab is 24 5 units. [7]",
            "4": "4 0606/02/o/n/06 \u00a9 ucles 20066  a curve has equation   y  =  x3 + ax + b,   where a and b  are constants. the gradient of the curve at the  point (2, 7) is 3. find  (i) the value of a and of b, [5]  (ii) the coordinates of the other point on the curve where the gradient is 3. [2] 7 (a) find the value of m for which the line   y = mx \u2013 3   is a tangent to the curve   y = x + 1 x    and find  the x-coordinate of the point at which this tangent touches the curve. [5]  (b) find the value of c and of d for which   {x : \u2013 5 < x < 3}   is the solution set of   x2 + cx < d. [2] 8 given that   a = 41 32\u2212 \u2212\u239b \u239d\u239c\u239e \u23a0\u239f ,   use the inverse matrix of a to   (i) solve the simultaneous equations  y  \u2013 4x + 8  =  0,  2 y \u2013 3x + 1  =  0,  (ii) find the matrix b such that   ba = \u2212 \u2212\u239b \u239d\u239c\u239e \u23a0\u239f23 91.  [8] 9 (a) express   258 352\u2212() \u2212 \u2212   in the form p + q 5, where p and q are integers. [4]  (b) given that   a bb aabx xy y 3 126 \u2212 +\u00d7 ()= ,   find the value of x and of y. [4] 10 (a) how many different four-digit numbers can be formed from the digits 1, 2, 3, 4, 5, 6,  7, 8, 9 if no digit may be repeated? [2]  (b) in a group of 13 entertainers, 8 are singers and 5 are comedians. a concert is to be given by 5 of these entertainers. in the concert there must be at least 1 comedian and there must be more singers than comedians. find the number of different ways that the 5 entertainers can be selected. [6] 11 the equation of a curve is    yxx =\u2212e2.  (i) show that   d dey xxx =\u2212()\u2212 1 22 2. [3]  (ii) find an expression for d2y dx2 . [2]  the curve has a stationary point at m.  (iii) find the coordinates of m. [2]  (iv) determine the nature of the stationary point at m. [2]",
            "5": "5 0606/02/o/n/06 \u00a9 ucles 200612 answer only one of the following two alternatives.  either r cm /h9258radl om n   the diagram shows a sector of a circle, centre o and radius r cm. angle lom is \u03b8 radians. the tangent  to the circle at l meets the line through o and m at n. the shaded region shown has perimeter p cm  and area a cm2. obtain an expression, in terms of r and \u03b8, for  (i) p, [4]  (ii) a. [3]  given that \u03b8 = 1.2 and that p = 83, find the value of  (iii) r, [2]  (iv) a. [1]  or solutions to this question by accurate drawing will not be accepted. y xa (3, 3)  b (6, 3) coe (10, k)d   the diagram shows an isosceles triangle abc in which a is the point (3, 3), b is the point (6, 3) and  c lies below the x-axis. given that the area of triangle abc is 6 square units,  (i) find the coordinates of c. [3]  the line cb is extended to the point d so that b is the mid-point of cd.  (ii) find the coordinates of d. [2]  a line is drawn from d, parallel to ac, to the point e (10, k) and c is joined to e.  (iii) find the value of k. [3]  (iv) prove that angle ced is not a right angle. [2]",
            "6": "6 0606/02/o/n/06blank page",
            "7": "7 0606/02/o/n/06blank page",
            "8": "8 0606/02/o/n/06blank 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. university of cambridge international examinations is part of the university of cambridge local examinations syndicate (ucles), which is itself a department  of the university of cambridge."
        }
    },
    "2007": {
        "0606_s07_qp_1.pdf": {
            "1": "this document consists of 6 printed pages and 2 blank pages. sp (slm/cgw) t35481/2 \u00a9 ucles 2007 [turn overuniversity of cambridge international examinations international general certificate of secondary education read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. *1398595418*additional mathematics 0606/01 paper 1 may/june 2007  2 hours additional materials: answer booklet/paper graph paper electronic calculator mathematical tables",
            "2": "2 0606/01/m/j/07 \u00a9 ucles 2007mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1. sec2 a = 1 + tan2 a. cosec2 a = 1 + cot2 a. formulae for \u2206 abc a sin a = b sin b = c sin c . a2 = b2 + c2 \u2013 2bc cos a. \u2206 = 1  2 bc sin a .",
            "3": "3 0606/01/m/j/07 \u00a9 ucles 2007 [turn over1 (a) a bc/h5105   the diagram above shows a universal set /h5105 and the three sets a, b and c.   (i) copy the above diagram and shade the region representing ( a  c/h11032)  b. [1]   (ii) a bc/h5105    express, in set notation, the set represented by the shaded region in the diagram above. [1]  (b) x y/h5105   the diagram shows a universal set /h5105 and the sets x and y. show, by means of two diagrams, that  the set (x  y)/h11032 is not the same as the set x/h11032  y /h11032. [2] 2 find the equation of the normal to the curve   y = 2x + 4 x \u2013 2   at the point where x = 4. [5] 3 the straight line   3 x = 2y + 18   intersects the curve   2 x2 \u2013 23x + 2y + 50 = 0   at the points a and b.  given that a lies below the x-axis and that the point p lies on ab such that ap : pb = 1 : 2, find the  coordinates of p. [6] 4 (i) find the first three terms, in ascending powers of u, in the expansion of   (2 + u)5. [2]  (ii) by replacing u with   2x \u2013 5x2,   find the coefficient of  x2  in the expansion of   (2 + 2 x \u2013 5x2)5.  [4]",
            "4": "4 0606/01/m/j/07 \u00a9 ucles 20075 a curve has the equation   yx x=+9 .  (i) find expressions for   dy dx   and   d2y dx2 . [4]  (ii) show that the curve has a stationary value when x = 9. [1]  (iii) find the nature of this stationary value. [2] 6 a b oj i  the diagram shows a large rectangular television screen in which one corner is taken as the origin o  and i and j are unit vectors along two of the edges. in a game, an alien spacecraft appears at the point  a with position vector 12 j cm and moves across the screen with velocity (40 i + 15j) cm per second. a  player fires a missile from a point b; the missile is fired 0.5 seconds after the spacecraft appears on the  screen. the point b has position vector 46 i cm and the velocity of the missile is ( ki +30j) cm per second,  where k is a constant. given that the missile hits the spacecraft,  (i) show that the spacecraft moved across the screen for 1.8 seconds before impact, [4]  (ii) find the value of k. [3] 7 (a) use the substitution   u = 5x   to solve the equation   5x + 1 = 8 + 4 (5\u2013x). [5]  (b) given that   log( p \u2013 q) = log p \u2013 log q ,   express p in terms of q. [3] 8 (a) solve, for 0 /h11088 x /h11088 2, the equation   1 + 5cos 3x = 0,   giving your answer in radians correct to  2 decimal places. [3]  (b) find all the angles between 0\u00ba and 360\u00ba such that     sec y + 5tan y = 3cos y. [5]",
            "5": "5 0606/01/m/j/07 \u00a9 ucles 2007 [turn over9 x 0.100 0.125 0.160 0.200 0.400 y 0.050 0.064 0.085 0.111 0.286  the table above shows experimental values of the variables x and y.  (i) on graph paper draw the graph of  1 y  against  1 x . [3]  hence,  (ii) express y in terms of x, [4]  (iii) find the value of x for which y = 0.15. [2] 10 a bed c 8m5m5m  the diagram shows an isosceles triangle abc in which ab = 8 m, bc = ca = 5 m. abda is a sector of  the circle, centre a and radius 8 m. cbec is a sector of the circle, centre c and radius 5 m.  (i) show that angle bce is 1.287 radians correct to 3 decimal places. [2]  (ii) find the perimeter of the shaded region. [4]  (iii) find the area of the shaded region. [4] [question 11 is printed on the next page.]",
            "6": "6 0606/01/m/j/07 \u00a9 ucles 200711 answer only one of the following two alternatives.  either y y = 3  sin x + 4  cos  x x o \u03c0 2  the graph shows part of the curve   y = 3sin x + 4 cos x   for 0 /h11088 x /h11088 \u03c0 2 radians.  (i) find the coordinates of the maximum point of the curve. [5]  (ii) find the area of the shaded region. [5]  or y y = (3x + 2)212 x oba c  the diagram, which is not drawn to scale, shows part of the curve   y = 12 (3x + 2)2 ,   intersecting the  y-axis at a. the tangent to the curve at a meets the x-axis at b. the point c lies on the curve and bc is  parallel to the y-axis.  (i) find the x-coordinate of b. [4]  (ii) find the area of the shaded region. [6]",
            "7": "7 0606/01/m/j/07blank page",
            "8": "8 0606/01/m/j/07blank 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. 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."
        },
        "0606_s07_qp_2.pdf": {
            "1": "this document consists of 5 printed pages and 3 blank pages. sp (slm/cgw) t31723/2 \u00a9 ucles 2007 [turn overuniversity of cambridge international examinations international general certificate of secondary education read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. *9948893586*additional mathematics 0606/02 paper 2 may/june 2007  2 hours additional materials: answer booklet/paper electronic calculator mathematical tables",
            "2": "2 0606/02/m/j/07 \u00a9 ucles 2007mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1. sec2 a = 1 + tan2 a. cosec2 a = 1 + cot2 a. formulae for \u2206 abc a sin a = b sin b = c sin c . a2 = b2 + c2 \u2013 2bc cos a. \u2206 = 1  2 bc sin a .",
            "3": "3 0606/02/m/j/07 \u00a9 ucles 2007 [turn over1 a triangle has a base of length (13 \u2013 2 x) m and a perpendicular height of x m. calculate the range of  values of x for which the area of the triangle is greater than 3 m2. [3] 2 0135y x 2\u2013 \u03c0 4\u2013 \u03c0 4 \u03c0 2 \u03c0  the diagram shows part of the graph of y = a tan (bx) + c. find the value of    (i) c,           (ii) b,           (iii) a. [3] 3 the roots of the equation   xx228 2 0\u2212 +=    are p and q, where p >  q. without using a calculator,  express p q  in the form  mn+ , where m and n are integers. [5] 4 an artist has 6 watercolour paintings and 4 oil paintings. she wishes to select 4 of these 10 paintings  for an exhibition.   (i) find the number of different selections she can make. [2]  (ii) in how many of these selections will there be more watercolour paintings than oil paintings? [3] 5 (i) express  1 32  as a power of 2. [1]  (ii) express  ()641 x as a power of 2. [1]  (iii) hence solve the equation  ()64 21 321 x x= . [3] 6 (i) differentiate x2 ln x with respect to x. [2]  (ii) use your result to show that  /h20885e 14x ln x dx = e2 + 1. [4]",
            "4": "4 0606/02/m/j/07 \u00a9 ucles 20077 given that a = /h20898 2 3  \u20132 \u20131/h20899  and b = /h20898 8 10 \u2013 4 2/h20899, find the matrices x and y such that   (i) x = a2 + 2b, [3]  (ii) ya = b. [4] 8 the equation of the curve c is   2y = x2 + 4.   the equation of the line l is   y  = 3x \u2013 k,   where k is an  integer.   (i) find the largest value of the integer k for which l intersects c. [4]  (ii) in the case where k = \u2013 2, show that the line joining the points of intersection of l and c is bisected  by the line   y = 2x + 5. [4] 9 the position vectors, relative to an origin o, of three points  p, q and r are i + 3j , 5i + 11j and 9i + 9j  respectively.  (i) by finding the magnitude of the vectors \u2192pr, \u2192rq and \u2192qp, show that angle pqr is 90\u00b0. [4]  (ii) find the unit vector parallel to \u2192pr. [2]  (iii) given that \u2192oq = m\u2192op + n\u2192or, where m and n are constants, find the value of m and of n. [3] 10 the functions f and g are defined, for x /h9280 /h11938, by     f  :  x a  3x \u2013 2,    g : x a  7x \u2013 a x + 1 , where x \u2260 \u20131 and a is a positive constant.  (i) obtain expressions for f\u20131 and g\u20131. [3]  (ii) determine the value of a for which f\u20131g(4) = 2. [3]  (iii) if a = 9, show that there is only one value of x for which g(x) = g\u20131(x). [3] 11 a particle, moving in a straight line, passes through a fixed point o with velocity 14 ms\u20131. the  acceleration, a ms\u20132, of the particle, t seconds after passing through o, is given by   a = 2t \u2013 9.   the  particle subsequently comes to instantaneous rest, firstly at a and later at  b. find   (i) the acceleration of the particle at a and at b, [4]  (ii) the greatest speed of the particle as it travels from a to b, [2]  (iii) the distance ab. [4]",
            "5": "5 0606/02/m/j/07 \u00a9 ucles 200712 answer only one of the following two alternatives.  either  solutions to this question by accurate drawing will not be accepted. o dcb a e (3,  4)(\u20131, 6) xy  the diagram shows a quadrilateral abcd. the point e lies on ad such that angle aeb = 90\u00b0. the line  ec is parallel to the x-axis and the line cd is parallel to the y-axis. the points a and e are (\u2013 1, 6) and  (3, 4) respectively. given that the gradient of ab is 1 3 ,  (i) find the coordinates of b. [5]  given also that the area of triangle ebc is 24 units2,   (ii) find the coordinates of c, [3]  (iii) find the coordinates of d. [2]  or   (a) the expression   f(x) = x3 + ax2 + bx + c   leaves the same remainder, r, when it is divided by    x + 2   and when it is divided by   x \u2013 2.   (i) evaluate b. [2]   f(x) also leaves the same remainder, r, when divided by   x \u20131.    (ii) evaluate a. [2]   f(x) leaves a remainder of 4 when divided by   x \u2013 3.   (iii) evaluate c. [1]  (b) solve the equation   x3 + 3x2 = 2,   giving your answers to 2 decimal places where necessary. [5]",
            "6": "6 0606/02/m/j/07blank page",
            "7": "7 0606/02/m/j/07blank page",
            "8": "8 0606/02/m/j/07blank 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. 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."
        },
        "0606_w07_qp_1.pdf": {
            "1": "this document consists of 5 printed pages and 3 blank pages. sp (sc) t44477/2 \u00a9 ucles 2007 [turn overuniversity of cambridge international examinations international general certificate of secondary education read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. *1452322200*additional mathematics 0606/01 paper 1 october/november 2007  2 hours additional materials: answer booklet/paper graph paper (1 sheet) electronic calculator mathematical tables",
            "2": "2 0606/01/o/n/07 \u00a9 ucles 2007mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1. sec2 a = 1 + tan2 a. cosec2 a = 1 + cot2 a. formulae for \u2206 abc a sin a = b sin b = c sin c . a2 = b2 + c2 \u2013 2bc cos a. \u2206 = 1  2 bc sin a .",
            "3": "3 0606/01/o/n/07 \u00a9 ucles 2007 [turn over1 given that  a = (2 \u20131 3 1),  find the value of each of the constants m and n for which a2 + ma = ni,  where i is the identity matrix. [4] 2 show that 1\u2013\u2013\u2013\u2013\u2013\u2013\u20131 \u2013 cos \u03b8  \u2013  1\u2013\u2013\u2013\u2013\u2013\u2013\u20131 + cos \u03b8   \u2261  2cosec \u03b8 cot \u03b8.   [4] 3 given that  p = 3 + 1 3 \u2013 1 ,  express in its simplest surd form,  (i) p, [3]  (ii) p \u2013 1\u2013p. [2] 4 a badminton team of 4 men and 4 women is to be selected from 9 men and 6 women.   (i) find the total number of ways in which the team can be selected if there are no restrictions on the  selection. [3]  two of the men are twins.  (ii) find the number of ways in which the team can be selected if exactly one of the twins is in the team. [3] 5 in this question, i is a unit vector due east, and j is a unit vector due north.  a plane flies from p to q where \u2192pq = (960i + 400j) km. a constant wind is blowing with velocity  (\u201360i + 60j) km h\u20131. given that the plane takes 4 hours to travel from p to q, find   (i) the velocity, in still air, of the plane, giving your answer in the form ( ai + bj) km h\u20131, [4]  (ii) the bearing, to the nearest degree, on which the plane must be directed. [2] 6 a curve is such that  dydx = 6 4x + 1 ,  and (6, 20) is a point on the curve.  (i) find the equation of the curve. [4]  a line with gradient \u2013 1 2 is a normal to the curve.  (ii) find the coordinates of the points at which this normal meets the coordinate axes. [4]",
            "4": "4 0606/01/o/n/07 \u00a9 ucles 20077 (i) use the substitution   u = 2x to solve the equation   22x = 2x + 2 + 5. [5]  (ii) solve the equation   2log93 + log5(7y \u2013 3) = log28. [4] 8 (a) the remainder when the expression   x3 \u2013 11x2 + kx \u2013 30   is divided by   x \u2013 1   is 4 times the  remainder when this expression is divided by   x \u2013 2.   find the value of the constant k. [4]  (b) solve the equation   x3 \u2013 4x2 \u2013 8x + 8 = 0,   expressing non-integer solutions in the form    a \u00b1 b,   where a and b are integers. [5] 9  x 2468 1 0 y 14.4 10.8 11.2 12.6 14.4  the table shows experimental values of two variables, x and y.  (i) using graph paper, plot xy against x2. [2]  (ii) use the graph of xy against x2 to express y in terms of x. [4]  (iii) find the value of y for which  y = 83\u2013\u2013x. [3] 10  adbc 0.8 rad 10 cm10 cm  the diagram shows a sector abc of the circle, centre a and radius 10 cm, in which angle  bac = 0.8 radians. the arc cd of a circle has centre b and the point d lies on ab.  (i) show that the length of the straight line bc is 7.79 cm, correct to 2 decimal places. [2]  (ii) find the perimeter of the shaded region. [4]  (iii) find the area of the shaded region. [4]",
            "5": "5 0606/01/o/n/07 \u00a9 ucles 200711 answer only one of the following two alternatives.  either  a curve has the equation   y = xe2x.  (i) obtain expressions for  dy dx  and  d2y dx2 . [5]  (ii) show that the y-coordinate of the stationary point of the curve is   \u2013 1 2e . [3]  (iii) determine the nature of this stationary point. [2]  or  (i) show that   d dx (ln x\u2013\u2013\u2013x2) = 1 \u2013 2 lnx\u2013\u2013\u2013\u2013\u2013\u2013\u2013x3 . [3]  (ii) show that the y-coordinate of the stationary point of the curve  y = ln x\u2013\u2013\u2013x2  is  1\u2013\u20132e . [3]  (iii) use the result from part  (i) to find   \u222b (ln x\u2013\u2013\u2013x3) dx. [4]",
            "6": "6 0606/01/o/n/07blank page",
            "7": "7 0606/01/o/n/07blank page",
            "8": "8 0606/01/o/n/07blank 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. 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."
        },
        "0606_w07_qp_2.pdf": {
            "1": "this document consists of 6 printed pages and 2 blank pages. sp (sc) t44479/1 \u00a9 ucles 2007 [turn overuniversity of cambridge international examinations international general certificate of secondary education read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case ofangles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. *8975290358*additional mathematics 0606/02 paper 2 october/november 2007  2 hours additional materials: answer booklet/paper electronic calculator mathematical tables",
            "2": "2 0606/02/o/n/07 \u00a9 ucles 2007mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  . 2. trigonometry identities sin2 a + cos2 a = 1. sec2 a = 1 + tan2 a. cosec2 a = 1 + cot2 a. formulae for \u2206 abc a sin a = b sin b = c sin c . a2 = b2 + c2 \u2013 2bc cos a. \u2206 = 1  2 bc sin a .",
            "3": "3 0606/02/o/n/07 \u00a9 ucles 2007 [turn over1 the two variables x and y are related by the equation   yx2 = 800.  (i) obtain an expression for   dy dx   in terms of x. [2]  (ii) hence find the approximate change in y as x increases from 10 to 10 + p, where p is small. [2] 2 solve the equation   3sin  (x\u20132 \u2013 1) = 1   for 0 < x < 6\u03c0  radians. [5]     3 (i) express  9 x + 1  as a power of 3.  [1]  (ii) express  3272x  as a power of 3. [1]  (iii) express  54 \u00d7 3272x\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u20139x + 1 + 216(32x \u2013 1)  as a fraction in its simplest form. [3] 4 a cycle shop sells three models of racing cycles, a, b and c. the table below shows the numbers of  each model sold over a four-week period and the cost of each model in $.           model weekabc 1  8 1 2 4 2  7 1 0 231 0 1 2 04  6   8 4 cost ($) 300 500 800  in the first two weeks the shop banked 30% of all money received, but in the last two weeks the shop  only banked  20% of all money received.    (i) write down three matrices such that matrix multiplication will give the total amount of money banked over the four-week period. [2]  (ii) hence evaluate this total amount. [4] 5 (i) expand   (1 + x) 5. [1]  (ii) hence express   (1 +   2)5   in the form   a + b   2,   where a and b are integers. [3]  (iii) obtain the corresponding result for   (1 \u2013   2)5   and hence evaluate   (1 +   2)5 + (1 \u2013   2)5. [2]",
            "4": "4 0606/02/o/n/07 \u00a9 ucles 20076 two circular flower beds have a combined area of  29\u03c0\u2013\u2013\u20132 m2.  the sum of the circumferences of the two  flower beds is 10\u03c0   m. determine the radius of each flower bed. [6] 7 the position vectors of points a and b, relative to an origin o, are  2i + 4j  and  6i + 10j  respectively.   the position vector of c, relative to o, is   ki + 25j,   where k is a positive constant.  (i) find the value of k for which the length of bc is 25 units. [3]  (ii) find the value of k for which abc is a straight line. [3] 8 given that x /h9280 /h11938 and that    /h5105 = {x : 2 < x < 10} ,      a = {x : 3x + 2 < 20}     and b = {x : x2 < 11x \u2013 28} ,   find the set of values of x which define   (i) a /h20669 b,  (ii) (a /h33371 b)/h11032.  [7] 9 a particle travels in a straight line so that, t s after passing through a fixed point o, its speed, v ms\u20131, is   given by   v = 8cos (t\u20132).  (i) find the acceleration of the particle when t = 1. [3]  the particle first comes to instantaneous rest at the point p.  (ii) find the distance op.  [4]",
            "5": "5 0606/02/o/n/07 \u00a9 ucles 2007 [turn over10  y x om x  the diagram shows part of the curve   y = 4   x \u2013 x.   the origin o lies on the curve and the curve  intersects the positive x-axis at x. the maximum point of the curve is at m. find   (i) the coordinates of x and of m, [5]  (ii) the area of the shaded region. [4] 11 solutions to this question by accurate drawing will not be accepted.  y x ocb a (6, \u20133)  the diagram shows a triangle abc in which a is the point (6, \u20133). the line ac passes through the  origin o. the line ob is perpendicular to ac.    (i) find the equation of ob. [2]  the area of triangle aob is 15 units2.    (ii) find the coordinates of b. [3]  the length of ao is 3 times the length of oc.  (iii) find the coordinates of c. [2]  the point d is such that the quadrilateral abcd is a kite.    (iv) find the area of abcd. [2]",
            "6": "6 0606/02/o/n/07 \u00a9 ucles 200712 answer only one of the following two alternatives.  either   the function f is defined, for x > 0, by   f : x /h21739 ln x.    (i) state the range of f. [1]  (ii) state the range of f \u20131. [1]  (iii) on the same diagram, sketch and label the graphs of  y = f(x)  and  y = f \u20131(x). [2]  the function g is defined, for x > 0, by   g : x /h21739 3x + 2.  (iv) solve the equation   fg ( x) = 3. [2]  (v) solve the equation   f \u20131g\u20131 (x) = 7. [4]  or (i) find the values of k for which   y = kx + 2   is a tangent to the curve   y = 4x 2 + 2x + 3. [4]  (ii) express   4x2 + 2x + 3   in the form   a(x + b)2 + c,   where a, b and c are constants. [3]  (iii) determine, with explanation, whether or not the curve   y = 4x2 + 2x + 3   meets the x-axis. [2]  the function f is defined by   f : x /h21739 4x2 + 2x + 3   where  x /h11091 p.   (iv) determine the smallest value of p for which f has an inverse. [1]",
            "7": "7 0606/02/o/n/07blank page",
            "8": "8 0606/02/o/n/07blank 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. 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."
        }
    },
    "2008": {
        "0606_s08_qp_1.pdf": {
            "1": "this document consists of 6 printed pages and 2 blank pages. spa (nf/dt) t56698 \u00a9 ucles 2008 [turn overuniversity of cambridge international examinations international general certificate of secondary education read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. *8575667431*additional mathematics 0606/01 paper 1 may/june 2008  2 hours additional materials: answer booklet/paper electronic calculator mathematical tables",
            "2": "2 0606/01/m/j/08 \u00a9 ucles 2008mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1. sec2 a = 1 + tan2 a. cosec2 a = 1 + cot2 a. formulae for \u2206 abc a sin a = b sin b = c sin c . a2 = b2 + c2 \u2013 2bc cos a. \u2206 = 1  2 bc sin a .",
            "3": "3 0606/01/m/j/08 \u00a9 ucles 2008 [turn over1 express   83 2 43 2\u2212 +   in the form  ab+ 2,  where a and b are integers. [3] 2 a committee of 5 people is to be selected from 6 men and 4 women. find  (i) the number of different ways in which the committee can be selected, [1]  (ii) the number of these selections with more women than men. [4] 3 the line   y = 3x + k   is a tangent to the curve   x2 + xy + 16 = 0.  (i) find the possible values of k. [3]  (ii) for each of these values of  k, find the coordinates of the point of contact of the tangent with the  curve. [2] 4 variables x and y are such that, when e y is plotted against x2, a straight line graph passing through the  points (0.2, 1) and (0.5, 1.6) is obtained.  (i) find the value of e y when x = 0. [2]  (ii) express y in terms of x. [3] 5 variables x and y are connected by the equation   y = x tan x.   given that x is increasing at the rate of  2 units per second, find the rate of increase of y when  x = \u03c0 4. [5] 6 solve the equation   x2 (2x + 3) = 17x \u2013 12. [6]",
            "4": "4 0606/01/m/j/08 \u00a9 ucles 20087 ob ca 4 cm  the diagram shows a sector oab of a circle, centre o, radius 4 cm. the tangent to the circle at a meets  the line ob extended at c. given that the area of the sector oab is 10 cm2, calculate  (i) the angle aob in radians, [2]  (ii) the perimeter of the shaded region. [4] 8 (i) given that   log9 x = a log3 x,   find a. [1]  (ii) given that   log27 y = b log3 y,   find b. [1]  (iii) hence solve, for x and y, the simultaneous equations 6log9 x + 3 log27  y = 8, log3 x + 2 log9 y = 2.  [4] 9 a curve is such that   dy dx = 2 cos /h208982x \u2013 \u03c0 2/h20899.   the curve passes through the point /h20898\u03c0 2, 3/h20899.  (i) find the equation of the curve. [4]  (ii) find the equation of the normal to the curve at the point where  x = 3\u03c0 4. [4]",
            "5": "5 0606/01/m/j/08 \u00a9 ucles 2008 [turn over10 in this question,  i is a unit vector due east and j is a unit vector due north.  at 0900 hours a ship sails from the point p with position vector (2 i + 3j) km relative to an origin o.  the ship sails north-east with a speed of 15 2 km h\u20131.  (i) find, in terms of i and j, the velocity of the ship. [2]  (ii) show that the ship will be at the point with position vector (24.5 i + 25.5j) km at 1030 hours. [1]  (iii) find, in terms of i, j and t, the position of the ship t hours after leaving p. [2]  at the same time as the ship leaves p, a submarine leaves the point q with position vector   (47i \u2013 27j) km. the submarine proceeds with a speed of 25 km h\u20131 due north to meet the ship.    (iv) find, in terms of i and j, the velocity of the ship relative to the submarine. [2]  (v) find the position vector of the point where the submarine meets the ship. [2] 11 solve the equation   (i) 3 sin x + 5 cos x = 0 for   0\u00b0 < x < 360\u00b0, [3]  (ii) 3 tan2 y \u2013 sec y \u2013 1 = 0 for   0\u00b0 < y < 360\u00b0, [5]  (iii) sin(2z \u2013 0.6) = 0.8 for   0 < z < 3 radians. [4] [question 12 is printed on the next page.]",
            "6": "6 0606/01/m/j/08 \u00a9 ucles 200812 answer only one of the following two alternatives.  either  a curve has equation   y = (x2 \u2013 3)e\u2013x.  (i) find the coordinates of the points of intersection of the curve with the x-axis. [2]  (ii) find the coordinates of the stationary points of the curve. [5]  (iii) determine the nature of these stationary points. [3]  or a particle moves in a straight line such that its displacement, s m, from a fixed point o at a time t s, is  given by s = ln(t + 1)   for   0 /h11088 t /h11088 3,s =  1 2ln (t \u2013 2) \u2013 ln(t + 1) + ln 16   for t > 3.  find  (i) the initial velocity of the particle, [2]  (ii) the velocity of the particle when t = 4, [2]  (iii) the acceleration of the particle when t = 4, [2]  (iv) the value of t when the particle is instantaneously at rest, [2]  (v) the distance travelled by the particle in the 4th second. [2]",
            "7": "7 0606/01/m/j/08blank page",
            "8": "8 0606/01/m/j/08blank 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. 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."
        },
        "0606_s08_qp_2.pdf": {
            "1": "this document consists of 5 printed pages and 3 blank pages. spa (nf/dt) t56699 \u00a9 ucles 2008 [turn overuniversity of cambridge international examinations international general certificate of secondary education read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. *0132636683*additional mathematics 0606/02 paper 2 may/june 2008  2 hours additional materials: answer booklet/paper electronic calculator mathematical tables",
            "2": "2 0606/02/m/j/08 \u00a9 ucles 2008mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1. sec2 a = 1 + tan2 a. cosec2 a = 1 + cot2 a. formulae for \u2206 abc a sin a = b sin b = c sin c . a2 = b2 + c2 \u2013 2bc cos a. \u2206 = 1  2 bc sin a .",
            "3": "3 0606/02/m/j/08 \u00a9 ucles 2008 [turn over1 the equation of a curve is given by   y = x2 + ax + 3,   where a is a constant. given that this equation  can also be written as   y = (x + 4)2 + b,   find  (i) the value of a and of b, [2]  (ii) the coordinates of the turning point of the curve. [1] 2 (a) illustrate the following statements using a separate venn diagram for each.   (i) a \u2229 b = \u2205, (ii)    (c \u222a d) \u2282 e. [2]  (b) y x/h5105   express, in set notation, the set represented by the shaded region. [2] 3 find the coordinates of the points where the straight line   y = 2x \u2013 3   intersects the curve x2 + y2 + xy + x = 30. [5] 4 (i) sketch, on the same diagram, the graphs of   y = x \u2013 3   and   y = /h209192x \u2013 9 /h20919. [3]  (ii) solve the equation   /h209192x \u2013 9 /h20919 = x \u2013 3. [2] 5 find the coefficient of x3 in the expansion of   (i) (1 + 3x)8,  [2]  (ii) (1 \u2013 4x)(1 + 3x)8. [3] 6 (a) given that sin x = p,  find an expression, in terms of p, for  sec2 x. [2]  (b) prove that   sec a cosec a \u2013  cot a \u2261 tan a . [4]",
            "4": "4 0606/02/m/j/08 \u00a9 ucles 20087 y x op (x, y) y=42 x2  the diagram shows part of the curve   y x=42 2.   the point p (x, y) lies on this curve.  (i) write down an expression, in terms of x, for (op)2. [1]  (ii) denoting (op)2 by s, find an expression for  ds dx . [2]  (iii) find the value of x for which s has a stationary value and the corresponding value of op. [3] 8 solve the equation  (i) 22x + 1 = 20, [3]  (ii) 5 25125 2541 3 2y yy y\u2212 + \u2212= . [4] 9 given that   a = /h208984 1 2 3/h20899,   b = /h208983 \u201350 2/h20899   and   c = /h2089841/h20899,   calculate  (i) ab, [2]  (ii) bc, [2]  (iii) the matrix x such that ax = b.  [4] 10 (a) find   (i) /h2084812 (2x \u2013 1)4 dx, [2]   (ii) /h20848x(x \u20131)2dx. [3]  (b) (i) given that   yx x=\u2212 + 25 4() ,   show that   d dy xx x=+ +31 4() . [3]   (ii) hence find   /h20848()x x+ +1 4dx. [2]",
            "5": "5 0606/02/m/j/08 \u00a9 ucles 200811 the function f is defined by f(x) = (x + 1)2 + 2  for  x /h11091 \u20131.  find  (i) the range of f, [1]  (ii) f 2(1), [1]  (iii) an expression for f \u20131(x) . [3]  the function g is defined by g(x) = 20 x + 1   for   x /h11091 0.  find  (iv) g\u20131 (2), [2]  (v) the value of x for which fg(x) = 38. [4] 12 answer only one of the following two alternatives.  either  the diagram shows the curve   y = 4x \u2013 x2,   which crosses the x-axis at the origin o and the point a.  the tangent to the curve at the point (1, 3) crosses the x-axis at the point b.  (i) find the coordinates of a and of b. [5]  (ii) find the area of the shaded region. [5]  or  solutions to this question by accurate drawing will not be accepted. the points a (\u20132, 2), b ( 4, 4) and c (5, 2) are the vertices of a triangle. the perpendicular  bisector of ab and the line through  a parallel to bc intersect at the point d. find the area of the  quadrilateral abcd. [10]",
            "6": "6 0606/02/m/j/08blank page",
            "7": "7 0606/02/m/j/08blank page",
            "8": "8 0606/02/m/j/08blank 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. 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."
        },
        "0606_w08_qp_1.pdf": {
            "1": "this document consists of 5 printed pages and 3 blank pages. spa (cm/dt) t56700 \u00a9 ucles 2008 [turn overuniversity of cambridge international examinations international general certificate of secondary education read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. *9606941300*additional mathematics 0606/01 paper 1 october/november 2008  2 hours additional materials: answer booklet/paper electronic calculator mathematical tables",
            "2": "2 0606/01/o/n/08 \u00a9 ucles 2008mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1. sec2 a = 1 + tan2 a. cosec2 a = 1 + cot2 a. formulae for \u2206 abc a sin a = b sin b = c sin c . a2 = b2 + c2 \u2013 2bc cos a. \u2206 = 1  2 bc sin a .",
            "3": "3 0606/01/o/n/08 \u00a9 ucles 2008 [turn over1 b a c/h5105  (i) copy the venn diagram above and shade the region that represents  a \u222a (b \u2229 c). [1]  (ii) copy the venn diagram above and shade the region that represents  a \u2229 (b \u222a c). [1]  (iii) copy the venn diagram above and shade the region that represents  ( a \u222a b \u222a c)/h11032. [1] 2 find the set of values of x for which   (2x + 1)2 > 8x + 9. [4] 3 prove that   sin a 1 + cos a + 1 + cos a sin a \u2261 2 cosec a. [4] 4 a function f is such that   f(x) = ax3 + bx2 + 3x + 4.   when f(x) is divided by   x \u2013 1,   the remainder  is 3. when f(x) is divided by   2x + 1,   the remainder is 6. find the value of a and of b. [5] 5 given that a = 5i \u2013 12j and that b = pi + j, find  (i) the unit vector in the direction of a, [2]  (ii) the values of the constants p and q such that qa + b = 19i \u2013 23j. [3] 6 (i) solve the equation   2 t = 9 + 5 t . [3]  (ii) hence, or otherwise, solve the equation   2 x1 2 = 9 + 5x\u2013 12 . [3] 7 (i) express   4x2 \u2013 12x + 3   in the form   ( ax + b)2 + c,   where   a, b and c are constants and a > 0.  [3]  (ii) hence, or otherwise, find the coordinates of the stationary point of the curve   y = 4x2 \u2013 12x + 3.  [2]  (iii) given that   f( x) = 4x2 \u2013 12x + 3,   write down the range of f. [1]",
            "4": "4 0606/01/o/n/08 \u00a9 ucles 20088 a curve is such that   d2y dx2 = 4e\u20132x.   given that dy dx = 3 when x = 0 and that the curve passes through the  point (2, e\u20134), find the equation of the curve. [6] 9 (i) find, in ascending powers of x, the first 3 terms in the expansion of   (2 \u2013 3 x)5. [3]  the first 3 terms in the expansion of   ( a + bx)(2 \u2013 3x)5   in ascending powers of x are 64 \u2013 192x + cx2.  (ii) find the value of a, of b and of c. [5] 10 (a) functions f and g are defined, for x /h9280 /h11938, by f(x) = 3 \u2013 x, g(x) = x x + 2 ,   where x \u2260 \u20132.   (i) find fg(x). [2]   (ii) hence find the value of x for which  fg(x) = 10. [2]  (b) a function h is defined, for x /h9280 /h11938, by   h(x) = 4 + ln x,   where   x > 1.   (i) find the range of h. [1]   (ii) find the value of h\u20131(9). [2]   (iii) on the same axes, sketch the graphs of y = h(x) and y = h\u20131(x). [3] 11 solve the equation   (i) tan 2x \u2013 3 cot 2x = 0,   for   0\u00b0 < x < 180\u00b0, [4]  (ii) cosec y = 1 \u2013 2cot2 y,   for   0\u00b0 /h11088 y /h11088 360\u00b0, [5]  (iii) sec(z + \u03c0 2) = \u20132,   for   0 < z < \u03c0 radians. [3]",
            "5": "5 0606/01/o/n/08 \u00a9 ucles 200812 answer only one of the following two alternatives.  either  a curve has equation   y = x2 x + 1 .  (i) find the coordinates of the stationary points of the curve. [5]  the normal to the curve at the point where x = 1 meets the x-axis at m. the tangent to the curve at the  point where x = \u20132 meets the y-axis at n.  (ii) find the area of the triangle mno, where o is the origin. [6]  or  a curve has equation  y = ex \u2013 2 \u2013 2x + 6.  (i) find the coordinates of the stationary point of the curve and determine the nature of the stationary  point. [6]  the area of the region enclosed by the curve, the positive x-axis, the positive y-axis and the line x = 3  is  k + e \u2013 e\u20132.  (ii) find the value of k. [5]",
            "6": "6 0606/01/o/n/08blank page",
            "7": "7 0606/01/o/n/08blank page",
            "8": "8 0606/01/o/n/08blank 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. 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."
        },
        "0606_w08_qp_2.pdf": {
            "1": "this document consists of 6 printed pages and 2 blank pages. spa (cm/dt) t56701 \u00a9 ucles 2008 [turn overuniversity of cambridge international examinations international general certificate of secondary education read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. *6283117453*additional mathematics 0606/02 paper 2 october/november 2008  2 hours additional materials: answer booklet/paper graph paper (1 sheet) electronic calculator mathematical tables",
            "2": "2 0606/02/o/n/08 \u00a9 ucles 2008mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1. sec2 a = 1 + tan2 a. cosec2 a = 1 + cot2 a. formulae for \u2206 abc a sin a = b sin b = c sin c . a2 = b2 + c2 \u2013 2bc cos a. \u2206 = 1  2 bc sin a .",
            "3": "3 0606/02/o/n/08 \u00a9 ucles 2008 [turn over1 given that   a = /h20898 13 6  7 4/h20899,   find the inverse matrix a\u20131 and hence solve the simultaneous equations 13x + 6y = 41,  7x + 4y = 24.  [4] 2 variables x and y are connected by the equation   y = (2x \u2013 9)3.   given that x is increasing at the rate of  4 units per second, find the rate of increase of  y when x = 7. [4] 3 find the set of values of m for which the line   y = mx + 2   does not meet the curve   y = x2 \u2013 5x + 18.  [5] 4 (i) differentiate  x ln x  with respect to x. [2]  (ii) hence find   /h20848ln x dx. [3] 5 solve the equation  (i) 4x 25\u2013x = 24x 8x\u20133 , [3]  (ii) lg (2y + 10) + lg y = 2. [3] 6 (a) a sports team of 3 attackers, 2 centres and 4 defenders is to be chosen from a squad of 5 attackers, 3 centres and 6 defenders.  calculate the number of different ways in which this can be done. [3]  (b) how many different 4-digit numbers greater than 3000 can be formed using the six digits 1, 2, 3, 4, 5 and 6 if no digit can be used more than once? [3]",
            "4": "4 0606/02/o/n/08 \u00a9 ucles 20087 q p1.4 ms \u2013148 m  the diagram shows a river with parallel banks. the river is 48 m wide and is flowing with a speed of  1.4 ms\u20131. a boat travels in a straight line from a point p on one bank to a point q which is on the other  bank directly opposite p. given that the boat takes 10 seconds to cross the river, find  (i) the speed of the boat in still water, [4]  (ii) the angle to the bank at which the boat should be steered. [2] 8 the function f is defined, for 0 /h11088 x /h11088 2 \u03c0, by f(x) = 3 + 5 sin 2x.  state  (i) the amplitude of f, [1]  (ii) the period of f, [1]  (iii) the maximum and minimum values of f. [2]  sketch the graph of  y = f(x). [3] 9 the line   y = 2x \u2013 9   intersects the curve   x2 + y2 + xy + 3x = 46 at the points a and b. find the  equation of the perpendicular bisector of ab. [8]",
            "5": "5 0606/02/o/n/08 \u00a9 ucles 2008 [turn over10 y x oy = x   \u2212 8x  + 16x32  the diagram shows part of the curve   y = x3 \u2013 8x2 + 16x.  (i) show that the curve has a minimum point at (4, 0) and find the coordinates of the maximum  point. [4]  (ii) find the area of the shaded region enclosed by the x-axis and the curve. [4] 11 the table shows experimental values of two variables x and y. x 2468 y 2.25 0.81 0.47 0.33  (i) using graph paper, plot xy against 1 x and draw a straight line graph . [3]  (ii) use your graph to express y in terms of x. [5]  (iii) estimate the value of x and of y for which  xy = 4. [3] [question 12 is printed on the next page.]",
            "6": "6 0606/02/o/n/08 \u00a9 ucles 200812 answer only one of the following two alternatives.  either od cb a 6 cm0.6 rad2 cm  the diagram shows a sector aob of a circle with centre o and radius 6 cm. angle aob = 0.6 radians.  the point d lies on ob such that the length of od is 2 cm. the point c lies on oa such that ocd is a  right angle.  (i) show that the length of oc is approximately 1.65 cm and find the length of cd. [4]  (ii) find the perimeter of the shaded region. [3]  (iii) find the area of the shaded region. [3]  or  a particle moves in a straight line so that t seconds after passing a fixed point o its acceleration,  a ms\u20132, is given by   a = 4t \u2013 12. given that its speed at o is 16 ms\u20131, find  (i) the values of t at which the particle is stationary, [5]  (ii) the distance the particle travels in the fifth second. [5]",
            "7": "7 0606/02/o/n/08blank page",
            "8": "8 0606/02/o/n/08blank 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. 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."
        }
    },
    "2009": {
        "0606_s09_qp_1.pdf": {
            "1": "this document consists of 6 printed pages and 2 blank pages. sp (sm) v06774 \u00a9 ucles 2009 [turn overuniversity of cambridge international examinations international general certificate of secondary education read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. *6942311642*additional mathematics 0606/01 paper 1 may/june 2009  2 hours additional materials: answer booklet/paper graph paper (2 sheets) electronic calculator mathematical tables",
            "2": "2 0606/01/m/j/09 \u00a9 ucles 2009mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1) an\u20131 b + (n2) an\u20132 b2 + \u2026 + (n r) an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1. sec2 a = 1 + tan2 a. cosec2 a = 1 + cot2 a. formulae for \u2206 abc a sin a = b sin b = c sin c . a2 = b2 + c2 \u2013 2bc cos a. \u2206 = 1  2 bc sin a .",
            "3": "3 0606/01/m/j/09 \u00a9 ucles 2009 [turn over1   15 cm15 cm12 cm ba o  the diagram shows a sector aob of a circle, centre o, radius 15 cm. the length of the arc ab is 12 cm.    (i) find, in radians, angle aob. [2]  (ii) find the area of the sector aob. [2] 2 the equation of a curve is    y = x3 \u2013 8.    find the equation of the normal to the curve at the point where the curve crosses the x-axis. [4] 3 show that   1 \u2013 cos2/h9258 sec2/h9258  \u2013 1 = 1 \u2013 sin2/h9258. [4] 4 the line    y = 5x \u2013 3    is a tangent to the curve    y = kx2 \u2013 3x + 5    at the point a. find  (i) the value of k, [3]  (ii) the coordinates of a. [2] 5 (a) solve the equation  92x \u2013 1 = 27x. [3]  (b) given that   ab\u20131 22 3 ab3\u20132 3  = a pbq,  find the value of p and of q. [2] 6 solve the equation      2 x3 + 3x2 \u2013 32x + 15 = 0. [6] 7 (i)   find   d\u2013dx(xe3x \u2013e3x\u2013\u2013\u20133) . [3]  (ii) hence find      \u222bxe3xdx. [3]",
            "4": "4 0606/01/m/j/098 a curve has equation  y = 2x x2 + 9  .  (i) find the x-coordinate of each of the stationary points of the curve. [4]  (ii) given that x is increasing at the rate of 2 units per second, find the rate of increase of y when x = 1. [3] 9 at 10 00 hours, a ship p leaves a point a with position vector    (\u2013 4 i + 8j)  km relative to an origin o,  where i is a unit vector due east and j is a unit vector due north. the ship sails north-east with a speed  of 10\u221a 2 km h\u20131. find    (i) the velocity vector of p, [2]    (ii) the position vector of p at 12 00 hours. [2]  at 12 00 hours, a second ship q leaves a point b with position vector    (19i + 34j) km    travelling with velocity vector    (8 i + 6j) km h \u20131.  (iii) find the velocity of p relative to q. [2]  (iv) hence, or otherwise, find the time at which p and q meet and the position vector of the point  where this happens. [3] \u00a9 ucles 2009",
            "5": "5 0606/01/m/j/09 \u00a9 ucles 200910 solutions to this question by accurate drawing will not be accepted. cy x q o a (\u2013 4, 0)p (1, 10) b (8,   9)  the diagram shows the line ab passing through the points a(\u2013 4, 0) and b(8, 9). the line through the  point p(1, 10), perpendicular to ab, meets ab at c and the x-axis at q. find  (i) the coordinates of c and of q, [7]  (ii) the area of triangle acq. [2] 11 the table shows experimental values of variables s and t.   t 5 15 30 70 100 s 1305 349 152 55 36    (i) by plotting a suitable straight line graph, show that s and t are related by the equation s = kt n,    where k and n are constants. [4]  (ii) use your graph to find the value of k and of n. [4]  (iii) estimate the value of s when t  = 50. [2] [turn over",
            "6": "6 0606/01/m/j/0912 answer only one of the following two alternatives.  either  (i) state the amplitude of  1 + sin (x\u20133). [1]  (ii) state, in radians, the period of  1 + sin (x\u20133). [1] y xx 3 oaby = 1.5 y = 1  + sin (\u2013)  the diagram shows the curve  y = 1 + sin (x\u20133)  meeting the line y = 1.5 at points a and b. find  (iii) the x-coordinate of a and of b, [3]  (iv) the area of the shaded region. [6]  or  a particle moves in a straight line such that t s after passing through a fixed point o, its velocity, v m s\u20131, is given by  v = k cos 4t,  where k is a positive constant. find  (i) the value of t when the particle is first instantaneously at rest, [1]  (ii) an expression for the acceleration of the particle t s after passing through o. [2]  given that the acceleration of the particle is 12 m s\u20132 when t = 3\u03c0 8 ,  (iii) find the value of k. [2]  using your value for k,  (iv) sketch the velocity-time curve for the particle for 0 /h33355 t /h33355 \u03c0, [2]  (v) find the displacement of the particle from o when t = \u03c0 24 . [4] \u00a9 ucles 2009",
            "7": "7 0606/01/m/j/09blank page",
            "8": "8 0606/01/m/j/09blank 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. 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."
        },
        "0606_s09_qp_2.pdf": {
            "1": "this document consists of 6 printed pages and 2 blank pages. sp (sm) v07190/1 \u00a9 ucles 2009 [turn overuniversity of cambridge international examinations international general certificate of secondary education read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case ofangles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. *3058027732*additional mathematics 0606/02 paper 2 may/june 2009  2 hours additional materials: answer paper graph paper (1 sheet) electronic calculator mathematical tables",
            "2": "2 0606/02/m/j/09 \u00a9 ucles 2009mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1) an\u20131 b + (n2) an\u20132 b2 + \u2026 + (n r) an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  . 2. trigonometry identities sin2 a + cos2 a = 1. sec2 a = 1 + tan2 a. cosec2 a = 1 + cot2 a. formulae for \u2206 abc a sin a = b sin b = c sin c . a2 = b2 + c2 \u2013 2bc cos a. \u2206 = 1  2 bc sin a .",
            "3": "3 0606/02/m/j/09 \u00a9 ucles 2009 [turn over1 (a)  x/h5105 y   express, in set notation, the set represented by the shaded region. [1]  (b)  in a class of 30 students, 17 are studying politics, 14 are studying economics and 10 are studying  both of these subjects.   (i) illustrate this information using a venn diagram. [1]   find the number of students studying   (ii) neither of these subjects, [1]   (iii) exactly one of these subjects. [1] 2 given that  a = /h208987 6 3 4/h20899,  find a1\u2212 and hence solve the simultaneous equations 7x + 6y = 17, 3x + 4y =   3.  [4] 3 sketch the graph of   y = /h20919 x2 \u2013 8x + 12 /h20919/h20919. [4] 4 find the coefficient of x4 in the expansion of   (i) (1 + 2x)6, [2]  (ii) /h208981 \u2013 x  4/h20899(1 + 2x)6. [3]",
            "4": "4 0606/02/m/j/09 \u00a9 ucles 20095  two variables, x and y, are related by the equation y = 6x2 + 32 x3 .  (i) obtain an expression for  dy dx . [2]  (ii) use your expression to f ind the approximate change in the value of y when x increases from  2 to 2.04. [3] 6 the function f is defined by   f(x) = 2 + x \u2013 3   for x /h11091 3. find  (i) the range of f, [1]  (ii) an expression for f \u20131(x). [2]  the function g is def ined by   g(x) = 12 x + 2   for x /h11022 0. find  (iii) gf(12). [2] 7 given that    logp  x = 9    and    logpy = 6,    find  (i) logp x, [1]  (ii) logp (1 x) , [1]  (iii) logp (xy ), [2]  (iv) logy x. [2]",
            "5": "5 0606/02/m/j/09 \u00a9 ucles 2009 [turn over8  y xt unitsy = 27  \u2013 x2p q os r   the diagram shows part of the curve   y = 27 \u2013 x2.   the points p and s lie on this curve. the points q  and r lie on the x-axis and pqrs is a rectangle. the length of oq is t units.  (i) find the length of pq in terms of t and hence show that the area, a square units, of pqrs is given  by      a = 54t \u2013 2t 3. [2]  (ii) given that  t can vary, find the value of t for which a has a stationary value. [3]  (iii) find this stationary value of a and determine its nature. [3] 9 a musician has to play 4 pieces from a list of 9. of these 9 pieces 4 were written by beethoven, 3 by  handel and 2 by sibelius. calculate the number of ways the 4 pieces can be chosen if   (i)  there are no restrictions, [2]  (ii) there must be 2 pieces by beethoven, 1 by handel and 1 by sibelius, [3]  (iii) there must be at least one piece by each composer. [4] 10 the line      2 x + y = 12      intersects the curve      x2 + 3xy + y2 = 176      at the points a and b. find the equation of the perpendicular bisector of ab. [9] 11 (a) find all the angles between 0\u00ba and 360\u00ba which satisfy   (i) 2sin x \u2013 3cos x = 0, [3]     (ii) 2sin2 y \u2013 3cos y = 0. [5]  (b)  given that    0 /h33355 z /h33355 3 radians,    find, correct to 2 decimal places, all the values of z for which  sin(2z + 1) = 0.9.  [3]",
            "6": "6 0606/02/m/j/09 \u00a9 ucles 200912 answer only one of the following two alternatives.  either  the point p(0, 5) lies on the curve for which   dy dx = e1 2x.  the point q, with x-coordinate 2, also lies  on the curve.     (i) find, in terms of e, the y-coordinate of q. [5]  the tangents to the curve at the points p and q intersect at the point r.    (ii) find, in terms of e, the x-coordinate of r. [5]  or     b oac dy y = e      + 5 x  x\u00b9\u00b2   the diagram shows part of the curve y =  e1 2x+ 5 crossing the y-axis at a. the normal to the curve  at a meets the x-axis at b.   (i) find the coordinates of b. [4]   the line through b, parallel to the y-axis, meets the curve at c. the line through c, parallel to the x-axis, meets the y-axis at d.    (ii) find the area of the shaded region. [6]",
            "7": "7 0606/02/m/j/09blank page",
            "8": "8 0606/02/m/j/09blank 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. 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."
        },
        "0606_w09_qp_01.pdf": {
            "1": "this document consists of 5 printed pages and 3 blank pages. dc (slm) 11532/2 \u00a9 ucles 2009 [turn overuniversity of cambridge international examinations international general certificate of secondary education read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. * 8 1 6086321 0 *additional mathematics 0606/01 paper 1 october/november 2009  2 hours additional materials: answer booklet/paper electronic calculator  mathematical tables",
            "2": "2 0606/01/o/n/09 \u00a9 ucles 2009mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2 . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1. sec2 a = 1 + tan2 a. cosec2 a = 1 + cot2 a. formulae for \u2206abc a sin a = b sin b = c sin c . a2 = b2 + c2 \u2013 2bc cos a. \u2206 = 1  2 bc sin a .",
            "3": "3 0606/01/o/n/09 \u00a9 ucles 2009 [turn over1 given that  f (x) = 2x3 \u2013 7x2 + 7ax + 16  is divisible by  x \u2013 a,  find  (i) the value of the constant a, [2]  (ii) the remainder when f  (x) is divided by  2 x + 1. [2] 2                       place team1st 2nd 3rd 4th harriers 6 3 1 2 strollers 3 2 4 3 road runners 2 5 5 0 olympians 1 2 2 7  the table shows the results achieved by four teams in twelve events of an athletics match. in each  event, 1st  place scores 5 points, 2nd place scores 3 points, 3rd place scores 2 points and 4th place scores 1 point.    (i) write down two matrices whose product shows the total number of points scored by each team. [2]  (ii) evaluate this product of matrices. [2] 3 find the values of k for which the equation  x 2 \u2013 2(2k + 1) x + (k + 2) = 0  has two equal roots. [4] 4 solve the simultaneous equations     x + 3y = 13,     x 2 + 3y2 = 43. [5] 5     ba c3 +    2 3 \u2013    2  the diagram shows a triangle abc, where angle b is a right angle,  the length of ab = 3 + 2 and the  length of bc = 3 \u2013 2.    (i) find the length of  ac in the form  k, where k is an integer. [2]  (ii) find  tan a  in the form  ab c+2,  where a, b and c are integers. [3]",
            "4": "4 0606/01/o/n/09 \u00a9 ucles 20096 set a is such that  a = {x : 3x2 \u2013 10x \u2013 8 \ue0f8 0}.    (i) find the set of values of x which define the set a. [3]    set b is such that  b = {x : 7 \u2013 2x \ue0f8 1}.  (ii) find the set of values of x which define the set a \ue0f9 b. [2] 7 a committee of 8 people is to be selected from 7 teachers and 6 students. find the number of different  ways in which the committee can be selected if    (i) there are no restrictions, [2]  (ii) there are to be more teachers than students on the committee. [4] 8 the number, n, of bacteria present in an experiment, t minutes after measurements begin, is given by   n = 1000e\u2013kt,  where k is a constant.  (i) state the number of bacteria when t = 0. [1]  when t = 0, the number of bacteria is decreasing at the rate of 20 per minute. find  (ii) the value of  k, [3]  (iii) the time taken for the number of bacteria to decrease by 50%. [3] 9 differentiate, with respect to x,  (i) (1 \u2013 2x)20, [2]  (ii) x2ln x, [3]  (iii) tan(2x + 1)__________ x  . [3]      10 a curve has equation  y = 3x 3 \u2013 2x 2 + 2x.    (i) show that the equation of the tangent to the curve at the point  where  x = 1 is     y = 7x \u2013 4. [4]  (ii) find the coordinates of the point where this tangent meets the curve again. [5]",
            "5": "5 0606/01/o/n/09 \u00a9 ucles 200911 (a) show that   tan \ue075 + cot \ue075 = cosec \ue075 sec\ue075. [3]  (b) solve the equation     (i) tan x = 3 sin x  for  0 \u00b0 \ue02c x \ue02c 360 \u00b0, [4]   (ii) 2cot2 y + 3 cosec y = 0  for  0 \ue02c y \ue02c 2 \u03c0 radians. [5] 12 answer only one of the following two alternatives.  either  a solid circular cylinder has radius r cm and height h cm. the volume of the cylinder is 1000 cm3.  (i) find an expression for h in terms of r. [2]  (ii) hence show that the total surface area, a cm2, of the cylinder is given by      a = 2\u03c0\u2009r2 + 2000 r. [2]  (iii) given that r varies, find, correct to 2 decimal places, the value of r when a has a stationary value. [4]  (iv) find this stationary value of a and determine its nature. [3]  or y x oa by = x + cos  2x  the diagram shows part of the curve  y = x + cos 2x. the curve has a maximum point at a and a  minimum point at b.  (i) find the x-coordinate of the point a and of the point b. [6]  (ii) find, in terms of \u03c0, the area of the shaded region. [5]   ",
            "6": "6 0606/01/o/n/09blank page",
            "7": "7 0606/01/o/n/09blank page",
            "8": "8 0606/01/o/n/09blank 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. 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."
        },
        "0606_w09_qp_02.pdf": {
            "1": "this document consists of 5 printed pages and 3 blank pages. dc (cw) 15823 \u00a9 ucles 2009 [turn overuniversity of cambridge international examinations international general certificate of secondary education read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. * 399303 2000 *additional mathematics 0606/02 paper 2 october/november 2009  2 hours additional materials: answer booklet/paper graph paper (2 sheets)  electronic calculator mathematical tables",
            "2": "2 0606/02/o/n/09 \u00a9 ucles 2009mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2 . binomial theorem (a + b)n = an +(n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  . 2. trigonometry identities sin2 a + cos2 a = 1. sec2 a = 1 + tan2 a. cosec2 a = 1 + cot2 a. formulae for \u2206abc a sin a = b sin b = c sin c . a2 = b2 + c2 \u2013 2bc cos a. \u2206 = 1  2 bc sin a .",
            "3": "3 0606/02/o/n/09 \u00a9 ucles 2009 [turn over1 a function f is defined by  f: x \ue0b0 e x\u20131,  where x \ue02e 0.  (i) state the range of f. [1]  (ii) find an expression for f \u20131. [2]  (iii) state the domain of f \u20131. [1] 2 (i) find the first four terms, in ascending powers of x, in the expansion of   \ue0312  \u2013 x  2\ue0326 . [4]  (ii) find the coefficient of x3 in the expansion of   (l + x)2 \ue0312  \u2013 x  2\ue0326 . [2] 3 the table shows experimental values of the variables x and y which are related by the equation    y = a x2 + b x ,  where a and b are constants. x 2  4 6 8 10 y 6.24  2.82 1.79 1.33 1.05  (i) using graph paper, plot x2y against x and draw a straight line graph . [3]  (ii) use your graph to estimate the value of a and of b. [4] 4 find the coordinates and the nature of the stationary points of the curve    y = x3 + 3x2 \u2013 45x + 60. [7] 5 relative to an origin o, the position vectors of  points a and b are \ue0317 24\ue032 and \ue03110 20\ue032 respectively.  find  (i) the length of  oa, [2]  (ii) the length of  ab. [2]  given that abc is a straight line and that the length of ac is equal to the length of oa, find  (iii)  the position vector of the point c. [3] 6 (i) given that   y = xx4+ 12,   show that   dy dx = kx x(+2) 4+ 12,   where k is a constant  to be found. [4]  (ii) hence evaluate  6 \u20132\ue0653+6 4+12x x dx . [3]",
            "4": "4 0606/02/o/n/09 \u00a9 ucles 20097 (i) using graph paper, draw the curve  y = sin 2x  for  0\u00b0 \ue0f8 x \ue0f8 360 \u00b0. [3]  in order to solve the equation  1 + sin 2x = 2cos x  another curve must be added to your diagram.   (ii) write down the equation of this curve and add this curve to your diagram. [3]  (iii) state the number of values of x which satisfy the equation  1 + sin 2x = 2cos x  for  0 \u00b0 \ue0f8 x \ue0f8 360 \u00b0 .  [1] 8  it is given that a = \ue0312 \u20131 4 3\ue032,  b = \ue0311 \u201332 0\ue032 and c = \ue0315 \u20132\ue032. find  (i) ab, [2]  (ii) bc, [2]  (iii) a\u20131, and hence find the matrix x such that ax = b. [4]   9 a particle moves in a straight line so that, t seconds after passing through a fixed point o, its velocity,   v ms\u20131, is given by   v = 20 (2t + 4)2.   find  (i) the velocity of the particle at o, [1]  (ii) the acceleration of the particle when  t = 3, [3]  (iii) the distance travelled by the particle in the first 8 seconds. [4] 10 (a) solve   lg(7x \u2013 3) + 2 lg5 = 2 + lg(x + 3). [4]  (b) use the substitution  u = 3x  to solve the equation   3x+1 + 32\u2013 x = 28 . [5]",
            "5": "5 0606/02/o/n/09 \u00a9 ucles 200911 answer only one of the following two alternatives.  either 3 cm 3 cm\ufffd3 cmq bpd ca \ufffd3 cm \u03c0 3_  in the diagram, acb is an arc of a circle with centre p, and adb is an arc of a circle with centre  q.   angle aqb = \u03c0 3,  aq = bq = 3 cm and ap = bp = 3 cm.   (i) show that angle apb = 2\u03c0 3. [2]  (ii) find the perimeter of the shaded region. [3]  (iii) find the area of the shaded region. [5]  or  solutions to this question by accurate drawing will not be accepted. ab (8, 1) (\u20132,  1)e fy x oc(6,  9) d  the diagram shows a parallelogram with vertices a(\u20132, 1), b(8, 1), c(6, 9) and d.  (i) find the coordinates of d. [2]  the point e lies on the diagonal db such that de =  1  4 db .  (ii) find the coordinates of e. [2]  the point f is such that ef is parallel to ab.   the area of trapezium aefb is  11  2 \ue033 (the area of parallelogram abcd).  (iii) find the coordinates of f. [6]",
            "6": "6 0606/02/o/n/09blank page",
            "7": "7 0606/02/o/n/09blank page",
            "8": "8 0606/02/o/n/09blank 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. 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."
        },
        "0606_w09_qp_1.pdf": {
            "1": "this document consists of 5 printed pages and 3 blank pages. dc (slm) 11532/2 \u00a9 ucles 2009 [turn overuniversity of cambridge international examinations international general certificate of secondary education read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. * 8 1 6086321 0 *additional mathematics 0606/01 paper 1 october/november 2009  2 hours additional materials: answer booklet/paper electronic calculator  mathematical tables",
            "2": "2 0606/01/o/n/09 \u00a9 ucles 2009mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2 . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1. sec2 a = 1 + tan2 a. cosec2 a = 1 + cot2 a. formulae for \u2206abc a sin a = b sin b = c sin c . a2 = b2 + c2 \u2013 2bc cos a. \u2206 = 1  2 bc sin a .",
            "3": "3 0606/01/o/n/09 \u00a9 ucles 2009 [turn over1 given that  f (x) = 2x3 \u2013 7x2 + 7ax + 16  is divisible by  x \u2013 a,  find  (i) the value of the constant a, [2]  (ii) the remainder when f  (x) is divided by  2 x + 1. [2] 2                       place team1st 2nd 3rd 4th harriers 6 3 1 2 strollers 3 2 4 3 road runners 2 5 5 0 olympians 1 2 2 7  the table shows the results achieved by four teams in twelve events of an athletics match. in each  event, 1st  place scores 5 points, 2nd place scores 3 points, 3rd place scores 2 points and 4th place scores 1 point.    (i) write down two matrices whose product shows the total number of points scored by each team. [2]  (ii) evaluate this product of matrices. [2] 3 find the values of k for which the equation  x 2 \u2013 2(2k + 1) x + (k + 2) = 0  has two equal roots. [4] 4 solve the simultaneous equations     x + 3y = 13,     x 2 + 3y2 = 43. [5] 5     ba c3 +    2 3 \u2013    2  the diagram shows a triangle abc, where angle b is a right angle,  the length of ab = 3 + 2 and the  length of bc = 3 \u2013 2.    (i) find the length of  ac in the form  k, where k is an integer. [2]  (ii) find  tan a  in the form  ab c+2,  where a, b and c are integers. [3]",
            "4": "4 0606/01/o/n/09 \u00a9 ucles 20096 set a is such that  a = {x : 3x2 \u2013 10x \u2013 8 \ue0f8 0}.    (i) find the set of values of x which define the set a. [3]    set b is such that  b = {x : 7 \u2013 2x \ue0f8 1}.  (ii) find the set of values of x which define the set a \ue0f9 b. [2] 7 a committee of 8 people is to be selected from 7 teachers and 6 students. find the number of different  ways in which the committee can be selected if    (i) there are no restrictions, [2]  (ii) there are to be more teachers than students on the committee. [4] 8 the number, n, of bacteria present in an experiment, t minutes after measurements begin, is given by   n = 1000e\u2013kt,  where k is a constant.  (i) state the number of bacteria when t = 0. [1]  when t = 0, the number of bacteria is decreasing at the rate of 20 per minute. find  (ii) the value of  k, [3]  (iii) the time taken for the number of bacteria to decrease by 50%. [3] 9 differentiate, with respect to x,  (i) (1 \u2013 2x)20, [2]  (ii) x2ln x, [3]  (iii) tan(2x + 1)__________ x  . [3]      10 a curve has equation  y = 3x 3 \u2013 2x 2 + 2x.    (i) show that the equation of the tangent to the curve at the point  where  x = 1 is     y = 7x \u2013 4. [4]  (ii) find the coordinates of the point where this tangent meets the curve again. [5]",
            "5": "5 0606/01/o/n/09 \u00a9 ucles 200911 (a) show that   tan \ue075 + cot \ue075 = cosec \ue075 sec\ue075. [3]  (b) solve the equation     (i) tan x = 3 sin x  for  0 \u00b0 \ue02c x \ue02c 360 \u00b0, [4]   (ii) 2cot2 y + 3 cosec y = 0  for  0 \ue02c y \ue02c 2 \u03c0 radians. [5] 12 answer only one of the following two alternatives.  either  a solid circular cylinder has radius r cm and height h cm. the volume of the cylinder is 1000 cm3.  (i) find an expression for h in terms of r. [2]  (ii) hence show that the total surface area, a cm2, of the cylinder is given by      a = 2\u03c0\u2009r2 + 2000 r. [2]  (iii) given that r varies, find, correct to 2 decimal places, the value of r when a has a stationary value. [4]  (iv) find this stationary value of a and determine its nature. [3]  or y x oa by = x + cos  2x  the diagram shows part of the curve  y = x + cos 2x. the curve has a maximum point at a and a  minimum point at b.  (i) find the x-coordinate of the point a and of the point b. [6]  (ii) find, in terms of \u03c0, the area of the shaded region. [5]   ",
            "6": "6 0606/01/o/n/09blank page",
            "7": "7 0606/01/o/n/09blank page",
            "8": "8 0606/01/o/n/09blank 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. 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."
        },
        "0606_w09_qp_2.pdf": {
            "1": "this document consists of 5 printed pages and 3 blank pages. dc (cw) 15823 \u00a9 ucles 2009 [turn overuniversity of cambridge international examinations international general certificate of secondary education read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. * 399303 2000 *additional mathematics 0606/02 paper 2 october/november 2009  2 hours additional materials: answer booklet/paper graph paper (2 sheets)  electronic calculator mathematical tables",
            "2": "2 0606/02/o/n/09 \u00a9 ucles 2009mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2 . binomial theorem (a + b)n = an +(n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  . 2. trigonometry identities sin2 a + cos2 a = 1. sec2 a = 1 + tan2 a. cosec2 a = 1 + cot2 a. formulae for \u2206abc a sin a = b sin b = c sin c . a2 = b2 + c2 \u2013 2bc cos a. \u2206 = 1  2 bc sin a .",
            "3": "3 0606/02/o/n/09 \u00a9 ucles 2009 [turn over1 a function f is defined by  f: x \ue0b0 e x\u20131,  where x \ue02e 0.  (i) state the range of f. [1]  (ii) find an expression for f \u20131. [2]  (iii) state the domain of f \u20131. [1] 2 (i) find the first four terms, in ascending powers of x, in the expansion of   \ue0312  \u2013 x  2\ue0326 . [4]  (ii) find the coefficient of x3 in the expansion of   (l + x)2 \ue0312  \u2013 x  2\ue0326 . [2] 3 the table shows experimental values of the variables x and y which are related by the equation    y = a x2 + b x ,  where a and b are constants. x 2  4 6 8 10 y 6.24  2.82 1.79 1.33 1.05  (i) using graph paper, plot x2y against x and draw a straight line graph . [3]  (ii) use your graph to estimate the value of a and of b. [4] 4 find the coordinates and the nature of the stationary points of the curve    y = x3 + 3x2 \u2013 45x + 60. [7] 5 relative to an origin o, the position vectors of  points a and b are \ue0317 24\ue032 and \ue03110 20\ue032 respectively.  find  (i) the length of  oa, [2]  (ii) the length of  ab. [2]  given that abc is a straight line and that the length of ac is equal to the length of oa, find  (iii)  the position vector of the point c. [3] 6 (i) given that   y = xx4+ 12,   show that   dy dx = kx x(+2) 4+ 12,   where k is a constant  to be found. [4]  (ii) hence evaluate  6 \u20132\ue0653+6 4+12x x dx . [3]",
            "4": "4 0606/02/o/n/09 \u00a9 ucles 20097 (i) using graph paper, draw the curve  y = sin 2x  for  0\u00b0 \ue0f8 x \ue0f8 360 \u00b0. [3]  in order to solve the equation  1 + sin 2x = 2cos x  another curve must be added to your diagram.   (ii) write down the equation of this curve and add this curve to your diagram. [3]  (iii) state the number of values of x which satisfy the equation  1 + sin 2x = 2cos x  for  0 \u00b0 \ue0f8 x \ue0f8 360 \u00b0 .  [1] 8  it is given that a = \ue0312 \u20131 4 3\ue032,  b = \ue0311 \u201332 0\ue032 and c = \ue0315 \u20132\ue032. find  (i) ab, [2]  (ii) bc, [2]  (iii) a\u20131, and hence find the matrix x such that ax = b. [4]   9 a particle moves in a straight line so that, t seconds after passing through a fixed point o, its velocity,   v ms\u20131, is given by   v = 20 (2t + 4)2.   find  (i) the velocity of the particle at o, [1]  (ii) the acceleration of the particle when  t = 3, [3]  (iii) the distance travelled by the particle in the first 8 seconds. [4] 10 (a) solve   lg(7x \u2013 3) + 2 lg5 = 2 + lg(x + 3). [4]  (b) use the substitution  u = 3x  to solve the equation   3x+1 + 32\u2013 x = 28 . [5]",
            "5": "5 0606/02/o/n/09 \u00a9 ucles 200911 answer only one of the following two alternatives.  either 3 cm 3 cm\ufffd3 cmq bpd ca \ufffd3 cm \u03c0 3_  in the diagram, acb is an arc of a circle with centre p, and adb is an arc of a circle with centre  q.   angle aqb = \u03c0 3,  aq = bq = 3 cm and ap = bp = 3 cm.   (i) show that angle apb = 2\u03c0 3. [2]  (ii) find the perimeter of the shaded region. [3]  (iii) find the area of the shaded region. [5]  or  solutions to this question by accurate drawing will not be accepted. ab (8, 1) (\u20132,  1)e fy x oc(6,  9) d  the diagram shows a parallelogram with vertices a(\u20132, 1), b(8, 1), c(6, 9) and d.  (i) find the coordinates of d. [2]  the point e lies on the diagonal db such that de =  1  4 db .  (ii) find the coordinates of e. [2]  the point f is such that ef is parallel to ab.   the area of trapezium aefb is  11  2 \ue033 (the area of parallelogram abcd).  (iii) find the coordinates of f. [6]",
            "6": "6 0606/02/o/n/09blank page",
            "7": "7 0606/02/o/n/09blank page",
            "8": "8 0606/02/o/n/09blank 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. 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."
        }
    },
    "2010": {
        "0606_s10_qp_11.pdf": {
            "1": "university of cambridge international examinations international general certificate of secondary education read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. *3914377199*additional mathematics 0606/11 paper 1 may/june 2010  2 hours additional materials: answer booklet/paper electronic calculator this document consists of 5 printed pages and 3 blank pages. dc (leo/kn) 25698/1 \u00a9 ucles 2010 [turn over",
            "2": "2 0606/11/m/j/10 \u00a9 ucles 2010mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb a c   a = \u2212 \u22122 4  2 . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1. sec2 a = 1 + tan2 a. cosec2 a = 1 + cot2 a. formulae for \u2206abc a sin a = b sin b = c sin c . a2 = b2 + c2 \u2013 2bc cos a. \u2206 = 1  2 bc sin a .",
            "3": "3 0606/11/m/j/10 \u00a9 ucles 2010 [turn over1 differentiate with respect to x  (i)   1 + x3, [2]  (ii) x2 cos 2x. [3] 2 (i) find the first 3 terms of the expansion, in ascending powers of x, of  (1 + 3x)6. [2]  (ii) hence find the coefficient of x2 in the expansion of  (1 + 3 x)6 (1 \u2013 3x \u2013 5x2). [3] 3 find the set of values of k for which the equation  x2 + (k \u2013 2)x + (2k \u2013 4) = 0 has real roots. [5] 4 (a) ab c/h5105   (i) copy the venn diagram above and shade the region that represents ( a \u2229 b) \u222a c. [1]   (ii) copy the venn diagram above and shade the region that represents a\u02b9 \u2229 b\u02b9. [1]   (iii) copy the venn diagram above and shade the region that represents ( a \u222a b) \u2229 c. [1]  (b) it is given that the universal set  /h5105 = {x : 2 /h11088 x /h11088 20, x is an integer},      x = {x : 4 < x < 15, x is an integer},      y = {x : x /h11091 9, x is an integer},      z = {x : x is a multiple of 5}.   (i) list the elements of x \u2229 y. [1]     (ii) list the elements of x \u222a y. [1]   (iii) find (x \u222a y)\u02b9 \u2229 z. [1] 5 solve the equation  3 x(x2 + 6) = 8 \u2013 17x2. [6]",
            "4": "4 0606/11/m/j/10 \u00a9 ucles 20106 given that  log8 p = x  and  log8 q = y,  express in terms of x and/or y  (i) log8    p + log8 q2, [2]  (ii) log8 /h20920q\u20138/h20921, [2]  (iii) log2 (64p). [3] 7 the function f is defined by      f ( x) = (2x + 1)2 \u2013 3    for  x /h11091 \u2013 1 2 .  find  (i) the range of f, [1]    (ii) an expression for f\u20131 (x). [3]   the function g is defined by      g ( x) = 3 1 + x     for  x > \u20131.  (iii) find the value of x for which fg(x) = 13. [4] 8 (a) solve the equation (23 \u2013 4x) (4x + 4) = 2. [3]  (b) (i) simplify    108 \u2013 12\u2013\u2013  3 , giving your answer in the form k  3, where k is an integer. [2]   (ii) simplify    5+ 3\u2013\u2013\u2013\u2013\u2013  5\u2013 2 , giving your answer in the form a  5 + b, where a and b are integers. [3] 9 (a)  variables x and y are related by the equation  y = 5x + 2 \u2013 4e\u2013x.   (i) find dy\u2013\u2013dx . [2]   (ii) hence find the approximate change in y when x increases from 0 to p, where p is small. [2]  (b) a square of area a cm2 has a side of length x cm. given that the area is increasing at a constant rate  of 0.5 cm2 s\u20131, find the rate of increase of x when a = 9. [4]",
            "5": "5 0606/11/m/j/10 \u00a9 ucles 201010 solve  (i) 4 sin x = cos x   for   0\u00b0 < x < 360\u00b0, [3]  (ii) 3 + sin y = 3 cos2 y   for   0\u00b0 < y < 360\u00b0, [5]  (iii) sec /h20920z\u20133/h20921 = 4   for   0 < z < 5 radians. [3] 11 answer only one of the following two alternatives.  either  a curve has equation  y = ln x\u2013\u2013\u2013x2 , where x > 0.  (i) find the exact coordinates of the stationary point of the curve. [6]  (ii) show that  d2y\u2013\u2013\u2013dx2 can be written in the form  a ln x + b\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013x4 ,  where a and b are integers. [3]  (iii) hence, or otherwise, determine the nature of the stationary point of the curve. [2]  or   a curve is such that  dy\u2013\u2013dx = 6 cos /h209202x + \u03c0\u20132/h20921 for \u2013 \u03c0\u20134 /h11088 x /h11088 5\u03c0\u2013\u20134 . the curve passes through the point /h20920\u03c0\u20134, 5/h20921.  find  (i) the equation of the curve, [4]  (ii) the x-coordinates of the stationary points of the curve, [3]  (iii) the equation of the normal to the curve at the point on the curve where  x = 3\u03c0\u2013\u20134. [4]",
            "6": "6 0606/11/m/j/10 \u00a9 ucles 2010blank page",
            "7": "7 0606/11/m/j/10 \u00a9 ucles 2010blank page",
            "8": "8 0606/11/m/j/10 \u00a9 ucles 2010blank 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. 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."
        },
        "0606_s10_qp_12.pdf": {
            "1": "read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case ofangles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.additional mathematics 0606/12 paper 1 may/june 2010  2 hours additional materials: answer booklet/paper electronic calculator  graph paper (2 sheets) this document consists of 6 printed pages and 2 blank pages. dc (sm/kn) 25700 \u00a9 ucles 2010 [turn over *6316616089*university of cambridge international examinations international general certificate of secondary education",
            "2": "2 0606/12/m/j/10 \u00a9 ucles 2010mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb a c   a = \u2212 \u22122 4  2 . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1. sec2 a = 1 + tan2 a. cosec2 a = 1 + cot2 a. formulae for \u2206abc a sin a = b sin b = c sin c . a2 = b2 + c2 \u2013 2bc cos a. \u2206 = 1  2 bc sin a .",
            "3": "3 0606/12/m/j/10 \u00a9 ucles 2010 [turn over1 find the coordinates of the points of intersection of the curve  y2 + y = 10x \u2013 8x2  and the straight line   y + 4x + 1 = 0. [5] 2 the expression  6 x3 + ax2 \u2013 (a + 1)x + b  has a remainder of 15 when divided by  x + 2  and a remainder  of 24 when divided by  x + 1.  show that a = 8 and find the value of b. [5] 3 given that  joa = /h20898\u201317 25/h20899  and  job = /h208984 5/h20899, find  (i) the unit vector parallel to jab, [3]   (ii) the vector joc, such that jac = 3jab. [2] 4 oy2 sec x\u00d7 \u00d7(2.4, 1.6)(1.3, 3.8)  variables x and y are such that, when y2 is plotted against sec x, a straight line graph passing through the  points (2.4, 1.6) and (1.3, 3.8) is obtained.  (i) express y2 in terms of sec x. [3]  (ii) hence find the exact value of  cos x  when y = 2. [2]",
            "4": "4 0606/12/m/j/10 \u00a9 ucles 20105 y x oa by = 6 \u2013  33\u2013x  the diagram shows part of the curve  y = 6 \u2013 3\u2013x  which passes through the point a where x = 3. the  normal to the curve at the point a meets the x-axis at the point b. find the coordinates of the point b.  [5] 6 (a) (i) on the same diagram, sketch the curves  y = cos x  and  y = 1 + cos 2x  for  0 /h11088 x /h11088 2\u03c0. [3]     (ii) hence state the number of solutions of the equation      cos 2x \u2013 cos x + 1 = 0  where  0 /h11088 x /h11088 2\u03c0. [1]  (b) the function f is given by  f( x) = 5sin 3x.  find   (i) the amplitude of f, [1]   (ii) the period of f. [1] 7 the table shows values of the variables p and v which are related by the equation  p = kv n,  where k and  n are constants. v 10 50 110 230 p 1412 151 53 19  (i) using graph paper, plot  lg p  against  lg v  and draw a straight line graph. [3]  use your graph to estimate  (ii) the value of n, [2]  (iii) the value of p when v = 170. [2]",
            "5": "5 0606/12/m/j/10 \u00a9 ucles 2010 [turn over8 given that  a = /h208984 3 1 2/h20899  and  b = /h20898\u20132 0  1 4/h20899,  find  (i) 3a \u2013 2b, [2]  (ii) a\u20131, [2]  (iii) the matrix x such that xb\u20131 = a. [3] 9 oa bx y8 cm 3 cm  the diagram shows a sector oxy of a circle centre o, radius 3 cm and a sector oab of a circle  centre o, radius 8 cm. the point x lies on the line oa and the point y lies on the line  ob. the perimeter  of the region xabyx is 15. 5 cm. find  (i) the angle aob in radians, [3]  (ii) the ratio of the area of the sector oxy to the area of the region xabyx in the form p : q, where  p and q are integers. [4] 10 a music student needs to select 7 pieces of music from 6 classical pieces and 4 modern pieces. find the number of different selections that she can make if  (i) there are no restrictions, [1]  (ii) there are to be only 2 modern pieces included, [2]  (iii) there are to be more classical pieces than modern pieces. [4]",
            "6": "6 0606/12/m/j/10 \u00a9 ucles 201011 a particle moves in a straight line such that its displacement, x m, from a fixed point o on the line at  time t seconds is given by  x = 12{1n (2t + 3)}.  find  (i) the value of t when the displacement of the particle from o is 48 m, [3]  (ii) the velocity of the particle when t = 1, [3]  (iii) the acceleration of the particle when t =1. [3] 12 answer only one of the following two alternatives.  either y y = 5 x oab      , 7 c\u03c0\u2013\u20134  the diagram shows part of a curve for which  dy\u2013\u2013dx = 8 cos 2x.  the curve passes through the   point  b /h20920\u03c0\u20134, 7/h20921.  the line  y = 5  meets the curve at the points a and c.  (i) show that the curve has equation  y = 3 + 4 sin 2x. [3]  (ii) find the x-coordinate of the point a and of the point c. [4]  (iii) find the area of the shaded region. [5]  or  a curve is such that  dy\u2013\u2013dx = 6e3x \u2013 12.  the curve passes through the point (0, 1).  (i) find the equation of the curve. [4]  (ii) find the coordinates of the stationary point of the curve. [3]  (iii) determine the nature of the stationary point. [2]  (iv) find the coordinates of the point where the tangent to the curve at the point (0, 1) meets the  x-axis. [3]",
            "7": "7 0606/12/m/j/10 \u00a9 ucles 2010blank page",
            "8": "8 0606/12/m/j/10 \u00a9 ucles 2010blank 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. 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."
        },
        "0606_s10_qp_13.pdf": {
            "1": "read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case ofangles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.additional mathematics 0606/13 paper 1 may/june 2010  2 hours additional materials: answer booklet/paper electronic calculator  graph paper (2 sheets) this document consists of 6 printed pages and 2 blank pages. dc (sm/kn) 25701 \u00a9 ucles 2010 [turn over *5581385216*university of cambridge international examinations international general certificate of secondary education",
            "2": "2 0606/13/m/j/10 \u00a9 ucles 2010mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb a c   a = \u2212 \u22122 4  2 . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1. sec2 a = 1 + tan2 a. cosec2 a = 1 + cot2 a. formulae for \u2206abc a sin a = b sin b = c sin c . a2 = b2 + c2 \u2013 2bc cos a. \u2206 = 1  2 bc sin a .",
            "3": "3 0606/13/m/j/10 \u00a9 ucles 2010 [turn over1 find the coordinates of the points of intersection of the curve  y2 + y = 10x \u2013 8x2  and the straight line   y + 4x + 1 = 0. [5] 2 the expression  6 x3 + ax2 \u2013 (a + 1)x + b  has a remainder of 15 when divided by  x + 2  and a remainder  of 24 when divided by  x + 1.  show that a = 8 and find the value of b. [5] 3 given that  joa = /h20898\u201317 25/h20899  and  job = /h208984 5/h20899, find  (i) the unit vector parallel to jab, [3]   (ii) the vector joc, such that jac = 3jab. [2] 4 oy2 sec x\u00d7 \u00d7(2.4, 1.6)(1.3, 3.8)  variables x and y are such that, when y2 is plotted against sec x, a straight line graph passing through the  points (2.4, 1.6) and (1.3, 3.8) is obtained.  (i) express y2 in terms of sec x. [3]  (ii) hence find the exact value of  cos x  when y = 2. [2]",
            "4": "4 0606/13/m/j/10 \u00a9 ucles 20105 y x oa by = 6 \u2013  33\u2013x  the diagram shows part of the curve  y = 6 \u2013 3\u2013x  which passes through the point a where x = 3. the  normal to the curve at the point a meets the x-axis at the point b. find the coordinates of the point b.  [5] 6 (a) (i) on the same diagram, sketch the curves  y = cos x  and  y = 1 + cos 2x  for  0 /h11088 x /h11088 2\u03c0. [3]     (ii) hence state the number of solutions of the equation      cos 2x \u2013 cos x + 1 = 0  where  0 /h11088 x /h11088 2\u03c0. [1]  (b) the function f is given by  f( x) = 5sin 3x.  find   (i) the amplitude of f, [1]   (ii) the period of f. [1] 7 the table shows values of the variables p and v which are related by the equation  p = kv n,  where k and  n are constants. v 10 50 110 230 p 1412 151 53 19  (i) using graph paper, plot  lg p  against  lg v  and draw a straight line graph. [3]  use your graph to estimate  (ii) the value of n, [2]  (iii) the value of p when v = 170. [2]",
            "5": "5 0606/13/m/j/10 \u00a9 ucles 2010 [turn over8 given that  a = /h208984 3 1 2/h20899  and  b = /h20898\u20132 0  1 4/h20899,  find  (i) 3a \u2013 2b, [2]  (ii) a\u20131, [2]  (iii) the matrix x such that xb\u20131 = a. [3] 9 oa bx y8 cm 3 cm  the diagram shows a sector oxy of a circle centre o, radius 3 cm and a sector oab of a circle  centre o, radius 8 cm. the point x lies on the line oa and the point y lies on the line  ob. the perimeter  of the region xabyx is 15. 5 cm. find  (i) the angle aob in radians, [3]  (ii) the ratio of the area of the sector oxy to the area of the region xabyx in the form p : q, where  p and q are integers. [4] 10 a music student needs to select 7 pieces of music from 6 classical pieces and 4 modern pieces. find the number of different selections that she can make if  (i) there are no restrictions, [1]  (ii) there are to be only 2 modern pieces included, [2]  (iii) there are to be more classical pieces than modern pieces. [4]",
            "6": "6 0606/13/m/j/10 \u00a9 ucles 201011 a particle moves in a straight line such that its displacement, x m, from a fixed point o on the line at  time t seconds is given by  x = 12{1n (2t + 3)}.  find  (i) the value of t when the displacement of the particle from o is 48 m, [3]  (ii) the velocity of the particle when t = 1, [3]  (iii) the acceleration of the particle when t =1. [3] 12 answer only one of the following two alternatives.  either y y = 5 x oab      , 7 c\u03c0\u2013\u20134  the diagram shows part of a curve for which  dy\u2013\u2013dx = 8 cos 2x.  the curve passes through the   point  b /h20920\u03c0\u20134, 7/h20921.  the line  y = 5  meets the curve at the points a and c.  (i) show that the curve has equation  y = 3 + 4 sin 2x. [3]  (ii) find the x-coordinate of the point a and of the point c. [4]  (iii) find the area of the shaded region. [5]  or  a curve is such that  dy\u2013\u2013dx = 6e3x \u2013 12.  the curve passes through the point (0, 1).  (i) find the equation of the curve. [4]  (ii) find the coordinates of the stationary point of the curve. [3]  (iii) determine the nature of the stationary point. [2]  (iv) find the coordinates of the point where the tangent to the curve at the point (0, 1) meets the  x-axis. [3]",
            "7": "7 0606/13/m/j/10 \u00a9 ucles 2010blank page",
            "8": "8 0606/13/m/j/10 \u00a9 ucles 2010blank 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. 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."
        },
        "0606_s10_qp_21.pdf": {
            "1": "university of cambridge international examinations international general certificate of secondary education read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. *1406924476*additional mathematics 0606/21 paper 2 may/june 2010  2 hours additional materials: answer booklet/paper electronic calculator this document consists of 6 printed pages and 2 blank pages. dc (leo/kn) 25699/1 \u00a9 ucles 2010 [turn over",
            "2": "2 0606/21/m/j/10 \u00a9 ucles 2010mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb a c   a = \u2212 \u22122 4  2 . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1. sec2 a = 1 + tan2 a. cosec2 a = 1 + cot2 a. formulae for \u2206abc a sin a = b sin b = c sin c . a2 = b2 + c2 \u2013 2bc cos a. \u2206 = 1  2 bc sin a .",
            "3": "3 0606/21/m/j/10 \u00a9 ucles 2010 [turn over1 oy\u2013\u2013x2 x3\u00d7 \u00d7(7, 1)(3, 9)  the variables x and y are related so that, when y\u2013\u2013x2 is plotted against x3, a straight line graph passing   through (3, 9) and (7, 1) is obtained. express y in terms of x. [4] 2 in a singing competition there are 8 contestants. each contestant sings in the first round of this  competition.  (i) in how many different orders could the contestants sing? [1]  after the first round 5 contestants are chosen.  (ii) in how many different ways can these 5 contestants be chosen? [2]  these 5 contestants sing again and then first, second and third prizes are awarded to three of them.  (iii) in how many different ways can the prizes be awarded? [2] 3 it is given that  x \u2013 1  is a factor of f( x), where  f(x) = x3 \u2013 6x2 + ax + b.  (i) express b in terms of a. [2]  (ii) show that the remainder when f( x) is divided by  x \u2013 3  is twice the remainder when f( x) is divided  by  x \u2013 2. [4]",
            "4": "4 0606/21/m/j/10 \u00a9 ucles 20104 (a) given that  sin x = p  and  cos x = 2p,  where x is acute, find the exact value of p and the exact value  of cosec x. [3]   (b) prove that  (cot x + tan x) (cot x \u2013 tan x) = 1\u2013\u2013\u2013\u2013\u2013sin2 x \u2013 1\u2013\u2013\u2013\u2013\u2013cos2 x . [3] 5 given that a curve has equation  y = x2 + 64   x,  find the coordinates of the point on the curve where    d2y\u2013\u2013\u2013dx2 = 0. [7] 6 the line  y = x + 4  intersects the curve  2 x2 + 3xy \u2013 y2 + 1 = 0  at the points a and b. find the length of  the line ab. [7] 7 solutions to this question by accurate drawing will not be accepted. oy xc(4, 10) da(\u20131, 5)b(\u20132, 6)  in the diagram the points a(\u20131, 5), b(\u20132, 6), c(4, 10) and d are the vertices of a quadrilateral in which  ad is parallel to the x-axis. the perpendicular bisector of bc passes through d. find the area of the  quadrilateral abcd. [8]",
            "5": "5 0606/21/m/j/10 \u00a9 ucles 2010 [turn over8 (a) given that  a = /h208982      3 7 1    \u20135 4 /h20899  and  b = /h208982 18 6/h20899,  calculate   (i) 2a, [1]   (ii) b2, [2]   (iii) ba. [2]  (b) (i) given that  c = /h208982 17 6/h20899,  find c\u20131. [2]   (ii) given also that  d = /h20898  4 3\u20132 \u20131/h20899,  find the matrix x such that xc = d. [2] 9 a particle starts from rest and moves in a straight line so that, t seconds after leaving a fixed point o, its  velocity, v ms\u20131, is given by     v = 4 sin 2t.  (i) find the distance travelled by the particle before it first comes to instantaneous rest. [5]  (ii) find the acceleration of the particle when t = 3. [3] 10 in this question, /h2089810/h20899 is a unit vector due east and /h2089801/h20899 is a unit vector due north.  a lighthouse has position vector /h208982748/h20899 km relative to an origin o. a boat moves in such a way that its   position vector is given by /h20898  4 + 8t12 + 6t/h20899 km, where t is the time, in hours, after 1200.  (i) show that at 1400 the boat is 25 km from the lighthouse. [4]  (ii) find the length of time for which the boat is less than 25 km from the lighthouse. [4]",
            "6": "6 0606/21/m/j/10 \u00a9 ucles 201011 answer only one of the following two alternatives.  either b o acd 0.8\u03c0 6 cm  the diagram represents a company logo abcda, consisting of a sector oabco of a circle, centre o  and radius 6 cm, and a triangle aod.  angle aoc = 0.8\u03c0 radians and c is the mid-point of od. find  (i) the perimeter of the logo, [7]  (ii) the area of the logo. [5]  or  y op(1, 8) y = x3 \u2013 6x2 + 8x + 5 q x  the diagram shows part of the curve  y = x3 \u2013 6x2 + 8x + 5.  the tangent to the curve at the point p(1, 8)  cuts the curve at the point q.  (i) show that the x-coordinate of q is 4.  [6]  (ii) find the area of the shaded region. [6]",
            "7": "7 0606/21/m/j/10 \u00a9 ucles 2010blank page",
            "8": "8 0606/21/m/j/10 \u00a9 ucles 2010blank 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. 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."
        },
        "0606_s10_qp_22.pdf": {
            "1": "university of cambridge international examinations international general certificate of secondary education read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. *0316746513*additional mathematics 0606/22 paper 2 may/june 2010  2 hours additional materials: answer booklet/paper electronic calculator  graph paper (2 sheets) this document consists of 6 printed pages and 2 blank pages. dc (leo/kn) 25706 \u00a9 ucles 2010 [turn over",
            "2": "2 0606/22/m/j/10 \u00a9 ucles 2010mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb a c   a = \u2212 \u22122 4  2 . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1. sec2 a = 1 + tan2 a. cosec2 a = 1 + cot2 a. formulae for \u2206abc a sin a = b sin b = c sin c . a2 = b2 + c2 \u2013 2bc cos a. \u2206 = 1  2 bc sin a .",
            "3": "3 0606/22/m/j/10 \u00a9 ucles 2010 [turn over1 find  \u222b   (2 + 5x \u2013 1\u2013\u2013\u2013\u2013\u2013\u2013(x \u2013 2)2) dx. [3] 2 (a) ab c/h5105   copy the diagram and shade the region which represents the set  a \u222a (b \u2229 c/h11032). [1]  (b) xy/h5105   express, in set notation, the set represented by the shaded region. [1]  (c) the universal set /h5105 and the sets p and q are such that n( /h5105) = 30, n(p) = 18 and n(q) = 16. given  that n(p \u222a q)/h11032 = 2, find n(p \u2229 q). [2] 3 the volume v cm3 of a spherical ball of radius r cm is given by  v = 4\u20133 \u03c0r3.  given that the radius is  increasing at a constant rate of 1\u2013\u03c0  cm s\u20131, find the rate at which the volume is increasing when v = 288\u03c0.  [4]",
            "4": "4 0606/22/m/j/10 \u00a9 ucles 20104 a \u03b8 b c16\u2013\u2013 2 7  3  the diagram shows a right-angled triangle abc in which the length of ab is 16\u2013\u2013   2 , the length of bc is  7  3 and angle bca is \u03b8.  (i) find tan \u03b8 in the form  a  6\u2013\u2013\u2013\u2013b ,  where a and b are integers. [2]  (ii) calculate the length of ac, giving your answer in the form c  d, where c and d are integers and d is  as small as possible. [3] 5 solve the equation  2 x3 \u2013 3x2 \u2013 11x + 6 = 0. [6] 6 rq (x, y) p oy = 12 \u2013 2xy x  the diagram shows part of the line  y = 12 \u2013 2x.  the point q ( x, y) lies on this line and the points p and  r lie on the coordinate axes such that  opqr is a rectangle.  (i) write down an expression, in terms of x, for the area a of the rectangle opqr. [2]  (ii) given that x can vary, find the value of x for which a has a stationary value. [3]  (iii) find this stationary value of a and determine its nature. [2]",
            "5": "5 0606/22/m/j/10 \u00a9 ucles 2010 [turn over7 (i) sketch the graph of  y = \u23d03x + 9 \u23d0  for \u20135 < x < 2, showing the coordinates of the points where the  graph meets the axes. [3]  (ii) on the same diagram, sketch the graph of  y = x + 6. [1]  (iii) solve the equation  \u23d03x + 9\u23d0= x + 6. [3] 8 (a) (i) write down the first 4 terms, in ascending powers of x, of the expansion of  (1 \u2013 3 x)7. [3]   (ii) find the coefficient of x3 in the expansion of  (5 + 2 x)(1 \u2013 3x)7. [2]  (b) find the term which is independent of x in the expansion of  /h20920x2 + 2\u2013\u2013x/h209219. [3] 9 (i) given that  y = x + 2\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013 (4x + 12)\u00bd, show that  dy\u2013\u2013dx = k(x + 4)\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013 (4x + 12)3/2,  where k is a constant to be found. [5]  (ii) hence evaluate  \u222b 113x + 4\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013 (4x + 12)3/2 dx. [3] 10 (a) given that  logp x = 6  and  logp y = 4,  find the value of   (i) logp /h20920x2 \u2013\u2013\u2013y/h20921, [2]   (ii) logy x. [2]  (b) find the value of 2z, where z = 5 + log23. [3]  (c) express    512  as a power of 4. [2] 11 (a) solve, for  0 < x < 3  radians, the equation  4 sin x \u2013 3 = 0,  giving your answers correct to 2 decimal  places. [3]  (b) solve, for  0\u00b0 < y < 360\u00b0,  the equation  4 cosec y = 6 sin y + cot y. [6]",
            "6": "6 0606/22/m/j/10 \u00a9 ucles 201012 answer only one of the following two alternatives.  either  it is given that  f( x) = 4x2 + kx + k.  (i) find the set of values of k for which the equation f( x) = 3 has no real roots. [5]  in the case where k = 10,  (ii) express f(x) in the form  ( ax + b)2 + c, [3]  (iii) find the least value of f( x) and the value of x for which this least value occurs. [2]  or  the functions f, g and h are defined, for x \u2208 /h11938, by     f (x) = x2 + 1,     g ( x) = 2x \u2013 5,     h ( x) = 2x.  (i) write down the range of f. [1]  (ii) find the value of gf(3). [2]  (iii) solve the equation  fg( x) = g\u20131 (15). [5]  (iv) on the same axes, sketch the graph of y = h(x) and the graph of the inverse function y = h\u20131(x),  indicating clearly which graph represents h and which graph represents h\u20131. [2]",
            "7": "7 0606/22/m/j/10 \u00a9 ucles 2010blank page",
            "8": "8 0606/22/m/j/10 \u00a9 ucles 2010blank 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. 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."
        },
        "0606_s10_qp_23.pdf": {
            "1": "university of cambridge international examinations international general certificate of secondary education read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. *366157799 4*additional mathematics 0606/23 paper 2 may/june 2010  2 hours additional materials: answer booklet/paper electronic calculator  graph paper (2 sheets) this document consists of 6 printed pages and 2 blank pages. dc (leo/kn) 25707 \u00a9 ucles 2010 [turn over",
            "2": "2 0606/23/m/j/10 \u00a9 ucles 2010mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb a c   a = \u2212 \u22122 4  2 . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1. sec2 a = 1 + tan2 a. cosec2 a = 1 + cot2 a. formulae for \u2206abc a sin a = b sin b = c sin c . a2 = b2 + c2 \u2013 2bc cos a. \u2206 = 1  2 bc sin a .",
            "3": "3 0606/23/m/j/10 \u00a9 ucles 2010 [turn over1 find  \u222b   (2 + 5x \u2013 1\u2013\u2013\u2013\u2013\u2013\u2013(x \u2013 2)2) dx. [3] 2 (a) ab c/h5105   copy the diagram and shade the region which represents the set  a \u222a (b \u2229 c/h11032). [1]  (b) xy/h5105   express, in set notation, the set represented by the shaded region. [1]  (c) the universal set /h5105 and the sets p and q are such that n( /h5105) = 30, n(p) = 18 and n(q) = 16. given  that n(p \u222a q)/h11032 = 2, find n(p \u2229 q). [2] 3 the volume v cm3 of a spherical ball of radius r cm is given by  v = 4\u20133 \u03c0r3.  given that the radius is  increasing at a constant rate of 1\u2013\u03c0  cm s\u20131, find the rate at which the volume is increasing when v = 288\u03c0.  [4]",
            "4": "4 0606/23/m/j/10 \u00a9 ucles 20104 a \u03b8 b c16\u2013\u2013 2 7  3  the diagram shows a right-angled triangle abc in which the length of ab is 16\u2013\u2013   2 , the length of bc is  7  3 and angle bca is \u03b8.  (i) find tan \u03b8 in the form  a  6\u2013\u2013\u2013\u2013b ,  where a and b are integers. [2]  (ii) calculate the length of ac, giving your answer in the form c  d, where c and d are integers and d is  as small as possible. [3] 5 solve the equation  2 x3 \u2013 3x2 \u2013 11x + 6 = 0. [6] 6 rq (x, y) p oy = 12 \u2013 2xy x  the diagram shows part of the line  y = 12 \u2013 2x.  the point q ( x, y) lies on this line and the points p and  r lie on the coordinate axes such that  opqr is a rectangle.  (i) write down an expression, in terms of x, for the area a of the rectangle opqr. [2]  (ii) given that x can vary, find the value of x for which a has a stationary value. [3]  (iii) find this stationary value of a and determine its nature. [2]",
            "5": "5 0606/23/m/j/10 \u00a9 ucles 2010 [turn over7 (i) sketch the graph of  y = \u23d03x + 9 \u23d0  for \u20135 < x < 2, showing the coordinates of the points where the  graph meets the axes. [3]  (ii) on the same diagram, sketch the graph of  y = x + 6. [1]  (iii) solve the equation  \u23d03x + 9\u23d0= x + 6. [3] 8 (a) (i) write down the first 4 terms, in ascending powers of x, of the expansion of  (1 \u2013 3 x)7. [3]   (ii) find the coefficient of x3 in the expansion of  (5 + 2 x)(1 \u2013 3x)7. [2]  (b) find the term which is independent of x in the expansion of  /h20920x2 + 2\u2013\u2013x/h209219. [3] 9 (i) given that  y = x + 2\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013 (4x + 12)\u00bd, show that  dy\u2013\u2013dx = k(x + 4)\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013 (4x + 12)3/2,  where k is a constant to be found. [5]  (ii) hence evaluate  \u222b 113x + 4\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013\u2013 (4x + 12)3/2 dx. [3] 10 (a) given that  logp x = 6  and  logp y = 4,  find the value of   (i) logp /h20920x2 \u2013\u2013\u2013y/h20921, [2]   (ii) logy x. [2]  (b) find the value of 2z, where z = 5 + log23. [3]  (c) express    512  as a power of 4. [2] 11 (a) solve, for  0 < x < 3  radians, the equation  4 sin x \u2013 3 = 0,  giving your answers correct to 2 decimal  places. [3]  (b) solve, for  0\u00b0 < y < 360\u00b0,  the equation  4 cosec y = 6 sin y + cot y. [6]",
            "6": "6 0606/23/m/j/10 \u00a9 ucles 201012 answer only one of the following two alternatives.  either  it is given that  f( x) = 4x2 + kx + k.  (i) find the set of values of k for which the equation f( x) = 3 has no real roots. [5]  in the case where k = 10,  (ii) express f(x) in the form  ( ax + b)2 + c, [3]  (iii) find the least value of f( x) and the value of x for which this least value occurs. [2]  or  the functions f, g and h are defined, for x \u2208 /h11938, by     f (x) = x2 + 1,     g ( x) = 2x \u2013 5,     h ( x) = 2x.  (i) write down the range of f. [1]  (ii) find the value of gf(3). [2]  (iii) solve the equation  fg( x) = g\u20131 (15). [5]  (iv) on the same axes, sketch the graph of y = h(x) and the graph of the inverse function y = h\u20131(x),  indicating clearly which graph represents h and which graph represents h\u20131. [2]",
            "7": "7 0606/23/m/j/10 \u00a9 ucles 2010blank page",
            "8": "8 0606/23/m/j/10 \u00a9 ucles 2010blank 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. 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."
        },
        "0606_w10_qp_11.pdf": {
            "1": "this document consists of 6 printed pages and 2 blank pages. dc (slm) 34223 \u00a9 ucles 2010 [turn overuniversity of cambridge international examinations international general certificate of secondary education read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. *0523546408*additional mathematics 0606/11 paper 1 october/november 2010  2 hours additional materials: answer booklet/paper electronic calculator  graph paper (1 sheet)",
            "2": "2 0606/11/o/n/10 \u00a9 ucles 2010mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/11/o/n/10 \u00a9 ucles 2010 [turn over1 the equation of a curve is given by  y = 2x2 + ax + 14, where a is a constant.  given that this equation can also be written as  y = 2(x \u2013 3)2 + b, where b is a constant, find  (i) the value of a and of b, [2]  (ii) the minimum value of y. [1] 2 (i) sketch, on the same set of axes, the graphs of  y = cos x and  y = sin 2x for 0\u00b0 /h11088 x /h11088 180\u00b0. [2]  (ii) hence write down the number of solutions of the equation sin 2 x \u2013 cos x = 0 for 0\u00b0 /h11088 x /h11088 180\u00b0.  [1] 3 show that  cos x 1 \u2013 sin x  +  cos x 1 + sin x   =  2 sec x. [4] 4 factorise completely the expression  2 x3 \u2013 11x2 \u2013 20x \u2013 7. [5] 5 a curve has the equation  y = 2x sin x + \u03c0 3.  the curve passes through the point p (\u03c0 2, a).  (i) find, in terms of \u03c0, the value of a. [1]  (ii) using your value of a, find the equation of the normal to the curve at p. [5] 6 (i) find, in ascending powers of x, the first 3 terms in the expansion of  (2 \u2013 5 x)6, giving your answer  in the form a + bx + cx2, where a, b and c are integers. [3]  (ii) find the coefficient of x in the expansion of  (2 \u2013 5 x)6 (1 + x 2)10 . [3] 7 (a) sets a and b are such that     a = {x : sin x = 0.5 for 0\u00b0 /h11088 x /h11088 360\u00b0},    b = {x : cos (x \u2013 30\u00b0) = \u2013 0.5 for 0\u00b0 /h11088 x /h11088 360\u00b0}.   find the elements of    (i) a, [2]   (ii) ab. [2]  (b) set c is such that    c = {x : sec2 3x = 1 for 0\u00b0 /h11088 x /h11088 180\u00b0}.   find n(c). [3]",
            "4": "4 0606/11/o/n/10 \u00a9 ucles 20108 variables x and y are such that, when ln y is plotted against ln x, a straight line graph passing through the  points (2, 5.8) and (6, 3.8) is obtained. 1ny 1nx o(2, 5.8) (6, 3.8)  (i) find the value of ln y when lnx = 0. [2]  (ii) given that y = axb, find the value of a and of b. [5] 9 x cm x cm4x cma cm2  the figure shows a rectangular metal block of length 4 x cm, with a cross-section which is a square of  side x cm and area a cm2. the block is heated and the area of the cross-section increases at a constant  rate of 0.003  cm2s\u20131. find  (i)  da dx in terms of x, [1]  (ii) the rate of increase of x when x = 5, [3]  (iii) the rate of increase of the volume of the block when x = 5. [4]",
            "5": "5 0606/11/o/n/10 \u00a9 ucles 2010 [turn over10 p\u03c0\u20133 edcb a o 4 cm  the diagram shows a circle, centre o, radius 4 cm, enclosed within a sector pbcdp of a circle, centre  p. the circle centre o touches the sector at points a, c and e. angle bpd is \u03c0 3 radians.  (i) show that pa  = 4 3cm and pb = 12 cm. [2]    find, to 1 decimal place,  (ii) the area of the shaded region , [4]  (iii) the perimeter of the shaded region . [4] 11 (i) find  /h208851 1+x dx. [2]  (ii) given that  y = 2x 1+x, show that  dy dx = a 1+x + bx /h208981+x/h208993, where a and b are to be found. [4]  (iii) hence find  /h20885x /h208981+x/h208993  dx and evaluate  /h208853 0x /h208981+x/h208993  dx. [4]",
            "6": "6 0606/11/o/n/10 \u00a9 ucles 201012 answer only one of the following two alternatives. either  a curve is such that  dy dx = 4x2 \u2013 9. the curve passes through the point (3, 1).   (i) find the equation of the curve. [4]  the curve has stationary points at a and b.  (ii) find the coordinates of a and of b. [3]  (iii) find the equation of the perpendicular bisector of the line ab. [4] or  a curve has the equation  y = ae2x + be\u2013x where  x /h11091 0. at the point where  x = 0,  y  = 50 and  dy dx = \u2013 20.  (i) show that a = 10 and find the value of b. [5]  (ii) using the values of a and b found in part (i), find the coordinates of the stationary point on the  curve. [4]  (iii) determine the nature of the stationary point, giving a reason for your answer. [2]",
            "7": "7 0606/11/o/n/10 \u00a9 ucles 2010blank page",
            "8": "8 0606/11/o/n/10 \u00a9 ucles 2010blank 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. 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."
        },
        "0606_w10_qp_12.pdf": {
            "1": "this document consists of 6 printed pages and 2 blank pages. dc (slm) 34224 \u00a9 ucles 2010 [turn overuniversity of cambridge international examinations international general certificate of secondary education read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. *3899679080*additional mathematics 0606/12 paper 1 october/november 2010  2 hours additional materials: answer booklet/paper electronic calculator  graph paper (1 sheet)",
            "2": "2 0606/12/o/n/10 \u00a9 ucles 2010mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/12/o/n/10 \u00a9 ucles 2010 [turn over1 the equation of a curve is given by  y = 2x2 + ax + 14, where a is a constant.  given that this equation can also be written as  y = 2(x \u2013 3)2 + b, where b is a constant, find  (i) the value of a and of b, [2]  (ii) the minimum value of y. [1] 2 (i) sketch, on the same set of axes, the graphs of  y = cos x and  y = sin 2x for 0\u00b0 /h11088 x /h11088 180\u00b0. [2]  (ii) hence write down the number of solutions of the equation sin 2 x \u2013 cos x = 0 for 0\u00b0 /h11088 x /h11088 180\u00b0.  [1] 3 show that  cos x 1 \u2013 sin x  +  cos x 1 + sin x   =  2 sec x. [4] 4 factorise completely the expression  2 x3 \u2013 11x2 \u2013 20x \u2013 7. [5] 5 a curve has the equation  y = 2x sin x + \u03c0 3.  the curve passes through the point p (\u03c0 2, a).  (i) find, in terms of \u03c0, the value of a. [1]  (ii) using your value of a, find the equation of the normal to the curve at p. [5] 6 (i) find, in ascending powers of x, the first 3 terms in the expansion of  (2 \u2013 5 x)6, giving your answer  in the form a + bx + cx2, where a, b and c are integers. [3]  (ii) find the coefficient of x in the expansion of  (2 \u2013 5 x)6 (1 + x 2)10 . [3] 7 (a) sets a and b are such that     a = {x : sin x = 0.5 for 0\u00b0 /h11088 x /h11088 360\u00b0},    b = {x : cos (x \u2013 30\u00b0) = \u2013 0.5 for 0\u00b0 /h11088 x /h11088 360\u00b0}.   find the elements of    (i) a, [2]   (ii) ab. [2]  (b) set c is such that    c = {x : sec2 3x = 1 for 0\u00b0 /h11088 x /h11088 180\u00b0}.   find n(c). [3]",
            "4": "4 0606/12/o/n/10 \u00a9 ucles 20108 variables x and y are such that, when ln y is plotted against ln x, a straight line graph passing through the  points (2, 5.8) and (6, 3.8) is obtained. 1ny 1nx o(2, 5.8) (6, 3.8)  (i) find the value of ln y when lnx = 0. [2]  (ii) given that y = axb, find the value of a and of b. [5] 9 x cm x cm4x cma cm2  the figure shows a rectangular metal block of length 4 x cm, with a cross-section which is a square of  side x cm and area a cm2. the block is heated and the area of the cross-section increases at a constant  rate of 0.003  cm2s\u20131. find  (i)  da dx in terms of x, [1]  (ii) the rate of increase of x when x = 5, [3]  (iii) the rate of increase of the volume of the block when x = 5. [4]",
            "5": "5 0606/12/o/n/10 \u00a9 ucles 2010 [turn over10 p\u03c0\u20133 edcb a o 4 cm  the diagram shows a circle, centre o, radius 4 cm, enclosed within a sector pbcdp of a circle, centre  p. the circle centre o touches the sector at points a, c and e. angle bpd is \u03c0 3 radians.  (i) show that pa  = 4 3cm and pb = 12 cm. [2]    find, to 1 decimal place,  (ii) the area of the shaded region , [4]  (iii) the perimeter of the shaded region . [4] 11 (i) find  /h208851 1+x dx. [2]  (ii) given that  y = 2x 1+x, show that  dy dx = a 1+x + bx /h208981+x/h208993, where a and b are to be found. [4]  (iii) hence find  /h20885x /h208981+x/h208993  dx and evaluate  /h208853 0x /h208981+x/h208993  dx. [4]",
            "6": "6 0606/12/o/n/10 \u00a9 ucles 201012 answer only one of the following two alternatives. either  a curve is such that  dy dx = 4x2 \u2013 9. the curve passes through the point (3, 1).   (i) find the equation of the curve. [4]  the curve has stationary points at a and b.  (ii) find the coordinates of a and of b. [3]  (iii) find the equation of the perpendicular bisector of the line ab. [4] or  a curve has the equation  y = ae2x + be\u2013x where  x /h11091 0. at the point where  x = 0,  y  = 50 and  dy dx = \u2013 20.  (i) show that a = 10 and find the value of b. [5]  (ii) using the values of a and b found in part (i), find the coordinates of the stationary point on the  curve. [4]  (iii) determine the nature of the stationary point, giving a reason for your answer. [2]",
            "7": "7 0606/12/o/n/10 \u00a9 ucles 2010blank page",
            "8": "8 0606/12/o/n/10 \u00a9 ucles 2010blank 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. 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."
        },
        "0606_w10_qp_13.pdf": {
            "1": "this document consists of 5 printed pages and 3 blank pages. dc (slm) 34235 \u00a9 ucles 2010 [turn overuniversity of cambridge international examinations international general certificate of secondary education read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. * 0 5 1 3 2 6 0 4 5 1 *additional mathematics 0606/13 paper 1 october/november 2010  2 hours additional materials: answer booklet/paper electronic calculator  graph paper (1 sheet)",
            "2": "2 0606/13/o/n/10 \u00a9 ucles 2010mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb ac a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/13/o/n/10 \u00a9 ucles 2010 [turn over1 show that sec x \u2013 cos x = sin x tan x. [3] 2 a 4-digit number is formed by using four of the seven digits 2, 3, 4, 5, 6, 7 and 8. no digit can be used  more than once in any one number. find how many different 4-digit numbers can be formed if  (i) there are no restrictions, [2]  (ii) the number is even. [2] 3 the line y = mx + 2 is a tangent to the curve y = x2 + 12x + 18. find the possible values of m. [4] 4 the remainder when the expression x3 + kx2 \u2013 5x \u2013 3 is divided by x \u2013 2 is 5 times the remainder when  the expression is divided by x + 1.  find the value of k. [4] 5 solve the simultaneous equations      log3 a = 2 log3 b,     log3 (2a \u2013 b) = 1. [5] 6 solve the equation 3x3 + 7x2 \u2013 22x \u2013 8 = 0. [6] 7 (i) sketch the graph of  y = |3x \u2013 5|, for \u20132 \ue03c x \ue03c 3, showing the coordinates of the points where the  graph meets the axes.  [3]  (ii)  on the same diagram, sketch the graph of  y = 8x. [1]  (iii) solve the equation 8 x = |3x \u2013 5|. [3] 8 (a) a function f is defined, for x  \ue052, by      f(x) = x2 + 4x \u2013 6.   (i) find the least value of f( x) and the value of x for which it occurs. [2]   (ii) hence write down a suitable domain for f( x) in order that f\u20131(x) exists. [1]  (b) functions g and h are defined, for x  \ue052, by    g(x) = x 2 \u2013 1,    h(x) = x2 \u2013 x.   (i) find g\u20131(x). [2]   (ii) solve gh(x) = g\u20131(x). [3]",
            "4": "4 0606/13/o/n/10 \u00a9 ucles 20109 (a) find  \ue045(x1 3 \u2013 3)2 dx. [3]  (b) (i) given that  y = x x26+, find  dy dx. [3]   (ii) hence find \ue045x2 + 3 x26+  dx. [2] 10 a particle travels in a straight line so that, t s after passing through a fixed point o, its displacement s m  from o is given by s = ln(t2 + 1).  (i) find the value of t when s = 5. [2]  (ii) find the distance travelled by the particle during the third second. [2]  (iii) show that, when t = 2, the velocity of the particle is 0.8 ms\u20131. [2]  (iv) find the acceleration of the particle when t = 2. [3] 11 solve the equation  (i) 3 sin x \u2013 4 cos x = 0,  for 0\u00b0 \ue03c x \ue03c 360\u00b0, [3]  (ii) 11 sin y + 1 = 4 cos2 y,  for 0\u00b0 \ue03c y \ue03c 360\u00b0, [4]  (iii) sec (2z + \u03c0  3) = \u20132,  for  0 \ue03c z \ue03c \u03c0 radians. [4]",
            "5": "5 0606/13/o/n/10 \u00a9 ucles 201012 answer only one of the following two alternatives. either a curve has the equation  y = a sin 2x  + b cos 3x . the curve passes through the point with coordinates (\u03c0  12, 3) and has a gradient of  \u2013 4 when  x  = \u03c0  3.  (i) show that a = 4 and find the value of b. [6] (ii) given that, for  0 \ue03c x \ue03c \u03c0  3, the curve lies above the x-axis, find the area of the region enclosed by the   curve, the y-axis and the line x = \u03c0  3. [5] or y x ob y = 4x2 \u2013 2x3c a the diagram shows the curve y = 4x2 \u2013 2x3. the point a lies on the curve and the x-coordinate of a is 1.   the curve crosses the x-axis at the point b. the normal to the curve at the point a crosses the y-axis at the  point c.   (i) show that the coordinates of c are (0, 2.5). [5]  (ii) find the area of the shaded region. [6]",
            "6": "6 0606/13/o/n/10 \u00a9 ucles 2010blank page",
            "7": "7 0606/13/o/n/10 \u00a9 ucles 2010blank page",
            "8": "8 0606/13/o/n/10 \u00a9 ucles 2010blank 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. 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."
        },
        "0606_w10_qp_21.pdf": {
            "1": "this document consists of 6 printed pages and 2 blank pages. dc (cw/dj) 34225 \u00a9 ucles 2010 [turn overuniversity of cambridge international examinations international general certificate of secondary education *2915442350*additional mathematics 0606/21 paper 2 october/november 2010  2 hours additional materials: answer booklet/paper  electronic calculator read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/21/o/n/10 \u00a9 ucles 2010mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/21/o/n/10 \u00a9 ucles 2010 [turn over1 solve the equation /h209042x + 10 /h20904 = 7. [3] 2 the expression x3 + ax2 \u2013 15x + b has a factor x \u2013 2 and leaves a remainder of 75 when divided by  x + 3. find the value of a and of b. [5] 3 a number, n0, of fish of a particular species are introduced to a lake. the number, n, of these fish in the  lake, t weeks after their introduction, is given by n = n0e\u2013kt, where k is a constant. calculate  (i) the value of k if, after 34 weeks, the number of these fish has fallen to 1 2 of the number introduced,  [2]  (ii) the number of weeks it takes for the number of these fish to have fallen to 15 of the number  introduced. [3] 4 students take three multiple-choice tests, each with ten questions. a correct answer earns 5 marks. if no  answer is given 1 mark is scored. an incorrect answer loses 2 marks. a student\u2019s final total mark is the sum of 20% of the mark in test 1, 30% of the mark in test 2 and 50% of the mark in test 3. one student\u2019s responses are summarized in the table below. test 1 test 2 test 3 correct answer 7 6 5no answer 1 3 5incorrect answer 2 1 0  write down three matrices such that matrix multiplication will give this student\u2019s final total mark and hence find this total mark. [5] 5 find the set of values of m for which the line y = mx \u2013 2 cuts the curve y = x 2 + 8x + 7 in two distinct  points. [6]",
            "4": "4 0606/21/o/n/10 \u00a9 ucles 20106 a 4-digit number is formed by using four of the seven digits 1, 3, 4, 5, 7, 8 and 9. no digit can be used  more than once in any one number. find how many different 4-digit numbers can be formed if  (i) there are no restrictions, [2]  (ii) the number is less than 4000,  [2]  (iii) the number is even and less than 4000. [2] 7 45 cm 60 cmx cmx cmx cm  a rectangular sheet of metal measures 60 cm by 45 cm. a scoop is made by cutting out squares, of side  x cm, from two corners of the sheet and folding the remainder as shown.  (i) show that the volume, v cm3, of the scoop is given by     v = 2700x \u2013 165x2 + 2x3. [2]  (ii) given that x can vary, find the value of x for which v has a stationary value. [4] 8 solve the equation  (i) lg(5x + 10) + 2 lg3 = 1 + lg(4x + 12), [4]  (ii) 92y 37\u2013y = 34y+3 27y\u20132 . [3]",
            "5": "5 0606/21/o/n/10 \u00a9 ucles 2010 [turn over9 a plane, whose speed in still air is 250 kmh\u20131, flies directly from a to b, where b is 500 km from a on  a bearing of 060\u00b0. there is a constant wind of 80 kmh\u20131 blowing from the south. find, to the nearest  minute, the time taken for the flight. [7] 10 solutions to this question by accurate drawing will not be accepted. y x ob(6,5) a(1,4) c d  the diagram shows a quadrilateral abcd in which a is the point (1, 4) and b is the point (6, 5). angle  abc is a right angle and the point c lies on the x-axis. the line ad is parallel to the y-axis and the line  cd is parallel to ba. find   (i) the equation of the line cd, [5]  (ii) the area of the quadrilateral abcd. [4] 11 solve the equation  (i) 5 sin x \u2013 3 cos x = 0, for 0\u00b0 /h33355 x /h33355 360\u00b0, [3]  (ii) 2 cos2 y \u2013 sin y \u2013 1 = 0, for 0\u00b0 /h33355 y /h33355 360\u00b0, [5]  (iii) 3 sec z = 10, for 0 /h33355 z /h33355 6 radians. [3]",
            "6": "6 0606/21/o/n/10 \u00a9 ucles 201012 answer only one of the following two alternatives.  either  the functions f and g are defined, for x /h11022 1, by  f(x) = (x + 1)2 \u2013 4,  g(x) = 3x + 5 x \u2013 1 .  find  (i) fg(9), [2]  (ii) expressions for f\u20131(x) and g\u20131(x), [4]  (iii) the value of x for which g(x) = g\u20131(x). [4]  or a particle moves in a straight line so that, at time t s after passing a fixed point o, its velocity is v ms \u20131,  where v = 6t + 4 cos 2t.  find  (i) the velocity of the particle at the instant it passes o, [1]  (ii) the acceleration of the particle when t = 5, [4]  (iii) the greatest value of the acceleration, [1]  (iv) the distance travelled in the fifth second. [4]",
            "7": "7 0606/21/o/n/10 \u00a9 ucles 2010blank page",
            "8": "8 0606/21/o/n/10 \u00a9 ucles 2010blank 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. 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."
        },
        "0606_w10_qp_22.pdf": {
            "1": "this document consists of 6 printed pages and 2 blank pages. dc (slm) 34222 \u00a9 ucles 2010 [turn overuniversity of cambridge international examinations international general certificate of secondary education *9337164288*additional mathematics 0606/22 paper 2 october/november 2010  2 hours additional materials: answer booklet/paper  electronic calculator read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/22/o/n/10 \u00a9 ucles 2010mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/22/o/n/10 \u00a9 ucles 2010 [turn over1 solve the equation /h209042x + 10 /h20904 = 7. [3] 2 the expression x3 + ax2 \u2013 15x + b has a factor x \u2013 2 and leaves a remainder of 75 when divided by  x + 3. find the value of a and of b. [5] 3 a number, n0, of fish of a particular species are introduced to a lake. the number, n, of these fish in the  lake, t weeks after their introduction, is given by n = n0e\u2013kt, where k is a constant. calculate  (i) the value of k if, after 34 weeks, the number of these fish has fallen to 1 2 of the number introduced,  [2]  (ii) the number of weeks it takes for the number of these fish to have fallen to 15 of the number  introduced. [3] 4 students take three multiple-choice tests, each with ten questions. a correct answer earns 5 marks. if no  answer is given 1 mark is scored. an incorrect answer loses 2 marks. a student\u2019s final total mark is the sum of 20% of the mark in test 1, 30% of the mark in test 2 and 50% of the mark in test 3. one student\u2019s responses are summarized in the table below. test 1 test 2 test 3 correct answer 7 6 5no answer 1 3 5incorrect answer 2 1 0  write down three matrices such that matrix multiplication will give this student\u2019s final total mark and hence find this total mark. [5] 5 find the set of values of m for which the line y = mx \u2013 2 cuts the curve y = x 2 + 8x + 7 in two distinct  points. [6]",
            "4": "4 0606/22/o/n/10 \u00a9 ucles 20106 a 4-digit number is formed by using four of the seven digits 1, 3, 4, 5, 7, 8 and 9. no digit can be used  more than once in any one number. find how many different 4-digit numbers can be formed if  (i) there are no restrictions, [2]  (ii) the number is less than 4000,  [2]  (iii) the number is even and less than 4000. [2] 7 45 cm 60 cmx cmx cmx cm  a rectangular sheet of metal measures 60 cm by 45 cm. a scoop is made by cutting out squares, of side  x cm, from two corners of the sheet and folding the remainder as shown.  (i) show that the volume, v cm3, of the scoop is given by     v = 2700x \u2013 165x2 + 2x3. [2]  (ii) given that x can vary, find the value of x for which v has a stationary value. [4] 8 solve the equation  (i) lg(5x + 10) + 2 lg3 = 1 + lg(4x + 12), [4]  (ii) 92y 37\u2013y = 34y+3 27y\u20132 . [3]",
            "5": "5 0606/22/o/n/10 \u00a9 ucles 2010 [turn over9 a plane, whose speed in still air is 250 kmh\u20131, flies directly from a to b, where b is 500 km from a on  a bearing of 060\u00b0. there is a constant wind of 80 kmh\u20131 blowing from the south. find, to the nearest  minute, the time taken for the flight. [7] 10 solutions to this question by accurate drawing will not be accepted. y x ob(6,5) a(1,4) c d  the diagram shows a quadrilateral abcd in which a is the point (1, 4) and b is the point (6, 5). angle  abc is a right angle and the point c lies on the x-axis. the line ad is parallel to the y-axis and the line  cd is parallel to ba. find   (i) the equation of the line cd, [5]  (ii) the area of the quadrilateral abcd. [4] 11 solve the equation  (i) 5 sin x \u2013 3 cos x = 0, for 0\u00b0 /h33355 x /h33355 360\u00b0, [3]  (ii) 2 cos2 y \u2013 sin y \u2013 1 = 0, for 0\u00b0 /h33355 y /h33355 360\u00b0, [5]  (iii) 3 sec z = 10, for 0 /h33355 z /h33355 6 radians. [3]",
            "6": "6 0606/22/o/n/10 \u00a9 ucles 201012 answer only one of the following two alternatives.  either  the functions f and g are defined, for x /h11022 1, by  f(x) = (x + 1)2 \u2013 4,  g(x) = 3x + 5 x \u2013 1 .  find  (i) fg(9), [2]  (ii) expressions for f\u20131(x) and g\u20131(x), [4]  (iii) the value of x for which g(x) = g\u20131(x). [4]  or a particle moves in a straight line so that, at time t s after passing a fixed point o, its velocity is v ms \u20131,  where v = 6t + 4 cos 2t.  find  (i) the velocity of the particle at the instant it passes o, [1]  (ii) the acceleration of the particle when t = 5, [4]  (iii) the greatest value of the acceleration, [1]  (iv) the distance travelled in the fifth second. [4]",
            "7": "7 0606/22/o/n/10 \u00a9 ucles 2010blank page",
            "8": "8 0606/22/o/n/10 \u00a9 ucles 2010blank 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. 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."
        },
        "0606_w10_qp_23.pdf": {
            "1": "this document consists of 7 printed pages and 1 blank page. dc (cw/dj) 34220 \u00a9 ucles 2010 [turn overuniversity of cambridge international examinations international general certificate of secondary education *8579300390*additional mathematics 0606/23 paper 2 october/november 2010  2 hours additional materials: answer booklet/paper  graph paper (1 sheet)  electronic calculator read these instructions first if you have been given an answer booklet, follow the instructions on the front cover of the booklet. write your centre number, candidate number and name on all the work you hand in.write in dark blue or black pen.y ou may use a soft pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. write your answers on the separate answer booklet/paper provided.give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/23/o/n/10 \u00a9 ucles 2010mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/23/o/n/10 \u00a9 ucles 2010 [turn over1 the two variables x and y are such that y = 10 (x + 4)3 .  (i) find an expression for dy d x . [2]  (ii) hence find the approximate change in y as x increases from 6 to 6 + p, where p is small. [2] 2 find the equation of the curve which passes through the point (4, 22) and for which dy d x = 3x(x \u2013 2).   [4] 3 (a) 0 0\u00ba 60\u00ba 120\u00ba 180\u00ba 240\u00ba 300\u00ba 360\u00bax12345678910y  the diagram shows the curve y = a cos bx + c for 0\u00b0 /h33355 x /h33355 360\u00b0. find the value of   (i) a,    (ii)    b,    (iii)    c. [3]  (b) given that f( x) = 6 sin 2x + 7, state   (i) the period of f, [1]   (ii) the amplitude of f. [1]",
            "4": "4 0606/23/o/n/10 \u00a9 ucles 20104 (i) find, in ascending powers of x, the first 4 terms of the expansion of (1 + x)6. [2]  (ii) hence find the coefficient of p3 in the expansion of (1 + p \u2013 p2)6. [3] 5 (a) given that a = (2 \u20134 1) and b = /h20898 3 \u20131  0 5\u20132 7/h20899 , find the matrix product ab. [2]  (b) given that c = /h20898 3 5\u20132 \u20134/h20899  and d = /h208986 \u201342 8/h20899 , find   (i) the inverse matrix c\u20131, [2]   (ii) the matrix x such that cx = d. [2] 6 (a) a/h5105 b   copy the diagram above and shade the region which represents the set a/h11032 /h33371 b. [1]  (b) the sets p, q and r are such that     p /h33370 q = /h11083 and p /h33371 q /h20666 r.   draw a venn diagram showing the sets p, q and r. [2] (c) in a group of 50 students f denotes the set of students who speak french and s denotes the set of  students who speak spanish. it is given that n( f) = 24, n(s ) = 18, n(f /h33370 s) = x and n(f/h11032 /h33370 s/h11032) = 3x.  write down an equation in x and hence find the number of students in the group who speak neither  french nor spanish. [3] 7 the line y = 2x \u2013 6 meets the curve 4 x 2 + 2xy \u2013 y2 = 124 at the points a and b. find the length of the  line ab. [7]",
            "5": "5 0606/23/o/n/10 \u00a9 ucles 2010 [turn over8 (i) show that (5 + 3\u221a\u23af2 )2 = 43 + 30\u221a\u23af2 . [1]  hence find, without using a calculator, the positive square root of  (ii) 86 + 60\u221a\u23af2 , giving your answer in the form a + b\u221a\u23af2 , where a and b are integers, [2]  (iii) 43 \u2013 30\u221a\u23af2 , giving your answer in the form c + d\u221a\u23af2 , where c and d are integers, [1]  (iv) 1 43 + 30\u221a\u23af2, giving your answer in the form f + g\u221a\u23af2 h, where f, g and h are integers. [3] 9 x ab cod 30 cm8 cm  the diagram shows a rectangle abcd and an arc axb of a circle with centre at o, the mid-point of  dc.  the lengths of dc and bc are 30 cm and 8 cm respectively. find  (i) the length of oa, [2]  (ii) the angle aob, in radians, [2]  (iii) the perimeter of figure adocbxa, [2]  (iv) the area of figure adocbxa. [2] 10 the equation of a curve is y = x2ex. the tangent to the curve at the point p(1, e) meets the y-axis at the  point a. the normal to the curve at p meets the x-axis at the point b. find the area of the triangle oab,  where o is the origin. [9]",
            "6": "6 0606/23/o/n/10 \u00a9 ucles 201011 b xq p aob a  in the diagram  \u23af \u2192oa = a,  \u23af \u2192ob = b,  \u23af \u2192op = 2a and  \u23af \u2192oq = 3b.  (i) given that  \u23af \u2192ax = l \u23af \u2192aq, express  \u23af \u2192ox in terms of l, a and b. [3]  (ii) given that  \u23af \u2192bx = k \u23af \u2192bp,  express  \u23af \u2192ox in terms of k, a and b. [3]  (iii) hence find the value of l and of k. [3]",
            "7": "7 0606/23/o/n/10 \u00a9 ucles 201012 answer only one of the following two alternatives.  either   the table shows values of the variables v and p which are related by the equation p = a v2 + b v , where a  and b are constants. v 2468 p 6.22 2.84 1.83 1.35  (i) using graph paper, plot v2 p on the y-axis against v on the x-axis and draw a straight line graph.  [2]  (ii) use your graph to estimate the value of a and of b . [4]  in another method of finding a and b from a straight line graph, 1 v is plotted along the x-axis. in this  case, and without drawing a second graph,  (iii) state the variable that should be plotted on the y-axis, [2]  (iv) explain how the values of a and b could be obtained. [2]  or the table shows experimental values of two variables r and t. t 2 8 24 54 r 22 134 560 1608  (i) using the y-axis for ln r and the x-axis for ln t, plot ln r against ln t to obtain a straight line graph.  [2]  (ii) find the gradient and the intercept on the y-axis of this graph and express r in terms of t. [6]  another method of finding the relationship between r and t from a straight line graph is to plot lg r on  the y-axis and lg t on the x -axis. without drawing this second graph, find the value of the gradient and  of the intercept on the y-axis for this graph. [2]",
            "8": "8 0606/23/o/n/10 \u00a9 ucles 2010blank 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. 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."
        }
    },
    "2011": {
        "0606_s11_qp_11.pdf": {
            "1": "this document consists of 16 printed pages. dc (sm/dj) 42191/2 \u00a9 ucles 2011 [turn overuniversity of cambridge international examinations international general certificate of secondary education read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid.do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. *6061060040* additional mathematics  0606/11 paper 1 may/june 2011  2 hours candidates answer on the question paper. additional materials: electronic calculator for examiner\u2019s use 1 23456789 101112 total",
            "2": "2 0606/11/m/j/11 \u00a9 ucles 2011mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use 0606/11/m/j/111 show that     1 1 \u2013 cos\u03b8 + 1 1 + cos\u03b8 = 2cosec2\u03b8. [3] 2 express  lg a + 3lg b \u2013 3  as a single logarithm. [3]",
            "4": "4 \u00a9 ucles 2011for examiner\u2019 s use 0606/11/m/j/113 (a) shade the region corresponding to the set given below each venn diagram. a (a\u222ab)\u2229c\u02b9b ca (a\u222ab\u222ac)\u02b9b ca (a\u2229b)\u222a(b\u2229c)\u222a(c\u2229a)b c/h5105/h5105/h5105  [3]  (b) given that  p = {p : tan p = 1 for 0\u00ba /h11088 p /h11088 540\u00ba}, find n(p). [1] 4 (a) solve the equation  163x\u20132 = 82x. [3]",
            "5": "5 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use 0606/11/m/j/11 (b) given that  ab   4 32 52 52 5\u2013 \u2013 a  b1 33 5 = apbq, find the value of p and of q. [2] 5 (i) y 456 3 210 45\u00b0 90\u00b0 135\u00b0 180\u00b0 \u20131 \u20132 \u20133 \u20134x   on the diagram above, sketch the curve  y = 1 + 3sin2x  for  0\u00ba /h11088 x /h11088 180\u00ba. [3]  (ii) y 456 3 210 45\u00b0 90\u00b0 135\u00b0 180\u00b0 \u20131 \u20132 \u20133 \u20134x   on the diagram above, sketch the curve y = /h208411 + 3sin2x/h20841 for 0\u00ba /h11088 x /h11088 180\u00ba. [1]  (iii) write down the number of solutions of the equation /h208411 + 3sin2x/h20841 = 1 for 0\u00ba /h11088 x /h11088 180\u00ba. [1]",
            "6": "6 \u00a9 ucles 2011for examiner\u2019 s use 0606/11/m/j/116 the curves y = x2 and 3y = \u20132x2 + 20x \u2013 20 meet at the point a. y xa oy = x2 3y = \u20132x2 + 20x \u2013 20  (i) show that the x-coordinate of a is 2. [1]  (ii) show that the gradients of the two curves are equal at a. [3]  (iii) find the equation of the tangent to the curves at a. [1]",
            "7": "7 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use 0606/11/m/j/117 the points a and b have coordinates (\u20132, 15) and (3, 5) respectively. the perpendicular to  the line ab at the point a (\u20132, 15) crosses the y-axis at the point c. find the area of the  triangle abc. [6]",
            "8": "8 \u00a9 ucles 2011for examiner\u2019 s use 0606/11/m/j/118 (a) the matrices a, b and c are given by a = /h208982 1 1 32 5/h20899, b = /h208982  1  3  41  5  6  7/h20899   and c = /h208989 10/h20899. write down, but do not evaluate, matrix products which may be calculated    from the matrices a, b and c. [2]  (b) given that  x = /h208982 43 5/h20899 and y = /h208982x 3 y  x 4y/h20899, find the value of x and of y such that    x-1y = /h20898\u201312x + 3y 6\u20137x + 3y 6/h20899. [6]",
            "9": "9 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use 0606/11/m/j/119 a body moves in a straight line such that, t s after passing through a fixed point o, its  displacement from o is s m. the velocity v ms\u20131 of the body is such that v = 5cos4t.  (i) write down the velocity of the body as it passes through o. [1]  (ii) find the value of t when the acceleration of the body is first equal to 10 ms\u20132. [4]  (iii) find the value of s when t = 5. [4]",
            "10": "10 \u00a9 ucles 2011for examiner\u2019 s use 0606/11/m/j/1110 (a) a curve is such that dy dx = ae1\u2013x \u2013 3x2, where a is a constant. at the point (1, 4), the gradient  of the curve is 2.   (i) find the value of a. [1]   (ii) find the equation of the curve. [5]",
            "11": "11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use 0606/11/m/j/11 (b) (i) find /h20848(7x + 8)1 3dx. [2]   (ii) hence evaluate 8 0/h20848(7x + 8)13dx. [2]",
            "12": "12 \u00a9 ucles 2011for examiner\u2019 s use 0606/11/m/j/1111 (a) the function f is such that f( x) = 2x2 \u2013 8x + 5.   (i) show that f(x) = 2(x + a)2 + b, where a and b are to be found. [2]   (ii) hence, or otherwise, write down a suitable domain for f so that f\u20131 exists. [1]  (b) the functions g and h are defined respectively by g(x) = x2 + 4,       x /h11091 0,       h(x) = 4x \u2013 25, x /h11091 0.   (i) write down the range of g and of h\u20131. [2]",
            "13": "13 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use 0606/11/m/j/11  (ii) on the axes below, sketch the graphs of y = g(x) and y = g\u20131(x), showing the coordinates  of any points where the curves meet the coordinate axes. [3] y x o   (iii) find the value of x for which gh(x) = 85. [4]",
            "14": "14 \u00a9 ucles 2011for examiner\u2019 s use 0606/11/m/j/1112 answer only one of the following two alternatives. either  the equation of a curve is y = (x \u2013 1)(x2 \u2013 6x + 2).  (i) find the x-coordinates of the stationary points on the curve and determine the nature of each  of these stationary points. [6]  (ii) given that z = y2 and that z is increasing at the constant rate of 10 units per second, find the  rate of change of y when x = 2. [2]   (iii) hence find the rate of change of x when x = 2. [2] or  the diagram shows a cuboid with a rectangular base of sides x cm and 2x cm. the height of the  cuboid is y cm and its volume is 72 cm3. y cm x cm 2x cm  (i) show that the surface area a cm2 of the cuboid is given by  a = 4x2 + 216 x.  [3]  (ii) given that x can vary, find the dimensions of the cuboid when a is a minimum. [4]  (iii) given that x increases from 2 to 2 + p, where p is small, find, in terms of p, the corresponding  approximate change in a, stating whether this change is an increase or a decrease. [3]",
            "15": "15 \u00a9 ucles 2011for examiner\u2019 s use 0606/11/m/j/11start your answer to question 12 here. indicate which question you are answering.   either or .. ",
            "16": "16 \u00a9 ucles 2011 0606/11/m/j/11for examiner\u2019 s use 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. 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.continue your answer here if necessary. .. "
        },
        "0606_s11_qp_12.pdf": {
            "1": "this document consists of 16 printed pages. dc (nh/cgw) 42186/1 \u00a9 ucles 2011 [turn overread these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid.do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. *6732187560* additional mathematics 0606/12 paper 1 may/june 2011  2 hours candidates answer on the question paper. additional materials electronic calculator for examiner\u2019s use 1 23456789 101112 totaluniversity of cambridge international examinations international general certificate of secondary education",
            "2": "2 0606/12/m/j/11 \u00a9 ucles 2011mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb a c   a = \u2212 \u22122 4  2 . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use 0606/12/m/j/111 find the value of k for which the x-axis is a tangent to the curve      y = x2 + (2k + 10)x + k  2 + 5. [3]",
            "4": "4 \u00a9 ucles 2011for examiner\u2019 s use 0606/12/m/j/112 the coefficient of  x3  in the expansion of  (2 + ax)5  is 10 times the coefficient of  x2  in the  expansion of  /h208981 + ax 3/h208994  . find the value of a. [4]",
            "5": "5 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use 0606/12/m/j/113 (a) 5 4 3 2 1 \u03c0 \u03c0 x  2y  o   the figure shows the graph of  y = k + m sin px  for  0 /h11088 x /h11088 \u03c0, where k, m and p are positive  constants. complete the following statements.   k = ..    m = ..    p = .. [3]  (b) the function g is such that  g(x) = 1 + 5cos3x . write down   (i) the amplitude of g, [1]   (ii) the period of g in terms of \u03c0. [1]",
            "6": "6 \u00a9 ucles 2011for examiner\u2019 s use 0606/12/m/j/114 you must not use a calculator in question 4.  in the triangle abc, angle b = 90\u00b0, ab = 4 + 2 2  and  bc = 1 + 2 .  (i) find tan c, giving your answer in the form  k 2 . [2]  (ii) find the area of the triangle abc, giving your answer in the form  p + q 2, where p  and q  are integers. [2]  (iii) find the area of the square whose side is of length ac, giving your answer in the form s + t 2, where s  and t  are integers. [2]",
            "7": "7 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use 0606/12/m/j/115 (i) show that  2x \u2013 1  is a factor of  2 x3 \u2013 5x2 + 10x \u2013 4. [2]  (ii) hence show that  2x3 \u2013 5x2 + 10x \u2013 4 = 0  has only one real root and state the value of this  root. [4]",
            "8": "8 \u00a9 ucles 2011for examiner\u2019 s use 0606/12/m/j/116 the figure shows the graph of a straight line with  1g y  plotted against x. the  straight line passes  through the points a (5,3) and b (15,5). a (5,3)b (15,5) x lg y   o  (i) express  lg y  in terms of x. [3]  (ii) show that  y = a (10bx)  where a and b are to be found. [3]",
            "9": "9 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use 0606/12/m/j/117 a team of 6 members is to be selected from 6 women and 8 men.  (i) find the number of different teams that can be selected.  [1]  (ii) find the number of different teams that consist of 2 women and 4 men. [3]  (iii) find the number of different teams that contain no more than 1 woman. [3]",
            "10": "10 \u00a9 ucles 2011for examiner\u2019 s use 0606/12/m/j/118 (i) sketch the curve  y = (2x \u2013 5)(2x + 1) for  \u20131 /h11088 x /h11088 3, stating the coordinates of the points  where the curve meets the coordinate axes. [4]  (ii) state the coordinates of the stationary point on the curve. [1]  (iii) using your answers to parts (i) and (ii), sketch the curve  y = \u23d0(2x \u2013 5)(2x + 1) \u23d0 for  \u20131 /h11088 x /h11088 3. [2]",
            "11": "11 \u00a9 ucles 2011for examiner\u2019 s use 0606/12/m/j/11 [turn over9 the figure shows a circle, centre o, radius r cm. the length of the arc ab of the circle is 9 \u03c0 cm.   angle aob is \u03b8 radians and is 3 times angle oba.      \u03b8 rada bor cm 9\u03c0 cm  (i) show that  \u03b8  = 3\u03c0 5 . [2]  (ii) find the value of r. [2]  (iii) find the area of the shaded region. [3]",
            "12": "12 \u00a9 ucles 2011for examiner\u2019 s use 0606/12/m/j/1110 relative to an origin o, points a and b have position vectors  /h208985 \u20136/h20899  and   /h2089829 \u201313/h20899  respectively.  (i) find a unit vector parallel to  ab. [3]  the points a, b and c  lie on a straight line such that  2 ac = 3ab.  (ii) find the position vector of the point c. [4]",
            "13": "13 \u00a9 ucles 2011for examiner\u2019 s use 0606/12/m/j/11 [turn over11 solve  (i) 2cot2 x \u2013 5cosec  x \u2013 1 = 0  for  0\u00b0 < x < 180\u00b0, [5]  (ii) 5cos 2y \u2013 4sin 2y = 0  for  0\u00b0 < y < 180\u00b0, [4]  (iii) cos /h20898z + \u03c0 6/h20899 = \u2013 1 2  for  0 < z < 2\u03c0 radians. [3]",
            "14": "14 \u00a9 ucles 2011for examiner\u2019 s use 0606/12/m/j/1112 answer only one of the following two alternatives.  either  the tangent to the curve  y = 3x3 + 2x2 \u2013 5x + 1  at the point where  x = \u20131  meets the y-axis at the  point a.  (i) find the coordinates of the point a. [3]  the curve meets the y-axis at the point b. the normal to the curve at b meets the x-axis at the  point c. the tangent to the curve at the point where  x = \u20131  and the normal to the curve at b meet  at the point d.  (ii) find the area of the triangle acd. [7]  or    r qy y = x (x  \u2013 3)2 x op  the diagram shows  the curve  y = x (x \u2013 3)2 . the curve has a maximum at the point p and  touches the x-axis at the point q. the tangent at p and the normal at q meet at the point r. find  the area of the shaded region pqr. [10]",
            "15": "15 \u00a9 ucles 2011for examiner\u2019 s use 0606/12/m/j/11start your answer to question 12 here. indicate which question you are answering.  either or ... [turn over",
            "16": "16 \u00a9 ucles 2011for examiner\u2019 s use 0606/12/m/j/11continue your answer here if necessary.  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. 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."
        },
        "0606_s11_qp_21.pdf": {
            "1": "this document consists of 14 printed pages and 2 blank pages. dc (nh/sw) 42198/1 \u00a9 ucles 2011 [turn overuniversity of cambridge international examinations international general certificate of secondary education *1668603243* additional mathematics 0606/21 paper 2 may/june 2011  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid.do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.for examiner\u2019s use 1 23456789 1011 total",
            "2": "2 0606/21/m/j/11 \u00a9 ucles 2011mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb a c   a = \u2212 \u22122 4  2 . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/21/m/j/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use1 without using a calculator, express (5 + 2   3)2 2 +   3 in the form p + q   3, where p and q are integers.  [4] 2 (i) find the coefficient of x3 in the expansion of /h208981 \u2013 x 2/h2089912 .  [2]  (ii) find the coefficient of x3 in the expansion of (1 + 4 x) /h208981 \u2013 x 2/h2089912 .  [3]",
            "4": "4 0606/21/m/j/11 \u00a9 ucles 2011for examiner\u2019 s use3 relative to an origin o, the position vectors of the points a and b are i \u2013 4j and 7i + 20j  respectively.  the point c lies on ab and is such that \u2192ac = 2 3 \u2192ab. find the position vector of c  and the magnitude of this vector. [5]",
            "5": "5 0606/21/m/j/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use4 find the set of values of k for which the line  y = 2x \u2013 5  cuts the curve  y = x2 + kx + 11  in two  distinct points. [6]",
            "6": "6 0606/21/m/j/11 \u00a9 ucles 2011for examiner\u2019 s use5 the expression  x3 + 8x2 + px \u2013 25  leaves a remainder of r when divided by  x \u2013 1  and a  remainder of  \u2013 r  when divided by  x + 2.  (i) find the value of p. [4]  (ii) hence find the remainder when the expression is divided by x + 3. [2]",
            "7": "7 0606/21/m/j/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use6 (a) a shelf contains 8 different travel books, of which 5 are about europe and 3 are about africa.   (i) find the number of different ways the books can be arranged if there are no restrictions.  [2]   (ii) find the number of different ways the books can be arranged if the 5 books about europe are kept together. [2]  (b) 3 dvds and 2 videotapes are to be selected from a collection of 7 dvds and 5 videotapes.   calculate the number of different selections that could be made. [3]",
            "8": "8 0606/21/m/j/11 \u00a9 ucles 2011for examiner\u2019 s use7 the variables x and y are related so that when lg y is plotted against lg x a straight line graph  passing through the points (4, 12) and (6, 17) is obtained.   (4,12)lg y lg xo(6,17)  (i) express y in terms of x, giving your answer in the form  y = axb.  [6]  (ii) find the value of x when y = 300. [2]",
            "9": "9 0606/21/m/j/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use8 the temperature, t \u00b0 celsius, of an object, t minutes after it is removed from a heat source, is  given by t = 55e\u20130.1t + 15.  (i) find the temperature of the object at the instant it is removed from the heat source. [1]  (ii) find the temperature of the object when t = 8. [1]  (iii) find the value of t when t = 25. [3]  (iv) find the rate of change of t when t = 16. [3]",
            "10": "10 0606/21/m/j/11 \u00a9 ucles 2011for examiner\u2019 s use9 a coastguard station receives a distress call from a ship which is travelling at 15 km h\u20131 on a  bearing of 150\u00b0. a lifeboat leaves the coastguard station at 15 00 hours; at this time the ship is at a  distance of 30 km on a bearing of 270\u00b0. the lifeboat travels in a straight line at constant speed and reaches the ship at 15 40 hours.    (i) find the speed of the lifeboat. [5]  (ii) find the bearing on which the lifeboat travelled. [3]",
            "11": "11 0606/21/m/j/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use10 (i) solve the equation     3 sin x + 4 cos x = 0     for     0\u00b0 < x < 360\u00b0. [3]  (ii) solve the equation     6 cos y + 6 sec y = 13     for     0\u00b0 < y < 360\u00b0. [5]  (iii) solve the equation     sin(2 z \u2013 3) = 0.7     for     0 < z < \u03c0  radians. [3]",
            "12": "12 0606/21/m/j/11 \u00a9 ucles 2011for examiner\u2019 s use11 answer only one of the following two alternatives.  either 1.8 radc a beod 12  cm   the diagram shows an isosceles triangle aob and a sector ocdeo of a circle with centre o. the  line ab is a tangent to the circle. angle aob = 1.8 radians and the radius of the circle is 12 cm.  (i) show that the distance ac = 7.3 cm to 1 decimal place. [2]  (ii) find the perimeter of the shaded region. [6]  (iii) find the area of the shaded region. [4]  or y x y = x  sin xqp o  the diagram shows part of the curve  y = x sin x  and the normal to the curve at the point   p /h20898\u03c0 2 , \u03c0 2/h20899.  the curve passes through the point q(\u03c0, 0).  (i) show that the normal to the curve at p passes through the point q. [4]  (ii) given that d dx (x cos x) = cos x \u2013 x sin x, find /h20848x sin xdx. [3]  (iii) find the area of the shaded region. [5]",
            "13": "13 0606/21/m/j/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s usestart your answer to question 11 here. indicate which question you are answering.  either or .. ",
            "14": "14 0606/21/m/j/11 \u00a9 ucles 2011for examiner\u2019 s usecontinue your answer here if necessary. ..",
            "15": "15 0606/21/m/j/11 \u00a9 ucles 2011blank page",
            "16": "16 0606/21/m/j/11 \u00a9 ucles 2011permission 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. 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.blank page"
        },
        "0606_s11_qp_22.pdf": {
            "1": "this document consists of 16 printed pages. dc (nh/sw) 42199/1 \u00a9 ucles 2011 [turn over *7560400886* additional mathematics 0606/22 paper 2 may/june 2011  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid.do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.for examiner\u2019s use 1 23456789 1011 totaluniversity of cambridge international examinations international general certificate of secondary education",
            "2": "2 0606/22/m/j/11 \u00a9 ucles 2011mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb a c   a = \u2212 \u22122 4  2 . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/22/m/j/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use1 (i) given that  y = sin 3x, find dy dx. [1]  (ii) hence find the approximate increase in y as x increases from \u03c0 9 to \u03c0 9 + p, where p is small.    [2] 2 (a) an outdoor club has three sections, walking, biking and rock-climbing. using /h5105 to denote  the set of all members of the club and w, b and r to denote the members of the walking, biking and rock-climbing sections respectively, write each of the following statements using set notation.   (i) there are 72 members in the club. [1]   (ii) every member of the rock-climbing section is also a member of the walking section.     [1]  (b) (i)    x y/h5105   on the diagram shade the region which  represents the set x  y \u02b9. [1]   (ii) using set notation express the set x  y \u02b9 in an alternative way.  [1]",
            "4": "4 0606/22/m/j/11 \u00a9 ucles 2011for examiner\u2019 s use3 (i) given that a = /h20898  2 1 \u20132 5/h20899, find the inverse of the matrix a + i, where i is the identity matrix.    [3]  (ii) hence, or otherwise, find the matrix x such that ax + x = b, where b = /h2089814  4/h20899. [2]",
            "5": "5 0606/22/m/j/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use4 (a) prove that 1 1 \u2013 sin x \u2013 1 1 + sin x = 2 tan x sec x.  [3]  (b) an acute angle x is such that  sin x = p.  given that  sin 2 x = 2 sin x cos x, find an expression,  in terms of p, for cosec 2x. [3]",
            "6": "6 0606/22/m/j/11 \u00a9 ucles 2011for examiner\u2019 s use5 (i) given that y = x 2x + 15 , show that dy dx = k(x + 5)\u2013\u2013\u2013\u2013\u2013\u2013\u20132x + 15, where k is a constant to be found. [3]      (ii) hence find /h20848x + 5\u2013\u2013\u2013\u2013\u2013\u2013\u20132x + 15dx  and evaluate 5 \u20133/h20848x + 5\u2013\u2013\u2013\u2013\u2013\u2013\u20132x + 15dx.  [3]",
            "7": "7 0606/22/m/j/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use6 the line  y = 3x \u2013 9  intersects the curve  49 x2 \u2013 y2 + 42x + 8y = 247 at the points a and b.    find the length of the line ab.  [7]",
            "8": "8 0606/22/m/j/11 \u00a9 ucles 2011for examiner\u2019 s use7 a particle moves in a straight line so that, t s after passing through a fixed point o, its velocity,   v ms\u20131, is given by v = 60\u2013\u2013\u2013\u2013\u2013\u2013\u2013(3t + 4)2.  (i) find the velocity of the particle as it passes through o. [1]  (ii) find the acceleration of the particle when t = 2. [3]  (iii) find an expression for the displacement of the particle from o, t s after it has passed  through o.  [4]",
            "9": "9 0606/22/m/j/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use8 (a) (i) solve  3x = 200, giving your answer to 2 decimal places. [2]   (ii) solve  log5 (5y + 40) \u2013 log5 (y + 2) = 2.  [4]  (b) given that (24z3)2 \u2013\u2013\u2013\u2013\u2013\u2013\u201327 \u00d7 12z = 2a3bzc, evaluate a, b and c.  [3]",
            "10": "10 0606/22/m/j/11 \u00a9 ucles 2011for examiner\u2019 s use9 solutions to this question by accurate drawing will not be accepted. y xd c x = 14 b (\u20132, \u201310)a (4, 2) m o  the diagram shows the quadrilateral abcd in which a is the point (4, 2) and b is the point  (\u20132, \u201310). the points c and d lie on the line x = 14.  the diagonal ac is perpendicular to ab and  passes through the mid-point, m, of the diagonal  bd.  find the area of the quadrilateral abcd.   [9]",
            "11": "11 0606/22/m/j/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s usecontinue your answer here if necessary.",
            "12": "12 0606/22/m/j/11 \u00a9 ucles 2011for examiner\u2019 s use10 (a) (i) express 18 + 16x \u2013 2x2 in the form a + b(x + c)2, where a, b and c are integers.  [3]   a function f is defined by  f : x \u2192 18 + 16x \u2013 2x2 for x  /h11938.   (ii) write down the coordinates of the stationary point on the graph of  y = f(x). [1]   (iii) sketch the graph of  y = f(x). [2]",
            "13": "13 0606/22/m/j/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use (b) a function g is defined by  g : x \u2192 (x + 3)2 \u2013 7 for x > \u20133.   (i) find an expression for  g\u20131 (x).  [2]   (ii) solve the equation  g\u20131 (x) = g(0).  [3]",
            "14": "14 0606/22/m/j/11 \u00a9 ucles 2011for examiner\u2019 s use11 answer only one of the following two alternatives.  either  (a) using an equilateral triangle  of side 2 units, find the exact value of sin 60\u00b0 and of cos 60\u00b0.    [3]  (b) p qx cm60\u00b0 60\u00b0 x cm y cms r   pqrs is a trapezium in which pq = rs = x cm and qr = y cm.   angle qps = angle rsp = 60\u00b0 and qr is parallel to ps.   (i) given that the perimeter of the trapezium is 60 cm, express y in terms of  x. [2]   (ii) given that the area of the trapezium is a cm2 , show that         a  =   3(30x \u2013 x2) 2 . [3]   (iii) given that x can vary, find the value of x for which a has a stationary value and  determine the nature of this stationary value. [4]  or     r cm h cm           for a sphere of radius r: v olume = 4 3 \u03c0 r3 surface area = 4 \u03c0 r2  the diagram shows a solid object in the form of a cylinder of height h cm and radius r cm on top  of a hemisphere of radius r cm. given that the volume of the object is 2880 \u03c0 cm3,  (i) express h in terms of r, [2]  (ii) show that the external surface area, a cm2, of the object is given by         a = 5 3 \u03c0 r2 + 5760\u03c0 r .  [3]  given that r can vary,  (iii) find the value of r for which a has a stationary value, [4]  (iv) find this stationary value of a, leaving your answer in terms of \u03c0,  [2]  (v) determine the nature of this stationary value. [1]",
            "15": "15 0606/22/m/j/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s usestart your answer to question 11 here. indicate which question you are answering.  either or .. ",
            "16": "16 0606/22/m/j/11 \u00a9 ucles 2011for examiner\u2019 s usecontinue your answer here if necessary.  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. 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."
        },
        "0606_w11_qp_11.pdf": {
            "1": "this document consists of 14 printed pages and 2 blank pages. dc (nf/cgw) 48822 \u00a9 ucles 2011 [turn overuniversity of cambridge international examinations international general certificate of secondary education *6409782612* additional mathematics 0606/11 paper 1 october/november 2011  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. for examiner\u2019s use  1  2 3 4 5 6 7 8 910 total",
            "2": "2 0606/11/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use mathematical formulae  1. algebra quadratic equation  for the equation ax2 + bx + c  = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! .  2. trigonometry identities  sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/11/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use1 (a) sets a and b are such that n( a) = 15 and n(b) = 7. find the greatest and least possible  values of   (i) n(a  b), [2]   (ii) n(a  b). [2]  (b) on a venn diagram draw 3 sets p, q and r such that      p  q = \u2205 and p  r = p. [2]",
            "4": "4 0606/11/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use2 the function f is such that f( x) = 4x3 \u2013 8x2 + ax + b, where a and b are constants. it is given  that 2x \u2013 1 is a factor of f( x) and that when f( x) is divided by x + 2 the remainder is 20. find the  remainder when f( x) is divided by x \u2013 1. [6]",
            "5": "5 0606/11/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use3 variables t and n are such that when 1g n is plotted against 1g t, a straight line graph passing  through the points (0.45, 1.2) and (1, 3.4) is obtained. lg n lg t(0.45,  1.2)(1, 3.4) o  (i) express the equation of the straight line graph in the form 1g n = m 1g t + 1g c, where m and c  are constants to be found. [4]  (ii) hence express n in terms of t. [1]",
            "6": "6 0606/11/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use4 six-digit numbers are to be formed using the digits 3, 4, 5, 6, 7 and 9. each digit may only be  used once in any number.  (i) find how many different six-digit numbers can be formed. [1]  find how many of these six-digit numbers are  (ii) even, [1]  (iii) greater than 500 000, [1]  (iv) even and greater than 500 000. [3]",
            "7": "7 0606/11/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use5 a particle moves in a straight line such that its displacement, x m, from a fixed point o at time  t s, is given by x = 3 + sin 2t, where t /h11091 0.  (i) find the velocity of the particle when t = 0. [2]  (ii) find the value of t when the particle is first at rest. [2]  (iii) find the distance travelled by the particle before it first comes to rest. [2]  (iv) find the acceleration of the particle when t = 3\u03c0 4. [2]",
            "8": "8 0606/11/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use6 (a) xy o (0,  p)(q, 1) (\u2013 /pi1  ,  \u20135)12   the diagram shows part of the graph y = p + 3tan3x passing through the points (\u2013 \u03c0 12, \u20135), (0, p)  and (q, 1). find the value of p and of q. [4]  (b) it is given that f( x) = a cos(bx)+c, where a, b and c are integers. the maximum value of f is  11, the minimum value of f is 3 and the period of f is 72 \u00b0. find the value of a, of b and of c.  [4]",
            "9": "9 0606/11/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use7 the coefficient of x2 in the expansion of /h208981 + x 5/h20899n , where n is a positive integer, is 3 5.  (i) find the value of n. [4]  (ii) using this value of n, find the term independent of x in the expansion of      /h208981 + x 5/h20899 n  /h208982 \u2013 3 x/h20899 2 . [4]",
            "10": "10 0606/11/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use8 (a) find  /h20885(ex + 1)2 dx  and hence evaluate  /h208852 0(ex + 1)2 dx. [6]  (b) a curve is such that dy dx = (4x +1)\u20131 2. given that the curve passes through the point with    coordinates (2, 4.5), find the equation of the curve. [5]",
            "11": "11 0606/11/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use9 (i) solve  1 + cot2 x = 8 sin x  for 0\u00b0 /h11088 x /h11088 360\u00b0. [5]  (ii) solve  4 sin(2y \u2013 0.3) + 5 cos(2y \u2013 0.3) = 0  for  0 /h11088 y /h11088 \u03c0 radians. [5]",
            "12": "12 0606/11/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use10 answer only one of the following two alternatives.  either a b g def c\u03b8 \u03b8\u03b8 r cmr cm  the figure shows a sector  abc of a circle centre c, radius 2r cm, where angle acb is 3\u03b8 radians.  the points d, e, f and g lie on an arc of a circle centre c, radius r cm. the points d and g are  the midpoints of ca and cb respectively. angles dce and fcg are each \u03b8 radians. the area of  the shaded region is 5 cm2.  (i) by first expressing \u03b8 in terms of r, show that the perimeter, p cm, of the shaded region is   given by p = 4r + 8 r. [6]  (ii) given that r can vary, show that the stationary value of p can be written in the form  k2, where k is a constant to be found. [4]  (iii) determine the nature of this stationary value and find the value of \u03b8 for which it occurs. [2]  or 10 cm r cm \u03b8 \u03b8oa bdce f  the figure shows a sector oab of a circle, centre o, radius 10 cm. angle aob = 2\u03b8 radians  where 0 < \u03b8 < \u03c0 2. a circle centre c, radius r cm, touches the arc ab at the point d. the lines oa  and ob are tangents to the circle at the points e and f respectively.  (i) write down, in terms of r, the length of oc. [1]  (ii) hence show that r = 10 sin \u03b8 1 + sin \u03b8 .  [2]  (iii) given that \u03b8 can vary, find dr d\u03b8 when r = 10 3. [6]  (iv) given that r is increasing at 2 cms\u20131, find the rate at which \u03b8 is increasing when \u03b8 = \u03c0 6 . [3]",
            "13": "13 0606/11/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s usestart your answer to question 10 here. indicate which question you are answering.       either or ... ..",
            "14": "14 0606/11/o/n/11 \u00a9 ucles 2011for examiner\u2019 s usecontinue your answer here if necessary. ... ...",
            "15": "15 0606/11/o/n/11 \u00a9 ucles 2011blank page",
            "16": "16 0606/11/o/n/11 \u00a9 ucles 2011permission 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. 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.blank page"
        },
        "0606_w11_qp_12.pdf": {
            "1": "this document consists of 16 printed pages. dc (leo/cgw) 48824 \u00a9 ucles 2011 [turn overuniversity of cambridge international examinations international general certificate of secondary education *6890064064* additional mathematics 0606/12 paper 1 october/november 2011  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.for examiner\u2019s use  1  2 3 4 5 6 7 8 910 11 total",
            "2": "2 0606/12/o/n/11 \u00a9 ucles 2011mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/12/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use1 show that     1 tan \u03b8 + cot \u03b8 = sin \u03b8 cos \u03b8. [3]",
            "4": "4 0606/12/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use2 find the coordinates of the points where the line   2 y = x \u2013 1 meets the curve   x2 + y2 = 29. [5]",
            "5": "5 0606/12/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use3 (i) express logx2 in terms of a logarithm to base 2. [1]  (ii) using the result of part (i), and the substitution   u = log2x, find the values of x which satisfy  the equation   log2x = 3 \u2013 2 logx2. [4]",
            "6": "6 0606/12/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use4 a curve has equation y = (3x2 + 15)2 3. find the equation of the normal to the curve at the point  where x = 2. [6]",
            "7": "7 0606/12/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use5 variables x and y are such that, when y2 is plotted against 2x, a straight line graph is obtained.  this line has a gradient of 5 and passes through the point (16,81). o(16,81) 2 xy 2  (i) express y2 in terms of 2x. [3]  (ii) find the value of x when y = 6. [3]",
            "8": "8 0606/12/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use6 (i) given that   (3 + x)5 + (3 \u2013 x)5 = a + bx2 + cx4, find the value of a, of b and of c. [4]  (ii) hence, using the substitution   y = x2, solve, for x, the equation         (3 + x)5 + (3 \u2013 x)5 = 1086. [4]",
            "9": "9 0606/12/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use7 (i) show that /h208984 \u2013 x/h208992 x can be written in the form px\u2013 1 2 + q + rx12 , where p, q and r are   integers to be found. [3]  (ii) a curve is such that dy dx = /h208984 \u2013 x/h208992 x for x > 0.  given that the curve passes through the   point (9, 30), find the equation of the curve. [5]",
            "10": "10 0606/12/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use8 the line cd is the perpendicular bisector of the line joining the point a (\u20131, \u20135) and the  point b  (5,3).  (i) find the equation of the line cd. [4]",
            "11": "11 0606/12/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use (ii) given that m is the midpoint of ab, that 2 cm = md, and that the x-coordinate of c is \u2013 2,  find the coordinates of d. [3]  (iii) find the area of the triangle cad. [2]",
            "12": "12 0606/12/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use9 (i) given that y = x sin 4x, find dy dx . [3]  (ii) hence find /h20885 x cos 4x dx and evaluate  0\u03c0 8/h20885 x cos 4 x dx. [6]",
            "13": "13 0606/12/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use10 (i) solve   2 sec2 x = 5 tan x + 5,  for 0\u00b0 < x < 360\u00b0. [5]  (ii) solve   2 sin /h20898y 2 + \u03c0 3/h20899 = 1,  for  0 < y < 4\u03c0 radians. [5]",
            "14": "14 0606/12/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use11 answer only one of the following two alternatives. either  a curve has equation y = e\u2013x (acos 2 x + bsin 2x). at the point (0, 4) on the curve, the gradient of  the tangent is 6.  (i) find the value of a. [1]  (ii) show that b = 5 . [5]  (iii) find the value of x, where 0 <  x < \u03c0 2 radians, for which y has a stationary value. [5] or  a curve has equation y = 1n(x2 \u2013 1) x2 \u2013 1, for x > 1.  (i) show that dy dx = k\u200ax(1 \u2013 1n(x2 \u20131)) (x2 \u2013 1)2, where k is a constant to be found. [4]  (ii) hence find the approximate change in y when x increases from 5 to 5 + p, where  p is  small. [2]  (iii) find, in terms of e, the coordinates of the stationary point on the curve. [5] start your answer to question 11 here. indicate which question you are answering.       either or .. ",
            "15": "15 0606/12/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s usecontinue your answer to question 11 here. .. ",
            "16": "16 0606/12/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use 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. 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.continue your answer here if necessary. .. "
        },
        "0606_w11_qp_13.pdf": {
            "1": "this document consists of 16 printed pages. dc (nf/cgw) 48825 \u00a9 ucles 2011 [turn overuniversity of cambridge international examinations international general certificate of secondary education *8208281311* additional mathematics 0606/13 paper 1 october/november 2011  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.for examiner\u2019s use  1  2 3 4 5 6 7 8 910 11 12 total",
            "2": "2 0606/13/o/n/11 \u00a9 ucles 2011for examiner\u2019 s usemathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/13/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use 1 given that 6x3 2y45  4 2x12 y\u20131 = axp yq, find the values of the constants a, p and q.  [3] 2 express /h20881/h33701/h33701/h33702 in the form k cos \u03b8, where k is a constant to be found.  [4]1 \u2013 cos2 \u03b8 4 sec2 \u03b8 \u2013 4",
            "4": "4 0606/13/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use3 (i) given that a = /h20898  4 3 \u2013 8 \u20132/h20899 , find a\u20131.  [2]  (ii) hence find the matrix m such that /h20898  4 3\u2013 8 \u20132/h20899 m = /h208981 42 3/h20899 .  [3]",
            "5": "5 0606/13/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use4 (a) sets a and b are such that n( a) = 11, n(b) = 13 and n(a  b) = 18.   find n(a  b).  [2]  (b) sets /h5105, x and y are such that /h5105 = {\u03b8:0 /h33355 \u03b8 /h33355 2\u03c0}, x = {\u03b8:sin \u03b8 = \u2013 0.5}, y = /h20902\u03b8:sec2 \u03b8 = 4 3/h20903 .   (i) find, in terms of \u03c0, the elements of the set x.  [1]   (ii) find, in terms of \u03c0, the elements of the set y.  [2]   (iii) use set notation to describe the relationship between the sets x and y.  [1]",
            "6": "6 0606/13/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use5 it is given that lg p3 q = 10a and lg  p  q2 = a.  (i) find, in terms of a, expressions for lg p  and lg q.  [5]  (ii) find the value of logp q.  [1]",
            "7": "7 0606/13/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use6 a curve has equation      y = 6 cos x 2 + 4 sin x 2 , for 0 /h11021 x /h11021 2\u03c0  radians.  (i) find the x-coordinate of the stationary point on the curve.  [5]  (ii) determine the nature of this stationary point.  [2]",
            "8": "8 0606/13/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use7  xy b ca om (1,3) (\u2013 4,2)  the figure shows a right-angled triangle abc, where the point a has coordinates (\u2013 4,2) , the  angle b is 90\u00b0 and the point c lies on the x-axis. the point m(1,3) is the midpoint of ab. find  the area of the triangle abc. [7]",
            "9": "9 0606/13/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use8 vectors a and b are such that a = /h208983 + m 5 \u2013 2n/h20899 and b = /h208984 \u2013 2n 10 + 3m/h20899 .  (i) given that 3 a + b = /h208981 + n \u20135/h20899 , find the value of m and of n.  [4]  (ii) show that the magnitude of b is k \u221a\u23af5, where k is an integer to be found.  [2]  (iii) find the unit vector in the direction of b.  [1]",
            "10": "10 0606/13/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use9 the function f is defined, for 0\u00b0 /h33355 x /h33355 360\u00b0, by f(x) = 2 sin 3x \u20131.  (i) state the amplitude and period of f.  [2]  (ii) state the maximum value of f and the corresponding values of x.  [3]  (iii) sketch the graph of f.  [2]",
            "11": "11 0606/13/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use10 (a) differentiate tan (3 x + 2) with respect to x.  [2]  (b) differentiate (\u221a\u23afx + 1 )2 3 with respect to x.  [3]  (c) differentiate ln (x3 \u2013 1) 2x + 3 with respect to x.  [3]",
            "12": "12 0606/13/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use11 a particle moves in a straight line so that, t s after leaving a fixed point o, its velocity v ms\u20131 is  given by v = 3e2t + 4t.  (i) find the initial velocity of the particle.  [1]  (ii) find the initial acceleration of the particle.  [3]",
            "13": "13 0606/13/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use (iii) find the distance travelled by the particle in the third second.  [4]",
            "14": "14 0606/13/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use12 answer only one of the following two alternatives.  either  a function f is such that f( x) = ln (5x \u2013 10), for x /h11022 2.  (i) state the range of f.  [1]  (ii) find f\u20131 (x).  [3]  (iii) state the range of f\u20131.  [1]  (iv) solve f(x) = 0.  [2]  a function g is such that g( x) = 2x \u2013 ln 2, for x /h20678 /h11938.  (v) solve gf(x) = f(x2).  [5]  or  a function f is such that f( x) = 4e\u2013x + 2, for x /h20678 /h11938.  (i) state the range of f.  [1]  (ii) solve f(x) = 26.  [2]  (iii) find f\u20131(x).  [3]  (iv) state the domain of f\u20131.  [1]  a function g is such that g( x) = 2ex \u2013 4, for x /h20678 /h11938.  (v) using the substitution t = ex or otherwise, solve g(x) = f(x).  [5] start your answer to question 12 here.indicate which question you are answering.        either or ... .",
            "15": "15 0606/13/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s usecontinue your answer to question 12 here. .",
            "16": "16 0606/13/o/n/11 \u00a9 ucles 2011for examiner\u2019s use 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. 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.continue your answer here if necessary. ..."
        },
        "0606_w11_qp_21.pdf": {
            "1": "this document consists of 18 printed pages and 2 blank pages. dc (nf/cgw) 48828 \u00a9 ucles 2011 [turn overuniversity of cambridge international examinations international general certificate of secondary education *1741350364* additional mathematics 0606/21 paper 2 october/november 2011  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.for examiner\u2019s use  1  2 3 4 5 6 7 8 910 11 12 total",
            "2": "2 0606/21/o/n/11 \u00a9 ucles 2011for examiner\u2019 s usemathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c  = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/21/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use1 solve the equation    |4 x \u2013 5| = 21. [3] 2 given that the straight line   y = 3x + c   is a tangent to the curve   y = x2 + 9x + k,   express k in  terms of c. [4]",
            "4": "4 0606/21/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use3 32 2+\u221a3\u03b8  without using a calculator, find the value of cos \u03b8, giving your answer in the form a + b 3 c, where  a, b and c  are integers. [5]",
            "5": "5 0606/21/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use4 (i) given that  y = 1 x2 + 3 , show that  dy dx = kx (x2 + 3)2 , where k is a constant to be found. [2]  (ii) hence find  /h20885 6x (x2 + 3)2 dx  and evaluate  /h208853 16x (x2 + 3)2 dx. [3]",
            "6": "6 0606/21/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use5 (a) the functions f and g are defined, for x  /h11938, by f : x /h21739 2x + 3, g : x /h21739 x2 \u2013 1.   find fg(4). [2]  (b) the functions h and k are defined, for x > 0, by h : x /h21739 x + 4, k : x /h21739 x.   express each of the following in terms of h and k.   (i)  x /h21739 x + 4  [1]   (ii) x /h21739 x + 8 [1]   (iii) x /h21739 x2 \u2013 4 [2]",
            "7": "7 0606/21/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use6 solutions to this question by accurate drawing will not be accepted.  the points a(1, 4), b(3, 8), c(13, 13) and d are the vertices of a trapezium in which ab is  parallel to dc and angle bad is 90\u00b0. find the coordinates of d. [6]",
            "8": "8 0606/21/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use7 (a) given that tan x = p, find an expression, in terms of p, for cosec2x. [3]  (b) prove that    (1 + sec \u03b8\u200a\u200a)(1 \u2013 cos\u03b8\u200a\u200a) = sin\u03b8 tan\u03b8. [4]",
            "9": "9 0606/21/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use8 a x bp ba o  in the diagram oa = a,  ob = b and  ap = 2 5 ab.  (i) given that ox = \u03bcop, where \u03bc is a constant, express ox in terms of \u03bc, a and b. [3]  (ii) given also that ax = \u03bbob, where \u03bb is a constant, use a vector method to find the value of \u03bc  and of \u03bb. [5]",
            "10": "10 0606/21/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use9 the table shows experimental values of two variables x and y. x 12345 y 3.40 2.92 2.93 3.10 3.34  it is known that x and y are related by the equation  y =  a x + bx, where a and b are constants.  (i) complete the following table. x x y x  [1]  (ii) on the grid on page 11 plot yx against x x and draw a straight line graph. [2]  (iii) use your graph to estimate the value of a and of b. [3]  (iv) estimate the value of y when x is 1.5. [1]",
            "11": "11 0606/21/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use 212345678 o4 6 8 10 12 x \u221a xy \u221a x",
            "12": "12 0606/21/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use10 it is given that a = /h208983 2 1 \u20135/h20899 and b = /h20898\u20131 4\u20132 3/h20899.  (i) find 2a \u2013 b. [2]  (ii) find ba. [2]",
            "13": "13 0606/21/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use (iii) find the inverse matrix, a\u20131. [2]  (iv) use your answer to part (iii)  to solve the simultaneous equations  3x + 2y = 23,  x \u2013 \u200a5y = 19.  [2]",
            "14": "14 0606/21/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use11 (a) (i) solve 52x+3 252x = 252\u2013x 125x . [3]   (ii) solve 1g y + 1g(y \u2013 15) = 2. [4]",
            "15": "15 0606/21/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use (b) without using a calculator, and showing each stage of your working, find the value of   2 log12 4 \u2013 1 2 log12 81 + 4 log12 3. [3]",
            "16": "16 0606/21/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use12 answer only one of the following two alternatives.  either y x ap (1,1n  2) y =1n (x+1)   \u2013 1n x c ob d  the diagram shows part of the curve   y = 1n (x +1) \u2013 1n x. the tangent to the curve at the point  p (1, 1n 2) meets the x-axis at a and the y-axis at b. the normal to the curve at p meets the  x-axis at c and the y-axis at d.  (i) find, in terms of 1n 2, the coordinates of a, b, c and d. [8]  (ii) given that area of triangle bpd area of triangle apc = 1 k, express k in terms of 1n 2. [3]  or  a curve has equation   y = xex. the curve has a stationary point at p.  (i) find, in terms of e, the coordinates of p and determine the nature of this stationary point. [5]  the normal to the curve at the point q (1, e) meets the x-axis at r and the y-axis at s.  (ii) find, in terms of e, the area of triangle ors, where o is the origin. [6]",
            "17": "17 0606/21/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s usestart your answer to question 12 here. indicate which question you are answering.       either or  ...  ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...",
            "18": "18 0606/21/o/n/11 \u00a9 ucles 2011for examiner\u2019 s usecontinue your answer here if necessary.  ...  ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...",
            "19": "19 0606/21/o/n/11 \u00a9 ucles 2011blank page",
            "20": "20 0606/21/o/n/11 \u00a9 ucles 2011permission 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. 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.blank page"
        },
        "0606_w11_qp_22.pdf": {
            "1": "this document consists of 16 printed pages. dc (nf/cgw) 48833 \u00a9 ucles 2011 [turn overuniversity of cambridge international examinations international general certificate of secondary education *8134180748* additional mathematics 0606/22 paper 2 october/november 2011  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.for examiner\u2019s use  1  2 3 4 5 6 7 8 910 11 total",
            "2": "2 0606/22/o/n/11 \u00a9 ucles 2011mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/22/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use1 (a) the universal set /h5105 and the sets a and b shown in the venn diagram below are such that n(a) = 15,   n(b) = 20,   n(a /h11032  b) = 6 and   n(/h5105) = 30.   in the venn diagram below insert the number of elements in the set represented by each of  the four regions. [4] a/h5105 b  (b) in the venn diagram below shade the region that represents ( p  q)  r/h11032. [1] p rq/h5105",
            "4": "4 0606/22/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use2 (i) on the grid below, draw on the same axes, for 0\u00b0 /h11088 x /h11088 180\u00b0, the graphs of y = sin x  and y = 1 + cos 2x. [3]  (ii) state the number of roots of the equation sin x = 1 + cos 2x for 0\u00b0 /h11088 x /h11088 180\u00b0. [1]  (iii) without extending your graphs state the number of roots of the equation sin x = 1 + cos 2x  for 0\u00b0 /h11088 x /h11088 360\u00b0. [1]",
            "5": "5 0606/22/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use3 it is given that 2 x \u2013 1 is a factor of the expression 4 x3 + ax2 \u2013 11x + b and that the remainder  when the expression is divided by x + 2 is 25. find the remainder when the expression is divided  by x + 1. [6]",
            "6": "6 0606/22/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use4 it is given that a = /h208983 \u20132 1 \u20135/h20899, b = /h20898 1 \u20134 2\u20133 5 0/h20899 and c = /h20898 4 2\u20137/h20899.  (i) calculate ab. [2]  (ii) calculate bc. [2]  (iii) find the inverse matrix, a\u20131. [2]",
            "7": "7 0606/22/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use5 four boys and three girls are to be seated in a row. calculate the number of different ways that  this can be done if  (i) the boys and girls sit alternately, [2]  (ii) the boys sit together and the girls sit together, [2]  (iii) a boy sits at each end of the row. [2]",
            "8": "8 0606/22/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use6 the length of a rectangular garden is x m and the width of the garden is 10 m less than the length.  (i) given that the perimeter of the garden is greater than 140 m, write down a linear inequality  in x. [1]  (ii) given that the area of the garden is less than 3000 m2, write down a quadratic inequality in x.  [1]  (iii) by solving these two inequalities, find the set of possible values of x. [4]",
            "9": "9 0606/22/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use7  de c b aof 8 cm20 cm 6 cm\u03b8  in the diagram ad and be are arcs of concentric circles centre o, where oa = 6 cm and  ab = 8 cm. the area of the region abed is 32 cm2. the triangle ocf is isosceles with  oc = of = 20 cm.   (i) find the angle /h9258 in radians. [3]  (ii) find the perimeter of the region bcfe. [5]",
            "10": "10 0606/22/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use8 a particle travels in a straight line so that, t s after passing through a fixed point o, its velocity,  v ms\u20131, is given by v = 12cos (t 3).  (i) find the value of t when the velocity of the particle first equals 2 ms\u20131. [2]  (ii) find the acceleration of the particle when t = 3. [3]  (iii) find the distance of the particle from o when it first comes to instantaneous rest. [4]",
            "11": "11 0606/22/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use9 it is given that f( x) = 2x2 \u2013 12x + 10.  (i) find the value of a, of b and of c for which f(x) = a(x + b)2 + c. [3]  (ii) sketch the graph of y = |f(x)| for \u20131 /h11088 x /h11088 7. [4]  (iii) find the set of values of k for which the equation |f( x)| = k has 4 distinct roots. [2]",
            "12": "12 0606/22/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use10 y xp oqy  =  x3  \u2013  9x2  +  24x   +  2  the diagram shows part of the curve y = x3 \u2013 9x2 + 24x + 2 cutting the y-axis at the point p. the  curve has a minimum point at q.  (i) find the coordinates of the point q. [4]",
            "13": "13 0606/22/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use (ii) find the area of the region enclosed by the curve and the line pq. [6]",
            "14": "14 0606/22/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use11 answer only one of the following two alternatives. either ob xt as  in the diagram above  \u23af \u2192oa = a,  \u23af \u2192ob = b,  \u23af \u2192os = 3 5  \u23af \u2192oa and  \u23af \u2192ot = 75 \u23af \u2192ob.  (i) given that  \u23af \u2192ax = l \u23af \u2192ab, where l is a constant, express  \u23af \u2192ox in terms of l, a and b. [2]  (ii) given that  \u23af \u2192sx = k \u23af \u2192st,  where k is a constant, express  \u23af \u2192ox in terms of k, a and b. [4]  (iii) hence evaluate l and k. [4] or oc d rqp  in the diagram above  \u23af \u2192oc = c and   \u23af \u2192od = d. the points p and q lie on oc and od produced  respectively, so that oc : cp = 1 : 2 and od : dq = 2 : 1. the line cd is extended to r so that  cd = dr.  (i) find, in terms of c and/or d, the vectors  \u23af \u2192op,  \u23af \u2192oq and  \u23af \u2192or. [5]  (ii) show that the points p, q and r are collinear and find the ratio pq : qr. [5]",
            "15": "15 0606/22/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s usestart your answer to question 11 here. indicate which question you are answering.        either or .. ",
            "16": "16 0606/22/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use 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. 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.continue your answer here if necessary. .. "
        },
        "0606_w11_qp_23.pdf": {
            "1": "this document consists of 16 printed pages. dc (leo/cgw) 48835 \u00a9 ucles 2011 [turn overuniversity of cambridge international examinations international general certificate of secondary education *9273068136* additional mathematics 0606/23 paper 2 october/november 2011  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.for examiner\u2019s use  1  2 3 4 5 6 7 8 910 11 12 total",
            "2": "2 0606/23/o/n/11 \u00a9 ucles 2011for examiner\u2019 s usemathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2. binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/23/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use1 solve the inequality x(2x \u2013 1) /h11022 15.  [3] 2 (i) given that y = (12 \u2013 4x)5, find dy dx  .  [2]  (ii) hence find the approximate change in y as x increases from 0.5 to 0.5 + p, where p is small.  [2]",
            "4": "4 0606/23/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use3 (i) find the coefficient of x3 in the expansion of (1 \u2013 2 x)7.  [2]  (ii) find the coefficient of x3 in the expansion of (1 + 3 x2)(1 \u2013 2x)7.  [3]",
            "5": "5 0606/23/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use4 without using a calculator, find the positive root of the equation (5 \u2013 2 \u221a\u23af2)x2 \u2013 (4 + 2 \u221a\u23af2)x \u2013 2 = 0,  giving your answer in the form a + b \u221a\u23af2, where a and b are integers.  [6]",
            "6": "6 0606/23/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use5 a school council of 6 people is to be chosen from a group of 8 students and 6 teachers. calculate  the number of different ways that the council can be selected if  (i) there are no restrictions,  [2]  (ii) there must be at least 1 teacher on the council and more students than teachers.  [3]  after the council is chosen, a chairperson and a secretary have to be selected from the 6 council members.  (iii) calculate the number of different ways in which a chairperson and a secretary can be selected.  [1]",
            "7": "7 0606/23/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use6 (i) in the space below sketch the graph of   y = /h20919(2x + 3)(2x \u2013 7)/h20919.  [4]  (ii) how many values of x satisfy the equation /h20919(2x + 3)(2x \u2013 7)/h20919 = 2x ? [2]",
            "8": "8 0606/23/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use7  (1,3) o (3,\u20131)xxy  the variables x and y are related in such a way that when  y x is plotted against x a straight line is   obtained, as shown in the graph. the line passes through the points (1, 3) and (3, \u20131).  (i) express y in terms of x.  [4]  (ii) find the value of x and of y such that  y x = \u2013 9.  [2]",
            "9": "9 0606/23/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use8 a sector of a circle, of radius r cm, has a perimeter of 200 cm.  (i) express the area, a cm2, of the sector in terms of r.  [3]  (ii) given that r can vary, find the stationary value of a.  [3]",
            "10": "10 0606/23/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use9 an aircraft, whose speed in still air is 350 kmh\u20131, flies in a straight line from a to b, a distance of  480 km. there is a wind of 50 kmh\u20131 blowing from the north. the pilot sets a course of 130\u00b0.  (i) calculate the time taken to fly from a to b.  [5]  (ii) calculate the bearing of b from a.  [3]",
            "11": "11 0606/23/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use10 the line y = 2x + 10 intersects the curve 2 x2 + 3xy \u2013 5y + y2 = 218 at the points a and b.  find the equation of the perpendicular bisector of ab.  [9]",
            "12": "12 0606/23/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use11 (i) solve      4 cot 1 2 x = 1, for 0\u00b0 /h11021 x /h11021 360\u00b0.  [3]  (ii) solve      3(1 \u2013 tan y cos y) = 5 cos2 y \u2013 2, for 0\u00b0 /h11021 y /h11021 360\u00b0. [5]",
            "13": "13 0606/23/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s use (iii) solve      3 sec2 z = 4, for 0 /h11021 z /h11021 2 \u03c0  radians.  [3]",
            "14": "14 0606/23/o/n/11 \u00a9 ucles 2011for examiner\u2019 s use12 answer only one of the following two alternatives.  either oy x (1, 0) qp (e, 1)y=ln  x  the diagram shows part of the curve y = ln x cutting the x-axis at the point (1, 0). the normal to  the curve at the point p(e, 1) cuts the x-axis at the point q.  (i) show that q is the point /h20898e + 1 e , 0/h20899 .  [4]  (ii) show that d dx (x ln x) = 1 + ln x.  [1]  (iii) hence find /h20885ln xdx and the area of the shaded region. [5]  or y x oba (0,1)y = e x cos  x (/pi1 , 0)2  the diagram shows part of the curve y = ex cos x, cutting the x-axis at the point /h20898\u03c0 2, 0/h20899 . the  normal to the curve at the point a(0, 1) cuts the x-axis at the point b.  (i) find the coordinates of b.  [4]  (ii) show that d dx [ex (cos x + sin x)] = 2ex cos x.  [2]  (iii) hence find /h20885ex cos xdx and the area of the shaded region.  [4]",
            "15": "15 0606/23/o/n/11 \u00a9 ucles 2011 [turn overfor examiner\u2019 s usestart your answer to question 12 here. indicate which question you are answering.       either or ...",
            "16": "16 0606/23/o/n/11 \u00a9 ucles 2011for examiner\u2019s use 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. 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.continue your answer here if necessary. ..."
        }
    },
    "2012": {
        "0606_s12_qp_11.pdf": {
            "1": "this document consists of 16 printed pages. dc (slm) 57494 \u00a9 ucles 2012 [turn overuniversity of cambridge international examinations international general certificate of secondary education read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid.do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. *1445389868* additional mathematics  0606/11 paper 1 may/june 2012  2 hours candidates answer on the question paper. additional materials: electronic calculator for examiner\u2019s use 1 23456789 1011 total",
            "2": "2 0606/11/m/j/12 \u00a9 ucles 2012mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2 binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/11/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use1 (i) sketch the graph of   y = /h208952x \u2013 5/h20895, showing the coordinates of the points where the graph  meets the coordinate axes. [2] y x o  (ii) solve   /h208952x \u2013 5/h20895 = 3 . [2]",
            "4": "4 0606/11/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use2 the expression   2x3 + ax2 + bx \u2013 30   is divisible by   x + 2   and leaves a remainder of  \u201335  when  divided by   2x \u2013 1. find the values of the constants a and b. [5]",
            "5": "5 0606/11/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use3 find the set of values of k for which the line   y = 2x + k   cuts the curve   y = x2 + kx + 5   at two  distinct points.  [6]",
            "6": "6 0606/11/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use4 (a) arrangements containing 5 different letters from the word amplitude are to be made.  find   (i) the number of 5-letter arrangements if there are no restrictions, [1]   (ii) the number of 5-letter arrangements which start with the letter a and end with theletter e.  [1]  (b) tickets for a concert are given out randomly to a class containing 20 students. no student is given more than one ticket. there are 15 tickets.   (i) find the number of ways in which this can be done. [1]",
            "7": "7 0606/11/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use  there are 12 boys and 8 girls in the class. find the number of different ways in which   (ii) 10 boys and 5 girls get tickets,  [3]   (iii) all the boys get tickets. [1]",
            "8": "8 0606/11/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use5 (i) find the equation of the tangent to the curve     y = x3 + 2x2 \u2013 3x + 4     at the point where the  curve crosses the y-axis. [4]  (ii) find the coordinates of the point where this tangent meets the curve again. [3]",
            "9": "9 0606/11/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use6 (i) given that   15cos2  \u03b8  + 2sin2 \u03b8  = 7, show that   tan2 \u03b8  = 8 5. [4]  (ii) solve   15cos2 \u03b8 + 2sin2 \u03b8  = 7   for   0 /h11088 \u03b8 /h11088 \u03c0   radians. [3]",
            "10": "10 0606/11/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use7 the table shows values of variables x and y. x 1 3 6 10 14 y 2.5 4.5 0 \u201320 \u201356  (i) by plotting a suitable straight line graph, show that y and x are related by the equation y = ax + bx2, where a  and b  are constants. [4]",
            "11": "11 0606/11/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use (ii) use your graph to find the value of a  and of b. [4] 8 (a) find the value of x for which    2lg x \u2013 lg(5x + 60) = 1 . [5]  (b) solve    log5 y = 4logy 5 . [4]",
            "12": "12 0606/11/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use9 find the values of the positive constants p and q such that, in the binomial expansion of  ( p + qx)10, the coefficient of x5 is 252 and the coefficient of x3 is 6 times the coefficient of x2.  [8]",
            "13": "13 0606/11/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use10 variables x and y are such that   y = e2x + e\u20132x .  (i) find  dy dx. [2]  (ii) by using the substitution   u = e2x ,  find the value of y  when  dy dx = 3. [4]  (iii) given that x  is decreasing at the rate of 0.5 units s\u20131, find the corresponding rate of change  of y  when x = 1. [3]",
            "14": "14 0606/11/m/j/12 \u00a9 ucles 2012for examiner\u2019 s useanswer only one of the following two alternatives. 11 either the diagram shows part of the curve    y = 9x 2 \u2013 x3, which meets the x-axis at the origin o and at  the point a. the line    y \u2013 2x + 18 = 0   passes through a  and meets the y-axis at the point b. y o ba xy = 9x2 \u2013 x3 y \u2013 2x + 18 = 0not to scale  (i) show that, for  x  /h11091 0,  9x2 \u2013 x3 /h11088 108. [4]  (ii) find the area of the shaded region bounded by the curve, the line ab  and the y-axis. [6]  or  the diagram shows part of the curve    y = 2sin 3 x . the normal to the curve    y = 2sin 3 x     at the  point where  x = \u03c0 9 meets the y-axis at the point p. y op \u03c0 9xy = 2sin 3x not to scale  (i) find the coordinates of p. [5]  (ii) find the area of the shaded region bounded by the curve, the normal and the y-axis. [5]",
            "15": "15 0606/11/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s usestart your answer to question 11 here. indicate which question you are answering.   either or ...",
            "16": "16 0606/11/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use 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. 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.continue your answer here if necessary. ..."
        },
        "0606_s12_qp_12.pdf": {
            "1": "this document consists of 20 printed pages. dc (slm) 57493 \u00a9 ucles 2012 [turn overuniversity of cambridge international examinations international general certificate of secondary education *4520603884* additional mathematics  0606/12 paper 1 may/june 2012  2 hours candidates answer on the question paper. additional materials electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid.do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.for examiner\u2019s use 1 23456789 101112 total",
            "2": "2 0606/12/m/j/12 \u00a9 ucles 2012mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2 binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/12/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use1 (i) find /h208857x \u2013 5  dx. [3]  (ii) hence evaluate 3 2/h208857x \u2013 5  dx. [2]",
            "4": "4 0606/12/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use2 using the substitution  u = 2x, find the values of x such that    22x+2 = 5 (2x) \u2013 1 . [5]",
            "5": "5 0606/12/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use3 show that   cot a + sin a 1 + cos a  = cosec a . [4]",
            "6": "6 0606/12/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use4 solve the simultaneous equations   5 x + 3y = 2  and  2 x  \u2013  3 y = 1 . [5]",
            "7": "7 0606/12/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use5 differentiate the following with respect to x.  (i) (2 \u2013 x2)1n(3x + 1) [3]  (ii) 4 \u2013 tan 2x 5x [3]",
            "8": "8 0606/12/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use6 you must not use a calculator in this question.  (i) express 8   3 + 1 in the form a(  3 \u2013 1), where a is an integer. [2]  an equilateral triangle has sides of length 8   3 + 1.  (ii) show that the height of the  triangle is 6 \u2013 2   3. [2]",
            "9": "9 0606/12/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use (iii) hence, or otherwise, find the area of the triangle in the form p  3 \u2013 q, where p and  q are  integers. [2]",
            "10": "10 0606/12/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use7 (i) sketch the graph of  y = |x2 \u2013 x \u2013 6|, showing the coordinates of the points where the curve  meets the coordinate axes. [3]  (ii) solve |x2 \u2013 x \u2013 6| = 6. [3]",
            "11": "11 0606/12/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use [turn over8 oa bx2\u03c0 3rad10 cm  the figure shows a circle, centre o, with radius 10 cm. the lines xa and xb are tangents to the   circle at a and b respectively, and angle aob is 2\u03c0 3 radians.  (i) find the perimeter of the shaded region. [3]  (ii) find the area of the shaded region. [4]",
            "12": "12 0606/12/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use9 variables n and x are such that  n = 200 + 50e x 100 .  (i) find the value of n when x = 0. [1]  (ii) find the value of x when n = 600. [3]",
            "13": "13 0606/12/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use [turn over (iii) find the value of n when  dn dx = 45. [4]",
            "14": "14 0606/12/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use10 (a) it is given that  f( x) = 1 2 + x for x /hs11005 \u20132, x/h33528/h11938.   (i) find f  \u2033(x). [2]   (ii) find f  \u20131 (x). [2]   (iii) solve f  2(x) = \u20131. [3]",
            "15": "15 0606/12/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use (b) the functions g, h and k are defined, for x/h33528/h11938, by     g(x) = 1 x + 5,  x /hs11005 \u20135,     h(x) = x2 \u20131,     k(x) = 2x + 1.   express the following in terms of g, h and/or k.   (i) 1 (x2\u20131) + 5 [1]   (ii) 2 x + 5 + 1 [1] [turn over",
            "16": "16 0606/12/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use11 the point p lies on the line joining a(\u20131, \u20135) and b(11, 13) such that ap = 1 3ab.  (i) find the equation of the line perpendicular to ab and passing through p. [5]  the line perpendicular to ab passing through p and the line parallel to the x-axis passing through  b intersect at the point q.  (ii) find the coordinates of the point q. [2]",
            "17": "17 0606/12/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use (iii) find the area of the triangle pbq. [2]",
            "18": "18 0606/12/m/j/12 \u00a9 ucles 2012for examiner\u2019 s useanswer only one of the following two alternatives. 12 either at 12 00 hours, a ship has position vector   (54i + 16j) km relative to a lighthouse, where i is  a unit vector due east and j is a unit vector due north. the ship is travelling with a speed of  20 km h \u20131 in the direction   3 i +4j.  (i) show that the position vector of the ship at 15 00 hours is   (90 i + 64j) km. [2]  (ii) find the position vector of the ship t hours after 12 00 hours. [2]  a speedboat leaves the lighthouse at 14 00 hours and travels in a straight line to intercept the ship.  given that the speedboat intercepts the ship at 16 00 hours, find  (iii) the speed of the speedboat, [3]  (iv) the velocity of the speedboat relative to the ship, [1]  (v) the angle the direction of the speedboat makes with north. [2]  or ra o bpq  the position vectors of points a and b relative to an origin o are a and b respectively. the point  p is such that  op = 5 4 ob . the point q is such that  aq = 1 3 ab . the point r lies on oa such  that rqp is a straight line where  or =\u03bboa  and  qr = \u03bcpr .  (i) express oq and pq in terms of a and b. [2]  (ii) express qr in terms of \u03bb, a and b. [2]  (iii) express qr in terms of \u03bc , a and b. [3]  (iv) hence find the value of \u03bb and of \u03bc. [3]",
            "19": "19 0606/12/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s usestart your answer to question 12 here. indicate which question you are answering.   either or ...",
            "20": "20 0606/12/m/j/12 \u00a9 ucles 2012for examiner\u2019 s usecontinue your answer here if necessary. ... 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. 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."
        },
        "0606_s12_qp_13.pdf": {
            "1": "this document consists of 16 printed pages. dc (slm) 57492 \u00a9 ucles 2012 [turn overuniversity of cambridge international examinations international general certificate of secondary education *1237304545* additional mathematics  0606/13 paper 1 may/june 2012  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid.do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.for examiner\u2019s use 1 23456789 1011 total",
            "2": "2 0606/13/m/j/12 \u00a9 ucles 2012mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2 binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/13/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use1 (i) sketch the graph of   y = /h208952x \u2013 5/h20895, showing the coordinates of the points where the graph  meets the coordinate axes. [2] y x o  (ii) solve   /h208952x \u2013 5/h20895 = 3 . [2]",
            "4": "4 0606/13/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use2 the expression   2x3 + ax2 + bx \u2013 30   is divisible by   x + 2   and leaves a remainder of  \u201335  when  divided by   2x \u2013 1. find the values of the constants a and b. [5]",
            "5": "5 0606/13/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use3 find the set of values of k for which the line   y = 2x + k   cuts the curve   y = x2 + kx + 5   at two  distinct points.  [6]",
            "6": "6 0606/13/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use4 (a) arrangements containing 5 different letters from the word amplitude are to be made.  find   (i) the number of 5-letter arrangements if there are no restrictions, [1]   (ii) the number of 5-letter arrangements which start with the letter a and end with theletter e.  [1]  (b) tickets for a concert are given out randomly to a class containing 20 students. no student is given more than one ticket. there are 15 tickets.   (i) find the number of ways in which this can be done. [1]",
            "7": "7 0606/13/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use  there are 12 boys and 8 girls in the class. find the number of different ways in which   (ii) 10 boys and 5 girls get tickets,  [3]   (iii) all the boys get tickets. [1]",
            "8": "8 0606/13/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use5 (i) find the equation of the tangent to the curve     y = x3 + 2x2 \u2013 3x + 4     at the point where the  curve crosses the y-axis. [4]  (ii) find the coordinates of the point where this tangent meets the curve again. [3]",
            "9": "9 0606/13/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use6 (i) given that   15cos2  \u03b8  + 2sin2 \u03b8  = 7, show that   tan2 \u03b8  = 8 5. [4]  (ii) solve   15cos2 \u03b8 + 2sin2 \u03b8  = 7   for   0 /h11088 \u03b8 /h11088 \u03c0   radians. [3]",
            "10": "10 0606/13/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use7 the table shows values of variables x and y. x 1 3 6 10 14 y 2.5 4.5 0 \u201320 \u201356  (i) by plotting a suitable straight line graph, show that y and x are related by the equation y = ax + bx2, where a  and b  are constants. [4]",
            "11": "11 0606/13/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use (ii) use your graph to find the value of a  and of b. [4] 8 (a) find the value of x for which    2lg x \u2013 lg(5x + 60) = 1 . [5]  (b) solve    log5 y = 4logy 5 . [4]",
            "12": "12 0606/13/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use9 find the values of the positive constants p and q such that, in the binomial expansion of  ( p + qx)10, the coefficient of x5 is 252 and the coefficient of x3 is 6 times the coefficient of x2.  [8]",
            "13": "13 0606/13/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use10 variables x and y are such that   y = e2x + e\u20132x .  (i) find  dy dx. [2]  (ii) by using the substitution   u = e2x ,  find the value of y  when  dy dx = 3. [4]  (iii) given that x  is decreasing at the rate of 0.5 units s\u20131, find the corresponding rate of change  of y  when x = 1. [3]",
            "14": "14 0606/13/m/j/12 \u00a9 ucles 2012for examiner\u2019 s useanswer only one of the following two alternatives. 11 either the diagram shows part of the curve    y = 9x 2 \u2013 x3, which meets the x-axis at the origin o and at  the point a. the line    y \u2013 2x + 18 = 0   passes through a  and meets the y-axis at the point b. y o ba xy = 9x2 \u2013 x3 y \u2013 2x + 18 = 0not to scale  (i) show that, for  x  /h11091 0,  9x2 \u2013 x3 /h11088 108. [4]  (ii) find the area of the shaded region bounded by the curve, the line ab  and the y-axis. [6]  or  the diagram shows part of the curve    y = 2sin 3 x . the normal to the curve    y = 2sin 3 x     at the  point where  x = \u03c0 9 meets the y-axis at the point p. y op \u03c0 9xy = 2sin 3x not to scale  (i) find the coordinates of p. [5]  (ii) find the area of the shaded region bounded by the curve, the normal and the y-axis. [5]",
            "15": "15 0606/13/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s usestart your answer to question 11 here. indicate which question you are answering.   either or ...",
            "16": "16 0606/13/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use 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. 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.continue your answer here if necessary. ..."
        },
        "0606_s12_qp_21.pdf": {
            "1": "this document consists of 16 printed pages. dc (slm) 57491 \u00a9 ucles 2012 [turn overuniversity of cambridge international examinations international general certificate of secondary education *0050607792* additional mathematics 0606/21 paper 2 may/june 2012  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid.do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.for examiner\u2019s use 1 23456789 101112 total",
            "2": "2 0606/21/m/j/12 \u00a9 ucles 2012mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2 binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/21/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use1 (i) given that a = /h208984 \u20133 2 5/h20899, find the inverse matrix a\u20131. [2]  (ii) use your answer to part (i) to solve the simultaneous equations     4x \u2013 3y = \u201310,     2x + 5y = 21. [2]",
            "4": "4 0606/21/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use2 a cuboid has a square base of side (2 +   3) cm and a volume of (16 + 9   3) cm3. without using a  calculator, find the height of the cuboid in the form ( a + b   3) cm, where a and b are integers.  [4]",
            "5": "5 0606/21/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use3 (a) 12 10 8 6 4 2 o 180\u00b0y x   the diagram shows a sketch of the curve  y = asin(bx) + c  for 0\u00b0 /h11088 x /h11088 180\u00b0. find the  values of a, b and c. [3]  (b) given that  f( x) = 5cos3x + 1, for all x, state   (i) the period of f, [1]   (ii) the amplitude of f. [1]",
            "6": "6 0606/21/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use4 (i) find   d dx(x2 lnx). [2]  (ii) hence, or otherwise, find   /h20885xlnx d x. [3]",
            "7": "7 0606/21/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use5 (a) solve the equation   32x = 1000, giving your answer to 2 decimal places. [2]  (b) solve the equation   362y\u20135 63y = 62y\u20131 216 y+6. [4]",
            "8": "8 0606/21/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use6 by shading the venn diagrams below, investigate whether each of the following statements is true  or false. state your conclusions clearly.  (i) a  b/h11032 = (a/h11032  b)/h11032 [2] b a/h5105 b a/h5105 a  b/h11032 (a/h11032  b)/h11032  (ii) x  y = x/h11032  y/h11032 [2] y x/h5105 y x/h5105 x  y x/h11032  y/h11032  (iii) (p  q)  (q  r) = q  (p  r) [2] q rp/h5105 q rp/h5105 (p  q)  (q  r) q  (p  r)",
            "9": "9 0606/21/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use7 given that    f( x) = x2  \u2013  648   x , find the value of x for which f /h11033(x) = 0. [6]",
            "10": "10 0606/21/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use8 relative to an origin o, the position vectors of the points a and b are 2i \u2013 3j and 11i + 42j  respectively.  (i) write down an expression for \u2192ab. [2]  the point c lies on ab such that \u2192ac = 1 3\u2192ab.  (ii) find the length of \u2192oc. [4]  the point d lies on \u2192oa such that \u2192dc is parallel to \u2192ob.  (iii) find the position vector of d. [2]",
            "11": "11 0606/21/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use9 a particle moves in a straight line so that, t s after passing through a fixed point o, its velocity,  v ms\u20131, is given by  v = 2t \u2013 11 + 6 t + 1 . find the acceleration of the particle when it is at  instantaneous rest. [7]",
            "12": "12 0606/21/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use10 solutions to this question by accurate drawing will not be accepted. o dc (\u20133, 2)b (7, 7) a (11, 4)y x  the diagram shows a trapezium abcd with vertices a(11, 4), b(7, 7), c(\u20133, 2) and d. the side  ad is parallel to bc and the side cd is perpendicular to bc. find the area of the trapezium  abcd. [9]",
            "13": "13 0606/21/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use11  b a cd1 rad 12 cm  the diagram shows a right-angled triangle abc and a sector cbdc of a circle with centre c and  radius 12 cm. angle acb = 1 radian and acd is a straight line.  (i) show that the length of ab is approximately 10.1 cm. [1]  (ii) find the perimeter of the shaded region. [5]  (iii) find the area of the shaded region. [4]",
            "14": "14 0606/21/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use12 answer only one of the following two alternatives.  either  the equation of a curve is     y = 2x2 \u2013 20x + 37.  (i) express y in the form a(x + b)2 + c, where a, b and c are integers. [3]  (ii) write down the coordinates of the stationary point on the curve. [1]  a function f is defined by     f : x /h21739 2x2 \u2013 20x + 37 for x /h11022 k. given that the function f\u20131(x) exists,  (iii) write down the least possible value of k, [1]  (iv) sketch the graphs of y = f(x) and y = f\u20131(x) on the axes provided, [2]  (v) obtain an expression for f\u20131. [3]  or  a function g is defined by     g : x /h21739 5x2 + px + 72, where p is a constant. the function can also  be written as     g : x /h21739 5(x \u2013 4)2 + q.  (i) find the value of p and of q. [3]  (ii) find the range of the function g. [1]  (iii) sketch the graph of the function on the axes provided. [2]  (iv) given that the function h is defined by h : x /h21739 ln x, where x /h11022 0, solve the equation  gh(x) = 12. [4] start your answer to question 12 here. indicate which question you are answering.  either or .. ..",
            "15": "15 0606/21/m/j/12 \u00a9 ucles 2012 [turn overcontinue your answer here.   oy x",
            "16": "16 0606/21/m/j/12 \u00a9 ucles 2012permission 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. 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.continue your answer here if necessary.  "
        },
        "0606_s12_qp_22.pdf": {
            "1": "this document consists of 16 printed pages. dc (slm) 57489 \u00a9 ucles 2012 [turn over *0104471722*university of cambridge international examinations international general certificate of secondary education additional mathematics 0606/22 paper 2 may/june 2012  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid.do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.for examiner\u2019s use 1 23456789 1011 total",
            "2": "2 0606/22/m/j/12 \u00a9 ucles 2012mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb a c   a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/22/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use1 it is given that p is the set of prime numbers, s is the set of square numbers and n is the set of  numbers between 10 and 90. write each of the following statements using set notation.  (i) 7 is a prime number. [1]  (ii) 8 is not a square number. [1]  (iii) there are 6 square numbers between 10 and 90. [1] 2 (i) given that    y = (4x + 1)3, find dy dx. [2]  (ii) hence find the approximate increase in y as x increases from 6 to 6 + p, where p  is small. [2]",
            "4": "4 0606/22/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use3 find the values of m for which the line    y = mx \u2013 5 is a tangent to the curve       y = x2 + 3x + 4. [5]",
            "5": "5 0606/22/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use4 in a competition the contestants search for hidden targets which are classed as difficult, medium  or easy. in the first round, finding a difficult target scores 5 points, a medium target 3 points and an easy target 1 point. the number of targets found by the two contestants, claire and denise, are shown in the table. target contestantdifficult medium easy claire 4 1 7 denise 2 5 1  in the second round, finding a difficult target scores 8 points, a medium target 4 points and an  easy target 2 points. in the second round claire finds 2 difficult, 5 medium and 2 easy targets whilst denise finds 4 difficult, 3 medium and 6 easy targets.  (i) write down the sum of two matrix products which, on evaluation, would give the total score for each contestant. [3]  (ii) use matrix multiplication and addition to calculate the total score for each contestant. [2]",
            "6": "6 0606/22/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use5 it is given that x \u2013 2 is a factor of     f( x) = x3 + kx2 \u2013 8x \u2013 8.  (i) find the value of the integer k. [2]  (ii) using your value of k, find the non-integer roots of the equation f( x) = 0 in the form a \u00b1  b, where a and b are integers. [5]",
            "7": "7 0606/22/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use6 (a) find the coefficient of x3 in the expansion of   (i) (1 \u2013 2x)7, [2]   (ii) (3 + 4x)(1 \u2013 2x)7. [3]  (b) find the term independent of x in the expansion of     /h20898x + 3\u2013\u2013x2/h208996 . [3]",
            "8": "8 0606/22/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use7 the table shows experimental values of variables x and y. x 5 30 150 400 y 8.9 21.9 48.9 80.6  (i) by plotting a suitable straight line graph, show that y and x are related by the equation  y = axb, where a and b are constants. [4]",
            "9": "9 0606/22/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use (ii) use your graph to estimate the value of a and of b. [4]  (iii) estimate the value of y when x = 100. [2]",
            "10": "10 0606/22/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use8 an open rectangular cardboard box with a square base is to have a volume of 256 cm3. find the  dimensions of the box if the area of cardboard used is as small as possible. [7]",
            "11": "11 0606/22/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use9 (a) solve the equation   (i) 3 sin x \u2013 5 cos x = 0 for 0\u00b0 < x < 360\u00b0, [3]   (ii) 5 sin2 y + 9 cos y \u2013 3 = 0 for 0\u00b0 < y < 360\u00b0. [5]",
            "12": "12 0606/22/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use (b) solve  sin(3 \u2013 z) = 0.8 for 0 < z < \u03c0 radians. [4] 10 (a) a team of 7 people is to be chosen from 5 women and 7 men. calculate the number of  different ways in which this can be done if   (i) there are no restrictions, [1]   (ii) the team is to contain more women than men. [3]",
            "13": "13 0606/22/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use (b) (i) how many different 4-digit numbers, less than 5000, can be formed using 4 of the 6  digits 1, 2, 3, 4, 5 and 6 if no digit can be used more than once? [2]   (ii) how many of these 4-digit numbers are divisible by 5? [2]",
            "14": "14 0606/22/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use11 answer only one of the following two alternatives.  either y y = sin     x1 2 xqp       , o3\u03c0 2\u221a2 2/h20898/h20899  the diagram shows part of the curve y = sin 1 2 x. the tangent to the curve at the point p /h208983\u03c0 2,   2 2/h20899  cuts the x -axis at the point q.  (i) find the coordinates of q. [4]  (ii) find the area of the shaded region bounded by the curve, the tangent and the x-axis. [7]  or  (i) given that y = xe\u2013x, find dy dx and hence show that /h20885xe\u2013x dx = \u2013xe\u2013x \u2013 e\u2013x + c. [4] y x or  2, y = xe\u2013x2 e2/h20898/h20899  the diagram shows part of the curve y = xe\u2013x and the tangent to the curve at the point r /h208982, 2\u2013\u2013e2/h20899.  (ii) find the area of the shaded region bounded by the curve, the tangent and the y-axis. [7]",
            "15": "15 0606/22/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s usestart your answer to question 11 here. indicate which question you are answering.  either or ... ",
            "16": "16 0606/22/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use 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. 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.continue your answer here if necessary. "
        },
        "0606_s12_qp_23.pdf": {
            "1": "this document consists of 16 printed pages. dc (slm) 57480 \u00a9 ucles 2012 [turn overuniversity of cambridge international examinations international general certificate of secondary education *1194717369* additional mathematics 0606/23 paper 2 may/june 2012  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid.do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.for examiner\u2019s use 1 23456789 101112 total",
            "2": "2 0606/23/m/j/12 \u00a9 ucles 2012mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2 binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/23/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use1 (i) given that a = /h208984 \u20133 2 5/h20899, find the inverse matrix a\u20131. [2]  (ii) use your answer to part (i) to solve the simultaneous equations     4x \u2013 3y = \u201310,     2x + 5y = 21. [2]",
            "4": "4 0606/23/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use2 a cuboid has a square base of side (2 +   3) cm and a volume of (16 + 9   3) cm3. without using a  calculator, find the height of the cuboid in the form ( a + b   3) cm, where a and b are integers.  [4]",
            "5": "5 0606/23/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use3 (a) 12 10 8 6 4 2 o 180\u00b0y x   the diagram shows a sketch of the curve  y = asin(bx) + c  for 0\u00b0 /h11088 x /h11088 180\u00b0. find the  values of a, b and c. [3]  (b) given that  f( x) = 5cos3x + 1, for all x, state   (i) the period of f, [1]   (ii) the amplitude of f. [1]",
            "6": "6 0606/23/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use4 (i) find   d dx(x2 lnx). [2]  (ii) hence, or otherwise, find   /h20885xlnx d x. [3]",
            "7": "7 0606/23/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use5 (a) solve the equation   32x = 1000, giving your answer to 2 decimal places. [2]  (b) solve the equation   362y\u20135 63y = 62y\u20131 216 y+6. [4]",
            "8": "8 0606/23/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use6 by shading the venn diagrams below, investigate whether each of the following statements is true  or false. state your conclusions clearly.  (i) a  b/h11032 = (a/h11032  b)/h11032 [2] b a/h5105 b a/h5105 a  b/h11032 (a/h11032  b)/h11032  (ii) x  y = x/h11032  y/h11032 [2] y x/h5105 y x/h5105 x  y x/h11032  y/h11032  (iii) (p  q)  (q  r) = q  (p  r) [2] q rp/h5105 q rp/h5105 (p  q)  (q  r) q  (p  r)",
            "9": "9 0606/23/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use7 given that    f( x) = x2  \u2013  648   x , find the value of x for which f /h11033(x) = 0. [6]",
            "10": "10 0606/23/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use8 relative to an origin o, the position vectors of the points a and b are 2i \u2013 3j and 11i + 42j  respectively.  (i) write down an expression for \u2192ab. [2]  the point c lies on ab such that \u2192ac = 1 3\u2192ab.  (ii) find the length of \u2192oc. [4]  the point d lies on \u2192oa such that \u2192dc is parallel to \u2192ob.  (iii) find the position vector of d. [2]",
            "11": "11 0606/23/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use9 a particle moves in a straight line so that, t s after passing through a fixed point o, its velocity,  v ms\u20131, is given by  v = 2t \u2013 11 + 6 t + 1 . find the acceleration of the particle when it is at  instantaneous rest. [7]",
            "12": "12 0606/23/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use10 solutions to this question by accurate drawing will not be accepted. o dc (\u20133, 2)b (7, 7) a (11, 4)y x  the diagram shows a trapezium abcd with vertices a(11, 4), b(7, 7), c(\u20133, 2) and d. the side  ad is parallel to bc and the side cd is perpendicular to bc. find the area of the trapezium  abcd. [9]",
            "13": "13 0606/23/m/j/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use11  b a cd1 rad 12 cm  the diagram shows a right-angled triangle abc and a sector cbdc of a circle with centre c and  radius 12 cm. angle acb = 1 radian and acd is a straight line.  (i) show that the length of ab is approximately 10.1 cm. [1]  (ii) find the perimeter of the shaded region. [5]  (iii) find the area of the shaded region. [4]",
            "14": "14 0606/23/m/j/12 \u00a9 ucles 2012for examiner\u2019 s use12 answer only one of the following two alternatives.  either  the equation of a curve is     y = 2x2 \u2013 20x + 37.  (i) express y in the form a(x + b)2 + c, where a, b and c are integers. [3]  (ii) write down the coordinates of the stationary point on the curve. [1]  a function f is defined by     f : x /h21739 2x2 \u2013 20x + 37 for x /h11022 k. given that the function f\u20131(x) exists,  (iii) write down the least possible value of k, [1]  (iv) sketch the graphs of y = f(x) and y = f\u20131(x) on the axes provided, [2]  (v) obtain an expression for f\u20131. [3]  or  a function g is defined by     g : x /h21739 5x2 + px + 72, where p is a constant. the function can also  be written as     g : x /h21739 5(x \u2013 4)2 + q.  (i) find the value of p and of q. [3]  (ii) find the range of the function g. [1]  (iii) sketch the graph of the function on the axes provided. [2]  (iv) given that the function h is defined by h : x /h21739 ln x, where x /h11022 0, solve the equation  gh(x) = 12. [4] start your answer to question 12 here. indicate which question you are answering.  either or .. ..",
            "15": "15 0606/23/m/j/12 \u00a9 ucles 2012 [turn overcontinue your answer here.   oy x",
            "16": "16 0606/23/m/j/12 \u00a9 ucles 2012permission 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. 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.continue your answer here if necessary.  "
        },
        "0606_w12_qp_11.pdf": {
            "1": "this document consists of 16 printed pages. dc (nh/jg) 50034/5 \u00a9 ucles 2012 [turn over *0835058084* additional mathematics  0606/11 paper 1 october/november 2012  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.for examiner\u2019s use  1  2 3 4 5 6 7 8 9101112 totaluniversity of cambridge international examinations international general certificate of secondary education",
            "2": "2 \u00a9 ucles 2012 0606/11/o/n/12for examiner\u2019 s use mathematical formulae  1. algebra quadratic equation  for the equation ax2 + bx + c  = 0, xbb a c a=\u2212 \u221224 2 binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2. trigonometry identities  sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 [turn over \u00a9 ucles 2012 0606/11/o/n/12for examiner\u2019 s use1 (i) sketch the graph of  y = |3 + 5x|, showing the coordinates of the points where your graph  meets the coordinate axes. [2]  (ii) solve the equation  |3 + 5 x| = 2. [2] 2 find the values of k for which the line  y = k \u2013 6x is a tangent to the curve y = x(2x + k). [4]",
            "4": "4 \u00a9 ucles 2012 0606/11/o/n/12for examiner\u2019 s use3 given that p = logq 32, express, in terms of p,  (i) logq 4, [2]  (ii) logq 16q. [2] 4 using the substitution u = 5x, or otherwise, solve      52x+1 = 7(5x) \u2013 2. [5]",
            "5": "5 [turn over \u00a9 ucles 2012 0606/11/o/n/12for examiner\u2019 s use5 given that  y = x2 cos 4x , find  (i) dy dx , [3]  (ii) the approximate change in y when x increases from \u03c0 4 to \u03c0 4 + p, where p is small. [2]",
            "6": "6 \u00a9 ucles 2012 0606/11/o/n/12for examiner\u2019 s use6 (i) find the first 3 terms, in descending powers of x, in the expansion of /h20898x + 2 x2/h208996 . [3]  (ii) hence find the term independent of x in the expansion of /h208982 \u2013 4 x3/h20899 /h20898x + 2 x2/h208996 . [2]",
            "7": "7 [turn over \u00a9 ucles 2012 0606/11/o/n/12for examiner\u2019 s use7 do not use a calculator in any part of this question.  (a) (i) show that 3 5 \u2013 2 2 is a square root of 53 \u2013 12 10. [1]   (ii) state the other square root of 53 \u2013 12 10. [1]  (b) express 63 + 7 2 43 + 5 2 in the form a + b 6, where a and b are integers to be found. [4]",
            "8": "8 \u00a9 ucles 2012 0606/11/o/n/12for examiner\u2019 s use8 the points a(\u20133, 6), b(5, 2) and c lie on a straight line such that b is the mid-point of ac.  (i) find the coordinates of c. [2]  the point d lies on the y-axis and the line cd is perpendicular to ac.  (ii) find the area of the triangle acd. [5]",
            "9": "9 [turn over \u00a9 ucles 2012 0606/11/o/n/12for examiner\u2019 s use9 a function g is such that g( x) = 1 2x \u2013 1  for 1 /h11088 x /h11088 3.  (i) find the range of g. [1]  (ii) find g\u20131(x). [2]  (iii) write down the domain of g\u20131(x). [1]  (iv) solve g2(x) = 3. [3]",
            "10": "10 \u00a9 ucles 2012 0606/11/o/n/12for examiner\u2019 s use10 the table shows values of the variables x and y. x 10\u00b0 30\u00b0 45\u00b0 60\u00b0 80\u00b0 y 11.2 16 19.5 22.4 24.7  (i) using the graph paper below, plot a suitable straight line graph to show that, for  10\u00b0 /h11088 x /h11088 80\u00b0,      y = a sin x + b, where a and b are positive constants. [4]",
            "11": "11 [turn over \u00a9 ucles 2012 0606/11/o/n/12for examiner\u2019 s use (ii) use your graph to find the value of a and of b. [3]  (iii) estimate the value of y when x = 50. [2]  (iv) estimate the value of x when y = 12. [2]",
            "12": "12 \u00a9 ucles 2012 0606/11/o/n/12for examiner\u2019 s use11 (a) solve cosec /h208982x \u2013 \u03c0 3/h20899 = 2 for 0 < x < \u03c0 radians. [4]  (b) (i) given that 5(cos y + sin y)(2 cos y \u2013 sin y) = 7, show that 12 tan2 y \u2013 5 tan y \u2013 3 = 0. [4]",
            "13": "13 [turn over \u00a9 ucles 2012 0606/11/o/n/12for examiner\u2019 s use (ii) hence solve  5(cos y + sin y)(2 cos y \u2013 sin y) = 7 for 0\u00b0 < x < 180\u00b0. [3]",
            "14": "14 \u00a9 ucles 2012 0606/11/o/n/12for examiner\u2019 s use12 answer only one of the following two alternatives.  either y y = (12 \u2013 6x)(1 + x)2 x aoc b  the diagram shows part of the graph of y = (12 \u2013 6x)(1 + x)2, which meets the x-axis at the  points a and b. the point c is the maximum point of the curve.  (i) find the coordinates of each of a, b and c. [6]  (ii) find the area of the shaded region. [5]  or y xa ob  the diagram shows part of a curve such that  dy dx = 3x2 \u2013 6x \u2013 9. points a and b are stationary  points of the curve and lines from a and b are drawn perpendicular to the x-axis. given that the  curve passes through the point (0, 30), find  (i) the equation of the curve, [4]  (ii) the x-coordinate of a and of b, [3]  (iii) the area of the shaded region. [4]",
            "15": "15 [turn over \u00a9 ucles 2012 0606/11/o/n/12for examiner\u2019 s usestart your answer to question 12 here. indicate which question you are answering.   either or ... ..",
            "16": "16 \u00a9 ucles 2012 0606/11/o/n/12for examiner\u2019 s usecontinue your answer here if necessary. ... . 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. 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."
        },
        "0606_w12_qp_12.pdf": {
            "1": "this document consists of 16 printed pages. dc (cw/sw) 50035/5 \u00a9 ucles 2012 [turn overuniversity of cambridge international examinations international general certificate of secondary education *8006817548* additional mathematics  0606/12 paper 1 october/november 2012  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.for examiner\u2019s use  1  2 3 4 5 6 7 8 910 11 total",
            "2": "2 0606/12/o/n/12 \u00a9 ucles 2012mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2 binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/12/o/n/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use1 it is given that   a = 4 3 , b = \u20131 2 and c = 21 2 .  (i) find | a + b + c|. [2]  (ii) find \u03bb and \u03bc such that   \u03bb a + \u03bc b = c. [3]",
            "4": "4 0606/12/o/n/12 \u00a9 ucles 2012for examiner\u2019 s use2 (i) find the inverse of the matrix   2 \u20131 \u20131 1.5 . [2]  (ii) hence find the matrix a such that     2 \u20131\u20131 1.5  a =    1 6\u20130.5 4 . [3] 3 (i) show that   cot\u03b8  + sin\u03b8 1 + cos\u03b8 = cosec\u03b8. [5]  (ii) explain why the equation   cot\u03b8 + sin\u03b8 1 + cos\u03b8 = 1 2   has no solution. [1]",
            "5": "5 0606/12/o/n/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use4 given that loga pq = 9  and loga p2q = 15, find the value of  (i) loga p  and of loga q, [4]  (ii) logp a + logq a. [2]",
            "6": "6 0606/12/o/n/12 \u00a9 ucles 2012for examiner\u2019 s use5 the line x \u2013 2y = 6 intersects the curve   x2 + xy + 10y + 4y2 = 156 at the points a and b.  find the length of ab. [7]",
            "7": "7 0606/12/o/n/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use6 15\u00b04 \u000b\u00a5\u0016 \u000e 1\f\u0016\u00a5\u0015 \u000e 4 \u0219  using sin15\u00b0 = 2 4 (3 \u2013 1) and without using a calculator, find the value of sin \u03b8 in the form  a + b2, where a and b are integers. [5]",
            "8": "8 0606/12/o/n/12 \u00a9 ucles 2012for examiner\u2019 s use7 solutions to this question by accurate drawing will not be accepted. e d b (8, 4)a (\u20135, 4) o xy c (6, 8)  the vertices of the trapezium abcd  are the points a(\u20135, 4), b(8, 4), c(6, 8) and d. the line ab  is parallel to the line dc. the lines ad and bc are extended to meet at e and angle aeb = 90\u00b0.  (i) find the coordinates of d and of  e. [6]",
            "9": "9 0606/12/o/n/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use (ii) find the area of the trapezium abcd . [2]",
            "10": "10 0606/12/o/n/12 \u00a9 ucles 2012for examiner\u2019 s use8 1.5 rad a c d bo 10 cm 18 cm  the diagram shows an isosceles triangle obd  in which ob = od = 18 cm and angle  bod  = 1.5 radians. an arc of the circle, centre o and radius 10 cm, meets ob at a and od at c.  (i) find the area of the shaded region. [3]  (ii) find the perimeter of the shaded region. [4]",
            "11": "11 0606/12/o/n/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use9 (a) (i) using the axes below, sketch for 0 /h11088 x /h11088 \u03c0, the graphs of      y = sin 2x   and   y = 1 + cos 2x. [4] 3 xy 2 1 o \u20131\u009b 4 \u20132 \u20133\u009b 23\u009b 4\u009b   (ii) write down the solutions of the equation   sin 2 x \u2013 cos 2 x = 1, for 0 /h11088 x /h11088 \u03c0. [2]  (b) (i) write down the amplitude and period of   5 cos 4 x \u2013 3. [2]   (ii) write down the period of   4 tan 3 x. [1]",
            "12": "12 0606/12/o/n/12 \u00a9 ucles 2012for examiner\u2019 s use10 a function f is such that   f( x) = 4 x3 + 4x2 + ax + b. it is given that 2 x \u2013 1 is a factor of both f( x)  and f\u200a\u200a\u02b9(x).  (i) show that b = 2 and find the value of a. [5]  using the values of a and b from part (i),  (ii) find the remainder when f( x) is divided by x + 3, [2]",
            "13": "13 0606/12/o/n/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use (iii) express f( x) in the form   f( x) = (2 x \u2013 1)( px2 + qx + r), where p, q and r are integers to be  found, [2]  (iv) find the values of x for which f( x) = 0. [2]",
            "14": "14 0606/12/o/n/12 \u00a9 ucles 2012for examiner\u2019 s use11 answer only one of the following two alternatives.  either  a curve is such that   y = 5x2 1 + x2  .  (i) show that   dy dx = kx (1 + x2)2  , where k is an integer to be found. [4]  (ii) find the coordinates of the stationary point on the curve and determine the nature of this  stationary point. [3]  (iii) by using your result from part (i), find  /h20885x (1 + x2)2 dx and hence evaluate  /h208852 \u20131x (1 + x2)2 dx.  [4]  or  a curve is such that   y = ax2 + b x2 \u2013 2  , where a and b are constants.  (i) show that   dy dx = \u2013 2x(2a + b) (x2 \u2013 2)2  . [4]  it is given that y = \u20133 and  dy dx = \u201310 when x = 1.  (ii) find the value of a and of b. [3]  (iii) using your values of a and b, find the coordinates of the stationary point on the curve, and  determine the nature of this stationary point. [4] start your answer to question 11 here. indicate which question you are answering.       either or .. ",
            "15": "15 0606/12/o/n/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s usecontinue your answer here. .. ..",
            "16": "16 0606/12/o/n/12 \u00a9 ucles 2012for examiner\u2019 s use 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. 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.continue your answer here if necessary. .. .."
        },
        "0606_w12_qp_13.pdf": {
            "1": "this document consists of 16 printed pages. dc (sjf/cgw) 50036/5 \u00a9 ucles 2012 [turn over *5843670487* additional mathematics  0606/13 paper 1 october/november 2012  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.for examiner\u2019s use  1  2 3 4 5 6 7 8 910 11 totaluniversity of cambridge international examinations international general certificate of secondary education",
            "2": "2 0606/13/o/n/12 \u00a9 ucles 2012for examiner\u2019 s usemathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2 binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/13/o/n/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use1 (a) on the venn diagrams below, shade the region corresponding to the set given below each  venn diagram. q p pf(qer)r/h5105 q p pe(qfr)r/h5105 [2]  (b) it is given that sets /h5105, b, s and f are such that    /h5105 = {students in a school},    b = {students who are boys},   s = {students in the swimming team},   f = {students in the football team}.  express each of the following statements in set notation.  (i) all students in the football team are boys. [1]      (ii) there are no students who are in both the swimming team and the football team. [1]  ",
            "4": "4 0606/13/o/n/12 \u00a9 ucles 2012for examiner\u2019 s use2 the rate of change of a variable x with respect to time t is  4cos2t.  (i) find the rate of change of x with respect to t when t = \u03c0 6 . [1]  the rate of change of a variable y with respect to time t is 3sint.  (ii) using your result from part (i), find the rate of change of y with respect to x when t = \u03c0 6 . [3] 3 a committee of 7 members is to be selected from 6 women and 9 men. find the number of  different committees that may be selected if  (i) there are no restrictions, [1]  (ii) the committee must consist of 2 women and 5 men, [2]  (iii) the committee must contain at least 1 woman. [3]",
            "5": "5 0606/13/o/n/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use4 (i) on the axes below sketch, for 0 /h33355 x /h33355 \u03c0, the graphs of y = tan x    and     y = 1 + 3sin 2x. [3] 8 6 4 2 o \u20132 \u20134 \u20136 \u20138x y  \u009b\u0003 \u009b\u0003 \u0015\u009b\u0003 \u0017\u0016\u009b \u0017  write down  (ii) the coordinates of the stationary points on the curve   y = 1 + 3sin 2x for 0 /h33355 x /h33355 \u03c0, [2]  (iii) the number of solutions of the equation tan x = 1 + 3sin 2x for 0 /h33355 x /h33355 \u03c0. [1]",
            "6": "6 0606/13/o/n/12 \u00a9 ucles 2012for examiner\u2019 s use5 a pilot flies his plane directly from a point a to a point b, a distance of 450 km. the bearing of b  from a is 030\u00b0. a wind of 80 km h\u20131 is blowing from the east. given that the plane can travel at  320 km h\u20131 in still air, find  (i) the bearing on which the plane must be steered, [4]  (ii) the time taken to fly from a to b. [4]",
            "7": "7 0606/13/o/n/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use6 in the expansion of ( p + x)6, where p is a positive integer, the coefficient of x2 is equal to  1.5 times the coefficient of x3.  (i) find the value of p. [4]  (ii) use your value of p to find the term independent of x in the expansion of ( p + x)6 /h208981\u2013 1 x /h208992 . [3]",
            "8": "8 0606/13/o/n/12 \u00a9 ucles 2012for examiner\u2019 s use7 a particle p moves along the x-axis such that its distance, x m, from the origin o at time t s is   given by   x = t t2 + 1 for t /h33356 0.  (i) find the greatest distance of p from o. [4]      (ii) find the acceleration of p at the instant when p is at its greatest distance from o. [3]",
            "9": "9 0606/13/o/n/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use8 (i) given that   3 x3 + 5x2 + px + 8 /h11013 (x \u2013 2)(ax2 + bx + c), find the value of each of the integers  a, b, c and p. [5]      (ii) using the values found in part (i), factorise completely   3 x3 + 5x2 + px + 8. [2]    ",
            "10": "10 0606/13/o/n/12 \u00a9 ucles 2012for examiner\u2019 s use9 20 cm 20 cm10 cm10 cm     rad cd a bo/ \u20146  the diagram shows four straight lines, ad, bc, ac and bd. lines ac and bd intersect at o  such that angle aob is \u03c0 6 radians. ab is an arc of the circle, centre  o and radius 10 cm, and  cd is an arc of the circle, centre o and radius 20 cm.  (i) find the perimeter of abcd. [4]    ",
            "11": "11 0606/13/o/n/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use (ii) find the area of abcd. [4]    ",
            "12": "12 0606/13/o/n/12 \u00a9 ucles 2012for examiner\u2019 s use10 (i) solve   tan2 x \u2013 2sec x + 1 = 0  for 0\u00b0 /h33355 x /h33355 360\u00b0. [4]  (ii) solve   cos2 3y = 5sin2 3y  for 0 /h33355 y /h33355 2 radians. [4]",
            "13": "13 0606/13/o/n/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use (iii) solve   2cosec /h20898z + \u03c0 4 /h20899 = 5  for 0 /h33355 z /h33355 6 radians. [4]",
            "14": "14 0606/13/o/n/12 \u00a9 ucles 2012for examiner\u2019 s use11 answer only one of the following two alternatives.  either  the tangent to the curve   y = 5ex + 3e\u2013x  at the point where x = 1n 3 5, meets the x-axis at the  point p.  (i) find the coordinates of p. [5]  the area of the region enclosed by the curve   y = 5ex + 3e\u2013x, the y-axis, the positive x-axis and  the line x = a is 12 square units.  (ii) show that   5e2a \u2013 14ea \u2013 3 = 0. [3]  (iii) hence find the value of a. [3]  or  (i) given that   y = 3e2x 1 + e2x , show that   dy dx = ae2x (1 + e2x)2 , where a is a constant to be found. [4]  (ii) find the equation of the tangent to the curve   y = 3e2x 1 + e2x  at the point where the curve  crosses the y-axis. [3]  (iii) using your result from part (i), find /h20885e2x (1 + e2x)2 dx and hence evaluate /h20885 01n3e2x (1 + e2x)2 dx.    [4] start your answer to question 11 here. indicate which question you are answering.       either or ... ...",
            "15": "15 0606/13/o/n/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s usecontinue your answer here. .",
            "16": "16 0606/13/o/n/12 \u00a9 ucles 2012for examiner\u2019s use 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. 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.continue your answer here if necessary. ..."
        },
        "0606_w12_qp_21.pdf": {
            "1": "this document consists of 17 printed pages and 3 blank pages. dc (leo/jg) 50026/6 \u00a9 ucles 2012 [turn overuniversity of cambridge international examinations international general certificate of secondary education *1269823337* additional mathematics  0606/21 paper 2 october/november 2012  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. for examiner\u2019s use  1  2 3 4 5 6 7 8 910 11 total",
            "2": "2 \u00a9 ucles 2012 0606/21/o/n/12for examiner\u2019 s usemathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c  = 0, xbb a c a=\u2212 \u221224 2 binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 \u00a9 ucles 2012 [turn over 0606/21/o/n/12for examiner\u2019 s use1 solve the inequality 4 x \u2013 9 > 4x(5 \u2013 x). [4]",
            "4": "4 \u00a9 ucles 2012 0606/21/o/n/12for examiner\u2019 s use2 (a) it is given that /h5105 is the set of integers, p is the set of prime numbers between 10 and  50, f is the set of multiples of 5, and t is the set of multiples of 10. write the following  statements using set notation.   (i) there are 11 prime numbers between 10 and 50. [1]   (ii) 18 is not a multiple of 5. [1]   (iii) all multiples of 10 are multiples of 5. [1]  (b) (i) in the venn diagram below shade the region that represents ( a/h11032  b)  (a  b/h11032). [1] a/h5105 b   (ii) in the venn diagram below shade the region that represents q  (r  s/h11032). [1] q/h5105 r s",
            "5": "5 \u00a9 ucles 2012 [turn over 0606/21/o/n/12for examiner\u2019 s use3 (i) on the grid below draw, for 0\u00b0 /h11088 x /h11088 360\u00b0, the graphs of   y = 3 sin 2x   and   y = 2 + cos x.  [4]  (ii) state the number of values of x for which   3 sin 2x = 2 + cos x  in the interval 0\u00b0 /h11088 x /h11088 360\u00b0.  [1]",
            "6": "6 \u00a9 ucles 2012 0606/21/o/n/12for examiner\u2019 s use4 it is given that   f( x) = 4 + 8x \u2013 x2.  (i) find the value of a and of b for which f(x) = a \u2013 (x + b)2 and hence write down the coordinates  of the stationary point of the curve y = f(x). [3]  (ii) on the axes below, sketch the graph of y = f(x), showing the coordinates of the point where  your graph intersects the y-axis. [2] y x o",
            "7": "7 \u00a9 ucles 2012 [turn over 0606/21/o/n/12for examiner\u2019 s use5 it is given that a = /h208984 \u20132 8 \u20133/h20899, b = /h208982  0 45 \u20131 4/h20899 and c = /h20898 5\u20132 3/h20899.  (i) calculate  abc. [4]  (ii) calculate a\u20131 b. [4]",
            "8": "8 \u00a9 ucles 2012 0606/21/o/n/12for examiner\u2019 s use6 the normal to the curve   y = x3 + 6x2 \u2013 34x + 44 at the point p (2, 8) cuts the x-axis at a and the  y-axis at b. show that the mid-point of the line ab lies on the line   4 y = x + 9. [8]",
            "9": "9 \u00a9 ucles 2012 [turn over 0606/21/o/n/12for examiner\u2019 s use7 in this question /h208981 0/h20899 is a unit vector due east and /h2089801/h20899 is a unit vector due north. at 12 00 a  coastguard, at point o, observes a ship with position vector /h208981612/h20899 km relative to o. the ship is  moving at a steady speed of 10  kmh\u20131 on a bearing of 330\u00b0.  (i) find the value of p such that /h20898\u20135 p/h20899 kmh\u20131 represents the velocity of the ship. [2]  (ii) write down, in terms of t, the position vector of the ship, relative to o, t hours after 12 00.  [2]  (iii) find the time  when the ship is due north of o. [2]  (iv) find the distance of the ship from o at this time. [2]",
            "10": "10 \u00a9 ucles 2012 0606/21/o/n/12for examiner\u2019 s use8 prs q ox cmy cm 1 rad  in the diagram pq and rs are arcs of concentric circles with centre o and angle  poq = 1 radian.  the radius of the larger circle is x cm and the radius of the smaller circle is y cm.  (i) given that the perimeter of the shaded region is 20 cm, express y in terms of x. [2]  (ii) given that the area of the shaded region is 16  cm2, express y2 in terms of x2. [2]",
            "11": "11 \u00a9 ucles 2012 [turn over 0606/21/o/n/12for examiner\u2019 s use (iii) find the value of x and of y. [4]",
            "12": "12 \u00a9 ucles 2012 0606/21/o/n/12for examiner\u2019 s use9 (a) an art gallery displays 10 paintings in a row. of these paintings, 5 are by picasso, 4 by  monet and 1 by turner.   (i) find the number of different ways the paintings can be displayed if there are no restrictions. [1]   (ii) find the number of different ways the paintings can be displayed if the paintings by each of the artists are kept together.  [3]  (b) a committee of  4 senior students and 2 junior students is to be selected from a group     of 6 senior students and 5 junior students.   (i) calculate the number of different committees which can be selected. [3]",
            "13": "13 \u00a9 ucles 2012 [turn over 0606/21/o/n/12for examiner\u2019 s use  one of the 6 senior students is a cousin of one of the 5 junior students.   (ii) calculate the number of different committees which can be selected if at most one of  these cousins is included. [3]",
            "14": "14 \u00a9 ucles 2012 0606/21/o/n/12for examiner\u2019 s use10 (i) the remainder when the expression x3 + 9x2 + bx + c is divided by x \u2013 2 is twice the  remainder when the expression is divided by x \u2013 1. show that c = 24. [5]  (ii) given that x + 8 is a factor of   x3 + 9x2 + bx + 24, show that the equation   x3 + 9x2 + bx + 24 = 0 has only one real root. [4]",
            "15": "15 0606/21/o/n/12 \u00a9 ucles 2012 [turn overblank page question 11 is printed on the next page.",
            "16": "16 \u00a9 ucles 2012 0606/21/o/n/12for examiner\u2019 s use11 answer only one of the following alternatives. either  a particle travels in a straight line so that, t s after passing through a fixed point o, its  displacement, s m, from o is given by s = t2 \u2013 10t + 10ln(l + t), where t > 0.  (i) find the distance travelled in the twelfth second. [2]  (ii) find the value of t when the particle is at instantaneous rest. [5]  (iii) find the acceleration of the particle when t = 9. [3] or  a particle travels in a straight line so that, t s after passing through a fixed point o, its velocity,  v cms\u20131, is given by v = 4e2t \u2013 24t.  (i) find the velocity of the particle as it passes through o. [1]  (ii) find the distance travelled by the particle in the third second. [4]  (iii) find an expression for the acceleration of the particle and hence find the stationary value of  the velocity. [5] start your answer to question 11 here. indicate which question you are answering.       either or  ...  ... ... ... ... ... ... ... ... ... ...",
            "17": "17 \u00a9 ucles 2012 [turn over 0606/21/o/n/12for examiner\u2019 s usecontinue your answer here. .. ",
            "18": "18 \u00a9 ucles 2012 0606/21/o/n/12for examiner\u2019 s usecontinue your answer here if necessary. .. ",
            "19": "19 0606/21/o/n/12 \u00a9 ucles 2012blank page",
            "20": "20 0606/21/o/n/12 \u00a9 ucles 2012permission 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. 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.blank page"
        },
        "0606_w12_qp_23.pdf": {
            "1": "this document consists of 16 printed pages. dc (leo/jg) 50029/6 \u00a9 ucles 2012 [turn over *4183751999* additional mathematics  0606/23 paper 2 october/november 2012  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid. answer all questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.for examiner\u2019s use  1  2 3 4 5 6 7 8 910 11 12 totaluniversity of cambridge international examinations international general certificate of secondary education",
            "2": "2 0606/23/o/n/12 \u00a9 ucles 2012for examiner\u2019 s usemathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xbb a c a=\u2212 \u221224 2 binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/23/o/n/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use1 solve the equation  |5x + 7| = 13. [3] 2 (i) given that  a = /h208987 8 4 6/h20899, find the inverse matrix, a\u20131. [2]  (ii) use your answer to part (i) to solve the simultaneous equations      7 x + 8y = 39,      4 x + 6y = 23. [2]",
            "4": "4 0606/23/o/n/12 \u00a9 ucles 2012for examiner\u2019 s use3 without using a calculator, simplify (33 \u2013 1)2 23 \u2013 3, giving your answer in the form a3 + b 3, where a and b are integers. [4]",
            "5": "5 0606/23/o/n/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use4 the points x, y and z are such that \u2192xy = 3\u2192yz. the position vectors of x and z, relative to an   origin o, are /h208984 \u201327/h20899 and /h2089820 \u20137/h20899 respectively. find the unit vector in the direction \u2192oy. [5]",
            "6": "6 0606/23/o/n/12 \u00a9 ucles 2012for examiner\u2019 s use5 find the set of values of m for which the line   y = mx + 2   does not meet the curve  y = mx2 + 7x + 11. [6]",
            "7": "7 0606/23/o/n/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use6 (a) given that cos x = p, find an expression, in terms of p, for tan2 x. [3]  (b) prove that   (cot \u03b8 + tan \u03b8)2 = sec2 \u03b8 + cosec2 \u03b8. [3]",
            "8": "8 0606/23/o/n/12 \u00a9 ucles 2012for examiner\u2019 s use7 (a) find /h20885(x + 3) x dx. [3]  (b) find /h2088520 (2x + 5)2 dx and hence evaluate /h20885 01020 (2x + 5)2 dx. [4]",
            "9": "9 0606/23/o/n/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use8 solutions to this question by accurate drawing will not be accepted.  the points a (4, 5), b(\u20132, 3), c(1, 9) and d are the vertices of a trapezium in which bc is  parallel to ad and angle bcd is 90\u00b0. find the area of the trapezium. [8]",
            "10": "10 0606/23/o/n/12 \u00a9 ucles 2012for examiner\u2019 s use9 the table shows experimental values of two variables x and y. x 1234 y 9.41 1.29 \u2013 0.69 \u2013 1.77  it is known that x and y are related by the equation   y = a x2 + bx, where a and b  are constants.  (i) a straight line graph is to be drawn to represent this information. given that x2y is plotted  on the vertical axis, state the variable to be plotted on the horizontal axis. [1]  (ii) on the grid opposite, draw this straight line graph. [3]  (iii) use your graph to estimate the value of a and of b. [3]  (iv) estimate the value of y when x is 3.7. [2]",
            "11": "11 0606/23/o/n/12 \u00a9 ucles 2012 [turn over",
            "12": "12 0606/23/o/n/12 \u00a9 ucles 2012for examiner\u2019 s use10 ad bc 200  m80 m x m  a track runs due east from a to b, a distance of 200 m. the point c is 80 m due north of b.  a cyclist travels on the track from a to d, where d is x m due west of b. the cyclist then travels  in a straight line across rough ground from d to c. the cyclist travels at 10 m s\u20131 on the track  and at 6 m s\u20131 across rough ground.  (i) show that the time taken, t s, for the cyclist to travel from a to c is given by  t = 200 \u2013 x 10 + (x2 + 6400) 6 [2]  (ii) given that x can vary, find the value of x for which t has a stationary value and the  corresponding value of t. [6]",
            "13": "13 0606/23/o/n/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s use11 (a) solve (2x\u20132)1 2 = 100, giving your answer to 1 decimal place.  [3]  (b) solve logy 2 = 3 \u2013 logy 256. [3]  (c) solve 65z\u20132 36z = 216z\u20131 363\u2013z. [4]",
            "14": "14 0606/23/o/n/12 \u00a9 ucles 2012for examiner\u2019 s use12 answer only one of the following alternatives. either  (i) express   4x2 + 32x + 55 in the form ( ax + b)2 + c, where a, b and c are constants and a is  positive. [3]  the functions f and g are defined by   f : x /h21739 4x2 + 32x + 55 for x > \u2013 4,   g : x /h21739 1 x for x > 0.  (ii) find f\u20131(x). [3]  (iii) solve the equation fg( x) = 135. [4] or the functions h and k are defined by   h : x /h21739  2x \u2013 7  for x /h11091 c,   k : x /h21739 3x \u2013 4 x \u2013 2 for x > 2.  (i) state the least possible value of c. [1]  (ii) find h\u20131(x). [2]  (iii) solve the equation k( x) = x. [3]  (iv) find an expression for the function k2, in the form k2 : x /h21739 a + b x where a and b are  constants. [4]",
            "15": "15 0606/23/o/n/12 \u00a9 ucles 2012 [turn overfor examiner\u2019 s usestart your answer to question 12 here. indicate which question you are answering.  either or ... ",
            "16": "16 0606/23/o/n/12 \u00a9 ucles 2012for examiner\u2019s use 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. 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.continue your answer here if necessary. ..."
        }
    },
    "2013": {
        "0606_s13_qp_11.pdf": {
            "1": "this document consists of 16 printed pages. dc (rw/sw) 57083/4 \u00a9 ucles 2013 [turn overuniversity of cambridge international examinations international general certificate of secondary education read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid.do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. * 5 5 4 4 6 5 2 3 1 5 * additional mathematics  0606/11 paper 1 may/june 2013  2 hours candidates answer on the question paper. additional materials: electronic calculator",
            "2": "2 0606/11/m/j/13 \u00a9 ucles 2013mathematical formulae 1.\u2002algebra quadratic\u2002equation  for the equation ax2 + bx + c = 0, xab b ac 242!=- - . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/11/m/j/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use1\u2002 on the axes below sketch, for 0 2rxg g , the graph of \u2002 (i)\u2002 cos y x 1 = - , [2] \u2002 (ii)\u2002 sin y x 2= . [2] \u20132\u201310y x12 \ufffd 2\ufffd 3\ufffd 22\ufffd \u2002 (iii)\u2002 state the number of solutions of the equation cos sinx x 2 1- = , for r 0 2xg g . [1]",
            "4": "4 0606/11/m/j/13 \u00a9 ucles 2013 for examiner\u2019 s use2\u2002 variables x and y are such that y abx= , where a and b are constants. the diagram shows the  graph of ln y against x, passing through the points (2, 4) and (8, 10). (2, 4)(8, 10) x oln y \u2002 find the value of a and of b. [5]",
            "5": "5 0606/11/m/j/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use3\u2002 a committee of 6 members is to be selected from 5 men and 9 women.  find the number of  different committees that could be selected if \u2002 (i)\u2002 there are no restrictions, [1] \u2002 (ii)\u2002 there are exactly 3 men and 3 women on the committee, [2] \u2002 (iii)\u2002 there is at least 1 man on the committee. [3]",
            "6": "6 0606/11/m/j/13 \u00a9 ucles 2013 for examiner\u2019 s use4\u2002 (i)\u2002 given that  logx21 4=, find the value of x. [1] \u2002 (ii)\u2002 solve  log logy y 2 5 1221 4 4- - = ^ h . [4]",
            "7": "7 0606/11/m/j/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use5\u2002 (i)\u2002 find  xx 16d2-c my . [2] \u2002 (ii)\u2002 hence find the value of the positive constant k for which 2 xx 16d kk 23- =c my . [4]",
            "8": "8 0606/11/m/j/13 \u00a9 ucles 2013 for examiner\u2019 s use6\u2002 (i)\u2002 given that a2 315=-c m , find a1 -. [2] \u2002 (ii)\u2002 using your answer from part (i), or otherwise, find the values of a, b, c and d such that a cb d 17 175a-= c c m m . [5]",
            "9": "9 0606/11/m/j/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use7\u2002 calculators\u2002must\u2002not\u2002be\u2002used\u2002in\u2002this\u2002question. b 5 \u2013 2 ac 5 + 1 \u2002 the diagram shows a triangle abc in which angle 90ca= . sides ab and ac are 5 2- and  5 1+ respectively. find \u2002 (i)\u2002 tan b in the form a b 5+ , where a and b are integers, [3] \u2002 (ii)\u2002 secb2 in the form c d 5+ , where c and d are integers. [4]",
            "10": "10 0606/11/m/j/13 \u00a9 ucles 2013 for examiner\u2019 s use8\u2002 \u03b8 radma d b fe c6 cm 16 cm 16 cm \u2002 the diagram shows a square abcd of side 16 cm. m is the mid-point of ab. the points e and f  are on ad and bc respectively such that ae bf= =  6 cm. ef is an arc of the circle centre m,  such that angle emf is i radians. \u2002 (i)\u2002 show that . 1 855i=  radians, correct to 3 decimal places. [2] \u2002 (ii)\u2002 calculate the perimeter of the shaded region. [4]",
            "11": "11 0606/11/m/j/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use\u2002 (iii)\u2002 calculate the area of the shaded region. [3]",
            "12": "12 0606/11/m/j/13 \u00a9 ucles 2013 for examiner\u2019 s use9\u2002 ba cop qa b c \u2002 the figure shows points a, b and c with position vectors a, b and c respectively, relative to  an origin o. the point p lies on ab such that 3:4 : ap ab= . the point q lies on oc such that  2:3 : oq qc= . \u2002 (i)\u2002 express ap in terms of a and b and hence show that 3 op41a b= + ^ h . [3] \u2002 (ii)\u2002 find pq in terms of a, b and c. [3]",
            "13": "13 0606/11/m/j/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use\u2002 (iii)\u2002 given that pq bc5 6= , find c in terms of a and b. [2]",
            "14": "14 0606/11/m/j/13 \u00a9 ucles 2013 for examiner\u2019 s use10\u2002 the point a, whose x-coordinate is 2, lies on the curve with equation y x x x 4 13 2= - + + . \u2002 (i)\u2002 find the equation of the tangent to the curve at a. [4] \u2002 this tangent meets the curve again at the point b. \u2002 (ii)\u2002 find the coordinates of b. [4]",
            "15": "15 0606/11/m/j/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use\u2002 (iii)\u2002 find the equation of the perpendicular bisector of the line ab. [4] question\u200211\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.",
            "16": "16 0606/11/m/j/13 \u00a9 ucles 2013for examiner\u2019 s use11\u2002 (a)\u2002 solve  rsinx 231 + = -` j  for r 0 2xg g  radians. [4] \u2002 (b)\u2002 solve  tan coty y2- =  for y 0 180c cg g . [6] 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. 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."
        },
        "0606_s13_qp_12.pdf": {
            "1": "this document consists of 17 printed pages and 3 blank pages. dc (leo/sw) 57088/3 \u00a9 ucles 2013 [turn overuniversity of cambridge international examinations international general certificate of secondary education * 6 1 1 1 6 3 9 0 6 5 * additional mathematics 0606/12 paper 1 may/june 2013  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid.do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/12/m/j/13 \u00a9 ucles 2013mathematical formulae 1.\u2002algebra quadratic\u2002equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2 . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/12/m/j/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use1 /h5105 a b \u2002 the v enn diagram shows the universal set \ue025, the set a and the set b. given that n( b ) = 5, n( a\ue039) = 10  and n(\ue025) = 26, find \u2002 (i)\u2002 n( )a b+,  [1] \u2002 (ii)\u2002 n(a), [1] \u2002 (iii)\u2002 n ( )b a+l . [1]",
            "4": "4 0606/12/m/j/13 \u00a9 ucles 2013 for examiner\u2019 s use2\u2002 a 4-digit number is to be formed from the digits 1, 2, 5, 7, 8 and 9. each digit may only be used  once. find the number of different 4-digit numbers that can be formed if \u2002 (i)\u2002 there are no restrictions, [1] \u2002 (ii)\u2002 the 4-digit numbers are divisible by 5, [2] \u2002 (iii)\u2002 the 4-digit numbers are divisible by 5 and are greater than 7000. [2]",
            "5": "5 0606/12/m/j/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use3\u2002 show that    (1 \u2013 cos \u03b8 \u2013 sin \u03b8 )2 \u2013 2(1 \u2013 sin \u03b8 )(1 \u2013 cos \u03b8 ) = 0. [3]",
            "6": "6 0606/12/m/j/13 \u00a9 ucles 2013 for examiner\u2019 s use4\u2002 find the set of values of k for which the curve    y = 2x2 + kx + 2k \u2013 6    lies above the x-axis for  all values of x. [4]",
            "7": "7 0606/12/m/j/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use5\u2002 the line    3x + 4y = 15    cuts the curve    2 xy = 9    at the points a and b. find the length of the  line ab. [6]",
            "8": "8 0606/12/m/j/13 \u00a9 ucles 2013 for examiner\u2019 s use6\u2002 the normal to the curve    y + 2 = 3 tan x, at the point on the curve where    x = 43r, cuts the  y-axis at the point p. find the coordinates of p. [6]",
            "9": "9 0606/12/m/j/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use7\u2002 it is given that    f(x) = 6x3 \u2013 5x2 + ax + b    has a factor of x + 2 and leaves a remainder of 27  when divided by x \u2013 1. \u2002 (i)\u2002 show that b = 40 and find the value of a. [4] \u2002 (ii)\u2002 show that    f(x) = (x + 2)(px2 + qx + r), where p, q and r are integers to be found. [2] \u2002 (iii)\u2002 hence solve f(x) = 0. [2]",
            "10": "10 0606/12/m/j/13 \u00a9 ucles 2013 for examiner\u2019 s use8\u2002 (a)\u2002 given that the matrix a = 4 32 5 \u2013c m , find  \u2002 \u2002 (i)\u2002 a2,  [2] \u2002 \u2002 (ii)\u2002 3a + 4i, where i is the identity matrix. [2]",
            "11": "11 0606/12/m/j/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use\u2002 (b)\u2002 (i)\u2002 find the inverse matrix of 6 91 3 \u2013c m . [2] \u2002 \u2002 (ii)\u2002 hence solve the equations      6x + y = 5,      \u20139x + 3y = 23. [3]",
            "12": "12 0606/12/m/j/13 \u00a9 ucles 2013 for examiner\u2019 s use9\u2002 (i)\u2002 given that n is a positive integer, find the first 3 terms in the expansion of x 121n +c m  in  ascending powers of x. [2] \u2002 (ii)\u2002 given that the coefficient of x2 in the expansion of (1 \u2013 x) x 121n +c m  is 425, find the value  of n. [5]",
            "13": "13 0606/12/m/j/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use10\u2002 (a)\u2002 (i)\u2002 find d x x2 5- y . [2] \u2002 \u2002 (ii)\u2002 hence evaluate d x x2 5 315- y . [2]",
            "14": "14 0606/12/m/j/13 \u00a9 ucles 2013 for examiner\u2019 s use\u2002 (b)\u2002 (i)\u2002\u2002 find ddlnxx x3^ h . [2] \u2002 \u2002 (ii)\u2002 hence find d ln x x x2y . [3]",
            "15": "15 0606/12/m/j/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use11\u2002 (a)\u2002 solve      cos2x + 2sec2x + 3 = 0 for x 0 360g gc c . [5] \u2002 (b)\u2002 solve      sin y622 r-` j  = 1 for 0 yg g r. [4]",
            "16": "16 0606/12/m/j/13 \u00a9 ucles 2013 for examiner\u2019 s use12\u2002 a particle p moves in a straight line such that, t s after leaving a point o, its velocity v m s\u20131 is  given by v = 36t \u20133t2 for t h 0. \u2002 (i)\u2002 find the value of t when the velocity of p stops increasing. [2] \u2002 (ii)\u2002 find the value of t when p comes to instantaneous rest. [2] \u2002 (iii)\u2002 find the distance of p from o when p is at instantaneous rest. [3]",
            "17": "17 0606/12/m/j/13 \u00a9 ucles 2013 for examiner\u2019 s use\u2002 \u2002 (iv)\u2002 find the speed of p when p is again at o. [4]",
            "18": "18 0606/12/m/j/13 \u00a9 ucles 2013blank\u2002page",
            "19": "19 0606/12/m/j/13 \u00a9 ucles 2013blank\u2002page",
            "20": "20 0606/12/m/j/13 \u00a9 ucles 2013permission 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. 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.blank\u2002page"
        },
        "0606_s13_qp_13.pdf": {
            "1": "this document consists of 16 printed pages. dc (tl/sw) 71814 \u00a9 ucles 2013 [turn overuniversity of cambridge international examinations international general certificate of secondary education read these instructions first write your centre number, candidate number and name on all the work you hand in. write in dark blue or black pen.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid.do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80. *6607517764* additional mathematics  0606/13 paper 1 may/june 2013  2 hours candidates answer on the question paper. additional materials: electronic calculator",
            "2": "2 0606/13/m/j/13 \u00a9 ucles 2013mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xabb a c 242!=-- . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u03b4abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u03b4 = 1  2 bc sin a",
            "3": "3 0606/13/m/j/13 \u00a9 ucles 2013 [turn overfor examiner\u2019 s use1 on the axes below sketch, for 02 r xgg , the graph of  (i) cosyx 1 =- , [2]  (ii) sinyx 2 = . [2] \u20132\u201310y x12 \u009b 2\u009b 3\u009b 22\u009b  (iii) state the number of solutions of the equation cos sinxx 21 -= , for r 02xgg . [1]",
            "4": "4 0606/13/m/j/13 \u00a9 ucles 2013for examiner\u2019 s use2 variables x and y are such that ya bx= , where a and b are constants. the diagram shows the  graph of ln y against x, passing through the points (2, 4) and (8, 10). (2, 4)(8, 10) x oln y  find the value of a and of b. [5]",
            "5": "5 0606/13/m/j/13 \u00a9 ucles 2013 [turn overfor examiner\u2019 s use3 a committee of 6 members is to be selected from 5 men and 9 women.  find the number of  different committees that could be selected if  (i) there are no restrictions, [1]  (ii) there are exactly 3 men and 3 women on the committee, [2]  (iii) there is at least 1 man on the committee. [3]",
            "6": "6 0606/13/m/j/13 \u00a9 ucles 2013for examiner\u2019 s use4 (i) given that  logx21 4=, find the value of x. [1]  (ii) solve  log logyy 25 1 221 44-- =^h . [4]",
            "7": "7 0606/13/m/j/13 \u00a9 ucles 2013 [turn overfor examiner\u2019 s use5 (i) find  xx 16d2-cmy . [2]  (ii) hence find the value of the positive constant k for which 2 xx 16d kk 23-=cmy . [4]",
            "8": "8 0606/13/m/j/13 \u00a9 ucles 2013for examiner\u2019 s use6 (i) given that a2 315=- cm , find a1 -. [2]  (ii) using your answer from part (i), or otherwise, find the values of a, b, c and d such that a cb d 17 175a-=ccmm . [5]",
            "9": "9 0606/13/m/j/13 \u00a9 ucles 2013 [turn overfor examiner\u2019 s use7 calculators must not be used in this question. b 5 \u2013 2 ac 5 + 1  the diagram shows a triangle abc in which angle 90c a= . sides ab and ac are 52- and  51+ respectively. find  (i) tan b in the form ab 5 + , where a and b are integers, [3]  (ii) secb2 in the form cd 5 + , where c and d are integers. [4]",
            "10": "10 0606/13/m/j/13 \u00a9 ucles 2013for examiner\u2019 s use8  \u0219 radma d b fe c6 cm 16 cm 16 cm  the diagram shows a square abcd of side 16 cm. m is the mid-point of ab. the points e and f  are on ad and bc respectively such that ae bf==  6 cm. ef is an arc of the circle centre m,  such that angle emf is i radians.  (i) show that . 1 855 i=  radians, correct to 3 decimal places. [2]  (ii) calculate the perimeter of the shaded region. [4]",
            "11": "11 0606/13/m/j/13 \u00a9 ucles 2013 [turn overfor examiner\u2019 s use (iii) calculate the area of the shaded region. [3]",
            "12": "12 0606/13/m/j/13 \u00a9 ucles 2013for examiner\u2019 s use9  ba cop qa b c  the figure shows points a, b and c with position vectors a, b and c respectively, relative to  an origin o. the point p lies on ab such that 3:4 :ap ab = . the point q lies on oc such that  2:3 :oq qc = .  (i) express ap in terms of a and b and hence show that 3 op41ab=+^h . [3]  (ii) find pq in terms of a, b and c. [3]",
            "13": "13 0606/13/m/j/13 \u00a9 ucles 2013 [turn overfor examiner\u2019 s use (iii) given that pq bc56= , find c in terms of a and b. [2]",
            "14": "14 0606/13/m/j/13 \u00a9 ucles 2013for examiner\u2019 s use10 the point a, whose x-coordinate is 2, lies on the curve with equation yx x x 4132=- + + .  (i) find the equation of the tangent to the curve at a. [4]  this tangent meets the curve again at the point b.  (ii) find the coordinates of b. [4]",
            "15": "15 0606/13/m/j/13 \u00a9 ucles 2013 [turn overfor examiner\u2019 s use (iii) find the equation of the perpendicular bisector of the line ab. [4] question 11 is printed on the next page.",
            "16": "16 0606/13/m/j/13 \u00a9 ucles 2013for examiner\u2019 s use11 (a) solve  rsinx 231 += -`j  for r 02xgg  radians. [4]  (b) solve  tan cotyy2-=  for y 0 180ccgg . [6] 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. 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."
        },
        "0606_s13_qp_21.pdf": {
            "1": "this document consists of 16 printed pages. dc (nh/sw) 57089/6 \u00a9 ucles 2013 [turn over * 5 2 7 2 7 0 5 0 4 6 * additional mathematics 0606/21 paper 2 may/june 2013  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid.do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.university of cambridge international examinations international general certificate of secondary education",
            "2": "2 0606/21/m/j/13 \u00a9 ucles 2013mathematical formulae 1.\u2002algebra quadratic\u2002equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2 . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/21/m/j/13 \u00a9 ucles 2013 [turn over for examiner\u2019s use1\u2002 prove that cossin 12 ii+c m  + 2 4cossintan122 iii-= + c m . [4]",
            "4": "4 0606/21/m/j/13 \u00a9 ucles 2013 for examiner\u2019s use2 t s 24 20 516 ov ms\u20131 \u2002 the velocity-time graph represents the motion of a particle moving in a straight line. \u2002 (i)\u2002 find the acceleration during the first 5 seconds. [1] \u2002 (ii)\u2002 find the length of time for which the particle is travelling with constant velocity . [1] \u2002 (iii)\u2002 find the total distance travelled by the particle. [3]",
            "5": "5 0606/21/m/j/13 \u00a9 ucles 2013 [turn over for examiner\u2019s use3\u2002 variables x and y are related by the equation sin y 10 42= -  x, where x02g gr. given that \u2002 x is increasing at a rate of 0.2 radians per second, find the corresponding rate of change of y  when y = 8. [6]",
            "6": "6 0606/21/m/j/13 \u00a9 ucles 2013 for examiner\u2019s use4\u2002 (i)\u2002 sketch the graph of y x 4 2= -  on the axes below, showing the coordinates of the points  where the graph meets the axes. [3] x oy \u2002 (ii)\u2002 solve the equation x x4 2- = . [3]",
            "7": "7 0606/21/m/j/13 \u00a9 ucles 2013 [turn over for examiner\u2019s use5 x cmr uq pt s \u2002 a piece of wire of length 96  cm is formed into the rectangular shape pqrstu shown in the  diagram. it is given that pq = tu = sr = x cm. it may be assumed that pq and tu coincide  and that ts and qr have the same length. \u2002 (i)\u2002 show that the area, acm2, enclosed by the wire is given by ax x 296 32 =-. [2] \u2002 (ii)\u2002 given that x can vary, find the stationary value of a and determine the nature of this  stationary value. [4]",
            "8": "8 0606/21/m/j/13 \u00a9 ucles 2013 for examiner\u2019s use6\u2002 find the equation of the normal to the curve yxx 282 =-+ at the point on the curve where x = 4.  [6]",
            "9": "9 0606/21/m/j/13 \u00a9 ucles 2013 [turn over for examiner\u2019s use7\u2002 (i)\u2002 find the first four terms in the expansion of ( ) x 26+  in ascending powers of x. [3] \u2002 (ii)\u2002 hence find the coefficient of x3 in the expansion of x x x 1 3 1 26+ - +^ ^ ^ h h h . [4]",
            "10": "10 0606/21/m/j/13 \u00a9 ucles 2013 for examiner\u2019s use8\u2002 the line\u2002 2 8 y x= -  cuts the curve 2 5 32 0x y xy2 2+ - + =  at the points a and b. find the  length of the line ab. [7]",
            "11": "11 0606/21/m/j/13 \u00a9 ucles 2013 [turn over for examiner\u2019s use9\u2002 it is given that x \u2208 \ue052\u2002and that \ue025 = {x : \u2212 5 < x < 12}, \u2002    s = {x : 5x + 24 > x2}, \u2002    t = {x : 2x + 7 > 15}. \u2002 find the values of x such that \u2002 (i)\u2002 x s!, [3] \u2002 (ii)\u2002 x s tj! , [2] \u2002 (iii)\u2002 ( )x s tk! l. [3]",
            "12": "12 0606/21/m/j/13 \u00a9 ucles 2013 for examiner\u2019s use10\u2002 a plane, whose speed in still air is 240 kmh\u20131, flies directly from a to b, where b is 500 km from  a on a bearing of 032\u00b0. there is a constant wind of 50 kmh\u20131 blowing from the west. \u2002 (i)\u2002 find the bearing on which the plane is steered. [4]",
            "13": "13 0606/21/m/j/13 \u00a9 ucles 2013 [turn over for examiner\u2019s use\u2002 (ii)\u2002 find, to the nearest minute, the time taken for the flight. [4]",
            "14": "14 0606/21/m/j/13 \u00a9 ucles 2013 for examiner\u2019s use11\u2002 a one-one function f is defined by ( ) ( 1) 5x xf2= - -  for x kh. \u2002 (i)\u2002 state the least value that k can take. [1] \u2002 for this least value of k \u2002 (ii)\u2002 write down the range of f, [1] \u2002 (iii)\u2002 find ( )x f1 -, [2]",
            "15": "15 0606/21/m/j/13 \u00a9 ucles 2013 [turn over for examiner\u2019s use\u2002 (iv)\u2002 sketch and label, on the axes below, the graph of ( ) y x f=  and of ( ) y x f1=-, [2] x oy y = x \u2002 (v)\u2002 find the value of x for which ( ) ( )x xf f1=-. [2] question\u200212\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.",
            "16": "16 0606/21/m/j/13 \u00a9 ucles 2013 for examiner\u2019s use12\u2002 the function   ( )x x x ax bf3 2= + + +    is divisible by x3- and leaves a remainder  of 20 when divided by x1+. \u2002 (i)\u2002 show that b6= and find the value of a. [4] \u2002 (ii)\u2002 using your value of a and taking b as 6, find the non-integer roots of the equation ( ) 0xf=  in the form p q! , where p and q are integers. [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. 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."
        },
        "0606_s13_qp_22.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (nh/sw) 57090/3 \u00a9 ucles 2013 [turn over * 5 8 9 9 8 3 2 6 4 7 * additional mathematics 0606/22 paper 2 may/june 2013  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid.do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.university of cambridge international examinations international general certificate of secondary education",
            "2": "2 0606/22/m/j/13 \u00a9 ucles 2013mathematical formulae 1.\u2002algebra quadratic\u2002equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2 . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/22/m/j/13 \u00a9 ucles 2013 [turn over for examiner\u2019s use1 (4, 18) (1, 3) x2 oy \u2002 variables x and y are such that when y is plotted against x2 a straight line graph passing  through the points (1, 3) and (4, 18) is obtained. express y in terms of x. [4]",
            "4": "4 0606/22/m/j/13 \u00a9 ucles 2013 for examiner\u2019s use2\u2002 (a)\u2002 solve the equation 3p+1 = 0.7 , giving your answer to 2 decimal places. [3] \u2002 (b)\u2002 express   (4 ) yy x 833 2#   in the form 2a \u00d7 xb \u00d7 yc, where a, b and c are constants. [3]",
            "5": "5 0606/22/m/j/13 \u00a9 ucles 2013 [turn over for examiner\u2019s use3\u2002 (a) oy x oya xoy x oy x oy x oy xb c d e f \u2002 \u2002 (i)\u2002 write down the letter of each graph which does not represent a function. [2] \u2002 \u2002 (ii)\u2002 write down the letter of each graph which represents a function that does not have an  inverse. [2] \u2002 (b) x o 55y y = f(x) \u2002 \u2002 the diagram shows the graph of a function y = f(x). on the same axes sketch the graph of  y = f \u20131(x). [2]",
            "6": "6 0606/22/m/j/13 \u00a9 ucles 2013 for examiner\u2019s use4\u2002 the position vectors of the points a and b, relative to an origin o, are 4i \u2013 21j and 22i \u2013 30j  respectively. the point  c lies on ab such that ab ac 3= . \u2002 (i)\u2002 find the position vector of c relative to o. [4] \u2002 \u2002 (ii)\u2002 find the unit vector in the direction oc. [2]",
            "7": "7 0606/22/m/j/13 \u00a9 ucles 2013 [turn over for examiner\u2019s use5\u2002 calculators\u2002must\u2002not\u2002be\u2002used\u2002in\u2002this\u2002question. a b d x xc5 4 + 7 2 \u2002 the diagram shows a trapezium abcd in which ad = 7 cm and ab = 4 5 cm+^ h . ax is  perpendicular to dc with dx = 2 cm and xc = x cm. given that the area of trapezium abcd is  15 5 2 cm2+ ^ h , obtain an expression for x in the form a + b 5, where a and b are integers. [6]",
            "8": "8 0606/22/m/j/13 \u00a9 ucles 2013 for examiner\u2019s use6 or \ufffd 3 ra b \u2002 the shaded region in the diagram is\u2002a segment of a circle with centre o and radius r cm. \u2002 angle aob = 3r radians. \u2002 (i)\u2002 show that the perimeter of the segment is r 33r+c m  cm. [2] \u2002 (ii)\u2002 given that the perimeter of the segment is 26 cm, find the value of r and the area of the  segment. [5]",
            "9": "9 0606/22/m/j/13 \u00a9 ucles 2013 [turn over for examiner\u2019s use7\u2002 differentiate, with respect to x, \u2002 (i)\u2002 (3 \u2212 5x)12, [2] \u2002 (ii)\u2002 x2 sin x, [2] \u2002 (iii)\u2002 1tanx ex2+ . [4]",
            "10": "10 0606/22/m/j/13 \u00a9 ucles 2013 for examiner\u2019s use8\u2002 solutions\u2002to\u2002this\u2002question\u2002by\u2002accurate\u2002drawing\u2002will\u2002not\u2002be\u2002accepted. \u2002 the points a(\u2212 6, 2), b(2, 6) and c are the vertices of a triangle. \u2002 (i)\u2002 find the equation of the line ab in the form y = mx + c . [2] \u2002 (ii)\u2002 given that angle abc = 90\u00b0, find the equation of bc. [2]",
            "11": "11 0606/22/m/j/13 \u00a9 ucles 2013 [turn over for examiner\u2019s use\u2002 (iii)\u2002 given that the length of ac is 10 units, find the coordinates of each of the two possible  positions of point c. [4]",
            "12": "12 0606/22/m/j/13 \u00a9 ucles 2013 for examiner\u2019s use9\u2002 (a)\u2002 the graph of y = k(3x) + c passes through the points (0, 14) and (\u2212 2, 6). find the value of\u2002 k  and of c. [3] \u2002 (b)\u2002 the variables x and y are connected by the equation y = ex + 25 \u2212 24e\u2013x. \u2002 \u2002 (i)\u2002 find the value of y when x = 4. [1] \u2002 \u2002 (ii)\u2002 find the value of ex when y = 20 and hence find the corresponding value of x. [4]",
            "13": "13 0606/22/m/j/13 \u00a9 ucles 2013 [turn over for examiner\u2019s use10\u2002 (a)\u2002 the function f is defined, for 0\u00b0  x  360\u00b0, by f(x) = 1 + 3 cos 2x. \u2002 \u2002 (i)\u2002 sketch the graph of y = f(x) on the axes below. [4] o \u201355y x90\u00b0 180\u00b0 270\u00b0 360\u00b0 \u2002 \u2002 (ii)\u2002 state the amplitude of f. [1] \u2002 \u2002 (iii)\u2002 state the period of f. [1] \u2002 (b)\u2002 given that cos x = p , where 270\u00b0 < x < 360\u00b0,  find cosec x in terms of p. [3]",
            "14": "14 0606/22/m/j/13 \u00a9 ucles 2013 for examiner\u2019s use11\u2002 a curve has equation y = 3x +  ( )x 41 3- . \u2002 (i)\u2002 find xy dd and  xy dd 22  . [4] \u2002 (ii)\u2002 show that the coordinates of the stationary points of the curve are (5, 16) and (3, 8). [2] \u2002 (iii)\u2002 determine the nature of each of these stationary points. [2]",
            "15": "15 0606/22/m/j/13 \u00a9 ucles 2013 for examiner\u2019s use\u2002 (iv)\u2002 find \u222b ( )x x3 41 3+ -c m dx. [2] \u2002 (v)\u2002 hence find the area of the region enclosed by the curve, the line x = 5, the x-axis and the  line x = 6 . [2]",
            "16": "16 0606/22/m/j/13 \u00a9 ucles 2013permission 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. 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.blank\u2002page"
        },
        "0606_s13_qp_23.pdf": {
            "1": "this document consists of 16 printed pages. dc (jf/sw) 71796 \u00a9 ucles 2013 [turn over * 8 4 8 5 2 9 6 2 9 8 * additional mathematics 0606/23 paper 2 may/june 2013  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid.do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.university of cambridge international examinations international general certificate of secondary education",
            "2": "2 0606/23/m/j/13 \u00a9 ucles 2013mathematical formulae 1.\u2002algebra quadratic\u2002equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2 . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/23/m/j/13 \u00a9 ucles 2013 [turn over for examiner\u2019s use1\u2002 prove that cossin 12 ii+c m  + 2 4cossintan122 iii-= + c m . [4]",
            "4": "4 0606/23/m/j/13 \u00a9 ucles 2013 for examiner\u2019s use2 t s 24 20 516 ov ms\u20131 \u2002 the velocity-time graph represents the motion of a particle moving in a straight line. \u2002 (i)\u2002 find the acceleration during the first 5 seconds. [1] \u2002 (ii)\u2002 find the length of time for which the particle is travelling with constant velocity . [1] \u2002 (iii)\u2002 find the total distance travelled by the particle. [3]",
            "5": "5 0606/23/m/j/13 \u00a9 ucles 2013 [turn over for examiner\u2019s use3\u2002 variables x and y are related by the equation sin y 10 42= -  x, where x02g gr. given that \u2002 x is increasing at a rate of 0.2 radians per second, find the corresponding rate of change of y  when y = 8. [6]",
            "6": "6 0606/23/m/j/13 \u00a9 ucles 2013 for examiner\u2019s use4\u2002 (i)\u2002 sketch the graph of y x 4 2= -  on the axes below, showing the coordinates of the points  where the graph meets the axes. [3] x oy \u2002 (ii)\u2002 solve the equation x x4 2- = . [3]",
            "7": "7 0606/23/m/j/13 \u00a9 ucles 2013 [turn over for examiner\u2019s use5 x cmr uq pt s \u2002 a piece of wire of length 96  cm is formed into the rectangular shape pqrstu shown in the  diagram. it is given that pq = tu = sr = x cm. it may be assumed that pq and tu coincide  and that ts and qr have the same length. \u2002 (i)\u2002 show that the area, acm2, enclosed by the wire is given by ax x 296 32 =-. [2] \u2002 (ii)\u2002 given that x can vary, find the stationary value of a and determine the nature of this  stationary value. [4]",
            "8": "8 0606/23/m/j/13 \u00a9 ucles 2013 for examiner\u2019s use6\u2002 find the equation of the normal to the curve yxx 282 =-+ at the point on the curve where x = 4.  [6]",
            "9": "9 0606/23/m/j/13 \u00a9 ucles 2013 [turn over for examiner\u2019s use7\u2002 (i)\u2002 find the first four terms in the expansion of ( ) x 26+  in ascending powers of x. [3] \u2002 (ii)\u2002 hence find the coefficient of x3 in the expansion of x x x 1 3 1 26+ - +^ ^ ^ h h h . [4]",
            "10": "10 0606/23/m/j/13 \u00a9 ucles 2013 for examiner\u2019s use8\u2002 the line\u2002 2 8 y x= -  cuts the curve 2 5 32 0x y xy2 2+ - + =  at the points a and b. find the  length of the line ab. [7]",
            "11": "11 0606/23/m/j/13 \u00a9 ucles 2013 [turn over for examiner\u2019s use9\u2002 it is given that x \u2208 \ue052\u2002and that \ue025 = {x : \u2212 5 < x < 12}, \u2002    s = {x : 5x + 24 > x2}, \u2002    t = {x : 2x + 7 > 15}. \u2002 find the values of x such that \u2002 (i)\u2002 x s!, [3] \u2002 (ii)\u2002 x s tj! , [2] \u2002 (iii)\u2002 ( )x s tk! l. [3]",
            "12": "12 0606/23/m/j/13 \u00a9 ucles 2013 for examiner\u2019s use10\u2002 a plane, whose speed in still air is 240 kmh\u20131, flies directly from a to b, where b is 500 km from  a on a bearing of 032\u00b0. there is a constant wind of 50 kmh\u20131 blowing from the west. \u2002 (i)\u2002 find the bearing on which the plane is steered. [4]",
            "13": "13 0606/23/m/j/13 \u00a9 ucles 2013 [turn over for examiner\u2019s use\u2002 (ii)\u2002 find, to the nearest minute, the time taken for the flight. [4]",
            "14": "14 0606/23/m/j/13 \u00a9 ucles 2013 for examiner\u2019s use11\u2002 a one-one function f is defined by ( ) ( 1) 5x xf2= - -  for x kh. \u2002 (i)\u2002 state the least value that k can take. [1] \u2002 for this least value of k \u2002 (ii)\u2002 write down the range of f, [1] \u2002 (iii)\u2002 find ( )x f1 -, [2]",
            "15": "15 0606/23/m/j/13 \u00a9 ucles 2013 [turn over for examiner\u2019s use\u2002 (iv)\u2002 sketch and label, on the axes below, the graph of ( ) y x f=  and of ( ) y x f1=-, [2] x oy y = x \u2002 (v)\u2002 find the value of x for which ( ) ( )x xf f1=-. [2] question\u200212\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.",
            "16": "16 0606/23/m/j/13 \u00a9 ucles 2013 for examiner\u2019s use12\u2002 the function   ( )x x x ax bf3 2= + + +    is divisible by x3- and leaves a remainder  of 20 when divided by x1+. \u2002 (i)\u2002 show that b6= and find the value of a. [4] \u2002 (ii)\u2002 using your value of a and taking b as 6, find the non-integer roots of the equation ( ) 0xf=  in the form p q! , where p and q are integers. [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. 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."
        },
        "0606_w13_qp_11.pdf": {
            "1": "this document consists of 16 printed pages. dc (cw/cgw) 67138/4 \u00a9 ucles 2013 [turn overuniversity of cambridge international examinations international general certificate of secondary education * 2 6 4 7 3 8 5 2 4 6 * additional mathematics  0606/11 paper 1 october/november 2013  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid.do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/11/o/n/13 \u00a9 ucles 2013mathematical formulae 1.\u2002algebra quadratic\u2002equation  for the equation ax2 + bx + c = 0, xab b ac 242!=- - . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/11/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use1\u2002 the diagram shows the graph of ( ) sin y a bx c= +  for 0 2xg g r, where a, b and c are positive  integers. 4 3 2 1 oy x \u20131 \u20132 \u20133\ufffd 2\ufffd \u2002 state the value of a, of b and of c. [3] \u2002 a = b = c =  2\u2002 find the set of values of k for which the curve ( ) ( ) y k x x k 1 3 12= + - + +  lies below the  x-axis. [4]",
            "4": "4 0606/11/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use3\u2002 show that 1 12cossin sincossecii iii+++= . [4]",
            "5": "5 0606/11/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use4\u2002 the sets a and b are such that : , cos a x x x210 6 0 2 \u00b0 \u00b0g g = =$ ., : , tan b x x x 3 0 6 0 2 \u00b0 \u00b0g g = =\" ,. \u2002 (i)\u2002 find n(a). [1] \u2002 (ii)\u2002 find n(b). [1] \u2002 (iii)\u2002 find the elements of a , b. [1] \u2002 (iv)\u2002 find the elements of a + b. [1]",
            "6": "6 0606/11/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use5\u2002 (i)\u2002 find (9 3 ) sin x xd +y . [3] \u2002 (ii)\u2002 hence show that r ( ) sin x x a b 9 3 d 9r + = +ry , where a and b are constants to be found. [3]",
            "7": "7 0606/11/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use6\u2002 the function ( ) 4 2x ax x bxf3 2= + + - , where a and b are constants, is such that x2 1-  is a  factor. given that the remainder when ( )xf is divided by x2- is twice the remainder when ( )xf  is divided by x1+, find the value of a and of b. [6]",
            "8": "8 0606/11/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use7\u2002 (a)\u2002 (i)\u2002 find how many different 4-digit numbers can be formed from the digits \u2002 \u2002 \u2002 1, 3, 5, 6, 8 and 9  if each digit may be used only once. [1] \u2002 \u2002 (ii)\u2002 find how many of these 4-digit numbers are even. [1] \u2002 (b)\u2002 a team of 6 people is to be selected from 8 men and 4 women. find the number of different  teams that can be selected if \u2002 \u2002 (i)\u2002 there are no restrictions, [1] \u2002 \u2002 (ii)\u2002 the team contains all 4 women, [1] \u2002 \u2002 (iii)\u2002 the team contains at least 4 men. [3]",
            "9": "9 0606/11/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use8\u2002 (i)\u2002 on the grid below, sketch the graph of ( ) ( ) y x x 2 3 = - + for x5 4g g- , and  \u2002 \u2002 state the coordinates of the points where the curve meets the coordinate axes. [4] y x \u20135 \u20134 \u20133 \u20132 \u20131 1 3 24 o \u2002 (ii)\u2002 find the coordinates of the stationary point on the curve ( ) ( ) y x x 2 3 = - + . [2] \u2002 (iii)\u2002 given that k is a positive constant, state the set of values of k for which  \u2002 \u2002 ( ) ( )x x k 2 3- + =  has 2 solutions only. [1]",
            "10": "10 0606/11/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use9\u2002 (a)\u2002 differentiate ( ) lnx x4 2 13+  with respect to x. [3] \u2002 (b)\u2002 (i)\u2002 given that yxx 22=+, show that xy xx 24 dd 3= ++ ^ h. [4]",
            "11": "11 0606/11/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use\u2002 \u2002 (ii)\u2002 hence find yxxx 25 20d3++c edd^ h. [2] \u2002 \u2002 (iii)\u2002 hence evaluate  27yxxx 25 20d 27 3++c edd^ h. [2]",
            "12": "12 0606/11/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use10\u2002 solutions\u2002to\u2002this\u2002question\u2002by\u2002accurate\u2002drawing\u2002will\u2002not\u2002be\u2002accepted. \u2002 the points ( , )a 3 2-  and ( , )b1 4 are vertices of an isosceles triangle abc , where angle \u00b0 b 90= . \u2002 (i)\u2002 find the length of the line ab. [1] \u2002 (ii)\u2002 find the equation of the line bc. [3]",
            "13": "13 0606/11/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use\u2002 \u2002 (iii)\u2002 find the coordinates of each of the two possible positions of c. [6]",
            "14": "14 0606/11/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use11\u2002 (a)\u2002 it is given that the matrix 2 431a=j lkkn poo. \u2002 \u2002 (i)\u2002 find a + 2i. [1] \u2002 \u2002 (ii)\u2002 find a 2. [2] \u2002 \u2002 (iii)\u2002 using your answer to part (ii) find the matrix b such that a2b = i. [2]",
            "15": "15 0606/11/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use\u2002 (b)\u2002 given that the matrix cx xx 11 2=- +- x1-j lkkn poo, show that det 0c!. [4] 12\u2002 (a)\u2002 a function f is such that ( ) 3 1x xf2= -   for x 10 8g g- . \u2002 \u2002 (i)\u2002 find the range of f. [3] \u2002 \u2002 (ii)\u2002 write down a suitable domain for f for which f1 - exists. [1] question\u200212(b)\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.",
            "16": "16 0606/11/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use\u2002 (b)\u2002 functions g and h are defined by ( ) 4 2xg ex= -  for  xrd , ( ) 5 lnx xh=  for  x02. \u2002 \u2002 (i)\u2002 find ( )x g1 -. [2] \u2002 \u2002 (ii)\u2002 solve ( ) 18xgh= . [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. 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."
        },
        "0606_w13_qp_12.pdf": {
            "1": "this document consists of 16 printed pages. dc (sjw/cgw) 80816 \u00a9 ucles 2013 [turn overuniversity of cambridge international examinations international general certificate of secondary education * 0 9 8 6 6 1 0 4 7 5 * additional mathematics  0606/12 paper 1 october/november 2013  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid.do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/12/o/n/13 \u00a9 ucles 2013mathematical formulae 1.\u2002algebra quadratic\u2002equation  for the equation ax2 + bx + c = 0, xab b ac 242!=- - . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/12/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use1\u2002 the diagram shows the graph of ( ) sin y a bx c= +  for 0 2xg g r, where a, b and c are positive  integers. 4 3 2 1 oy x \u20131 \u20132 \u20133\ufffd 2\ufffd \u2002 state the value of a, of b and of c. [3] \u2002 a = b = c =  2\u2002 find the set of values of k for which the curve ( ) ( ) y k x x k 1 3 12= + - + +  lies below the  x-axis. [4]",
            "4": "4 0606/12/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use3\u2002 show that 1 12cossin sincossecii iii+++= . [4]",
            "5": "5 0606/12/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use4\u2002 the sets a and b are such that : , cos a x x x210 6 0 2 \u00b0 \u00b0g g = =$ ., : , tan b x x x 3 0 6 0 2 \u00b0 \u00b0g g = =\" ,. \u2002 (i)\u2002 find n(a). [1] \u2002 (ii)\u2002 find n(b). [1] \u2002 (iii)\u2002 find the elements of a , b. [1] \u2002 (iv)\u2002 find the elements of a + b. [1]",
            "6": "6 0606/12/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use5\u2002 (i)\u2002 find (9 3 ) sin x xd +y . [3] \u2002 (ii)\u2002 hence show that r ( ) sin x x a b 9 3 d 9r + = +ry , where a and b are constants to be found. [3]",
            "7": "7 0606/12/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use6\u2002 the function ( ) 4 2x ax x bxf3 2= + + - , where a and b are constants, is such that x2 1-  is a  factor. given that the remainder when ( )xf is divided by x2- is twice the remainder when ( )xf  is divided by x1+, find the value of a and of b. [6]",
            "8": "8 0606/12/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use7\u2002 (a)\u2002 (i)\u2002 find how many different 4-digit numbers can be formed from the digits \u2002 \u2002 \u2002 1, 3, 5, 6, 8 and 9  if each digit may be used only once. [1] \u2002 \u2002 (ii)\u2002 find how many of these 4-digit numbers are even. [1] \u2002 (b)\u2002 a team of 6 people is to be selected from 8 men and 4 women. find the number of different  teams that can be selected if \u2002 \u2002 (i)\u2002 there are no restrictions, [1] \u2002 \u2002 (ii)\u2002 the team contains all 4 women, [1] \u2002 \u2002 (iii)\u2002 the team contains at least 4 men. [3]",
            "9": "9 0606/12/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use8\u2002 (i)\u2002 on the grid below, sketch the graph of ( ) ( ) y x x 2 3 = - + for x5 4g g- , and  \u2002 \u2002 state the coordinates of the points where the curve meets the coordinate axes. [4] y x \u20135 \u20134 \u20133 \u20132 \u20131 1 3 24 o \u2002 (ii)\u2002 find the coordinates of the stationary point on the curve ( ) ( ) y x x 2 3 = - + . [2] \u2002 (iii)\u2002 given that k is a positive constant, state the set of values of k for which  \u2002 \u2002 ( ) ( )x x k 2 3- + =  has 2 solutions only. [1]",
            "10": "10 0606/12/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use9\u2002 (a)\u2002 differentiate ( ) lnx x4 2 13+  with respect to x. [3] \u2002 (b)\u2002 (i)\u2002 given that yxx 22=+, show that xy xx 24 dd 3= ++ ^ h. [4]",
            "11": "11 0606/12/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use\u2002 \u2002 (ii)\u2002 hence find yxxx 25 20d3++c edd^ h. [2] \u2002 \u2002 (iii)\u2002 hence evaluate  27yxxx 25 20d 27 3++c edd^ h. [2]",
            "12": "12 0606/12/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use10\u2002 solutions\u2002to\u2002this\u2002question\u2002by\u2002accurate\u2002drawing\u2002will\u2002not\u2002be\u2002accepted. \u2002 the points ( , )a 3 2-  and ( , )b1 4 are vertices of an isosceles triangle abc , where angle \u00b0 b 90= . \u2002 (i)\u2002 find the length of the line ab. [1] \u2002 (ii)\u2002 find the equation of the line bc. [3]",
            "13": "13 0606/12/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use\u2002 \u2002 (iii)\u2002 find the coordinates of each of the two possible positions of c. [6]",
            "14": "14 0606/12/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use11\u2002 (a)\u2002 it is given that the matrix 2 431a=j lkkn poo. \u2002 \u2002 (i)\u2002 find a + 2i. [1] \u2002 \u2002 (ii)\u2002 find a 2. [2] \u2002 \u2002 (iii)\u2002 using your answer to part (ii) find the matrix b such that a2b = i. [2]",
            "15": "15 0606/12/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use\u2002 (b)\u2002 given that the matrix cx xx 11 2=- +- x1-j lkkn poo, show that det 0c!. [4] 12\u2002 (a)\u2002 a function f is such that ( ) 3 1x xf2= -   for x 10 8g g- . \u2002 \u2002 (i)\u2002 find the range of f. [3] \u2002 \u2002 (ii)\u2002 write down a suitable domain for f for which f1 - exists. [1] question\u200212(b)\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.",
            "16": "16 0606/12/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use\u2002 (b)\u2002 functions g and h are defined by ( ) 4 2xg ex= -  for  xrd , ( ) 5 lnx xh=  for  x02. \u2002 \u2002 (i)\u2002 find ( )x g1 -. [2] \u2002 \u2002 (ii)\u2002 solve ( ) 18xgh= . [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. 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."
        },
        "0606_w13_qp_13.pdf": {
            "1": "* 0 7 4 8 0 0 0 4 4 7 * this document consists of 16 printed pages. dc (nh/cgw) 67137/4 \u00a9 ucles 2013 [turn overuniversity of cambridge international examinations international general certificate of secondary education additional mathematics 0606/13 paper 1 october/november 2013  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid.do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/13/o/n/13 \u00a9 ucles 2013mathematical formulae 1.\u2002algebra quadratic\u2002equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2 . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/13/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use1\u2002 the coefficient of x2 in the expansion of px26+^ h  is 60. \u2002 (i)\u2002 find the value of the positive constant p. [3] \u2002 (ii)\u2002 using your value of p, find the coefficient of x2 in the expansion of x px3 26- +^ ^ h h . [3]",
            "4": "4 0606/13/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use2\u2002 solve lg lgy y2 5 60 1- + = ^ h . [5]",
            "5": "5 0606/13/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use3\u2002 show that tan sin sin sec2 2 4 2i i i i- = . [4]",
            "6": "6 0606/13/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use4\u2002 a curve has equation ey x3x 22 = +^ h . \u2002 (i)\u2002 show that dd e xy xa x 32x 32 = ++ ^^ hh, where a is a constant to be found. [4] \u2002 (ii)\u2002 find the exact coordinates of the point on the curve where dd xy0=. [2]",
            "7": "7 0606/13/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use5\u2002 for xr!, the functions f and g are defined by \u2002   fx x 23= ^ h , \u2002   g x x x 4 52= - ^ h . \u2002 (i)\u2002 express f212c m as a power of 2. [2] \u2002 (ii)\u2002 find the values of x for which f and g are increasing at the same rate with respect to x. [4]",
            "8": "8 0606/13/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use6\u2002 do\u2002not\u2002use\u2002a\u2002calculator\u2002in\u2002this\u2002question. \u2002 the diagram shows part of the curve y x42= - . o4y xy = 4 \u2013 x 2 2 \u2002 show that the area of the shaded region can be written in the form p2, where p is an integer to  be found. [6]",
            "9": "9 0606/13/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use7\u2002 it is given that at t t t2 12 2=- +c m . \u2002 (i)\u2002 find the value of t for which det a = 1. [3] \u2002 (ii)\u2002 in the case when t3=, find a\u20131 and hence solve      x y3 5+ = ,      x y7 3 11+ = .  [5]",
            "10": "10 0606/13/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use8\u2002 the diagram shows two concentric circles, centre o, radii 4 cm and 6 cm. the points a and b lie  on the larger circle and the points c and d lie on the smaller circle such that oda and ocb are  straight lines. a d 4 cmrad2 cm bc oi \u2002 (i)\u2002 given that the area of triangle ocd is 7.5 cm2, show that 1.215i=  radians, to 3 decimal  places. [2] \u2002 (ii)\u2002 find the perimeter of the shaded region. [4]",
            "11": "11 0606/13/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use\u2002 (iii)\u2002 find the area of the shaded region. [3]",
            "12": "12 0606/13/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use9\u2002 (a)\u2002 (i)\u2002 solve  sin cosx x 6 52= +    for x 0 180\u00b0 \u00b01 1 . [4] \u2002 \u2002 (ii)\u2002 hence, or otherwise, solve  cos siny y 6 52= +   for y 0 180\u00b0 \u00b01 1 . [3]",
            "13": "13 0606/13/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use\u2002 (b)\u2002 solve  cot cotz z 4 3 02- =   for  z 01 1 r radians. [4]",
            "14": "14 0606/13/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use10\u2002 the variables s and t are related by the equation t ksn= , where k and n are constants. the table  below shows values of variables s and t. s 2 4 6 8 t 25.00 6.25 2.78 1.56 \u2002 (i)\u2002 a straight line graph is to be drawn for this information with lg t plotted on the vertical axis.  state the variable which must be plotted on the horizontal axis. [1] \u2002 (ii)\u2002 draw this straight line graph on the grid below. [3] o121g t",
            "15": "15 0606/13/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use\u2002 (iii)\u2002 use your graph to find the value of k and of n. [4] \u2002 (iv)\u2002 estimate the value of s when t = 4. [2] question\u200211\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.",
            "16": "16 0606/13/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use 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. 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.11\u2002 (i)\u2002 given that e e dx225 43x xk2 2 0\u2013- = <c m , where k is a constant, show that     4e 12e 5 0k k4 2- + = . [5] \u2002 (ii)\u2002 using a substitution of eyk2= , or otherwise, find the possible values of k. [4]"
        },
        "0606_w13_qp_21.pdf": {
            "1": "this document consists of 18 printed pages and 2 blank pages. dc (leg/sw) 67890/2 \u00a9 ucles 2013 [turn overuniversity of cambridge international examinations international general certificate of secondary education * 0 9 1 7 8 8 6 3 7 4 * additional mathematics 0606/21 paper 2 october/november 2013  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid.do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/21/o/n/13 \u00a9 ucles 2013mathematical formulae 1.\u2002algebra quadratic\u2002equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2 . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/21/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use1\u2002 find the set of values of x for which x x 6 521- . [3]",
            "4": "4 0606/21/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use2\u2002do\u2002not\u2002use\u2002a\u2002calculator\u2002in\u2002this\u2002question. \u2002 express 54 5 122 -- ^ h in the form p q5+, where p and q are integers. [4]",
            "5": "5 0606/21/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use3\u2002 (i)\u2002 given that y x4158 = -j lkkn poo, find dd xy. [2] \u2002 (ii)\u2002 hence find the approximate change in y as x increases from 12 to p 12+, where p is small.  [2]",
            "6": "6 0606/21/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use4\u2002 given that logx 5p= and logy 2p=, find \u2002 (i)\u2002 logxp2, [1] \u2002 (ii)\u2002 logx1 p, [1] \u2002 (iii)\u2002 log pxy. [2]",
            "7": "7 0606/21/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use5\u2002 solve the simultaneous equations \u2002     , 25641024yx = \u2002     3 9 243.x y2#=  [5]",
            "8": "8 0606/21/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use6\u2002 (a)\u2002 (i)\u2002 find the coefficient of x3 in the expansion of x 1 26-^ h . [2] \u2002 \u2002 (ii)\u2002 find the coefficient of x3 in the expansion of x12+e o x 1 26-^ h . [3] \u2002 (b)\u2002 expand x x214 + e o  in a series of powers of x with integer coefficients. [3]",
            "9": "9 0606/21/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use7\u2002 x cm \u2002 the diagram shows a box in the shape of a cuboid with a square cross-section of side x cm. the  volume of the box is 3500 cm3. four pieces of tape are fastened round the box as shown. the  pieces of tape are parallel to the edges of the box. \u2002 (i)\u2002 given that the total length of the four pieces of tape is l cm, show that l x x147000 2= + . [3] \u2002 (ii)\u2002 given that x can vary, find the stationary value of l and determine the nature of this stationary  value. [5]",
            "10": "10 0606/21/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use8\u2002 the table shows experimental values of two variables x and y. x 2 4 6 8 y 9.6 38.4 105 232 \u2002 it is known that x and y are related by the equation y ax bx3= + , where a and b are constants. \u2002 (i)\u2002 a straight line graph is to be drawn for this information with xy on the vertical axis. state the  variable which must be plotted on the horizontal axis. [1] \u2002 (ii)\u2002 draw this straight line graph on the grid below. [2] o102030y x",
            "11": "11 0606/21/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use\u2002 (iii)\u2002 use your graph to estimate the value of a and of b. [3] \u2002 (iv)\u2002 estimate the value of x for which y x2 25= . [2]",
            "12": "12 0606/21/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use9\u2002 40 m 70 m1.8 m s\u20131 pq \u2002 the diagram shows a river with parallel banks. the river is 40 m wide and is flowing with a  speed of 1.8 ms\u20131. a canoe travels in a straight line from a point p on one bank to a point q on  the opposite bank 70 m downstream from p. given that the canoe takes 12 s to travel from p to q,  calculate the speed of the canoe in still water and the angle to the bank that the canoe was steered. [8]",
            "13": "13 0606/21/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use",
            "14": "14 0606/21/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use10 1.4 rado a b12 cm \u2002 the diagram shows a circle with centre o and a chord ab. the radius of the circle is 12 cm and  angle aob is 1.4 radians. \u2002 (i)\u2002 find the perimeter of the shaded region. [5]",
            "15": "15 0606/21/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use\u2002 (ii)\u2002 find the area of the shaded region. [4]",
            "16": "16 0606/21/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use11 o qp (9, e3)y xyex 3= \u2002 the diagram shows part of the curve e yx 3= . the tangent to the curve at , ep93^ h  meets the  x-axis at q. \u2002 (i)\u2002 find the coordinates of q. [4]",
            "17": "17 0606/21/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use\u2002 (ii)\u2002 find the area of the shaded region bounded by the curve, the coordinate axes and the tangent  to the curve at p. [6]",
            "18": "18 0606/21/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use12\u2002 (a)\u2002 solve the equation    coseccosxx270 + =  for 0\u00b0 360\u00b0 xg g  . [4] \u2002 (b)\u2002 solve the equation    sin y 7 2 1 5 - = ^ h  for  y0 5g g  radians. [5]",
            "19": "19 0606/21/o/n/13 \u00a9 ucles 2013blank\u2002page",
            "20": "20 0606/21/o/n/13 \u00a9 ucles 2013permission 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. 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.blank\u2002page"
        },
        "0606_w13_qp_22.pdf": {
            "1": "this document consists of 18 printed pages and 2 blank pages. dc (sjw/sw) 81064 \u00a9 ucles 2013 [turn overuniversity of cambridge international examinations international general certificate of secondary education * 3 0 3 1 9 4 4 7 2 3 * additional mathematics 0606/22 paper 2 october/november 2013  2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid.do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/22/o/n/13 \u00a9 ucles 2013mathematical formulae 1.\u2002algebra quadratic\u2002equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2 . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/22/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use1\u2002 find the set of values of x for which x x 6 521- . [3]",
            "4": "4 0606/22/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use2\u2002do\u2002not\u2002use\u2002a\u2002calculator\u2002in\u2002this\u2002question. \u2002 express 54 5 122 -- ^ h in the form p q5+, where p and q are integers. [4]",
            "5": "5 0606/22/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use3\u2002 (i)\u2002 given that y x4158 = -j lkkn poo, find dd xy. [2] \u2002 (ii)\u2002 hence find the approximate change in y as x increases from 12 to p 12+, where p is small.  [2]",
            "6": "6 0606/22/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use4\u2002 given that logx 5p= and logy 2p=, find \u2002 (i)\u2002 logxp2, [1] \u2002 (ii)\u2002 logx1 p, [1] \u2002 (iii)\u2002 log pxy. [2]",
            "7": "7 0606/22/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use5\u2002 solve the simultaneous equations \u2002     , 25641024yx = \u2002     3 9 243.x y2#=  [5]",
            "8": "8 0606/22/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use6\u2002 (a)\u2002 (i)\u2002 find the coefficient of x3 in the expansion of x 1 26-^ h . [2] \u2002 \u2002 (ii)\u2002 find the coefficient of x3 in the expansion of x12+e o x 1 26-^ h . [3] \u2002 (b)\u2002 expand x x214 + e o  in a series of powers of x with integer coefficients. [3]",
            "9": "9 0606/22/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use7\u2002 x cm \u2002 the diagram shows a box in the shape of a cuboid with a square cross-section of side x cm. the  volume of the box is 3500 cm3. four pieces of tape are fastened round the box as shown. the  pieces of tape are parallel to the edges of the box. \u2002 (i)\u2002 given that the total length of the four pieces of tape is l cm, show that l x x147000 2= + . [3] \u2002 (ii)\u2002 given that x can vary, find the stationary value of l and determine the nature of this stationary  value. [5]",
            "10": "10 0606/22/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use8\u2002 the table shows experimental values of two variables x and y. x 2 4 6 8 y 9.6 38.4 105 232 \u2002 it is known that x and y are related by the equation y ax bx3= + , where a and b are constants. \u2002 (i)\u2002 a straight line graph is to be drawn for this information with xy on the vertical axis. state the  variable which must be plotted on the horizontal axis. [1] \u2002 (ii)\u2002 draw this straight line graph on the grid below. [2] o102030y x",
            "11": "11 0606/22/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use\u2002 (iii)\u2002 use your graph to estimate the value of a and of b. [3] \u2002 (iv)\u2002 estimate the value of x for which y x2 25= . [2]",
            "12": "12 0606/22/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use9\u2002 40 m 70 m1.8 m s\u20131 pq \u2002 the diagram shows a river with parallel banks. the river is 40 m wide and is flowing with a  speed of 1.8 ms\u20131. a canoe travels in a straight line from a point p on one bank to a point q on  the opposite bank 70 m downstream from p. given that the canoe takes 12 s to travel from p to q,  calculate the speed of the canoe in still water and the angle to the bank that the canoe was steered. [8]",
            "13": "13 0606/22/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use",
            "14": "14 0606/22/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use10 1.4 rado a b12 cm \u2002 the diagram shows a circle with centre o and a chord ab. the radius of the circle is 12 cm and  angle aob is 1.4 radians. \u2002 (i)\u2002 find the perimeter of the shaded region. [5]",
            "15": "15 0606/22/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use\u2002 (ii)\u2002 find the area of the shaded region. [4]",
            "16": "16 0606/22/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use11 o qp (9, e3)y xyex 3= \u2002 the diagram shows part of the curve e yx 3= . the tangent to the curve at , ep93^ h  meets the  x-axis at q. \u2002 (i)\u2002 find the coordinates of q. [4]",
            "17": "17 0606/22/o/n/13 \u00a9 ucles 2013 [turn\u2002over for examiner\u2019 s use\u2002 (ii)\u2002 find the area of the shaded region bounded by the curve, the coordinate axes and the tangent  to the curve at p. [6]",
            "18": "18 0606/22/o/n/13 \u00a9 ucles 2013 for examiner\u2019 s use12\u2002 (a)\u2002 solve the equation    coseccosxx270 + =  for 0\u00b0 360\u00b0 xg g  . [4] \u2002 (b)\u2002 solve the equation    sin y 7 2 1 5 - = ^ h  for  y0 5g g  radians. [5]",
            "19": "19 0606/22/o/n/13 \u00a9 ucles 2013blank\u2002page",
            "20": "20 0606/22/o/n/13 \u00a9 ucles 2013permission 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. 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.blank\u2002page"
        },
        "0606_w13_qp_23.pdf": {
            "1": "this document consists of 19 printed pages and 1 blank page. dc (kn/sw) 67884/4 \u00a9 ucles 2013\b [turn overuniversity of cambridge international examinations international general certificate of secondary education * 7 1 3 2 3 9 8 2 2 2 * additional mathematics\b 0606/23 paper 2\b october/november 2013 \b 2 hours candidates answer on the question paper. additional materials: electronic 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.y ou may use a pencil for any diagrams or graphs.do not use staples, paper clips, highlighters, glue or correction fluid.do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.the use of an electronic calculator is expected, where appropriate.y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/23/o/n/13 \u00a9\bucles\b2013mathematical formulae 1.\balgebra quadratic\bequation \b for\bthe\bequation\b ax2\b+\bbx\b+\bc\b=\b0, xb b ac a=\u2212 \u221224 2 binomial theorem (a\b+\bb)n\b=\ban\b+\b(n 1)an\u20131\bb\b+\b(n 2)an\u20132\bb2\b+\b\u2026\b+\b(n r)an\u2013r\bbr\b+\b\u2026\b+\b bn, \b where\b n\bis\ba\bpositive\binteger\band\b(n r)\b=\bn! (n\b\u2013\br)!r! 2.\btrigonometry identities sin2\ba\b+\bcos2\ba\b=\b1 sec2\ba\b=\b1\b+\btan2\ba cosec2\ba\b=\b1\b+\bcot2\ba formulae for \u2206abc a sin\ba = b sin\bb = c sin\bc a2\b=\bb2\b+\bc2\b\u2013\b2bc\bcos\b a \u2206\b=\b1\b 2\bbc\bsin\ba",
            "3": "3 0606/23/o/n/13 \u00a9\bucles\b2013 [turn\bover for examiner\u2019 s use1\bfind\bthe\bcoordinates\bof\bthe\bstationary\bpoints\bon\bthe\bcurve\b\b\b y\b=\bx3\b\u2013\b6x2\b\u2013\b36 x\b+\b16.\b \b [5]",
            "4": "4 0606/23/o/n/13 \u00a9\bucles\b2013 for examiner\u2019 s use2\b (i)\bfind\bhow\bmany\bdifferent\bnumbers\bcan\bbe\bformed\busing\b4\bof\bthe\bdigits\b \b \b1,\b2,\b3,\b4,\b5,\b6\band\b7\bif\bno\bdigit\bis\brepeated.\b [1] \bfind\bhow\bmany\bof\bthese\b4-digit\bnumbers\bare \b (ii)\bodd,\b [1] \b (iii)\bodd\band\bless\bthan\b3000.\b [3]",
            "5": "5 0606/23/o/n/13 \u00a9\bucles\b2013 [turn\bover for examiner\u2019 s use3\bfind\bthe\bset\bof\bvalues\bof\b k\bfor\bwhich\bthe\bline\b\b\b y\b=\b3x\b\u2013\bk\b\b\bdoes\bnot\bmeet\bthe\bcurve\b\b\b y\b=\bkx2\b+\b11 x\b\u2013\b6. \b [6]",
            "6": "6 0606/23/o/n/13 \u00a9\bucles\b2013 for examiner\u2019 s use4 y xo(0, 3) ,23rc m \b (a)\b (i)\b the\bdiagram\bshows\bthe\bgraph\bof\b y\b=\ba\b+\bc\btan( bx)\bpassing\bthrough\bthe\bpoints\b(0,\b3)\band \b \b \b ,23re o.\bfind\bthe\bvalue\bof\b a\band\bof\b b.\b [2] \b \b (ii)\b given\bthat\bthe\bpoint\b ,87re o\balso\blies\bon\bthe\bgraph,\bfind\bthe\bvalue\bof\b c.\b [1]",
            "7": "7 0606/23/o/n/13 \u00a9\bucles\b2013 [turn\bover for examiner\u2019 s use\b (b)\bgiven\bthat\b ( ) 8 5 3 cosx x f= - ,\bstate\bthe\bperiod\band\bthe\bamplitude\bof\bf.\b [2] \b \bperiod\b...\b\b\bamplitude\b...",
            "8": "8 0606/23/o/n/13 \u00a9\bucles\b2013 for examiner\u2019 s use5\b (a)\b (i)\b in\bthe\bvenn\bdiagram\bbelow\bshade\bthe\bregion\bthat\brepresents\b a bj l ^ h.\b [1] a b/h5105 \b \b (ii)\b in\bthe\bvenn\bdiagram\bbelow\bshade\bthe\bregion\bthat\brepresents\b p q rk k l.\b [1] p q r/h5105 \b (b)\bexpress,\bin\bset\bnotation,\bthe\bset\brepresented\bby\bthe\bshaded\bregion.\b [1] s t/h5105 \b answer\b\b\b...",
            "9": "9 0606/23/o/n/13 \u00a9\bucles\b2013 [turn\bover for examiner\u2019 s use\b (c)\bthe\buniversal\bset\b \ue025\band\bthe\bsets\b v\band\b w\bare\bsuch\bthat\bn( \ue025)\b=\b40,\bn( v )\b=\b18\band\bn( w)\b=\b14.\b given\bthat\b n ( )v w xk =\band\b n(( )v wj )x3=l\bfind\bthe\bvalue\bof\b x. \b \byou\bmay\buse\bthe\bvenn\bdiagram\bbelow\bto\bhelp\byou.\b [3] vw/h5105",
            "10": "10 0606/23/o/n/13 \u00a9\bucles\b2013 for examiner\u2019 s use6\bthe\bexpression\b\b\b2 x3\b+\bax2\b+\bbx\b+\b21\b\b\bhas\ba\bfactor\b\b\b x\b+\b3\b\b\band\bleaves\ba\bremainder\bof\b65\bwhen\b divided\bby\b\b\b x\b\u2013\b2. \b (i)\bfind\bthe\bvalue\bof\b a\band\bof\b b.\b [5] \b (ii)\bhence\bfind\bthe\bvalue\bof\bthe\bremainder\bwhen\bthe\bexpression\bis\bdivided\bby\b2 x\b+\b1.\b [2]",
            "11": "11 0606/23/o/n/13 \u00a9\bucles\b2013 [turn\bover for examiner\u2019 s use7\bthe\bline\b\b\b4 x\b+\by\b=\b16\b\b\bintersects\bthe\bcurve\b\b\bx y4 81 - =\b\b\bat\bthe\bpoints\b a\band\b b.\bthe\b x-coordinate\bof\b \b a\bis\bless\bthan\bthe\b x-coordinate\bof\b b.\bgiven\bthat\bthe\bpoint\b c\blies\bon\bthe\bline\b ab\bsuch\bthat\b ac :\bcb\b=\b1\b:\b2,\bfind\bthe\bcoordinates\bof\b c.\b\b [8]",
            "12": "12 0606/23/o/n/13 \u00a9\bucles\b2013 for examiner\u2019 s use8\b solutions\bto\bthis\bquestion\bby\baccurate\bdrawing\bwill\bnot\bbe\baccepted. xy x d c (10, 4) b (6, \u20134)a (\u20134, 6) o \bthe\bdiagram\bshows\ba\bquadrilateral\b abcd,\bwith\bvertices\b a(\u2212\b4,\b6),\b b(6,\b\u2212\b4),\b c(10,\b4)\band\b d. \b the\bangle\b adc\b=\b90\u00b0.\bthe\blines\b bc\band\b ad\bare\bextended\bto\bintersect\bat\bthe\bpoint\b x. \b (i)\bgiven\bthat\b c\bis\bthe\bmidpoint\bof\b bx,\bfind\bthe\bcoordinates\bof\b d.\b [7]",
            "13": "13 0606/23/o/n/13 \u00a9\bucles\b2013 [turn\bover for examiner\u2019 s use\b \b (ii)\b hence\bcalculate\bthe\barea\bof\bthe\bquadrilateral\b abcd.\b [2]",
            "14": "14 0606/23/o/n/13 \u00a9\bucles\b2013 for examiner\u2019 s use9\ba\bparticle\btravels\bin\ba\bstraight\bline\bso\bthat,\b t s\bafter\bpassing\bthrough\ba\bfixed\bpoint\b o,\bits\bvelocity,\b v\bms\u20131,\bis\bgiven\bby\b\b sin v t 3 6 2= + . \b (i)\bfind\bthe\bvelocity\bof\bthe\bparticle\bwhen\b t4r=.\b [1] \b (ii)\bfind\bthe\bacceleration\bof\bthe\bparticle\bwhen\b t\b=\b2.\b [3]",
            "15": "15 0606/23/o/n/13 \u00a9\bucles\b2013 [turn\bover for examiner\u2019 s use\bthe\bparticle\bfirst\bcomes\bto\binstantaneous\brest\bat\bthe\bpoint\b p. \b (iii)\bfind\bthe\bdistance\b op.\b \b [5]",
            "16": "16 0606/23/o/n/13 \u00a9\bucles\b2013 for examiner\u2019 s use10 120  cm30 cm h cm \b\b\b\b\b\b\b\b\b\b\b\bthe\bvolume\bof\ba\bcone\bof\b height\bh\band\bradius r\bis r h31 2r \bthe\bdiagram\bshows\ba\bcontainer\bin\bthe\bshape\bof\ba\bcone\bof\bheight\b120\bcm\band\bradius\b30\bcm.\bwater\bis\b poured\binto\bthe\bcontainer\bat\ba\brate\bof\b 20 cm s3 1r-. \b (i)\bat\bthe\binstant\bwhen\bthe\bdepth\bof\bwater\bin\bthe\bcone\bis\b h\bcm\bthe\bvolume\bof\bwater\bin\bthe\bcone\bis\b v cm3.\bshow\bthat\b vh 483r=.\b \b [3]",
            "17": "17 0606/23/o/n/13 \u00a9\bucles\b2013 [turn\bover for examiner\u2019 s use\b (ii)\bfind\bthe\brate\bat\bwhich\b h\bis\bincreasing\bwhen\b h\b=\b50.\b \b [3] \b (iii)\bfind\bthe\brate\bat\bwhich\bthe\bcircular\barea\bof\bthe\bwater\u2019s\bsurface\bis\bincreasing\bwhen\b h\b=\b50.\b [4]",
            "18": "18 0606/23/o/n/13 \u00a9\bucles\b2013 for examiner\u2019 s use11\bin\bthis\bquestion\b i\bis\ba\bunit\bvector\bdue\beast\band\b j\bis\ba\bunit\bvector\bdue\bnorth. \bat\btime\b t =\b0\bboat\b a\bleaves\bthe\borigin\b o\band\btravels\bwith\bvelocity\b(2 i\b+\b4j)\bkmh\u20131.\balso\bat\btime\b t\b=\b0\b boat\b b\b leaves\b the\b point\b with\b position\b vector\b (\u201321 i\b +\b 22j)\bkm\b and\b travels\b with\b velocity\b (5i\b+\b3j)\bkmh\u20131. \b (i)\bwrite\bdown\bthe\bposition\bvectors\bof\bboats\b a\band\b b\bafter\b t\bhours.\b [2] \b (ii)\bshow\bthat\b a\band\b b\bare\b25\bkm\bapart\bwhen\b t\b=\b2.\b [3]",
            "19": "19 0606/23/o/n/13 \u00a9\bucles\b2013 [turn\bover for examiner\u2019 s use\b (iii)\bfind\bthe\blength\bof\btime\bfor\bwhich\b a\band\b b\bare\bless\bthan\b25\bkm\bapart.\b [5]",
            "20": "20 0606/23/o/n/13 \u00a9\bucles\b2013permission 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. 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.blank\bpage"
        }
    },
    "2014": {
        "0606_s14_qp_11.pdf": {
            "1": "this document consists of 16 printed pages. dc (lk/cgw) 73326/4 \u00a9 ucles 2014  [turn overcambridge international examinations cambridge international general certificate of secondary education * 9 7 8 0 7 1 0 6 7 7 * additional mathematics  0606/11 paper 1  may/june 2014  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/11/m/j/14 \u00a9 ucles 2014mathematical formulae 1.\u2002algebra quadratic\u2002equation  for the equation ax2 + bx + c = 0, xab b ac 242!=- - binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/11/m/j/14 \u00a9 ucles 2014 [turn\u2002over1\u2002show that   . tansincossec1iiii ++=  [4]",
            "4": "4 0606/11/m/j/14 \u00a9 ucles 20142\u2002vectors a, b and c are such that , a nd a b c4 32 25 2= = =-j lkkj lkkj lkkn poon poon poo. \u2002 \u2002(i)\u2002show that . a b c = +  [2] \u2002(ii)\u2002given that a b c7 m n+ = , find the value of m and of .n [3]",
            "5": "5 0606/11/m/j/14 \u00a9 ucles 2014 [turn\u2002over3\u2002(a)\u2002on the venn diagrams below, shade the regions indicated.   a cb/h5105 a cb/h5105 a cb/h5105  (i)\u2002 c a b+ +  (ii)\u2002 a b c , + l ^ h  (iii)\u2002 a b c , + l ^ h    [3] \u2002(b)\u2002sets p and q are such that  \u2002 \u2002   : p x x x 2 02= + = \" , and : q x x x 2 7 02= + + = \" ,, where xr!. \u2002 \u2002(i)\u2002find .pn^ h [1] \u2002 \u2002(ii)\u2002find .qn^ h [1]",
            "6": "6 0606/11/m/j/14 \u00a9 ucles 20144\u2002find the set of values of k for which the line y k x4 3= -^ h  does not intersect the curve  . y x x 4 8 82= + - [5]",
            "7": "7 0606/11/m/j/14 \u00a9 ucles 2014 [turn\u2002over5\u2002(i)\u2002given that yex2= , find xy dd. [2] \u2002(ii)\u2002use your answer to part (i) to find x xe dx2y . [2] \u2002(iii)\u2002hence evaluate x xe dx 02 2y . [2]",
            "8": "8 0606/11/m/j/14 \u00a9 ucles 20146\u2002matrices a and b are such that a\u2002=\u20021 7 44 6 2-j lk kkn po oo and b = 2 31 5j lkkn poo. \u2002(i)\u2002\u2002\u2002find ab. [2] \u2002(ii)\u2002find b1-. [2] \u2002(iii)\u2002using your answer to part (ii), solve the simultaneous equations      , .x y x y4 2 3 6 10 22+ = - + = - [3]",
            "9": "9 0606/11/m/j/14 \u00a9 ucles 2014 [turn\u2002over7\u2002a curve is such that  xyx x4 11 dd 2= + +^ h for x02. the curve passes through the point ,21 65j lkkn poo. \u2002(i)\u2002find the equation of the curve.  [4] \u2002(ii)\u2002find the equation of the normal to the curve at the point where x1=.  [4]",
            "10": "10 0606/11/m/j/14 \u00a9 ucles 20148\u2002the table shows values of variables v and p. v 10 50 100 200 p 95.0 8.5 3.0 1.1 \u2002(i)\u2002by plotting a suitable straight line graph, show that v and p are related by the equation p k vn= ,  where k and n are constants.  [4] \u2002 \u2002",
            "11": "11 0606/11/m/j/14 \u00a9 ucles 2014 [turn\u2002over\u2002 use your graph to find \u2002(ii)\u2002the value of n, [2] \u2002(iii)\u2002the value of p when v35= . [2]",
            "12": "12 0606/11/m/j/14 \u00a9 ucles 20149\u2002(a)\u2002the diagram shows the velocity-time graph of a particle p moving in a straight line with velocity  vms1- at time ts after leaving a fixed point. 5 0 10 20 30 40 50 60 70t s1015v ms\u20131 \u2002 \u2002 find the distance travelled by the particle p. [2] \u2002(b)\u2002the diagram shows the displacement-time graph of a particle q moving in a straight line with  displacement sm from a fixed point at time ts. 5 0 5 10 15 20 25 30 t s1015s m 20",
            "13": "13 0606/11/m/j/14 \u00a9 ucles 2014 [turn\u2002over  on the axes below, plot the corresponding velocity-time graph for the particle q. [3] 1 0 5 10 15 20 25 30t s23v ms\u20131 \u2002(c)\u2002the displacement s m of a particle r, which is moving in a straight line, from a fixed point at  time t s is given by ln s t t 4 16 1 13 = - + +^ h .     \u2002 \u2002(i)\u2002\u2002find the value of t for which the particle r is instantaneously at rest.  [3] \u2002 \u2002(ii)\u2002find the value of t for which the acceleration of the particle r is .025ms2-. [2]",
            "14": "14 0606/11/m/j/14 \u00a9 ucles 201410\u2002(a)\u2002how many even numbers less than 500 can be formed using the digits 1, 2, 3, 4 and 5?  each digit  may be used only once in any number.  [4] \u2002(b)\u2002a committee of 8 people is to be chosen from 7 men and 5 women.  find the number of different  committees that could be selected if  \u2002 \u2002(i)\u2002 the committee contains at least 3 men and at least 3 women,  [4] \u2002 \u2002(ii)\u2002the oldest man or the oldest woman, but not both, must be included in the committee.  [2]",
            "15": "15 0606/11/m/j/14 \u00a9 ucles 2014 [turn\u2002over11\u2002(a)\u2002solve         sin c os x x 5 2 3 2 0 + =   for x 0 180 c cg g . [4] \u2002(b)\u2002solve         cot c osec y y 2 3 02+ =   for y 0 360 c cg g . [4] question\u200211(c)\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.",
            "16": "16 0606/11/m/j/14 \u00a9 ucles 2014permission 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. 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.\u2002(c)\u2002solve         3cos . z1 2 2 + =^ h   for z0 6g g  radians.  [4]"
        },
        "0606_s14_qp_12.pdf": {
            "1": "additional mathematics \b 0606/12 paper \b1\b may/june 2014 \b 2 hours candidates \banswer \bon\bthe\bquestion \bpaper. additional \bmaterials: \b electronic \bcalculator read these instructions first write \byour\bcentre \bnumber, \bcandidate \bnumber \band\bname \bon\ball\bthe\bwork \byou\bhand \bin. write \bin\bdark\bblue\bor\bblack \bpen. y ou\bmay\buse\ban\bhb\bpencil \bfor\bany\bdiagrams \bor\bgraphs. do\bnot\buse\bstaples, \bpaper \bclips, \bglue\bor\bcorrection \bfluid. do\bnot \bwrite \bin\bany \bbarcodes. answer \ball\bthe\bquestions. give \bnon-exact \bnumerical \banswers \bcorrect \bto\b3\bsignificant \bfigures, \bor\b1\bdecimal \bplace \bin\bthe\bcase \bof\b angles \bin\bdegrees, \bunless \ba\bdifferent \blevel\bof\baccuracy \bis\bspecified \bin\bthe\bquestion. the\buse\bof\ban\belectronic \bcalculator \bis\bexpected, \bwhere \bappropriate. y ou\bare\breminded \bof\bthe\bneed \bfor\bclear \bpresentation \bin\byour\banswers. at\bthe\bend\bof\bthe\bexamination, \bfasten \ball\byour\bwork \bsecurely \btogether. the\bnumber \bof\bmarks \bis\bgiven \bin\bbrackets \b[\b]\bat\bthe\bend\bof\beach \bquestion \bor\bpart\bquestion. the\btotal\bnumber \bof\bmarks \bfor\bthis\bpaper \bis\b80. this\bdocument \bconsists \bof\b15\bprinted \bpages \band\b1\bblank \bpage. dc\b(nf/cgw) \b73328/3 \u00a9\bucles \b2014\b [turn overcambridge international examinations cambridge \binternational \bgeneral \bcertificate \bof\bsecondary \beducation * 2 8 0 6 8 4 6 6 6 5 *",
            "2": "2 0606/12/m/j/14 \u00a9 ucles 2014mathematical formulae 1.\u2002algebra quadratic equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/12/m/j/14 \u00a9 ucles 2014 [turn\u2002over1\u2002show that     sincos cossin aa aa 11 +++     can be written in the form secp a , where p is an integer to be  \u2002 found.  [4]",
            "4": "4 0606/12/m/j/14 \u00a9 ucles 20142\u2002(a)\u2002on the venn diagrams below, draw sets a and b as indicated. \u2002 \u2002 (i)\u2002  (ii) /h5105 /h5105 a /h20666 b a /h20669 b = /h11632  [2] \u2002(b)\u2002the universal set % and sets  p and q are such that n( %) = 20, ( )p q 15 n,= , ( )p 13 n=  and  ( )p q 4 n+=.  find \u2002 \u2002 (i)\u2002 ( )qn , [1] \u2002 \u2002(ii)\u2002 ( )p qn, l ^ h , [1] \u2002 \u2002(iii)\u2002 ( )p qn+ l. [1]",
            "5": "5 0606/12/m/j/14 \u00a9 ucles 2014 [turn\u2002over3\u2002(i)\u2002sketch the graph of     y x x 2 1 2 = + - ^ ^ h h      for x2 3g g- , showing the coordinates of the  points where the curve meets the x- and y-axes.  [3] \u2002(ii)\u2002find the non-zero values of k for which the equation x k x 2 1 2 + = - ^ ^ h h  has two solutions only.  [2]",
            "6": "6 0606/12/m/j/14 \u00a9 ucles 20144\u2002the region enclosed by the curve     sin y x 2 3= ,     the x-axis and the line x = a , where \u2002  a 0 11 1  radian, lies entirely above the x-axis. given that the area of this region is 31 square unit,  find the value of a. [6]",
            "7": "7 0606/12/m/j/14 \u00a9 ucles 2014 [turn\u2002over5\u2002(i)\u2002given that 2 481 x y5#=, show that x y5 2 3\u2013 + = . [3] \u2002(ii)\u2002solve the simultaneous equations  2 481 x y5#= and 7 49 1x y 2# =. [4]",
            "8": "8 0606/12/m/j/14 \u00a9 ucles 20146\u2002(a)\u2002matrices x, y and z are such that x2 13 2=c m , y1 4 63 5 7=f p   and z 1 2 3=^ h .  write  \u2002 \u2002 down all the matrix products which are possible using any two of these matrices. do not  \u2002 \u2002 evaluate these products.  [2] \u2002(b)\u2002matrices a and b are such that a5 42 1=--c m  and ab3 69 3=- -c m .  find the matrix b. [5]",
            "9": "9 0606/12/m/j/14 \u00a9 ucles 2014 [turn\u2002over7\u2002the diagram shows a circle, centre o, radius 8  cm. points p and q lie on the circle such that the chord  pq = 12  cm and angle poq i= radians. p q o8 cm12 cm \u03b8 rad \u2002(i)\u2002show that .1696 i= , correct to 3 decimal places.  [2] \u2002(ii)\u2002find the perimeter of the shaded region.  [3] \u2002(iii)\u2002find the area of the shaded region.  [3]",
            "10": "10 0606/12/m/j/14 \u00a9 ucles 20148\u2002(a)\u2002(i)\u2002how many different 5-digit numbers can be formed using the digits 1, 2, 4, 5, 7 and 9 if no  digit is repeated?  [1] \u2002 \u2002(ii)\u2002how many of these numbers are even?  [1] \u2002 \u2002(iii)\u2002how many of these numbers are less than 60  000 and even?  [3] \u2002(b)\u2002how many different groups of 6 children can be chosen from a class of 18 children if the class  contains one set of twins who must not be separated?  [3]",
            "11": "11 0606/12/m/j/14 \u00a9 ucles 2014 [turn\u2002over9\u2002a solid circular cylinder has a base radius of r cm and a volume of 4000  cm3. \u2002(i)\u2002show that the total surface area, a cm2, of the cylinder is given by arr800022r = + . [3] \u2002(ii)\u2002given that r can vary, find the minimum total surface area of the cylinder, justifying that this area  is a minimum.  [6]",
            "12": "12 0606/12/m/j/14 \u00a9 ucles 201410\u2002in this question i is a unit vector due east and j is a unit vector due north. \u2002 at 12  00 hours, a ship leaves a port p and travels with a speed of 26  kmh\u20131 in the direction i j5 12+ . \u2002(i)\u2002show that the velocity of the ship is i j10 24+ ^ h  kmh\u20131. [2] \u2002(ii)\u2002write down the position vector of the ship, relative to p, at 16  00 hours.  [1] \u2002(iii)\u2002find the position vector of the ship, relative to p, t hours after 16  00 hours.  [2] \u2002 at 16  00 hours, a speedboat leaves a lighthouse which has position vector i j120 81+ ^ h  km, relative to  p, to intercept the ship. the speedboat has a velocity of i j22 30 - +^ h  kmh\u20131. \u2002(iv)\u2002find the position vector, relative to p, of the speedboat t hours after 16  00 hours.  [1]",
            "13": "13 0606/12/m/j/14 \u00a9 ucles 2014 [turn\u2002over\u2002(v)\u2002find the time at which the speedboat intercepts the ship and the position vector , relative to p, of  the point of interception.  [4]",
            "14": "14 0606/12/m/j/14 \u00a9 ucles 201411\u2002(a)\u2002solve     tan t an x x5 02+ =    for \u00b0 \u00b0x 0 180 g g . [3] \u2002(b)\u2002solve     cos s in y y 2 1 02- = -    for \u00b0 \u00b0y 0 360 g g . [4]",
            "15": "15 0606/12/m/j/14 \u00a9 ucles 2014\u2002(c)\u2002solve     secz2 26r- =` j   for z0g g r radians.  [4]",
            "16": "16 0606/12/m/j/14 \u00a9 ucles 2014permission \bto\breproduce \bitems \bwhere \bthird-party \bowned \bmaterial \bprotected \bby\bcopyright \bis\bincluded \bhas\bbeen \bsought \band\bcleared \bwhere \bpossible. \bevery \b reasonable \beffort \bhas\bbeen \bmade \bby\bthe\bpublisher \b(ucles) \bto\btrace \bcopyright \bholders, \bbut\bif\bany\bitems \brequiring \bclearance \bhave \bunwittingly \bbeen \bincluded, \bthe\b publisher \bwill\bbe\bpleased \bto\bmake \bamends \bat\bthe\bearliest \bpossible \bopportunity. university \bof\bcambridge \binternational \bexaminations \bis\bpart\bof\bthe\bcambridge \bassessment \bgroup. \bcambridge \bassessment \bis\bthe\bbrand \bname \bof\buniversity \bof\b cambridge \blocal \bexaminations \bsyndicate \b(ucles), \bwhich \bis\bitself \ba\bdepartment \bof\bthe\buniversity \bof\bcambridge.blank\u2002page"
        },
        "0606_s14_qp_13.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (cw/cgw) 73329/3 \u00a9 ucles 2014 [turn overcambridge international examinations cambridge international general certificate of secondary education *4354645867* additional mathematics  0606/13 paper 1 may/june 2014  2 hours candidates answer on the question paper. additional materials: electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/13/m/j/14 \u00a9 ucles 2014mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, xabb a c 242!=-- binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/13/m/j/14 \u00a9 ucles 2014 [turn over1 (i) show that yx x36 52=- + can be written in the form () ya x b c2=- + , where a, b and c  are constants to be found. [3]  (ii) hence, or otherwise, find the coordinates of the stationary point of the curve yx x36 52=- + .    [1] 2 given that 24 8 1xyx y4## =-and 331 xy=+, find the value of x and of y. [4]",
            "4": "4 0606/13/m/j/14 \u00a9 ucles 20143 (i) find, in terms of p, the remainder when  xp xp x 2132 2+++   is divided by x3+. [2]  (ii) hence find the set of values of p for which this remainder is negative. [3]",
            "5": "5 0606/13/m/j/14 \u00a9 ucles 2014 [turn over4 the diagram shows a thin square sheet of metal measuring 24 cm by 24 cm. a square of side x cm is  cut off from each corner. the remainder is then folded to form an open box, x cm deep, whose square  base is shown shaded in the diagram. 24 cm 24 cm x cm x cm  (i) show that the volume, v cm3, of the box is given by vx x x49 65 7 632=- + . [2]  (ii) given that x can vary, find the maximum volume of the box. [4]",
            "6": "6 0606/13/m/j/14 \u00a9 ucles 20145 (i) the first three terms in the expansion of () x 256- , in ascending powers of x, are pq xr x2++ .  find the value of each of the integers p, q and r. [3]  (ii) in the expansion of () () xa b x 2563-+ , the constant term is equal to 512 and the  coefficient of x is zero. find the value of each of the constants a and b. [4]",
            "7": "7 0606/13/m/j/14 \u00a9 ucles 2014 [turn over6 find the equation of the normal to the curve () yx x 12231=- at the point on the curve  where x2=. [6]",
            "8": "8 0606/13/m/j/14 \u00a9 ucles 20147 (a) a 5-character password is to be chosen from the letters a, b, c, d, e and the digits 4, 5, 6, 7.  each letter or digit may be used only once. find the number of different passwords that can be chosen if   (i)  there are no restrictions, [1]   (ii) the password contains 2 letters followed by 3 digits. [2]  (b) a school has 3 concert tickets to give out at random to a class of 18 boys and 15 girls.  find the number of ways in which this can be done if   (i) there are no restrictions, [1]   (ii) 2 of the tickets are given to boys and 1 ticket is given to a girl, [2]",
            "9": "9 0606/13/m/j/14 \u00a9 ucles 2014 [turn over  (iii) at least 1 boy gets a ticket. [2]",
            "10": "10 0606/13/m/j/14 \u00a9 ucles 20148 a particle moves in a straight line such that, t s after passing through a fixed point o, its velocity,  vms1-, is given by v54 et2=--.  (i) find the velocity of the particle at o. [1]  (ii) find the value of t when the acceleration of the particle is 6ms2-. [3]  (iii) find the distance of the particle from o when . t15= . [5]  (iv) explain why the particle does not return to o. [1]",
            "11": "11 0606/13/m/j/14 \u00a9 ucles 2014 [turn over9 solve  (i) sin cos cosxx x 32 =      for \u00b0\u00b0x 0 180gg , [4]  (ii) sin cosyy 10 82+=      for \u00b0\u00b0y 0 360gg . [5]",
            "12": "12 0606/13/m/j/14 \u00a9 ucles 201410 the table shows experimental values of x and y. x 1.50 1.75 2.00 2.25 y 3.9 8.3 19.5 51.7  (i) complete the following table. x2 1g y  [1]  (ii) by plotting a suitable straight line graph on the grid on page 13, show that x and y are related    by the equation ya bx2= , where a and b are constants. [2]  (iii) use your graph to find the value of a and of b. [4]  (iv) estimate the value of y when . x12 5= . [2]",
            "13": "13 0606/13/m/j/14 \u00a9 ucles 2014 [turn over2 1 \u201310 1 2 3 4 5 6",
            "14": "14 0606/13/m/j/14 \u00a9 ucles 201411 the diagram shows the graph of cos sinyx x 33 3 =+ , which crosses the x-axis at a and has a  maximum point at b. b a xy ocos sinyx x 33 3 =+  (i) find the x-coordinate of a. [3]  (ii) find xy dd and hence find the x-coordinate of b. [4]",
            "15": "15 0606/13/m/j/14 \u00a9 ucles 2014 (iii) showing all your working, find the area of the shaded region bounded by the curve, the x-axis  and the line through b parallel to the y-axis. [5]",
            "16": "16 0606/13/m/j/14 \u00a9 ucles 2014permission 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. 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.blank page"
        },
        "0606_s14_qp_21.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (rw/sw) 73390/3 \u00a9 ucles 2014  [turn overcambridge international examinations cambridge international general certificate of secondary education * 8 6 5 2 2 2 4 7 5 1 * additional mathematics  0606/21 paper 2  may/june 2014  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of   angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/21/m/j/14 \u00a9 ucles 2014mathematical formulae 1.\u2002algebra quadratic \u2002equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/21/m/j/14 \u00a9 ucles 2014 [turn\u2002over1\u2002find the set of values of x for which  x x x 21+^ h . [3] 2\u2002without\u2002using\u2002a\u2002calculator , express  6 1 32+-^ h   in the form  a b 3+ , where a and b are integers to  be found.  [4]",
            "4": "4 0606/21/m/j/14 \u00a9 ucles 20143\u2002(i)\u2002on the axes below, sketch the graph of  y x x4 2 = - + ^ ^ h h   showing the coordinates of the points  where the curve meets the x-axis.  [2] y x o \u2002(ii)\u2002find the set of values of k for which  x x k 4 2- + = ^ ^ h h   has four solutions.  [3]",
            "5": "5 0606/21/m/j/14 \u00a9 ucles 2014 [turn\u2002over4\u2002the expression x ax bx2 123 2+ + +  has a factor x4- and leaves a remainder of 12- when divided by  x1-. find the value of each of the constants a and b. [5]",
            "6": "6 0606/21/m/j/14 \u00a9 ucles 20145\u2002(i)\u2002express  x x2 62- +   in the form  p x q r2- +^ h , where p, q and r are constants to be found.  [3] \u2002(ii)\u2002hence state the least value of  x x2 62- +   and the value of x at which this occurs.  [2]",
            "7": "7 0606/21/m/j/14 \u00a9 ucles 2014 [turn\u2002over6\u2002(a)\u2002find the coefficient of x5 in the expansion of  x 3 28-^ h . [2] \u2002(b)\u2002(i)\u2002write down the first three terms in the expansion of  x 1 26+^ h   in ascending powers of x. [2] \u2002 \u2002(ii)\u2002in the expansion of  ax x 1 1 26+ +^ ^ h h , the coefficient of x2 is 1.5 times the coefficient of x.  find the value of the constant a. [4]",
            "8": "8 0606/21/m/j/14 \u00a9 ucles 20147\u2002given that a curve has equation  yxx12 = + , where x02, find \u2002(i)\u2002xy dd , [2] \u2002(ii)\u2002xy dd 22  . [2] \u2002 hence, or otherwise, find \u2002(iii)\u2002the coordinates and nature of the stationary point of the curve.  [4]",
            "9": "9 0606/21/m/j/14 \u00a9 ucles 2014 [turn\u2002over8\u2002a sector of a circle of radius r cm has an angle of i radians, where r1i . the perimeter of the sector  is 30  cm. \u2002(i)\u2002show that the area, a cm2, of the sector is given by  a r r 152= - . [3] \u2002(ii)\u2002given that r can vary, find the maximum area of the sector.  [3]",
            "10": "10 0606/21/m/j/14 \u00a9 ucles 20149\u2002solutions \u2002to\u2002this\u2002question\u2002by\u2002accurate\u2002drawing\u2002will\u2002not\u2002be\u2002accepted. \u2002 the points ,a p 1^ h , ,b1 6^ h , ,c q4^ h  and ,d5 4^ h , where p and q are constants, are the vertices of a kite  abcd . the diagonals of the kite, ac and bd, intersect at the point e. the line ac is the perpendicular  bisector of bd. find \u2002(i)\u2002the coordinates of e, [2] \u2002(ii)\u2002the equation of the diagonal ac, [3]",
            "11": "11 0606/21/m/j/14 \u00a9 ucles 2014 [turn\u2002over\u2002(iii)\u2002the area of the kite abcd . [3]",
            "12": "12 0606/21/m/j/14 \u00a9 ucles 201410\u2002find  xy dd  when \u2002(i)\u2002 cos sin y xx23=j lkkn poo, [4] \u2002(ii)\u2002lntanyxx l=+. [4]",
            "13": "13 0606/21/m/j/14 \u00a9 ucles 2014 [turn\u2002over11\u2002(a)\u2002solve 2641 x x52=-. [4] \u2002(b)\u2002by changing the base of log 4a2, express  log log 4 2la a 2+ ^ ^ h h   as a single logarithm to base  a. [4]",
            "14": "14 0606/21/m/j/14 \u00a9 ucles 201412\u2002the functions f and g are defined by     xxx 12f=+^ h  for x02,     x x 1 g= + ^ h  for x 12-. \u2002(i)\u2002find 8fg^ h. [2] \u2002(ii)\u2002find an expression for xf2^ h, giving your answer in the form bx cax +, where a, b and c are integers  to be found.  [3] \u2002(iii)\u2002find an expression for x g1-^ h, stating its domain and range.  [4]",
            "15": "15 0606/21/m/j/14 \u00a9 ucles 2014\u2002(iv)\u2002on the same axes, sketch the graphs of y xg= ^ h and y xg1=-^ h, indicating the geometrical  relationship between the graphs.  [3] y x o",
            "16": "16 0606/21/m/j/14 \u00a9 ucles 2014blank\u2002page 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. 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."
        },
        "0606_s14_qp_22.pdf": {
            "1": "additional mathematics \b 0606/22 paper \b2\b may/june 2014 \b 2 hours candidates \banswer \bon\bthe\bquestion \bpaper. additional \bmaterials: \b electronic \bcalculator read these instructions first write \byour\bcentre \bnumber, \bcandidate \bnumber \band\bname \bon\ball\bthe\bwork \byou\bhand \bin. write \bin\bdark\bblue\bor\bblack \bpen. y ou\bmay\buse\ban\bhb\bpencil \bfor\bany\bdiagrams \bor\bgraphs. do\bnot\buse\bstaples, \bpaper \bclips, \bglue\bor\bcorrection \bfluid. do\bnot \bwrite \bin\bany \bbarcodes. answer \ball\bthe\bquestions. give \bnon-exact \bnumerical \banswers \bcorrect \bto\b3\bsignificant \bfigures, \bor\b1\bdecimal \bplace \bin\bthe\bcase \bof\b angles \bin\bdegrees, \bunless \ba\bdifferent \blevel\bof\baccuracy \bis\bspecified \bin\bthe\bquestion. the\buse\bof\ban\belectronic \bcalculator \bis\bexpected, \bwhere \bappropriate. y ou\bare\breminded \bof\bthe\bneed \bfor\bclear \bpresentation \bin\byour\banswers. at\bthe\bend\bof\bthe\bexamination, \bfasten \ball\byour\bwork \bsecurely \btogether. the\bnumber \bof\bmarks \bis\bgiven \bin\bbrackets \b[\b]\bat\bthe\bend\bof\beach \bquestion \bor\bpart\bquestion. the\btotal\bnumber \bof\bmarks \bfor\bthis\bpaper \bis\b80. this\bdocument \bconsists \bof\b14\bprinted \bpages \band\b2\bblank \bpages. dc\b(nf/sw) \b73391/3 \u00a9\bucles \b2014\b [turn overcambridge international examinations cambridge \binternational \bgeneral \bcertificate \bof\bsecondary \beducation * 7 0 2 4 7 0 9 2 3 8 *",
            "2": "2 0606/22/m/j/14 \u00a9 ucles 2014mathematical formulae 1.\u2002algebra quadratic equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/22/m/j/14 \u00a9 ucles 2014 [turn\u2002over1\u2002without\u2002using\u2002a\u2002calculator , express  52 5 12+ -^ h in the form a b 5+ , where a and b are  \u2002 constants to be found.  [4] 2\u2002find the values of k for which the line     y k x2 0 + - =     is a tangent to the curve y x x 2 9 42= - +.  [5]",
            "4": "4 0606/22/m/j/14 \u00a9 ucles 20143\u2002(i)\u2002given that  x1+ is a factor of    x x x d 3 14 73 2- - +, show that d = 10.  [1] \u2002(ii)\u2002show that     x x x 3 14 7 103 2- - +    can be written in the form   x ax bx c12+ + + ^ ^h h, where a, b  and c are constants to be found.  [2] \u2002(iii)\u2002hence solve the equation    x x x 3 14 7 10 03 2- - + = . [2]",
            "5": "5 0606/22/m/j/14 \u00a9 ucles 2014 [turn\u2002over4\u2002(i)\u2002express     x x12 6 52- +      in the form p x q r2- +^ h , where p, q and r are constants  to be found.  [3] \u2002(ii)\u2002hence find the greatest value of   x x12 6 51 2- +   and state the value of x at which this  \u2002 \u2002 occurs.  [2]",
            "6": "6 0606/22/m/j/14 \u00a9 ucles 20145\u2002(i)\u2002find and simplify the first three terms of the expansion, in ascending powers of x, of x 1 45-^ h .  [2] \u2002(ii)\u2002the first three terms in the expansion of   x ax bx 1 4 15 2- + + ^ ^h h   are  x x 1 23 2222- + . find the  value of each of the constants a and b. [4]",
            "7": "7 0606/22/m/j/14 \u00a9 ucles 2014 [turn\u2002over6\u2002(a)\u2002(i)\u2002state the value of u for which lgu 0=. [1] \u2002 \u2002(ii)\u2002hence solve lgx2 3 0 + = . [2] \u2002(b)\u2002express   log log loga 2 15 5a 3 3-^ ^ h h ,    where a > 1, as a single logarithm to base 3.  [4]",
            "8": "8 0606/22/m/j/14 \u00a9 ucles 20147\u2002differentiate with respect to x \u2002(i)\u2002xex4 3, [2] \u2002(ii)\u2002ln cosx 2+^ h , [2] \u2002(iii)\u2002sin xx 1+. [3]",
            "9": "9 0606/22/m/j/14 \u00a9 ucles 2014 [turn\u2002over8\u2002the line     y x 5= -      meets the curve     x y x2 35 02 2+ + - =      at the points a and b. find the  exact  length of ab. [6]",
            "10": "10 0606/22/m/j/14 \u00a9 ucles 20149\u2002a curve is such that xyx2 1dd21 = +^ h . the curve passes through the point (4, 10). \u2002(i)\u2002find the equation of the curve.  [4] \u2002(ii)\u2002find y xdy  and hence evaluate y xd. 01 5y . [5]",
            "11": "11 0606/22/m/j/14 \u00a9 ucles 2014 [turn\u2002over10\u2002two variables x and y are connected by the relationship y a bx= , where a and b are constants. \u2002(i)\u2002transform the relationship y a bx=  into a straight line form.  [2] \u2002 an experiment was carried out measuring values of y for certain values of x. the values of lny and x  were plotted and a line of best fit was drawn. the graph is shown on the grid below. ln y x101 \u2013123456 23456 \u2002(ii)\u2002use the graph to determine the value of a and the value of b, giving each to 1 significant figure.  [4] \u2002(iii)\u2002find x when y = 220.  [2]",
            "12": "12 0606/22/m/j/14 \u00a9 ucles 201411\u2002the functions f and g are defined, for real values of x greater than 2, by  ( )x 2 1 fx= - ,  ( )x x x1 g= +^ h . \u2002(i)\u2002state the range of f.  [1] \u2002(ii)\u2002find an expression for ( )x f1-, stating its domain and range.  [4]",
            "13": "13 0606/22/m/j/14 \u00a9 ucles 2014 [turn\u2002over\u2002(iii)\u2002find an expression for ( )xgf  and explain why the equation ( )x 0 gf= has no solutions.  [4]",
            "14": "14 0606/22/m/j/14 \u00a9 ucles 201412\u2002a curve has equation y x x x9 243 2= - + . \u2002(i)\u2002find the set of values of x for which xy0ddh. [4] \u2002 the normal to the curve at the point on the curve where x = 3 cuts the y-axis at the point p. \u2002(ii)\u2002find the equation of the normal and the coordinates of p. [5]",
            "15": "15 0606/22/m/j/14 \u00a9 ucles 2014blank\u2002page",
            "16": "16 0606/22/m/j/14 \u00a9 ucles 2014blank\u2002page permission \bto\breproduce \bitems \bwhere \bthird-party \bowned \bmaterial \bprotected \bby\bcopyright \bis\bincluded \bhas\bbeen \bsought \band\bcleared \bwhere \bpossible. \bevery \b reasonable \beffort \bhas\bbeen \bmade \bby\bthe\bpublisher \b(ucles) \bto\btrace \bcopyright \bholders, \bbut\bif\bany\bitems \brequiring \bclearance \bhave \bunwittingly \bbeen \bincluded, \bthe\b publisher \bwill\bbe\bpleased \bto\bmake \bamends \bat\bthe\bearliest \bpossible \bopportunity. cambridge \binternational \bexaminations \bis\bpart\bof\bthe\bcambridge \bassessment \bgroup. \bcambridge \bassessment \bis\bthe\bbrand \bname \bof\buniversity \bof\bcambridge \blocal \b examinations \bsyndicate \b(ucles), \bwhich \bis\bitself \ba\bdepartment \bof\bthe\buniversity \bof\bcambridge."
        },
        "0606_s14_qp_23.pdf": {
            "1": "this document consists of 16 printed pages. dc (nh/cgw) 73394/4 \u00a9 ucles 2014  [turn overcambridge international examinations cambridge international general certificate of secondary education * 9 1 0 4 5 3 8 9 2 1 * additional mathematics  0606/23 paper 2  may/june 2014  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/23/m/j/14 \u00a9 ucles 2014mathematical formulae 1.\u2002algebra quadratic equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/23/m/j/14 \u00a9 ucles 2014 [turn\u2002over1 r cm1.6 rad500  cm2 \u2002 the diagram shows a sector of a circle of radius r cm. the angle of the sector is 1.6 radians and the area  of the sector is 500cm2. \u2002(i)\u2002find the value of r. [2]  (ii) hence find the perimeter of the sector.  [2]",
            "4": "4 0606/23/m/j/14 \u00a9 ucles 20142\u2002using the substitution logu x3= , solve, for x, the equation \u2002log logx12 3 4x 3- = . [5]",
            "5": "5 0606/23/m/j/14 \u00a9 ucles 2014 [turn\u2002over3\u2002in a motor racing competition, the winning driver in each race scores 5 points, the second and third  placed drivers score 3 and 1 points respectively. each team has two members. the results of the drivers  in one team, over a number of races, are shown in the table below .   driver  1st place  2nd place  3rd place   alan  3 1 4   brian  1 4 0 \u2002(i)\u2002write down two matrices whose product under matrix multiplication will give the number of  points scored by each of the drivers. hence calculate the number of points scored by alan and by  brian.  [3] \u2002(ii)\u2002the points scored by alan and by brian are added to give the number of points scored by the team.  using your answer to part \u2002(i),\u2002write down two matrices whose product would give the number of  points scored by the team.  [1]",
            "6": "6 0606/23/m/j/14 \u00a9 ucles 20144\u2002(a)\u2002illustrate the following statements using the venn diagrams below.     (i) a b a ,= (ii) a b c ++ q= [2] /h5105 /h5105a b a ,= a b c ++ q= \u2002(b)\u2002it is given that \ue025 is the set of integers between 1 and 100 inclusive. s and c are subsets of \ue025, where  s is the set of square numbers and c is the set of cube numbers. write the following statements  using set notation. \u2002 \u2002 (i)\u200250 is not a cube number.  [1] \u2002 \u2002(ii)\u200264 is both a square number and a cube number.  [1] \u2002 \u2002(iii)\u2002there are 90 integers between 1 and 100 inclusive which are not square numbers.  [1]",
            "7": "7 0606/23/m/j/14 \u00a9 ucles 2014 [turn\u2002over5\u2002do\u2002not\u2002use\u2002a\u2002calculator \u2002in\u2002this\u2002question. \u2002(i)\u2002show that 2 2 4 8 2 2 3 02+ - + = ^ ^ h h . [2] \u2002(ii)\u2002solve the equation x x 2 2 2 2 0 3 4 22+ - + =+ ^ ^ h h , giving your answer in the form a b 2+   where a and b are integers.  [3]",
            "8": "8 0606/23/m/j/14 \u00a9 ucles 20146\u2002find the coordinates of the points of intersection of the curve x y8 101 - =  and the line x y 9 + = .  [6]",
            "9": "9 0606/23/m/j/14 \u00a9 ucles 2014 [turn\u2002over7\u2002(a)\u2002prove that    sec c osectan c ot sin c os1 i ii i i i ++=+. [3] \u2002(b)\u2002given that tanx125=-  and \u00b0 \u00b0x 90 1801 1 , find the exact value of sinx and of cosx, giving \u2002 \u2002 each answer as a fraction.  [3] \u2002 \u2002 answer    sinx=            cosx=",
            "10": "10 0606/23/m/j/14 \u00a9 ucles 20148\u2002a curve is such that xyx x6 8 3dd2= - +. \u2002(i)\u2002show that the curve has no stationary points.  [2] \u2002 given that the curve passes through the point p(2, 10), \u2002(ii)\u2002find the equation of the tangent to the curve at the point p, [2] \u2002(iii)\u2002find the equation of the curve.  [4]",
            "11": "11 0606/23/m/j/14 \u00a9 ucles 2014 [turn\u2002over9\u2002solutions \u2002to\u2002this\u2002question\u2002by\u2002accurate\u2002drawing\u2002will\u2002not\u2002be\u2002accepted. \u2002 the points ( , ) a2 11 , ( , ) b 2 3-  and ( , ) c2 1- are the vertices of a triangle. \u2002(i)\u2002find the equation of the perpendicular bisector of ab. [4] \u2002 the line through  a parallel to bc intersects the perpendicular bisector of ab at the point d.  \u2002(ii)\u2002find the area of the quadrilateral abcd.  [6]",
            "12": "12 0606/23/m/j/14 \u00a9 ucles 201410\u2002(i)\u2002given that y xx 212 2= +, show that xy xk 21dd 2 3= + ^ h, where k is a constant to be found.  [5]",
            "13": "13 0606/23/m/j/14 \u00a9 ucles 2014 [turn\u2002over\u2002(ii)\u2002hence find  xx 216d 2 3+c edd^ h and evaluate  xx 216d 2 310 + 2c edd^ h. [3]",
            "14": "14 0606/23/m/j/14 \u00a9 ucles 201411 m npa b o \u2002 in the diagram oaa2=  and obb5= . the point m is the midpoint of oa and the point n lies on ob  such that : :onnb 3 2= . \u2002(i)\u2002find an expression for the vector mb in terms of a and b. [2] \u2002 the point p lies on an such that ap anm= . \u2002(ii)\u2002find an expression for the vector ap in terms of m, a and b. [2]",
            "15": "15 0606/23/m/j/14 \u00a9 ucles 2014 [turn\u2002over\u2002(iii)\u2002find an expression for the vector mp in terms of m, a and b. [2] \u2002(iv)\u2002given that m, p and b are collinear, find the value of m. [4] question \u200212\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.",
            "16": "16 0606/23/m/j/14 \u00a9 ucles 2014permission 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. 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.12\u2002the function f is such that ( )x x 2 3 f= + - for x4 28g g . \u2002(i)\u2002find the range of f.  [2] \u2002(ii)\u2002find ( )12f2. [2] \u2002(iii)\u2002find an expression for ( )x f1-. [2] \u2002 the function g is defined by ( )xx120g=  for x0h. \u2002(iv)\u2002find the value of x for which ( )x 20 gf= . [3]"
        },
        "0606_w14_qp_11.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (lk/slm) 81862/3 \u00a9 ucles 2014  [turn overcambridge international examinations cambridge international general certificate of secondary education * 8 0 2 3 6 5 2 7 1 3 * additional mathematics  0606/11 paper 1  october/november 2014  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/11/o/n/14 \u00a9 ucles 2014mathematical formulae 1.\u2002algebra quadratic \u2002equation  for the equation ax2 + bx + c = 0, xab b ac 242!=- - . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/11/o/n/14 \u00a9 ucles 2014 [turn\u2002over1\u2002find the coordinates of the stationary point on the curve y xx16 2= + .\u2002 [4] 2\u2002(a)\u2002on the axes below, sketch the curve cos y x3 2 1 = -   for x 0 180 \u00b0 \u00b0g g . [3] o2 \u20132 \u20134 \u2013646 45\u00b0 90\u00b0 135\u00b0 180\u00b0y x \u2002(b)\u2002(i)\u2002state the amplitude of sinx 1 4 2 - . [1] \u2002 \u2002(ii)\u2002state the period of tanx 5 3 1+. [1]",
            "4": "4 0606/11/o/n/14 \u00a9 ucles 20143\u2002a curve is such thaty x x 32 d d=+  for x 32-. the curve passes through the point ( , ) 6 10 . \u2002(i)\u2002find the equation of the curve.  [4] \u2002(ii)\u2002find the x-coordinate of the point on the curve where y = 6. [1]",
            "5": "5 0606/11/o/n/14 \u00a9 ucles 2014 [turn\u2002over4\u2002(i)\u2002using the substitution y5x= , show that the equation ( ) 5 5 2 2 5x x x 2 1 1- + =+ +can be  \u2002 \u2002 written in the form  ay by 2 02+ + =, where a and b are constants to be found.  [2] \u2002(ii)\u2002hence solve the equation ( ) 5 5 2 2 5x x x 2 1 1- + =+ + . [4]",
            "6": "6 0606/11/o/n/14 \u00a9 ucles 20145\u2002(i)\u2002find the equation of the tangent to the curve nl y x x3= - at the point on the curve  where x1=. [4] \u2002(ii)\u2002show that this tangent bisects the line joining the points \u2002( , ) 2 16-\u2002and ( , ) 12 2. [2]",
            "7": "7 0606/11/o/n/14 \u00a9 ucles 2014 [turn\u2002over6\u2002(i)\u2002given that the coefficient of x2 in the expansion of ( ) px 26+ is 60, find the value of the positive  constant p. [3] \u2002(ii)\u2002using your value of p, find the coefficient of x2 in the expansion of ( ) ( )x px3 26- + . [3]",
            "8": "8 0606/11/o/n/14 \u00a9 ucles 20147\u2002matrices a and b are such that a ab b3 2a=-j lkkn poo and bab ba 2 2=-j lkkn poo , where a and b are non-zero constants. \u2002(i)\u2002find a1\u2013. [2] \u2002(ii)\u2002using your answer to part (i),\u2002find the matrix x such that  xa\u2002=\u2002b. [4]",
            "9": "9 0606/11/o/n/14 \u00a9 ucles 2014 [turn\u2002over8\u2002the point p lies on the line joining ( , ) a 2 3-  and ( , ) b1019 such that : :appb 1 3= . \u2002(i)\u2002show that the x-coordinate of p is 1 and find the y-coordinate of p. [2] \u2002(ii)\u2002find the equation of the line through p which is perpendicular to ab. [3] \u2002 the line through p which is perpendicular to ab meets the y-axis at the point q. \u2002(iii)\u2002find the area of the triangle aqb . [3]",
            "10": "10 0606/11/o/n/14 \u00a9 ucles 20149\u2002the table shows experimental values of variables x and y. x 2 2.5 3 3.5 4 y 18.8 29.6 46.9 74.1 117.2 \u2002(i)\u2002by plotting a suitable straight line graph on the grid below, show that x and y are related by the  equation y abx= , where a and b are constants.  [4]",
            "11": "11 0606/11/o/n/14 \u00a9 ucles 2014 [turn\u2002over\u2002(ii)\u2002use your graph to find the value of a and of b. [4]",
            "12": "12 0606/11/o/n/14 \u00a9 ucles 201410\u2002(a)\u2002(i)\u2002find how many different 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5 and 6 if  no digit is repeated.  [1] \u2002 \u2002(ii)\u2002how many of the 4-digit numbers found in part (i) are greater than 6000?  [1] \u2002 \u2002(iii)\u2002how many of the 4-digit numbers found in part (i) are greater than 6000 and are odd?  [1] \u2002(b)\u2002a quiz team of 10 players is to be chosen from a class of 8 boys and 12 girls. \u2002 \u2002 (i)\u2002find the number of different teams that can be chosen if the team has to have equal numbers  of girls and boys.  [3] \u2002 \u2002(ii)\u2002find the number of different teams that can be chosen if the team has to include the youngest  and oldest boy and the youngest and oldest girl.  [2]",
            "13": "13 0606/11/o/n/14 \u00a9 ucles 2014 [turn\u2002over11\u2002(a)\u2002solve cos c ot x x 2 3 3=   for \u00b0 \u00b0x 0 90g g . [5] \u2002(b)\u2002solve sec y22r+ = -j lkkn poo   for y0g g r radians.  [4]",
            "14": "14 0606/11/o/n/14 \u00a9 ucles 201412 a br op q \u2002 the position vectors of points a and b relative to an origin o are a and b respectively. the point p  is such that op oan= . the point q is such that oq obm= . the lines aq and bp intersect at the  point  r. \u2002(i)\u2002express aq in terms of m, a and b. [1] \u2002(ii)\u2002express bp in terms of n, a and b. [1] \u2002 it is given that ar aq 3=  and br bp 8 7= . \u2002(iii)\u2002express or in terms of m, a and b. [2]",
            "15": "15 0606/11/o/n/14 \u00a9 ucles 2014\u2002(iv)\u2002express or in terms of n, a and b. [2] \u2002(v)\u2002hence find the value of n and of  m. [3]",
            "16": "16 0606/11/o/n/14 \u00a9 ucles 2014permission 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. 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\u2002page"
        },
        "0606_w14_qp_12.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (lk/slm) 97555 \u00a9 ucles 2014  [turn overcambridge international examinations cambridge international general certificate of secondary education * 6 9 4 1 6 5 4 3 4 9 * additional mathematics  0606/12 paper 1  october/november 2014  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/12/o/n/14 \u00a9 ucles 2014mathematical formulae 1.\u2002algebra quadratic \u2002equation  for the equation ax2 + bx + c = 0, xab b ac 242!=- - . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/12/o/n/14 \u00a9 ucles 2014 [turn\u2002over1\u2002find the coordinates of the stationary point on the curve y xx16 2= + .\u2002 [4] 2\u2002(a)\u2002on the axes below, sketch the curve cos y x3 2 1 = -   for x 0 180 \u00b0 \u00b0g g . [3] o2 \u20132 \u20134 \u2013646 45\u00b0 90\u00b0 135\u00b0 180\u00b0y x \u2002(b)\u2002(i)\u2002state the amplitude of sinx 1 4 2 - . [1] \u2002 \u2002(ii)\u2002state the period of tanx 5 3 1+. [1]",
            "4": "4 0606/12/o/n/14 \u00a9 ucles 20143\u2002a curve is such thaty x x 32 d d=+  for x 32-. the curve passes through the point ( , ) 6 10 . \u2002(i)\u2002find the equation of the curve.  [4] \u2002(ii)\u2002find the x-coordinate of the point on the curve where y = 6. [1]",
            "5": "5 0606/12/o/n/14 \u00a9 ucles 2014 [turn\u2002over4\u2002(i)\u2002using the substitution y5x= , show that the equation ( ) 5 5 2 2 5x x x 2 1 1- + =+ +can be  \u2002 \u2002 written in the form  ay by 2 02+ + =, where a and b are constants to be found.  [2] \u2002(ii)\u2002hence solve the equation ( ) 5 5 2 2 5x x x 2 1 1- + =+ + . [4]",
            "6": "6 0606/12/o/n/14 \u00a9 ucles 20145\u2002(i)\u2002find the equation of the tangent to the curve nl y x x3= - at the point on the curve  where x1=. [4] \u2002(ii)\u2002show that this tangent bisects the line joining the points \u2002( , ) 2 16-\u2002and ( , ) 12 2. [2]",
            "7": "7 0606/12/o/n/14 \u00a9 ucles 2014 [turn\u2002over6\u2002(i)\u2002given that the coefficient of x2 in the expansion of ( ) px 26+ is 60, find the value of the positive  constant p. [3] \u2002(ii)\u2002using your value of p, find the coefficient of x2 in the expansion of ( ) ( )x px3 26- + . [3]",
            "8": "8 0606/12/o/n/14 \u00a9 ucles 20147\u2002matrices a and b are such that a ab b3 2a=-j lkkn poo and bab ba 2 2=-j lkkn poo , where a and b are non-zero constants. \u2002(i)\u2002find a1\u2013. [2] \u2002(ii)\u2002using your answer to part (i),\u2002find the matrix x such that  xa\u2002=\u2002b. [4]",
            "9": "9 0606/12/o/n/14 \u00a9 ucles 2014 [turn\u2002over8\u2002the point p lies on the line joining ( , ) a 2 3-  and ( , ) b1019 such that : :appb 1 3= . \u2002(i)\u2002show that the x-coordinate of p is 1 and find the y-coordinate of p. [2] \u2002(ii)\u2002find the equation of the line through p which is perpendicular to ab. [3] \u2002 the line through p which is perpendicular to ab meets the y-axis at the point q. \u2002(iii)\u2002find the area of the triangle aqb . [3]",
            "10": "10 0606/12/o/n/14 \u00a9 ucles 20149\u2002the table shows experimental values of variables x and y. x 2 2.5 3 3.5 4 y 18.8 29.6 46.9 74.1 117.2 \u2002(i)\u2002by plotting a suitable straight line graph on the grid below, show that x and y are related by the  equation y abx= , where a and b are constants.  [4]",
            "11": "11 0606/12/o/n/14 \u00a9 ucles 2014 [turn\u2002over\u2002(ii)\u2002use your graph to find the value of a and of b. [4]",
            "12": "12 0606/12/o/n/14 \u00a9 ucles 201410\u2002(a)\u2002(i)\u2002find how many different 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5 and 6 if  no digit is repeated.  [1] \u2002 \u2002(ii)\u2002how many of the 4-digit numbers found in part (i) are greater than 6000?  [1] \u2002 \u2002(iii)\u2002how many of the 4-digit numbers found in part (i) are greater than 6000 and are odd?  [1] \u2002(b)\u2002a quiz team of 10 players is to be chosen from a class of 8 boys and 12 girls. \u2002 \u2002 (i)\u2002find the number of different teams that can be chosen if the team has to have equal numbers  of girls and boys.  [3] \u2002 \u2002(ii)\u2002find the number of different teams that can be chosen if the team has to include the youngest  and oldest boy and the youngest and oldest girl.  [2]",
            "13": "13 0606/12/o/n/14 \u00a9 ucles 2014 [turn\u2002over11\u2002(a)\u2002solve cos c ot x x 2 3 3=   for \u00b0 \u00b0x 0 90g g . [5] \u2002(b)\u2002solve sec y22r+ = -j lkkn poo   for y0g g r radians.  [4]",
            "14": "14 0606/12/o/n/14 \u00a9 ucles 201412 a br op q \u2002 the position vectors of points a and b relative to an origin o are a and b respectively. the point p  is such that op oan= . the point q is such that oq obm= . the lines aq and bp intersect at the  point  r. \u2002(i)\u2002express aq in terms of m, a and b. [1] \u2002(ii)\u2002express bp in terms of n, a and b. [1] \u2002 it is given that ar aq 3=  and br bp 8 7= . \u2002(iii)\u2002express or in terms of m, a and b. [2]",
            "15": "15 0606/12/o/n/14 \u00a9 ucles 2014\u2002(iv)\u2002express or in terms of n, a and b. [2] \u2002(v)\u2002hence find the value of n and of  m. [3]",
            "16": "16 0606/12/o/n/14 \u00a9 ucles 2014permission 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. 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\u2002page"
        },
        "0606_w14_qp_13.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (lk/slm) 81861/3 \u00a9 ucles 2014  [turn overcambridge international examinations cambridge international general certificate of secondary education * 8 5 3 8 8 2 7 9 5 0 * additional mathematics  0606/13 paper 1  october/november 2014  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/13/o/n/14 \u00a9 ucles 2014mathematical formulae 1.\u2002algebra quadratic \u2002equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2 . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/13/o/n/14 \u00a9 ucles 2014 [turn\u2002over1\u2002the diagram shows the graph of cos y a bx c = +   for \u00b0 \u00b0x 0 360 g g , where a, b and c are  positive integers.  oy x180\u00b017 360\u00b0 \u2002 state the value of each of a, b and c. [3] \u2002  a =   b =   c =",
            "4": "4 0606/13/o/n/14 \u00a9 ucles 20142\u2002the line   y x4 8= +   cuts the curve   xy x 4 2= +   at the points a and b. find the exact length  of ab. [5]",
            "5": "5 0606/13/o/n/14 \u00a9 ucles 2014 [turn\u2002over3\u2002the universal set \ue025 is the set of real numbers. sets a, b and c are such that     a = :x x x5 6 02+ + = \" ,,     b = :x x x x3 2 1 0 - + + = ^ ^ ^ h h h \" ,,     c = :x x x3 02+ + = \" ,. \u2002(i)\u2002state the value of each of n( a), n(b) and n( c). [3] \u2002 \u2002 na= ^ h \u2002 \u2002 \u2002 \u2002 nb= ^ h \u2002 \u2002 \u2002 \u2002 nc= ^ h \u2002(ii)\u2002list the elements in the set a b,. [1] \u2002(iii)\u2002list the elements in the set a b+. [1] \u2002(iv)\u2002describe the set cl. [1]",
            "6": "6 0606/13/o/n/14 \u00a9 ucles 20144\u2002(a)\u2002solve sin c os x x 3 5 0 + =   for \u00b0 \u00b0x 0 360 g g . [3] \u2002(b)\u2002solve cosec y342r+ =j lkkn poo   for y0g g r radians.  [5]",
            "7": "7 0606/13/o/n/14 \u00a9 ucles 2014 [turn\u2002over5\u2002(a)\u2002a drinks machine sells coffee, tea and cola.  coffee costs $0.50, tea costs $0.40 and cola costs  $0.45. the table below shows the numbers of drinks sold over a 4-day period. coffee tea cola tuesday 12 2 1 wednesday 9 3 0 thursday 8 5 1 friday 11 2 0 \u2002 \u2002 (i)\u2002write down 2 matrices whose product will give the amount of money the drinks machine  took each day and evaluate this product.  [4] \u2002 \u2002(ii)\u2002hence write down the total amount of money taken by the machine for this 4-day period.  [1] \u2002(b)\u2002matrices x and y are such that x = 2 54 1-j lkkn poo and xy = i, where i is the identity matrix. find the  \u2002 \u2002 matrix y. [3]",
            "8": "8 0606/13/o/n/14 \u00a9 ucles 20146\u2002the diagram shows a sector, aob , of a circle centre o, radius 12  cm. angle . aob 0 9=  radians. the  point c lies on oa such that oc = cb. 0.9 radoca b12 cm \u2002(i)\u2002show that oc = 9.65  cm correct to 3 significant figures.  [2] \u2002(ii)\u2002find the perimeter of the shaded region.  [3]",
            "9": "9 0606/13/o/n/14 \u00a9 ucles 2014 [turn\u2002over\u2002(iii)\u2002find the area of the shaded region.  [3] 7\u2002solve the equation   log l og x x 1 2 18 95 5+ = - ^ h . [5]",
            "10": "10 0606/13/o/n/14 \u00a9 ucles 20148\u2002(i) given that f l n x x x3= ^ h , show that f ln x x 3 1= + l^ ^h h . [3] \u2002(ii)\u2002hence find ln dx x 1+^ hy . [2] \u2002(iii)\u2002hence find lndx x 12y  in the form lnp q+ , where p and q are integers.  [3]",
            "11": "11 0606/13/o/n/14 \u00a9 ucles 2014 [turn\u2002over9\u2002(a)\u2002given that the first 3 terms in the expansion of qx5p-^ h  are x rx 625 15002- + , find the value of  each of the integers p, q and r. [5] \u2002(b)\u2002find the value of the term that is independent of x in the expansion of xx241 312 +j lkkn poo. [3]",
            "12": "12 0606/13/o/n/14 \u00a9 ucles 201410\u2002(a)\u2002solve the following simultaneous equations. 2551yx 3 2=- 27381yx 1=-  [5]",
            "13": "13 0606/13/o/n/14 \u00a9 ucles 2014 [turn\u2002over\u2002(b)\u2002the diagram shows a triangle abc  such that ab 2 3= +^ h  cm, bc 1 2 3 = +^ h  cm  and ac 2= cm. b ca 2 cm 1 2 3 cm +^ h2 3 cm +^ h \u2002 \u2002 without using a calculator, find the value of cosa in the form a b 3+ , where a and b are  constants to be found.  [4]",
            "14": "14 0606/13/o/n/14 \u00a9 ucles 201411\u2002the diagram shows part of the curve y x x5 12= + - ^ ^ h h . o xy y = (x + 5)(x \u2013 1)2 \u2002(i)\u2002find the x-coordinates of the stationary points of the curve.  [5]",
            "15": "15 0606/13/o/n/14 \u00a9 ucles 2014\u2002(ii)\u2002find d x x x5 12+ -^ ^ h h y . [3] \u2002(iii)\u2002hence find the area enclosed by the curve and the x-axis.   [2] \u2002(iv)\u2002find the set of positive values of k for which the equation x k x5 12+ = - ^ ^ h h has only one real  solution.  [2] ",
            "16": "16 0606/13/o/n/14 \u00a9 ucles 2014permission 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. 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\u2002page"
        },
        "0606_w14_qp_21.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (cw/slm) 81813/3 \u00a9 ucles 2014  [turn overcambridge international examinations cambridge international general certificate of secondary education * 9 5 8 5 8 0 0 3 2 6 * additional mathematics  0606/21 paper 2  october/november 2014  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of   angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/21/o/n/14 \u00a9 ucles 2014mathematical formulae 1.\u2002algebra quadratic \u2002equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/21/o/n/14 \u00a9 ucles 2014 [turn\u2002over1\u2002(a)\u2002on each of the venn diagrams below shade the region which represents the given set. a cb/h5105a cb/h5105  ( )a b c + , l (a b c + , ) l  [2] \u2002(b)\u2002in a year group of  98 pupils, f is the set of pupils who play football and h is the set of pupils who  play hockey. there are 60 pupils who play football and 50 pupils who play hockey. the number  that play both sports is x and the number that play neither is   x 30 2- . find the value of x. [3]",
            "4": "4 0606/21/o/n/14 \u00a9 ucles 20142\u2002solve the inequality   ( ) x x x 9 2 1 12 21 + - + . [3] 3\u2002solve the following simultaneous equations. ( ) log log x y 3 22 2+ = + ( ) log x y 32+ =  [5]",
            "5": "5 0606/21/o/n/14 \u00a9 ucles 2014 [turn\u2002over4\u2002the functions f and g are defined for real values of x by    ( )x x 1 3 f= - - for , x 12   ( )xxx 2 32g=-- for . x 22 \u2002(i)\u2002find gf(37).  [2] \u2002(ii)\u2002find an expression for ( )x f1-. [2] \u2002(iii)\u2002find an expression for ( ).x g1- [2]",
            "6": "6 0606/21/o/n/14 \u00a9 ucles 20145\u2002the number of bacteria b in a culture, t days after the first observation, is given by  b 500 400e.t0 2= + . \u2002(i)\u2002find the initial number present.  [1] \u2002(ii)\u2002find the number present after 10 days.  [1] \u2002(iii)\u2002find the rate at which the bacteria are increasing after 10 days.  [2] \u2002(iv)\u2002find the value of t when b10000= . [3]",
            "7": "7 0606/21/o/n/14 \u00a9 ucles 2014 [turn\u2002over6\u2002(i)\u2002calculate the coordinates of the points where the line y x 2= + cuts the curve . x y 102 2+ =  [4] \u2002(ii)\u2002find the exact values of m for which the line y m x5 = + is a tangent to the curve . x y 102 2+ =  [4]",
            "8": "8 0606/21/o/n/14 \u00a9 ucles 20147\u2002a particle moving in a straight line passes through a fixed point o. the displacement, x metres, of the  particle, t seconds after it passes through o, is given by . sin x t t 2= + \u2002(i)\u2002find an expression for the velocity, vms1-, at time t. [2]  when the particle is first at instantaneous rest, find \u2002(ii)\u2002the value of t, [2] \u2002(iii)\u2002its displacement and acceleration.  [3]",
            "9": "9 0606/21/o/n/14 \u00a9 ucles 2014 [turn\u2002over8\u2002(i)\u2002given that yxx 222 =+ , show that( ) xy xkx 2 dd 2 2=+ , where k is a constant to be found.  [3] \u2002(ii)\u2002hence find ( ) xxx2d2 2+c edd . [2]",
            "10": "10 0606/21/o/n/14 \u00a9 ucles 20149\u2002integers a and b are such that ( )a a b 3 5 5 512+ + - = . find the possible values of a and the  corresponding values of b. [6]",
            "11": "11 0606/21/o/n/14 \u00a9 ucles 2014 [turn\u2002over10\u2002(i)\u2002prove that . sec c osec cot t an x x x x- =  [4] \u2002(ii)\u2002use the result from part (i) to solve the equation sec c osec cot x x x 3=   for 0\u00b0 x1 1  360\u00b0.  [4]",
            "12": "12 0606/21/o/n/14 \u00a9 ucles 201411 pq os r0.8 rad5 cm x cm \u2002 the diagram shows a sector opq  of a circle with centre o and radius x cm. angle poq  is 0.8 radians.  the point s lies on oq such that os = 5 cm. the point r lies on op such that angle ors is a right  angle. given that the area of triangle ors is one-fifth of the area of sector opq , find \u2002(i)\u2002the area of sector opq  in terms of x and hence show that the value of x is 8.837 correct to  4 significant figures,  [5]",
            "13": "13 0606/21/o/n/14 \u00a9 ucles 2014 [turn\u2002over\u2002(ii)\u2002the perimeter of pqsr , [3] \u2002(iii)\u2002the area of pqsr . [2]",
            "14": "14 0606/21/o/n/14 \u00a9 ucles 201412\u2002(i)\u2002show that x2- is a factor of x x3 14 323 2- + . [1] \u2002(ii)\u2002hence factorise x x3 14 323 2- + completely.  [4]",
            "15": "15 0606/21/o/n/14 \u00a9 ucles 2014\u2002 the diagram below shows part of the curve y xx3 1432 2= - +  cutting the x-axis at the points p and q. y x p qoy = 3x \u2013 14 + 32 x2 \u2002(iii)\u2002state the x-coordinates of p and q. [1] \u2002(iv)\u2002find ( ) xxx 3 1432d2- + y and hence determine the area of the shaded region.  [4]",
            "16": "16 0606/21/o/n/14 \u00a9 ucles 2014blank\u2002page 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. 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."
        },
        "0606_w14_qp_22.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (lk/slm) 97553 \u00a9 ucles 2014  [turn overcambridge international examinations cambridge international general certificate of secondary education * 4 9 9 3 1 9 7 9 6 9 * additional mathematics  0606/22 paper 2  october/november 2014  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of   angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/22/o/n/14 \u00a9 ucles 2014mathematical formulae 1.\u2002algebra quadratic \u2002equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/22/o/n/14 \u00a9 ucles 2014 [turn\u2002over1\u2002(a)\u2002on each of the venn diagrams below shade the region which represents the given set. a cb/h5105a cb/h5105  ( )a b c + , l (a b c + , ) l  [2] \u2002(b)\u2002in a year group of  98 pupils, f is the set of pupils who play football and h is the set of pupils who  play hockey. there are 60 pupils who play football and 50 pupils who play hockey. the number  that play both sports is x and the number that play neither is   x 30 2- . find the value of x. [3]",
            "4": "4 0606/22/o/n/14 \u00a9 ucles 20142\u2002solve the inequality   ( ) x x x 9 2 1 12 21 + - + . [3] 3\u2002solve the following simultaneous equations. ( ) log log x y 3 22 2+ = + ( ) log x y 32+ =  [5]",
            "5": "5 0606/22/o/n/14 \u00a9 ucles 2014 [turn\u2002over4\u2002the functions f and g are defined for real values of x by    ( )x x 1 3 f= - - for , x 12   ( )xxx 2 32g=-- for . x 22 \u2002(i)\u2002find gf(37).  [2] \u2002(ii)\u2002find an expression for ( )x f1-. [2] \u2002(iii)\u2002find an expression for ( ).x g1- [2]",
            "6": "6 0606/22/o/n/14 \u00a9 ucles 20145\u2002the number of bacteria b in a culture, t days after the first observation, is given by  b 500 400e.t0 2= + . \u2002(i)\u2002find the initial number present.  [1] \u2002(ii)\u2002find the number present after 10 days.  [1] \u2002(iii)\u2002find the rate at which the bacteria are increasing after 10 days.  [2] \u2002(iv)\u2002find the value of t when b10000= . [3]",
            "7": "7 0606/22/o/n/14 \u00a9 ucles 2014 [turn\u2002over6\u2002(i)\u2002calculate the coordinates of the points where the line y x 2= + cuts the curve . x y 102 2+ =  [4] \u2002(ii)\u2002find the exact values of m for which the line y m x5 = + is a tangent to the curve . x y 102 2+ =  [4]",
            "8": "8 0606/22/o/n/14 \u00a9 ucles 20147\u2002a particle moving in a straight line passes through a fixed point o. the displacement, x metres, of the  particle, t seconds after it passes through o, is given by . sin x t t 2= + \u2002(i)\u2002find an expression for the velocity, vms1-, at time t. [2]  when the particle is first at instantaneous rest, find \u2002(ii)\u2002the value of t, [2] \u2002(iii)\u2002its displacement and acceleration.  [3]",
            "9": "9 0606/22/o/n/14 \u00a9 ucles 2014 [turn\u2002over8\u2002(i)\u2002given that yxx 222 =+ , show that( ) xy xkx 2 dd 2 2=+ , where k is a constant to be found.  [3] \u2002(ii)\u2002hence find ( ) xxx2d2 2+c edd . [2]",
            "10": "10 0606/22/o/n/14 \u00a9 ucles 20149\u2002integers a and b are such that ( )a a b 3 5 5 512+ + - = . find the possible values of a and the  corresponding values of b. [6]",
            "11": "11 0606/22/o/n/14 \u00a9 ucles 2014 [turn\u2002over10\u2002(i)\u2002prove that . sec c osec cot t an x x x x- =  [4] \u2002(ii)\u2002use the result from part (i) to solve the equation sec c osec cot x x x 3=   for 0\u00b0 x1 1  360\u00b0.  [4]",
            "12": "12 0606/22/o/n/14 \u00a9 ucles 201411 pq os r0.8 rad5 cm x cm \u2002 the diagram shows a sector opq  of a circle with centre o and radius x cm. angle poq  is 0.8 radians.  the point s lies on oq such that os = 5 cm. the point r lies on op such that angle ors is a right  angle. given that the area of triangle ors is one-fifth of the area of sector opq , find \u2002(i)\u2002the area of sector opq  in terms of x and hence show that the value of x is 8.837 correct to  4 significant figures,  [5]",
            "13": "13 0606/22/o/n/14 \u00a9 ucles 2014 [turn\u2002over\u2002(ii)\u2002the perimeter of pqsr , [3] \u2002(iii)\u2002the area of pqsr . [2]",
            "14": "14 0606/22/o/n/14 \u00a9 ucles 201412\u2002(i)\u2002show that x2- is a factor of x x3 14 323 2- + . [1] \u2002(ii)\u2002hence factorise x x3 14 323 2- + completely.  [4]",
            "15": "15 0606/22/o/n/14 \u00a9 ucles 2014\u2002 the diagram below shows part of the curve y xx3 1432 2= - +  cutting the x-axis at the points p and q. y x p qoy = 3x \u2013 14 + 32 x2 \u2002(iii)\u2002state the x-coordinates of p and q. [1] \u2002(iv)\u2002find ( ) xxx 3 1432d2- + y and hence determine the area of the shaded region.  [4]",
            "16": "16 0606/22/o/n/14 \u00a9 ucles 2014blank\u2002page 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. 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."
        },
        "0606_w14_qp_23.pdf": {
            "1": "additional mathematics \b 0606/23 paper \b2\b october/november 2014 \b 2 hours candidates \banswer \bon\bthe\bquestion \bpaper. additional \bmaterials: \b electronic \bcalculator read these instructions first write \byour\bcentre \bnumber, \bcandidate \bnumber \band\bname \bon\ball\bthe\bwork \byou\bhand \bin. write \bin\bdark\bblue\bor\bblack \bpen. y ou\bmay\buse\ban\bhb\bpencil \bfor\bany\bdiagrams \bor\bgraphs. do\bnot\buse\bstaples, \bpaper \bclips, \bglue\bor\bcorrection \bfluid. do\bnot \bwrite \bin\bany \bbarcodes. answer \ball\bthe\bquestions. give \bnon-exact \bnumerical \banswers \bcorrect \bto\b3\bsignificant \bfigures, \bor\b1\bdecimal \bplace \bin\bthe\bcase \bof\b angles \bin\bdegrees, \bunless \ba\bdifferent \blevel\bof\baccuracy \bis\bspecified \bin\bthe\bquestion. the\buse\bof\ban\belectronic \bcalculator \bis\bexpected, \bwhere \bappropriate. y ou\bare\breminded \bof\bthe\bneed \bfor\bclear \bpresentation \bin\byour\banswers. at\bthe\bend\bof\bthe\bexamination, \bfasten \ball\byour\bwork \bsecurely \btogether. the\bnumber \bof\bmarks \bis\bgiven \bin\bbrackets \b[\b]\bat\bthe\bend\bof\beach \bquestion \bor\bpart\bquestion. the\btotal\bnumber \bof\bmarks \bfor\bthis\bpaper \bis\b80. this\bdocument \bconsists \bof\b16\bprinted \bpages. dc\b(nf/slm) \b81812/2 \u00a9\bucles \b2014\b [turn overcambridge international examinations cambridge \binternational \bgeneral \bcertificate \bof\bsecondary \beducation * 2 2 4 9 2 3 9 0 5 9 *",
            "2": "2 0606/23/o/n/14 \u00a9 ucles 2014mathematical formulae 1.\u2002algebra quadratic \u2002equation  for the equation ax2 + bx + c = 0, xb b ac a=\u2212 \u221224 2 binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a\b=\bb sin b\b=\bc sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/23/o/n/14 \u00a9 ucles 2014 [turn\u2002over1\u2002the expression     x x x x p 3 8 33 f3 2= + - + ^ h      has a factor of  x2-. \u2002(i)\u2002show that  p10=  and express xf^ h as a product of a linear factor and a quadratic factor.  [4] \u2002(ii)\u2002hence solve the equation ( )x 0 f=. [2]",
            "4": "4 0606/23/o/n/14 \u00a9 ucles 20142\u2002a committee of four is to be selected from 7 men and 5 women. find the number of different  committees that could be selected if  \u2002(i)\u2002there are no restrictions,  [1] \u2002(ii)\u2002there must be two male and two female members.  [2] \u2002 a brother and sister, ken and betty, are among the 7 men and 5 women. \u2002(iii)\u2002find how many different committees of four could be selected so that there are two male and two  female members which must include either ken or betty but not both.  [4]",
            "5": "5 0606/23/o/n/14 \u00a9 ucles 2014 [turn\u2002over3\u2002points a and b have coordinates (\u22122,  10) and (4,  2) respectively. c is the mid-point of the line ab. \u2002 point d is such that  cd12 9=c m . \u2002(i)\u2002find the coordinates of  c and of d. [3] \u2002(ii)\u2002show that cd is perpendicular to ab. [3] \u2002(iii)\u2002find the area of triangle abd . [2]",
            "6": "6 0606/23/o/n/14 \u00a9 ucles 20144\u2002the profit $ p made by a company in its nth year is modelled by  p 1000eanb=+. \u2002 in the first year the company made $2000 profit. \u2002(i)\u2002show that ln a b 2 + = . [1] \u2002 in the second year the company made $3297 profit. \u2002(ii)\u2002find another linear equation connecting  a and b. [2] \u2002(iii)\u2002solve the two equations from parts (i) and (ii) to find the value of a and of  b. [2] \u2002(iv)\u2002using your values for a and b, find the profit in the 10th year.  [2]",
            "7": "7 0606/23/o/n/14 \u00a9 ucles 2014 [turn\u2002over5\u2002 r oba3a pqx \u2002 in the diagram b op=, a pq=\u2002and a or 3= . the lines oq and pr intersect at x. \u2002(i)\u2002given that ox oqn= , express ox in terms of n, a and b.\u2002 [1] \u2002(ii)\u2002given that rx rpm= , express ox in terms of m, a and b.\u2002 [2] \u2002(iii)\u2002hence find the value of   n and of m and state the value of the ratio pr xx. [3]",
            "8": "8 0606/23/o/n/14 \u00a9 ucles 20146\u2002variables x and y are such that, when lny  is plotted against 3x, a straight line graph passing through  (4, 19) and (9,  39) is obtained. ln y o 3x(4, 19)(9, 39) \u2002(i)\u2002find the equation of this line in the form lny m c 3x= + , where m and c are constants to be found.  [3] \u2002(ii)\u2002find y when . x 0 5= . [2]",
            "9": "9 0606/23/o/n/14 \u00a9 ucles 2014 [turn\u2002over\u2002(iii)\u2002find x when y2000= . [3]",
            "10": "10 0606/23/o/n/14 \u00a9 ucles 20147\u2002the functions f and g are defined for real values of x by   xx21 f= + ^ h  for x12,  x x 2 g2= + ^ h . \u2002 find an expression for \u2002(i)\u2002 x f1-^ h, [2] \u2002(ii)\u2002 xgf^ h, [2] \u2002(iii)\u2002 xfg^ h. [2]",
            "11": "11 0606/23/o/n/14 \u00a9 ucles 2014 [turn\u2002over\u2002(iv)\u2002show that xxx 23 2ff=++^ h  and solve x xff= ^ h . [4]",
            "12": "12 0606/23/o/n/14 \u00a9 ucles 20148\u2002a particle moving in a straight line passes through a fixed point o. the displacement, x metres, of the  particle, t seconds after it passes through o, is given by     cos x t t 5 3 2 3 = - +.  \u2002(i)\u2002find expressions for the velocity and acceleration of the particle after t seconds.  [3] \u2002(ii)\u2002find the maximum velocity of the particle and the value of t at which this first occurs.  [3]",
            "13": "13 0606/23/o/n/14 \u00a9 ucles 2014 [turn\u2002over\u2002(iii)\u2002find the value of t when the velocity of the particle is first equal to 2  ms\u22121 and its acceleration at  this time.\u2002 [3]",
            "14": "14 0606/23/o/n/14 \u00a9 ucles 20149\u2002(i)\u2002determine the coordinates and nature of each of the two turning points on the  \u2002 \u2002 curve     y xx421= +-. [6]",
            "15": "15 0606/23/o/n/14 \u00a9 ucles 2014 [turn\u2002over\u2002(ii)\u2002find the equation of the normal to the curve at the point (3,  13) and find the x-coordinate of the  point where this normal cuts the curve again.  [6]",
            "16": "16 0606/23/o/n/14 \u00a9 ucles 201410\u2002(i)\u2002prove that     cos c oscosecx xx11 1122 -++= . [3] \u2002(ii)\u2002hence solve the equation     cos c os x x 11 118-++=  for \u00b0 \u00b0x 0 3601 1 . [4] permission \bto\breproduce \bitems \bwhere \bthird-party \bowned \bmaterial \bprotected \bby\bcopyright \bis\bincluded \bhas\bbeen \bsought \band\bcleared \bwhere \bpossible. \bevery \b reasonable \beffort \bhas\bbeen \bmade \bby\bthe\bpublisher \b(ucles) \bto\btrace \bcopyright \bholders, \bbut\bif\bany\bitems \brequiring \bclearance \bhave \bunwittingly \bbeen \bincluded, \bthe\b publisher \bwill\bbe\bpleased \bto\bmake \bamends \bat\bthe\bearliest \bpossible \bopportunity. cambridge \binternational \bexaminations \bis\bpart\bof\bthe\bcambridge \bassessment \bgroup. \bcambridge \bassessment \bis\bthe\bbrand \bname \bof\buniversity \bof\bcambridge \blocal \b examinations \bsyndicate \b(ucles), \bwhich \bis\bitself \ba\bdepartment \bof\bthe\buniversity \bof\bcambridge."
        }
    },
    "2015": {
        "0606_m15_qp_12.pdf": {
            "1": "this document consists of 16 printed pages. dc (cw/sg) 99296/4 \u00a9 ucles 2015  [turn overcambridge international examinations cambridge international general certificate of secondary education * 0 9 8 5 1 4 8 7 5 5 * additional mathematics  0606/12 paper 1  february/march 2015  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/12/f/m/15 \u00a9 ucles 2015mathematical formulae 1.\u2002algebra quadratic equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/12/f/m/15 \u00a9 ucles 2015 [turn\u2002over1\u2002a sports club has members who play a variety of sports. sets c, f and t are such that   c = { members who play cricket},   f = { members who play football},   t = { members who play tennis}.  describe the following in words. \u2002(i)\u2002c f, [1] \u2002(ii)\u2002tl [1] \u2002(iii)\u2002f t+ q= [1] \u2002(iv)\u2002 ( )c t 10 n+=  [1]",
            "4": "4 0606/12/f/m/15 \u00a9 ucles 20152\u2002find the values of k for which the line y k x3 = - does not meet the curve y x x k 2 32= - +. [5]",
            "5": "5 0606/12/f/m/15 \u00a9 ucles 2015 [turn\u2002over3\u2002(i)\u2002on the axes below sketch the graph of y x 4 5= - ,stating the coordinates of the points  where the graph meets the coordinate axes.  [3] y xo \u2002(ii)\u2002solve x 4 5 9 - = . [3]",
            "6": "6 0606/12/f/m/15 \u00a9 ucles 20154\u2002(i)\u2002write down, in ascending powers of x, the first 3 terms in the expansion of ( ) x 3 26+ .  give each term in its simplest form.  [3] \u2002(ii)\u2002hence find the coefficient of x2 in the expansion of ( ) ( )x x2 3 26- + . [2]",
            "7": "7 0606/12/f/m/15 \u00a9 ucles 2015 [turn\u2002over5\u2002 (2, 1)(3, 5)e y o x \u2002 variables x and y are such that when ey is plotted against x a straight line graph is obtained. the  diagram shows this straight line graph which passes through the points (2, 1) and (3, 5). \u2002(i)\u2002express y in terms of x. [4] \u2002(ii)\u2002state the values of x for which y exists.  [1] \u2002(iii)\u2002find the value of x when lny 6= . [1]",
            "8": "8 0606/12/f/m/15 \u00a9 ucles 20156\u2002(i)\u2002given thattanyxx2= ,find xy dd. [3] \u2002(ii)\u2002hence find the equation of the normal to the curvetanyxx2= at the point where x8r=. [3]",
            "9": "9 0606/12/f/m/15 \u00a9 ucles 2015 [turn\u2002over7\u2002the polynomial ( )x a x bx x 3 4 p3 2= + - - has a factor of x2 1- and leaves a remainder  of 10- when divided by x2+. \u2002(i)\u2002show that a10=  and find the value of b. [4] \u2002(ii)\u2002given that ( ) ( ) ( ) x x rx sx t 2 1 p2= - + + ,find the value of each of the integers  r, s and t. [2] \u2002(iii)\u2002hence find the exact solutions of ( )x 0 p=. [3]",
            "10": "10 0606/12/f/m/15 \u00a9 ucles 20158\u2002(a)\u2002a function f is such that ( ) sin 2 fi i=  for 02g gir. \u2002 \u2002 (i)\u2002write down the range of f.  [1] \u2002 \u2002(ii)\u2002write down a suitable restricted domain for f such that f1- exists.  [1] \u2002(b)\u2002functions g and h are such that     ( ) ln x x 2 4 g= +  for x02,     ( )x x 4 h2= +  for  x02. \u2002 \u2002 (i)\u2002find g1-, stating its domain and its range.  [4] \u2002 \u2002(ii)\u2002solve ( )x 10 gh= . [3]",
            "11": "11 0606/12/f/m/15 \u00a9 ucles 2015 [turn\u2002over\u2002 \u2002(iii)\u2002solve ( ) ( ) x xg h=l l . [3]",
            "12": "12 0606/12/f/m/15 \u00a9 ucles 20159 x cm x cm y cmx cm \u2002 the diagram shows an empty container in the form of an open triangular prism. the triangular faces  are equilateral with a side of x cm and the length of each rectangular face is y cm. the container is  made from thin sheet metal. when full, the container holds 200 3 cm3. \u2002(i)\u2002show that a cm2 , the total area of the thin sheet metal used, is given by  axx 23 16002 = + . [5]",
            "13": "13 0606/12/f/m/15 \u00a9 ucles 2015 [turn\u2002over\u2002(ii)\u2002given that x and y can vary, find the stationary value of a and determine its nature.  [6]",
            "14": "14 0606/12/f/m/15 \u00a9 ucles 201510\u2002do\u2002not\u2002use\u2002a\u2002calculator \u2002in\u2002this\u2002question. a b c\u03b8( ) cm 1 2 5+ ( ) cm 2 5+ \u2002 the diagram shows triangle abc  which is right-angled at the point b. the side ab 1 2 5 = +^ h  cm  and the side bc 5 2= +^ h  cm. angle bcai=. \u2002(i)\u2002find tani in the form a b 5+ , where a and b are integers to be found.  [3] \u2002(ii)\u2002hence find sec2i in the form c d 5+ , where c and d are integers to be found.  [3]",
            "15": "15 0606/12/f/m/15 \u00a9 ucles 2015 [turn\u2002over11\u2002(a)\u2002(i)\u2002show thatcot t ancoseccosx xxx+= . [3] \u2002 \u2002(ii)\u2002hence solve .cot t ancosec y yy 3 330 5+=    for y0g g r radians, giving your answers in  terms of r. [3] question \u200211(b)\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.",
            "16": "16 0606/12/f/m/15 \u00a9 ucles 2015\u2002(b)\u2002solve sin c os z z 2 8 52+ =   for z 0 360 \u00b0 \u00b01 1 . [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."
        },
        "0606_m15_qp_22.pdf": {
            "1": "this document consists of 16 printed pages. dc (ac/fd) 99297/4 \u00a9 ucles 2015  [turn overcambridge international examinations cambridge international general certificate of secondary education * 8 4 7 5 1 4 8 9 1 2 * additional mathematics  0606/22 paper 2  february/march 2015  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/22/f/m/15 \u00a9 ucles 2015mathematical formulae 1.\u2002algebra quadratic equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a ",
            "3": "3 0606/22/f/m/15 \u00a9 ucles 2015 [turn\u2002over1\u2002(i)\u2002state the amplitude of cosx 4 3 -. [1] \u2002(ii)\u2002state the period of cosx 4 3 -. [1] \u2002(iii)\u2002the function f is defined, for x 0 360 c cg g , by ( ) cos x x 4 3 f= - . sketch the graph of ( ) y x f=  on  the axes below.  [2] 90\u00b005y x \u20135180\u00b0 270\u00b0 360\u00b0 \u2002",
            "4": "4 0606/22/f/m/15 \u00a9 ucles 20152\u2002(a)\u2002jean has nine different flags. \u2002 \u2002 (i)\u2002\u2002find the number of different ways in which jean can choose three flags from her nine flags.   [1] \u2002 \u2002(ii)\u2002jean has five flagpoles in a row. she puts one of her nine flags on each flagpole. calculate the  number of different five-flag arrangements she can make.  [1] \u2002(b)\u2002\u2002\u2002the six digits of the number 738925 are rearranged so that the resulting six-digit number is even.  find the number of different ways in which this can be done.   [2] \u2002",
            "5": "5 0606/22/f/m/15 \u00a9 ucles 2015 [turn\u2002over3\u2002\u2002solve the simultaneous equations ., y xx x y y 2 43 2 162 2 - =- + =  [5]",
            "6": "6 0606/22/f/m/15 \u00a9 ucles 20154\u2002\u2002(i)\u2002differentiate   sin c osx x    with respect to x, giving your answer in terms of sin x. [3] \u2002(ii)\u2002hence find sinx xd2y . [3]",
            "7": "7 0606/22/f/m/15 \u00a9 ucles 2015 [turn\u2002over5\u2002\u2002the position vectors of the points a and b relative to an origin o are \u22122i + 17j and 6i + 2j respectively. \u2002(i)\u2002find the vector ab. [1] \u2002(ii)\u2002find the unit vector in the direction of ab.  [2] \u2002(iii)\u2002the position vector of the point c relative to the origin o is such that m oc oa ob = + , where m  is a constant. given that c lies on the x-axis, find the vector oc.  [3]",
            "8": "8 0606/22/f/m/15 \u00a9 ucles 20156\u2002 b c o\u03b8 rad 20 cma \u2002 aob  is a sector of a circle with centre o and radius 20  cm. angle aob  = \u03b8 radians. aoc  is a straight  line and triangle obc  is isosceles with ob = oc.  \u2002 \u2002(i)\u2002given that the length of the arc ab is 15\u03c0 cm, find the exact value of \u03b8.  [2] \u2002(ii)\u2002find the area of the shaded region.  [4]",
            "9": "9 0606/22/f/m/15 \u00a9 ucles 2015 [turn\u2002over7\u2002it is given that a = 1 35 10- -j lkkn poo and b = 3 45 10j lkkn poo. \u2002(i)\u2002find a2 + b. [2] \u2002(ii)\u2002find det b. [1] \u2002(iii)\u2002find the inverse matrix, b\u22121. [2] \u2002(iv)\u2002find the matrix x, given that bx = a. [2]",
            "10": "10 0606/22/f/m/15 \u00a9 ucles 20158\u2002solutions \u2002to\u2002this\u2002question\u2002by\u2002accurate\u2002drawing\u2002will\u2002not\u2002be\u2002accepted. \u2002 the points a and b have coordinates (2, \u22121) and (6, 5) respectively. \u2002(i)\u2002find the equation of the perpendicular bisector of ab, giving your answer in the form ax by c + = ,  where a, b and c are integers.  [4] \u2002 the point c has coordinates (10, \u22122). \u2002(ii)\u2002find the equation of the line through c which is parallel to ab.    [2] \u2002",
            "11": "11 0606/22/f/m/15 \u00a9 ucles 2015 [turn\u2002over\u2002(iii)\u2002calculate the length of bc. [2] \u2002(iv)\u2002show that triangle abc  is isosceles.    [1]",
            "12": "12 0606/22/f/m/15 \u00a9 ucles 20159\u2002 y =4 (2x + 1)2+ 2xy a oy = 4x x \u2002 the diagram shows part of the curve ( )yxx2 1422=++  and the line y = 4x. \u2002(i)\u2002find the coordinates of a, the stationary point of the curve.    [5] \u2002(ii)\u2002verify that a is also the point of intersection of the curve ( )yxx2 1422=++  and the line y = 4x.  [1]",
            "13": "13 0606/22/f/m/15 \u00a9 ucles 2015 [turn\u2002over\u2002(iii)\u2002without\u2002using\u2002a\u2002calculator , find the area of the shaded region enclosed by the line y = 4x, the  curve and the y-axis.  [6]",
            "14": "14 0606/22/f/m/15 \u00a9 ucles 201510\u2002(a)\u2002(i)\u2002sketch the graph of y 5 ex= -  on the axes below, showing the exact coordinates of any  points where the graph meets the  coordinate axes.   [3] o xy \u2002 \u2002(ii)\u2002find the range of values of k for which the equation k5 ex- =  has no solutions.   [1] \u2002(b)\u2002simplify log l og log 2 821 a a a+ +j lkkn poo, giving your answer in the form logp 2a, where p is a  constant.  [2] \u2002(c)\u2002solve the equation log l ogx x 4 13 9- = . [4]",
            "15": "15 0606/22/f/m/15 \u00a9 ucles 2015 [turn\u2002over11\u2002\u2002(a)\u2002a particle p moves in a straight line. starting from rest, p moves with constant acceleration for  30 seconds after which it moves with constant velocity, k ms\u22121, for 90 seconds. p then moves  with constant deceleration until it comes to rest; the magnitude of the deceleration is twice the  magnitude of the initial acceleration. \u2002 \u2002 (i)\u2002use the information to complete the velocity-time graph.    [2] t secondsv ms \u20131 k o \u2002 \u2002(ii)\u2002given that the particle travels 450 metres while it is accelerating, find the value of k and the  acceleration of the particle.    [4] question \u200211(b)\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page. \u2002",
            "16": "16 0606/22/f/m/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.\u2002(b)\u2002a body q moves in a straight line such that, t seconds after passing a fixed point, its acceleration,  a ms\u22122, is given by a t3 62= + . when t = 0, the velocity of the body is 5  ms\u22121. find the velocity  when t = 3. [5] "
        },
        "0606_s15_qp_11.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (rw/sw) 91459/2 \u00a9 ucles 2015  [turn overcambridge international examinations cambridge international general certificate of secondary education * 1 1 1 2 0 1 6 0 6 9 * additional mathematics  0606/11 paper 1  may/june 2015  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/11/m/j/15 \u00a9 ucles 2015mathematical formulae 1.\u2002algebra quadratic \u2002equation  for the equation ax2 + bx + c = 0, xab b ac 242!=- - binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/11/m/j/15 \u00a9 ucles 2015 [turn\u2002over1\u2002(i)\u2002state the period of sinx2. [1] \u2002(ii)\u2002state the amplitude of cos x 1 2 3 + . [1] \u2002(iii)\u2002on the axes below, sketch the graph of \u2002 \u2002 (a)\u2002 sin y x 2=      for \u00b0 \u00b0x 0 180 g g , [1] \u2002 \u2002(b)\u2002 cos y x 1 2 3 = +      for \u00b0 \u00b0x 0 180 g g . [2] o \u2013245\u00b0 90\u00b0 135\u00b0 180\u00b024 \u20134y x \u2002(iv)\u2002state the number of solutions of     sin c os x x2 2 3 1 - =  for \u00b0 \u00b0x 0 180 g g . [1]",
            "4": "4 0606/11/m/j/15 \u00a9 ucles 20152\u2002do\u2002not\u2002use\u2002a\u2002calculator \u2002in\u2002this\u2002question . 4 3 2+^ h c b cm  cma 5 28+^ hradi \u2002 the diagram shows the triangle abc  where angle b is a right angle, ab 4 3 2 = +^ h  cm,  bc 8 5 2 = +^ h  cm and angle bac i= radians. showing all your working, find \u2002(i)\u2002tani in the form a b 2+ , where a and b are integers,  [2] \u2002(ii)\u2002sec2i in the form c d 2+ , where c and d are integers.  [3]",
            "5": "5 0606/11/m/j/15 \u00a9 ucles 2015 [turn\u2002over3\u2002(i)\u2002find the first 4 terms in the expansion of     x226+^ h      in ascending powers of x. [3] \u2002(ii)\u2002find the term independent of x in the expansion of     xx2 13 26 22 + -^ ch m. [3]",
            "6": "6 0606/11/m/j/15 \u00a9 ucles 20154\u2002(a)\u2002given that the matrix k2 4 0x=-j lkkn poo, find x2 in terms of the constant k. [2] \u2002(b)\u2002given that the matrix a b1 5a=j lkkn poo and the matrix 65 3261 31a1= -- -j lk kkn po oo, find the value of each of the  \u2002 \u2002 integers a and b. [3]",
            "7": "7 0606/11/m/j/15 \u00a9 ucles 2015 [turn\u2002over5\u2002the curve      y x y x 42= + -     intersects the line      y x3 1= -      at the points a and b. find the  equation of the perpendicular bisector of the line ab. [8]",
            "8": "8 0606/11/m/j/15 \u00a9 ucles 20156\u2002the polynomial      x ax x bx 15 2 f3 2= - + - ^ h      has a factor of      x2 1-     and a remainder of 5 when  divided by     x1-. \u2002(i)\u2002show that b8= and find the value of a. [4] \u2002(ii)\u2002using the values of a and b from part (i), express xf^ h in the form x2 1- ^ h  xg^ h, where xg^ h is a  quadratic factor to be found.  [2] \u2002(iii)\u2002show that the equation x 0 f= ^ h  has only one real root.  [2]",
            "9": "9 0606/11/m/j/15 \u00a9 ucles 2015 [turn\u2002over7\u2002the point a, where x0=, lies on the curve lnyxx 14 32 =-+ ^ h. the normal to the curve at a meets the  x-axis at the point b. \u2002(i)\u2002find the equation of this normal.  [7] \u2002(ii)\u2002find the area of the triangle aob , where o is the origin.  [2]",
            "10": "10 0606/11/m/j/15 \u00a9 ucles 20158\u2002it is given that  x 3 f ex2= ^ h      for x0h, \u2002\u2002 \u2002 \u2002 x x 2 5 g2= + + ^ ^h h \u2002\u2002\u2002\u2002\u2002for x0h. \u2002(i)\u2002write down the range of f and of g.  [2] \u2002(ii)\u2002find g1-, stating its domain.  [3] \u2002(iii)\u2002find the exact solution of x 41 gf= ^ h . [4]",
            "11": "11 0606/11/m/j/15 \u00a9 ucles 2015 [turn\u2002over\u2002(iv)\u2002evaluate ln4 fl^ h . [2]",
            "12": "12 0606/11/m/j/15 \u00a9 ucles 20159 ocd by xy = x3 \u2013 5x2 + 3x + 10y = 3x + 10 a \u2002 the diagram shows parts of the line      y x3 10= +      and the curve      y x x x 5 3 103 2= - + + .  the line and the curve both pass through the point a on the y-axis. the curve has a maximum at the  point b and a minimum at the point c. the line through c, parallel to the y-axis, intersects the line       y x3 10= +      at the point d. \u2002(i)\u2002show that the line ad is a tangent to the curve at a. [2] \u2002(ii)\u2002find the x-coordinate of b and of c. [3]",
            "13": "13 0606/11/m/j/15 \u00a9 ucles 2015 [turn\u2002over\u2002(iii)\u2002find the area of the shaded region abcd , showing all your working.  [5]",
            "14": "14 0606/11/m/j/15 \u00a9 ucles 201510\u2002(a)\u2002solve     sin c osec x x 4 =      for \u00b0 \u00b0x 0 360 g g . [3] \u2002(b)\u2002solve     tan s ec y y3 2 3 2 02- - =     for \u00b0 \u00b0y 0 180 g g . [6]",
            "15": "15 0606/11/m/j/15 \u00a9 ucles 2015\u2002(c)\u2002solve     tanz33r- =` j      for z0 2g g r radians.  [3]",
            "16": "16 0606/11/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.blank\u2002page"
        },
        "0606_s15_qp_12.pdf": {
            "1": "additional mathematics \b 0606/12 paper \b1\b may/june 2015 \b 2 hours candidates \banswer \bon\bthe\bquestion \bpaper. additional \bmaterials: \b electronic \bcalculator read these instructions first write \byour\bcentre \bnumber, \bcandidate \bnumber \band\bname \bon\ball\bthe\bwork \byou\bhand \bin. write \bin\bdark\bblue\bor\bblack \bpen. y ou\bmay\buse\ban\bhb\bpencil \bfor\bany\bdiagrams \bor\bgraphs. do\bnot\buse\bstaples, \bpaper \bclips, \bglue\bor\bcorrection \bfluid. do\bnot \bwrite \bin\bany \bbarcodes. answer \ball\bthe\bquestions. give \bnon-exact \bnumerical \banswers \bcorrect \bto\b3\bsignificant \bfigures, \bor\b1\bdecimal \bplace \bin\bthe\bcase \bof\b angles \bin\bdegrees, \bunless \ba\bdifferent \blevel\bof\baccuracy \bis\bspecified \bin\bthe\bquestion. the\buse\bof\ban\belectronic \bcalculator \bis\bexpected, \bwhere \bappropriate. y ou\bare\breminded \bof\bthe\bneed \bfor\bclear \bpresentation \bin\byour\banswers. at\bthe\bend\bof\bthe\bexamination, \bfasten \ball\byour\bwork \bsecurely \btogether. the\bnumber \bof\bmarks \bis\bgiven \bin\bbrackets \b[\b]\bat\bthe\bend\bof\beach \bquestion \bor\bpart\bquestion. the\btotal\bnumber \bof\bmarks \bfor\bthis\bpaper \bis\b80. this\bdocument \bconsists \bof\b16\bprinted \bpages. dc\b(cw/jg) \b91463/2 \u00a9\bucles \b2015\b [turn overcambridge international examinations cambridge \binternational \bgeneral \bcertificate \bof\bsecondary \beducation * 9 9 3 7 8 4 8 4 1 4 *",
            "2": "2 0606/12/m/j/15 \u00a9 ucles 2015mathematical formulae 1.\u2002algebra quadratic equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/12/m/j/15 \u00a9 ucles 2015 [turn\u2002over1\u2002given that the graph of ( ) y k x k x 2 5 12= + + + does not meet the x-axis, find the possible values  of k. [4] 2\u2002show that cosectan c otsecii ii+= . [4]",
            "4": "4 0606/12/m/j/15 \u00a9 ucles 20153\u2002find the inverse of the matrix 4 52 3j lkkn poo and hence solve the simultaneous equations x y4 2 8 0 + - =,  x y5 3 9 0 + - =. [5]",
            "5": "5 0606/12/m/j/15 \u00a9 ucles 2015 [turn\u2002over4 1.7rad 2.4rada cb 12 cmo \u2002 the diagram shows a circle, centre o, radius 12  cm. the points a, b and c lie on the circumference of  this circle such that angle aob  is 1.7 radians and angle aoc  is 2.4 radians. \u2002(i)\u2002find the area of the shaded region.  [4] \u2002(ii)\u2002find the perimeter of the shaded region.  [5]",
            "6": "6 0606/12/m/j/15 \u00a9 ucles 20155\u2002(a)\u2002a security code is to be chosen using 6 of the following:    \u2022 the letters a, b and c    \u2022 the numbers 2, 3 and 5    \u2022 the symbols * and $. \u2002 \u2002 none of the above may be used more than once. find the number of different security codes that  may be chosen if \u2002 \u2002 (i)\u2002there are no restrictions,  [1] \u2002 \u2002(ii)\u2002the security code starts with a letter and finishes with a symbol,  [2] \u2002 \u2002(iii)\u2002the two symbols are next to each other in the security code.  [3]",
            "7": "7 0606/12/m/j/15 \u00a9 ucles 2015 [turn\u2002over\u2002(b)\u2002two teams, each of 4 students, are to be selected from a class of 8 boys and 6 girls. find the  number of different ways the two teams may be selected if \u2002 \u2002 (i)\u2002there are no restrictions,  [2] \u2002 \u2002(ii)\u2002one team is to contain boys only and the other team is to contain girls only . [2]",
            "8": "8 0606/12/m/j/15 \u00a9 ucles 20156\u2002a particle moves in a straight line such that its displacement, x m, from a fixed point o after t s, is  given by ln x t t 10 4 42= + - ^ h . \u2002(i)\u2002find the initial displacement of the particle from o. [1] \u2002(ii)\u2002find the values of t when the particle is instantaneously at rest.  [4]",
            "9": "9 0606/12/m/j/15 \u00a9 ucles 2015 [turn\u2002over\u2002(iii)\u2002find the value of t when the acceleration of the particle is zero.  [5]",
            "10": "10 0606/12/m/j/15 \u00a9 ucles 20157 a x c d7a4ab b \u2002 in the diagram ab = 4a, bc = b and dc = 7a. the lines ac and db intersect at the point x. find, in  terms of a and b, \u2002(i)\u2002da, [1] \u2002(ii)\u2002db. [1] \u2002 given that ax acm= , find, in terms of a, b and m, \u2002(iii)\u2002ax, [1] \u2002(iv)\u2002dx. [2]",
            "11": "11 0606/12/m/j/15 \u00a9 ucles 2015 [turn\u2002over\u2002 given that dx dbn= , \u2002(v)\u2002find the value of m and of n. [4]",
            "12": "12 0606/12/m/j/15 \u00a9 ucles 20158\u2002(i)\u2002find x 10e e dx x2 2+-^ hy . [2] \u2002(ii)\u2002hence find ( ) x 10e e dx x kk2 2+- -y  in terms of the constant k. [2] \u2002(iii)\u2002given that ( ) x 10 60 e e dx x kk2 2+ = -- -y , show that 11 11 120 0 e ek k2 2- + =-. [2]",
            "13": "13 0606/12/m/j/15 \u00a9 ucles 2015 [turn\u2002over\u2002(iv)\u2002using a substitution of yek2=  or otherwise, find the value of k in the form lna b , where  a and b are constants.  [3]",
            "14": "14 0606/12/m/j/15 \u00a9 ucles 20159\u2002a curve has equation cos y x x 4 3 2 = + . the normal to the curve at the point where x4r= meets  the x- and y-axes at the points a and b respectively. find the exact area of the triangle aob ,  where o is the origin.  [8]",
            "15": "15 0606/12/m/j/15 \u00a9 ucles 2015 [turn\u2002over10\u2002(a)\u2002solve cos s ec x x 2 3 3=   for \u00b0 \u00b0x 0 120 g g . [3] \u2002(b)\u2002solve cosec c ot y y 3 5 5 02+ - =  for \u00b0 \u00b0y 0 360 g g . [5] question \u200210(c)\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.",
            "16": "16 0606/12/m/j/15 \u00a9 ucles 2015\u2002(c)\u2002solve sinz 231r+ =j lkkn poo    for   z0 2g g r radians.  [4] permission \bto\breproduce \bitems \bwhere \bthird-party \bowned \bmaterial \bprotected \bby\bcopyright \bis\bincluded \bhas\bbeen \bsought \band\bcleared \bwhere \bpossible. \bevery \breasonable \b effort \bhas\bbeen \bmade \bby\bthe\bpublisher \b(ucles) \bto\btrace \bcopyright \bholders, \bbut\bif\bany\bitems \brequiring \bclearance \bhave \bunwittingly \bbeen \bincluded, \bthe\bpublisher \bwill\b be\bpleased \bto\bmake \bamends \bat\bthe\bearliest \bpossible \bopportunity. to\bavoid \bthe\bissue \bof\bdisclosure \bof\banswer-related \binformation \bto\bcandidates, \ball\bcopyright \backnowledgements \bare\breproduced \bonline \bin\bthe\bcambridge \binternational \b examinations \bcopyright \backnowledgements \bbooklet. \bthis\bis\bproduced \bfor\beach \bseries \bof\bexaminations \band\bis\bfreely \bavailable \bto\bdownload \bat\bwww.cie.org.uk \bafter\b the\blive\bexamination \bseries. cambridge \binternational \bexaminations \bis\bpart\bof\bthe\bcambridge \bassessment \bgroup. \bcambridge \bassessment \bis\bthe\bbrand \bname \bof\buniversity \bof\bcambridge \blocal \b examinations \bsyndicate \b(ucles), \bwhich \bis\bitself \ba\bdepartment \bof\bthe\buniversity \bof\bcambridge."
        },
        "0606_s15_qp_13.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (st/sw) 105918 \u00a9 ucles 2015  [turn overcambridge international examinations cambridge international general certificate of secondary education * 7 5 5 2 6 5 9 0 8 8 * additional mathematics  0606/13 paper 1  may/june 2015  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/13/m/j/15 \u00a9 ucles 2015mathematical formulae 1.\u2002algebra quadratic \u2002equation  for the equation ax2 + bx + c = 0, xab b ac 242!=- - binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/13/m/j/15 \u00a9 ucles 2015 [turn\u2002over1\u2002(i)\u2002state the period of sinx2. [1] \u2002(ii)\u2002state the amplitude of cos x 1 2 3 + . [1] \u2002(iii)\u2002on the axes below, sketch the graph of \u2002 \u2002 (a)\u2002 sin y x 2=      for \u00b0 \u00b0x 0 180 g g , [1] \u2002 \u2002(b)\u2002 cos y x 1 2 3 = +      for \u00b0 \u00b0x 0 180 g g . [2] o \u2013245\u00b0 90\u00b0 135\u00b0 180\u00b024 \u20134y x \u2002(iv)\u2002state the number of solutions of     sin c os x x2 2 3 1 - =  for \u00b0 \u00b0x 0 180 g g . [1]",
            "4": "4 0606/13/m/j/15 \u00a9 ucles 20152\u2002do\u2002not\u2002use\u2002a\u2002calculator \u2002in\u2002this\u2002question . 4 3 2+^ h c b cm  cma 5 28+^ hradi \u2002 the diagram shows the triangle abc  where angle b is a right angle, ab 4 3 2 = +^ h  cm,  bc 8 5 2 = +^ h  cm and angle bac i= radians. showing all your working, find \u2002(i)\u2002tani in the form a b 2+ , where a and b are integers,  [2] \u2002(ii)\u2002sec2i in the form c d 2+ , where c and d are integers.  [3]",
            "5": "5 0606/13/m/j/15 \u00a9 ucles 2015 [turn\u2002over3\u2002(i)\u2002find the first 4 terms in the expansion of     x226+^ h      in ascending powers of x. [3] \u2002(ii)\u2002find the term independent of x in the expansion of     xx2 13 26 22 + -^ ch m. [3]",
            "6": "6 0606/13/m/j/15 \u00a9 ucles 20154\u2002(a)\u2002given that the matrix k2 4 0x=-j lkkn poo, find x2 in terms of the constant k. [2] \u2002(b)\u2002given that the matrix a b1 5a=j lkkn poo and the matrix 65 3261 31a1= -- -j lk kkn po oo, find the value of each of the  \u2002 \u2002 integers a and b. [3]",
            "7": "7 0606/13/m/j/15 \u00a9 ucles 2015 [turn\u2002over5\u2002the curve      y x y x 42= + -     intersects the line      y x3 1= -      at the points a and b. find the  equation of the perpendicular bisector of the line ab. [8]",
            "8": "8 0606/13/m/j/15 \u00a9 ucles 20156\u2002the polynomial      x ax x bx 15 2 f3 2= - + - ^ h      has a factor of      x2 1-     and a remainder of 5 when  divided by     x1-. \u2002(i)\u2002show that b8= and find the value of a. [4] \u2002(ii)\u2002using the values of a and b from part (i), express xf^ h in the form x2 1- ^ h  xg^ h, where xg^ h is a  quadratic factor to be found.  [2] \u2002(iii)\u2002show that the equation x 0 f= ^ h  has only one real root.  [2]",
            "9": "9 0606/13/m/j/15 \u00a9 ucles 2015 [turn\u2002over7\u2002the point a, where x0=, lies on the curve lnyxx 14 32 =-+ ^ h. the normal to the curve at a meets the  x-axis at the point b. \u2002(i)\u2002find the equation of this normal.  [7] \u2002(ii)\u2002find the area of the triangle aob , where o is the origin.  [2]",
            "10": "10 0606/13/m/j/15 \u00a9 ucles 20158\u2002it is given that  x 3 f ex2= ^ h      for x0h, \u2002\u2002 \u2002 \u2002 x x 2 5 g2= + + ^ ^h h \u2002\u2002\u2002\u2002\u2002for x0h. \u2002(i)\u2002write down the range of f and of g.  [2] \u2002(ii)\u2002find g1-, stating its domain.  [3] \u2002(iii)\u2002find the exact solution of x 41 gf= ^ h . [4]",
            "11": "11 0606/13/m/j/15 \u00a9 ucles 2015 [turn\u2002over\u2002(iv)\u2002evaluate ln4 fl^ h . [2]",
            "12": "12 0606/13/m/j/15 \u00a9 ucles 20159 ocd by xy = x3 \u2013 5x2 + 3x + 10y = 3x + 10 a \u2002 the diagram shows parts of the line      y x3 10= +      and the curve      y x x x 5 3 103 2= - + + .  the line and the curve both pass through the point a on the y-axis. the curve has a maximum at the  point b and a minimum at the point c. the line through c, parallel to the y-axis, intersects the line       y x3 10= +      at the point d. \u2002(i)\u2002show that the line ad is a tangent to the curve at a. [2] \u2002(ii)\u2002find the x-coordinate of b and of c. [3]",
            "13": "13 0606/13/m/j/15 \u00a9 ucles 2015 [turn\u2002over\u2002(iii)\u2002find the area of the shaded region abcd , showing all your working.  [5]",
            "14": "14 0606/13/m/j/15 \u00a9 ucles 201510\u2002(a)\u2002solve     sin c osec x x 4 =      for \u00b0 \u00b0x 0 360 g g . [3] \u2002(b)\u2002solve     tan s ec y y3 2 3 2 02- - =     for \u00b0 \u00b0y 0 180 g g . [6]",
            "15": "15 0606/13/m/j/15 \u00a9 ucles 2015\u2002(c)\u2002solve     tanz33r- =` j      for z0 2g g r radians.  [3]",
            "16": "16 0606/13/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.blank\u2002page"
        },
        "0606_s15_qp_21.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (leg/sw) 91464/2 \u00a9 ucles 2015  [turn overcambridge international examinations cambridge international general certificate of secondary education * 8 4 5 6 9 2 9 6 2 4 * additional mathematics  0606/21 paper 2  may/june 2015  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of   angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/21/m/j/15 \u00a9 ucles 2015mathematical formulae 1.\u2002algebra quadratic \u2002equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/21/m/j/15 \u00a9 ucles 2015 [turn\u2002over1\u2002(a)\u2002write  log x27 as a logarithm to base 3.  [2] \u2002(b)\u2002given that  log log log y3 1 5 3 1a a a= - + ^ h , express y in terms of a. [3]",
            "4": "4 0606/21/m/j/15 \u00a9 ucles 20152\u2002(a) o x 24y \u2002 \u2002 the diagram shows the graph of f () y x=  passing through 0,4^ h  and touching the x-axis at ,2 0^ h .  given that the graph of f () y x= is a straight line, write down the two possible expressions for f ()x.  [2] \u2002(b)\u2002on the axes below, sketch the graph of e y 3x= +-, stating the coordinates of any point of  intersection with the coordinate axes.  [3] o xy",
            "5": "5 0606/21/m/j/15 \u00a9 ucles 2015 [turn\u2002over3\u2002(a)\u2002find the matrix a if     a4 54 30 21 5 6552 318 219+-- -= c c m m. [2] \u2002(b)\u2002\u2002 p30 70 50 4025 15 40 2065 80 30 75=f p          q 650 500 450 225 =^ h \u2002 \u2002 the matrix p represents the number of 4 different televisions that are on sale in each of 3 shops.  the matrix q represents the value of each television in dollars. \u2002 \u2002 (i)\u2002state, without evaluation, what is represented by the matrix qp. [1] \u2002 \u2002(ii)\u2002given that the matrix r1 1 1=f p, state, without evaluation, what is represented by the matrix  qpr . [1]",
            "6": "6 0606/21/m/j/15 \u00a9 ucles 20154\u2002 rad43r8 cm o qp t \u2002 the diagram shows a circle, centre o, radius  8 cm. the points p and q lie on the circle. the lines pt and qt  are tangents to the circle and angle  poq43r=  radians. \u2002(i)\u2002find the length of pt. [2] \u2002(ii)\u2002find the area of the shaded region.  [3] \u2002(iii)\u2002find the perimeter of the shaded region.  [2]",
            "7": "7 0606/21/m/j/15 \u00a9 ucles 2015 [turn\u2002over5\u2002(a)\u2002a lock can be opened using only the number 4351. state whether this is a permutation or a \u2002 \u2002 combination of digits, giving a reason for your answer.  [1] \u2002(b)\u2002there are twenty numbered balls in a bag. two of the balls are numbered 0, six are numbered 1,  five are numbered 2 and seven are numbered 3, as shown in the table below . number on ball 0 1 2 3 frequency 2 6 5 7 \u2002 \u2002 four of these balls are chosen at random, without replacement. calculate the number of ways this  can be done so that \u2002 \u2002 (i)\u2002the four balls all have the same number,  [2] \u2002 \u2002(ii)\u2002the four balls all have different numbers,  [2] \u2002 \u2002(iii)\u2002the four balls have numbers that total 3.  [3]",
            "8": "8 0606/21/m/j/15 \u00a9 ucles 20156\u2002a particle p is projected from the origin o so that it moves in a straight line. at time t seconds after  projection, the velocity of the particle, v ms\u20131, is given by     v t t 2 14 1 22= - + . \u2002(i)\u2002find the time at which p first comes to instantaneous rest.  [2] \u2002(ii)\u2002find an expression for the displacement of p from o at time t seconds.  [3] \u2002(iii)\u2002find the acceleration of p when t = 3. [2]",
            "9": "9 0606/21/m/j/15 \u00a9 ucles 2015 [turn\u2002over7\u2002(a)\u2002the four points o, a, b and c are such that a oa 5= ,       b ob 15= ,       b a oc 24 3 = - . \u2002 \u2002 show that b lies on the line  ac. [3] \u2002(b)\u2002relative to an origin o, the position vector of the point p is   i \u2013 4j   and the position vector of the  point q is   3i + 7j. find \u2002 \u2002 (i)\u2002pq, [2] \u2002 \u2002(ii)\u2002the unit vector in the direction pq, [1] \u2002 \u2002(iii)\u2002the position vector of m, the mid-point of pq. [2]",
            "10": "10 0606/21/m/j/15 \u00a9 ucles 20158\u2002(a)\u2002(i)\u2002find e d xx4 3+y . [2] \u2002 \u2002(ii)\u2002hence evaluate e d x .x4 3 2 53+y . [2] \u2002(b)\u2002(i)\u2002find d cosxx3j lkkn poo y . [2] \u2002 \u2002(ii)\u2002hence evaluate d cosxx3 06r j lkkn poo y . [2]",
            "11": "11 0606/21/m/j/15 \u00a9 ucles 2015 [turn\u2002over\u2002(c)\u2002find d x x x12 +-^ hy . [4]",
            "12": "12 0606/21/m/j/15 \u00a9 ucles 20159\u2002(a)\u2002find the set of values of x for which   x x4 19 5 02g + - . [3] \u2002(b)\u2002(i)\u2002express x x 8 92+ -  in the form x a b2+ +^ h , where a and b are integers.  [2] \u2002 \u2002(ii)\u2002use your answer to part (i) to find the greatest value of x x 9 82- -  and the value of x at  which this occurs.  [2]",
            "13": "13 0606/21/m/j/15 \u00a9 ucles 2015 [turn\u2002over\u2002 \u2002(iii)\u2002sketch the graph of y x x 9 82= - -, indicating the coordinates of any points of intersection  with the coordinate axes.  [2] o xy",
            "14": "14 0606/21/m/j/15 \u00a9 ucles 201510\u2002the relationship between experimental values of two variables, x and y, is given by y a bx= , where a  and b are constants. \u2002(i)\u2002by transforming the relationship y a bx= , show that plotting lny against x should produce a  straight line graph.  [2] \u2002(ii)\u2002the diagram below shows the results of plotting ln  y against x for 7 different pairs of values of  variables, x and y. a line of best fit has been drawn. 6 1 0 2 3 4 5 6x810ln y 1112 579 \u2002 \u2002 by taking readings from the diagram, find the value of a and of b, giving each value correct to  1 significant figure.  [4] \u2002(iii)\u2002estimate the value of y when x = 2.5.  [2]",
            "15": "15 0606/21/m/j/15 \u00a9 ucles 201511 a b c/h5105 \u2002 the venn diagram above shows the sets a, b and c. it is given that \u2002 \u2002 na b c 48 , , = ^ h ,  \u2002 \u2002 na 30= ^ h ,  n()b 25= ,  n()c 15= , \u2002 \u2002 n( )a b 7 +=, nb c 6 += ^ h , na b c 16 + + = l l^ h . \u2002(i)\u2002find the value of x, where nx a b c+ + = ^ h . [3]  \u2002(ii)\u2002find the value of y, where ny a b c+ + = l ^ h . [3] \u2002(iii)\u2002hence show that a b c + + q= l l . [1] \u2002",
            "16": "16 0606/21/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.blank\u2002page"
        },
        "0606_s15_qp_22.pdf": {
            "1": "this document consists of 16 printed pages. dc (nh/sw) 91465/1 \u00a9 ucles 2015  [turn over * 8 8 7 8 4 1 0 8 4 3 * additional mathematics  0606/22 paper 2  may/june 2015  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge international examinations cambridge international general certificate of secondary education",
            "2": "2 0606/22/m/j/15 \u00a9 ucles 2015mathematical formulae 1.\u2002algebra quadratic equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/22/m/j/15 \u00a9 ucles 2015 [turn\u2002over1\u2002the universal set contains all the integers from 0 to 12 inclusive. given that  a = {1, 2, 3, 8, 12},    b = {0, 2, 3, 4, 6}    and   c = {1, 2, 4, 6, 7, 9, 10}, \u2002(i)\u2002complete the venn diagram,  [3] a b c/h5105 \u2002(ii)\u2002state the value of ( )a b c nk kl l , [1] \u2002(iii)\u2002write down the elements of the set a b ck kl . [1]",
            "4": "4 0606/22/m/j/15 \u00a9 ucles 20152\u2002the table shows the number of passengers in economy class and in business class on 3 flights from  london to paris. the table also shows the departure times for the 3 flights and the cost of a single ticket  in each class. departure time number of passengers in  economy classnumber of passengers in  business class 09 30 60 50 13 30 70 52 15 45 58 34 single ticket price (\u00a3) 120 300 \u2002(i)\u2002write down a matrix, p, for the numbers of passengers and a matrix, q, of single ticket prices,  such that the matrix product qp can be found.  [2] \u2002(ii)\u2002find the matrix product qp. [2] \u2002(iii)\u2002given that  1 1 1r=j lk kkn po oo, explain what information is found by evaluating the matrix product qpr . [1]",
            "5": "5 0606/22/m/j/15 \u00a9 ucles 2015 [turn\u2002over3\u2002do\u2002not\u2002use\u2002a\u2002calculator \u2002in\u2002this\u2002question. acmbc ( )6 3 5+ \u2002 the diagram shows the right-angled triangle abc , where 6 3 5 ab= +^ h cm and angle b = 90\u00b0. the \u2002 area of this triangle is 236 155cm2 +j lkkn poo . \u2002(i)\u2002find the length of the side bc in the form 5 a b cm +^ h , where a and b are integers.  [3] \u2002(ii)\u2002find ac2^ h  in the form 5 c d cm2+^ h , where c and d are integers.  [2]",
            "6": "6 0606/22/m/j/15 \u00a9 ucles 20154\u2002\u2002a river, which is 80  m wide, flows at 2  ms\u20131 between parallel, straight banks. a man wants to row his  boat straight across the river and land on the other bank directly opposite his starting point. he is able  to row his boat in still water at 3  ms\u20131. find \u2002(i)\u2002the direction in which he must row his boat,  [2] \u2002(ii)\u2002the time it takes him to cross the river.  [3]",
            "7": "7 0606/22/m/j/15 \u00a9 ucles 2015 [turn\u2002over5\u2002solve the simultaneous equations     2 3 7 , 4.x y xy x y2 2+ = + = [5] 6\u2002(a)\u2002solve 641 2x=-. [2] \u2002(b)\u2002solve 2 8 16 64 2 4 log l og log l og log y y y2 a a a a a+ + - = . [4]",
            "8": "8 0606/22/m/j/15 \u00a9 ucles 20157\u2002in the expansion of 1 2 xn+^ h , the coefficient of x4 is ten times the coefficient of x2. find the value of  the positive integer, n. [6]",
            "9": "9 0606/22/m/j/15 \u00a9 ucles 2015 [turn\u2002over8 b a c o xy y = x + 10 y = x2\u2013 6x + 10 \u2002 the graph of  6 10 y x x2= - +  cuts the y-axis at a. the graphs of  6 10 y x x2= - +  and 10 y x= +   cut one another at a and b. the line bc is perpendicular to the x-axis. calculate the area of the shaded  region enclosed by the curve and the line ab, showing all your working.  [8]",
            "10": "10 0606/22/m/j/15 \u00a9 ucles 20159\u2002solutions \u2002by\u2002accurate\u2002drawing\u2002will\u2002not\u2002be\u2002accepted. oy = mx + 4 24 \u20131qrp (2, 10) xy \u2002 the line 4 y m x= +  meets the lines 2x= and 1 x=-  at the points p and q respectively. the point r is  such that qr is parallel to the y-axis and the gradient of rp is 1. the point p has coordinates (2, 10). \u2002(i)\u2002find the value of m. [2] \u2002(ii)\u2002find the  y-coordinate of q. [1] \u2002(iii)\u2002find the coordinates of r. [2]",
            "11": "11 0606/22/m/j/15 \u00a9 ucles 2015 [turn\u2002over\u2002(iv)\u2002find the equation of the line through p, perpendicular to pq, giving your answer in the form  ax by c + = , where a, b and c are integers . [3] \u2002(v)\u2002find the coordinates of the midpoint, m, of the line pq. [2] \u2002(vi)\u2002find the area of triangle qrm . [2]",
            "12": "12 0606/22/m/j/15 \u00a9 ucles 201510\u2002(a)\u2002the function f is defined by  : s in x xf7  for 0\u00b0 360\u00b0xg g . on the axes below, sketch the  graph of ( ) y x f= . [2] o 90\u00b0 180\u00b0 270\u00b0 360\u00b0 xy \u2002(b)\u2002the functions g and hg are defined, for  1xh, by     4 3 , .ln x x x xg hg= - =^ ^ ^h h h \u2002 \u2002 (i)\u2002show that  43xhex =+^ h . [2]",
            "13": "13 0606/22/m/j/15 \u00a9 ucles 2015 [turn\u2002over\u2002 \u2002(ii) o x 1y = g(x)y \u2002 \u2002 the diagram shows the graph of  y xg= ^ h. given that g and h are inverse functions, sketch, on the  same diagram, the graph of  y xh= ^ h. give the coordinates of any point where your graph meets  the coordinate axes.  [2] \u2002 \u2002(iii)\u2002state the domain of h.  [1] \u2002 \u2002(iv)\u2002state the range of h.  [1]",
            "14": "14 0606/22/m/j/15 \u00a9 ucles 201511 o ab c d q psrh 48 \u2002 the diagram shows a cuboid of height h units inside a right pyramid opqrs  of height 8 units and with  square base of side 4 units. the base of the cuboid sits on the square base pqrs  of the pyramid. the  points a, b, c and d are corners of the cuboid and lie on the edges op, oq, or and os, respectively,  of the pyramid opqrs . the pyramids opqrs  and oabcd  are similar. \u2002(i)\u2002find an expression for ad in terms of h and hence show that the volume v of the cuboid is given \u2002 \u2002 by 44 16 vhh h32= - +  units3. [4]",
            "15": "15 0606/22/m/j/15 \u00a9 ucles 2015 [turn\u2002over\u2002(ii)\u2002given that h can vary, find the value of h for which v is a maximum.  [4] question \u200212\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.",
            "16": "16 0606/22/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\u2002(i)\u2002show that x = \u20132 is a root of the polynomial equation 15 26 11 6 0 x x x3 2+ - - = . [1] \u2002(ii)\u2002find the remainder when 15 26 11 6 x x x3 2+ - - is divided by x \u2013 3. [2] \u2002(iii)\u2002find the value of p and of q such that 15 26 11 6 x x x3 2+ - - is a factor of \u2002 \u2002 15 37 6 x px x qx4 2 3+ - + + . [4]"
        },
        "0606_s15_qp_23.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (nf/sw) 105994 \u00a9 ucles 2015  [turn overcambridge international examinations cambridge international general certificate of secondary education * 5 7 8 8 7 7 5 7 0 7 * additional mathematics  0606/23 paper 2  may/june 2015  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of   angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/23/m/j/15 \u00a9 ucles 2015mathematical formulae 1.\u2002algebra quadratic \u2002equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/23/m/j/15 \u00a9 ucles 2015 [turn\u2002over1\u2002(a)\u2002write  log x27 as a logarithm to base 3.  [2] \u2002(b)\u2002given that  log log log y3 1 5 3 1a a a= - + ^ h , express y in terms of a. [3]",
            "4": "4 0606/23/m/j/15 \u00a9 ucles 20152\u2002(a) o x 24y \u2002 \u2002 the diagram shows the graph of f () y x=  passing through 0,4^ h  and touching the x-axis at ,2 0^ h .  given that the graph of f () y x= is a straight line, write down the two possible expressions for f ()x.  [2] \u2002(b)\u2002on the axes below, sketch the graph of e y 3x= +-, stating the coordinates of any point of  intersection with the coordinate axes.  [3] o xy",
            "5": "5 0606/23/m/j/15 \u00a9 ucles 2015 [turn\u2002over3\u2002(a)\u2002find the matrix a if     a4 54 30 21 5 6552 318 219+-- -= c c m m. [2] \u2002(b)\u2002\u2002 p30 70 50 4025 15 40 2065 80 30 75=f p          q 650 500 450 225 =^ h \u2002 \u2002 the matrix p represents the number of 4 different televisions that are on sale in each of 3 shops.  the matrix q represents the value of each television in dollars. \u2002 \u2002 (i)\u2002state, without evaluation, what is represented by the matrix qp. [1] \u2002 \u2002(ii)\u2002given that the matrix r1 1 1=f p, state, without evaluation, what is represented by the matrix  qpr . [1]",
            "6": "6 0606/23/m/j/15 \u00a9 ucles 20154\u2002 rad43r8 cm o qp t \u2002 the diagram shows a circle, centre o, radius  8 cm. the points p and q lie on the circle. the lines pt and qt  are tangents to the circle and angle  poq43r=  radians. \u2002(i)\u2002find the length of pt. [2] \u2002(ii)\u2002find the area of the shaded region.  [3] \u2002(iii)\u2002find the perimeter of the shaded region.  [2]",
            "7": "7 0606/23/m/j/15 \u00a9 ucles 2015 [turn\u2002over5\u2002(a)\u2002a lock can be opened using only the number 4351. state whether this is a permutation or a \u2002 \u2002 combination of digits, giving a reason for your answer.  [1] \u2002(b)\u2002there are twenty numbered balls in a bag. two of the balls are numbered 0, six are numbered 1,  five are numbered 2 and seven are numbered 3, as shown in the table below . number on ball 0 1 2 3 frequency 2 6 5 7 \u2002 \u2002 four of these balls are chosen at random, without replacement. calculate the number of ways this  can be done so that \u2002 \u2002 (i)\u2002the four balls all have the same number,  [2] \u2002 \u2002(ii)\u2002the four balls all have different numbers,  [2] \u2002 \u2002(iii)\u2002the four balls have numbers that total 3.  [3]",
            "8": "8 0606/23/m/j/15 \u00a9 ucles 20156\u2002a particle p is projected from the origin o so that it moves in a straight line. at time t seconds after  projection, the velocity of the particle, v ms\u20131, is given by     v t t 2 14 1 22= - + . \u2002(i)\u2002find the time at which p first comes to instantaneous rest.  [2] \u2002(ii)\u2002find an expression for the displacement of p from o at time t seconds.  [3] \u2002(iii)\u2002find the acceleration of p when t = 3. [2]",
            "9": "9 0606/23/m/j/15 \u00a9 ucles 2015 [turn\u2002over7\u2002(a)\u2002the four points o, a, b and c are such that a oa 5= ,       b ob 15= ,       b a oc 24 3 = - . \u2002 \u2002 show that b lies on the line  ac. [3] \u2002(b)\u2002relative to an origin o, the position vector of the point p is   i \u2013 4j   and the position vector of the  point q is   3i + 7j. find \u2002 \u2002 (i)\u2002pq, [2] \u2002 \u2002(ii)\u2002the unit vector in the direction pq, [1] \u2002 \u2002(iii)\u2002the position vector of m, the mid-point of pq. [2]",
            "10": "10 0606/23/m/j/15 \u00a9 ucles 20158\u2002(a)\u2002(i)\u2002find e d xx4 3+y . [2] \u2002 \u2002(ii)\u2002hence evaluate e d x .x4 3 2 53+y . [2] \u2002(b)\u2002(i)\u2002find d cosxx3j lkkn poo y . [2] \u2002 \u2002(ii)\u2002hence evaluate d cosxx3 06r j lkkn poo y . [2]",
            "11": "11 0606/23/m/j/15 \u00a9 ucles 2015 [turn\u2002over\u2002(c)\u2002find d x x x12 +-^ hy . [4]",
            "12": "12 0606/23/m/j/15 \u00a9 ucles 20159\u2002(a)\u2002find the set of values of x for which   x x4 19 5 02g + - . [3] \u2002(b)\u2002(i)\u2002express x x 8 92+ -  in the form x a b2+ +^ h , where a and b are integers.  [2] \u2002 \u2002(ii)\u2002use your answer to part (i) to find the greatest value of x x 9 82- -  and the value of x at  which this occurs.  [2]",
            "13": "13 0606/23/m/j/15 \u00a9 ucles 2015 [turn\u2002over\u2002 \u2002(iii)\u2002sketch the graph of y x x 9 82= - -, indicating the coordinates of any points of intersection  with the coordinate axes.  [2] o xy",
            "14": "14 0606/23/m/j/15 \u00a9 ucles 201510\u2002the relationship between experimental values of two variables, x and y, is given by y a bx= , where a  and b are constants. \u2002(i)\u2002by transforming the relationship y a bx= , show that plotting lny against x should produce a  straight line graph.  [2] \u2002(ii)\u2002the diagram below shows the results of plotting ln  y against x for 7 different pairs of values of  variables, x and y. a line of best fit has been drawn. 6 1 0 2 3 4 5 6x810ln y 1112 579 \u2002 \u2002 by taking readings from the diagram, find the value of a and of b, giving each value correct to  1 significant figure.  [4] \u2002(iii)\u2002estimate the value of y when x = 2.5.  [2]",
            "15": "15 0606/23/m/j/15 \u00a9 ucles 201511 a b c/h5105 \u2002 the venn diagram above shows the sets a, b and c. it is given that \u2002 \u2002 na b c 48 , , = ^ h ,  \u2002 \u2002 na 30= ^ h ,  n()b 25= ,  n()c 15= , \u2002 \u2002 n( )a b 7 +=, nb c 6 += ^ h , na b c 16 + + = l l^ h . \u2002(i)\u2002find the value of x, where nx a b c+ + = ^ h . [3]  \u2002(ii)\u2002find the value of y, where ny a b c+ + = l ^ h . [3] \u2002(iii)\u2002hence show that a b c + + q= l l . [1] \u2002",
            "16": "16 0606/23/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.blank\u2002page"
        },
        "0606_w15_qp_11.pdf": {
            "1": "this document consists of 16 printed pages. dc (leg/cgw) 98539/3 \u00a9 ucles 2015  [turn overuniversity of cambridge international examinations international general certificate of secondary education * 6 1 3 3 6 0 6 8 8 6 * additional mathematics  0606/11 paper 1  october/november 2015  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/11/o/n/15 \u00a9 ucles 2015mathematical formulae 1.\u2002algebra quadratic \u2002equation  for the equation ax2 + bx + c = 0, xab b ac 242!=- - . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/11/o/n/15 \u00a9 ucles 2015 [turn\u2002over1\u2002find the range of values of k for which the equation   kx k x xk 8 22+ = -    has 2 real distinct roots.  [4]",
            "4": "4 0606/11/o/n/15 \u00a9 ucles 20152\u2002a curve, showing the relationship between two variables x and y, passes through the point  , p 1 3-^ h . \u2002 the curve has a gradient of 2 at p. given that     dd xy522 =- ,     find the equation of the curve.  [4]",
            "5": "5 0606/11/o/n/15 \u00a9 ucles 2015 [turn\u2002over3\u2002show that sec c osec sec cosec 1 12 2i i i i - + - = . [5]",
            "6": "6 0606/11/o/n/15 \u00a9 ucles 20154\u2002(a)\u20026 books are to be chosen from 8 different books. \u2002 \u2002 (i)\u2002find the number of different selections of 6 books that could be made.  [1] \u2002 \u2002 a clock is to be displayed on a shelf with 3 of the 8 different books on each side of it. find the  number of ways this can be done if \u2002 \u2002 (ii)\u2002there are no restrictions on the choice of books,  [1] \u2002 \u2002(iii)\u20023 of the 8 books are music books which have to be kept together.  [2] \u2002(b)\u2002a team of 6 tennis players is to be chosen from 10 tennis players consisting of 7 men and  3 women.  find the number of different teams that could be chosen if the team must include at  least 1 woman.  [3]",
            "7": "7 0606/11/o/n/15 \u00a9 ucles 2015 [turn\u2002over5\u2002variables x and y are such that   ln y x x 3 2 12= - + ^ ^h h. \u2002 \u2002 (i)\u2002find the value of  dd xy  when  x2=. [4] \u2002 \u2002 (ii)\u2002\u2002hence find the approximate change in y when x changes from 2 to 2.03.  [2]",
            "8": "8 0606/11/o/n/15 \u00a9 ucles 20156\u2002it is given that  \ue025 = ,where isanintege r x x x 1 12|g g \" ,  and that sets a, b, c and d are such that  \u2002    a = multiple s of 3 \" ,, \u2002    b = prime numbers \" ,, \u2002    c = odd integers \" ,, \u2002    d = even integers \" ,. \u2002 write down the following sets in terms of their elements. \u2002(i)\u2002a b+ [1] \u2002(ii)\u2002a c, [1] \u2002(iii)\u2002a c+l  [1] \u2002(iv)\u2002d b, l ^ h  [1] \u2002(v)\u2002write down a set  e such that e d1. [1]",
            "9": "9 0606/11/o/n/15 \u00a9 ucles 2015 [turn\u2002over7\u2002two variables, x and y, are such that  y a xb= , where a and b are constants. when lny is plotted  against lnx, a straight line graph is obtained which passes through the points . , . 1 4 5 8 ^ h  and . , . 2 2 6 0 ^ h . \u2002(i)\u2002find the value of a and of b. [4] \u2002(ii)\u2002calculate the value of y when x = 5. [2]",
            "10": "10 0606/11/o/n/15 \u00a9 ucles 20158\u2002find the equation of the tangent to the curve  y xx 52 1 2= +-  at the point where  x = 2. [7]",
            "11": "11 0606/11/o/n/15 \u00a9 ucles 2015 [turn\u2002over9\u2002you\u2002are\u2002not\u2002allowed\u2002to\u2002use\u2002a\u2002calculator \u2002in\u2002this\u2002question. \u2002(i)\u2002find  dx x4+ y . [2] \u2002(ii) ab y = \u221a4  + xy x 5 o \u2002 \u2002 the diagram shows the graph of  y x 4= + , which meets the y-axis at the point a and the line    x5= at the point b. using your answer to part (i), find the area of the region enclosed by the  curve and the straight line ab. [5]",
            "12": "12 0606/11/o/n/15 \u00a9 ucles 201510 a e dbc 10 cm \u2002 the diagram shows two circles, centres a and b, each of radius 10  cm. the point b lies on the  circumference of the circle with centre a. the two circles intersect at the points c and d. the point e  lies on the circumference of the circle centre b such that abe is a diameter.  \u2002(i)\u2002explain why triangle abc  is equilateral.  [1] \u2002(ii)\u2002write down, in terms of r, angle cbe . [1] \u2002(iii)\u2002find the perimeter of the shaded region.  [5]",
            "13": "13 0606/11/o/n/15 \u00a9 ucles 2015 [turn\u2002over\u2002(iv)\u2002find the area of the shaded region.  [3]",
            "14": "14 0606/11/o/n/15 \u00a9 ucles 201511\u2002(a)\u2002a function f is such that  fx x x6 42= + + ^ h   for  x0h. \u2002 \u2002 (i)\u2002show that  x x 6 42+ +   can be written in the form  x a b2+ +^ h , where a and b are integers.  [2] \u2002 \u2002 (ii)\u2002write down the range of f.  [1] \u2002 \u2002(iii)\u2002find  f1-  and state its domain.  [3]",
            "15": "15 0606/11/o/n/15 \u00a9 ucles 2015 [turn\u2002over\u2002(b)\u2002functions g and h are such that, for  xrd ,     g exx= ^ h       and      hx x 5 2= + ^ h . \u2002 \u2002 solve  h g x 372= ^ h . [4] question \u200212\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.",
            "16": "16 0606/11/o/n/15 \u00a9 ucles 201512\u2002the line     x y2 1 0 - + =     meets the curve     x y 3 192+ =      at the points a and b.  the  perpendicular bisector of the line ab meets the x-axis at the point c. find the area of the triangle abc .  [9] 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."
        },
        "0606_w15_qp_12.pdf": {
            "1": "this document consists of 16 printed pages. dc (slm) 115230 \u00a9 ucles 2015  [turn overuniversity of cambridge international examinations international general certificate of secondary education * 8 9 4 7 2 6 6 4 7 2 * additional mathematics  0606/12 paper 1  october/november 2015  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/12/o/n/15 \u00a9 ucles 2015mathematical formulae 1.\u2002algebra quadratic \u2002equation  for the equation ax2 + bx + c = 0, xab b ac 242!=- - . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/12/o/n/15 \u00a9 ucles 2015 [turn\u2002over1\u2002find the range of values of k for which the equation   kx k x xk 8 22+ = -    has 2 real distinct roots.  [4]",
            "4": "4 0606/12/o/n/15 \u00a9 ucles 20152\u2002a curve, showing the relationship between two variables x and y, passes through the point  , p 1 3-^ h . \u2002 the curve has a gradient of 2 at p. given that     dd xy522 =- ,     find the equation of the curve.  [4]",
            "5": "5 0606/12/o/n/15 \u00a9 ucles 2015 [turn\u2002over3\u2002show that sec c osec sec cosec 1 12 2i i i i - + - = . [5]",
            "6": "6 0606/12/o/n/15 \u00a9 ucles 20154\u2002(a)\u20026 books are to be chosen from 8 different books. \u2002 \u2002 (i)\u2002find the number of different selections of 6 books that could be made.  [1] \u2002 \u2002 a clock is to be displayed on a shelf with 3 of the 8 different books on each side of it. find the  number of ways this can be done if \u2002 \u2002 (ii)\u2002there are no restrictions on the choice of books,  [1] \u2002 \u2002(iii)\u20023 of the 8 books are music books which have to be kept together.  [2] \u2002(b)\u2002a team of 6 tennis players is to be chosen from 10 tennis players consisting of 7 men and  3 women.  find the number of different teams that could be chosen if the team must include at  least 1 woman.  [3]",
            "7": "7 0606/12/o/n/15 \u00a9 ucles 2015 [turn\u2002over5\u2002variables x and y are such that   ln y x x 3 2 12= - + ^ ^h h. \u2002 \u2002 (i)\u2002find the value of  dd xy  when  x2=. [4] \u2002 \u2002 (ii)\u2002\u2002hence find the approximate change in y when x changes from 2 to 2.03.  [2]",
            "8": "8 0606/12/o/n/15 \u00a9 ucles 20156\u2002it is given that  \ue025 = ,where isanintege r x x x 1 12|g g \" ,  and that sets a, b, c and d are such that  \u2002    a = multiple s of 3 \" ,, \u2002    b = prime numbers \" ,, \u2002    c = odd integers \" ,, \u2002    d = even integers \" ,. \u2002 write down the following sets in terms of their elements. \u2002(i)\u2002a b+ [1] \u2002(ii)\u2002a c, [1] \u2002(iii)\u2002a c+l  [1] \u2002(iv)\u2002d b, l ^ h  [1] \u2002(v)\u2002write down a set  e such that e d1. [1]",
            "9": "9 0606/12/o/n/15 \u00a9 ucles 2015 [turn\u2002over7\u2002two variables, x and y, are such that  y a xb= , where a and b are constants. when lny is plotted  against lnx, a straight line graph is obtained which passes through the points . , . 1 4 5 8 ^ h  and . , . 2 2 6 0 ^ h . \u2002(i)\u2002find the value of a and of b. [4] \u2002(ii)\u2002calculate the value of y when x = 5. [2]",
            "10": "10 0606/12/o/n/15 \u00a9 ucles 20158\u2002find the equation of the tangent to the curve  y xx 52 1 2= +-  at the point where  x = 2. [7]",
            "11": "11 0606/12/o/n/15 \u00a9 ucles 2015 [turn\u2002over9\u2002you\u2002are\u2002not\u2002allowed\u2002to\u2002use\u2002a\u2002calculator \u2002in\u2002this\u2002question. \u2002(i)\u2002find  dx x4+ y . [2] \u2002(ii) ab y = \u221a4  + xy x 5 o \u2002 \u2002 the diagram shows the graph of  y x 4= + , which meets the y-axis at the point a and the line    x5= at the point b. using your answer to part (i), find the area of the region enclosed by the  curve and the straight line ab. [5]",
            "12": "12 0606/12/o/n/15 \u00a9 ucles 201510 a e dbc 10 cm \u2002 the diagram shows two circles, centres a and b, each of radius 10  cm. the point b lies on the  circumference of the circle with centre a. the two circles intersect at the points c and d. the point e  lies on the circumference of the circle centre b such that abe is a diameter.  \u2002(i)\u2002explain why triangle abc  is equilateral.  [1] \u2002(ii)\u2002write down, in terms of r, angle cbe . [1] \u2002(iii)\u2002find the perimeter of the shaded region.  [5]",
            "13": "13 0606/12/o/n/15 \u00a9 ucles 2015 [turn\u2002over\u2002(iv)\u2002find the area of the shaded region.  [3]",
            "14": "14 0606/12/o/n/15 \u00a9 ucles 201511\u2002(a)\u2002a function f is such that  fx x x6 42= + + ^ h   for  x0h. \u2002 \u2002 (i)\u2002show that  x x 6 42+ +   can be written in the form  x a b2+ +^ h , where a and b are integers.  [2] \u2002 \u2002 (ii)\u2002write down the range of f.  [1] \u2002 \u2002(iii)\u2002find  f1-  and state its domain.  [3]",
            "15": "15 0606/12/o/n/15 \u00a9 ucles 2015 [turn\u2002over\u2002(b)\u2002functions g and h are such that, for  xrd ,     g exx= ^ h       and      hx x 5 2= + ^ h . \u2002 \u2002 solve  h g x 372= ^ h . [4] question \u200212\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.",
            "16": "16 0606/12/o/n/15 \u00a9 ucles 201512\u2002the line     x y2 1 0 - + =     meets the curve     x y 3 192+ =      at the points a and b.  the  perpendicular bisector of the line ab meets the x-axis at the point c. find the area of the triangle abc .  [9] 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."
        },
        "0606_w15_qp_13.pdf": {
            "1": "this document consists of 16 printed pages. dc (ac/cgw) 98537/3 \u00a9 ucles 2015 \b [turn overcambridge international examinations cambridge international general certificate of secondary education * 1 8 0 7 0 4 5 4 9 1 * additional mathematics  0606/13 paper 1  october/november 2015  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/13/o/n/15 \u00a9\bucles\b2015mathematical formulae 1.\u2002algebra quadratic \u2002equation \bfor\bthe\bequation\bax2\b+\bbx\b+\bc\b=\b0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a\b+\bb)n\b=\ban\b+\b(n 1)an\u20131\bb\b+\b(n 2)an\u20132\bb2\b+\b\u2026\b+\b(n r)an\u2013r\bbr\b+\b\u2026\b+\bbn, \bwhere\bn\bis\ba\bpositive\binteger\band\b(n r)\b=\bn! (n\b\u2013\br)!r!\b 2.\u2002trigonometry identities sin2\ba\b+\bcos2\ba\b=\b1 sec2\ba\b=\b1\b+\btan2\ba cosec2\ba\b=\b1\b+\bcot2\ba formulae for \u2206abc a sin\ba = b sin\bb = c sin\bc  a2\b=\bb2\b+\bc2\b\u2013\b2bc\bcos\ba \u2206\b=\b1\b 2\bbc\bsin\ba",
            "3": "3 0606/13/o/n/15 \u00a9\bucles\b2015 [turn\u2002over1\u2002on\bthe\bvenn\bdiagrams\bbelow,\bshade\bthe\bregions\bindicated. \u2002(i)\u2002 \u2002a b c a /h20669 /h20871b /h20668 c/h20872/h5105 \b[1] \u2002(ii)\u2002 \u2002a b c a /h20668 /h20871b /h20669 c/h20872/h5105 \b[1] \u2002(iii)\u2002 \u2002a b c /h20871a /h20668b/h20872' /h20669 c/h5105 \b[1]",
            "4": "4 0606/13/o/n/15 \u00a9\bucles\b20152\u2002solve cos x 2 3412 r- =j lkkn poofor\b\b x03g gr.\b [4]",
            "5": "5 0606/13/o/n/15 \u00a9\bucles\b2015 [turn\u2002over3\u2002(a)\u2002matrices\ba\u2002and\u2002b\u2002are\bsuch\bthat\b2 41 3a=j lkkn poo\band\b3 68 01 2b=j lkkn poo.\bfind\bab.\b [2] \u2002(b)\u2002given\bthat\bmatrix\b4 26 8x=-j lkkn poo,\bfind\bthe\binteger\bvalue\bof\bm\band\bof\bn\bsuch\bthat\b m n x x i2= + ,\b where\bi\bis\bthe\bidentity\bmatrix.\b [5] \u2002(c)\u2002given\bthat\bmatrix\ba a32y=j lkkn poo,\bfind\bthe\bvalues\bof\ba\bfor\bwhich\bdet\by\b=\b0.\b [2]",
            "6": "6 0606/13/o/n/15 \u00a9\bucles\b20154\u2002you\u2002are\u2002not\u2002allowed\u2002to\u2002use\u2002a\u2002calculator \u2002in\u2002this\u2002question. a bc (4\u221a3+1)  cm \u2002the\bdiagram\bshows\btriangle\babc\bwith\bside\b ( ) ab 4 3 1 = + \bcm.\bangle  b\bis\ba\bright\bangle.\bit\bis\bgiven \u2002that\bthe\barea\bof\bthis\btriangle\bis\b247\bcm2. \u2002(i)\u2002find\bthe\blength\bof\bthe\bside\bbc\bin\bthe\bform\b( )a b3+\bcm,\bwhere\ba\band\bb\bare\bintegers.\b [3] \u2002(ii)\u2002hence\bfind\bthe\blength\bof\bthe\bside\bac\bin\bthe\bform\bp2\bcm,\bwhere\bp\bis\ban\binteger.\b [2]",
            "7": "7 0606/13/o/n/15 \u00a9\bucles\b2015 [turn\u2002over5\u2002find\bthe\bequation\bof\bthe\bnormal\bto\bthe\bcurve tan y x 5 3= - at\bthe\bpoint\bwhere\bx4r=.\b [5]",
            "8": "8 0606/13/o/n/15 \u00a9\bucles\b20156\u2002(i)\u2002\u2002on\bthe\baxes\bbelow,\bsketch\bthe\bgraph\bof y x x4 122= - -showing\bthe\bcoordinates \bof\bthe\b points\bwhere\bthe\bgraph\bmeets\bthe\baxes.\b [3] y x o \u2002(ii)\u2002find\bthe\bcoordinates \bof\bthe\bstationary\bpoint\bon\bthe\bcurve y x x4 122= - -.\b [2] \u2002(iii)\u2002find\bthe\bvalues\bof\bk\bsuch\bthat\bthe\bequation x x k 4 122- - =has\bonly\b2\bsolutions.\b [2]",
            "9": "9 0606/13/o/n/15 \u00a9\bucles\b2015 [turn\u2002over7\u2002a\bcurve,\bshowing\bthe\brelationship \bbetween\btwo\bvariables\bx\band\by,\bis\bsuch\bthat\bddcosxyx 6 322 =.\bgiven \u2002that\bthe\bcurve\bhas\ba\bgradient\bof\b4 3\bat\bthe\bpoint\b,9 31 r- c m,\bfind\bthe\bequation\bof\bthe\bcurve.\b [6]",
            "10": "10 0606/13/o/n/15 \u00a9\bucles\b20158\u2002(a)\u2002given\bthat\bthe\bfirst\b4\bterms\bin\bthe\bexpansion\bof\b( ) kx 28+\bare\b x px qx 256 2562 3+ + +,\bfind\bthe\b value\bof\bk,\bof\bp\band\bof\bq.\b [3] \u2002(b)\u2002find\bthe\bterm\bthat\bis\bindependent \bof x\bin\bthe\bexpansion\bof\bxx2 29 -c m.\b [3]",
            "11": "11 0606/13/o/n/15 \u00a9\bucles\b2015 [turn\u2002over9\u2002(a)\u2002five\bdifferent\bbooks\bare\bto\bbe\barranged\bon\ba\bshelf.\bthere\bare\b2\bmathematics \bbooks\band\b3\bhistory\b books.\bfind\bthe\bnumber\bof\bdifferent\barrangements \bof\bbooks\bif \u2002 \u2002 (i)\u2002the mathematics books are next to each other,  [2] \u2002 \u2002(ii)\u2002the mathematics books are not next to each other.   [2] \u2002(b)\u2002\u2002to\bcompete\bin\ba\bquiz,\ba\bteam\bof\b5\bis\bto\bbe\bchosen\bfrom\ba\bgroup\bof\b9\bmen\band\b6\bwomen.\bfind\bthe\b number\bof\bdifferent\bteams\bthat\bcan\bbe\bchosen\bif \u2002 \u2002 (i)\u2002there are no restrictions,  [1] \u2002 \u2002 (ii)\bat\bleast\btwo\bmen\bmust\bbe\bon\bthe\bteam.\b [3]",
            "12": "12 0606/13/o/n/15 \u00a9\bucles\b201510\u2002 6 cm c ab y x6 cm 10 cm \u2002the\bdiagram\bshows\ban\bisosceles\btriangle\babc\bsuch\bthat\bac =\b10\bcm\band\bab =\bbc =\b6\bcm. \u2002 bx\bis\ban\barc\bof\ba\bcircle,\bcentre\bc,\band\bby\bis\ban\barc\bof\ba\bcircle,\bcentre\ba. \u2002(i)\u2002show\bthat\bangle\babc\b=\b1.970\bradians,\bcorrect\bto\b3\bdecimal\bplaces.\b [2] \u2002(ii)\u2002find\bthe\bperimeter\bof\bthe\bshaded\bregion.\b [4]",
            "13": "13 0606/13/o/n/15 \u00a9\bucles\b2015 [turn\u2002over\u2002(iii)\u2002find\bthe\barea\bof\bthe\bshaded\bregion.\b [3]",
            "14": "14 0606/13/o/n/15 \u00a9\bucles\b201511\u2002the\bline x y 2 0- + =intersects\bthe\bcurve x y x 2 2 1 02 2- + + = at\bthe\bpoints\ba\band\bb.\bthe\b perpendicular \bbisector\bof\bthe\bline\bab\bintersects\bthe\bcurve\bat\bthe\bpoints\bc\band\bd.\bfind\bthe\blength\bof\bthe\b line\bcd\bin\bthe\bform\ba5,\bwhere\ba\bis\ban\binteger.\b [10]",
            "15": "15 0606/13/o/n/15 \u00a9\bucles\b2015 [turn\u2002overquestion \u200212\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.",
            "16": "16 0606/13/o/n/15 \u00a9\bucles\b2015permission \bto\breproduce\bitems\bwhere\bthird-party \bowned\bmaterial\bprotected\bby\bcopyright\bis\bincluded\bhas\bbeen\bsought\band\bcleared\bwhere\bpossible.\bevery\breasonable \beffort\bhas\bbeen\b made\bby\bthe\bpublisher\b(ucles)\bto\btrace\bcopyright\bholders,\bbut\bif\bany\bitems\brequiring\bclearance\bhave\bunwittingly \bbeen\bincluded,\bthe\bpublisher\bwill\bbe\bpleased\bto\bmake\bamends\bat\b the\bearliest\bpossible\bopportunity. to\bavoid\bthe\bissue\bof\bdisclosure\bof\banswer-related \binformation \bto\bcandidates, \ball\bcopyright\backnowledgements \bare\breproduced \bonline\bin\bthe\bcambridge \binternational \bexaminations \b copyright\backnowledgements \bbooklet.\bthis\bis\bproduced\bfor\beach\bseries\bof\bexaminations \band\bis\bfreely\bavailable\bto\bdownload\bat\bwww.cie.org.uk \bafter\bthe\blive\bexamination \bseries. cambridge \binternational \bexaminations \bis\bpart\bof\bthe\bcambridge \bassessment \bgroup.\bcambridge \bassessment \bis\bthe\bbrand\bname\bof\buniversity\bof\bcambridge \blocal\bexaminations \b syndicate\b(ucles),\bwhich\bis\bitself\ba\bdepartment \bof\bthe\buniversity\bof\bcambridge.12\u2002(a)\u2002given\bthat\b2 4 128x x y 2 1# =- +\band\b2791yy x 42 =-- ,\bfind\bthe\bvalue\bof\beach\bof\bthe\bintegers\b\bx\band\by.\b\b[4] \u2002(b)\u2002solve ( )2 5 5 1 0z z2+ - =.\b [4]"
        },
        "0606_w15_qp_21.pdf": {
            "1": "this document consists of 16 printed pages. dc (ac/cgw) 98388/4 \u00a9 ucles 2015 \b [turn overcambridge international examinations cambridge international general certificate of secondary education * 4 0 3 3 8 5 4 1 1 6 * additional mathematics  0606/21 paper 2  october/november 2015  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of   angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/21/o/n/15 \u00a9\bucles\b2015mathematical formulae 1.\u2002algebra quadratic\u2002equation \bfor\bthe\bequation\bax2\b+\bbx\b+\bc\b=\b0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a\b+\bb)n\b=\ban\b+\b(n 1)an\u20131\bb\b+\b(n 2)an\u20132\bb2\b+\b\u2026\b+\b(n r)an\u2013r\bbr\b+\b\u2026\b+\bbn, \bwhere\bn\bis\ba\bpositive\binteger\band\b(n r)\b=\bn! (n\b\u2013\br)!r!\b 2.\u2002trigonometry identities sin2\ba\b+\bcos2\ba\b=\b1 sec2\ba\b=\b1\b+\btan2\ba cosec2\ba\b=\b1\b+\bcot2\ba formulae for \u2206abc a sin\ba = b sin\bb = c sin\bc  a2\b=\bb2\b+\bc2\b\u2013\b2bc\bcos\ba \u2206\b=\b1\b 2\bbc\bsin\ba",
            "3": "3 0606/21/o/n/15 \u00a9\bucles\b2015 [turn\u2002over1\u2002it\bis\bgiven\bthat\b\b( )x x x x 4 4 15 18 f3 2= - - + . \u2002(i)\u2002show\bthat\bx2+\b\bis\ba\bfactor\bof\b( )xf.\b [1] \u2002(ii)\u2002hence\bfactorise\b( )xf\bcompletely \band\bsolve\bthe\bequation\b( )x 0 f=.\b [4]",
            "4": "4 0606/21/o/n/15 \u00a9\bucles\b20152\u2002(i)\u2002find,\bin\bthe\bsimplest\bform,\bthe\bfirst\b3\bterms\bof\bthe\bexpansion\bof\b( ) x 2 36-,\bin\bascending\bpowers\b of\bx.\b [3] \u2002(ii)\u2002find\bthe\bcoefficient \bof\bx2\bin\bthe\bexpansion\bof\b( ) ( )x x 1 2 2 36+ - .\b [2]",
            "5": "5 0606/21/o/n/15 \u00a9\bucles\b2015 [turn\u2002over3\u2002relative\bto\ban\borigin  o,\bpoints\ba, b\band\bc\bhave\bposition\bvectors\b5 4c m,\b10 12-c m\band\b6 18-c m\brespectively. \ball\b distances\bare\bmeasured\bin\bkilometres. \ba\bman\bdrives\bat\ba\bconstant\bspeed\bdirectly\bfrom  a\bto\bb in\b20\bminutes. \u2002(i)\u2002calculate\bthe\bspeed\bin\bkmh\u20131\bat\bwhich\bthe\bman\bdrives\bfrom\ba\bto\bb.\b [3] \u2002he\bnow\bdrives\bdirectly\bfrom  b\bto\bc\bat\bthe\bsame\bspeed. \u2002(ii)\u2002find\bhow\blong\bit\btakes\bhim\bto\bdrive\bfrom  b\bto\bc.\b\b [3]",
            "6": "6 0606/21/o/n/15 \u00a9\bucles\b20154\u2002(a)\u2002given\bthat\b2 3 75 41 22 34 01 and a b =- =--f c p m,\bcalculate\b2ba.\b [3] \u2002(b)\u2002the\bmatrices\bc\band\bd\bare\bgiven\bby\b1 12 63 12 4and c d =-=-c c m m.\b \u2002 \u2002(i)\u2002find\bc\u20131.\b [2] \u2002 \u2002(ii)\u2002hence\bfind\bthe\bmatrix\u2002x\bsuch\bthat\bcx\u2002+\u2002d\u2002=\u2002i,\bwhere\bi\bis\bthe\bidentity\bmatrix.\b [3]",
            "7": "7 0606/21/o/n/15 \u00a9\bucles\b2015 [turn\u2002over5\u2002(a)\bsolve\bthe\bfollowing\bequations\bto\bfind\bp\band\bq. 8 2 4q p p q1 2 1 7 4# =- + -81= 9 3# \b[4] \u2002(b)\u2002solve\bthe\bequation\b\b\b\b\b ( ) ( ) x x3 2 1 2 2 g lg lg l- + + = -.\b [5]",
            "8": "8 0606/21/o/n/15 \u00a9\bucles\b20156\u2002y x4 235 1 00 \u03c0 \u03c0 23\u03c0 2\u03c0 2 \bthe\bfigure\bshows\bpart\bof\bthe\bgraph\bof sin y a b c x = + . \u2002(i)\u2002find\bthe\bvalue\bof\beach\bof\bthe\bintegers\ba,\bb\band\bc.\b\b [3] \u2002using\byour\bvalues\bof\ba,\bb\band\bc find \u2002(ii)\u2002dd xy,\b\b [2]",
            "9": "9 0606/21/o/n/15 \u00a9\bucles\b2015 [turn\u2002over\u2002(iii)\u2002the\bequation\bof\bthe\bnormal\bto\bthe\bcurve\bat\b,23r` j.\b [3]",
            "10": "10 0606/21/o/n/15 \u00a9\bucles\b20157 8 cm h cm 6 cmr cm \u2002a\bcone,\bof\bheight\b8\bcm\band\bbase\bradius\b6\bcm,\bis\bplaced\bover\ba\bcylinder\bof\bradius\br\bcm\band\bheight\bh\bcm\b and\bis\bin\bcontact\bwith\bthe\bcylinder\balong\bthe\bcylinder\u2019s\bupper\brim.\bthe\barrangement \bis\bsymmetrical \band\b the\bdiagram\bshows\ba\bvertical\bcross-section \bthrough\bthe\bvertex\bof\bthe\bcone.\b \u2002(i)\u2002use\bsimilar\btriangles\bto\bexpress\bh\bin\bterms\bof r.\b [2] \u2002(ii)\u2002hence\bshow\bthat\bthe\bvolume,\bv\bcm3,\bof\bthe\bcylinder\bis\bgiven\bby\bv r r 82 34 3r r= - .\b [1]",
            "11": "11 0606/21/o/n/15 \u00a9\bucles\b2015 [turn\u2002over\u2002(iii)\u2002given\bthat\br\bcan\bvary,\bfind\bthe\bvalue\bof\br which\bgives\ba\bstationary\bvalue\bof\bv.\bfind\bthis\bstationary\b value\bof\bv\bin\bterms\bof\b\u03c0\band\bdetermine\bits\bnature.\b [6]",
            "12": "12 0606/21/o/n/15 \u00a9\bucles\b20158\u2002solutions\u2002to\u2002this\u2002question\u2002by\u2002accurate\u2002drawing\u2002will\u2002not\u2002be\u2002accepted. \u2002two\bpoints\ba\band\bb\bhave\bcoordinates \b(\u20133,\b2)\band\b(9,\b8)\brespectively. \u2002(i)\u2002find\bthe\bcoordinates \bof\bc, the\bpoint\bwhere\bthe\bline\bab\bcuts\bthe\by-axis.\b [3] \u2002(ii)\u2002find\bthe\bcoordinates \bof\bd,\bthe\bmid-point\bof\bab.\b [1]",
            "13": "13 0606/21/o/n/15 \u00a9\bucles\b2015 [turn\u2002over\u2002(iii)\u2002find\bthe\bequation\bof\bthe\bperpendicular \bbisector\bof\bab.\b [2] \u2002the\bperpendicular \bbisector\bof\bab\bcuts\bthe\by-axis\bat\bthe\bpoint\be.\b \u2002(iv)\u2002find\bthe\bcoordinates \bof\be.\b [1] \u2002(v)\u2002show\bthat\bthe\barea\bof\btriangle\babe\bis\bfour\btimes\bthe\barea\bof\btriangle  ecd.\b \b[3]",
            "14": "14 0606/21/o/n/15 \u00a9\bucles\b20159\b\bsolve\bthe\bfollowing\bequations. \u2002(i)\u2002sin c os x x 4 2 5 2 0 + = \bfor\b x 0 180 c cg g \b [3] \u2002(ii)\u2002cot c osec y y3 32+ = \bfor\b y 0 360 c cg g \b [5]",
            "15": "15 0606/21/o/n/15 \u00a9\bucles\b2015 [turn\u2002over\u2002(iii)\u2002cos z4 21 r+ = - ` j \bfor\b z0 2g g r\bradians,\bgiving\beach\banswer\bas\ba\bmultiple\bof\b\u03c0\b [4] question\u200210\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.\u2002",
            "16": "16 0606/21/o/n/15 \u00a9\bucles\b2015permission \bto\breproduce\bitems\bwhere\bthird-party \bowned\bmaterial\bprotected\bby\bcopyright\bis\bincluded\bhas\bbeen\bsought\band\bcleared\bwhere\bpossible.\bevery\breasonable \beffort\bhas\bbeen\b made\bby\bthe\bpublisher\b(ucles)\bto\btrace\bcopyright\bholders,\bbut\bif\bany\bitems\brequiring\bclearance\bhave\bunwittingly \bbeen\bincluded,\bthe\bpublisher\bwill\bbe\bpleased\bto\bmake\bamends\bat\b the\bearliest\bpossible\bopportunity. to\bavoid\bthe\bissue\bof\bdisclosure\bof\banswer-related \binformation \bto\bcandidates, \ball\bcopyright\backnowledgements \bare\breproduced \bonline\bin\bthe\bcambridge \binternational \bexaminations \b copyright\backnowledgements \bbooklet.\bthis\bis\bproduced\bfor\beach\bseries\bof\bexaminations \band\bis\bfreely\bavailable\bto\bdownload\bat\bwww.cie.org.uk \bafter\bthe\blive\bexamination \bseries. cambridge \binternational \bexaminations \bis\bpart\bof\bthe\bcambridge \bassessment \bgroup.\bcambridge \bassessment \bis\bthe\bbrand\bname\bof\buniversity\bof\bcambridge \blocal\bexaminations \b syndicate\b(ucles),\bwhich\bis\bitself\ba\bdepartment \bof\bthe\buniversity\bof\bcambridge.10\u2002a\bparticle\bis\bmoving\bin\ba\bstraight\bline\bsuch\bthat\bits\bvelocity,\bv\bms\u20131,\bt seconds\bafter\bpassing\ba\b fixed\bpoint\bo\bis\b\b\b\bv 6 1 e et t2 2= - --. \u2002(i)\u2002find\ban\bexpression \bfor\bthe\bdisplacement, \bs\bm,\bfrom\bo\bof\bthe\bparticle  after\bt seconds.\b [3] \u2002(ii)\u2002using\bthe\bsubstitution \buet2= , or\botherwise,\bfind\bthe\btime\bwhen\bthe\bparticle\bis\bat\brest.\b [3] \u2002(iii)\u2002find\bthe\bacceleration \bat\bthis\btime.\b [2]"
        },
        "0606_w15_qp_22.pdf": {
            "1": "this document consists of 16 printed pages. dc (slm) 115963 \u00a9 ucles 2015 \b [turn overcambridge international examinations cambridge international general certificate of secondary education * 9 3 3 4 9 5 4 2 0 2 * additional mathematics  0606/22 paper 2  october/november 2015  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of   angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/22/o/n/15 \u00a9\bucles\b2015mathematical formulae 1.\u2002algebra quadratic\u2002equation \bfor\bthe\bequation\bax2\b+\bbx\b+\bc\b=\b0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a\b+\bb)n\b=\ban\b+\b(n 1)an\u20131\bb\b+\b(n 2)an\u20132\bb2\b+\b\u2026\b+\b(n r)an\u2013r\bbr\b+\b\u2026\b+\bbn, \bwhere\bn\bis\ba\bpositive\binteger\band\b(n r)\b=\bn! (n\b\u2013\br)!r!\b 2.\u2002trigonometry identities sin2\ba\b+\bcos2\ba\b=\b1 sec2\ba\b=\b1\b+\btan2\ba cosec2\ba\b=\b1\b+\bcot2\ba formulae for \u2206abc a sin\ba = b sin\bb = c sin\bc  a2\b=\bb2\b+\bc2\b\u2013\b2bc\bcos\ba \u2206\b=\b1\b 2\bbc\bsin\ba",
            "3": "3 0606/22/o/n/15 \u00a9\bucles\b2015 [turn\u2002over1\u2002it\bis\bgiven\bthat\b\b( )x x x x 4 4 15 18 f3 2= - - + . \u2002(i)\u2002show\bthat\bx2+\b\bis\ba\bfactor\bof\b( )xf.\b [1] \u2002(ii)\u2002hence\bfactorise\b( )xf\bcompletely \band\bsolve\bthe\bequation\b( )x 0 f=.\b [4]",
            "4": "4 0606/22/o/n/15 \u00a9\bucles\b20152\u2002(i)\u2002find,\bin\bthe\bsimplest\bform,\bthe\bfirst\b3\bterms\bof\bthe\bexpansion\bof\b( ) x 2 36-,\bin\bascending\bpowers\b of\bx.\b [3] \u2002(ii)\u2002find\bthe\bcoefficient \bof\bx2\bin\bthe\bexpansion\bof\b( ) ( )x x 1 2 2 36+ - .\b [2]",
            "5": "5 0606/22/o/n/15 \u00a9\bucles\b2015 [turn\u2002over3\u2002relative\bto\ban\borigin  o,\bpoints\ba, b\band\bc\bhave\bposition\bvectors\b5 4c m,\b10 12-c m\band\b6 18-c m\brespectively. \ball\b distances\bare\bmeasured\bin\bkilometres. \ba\bman\bdrives\bat\ba\bconstant\bspeed\bdirectly\bfrom  a\bto\bb in\b20\bminutes. \u2002(i)\u2002calculate\bthe\bspeed\bin\bkmh\u20131\bat\bwhich\bthe\bman\bdrives\bfrom\ba\bto\bb.\b [3] \u2002he\bnow\bdrives\bdirectly\bfrom  b\bto\bc\bat\bthe\bsame\bspeed. \u2002(ii)\u2002find\bhow\blong\bit\btakes\bhim\bto\bdrive\bfrom  b\bto\bc.\b\b [3]",
            "6": "6 0606/22/o/n/15 \u00a9\bucles\b20154\u2002(a)\u2002given\bthat\b2 3 75 41 22 34 01 and a b =- =--f c p m,\bcalculate\b2ba.\b [3] \u2002(b)\u2002the\bmatrices\bc\band\bd\bare\bgiven\bby\b1 12 63 12 4and c d =-=-c c m m.\b \u2002 \u2002(i)\u2002find\bc\u20131.\b [2] \u2002 \u2002(ii)\u2002hence\bfind\bthe\bmatrix\u2002x\bsuch\bthat\bcx\u2002+\u2002d\u2002=\u2002i,\bwhere\bi\bis\bthe\bidentity\bmatrix.\b [3]",
            "7": "7 0606/22/o/n/15 \u00a9\bucles\b2015 [turn\u2002over5\u2002(a)\bsolve\bthe\bfollowing\bequations\bto\bfind\bp\band\bq. 8 2 4q p p q1 2 1 7 4# =- + -81= 9 3# \b[4] \u2002(b)\u2002solve\bthe\bequation\b\b\b\b\b ( ) ( ) x x3 2 1 2 2 g lg lg l- + + = -.\b [5]",
            "8": "8 0606/22/o/n/15 \u00a9\bucles\b20156\u2002y x4 235 1 00 \u03c0 \u03c0 23\u03c0 2\u03c0 2 \bthe\bfigure\bshows\bpart\bof\bthe\bgraph\bof sin y a b c x = + . \u2002(i)\u2002find\bthe\bvalue\bof\beach\bof\bthe\bintegers\ba,\bb\band\bc.\b\b [3] \u2002using\byour\bvalues\bof\ba,\bb\band\bc find \u2002(ii)\u2002dd xy,\b\b [2]",
            "9": "9 0606/22/o/n/15 \u00a9\bucles\b2015 [turn\u2002over\u2002(iii)\u2002the\bequation\bof\bthe\bnormal\bto\bthe\bcurve\bat\b,23r` j.\b [3]",
            "10": "10 0606/22/o/n/15 \u00a9\bucles\b20157 8 cm h cm 6 cmr cm \u2002a\bcone,\bof\bheight\b8\bcm\band\bbase\bradius\b6\bcm,\bis\bplaced\bover\ba\bcylinder\bof\bradius\br\bcm\band\bheight\bh\bcm\b and\bis\bin\bcontact\bwith\bthe\bcylinder\balong\bthe\bcylinder\u2019s\bupper\brim.\bthe\barrangement \bis\bsymmetrical \band\b the\bdiagram\bshows\ba\bvertical\bcross-section \bthrough\bthe\bvertex\bof\bthe\bcone.\b \u2002(i)\u2002use\bsimilar\btriangles\bto\bexpress\bh\bin\bterms\bof r.\b [2] \u2002(ii)\u2002hence\bshow\bthat\bthe\bvolume,\bv\bcm3,\bof\bthe\bcylinder\bis\bgiven\bby\bv r r 82 34 3r r= - .\b [1]",
            "11": "11 0606/22/o/n/15 \u00a9\bucles\b2015 [turn\u2002over\u2002(iii)\u2002given\bthat\br\bcan\bvary,\bfind\bthe\bvalue\bof\br which\bgives\ba\bstationary\bvalue\bof\bv.\bfind\bthis\bstationary\b value\bof\bv\bin\bterms\bof\b\u03c0\band\bdetermine\bits\bnature.\b [6]",
            "12": "12 0606/22/o/n/15 \u00a9\bucles\b20158\u2002solutions\u2002to\u2002this\u2002question\u2002by\u2002accurate\u2002drawing\u2002will\u2002not\u2002be\u2002accepted. \u2002two\bpoints\ba\band\bb\bhave\bcoordinates \b(\u20133,\b2)\band\b(9,\b8)\brespectively. \u2002(i)\u2002find\bthe\bcoordinates \bof\bc, the\bpoint\bwhere\bthe\bline\bab\bcuts\bthe\by-axis.\b [3] \u2002(ii)\u2002find\bthe\bcoordinates \bof\bd,\bthe\bmid-point\bof\bab.\b [1]",
            "13": "13 0606/22/o/n/15 \u00a9\bucles\b2015 [turn\u2002over\u2002(iii)\u2002find\bthe\bequation\bof\bthe\bperpendicular \bbisector\bof\bab.\b [2] \u2002the\bperpendicular \bbisector\bof\bab\bcuts\bthe\by-axis\bat\bthe\bpoint\be.\b \u2002(iv)\u2002find\bthe\bcoordinates \bof\be.\b [1] \u2002(v)\u2002show\bthat\bthe\barea\bof\btriangle\babe\bis\bfour\btimes\bthe\barea\bof\btriangle  ecd.\b \b[3]",
            "14": "14 0606/22/o/n/15 \u00a9\bucles\b20159\b\bsolve\bthe\bfollowing\bequations. \u2002(i)\u2002sin c os x x 4 2 5 2 0 + = \bfor\b x 0 180 c cg g \b [3] \u2002(ii)\u2002cot c osec y y3 32+ = \bfor\b y 0 360 c cg g \b [5]",
            "15": "15 0606/22/o/n/15 \u00a9\bucles\b2015 [turn\u2002over\u2002(iii)\u2002cos z4 21 r+ = - ` j \bfor\b z0 2g g r\bradians,\bgiving\beach\banswer\bas\ba\bmultiple\bof\b\u03c0\b [4] question\u200210\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.\u2002",
            "16": "16 0606/22/o/n/15 \u00a9\bucles\b2015permission \bto\breproduce\bitems\bwhere\bthird-party \bowned\bmaterial\bprotected\bby\bcopyright\bis\bincluded\bhas\bbeen\bsought\band\bcleared\bwhere\bpossible.\bevery\breasonable \beffort\bhas\bbeen\b made\bby\bthe\bpublisher\b(ucles)\bto\btrace\bcopyright\bholders,\bbut\bif\bany\bitems\brequiring\bclearance\bhave\bunwittingly \bbeen\bincluded,\bthe\bpublisher\bwill\bbe\bpleased\bto\bmake\bamends\bat\b the\bearliest\bpossible\bopportunity. to\bavoid\bthe\bissue\bof\bdisclosure\bof\banswer-related \binformation \bto\bcandidates, \ball\bcopyright\backnowledgements \bare\breproduced \bonline\bin\bthe\bcambridge \binternational \bexaminations \b copyright\backnowledgements \bbooklet.\bthis\bis\bproduced\bfor\beach\bseries\bof\bexaminations \band\bis\bfreely\bavailable\bto\bdownload\bat\bwww.cie.org.uk \bafter\bthe\blive\bexamination \bseries. cambridge \binternational \bexaminations \bis\bpart\bof\bthe\bcambridge \bassessment \bgroup.\bcambridge \bassessment \bis\bthe\bbrand\bname\bof\buniversity\bof\bcambridge \blocal\bexaminations \b syndicate\b(ucles),\bwhich\bis\bitself\ba\bdepartment \bof\bthe\buniversity\bof\bcambridge.10\u2002a\bparticle\bis\bmoving\bin\ba\bstraight\bline\bsuch\bthat\bits\bvelocity,\bv\bms\u20131,\bt seconds\bafter\bpassing\ba\b fixed\bpoint\bo\bis\b\b\b\bv 6 1 e et t2 2= - --. \u2002(i)\u2002find\ban\bexpression \bfor\bthe\bdisplacement, \bs\bm,\bfrom\bo\bof\bthe\bparticle  after\bt seconds.\b [3] \u2002(ii)\u2002using\bthe\bsubstitution \buet2= , or\botherwise,\bfind\bthe\btime\bwhen\bthe\bparticle\bis\bat\brest.\b [3] \u2002(iii)\u2002find\bthe\bacceleration \bat\bthis\btime.\b [2]"
        },
        "0606_w15_qp_23.pdf": {
            "1": "this document consists of 16 printed pages. dc (kn/cgw) 98325/2 \u00a9 ucles 2015  [turn overcambridge international examinations cambridge international general certificate of secondary education * 1 2 9 6 1 1 8 2 2 1 * additional mathematics  0606/23 paper 2  october/november 2015  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles in  degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/23/o/n/15 \u00a9 ucles 2015mathematical formulae 1.\u2002algebra quadratic \u2002equation  for the equation ax2 + bx + c = 0, xb b ac a=\u2212 \u221224 2 binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/23/o/n/15 \u00a9 ucles 2015 [turn\u2002over1\u2002find the equation of the tangent to the curve     y x x x 3 5 73 2= + - -      at the point where  x = 2. [5]",
            "4": "4 0606/23/o/n/15 \u00a9 ucles 20152\u2002find the values of k for which the line     y x k 2 2= + +     cuts the curve     ( ) y x k x 2 2 82= + + +       in two distinct points.  [6]",
            "5": "5 0606/23/o/n/15 \u00a9 ucles 2015 [turn\u2002over3\u2002(a)\u2002given that  yxx 223 =- , find xy dd . [3] \u2002(b)\u2002given that y x x4 6= + , show that ( ) xy xk x 4 61 dd=++ and state the value of k. [3]",
            "6": "6 0606/23/o/n/15 \u00a9 ucles 20154\u2002solve the following simultaneous equations, giving your answers for both x and y in the form  a b 3+ , where a and b are integers. \u2002     x y2 9+ = \u2002     x y3 2 5 + =  [5]",
            "7": "7 0606/23/o/n/15 \u00a9 ucles 2015 [turn\u2002over5\u2002the roots of the equation     x ax bx c 03 2+ + + =      are 1, 3 and 3. show that c 9\u2013=  and find the  value of a and of b. [4]",
            "8": "8 0606/23/o/n/15 \u00a9 ucles 20156\u2002\u2002solve the following equation. \u2002     ( ) loglogx29 15 322 x2- = +  [5]",
            "9": "9 0606/23/o/n/15 \u00a9 ucles 2015 [turn\u2002over7\u2002the velocity, vms1-, of a particle travelling in a straight line, t seconds after passing through a fixed  \u2002 point o, is given by ( )vt210 2=+ . \u2002(i)\u2002find the acceleration of the particle when t = 3. [3] \u2002(ii)\u2002explain why the particle never comes to rest.  [1] \u2002(iii)\u2002find an expression for the displacement of the particle from o after time t s. [3] \u2002(iv)\u2002find the distance travelled by the particle between t = 3 and t = 8. [2]",
            "10": "10 0606/23/o/n/15 \u00a9 ucles 20158\u2002(i)\u2002prove that     sec c osec sec c osec x x x x2 2 2 2+ = . [4] \u2002(ii)\u2002hence, or otherwise, solve  sec c osec tan x x x 42 2 2+ =      for x 90 2701 1c c . [4]",
            "11": "11 0606/23/o/n/15 \u00a9 ucles 2015 [turn\u2002over9\u2002given that ( )x x x 3 12 2 f2= + +, \u2002(i)\u2002find values of a, b and c such that ( ) ( ) x a x b c f2= + +, [3] \u2002(ii)\u2002state the minimum value of f( x) and the value of x at which it occurs,  [2] \u2002(iii)\u2002solve  y10 f= c m , giving each answer for y correct to 2 decimal places.  [3]",
            "12": "12 0606/23/o/n/15 \u00a9 ucles 201510\u2002\u2002(i)\u2002given that exkxddex x 2 22 2=- - ^ h , state the value of k. [1]  \u2002(ii)\u2002using your result from part (i), find x x3 e dx22-y . [2] \u2002(iii)\u2002hence find the area enclosed by the curve y x3 ex22=-, the x-axis and the lines x1= and  x 2= . [2]",
            "13": "13 0606/23/o/n/15 \u00a9 ucles 2015 [turn\u2002over\u2002(iv)\u2002find the coordinates of the stationary points on the curve y x3 ex22=-. [4]",
            "14": "14 0606/23/o/n/15 \u00a9 ucles 201511\u2002the trees in a certain forest are dying because of an unknown virus.   \u2002 the number of trees, n, surviving t years after the onset of the virus is shown in the table below. t 1 2 3 4 5 6 n 2000 1300 890 590 395 260 \u2002 the relationship between n and t is thought to be of the form  n abt=-. \u2002(i)\u2002transform this relationship into straight line form.  [1] \u2002(ii)\u2002using the given data, draw this straight line on the grid below.  [3] ",
            "15": "15 0606/23/o/n/15 \u00a9 ucles 2015 [turn\u2002over\u2002(iii)\u2002use your graph to estimate the value of a and of b. [3] \u2002 if the trees continue to die in the same way, find \u2002(iv)\u2002the number of trees surviving after 10 years,  [1] \u2002(v)\u2002the number of years taken until there are only 10 trees surviving.  [2] question \u200212\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.",
            "16": "16 0606/23/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.12\u2002a plane that can travel at 250  kmh\u20131 in still air sets off on a bearing of 070\u00b0. a wind with speed w kmh\u20131  from the south blows the plane off course so that the plane actually travels on a bearing of 060\u00b0. \u2002 find, in kmh\u20131, the resultant speed v of the plane and the windspeed w. [5]"
        }
    },
    "2016": {
        "0606_m16_qp_12.pdf": {
            "1": "this document consists of 16 printed pages. dc (leg/fd) 106873/3 \u00a9 ucles 2016  [turn overcambridge international examinations cambridge international general certificate of secondary education * 9 2 4 2 8 1 9 0 7 2 * additional mathematics  0606/12 paper 1  february/march 2016  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/12/f/m/16 \u00a9 ucles 2016mathematical formulae 1.\u2002algebra quadratic equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/12/f/m/16 \u00a9 ucles 2016 [turn\u2002over1\u2002find the values of a for which the line    y xa 9 = +     intersects the curve    y x x 2 3 12=- + +     at  2 distinct points.  [4] 2\u2002given that     p q rp q rp q ra b c 312 3221 = -- - , find the values of  a, b and c. [3]",
            "4": "4 0606/12/f/m/16 \u00a9 ucles 20163\u2002solve    log l ogx x 35 25+ = . [3]",
            "5": "5 0606/12/f/m/16 \u00a9 ucles 2016 [turn\u2002over4\u2002(i)\u2002on the axes below, sketch the graphs of    y x2= -   and  y x 3 2= + . [4] \u201399 \u20136 6xy 0 \u2002(ii)\u2002solve   x x 3 2 2 + = -. [3]",
            "6": "6 0606/12/f/m/16 \u00a9 ucles 20165\u2002(a)\u2002a 6-character password is to be chosen from the following 9 characters. letters a b e f numbers 5 8 9 symbols * $ \u2002 \u2002 each character may be used only once in any password. \u2002 \u2002 find the number of different 6-character passwords that may be chosen if \u2002 \u2002 (i)\u2002there are no restrictions,  [1] \u2002 \u2002(ii)\u2002the password must consist of 2 letters, 2 numbers and 2 symbols, in that order , [2] \u2002 \u2002(iii)\u2002the password must start and finish with a symbol.  [2]",
            "7": "7 0606/12/f/m/16 \u00a9 ucles 2016 [turn\u2002over\u2002(b)\u2002an examination consists of a section a, containing 10 short questions, and a section b, containing  5 long questions. candidates are required to answer 6 questions from section a and 3 questions  from section b. find the number of different selections of questions that can be made if \u2002 \u2002 (i)\u2002 there are no further restrictions,  [2] \u2002 \u2002(ii)\u2002candidates must answer the first 2 questions in section a and the first question in section b.  [2]",
            "8": "8 0606/12/f/m/16 \u00a9 ucles 20166\u2002a function f is such that    f ex 6x4= + ^ h     for  xr!. \u2002(i)\u2002write down the range of f.  [1] \u2002(ii)\u2002find    fx1-^ h  and state its domain and range.  [4] \u2002(iii)\u2002find    fxl^ h. [1] \u2002(iv)\u2002hence find the exact solution of f f x x= l ^ ^h h . [2]",
            "9": "9 0606/12/f/m/16 \u00a9 ucles 2016 [turn\u2002over7\u2002the polynomial    fx ax x x b 7 93 2+ - + = ^ h    is divisible by x2 1-.  the remainder when  fx^ h  is  divided by  x2-  is 5 times the remainder when  fx^ h  is divided by  x1+. \u2002(i)\u2002show that  a6=  and find the value of b.  [4] \u2002(ii)\u2002using the values from part (i), show that   fx x cx dx e 2 12= - + + ^ ^ ^ h h h, where c, d and e are  integers to be found.  [2] \u2002(iii)\u2002hence factorise   fx^ h  completely.  [2]",
            "10": "10 0606/12/f/m/16 \u00a9 ucles 20168\u2002 lg y lg x 0(1.3, 3)(2.55, 4.5) \u2002 the variables x and y are such that when lgy is plotted against lgx the straight line graph shown  above is obtained. \u2002(i)\u2002given that  y a xb=  , find the value of a and of b. [5]",
            "11": "11 0606/12/f/m/16 \u00a9 ucles 2016 [turn\u2002over\u2002(ii)\u2002find the value of lg y when x100= . [2] \u2002(iii)\u2002find the value of x when y = 8000.  [2] ",
            "12": "12 0606/12/f/m/16 \u00a9 ucles 20169\u2002 a c o br cm irad \u2002 the diagram shows a circle, centre o, radius r cm. points a, b and c are such that a and b lie on the  circle and the tangents at a and b meet at c. angle aob  = i radians. \u2002(i)\u2002given that the area of the major sector aob  is 7 times the area of the minor sector aob , find the  value of i. [2] \u2002(ii)\u2002given also that the perimeter of the minor sector aob  is 20  cm, show that the value of r, correct  to 2 decimal places, is 7.18.  [2]",
            "13": "13 0606/12/f/m/16 \u00a9 ucles 2016 [turn\u2002over\u2002(iii)\u2002using the values of i and r from parts (i) and (ii), find the perimeter of the shaded region abc .  [3] \u2002(iv)\u2002find the area of the shaded region  abc . [3]",
            "14": "14 0606/12/f/m/16 \u00a9 ucles 201610\u2002(i)\u2002find dd( )xx x2 123 1-1 j lkkn poo. [3] \u2002(ii)\u2002hence, show that   d x x xxpx q c 2 1152 1 21 23 - =-+ + ^^^ hhh y  , where c is a constant of integration,  \u2002 \u2002 and p and q are integers to be found.  [6]",
            "15": "15 0606/12/f/m/16 \u00a9 ucles 2016 [turn\u2002over\u2002(iii)\u2002hence find d x x x 2 1 .0 5121 - ^ h y . [2] \u2002 question \u200211\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.",
            "16": "16 0606/12/f/m/16 \u00a9 ucles 201611\u2002(i)\u2002show that     cosec c osectan11 1122 i ii--+= . [4] \u2002(ii)\u2002hence solve     cosec c osectan11 116i ii--+= +      for 0 3601 1i c c . [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."
        },
        "0606_m16_qp_22.pdf": {
            "1": "this document consists of 16 printed pages. dc (nf/fd) 106874/3 \u00a9 ucles 2016  [turn overcambridge international examinations cambridge international general certificate of secondary education * 5 7 6 4 7 8 3 2 7 3 * additional mathematics  0606/22 paper 2  february/ march 2016  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together . 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 80.",
            "2": "2 0606/22/f/m/16 \u00a9 ucles 2016mathematical formulae 1.\u2002algebra quadratic equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/22/f/m/16 \u00a9 ucles 2016 [turn\u2002over1\u2002two variables x and y are such that yx95=-  for x92. \u2002(i)\u2002find an expression for xy dd . [2] \u2002(ii)\u2002hence, find the approximate change in y as x increases from 13 to 13 + h, where h is small.  [2]",
            "4": "4 0606/22/f/m/16 \u00a9 ucles 20162\u2002the sets a, b and c are such that , , , , , .c a b c a b b b c a b2 12 14 19n n n n+ + , ,q1 = = = = =^ ^ ^ ^h h h h \u2002 complete the venn diagram to show the sets a, b and c and hence state a b c n+ +l l ^ h . \ue025      a b c n+ +l l ^ h  = .  [4]",
            "5": "5 0606/22/f/m/16 \u00a9 ucles 2016 [turn\u2002over3\u2002find the equation of the curve which passes through the point (1,  7) and for which xy xx9 3 dd 24 =- . [4]",
            "6": "6 0606/22/f/m/16 \u00a9 ucles 20164\u2002(a)\u2002 cos x a bx c f + = ^ h    has a period of 60\u00b0, an amplitude of 10 and is such that f (0) = 14.  state  the values of a, b and c. [2] \u2002(b)\u2002sketch the graph of sin y x 3 4 2 = -  for \u00b0x 0 180\u00b0 g g  on the axes below.  [3] 45\u00b0oy x90\u00b0 135\u00b0 180\u00b0",
            "7": "7 0606/22/f/m/16 \u00a9 ucles 2016 [turn\u2002over5\u2002(i)\u2002find, in ascending powers of x, the first 3 terms of the expansion of kx37+^ h , where k is a \u2002 \u2002 constant. give each term in its simplest form.  [3] \u2002(ii)\u2002given that, in the expansion of kx37+^ h , the coefficient of x2 is twice the coefficient of x, \u2002 \u2002 find the value of k. [2]",
            "8": "8 0606/22/f/m/16 \u00a9 ucles 20166\u2002do\u2002not\u2002use\u2002a\u2002calculator \u2002in\u2002this\u2002question. x1 3 3+ 6 2 3+ 5 3- \u2002 the diagram shows two parallelograms that are similar. the base and height, in centimetres, of each  \u2002 parallelogram is shown. given that x, the height of the smaller parallelogram, is p q 63+ , find the  value of each of the integers p and q. [5]",
            "9": "9 0606/22/f/m/16 \u00a9 ucles 2016 [turn\u2002over7\u2002(a)\u2002given that 4 26 08 4a=-j lkkn poo  and 6 71 22 1b=-j lkkn poo\u2002, find  a \u2212 3b. [2] \u2002(b)\u2002given that 2 40 1c=-j lkkn poo  and 4 33 5d=- -j lkkn poo , find \u2002 \u2002 (i)\u2002the inverse matrix c\u22121, [2] \u2002 \u2002(ii)\u2002the matrix x such that xd\u22121 = c. [3]",
            "10": "10 0606/22/f/m/16 \u00a9 ucles 20168\u2002the line   2 y = x + 2   meets the curve   x x y y 3 122 2+ - =    at the points a and b. \u2002(i)\u2002find the coordinates of the points a and b. [5] \u2002(ii)\u2002given that the point  c has coordinates (0,  6), show that the triangle abc  is right-angled.  [2]",
            "11": "11 0606/22/f/m/16 \u00a9 ucles 2016 [turn\u2002over9\u2002 p 1 mx m q t rrads i \u2002 pqrs  is a quadrilateral with ps parallel to qr. the perimeter of pqrs  is 3 m. the length of pq is 1 m  and the length of ps is x m. the point t is on qr such that st is parallel to pq. angle srt is q radians. \u2002(i)\u2002find an expression for x in terms of q. [3] \u2002(ii)\u2002show that the area, a m2, of pqrs  is given by coseca 12i= -  . [2] \u2002(iii)\u2002hence find the exact value of q  when  a 133= -c m  m2. [2]",
            "12": "12 0606/22/f/m/16 \u00a9 ucles 201610\u2002(a)\u2002the vectors p and q are such that p = 11i \u2212 24j and q = 2i + aj. \u2002 \u2002 (i)\u2002find the value of each of the constants a and b such that p + 2q = (a + b)i \u2212 20j. [3] \u2002 \u2002(ii)\u2002using the values of a and b found in part (i), find the unit vector in the direction p + 2q. [2]",
            "13": "13 0606/22/f/m/16 \u00a9 ucles 2016 [turn\u2002over (b)\u2002 o bca a b \u2002 \u2002 the points a and b have position vectors a and b with respect to an origin o. the point c lies on  ab and is such that ab : ac is 1 : l. find an expression for oc in terms of a, b and l. [3] \u2002(c)\u2002the points s and t have position vectors s and t with respect to an origin o. the points o, s and t  do not lie in a straight line. given that the vector   2 s + mt   is parallel to the vector   ( m + 3)s + 9t,    where m is a positive constant, find the value of m. [3]",
            "14": "14 0606/22/f/m/16 \u00a9 ucles 201611\u2002a curve has equation      yxx 12=+ . \u2002(i)\u2002find the coordinates of the stationary points of the curve.  [5]",
            "15": "15 0606/22/f/m/16 \u00a9 ucles 2016 [turn\u2002over\u2002(ii)\u2002show that xy xpx qx 1 dd 22 23 3= ++ ^ h , where p and q are integers to be found, and determine the nature of    the stationary points of the curve.  [5] question \u200212\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.",
            "16": "16 0606/22/f/m/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\u2002a particle p is projected from the origin o so that it moves in a straight line. at time t seconds \u2002 after projection, the velocity of the particle, v ms\u22121, is given by v t t 9 63 9 02= - +  . \u2002(i)\u2002show that p first comes to instantaneous rest when t = 2. [2] \u2002(ii)\u2002find the acceleration of p when t = 3.5. [2] \u2002(iii)\u2002find an expression for the displacement of p from o at time t seconds.  [3] \u2002(iv)\u2002find the distance travelled by p    (a) in the first 2 seconds,  [2]   (b) in the first 3 seconds.  [2]"
        },
        "0606_s16_qp_11.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (lk/sw) 106867/3 \u00a9 ucles 2016  [turn overcambridge international examinations cambridge international general certificate of secondary education * 5 4 7 0 3 1 2 3 7 2 * additional mathematics  0606/11 paper 1  may/june 2016  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/11/m/j/16 \u00a9 ucles 2016mathematical formulae 1.\u2002algebra quadratic \u2002equation  for the equation ax2 + bx + c = 0, xab b ac 242!=- - binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/11/m/j/16 \u00a9 ucles 2016 [turn\u2002over1\u2002find the value of k for which the curve y x x k 2 32= - + \u2002(i)\u2002passes through the point ( , ) 4 7- , [1] \u2002(ii)\u2002meets the x-axis at one point only.  [2] 2\u2002(a)\u2002solve the equation 16 8x x3 1 2=- + . [3]  \u2002(b)\u2002given that  a ba b3 32 2131 21 -- ` j  = a p b q, find the value of each of the constants p and q. [2]",
            "4": "4 0606/11/m/j/16 \u00a9 ucles 20163\u2002find the equation of the normal to the curve ( )n y x 1 2 72= -  at the point where the curve crosses the positive x-axis. give your answer in the form ax b cy 0 + + = , where a, b and c are integers.  [5]",
            "5": "5 0606/11/m/j/16 \u00a9 ucles 2016 [turn\u2002over4\u2002(a)\u2002given the matrices a1 32 0=-j lkkn poo and b3 10 2=j lkkn poo , find a b 22-  . [3] \u2002(b)\u2002using a matrix method, solve the equations      x y4 1+ =  ,     x y10 3 1+ =  . [4]",
            "6": "6 0606/11/m/j/16 \u00a9 ucles 20165\u2002do\u2002not\u2002use\u2002a\u2002calculator \u2002in\u2002this\u2002question. \u2002(i)\u2002show that    ddee exx px4x x x4 4 4- =j lkkn poo  , where p is an integer to be found.  [4] \u2002(ii)\u2002hence find the exact value of e dx xnx4 01 2y  , giving your answer in the form nacb1 2+ , where \u2002 \u2002 a, b and c are integers to be found.  [4]",
            "7": "7 0606/11/m/j/16 \u00a9 ucles 2016 [turn\u2002over6\u2002the function f is defined by    ( )fx x 2 5= - +    for x5 01g-  . \u2002(i)\u2002write down the range of f.  [2] \u2002(ii)\u2002find ( ) fx1- and state its domain and range.  [4] \u2002 the function g is defined by     ( )gxx4=     for x5 11g- -  . \u2002(iii)\u2002solve ( )fgx 0= . [3]",
            "8": "8 0606/11/m/j/16 \u00a9 ucles 20167\u2002 75 m 2.4 ms\u2013130 m ba \u2002 the diagram shows a river with parallel banks. the river is 75  m wide and is flowing with a speed of  2.4 ms\u20131. a speedboat travels in a straight line from a point a on one bank to a point b on the opposite  bank, 30  m downstream from a. the speedboat can travel at a speed of 4.5  ms\u20131 in still water. \u2002(i)\u2002find the angle to the bank and the direction in which the speedboat is steered.  [4]",
            "9": "9 0606/11/m/j/16 \u00a9 ucles 2016 [turn\u2002over\u2002(ii)\u2002find the time the speedboat takes to travel from a to b. [4]",
            "10": "10 0606/11/m/j/16 \u00a9 ucles 20168\u2002solutions \u2002to\u2002this\u2002question\u2002by\u2002accurate\u2002drawing\u2002will\u2002not\u2002be\u2002accepted. \u2002 three points have coordinates ( , ) a 8 6-  , ( , ) b4 2  and ( , ) c 1 7-  . the line through c perpendicular to  ab intersects ab at the point p. \u2002(i)\u2002find the equation of the line ab. [2] \u2002(ii)\u2002find the equation of the line cp. [2] \u2002(iii)\u2002show that p is the midpoint of ab. [3]",
            "11": "11 0606/11/m/j/16 \u00a9 ucles 2016 [turn\u2002over\u2002(iv)\u2002calculate the length of cp. [1] \u2002(v)\u2002hence find the area of the triangle abc . [2]",
            "12": "12 0606/11/m/j/16 \u00a9 ucles 20169\u2002(i)\u2002show that   cos c ot cot c os x x x x 2 1 2 + = +    can be written in the form ( ) ( ) cos c os sin a x x x b 0 - - = ,   where a and b are constants to be found.  [4] \u2002(ii)\u2002hence, or otherwise, solve   cos c ot cot c os x x x x 2 1 2 + = +   for x 01 1 r . [3]",
            "13": "13 0606/11/m/j/16 \u00a9 ucles 2016 [turn\u2002over10\u2002(i)\u2002given that ( )fx x kx p 43= + + is exactly divisible by  x2+ and ( )fxl is exactly divisible by  x2 1- , find the value of k and of p. [4] \u2002(ii)\u2002using the values of k and p found in part (i), show that ( ) ( ) ( ) fx x ax bx c 22= + + +  , where a, b and c are integers to be found.  [2] \u2002(iii)\u2002hence show that ( )fx 0=  has only one solution and state this solution.  [2]",
            "14": "14 0606/11/m/j/16 \u00a9 ucles 201611 b o2\u03b8 rada r cm \u2002 the diagram shows a circle, centre o, radius r cm. the points a and b lie on the circle such that  angle aob 2i=  radians. \u2002(i)\u2002find, in terms of r and i, an expression for the length of the chord ab. [1] \u2002(ii)\u2002given that the perimeter of the shaded region is 20  cm, show that sinr10 i i=+ . [2]",
            "15": "15 0606/11/m/j/16 \u00a9 ucles 2016\u2002(iii)\u2002given that r and i can vary, find the value of ddr i when i = 6r . [4] \u2002(iv)\u2002given that r is increasing at the rate of 15  cm s\u20131, find the corresponding rate of change of  i when i = 6r . [3]",
            "16": "16 0606/11/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\u2002page"
        },
        "0606_s16_qp_12.pdf": {
            "1": "additional mathematics \b 0606/12 paper \b1\b may/june 2016 \b 2 hours candidates \banswer \bon\bthe\bquestion \bpaper. additional \bmaterials: \b electronic \bcalculator read these instructions first write \byour\bcentre \bnumber, \bcandidate \bnumber \band\bname \bon\ball\bthe\bwork \byou\bhand \bin. write \bin\bdark\bblue\bor\bblack \bpen. y ou\bmay\buse\ban\bhb\bpencil \bfor\bany\bdiagrams \bor\bgraphs. do\bnot\buse\bstaples, \bpaper \bclips, \bglue\bor\bcorrection \bfluid. do\bnot \bwrite \bin\bany \bbarcodes. answer \ball\bthe\bquestions. give \bnon-exact \bnumerical \banswers \bcorrect \bto\b3\bsignificant \bfigures, \bor\b1\bdecimal \bplace \bin\bthe\bcase \bof\b angles \bin\bdegrees, \bunless \ba\bdifferent \blevel\bof\baccuracy \bis\bspecified \bin\bthe\bquestion. the\buse\bof\ban\belectronic \bcalculator \bis\bexpected, \bwhere \bappropriate. y ou\bare\breminded \bof\bthe\bneed \bfor\bclear \bpresentation \bin\byour\banswers. at\bthe\bend\bof\bthe\bexamination, \bfasten \ball\byour\bwork \bsecurely \btogether. the\bnumber \bof\bmarks \bis\bgiven \bin\bbrackets \b[\b]\bat\bthe\bend\bof\beach \bquestion \bor\bpart\bquestion. the\btotal\bnumber \bof\bmarks \bfor\bthis\bpaper \bis\b80. this\bdocument \bconsists \bof\b16\bprinted \bpages. dc\b(st/sw) \b106862/3 \u00a9\bucles \b2016\b [turn overcambridge international examinations cambridge \binternational \bgeneral \bcertificate \bof\bsecondary \beducation * 0 9 9 3 8 1 1 3 1 0 *",
            "2": "2 0606/12/m/j/16 \u00a9 ucles 2016mathematical formulae 1.\u2002algebra quadratic equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/12/m/j/16 \u00a9 ucles 2016 [turn\u2002over1\u2002(a)\u2002the universal set \ue025 is the set of real numbers and sets x, y and z are such that    x = {integer multiples of 5},    y = {integer multiples of 10},    z = {r, 2, e}.   use set notation to complete the two statements below.   y ... x y \ue0f9\u2009z = ...  [2] \u2002(b)\u2002\u2002on each of the venn diagrams below, shade the region indicated. a b (a  /h33370 b) /h33371 c a  /h33370 (b /h33371 c )c/h5105 a b c/h5105 [2]",
            "4": "4 0606/12/m/j/16 \u00a9 ucles 20162\u2002(i)\u2002the first 3 terms in the expansion of x2415 -c m  are ab xc 2+ +x. find the value of each of the  integers a, b and c. [3] \u2002(ii)\u2002hence find the term independent of x in the expansion of xx 2413 45 - +c ^m h. [2]",
            "5": "5 0606/12/m/j/16 \u00a9 ucles 2016 [turn\u2002over3\u2002vectors\u2002\u2002a,\u2002b\u2002and\u2002c\u2002are such that \u2002\u2002\u2002a\u2002=\u2002y2j lkkn poo,  b\u2002=\u20021 3j lkkn poo\u2002\u2002and c\u2002=\u20025 5-j lkkn poo. \u2002(i)\u2002given that a b c = - , find the possible values of y. [3] \u2002\u2002\u2002(ii)\u2002given that\u2002b c b c b c 4 2 n m + + - = - ^ ^ ^ h h h, find the value of n and of m. [3]",
            "6": "6 0606/12/m/j/16 \u00a9 ucles 20164\u2002do\u2002not\u2002use\u2002a\u2002calculator\u2002in\u2002this\u2002question. \u2002 find the positive value of x for which  x x 4 5 2 5 1 02+ + - - = ^ ^ h h , giving your answer in the   form ba 5+, where a and b are integers.  [6]",
            "7": "7 0606/12/m/j/16 \u00a9 ucles 2016 [turn\u2002over5\u2002\u2002(i)\u2002show that cos sec sin tan 1 1 i i i i - + = ^ ^ h h . [4] \u2002(ii)\u2002hence solve the equation  cos sec sin 1 1 i i i - + = ^ ^ h h  for 0g gir radians.  [3]",
            "8": "8 0606/12/m/j/16 \u00a9 ucles 20166 show that  xx4 1ddex3+ ^ h  can be written in the form  xpx q 4 1ex3 ++ ^ h, where p and q are   integers to be found.  [5]",
            "9": "9 0606/12/m/j/16 \u00a9 ucles 2016 [turn\u2002over7 a ob y = 1 \u2013 2cos3 xy x   the diagram shows part of the graph of y x 1 32cos= - , which crosses the x-axis at the point a and  has a maximum at the point b. \u2002(i)\u2002find the coordinates of a. [2] \u2002(ii)\u2002find the coordinates of b. [2] \u2002(iii)\u2002showing all your working, find the area of the shaded region bounded by the curve, the x-axis  and the perpendicular from b to the x-axis.  [4]",
            "10": "10 0606/12/m/j/16 \u00a9 ucles 20168 0.2 1 2 3 4 x20.40.6lg y 00.70.80.91.0 0.10.30.5 0.0(1, 0.73) (4, 0.10)   variables x and y are such that when lgy is plotted against x2, the straight line graph shown above is  obtained.  \u2002(i)\u2002given that y a bx2= , find the value of a and of b. [4] \u2002(ii)\u2002find the value of y when x = 1.5.  [2] \u2002(iii)\u2002find the positive value of x when y = 2. [2]",
            "11": "11 0606/12/m/j/16 \u00a9 ucles 2016 [turn\u2002over9 a curve passes through the point ,234-c m  and is such that  xxy3 10dd 21= +-^ h . \u2002(i)\u2002find the equation of the curve.  [4]  the normal to the curve, at the point where x5=, meets the line y35=-  at the point p. \u2002(ii)\u2002find the  x-coordinate of p. [6]",
            "12": "12 0606/12/m/j/16 \u00a9 ucles 201610\u2002 x cm y cmb ca d   the diagram shows a badge, made of thin sheet metal, consisting of two semi-circular pieces, centres  b and c, each of radius x cm.  they are attached to each other by a rectangular piece of thin sheet  metal, abcd , such that ab and cd are the radii of the semi-circular pieces and ad = bc = y cm.    \u2002(i)\u2002given that the area of the badge is 20  cm2, show that the perimeter, p cm, of the badge is given  \u2002 \u2002 by p xx240= + .   [4]",
            "13": "13 0606/12/m/j/16 \u00a9 ucles 2016 [turn\u2002over\u2002(ii)\u2002given that x can vary, find the minimum value of p, justifying that this value is a minimum.  [5]",
            "14": "14 0606/12/m/j/16 \u00a9 ucles 201611\u2002(a)\u2002\u2002 101020v ms\u20131 30 20 30 40 50 60t s o \u2002 \u2002 the diagram shows the velocity-time graph of a particle p moving in a straight line with velocity  v ms\u20131 at time t s after leaving a fixed point. \u2002 \u2002(i)\u2002find the distance travelled by the particle p. [2] \u2002 \u2002(ii)\u2002write down the deceleration of the particle when t = 30.  [1]",
            "15": "15 0606/12/m/j/16 \u00a9 ucles 2016 [turn\u2002over\u2002(b)\u2002\u2002the diagram shows a velocity-time graph of a particle q moving in a straight line with velocity  v ms\u20131, at time t s after leaving a fixed point. 5 10 15 2036v ms\u20131 t s o \u2002 \u2002 the displacement of q at time t s is s m. on the axes below, draw the corresponding  displacement-time graph for q. [2] 5 10 15 20306090s m t s o question\u200211(c)\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.",
            "16": "16 0606/12/m/j/16 \u00a9 ucles 2016\u2002(c)\u2002the velocity, v ms\u20131, of a particle r moving in a straight line, t s after passing through a fixed  point o, is given by v4 6et2= + . \u2002 \u2002(i)\u2002\u2002explain why the particle is never at rest.  [1] \u2002 \u2002(ii)\u2002find the exact value of t for which the acceleration of r is 12 ms\u20132. [2] \u2002 \u2002(iii)\u2002showing all your working, find the distance travelled by r in the interval between . t0 4=   and . t0 5= . [4] permission \bto\breproduce \bitems \bwhere \bthird-party \bowned \bmaterial \bprotected \bby\bcopyright \bis\bincluded \bhas\bbeen \bsought \band\bcleared \bwhere \bpossible. \bevery \breasonable \b effort \bhas\bbeen \bmade \bby\bthe\bpublisher \b(ucles) \bto\btrace \bcopyright \bholders, \bbut\bif\bany\bitems \brequiring \bclearance \bhave \bunwittingly \bbeen \bincluded, \bthe\bpublisher \bwill\b be\bpleased \bto\bmake \bamends \bat\bthe\bearliest \bpossible \bopportunity. to\bavoid \bthe\bissue \bof\bdisclosure \bof\banswer-related \binformation \bto\bcandidates, \ball\bcopyright \backnowledgements \bare\breproduced \bonline \bin\bthe\bcambridge \binternational \b examinations \bcopyright \backnowledgements \bbooklet. \bthis\bis\bproduced \bfor\beach \bseries \bof\bexaminations \band\bis\bfreely \bavailable \bto\bdownload \bat\bwww.cie.org.uk \bafter\b the\blive\bexamination \bseries. cambridge \binternational \bexaminations \bis\bpart\bof\bthe\bcambridge \bassessment \bgroup. \bcambridge \bassessment \bis\bthe\bbrand \bname \bof\buniversity \bof\bcambridge \blocal \b examinations \bsyndicate \b(ucles), \bwhich \bis\bitself \ba\bdepartment \bof\bthe\buniversity \bof\bcambridge."
        },
        "0606_s16_qp_13.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (slm) 122174 \u00a9 ucles 2016  [turn overcambridge international examinations cambridge international general certificate of secondary education * 5 8 7 0 4 3 8 4 3 5 * additional mathematics  0606/13 paper 1  may/june 2016  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/13/m/j/16 \u00a9 ucles 2016mathematical formulae 1.\u2002algebra quadratic \u2002equation  for the equation ax2 + bx + c = 0, xab b ac 242!=- - binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/13/m/j/16 \u00a9 ucles 2016 [turn\u2002over1\u2002find the value of k for which the curve y x x k 2 32= - + \u2002(i)\u2002passes through the point ( , ) 4 7- , [1] \u2002(ii)\u2002meets the x-axis at one point only.  [2] 2\u2002(a)\u2002solve the equation 16 8x x3 1 2=- + . [3]  \u2002(b)\u2002given that  a ba b3 32 2131 21 -- ` j  = a p b q, find the value of each of the constants p and q. [2]",
            "4": "4 0606/13/m/j/16 \u00a9 ucles 20163\u2002find the equation of the normal to the curve ( )n y x 1 2 72= -  at the point where the curve crosses the positive x-axis. give your answer in the form ax b cy 0 + + = , where a, b and c are integers.  [5]",
            "5": "5 0606/13/m/j/16 \u00a9 ucles 2016 [turn\u2002over4\u2002(a)\u2002given the matrices a1 32 0=-j lkkn poo and b3 10 2=j lkkn poo , find a b 22-  . [3] \u2002(b)\u2002using a matrix method, solve the equations      x y4 1+ =  ,     x y10 3 1+ =  . [4]",
            "6": "6 0606/13/m/j/16 \u00a9 ucles 20165\u2002do\u2002not\u2002use\u2002a\u2002calculator \u2002in\u2002this\u2002question. \u2002(i)\u2002show that    ddee exx px4x x x4 4 4- =j lkkn poo  , where p is an integer to be found.  [4] \u2002(ii)\u2002hence find the exact value of e dx xnx4 01 2y  , giving your answer in the form nacb1 2+ , where \u2002 \u2002 a, b and c are integers to be found.  [4]",
            "7": "7 0606/13/m/j/16 \u00a9 ucles 2016 [turn\u2002over6\u2002the function f is defined by    ( )fx x 2 5= - +    for x5 01g-  . \u2002(i)\u2002write down the range of f.  [2] \u2002(ii)\u2002find ( ) fx1- and state its domain and range.  [4] \u2002 the function g is defined by     ( )gxx4=     for x5 11g- -  . \u2002(iii)\u2002solve ( )fgx 0= . [3]",
            "8": "8 0606/13/m/j/16 \u00a9 ucles 20167\u2002 75 m 2.4 ms\u2013130 m ba \u2002 the diagram shows a river with parallel banks. the river is 75  m wide and is flowing with a speed of  2.4 ms\u20131. a speedboat travels in a straight line from a point a on one bank to a point b on the opposite  bank, 30  m downstream from a. the speedboat can travel at a speed of 4.5  ms\u20131 in still water. \u2002(i)\u2002find the angle to the bank and the direction in which the speedboat is steered.  [4]",
            "9": "9 0606/13/m/j/16 \u00a9 ucles 2016 [turn\u2002over\u2002(ii)\u2002find the time the speedboat takes to travel from a to b. [4]",
            "10": "10 0606/13/m/j/16 \u00a9 ucles 20168\u2002solutions \u2002to\u2002this\u2002question\u2002by\u2002accurate\u2002drawing\u2002will\u2002not\u2002be\u2002accepted. \u2002 three points have coordinates ( , ) a 8 6-  , ( , ) b4 2  and ( , ) c 1 7-  . the line through c perpendicular to  ab intersects ab at the point p. \u2002(i)\u2002find the equation of the line ab. [2] \u2002(ii)\u2002find the equation of the line cp. [2] \u2002(iii)\u2002show that p is the midpoint of ab. [3]",
            "11": "11 0606/13/m/j/16 \u00a9 ucles 2016 [turn\u2002over\u2002(iv)\u2002calculate the length of cp. [1] \u2002(v)\u2002hence find the area of the triangle abc . [2]",
            "12": "12 0606/13/m/j/16 \u00a9 ucles 20169\u2002(i)\u2002show that   cos c ot cot c os x x x x 2 1 2 + = +    can be written in the form ( ) ( ) cos c os sin a x x x b 0 - - = ,   where a and b are constants to be found.  [4] \u2002(ii)\u2002hence, or otherwise, solve   cos c ot cot c os x x x x 2 1 2 + = +   for x 01 1 r . [3]",
            "13": "13 0606/13/m/j/16 \u00a9 ucles 2016 [turn\u2002over10\u2002(i)\u2002given that ( )fx x kx p 43= + + is exactly divisible by  x2+ and ( )fxl is exactly divisible by  x2 1- , find the value of k and of p. [4] \u2002(ii)\u2002using the values of k and p found in part (i), show that ( ) ( ) ( ) fx x ax bx c 22= + + +  , where a, b and c are integers to be found.  [2] \u2002(iii)\u2002hence show that ( )fx 0=  has only one solution and state this solution.  [2]",
            "14": "14 0606/13/m/j/16 \u00a9 ucles 201611 b o2\u03b8 rada r cm \u2002 the diagram shows a circle, centre o, radius r cm. the points a and b lie on the circle such that  angle aob 2i=  radians. \u2002(i)\u2002find, in terms of r and i, an expression for the length of the chord ab. [1] \u2002(ii)\u2002given that the perimeter of the shaded region is 20  cm, show that sinr10 i i=+ . [2]",
            "15": "15 0606/13/m/j/16 \u00a9 ucles 2016\u2002(iii)\u2002given that r and i can vary, find the value of ddr i when i = 6r . [4] \u2002(iv)\u2002given that r is increasing at the rate of 15  cm s\u20131, find the corresponding rate of change of  i when i = 6r . [3]",
            "16": "16 0606/13/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\u2002page"
        },
        "0606_s16_qp_21.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (rw/sg) 106861/1 \u00a9 ucles 2016  [turn overcambridge international examinations cambridge international general certificate of secondary education * 3 9 1 1 9 9 9 3 9 1 * additional mathematics  0606/21 paper 2  may/june 2016  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of   angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together . 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 80.",
            "2": "2 0606/21/m/j/16 \u00a9 ucles 2016mathematical formulae 1.\u2002algebra quadratic \u2002equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/21/m/j/16 \u00a9 ucles 2016 [turn\u2002over1\u2002find the values of x for which x x4 2 72 - +^ ^ h h . [3] 2\u2002(a)\u2002illustrate the statements    a bf and b cf     using the venn diagram below. \u2002 [1] /h5105 \u2002(b)\u2002it is given that \u2002   the elements of set \ue025  are the letters of the alphabet,    the elements of set p  are the letters in the word maths ,    the elements of set q are the letters in the word exam . \u2002 \u2002 (i)\u2002write the following using set notation. \u2002    the letter h is in the word maths . [1] \u2002 \u2002(ii)\u2002write the following using set notation. \u2002    the number of letters occurring in both of the words maths  and exam is two.  [1] \u2002 \u2002(iii)\u2002list the elements of the set p qk l. [1]",
            "4": "4 0606/21/m/j/16 \u00a9 ucles 20163\u2002do\u2002not\u2002use\u2002a\u2002calculator \u2002in\u2002this\u2002question. \u2002(i)\u2002find the value of   logp- p2. [1] \u2002(ii)\u2002find   lg101 nj lkkn poo. [1] \u2002(iii)\u2002show that  loglg lglgy1020 4 52 -=^ h , where y is a constant to be found.  [2] \u2002(iv)\u2002solve  log l og log x x2 3 600r r r+ = . [2]",
            "5": "5 0606/21/m/j/16 \u00a9 ucles 2016 [turn\u2002over4 a b c\u03b8 rad \u2002 the diagram shows 3 circles with centres a, b and c, each of radius 5  cm. each circle touches the other  two circles. angle bac  is \u03b8 radians. \u2002(i)\u2002write down the value of \u03b8. [1] \u2002(ii)\u2002find the area of the shaded region between the circles.  [4]",
            "6": "6 0606/21/m/j/16 \u00a9 ucles 20165\u2002do\u2002not\u2002use\u2002a\u2002calculator \u2002in\u2002this\u2002question. \u2002(a)\u2002express  78 5- in the form a b+ , where a and b are integers.  [3] \u2002(b)\u2002given that   p q 28 3 2 32+ = +^ h , where p and q are integers, find the values of p and of q. [3]",
            "7": "7 0606/21/m/j/16 \u00a9 ucles 2016 [turn\u2002over6\u2002(i)\u2002express  x x4 8 52+ -   in the form  p x q r2+ +^ h , where p, q and r are constants to \u2002be found.  [3] \u2002(ii)\u2002state the coordinates of the vertex of \u2002\u2002y x x 4 8 52= + - .\u2002 [2] \u2002(iii)\u2002on the axes below, sketch the graph of  y x x 4 8 52= + -, showing the coordinates of the points  where the curve meets the axes.  [3] o xy",
            "8": "8 0606/21/m/j/16 \u00a9 ucles 20167\u2002o, p, q and r are four points such that  p op=,  qoq=  and  q p or 3 2= - . \u2002(i)\u2002find,\u2002in terms of \u2002p\u2002and\u2002q, \u2002  (a) pq, [1] \u2002  (b) qr. [1] \u2002(ii)\u2002justifying your answer, what can be said about the positions of the points p, q and r? [2] \u2002(iii)\u2002given that \u2002 i j op 3= +\u2002and\u2002that\u2002 i j oq 2= + , find the unit vector in the direction or. [3]",
            "9": "9 0606/21/m/j/16 \u00a9 ucles 2016 [turn\u2002over8\u2002(a)\u2002(i)\u2002use the binomial theorem to expand a b4+^ h , giving each term in its simplest form.  [2] \u2002 \u2002(ii)\u2002hence find the term independent of x in the expansion of xx2514 +j lkkn poo. [2] \u2002(b)\u2002the coefficient of x3 in the expansion of x12n +j lkkn poo equals n 125. find the value of the positive  integer  n. [3]",
            "10": "10 0606/21/m/j/16 \u00a9 ucles 20169\u2002(a)\u2002given that  tan y a bx c = +    has period r 4 radians and passes through the points ,0 2-^ h  and \u2002 \u2002r,160j lkkn poo, find the value of each of the constants a, b and c. [3]  a = ...    b = ...    c = ... \u2002(b)\u2002(i)\u2002on the axes below, draw the graph of cos y x2 3 1 = +  for r rx32 32g g-  radians.  [3] 32r-2r-3r-6r-6r 3r 2r 32ry x \u201344 o \u2002 \u2002(ii)\u2002using your graph, or otherwise, find the exact solutions of cos x 2 3 1 12+ = ^ h  for  \u2002 \u2002 \u2002r rx32 32g g-  radians.  [2]",
            "11": "11 0606/21/m/j/16 \u00a9 ucles 2016 [turn\u2002over10\u2002(a)\u2002(i)\u2002find how many 5-digit even numbers can be made using each of the digits 1, 2, 3, 4, 5 once  only.  [2] \u2002 \u2002(ii)\u2002find how many different 3-digit numbers can be made using the digits 1, 2, 3, 4, 5 if each  digit can be used once only.  [2] \u2002(b)\u2002a man and two women are to sit in a row of five empty chairs. calculate the number of ways they  can be seated if \u2002 \u2002 (i)\u2002the two women must sit next to each other,  [2] \u2002 \u2002(ii)\u2002all three people must sit next to each other.  [2]",
            "12": "12 0606/21/m/j/16 \u00a9 ucles 201611\u2002(i)\u2002find   x x x 3 d23- ^ hy . [2] \u2002 the diagram shows part of the curve y x x 323= -    and the lines y x3=    and   y x2 27 3= - . the curve  and the line y x3=  meet the x-axis at o and the curve and the line y x2 27 3= -  meet the x-axis at a. y x x 323 = -y x2 27 3= - y x3=y o a xb \u2002(ii)\u2002find the coordinates of a. [1] \u2002(iii)\u2002verify that the coordinates of b are ,3 9^ h . [1]",
            "13": "13 0606/21/m/j/16 \u00a9 ucles 2016 [turn\u2002over\u2002(iv)\u2002find the area of the shaded region.  [4]",
            "14": "14 0606/21/m/j/16 \u00a9 ucles 201612\u2002a curve has equation  yxxx12 512 =--- . \u2002(i)\u2002find  xy dd. [3] \u2002(ii)\u2002find  xy dd 22 . [2]",
            "15": "15 0606/21/m/j/16 \u00a9 ucles 2016\u2002(iii)\u2002find the coordinates of the stationary points of the curve and determine their nature.  [5]",
            "16": "16 0606/21/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\u2002page"
        },
        "0606_s16_qp_22.pdf": {
            "1": "this document consists of 12 printed pages. dc (kn/sw) 106860/4 \u00a9 ucles 2016  [turn over * 9 6 6 2 4 0 1 7 0 8 * additional mathematics  0606/22 paper 2  may/june 2016  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge international examinations cambridge international general certificate of secondary education",
            "2": "2 0606/22/m/j/16 \u00a9 ucles 2016mathematical formulae 1.\u2002algebra quadratic equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/22/m/j/16 \u00a9 ucles 2016 [turn\u2002over1\u2002(i)\u2002given that  x k x k2 4 3 02+ + - =   has no real roots, show that k satisfies  k k 4 3 021 - + .  [2] \u2002(ii)\u2002solve the inequality         k k 4 3 021 - + .  [2] 2\u2002variables x and y are related by the equation  yxx 35 1=-- . \u2002(i)\u2002find xy dd, simplifying your answer.  [2] \u2002(ii)\u2002hence find the approximate change in x when y increases from 9 by the small amount 0.07.  [3]",
            "4": "4 0606/22/m/j/16 \u00a9 ucles 20163\u2002a team of 3 people is to be selected from 7 women and 6 men. find the number of different teams that  could be selected if there must be more women than men on the team.  [3] 4\u2002\u2002do\u2002not\u2002use\u2002a\u2002calculator \u2002in\u2002this\u2002question. \u2002 \u2002 the polynomial p()x x x qx 2 3 563 2= - + +  has a factor x \u2013 2. \u2002(i)\u2002show that q = \u221230.  [1] \u2002(ii)\u2002factorise p ()x completely and hence state all the solutions of p()x 0= . [4] ",
            "5": "5 0606/22/m/j/16 \u00a9 ucles 2016 [turn\u2002over5\u2002the coordinates of three points are a(\u22122, 6), b(6, 10) and c(p, 0). \u2002(i)\u2002find the coordinates of m, the mid-point of ab. [2] \u2002(ii)\u2002given that cm is perpendicular to ab, find the value of the constant p. [2] \u2002(iii)\u2002find angle mcb . [3]",
            "6": "6 0606/22/m/j/16 \u00a9 ucles 20166 o a b5 cm radi \u2002 the diagram shows a sector of a circle with centre o and radius 5  cm. the length of the arc ab is 7 cm.  angle aob  is \u03b8 radians. \u2002(i)\u2002explain why \u03b8 must be greater than 1 radian.  [1] \u2002(ii)\u2002find the value of \u03b8. [2] \u2002(iii)\u2002calculate the area of the sector aob . [2] \u2002(iv)\u2002calculate the area of the shaded segment.  [2]",
            "7": "7 0606/22/m/j/16 \u00a9 ucles 2016 [turn\u2002over7\u2002the matrix a is 4 35 2j lkkn poo and the matrix b is 4 12 3j lkkn poo.  \u2002(i)\u2002find the matrix c such that 3a bc= + . [2] \u2002(ii)\u2002show that ( )det det det ab a b# = . [4] \u2002(iii)\u2002find the matrix ( )ab1-. [2]",
            "8": "8 0606/22/m/j/16 \u00a9 ucles 20168\u2002find the coordinates of the points of intersection of the curve y x45 30 + + = and the line  \u2002 y x15 10 = + . [6]",
            "9": "9 0606/22/m/j/16 \u00a9 ucles 2016 [turn\u2002over9\u2002(a)\u2002find   xx xx1d23 2+ +y . [3] \u2002(b)\u2002(i)\u2002find ( )sin x x5 dr+ y . [2] \u2002 \u2002(ii)\u2002hence evaluate ( )sinx x5 d0 5r+ -ry . [2]",
            "10": "10 0606/22/m/j/16 \u00a9 ucles 201610\u2002(a)\u2002\u2002the graph of the curve ( ) ( ) y p q 4 4x x2= -  passes through the points (0, 2) and (0.5, 14). find the  value of  p and of q. [3] \u2002(b)\u2002the variables x and y are connected by the equation ( ) y 10 2 10x x2= - . using the substitution  u10x= , or otherwise, find the exact value of x when y = 24.  [3] \u2002(c)\u2002solve   ( ) log l og x x1 32 2+ - = . [3]",
            "11": "11 0606/22/m/j/16 \u00a9 ucles 2016 [turn\u2002over11\u2002(a)\u2002a function f is defined, for all real x, by      ( )x x x f2= - . \u2002 \u2002 find the greatest value of f  (x) and the value of x for which this occurs.  [3] \u2002(b)\u2002the domain of g()x x x2= -  is such that ( )x g1- exists. explain why x1h is a suitable domain  for g( x). [1] \u2002(c)\u2002the functions h and k are defined by \u2002    : ( ) lgx x 2 h7 + for x 22-, \u2002    :x x 5 1 k7+ -  for x 1 1011 1 . \u2002 \u2002 (i)\u2002find hk(10).  [2] \u2002 \u2002(ii)\u2002find ( )x k1-, stating its domain and range.  [5]  question \u200212\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.",
            "12": "12 0606/22/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.12\u2002\u2002solve the equation \u2002(i)\u2002sin c os a a 8 2 72+ =   for  a 0 180 g gc c , [4] \u2002(ii)\u2002 ( ) . cosec b3 1 2 5 + =    for   b0g g r radians.  [4]"
        },
        "0606_s16_qp_23.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (st/sg) 125570 \u00a9 ucles 2016  [turn overcambridge international examinations cambridge international general certificate of secondary education * 1 5 0 9 9 5 0 9 3 3 * additional mathematics  0606/23 paper 2  may/june 2016  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of   angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together . 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 80.",
            "2": "2 0606/23/m/j/16 \u00a9 ucles 2016mathematical formulae 1.\u2002algebra quadratic \u2002equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/23/m/j/16 \u00a9 ucles 2016 [turn\u2002over1\u2002find the values of x for which x x4 2 72 - +^ ^ h h . [3] 2\u2002(a)\u2002illustrate the statements    a bf and b cf     using the venn diagram below. \u2002 [1] /h5105 \u2002(b)\u2002it is given that \u2002   the elements of set \ue025  are the letters of the alphabet,    the elements of set p  are the letters in the word maths ,    the elements of set q are the letters in the word exam . \u2002 \u2002 (i)\u2002write the following using set notation. \u2002    the letter h is in the word maths . [1] \u2002 \u2002(ii)\u2002write the following using set notation. \u2002    the number of letters occurring in both of the words maths  and exam is two.  [1] \u2002 \u2002(iii)\u2002list the elements of the set p qk l. [1]",
            "4": "4 0606/23/m/j/16 \u00a9 ucles 20163\u2002do\u2002not\u2002use\u2002a\u2002calculator \u2002in\u2002this\u2002question. \u2002(i)\u2002find the value of   logp- p2. [1] \u2002(ii)\u2002find   lg101 nj lkkn poo. [1] \u2002(iii)\u2002show that  loglg lglgy1020 4 52 -=^ h , where y is a constant to be found.  [2] \u2002(iv)\u2002solve  log l og log x x2 3 600r r r+ = . [2]",
            "5": "5 0606/23/m/j/16 \u00a9 ucles 2016 [turn\u2002over4 a b c\u03b8 rad \u2002 the diagram shows 3 circles with centres a, b and c, each of radius 5  cm. each circle touches the other  two circles. angle bac  is \u03b8 radians. \u2002(i)\u2002write down the value of \u03b8. [1] \u2002(ii)\u2002find the area of the shaded region between the circles.  [4]",
            "6": "6 0606/23/m/j/16 \u00a9 ucles 20165\u2002do\u2002not\u2002use\u2002a\u2002calculator \u2002in\u2002this\u2002question. \u2002(a)\u2002express  78 5- in the form a b+ , where a and b are integers.  [3] \u2002(b)\u2002given that   p q 28 3 2 32+ = +^ h , where p and q are integers, find the values of p and of q. [3]",
            "7": "7 0606/23/m/j/16 \u00a9 ucles 2016 [turn\u2002over6\u2002(i)\u2002express  x x4 8 52+ -   in the form  p x q r2+ +^ h , where p, q and r are constants to \u2002be found.  [3] \u2002(ii)\u2002state the coordinates of the vertex of \u2002\u2002y x x 4 8 52= + - .\u2002 [2] \u2002(iii)\u2002on the axes below, sketch the graph of  y x x 4 8 52= + -, showing the coordinates of the points  where the curve meets the axes.  [3] o xy",
            "8": "8 0606/23/m/j/16 \u00a9 ucles 20167\u2002o, p, q and r are four points such that  p op=,  qoq=  and  q p or 3 2= - . \u2002(i)\u2002find,\u2002in terms of \u2002p\u2002and\u2002q, \u2002  (a) pq, [1] \u2002  (b) qr. [1] \u2002(ii)\u2002justifying your answer, what can be said about the positions of the points p, q and r? [2] \u2002(iii)\u2002given that \u2002 i j op 3= +\u2002and\u2002that\u2002 i j oq 2= + , find the unit vector in the direction or. [3]",
            "9": "9 0606/23/m/j/16 \u00a9 ucles 2016 [turn\u2002over8\u2002(a)\u2002(i)\u2002use the binomial theorem to expand a b4+^ h , giving each term in its simplest form.  [2] \u2002 \u2002(ii)\u2002hence find the term independent of x in the expansion of xx2514 +j lkkn poo. [2] \u2002(b)\u2002the coefficient of x3 in the expansion of x12n +j lkkn poo equals n 125. find the value of the positive  integer  n. [3]",
            "10": "10 0606/23/m/j/16 \u00a9 ucles 20169\u2002(a)\u2002given that  tan y a bx c = +    has period r 4 radians and passes through the points ,0 2-^ h  and \u2002 \u2002r,160j lkkn poo, find the value of each of the constants a, b and c. [3]  a = ...    b = ...    c = ... \u2002(b)\u2002(i)\u2002on the axes below, draw the graph of cos y x2 3 1 = +  for r rx32 32g g-  radians.  [3] 32r-2r-3r-6r-6r 3r 2r 32ry x \u201344 o \u2002 \u2002(ii)\u2002using your graph, or otherwise, find the exact solutions of cos x 2 3 1 12+ = ^ h  for  \u2002 \u2002 \u2002r rx32 32g g-  radians.  [2]",
            "11": "11 0606/23/m/j/16 \u00a9 ucles 2016 [turn\u2002over10\u2002(a)\u2002(i)\u2002find how many 5-digit even numbers can be made using each of the digits 1, 2, 3, 4, 5 once  only.  [2] \u2002 \u2002(ii)\u2002find how many different 3-digit numbers can be made using the digits 1, 2, 3, 4, 5 if each  digit can be used once only.  [2] \u2002(b)\u2002a man and two women are to sit in a row of five empty chairs. calculate the number of ways they  can be seated if \u2002 \u2002 (i)\u2002the two women must sit next to each other,  [2] \u2002 \u2002(ii)\u2002all three people must sit next to each other.  [2]",
            "12": "12 0606/23/m/j/16 \u00a9 ucles 201611\u2002(i)\u2002find   x x x 3 d23- ^ hy . [2] \u2002 the diagram shows part of the curve y x x 323= -    and the lines y x3=    and   y x2 27 3= - . the curve  and the line y x3=  meet the x-axis at o and the curve and the line y x2 27 3= -  meet the x-axis at a. y x x 323 = -y x2 27 3= - y x3=y o a xb \u2002(ii)\u2002find the coordinates of a. [1] \u2002(iii)\u2002verify that the coordinates of b are ,3 9^ h . [1]",
            "13": "13 0606/23/m/j/16 \u00a9 ucles 2016 [turn\u2002over\u2002(iv)\u2002find the area of the shaded region.  [4]",
            "14": "14 0606/23/m/j/16 \u00a9 ucles 201612\u2002a curve has equation  yxxx12 512 =--- . \u2002(i)\u2002find  xy dd. [3] \u2002(ii)\u2002find  xy dd 22 . [2]",
            "15": "15 0606/23/m/j/16 \u00a9 ucles 2016\u2002(iii)\u2002find the coordinates of the stationary points of the curve and determine their nature.  [5]",
            "16": "16 0606/23/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\u2002page"
        },
        "0606_w16_qp_11.pdf": {
            "1": "this document consists of 16 printed pages. dc (cw/sg) 116669/2 \u00a9 ucles 2016  [turn overcambridge international examinations cambridge international general certificate of secondary education * 0 8 7 2 6 9 0 5 1 6 * additional mathematics  0606/11 paper 1  october/november 2016  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/11/o/n/16 \u00a9 ucles 2016mathematical formulae 1.\u2002algebra quadratic \u2002equation  for the equation ax2 + bx + c = 0, xab b ac 242!=- - . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/11/o/n/16 \u00a9 ucles 2016 [turn\u2002over1\u2002(a)\u2002sets \ue025, a and b are such that n(\ue025) , ( ) , ( ) a b a b 26 7 3 n n + + = = = l   and  ( )b 15 n=  . \u2002 \u2002 using a venn diagram, or otherwise, find \u2002 \u2002 (i)\u2002 ( )an , [1] \u2002 \u2002(ii)\u2002 ( )a bn,, [1] \u2002 \u2002(iii)\u2002 ( )a bn, l. [1] \u2002(b)\u2002it is given that  \ue025 { : } x x0 301 1 =  ,  p = {multiples of 5},  q = {multiples of 6} and  r = {multiples of 2}. use set notation to complete the following statements. \u2002 \u2002 (i)\u2002q  ...   r, [1] \u2002 \u2002(ii)\u2002p q+= ...  [1]",
            "4": "4 0606/11/o/n/16 \u00a9 ucles 20162\u2002given that   ( ) p qrp q rp q ra b c 53231 21 23 =-- , find the value of each of the integers a, b and c. [3] 3\u2002by using the substitution log y x3= , or otherwise, find the values of x for which  ( )log l og log x x 3 9 032 35 3+ - = . [6]",
            "5": "5 0606/11/o/n/16 \u00a9 ucles 2016 [turn\u2002over4\u2002(i)\u2002find the first 3 terms in the expansion of   xx231 25 -j lkkn poo , in descending powers of x. [3] \u2002(ii)\u2002hence find the coefficient of x7 in the expansion of xxx31231 325 + -j lkkj lkkn poon poo . [2]",
            "6": "6 0606/11/o/n/16 \u00a9 ucles 20165\u2002(i)\u2002find the equation of the normal to the curve  ( )ln y x213 2 = +   at the point p where  x31=-  . [4] \u2002 the normal to the curve at the point p intersects the y-axis at the point q. the curve ( )ln y x213 2 = +   intersects the y-axis at the point r . \u2002(ii)\u2002find the area of the triangle pqr . [3]",
            "7": "7 0606/11/o/n/16 \u00a9 ucles 2016 [turn\u2002over6\u2002(a)\u2002matrices x, y and z are such that  x2 4 63 1 5= -j lk kkn po oo\u2002,  y 1 1 0 = -^ h     and z0 51 3=-j lkkn poo . \u2002 \u2002 write down all the matrix products which are possible using any two of these matrices. do not  evaluate these products.  [2] \u2002(b)\u2002matrices a, b and c are such that  a1 2 4 7=-j lkkn poo ,  b4 102 4=-j lkkn poo  and  ac b=. \u2002 \u2002 (i)\u2002find a1- . [2] \u2002 \u2002(ii)\u2002hence find c. [3]",
            "8": "8 0606/11/o/n/16 \u00a9 ucles 20167 y x oab ccosy x26r= -j lkkn poo \u2002 the diagram shows part of the graph of cos y x26r= -j lkkn poo. the graph intersects the y-axis at the  \u2002 point  a, has a maximum point at b and intersects the x-axis at the point c. \u2002(i)\u2002find the coordinates of a. [1] \u2002(ii)\u2002find the coordinates of b. [2]",
            "9": "9 0606/11/o/n/16 \u00a9 ucles 2016 [turn\u2002over\u2002(iii)\u2002find the coordinates of c. [2] \u2002(iv)\u2002find cosx x 26dr-j lkkn poo y  . [1] \u2002(v)\u2002hence find the area of the shaded region.  [2]",
            "10": "10 0606/11/o/n/16 \u00a9 ucles 20168 irad 12 cmb ca do \u2002 the diagram shows a sector aob  of the circle, centre o, radius 12  cm, together with points c and  d such that abcd  is a rectangle. the angle aob  is i radians and the perimeter of the sector aob  is  47 cm. \u2002(i)\u2002show that .1 92i=  radians correct to 2 decimal places.  [2] \u2002(ii)\u2002find the length of cd. [2]",
            "11": "11 0606/11/o/n/16 \u00a9 ucles 2016 [turn\u2002over\u2002(iii)\u2002given that the total area of the shape is 425  cm2, find the length of ad. [5]",
            "12": "12 0606/11/o/n/16 \u00a9 ucles 20169\u2002do\u2002not\u2002use\u2002a\u2002calculator \u2002in\u2002this\u2002question. \u2002 the polynomial p( x) is   ax x bx4 183 2- + + .   it is given that p( x) and ( )xpl are both divisible  by x2 3- . \u2002(i)\u2002show that a4= and find the value of b. [4] \u2002(ii)\u2002using the values of a and b from part (i), factorise p( x) completely.  [2]",
            "13": "13 0606/11/o/n/16 \u00a9 ucles 2016 [turn\u2002over\u2002(iii)\u2002hence find the values of x for which p( x) x2= +  . [3]",
            "14": "14 0606/11/o/n/16 \u00a9 ucles 201610\u2002(a) v ms\u20131 u 0 20 30u 2 t s \u2002 \u2002 the diagram shows part of the velocity-time graph for a particle, moving at vms1- in a straight  \u2002 \u2002 line, t s after passing through a fixed point. the particle travels at ums1-for 20  s and then  \u2002 \u2002 decelerates uniformly for 10  s to a velocity of u 2ms1-. in this 30  s interval, the particle travels  \u2002 \u2002 165 m. \u2002 \u2002 (i)\u2002find the value of u. [3] \u2002 \u2002(ii)\u2002find the acceleration of the particle between t = 20 and t = 30. [2]",
            "15": "15 0606/11/o/n/16 \u00a9 ucles 2016 [turn\u2002over\u2002(b)\u2002\u2002a particle p travels in a straight line such that,  t s after passing through a fixed point o, its  velocity, vms1-, is given by vt 832 = 4 e-j lkkn poo. \u2002 \u2002 (i)\u2002find the speed of p at o. [1] \u2002 \u2002(ii)\u2002find the value of t for which p is instantaneously at rest.  [2] \u2002 \u2002(iii)\u2002find the acceleration of p when t = 1. [4] question \u200211\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.",
            "16": "16 0606/11/o/n/16 \u00a9 ucles 201611\u2002the variables x and y are such that when lny is plotted against x, a straight line graph is obtained. this  line passes through the points , . , . ln ln x y x y 4 0 20 12 0 08 and = = = = . \u2002(i)\u2002given that y a bx= , find the value of a and of b. [5] \u2002(ii)\u2002find the value of y when x6= . [2] \u2002(iii)\u2002find the value of x when . y 1 1=  . [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."
        },
        "0606_w16_qp_12.pdf": {
            "1": "this document consists of 16 printed pages. dc (st/sg) 126424 \u00a9 ucles 2016  [turn overcambridge international examinations cambridge international general certificate of secondary education * 3 1 0 9 5 9 4 6 7 9 * additional mathematics  0606/12 paper 1  october/november 2016  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/12/o/n/16 \u00a9 ucles 2016mathematical formulae 1.\u2002algebra quadratic \u2002equation  for the equation ax2 + bx + c = 0, xab b ac 242!=- - . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/12/o/n/16 \u00a9 ucles 2016 [turn\u2002over1\u2002(a)\u2002sets \ue025, a and b are such that n(\ue025) , ( ) , ( ) a b a b 26 7 3 n n + + = = = l   and  ( )b 15 n=  . \u2002 \u2002 using a venn diagram, or otherwise, find \u2002 \u2002 (i)\u2002 ( )an , [1] \u2002 \u2002(ii)\u2002 ( )a bn,, [1] \u2002 \u2002(iii)\u2002 ( )a bn, l. [1] \u2002(b)\u2002it is given that  \ue025 { : } x x0 301 1 =  ,  p = {multiples of 5},  q = {multiples of 6} and  r = {multiples of 2}. use set notation to complete the following statements. \u2002 \u2002 (i)\u2002q  ...   r, [1] \u2002 \u2002(ii)\u2002p q+= ...  [1]",
            "4": "4 0606/12/o/n/16 \u00a9 ucles 20162\u2002given that   ( ) p qrp q rp q ra b c 53231 21 23 =-- , find the value of each of the integers a, b and c. [3] 3\u2002by using the substitution log y x3= , or otherwise, find the values of x for which  ( )log l og log x x 3 9 032 35 3+ - = . [6]",
            "5": "5 0606/12/o/n/16 \u00a9 ucles 2016 [turn\u2002over4\u2002(i)\u2002find the first 3 terms in the expansion of   xx231 25 -j lkkn poo , in descending powers of x. [3] \u2002(ii)\u2002hence find the coefficient of x7 in the expansion of xxx31231 325 + -j lkkj lkkn poon poo . [2]",
            "6": "6 0606/12/o/n/16 \u00a9 ucles 20165\u2002(i)\u2002find the equation of the normal to the curve  ( )ln y x213 2 = +   at the point p where  x31=-  . [4] \u2002 the normal to the curve at the point p intersects the y-axis at the point q. the curve ( )ln y x213 2 = +   intersects the y-axis at the point r . \u2002(ii)\u2002find the area of the triangle pqr . [3]",
            "7": "7 0606/12/o/n/16 \u00a9 ucles 2016 [turn\u2002over6\u2002(a)\u2002matrices x, y and z are such that  x2 4 63 1 5= -j lk kkn po oo\u2002,  y 1 1 0 = -^ h     and z0 51 3=-j lkkn poo . \u2002 \u2002 write down all the matrix products which are possible using any two of these matrices. do not  evaluate these products.  [2] \u2002(b)\u2002matrices a, b and c are such that  a1 2 4 7=-j lkkn poo ,  b4 102 4=-j lkkn poo  and  ac b=. \u2002 \u2002 (i)\u2002find a1- . [2] \u2002 \u2002(ii)\u2002hence find c. [3]",
            "8": "8 0606/12/o/n/16 \u00a9 ucles 20167 y x oab ccosy x26r= -j lkkn poo \u2002 the diagram shows part of the graph of cos y x26r= -j lkkn poo. the graph intersects the y-axis at the  \u2002 point  a, has a maximum point at b and intersects the x-axis at the point c. \u2002(i)\u2002find the coordinates of a. [1] \u2002(ii)\u2002find the coordinates of b. [2]",
            "9": "9 0606/12/o/n/16 \u00a9 ucles 2016 [turn\u2002over\u2002(iii)\u2002find the coordinates of c. [2] \u2002(iv)\u2002find cosx x 26dr-j lkkn poo y  . [1] \u2002(v)\u2002hence find the area of the shaded region.  [2]",
            "10": "10 0606/12/o/n/16 \u00a9 ucles 20168 irad 12 cmb ca do \u2002 the diagram shows a sector aob  of the circle, centre o, radius 12  cm, together with points c and  d such that abcd  is a rectangle. the angle aob  is i radians and the perimeter of the sector aob  is  47 cm. \u2002(i)\u2002show that .1 92i=  radians correct to 2 decimal places.  [2] \u2002(ii)\u2002find the length of cd. [2]",
            "11": "11 0606/12/o/n/16 \u00a9 ucles 2016 [turn\u2002over\u2002(iii)\u2002given that the total area of the shape is 425  cm2, find the length of ad. [5]",
            "12": "12 0606/12/o/n/16 \u00a9 ucles 20169\u2002do\u2002not\u2002use\u2002a\u2002calculator \u2002in\u2002this\u2002question. \u2002 the polynomial p( x) is   ax x bx4 183 2- + + .   it is given that p( x) and ( )xpl are both divisible  by x2 3- . \u2002(i)\u2002show that a4= and find the value of b. [4] \u2002(ii)\u2002using the values of a and b from part (i), factorise p( x) completely.  [2]",
            "13": "13 0606/12/o/n/16 \u00a9 ucles 2016 [turn\u2002over\u2002(iii)\u2002hence find the values of x for which p( x) x2= +  . [3]",
            "14": "14 0606/12/o/n/16 \u00a9 ucles 201610\u2002(a) v ms\u20131 u 0 20 30u 2 t s \u2002 \u2002 the diagram shows part of the velocity-time graph for a particle, moving at vms1- in a straight  \u2002 \u2002 line, t s after passing through a fixed point. the particle travels at ums1-for 20  s and then  \u2002 \u2002 decelerates uniformly for 10  s to a velocity of u 2ms1-. in this 30  s interval, the particle travels  \u2002 \u2002 165 m. \u2002 \u2002 (i)\u2002find the value of u. [3] \u2002 \u2002(ii)\u2002find the acceleration of the particle between t = 20 and t = 30. [2]",
            "15": "15 0606/12/o/n/16 \u00a9 ucles 2016 [turn\u2002over\u2002(b)\u2002\u2002a particle p travels in a straight line such that,  t s after passing through a fixed point o, its  velocity, vms1-, is given by vt 832 = 4 e-j lkkn poo. \u2002 \u2002 (i)\u2002find the speed of p at o. [1] \u2002 \u2002(ii)\u2002find the value of t for which p is instantaneously at rest.  [2] \u2002 \u2002(iii)\u2002find the acceleration of p when t = 1. [4] question \u200211\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.",
            "16": "16 0606/12/o/n/16 \u00a9 ucles 201611\u2002the variables x and y are such that when lny is plotted against x, a straight line graph is obtained. this  line passes through the points , . , . ln ln x y x y 4 0 20 12 0 08 and = = = = . \u2002(i)\u2002given that y a bx= , find the value of a and of b. [5] \u2002(ii)\u2002find the value of y when x6= . [2] \u2002(iii)\u2002find the value of x when . y 1 1=  . [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."
        },
        "0606_w16_qp_13.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (rw/ar) 116667/2 \u00a9 ucles 2016  [turn overcambridge international examinations cambridge international general certificate of secondary education * 8 7 6 7 8 8 5 4 6 1 * additional mathematics  0606/13 paper 1  october/november 2016  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/13/o/n/16 \u00a9 ucles 2016mathematical formulae 1.\u2002algebra quadratic \u2002equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/13/o/n/16 \u00a9 ucles 2016 [turn\u2002over1\u2002on the axes below, sketch the graph of   cos y x 2 3=    for \u00b0 x0 180 g g . [3] y 3 2 1 0 \u20131 \u20132 \u2013330\u00b0 60\u00b0 90\u00b0 120\u00b0 150\u00b0 180\u00b0x 2\u2002express     mm m mm 24 39 +-     in the form amb+, where a and b are integers to be found.  [3]",
            "4": "4 0606/13/o/n/16 \u00a9 ucles 20163\u2002(i)\u2002given that  x p x 3 1 2 32+ - =- ^ h , show that, for x to be real,  p p 3 9 02h - - . [3] \u2002(ii)\u2002hence find the set of values of p for which x is real, expressing your answer in exact form.  [3]",
            "5": "5 0606/13/o/n/16 \u00a9 ucles 2016 [turn\u2002over4\u2002(i)\u2002find, in ascending powers of x, the first 3 terms in the expansion of  x246 -j lkkn poo. [3] \u2002(ii)\u2002hence find the term independent of x in the expansion of  xx42 3226 + + -4 xj lkkj lkkn poon poo. [3]",
            "6": "6 0606/13/o/n/16 \u00a9 ucles 20165\u2002(i)\u2002given that   log xy25 9=, show that   log l og x y 53 3+ = . [3] \u2002(ii)\u2002hence solve the equations \u2002 \u2002   log xy25 9=, \u2002 \u2002   log l og x y 63 3# =- . [5]",
            "7": "7 0606/13/o/n/16 \u00a9 ucles 2016 [turn\u2002over6\u2002(i)\u2002find lnxx3 11dd 2- ^^ h h. [2] \u2002(ii)\u2002hence show that   lnxxx p x c3 113 11 d22 -= - + ^ h y , where p is a constant to be found, and c is a    constant of integration.  [1] \u2002(iii)\u2002given that  a lnxxx3 112 d22-= y , where a 22, find the value of a. [4]",
            "8": "8 0606/13/o/n/16 \u00a9 ucles 20167 0 1 2 3 4 512345ln y 1 x(1.5, 3.5) (4.0, 1.5) \u2002 the variables x and y are such that when lny is plotted against x1 the straight line graph shown above is  obtained. \u2002(i)\u2002given that   y a exb= ,   find the value of a and of b. [4]",
            "9": "9 0606/13/o/n/16 \u00a9 ucles 2016 [turn\u2002over\u2002(ii)\u2002find the value of y when . x 0 32= . [2] \u2002(iii)\u2002find the value of x when y20= . [2]",
            "10": "10 0606/13/o/n/16 \u00a9 ucles 20168\u2002(a)\u2002(i)\u2002show that     cosec sincosecsec2 i iii-= . [3] \u2002 \u2002(ii)\u2002hence solve     cosec sincosec4i ii -=  for \u00b0 \u00b00 3601 1i . [3]",
            "11": "11 0606/13/o/n/16 \u00a9 ucles 2016 [turn\u2002over\u2002(b)\u2002solve   rtanx 341 + =j lkkn poo  for  r x 0 21 1 , giving your answers in terms of r. [3]",
            "12": "12 0606/13/o/n/16 \u00a9 ucles 20169\u2002(a)\u2002a team of 5 students is to be chosen from a class of 10 boys and 8 girls. find the number of  different teams that may be chosen if \u2002 \u2002 (i)\u2002there are no restrictions,  [1] \u2002 \u2002(ii)\u2002the team must contain at least one boy and one girl.  [4]",
            "13": "13 0606/13/o/n/16 \u00a9 ucles 2016 [turn\u2002over\u2002(b)\u2002a computer password, which must contain 6 characters, is to be chosen from the following  10 characters:  symbols  ? ! *  numbers  3 5 7  letters  w x y z \u2002 \u2002 each character may be used once only in any password. find the number of possible passwords  that may be chosen if \u2002 \u2002 (i)\u2002there are no restrictions,  [1] \u2002 \u2002(ii)\u2002each password must start with a letter and finish with a number,  [2] \u2002 \u2002(iii)\u2002each password must contain at least one symbol.  [3]",
            "14": "14 0606/13/o/n/16 \u00a9 ucles 201610\u2002a curve y xf=^ h  is such that    x x 6 8 f ex2= - l^ h . \u2002(i)\u2002given that the curve passes through the point p ,0 3-^ h , find the equation of the curve.  [5] \u2002 the normal to the curve  y xf=^ h at p meets the line y x2 3= -  at the point q. \u2002(ii)\u2002find the area of the triangle opq , where o is the origin.  [5]",
            "15": "15 0606/13/o/n/16 \u00a9 ucles 201611\u2002a particle moving in a straight line has a velocity of v ms\u20131 such that, t s after leaving a fixed point,   v t t 4 8 32= - +. \u2002(i)\u2002find the acceleration of the particle when t3=. [2] \u2002(ii)\u2002find the values of t for which the particle is momentarily at rest.  [2] \u2002(iii)\u2002find the total distance the particle has travelled when . t1 5= . [5]",
            "16": "16 0606/13/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\u2002page"
        },
        "0606_w16_qp_21.pdf": {
            "1": "this document consists of 16 printed pages. dc (nh/jg) 116665/2 \u00a9 ucles 2016  [turn over * 1 0 7 8 7 6 6 1 6 2 * additional mathematics  0606/21 paper 2  october/november 2016  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of   angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge international examinations cambridge international general certificate of secondary education",
            "2": "2 0606/21/o/n/16 \u00a9 ucles 2016mathematical formulae 1.\u2002algebra quadratic \u2002equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/21/o/n/16 \u00a9 ucles 2016 [turn\u2002over1\u2002solve the equation  4 3x x- = . [3] 2\u2002without\u2002using\u2002a\u2002calculator , find the integers a and b such that  3 1 3 13 3a b ++-= - . [5]",
            "4": "4 0606/21/o/n/16 \u00a9 ucles 20163\u2002solve the equation  22101 lg lgxx-+= c m . [5] 4\u2002the number of bacteria, n, present in a culture can be modelled by the equation   7000 2000 n e0.05t= +-,  where t is measured in days. find \u2002(i)\u2002the number of bacteria when t = 10, [1]",
            "5": "5 0606/21/o/n/16 \u00a9 ucles 2016 [turn\u2002over\u2002(ii)\u2002the value of t when the number of bacteria reaches 7500,   [3] \u2002(iii)\u2002the rate at which the number of bacteria is decreasing after 8 days.  [3]",
            "6": "6 0606/21/o/n/16 \u00a9 ucles 20165\u2002the curve with equation  2 7 2 y x x x3 2= + - +  passes through the point a (\u22122, 16). find \u2002(i)\u2002the equation of the tangent to the curve at the point a, [3] \u2002(ii)\u2002the coordinates of the point where this tangent meets the curve again.  [5]",
            "7": "7 0606/21/o/n/16 \u00a9 ucles 2016 [turn\u2002over6\u2002(i)\u2002prove that  1 1 tancos cotsincos s inxx xxx x+-+= - . [4] \u2002(ii)\u2002hence solve the equation  1 13 4 180\u00b0 180\u00b0tancos cotsinsin c osxx xxx x x for 1 1+-+= - - . [4]",
            "8": "8 0606/21/o/n/16 \u00a9 ucles 20167 14 cmx cm p sr q x cm3 cm \u2002(i)\u2002show that the area, a cm2, of the trapezium pqrs  is given by 7 9x a x2= + - ^ h . [2]",
            "9": "9 0606/21/o/n/16 \u00a9 ucles 2016 [turn\u2002over\u2002(ii)\u2002given that x can vary, find the stationary value of a. [7]",
            "10": "10 0606/21/o/n/16 \u00a9 ucles 20168\u2002the function xf^ h is given by  13 1xxxf33 =+-^ h    for   0 g x g 3. \u2002(i)\u2002show that  1x xkxf3 22 = +l^ ^h h , where k is a constant to be determined.  [3] \u2002(ii)\u2002find   1 xxxd32 2+ ^ hy   and hence evaluate   1 xxxd32 12 2+ ^ hy  . [4]",
            "11": "11 0606/21/o/n/16 \u00a9 ucles 2016 [turn\u2002over\u2002(iii)\u2002find   f  \u22121(x), stating its domain.  [4]",
            "12": "12 0606/21/o/n/16 \u00a9 ucles 20169\u2002the line 4 y k x= - , where k is a positive constant, passes through the point p (0, \u22124) and is a tangent  to the curve  2 8 x y y2 2+ - = at the point t. find \u2002(i)\u2002the value of k, [5]",
            "13": "13 0606/21/o/n/16 \u00a9 ucles 2016 [turn\u2002over\u2002(ii)\u2002the coordinates of  t, [3] \u2002(iii)\u2002the length of tp. [2]",
            "14": "14 0606/21/o/n/16 \u00a9 ucles 201610\u2002the town of cambley is 5  km east and p km north of edwintown so that the position vector of cambley  from edwintown is 10005000 pm c  metres. manjit sets out from edwintown at the same time as raj sets out  from cambley. manjit sets out from edwintown on a bearing of 020\u00b0 at a speed of 2.5  ms\u20131 so that her  position vector relative to edwintown after t seconds is given by 2.5 20\u00b02.5 70\u00b0 coscos ttc m  metres. raj sets out  from cambley on a bearing of 310\u00b0 at 2  ms\u20131. \u2002(i)\u2002find the position vector of raj relative to edwintown after t seconds.  [2]",
            "15": "15 0606/21/o/n/16 \u00a9 ucles 2016 [turn\u2002over\u2002 manjit and raj meet after t seconds. \u2002(ii)\u2002find the value of t and of p. [5] question \u200211\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.",
            "16": "16 0606/21/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.11\u2002mr and mrs coldicott have 5 sons and 4 daughters. all 11 members of the family play tennis. six  members of the family enter a tennis competition where teams consist of 4 males and 2 females. \u2002 find the number of different teams of 4 males and 2 females that could be selected if \u2002(i)\u2002there are no further restrictions,  [2] \u2002(ii)\u2002mr and mrs coldicott must both be in the team,  [2] \u2002(iii)\u2002either mr or mrs coldicott is in the team but not both.  [3]"
        },
        "0606_w16_qp_22.pdf": {
            "1": "this document consists of 16 printed pages. dc (st/jg) 126423 \u00a9 ucles 2016  [turn over * 0 7 2 8 4 4 1 6 9 4 * additional mathematics  0606/22 paper 2  october/november 2016  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of   angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge international examinations cambridge international general certificate of secondary education",
            "2": "2 0606/22/o/n/16 \u00a9 ucles 2016mathematical formulae 1.\u2002algebra quadratic \u2002equation  for the equation ax2 + bx + c = 0, x b b  ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2.\u2002trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/22/o/n/16 \u00a9 ucles 2016 [turn\u2002over1\u2002solve the equation  4 3x x- = . [3] 2\u2002without\u2002using\u2002a\u2002calculator , find the integers a and b such that  3 1 3 13 3a b ++-= - . [5]",
            "4": "4 0606/22/o/n/16 \u00a9 ucles 20163\u2002solve the equation  22101 lg lgxx-+= c m . [5] 4\u2002the number of bacteria, n, present in a culture can be modelled by the equation   7000 2000 n e0.05t= +-,  where t is measured in days. find \u2002(i)\u2002the number of bacteria when t = 10, [1]",
            "5": "5 0606/22/o/n/16 \u00a9 ucles 2016 [turn\u2002over\u2002(ii)\u2002the value of t when the number of bacteria reaches 7500,   [3] \u2002(iii)\u2002the rate at which the number of bacteria is decreasing after 8 days.  [3]",
            "6": "6 0606/22/o/n/16 \u00a9 ucles 20165\u2002the curve with equation  2 7 2 y x x x3 2= + - +  passes through the point a (\u22122, 16). find \u2002(i)\u2002the equation of the tangent to the curve at the point a, [3] \u2002(ii)\u2002the coordinates of the point where this tangent meets the curve again.  [5]",
            "7": "7 0606/22/o/n/16 \u00a9 ucles 2016 [turn\u2002over6\u2002(i)\u2002prove that  1 1 tancos cotsincos s inxx xxx x+-+= - . [4] \u2002(ii)\u2002hence solve the equation  1 13 4 180\u00b0 180\u00b0tancos cotsinsin c osxx xxx x x for 1 1+-+= - - . [4]",
            "8": "8 0606/22/o/n/16 \u00a9 ucles 20167 14 cmx cm p sr q x cm3 cm \u2002(i)\u2002show that the area, a cm2, of the trapezium pqrs  is given by 7 9x a x2= + - ^ h . [2]",
            "9": "9 0606/22/o/n/16 \u00a9 ucles 2016 [turn\u2002over\u2002(ii)\u2002given that x can vary, find the stationary value of a. [7]",
            "10": "10 0606/22/o/n/16 \u00a9 ucles 20168\u2002the function xf^ h is given by  13 1xxxf33 =+-^ h    for   0 g x g 3. \u2002(i)\u2002show that  1x xkxf3 22 = +l^ ^h h , where k is a constant to be determined.  [3] \u2002(ii)\u2002find   1 xxxd32 2+ ^ hy   and hence evaluate   1 xxxd32 12 2+ ^ hy  . [4]",
            "11": "11 0606/22/o/n/16 \u00a9 ucles 2016 [turn\u2002over\u2002(iii)\u2002find   f  \u22121(x), stating its domain.  [4]",
            "12": "12 0606/22/o/n/16 \u00a9 ucles 20169\u2002the line 4 y k x= - , where k is a positive constant, passes through the point p (0, \u22124) and is a tangent  to the curve  2 8 x y y2 2+ - = at the point t. find \u2002(i)\u2002the value of k, [5]",
            "13": "13 0606/22/o/n/16 \u00a9 ucles 2016 [turn\u2002over\u2002(ii)\u2002the coordinates of  t, [3] \u2002(iii)\u2002the length of tp. [2]",
            "14": "14 0606/22/o/n/16 \u00a9 ucles 201610\u2002the town of cambley is 5  km east and p km north of edwintown so that the position vector of cambley  from edwintown is 10005000 pm c  metres. manjit sets out from edwintown at the same time as raj sets out  from cambley. manjit sets out from edwintown on a bearing of 020\u00b0 at a speed of 2.5  ms\u20131 so that her  position vector relative to edwintown after t seconds is given by 2.5 20\u00b02.5 70\u00b0 coscos ttc m  metres. raj sets out  from cambley on a bearing of 310\u00b0 at 2  ms\u20131. \u2002(i)\u2002find the position vector of raj relative to edwintown after t seconds.  [2]",
            "15": "15 0606/22/o/n/16 \u00a9 ucles 2016 [turn\u2002over\u2002 manjit and raj meet after t seconds. \u2002(ii)\u2002find the value of t and of p. [5] question \u200211\u2002is\u2002printed\u2002on\u2002the\u2002next\u2002page.",
            "16": "16 0606/22/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.11\u2002mr and mrs coldicott have 5 sons and 4 daughters. all 11 members of the family play tennis. six  members of the family enter a tennis competition where teams consist of 4 males and 2 females. \u2002 find the number of different teams of 4 males and 2 females that could be selected if \u2002(i)\u2002there are no further restrictions,  [2] \u2002(ii)\u2002mr and mrs coldicott must both be in the team,  [2] \u2002(iii)\u2002either mr or mrs coldicott is in the team but not both.  [3]"
        },
        "0606_w16_qp_23.pdf": {
            "1": "this document consists of 16 printed pages. dc (lk/sg) 116670/2 \u00a9 ucles 2016  [turn overcambridge international examinations cambridge international general certificate of secondary education * 3 6 6 6 4 5 3 2 4 9 * additional mathematics  0606/23 paper 2  october/november 2016  2 hours candidates answer on the question paper. additional materials:  electronic 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. y ou may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles in  degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. y ou are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/23/o/n/16 \u00a9 ucles 2016mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, xb b ac a=\u2212 \u221224 2 binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/23/o/n/16 \u00a9 ucles 2016 [turn over1 without using a calculator , show that  k5 35 3 32++= -   where k is an integer to be found.  [3] 2 solve the equation  e e 6x x3= . [3]",
            "4": "4 0606/23/o/n/16 \u00a9 ucles 20163 (i) show that dd cossin cos x xx x 1 11 +=+c m  . [4]  (ii) y x3 2 1 01 2y =1 1 + cos  x   the diagram shows part of the graph of cosyx 11=+. use the result from part (i) to find the area   enclosed by the graph and the lines , x x 0 2= =  and y0=. [2]",
            "5": "5 0606/23/o/n/16 \u00a9 ucles 2016 [turn over4 the cubic given by ( )px x ax bx 243 2= + + -  is divisible by x2-. when ( )px is divided by x1-  the remainder is 20-.  (i) form a pair of equations in a and b and solve them to find the value of a and of b. [4]  (ii) factorise ( )px completely and hence solve ( )px 0=. [4]",
            "6": "6 0606/23/o/n/16 \u00a9 ucles 20165 in this question all lengths are in centimetres. a b c60\u00b0  in the  triangle abc shown above, ac 3 1= + , bc 3 1= -  and angle \u00b0 acb 60= .  (i) without using a calculator , show that the length of ab 6= . [3]  (ii) show that angle \u00b0 cab 15= . [2]  (iii) without using a calculator , find the area of triangle abc.  [2]",
            "7": "7 0606/23/o/n/16 \u00a9 ucles 2016 [turn over6 a curve has equation tan y x 7= + .    find  (i) the equation of the tangent to the curve at the point where x4r= , [4]  (ii)  the values of x between 0 and r radians for which dd xyy=. [4]",
            "8": "8 0606/23/o/n/16 \u00a9 ucles 20167 in this question all lengths are in metres. h 0.5h + 2 r  a conical tent is to be made with height h , base radius  r and slant height 0.5 h + 2, as shown in the   diagram.   (i) show that . r h h 2 4 0 752 2= + - . [2]",
            "9": "9 0606/23/o/n/16 \u00a9 ucles 2016 [turn over the volume of the tent,  v, is given by r h31 2r .  (ii) given that h can vary find, correct to 2 decimal places, the value of h which gives a stationary  value of v. [5]  (iii) determine the nature of this stationary value.  [2]",
            "10": "10 0606/23/o/n/16 \u00a9 ucles 20168 10 cm6 cma ct b o  the points  a, b and c lie on a circle centre o, radius 6  cm. the tangents to the circle at a and c meet  at the point t. the length of ot is 10  cm. find  (i) the angle toa in radians,  [2]",
            "11": "11 0606/23/o/n/16 \u00a9 ucles 2016 [turn over (ii) the area of the region tabct,  [6]  (iii) the perimeter of the region tabct.  [2]",
            "12": "12 0606/23/o/n/16 \u00a9 ucles 20169 in this question i is a unit vector due east and j is a unit vector due north. units of length and velocity  are metres and metres per second respectively.  the initial position vectors of particles a and b, relative to a fixed point o, are i +5j and qi \u2013 15 j  respectively. a and b start moving at the same time. a moves with velocity pi \u2013 3j and b moves with  velocity 3 i \u2013 j.  (i) given that a travels with a speed of 5  ms\u20131, find the value of the positive constant p. [1]  (ii) find the direction of motion of b as a bearing correct to the nearest degree.  [2]  (iii) state the position vector of a after t seconds .  [1]  (iv) state the position vector of b after t seconds.  [1]",
            "13": "13 0606/23/o/n/16 \u00a9 ucles 2016 [turn over (v) find the time taken until a and b meet.  [2]  (vi) find the position vector of the point where a and b meet.  [1]  (vii) find the value of the constant q. [1]",
            "14": "14 0606/23/o/n/16 \u00a9 ucles 201610 the functions f and g are defined for x12 by   ( )f lnx x 2= + ,   ( )g ex 2 3x= +  .  (i) find ( )fgx. [1]  (ii) find ( )ffx. [1]  (iii) find ( )gx1-. [2]",
            "15": "15 0606/23/o/n/16 \u00a9 ucles 2016 [turn over (iv) solve the equation ( )fx 4=. [1]  (v) solve the equation ( )gfx 20= . [4] question 11 is printed on the next page.",
            "16": "16 0606/23/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.11 it is given that apq2 3=j lkkn poo and that a a i 5 22- = , where i is the identity matrix.  (i) find a relationship connecting the constants p and q. [4]  (ii) given that p and q are positive and that det a p3=- , find the value of p and of q. [4]"
        }
    },
    "2017": {
        "0606_m17_qp_12.pdf": {
            "1": "this document consists of 14 printed pages and 2 blank pages. dc (lk/sg) 129474/2 \u00a9 ucles 2017  [turn over *5331723388* additional mathematics  0606/12 paper 1  february/march 2017  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge international examinations cambridge international general certificate of secondary education",
            "2": "2 0606/12/f/m/17 \u00a9 ucles 2017 mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/12/f/m/17 \u00a9 ucles 2017 [turn over 1 (a) it is given that \ue025 = {: ,} xx x 03 5 r 11 !  and sets a and b are such that a = {multiples of 5} and b = {multiples of 7}.   (i) find   ()nab+. [1]   (ii) find   ()nab,. [1]  (b) it is given that sets x, y and z are such that xy y +=,   xz z +=   and yz+ q=.   on the venn diagram below, illustrate sets x, y and z. [3] /h5105",
            "4": "4 0606/12/f/m/17 \u00a9 ucles 2017 2 (i) on the axes below sketch, for \u00b0\u00b0x 0 360 gg , the graph of cos yx13 2 =+ . [3] 360\u00b0 270\u00b0 180\u00b0 xy o90\u00b0  (ii) write down the coordinates of the point where this graph first has a minimum value.  [1] 3 the first three terms in the expansion of ax 45 +j lkkn poo are bx cx 322++ . find the value of each of the  constants a, b and c. [5]",
            "5": "5 0606/12/f/m/17 \u00a9 ucles 2017 [turn over 4 (a) it is given that a1 23 4=-j lkkn poo.   (i) find a1-. [2]   (ii) using your answer to part (i), find the matrix m such that am = 1 45 2--j lkkn poo. [3]  (b) x is a 21 3- -j lkkn poo   and y is a2 41 3j lkkn poo, where a is a constant.   given that   det x = 4 det y,   find the value of a. [2]",
            "6": "6 0606/12/f/m/17 \u00a9 ucles 2017 5 (i) show that    cosecs in cotcos ii ii -= . [3]  (ii) hence solve the equation    cosecs in cos31ii i -= ,    for 0gi 2gr radians.  [4]",
            "7": "7 0606/12/f/m/17 \u00a9 ucles 2017 [turn over 6 (a) the letters of the word thursday are arranged in a straight line. find the number of different  arrangements of these letters if   (i) there are no restrictions,  [1]   (ii) the arrangement must start with the letter t and end with the letter y ,  [1]   (iii) the second letter in the arrangement must be y .  [1]  (b) 7 children have to be divided into two groups, one of 4 children and the other of 3 children. given  that there are 3 girls and 4 boys, find the number of different ways this can be done if   (i) there are no restrictions,  [1]   (ii) all the boys are in one group,  [1]   (iii) one boy and one girl are twins and must be in the same group.  [3]",
            "8": "8 0606/12/f/m/17 \u00a9 ucles 2017 7 (a) a vector v has a magnitude of 102 units and has the same direction as 8 15-j lkkn poo. find v in the form    a bj lkkn poo, where a and b are integers.  [2]  (b) vectors c4 3=j lkkn poo  and dpq pq5=- +j lkkn poo  are such that    cdp2272 +=j lkkn poo. find the possible values of the     constants p and q. [6]",
            "9": "9 0606/12/f/m/17 \u00a9 ucles 2017 [turn over 8 a curve  is such that ddsinxyx 4222 = . the curve has a gradient of 5 at the point where x2r=.  (i) find an expression for the gradient of the curve at the point (,)xy. [4]  the curve passes through the point p12rc,21-m.  (ii) find the equation of the curve.  [4]  (iii) find the equation of the normal to the curve at the point p, giving your answer in the form  ym xc=+ , where m and c are constants correct to 3 decimal places.  [3]",
            "10": "10 0606/12/f/m/17 \u00a9 ucles 2017 9 i rada bc o  the diagram shows a circle, centre o, radius 10  cm. points a, b and c lie on the circumference of the  circle such that ac bc= . the area of the minor sector aob  is cm202r and angle aob  is i radians.  (i) find the value of i in terms of r. [2]  (ii) find the perimeter of the shaded region.  [4]",
            "11": "11 0606/12/f/m/17 \u00a9 ucles 2017 [turn over  (iii) find the area of the shaded region.  [3]",
            "12": "12 0606/12/f/m/17 \u00a9 ucles 2017 10  y o xaby = (2x \u2013 5)3 2 y33=  the diagram shows part of the curve ()yx 2523=-  and the line y33= . the curve meets the  x-axis at the point a and the line y33=  at the point b. find the area of the shaded region enclosed     by the line ab and the curve, giving your answer in the form p 203, where p is an integer. you must  show all your working.  [8]",
            "13": "13 0606/12/f/m/17 \u00a9 ucles 2017 [turn over question 11 is printed on the next page.",
            "14": "14 0606/12/f/m/17 \u00a9 ucles 2017 11 it is given that e yabx= , where a and b are constants.  when lny is plotted against x a straight line  graph is obtained which passes through the points (1.0, 0.7) and (2.5, 3.7).  (i) find the value of a and of b. [6]  (ii) find the value of y when x2=. [2]",
            "15": "15 0606/12/f/m/17 \u00a9 ucles 2017 blank page",
            "16": "16 0606/12/f/m/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"
        },
        "0606_m17_qp_22.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (lk/sg) 129475/3 \u00a9 ucles 2017  [turn over *4214767259* additional mathematics  0606/22 paper 2  february/march 2017  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge international examinations cambridge international general certificate of secondary education",
            "2": "2 0606/22/f/m/17 \u00a9 ucles 2017 mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/22/f/m/17 \u00a9 ucles 2017 [turn over 1 solve the equation x 53 10 -= . [3] 2 the value, v dollars, of a car aged t years is given by e v12000.t02=-.  (i) write down the value of the car when it was new.  [1]  (ii) find the time it takes for the value to decrease to 32 of the value when it was new.  [2]",
            "4": "4 0606/22/f/m/17 \u00a9 ucles 2017 3 the polynomial ()px is   xxx x 23 84432-- +- .  (i) show that ()px can be written as    () () xx xx 14 432-- -+ . [1]  (ii) hence write ()px as a product of its linear factors, showing all your working.  [4]  4 find the set of values of k for which the line    yx k 3=+    and the curve    yx x 23 42=- +   do not  intersect.  [4]",
            "5": "5 0606/22/f/m/17 \u00a9 ucles 2017 [turn over 5 x 20 3 5+  the diagram shows a trapezium made from a rectangle and a right-angled triangle. the dimensions, in  centimetres, of the rectangle and triangle are shown. the area, in square centimetres, of the trapezium  is 13 55+ . without using a calculator , find the value of x in the form pq 5+ , where p and q are  integers.  [5]",
            "6": "6 0606/22/f/m/17 \u00a9 ucles 2017 6 (a) (i) express xx893-- 36`` jj    in the form axb, where a and b are constants to be found.  [2]   (ii) hence solve the equation xx8 625093-= --6 3`` jj . [2]  ",
            "7": "7 0606/22/f/m/17 \u00a9 ucles 2017 [turn over  (b) it is given that () () logl og ya xx24 31aa=+ -- ,   where a is a positive integer.   (i) explain why x must be greater than 0.75.  [1]   (ii) show that y can be written as ()log xx x 16 24 9a32-+ . [3]   (iii) find the value of x for which ()log yx 9a= . [2]",
            "8": "8 0606/22/f/m/17 \u00a9 ucles 2017 7 (a) calculate the magnitude and bearing of the resultant velocity of ms101- on a bearing of 240 \u00b0 and  ms51- due south.  [5]  (b) a car travelling east along a road at a velocity of kmh 381- passes a lorry travelling west on the  same road at a velocity of kmh 561-. write down the velocity of the lorry relative to the car.  [2]",
            "9": "9 0606/22/f/m/17 \u00a9 ucles 2017 [turn over 8 the points a(3, 7) and b(8, 4) lie on the line l. the line through the point c(6, \u22124) with gradient 61  meets the line l at the point d. calculate  (i) the coordinates of d, [6]  (ii) the equation of the line through d perpendicular to the line yx32 10 -= . [2]",
            "10": "10 0606/22/f/m/17 \u00a9 ucles 2017 9 (a) find ed xx21+y . [2]  (b) (i) given that lnyxx= , find dd xy. [3]   (ii) hence find () ln lndx xxx11 1 22-+j lkkn poo y . [3]",
            "11": "11 0606/22/f/m/17 \u00a9 ucles 2017 [turn over 10 solve, for \u00b0\u00b0x 0 360 gg , the equation  (i) (\u00b0 ) cotx21 043-= , [4]  (ii) sinc os cos xx x22-= . [5]",
            "12": "12 0606/22/f/m/17 \u00a9 ucles 2017 11 the functions f and g are defined by  ()ff or xxxx222 h =-, ()gf or xxx2102 h =-.  (i) state the range of g.  [1]  (ii) explain why fg(1) does not exist.  [2]  (iii) show that ()gfxa xbxc 2 2=+ + , where a, b and c are constants to be found.  [3]",
            "13": "13 0606/22/f/m/17 \u00a9 ucles 2017 [turn over  (iv) state the domain of gf.  [1]  (v) show that ()fxxx 28 12 =++ -. [4]",
            "14": "14 0606/22/f/m/17 \u00a9 ucles 2017 12 the diagram shows a shape made by cutting an equilateral triangle out of a rectangle of width x cm.  x cm  the perimeter of the shape is 20  cm.   (i) show that the area, a cm2, of the shape is given by      ax x 10463 2=-+j lkkn poo. [3]",
            "15": "15 0606/22/f/m/17 \u00a9 ucles 2017  (ii) given that x can vary, find the value of x which produces the maximum area and calculate this  maximum area. give your answers to 2 significant figures.  [4]",
            "16": "16 0606/22/f/m/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"
        },
        "0606_s17_qp_11.pdf": {
            "1": "this document consists of 12 printed pages. dc (rw/fd) 129466/3 \u00a9 ucles 2017  [turn over *9272080016* additional mathematics  0606/11 paper 1  may/june 2017  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge international examinations cambridge international general certificate of secondary education",
            "2": "2 0606/11/m/j/17 \u00a9 ucles 2017 mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, xabb ac 242!=-- binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/11/m/j/17 \u00a9 ucles 2017 [turn over 1 the line yk x5 =- , where k is a positive constant, is a tangent to the curve yx x42=+  at the point a.  (i) find the exact value of k. [3]  (ii) find the gradient of the normal to the curve at the point a, giving your answer in the form ab 5+ ,   where a and b are constants.  [2]",
            "4": "4 0606/11/m/j/17 \u00a9 ucles 2017 2 it is given that xx ax bx 48 p32=+ +- ^h . when xp^h is divided by   x3-   the remainder is 6.  given that   10p= l^h , find the value of a and of b. [5] 3 (a) simplify xy xy8103 6'- 3, giving your answer in the form xyab, where a and b are integers.  [2]  (b) (i) show that tt42 5221 23 -+ - ^^ hh  can be written in the form tq tr 2p-+^^ hh , where p, q and r  are constants to be found.  [3]   (ii) hence solve the equation   tt42 52 021 23 -+ -= ^^ hh . [1]",
            "5": "5 0606/11/m/j/17 \u00a9 ucles 2017 [turn over 4 (a) it is given that   x 35 fex4=+-^h    for xr!.   (i) state the range of f.  [1]   (ii) find   f1-   and state its domain.  [4]  (b) it is given that   xx 5 g2=+ ^h    and   ln xxh= ^h    for x02. solve x 2 hg = ^h . [3]",
            "6": "6 0606/11/m/j/17 \u00a9 ucles 2017 5 (a) oa m cb ba c   the diagram shows a figure oabc , where a oa=, b ob= and c oc=. the lines ac and ob  intersect at the point m where m is the midpoint of the line ac.   (i) find, in terms of a and c, the vector om. [2]   (ii) given that ::om mb 23= , find b in terms of a and c. [2]",
            "7": "7 0606/11/m/j/17 \u00a9 ucles 2017 [turn over  (b) vectors i and j are unit vectors parallel to the x-axis and y-axis respectively.   the vector p has a magnitude of 39  units and has the same direction as   ij10 24 -+ .   (i) find p in terms of i and j. [2]   (ii) find the vector q such that pq2+ is parallel to the positive y-axis and has a magnitude of  12 units.  [3]   (iii) hence show that q k5= , where k is an integer to be found.  [2]",
            "8": "8 0606/11/m/j/17 \u00a9 ucles 2017 6  oa d b c8 cm 12 cm  the diagram shows a circle, centre o, radius 12  cm. the points a and b lie on the circumference of the  circle and form a rectangle with the points c and d. the length of ad is 8 cm and the area of the minor  sector aob  is 150  cm2.  (i) show that angle aob  is 2.08 radians, correct to 2  decimal places.  [2]  (ii) find the area of the shaded region adcb . [6]  (iii) find the perimeter of the shaded region adcb . [3]",
            "9": "9 0606/11/m/j/17 \u00a9 ucles 2017 [turn over 7 show that the curve y x382 35 =+^h  has only one stationary point. find the coordinates of this stationary  point and determine its nature.  [8]",
            "10": "10 0606/11/m/j/17 \u00a9 ucles 2017 8 (i) on the axes below sketch the graphs of   yx 25=-    and   yx x 98 01 62=- . [5] \u20131 1 0 \u201310\u20135510y 2 3 4 5 6 x  (ii) solve x25 4 -= . [3]  (iii) hence show that the graphs of    yx 25=-     and    yx x 98 01 62=-     intersect at the points  where y4=. [1]  (iv) hence find the values of x for which xx x 92 58 01 62g-- . [2]",
            "11": "11 0606/11/m/j/17 \u00a9 ucles 2017 [turn over 9 (i) show that tans ecxx54343122+= +j lkkj lkkn poon poo . [1]  (ii) given that ddtans ecxxx 3 31 32=j lkkj lkk cn poon poo m , find   secxx3d2j lkkn poo y . [1]  (iii) oy xy = 5 + 4 tan2x 3j lkkn poo 2   the diagram shows part of the curve tan yx5432=+j lkkn poo. using the results from parts (i) and (ii),    find the exact area of the shaded region enclosed by the curve, the x-axis and the lines rx2= and  rx=. [5] question 10 is printed on the next page.",
            "12": "12 0606/11/m/j/17 \u00a9 ucles 2017 10 (a) given that yx41ex 23 =+, find xy dd. [3]  (b) variables x, y and t are such that   rrcoss in yx x 43233=+ ++j lkkj lkkn poon poo   and   ty10dd= .   (i) find the value of  xy dd when rx2=. [3]   (ii) find the value of  tx dd when rx2=. [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."
        },
        "0606_s17_qp_12.pdf": {
            "1": "this document consists of 12 printed pages. dc (lk/cgw) 129467/2 \u00a9 ucles 2017  [turn over *0147311657* additional mathematics  0606/12 paper 1  may/june 2017  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge international examinations cambridge international general certificate of secondary education",
            "2": "2 0606/12/m/j/17 \u00a9 ucles 2017 mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/12/m/j/17 \u00a9 ucles 2017 [turn over 1 on each of the venn diagrams below, shade the region which represents the given set. a b c (a + b) , c/h5105 a b c (a + b ) + c/h5105a b c (a , b) + c/h5105  [3] 2 it is given that ()yxx 154221 =++. showing all your working, find the exact value of dd xy when x3=.  [5]",
            "4": "4 0606/12/m/j/17 \u00a9 ucles 2017 3 vectors i and j are unit vectors parallel to the x-axis and y-axis respectively.  (a) the vector v has a magnitude of 35  units and has the same direction as ij2-. find v giving  your answer in the form ijab+, where a and b are integers.  [2]  (b) the velocity vector w makes an angle of 30\u00b0 with the positive x-axis and is such that w 2=.  find w giving your answer in the form ijcd+, where c and d are integers.  [2] 4 the first 3 terms in the expansion of x36n -j lkkn poo are ax bx 812++ . find the value of each of the constants  n, a and b. [5]",
            "5": "5 0606/12/m/j/17 \u00a9 ucles 2017 [turn over 5 a particle p moves in a straight line, such that its displacement, x m, from a fixed point o, t s after  passing o, is given by ()cos xt43 4 =- .  (i) find the velocity of p at time t. [1]  (ii) hence write down the maximum speed of p. [1]  (iii) find the smallest value of t for which the acceleration of p is zero.  [3]  (iv) for the value of t found in part (iii), find the distance of p from o. [1]",
            "6": "6 0606/12/m/j/17 \u00a9 ucles 2017 6 (i) show that cott ancoseccosiiii+= . [4]  it is given that cott ancosecd222 43 a 0 iiii+= y , where a 0411r.  (ii) using your answer to part (i) find the value of a, giving your answer in terms of r. [4]",
            "7": "7 0606/12/m/j/17 \u00a9 ucles 2017 [turn over 7 it is given that () ya 10bx= , where a and b are constants. the straight line graph obtained when lgy is  plotted against x passes through the points (.,.) 0522 and (.,.) 1037.  (i) find the value of a and of b. [5]  using your values of a and b, find  (ii) the value of y when . x06= , [2]  (iii) the value of x when y600= . [2]",
            "8": "8 0606/12/m/j/17 \u00a9 ucles 2017 8 (a) a 5-digit number is to be formed from the seven digits 1, 2, 3, 5, 6, 8 and 9. each digit can only be  used once in any 5-digit number. find the number of different 5-digit numbers that can be formed if   (i) there are no restrictions,  [1]   (ii) the number is divisible by 5,  [1]   (iii) the number is greater than 60  000, [1]   (iv) the number is greater than 60  000 and even.  [3]  (b) ranjit has 25 friends of whom 15 are boys and 10 are girls. ranjit wishes to hold a birthday party  but can only invite 7 friends. find the number of different ways these 7 friends can be selected if    (i) there are no restrictions,  [1]   (ii) only 2 of the 7 friends are boys,  [1]   (iii) the 25 friends include a boy and his sister who cannot be separated.  [3]",
            "9": "9 0606/12/m/j/17 \u00a9 ucles 2017 [turn over 9 (a) given that a3 1 41 2 5=-j lk kkn po oo, b1 32 0=-j lkkn poo and ca b= ,   (i) state the order of a, [1]   (ii) find c. [3]  (b) the matrix x5 412 7=- -j lkkn poo.   (i) find x1-. [2]   (ii) using x1-, find the coordinates of the point of intersection of the lines     , .yx yx12 52 6 74 52=- =- [4]",
            "10": "10 0606/12/m/j/17 \u00a9 ucles 2017 10 4 cma do cb8 cm  the diagram shows a circle, centre o, radius 8  cm. the points a, b, c and d lie on the circumference of  the circle such that ab is parallel to dc. the length of the arc ad is 4 cm and the length of the chord ab  is 15  cm.  (i) find, in radians, angle aod . [1]  (ii) hence show that angle . doc 143=  radians, correct to 2 decimal places.  [3]",
            "11": "11 0606/12/m/j/17 \u00a9 ucles 2017 [turn over  (iii) find the perimeter of the shaded region.  [3]  (iv) find the area of the shaded region.  [4] question 11 is printed on the next page.",
            "12": "12 0606/12/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 the curve ()fyx=  passes through the point 7,21 2j lkkn poo and is such that ()fexx21=-l .  (i) find the equation of the curve.  [4]  (ii) find the value of x for which f  \u02ba(x) = 4, giving your answer in the form ln ab 2 + , where a and b  are constants.  [4]"
        },
        "0606_s17_qp_13.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (kn/cgw) 129468/2 \u00a9 ucles 2017  [turn over *8262841617* additional mathematics  0606/13 paper 1  may/june 2017  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in  degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge international examinations cambridge international general certificate of secondary education",
            "2": "2 0606/13/m/j/17 \u00a9 ucles 2017 mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, xabb ac 242!=-- binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/13/m/j/17 \u00a9 ucles 2017 [turn over 1 (a) on the venn diagram below, shade the region which represents ab cb +, + ll ^^ hh . [1] a b c/h5105  (b) complete the venn diagram below to show the sets y and z such that zx y 11 . [1] x/h5105 2 given that  cos yx34 9 =+ , write down  (i) the amplitude of  y, [1]  (ii) the period of  y. [1]",
            "4": "4 0606/13/m/j/17 \u00a9 ucles 2017 3 (i) on the axes below, sketch the graph of   sin yx32=-    for  0 360 ggi cc . [3] 6y x4 2 0 90\u00b0 180\u00b0 270\u00b0 360\u00b0 \u20132 \u20134 \u20136  (ii) given that    sinxk 03 2 gg -     for x 0 360 ggcc , write down the value of k. [1]",
            "5": "5 0606/13/m/j/17 \u00a9 ucles 2017 [turn over 4 in this question, all dimensions are in centimetres. a b c3 + 2\u221a5 m 4 + 6\u221a5  the diagram shows an isosceles triangle abc , where  ab = ac. the point m is the mid-point of bc.   given that  am 32 5 =+   and  bc 46 5 =+ ,   find, without using a calculator ,  (i) the area of triangle abc , [2]  (ii)  tan abc , giving your answer in the form  cab 5+   where a, b and c are positive integers.  [3]",
            "6": "6 0606/13/m/j/17 \u00a9 ucles 2017 5 the normal to the curve yx 49=+ , at the point where x4=, meets the x- and y-axes at the points a  and b. find the coordinates of the mid-point of the line ab. [7]",
            "7": "7 0606/13/m/j/17 \u00a9 ucles 2017 [turn over 6 (a) given that   a = 3 21 4j lkkn poo,   b = 5 2 11 4 0-j lk kkn po oo  and  c = 5 32 1-j lkkn poo, find   (i) a + 3c, [2]   (ii) ba. [2]  (b) (i) given that  x = 1 43 2- -j lkkn poo, find x\u20131. [2]   (ii) hence find y, such that   xy = 5 1510 20-j lkkn poo. [3]",
            "8": "8 0606/13/m/j/17 \u00a9 ucles 2017 7 (a) show that   coss ectans intansin22 iiiiii++= . [4]",
            "9": "9 0606/13/m/j/17 \u00a9 ucles 2017 [turn over  (b) given that sin x3z =  and cosy3 z=  , find the numerical value of yx y 922 2- . [3]",
            "10": "10 0606/13/m/j/17 \u00a9 ucles 2017 8 it is given that ()xx ax xb 24 p32=+ ++ , where a and b are constants.  it is given also that  x21+  is a  factor of ()xp and that when ()xp is divided by x1- there is a remainder of 12-.  (i) find the value of a and of b. [5]  (ii) using your values of a and b, write ()xp in the form () () xx21 q+ , where ()xq is a quadratic  expression.  [2]  (iii) hence find the exact solutions of the equation ()x 0 p=. [2]",
            "11": "11 0606/13/m/j/17 \u00a9 ucles 2017 [turn over 9 it is given that x 56 15e edxx kk55-=- -^hy .  (i) show that 3 eekk55-=-. [5]  (ii) hence, using the substitution   yek5= ,   or otherwise, find the value of k. [3]",
            "12": "12 0606/13/m/j/17 \u00a9 ucles 2017 10 it is given that () ()ln yx x 10 25 1 =+ +.  (i) find xy dd. [4]  (ii)  hence show that ()()() ln ln xxax bxx c 51551 d+++- + = y , where a and b are integers and c is a     constant of integration.  [3]",
            "13": "13 0606/13/m/j/17 \u00a9 ucles 2017 [turn over  (iii) hence find ()lnxx51 d 051 + y , giving your answer in the form lndf 5+, where d and f are integers.    [2]",
            "14": "14 0606/13/m/j/17 \u00a9 ucles 2017 11 a curve has equation yx xx 6=- .  (i) find the coordinates of the stationary point of the curve.  [4]  (ii) determine the nature of this stationary point.  [2]  (iii) find the approximate change in y when x increases from 4 to h4+, where h is small.  [3]",
            "15": "15 0606/13/m/j/17 \u00a9 ucles 2017 12 a particle moves in a straight line, such that its velocity, vms1-, t s after passing a fixed point o, is  given by sin vt t32 26=+ + .  (i) find the acceleration of the particle at time t. [2]  (ii) hence find the smallest value of t for which the acceleration of the particle is zero.  [2]  (iii) find the displacement, x m from o, of the particle at time t. [5]",
            "16": "16 0606/13/m/j/17 \u00a9 ucles 201716 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"
        },
        "0606_s17_qp_21.pdf": {
            "1": "this document consists of 12 printed pages. dc (kn/fd) 129463/3 \u00a9 ucles 2017  [turn overcambridge international examinations cambridge international general certificate of secondary education *6595404132* additional mathematics  0606/21 paper 2  may/june 2017  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of   angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/21/m/j/17 \u00a9 ucles 2017 mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/21/m/j/17 \u00a9 ucles 2017 [turn over 1  find the equation of the curve which passes through the point (2, 17) and for which xyx41dd3=+ . [4] 2 do not use a calculator in this question.  (a) show that 24 2715930# +  can be written in the form a2, where a is an integer.  [3]  (b) solve the equation xx 31 23 += - ^^ hh , giving your answer in the form bc 3+ , where b and c  are integers.  [3]",
            "4": "4 0606/21/m/j/17 \u00a9 ucles 2017 3 the variables  x and y are such that ()lnyx 12=+ .  (i) find an expression for xy dd. [2]  (ii) hence, find the approximate change in y when x increases from 3 to h3+, where h is small.  [2] 4 (a) given that cos yx71 03 =- , where the angle x is measured in degrees, state   (i) the period of y, [1]   (ii) the amplitude of y. [1]  (b) 0 0\u00b0 45\u00b0 90\u00b0 135\u00b0 180\u00b0 225\u00b0 270\u00b0 315\u00b0 360\u00b024681012y x   find the equation of the curve shown, in the form () ya bx c g=+ , where ()xg is a trigonometric  function and a, b and c are integers to be found.  [4]",
            "5": "5 0606/21/m/j/17 \u00a9 ucles 2017 [turn over 5 (i) given that a is a constant, expand () ax24+ , in ascending powers of x, simplifying each term of  your expansion.  [2]  given also that the coefficient of x2 is equal to the coefficient of x3,   (ii) show that a3=,  [1]  (iii) use your expansion to show that the value of 1.974 is 15.1 to 1 decimal place.  [2]",
            "6": "6 0606/21/m/j/17 \u00a9 ucles 2017 6 four cinemas, p, q, r and s each sell adult, student and child tickets. the number of tickets sold by  each cinema on one weekday were     p: 90 adult, 10 student, 30 child      q: 45 student      r: 25 adult, 15 child      s: 10 adult, 100 child.  (i) given that 1111 l=^h , construct a matrix, m, of the number of tickets sold, such that the  matrix product lm can be found.  [1]  (ii) find the matrix product lm. [1]  (iii) state what information is represented by the matrix product lm. [1]  an adult ticket costs $5, a student ticket costs $4 and a child ticket costs $3.  (iv) construct a matrix, n, of the ticket costs, such that the matrix product lmn  can be found and  state what information is represented by the matrix product lmn . [2]",
            "7": "7 0606/21/m/j/17 \u00a9 ucles 2017 [turn over 7 (a) on each of the venn diagrams below shade the region which represents the given set. \u2229 \u2229\u2229 /h5105 /h5105x xpp' qq rr y' y    [2]  (b) in a group of students, each student studies at most two of art, music and design. no student  studies both music and design.     a denotes the set of students who study art,      m denotes the set of students who study music,      d denotes the set of students who study design.    (i) write the following using set notation.       no student studies both music and design.  [1]   there are 100 students in the group. 39 students study art, 45 study music and 36 study design.   12 students study both art and music. 25 students study both art and design.    (ii) complete the venn diagram below to represent this information and hence find the number of  students in the group who do not study any of these subjects.    /h5105a     [3]",
            "8": "8 0606/21/m/j/17 \u00a9 ucles 2017 8  (a) a football club has 30 players. in how many different ways can a captain and a vice-captain be  selected at random from these players?  [1]  (b) a team of 11 teachers is to be chosen from 2 mathematics teachers, 5 computing teachers and 9  science teachers. find the number of different teams that can be chosen if   (i) the team must have exactly 1 mathematics teacher,  [2]   (ii) the team must have exactly 1 mathematics teacher and at least 4 computing teachers.  [4]",
            "9": "9 0606/21/m/j/17 \u00a9 ucles 2017 [turn over 9  the curve xx yy y 34 3022+- +- = and the line () yx21=-  intersect at the points a and b.  (i) find the coordinates of a and of b. [5]  (ii) find the equation of the perpendicular bisector of the line ab, giving your answer in the form  ax by c += , where a, b and c are integers.  [4]",
            "10": "10 0606/21/m/j/17 \u00a9 ucles 2017 10 the table shows values of the variables t and p. t 1 1.5 2 2.5 p 4.39 8.33 15.8 30.0  (i) draw the graph of lnp against t on the grid below.  [2] 0.5123ln p 0 1 1.5 2 2.5 t  (ii) use the graph to estimate the value of p when . t22= . [2]  (iii) find the gradient of the graph and state the coordinates of the point where the graph meets the  vertical axis.  [2]  (iv) using your answers to part (iii), show that pa bt= , where a and b are constants to be found.  [3]  (v)  given that your equation in part (iv) is valid for values of t up to 10, find the smallest value of t,  correct to 1 decimal place, for which p is at least 1000.  [2]",
            "11": "11 0606/21/m/j/17 \u00a9 ucles 2017 [turn over 11 (i) prove that ()sinc ot tans ec xx xx+= . [4]  (ii) hence solve the equation ()sinc ot tan xx x 2 +=  for x 0 360 ggcc . [4] question 12 is printed on the next page.",
            "12": "12 0606/21/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.12  a particle moves in a straight line so that, t seconds after passing a fixed point o, its displacement, s m,  from o is given by     cos st t 13 5 =+ - .  (i) find the distance between the particle\u2019s first two positions of instantaneous rest.  [7]  (ii) find the acceleration when t = \u03c0. [2]"
        },
        "0606_s17_qp_22.pdf": {
            "1": "this document consists of 12 printed pages. dc (lk/fd) 129464/2 \u00a9 ucles 2017  [turn over *8715888044* additional mathematics  0606/22 paper 2  may/june 2017  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge international examinations cambridge international general certificate of secondary education",
            "2": "2 0606/22/m/j/17 \u00a9 ucles 2017 mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/22/m/j/17 \u00a9 ucles 2017 [turn over 1 solve xx53 13 += - . [3] 2 without using a calculator , express 35152 -+- j lkkn poo in the form ab 5+ , where a and b are integers.  [5]",
            "4": "4 0606/22/m/j/17 \u00a9 ucles 2017 3 without using a calculator , factorise the expression xx10 21 432-+ . [5] 4 the point p lies on the curve yx x 37 112=- +. the normal to the curve at p has equation yx k 5+= .  find the coordinates of p and the value of k. [6]",
            "5": "5 0606/22/m/j/17 \u00a9 ucles 2017 [turn over 5 (i) show that [. (. )]ddln lnxxx kx x 04 02 5554-= , where k is an integer to be found.  [2]  (ii) express ln x1253 in terms of lnx5. [1]  (iii) hence find ()ln d xx x 12543y . [2] 6 show that the roots of () px pq xq 02+- -=  are real for all real values of p and q.  [4]",
            "6": "6 0606/22/m/j/17 \u00a9 ucles 2017 7 (a) given that    ab7=, where a and b are positive constants, find,    (i) logba, [1]   (ii) logab. [1]  (b) solve the equation    logy41 81=- . [2]  (c) solve the equation     43216xx1 22 =- . [3]",
            "7": "7 0606/22/m/j/17 \u00a9 ucles 2017 [turn over 8 solutions to this question by accurate drawing will not be accepted.  the points a and b are (\u22128, 8) and (4, 0) respectively.   (i) find the equation of the line ab. [2]   (ii) calculate the length of ab. [2]  the point c is (0, 7) and d is the mid-point of ab.  (iii) show that angle adc  is a right angle.  [3]  the point e is such that ae4 7=-j lkkn poo.  (iv) write down the position vector of the point e. [1]   (v) show that acbe  is a parallelogram.  [2]",
            "8": "8 0606/22/m/j/17 \u00a9 ucles 2017 9 a function f is defined, for x3 2g, by    ()fxx x 26 52=- +.  (i) express ()fx in the form ()ax bc2-+ , where a, b and c are constants.  [3]  (ii) on the same axes, sketch the graphs of ()fyx=  and ()fyx1=-, showing the geometrical  relationship between them.  [3]  xy o  (iii) using your answer from part (i), find an expression for ()fx1-, stating its domain.  [3] ",
            "9": "9 0606/22/m/j/17 \u00a9 ucles 2017 [turn over 10 solve the equation  (i) sinx 4343r-=j lkkn poo  for x02ggr radians,  [4]  (ii) tans ec sec yy y 21 4322+= + for \u00b0\u00b0y 0 360 gg . [5]",
            "10": "10 0606/22/m/j/17 \u00a9 ucles 2017 11  ea ob d xy y = x3 + 4x2 \u2013 5x + 5 cy = 5   the diagram shows part of the curve yxxx 45 532=+ -+  and the line y = 5. the curve and the  line intersect at the points a, b and c. the points d and e are on the x-axis and the lines ae and  cd are parallel to the y-axis.  (i) find () d xxx x 45 532+- + y . [2]  (ii) find the area of each of the rectangles oeab  and obcd . [4]",
            "11": "11 0606/22/m/j/17 \u00a9 ucles 2017 [turn over  (iii) hence calculate the total area of the shaded regions enclosed between the line and the curve. you  must show all your working.  [4] question 12 is printed on the next page.",
            "12": "12 0606/22/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.12 the function g is defined, for x212-, by ()gxx213=+.  (i) show that ()gxl is always negative.  [2]  (ii) write down the range of g.  [1]   the function h is defined, for all real x, by ()hxk x3 =+ , where k is a constant.  (iii) find an expression for ()hgx. [1]  (iv) given that ()hg05=, find the value of k. [2]  (v) state the domain of hg.  [1]"
        },
        "0606_s17_qp_23.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (st/fc) 129465/2 \u00a9 ucles 2017  [turn over *7292744436* additional mathematics  0606/23 paper 2  may/june 2017  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of   angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge international examinations cambridge international general certificate of secondary education",
            "2": "2 0606/23/m/j/17 \u00a9 ucles 2017 mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/23/m/j/17 \u00a9 ucles 2017 [turn over 1 (a) solve the equation  . 72 5x25=+,  giving your answer correct to 2 decimal places.  [3]   (b) express   pqq 6255 123 41^^ hh  in the form pq5ab c, where a, b and c are constants.  [3]  ",
            "4": "4 0606/23/m/j/17 \u00a9 ucles 2017 2   y x oa y x ocy x ob y x od  the four graphs above are labelled a, b, c and d.  (i) write down the letter of each graph that represents a function, giving a reason for your choice.  [2]  (ii) write down the letter of each graph that represents a function which has an inverse, giving a  reason for your choice.  [2]",
            "5": "5 0606/23/m/j/17 \u00a9 ucles 2017 [turn over 3   oy3 (0.2, 5)(1, 13) 1 x  variables x and y are such that when y3 is plotted against x1, a straight line graph passing through the  points (0.2, 5) and (1, 13) is obtained. express y in terms of x. [4]  ",
            "6": "6 0606/23/m/j/17 \u00a9 ucles 2017 4  (a) vectors a, b and c are such that 5 6a=-j lkkn poo, 11 15b=-j lkkn poo and 3 a + c = b.   (i) find c. [1]   (ii) find the unit vector in the direction of b. [2]  (b)    p r q op q   in the diagram,  op p=  and  oq q=. the point r lies on pq such that pr = 3rq. find  or  in  terms of p and q, simplifying your answer.  [3]",
            "7": "7 0606/23/m/j/17 \u00a9 ucles 2017 [turn over 5  (a) how many 5-digit numbers are there that have 5 different digits and are divisible by 5?  [3]     (b) a committee of 8 people is to be selected from 9 men and 5 women. find the number of different  committees that can be selected if the committee must have at least 4 women.  [3]  ",
            "8": "8 0606/23/m/j/17 \u00a9 ucles 2017 6  the first three terms of the binomial expansion of ax2n-^h  are bx bx 64 16 1002- + . find the value of  each of the integers n, a and b. [7]  ",
            "9": "9 0606/23/m/j/17 \u00a9 ucles 2017 [turn over 7  differentiate with respect to x,  (i) cos xx 1410+^h , [4]  (ii) tanxex45- . [4]",
            "10": "10 0606/23/m/j/17 \u00a9 ucles 2017 8   \u03b8 radoa b2\ufffd cmr cmr cm  the diagram shows a circle, centre o of radius r cm, and a chord ab. angle aob  = \u03b8 radians. the  length of the major arc ab is 5 times the length of the minor arc ab. the minor arc ab has length  2r cm.  (i) find the value of \u03b8 and of r. [2]  (ii) calculate the exact perimeter of the shaded segment.  [2]  (iii) calculate the exact area of the shaded segment.  [4]",
            "11": "11 0606/23/m/j/17 \u00a9 ucles 2017 [turn over 9  the functions f and g are defined, for x12 , by ()fxx 91=- , ()xx 2 g2=+ .    (i) find an expression for  ()xf1-, stating its domain.  [3]  (ii) find the exact value of fg(7).  [2]  (iii) solve ()xx x 58 39 5 gf2=+ - . [4]   ",
            "12": "12 0606/23/m/j/17 \u00a9 ucles 2017 10  solve the equation  (a) sinx 21 =   for   xggrr-   radians,  [3]  (b) ()tany 32 15 1 += c    for   y 0 180 ggcc , [4]  ",
            "13": "13 0606/23/m/j/17 \u00a9 ucles 2017 [turn over  (c) cotc osec cosec zz z 37 122=- +   for   z 0 360 ggcc . [5]  ",
            "14": "14 0606/23/m/j/17 \u00a9 ucles 2017 11   q4y = 5x + 20 y = 5+ r xy opx10  the diagram shows part of the curve  yx51 0 =+   and the line  yx45 20 =+ . the line and curve  intersect at the points  p(0, 5)  and q. the line qr is parallel to the y-axis.   (i) find the coordinates of q. [4]",
            "15": "15 0606/23/m/j/17 \u00a9 ucles 2017   (ii) find the area of the shaded region. you must show all your working.  [6]",
            "16": "16 0606/23/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.blank page"
        },
        "0606_w17_qp_11.pdf": {
            "1": "this document consists of 16 printed pages. dc (nh/fc) 135359/3 \u00a9 ucles 2017  [turn over *1404301964* additional mathematics  0606/11 paper 1  october/november 2017  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge international examinations cambridge international general certificate of secondary education",
            "2": "2 0606/11/o/n/17 \u00a9 ucles 2017 mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, xabb ac 242!=-- . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/11/o/n/17 \u00a9 ucles 2017 [turn over 1 express in set notation the shaded regions shown in the venn diagrams below.  (i)   /h5105 a b     [1]  (ii)   /h5105 a b c     [1]  (iii)   /h5105 a b     [1]",
            "4": "4 0606/11/o/n/17 \u00a9 ucles 2017 2 the polynomial  p(x) is   ax bx x13 432+- +,   where a and b are integers. given that    x21-   is a  factor of ()xp and also a factor of ()xpl,  (i) find the value of a and of b. [5]  using your values of a and b,  (ii)  find the remainder when ()xp is divided by x1+. [2]",
            "5": "5 0606/11/o/n/17 \u00a9 ucles 2017 [turn over 3 (a) given that tl g221 21 r=-, express l in terms of t, g and r. [2]  (b) by using the substitution yx31=, or otherwise, solve  xx 43 032 31-+ =. [4]",
            "6": "6 0606/11/o/n/17 \u00a9 ucles 2017 4 when lg y is plotted against x2 a straight line is obtained which passes through the points (4,  3) and  (12, 7).  (i) find the gradient of the line.  [1]  (ii) use your answer to part (i) to express lg y in terms of x. [2]  (iii) hence express y in terms of x, giving your answer in the form  ya 10bx2= ^h  where a and b are  constants.  [3]",
            "7": "7 0606/11/o/n/17 \u00a9 ucles 2017 [turn over 5y y = 4e2x + 16e\u20132x x1oab  the diagram shows part of the graph of y41 6 eexx22=+- meeting the y-axis at the point a and the  line x = 1 at the point b.  (i) find the coordinates of a. [1]  (ii) find the y-coordinate of b. [1]  (iii) find x 41 6 ee dxx22+-^hy . [2]  (iv) hence find the area of the shaded region enclosed by the curve and the line ab. you must show all  your working.  [4]",
            "8": "8 0606/11/o/n/17 \u00a9 ucles 2017 6 (a) functions f and g are such that, for xrd, xx 3 f2=+ ^h , xx 41 g=- ^h .   (i) state the range of f.  [1]   (ii) solve ()x 4 fg=. [3]",
            "9": "9 0606/11/o/n/17 \u00a9 ucles 2017 [turn over  (b) a function h is such that xxx 421h=-+^h  for xrd, x4!.   (i)  find x h1-^h and state its range.  [4]   (ii) find xh2^h, giving your answer in its simplest form.  [3]",
            "10": "10 0606/11/o/n/17 \u00a9 ucles 2017 7 (i) write    lnxx 2121 -+j lkkn poo   as the difference of two logarithms.  [1]  a curve has equation   lnyxxx21214 =-++j lkkn poo   for x212.  (ii) using your answer to part (i) show that    xy xxba 41 dd 22 =-+,   where a and b are integers.  [4]",
            "11": "11 0606/11/o/n/17 \u00a9 ucles 2017 [turn over  (iii) hence find the x-coordinate of the stationary point on the curve.  [2]  (iv) determine the nature of this stationary point.  [2]",
            "12": "12 0606/11/o/n/17 \u00a9 ucles 2017 8 (a) 10 people are to be chosen, to receive concert tickets, from a group of 8 men and 6 women.   (i) find the number of different ways the 10 people can be chosen if 6 of them are men and 4 of  them are women.  [2]   the group of 8 men and 6 women contains a man and his wife.   (ii) find the number of different ways the 10 people can be chosen if both the man and his wife  are chosen or neither of them is chosen.  [3]",
            "13": "13 0606/11/o/n/17 \u00a9 ucles 2017 [turn over  (b) freddie has forgotten the 6-digit code that he uses to lock his briefcase. he knows that he did not  repeat any digit and that he did not start his code with a zero.   (i) find the number of different 6-digit numbers he could have chosen.  [1]   freddie also remembers that his 6-digit code is divisible by 5.   (ii) find the number of different 6-digit numbers he could have chosen.  [3]   freddie decides to choose a new 6-digit code for his briefcase once he has opened it. he plans to  have the 6-digit number divisible by 2 and greater than 600  000, again with no repetitions of digits.   (iii) find the number of different 6-digit numbers he can choose.  [3]",
            "14": "14 0606/11/o/n/17 \u00a9 ucles 2017 9 p a qb10 cm24 cm  the diagram shows a circle, centre a, radius 10  cm, intersecting a circle, centre b, radius 24  cm. the  two circles intersect at the points p and q. the radii ap and aq are tangents to the circle with centre b.  the radii bp and bq are tangents to the circle with centre a.  (i) show that angle p aq is 2.35 radians, correct to 3 significant figures.  [2]  (ii) find angle pbq  in radians.  [1]  (iii) find the perimeter of the shaded region.  [3]",
            "15": "15 0606/11/o/n/17 \u00a9 ucles 2017 [turn over  (iv) find the area of the shaded region.  [4] question 10 is printed on the next page.",
            "16": "16 0606/11/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.10 (a) solve    cosecs in xx 32 42 0 -=  for \u00b0x 0 180\u00b0 gg . [4]  (b) solve    tany 343r-=j lkkn poo  for y02gg r radians, giving your answers in terms of r. [4]"
        },
        "0606_w17_qp_12.pdf": {
            "1": "*4541912001* this document consists of 16 printed pages. dc (kn/sg) 135362/4 \u00a9 ucles 2017  [turn overcambridge international examinations cambridge international general certificate of secondary education additional mathematics  0606/12 paper 1  october/november 2017  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/12/o/n/17 \u00a9 ucles 2017 mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, xabb ac 242!=-- . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/12/o/n/17 \u00a9 ucles 2017 [turn over 1 (i) on the venn diagram below, draw sets x and y such that  xy 0 n+= ^ h .  /h5105  [1]  (ii) on the venn diagram below, draw sets a, b and c such that  ca b,1 l ^h . /h5105  [2]",
            "4": "4 0606/12/o/n/17 \u00a9 ucles 2017 2 the graph of   ()sin ya bx c =+    has an amplitude of 4, a period of r 3 and passes through the point    r,122j lkkn poo. find the value of each of the constants a, b and c. [4]",
            "5": "5 0606/12/o/n/17 \u00a9 ucles 2017 [turn over 3 (i) find, in ascending powers of x, the first 3 terms in the expansion of  x2425 -j lkkn poo.  [3]  (ii) hence find the term independent of x in the expansion of  x xx241 325 22 --j lkkj lkkn poon poo. [3]",
            "6": "6 0606/12/o/n/17 \u00a9 ucles 2017 4 given that lnyxx 132 22 =++ ^h , find the value of xy dd when x = 2, giving your answer as ln ab 14 + , where    a and b are fractions in their simplest form.  [6]",
            "7": "7 0606/12/o/n/17 \u00a9 ucles 2017 [turn over 5 when lgy is plotted against x, a straight line is obtained which passes through the points (0.6, 0.3) and  (1.1, 0.2).  (i) find lgy in terms of x. [4]  (ii) find y in terms of x, giving your answer in the form ya 10bx= ^h , where a and b are constants.  [3]",
            "8": "8 0606/12/o/n/17 \u00a9 ucles 2017 6 functions f and g are defined, for x02, by     () ln xxf= ,     ()xx 23 g2=+ .  (i) write down the range of f.  [1]  (ii) write down the range of g.  [1]  (iii) find the exact value of ()4 fg1-. [2]  (iv) find x g1-^h and state its domain.  [3]",
            "9": "9 0606/12/o/n/17 \u00a9 ucles 2017 [turn over 7 a polynomial  xp^h is   ax xb x 8532++ +,  where a and b are integers. it is given that  x21-  is a  factor of  xp^h  and that a remainder of \u201325 is obtained when  xp^h  is divided by  x + 2.  (i) find the value of a and of b. [5]  (ii) using your values of a and b, find the exact solutions of x 5 p= ^h . [2]",
            "10": "10 0606/12/o/n/17 \u00a9 ucles 2017 8 a b4 ms\u20131120  m 50 m  the diagram shows a river which is 120  m wide and is flowing at 4  ms\u20131. points a and b are on opposite  sides of the river such that b is 50  m downstream from a. a man needs to cross the river from a to b in  a boat which can travel at 5  ms\u20131 in still water.    (i) show that the man must point his boat upstream at an angle of approximately 65\u00b0 to the bank.    [4]",
            "11": "11 0606/12/o/n/17 \u00a9 ucles 2017 [turn over  (ii) find the time the man takes to cross the river from a to b. [6]",
            "12": "12 0606/12/o/n/17 \u00a9 ucles 2017 9 (a) 60 40 20x m 0 10 20 30 t s   the diagram shows the displacement-time graph of a particle p which moves in a straight line  such that, t s after leaving a fixed point o, its displacement from  o is x m. on the axes below, draw  the velocity-time graph of p. 6 4 2 0 10 20 30 t svelocity ms\u20131  [3]",
            "13": "13 0606/12/o/n/17 \u00a9 ucles 2017 [turn over  (b) a particle  q moves in a straight line such that its velocity, v ms\u20131, t s after passing through a fixed     point o, is given by e vt323 t5=+-, for t h 0.   (i)  find the velocity of q when   t = 0. [1]   (ii)  find the value of t when the acceleration of q is zero.  [3]   (iii) find the distance of q from o when  t = 0.5. [4]",
            "14": "14 0606/12/o/n/17 \u00a9 ucles 2017 10 6.2 cm 5 cm 5 cm a cdb ef  the diagram shows an isosceles triangle abc , where ab = ac = 5 cm. the arc bec  is part of the  circle centre a and has length 6.2  cm. the point d is the midpoint of the line bc. the arc bfc is a   semi-circle centre d.  (i) show that angle bac  is 1.24 radians.  [1]  (ii) find the perimeter of the shaded region.  [3]  (iii) find the area of the shaded region.  [4]",
            "15": "15 0606/12/o/n/17 \u00a9 ucles 2017 [turn over 11 (a) solve cot23 55 z+= c ^h   for 0 360 cggz c. [4] question 11(b) is printed on the next page.",
            "16": "16 0606/12/o/n/17 \u00a9 ucles 201716 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) (i) show that  cott ansecsiniiii+= . [3]   (ii)  hence solve   cott ansec 333 23 iii +=-   for  rr 22ggi - , giving your answers in terms of r.  [4]"
        },
        "0606_w17_qp_13.pdf": {
            "1": "*6581423218* this document consists of 15 printed pages and 1 blank page. dc (lk/fc) 135366/3 \u00a9 ucles 2017  [turn overcambridge international examinations cambridge international general certificate of secondary education additional mathematics  0606/13 paper 1  october/november 2017  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/13/o/n/17 \u00a9 ucles 2017 mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/13/o/n/17 \u00a9 ucles 2017 [turn over 1 given that   sec y22i =    and   tan x 5i=- ,   express y in terms of x. [2] 2 a curve is such that its gradient at the point ( x, y) is given by e10 3x5+.   given that the curve passes  though the point (0, 9), find the equation of the curve.  [4]",
            "4": "4 0606/13/o/n/17 \u00a9 ucles 2017 3 find the set of values of  k  for which the equation   kx xk34 02+- +=    has no real roots.  [4] 4 the graph of  ()cos ya bx c =+   has an amplitude of 3, a period of  4r and passes through the point     ,1225rcm .  find the value of each of the constants a, b and c. [4]",
            "5": "5 0606/13/o/n/17 \u00a9 ucles 2017 [turn over 5 (i) find () d xx71 053--y . [2]  (ii)  given that (7 10) d xx1425 a 653-=-y , find the exact value of a. [3]",
            "6": "6 0606/13/o/n/17 \u00a9 ucles 2017 6 when ln y is plotted against x2 a straight line is obtained which passes through the points (0.2, 2.4) and  (0.8, 0.9).  (i) express  ln y in the form px q2+, where  p and q are constants.  [3]  (ii) hence express y in terms of z, where ezx2= . [3]",
            "7": "7 0606/13/o/n/17 \u00a9 ucles 2017 [turn over 7 (i) find, in ascending powers of  x, the first 3 terms in the expansion of   x2426 -cm . give each term in  its simplest form.  [3]  (ii)  hence find the coefficient of x2 in the expansion of   x xx 24126 2 -+c cm m. [4]",
            "8": "8 0606/13/o/n/17 \u00a9 ucles 2017 8 it is given that () () yx x43 135=- - .  (i) show that   () ()dd xyxa xb 3132=- + ,   where a and b are integers to be found.  [5]  (ii) hence find, in terms of h, where h is small, the approximate change in y when x increases from   3 to 3 + h. [3]",
            "9": "9 0606/13/o/n/17 \u00a9 ucles 2017 [turn over 9 (a) a 6-digit number is to be formed using the digits 1, 3, 5, 6, 8, 9.  each of these digits may be used  only once in any 6-digit number. find how many different 6-digit numbers can be formed if   (i) there are no restrictions,  [1]   (ii) the number formed is even,  [1]   (iii) the number formed is even and greater than 300  000. [3]  (b) ruby wants to have a party for her friends. she can only invite 8 of her 15 friends.     (i)  find the number of different ways she can choose her friends for the party if there are no  restrictions.  [1]   two of her 15 friends are twins who cannot be separated.   (ii) find the number of different ways she can now choose her friends for the party.  [3]",
            "10": "10 0606/13/o/n/17 \u00a9 ucles 2017 10 (a) given that ,a nd ab abab41 2 53 413 188 4=-=-= cc c mm m, find the value of a and of b. [4]",
            "11": "11 0606/13/o/n/17 \u00a9 ucles 2017 [turn over  (b) it is given  that , xy3 45 11 42 0=--=-cc mm    and xz = y.   (i) find x1-. [2]   (ii) hence find z. [3]",
            "12": "12 0606/13/o/n/17 \u00a9 ucles 2017 11 a b d co 14.8  cm 10 cm  the diagram shows a circle, centre  o, radius 10  cm. the points a, b, c and d lie on the circumference  of the circle such that ab is parallel to dc. the length of the minor arc ab is 14.8  cm. the area of the  minor sector odc is 21.8  cm2.  (i) write down, in radians, angle aob . [1]  (ii) find, in radians, angle doc . [2]",
            "13": "13 0606/13/o/n/17 \u00a9 ucles 2017 [turn over  (iii) find the perimeter of the shaded region.  [4]  (iv) find the area of the shaded region.  [3]",
            "14": "14 0606/13/o/n/17 \u00a9 ucles 2017 12 the line   yx21=+    intersects the curve   xy y 14 2 =-    at the points p and q. the midpoint of the  line pq is the point m.  (i) show that the point ,10823-cm  lies on the perpendicular bisector of pq. [9]",
            "15": "15 0606/13/o/n/17 \u00a9 ucles 2017  the line pq intersects the y-axis at the point r. the perpendicular bisector of pq intersects the y-axis at  the point s.  (ii) find the area of the triangle rsm . [3]",
            "16": "16 0606/13/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"
        },
        "0606_w17_qp_21.pdf": {
            "1": "*7690408726* this document consists of 15 printed pages and 1 blank pag e. dc (cw) 135370/2 \u00a9 ucles 2017  [turn overadditional mathematics  0606/21 paper 2  october/november 2017  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of   angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge international examinations cambridge international general certificate of secondary education",
            "2": "2 0606/21/o/n/17 \u00a9 ucles 2017 mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n - r)!r!  2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/21/o/n/17 \u00a9 ucles 2017 [turn over 1 solve the inequality    () () xx15 122 -- . [4] 2 show that    sins intansec11 112iiii--+= . [4]",
            "4": "4 0606/21/o/n/17 \u00a9 ucles 2017 3 solve the equation    () () logl og xx10 52 755+= +- . [4]",
            "5": "5 0606/21/o/n/17 \u00a9 ucles 2017 [turn over 4 solve the following simultaneous equations for x and y, giving each answer in its simplest surd form. xy34+=     xy25 3 -=  [5]",
            "6": "6 0606/21/o/n/17 \u00a9 ucles 2017 5 (i) find   xx325 dd +`j . [2]  (ii) use your answer to part (i) to find   ()xx3230d2+y . [2]  (iii) hence evaluate ()xx3230d212 +y . [2]",
            "7": "7 0606/21/o/n/17 \u00a9 ucles 2017 [turn over 6 it is given that  p qm2 3=-cm  where p and q are integers.  (i) if det m =13, find an equation connecting p and q. [1]  (ii) given also that  p q pqm4 63 3 312 2 2=-- - -+eo , find a second equation connecting p and q. [2]  (iii) find the value of p and of q. [4]",
            "8": "8 0606/21/o/n/17 \u00a9 ucles 2017 7 find y in terms of x, given that    xyxx62 dd 22 3=+   and that when  x = 1, y = 3 and xy dd1=. [6]",
            "9": "9 0606/21/o/n/17 \u00a9 ucles 2017 [turn over 8 given that  () za a33 =+ +  and zb 79 32=+ , find the value of each of the integers a and b. [6]",
            "10": "10 0606/21/o/n/17 \u00a9 ucles 2017 9 (i) expand (1 + x)4, simplifying all coefficients.  [1]  (ii) expand (6 - x)4, simplifying  all coefficients.  [2]  (iii) hence express  (6 - x)4 - (1+ x)4 = 175 in the form ax3 + bx2 + cx + d = 0, where a, b, c and d  are integers.  [2]",
            "11": "11 0606/21/o/n/17 \u00a9 ucles 2017 [turn over  (iv) show that x = 2 is a solution of the equation in part (iii) and show that this equation has no other  real roots.  [5]",
            "12": "12 0606/21/o/n/17 \u00a9 ucles 2017 10 in this question i is a unit vector due east and j is a unit vector due north. units of length and velocity  are metres and metres per second respectively.  the initial position vectors of particles a and b, relative to a fixed point o, are 2 i + 4j and 10 i +14 j  respectively. particles a and b start moving at the same time. a moves with constant velocity i + j and  b moves with constant velocity -2i - 3j. find  (i) the position vector of  a after t seconds,  [1]  (ii) the position vector of  b after t seconds.  [1]  it is given that x is the distance between  a and b after t seconds.  (iii) show that   x\u200a\u200a2 = (8 - 3t)2 + (10 - 4t)2. [3]",
            "13": "13 0606/21/o/n/17 \u00a9 ucles 2017 [turn over  (iv) find the value of t for which  (8 - 3t)2 + (10 - 4t)2 has a stationary value and the corresponding  value of x. [4]",
            "14": "14 0606/21/o/n/17 \u00a9 ucles 2017 11 the line   y = kx + 3,   where  k is a positive constant, is a tangent to the curve   x2 - 2x + y2 = 8 at the  point  p.  (i) find the value of k. [4]  (ii) find the coordinates of p. [3]  (iii) find the equation of the normal to the curve at p. [2]",
            "15": "15 0606/21/o/n/17 \u00a9 ucles 2017 12 (i) differentiate   ()cosx1-  with respect to x. [2]  (ii) hence find  xy dd  given that   () tanc os yx x 41=+-. [2]  (iii) using your answer to part (ii) find the values of x in the range 0 g x g 2r such that   xy dd = 4. [6]",
            "16": "16 0606/21/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.blank page"
        },
        "0606_w17_qp_22.pdf": {
            "1": "*8047669716* this document consists of 15 printed pages and 1 blank page. dc (al/fc) 135371/2 \u00a9 ucles 2017  [turn overadditional mathematics  0606/22 paper 2  october/november 2017  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of   angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge international examinations cambridge international general certificate of secondary education",
            "2": "2 0606/22/o/n/17 \u00a9 ucles 2017 mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/22/o/n/17 \u00a9 ucles 2017 [turn over 1 if z23=+  find the integers a and b such that  az bz 132+= + . [5] ",
            "4": "4 0606/22/o/n/17 \u00a9 ucles 2017 2 solve the equation  x xxxx2 56. ... 15 05 0505+ +=-- . [5] 3 solve the inequality  x x 3 312+ - . [3]",
            "5": "5 0606/22/o/n/17 \u00a9 ucles 2017 [turn over 4 solve the simultaneous equations logl og xy4222+=^h , log yx742-= ^h .  [5]",
            "6": "6 0606/22/o/n/17 \u00a9 ucles 2017 5 naomi is going on holiday and intends to read 4 books during her time away. she selects these books  from 5 mystery, 3 crime and 2 romance books. find the number of ways in which she can make her  selection in each of the following cases.  (i) there are no restrictions.  [1]  (ii) she selects at least 2 mystery books.  [3]  (iii) she selects at least 1 book of each type.  [3]",
            "7": "7 0606/22/o/n/17 \u00a9 ucles 2017 [turn over 6 the volume of a closed cylinder of base radius x cm and height h cm is 500  cm3.  (i) express h in terms of x. [1]  (ii) show that the total surface area of the cylinder is given by  xx21000cm a22r=+ . [2]  (iii) given that x can vary, find the stationary value of a and show that this value is a minimum.  [5]",
            "8": "8 0606/22/o/n/17 \u00a9 ucles 2017 7 the gradient of the normal to a curve at the point with coordinates  ,xy^h   is given by  xx 13-.  (i) find the equation of the curve, given that the curve passes through the point  (1, \u221210).  [5]  (ii) find, in the form   ym xc=+ , the equation of the tangent to the curve at the point where  x4=. [4]",
            "9": "9 0606/22/o/n/17 \u00a9 ucles 2017 [turn over 8 the matrix a is 2 41 3cm .  (i) find 2a1-^h . [3]  (ii) hence solve the simultaneous equations yx245 0 ++ =, yx689 0 ++ =.  [4]",
            "10": "10 0606/22/o/n/17 \u00a9 ucles 2017 9 (i) find lnxxxdd^h . [2]  (ii) hence find lnxxd y . [2]",
            "11": "11 0606/22/o/n/17 \u00a9 ucles 2017 [turn over  (iii) hence, given that k02, show that ln ln xx kk41 d kk2=-^h y . [4]",
            "12": "12 0606/22/o/n/17 \u00a9 ucles 2017 10 (i) without using a calculator , solve the equation  cc671 032-+ =. [5]  it is given that tans in yx x 6 =+ .  (ii) find xy dd. [2]",
            "13": "13 0606/22/o/n/17 \u00a9 ucles 2017 [turn over  (iii) if  xy7dd= show that  cosc os xx 671 032-+ =. [2]  (iv) hence solve the equation  xy7dd= for x0gg r radians.  [2]",
            "14": "14 0606/22/o/n/17 \u00a9 ucles 2017 11 y x y = 4 + 3 x \u2013 x2y = mx + 8 o ab  the diagram shows the curve  yx x 432=+ - intersecting the positive x-axis at the point a. the  line ym x8 =+  is a tangent to the curve at the point b. find  (i) the coordinates of a, [2]  (ii) the value of m, [3]",
            "15": "15 0606/22/o/n/17 \u00a9 ucles 2017  (iii) the coordinates of b, [2]  (iv) the area of the shaded region, showing all your working.  [5]",
            "16": "16 0606/22/o/n/17 \u00a9 ucles 201716 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"
        },
        "0606_w17_qp_23.pdf": {
            "1": "*7407739830* this document consists of 16 printed pages. dc (nf/ar) 135372/4 \u00a9 ucles 2017  [turn overcambridge international examinations cambridge international general certificate of secondary education additional mathematics  0606/23 paper 2  october/november 2017  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles in  degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/23/o/n/17 \u00a9 ucles 2017 mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, xbb ac a=\u2212 \u221224 2 binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/23/o/n/17 \u00a9 ucles 2017 [turn over 1 (a) on each of the diagrams below, shade the region which represents the given set. a b c/h5105 a b c /h20871a /h20668 b/h20872 /h20669 c' /h20871a /h20669 b' /h20872 /h20668 c/h5105 [2]  (b)  p q r/h5105 7 42 8 1 3 65   the venn diagram shows the number of elements in each of its subsets.   complete the following.   n(p') =    n((q \ue0f8 r) \ue0f9 p) = ..   n(q' \ue0f8 p) =   [3]",
            "4": "4 0606/23/o/n/17 \u00a9 ucles 2017 2 solve the equation xx31 5 -= +. [3] 3 find integers p and q such that     pq31 31133-++=+ . [4]",
            "5": "5 0606/23/o/n/17 \u00a9 ucles 2017 [turn over 4 solve the simultaneous equations      logl og xy1133+= + ^h ,    logxy 23-=^h . [5]",
            "6": "6 0606/23/o/n/17 \u00a9 ucles 2017 5  d a o bx c  the diagram shows points o, a, b, c, d and x. the position vectors of a, b and c relative to o are   oa a=, ob b= and oc b23= . the vector cd a3= .  (i) if ox odm=  express ox in terms of  m, a and b. [1]  (ii) if ax abn=  express ox in terms of n, a and b. [2]  (iii) use your two expressions for ox to find the value of   m and of  n. [3]",
            "7": "7 0606/23/o/n/17 \u00a9 ucles 2017 [turn over  (iv) find the ratio xbax. [1]  (v) find the ratio xdox. [1]",
            "8": "8 0606/23/o/n/17 \u00a9 ucles 2017 6 the functions f and g are defined for real values of x by xx 21 f2=+ + ^^hh  , xxx 212g=--^h  , x21! .  (i) find 3 f2-^h . [2]  (ii) show that    xx gg1=-^^hh . [3]  (iii) solve  x198gf= ^h . [4]",
            "9": "9 0606/23/o/n/17 \u00a9 ucles 2017 [turn over 7 a particle moving in a straight line passes through a fixed point o. its velocity, vms1-, t s after passing  through o, is given by cos vt32 1 =-  for t0h.  (i) find the value of t when the particle is first at rest.  [2]  (ii) find the displacement from o of the particle when t4r=. [3]  (iii) find the acceleration of the particle when it is first at rest.  [3]",
            "10": "10 0606/23/o/n/17 \u00a9 ucles 2017 8 ab c 50 m1 ms\u20131 3 ms\u20131 a  a man, who can row a boat at 3  ms\u22121 in still water, wants to cross a river from a to b as shown in the  diagram. ab is perpendicular to both banks of the river. the river, which is 50  m wide, is flowing at  1 ms\u22121 in the direction shown. the man points his boat at an angle a\u00b0 to the bank. find  (i) the angle a, [2]  (ii) the resultant speed of the boat from a to b, [2]",
            "11": "11 0606/23/o/n/17 \u00a9 ucles 2017 [turn over  (iii) the time taken for the boat to travel from a to b. [2]  on another occasion the man points the boat in the same direction but the river speed has increased to  1.8 ms\u22121 and as a result he lands at the point c.  (iv) state the time taken for the boat to travel from a to c and hence find the distance  bc. [2]",
            "12": "12 0606/23/o/n/17 \u00a9 ucles 2017 9 (i) show that   ln ln xxx xx 13 dd 34=-cm  . [3]  (ii) find the exact coordinates of the stationary point of the curve   lnyxx 3=  . [3]",
            "13": "13 0606/23/o/n/17 \u00a9 ucles 2017 [turn over  (iii) use the result from part (i) to find   ln xxxd4j lkkn poo y  . [4]",
            "14": "14 0606/23/o/n/17 \u00a9 ucles 2017 10 (a) show that    cossin sincoscosecxx xxx112+++= . [3]  (b) solve the following equations.   (i) cotc osec yy 502+- =   for \u00b0\u00b0y 0 360 gg  [5]",
            "15": "15 0606/23/o/n/17 \u00a9 ucles 2017 [turn over   (ii) cosz2423 r+= - `j    for z0gg r radians  [4] question 11 is printed on the next page.",
            "16": "16 0606/23/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.11 the cubic equation  x3 + ax2 + bx \u2212 36 = 0  has a repeated positive integer root.  (i) if the repeated root is x = 3 find the other positive root and the value of a and of b. [4]  (ii) there are other possible values of a and b for which the cubic equation has a repeated positive  integer root. in each case state all three integer roots of the equation.  [4]"
        }
    },
    "2018": {
        "0606_m18_qp_12.pdf": {
            "1": "*5325132921* this document consists of 15 printed pages and 1 blank page. dc (sc/cgw) 144843/3 \u00a9 ucles 2018  [turn overadditional mathematics  0606/12 paper 1  february/march 2018  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge international examinations cambridge international general certificate of secondary education",
            "2": "2 0606/12/f/m/18 \u00a9 ucles 2018 mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/12/f/m/18 \u00a9 ucles 2018 [turn over 1 the remainder obtained when the polynomial    ()xx ax xb3 p32=+ -+     is divided by    x3+    is  twice the remainder obtained when ()xp is divided by    x2-.    given also that ()xp is divisible by     x1+,    find the value of a and of b. [5]",
            "4": "4 0606/12/f/m/18 \u00a9 ucles 2018 2 a curve has equation   sin yx45 3 =+ .  (i) find xy dd. [2]  (ii) hence find the equation of the tangent to the curve    sin yx45 3 =+     at the point where rx3=.   [3]",
            "5": "5 0606/12/f/m/18 \u00a9 ucles 2018 [turn over 3 do not use a calculator in this question.  (a) simplify    32 5 4562 5 + -- ^ ^^h hh,   giving your answer in the form ab 5+ , where a and b are    integers.  [3]  (b) in this part, all lengths are in centimetres. ba cab 62 3 =- bc 62 3 =+   the diagram shows the triangle abc  with ab 62 3 =-  and bc 62 3 =+ . given that     cosabc21=- , find the length of ac in the form cd , where c and d are integers.  [3]",
            "6": "6 0606/12/f/m/18 \u00a9 ucles 2018 4 it is given that   lnyxx 2412 =+- ^h.  (i) find the values of x for which y is not defined.  [2]  (ii) find xy dd. [3]  (iii) hence find the approximate increase in y when x increases from 2 to 2 + h, where h is small.  [2]",
            "7": "7 0606/12/f/m/18 \u00a9 ucles 2018 [turn over 5 the first 3 terms in the expansion of ax2n+^h  are equal to xb x 1024 12802-+ , where n, a and b are  constants.  (i) find the value of each of n, a and b. [5]  (ii) hence find the term independent of x in the expansion of ax xx21 n2 +-j lkk ^n poo h . [3]",
            "8": "8 0606/12/f/m/18 \u00a9 ucles 2018 6 a b com  the diagram shows the quadrilateral oabc  such that a oa=, b ob= and c oc=. it is given that  am : mc = 2 : 1 and om : mb = 3 : 2.  (i) find ac in terms of a and c. [1]  (ii) find om in terms of a and c. [2]  (iii) find om in terms of b. [1]",
            "9": "9 0606/12/f/m/18 \u00a9 ucles 2018 [turn over  (iv) find 51 0 ac+  in terms of b. [2]  (v) find ab in terms of a and c, giving your answer in its simplest form.  [2]",
            "10": "10 0606/12/f/m/18 \u00a9 ucles 2018 7 (a) find the values of a for which    detaaaa42163=-j lkkn poo . [3]  (b) it is given that 3421a=j lkkn poo and 20 35b=-j lkkn poo.   (i) find a\u20131. [2]   (ii) hence find the matrix c such that ac = b. [3]  (c) find the 2 # 2 matrix d such that 4 d + 3i = o. [1]",
            "11": "11 0606/12/f/m/18 \u00a9 ucles 2018 [turn over 8 a particle p, moving in a straight line, passes through a fixed point o at time t = 0 s. at time  t s after   leaving o, the displacement of the particle is x m and its velocity is v ms\u20131, where    , vt t 12 48 0 et2h =- .  (i) find x in terms of t. [4]  (ii) find the value of t when the acceleration of p is zero.  [3]  (iii) find the velocity of p when the acceleration is zero.  [2]",
            "12": "12 0606/12/f/m/18 \u00a9 ucles 2018 9 the table shows values of the variables x and y. x 2 4 6 8 10 y 736 271 100 37 13  the relationship between x and y is thought to be of the form ya ebx= , where a and b are constants.  (i) transform this relationship into straight line form.  [1]  (ii) hence, by plotting a suitable graph, show that the relationship ya ebx=  is correct.  [2]",
            "13": "13 0606/12/f/m/18 \u00a9 ucles 2018 [turn over  (iii) use your graph to find the value of a and of b. [4]  (iv) estimate the value of x when y = 500.  [2]  (v) estimate the value of y when x = 5. [2]",
            "14": "14 0606/12/f/m/18 \u00a9 ucles 2018 10 ab c d oy xyx x 21 32=+ - ^^ hh  the diagram shows the graph of    yx x 21 32=+ - ^^ hh .    the curve has a minimum at the point a, a  maximum at the point b and intersects the y-axis and the x-axis at the points c and d respectively.  (i) find the x-coordinate of a and of b. [5]  (ii) write down the coordinates of c and of d. [2]",
            "15": "15 0606/12/f/m/18 \u00a9 ucles 2018  (iii) showing all your working, find the area of the shaded region.  [5]",
            "16": "16 0606/12/f/m/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"
        },
        "0606_m18_qp_22.pdf": {
            "1": "this document consists of 14 printed pages and 2 blank pages. dc (kn/cgw) 144842/2 \u00a9 ucles 2018  [turn over *4569060243* additional mathematics  0606/22 paper 2  february/march 2018  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge international examinations cambridge international general certificate of secondary education",
            "2": "2 0606/22/f/m/18 \u00a9 ucles 2018 mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/22/f/m/18 \u00a9 ucles 2018 [turn over 1 (a) p q r/h5105   using set notation, write down the set represented by the shaded region.  [1]  (b)   \ue025  = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}       a  = { x: x is a prime number}       b  = { x: x is an even number}      c  = {1, 2, 3, 4, 8}   (i) complete the venn diagram to show the elements of each set.  [3] ab c/h5105   (ii) write down the value of  (( )) abcn,, l. [1]",
            "4": "4 0606/22/f/m/18 \u00a9 ucles 2018 2 determine the set of values of k for which the equation   () () kx kx 32 23 102-+ -+ =   has no real  roots.  [5] 3 a group of five people consists of two women, alice and betty, and three men, carl, david and ed.  (i) three of these five people are chosen at random to be a chairperson, a treasurer and a secretary.  find the number of ways in which this can be done if the chairperson and treasurer are both men.  [2]   these five people sit in a row of five chairs. find the number of different possible seating arrangements  if    (ii) david must sit in the middle,   [1]  (iii) alice and carl must sit together.   [2]",
            "5": "5 0606/22/f/m/18 \u00a9 ucles 2018 [turn over 4 (a) (i) state the amplitude of  15sin2 x \u2013 5. [1]   (ii) state the period of  15sin2 x \u2013 5. [1]  (b) 4 3 2 1 90 0  \u20131  \u20132  \u20133  \u20134\u201345 \u201390 \u2013135 \u2013180 45 135 180 xy   the diagram shows the graph of  () yx f=  for x 180 180 gg - cc c, where f  (x) is a trigonometric  function.   (i)  write down two possible expressions for the trigonometric function f( x). [2]   (ii) state the number of solutions of the equation  ()x 1 f=  for  x 180 180 gg - cc c. [1]",
            "6": "6 0606/22/f/m/18 \u00a9 ucles 2018 5 0.5 ms\u20131104  m ab c  a river is 104 metres wide and the current flows at 0.5  ms\u20131 parallel to its banks. a woman can swim at  1.6 ms\u20131 in still water. she swims from point a and aims for point b which is directly opposite, but she  is carried downstream to point c. calculate the time it takes the woman to swim across the river and the  distance downstream, bc, that she travels.  [4] 6 (i) differentiate  tanx13+j lkkn poo  with respect to x. [2]  (ii) hence find  secxx3d2j lkkn poo y . [2]",
            "7": "7 0606/22/f/m/18 \u00a9 ucles 2018 [turn over 7 a \u03b8 rad bd o c8 cm 1.4 rad  the diagram shows a circle with centre o and radius 8  cm. the points a, b, c and d lie on the  circumference of the circle. angle aob  = \u03b8 radians and angle cod  = 1.4 radians. the area of sector  aob  is 20  cm2.  (i) find angle \u03b8. [2]  (ii)  find the length of the arc ab. [2]  (iii)  find the area of the shaded segment.   [3]",
            "8": "8 0606/22/f/m/18 \u00a9 ucles 2018 8 (a)  solve the following equations.   (i) 51 4 ex34=+ [2]   (ii) ()lg lg lg yy27 23 -+ =  [4]  (b) write  () () logl oglogl og rpq 2r 222-   as a single logarithm to base 2.  [2]",
            "9": "9 0606/22/f/m/18 \u00a9 ucles 2018 [turn over 9 solutions to this question by accurate drawing will not be accepted.  p is the point (8, 2) and q is the point (11, 6).   (i) find the equation of the line l which passes through p and is perpendicular to the line pq.  [3]  the point r lies on l such that the area of triangle pqr  is 12.5 units2.   (ii) showing all your working, find the coordinates of each of the two possible positions of point r.    [6]",
            "10": "10 0606/22/f/m/18 \u00a9 ucles 2018 10 (a) the function f is defined by   ()xx 1 f2=+ ,   for all real values of x. the graph of y = f(x) is  given below. y x1y o 1 + x2=   (i) explain, with reference to the graph, why f does not have an inverse.  [1]   (ii) find ()xf2. [2]  (b) the function g is defined, for x > k, by   ()xx 1 g2=+    and g has an inverse.   (i)  write down a possible value for k. [1]   (ii)  find  ()xg1-. [2]",
            "11": "11 0606/22/f/m/18 \u00a9 ucles 2018 [turn over  (c) the function h is defined, for all real values of x, by   h( x) = 4ex + 2.   sketch the graph of  y = h(x).  hence, on the same axes, sketch the graph of  y = h\u20131(x). give the coordinates of any points where  your graphs meet the coordinate axes.  [4] oy x",
            "12": "12 0606/22/f/m/18 \u00a9 ucles 2018 11 (a) (i) show that  () () sincossins in aaaa 11-+ = cot a. [2]   (ii) hence solve   () () sinc ossins in xxxx 3313 13 -+ = 21  for  x 0 180 ggcc . [4]",
            "13": "13 0606/22/f/m/18 \u00a9 ucles 2018 [turn over  (b) solve   tans ec yy 10 102-- =  for  r y02gg   radians.  [5]",
            "14": "14 0606/22/f/m/18 \u00a9 ucles 2018 12 the volume, v, and surface area, s, of a sphere of radius r are given by   r vr34 3=    and   r sr42=    respectively.  the volume of a sphere increases at a rate of 200  cm3 per second. at the instant when the radius of the  sphere is 10  cm, find  (i) the rate of increase of the radius of the sphere,  [4]  (ii) the rate of increase of the surface area of the sphere.  [3]  ",
            "15": "15 0606/22/f/m/18 \u00a9 ucles 2018 blank page",
            "16": "16 0606/22/f/m/18 \u00a9 ucles 201816 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"
        },
        "0606_s18_qp_11.pdf": {
            "1": "*3936138431* this document consists of 16 printed pages. dc (sc/sg) 145845/2 \u00a9 ucles 2018  [turn overadditional mathematics  0606/11 paper 1  may/june 2018  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge international examinations cambridge international general certificate of secondary education",
            "2": "2 0606/11/m/j/18 \u00a9 ucles 2018 mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, xabb ac 242!=-- binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/11/m/j/18 \u00a9 ucles 2018 [turn over 1 solve the equations  yx 4 -= , xy xy841 6022+- -- =.  [5]",
            "4": "4 0606/11/m/j/18 \u00a9 ucles 2018 2 find the equation of the perpendicular bisector of the line joining the points (1, 3) and (4, -5). give  your answer in the form ax + by + c = 0, where a, b and c are integers.  [5]",
            "5": "5 0606/11/m/j/18 \u00a9 ucles 2018 [turn over 3 diagrams a to d show four different graphs. in each case the whole graph is shown and the scales on  the two axes are the same. y xa oy xb o y xc oy xd o  place ticks in the boxes in the table to indicate which descriptions, if any, apply to each graph. there  may be more than one tick in any row or column of the table.  [4] a b c d not a function one-one  function a function  that is its own  inverse a function  with no inverse",
            "6": "6 0606/11/m/j/18 \u00a9 ucles 2018 4 (i) the curve   sin ya bc x =+    has an amplitude of 4 and a period of r 3. given that the curve passes   through the point r,122j lkkn poo, find the value of each of the constants a, b and c. [4]  (ii) using your values of a, b and c, sketch the graph of sin ya bc x =+  for rx0gg  radians.  [3] y x 06 \u20136r",
            "7": "7 0606/11/m/j/18 \u00a9 ucles 2018 [turn over 5 the population, p, of a certain bacterium t days after the start of an experiment is modelled by   p = 800ekt, where k is a constant.  (i) state what the figure 800 represents in this experiment.  [1]  (ii) given that the population is 20  000 two days after the start of the experiment, calculate the value  of k. [3]  (iii) calculate the population three days after the start of the experiment.  [2]",
            "8": "8 0606/11/m/j/18 \u00a9 ucles 2018 6 (a) write   logl og log pq 223 3+ ^^ hh    as a single logarithm to base 3.  [3]  (b) given that   logl og 54 53 0aa2-+ = ^h ,   find the possible values of a. [3]",
            "9": "9 0606/11/m/j/18 \u00a9 ucles 2018 [turn over 7 (i) find the inverse of the matrix 4 52 3 --j lkkn poo. [2]  (ii) hence solve the simultaneous equations  8x - 4y - 5 = 0, -10x + 6y - 7 = 0.  [4]",
            "10": "10 0606/11/m/j/18 \u00a9 ucles 2018 8 (a) given that p = 2i - 5j and q = i - 3j, find the unit vector in the direction of 3 p - 4q. [4]  (b) b a1.25  kmh\u20131   a river flows between parallel banks at a speed of 1.25  kmh-1. a boy standing at point a on one  bank sends a toy boat across the river to his father standing directly opposite at point b. the toy  boat, which can travel at v kmh-1 in still water, crosses the river with resultant speed 2.73  kmh-1  along the line ab.   (i) calculate the value of v. [2]",
            "11": "11 0606/11/m/j/18 \u00a9 ucles 2018 [turn over   the direction in which the boy points the boat makes an angle i with the line ab.   (ii) find the value of i. [2]",
            "12": "12 0606/11/m/j/18 \u00a9 ucles 2018 9 (i) find the first 3 terms in the expansion of   xx21618 -j lkkn poo   in descending powers of x. [3]  (ii) hence find the coefficient of x4 in the expansion of   xxx2161118 22 -+j lkkj lkkn poon poo. [3]",
            "13": "13 0606/11/m/j/18 \u00a9 ucles 2018 [turn over 10 do not use a calculator in this question.  (a) simplify    6556 5 ++. [3]  (b) show that   32.05 7#^h    can be written in the form ab , where a and b are integers and a > b.  [2]  (c) solve the equation   xx24+= ,   giving your answers in simplest surd form.  [4]",
            "14": "14 0606/11/m/j/18 \u00a9 ucles 2018 11 y xa oyxx1627 2=+  the diagram shows part of the graph of   yxx1627 2=+ ,   which has a minimum at a.  (i) find the coordinates of a. [4]",
            "15": "15 0606/11/m/j/18 \u00a9 ucles 2018 [turn over  the points p and q lie on the curve    yxx1627 2=+     and have x-coordinates 1 and 3 respectively.  (ii) find the area enclosed by the curve and the line pq. you must show all your working.  [6] question 12 is printed on the next page.",
            "16": "16 0606/11/m/j/18 \u00a9 ucles 201816 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 a curve is such that   xyx25dd 22 21 =--^h .   given that the curve has a gradient of 6 at the point ,29 32j lkkn poo,   find the equation of the curve.  [8]"
        },
        "0606_s18_qp_12.pdf": {
            "1": "*1239049889* this document consists of 16 printed pages. dc (kn/sw) 145846/4 \u00a9 ucles 2018  [turn overadditional mathematics  0606/12 paper 1  may/june 2018  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge international examinations cambridge international general certificate of secondary education",
            "2": "2 0606/12/m/j/18 \u00a9 ucles 2018mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 \u00a9 ucles 2018 [turn over 0606/12/m/j/181 it is given that   tan yx13=+ .  (i) state the period of y. [1]  (ii) on the axes below, sketch the graph of   tan yx13=+    for  \u00b0x 0 180 \u00b0\u00b0gg . [3] 030 60 90 120 150 180y x",
            "4": "4 0606/12/m/j/18 \u00a9 ucles 2018 2 find the values of k for which the line  yk x 12=-   does not meet the curve  () yx kx 93 152=- ++ .  [5]",
            "5": "5 0606/12/m/j/18 \u00a9 ucles 2018 [turn over 3 the variables x and y are such that when e  y is plotted against x 2, a straight line graph passing through  the points (5, 3) and (3, 1) is obtained. find y in terms of x. [5]",
            "6": "6 0606/12/m/j/18 \u00a9 ucles 2018 4 a particle p moves so that its displacement, x metres from a fixed point o, at time t seconds, is given by  ()lnxt 53=+ .   (i) find the value of t when the displacement of p is 3m.  [2]  (ii) find the velocity of p when t = 0. [2]  (iii) explain why, after passing through o, the velocity of p is never negative.  [1]  (iv) find the acceleration of p when t = 0.  [2]",
            "7": "7 0606/12/m/j/18 \u00a9 ucles 2018 [turn over 5 (i) the first three terms in the expansion of  x3915 -j lkkn poo  can be written as  axb xc 2++ . find the value  of each of the constants a, b and c. [3]  (ii) use your values of a, b and c to find the term independent of x in the expansion of          ()xx 391295 2-+j lkkn poo . [3]",
            "8": "8 0606/12/m/j/18 \u00a9 ucles 2018 6 find the coordinates of the stationary point of the curve   yxx 212=-+. [6]",
            "9": "9 0606/12/m/j/18 \u00a9 ucles 2018 [turn over 7 a population, b, of a particular bacterium, t hours after measurements began, is given by b1000et 4 = .  (i) find the value of b when t = 0. [1]  (ii) find the time taken for b to double in size.  [3]  (iii) find the value of b when t = 8. [1]",
            "10": "10 0606/12/m/j/18 \u00a9 ucles 2018 8 (a) solve   coss in 34 42ii+=    for   \u00b0\u00b00 180 ggi . [4]  (b) solve   sinc os 23 2 zz=    for 22ggrrz -  radians.  [4]",
            "11": "11 0606/12/m/j/18 \u00a9 ucles 2018 [turn over 9 (a) (i) solve  lgx3=.  [1]   (ii) write  lg lg ab23-+   as a single logarithm.  [3]  (b) (i) solve  xx560 -+ =. [2]   (ii) hence, showing all your working, find the values of a such that  logl og a56 40a 4-+ =.  [3]",
            "12": "12 0606/12/m/j/18 \u00a9 ucles 2018 10 do not use a calculator in this question.  all lengths in this question are in centimetres. 60\u00b0ba c43 5- 43 5+  the diagram shows the triangle abc , where ab 43 5 =- , bc 43 5 =+  and angle \u00b0 abc 60= .   it is known that \u00b0 sin6023= , \u00b0 cos6021=, \u00b0 tan603= .  (i) find the exact value of ac. [4]",
            "13": "13 0606/12/m/j/18 \u00a9 ucles 2018 [turn over  (ii) hence show that   () cosecaqcbp43 52=+ ,   where p and q are integers.  [4] ",
            "14": "14 0606/12/m/j/18 \u00a9 ucles 2018 11 oy x baey83x4 =+  the diagram shows the graph of the curve   y3 8ex4 =+.   the curve meets the y-axis at the point a.   the normal to the curve at a meets the x-axis at the point b. find the area of the shaded region  enclosed by the curve, the line ab and the line through b parallel to the y-axis. give your answer in  the form ae , where a is a constant. you must show all your working.     [10]",
            "15": "15 0606/12/m/j/18 \u00a9 ucles 2018 [turn over question 12 is printed on the next page.",
            "16": "16 0606/12/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 do not use a calculator in this question.  (a) given that   68 3 9pp q q2 23##+ -   is equal to  2374# ,  find the value of each of the constants p and q.   [3]  (b) using the substitution  ux31 = , or otherwise, solve  xx43 01 32 3++ =. [4]  "
        },
        "0606_s18_qp_13.pdf": {
            "1": "*5006741950* this document consists of 16 printed pages. dc (nf/sg) 162658 \u00a9 ucles 2018  [turn overadditional mathematics  0606/13 paper 1  may/june 2018  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge international examinations cambridge international general certificate of secondary education",
            "2": "2 0606/13/m/j/18 \u00a9 ucles 2018 mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, xabb ac 242!=-- binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/13/m/j/18 \u00a9 ucles 2018 [turn over 1 solve the equations  yx 4 -= , xy xy841 6022+- -- =.  [5]",
            "4": "4 0606/13/m/j/18 \u00a9 ucles 2018 2 find the equation of the perpendicular bisector of the line joining the points (1, 3) and (4, -5). give  your answer in the form ax + by + c = 0, where a, b and c are integers.  [5]",
            "5": "5 0606/13/m/j/18 \u00a9 ucles 2018 [turn over 3 diagrams a to d show four different graphs. in each case the whole graph is shown and the scales on  the two axes are the same. y xa oy xb o y xc oy xd o  place ticks in the boxes in the table to indicate which descriptions, if any, apply to each graph. there  may be more than one tick in any row or column of the table.  [4] a b c d not a function one-one  function a function  that is its own  inverse a function  with no inverse",
            "6": "6 0606/13/m/j/18 \u00a9 ucles 2018 4 (i) the curve   sin ya bc x =+    has an amplitude of 4 and a period of r 3. given that the curve passes   through the point r,122j lkkn poo, find the value of each of the constants a, b and c. [4]  (ii) using your values of a, b and c, sketch the graph of sin ya bc x =+  for rx0gg  radians.  [3] y x 06 \u20136r",
            "7": "7 0606/13/m/j/18 \u00a9 ucles 2018 [turn over 5 the population, p, of a certain bacterium t days after the start of an experiment is modelled by   p = 800ekt, where k is a constant.  (i) state what the figure 800 represents in this experiment.  [1]  (ii) given that the population is 20  000 two days after the start of the experiment, calculate the value  of k. [3]  (iii) calculate the population three days after the start of the experiment.  [2]",
            "8": "8 0606/13/m/j/18 \u00a9 ucles 2018 6 (a) write   logl og log pq 223 3+ ^^ hh    as a single logarithm to base 3.  [3]  (b) given that   logl og 54 53 0aa2-+ = ^h ,   find the possible values of a. [3]",
            "9": "9 0606/13/m/j/18 \u00a9 ucles 2018 [turn over 7 (i) find the inverse of the matrix 4 52 3 --j lkkn poo. [2]  (ii) hence solve the simultaneous equations  8x - 4y - 5 = 0, -10x + 6y - 7 = 0.  [4]",
            "10": "10 0606/13/m/j/18 \u00a9 ucles 2018 8 (a) given that p = 2i - 5j and q = i - 3j, find the unit vector in the direction of 3 p - 4q. [4]  (b) b a1.25  kmh\u20131   a river flows between parallel banks at a speed of 1.25  kmh-1. a boy standing at point a on one  bank sends a toy boat across the river to his father standing directly opposite at point b. the toy  boat, which can travel at v kmh-1 in still water, crosses the river with resultant speed 2.73  kmh-1  along the line ab.   (i) calculate the value of v. [2]",
            "11": "11 0606/13/m/j/18 \u00a9 ucles 2018 [turn over   the direction in which the boy points the boat makes an angle i with the line ab.   (ii) find the value of i. [2]",
            "12": "12 0606/13/m/j/18 \u00a9 ucles 2018 9 (i) find the first 3 terms in the expansion of   xx21618 -j lkkn poo   in descending powers of x. [3]  (ii) hence find the coefficient of x4 in the expansion of   xxx2161118 22 -+j lkkj lkkn poon poo. [3]",
            "13": "13 0606/13/m/j/18 \u00a9 ucles 2018 [turn over 10 do not use a calculator in this question.  (a) simplify    6556 5 ++. [3]  (b) show that   32.05 7#^h    can be written in the form ab , where a and b are integers and a > b.  [2]  (c) solve the equation   xx24+= ,   giving your answers in simplest surd form.  [4]",
            "14": "14 0606/13/m/j/18 \u00a9 ucles 2018 11 y xa oyxx1627 2=+  the diagram shows part of the graph of   yxx1627 2=+ ,   which has a minimum at a.  (i) find the coordinates of a. [4]",
            "15": "15 0606/13/m/j/18 \u00a9 ucles 2018 [turn over  the points p and q lie on the curve    yxx1627 2=+     and have x-coordinates 1 and 3 respectively.  (ii) find the area enclosed by the curve and the line pq. you must show all your working.  [6] question 12 is printed on the next page.",
            "16": "16 0606/13/m/j/18 \u00a9 ucles 201816 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 a curve is such that   xyx25dd 22 21 =--^h .   given that the curve has a gradient of 6 at the point ,29 32j lkkn poo,   find the equation of the curve.  [8]"
        },
        "0606_s18_qp_21.pdf": {
            "1": "*6234149436* this document consists of 15 printed pages and 1 blank page. dc (nf/sw) 145871/1 \u00a9 ucles 2018  [turn overcambridge international examinations cambridge international general certificate of secondary education additional mathematics  0606/21 paper 2  may/june 2018  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of   angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/21/m/j/18 \u00a9 ucles 2018 mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/21/m/j/18 \u00a9 ucles 2018 [turn over 1 a, b and c are subsets of the same universal set.  (i) write each of the following statements in words.   (a) ab1y [1]   (b) ac+ q= [1]  (ii) write each of the following statements in set notation.   (a) there are 3 elements in set a or b or both.  [1]   (b) x is an element of a but it is not an element of c. [1]",
            "4": "4 0606/21/m/j/18 \u00a9 ucles 2018 2 the variables x and y are such that  lnyx 31=- ^h    for x312.  (i) find xy dd. [2]  (ii) hence find the approximate change in x when y increases from .ln12^h  to ..ln12 0125+ ^h . [3]",
            "5": "5 0606/21/m/j/18 \u00a9 ucles 2018 [turn over 3 a 7-character password is to be selected from the 12 characters shown in the table. each character may  be used only once. characters upper-case letters a b c d lower-case letters e f g h digits 1 2 3 4  find the number of different passwords  (i) if there are no restrictions,  [1]  (ii) that start with a digit,  [1]  (iii) that contain 4 upper-case letters and 3 lower-case letters such that all the upper-case letters are  together and all the lower-case letters are together.  [3]",
            "6": "6 0606/21/m/j/18 \u00a9 ucles 2018 4 do not use a calculator in this question.  it is given that x4+ is a factor of   xx xa x 23 12 p2 3=+ +- ^h .   when xp^h is divided by x1- the  remainder is b.  (i) show that a 23=-  and find the value of the constant b. [2]  (ii) factorise xp^h completely and hence state all the solutions of x 0 p= ^h . [4]",
            "7": "7 0606/21/m/j/18 \u00a9 ucles 2018 [turn over 5 the function f is defined by   xx251f=-^h    for . x252 .  (i) find an expression for xf1-^h. [2]  (ii) state the domain of xf1-^h. [1]  (iii) find an expression for xf2^h, giving your answer in the form cx dax b ++, where a, b, c and d are  integers to be found.  [3]",
            "8": "8 0606/21/m/j/18 \u00a9 ucles 2018 6  x rad o cda b 16 cm40 cm  in the diagram aob  and doc  are sectors of a circle centre o. the angle aob  is x radians. the length  of the arc ab is 40  cm and the radius ob is 16  cm.  (i) find the value of x. [2]  (ii) find the area of sector aob . [2]  (iii) given that the area of the shaded region abcd  is 140 cm2, find the length of oc. [3]",
            "9": "9 0606/21/m/j/18 \u00a9 ucles 2018 [turn over 7 differentiate with respect to x  (i) tanxx4 , [2]  (ii) x 1ex 231 -+ . [3]",
            "10": "10 0606/21/m/j/18 \u00a9 ucles 2018 8 an experiment was carried out recording values of y for certain values of x. the variables x and y are  thought to be connected by the relationship ya xn= , where a and n are constants.  (i) transform the relationship ya xn=  into straight line form.  [2]  the values of ln  y and ln  x were plotted and a line of best fit drawn. this is shown in the diagram  below. 0012345 2 4 6 8ln xln y  (ii) use the graph to find the value of a and of n, stating the coordinates of the points that you use.  [3]  (iii) find the value of x when y = 50.  [2]",
            "11": "11 0606/21/m/j/18 \u00a9 ucles 2018 [turn over 9 (i) express   xx51 432--    in the form px qr2++^h , where p, q and r are constants.  [3]  (ii) sketch the graph of  yx x 51 432=- -   on the axes below. show clearly any points where your  graph meets the coordinate axes.  [4] oy x  (iii) state the set of values of k for which   xx k 51 432-- =   has exactly four solutions.  [2]",
            "12": "12 0606/21/m/j/18 \u00a9 ucles 2018 10 a particle moves in a straight line such that its displacement, s metres, from a fixed point o at time  t seconds, is given by   cos st43=+ ,   where t0h. the particle is initially at rest.  (i) find the exact value of t when the particle is next at rest.  [2]  (ii) find the distance travelled by the particle between t4r=  and t2r= seconds.  [3]  (iii) find the greatest acceleration of the particle.  [2]",
            "13": "13 0606/21/m/j/18 \u00a9 ucles 2018 [turn over 11 (a) solve    coss in xx 10 392+=    for \u00b0\u00b0x 0 36011 . [5]  (b) solve    tans in yy 32 42=    for y 011 r radians.  [5]",
            "14": "14 0606/21/m/j/18 \u00a9 ucles 2018 12 in this question all lengths are in metres. 30\u00b0x ha b 5 c  a water container is in the shape of a triangular prism. the diagrams show the container and  its cross -section. the cross-section of the water in the container is an isosceles triangle abc , with  angle  abc  = angle bac  = 30\u00b0. the length of ab is x and the depth of water is h. the length of the  container is 5.  (i) show that xh23=  and hence find the volume of water in the container in terms of h. [3]",
            "15": "15 0606/21/m/j/18 \u00a9 ucles 2018  (ii) the container is filled at a rate of 0.5  m3 per minute. at the instant when h is 0.25  m, find    (a) the rate at which h is increasing,  [4]   (b) the rate at which x is increasing.  [2]",
            "16": "16 0606/21/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.blank page"
        },
        "0606_s18_qp_22.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (kn/sw) 145515/2 \u00a9 ucles 2018  [turn over *4401850851* additional mathematics  0606/22 paper 2  may/june 2018  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge international examinations cambridge international general certificate of secondary education",
            "2": "2 0606/22/m/j/18 \u00a9 ucles 2018 mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/22/m/j/18 \u00a9 ucles 2018 [turn over 1 (i)  show that   coscot sinc osec ii ii+= . [3]  (ii) hence solve   coscot sin4 ii i+=   for  \u00b0\u00b009 0 ggi . [2] ",
            "4": "4 0606/22/m/j/18 \u00a9 ucles 2018 2 (a)  on the venn diagram below, shade the region that represents ab+l. /h5105 a b  [1]  (b) the universal set  \ue025  and sets  p, q and r are such that     ()pq r ,, q=l , () pq r ++ q= l ,     n( ) qr 8 +=,  n( )rp 8 +=, n( ) pq 10 += ,     n(p) = 21, n(q) = 15, n(\ue025) = 30.   complete the venn diagram to show this information and state the value of n( r). /h5105 p q r   n(r) =   [4]",
            "5": "5 0606/22/m/j/18 \u00a9 ucles 2018 [turn over 3 it is given that   x + 3   is a factor of the polynomial   ()xx ax xb 22 4 p32=+ -+ .   the remainder when  p (x) is divided by   x \u2212 2   is  \u221215. find the remainder when p  (x) is divided by   x + 1. [6]",
            "6": "6 0606/22/m/j/18 \u00a9 ucles 2018 4 find the coordinates of the points where the line   yx23 6 -=    intersects the curve  x y 4952 2 += .  [5]",
            "7": "7 0606/22/m/j/18 \u00a9 ucles 2018 [turn over 5 (a)  four parts in a play are to be given to four of the girls chosen from the seven girls in a drama class.  find the number of different ways in which this can be done.  [2]  (b) three singers are chosen at random from a group of 5 chinese, 4 indian and 2 british singers. find  the number of different ways in which this can be done if   (i) no chinese singer is chosen,  [1]   (ii) one singer of each nationality is chosen,  [2]   (iii) the three singers chosen are all of the same nationality.  [2]",
            "8": "8 0606/22/m/j/18 \u00a9 ucles 2018 6 1.5 rad o c deba 5 cm  in the diagram,  abc  is an arc of the circle centre o, radius 5  cm, and angle aoc is 1.5 radians. ad and  ce are diameters of the circle and de is a straight line.  (i) find the total perimeter of the shaded regions.  [3]  (ii) find the total area of the shaded regions.  [3]",
            "9": "9 0606/22/m/j/18 \u00a9 ucles 2018 [turn over 7 vectors i and j are vectors parallel to the x-axis and y-axis respectively.  given that   a = 2i + 3j,   b = i \u2212 5j   and   c = 3i + 11j,   find  (i) the exact value of   ac+, [2]  (ii) the value of the constant m such that   a + mb   is parallel to j, [2]  (iii) the value of the constant n such that   na \u2212 b = c. [2]",
            "10": "10 0606/22/m/j/18 \u00a9 ucles 2018 8 (a)  a = 2 11 3- -j lkkn poo and b = 0 32 5- -j lkkn poo. find ( ba)\u22121. [4]  (b)  the matrix  x is such that xc = d, where c = 2 05 103 4-j lkkn poo and d = 454-^h .    (i)  state the order of the matrix c. [1]   (ii) find the matrix  x. [2]",
            "11": "11 0606/22/m/j/18 \u00a9 ucles 2018 [turn over 9 (i)  differentiate  sin xx4^h   with respect to x. [4]  (ii) hence find   sincossin xxxxxx x 8d43++c ^h m y .  [3]  ",
            "12": "12 0606/22/m/j/18 \u00a9 ucles 2018 10 (a) (i) on the axes below, sketch the graph of  () () yx x35 =+ -   showing the coordinates of the  points where the curve meets the x-axis.  [2] oy x   (ii) write down a suitable domain for the function  () () () xx x35 f=+ -   such that f  has an  inverse.  [1]  (b) the functions g and h are defined by      ()xx 31 g=-   for x > 1,     h()xx4=  for x \u2260 0.   (i) find hg  (x). [1]   (ii) find (hg)\u20131(x). [2]  (c) given that  p( a) = b  and that the function p has an inverse, write down  p\u20131 (b). [1]",
            "13": "13 0606/22/m/j/18 \u00a9 ucles 2018 [turn over 11 (a)  find   d xx21-3y .  [2]   (b) (i) find   sinxx4dy . [2]   (ii) hence evaluate    sinxx4drr 84y . [2]  (c) show that    x3 edlnx 3 08= y . [5]",
            "14": "14 0606/22/m/j/18 \u00a9 ucles 2018 12 in this question all lengths are in centimetres.  the volume of a cone of height h and base radius r is given by  r vr h31 2= .  it is known that  rsin12 462=-,  rcos12 462=+,  rtan1223=- . hr 6radr  a water cup is in the shape of a cone with its axis vertical. the diagrams show the cup and its   cross-section. the vertical angle of the cone is r 6 radians. the depth of water in the cup is h. the  surface of the water is a circle of radius r.   (i) find an expression for r in terms of h and show that the volume of water in the cup is given by     r()vh 374 33 =-. [4]",
            "15": "15 0606/22/m/j/18 \u00a9 ucles 2018  (ii) water is poured into the cup at a rate of 30  cm3 s\u20131. find, correct to 2 decimal places, the rate at  which the depth of water is increasing when h = 5. [4]",
            "16": "16 0606/22/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.blank page"
        },
        "0606_s18_qp_23.pdf": {
            "1": "*5291701669* this document consists of 15 printed pages and 1 blank page. dc (jm) 162865 \u00a9 ucles 2018  [turn overcambridge international examinations cambridge international general certificate of secondary education additional mathematics  0606/23 paper 2  may/june 2018  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of   angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/23/m/j/18 \u00a9 ucles 2018 mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/23/m/j/18 \u00a9 ucles 2018 [turn over 1 a, b and c are subsets of the same universal set.  (i) write each of the following statements in words.   (a) ab1y [1]   (b) ac+ q= [1]  (ii) write each of the following statements in set notation.   (a) there are 3 elements in set a or b or both.  [1]   (b) x is an element of a but it is not an element of c. [1]",
            "4": "4 0606/23/m/j/18 \u00a9 ucles 2018 2 the variables x and y are such that  ln yx 31=- ^h    for x312.  (i) find xy dd. [2]  (ii) hence find the approximate change in x when y increases from . ln12^h  to .. ln12 0125+ ^h . [3]",
            "5": "5 0606/23/m/j/18 \u00a9 ucles 2018 [turn over 3 a 7-character password is to be selected from the 12 characters shown in the table. each character may  be used only once. characters upper-case letters a b c d lower-case letters e f g h digits 1 2 3 4  find the number of different passwords  (i) if there are no restrictions,  [1]  (ii) that start with a digit,  [1]  (iii) that contain 4 upper-case letters and 3 lower-case letters such that all the upper-case letters are  together and all the lower-case letters are together.  [3]",
            "6": "6 0606/23/m/j/18 \u00a9 ucles 2018 4 do not use a calculator in this question.  it is given that x4+ is a factor of   xx xa x 23 12 p2 3=+ +- ^h .   when xp^h is divided by x1- the  remainder is b.  (i) show that a 23=-  and find the value of the constant b. [2]  (ii) factorise xp^h completely and hence state all the solutions of x 0 p= ^h . [4]",
            "7": "7 0606/23/m/j/18 \u00a9 ucles 2018 [turn over 5 the function f is defined by   xx251f=-^h    for . x 252 .  (i) find an expression for x f1-^h. [2]  (ii) state the domain of x f1-^h. [1]  (iii) find an expression for xf2^h, giving your answer in the form cx dax b ++, where a, b, c and d are  integers to be found.  [3]",
            "8": "8 0606/23/m/j/18 \u00a9 ucles 2018 6  x rad o cda b 16 cm40 cm  in the diagram aob  and doc  are sectors of a circle centre o. the angle aob  is x radians. the length  of the arc ab is 40  cm and the radius ob is 16  cm.  (i) find the value of x. [2]  (ii) find the area of sector aob . [2]  (iii) given that the area of the shaded region abcd  is 140 cm2, find the length of oc. [3]",
            "9": "9 0606/23/m/j/18 \u00a9 ucles 2018 [turn over 7 differentiate with respect to x  (i) tanxx4 , [2]  (ii) x 1ex 231 -+ . [3]",
            "10": "10 0606/23/m/j/18 \u00a9 ucles 2018 8 an experiment was carried out recording values of y for certain values of x. the variables x and y are  thought to be connected by the relationship ya xn= , where a and n are constants.  (i) transform the relationship ya xn=  into straight line form.  [2]  the values of ln  y and ln  x were plotted and a line of best fit drawn. this is shown in the diagram  below. 0012345 2 4 6 8ln xln y  (ii) use the graph to find the value of a and of n, stating the coordinates of the points that you use.  [3]  (iii) find the value of x when y = 50.  [2]",
            "11": "11 0606/23/m/j/18 \u00a9 ucles 2018 [turn over 9 (i) express   xx51 432--    in the form px qr2++^h , where p, q and r are constants.  [3]  (ii) sketch the graph of  yx x 51 432=- -   on the axes below. show clearly any points where your  graph meets the coordinate axes.  [4] oy x  (iii) state the set of values of k for which   xx k 51 432-- =   has exactly four solutions.  [2]",
            "12": "12 0606/23/m/j/18 \u00a9 ucles 2018 10 a particle moves in a straight line such that its displacement, s metres, from a fixed point o at time  t seconds, is given by   cos st43=+ ,   where t0h. the particle is initially at rest.  (i) find the exact value of t when the particle is next at rest.  [2]  (ii) find the distance travelled by the particle between t4r=  and t2r= seconds.  [3]  (iii) find the greatest acceleration of the particle.  [2]",
            "13": "13 0606/23/m/j/18 \u00a9 ucles 2018 [turn over 11 (a) solve    coss in xx 10 392+=    for \u00b0\u00b0x 0 36011 . [5]  (b) solve    tans in yy 32 42=    for y 011 r radians.  [5]",
            "14": "14 0606/23/m/j/18 \u00a9 ucles 2018 12 in this question all lengths are in metres. 30\u00b0x ha b 5 c  a water container is in the shape of a triangular prism. the diagrams show the container and  its cross -section. the cross-section of the water in the container is an isosceles triangle abc , with  angle  abc  = angle bac  = 30\u00b0. the length of ab is x and the depth of water is h. the length of the  container is 5.  (i) show that xh23=  and hence find the volume of water in the container in terms of h. [3]",
            "15": "15 0606/23/m/j/18 \u00a9 ucles 2018  (ii) the container is filled at a rate of 0.5  m3 per minute. at the instant when h is 0.25  m, find    (a) the rate at which h is increasing,  [4]   (b) the rate at which x is increasing.  [2]",
            "16": "16 0606/23/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.blank page"
        },
        "0606_w18_qp_11.pdf": {
            "1": "*0088942780* this document consists of 15 printed pages and 1 blank page. dc (rw/sg) 153502/3 \u00a9 ucles 2018  [turn overadditional mathematics  0606/11 paper 1  october/november 2018  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge international examinations cambridge international general certificate of secondary education",
            "2": "2 0606/11/o/n/18 \u00a9 ucles 2018 mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, xabb ac 242!=-- . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/11/o/n/18 \u00a9 ucles 2018 [turn over 1 (a) on the axes below, sketch the graph of   cos yx32 1 =- ,   for \u00b0\u00b0 \u00b0 x 0 360 gg . 5 4 3 2 1 0 \u20131 \u20132 \u20133 \u20134 \u20135 \u20136xy 90 180 270 360  [3]  (b) given that   sin yx46= ,   write down   (i) the amplitude of y, [1]   (ii) the period of y. [1]",
            "4": "4 0606/11/o/n/18 \u00a9 ucles 2018 2     ()xx xx a 25 4 p32=+ ++      ()xx ax b 43 q2=+ +  given that p( x) has a remainder of   2 when divided by   x21+   and that q( x) is divisible by   x2+,  (i) find the value of each of the constants a and b. [3]  given that   () () () xx x rp q =-    and using your values of a and b,  (ii) find the exact remainder when r( x) is divided by   x32-. [3]",
            "5": "5 0606/11/o/n/18 \u00a9 ucles 2018 [turn over 3 the coefficient of x2 in the expansion of   () ()xk x 236-+    is equal to 972. find the possible values of the  constant  k. [6]",
            "6": "6 0606/11/o/n/18 \u00a9 ucles 2018 4 (i) write   xx982-+    in the form   ()xp q2-- ,   where p and q are constants.  [2]  (ii) hence write down the coordinates of the minimum point on the curve   yx x982=- +. [1]  (iii) on the axes below, sketch the graph of    yx x982=- +,   showing the coordinates of the points  where the curve meets the coordinate axes. 20 16 812 4 0 \u20138\u20134 \u201312 \u201316xy 10 8 6 4 2 \u20132  [3]  (iv) write down the value of k for which   xx k 982-+ =   has exactly 3  solutions.  [1]",
            "7": "7 0606/11/o/n/18 \u00a9 ucles 2018 [turn over 5 r cm o\u03b8a brad  the diagram shows a circle with centre o and radius r cm. the minor arc ab is such that angle aob  is  i radians. the area of the minor sector aob  is 48  cm2.  (i) show that   r96 2i= . [2]  (ii) given that the minor arc ab has length 12  cm, find the value of r and of i. [3]  (iii) using your values of r and i, find the area of the shaded region.  [2]",
            "8": "8 0606/11/o/n/18 \u00a9 ucles 2018 6 a curve has equation   ()lnyxx 52232 =++.  (i) show that   lnxy 453dd=-    when x0=. [4]  (ii) hence find the equation of the tangent to the curve at the point where x0=. [2]",
            "9": "9 0606/11/o/n/18 \u00a9 ucles 2018 [turn over 7 (a) express   lg lgxy 23+-    as a single logarithm to base 10.  [3]  (b) (i) solve   xx6730 +- =. [2]   (ii) hence, given that   logl oga 6 373 0a 3+- =,   find the possible values of a. [4]",
            "10": "10 0606/11/o/n/18 \u00a9 ucles 2018 8 (i) find   ()xx54dd 223+ . [2]  (ii) hence find   ()xx x 54 d221+ y . [2]  given that   ()xx x 541519da 2 021+= y ,  (iii) find the value of the positive constant a. [4]",
            "11": "11 0606/11/o/n/18 \u00a9 ucles 2018 [turn over 9 variables s and t are such that   st43 et=+-.  (i) find the value of s when t0=. [1]  (ii) find the exact value of t when ts2dd=. [4]  (iii) find the approximate increase in s when t increases from ln5 to ln h5+, where h is small.  [3]",
            "12": "12 0606/11/o/n/18 \u00a9 ucles 2018 10 particle a is at the point with position vector 2 5-j lkkn poo at time t = 0 and moves with a speed of 10  ms-1 in the  same direction as 3 4j lkkn poo.  (i) given that a is at the point with position vector a38j lkkn poo when t = 6 s, find the value of the constant a. [3]  particle b is at the point with position vector 16 37j lkkn poo at time t = 0 and moves with velocity 4 2j lkkn poo ms-1.  (ii) write down, in terms of t, the position vector of b at time t s. [1]",
            "13": "13 0606/11/o/n/18 \u00a9 ucles 2018 [turn over  (iii) verify that particles a and b collide.  [4]  (iv) write down the position vector of the point of collision.  [1]",
            "14": "14 0606/11/o/n/18 \u00a9 ucles 2018 11 (a) () cos xx 32 f=-    for rx02gg .   (i) write down the range of f.  [2]   (ii) find the exact value of (.)25f1-. [3]",
            "15": "15 0606/11/o/n/18 \u00a9 ucles 2018  (b) ()xx 3 g2=-    for xr!.   find the exact solutions of ()x 6 g2=- . [4]",
            "16": "16 0606/11/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"
        },
        "0606_w18_qp_12.pdf": {
            "1": "*7206840868* this document consists of 16 printed pages. dc (st/jg) 153501/2 \u00a9 ucles 2018  [turn overcambridge international examinations cambridge international general certificate of secondary education additional mathematics  0606/12 paper 1  october/november 2018  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/12/o/n/18 \u00a9 ucles 2018 mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, xabb ac 242!=-- . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/12/o/n/18 \u00a9 ucles 2018 [turn over 1 solve   (\u00b0 ) sinx 12 50 0 ++ =   for \u00b0\u00b0x 180 180 gg - . [4] ",
            "4": "4 0606/12/o/n/18 \u00a9 ucles 2018 2 find the equation of the curve which has a gradient of 4 at the point (, ) 03- and is such that   xy5ddex 22 2=+ . [5]",
            "5": "5 0606/12/o/n/18 \u00a9 ucles 2018 [turn over 3 (i) on the axes below, sketch the graph of   yx 63=- ,   showing the coordinates of the points where the  graph meets the coordinate axes.  [2] 1012 8 46 2 0 \u20134\u20132 \u20136 \u20138 \u201310 \u201312xy 5 6 4 3 2 1 \u20131 \u20132  (ii) solve   x 63 2 -= . [3]  (iii) hence find the values of x for which   x 63 22 - . [1]",
            "6": "6 0606/12/o/n/18 \u00a9 ucles 2018 4   ()ln yx x1 23=+  (i) find the value of  xy dd when . x03= . you must show all your working.  [4]  (ii) hence find the approximate increase in y when x increases from 0.3 to .h 03+, where h is small.  [1]",
            "7": "7 0606/12/o/n/18 \u00a9 ucles 2018 [turn over 5 the 7th term in the expansion of ()ab x12+  in ascending powers of x is x9246. it is given that a and b are  positive constants.  (i)  show that ba1=. [2]  the 6th term in the expansion of ()ab x12+  in ascending powers of x is x1985.  (ii) find the value of a and of b. [4]",
            "8": "8 0606/12/o/n/18 \u00a9 ucles 2018 6 (i) find   ()xx5 125dd 232- . [2]  (ii) using your answer to part  (i), find   ()xx x 5 125 d231--y . [2]  (iii)  hence find   ()xxx5 125 d2 610 31--y . [2]",
            "9": "9 0606/12/o/n/18 \u00a9 ucles 2018 [turn over 7 (a) the vector v has a magnitude of 39 units and is in the same direction as 12 5-eo . write v in the    form a beo, where a and b are constants.  [2]  (b) vectors p and q are such that rs rp6=+ +eo  and r sq51 21=+ -eo , where r and s are constants. given that   pq230 0+= eo, find the value of r and of s. [4]",
            "10": "10 0606/12/o/n/18 \u00a9 ucles 2018 8   a aa43 4=+eo  (i) find the values of the constant a for which a1- does not exist.  [3]    (ii) given that a4=, find a1-. [2]  (iii) hence find the matrix b such that ab2 43 5=-eo . [3]",
            "11": "11 0606/12/o/n/18 \u00a9 ucles 2018 [turn over 9 the polynomial    ()xa xb xc x9 p32=+ +-     is divisible by x3+. it is given that ()03 6 p= l  and ()08 6 p = ll .  (i) find the value of each of the constants a, b and c.  [6]  (ii) using your values of a, b and c, find the remainder when ()xp is divided by x21-. [2]",
            "12": "12 0606/12/o/n/18 \u00a9 ucles 2018 10 y x 0y = a + 4 cos  bx6 6 mp r  the diagram shows part of the curve   cos ya bx 4 =+ ,   where a and b are positive constants. the curve  meets the y-axis at the point (,)06 and the x-axis at the point ,60rbl . the curve meets the x-axis again at the  point  p and has a minimum at the point m.  (i) find the value of a and of b. [3]",
            "13": "13 0606/12/o/n/18 \u00a9 ucles 2018 [turn over  using your values of a and b find,  (ii) the exact coordinates of p, [2]  (iii) the exact coordinates of m. [2]",
            "14": "14 0606/12/o/n/18 \u00a9 ucles 2018 11 r cm o   radip q  the diagram shows the sector opq  of a circle, centre o, radius r cm, where angle poq i= radians. the  perimeter of the sector is 10  cm.  (i) show that area, a cm2, of the sector is given by    ()a50 22ii=+. [5]",
            "15": "15 0606/12/o/n/18 \u00a9 ucles 2018 [turn over  it is given that i can vary and a has a maximum value.  (ii) find the maximum value of a. [5] question 12 is printed on the next page.",
            "16": "16 0606/12/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.12 the line   yx25=+    intersects the curve   yxy5 +=    at the points a and b. find the coordinates of the  point where the perpendicular bisector of the line ab intersects the line yx=. [9]"
        },
        "0606_w18_qp_13.pdf": {
            "1": "*3103611472* this document consists of 15 printed pages and 1 blank page. dc (st/jg) 153500/3 \u00a9 ucles 2018  [turn overcambridge international examinations cambridge international general certificate of secondary education additional mathematics  0606/13 paper 1  october/november 2018  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/13/o/n/18 \u00a9 ucles 2018 mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, xabb ac 242!=-- . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/13/o/n/18 \u00a9 ucles 2018 [turn over 1 (a) in the expansion of   ()px25+    the coefficient of x3 is equal to 258-  . find the value of the constant p.  [3]  (b) find the term independent of x in the expansion of   xx241 2 28 + eo . [3]",
            "4": "4 0606/13/o/n/18 \u00a9 ucles 2018 2  r cm oi radp q  the diagram shows a sector poq  of a circle, centre o, radius r cm, where angle poq i= radians. the  perimeter of the sector is 20  cm.    (i) show that the area, a cm2, of the sector is given by  ar r 102=- . [3]  it is given that r can vary and that a has a maximum value.  (ii) find the value of i for which a has a maximum value.    [3]",
            "5": "5 0606/13/o/n/18 \u00a9 ucles 2018 [turn over 3 do not use a calculator in this question.  in this question, all lengths are in centimetres.  a triangle abc  is such that angle \u00b0, ba b 90 53 5 == +  and  bc 53 5 =- .  (i) find, in its simplest surd form, the length of ac. [3]  (ii) find tanbca, giving your answer in the form ab 3+ , where a and b are integers.  [3]",
            "6": "6 0606/13/o/n/18 \u00a9 ucles 2018 4 in this question, the units of x are radians and the units of y are centimetres.  it is given that   ()cos yx 1310=+ .  (i) find the value of  xy dd when x2r=. [4]  given also that y is increasing at a rate of 6  cm s\u22121 when x2r=,  (ii) find the corresponding rate of change of x. [2]",
            "7": "7 0606/13/o/n/18 \u00a9 ucles 2018 [turn over 5 (i) show that   logl og 4293= . [2]  (ii) hence solve   logl ogx 4393+= . [3]",
            "8": "8 0606/13/o/n/18 \u00a9 ucles 2018 6 a particle p is moving in a straight line such that its displacement, s m, from a fixed point o at time t s, is  given by   st12 41 2 e.t05=+ --.  (i) find the value of t when p is instantaneously at rest.  [3]  (ii) find an expression for the acceleration of p at time t s. [2]  (iii) find the value of s when the acceleration of p is 0.3  ms\u22122. [3]  (iv) explain why the acceleration of the particle will always be positive.  [1]",
            "9": "9 0606/13/o/n/18 \u00a9 ucles 2018 [turn over 7  a b d o c  the diagram shows a quadrilateral oabc . the point d lies on ob such that   od db2=    and   ad mac= ,  where m is a scalar quantity. oa a=   ob b=   oc c=  (i) find ad in terms of m, a and c. [1]  (ii) find ad in terms of a and b. [2]  (iii) given that   ab c 15 16 9 =- ,   find the value of m. [3]",
            "10": "10 0606/13/o/n/18 \u00a9 ucles 2018 8   () sin xx54f=+    for   x02gg r radians    ()xx3gr=-    for   xr!  (i) write down the range of ()xf. [2]  (ii) find ()xf1- and write down its range.  [3]  (iii) solve   ()x21 1 fg= . [4]",
            "11": "11 0606/13/o/n/18 \u00a9 ucles 2018 [turn over 9 find the equation of the normal to the curve   ()lnyxx31 22 =+   at the point where x2=, giving your answer   in the form ym xc=+ , where m and c are correct to 2 decimal places. you must show all your working.  [8]",
            "12": "12 0606/13/o/n/18 \u00a9 ucles 2018 10 xy = 12 + x \u2013 x2y ob ay = x + 8  the diagram shows the curve   yx x 122=+ -   intersecting the line  yx 8=+    at the points a and b.  (i) find the coordinates of the points a and b. [3]  (ii) find   () xx x 12 d2+- y . [2]",
            "13": "13 0606/13/o/n/18 \u00a9 ucles 2018 [turn over  (iii) showing all your working, find the area of the shaded region.  [4]",
            "14": "14 0606/13/o/n/18 \u00a9 ucles 2018 11 the polynomial   ()xa xx bx 17 8 p32=+ +-    is divisible by   x21-   and has a remainder of  35-  when  divided by   x3+.  (i) by finding the value of each of the constants a and b, verify that  ab=. [4]  using your values of a and b,   (ii) find ()xp in the form  )() (xx21 q- , where ()xq is a quadratic expression,  [2]",
            "15": "15 0606/13/o/n/18 \u00a9 ucles 2018  (iii) factorise ()xp completely,  [1]  (iv) solve   sins in sin ab 17 8032ii i ++ -=    for   \u00b0\u00b00 18011i . [3]",
            "16": "16 0606/13/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"
        },
        "0606_w18_qp_21.pdf": {
            "1": "this document consists of 14 printed pages and 2 blank pag es. dc (st/jg) 153499/2 \u00a9 ucles 2018  [turn over *1207805813* additional mathematics  0606/21 paper 2  october/november 2018  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of   angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge international examinations cambridge international general certificate of secondary education",
            "2": "2 0606/21/o/n/18 \u00a9 ucles 2018 mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, xabb ac 242!=-- . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/21/o/n/18 \u00a9 ucles 2018 [turn over 1 solve the inequality   () ()xx29 101 -+ . [4] 2 (a) solve   31 0x 21=-b l. [3]  (b) solve   23eeyy12 32=-+. [4]",
            "4": "4 0606/21/o/n/18 \u00a9 ucles 2018 3 do not use a calculator in this question.  (a) simplify   () () 22 54 23 5 +- ,   giving your answer in the form ab c+ , where a, b and c are  integers.  [3]  (b) simplify   343 6 2- +,   giving your answer in the form pq32+ , where p and q are integers.  [4] ",
            "5": "5 0606/21/o/n/18 \u00a9 ucles 2018 [turn over 4  solve   secc ot tan xx x 5 =-    for \u00b0\u00b0x 0 36011 . [6]",
            "6": "6 0606/21/o/n/18 \u00a9 ucles 2018 5   a3 12 1=-eo .  (i) find a2. [2]  (ii) find constants p and q such that   pqaa i2+= . [4]",
            "7": "7 0606/21/o/n/18 \u00a9 ucles 2018 [turn over 6  a 5-digit code is to be formed from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9. each digit can be used once only in any  code. find how many codes can be formed if   (i) the first digit of the code is 6 and the other four digits are odd,  [2]  (ii) each of the first three digits is even,  [2]  (iii) the first and last digits are prime.  [2]",
            "8": "8 0606/21/o/n/18 \u00a9 ucles 2018 7 (i) show that   cosc oscoseccotxxxx11 112--+= . [4]  (ii) hence solve the equation   cosc ossecxxx11 11 --+=    for x02gg r radians.  [4]",
            "9": "9 0606/21/o/n/18 \u00a9 ucles 2018 [turn over 8 y x 0 5bae yxx 52=+-  the diagram shows part of the curve   yx ex52=+-,   the normal to the curve at the point a and the   line x5=. the normal to the curve at a meets the y-axis at the point b. the x-coordinate of a is 2.5.  (i) find the equation of the normal ab. [4]  (ii) showing all your working, find the area of the shaded region.  [6]",
            "10": "10 0606/21/o/n/18 \u00a9 ucles 2018 9 in this question, all lengths are in metres. y 2r  the diagram shows a window formed by a semi-circle of radius r on top of a rectangle with dimensions  2r by y. the total perimeter of the window is 5.  (i) find y in terms of r. [2]  (ii) show that the total area of the window is   arrr 52222 r=- - . [2]",
            "11": "11 0606/21/o/n/18 \u00a9 ucles 2018 [turn over  (iii) given that r can vary, find the value of r which gives a maximum area of the window and find this  area. (you are not required to show that this area is a maximum.)  [5] ",
            "12": "12 0606/21/o/n/18 \u00a9 ucles 2018 10 the line   yx12 2 =-    is a tangent to two curves. each curve has an equation of the form  yk kxx 62=+ +- , where k is a constant.  (i) find the two values of  k. [5]",
            "13": "13 0606/21/o/n/18 \u00a9 ucles 2018 [turn over  the line   yx12 2 =-    is a tangent to one curve at the point a and the other curve at the point b.   (ii) find the coordinates of a and of b. [3]  (iii) find the equation of the perpendicular bisector of ab. [3]",
            "14": "14 0606/21/o/n/18 \u00a9 ucles 2018 11 r nhx x x \u2013 215 9  there are 70 girls in a year group at a school. the venn diagram gives some  information about the numbers  of these girls who play rounders ( r), hockey ( h) and netball ( n).   n(r) = 28     n(h) = 38     n(n) = 35.  find the value of x and hence the number of girls who play netball only.  [6]",
            "15": "15 0606/21/o/n/18 \u00a9 ucles 2018 blank page",
            "16": "16 0606/21/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"
        },
        "0606_w18_qp_22.pdf": {
            "1": "*4429896348* this document consists of 15 printed pages and 1 blank page. dc (sc/cgw) 153503/3 \u00a9 ucles 2018  [turn overadditional mathematics  0606/22 paper 2  october/november 2018  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of   angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge international examinations cambridge international general certificate of secondary education",
            "2": "2 0606/22/o/n/18 \u00a9 ucles 2018 mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/22/o/n/18 \u00a9 ucles 2018 [turn over 1 solve the inequality   () () xx x 34 132 -+ +. [3] 2 /h5105 f c  there are 105 boys in a year group at a school. some boys play football ( f) and some play cricket ( c). \u2022 x boys play both football and cricket. \u2022 the number of boys that play neither game is the same as the number of boys that play both. \u2022 40 boys play cricket. \u2022 the number of boys that only play football is twice the number of boys that only play cricket.  complete the venn diagram and find the value of x. [5]",
            "4": "4 0606/22/o/n/18 \u00a9 ucles 2018 3 a curve has equation   sinyxx 23 =  .   find  (i) xy dd , [3]  (ii) the equation of the tangent to the curve at the point where rx4=. [3]",
            "5": "5 0606/22/o/n/18 \u00a9 ucles 2018 [turn over 4 solve  (i) 26x31=-, [3]  (ii) () loglogy14 132 y3+= +  . [5]",
            "6": "6 0606/22/o/n/18 \u00a9 ucles 2018 5 solve the simultaneous equations    482qp111=+ ,  39pq 31253=+ 27.  [5]",
            "7": "7 0606/22/o/n/18 \u00a9 ucles 2018 [turn over 6 (a) a 5-character code is to be formed from the 13 characters shown below. each character may be used  once only in any code.     letters  : a,  b,  c,  d,  e,  f     numbers: 1,  2,  3,  4,  5,  6,  7   find the number of different codes in which no two letters follow each other and no two numbers  follow each other.  [3]  (b) a netball team of 7 players is to be chosen from 10 girls. 3 of these 10 girls are sisters. find the number  of different ways the team can be chosen if the team does not contain all 3 sisters.  [3]",
            "8": "8 0606/22/o/n/18 \u00a9 ucles 2018 7 solve the quadratic equation    xx 13 13 02-+ ++ = `` jj ,   giving your answer in the form ab 3+ ,  where a and b are constants.  [6]",
            "9": "9 0606/22/o/n/18 \u00a9 ucles 2018 [turn over 8 (i) show that   sins intans ecxxxx11 112--+= . [4]  (ii) hence solve the equation   sins incose cxxx11 11 --+=    for \u00b0\u00b0x 0 360 gg . [4]",
            "10": "10 0606/22/o/n/18 \u00a9 ucles 2018 9 o ba (4, 4)y = 2\u221axy x  the diagram shows part of the curve   yx2= .   the normal to the curve at the point a (4, 4) meets the  x-axis at the point b.  (i) find the equation of the line  ab. [4]  (ii) find the coordinates of  b. [1]",
            "11": "11 0606/22/o/n/18 \u00a9 ucles 2018 [turn over  (iii) showing all your working, find the area of the shaded region.  [4]",
            "12": "12 0606/22/o/n/18 \u00a9 ucles 2018 10 two lines are tangents to the curve    yx x 12 42=- -.   the equation of each tangent is of the form  yk kx 21=+ -, where k is a constant.  (i) find the two possible values of k. [5]",
            "13": "13 0606/22/o/n/18 \u00a9 ucles 2018 [turn over  (ii) find the coordinates of the point of intersection of the two tangents.  [4]",
            "14": "14 0606/22/o/n/18 \u00a9 ucles 2018 11 the functions f and g are defined for real values of x1h  by  ()xx 43 f=- ,  ()xxx 3121g=-+.  (i) find ()xgf . [2]  (ii) find ()x g1-. [3]  (iii) solve ()xx 1 fg=- . [4]",
            "15": "15 0606/22/o/n/18 \u00a9 ucles 2018 12 a plane that can travel at 260  km/h in still air heads due north. a wind with speed 40  km/h from a bearing of  310\u00b0 blows the plane off course. find the resultant speed of the plane and its direction as a bearing correct to  1 decimal place.  [6]",
            "16": "16 0606/22/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.blank page"
        },
        "0606_w18_qp_23.pdf": {
            "1": "*7180504136* this document consists of 15 printed pages and 1 blank page. dc (st/sw) 153497/2 \u00a9 ucles 2018  [turn overcambridge international examinations cambridge international general certificate of secondary education additional mathematics  0606/23 paper 2  october/november 2018  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles in  degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/23/o/n/18 \u00a9 ucles 2018 mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, xabb ac 242!=-- . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/23/o/n/18 \u00a9 ucles 2018 [turn over 1  solve the equation   xx53 31 3 -= -+ . [3] 2  on each of the venn diagrams below, shade the region indicated. a b c a b ca b c(a /h33371 b /h33371 c)' (a /h33370 b) /h33371 c' a /h33370 b /h33370 c' [3]",
            "4": "4 0606/23/o/n/18 \u00a9 ucles 2018 3  (i) write   xx 872+-    in the form ()ax b2-- , where a and b are constants.  [3]  (ii) hence state the maximum value of   xx 872+-    and the value of x at which it occurs.  [2]  (iii)  using your answer to part (i) , or otherwise, solve the equation   zz 87 024+- = . [3]",
            "5": "5 0606/23/o/n/18 \u00a9 ucles 2018 [turn over 4     ()y xxx213 d d2 24=++  (i) find xy dd, given that xy1dd= when x1=. [3]  (ii) find y in terms of x, given that y3= when x1=. [3]",
            "6": "6 0606/23/o/n/18 \u00a9 ucles 2018 5 given that a2 13 4=eo  and b1 24 5=-eo , find  (i) a1-, [2]  (ii) the matrix c such that ca b=, [2]  (iii) the matrix d such that ad bi1+=-. [3]",
            "7": "7 0606/23/o/n/18 \u00a9 ucles 2018 [turn over 6  solve the simultaneous equations  ()log xy232+= , logl ogxy3122= - .   [5]",
            "8": "8 0606/23/o/n/18 \u00a9 ucles 2018 7  a squad of 20 boys, which includes 2 sets of twins, is available for selection for a cricket team of 11 players.  calculate the number of different teams that can be selected if  (i) there are no restrictions,  [1]  (ii) both sets of twins are selected,  [2]  (iii) one set of twins is selected but neither twin from the other set is selected,  [2]  (iv) exactly one twin from each set of twins is selected.  [2]",
            "9": "9 0606/23/o/n/18 \u00a9 ucles 2018 [turn over 8 variables x and y are such that when y2 is plotted against e2x a straight line is obtained which passes through  the points (1.5, 5.5) and (3.7, 12.1). find  (i) y in terms of e2x, [3]  (ii) the value of y when x3=, [1]  (iii) the value of x when y50= . [3]",
            "10": "10 0606/23/o/n/18 \u00a9 ucles 2018 9 (a) solve   sinx 243r+=bl    for x011 r radians.  [3]  (b)  solve   secc osec yy 34 =    for \u00b0\u00b0y 0 36011 . [3]",
            "11": "11 0606/23/o/n/18 \u00a9 ucles 2018 [turn over  (c)  solve   cott an cosec zz z 72-=    for \u00b0\u00b0z 0 36011 . [6]",
            "12": "12 0606/23/o/n/18 \u00a9 ucles 2018 10  the equation of a curve is   yx x32=+    for x 3h-.  (i) find xy dd . [3]  (ii) find the equation of the tangent to the curve   yx x32=+     at the point where x1=. [3]",
            "13": "13 0606/23/o/n/18 \u00a9 ucles 2018 [turn over  (iii) find the coordinates of the turning points of the curve   yx x32=+  . [4]",
            "14": "14 0606/23/o/n/18 \u00a9 ucles 2018 11  a line with equation   yx k 55=- ++    is a tangent to a curve with equation   yk xx 72=- -.   (i) find the two possible values of k. [5]  (ii) find, for each  of your values of k,   \u2022 the equation of the tangent   \u2022 the equation of the curve   \u2022 the coordinates of the point of contact of the tangent and the curve.  [5]",
            "15": "15 0606/23/o/n/18 \u00a9 ucles 2018    (iii) find the distance between the two points of contact.  [2]",
            "16": "16 0606/23/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.blank page"
        }
    },
    "2019": {
        "0606_m19_qp_12.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (jm/cb) 165270/2 \u00a9 ucles 2019  [turn over *6715046212*cambridge assessment international education cambridge international general certificate of secondary education additional mathematics  0606/12 paper 1  february/march 2019  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/12/f/m/19 \u00a9 ucles 2019 mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/12/f/m/19 \u00a9 ucles 2019 [turn over 1 (a) given that  \ue025{: }, xx12 0 11 =  a = {multiples of 3},  b = {multiples of 4},   find   (i)  n(),a [1]   (ii)  n( ). ab+  [1]  (b) on the venn diagram below, draw the sets p, q and r such that  pq1  and  . qr+ q= \t\t\t \t\t \ue025  [2]  (c) using set notation, describe the shaded areas shown in the venn diagrams below. s tx y z/h5105 /h5105   ..  ...  [2]",
            "4": "4 0606/12/f/m/19 \u00a9 ucles 2019 2 on the axes below, sketch the graph of the curve   yx x 25 32=- -,   stating the coordinates of any points  where the curve meets the coordinate axes. xy 10 \u2013100 \u20131 4  [4]",
            "5": "5 0606/12/f/m/19 \u00a9 ucles 2019 [turn over 3 (i) find the first 3 terms in the expansion, in ascending powers of x, of x396 -fp . give the terms in their  simplest form.  [3]  (ii) hence find the term independent of x in the expansion of xxx39262 --ff pp . [3]",
            "6": "6 0606/12/f/m/19 \u00a9 ucles 2019 4 the polynomial   ()xx ax bx 24 9 p32=+ +- ,   where a and b are constants.    when ()xpl is divided by    x +\u20093   there is a remainder of -24 .  (i) show that ab67 8 -=  . [2]  it is given that    2 x - 1    is a factor of p  (x).  (ii) find the value of a and of b. [4]  (iii) write p  (x) in the form () () xx21 q- , where q  (x) is a quadratic factor.  [2]  (iv) hence factorise p  (x) completely.  [1]",
            "7": "7 0606/12/f/m/19 \u00a9 ucles 2019 [turn over 5 it is given that . log xp4= giving your answer in its simplest form, find, in terms of p,  (i)  ()log x164, [2]  (ii)  logx 25647 fp . [2]  using your answers to parts  (i) and (ii),  (iii) solve   ()logl og xx162565447 -= fp ,   giving your answer correct to 2 decimal places.  [3]",
            "8": "8 0606/12/f/m/19 \u00a9 ucles 2019 6 (a) given that  a1 02 1=-eo ,  b1 2 34 5 1=- fp   and  c 32 0 =-` j, write down the matrix products which   are possible. you do not need to evaluate your products.  [2]  (b) it is given that   x2 52 3=-eo    and   y4 21 0=eo .   (i) find  x-1. [2]   (ii) hence find the matrix z such that  xz =\u2009y. [3]",
            "9": "9 0606/12/f/m/19 \u00a9 ucles 2019 [turn over 7 do not use a calculator in this question.  all lengths in this question are in centimetres. a b c d5 23+ 5 10 2- 5 63+  the diagram shows the trapezium abcd , where ab 23 5 =+ , dc 63 5 =+ , ad 10 25 =-  and  angle  adc = 90\u00b0.  (i) find the area of abcd , giving your answer in the form ab 5+ , where a and b are integers.  [3]  (ii) find cotbcd, giving your answer in the form cd 5+ , where c and d are fractions in their simplest  form.  [3]",
            "10": "10 0606/12/f/m/19 \u00a9 ucles 2019 8 (a) 05101520v 2 4 6 8 10 t  the diagram shows the velocity-time graph of a particle p moving in a straight line with velocity v ms-1 at  time t seconds after leaving a fixed point.  (i) write down the value of the acceleration of  p when t =\u20095. [1]  (ii) find the distance travelled by the particle  p between t =\u20090 and t =\u200910. [2]",
            "11": "11 0606/12/f/m/19 \u00a9 ucles 2019 [turn over  (b) a particle q moves such that its velocity, v ms-1, t seconds after leaving a fixed point, is given by   sin vt32 1 =- .   (i) find the speed of q when t7 12r= . [2]   (ii) find the least value of t for which the acceleration of q is zero.  [3]",
            "12": "12 0606/12/f/m/19 \u00a9 ucles 2019 9 the area of a sector of a circle of radius r cm is 36  cm2.  (i) show that the perimeter, p cm, of the sector is such that prr272=+ . [3]  (ii) hence, given that r can vary, find the stationary value of  p and determine its nature.  [4]",
            "13": "13 0606/12/f/m/19 \u00a9 ucles 2019 [turn over 10 a curve is such that when x = 0, both y =\u2009-5 and xy10dd= . given that   xy43ddex 22 2=+ ,   find  (i) the equation of the curve,  [7]  (ii) the equation of the normal to the curve at the point where x41=. [3]",
            "14": "14 0606/12/f/m/19 \u00a9 ucles 2019 11 (a) solve    sincos tan xx x21=    for \u00b0x 0 180\u00b0 gg . [3]",
            "15": "15 0606/12/f/m/19 \u00a9 ucles 2019  (b) (i) show that   seccotsincos iiii -= . [3]   (ii) hence solve    seccotsin333 21iii-=     for 32 32ggrri -  , where i is in radians.  [4]",
            "16": "16 0606/12/f/m/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"
        },
        "0606_m19_qp_22.pdf": {
            "1": "this document consists of 14 printed pages and 2 blank pages. dc (ks/tp) 165271/2 \u00a9 ucles 2019  [turn overcambridge assessment international education cambridge international general certificate of secondary education *1438509375* additional mathematics  0606/22 paper 2  february/march 2019  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/22/f/m/19 \u00a9 ucles 2019 mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/22/f/m/19 \u00a9 ucles 2019 [turn over 1 a band can play 25 different pieces of music. from these pieces of music, 8 are to be selected for a concert.  (i) find the number of different ways this can be done.  [1]  the 8 pieces of music are then arranged in order.  (ii) find the number of different arrangements possible.  [1]  the band has 15 members. three members are chosen at random to be the treasurer, secretary and agent.    (iii) find the number of ways in which this can be done.  [1] 2 variables x and y are related by the equation    yx eln x= .  (i) show that     .ln y x xxx dd el x =- [4]  (ii) hence find the approximate change in y as x increases from 2 to 2 + h, where h is small.  [2]",
            "4": "4 0606/22/f/m/19 \u00a9 ucles 2019 3 the function f is defined, for x 0 360 ggcc , by () sin xa bc x f=+ , where a, b and c are constants with  b02 and c02. the graph of () yxf=  meets the y-axis at the point (0, -1), has a period of 120\u00b0 and an  amplitude of 5.   (i) sketch the graph of  () yxf=   on the axes below.  [3] 60\u00b0 0\u00b0 120\u00b0 180\u00b0 240\u00b0 300\u00b0 360\u00b06 \u2013 6y x0  (ii) write down the value of each of the constants a, b and c. [2] a = .   b = .   c = .",
            "5": "5 0606/22/f/m/19 \u00a9 ucles 2019 [turn over 4 (a) find the values of x for which   . xx21 342g++` j  [3]  (b) show that, whatever the value of k, the equation    xkxk41022++ +=    has no real roots.  [3]",
            "6": "6 0606/22/f/m/19 \u00a9 ucles 2019 5 solutions to this question by accurate drawing will not be accepted.  the points a(3, 2), b(7, -4), c(2, -3) and d(k, 3) are such that cd is perpendicular to ab. find the   equation of the perpendicular bisector of cd. [6]",
            "7": "7 0606/22/f/m/19 \u00a9 ucles 2019 [turn over 6 the relationship between experimental values of two variables, x and y, is given by  ya bx= , where a and  b are constants.  (i) transform the relationship ya bx=  into straight line form.  [2]  the diagram shows lny plotted against x for ten different pairs of values of x and y. the line of best fit has  been drawn. 8 7 6 5 4 3 2 1 0 1 2 3 4 xln y  (ii) find the equation of the line of best fit and the value, correct to 1 significant figure, of a and of b. [4]  (iii) find the value, correct to 1 significant figure, of y when x = 2.7. [2]",
            "8": "8 0606/22/f/m/19 \u00a9 ucles 2019 7 (i) given that   yx x12=+ ,   show that   xy xax b 1dd p22 = ++ ` j ,   where a, b and p are positive constants.  [4]  (ii) explain why the graph of   yx x12=+    has no stationary points.  [2]",
            "9": "9 0606/22/f/m/19 \u00a9 ucles 2019 [turn over 8 relative to an origin o, the position vectors of the points a and b are 2 i + 12j and 6 i - 4j respectively.  (i) write down and simplify an expression for  ab. [2]  the point c lies on ab such that ac : cb is 1 : 3.  (ii) find the unit vector in the direction of  oc. [4]  the point d lies on oa  such that od : da is 1 : m.  (iii) find an expression for ad in terms of m, i and j. [2]",
            "10": "10 0606/22/f/m/19 \u00a9 ucles 2019 9 (a) it is given that   ()xx 65 g4=+    for all real x.   (i) explain why g is a function but does not have an inverse.  [2]   (ii) find  ()xg2 and state its domain.  [2]   it is given that   ()xx 65 h4=+   for  xkg.   (iii) state the greatest value of k such that h-1 exists.  [1]   (iv) for this value of k, find  h-1(x). [3]",
            "11": "11 0606/22/f/m/19 \u00a9 ucles 2019 [turn over  (b) the function p is defined by   ()x 32 pex=+    for all real x.   (i) state the range of p.  [1]   (ii) on the axes below, sketch and label the graphs of () yxp=  and () yxp1=-. state the coordinates  of any points of intersection with the coordinate axes.  [3] y x oyx=   (iii) hence explain why the equation  () () xxpp1=- has no solutions.  [1]",
            "12": "12 0606/22/f/m/19 \u00a9 ucles 2019 10  y x odab cyx x 15=+ + yx33-=  the diagram shows the curve   yx x 15=+ +    and the straight line   yx33-= . the curve and line  intersect at the points a and b. the lines bc and ad are perpendicular to the x-axis.  (i) using the substitution  u2 = x, or otherwise, find the coordinates of a and of b. you must show all your  working.  [6]",
            "13": "13 0606/22/f/m/19 \u00a9 ucles 2019 [turn over  (ii) find the area of the shaded region, showing all your working.  [6]",
            "14": "14 0606/22/f/m/19 \u00a9 ucles 2019 11 (a) find  ().xxxx1d626+y  [3]  (b) (i) find  () . cos4 5dii- y  [2]     (ii) hence evaluate    () . cos4 5d .1252ii- y  [2]",
            "15": "15 0606/22/f/m/19 \u00a9 ucles 2019 blank page",
            "16": "16 0606/22/f/m/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"
        },
        "0606_s19_qp_11.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (ce/cb) 165273/2 \u00a9 ucles 2019  [turn over *2049112309* additional mathematics  0606/11 paper 1  may/june 2019  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge assessment international education cambridge international general certificate of secondary education",
            "2": "2 0606/11/m/j/19 \u00a9 ucles 2019 mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, xabb ac 242!=-- binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/11/m/j/19 \u00a9 ucles 2019 [turn over 1 (a) on the venn diagrams below, shade the region indicated. a b ca b c/h5105 /h5105 ()ab c +, ()'ab c ,+  [2]  (b) on the venn diagram below, draw sets p, q and r such that pr1,  qr1   and   pq+ q=. \ue025   [2]",
            "4": "4 0606/11/m/j/19 \u00a9 ucles 2019 2 (i) write down the amplitude of   sinx 43 1-. [1]  (ii) write down the period of   sinx 43 1-. [1]  (iii) on the axes below, sketch the graph of   sin yx43 1 =-    for   \u00b0\u00b0 \u00b0 x 90 90 gg - . 6 4 2 \u201390 \u201360 \u201330 0 30 60 90 \u20132 \u20134 \u20136y x  [3]",
            "5": "5 0606/11/m/j/19 \u00a9 ucles 2019 [turn over 3 the polynomial   () () () xx xk 21 12 p=- +- ,   where k is a constant.  (i) write down the value of ()kp-. [1]  when p( x) is divided by   x + 3   the remainder is 23.  (ii) find the value of k. [2]  (iii) using your value of k, show that the equation ()x 25 p=-  has no real solutions.  [3]",
            "6": "6 0606/11/m/j/19 \u00a9 ucles 2019 4 (i) the first 3 terms, in ascending powers of x, in the expansion of   bx28+` j   can be written as    a + 256x +\u00a0cx2. find the value of each of the constants a, b and c. [4]  (ii) using the values found in part (i), find the term independent of x in the expansion of      bx xx22328+-` bj l. [3]",
            "7": "7 0606/11/m/j/19 \u00a9 ucles 2019 [turn over 5 a particle p is moving with a velocity of 20  ms-1 in the same direction as 43eo.  (i) find the velocity vector of p. [2]  at time t = 0 s, p has position vector 21eo relative to a fixed point o.  (ii) write down the position vector of p after t s. [2]  a particle q has position vector 1817eo  relative to o at time t = 0 s and has a velocity vector 128eo  ms-1.  (iii) given that p and q collide, find the value of t when they collide and the position vector of the point of  collision.  [3]",
            "8": "8 0606/11/m/j/19 \u00a9 ucles 2019 6 y xp oqyx x 32 12=- + yx25=+  the diagram shows the curve   yx x 32 12=- +   and the straight line   yx25=+    intersecting at the points  p and q. showing all your working, find the area of the shaded region.  [8]",
            "9": "9 0606/11/m/j/19 \u00a9 ucles 2019 [turn over 7 (a) solve   logl ogxx 1239+= . [3]  (b) solve   () ( logl og y31 0221 42 4-= ) y1-+ . [5]",
            "10": "10 0606/11/m/j/19 \u00a9 ucles 2019 8 it is given that   ()x 51 fex=-  for xrd .  (i) write down the range of f.  [1]  (ii) find f\u200a\u200a-1 and state its domain.  [3]  it is given also that   ()xx 4 g2=+    for   xrd .  (iii) find the value of fg(1).  [2]",
            "11": "11 0606/11/m/j/19 \u00a9 ucles 2019 [turn over  (iv) find the exact solutions of   ()x 40 g2= . [3]",
            "12": "12 0606/11/m/j/19 \u00a9 ucles 2019 9 in this question all lengths are in centimetres.  a closed cylinder has base radius r, height h and volume v.  it is given that the total surface area of the  cylinder is 600 r and that v, r and h can vary.  (i) show that   vr r 3003rr =- . [3]  (ii) find the stationary value of v and determine its nature.  [5]",
            "13": "13 0606/11/m/j/19 \u00a9 ucles 2019 [turn over 10 when lg y is plotted against x2 a straight line graph is obtained which passes through the points  (2, 4)  and    (6, 16).  (i) show that   y10ab x2=+, where a and b are constants.  [4]  (ii) find  y  when  x31= . [2]  (iii) find the positive value of  x  when  y = 2. [3]",
            "14": "14 0606/11/m/j/19 \u00a9 ucles 2019 11 it is given that   yx x12 32 21 =+ - ` `j j.  (i) show that   xy xpx qx 231 dd 212 = -++ ` j,   where p and q are integers.  [5]",
            "15": "15 0606/11/m/j/19 \u00a9 ucles 2019  (ii) hence find the equation of the normal to the curve   yx x12 32 21 =+ - ` `j j   at the point where x = 2,  giving your answer in the form ax + by + c = 0, where a, b and c are integers.  [4]",
            "16": "16 0606/11/m/j/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."
        },
        "0606_s19_qp_12.pdf": {
            "1": "this document consists of 16 printed pages. dc (jm/tp) 165274/2 \u00a9 ucles 2019  [turn over *0773973091* additional mathematics  0606/12 paper 1  may/june 2019  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge assessment international education cambridge international general certificate of secondary education",
            "2": "2 0606/12/m/j/19 \u00a9 ucles 2019 mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/12/m/j/19 \u00a9 ucles 2019 [turn over 1 (a) on the venn diagrams below, shade the region indicated. aa cbb c/h5105 /h5105 ab c ++ll l ()ab c ,+  [2]  (b)  \ue025 {: } xx0 360 \u00b0\u00b0gg =    {: .} cos px x20 5 ==    {: .} sin qx x05 ==   find pq+. [3]",
            "4": "4 0606/12/m/j/19 \u00a9 ucles 2019 2 do not use a calculator in this question.  find the coordinates of the points of intersection of the curve   () () yx x 23 12=+ -   and the line  () yx32 3 =+ . [5]",
            "5": "5 0606/12/m/j/19 \u00a9 ucles 2019 [turn over 3 the number, b, of a certain type of bacteria at time t days can be described by   b200 800 eett22=+-.  (i) find the value of b when t0=. [1]  (ii) at the instant when   tb1200dd= , show that   34 0 eett42-- =. [3]  (iii) using the substitution   uet2= , or otherwise, solve   34 0 eett42-- =. [2]",
            "6": "6 0606/12/m/j/19 \u00a9 ucles 2019 4 (a) given that    qp rpr qr 221223 -` `j j   can be written in the form   paqbr c,   find the value of each of the constants a,   b and c. [3]  (b) solve  , .xy xy34 43 1421 21 21 21-= +=- - [3]",
            "7": "7 0606/12/m/j/19 \u00a9 ucles 2019 [turn over 5 9.6 cm12 cma bcoradi  the diagram shows the right-angled triangle oab . the point c lies on the line ob. angle oab  2r= radians  and angle aob  = i radians. ac is an arc of the circle, centre o, radius 12  cm and ac has length 9.6  cm.  (i) find the value of i. [2]  (ii) find the area of the shaded region.  [4]",
            "8": "8 0606/12/m/j/19 \u00a9 ucles 2019 6 (a) eight books are to be arranged on a shelf. there are 4 mathematics books, 3 geography books and  1 french book.   (i) find the number of different arrangements of the books if there are no restrictions.  [1]   (ii) find the number of different arrangements if the mathematics books have to be kept together.  [3]   (iii) find the number of different arrangements if the mathematics books have to be kept together and  the geography books have to be kept together.  [3]",
            "9": "9 0606/12/m/j/19 \u00a9 ucles 2019 [turn over  (b) a team of 6 players is to be chosen from 8 men and 4 women. find the number of different ways this  can be done if   (i) there are no restrictions,  [1]   (ii) there is at least one woman in the team.  [2]",
            "10": "10 0606/12/m/j/19 \u00a9 ucles 2019 7 a pilot wishes to fly his plane from a point a to a point b on a bearing of 055\u00b0. there is a wind blowing at  120 km h\u20131 from the west. the plane can fly at 650  km h\u20131 in still air.  (i) find the direction in which the pilot must fly his plane in order to reach b. [4]  (ii) given that the distance between a and b is 1250  km, find the time it will take the pilot to fly from  a to b. [4]",
            "11": "11 0606/12/m/j/19 \u00a9 ucles 2019 [turn over 8 when e  y is plotted against x1, a straight line graph passing through the points (2,  20) and (4,  8) is obtained.  (i) find y in terms of x. [5]  (ii) hence find the positive values of x for which y is defined.  [1]  (iii) find the exact value of y when x = 3. [1]  (iv) find the exact value of x when y = 2. [2]",
            "12": "12 0606/12/m/j/19 \u00a9 ucles 2019 9 y x op qy = 5cos yx42 3 =+  the diagram shows the curve   cos yx42 3 =+    intersecting the line   y5=   at the points p and q.  (i) find, in terms of r, the x-coordinate of p and of q. [3]",
            "13": "13 0606/12/m/j/19 \u00a9 ucles 2019 [turn over  (ii) find the exact area of the shaded region. you must show all your working.  [6]",
            "14": "14 0606/12/m/j/19 \u00a9 ucles 2019 10 x cm4x cm h cm  the diagram shows an open container in the shape of a cuboid of width x cm, length 4 x cm and height h cm.   the volume of the container is 800  cm3.  (i) show that the external surface area, s cm2, of the open container is such that   sxx42000 2=+ . [4]",
            "15": "15 0606/12/m/j/19 \u00a9 ucles 2019 [turn over  (ii) given that x can vary, find the stationary value of s and determine its nature.  [5] question 11 is printed on the next page.",
            "16": "16 0606/12/m/j/19 \u00a9 ucles 2019 11 the normal to the curve   yx x23 132 =- + `` jj    at the point where x37=, meets the y-axis at the point p.  find the exact coordinates of the point p. [7] 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."
        },
        "0606_s19_qp_13.pdf": {
            "1": "this document consists of 16 printed pages. dc (kn/tp) 165276/2 \u00a9 ucles 2019  [turn over *6938333361* additional mathematics  0606/13 paper 1  may/june 2019  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge assessment international education cambridge international general certificate of secondary education",
            "2": "2 0606/13/m/j/19 \u00a9 ucles 2019 mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, xabb ac 242!=-- binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/13/m/j/19 \u00a9 ucles 2019 [turn over 1 describe, using set notation, the relationship between the sets shown in each of the venn diagrams below. a x y zb  . .  . ./h5105 /h5105  [3] 2 given that    pqrqr pqrp1 ab c 22 31=-`j,   find the value of each of the constants a, b and c. [3]",
            "4": "4 0606/13/m/j/19 \u00a9 ucles 2019 3 show that the line   ym x4 =+    will touch or intersect the curve   yx xm32=+ +   for all values of m.   [4]",
            "5": "5 0606/13/m/j/19 \u00a9 ucles 2019 [turn over 4 it is given that   ()lnyxx 1253 =-+   for  x12.  (i) find the value of  xy dd when x2=. you must show all your working.  [4]  (ii) find the approximate change in y as x increases from 2 to p2+, where p is small.  [1]",
            "6": "6 0606/13/m/j/19 \u00a9 ucles 2019 5 (i) on the axes below, sketch the graph of   yx x 31 452=- - ,   showing the coordinates of the points  where the graph meets the coordinate axes. y x 0 \u20131 6  [4]  (ii) find the exact value of k such that   xx k 31 452-- =   has 3 solutions only.  [3]",
            "7": "7 0606/13/m/j/19 \u00a9 ucles 2019 [turn over 6 (a) (i) show that   sectan coseccos iiii -= . [3]   (ii) solve   seccosectan222 23iii-=    for 0 180 ggi cc . [3]  (b) solve   rsin2312z+=bl    for r 0211z  radians.  [4]",
            "8": "8 0606/13/m/j/19 \u00a9 ucles 2019 7 do not use a calculator in this question.  in this question, all lengths are in centimetres. a b c25 1- 252+  the diagram shows the triangle abc  such that   ab 25 1 =- ,   bc 25=+    and angle abc 90= c.    (i) find the exact length of ac. [3]",
            "9": "9 0606/13/m/j/19 \u00a9 ucles 2019 [turn over  (ii) find tanacb, giving your answer in the form pq r+ , where p, q and r are integers.  [3]  (iii) hence find secacb2, giving your answer in the form   st u+    where s, t and u are integers.  [2]",
            "10": "10 0606/13/m/j/19 \u00a9 ucles 2019 8    xfex37|   for  xrd    xx21 g27| +   for   x0h  (i) write down the range of g.  [1]  (ii) show that   () ln 62 5 fg1=-. [3]  (iii) solve   () () xx 6 fg= l ll ,   giving your answer in the form lna, where a is an integer.  [3]",
            "11": "11 0606/13/m/j/19 \u00a9 ucles 2019 [turn over  (iv) on the axes below, sketch the graph of gy= and the graph of gy1=-, showing the points where the  graphs meet the coordinate axes. y x o  [3]",
            "12": "12 0606/13/m/j/19 \u00a9 ucles 2019 9 (a) jack has won 7 trophies for sport and wants to arrange them on a shelf. he has 2 trophies for cricket,   4 trophies for football and 1 trophy for swimming. find the number of different arrangements if   (i) there are no restrictions,  [1]   (ii) the football trophies are to be kept together,  [3]   (iii) the football trophies are to be kept together and the cricket trophies are to be kept together.  [3]",
            "13": "13 0606/13/m/j/19 \u00a9 ucles 2019 [turn over  (b) a team of 8 players is to be chosen from 6 girls and 8 boys. find the number of different ways the team  may be chosen if   (i) there are no restrictions,  [1]   (ii) all the girls are in the team,  [1]   (iii) at least 1 girl is in the team.  [2]",
            "14": "14 0606/13/m/j/19 \u00a9 ucles 2019 10 a curve is such that   xyx23dd 22 21 =+-` j.   the curve has a gradient of 5 at the point where x3= and passes    through the point ,21 31- eo .  (i)  find the equation of the curve.  [7]",
            "15": "15 0606/13/m/j/19 \u00a9 ucles 2019 [turn over  (ii)  find the equation of the normal to the curve at the point where x3=, giving your answer in the form    ax by c0 ++ =, where a, b and c are integers.  [4] question 11 is printed on the next page.",
            "16": "16 0606/13/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.11 a pilot wishes to fly his plane from a point a to a point b. the bearing of b from a is 050\u00b0. a wind is  blowing from the north at a speed of 120  km h\u20131. the plane can fly at 600  km h\u20131 in still air.  (i) find the bearing on which the pilot must fly his plane in order to reach b. [4]  (ii) given that the distance from a to b is 2500  km, find the time taken to fly from a to b. [4]"
        },
        "0606_s19_qp_21.pdf": {
            "1": "cambridge assessment international education cambridge international general certificate of secondary education *8109129254* this document consists of 15 printed pages and 1 blank page. dc (nf/tp) 165272/1 \u00a9 ucles 2019  [turn overadditional mathematics  0606/21 paper 2  may/june 2019  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of   angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/21/m/j/19 \u00a9 ucles 2019 mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/21/m/j/19 \u00a9 ucles 2019 [turn over 1 find the values of x for which   x(6x + 7) h 20. [3] 2 two variables x and y are such that    lnyxx 3=     for x 2 0.  (i) show that    ln xy xx 13 dd 4=-. [3]  (ii) hence find the approximate change in y as x increases from e to e  + h, where h is small.  [2]",
            "4": "4 0606/21/m/j/19 \u00a9 ucles 2019 3 (i) sketch the graph of   yx 53=-    on the axes below, showing the coordinates of the points where the  graph meets the coordinate axes. y x o [3]  (ii) solve the equation   xx53 2 -= -. [3] 4 without using a calculator , express   51532 +- ` j     in the form pq5+, where p and q are integers.  [4]",
            "5": "5 0606/21/m/j/19 \u00a9 ucles 2019 [turn over 5  v ms\u20131 o t s 410 k k + 6  the velocity-time graph represents the motion of a particle travelling in a straight line.  (i) find the acceleration during the last 6 seconds of the motion.  [1]  (ii) the particle travels with constant velocity for 23 seconds. find the value of k. [1]  (iii) using your answer to part (ii) , find the total distance travelled by the particle.  [3]",
            "6": "6 0606/21/m/j/19 \u00a9 ucles 2019 6 (a)   x xx xa3 23=+- -eo   given that a does not have an inverse, find the exact values of x. [3]  (b)   b0 4 53 1 2=-fp   and c0 31 42 5=-eo   (i) write down the order of matrix b. [1]   (ii) the matrix  bc9 3 612 8 315 3 20=- - -- fp . explain why cb bc! . [2]",
            "7": "7 0606/21/m/j/19 \u00a9 ucles 2019 [turn over 7 the variables x, y and u are such that    tanyu=    and   xu 13=+ .  (i) state the rate of change of y with respect to u. [1]  (ii)  hence find the rate of change of y with respect to x, giving your answer in terms of x. [4]",
            "8": "8 0606/21/m/j/19 \u00a9 ucles 2019 8  92radrb cde a8 cm  the diagram shows a right-angled triangle abc  with ab = 8 cm and angle abc2r= radians. the points  d   and e lie on ac and bc respectively. bad  and ecd  are sectors of the circles with centres a and c   respectively. angle bad92r=  radians.  (i) find the area of the shaded region.  [6]",
            "9": "9 0606/21/m/j/19 \u00a9 ucles 2019 [turn over  (ii) find the perimeter of the shaded region.  [3]",
            "10": "10 0606/21/m/j/19 \u00a9 ucles 2019 9 (a) eleven different television sets are to be displayed in a line in a large shop.   (i) find the number of different ways the televisions can be arranged.  [1]   of these television sets, 6 are made by company a and 5 are made by company b.   (ii) find the number of different ways the televisions can be arranged so that no two sets made by  company a are next to each other.  [2]  (b) a group of people is to be selected from 5 women and 3 men.   (i) calculate the number of different groups of 4 people that have exactly 3  women.  [2]   (ii) calculate the number of different groups of at most 4 people where the number of women is the  same as the number of men.  [2]",
            "11": "11 0606/21/m/j/19 \u00a9 ucles 2019 [turn over 10 solutions to this question by accurate drawing will not be accepted.  the points a and b have coordinates (  p, 3) and (1,  4) respectively and the line  l has equation   xy32+= .  (i) given that the gradient of ab is 31, find the value of p. [2]  (ii) show that l is the perpendicular bisector of  ab. [3]  (iii) given that ,cq 10-` j lies on l, find the value of q. [1]  (iv) find the area of triangle abc . [2]",
            "12": "12 0606/21/m/j/19 \u00a9 ucles 2019 11 (a) (i)  show that    sincosecc ot cos 11 iii i-=+. [4]   (ii) hence solve    sincosecc ot 25 iii-=    for 180 360 \u00b0\u00b011i . [2]",
            "13": "13 0606/21/m/j/19 \u00a9 ucles 2019 [turn over  (b) solve    tan3 421z-= - ` j   for  r02ggz    radians.  [3]",
            "14": "14 0606/21/m/j/19 \u00a9 ucles 2019 12 (a) given that  ax50 edx2 0= y ,  find the exact value of a. you must show all your working.  [4]",
            "15": "15 0606/21/m/j/19 \u00a9 ucles 2019  (b) a curve is such that   cosxyx 32 5dd=- .   the curve passes through the point ,558rrbl .   (i) find the equation of the curve.  [4]   (ii) find yxdy  and hence evaluate ryxdr 2y . [5]",
            "16": "16 0606/21/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.blank page"
        },
        "0606_s19_qp_22.pdf": {
            "1": "this document consists of 16 printed pages. dc (lk) 165275/2 \u00a9 ucles 2019  [turn over *3034680663* additional mathematics  0606/22 paper 2  may/june 2019  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge assessment international education cambridge international general certificate of secondary education",
            "2": "2 0606/22/m/j/19 \u00a9 ucles 2019 mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/22/m/j/19 \u00a9 ucles 2019 [turn over 1 given that   lnsinyxx 2=  ,   find an expression for dd xy . [4] 2 find the values of k for which the equation   ()kx kx k 102-+ -=    has real and distinct roots.  [4]",
            "4": "4 0606/22/m/j/19 \u00a9 ucles 2019 3 (i) given that   x2-   is a factor of   ax xx12 5632-+ +,   use the factor theorem to show that a4=. [2]  (ii) showing all your working, factorise   xx x 41 25 632-+ +   and hence solve   xx x 41 25 6032-+ += .  [4]",
            "5": "5 0606/22/m/j/19 \u00a9 ucles 2019 [turn over 4 a circle has diameter  x which is increasing at a constant rate of .c ms 0011-. find the exact rate of change of  the area of the circle when cm x6= . [5]",
            "6": "6 0606/22/m/j/19 \u00a9 ucles 2019 5  (i) express    xx51 512-+    in the form px qr2++` j , where p, q and r are constants.  [3]  (ii) hence state the least value of   . xx 30 22-+    and the value of x at which this occurs.  [2]",
            "7": "7 0606/22/m/j/19 \u00a9 ucles 2019 [turn over 6 (a) state the order of the matrix 0 51 84 18 6eo . [1]  (b) a2 14 3=--eo   (i) find a1-. [2]   (ii) hence, given that   aba = i,   find the matrix b. [3]",
            "8": "8 0606/22/m/j/19 \u00a9 ucles 2019 7 (a) solve   ()lgx 302-= . [2]   (b) (i) show that, for a02,   lnln ln aaa1 ()sinx25++bl    may be written as ()sinxk25++ , where k is an  integer.  [3]   (ii) hence find   lnln ln daaax1 ()sinx25++c ed ddbl . [3]",
            "9": "9 0606/22/m/j/19 \u00a9 ucles 2019 [turn over 8 (a) in the binomial expansion of   ax 26 -bl ,   the coefficient of x3 is 120 times the coefficient of x5. find   the possible values of the constant a.  [4]  (b) (i) expand   () x 1220+    in ascending powers of x, as far as the term in x3. simplify each term.  [2]   (ii) use your expansion to show that the value of 0.9820 is 0.67 to 2 decimal places.  [2]",
            "10": "10 0606/22/m/j/19 \u00a9 ucles 2019 9 (a) solve    sinc os xx 61 312-=   for  \u00b0\u00b0x 0 360 gg . [4]",
            "11": "11 0606/22/m/j/19 \u00a9 ucles 2019 [turn over  (b) (i)  show that, for y2211rr- ,    tantan yy 14 2+   can be written in the form sinay , where  a is an  integer.  [3]   (ii) hence solve     tantan yy 14302++=    for y2211rr-  radians.  [1]",
            "12": "12 0606/22/m/j/19 \u00a9 ucles 2019 10 (a) find the unit vector in the direction of ij51 5- . [2]  (b) the position vectors of points a and b relative to an origin o are 3 5-eo  and 12 7eo respectively. the   point c lies on ab such that  ac : cb is 2 : 1.   (i) find the position vector of c relative to o. [3]",
            "13": "13 0606/22/m/j/19 \u00a9 ucles 2019 [turn over   the point  d lies on ob such that  od : ob  is 1 : m and .dc6 125=eo .   (ii) find the value of m. [3]",
            "14": "14 0606/22/m/j/19 \u00a9 ucles 2019 11 the velocity, v m s\u22121, of a particle travelling in a straight line, t seconds after passing through a fixed   point o, is given by    v t14 3= +` j.  (i) explain why the direction of motion of the particle never changes.  [1]  (ii) showing all your working, find the acceleration of the particle when t5=. [3]  (iii) find an expression for the displacement of the particle from o after t seconds.  [3]  (iv) find the distance travelled by the particle in the fourth second.  [2]",
            "15": "15 0606/22/m/j/19 \u00a9 ucles 2019 [turn over 12 (a) the functions f and g are defined by     ()fxx 52=-  for x12,     ()gxx 492=-     for x02.   (i) state the range of g.  [1]   (ii) find the domain of gf.  [1]   (iii) showing all your working, find the exact solutions of   ()gfx 4=. [3] question 12(b) is printed on the next page.",
            "16": "16 0606/22/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. (b) the function h is defined by    ()hxx 12=-    for x 1g-.   (i) state the geometrical relationship between the graphs of ()h yx=  and ()h yx1=-. [1]   (ii) find an expression for  ()hx1-. [3]"
        },
        "0606_s19_qp_23.pdf": {
            "1": "this document consists of 16 printed pages. dc (sc/cb) 165277/2 \u00a9 ucles 2019  [turn over *9164116781* additional mathematics  0606/23 paper 2  may/june 2019  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of   angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge assessment international education cambridge international general certificate of secondary education",
            "2": "2 0606/23/m/j/19 \u00a9 ucles 2019 mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/23/m/j/19 \u00a9 ucles 2019 [turn over 1 find the values of x for which   9 x2 + 18x - 1 1 x + 1. [3] 2 differentiate   tanc osxx32   with respect to x. [4]",
            "4": "4 0606/23/m/j/19 \u00a9 ucles 2019 3 the points a, b and c have coordinates (4, 7), ( -3, 9) and (6, 4) respectively.   (i) find the equation of the line, l, that is parallel to the line ab and passes through c. give your answer  in the form ax + by = c, where a, b and c are integers.  [3]  (ii) the line l meets the x-axis at the point d and the y-axis at the point e. find the length of de. [2]",
            "5": "5 0606/23/m/j/19 \u00a9 ucles 2019 [turn over 4 the function f is defined, for 0\u00b0 g x g 360\u00b0, by   () sin xx 43 2 f=+ .  (i) sketch the graph of y = f(x) on the axes below. y x8 00\u00b0 60\u00b0 120\u00b0 180\u00b0 240\u00b0 300\u00b0 360\u00b0 \u20138  [3]  (ii) state the period of f.  [1]  (iii) state the amplitude of f.  [1]",
            "6": "6 0606/23/m/j/19 \u00a9 ucles 2019 5 (a) given that   a = 2 0 63 1 4-fp   and that , ao a +=   (i) state the order of the matrix a, [1]   (ii) write down the matrix o. [1]  (b) b = 1 31 2-eo   and c = . .. .04 0602 02 -eo  .   find the matrix product bc and state a relationship between b and c. [2]  (c) d = aa 14 5-eo  , where a is a positive integer. find d-1 in terms of a. [2]",
            "7": "7 0606/23/m/j/19 \u00a9 ucles 2019 [turn over 6 a curve has equation    yx x 35 23=- - ` j .  (i) find  xy dd and xy dd2 2 . [4]  (ii) find the exact value of the x-coordinate of each of the stationary points of the curve.  [2]  (iii) use the second derivative test to determine the nature of each of the stationary points.  [2]",
            "8": "8 0606/23/m/j/19 \u00a9 ucles 2019 7 50 cm d c oa b 94radr  the diagram shows a company logo, abcd . the logo is part of a sector, aob , of a circle, centre o and  radius 50  cm. the points c and d lie on ob and oa respectively. the lengths ad and bc are equal and   ad : ao  is 7 : 10. the angle aob  is 94r radians.  (i) find the perimeter of abcd . [5]",
            "9": "9 0606/23/m/j/19 \u00a9 ucles 2019 [turn over  (ii) find the area of abcd . [3]",
            "10": "10 0606/23/m/j/19 \u00a9 ucles 2019 8 (a) (i) given that    xpxxx qx rx1428 16 13 10 7f -= -++ + eo ,   find the value of each of the constants p,  q and r. [3]   (ii) explain why there is no term independent of x in the binomial expansion of   xpx1 28 -eo . [1]  (b) in the binomial expansion of   x12n -eo ,   where n is a positive integer, the coefficient of x is 30. form   an equation in n and hence find the value of n. [4]",
            "11": "11 0606/23/m/j/19 \u00a9 ucles 2019 [turn over 9 oy = 7yx162=-y x  the diagram shows the curve  y = 16 - x2  and the straight line y = 7. find the area of the shaded region.  you must show all your working.  [6]",
            "12": "12 0606/23/m/j/19 \u00a9 ucles 2019 10 o bap rq pq  the diagram shows a triangle oab . the point p is the midpoint of oa and the point q lies on ob such that    oq ob41= . the position vectors of p and q relative to o are p and q respectively.  (i) find, in terms of p and q, an expression for each of the vectors pq, qa and pb. [3]  (ii) given that pr pbm=  and that qr qan= , find an expression for pq in terms of m, n, p and q. [2]",
            "13": "13 0606/23/m/j/19 \u00a9 ucles 2019 [turn over  (iii) using your expressions for pq, find the value of m and of n. [4]",
            "14": "14 0606/23/m/j/19 \u00a9 ucles 2019 11 a particle travelling in a straight line passes through a fixed point o. the displacement, x metres, of the  particle, t seconds after it passes through o, is given by   sin xt t 5=+ .  (i) show that the particle is never at rest.  [2]  (ii) find the distance travelled by the particle between t3r= and t2r=. [2]",
            "15": "15 0606/23/m/j/19 \u00a9 ucles 2019 [turn over  (iii) find the acceleration of the particle when t = 4. [2]  (iv) find the value of t when the velocity of the particle is first at its minimum.  [2] question 12 is printed on the next page.",
            "16": "16 0606/23/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.12 do not use a calculator in this question.  the line   y = 4x - 6   intersects the curve   y = 10x3 - 19x2 - x  at the points a, b, and c. given that c is  the point (2, 2), find the coordinates of the midpoint of ab. [10]"
        },
        "0606_w19_qp_11.pdf": {
            "1": "this document consists of 16 printed pages. dc (ce/sw) 172295/2 \u00a9 ucles 2019  [turn over *3060253848* additional mathematics  0606/11 paper 1  october/november 2019  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge assessment international education cambridge international general certificate of secondary education",
            "2": "2 0606/11/o/n/19 \u00a9 ucles 2019 mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xabb ac 242!=-- . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/11/o/n/19 \u00a9 ucles 2019 [turn over 1 using set notation, describe the regions shaded on the venn diagrams below. /h5105 /h5105 a by x z  ..  ..  [2] 2 find the values of k for which the line   yk x3 =-    and the curve   yx xk 232=+ +   do not intersect.  [5]",
            "4": "4 0606/11/o/n/19 \u00a9 ucles 2019 3 given that   74 91xy# =   and   5 125251 x5y 32 # =  ,   calculate the value of x and of y. [5]",
            "5": "5 0606/11/o/n/19 \u00a9 ucles 2019 [turn over 4 it is given that   ()lnyxx 23412 =-+.  (i) find  xy dd . [3]  (ii) find the approximate change in y as x increases from 2 to h2+, where h is small.  [2]",
            "6": "6 0606/11/o/n/19 \u00a9 ucles 2019 5    ()x 31 fex2=+  for xrd     ()xx 1 g=+  for xrd  (i) write down the range of f and of g.  [2]  (ii) evaluate   ()0fg2. [2]  (iii) on the axes below, sketch the graphs of () yxf=  and () yxf1=-, stating the coordinates of the points  where the graphs meet the coordinate axes.  [3] y x o",
            "7": "7 0606/11/o/n/19 \u00a9 ucles 2019 [turn over 6 find the equation of the normal to the curve   yx 85=+    at the point where x21=, giving your answer in  the form , ax by c0 ++ = where a, b and c are integers.  [5]",
            "8": "8 0606/11/o/n/19 \u00a9 ucles 2019 7 when lgy is plotted against x, a straight line graph passing through the points (2.2, 3.6) and (3.4, 6) is  obtained.  (i) given that   , ya bx=  find the value of each of the constants a and b. [5]  (ii) find x when . y900=  [2]",
            "9": "9 0606/11/o/n/19 \u00a9 ucles 2019 [turn over 8 do not use a calculator in this question.  in this question, all lengths are in centimetres. 75+ 5 11 2+5 43+a b d c  the diagram shows the trapezium abcd  in which angle adc  is 90\u00b0 and ab is parallel to dc. it is given  that   , ab 43 5 =+    dc 11 25 =+    and   . ad 75=+  (i) find the perimeter of the trapezium, giving your answer in simplest surd form.  [3]  (ii) find the area of the trapezium, giving your answer in simplest surd form.  [3]",
            "10": "10 0606/11/o/n/19 \u00a9 ucles 2019 9 a db o15 cm 10 cm 10 cmc  the diagram shows a circle with centre o and radius 10  cm. the points a, b, c and d lie on the circle such  that the chord ab = 15 cm and the chord cd = 10 cm. the chord ab is parallel to the chord dc.  (i) show that the angle aob  is 1.70 radians correct to 2 decimal places.  [2]  (ii) find the perimeter of the shaded region.  [4]",
            "11": "11 0606/11/o/n/19 \u00a9 ucles 2019 [turn over  (iii) find the area of the shaded region.  [4]",
            "12": "12 0606/11/o/n/19 \u00a9 ucles 2019 10 y x oy = 2 + cos  3x y = 1.5  the diagram shows part of the graph of   cos yx23=+    and the straight line .. y15=  find the exact area of  the shaded region bounded by the curve and the straight line. you must show all your working.  [9]",
            "13": "13 0606/11/o/n/19 \u00a9 ucles 2019 [turn over continuation of working space for question 10",
            "14": "14 0606/11/o/n/19 \u00a9 ucles 2019 11 (a) jess wants to arrange 9 different books on a shelf. there are 4 mathematics books, 3  physics books and  2 chemistry books. find the number of different possible arrangements of the books if   (i) there are no restrictions,  [1]   (ii) a chemistry book is at each end of the shelf,  [2]   (iii) all the mathematics books are kept together and all the physics books are kept together.  [3]",
            "15": "15 0606/11/o/n/19 \u00a9 ucles 2019 [turn over  (b) a quiz team of 6 children is to be chosen from a class of 8 boys and 10 girls. find the number of ways  of choosing the team if   (i) there are no restrictions,  [1]   (ii) there are more boys than girls in the team.  [4] question 12 is printed on the next page.",
            "16": "16 0606/11/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.12 a curve is such that   sinxyx 23 dd 22r=+ bl . given that the curve has a gradient of 5 at the point ,335rrbl , find  the equation of the curve.  [8]"
        },
        "0606_w19_qp_12.pdf": {
            "1": "this document consists of 16 printed pages. dc (lk/tp) 172296/2 \u00a9 ucles 2019  [turn over *7218149806* additional mathematics  0606/12 paper 1  october/november 2019  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge assessment international education cambridge international general certificate of secondary education",
            "2": "2 0606/12/o/n/19 \u00a9 ucles 2019 mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, xabb ac 242!=-- . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/12/o/n/19 \u00a9 ucles 2019 [turn over 1 (i) on the axes below, sketch the graph of   cos yx23 1 =-   for \u00b0\u00b0x 90 90 gg - . y x 01 -1 -2 -3 -4234 30\u00b0 -30\u00b0 -60\u00b0 -90\u00b0 60\u00b0 90\u00b0  [3]  (ii) write down the amplitude of   cosx 23 1-. [1]  (iii) write down the period of   cosx 23 1-. [1]",
            "4": "4 0606/12/o/n/19 \u00a9 ucles 2019 2 when lgy2 is plotted against x, a straight line is obtained passing through the points  (5, 12)  and  (3, 20).   find y in terms of x, giving your answer in the form   y10ax b=+,   where a and b are integers.  [5]",
            "5": "5 0606/12/o/n/19 \u00a9 ucles 2019 [turn over 3 the first three terms in the expansion of   ()xx 1712144--bl    can be written as   ax bx 12++ . find the value  of each of the constants a and b. [6]",
            "6": "6 0606/12/o/n/19 \u00a9 ucles 2019 4 (i) on the axes below, sketch the graph of   yx x 29 52=- -   showing the coordinates of the points  where the graph meets the axes.  [4] y x o  (ii) find the values of k for which   xx k 29 52-- =   has exactly 2 solutions.  [3]",
            "7": "7 0606/12/o/n/19 \u00a9 ucles 2019 [turn over 5 (a) it is given that  f  : x x7  for   x0h,      g : x x57+ for   x0h.   identify each of the following functions with one of    f  -1,   g-1,   fg,   gf,   f  2,   g2.   (i) x5+ [1]   (ii) x5- [1]   (iii) x2 [1]   (iv) x10+  [1]  (b) it is given that      ()hxaxb 2=+    where a and b are constants.   (i) why is x22gg-  not a suitable domain for h( x)? [1]   (ii) given that ()h1 4= and ()h1 16= l , find the value of a and of b. [2]",
            "8": "8 0606/12/o/n/19 \u00a9 ucles 2019 6 (a) write   p pq rrqp 12 -3ak    in the form pqrab c, where a, b and c are constants.  [3]  (b) solve   logl og x27 3x 7+= . [4]",
            "9": "9 0606/12/o/n/19 \u00a9 ucles 2019 [turn over 7 it is given that    ()e yx 15x2=+ + ^ h .  (i) find dd xy. [3]  (ii) find the approximate change in y as x increases from 0.5 to .p 05+, where p is small.  [2]  (iii) given that y is increasing at a rate of 2 units per second when . x 05= , find the corresponding rate of  change in x. [2]",
            "10": "10 0606/12/o/n/19 \u00a9 ucles 2019 8 (a) five teams took part in a competition in which each team played each of the other 4 teams. the  following table represents the results after all the matches had been played. team won drawn lost a 2 1 1 b 1 3 0 c 1 1 2 d 0 1 3 e 3 0 1   points in the competition were awarded to the teams as follows      4 for each match won,      2 for each match drawn,      0 for each match lost.   (i) write down two matrices whose product under matrix multiplication will give the total number of  points awarded to each team.  [2]   (ii) evaluate the matrix product from part (i)  and hence state which team was awarded the most  points.  [2]",
            "11": "11 0606/12/o/n/19 \u00a9 ucles 2019 [turn over  (b) it is given that   a1 21 4=-cm     and    b5 10 2=-cm .   (i) find a-1. [2]   (ii) hence find the matrix c such that ac = b. [3]",
            "12": "12 0606/12/o/n/19 \u00a9 ucles 2019 9 a solid circular cylinder has a base radius of r cm and a height of h cm. the cylinder has a volume of  cm 12003r  and a total surface area of s cm2.  (i) show that srr22400 2rr=+ . [3]",
            "13": "13 0606/12/o/n/19 \u00a9 ucles 2019 [turn over  (ii) given that h and r can vary, find the stationary value of s and determine its nature.  [5]    ",
            "14": "14 0606/12/o/n/19 \u00a9 ucles 2019 10  18 cm 18 cmoab c10 cm  the diagram shows a circle centre o, radius 10  cm. the points a, b and c lie on the circumference of the  circle such that ab = bc = 18 cm.  (i) show that angle . aob 224=  radians correct to 2 decimal places.  [3]  (ii) find the perimeter of the shaded region.  [5]",
            "15": "15 0606/12/o/n/19 \u00a9 ucles 2019 [turn over continuation of working space for question 10(ii).  (iii) find the area of the shaded region.  [3] question 11 is printed on the next page.",
            "16": "16 0606/12/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.11 a curve is such that   ()dd xyx23 122 32 =--. given that the curve has a gradient of 6 at the point (3, 11), find     the equation of the curve.  [8]"
        },
        "0606_w19_qp_13.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (sc/fc) 172297/1 \u00a9 ucles 2019  [turn over *9428013313* additional mathematics  0606/13 paper 1  october/november 2019  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge assessment international education cambridge international general certificate of secondary education",
            "2": "2 0606/13/o/n/19 \u00a9 ucles 2019 mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, xabb ac 242!=-- . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/13/o/n/19 \u00a9 ucles 2019 [turn over 1 in a group of 145 students, the numbers studying mathematics, physics and chemistry are given below. all  students study at least one of the three subjects.     x students study all 3 subjects     24 students study both mathematics and chemistry     23 students study both physics and chemistry     28 students study both mathematics and physics     50 students study chemistry     75 students study physics     80 students study mathematics  (i) using the venn diagram, find the value of x. [4] /h5105mathematics physics chemistry  (ii) find the number of students who study mathematics only.  [1]",
            "4": "4 0606/13/o/n/19 \u00a9 ucles 2019 2 (i) on the axes below, sketch the graph of   cos yx54 3 =-    for \u00b0\u00b0 . x 90 90 gg - y x 02 - 2 - 4 - 6 - 8 - 1046 45\u00b0 -45\u00b0 -90\u00b0 90\u00b0  [4]  (ii) write down the amplitude of y. [1]  (iii) write down the period of y. [1]",
            "5": "5 0606/13/o/n/19 \u00a9 ucles 2019 [turn over 3 (i) differentiate   yx 312 31 =--` j   with respect to x. [2]  (ii) find the approximate change in y as x increases from 3 to ,p 3+ where p is small.  [1]  (iii) find the equation of the normal to the curve   yx 312 31 =--` j   at the point where . x 3=  [3]",
            "6": "6 0606/13/o/n/19 \u00a9 ucles 2019 4 it is given that . a5 42 1=-eo  (i) find a-1. [2]  (ii) hence find, in radians, the acute angles x and y such that  , .tant an tant anxy xy52 12 47+= -=  [5]",
            "7": "7 0606/13/o/n/19 \u00a9 ucles 2019 [turn over 5 (i) differentiate   () ()ln xx 3322++    with respect to x. [3]  (ii) hence find   () . lnxx x3d2+ y  [2]",
            "8": "8 0606/13/o/n/19 \u00a9 ucles 2019 6 x 1 1.5 2 2.5 3 y 6 14.3 48 228 1536  the table shows values of the variables x and y such that , ya bx2=  where a and b are constants.  (i) draw a straight line graph to show that . ya bx2=  [4]",
            "9": "9 0606/13/o/n/19 \u00a9 ucles 2019 [turn over  (ii) use your graph to find the value of a and of b. [4]  (iii) estimate the value of x when . y 100=  [2]",
            "10": "10 0606/13/o/n/19 \u00a9 ucles 2019 7 (a) a 5-digit code is to be chosen from the digits     1,  2,  3,  4,  5,  6,  7,  8 and 9.    each digit may be used  once only in any 5-digit code. find the number of different 5-digit codes that may be chosen if   (i) there are no restrictions,  [1]   (ii) the code is divisible by 5,  [1]   (iii) the code is even and greater than 70  000. [3]  (b) a team of 6 people is to be chosen from 8 men and 6 women. find the number of different teams that  may be chosen if   (i) there are no restrictions,  [1]   (ii) there are no women in the team,  [1]   (iii) there are a husband and wife who must not be separated.  [3]",
            "11": "11 0606/13/o/n/19 \u00a9 ucles 2019 [turn over 8 (a) given that   logxpa=   and  , logyqa=   find, in terms of p and q,   (i) , log axya2 [2]   (ii) logayx a3 eo, [2]   (iii) . logl ogaaxy+  [1]  (b) using the substitution , m 3x=  or otherwise, solve   . 33 40xx 12-+ =+ [3]",
            "12": "12 0606/13/o/n/19 \u00a9 ucles 2019 9 p q r os irad2r cmr cm  the diagram shows a sector opq  of the circle centre o, radius 3 r cm. the points s and r lie on op and oq  respectively such that ors is a sector of the circle centre o, radius 2 r cm. the angle poq i= radians. the  perimeter of the shaded region pqrs  is 100  cm.  (i) find i in terms of r. [2]  (ii) hence show that the area, a cm2, of the shaded region pqrs  is given by  . ar r 502=-  [2]",
            "13": "13 0606/13/o/n/19 \u00a9 ucles 2019 [turn over  (iii) given that r can vary and that a has a maximum value, find this value of a. [2]  (iv) given that a is increasing at the rate of 3  cm2 s-1 when r = 10, find the corresponding rate of change  of r. [3]  (v) find the corresponding rate of change of i when r = 10. [3]",
            "14": "14 0606/13/o/n/19 \u00a9 ucles 2019 10 (a) v ms-1 t s0 - 2020 5 10   the velocity-time graph for a particle p is shown by the two straight lines in the diagram.   (i) find the deceleration of p for  . t 51 0 gg  [2]   (ii) write down the value of t when the speed of p is zero.  [1]   (iii) find the distance p has travelled for . t 01 0 gg  [2]",
            "15": "15 0606/13/o/n/19 \u00a9 ucles 2019  (b) a particle q has a displacement of x m from a fixed point o, t s after leaving o. the velocity, v ms-1, of  q at time t s is given by   . v 61et2=+   (i) find an expression for x in terms of t. [3]   (ii) find the value of t when the acceleration of q is 24  ms-2. [3]",
            "16": "16 0606/13/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"
        },
        "0606_w19_qp_21.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank pag e. dc (nf/sg) 172320/3 \u00a9 ucles 2019  [turn over *5120051451*cambridge assessment international education cambridge international general certificate of secondary education additional mathematics  0606/21 paper 2  october/november 2019  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of   angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.",
            "2": "2 0606/21/o/n/19 \u00a9 ucles 2019 mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xabb ac 242!=-- . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/21/o/n/19 \u00a9 ucles 2019 [turn over 1 (i) on the axes below, draw the graph of  yx 23=- . y x 02468 -2-2 2 4 -4 [2]  (ii) solve the equation   x 72 30 -- =. [3] 2  y x0246 r 2r -2  the figure shows part of the graph of   cos yp qr x =+ . find the value of each of the integers p, q and r.     p=           q=           r= [3]",
            "4": "4 0606/21/o/n/19 \u00a9 ucles 2019 3 (a) solve   3 eexx21 43=+-. [3]  (b) solve   () () lg lg yy61 52 -+ += . [5]",
            "5": "5 0606/21/o/n/19 \u00a9 ucles 2019 [turn over 4 do not use a calculator in this question.  solve the following simultaneous equations, giving your answers for both x and y in the form ab 2+ ,  where a and b are integers. xy25+=      xy32 7 -=  [5]",
            "6": "6 0606/21/o/n/19 \u00a9 ucles 2019 5 a particle is moving in a straight line such that t seconds after passing a fixed point o its displacement, s m,  is given by   sinc os st t 32 42 4 =+ -.  (i) find expressions for the velocity and acceleration of the particle at time t. [3]  (ii) find the first time when the particle is instantaneously at rest.  [3]  (iii) find the acceleration of the particle at the time found in part (ii) . [2]",
            "7": "7 0606/21/o/n/19 \u00a9 ucles 2019 [turn over 6 do not use a calculator in this question.  the curve   xy x11 5 =+    cuts the line   yx 10=+    at the points a and b. the mid-point of ab is the  point  c. show that the point c lies on the line   xy 11+= . [7]",
            "8": "8 0606/21/o/n/19 \u00a9 ucles 2019 7 (a) (i) use the factor theorem to show that   x21-   is a factor of ()xp, where   ()xx x 49 5 p3=+ -. [1]   (ii) write ()xp as a product of linear and quadratic factors.  [2]",
            "9": "9 0606/21/o/n/19 \u00a9 ucles 2019 [turn over  (b) (i) show that   tansec sins ec xx xx 13 45 02-- =   can be written as   sins in xx 49 503+- =. [3]   (ii) using your answers to part (a)(ii)  and part (b)(i)  solve the equation      tansec sins ec xx xx 13 45 02-- =   for x0211 r radians.  [4]",
            "10": "10 0606/21/o/n/19 \u00a9 ucles 2019 8 the equation of a curve is given by   yx ex2=-.  (i) find   xy dd. [3]  (ii) find the exact coordinates of the stationary point on the curve   yx ex2=-. [2]",
            "11": "11 0606/21/o/n/19 \u00a9 ucles 2019 [turn over  (iii) find, in terms of e, the equation of the tangent to the curve   yx ex2=-   at the point ,11 e2 eo . [2]  (iv) using your answer to part (i) , find   xxedx2-y . [3]",
            "12": "12 0606/21/o/n/19 \u00a9 ucles 2019 9 given that   a5 92 3=--eo    and   b2 61 5=eo , find  (i) a1-, [2]  (ii) b2, [2]  (iii) the matrix c, where   bc ab1+=-, [3]",
            "13": "13 0606/21/o/n/19 \u00a9 ucles 2019 [turn over  (iv) the matrix d, where   bdai2=-. [3]",
            "14": "14 0606/21/o/n/19 \u00a9 ucles 2019 10 (i) expand   ()x34+    evaluating each coefficient.  [3]  in the expansion of   () xxpx34-+bl  the coefficient of x is zero.  (ii) find the value of the constant p. [2]  (iii) hence find the term independent of x. [1]  (iv) show that the coefficient of x2 is 90.  [2]",
            "15": "15 0606/21/o/n/19 \u00a9 ucles 2019 11 a plane, which can travel at a speed of 300  km h\u20131 in still air, heads due north. the plane is blown off course  by a wind so that it travels on a bearing of 010\u00b0 at a speed of 280  km h\u20131.  (i) find the speed of the wind.  [3]  (ii) find the direction of the wind as a bearing correct to the nearest degree.  [3]",
            "16": "16 0606/21/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.blank page"
        },
        "0606_w19_qp_22.pdf": {
            "1": "this document consists of 16 printed pages. dc (leg/sg) 172298/2 \u00a9 ucles 2019  [turn over *5192885901* additional mathematics  0606/22 paper 2  october/november 2019  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of   angles in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge assessment international education cambridge international general certificate of secondary education",
            "2": "2 0606/22/o/n/19 \u00a9 ucles 2019 mathematical formulae 1. algebra quadratic  equation  for the equation ax2 + bx + c = 0, x bb ac  a = \u2212 \u22122 4  2  binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r!  2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c  a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/22/o/n/19 \u00a9 ucles 2019 [turn over 1 on each of the venn diagrams below, shade the region indicated. /h5105 a b ab ab +, + ll^^ hh /h5105 a b c ab c +,^ h /h5105 a b c ab c++ l  [3]",
            "4": "4 0606/22/o/n/19 \u00a9 ucles 2019 2 given that   sinc os yx x 23 3 =+ ,   show that   dd ddsinxy xyyk x 3322 ++ = ,   where k is a constant to be  determined.  [5]",
            "5": "5 0606/22/o/n/19 \u00a9 ucles 2019 [turn over 3 a 5-digit code is formed using the following characters.    letters  a e i o u    numbers  1 2 3 4 5 6    symbols  @ \u2217 #  no character can be repeated in a code. find the number of possible codes if  (i) there are no restrictions,  [2]  (ii) the code starts with a symbol followed by two letters and then two numbers,  [2]  (iii) the first two characters are numbers, and no other numbers appear in the code.  [2]",
            "6": "6 0606/22/o/n/19 \u00a9 ucles 2019 4 find the values of k for which the line   yk x3 =+    does not meet the curve   yx x51 22=+ +. [5]",
            "7": "7 0606/22/o/n/19 \u00a9 ucles 2019 [turn over 5 at the point where x1= on the curve   y xk 12= +^ h,   the normal has a gradient of 31.  (i) find the value of the constant k. [4]  (ii) using your value of k, find the equation of the tangent to the curve at x2=. [3]",
            "8": "8 0606/22/o/n/19 \u00a9 ucles 2019 6 (i) show that   sectan tansec sin xx xx x 112 +++= . [5]",
            "9": "9 0606/22/o/n/19 \u00a9 ucles 2019 [turn over  (ii) hence solve the equation   sectan tansecsinxx xxx1113+++=+    for   x 0 180 ccgg . [4]",
            "10": "10 0606/22/o/n/19 \u00a9 ucles 2019 7 (a) the cubic equation   xa xb x40 032++ -=    has three positive integer roots. two of the roots are 2  and 4. find the other root and the value of each of the integers a and b.  [4]  (b) do not use a calculator in this question.   solve the equation   xx x 54 64 0032-= --    given that it has three integer roots, only one of which is  positive.  [4]",
            "11": "11 0606/22/o/n/19 \u00a9 ucles 2019 [turn over 8 (i) a particle a travels with a speed of 6.5  ms\u20131 in the direction ij51 2 -- . find the velocity, va, of a. [2]  (ii) a particle b travels with velocity ij12 9 =-vb. find the speed, in ms\u20131, of b. [2]  particle a starts moving from the point with position vector ij20 7-. at the same time particle b starts  moving from the point with position vector ij1 67 1 -+ .  (iii) find ra, the position vector of a after t seconds, and rb, the position vector of b after t seconds.  [2]  (iv) find the time when the particles collide and the position vector of the point of collision.  [3]",
            "12": "12 0606/22/o/n/19 \u00a9 ucles 2019 9 mp b (5,-1)a (-3,5)(r,s)  the diagram shows the points  a (\u20133, 5) and  b (5, \u20131). the mid-point of ab is m and the line pm is  perpendicular to ab. the point p has coordinates ( r, s).  (i) find the equation of the line pm in the form ym xc=+ , where m and c are exact constants.  [5]  (ii) hence find an expression for s in terms of r. [1]",
            "13": "13 0606/22/o/n/19 \u00a9 ucles 2019 [turn over  (iii) given that the length of pm is 10 units, find the value of  r and of s. [5]",
            "14": "14 0606/22/o/n/19 \u00a9 ucles 2019 10 (i) given that   lnyxx 2= ,   find dd xy. [3]  (ii) find the coordinates of the stationary point on the curve   lnyxx 2= . [3]",
            "15": "15 0606/22/o/n/19 \u00a9 ucles 2019 [turn over  (iii) using your answer to part (i) , find   dln xxx3y  . [3]  (iv) hence evaluate    12 dln xxx3 y  . [2] question 11 is printed on the next page.",
            "16": "16 0606/22/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.11 do not use a calculator in this question.  solve the quadratic equation   xx 53 35 302-+ ++ = ^^ hh ,   giving your answers in the form   ab 5+ ,    where a and b are constants.  [6]"
        },
        "0606_w19_qp_23.pdf": {
            "1": "this document consists of 15 printed pages and 1 blank page. dc (nh/fc) 172299/2 \u00a9 ucles 2019  [turn over *3629900230* additional mathematics  0606/23 paper 2  october/november 2019  2 hours candidates answer on the question paper. additional materials:  electronic 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. you may use an hb pencil for any diagrams or graphs. do not use staples, paper clips, glue or correction fluid. do not  write in any barcodes. answer all the questions. give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of  angles  in degrees, unless a different level of accuracy is specified in the question. the use of an electronic calculator is expected, where appropriate. you are reminded of the need for clear presentation in your answers. at the end of the examination, fasten all your work securely together. 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 80.cambridge assessment international education cambridge international general certificate of secondary education",
            "2": "2 0606/23/o/n/19 \u00a9 ucles 2019 mathematical formulae 1. algebra quadratic equation  for the equation ax2 + bx + c = 0, xabb ac 242!=-- . binomial theorem (a + b)n = an + (n 1)an\u20131 b + (n 2)an\u20132 b2 + \u2026 + (n r)an\u2013r br + \u2026 + bn,  where n is a positive integer and (n r) = n! (n \u2013 r)!r! . 2. trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc a sin a = b sin b = c sin c a2 = b2 + c2 \u2013 2bc cos a \u2206 = 1  2 bc sin a",
            "3": "3 0606/23/o/n/19 \u00a9 ucles 2019 [turn over 1 solve   xx32 4 += +. [3] 2 (i) show that   coscosc otcosxxxx1ecec--= . [3]  (ii) hence solve   coscosc ot xxx 12ec --=  for   \u00b0\u00b0x 0 18011 . [2]",
            "4": "4 0606/23/o/n/19 \u00a9 ucles 2019 3 the first four terms in the expansion of   () () ax bx 125++    are   xx cx 23 2 21023++ + , where a, b and c are  integers. show that   aa31 62 102-+ =   and hence find the values of a, b and c. [8]",
            "5": "5 0606/23/o/n/19 \u00a9 ucles 2019 [turn over 4 (i) given that   yx x 24 72=- -,   write y in the form ()ax bc2-+ , where a, b and c are constants.  [3]  (ii) hence write down the minimum value of y and the value of x at which it occurs.  [2]  (iii) using your answer to part (i) , solve the equation  pp24 70 -- =, giving your answer correct to  2 decimal places.  [3]",
            "6": "6 0606/23/o/n/19 \u00a9 ucles 2019 5 (a) solve   coty 3412 r-=bl    for y011 r radians.  [4]  (b) solve   cott an cose c zz z 77+=    for \u00b0\u00b0z 0 360 gg . [6]",
            "7": "7 0606/23/o/n/19 \u00a9 ucles 2019 [turn over 6 do not use a calculator in this question. c b a33\u2013 33+  (i) find tan acb  in the form rs 3+ , where r and s are integers.  [3]  (ii) find ac in the form tu, where t and u are integers and t1!. [3]",
            "8": "8 0606/23/o/n/19 \u00a9 ucles 2019 7 oy xx = 2 ()yxx36 22=++  the diagram shows part of the curve   ()yxx326 2=++    and the line x2=.  (i) find, correct to 2 decimal places, the coordinates of the stationary point.  [6]",
            "9": "9 0606/23/o/n/19 \u00a9 ucles 2019 [turn over  (ii) find the area of the shaded region, showing all your working.  [4]",
            "10": "10 0606/23/o/n/19 \u00a9 ucles 2019 8 the roots of the equation   xa xb x24 032++ +=    are 2, 3 and p, where p is an integer.  (i) find the value of p. [1]  (ii) show that a 1=- and find the value of b. [4]",
            "11": "11 0606/23/o/n/19 \u00a9 ucles 2019 [turn over  given that a curve has equation   yxxb x2432=- ++    find, using your value of b,  (iii) xy dd , [1]  (iv) the integer value of x for which the gradient of the curve is 2 and the corresponding value of y. [3]  the coordinates of the point p on the curve are given by the values of x and y found in part (iv) .  (v) find the equation of the tangent to the curve at p. [1]",
            "12": "12 0606/23/o/n/19 \u00a9 ucles 2019 9 b o a cd x  the diagram shows points o, a, b, c, d and x. the position vectors of a, b, and  c relative to o are , oa a=    ob b2=  and oc a3= . the vector cd b=.  (i) given that ax adm= , find ox in terms of m, a and b. [2]  (ii) given that bx bcn= , find ox in terms of n, a and b. [2]",
            "13": "13 0606/23/o/n/19 \u00a9 ucles 2019 [turn over  (iii) hence find the value of m and of n. [4]  (iv) find the ratio xdax. [1]",
            "14": "14 0606/23/o/n/19 \u00a9 ucles 2019 10 the functions f and g are defined by () () , () .ln xx x xx3232 4ff or ge forrx22 !=+ - =-  (i) solve ()x 5 gf=. [5]",
            "15": "15 0606/23/o/n/19 \u00a9 ucles 2019  (ii) find   ()x f1-. [2]  (iii) solve   () () xx fg1=-. [4]",
            "16": "16 0606/23/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.blank page"
        }
    },
    "2020": {
        "0606_m20_qp_12.pdf": {
            "1": "dc (nf/cb) 196735/3 r \u00a9 ucles 2020  [turn overthis document has 16 pages. blank pages are indicated. *6562346474* additional mathematics  0606/12 paper 1  february/march  2020  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].cambridge igcse\u2122",
            "2": "2 0606/12/f/m/20 \u00a9 ucles 2020 mathematical formulae 1.algebra quadratic equation    for the equation ax2 + bx + c = 0, xabb ac 242!=-- binomial theorem () \u2026\u2026 ab anabnabn rab b12nn nn nr rn 12 2+=++ ++ ++-- -j lkkj lkkj lkkn poon poon poo    where n is a positive integer and () !!! n r nr rn=-j lkkn poo arithmetic series ua n d sn al na n d1 21 212 1n n\u2212 \u2212=+ = += + ^^ ^ hh h #- geometric series ua r sra rr srar111 11nn nn1 1!\u2212\u2212 \u2212= = =3\u2212 ^ ^^h hh 2.trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc sins in sin aa bb cc== a2 = b2 + c2 \u2013 2bc cos a \u2206 = 21 bc sin a",
            "3": "3 0606/12/f/m/20 \u00a9 ucles 2020 [turn over 1 (a) on the axes below sketch the graph of    () () () y xxx32 41 =- --+ ,   showing the coordinates of  the points where the curve intersects the coordinate axes.  [3] oy x  (b) hence find the values of x for which   () () () xxx32 41 02 ---+ . [2]",
            "4": "4 0606/12/f/m/20 \u00a9 ucles 2020 2 find the values of k for which the line   yk x3 =+    is a tangent to the curve   yx xk 24 12=+ +- . [5]",
            "5": "5 0606/12/f/m/20 \u00a9 ucles 2020 [turn over 3 the first 3 terms in the expansion of    () ax35- ,  in ascending powers of x, can be written in the form    bx cx 812-+ . find the value of each of a, b and c. [5]",
            "6": "6 0606/12/f/m/20 \u00a9 ucles 2020 4 the tangent to the curve    ln yxx34623 =- - `j ,   at the point where , x 2= meets the y-axis at the   point  p. find the exact coordinates of p. [6]",
            "7": "7 0606/12/f/m/20 \u00a9 ucles 2020 [turn over 5 do not use a calculator in this question.  in this question all lengths are in centimetres. a b cd 24 3+53-  the diagram shows the isosceles triangle abc , where    ab ac=  and bc 24 3 =+ .   the height,  ad, of the triangle is 53- .  (a) find the area of the triangle abc , giving your answer in the form ab 3+ , where a and b are  integers.  [2]  (b) find , tanabc giving your answer in the form cd 3+ , where c and d are integers.  [3]  (c) find secabc2, giving your answer in the form ef 3+ , where e and f are integers.  [2]",
            "8": "8 0606/12/f/m/20 \u00a9 ucles 2020 6 solutions by accurate drawing will not be accepted.  the points a and b have coordinates (, ) 24-  and (, ) 610 respectively.  (a) find the equation of the perpendicular bisector of the line ab, giving your answer in the form  ax by c0 ++ =, where a, b and c are integers.  [4]  the point c has coordinates (, )p5  and lies on the perpendicular bisector of ab.  (b)  find the value of  p. [1]  it is given that the line ab bisects the line cd.  (c)  find the coordinates of d. [2]",
            "9": "9 0606/12/f/m/20 \u00a9 ucles 2020 [turn over 7 ()xa xx bx 31 2 p32=+ +-    has a factor of    x21+.   when ()xp is divided by   x3-  the remainder  is 105.  (a) find the value of a and of b. [5]  (b) using your values of a and b, write ()xp as a product of   x21+   and a quadratic factor.  [2]  (c) hence solve ()x 0 p=. [2]",
            "10": "10 0606/12/f/m/20 \u00a9 ucles 2020 8 in this question all distances are in km.  a ship  p sails from a point a, which has position vector 0 0eo, with a speed of 52  kmh-1 in the direction of   5 12-eo .  (a) find the velocity vector of the ship.  [1]  (b) write down the position vector of p at a time t hours after leaving a. [1]  at the same time that ship p sails from  a, a ship q sails from a point b, which has position vector 12 8eo ,   with velocity vector 25 45-eo  kmh-1.  (c) write down the position vector of  q at a time t hours after leaving b. [1]  (d) using your answers to parts (b)  and (c), find the displacement vector pq at time t hours.  [1]",
            "11": "11 0606/12/f/m/20 \u00a9 ucles 2020 [turn over  (e) hence show that pq tt34 168 2082=- + . [2]  (f) find the value of t when p and q are first 2  km  apart.  [2]",
            "12": "12 0606/12/f/m/20 \u00a9 ucles 2020 9 (a) (i) find how many different 4-digit numbers can be formed using the digits 2, 3, 5, 7, 8 and 9, if  each digit may be used only once in any number.  [1]   (ii) how many of the numbers found in part (i)  are divisible by 5?  [1]   (iii) how many of the numbers found in part (i)  are odd and greater than 7000?  [4]",
            "13": "13 0606/12/f/m/20 \u00a9 ucles 2020 [turn over  (b) the number of combinations of n items taken 3 at a time is 92 n. find the value of the constant n.  [4]",
            "14": "14 0606/12/f/m/20 \u00a9 ucles 2020 10 (a) solve   \u00b0 tan4 521a+= - `j   for 0 360 \u00b0\u00b0gga . [3]  (b) (i) show that   sins inseca11 11 2 iii--+= ,   where a is a constant to be found.  [3]",
            "15": "15 0606/12/f/m/20 \u00a9 ucles 2020 [turn over   (ii) hence solve   sins in 311 3118zz--+=-    for 33ggrrz -  radians.  [5] question 11 is on the next page.",
            "16": "16 0606/12/f/m/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 given that   .lnxx xx232 313124 da 1++--=j lkkn poo y    and that a 12, find the value of a. [7]"
        },
        "0606_m20_qp_22.pdf": {
            "1": "cambridge igcse\u2122*1552216622* dc (pq/cb) 196734/3 r \u00a9 ucles 2020  [turn overthis document has 16 pages. blank pages are indicated.additional mathematics  0606/22 paper 2  february/march  2020  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].",
            "2": "2 0606/22/f/m/20 \u00a9 ucles 2020 mathematical formulae 1.algebra quadratic equation    for the equation ax2 + bx + c = 0, xabb ac 242!=-- binomial theorem () \u2026\u2026 ab anabnabn rab b12nn nn nr rn 12 2+=++ ++ ++-- -j lkkj lkkj lkkn poon poon poo    where n is a positive integer and () !!! n r nr rn=-j lkkn poo arithmetic series ua n d sn al na n d1 21 212 1n n\u2212 \u2212=+ = += + ^^ ^ hh h #- geometric series ua r sra rr srar111 11nn nn1 1!\u2212\u2212 \u2212= = =3\u2212 ^ ^^h hh 2.trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc sins in sin aa bb cc== a2 = b2 + c2 \u2013 2bc cos a \u2206 = 21 bc sin a",
            "3": "3 0606/22/f/m/20 \u00a9 ucles 2020 [turn over 1 find the values of x for which   () () . xx xx 12 20 52 1121 -+ +-   [4]  2 variables x and y are such that, when 1g  y is plotted against ,x3 a straight line graph passing through the  points (6, 7) and (10, 9) is obtained. find y as a function of x. [4]",
            "4": "4 0606/22/f/m/20 \u00a9 ucles 2020 3 find the exact solution of   . 33 40xx21-- =+  [4] 4 the position vectors of three points, a, b and c, relative to an origin o, are ,5 7- -eo  10 4-eo  and x yeo respectively. given that , ac bc4=  find the unit vector in the direction of .oc  [5]",
            "5": "5 0606/22/f/m/20 \u00a9 ucles 2020 [turn over 5 (a) on the axes below, sketch the graph of   , yx 57=-    showing the coordinates of the points  where the graph meets the coordinate axes.  [3] oy x  (b) solve   . x5751 14 -- =  [3]",
            "6": "6 0606/22/f/m/20 \u00a9 ucles 2020 6 (a) a circle has a radius of 6  cm. a sector of this circle has a perimeter of 26 5r+`j  cm. find the area  of this sector.  [4]  (b)   o7 cma brad4r   the diagram shows the sector aob  of a circle with centre o and radius 7  cm.   angle aob4r= radians. find the perimeter of the shaded region.  [3]",
            "7": "7 0606/22/f/m/20 \u00a9 ucles 2020 [turn over 7 find the coordinates of the points of intersection of the curves   xy 512=-    and   . yx x212=- + [5]",
            "8": "8 0606/22/f/m/20 \u00a9 ucles 2020 8  12 0 - 1 - 2 - 3 - 4 - 5 - 6f(x) x2r 34r 38r 32r  the diagram shows the graph of   f()c os xa bx c =+    for x038ggr   radians.  (a) explain why f is a function.  [1]  (b) write down the range of f.  [1]  (c) find the value of each of the constants a, b and c. [4]",
            "9": "9 0606/22/f/m/20 \u00a9 ucles 2020 [turn over 9 variables x and y are such that   .sinyxx ex 23 =    use differentiation to find the approximate change in y  as x increases from 0.5 to .,h 05+ where h is small.  [6]",
            "10": "10 0606/22/f/m/20 \u00a9 ucles 2020 10 (a)  g()xx31=+    for . x 1h   (i) find an expression for g( ).x1- [2]   (ii) write down the range of g.1- [1]   (iii) find the domain of g.1- [2]",
            "11": "11 0606/22/f/m/20 \u00a9 ucles 2020 [turn over  (b)  ()x31- ()x 21n= h    for . x32h   the graph of ()xh y=  intersects the line yx= at two distinct points. on the axes below, sketch  the graph of  ()xh y=  and hence sketch the graph of h( ). yx1=-  [4] oy x",
            "12": "12 0606/22/f/m/20 \u00a9 ucles 2020 11  rh  a container is a circular cylinder, open at one end, with a base radius of r cm and a height of h cm. the  volume of the container is 1000  cm3. given that r and h can vary and that the total outer surface area of  the container has a minimum value, find this value.  [8]",
            "13": "13 0606/22/f/m/20 \u00a9 ucles 2020 [turn over 12 a particle p moves in a straight line such that, t seconds after passing through a fixed point o, its  acceleration, a ms2-, is given by . a 6=-  when , t 0= the velocity of p is ms181-.   (a) find the time at which p comes to instantaneous rest.  [3]  (b) find the distance travelled by p in the 3rd second.  [3]",
            "14": "14 0606/22/f/m/20 \u00a9 ucles 2020 13 (a) the sum of the first two terms of a geometric progression is 10 and the third term is 9.   (i) find the possible values of the common ratio and the first term.  [5]   (ii) find the sum to infinity of the convergent progression.  [1]",
            "15": "15 0606/22/f/m/20 \u00a9 ucles 2020  (b) in an arithmetic progression, u 101=-  and . u 144=  find   , uu uu100 101 102 200f +++ +    the sum  of the 100th to the 200th terms of the progression.  [4]",
            "16": "16 0606/22/f/m/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"
        },
        "0606_s20_qp_11.pdf": {
            "1": "cambridge igcse\u2122this document has 16 pages. blank pages are indicated. dc (leg/sw) 196733/3 r \u00a9 ucles 2020  [turn over *4440026581* additional mathematics  0606/11 paper 1  may/june  2020  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].",
            "2": "2 0606/11/m/j/20 \u00a9 ucles 2020 mathematical formulae 1.algebra quadratic equation    for the equation ax2 + bx + c = 0, xabb ac 242!=-- binomial theorem () \u2026\u2026 ab anabnabn rab b12nn nn nr rn 12 2+=++ ++ ++-- -j lkkj lkkj lkkn poon poon poo    where n is a positive integer and () !!! n r nr rn=-j lkkn poo arithmetic series ua n d sn al na n d1 21 212 1n n\u2212 \u2212=+ = += + ^^ ^ hh h #- geometric series ua r sra rr srar111 11nn nn1 1!\u2212\u2212 \u2212= = =3\u2212 ^ ^^h hh 2.trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc sins in sin aa bb cc== a2 = b2 + c2 \u2013 2bc cos a \u2206 = 21 bc sin a",
            "3": "3 0606/11/m/j/20 \u00a9 ucles 2020 [turn over 1 the diagram shows the graph of a cubic curve   f() yx= . y x 5 05 \u2013 1 \u2013 2() yx f=  (a) find an expression for f()x. [2]  (b) solve f()x 0g. [2]",
            "4": "4 0606/11/m/j/20 \u00a9 ucles 2020 2 (a) write down the period of cosx231-. [1]  (b) on the axes below, sketch the graph of   cos yx231 =-    for  \u00b0\u00b0x 360 360 gg - .  [3] y x \u2013 360\u00b0 \u2013 180\u00b0 180\u00b0 360\u00b0 \u2013 101 \u2013 22 \u2013 33",
            "5": "5 0606/11/m/j/20 \u00a9 ucles 2020 [turn over 3 the radius, r cm, of a circle is increasing at the rate of 5  cms\u20131. find, in terms of r, the rate at which the  area of the circle is increasing when  r3=. [4]",
            "6": "6 0606/11/m/j/20 \u00a9 ucles 2020 4 do not use a calculator in this question.  find the positive solution of the equation   xx 54 74 27 102++ -- = `` jj ,   giving your answer in  the form ab 7+ , where a and b are fractions in their simplest form.  [5]",
            "7": "7 0606/11/m/j/20 \u00a9 ucles 2020 [turn over 5 find the equation of the tangent to the curve lnyxx 2312 =+- `j  at the point where x1=. give your   answer in the form ym xc=+ , where m and c are constants correct to 3 decimal places.  [6]",
            "8": "8 0606/11/m/j/20 \u00a9 ucles 2020 6 the line   yx56=+    meets the curve   xy 8=   at the points a and b.  (a) find the coordinates of a and of b. [3]  (b) find the coordinates of the point where the perpendicular bisector of the line  ab meets the   line yx=. [5]",
            "9": "9 0606/11/m/j/20 \u00a9 ucles 2020 [turn over 7 12 cmradi 9.6 cmcd a bmo  the diagram shows an isosceles triangle oab  such that oa ob=  and angle aobi= radians. the  points c and d lie on oa and ob respectively. cd is an arc of length 9.6  cm of the circle, centre o,  radius 12  cm. the arc cd touches the line ab at the point m.  (a) find the value of i. [1]  (b) find the total area of the shaded regions.  [4]  (c) find the total perimeter of the shaded regions.  [3]",
            "10": "10 0606/11/m/j/20 \u00a9 ucles 2020 8 (a) show that   xx233 233 -++   can be written as   xx 4912 2-. [2]  (b) hence find   dxxx4912 2-y ,   giving your answer as a single logarithm and an arbitrary constant.  [3]",
            "11": "11 0606/11/m/j/20 \u00a9 ucles 2020 [turn over  (c) given that   a dl nxxx49125522-= y , where a 22, find the exact value of a. [4]",
            "12": "12 0606/11/m/j/20 \u00a9 ucles 2020 9 (a) an arithmetic progression has a second term of 14- and a sum to 21 terms of 84. find the first  term and the 21st term of this progression.  [5]",
            "13": "13 0606/11/m/j/20 \u00a9 ucles 2020 [turn over  (b) a geometric progression has a second term of p272 and a fifth term of p5. the common ratio, r, is  such that r 0111 .   (i) find r in terms of p. [2]   (ii) hence find, in terms of p, the sum to infinity of the progression.  [3]   (iii) given that the sum to infinity is 81, find the value of p. [2]",
            "14": "14 0606/11/m/j/20 \u00a9 ucles 2020 10 (a) (i) show that   secs eccot11 1122 iii--+= . [3]   (ii) hence solve   secs ec xx11 11 226--+=   for \u00b0x 90 90\u00b011- . [5]",
            "15": "15 0606/11/m/j/20 \u00a9 ucles 2020 [turn over  (b) solve   cose cy32r+=bl    for y02gg r radians, giving your answers in terms of r. [4] question 11 is printed on the next page.",
            "16": "16 0606/11/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.11 a curve is such that   ddcosxyx 5222 = .   this curve has a gradient of 43 at the point ,12 45rr-bl . find the  equation of this curve.  [8]"
        },
        "0606_s20_qp_12.pdf": {
            "1": "*5814812485* dc (nf/cb) 196732/3 r \u00a9 ucles 2020  [turn overthis document has 16 pages. blank pages are indicated.additional mathematics  0606/12 paper 1  may/june  2020  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].cambridge igcse\u2122",
            "2": "2 0606/12/m/j/20 \u00a9 ucles 2020 mathematical formulae 1.algebra quadratic equation    for the equation ax2 + bx + c = 0, xabb ac 242!=-- binomial theorem () \u2026\u2026 ab anabnabn rab b12nn nn nr rn 12 2+=++ ++ ++-- -j lkkj lkkj lkkn poon poon poo    where n is a positive integer and () !!! n r nr rn=-j lkkn poo arithmetic series ua n d sn al na n d1 21 212 1n n\u2212 \u2212=+ = += + ^^ ^ hh h #- geometric series ua r sra rr srar111 11nn nn1 1!\u2212\u2212 \u2212= = =3\u2212 ^ ^^h hh 2.trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc sins in sin aa bb cc== a2 = b2 + c2 \u2013 2bc cos a \u2206 = 21 bc sin a",
            "3": "3 0606/12/m/j/20 \u00a9 ucles 2020 [turn over 1 on the axes below, sketch the graph of   () () () yx xx212 =-++    showing the coordinates of the  points where the curve meets the axes.  [3] oy x",
            "4": "4 0606/12/m/j/20 \u00a9 ucles 2020 2 the volume, v, of a sphere of radius r is given by vr34 3r= .  the radius, r cm, of a sphere is increasing at the rate of 0.5  cms-1. find, in terms of r, the rate of change  of the volume of the sphere when . r025= . [4]",
            "5": "5 0606/12/m/j/20 \u00a9 ucles 2020 [turn over 3 (a) find the first 3 terms in the expansion of   x4166 -bl    in ascending powers of x. give each term in  its simplest form.  [3]  (b) hence find the term independent of x in the expansion of   xxx41616 2 --b bl l. [3]",
            "6": "6 0606/12/m/j/20 \u00a9 ucles 2020 4 (a) (i) find how many different 5-digit numbers can be formed using the digits 1, 2, 3, 5, 7 and 8, if  each digit may be used only once in any number.  [1]   (ii) how many of the numbers found in part (i)  are not divisible by 5?  [1]   (iii) how many of the numbers found in part (i)  are even and greater than 30  000?  [4]  (b) the number of combinations of n items taken 3 at a time is 6 times the number of combinations  of n items taken 2 at a time. find the value of the constant n. [4]",
            "7": "7 0606/12/m/j/20 \u00a9 ucles 2020 [turn over 5     :( ) xx 23 f27 +    for x02  (a) find the range of f.  [1]  (b) explain why f has an inverse.  [1]  (c) find f-1. [3]  (d) state the domain of f-1. [1]  (e) given that   :( ) lnxx 4 g7 +   for , x 02  find the exact solution of    ()x 49 fg= . [3]",
            "8": "8 0606/12/m/j/20 \u00a9 ucles 2020 6  oy xd (1, 0) ca bxy25+=-xy30+=  the diagram shows the straight line  xy25+=-  and part of the curve   xy30+= . the straight line  intersects the x-axis at the point a and intersects the curve at the point b. the point c lies on the curve.  the point d has coordinates (, ) 10. the line cd is parallel to the y-axis.  (a) find the coordinates of each of the points a and b. [3]",
            "9": "9 0606/12/m/j/20 \u00a9 ucles 2020 [turn over  (b) find the area of the shaded region, giving your answer in the form lnpq+ , where p and q are  positive integers.  [6]",
            "10": "10 0606/12/m/j/20 \u00a9 ucles 2020 7 (a) given that     yx x 15 22=- + `j ,    show that     xy xax bxc 25 2 dd2 =+++,    where a, b and c are  integers.  [5]",
            "11": "11 0606/12/m/j/20 \u00a9 ucles 2020 [turn over  (b) find the coordinates of the stationary point of the curve    yx x 15 22=- + `j , for x02. give  each coordinate correct to 2 significant figures.  [3]  (c) determine the nature of this stationary point.  [2]",
            "12": "12 0606/12/m/j/20 \u00a9 ucles 2020 8  o rbqpa  the diagram shows a triangle oab  such that oa a= and ob b=. the point p lies on oa such that   op oa43= . the point q is the mid-point of ab. the lines ob and pq are extended to meet at the    point  r. find, in terms of a and b,  (a) ab, [1]  (b) pq. give your answer in its simplest form.  [3]",
            "13": "13 0606/12/m/j/20 \u00a9 ucles 2020 [turn over  it is given that   npqq r=    and   , br kb=    where n and k are positive constants.  (c) find qr in terms of n, a and b. [1]  (d) find qr in terms of k, a and b. [2]  (e) hence find the value of n and of k. [3]",
            "14": "14 0606/12/m/j/20 \u00a9 ucles 2020 9 (a) a particle p moves in a straight line such that its displacement, x m, from a fixed point o at time t s  is given by   sin xt10 25 =- .   (i) find the speed of p when tr=. [1]   (ii) find the value of t for which p is first at rest.  [2]   (iii) find the acceleration of p when it is first at rest.  [2]",
            "15": "15 0606/12/m/j/20 \u00a9 ucles 2020 [turn over  (b)  v t sv ms\u20131 0 5 10 15 20 25   the diagram shows the velocity\u2013time graph for a particle q travelling in a straight line with  velocity v ms-1 at time t s. the particle accelerates at 3.5  ms-2 for the first 10  s of its motion and  then travels at constant velocity, v ms-1, for 10  s. the particle then decelerates at a constant rate  and comes to rest. the distance travelled during the interval t 20 25gg  is 112.5  m.   (i) find the value of v. [1]   (ii) find the velocity of q when t25= . [3]   (iii) find the value of t when q comes to rest.  [3] question 10 is printed on the next page.",
            "16": "16 0606/12/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 (a) solve   tanx31=-    for x22ggrr-  radians, giving your answers in terms of r. [4]  (b) use your answers to part (a)  to sketch the graph of    tan yx 43 4 =+    for   x22ggrr-  radians    on the axes below. show the coordinates of the points where the curve meets the axes. oy x r 2\u2013r 4\u2013r 2r 4 [3]"
        },
        "0606_s20_qp_13.pdf": {
            "1": "cambridge igcse\u2122dc (jc/ct) 196731/3 r \u00a9 ucles 2020  [turn overthis document has 16 pages. blank pages are indicated. *2037547431* additional mathematics  0606/13 paper 1  may/june  2020  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].",
            "2": "2 0606/13/m/j/20 \u00a9 ucles 2020 mathematical formulae 1.algebra quadratic equation    for the equation ax2 + bx + c = 0, xabb ac 242!=-- binomial theorem () \u2026\u2026 ab anabnabn rab b12nn nn nr rn 12 2+=++ ++ ++-- -j lkkj lkkj lkkn poon poon poo    where n is a positive integer and () !!! n r nr rn=-j lkkn poo arithmetic series ua n d sn al na n d1 21 212 1n n\u2212 \u2212=+ = += + ^^ ^ hh h #- geometric series ua r sra rr srar111 11nn nn1 1!\u2212\u2212 \u2212= = =3\u2212 ^ ^^h hh 2.trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc sins in sin aa bb cc== a2 = b2 + c2 \u2013 2bc cos a \u2206 = 21 bc sin a",
            "3": "3 0606/13/m/j/20 \u00a9 ucles 2020 [turn over 1   () e x 3 fx=+  for xr!    ()xx 95 g=-  for xr!  (a) find the range of f and of g.  [2]  (b) find the exact solution of   () () xx fg1=-l. [3]  (c) find the solution of   ()x 112 g2= . [2]",
            "4": "4 0606/13/m/j/20 \u00a9 ucles 2020 2 (a) given that   logl og xy2824+= ,   find the value of xy. [3]  (b) using the substitution y2x= , or otherwise, solve   22 21 0xx x 21 1-- +=++. [4]",
            "5": "5 0606/13/m/j/20 \u00a9 ucles 2020 [turn over 3 at time t s, a particle travelling in a straight line has acceleration ()t21 ms221+--. when t0=, the  particle is 4  m from a fixed point o and is travelling with velocity 8ms1- away from o.   (a) find the velocity of the particle at time t s. [3]  (b) find the displacement of the particle from o at time t s. [4]",
            "6": "6 0606/13/m/j/20 \u00a9 ucles 2020 4 (a) write   xx23 42+-    in the form ()ax bc2++ , where a, b and c are constants.  [3]  (b) hence write down the coordinates of the stationary point on the curve   yx x 23 42=+ -. [2]  (c) on the axes below, sketch the graph of   yx x 23 42=+ -,   showing the exact values of the  intercepts of the curve with the coordinate axes.  [3] oy x  (d) find the value of k for which   xx k 23 42+- =   has exactly 3 values of x. [1]",
            "7": "7 0606/13/m/j/20 \u00a9 ucles 2020 [turn over 5    ()xx ax xb 61 2 p32=+ ++ , where a and b are integers.  ()xp has a remainder of 11 when divided by x3- and a remainder of 21- when divided by x1+.  (a) given that   () () () xx qx2 p=- ,   find ()qx , a quadratic factor with numerical coefficients.  [6]  (b) hence solve   ()x 0 p=. [2]",
            "8": "8 0606/13/m/j/20 \u00a9 ucles 2020 6 (a) find the unit vector in the direction of 5 12-eo . [1]  (b) given that   kr4 12 310 5+-=-ee e oo o,   find the value of each of the constants k and r. [3]",
            "9": "9 0606/13/m/j/20 \u00a9 ucles 2020 [turn over  (c) relative to an origin o, the points a, b and c have position vectors p, 3qp- and 95qp-    respectively.   (i) find ab in terms of p and q. [1]   (ii) find ac in terms of p and q. [1]   (iii) explain why a, b and c all lie in a straight line.  [1]   (iv) find the ratio   ab : bc. [1]",
            "10": "10 0606/13/m/j/20 \u00a9 ucles 2020 7 o ac d bradi 12 cm10 cm  the diagram shows an isosceles triangle oab  such that oa ob 12cm ==  and angle aobi= radians.  points c and d lie on oa and ob respectively such that cd is an arc of the circle, centre o, radius  10 cm. the area of the sector ocd35cm2= .  (a) show that .07i= . [1]  (b) find the perimeter of the shaded region.  [4]  (c) find the area of the shaded region.  [3]",
            "11": "11 0606/13/m/j/20 \u00a9 ucles 2020 [turn over 8 (a) an arithmetic progression has a first term of 7 and a common difference of 0.4. find the least  number of terms so that the sum of the progression is greater than 300.  [4]   (b) the sum of the first two terms of a geometric progression is 9 and its sum to infinity is 36. given  that the terms of the progression are positive, find the common ratio.  [4]",
            "12": "12 0606/13/m/j/20 \u00a9 ucles 2020 9 xy 2= x3=yx53\u2013=y xo ba cd   the diagram shows part of the curve   xy 2=   intersecting the straight line   yx53=-    at the point a.  the straight line meets the x-axis at the point b. the point c lies on the x-axis and the point d lies on  the curve such that the line cd has equation   x3=.   find the exact area of the shaded region, giving  your answer in the form lnpq+ , where p and q are constants.  [8]",
            "13": "13 0606/13/m/j/20 \u00a9 ucles 2020 [turn over additional working space for question 9.",
            "14": "14 0606/13/m/j/20 \u00a9 ucles 2020 10 (a) given that   yx x2 =+ ,   show that   y x xax b 22 dd=++,   where a and b are constants.  [5]",
            "15": "15 0606/13/m/j/20 \u00a9 ucles 2020  (b) find the exact coordinates of the stationary point of the curve   yx x2 =+ . [3]  (c) determine the nature of this stationary point.  [2]",
            "16": "16 0606/13/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"
        },
        "0606_s20_qp_21.pdf": {
            "1": "cambridge igcse\u2122*3574984631* dc (pq/cb) 183937/5 \u00a9 ucles 2020  [turn overthis document has 16 pages. blank pages are indicated.additional mathematics  0606/21 paper 2  may/june  2020  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].",
            "2": "2 0606/21/m/j/20 \u00a9 ucles 2020 mathematical formulae 1. algebra quadratic equation  for the equation ax bx c02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o  where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ -  () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=-  ()() srarr111nn ! =--  () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/21/m/j/20 \u00a9 ucles 2020 [turn over 1 variables x and y are such that, when y4 is plotted against ,x1 a straight line graph passing through the  points (0.5, 9) and (3, 34) is obtained. find y as a function of x. [4] 2 (a) write   xx91 252-+    in the form () , px qr2-+  where p, q and r are constants.  [3]   (b) hence write down the coordinates of the minimum point of the curve   . yx x 91 252=- + [1]",
            "4": "4 0606/21/m/j/20 \u00a9 ucles 2020 3 do not use a calculator in this question.     p()xx xx 15 22 15 232=+ -+  (a) find the remainder when ()xp is divided by . x1+ [2]  (b) (i) show that x2+ is a factor of ()xp.  [1]   (ii) write ()xp as a product of linear factors.  [3]",
            "5": "5 0606/21/m/j/20 \u00a9 ucles 2020 [turn over 4 (a) in an examination, candidates must select 2 questions from the 5 questions in section a and select  4 questions from the 8 questions in section b. find the number of ways in which this can be done.  [2]  (b) the digits of the number 6  378 129 are to be arranged so that the resulting 7-digit number is even.  find the number of ways in which this can be done.   [2] 5 the vectors a and b are such that   ai ja=+    and    . bi j 12 b =+    (a) find the value of each of the constants a and b such that   () . ab ij 43 2 a -= +-  [3]   (b) hence find the unit vector in the direction of   . ba 4-  [2]",
            "6": "6 0606/21/m/j/20 \u00a9 ucles 2020 6 find the values of k for which the line   yk x7 =-    and the curve   yx x 38 52=+ +   do not intersect.  [6]",
            "7": "7 0606/21/m/j/20 \u00a9 ucles 2020 [turn over 7 (a) solve the simultaneous equations , 10 5xy2=+ 10 50xy34=+,   giving x and y in exact simplified form.  [4]  (b) solve   . xx21 0032 31-- = [3]",
            "8": "8 0606/21/m/j/20 \u00a9 ucles 2020 8 (a) expand   () ,x 25-    simplifying each coefficient.  [3]  (b) hence solve    eeee.()xx xx28 0 10 325 45 #=- +-  [4]",
            "9": "9 0606/21/m/j/20 \u00a9 ucles 2020 [turn over 9 a particle travels in a straight line. as it passes through a fixed point o, the particle is travelling at a  velocity of 3  ms\u20131. the particle continues at this velocity for 60 seconds then decelerates at a constant  rate for 15 seconds to a velocity of 1.6  ms\u20131. the particle then decelerates again at a constant rate for  5 seconds to reach point a, where it stops.    (a) sketch the velocity-time graph for this journey on the axes below.  [3] ov ms\u20131 t s  (b) find the distance between o and a.   [3]  (c) find the deceleration in the last 5 seconds.  [1]",
            "10": "10 0606/21/m/j/20 \u00a9 ucles 2020 10   oy x() yx 32=- yx432= (, ) bb 4 (, ) aa 0  the diagram shows part of the graphs of   yx432=    and   () yx 32=- .   the graph of () yx 32=-     meets the x-axis at the point a(a, 0) and the two graphs intersect at the point b(b, 4).  (a) find the value of a and of b. [2]",
            "11": "11 0606/21/m/j/20 \u00a9 ucles 2020 [turn over  (b) find the area of the shaded region.  [5]",
            "12": "12 0606/21/m/j/20 \u00a9 ucles 2020 11 the function f is defined by   ()x21+ f()n l x=    for . x 0h  (a) sketch the graph of f() yx=  and hence sketch the graph of f( ) yx1=- on the axes below.  [3] oy x  the function g is defined by   g()( ) xx 412=- +   for . x 4g  (b) (i) find an expression for g( )x1- and state its domain and range.  [4]",
            "13": "13 0606/21/m/j/20 \u00a9 ucles 2020 [turn over   (ii) find and simplify an expression for fg().x [2]   (iii)  explain why the function gf does not exist.  [1]",
            "14": "14 0606/21/m/j/20 \u00a9 ucles 2020 12 (a) find the x-coordinates of the stationary points of the curve   e( ). yx 23x36=+  [6]    (b) a curve has equation f() yx=  and has exactly two stationary points. given that f( ),xx 47=-ll   f( .)05 0=l  and f( ),30=l  use the second derivative test to determine the nature of each of the  stationary points of this curve.  [2]",
            "15": "15 0606/21/m/j/20 \u00a9 ucles 2020  (c) in this question all lengths are in centimetres. x 4xh   the diagram shows a solid cuboid with height h and a rectangular base measuring 4 x by x. the  volume of the cuboid is 40  cm3. given that x and h can vary and that the surface area of the cuboid  has a minimum value, find this value.       [5]",
            "16": "16 0606/21/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.blank page"
        },
        "0606_s20_qp_22.pdf": {
            "1": "cambridge igcse\u2122*0698096858* dc (pq/cb) 183938/6 \u00a9 ucles 2020  [turn overthis document has 12 pages. blank pages are indicated.additional mathematics  0606/22 paper 2  may/june  2020  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].",
            "2": "2 0606/22/m/j/20 \u00a9 ucles 2020 mathematical formulae 1. algebra quadratic equation  for the equation ax bx c02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o  where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ -  () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=-  ()() srarr111nn ! =--  () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/22/m/j/20 \u00a9 ucles 2020 [turn over 1 variables x and y are such that   e. sin yxx=+-   use differentiation to find the approximate change in   y as x increases from 4r to ,h4r+ where h is small.  [4] 2 do not use a calculator in this question.  the point ,p 15-`j  lies on the curve   . yx10 25 2=+   find the exact value of p, simplifying your  answer.  [5]",
            "4": "4 0606/22/m/j/20 \u00a9 ucles 2020 3 find the values of  k for which the line   yx 3=-    intersects the curve   yk xk x5122=+ +   at two  distinct points.  [6]  4 the three roots of ()x 0 p=, where   ()xp xa xb xc 232=+ ++    are , x21= xn= and , xn=-  where  a, b, c and n are integers. the y-intercept of the graph of ()xp y=  is 4. find (),xp  simplifying your  coefficients.  [5]",
            "5": "5 0606/22/m/j/20 \u00a9 ucles 2020 [turn over 5 solutions to this question by accurate drawing will not be accepted.  the points a and b are (4, 3) and (12, \u22127) respectively.  (a) find the equation of the line l, the perpendicular bisector of the line ab.  [4]  (b) the line parallel to ab which passes through the point (5, 12) intersects l at the point c. find the  coordinates of c. [4]",
            "6": "6 0606/22/m/j/20 \u00a9 ucles 2020 6 (a) find the equation of the tangent to the curve   tan yx22 7 =+    at the point where . x8r=   give your answer in the form , ax ybcr-= + where a, b and c are integers.  [5]  (b) this tangent intersects the x-axis at p and the y-axis at q. find the length of pq. [2]",
            "7": "7 0606/22/m/j/20 \u00a9 ucles 2020 [turn over 7 giving your answer in its simplest form, find the exact value of  (a) d,xx5210 04 +y  [4]  (b) ed .xnlx422 02+`jy  [5]",
            "8": "8 0606/22/m/j/20 \u00a9 ucles 2020 8 (a) solve   cotc osec xx 31 42 02-- =   for \u00b0\u00b0 . x 0 36011  [5]  (b) show that   .cotsinc ostanc os sinyyyyy y 244-=-  [4]",
            "9": "9 0606/22/m/j/20 \u00a9 ucles 2020 [turn over 9 (a) solve the equation   .279243xx 25 =- [3]   (b)           , logl og ba21 ab-=   where a 02 and . b 02   solve this equation for b, giving your answers in terms of a. [5]",
            "10": "10 0606/22/m/j/20 \u00a9 ucles 2020 10 (a) the first 5 terms of a sequence are given below. 4   2-   1   .05-    0.25   (i) find the 20th term of the sequence.  [2]   (ii) explain why the sum to infinity exists for this sequence and find the value of this sum.  [2]",
            "11": "11 0606/22/m/j/20 \u00a9 ucles 2020 [turn over  (b) the tenth term of an arithmetic progression is 15 times the second term. the sum of the first  6 terms of the progression is 87.   (i) find the common difference of the progression.  [4]   (ii) for this progression, the nth term is 6990. find the value of n. [3] question 11 is printed on the next page.",
            "12": "12 0606/22/m/j/20 \u00a9 ucles 2020 11  a bc1c2  the circles with centres c1 and c2 have equal radii of length r cm. the line c1c2 is a radius of both  circles. the two circles intersect at a and b.  (a) given that the perimeter of the shaded region is 4 r cm, find the value of r.  [4]  (b) find the exact area of the shaded region.  [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."
        },
        "0606_s20_qp_23.pdf": {
            "1": "cambridge igcse\u2122*5963414462* dc (pq/cb) 183935/5 \u00a9 ucles 2020  [turn overthis document has 16 pages. blank pages are indicated.additional mathematics  0606/23 paper 2  may/june  2020  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].",
            "2": "2 0606/23/m/j/20 \u00a9 ucles 2020 mathematical formulae 1. algebra quadratic equation  for the equation ax bx c02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o  where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ -  () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=-  ()() srarr111nn ! =--  () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/23/m/j/20 \u00a9 ucles 2020 [turn over1 solutions to this question by accurate drawing will not be accepted.  find the equation of the perpendicular bisector of the line joining the points (4, 7-) and ( 8-, 9).  [4] 2 find the set of values of k for which   xk xk 44 23 02-+ +=    has no real roots.  [5]",
            "4": "4 0606/23/m/j/20 \u00a9 ucles 2020 3 (a) on the axes below, sketch the graph of   () () () , yx xx216 =-+- -    showing the coordinates of  the points where the graph meets the coordinate axes. oy x  [2]  (b) hence solve   () () () . xx x 216 0g -+ --   [2]",
            "5": "5 0606/23/m/j/20 \u00a9 ucles 2020 [turn over 4 (a) (i) find how many different 5-digit numbers can be formed using five of the eight digits  1, 2, 3, 4, 5, 6, 7, 8   if each digit can be used once only.  [2]   (ii) find how many of these 5-digit numbers are greater than 60  000. [2]  (b) a team of 3 people is to be selected from 4 men and 5 women. find the number of different teams  that could be selected which include at least 2 women.  [2]",
            "6": "6 0606/23/m/j/20 \u00a9 ucles 2020 5 do not use a calculator in this question.  (a) simplify   .72128 [2]  (b) simplify   131 32 33 +-+ ,   giving your answer as a fraction with an integer denominator.  [4]",
            "7": "7 0606/23/m/j/20 \u00a9 ucles 2020 [turn over 6 (a) the curve   sin ya bx c =+    has a period of 180\u00b0, an amplitude of 20 and passes through the point   (90\u00b0, 3-). find the value of each of the constants a, b and c. [3]  (b) the function g is defined, for \u00b0\u00b0 , x 135 135 gg -  by   () . tan xx324 g=-    sketch the graph of   () yx g=  on the axes below, stating the coordinates of the point where the graph crosses the  y-axis.  [2] 0 135\u00b0y x \u00b0135-",
            "8": "8 0606/23/m/j/20 \u00a9 ucles 2020 7 variables x and y are connected by the relationship   , ya xn=    where a and n are constants.  (a) transform the relationship   ya xn=    to straight line form.  [2]  when lyn is plotted against lxn a straight line graph passing through the points (0, 0.5) and (3.2, 1.7)  is obtained.  (b) find the value of n and of a. [4]  (c)  find the value of y when . x 11=  [2]",
            "9": "9 0606/23/m/j/20 \u00a9 ucles 2020 [turn over 8 (a) differentiate   () sin xx43+- tan y=    with respect to x. [2]  (b) variables x and y are such that   en( ).lyx 225 x3=+   use differentiation to find the approximate  change in y as x increases from 1 to 1 + h, where h is small.  [6]",
            "10": "10 0606/23/m/j/20 \u00a9 ucles 2020 9 do not use a calculator in this question.   (a) find the term independent of x in the binomial expansion of   xx316 -bl . [2]   (b) in the expansion of   x12n +bl    the coefficient of x4 is half the coefficient of x6. find the value of  the positive constant n. [6]",
            "11": "11 0606/23/m/j/20 \u00a9 ucles 2020 [turn over 10 solve the equation  (a) sect an aa 51 48 02+- =   for   , a 0 180 \u00b0\u00b0gg  [4]  (b)  sinb 54820r-+ = bl    for   b44ggrr-    radians.  [4]",
            "12": "12 0606/23/m/j/20 \u00a9 ucles 2020 11 in this question all lengths are in centimetres.  the volume, v, of a cone of height h and base radius  r is given by   . vr h31 2r= 180w 90r  the diagram shows a large hollow cone from which a smaller cone of height 180 and base radius 90  has been removed. the remainder has been fitted with a circular base of radius 90 to form a container  for water. the depth of water in the container is w and the surface of the water is a circle of radius r.   (a) find an expression for r in terms of w and show that the volume v of the water in the container is  given by   . vw12180 4860003 rr =+ - `j  [3]   ",
            "13": "13 0606/23/m/j/20 \u00a9 ucles 2020 [turn over  (b) water is poured into the container at a rate of 10  000 cm3s\u22121. find the rate at which the depth of the  water is increasing when . w 10=  [4]",
            "14": "14 0606/23/m/j/20 \u00a9 ucles 2020 12 (a) (i) given that   f(),cosxx1=    show that   f( ). tans ec xx x =l   [3]    (ii) hence find   ed . tans ecxx x 3x3 4- `jy  [3]",
            "15": "15 0606/23/m/j/20 \u00a9 ucles 2020  (b) given that   ,lpxpx102 dn 25 += y    find the value of the positive constant p. [5]",
            "16": "16 0606/23/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.blank page"
        },
        "0606_w20_qp_11.pdf": {
            "1": "cambridge igcse\u2122*3081135600* dc (pq/fc) 187997/3 \u00a9 ucles 2020  [turn overthis document has 16 pages. blank pages are indicated.additional mathematics  0606/11 paper 1  october/november  2020  2 hours 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 calculator where appropriate.   \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.   \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].",
            "2": "2 0606/11/o/n/20 \u00a9 ucles 2020 mathematical formulae 1. algebra quadratic equation  for the equation ax bx c02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o  where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ -  () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=-  ()() srarr111nn ! =--  () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/11/o/n/20 \u00a9 ucles 2020 [turn over 1  - 2 - 1 0 424y x  the diagram shows the graph of () yx p= , where ()xp is a cubic function. find the two possible  expressions for ()xp. [3] 2 (a) write down the amplitude of   cosx143+ bl. [1]  (b) write down the period of   cosx143+ bl. [1]  (c) on the axes below, sketch the graph of   cos yx143=+ bl   for x 180 180 \u00b0\u00b0 \u00b0 gg - .  - 60 60 120 180xy 0 - 120 - 180123456  [3]",
            "4": "4 0606/11/o/n/20 \u00a9 ucles 2020 3 (a) write   p qp rqr 313231 -`` jj    in the form pq rab c, where a, b and c are constants.  [3]  (b) solve   xx65 1032 31-+ =. [3]",
            "5": "5 0606/11/o/n/20 \u00a9 ucles 2020 [turn over 4 it is given that   sintanyxx3= .   (a) find the exact value of xy dd when x3r=. [4]  (b) hence find the approximate change in y as x increases from 3r to h3r+, where h is small.  [1]    (c) given that x is increasing at the rate of  3 units per second, find the corresponding rate of change in  y when x3r=, giving your answer in its simplest surd form.  [2]",
            "6": "6 0606/11/o/n/20 \u00a9 ucles 2020 5 (a) (i) find how many different 4-digit numbers can be formed using the digits 1, 3, 4, 6, 7 and 9.    each digit may be used once only in any 4-digit number.  [1]   (ii) how many of these 4-digit numbers are even and greater than 6000?  [3]",
            "7": "7 0606/11/o/n/20 \u00a9 ucles 2020 [turn over  (b) a committee of 5 people is to be formed from 6 doctors, 4 dentists and 3 nurses. find the number  of different committees that could be formed if   (i) there are no restrictions,  [1]   (ii) the committee contains at least one doctor,  [2]   (iii) the committee contains all the nurses.  [1]",
            "8": "8 0606/11/o/n/20 \u00a9 ucles 2020 6 a particle p is initially at the point with position vector 30 10eo and moves with a constant speed of  10ms1- in the same direction as 4 3-eo .   (a) find the position vector of p after t s. [3]  as p starts moving, a particle q starts to move such that its position vector after t s is given by  t80 905 12-+ ee oo .  (b) write down the speed of q. [1]    (c) find the exact distance between p and q when t10= , giving your answer in its simplest surd  form.  [3]",
            "9": "9 0606/11/o/n/20 \u00a9 ucles 2020 [turn over 7 it is given that   () ()ln xx 52 3 f=+    for x232-.    (a)  write down the range of f.  [1]  (b) find f1- and state its domain.  [3]  (c) on the axes below, sketch the graph of () yx f=  and the graph of () yx f1=-. label each curve   and state the intercepts on the coordinate axes. oy x  [5]",
            "10": "10 0606/11/o/n/20 \u00a9 ucles 2020 8 (a) (i) show that   () () cose cs in sinsec11 22 ii ii+-= . [4]   (ii) hence solve   () () cose cs in sin 143 2ii i +- =   for   \u00b0\u00b0180 180 ggi - . [4]",
            "11": "11 0606/11/o/n/20 \u00a9 ucles 2020 [turn over  (b) solve   sinc os 332332 rrzz+= + ee oo    for 032ggrz  radians, giving your answers in terms of r.  [4]",
            "12": "12 0606/11/o/n/20 \u00a9 ucles 2020 9 (a) given that   lnx xx1 2313 da 1-+= eoy ,   where a 02, find the exact value of a, giving your answer  in simplest surd form.  [6]",
            "13": "13 0606/11/o/n/20 \u00a9 ucles 2020 [turn over  (b) find the exact value of   sinc os xx x 2312 d 0r 3 r+- + e bl o y . [5]",
            "14": "14 0606/11/o/n/20 \u00a9 ucles 2020 10 (a) an arithmetic progression has a second term of 8 and a fourth term of 18. find the least number of  terms for which the sum of this progression is greater than 1560.  [6]",
            "15": "15 0606/11/o/n/20 \u00a9 ucles 2020  (b) a geometric progression has a sum to infinity of 72. the sum of the first 3 terms of this progression  is 8333.    (i) find the value of the common ratio.  [5]   (ii) hence find the value of the first term.  [1]",
            "16": "16 0606/11/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"
        },
        "0606_w20_qp_12.pdf": {
            "1": "cambridge igcse\u2122*7394703437* dc (pq/fc) 187996/3 \u00a9 ucles 2020  [turn overthis document has 16 pages. blank pages are indicated.additional mathematics  0606/12 paper 1  october/november  2020  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].",
            "2": "2 0606/12/o/n/20 \u00a9 ucles 2020 mathematical formulae 1. algebra quadratic equation  for the equation ax bx c02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o  where n is a positive integer and () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ -  () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=-  ()() srarr111nn ! =--  () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/12/o/n/20 \u00a9 ucles 2020 [turn over 1 the curve   yx k 242=+ +   intersects the straight line () yk x4 =+  at two distinct points. find the  possible values of k. [4] 2 - 5 - 4 - 3 - 2 - 1 0 1 25y x  the diagram shows the graph of () yx f= , where ()xf is a cubic polynomial.  (a) find ()xf. [3]  (b) write down the values of x such that ()x 0 f1. [2]",
            "4": "4 0606/12/o/n/20 \u00a9 ucles 2020 3 (a) write down the amplitude of cosx231-. [1]  (b) write down the period of cosx231-. [1]  (c) on the axes below, sketch the graph of   cos yx231 =-    for   x3 ggrr-  radians.   - r 0 r 2r 3r1 - 1 - 2 - 323y x  [3]",
            "5": "5 0606/12/o/n/20 \u00a9 ucles 2020 [turn over 4 the 7th and 10th terms of an arithmetic progression are 158 and 149 respectively.  (a) find the common difference and the first term of the progression.  [3]  (b) find the least number of terms of the progression for their sum to be negative.  [3]",
            "6": "6 0606/12/o/n/20 \u00a9 ucles 2020 5 find the coefficient of x2 in the expansion of   xxxx325 -+bb ll . [5]",
            "7": "7 0606/12/o/n/20 \u00a9 ucles 2020 [turn over 6  ()xx x23 f2=+ -   for x 1h-     (a) given that the minimum value of xx232+-  occurs when x 1=- , explain why ()xf has an inverse.  [1]  (b) on the axes below, sketch the graph of () yx f=  and the graph of () yx f1=-. label each graph  and state the intercepts on the coordinate axes. oy x  [4]",
            "8": "8 0606/12/o/n/20 \u00a9 ucles 2020 7 a curve has equation   lnyxx 21352 =+- `j    for x3522.  (a) find the equation of the normal to the curve at the point where x 2= . [6]  (b) find the approximate change in y as x increases from 2 to h2+, where h is small.  [1]",
            "9": "9 0606/12/o/n/20 \u00a9 ucles 2020 [turn over 8 (a) find the number of ways in which 12 people can be put into 3 groups containing 3, 4 and 5 people  respectively.  [3]  (b) 4-digit numbers are to be formed using four of the digits 2, 3, 7, 8 and 9. each digit may be used  once only in any 4-digit number. find how many 4-digit numbers can be formed if   (i) there are no restrictions,  [1]   (ii) the number is even,  [1]   (iii) the number is greater than 7000 and odd.  [3]",
            "10": "10 0606/12/o/n/20 \u00a9 ucles 2020 9 a curve has equation   () yx x 21 43 =- +.   (a) show that   () xy xax b 434 dd=++,   where a and b are constants.  [5]  (b) hence write down the x-coordinate of the stationary point of the curve.  [1]  (c) determine the nature of this stationary point.  [2]",
            "11": "11 0606/12/o/n/20 \u00a9 ucles 2020 [turn over 10 the polynomial   ()xx ax bx 62 p32=+ ++ ,   where a and b are integers, has a factor of   x2-.      (a) given that   () () 12 0 pp=- ,  find the value of a and of b. [4]  (b) using your values of a and b,     (i) find the remainder when ()xp is divided by x21-,  [2]   (ii) factorise   ()xp. [2]",
            "12": "12 0606/12/o/n/20 \u00a9 ucles 2020 11 in this question all lengths are in centimetres and all angles are in radians. a b co r rr rd e f  the diagram shows the rectangle adef , where af de r == . the points b and c lie on ad such that     ab cd r == . the curve bc is an arc of the circle, centre o, radius r and has a length of 1.5 r.  (a) show that the perimeter of the shaded region is (. .) sin r 75 20 75 + . [5]",
            "13": "13 0606/12/o/n/20 \u00a9 ucles 2020 [turn over  (b) find the area of the shaded region, giving your answer in the form kr2, where k is a constant  correct to 2 decimal places.  [4] ",
            "14": "14 0606/12/o/n/20 \u00a9 ucles 2020 12 (a)  0v ms\u20131 t s 2030v 60 90   the diagram shows the velocity\u2013time graph of a particle p that travels 2775  m in 90  s, reaching a  final velocity of vms1-.   (i) find the value of v. [3]   (ii) write down the acceleration of p when t40= . [1]",
            "15": "15 0606/12/o/n/20 \u00a9 ucles 2020  (b) the acceleration, a ms2-, of a particle q travelling in a straight line, is given by   cos at62=    at  time t s. when t0= the particle is at point o and is travelling with a velocity of 10ms1-.   (i) find the velocity of q at time t. [3]   (ii) find the displacement of q from o at time t. [3]",
            "16": "16 0606/12/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.blank page"
        },
        "0606_w20_qp_13.pdf": {
            "1": "dc (pq/fc) 187995/4 \u00a9 ucles 2020  [turn overthis document has 16 pages. blank pages are indicated. *2950468632* additional mathematics  0606/13 paper 1  october/november  2020  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].cambridge igcse\u2122",
            "2": "2 0606/13/o/n/20 \u00a9 ucles 2020 mathematical formulae 1.algebra quadratic equation    for the equation ax2 + bx + c = 0, xabb ac 242!=-- binomial theorem () \u2026\u2026 ab anabnabn rab b12nn nn nr rn 12 2+=++ ++ ++-- -j lkkj lkkj lkkn poon poon poo    where n is a positive integer and () !!! n r nr rn=-j lkkn poo arithmetic series ua n d sn al na n d1 21 212 1n n\u2212 \u2212=+ = += + ^^ ^ hh h #- geometric series ua r sra rr srar111 11nn nn1 1!\u2212\u2212 \u2212= = =3\u2212 ^ ^^h hh 2.trigonometry identities sin2 a + cos2 a = 1 sec2 a = 1 + tan2 a cosec2 a = 1 + cot2 a formulae for \u2206abc sins in sin aa bb cc== a2 = b2 + c2 \u2013 2bc cos a \u2206 = 21 bc sin a",
            "3": "3 0606/13/o/n/20 \u00a9 ucles 2020 [turn over 1 (a) on the axes below, sketch the graph of   () () () yx xx21 3 =- +- ,   stating the intercepts on the  coordinate axes.   oy x  [3]  (b) hence write down the values of x such that   () () () xx x 21 302 -+ - .  [2]",
            "4": "4 0606/13/o/n/20 \u00a9 ucles 2020 2 (a)  given that   yx 1ex 223 =+- ,  find xy dd. [3]  (b) hence, given that y is increasing at the rate of 2 units per second, find the exact rate of change of x  when x2=. [3]",
            "5": "5 0606/13/o/n/20 \u00a9 ucles 2020 [turn over 3 (a)  () ()ln xx 42 1 f=-   (i) write down the largest possible domain for the function f.  [1]   (ii) find ()x f1- and its domain.  [3]  (b)  ()xx 5 g=+    for xr!       ()xx 23 h=-    for x23h    solve   ()x 7 gh =. [3]",
            "6": "6 0606/13/o/n/20 \u00a9 ucles 2020 4 (a) x m t s 0 50 65 85 12550100150   the diagram shows the x\u2013t graph for a runner, where displacement, x, is measured in metres and  time, t, is measured in seconds.     (i) on the axes below, draw the v\u2013t graph for the runner.  [3]  v ms\u20131 t s 01234 - 4- 3- 2- 150 65 85 125   (ii) find the total distance covered by the runner in 125  s. [1]",
            "7": "7 0606/13/o/n/20 \u00a9 ucles 2020 [turn over  (b) the displacement, x m, of a particle from a fixed point at time t s is given by   cos xt633r=+ bl .  find the acceleration of the particle when t32r= . [3] 5 given that the coefficient of x2 in the expansion of   () xx112n +- bl    is 425, find the value of the  positive integer n. [5]",
            "8": "8 0606/13/o/n/20 \u00a9 ucles 2020 6 it is known that   ya 10bx2#= ,   where a and b are constants. when lgy is plotted against x2, a  straight line passing through the points (3.63, 5.25) and (4.83, 6.88) is obtained.    (a)  find the value of a and of b. [4]  using your values of a and b, find   (b) the value of y when x2=,  [2]    (c) the positive value of x when y4=. [2]",
            "9": "9 0606/13/o/n/20 \u00a9 ucles 2020 [turn over 7 the polynomial   ()xa xb xx 19 4 p32=+ -+ ,   where a and b are constants, has a factor   x4+   and is  such that   () () 21 50 pp= .     (a) show that   () () () xx ax bxc 4 p2=+ ++ , where a, b and c are integers to be found.  [6]  (b) hence factorise ()xp. [1]  (c) find the remainder when ()xpl is divided by x. [1]",
            "10": "10 0606/13/o/n/20 \u00a9 ucles 2020 8 in this question all lengths are in centimetres. co ba r 0.5 r1.45  r  the diagram shows the figure abc . the arc ab is part of a circle, centre o, radius r, and is of length  1.45r. the point o lies on the straight line cb such that . co r05= .   (a) find, in radians, the angle aob . [1]  (b) find the area of abc , giving your answer in the form  kr2, where  k is a constant.  [3]",
            "11": "11 0606/13/o/n/20 \u00a9 ucles 2020 [turn over  (c) given that the perimeter of abc  is 12  cm, find the value of r. [4]",
            "12": "12 0606/13/o/n/20 \u00a9 ucles 2020 9  c o bba xa y  the diagram shows the triangle oac . the point b is the midpoint of oc. the point y lies on ac such  that oy intersects ab at the point x where ::axxb 31= . it is given that oa a= and b ob=.  (a) find ox in terms of a and b, giving your answer in its simplest form.  [3]  (b) find ac in terms of a and b. [1]",
            "13": "13 0606/13/o/n/20 \u00a9 ucles 2020 [turn over  (c) given that oy oxh= , find ay in terms of a, b and h. [1]  (d) given that ay acm= , find the value of h and of  m. [4]",
            "14": "14 0606/13/o/n/20 \u00a9 ucles 2020 10 (a) show that   xx11 31 02 +++   can be written as   xxx 31 31 051 2 2+++. [1]  (b) y p oqx = 2 xyxxx 31 31 051 2 2=+++   the diagram shows part of the curve   yxxx 31 31 051 2 2=+++,   the line   x2=   and a straight line of  gradient 1. the curve intersects the y-axis at the point p. the line of gradient 1 passes through p  and intersects the x-axis at the point q. find the area of the shaded region, giving your answer in  the form ln ab323 + `j , where a and b are constants.  [9]",
            "15": "15 0606/13/o/n/20 \u00a9 ucles 2020 [turn over additional working space for question 10 question 11 is printed on the next page.",
            "16": "16 0606/13/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.11 (a) given that   cost an xx 23 = ,   show that   sins in xx 23 202+- =. [3]  (b) hence solve   cost an 22 24 43rraa + += bb ll    for 011 ra  radians, giving your answers in  terms of r.  [4]"
        },
        "0606_w20_qp_21.pdf": {
            "1": "cambridge igcse\u2122dc (lk/sg) 187994/3 \u00a9 ucles 2020  [turn overthis document has 16 pages. blank pages are indicated.additional mathematics  0606/21 paper 2  october/november  2020  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ]. *8320369122*",
            "2": "2 0606/21/o/n/20 \u00a9 ucles 2020 mathematical formulae 1. algebra quadratic equation  for the equation ax bx c02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o  where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ -  () {( )} sn an an d l21 2121n=+ =+ - geometric series  ua rnn1=-  ()() srarr111nn ! =--  () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/21/o/n/20 \u00a9 ucles 2020 [turn over 1 solve the inequality   xx32 82++ . [3] 2 find the coordinates of the points of intersection of the curve   xx y92+=    and the line yx322 =- .  [5]",
            "4": "4 0606/21/o/n/20 \u00a9 ucles 2020 3 write     ggllxy32+-    as a single logarithm.  [3] 4 it is given that   ()lnsinc os yx x 3 =+    for   x 0211r.  (a) find xy dd. [3]  (b) find the value of x for which   xy 21 dd=-  . [3]",
            "5": "5 0606/21/o/n/20 \u00a9 ucles 2020 [turn over 5 the first three terms in the expansion of   () ab xx15++`j    are   xc x 32 2082-+ .   find the value of  each of the integers a, b and c. [7]",
            "6": "6 0606/21/o/n/20 \u00a9 ucles 2020 6 do not use a calculator in this question.  in this question all lengths are in centimetres.  31+ 15\u00b0a c b31-  in the diagram above  ac 31=- , ab 31=+ , angle \u00b0 abc 15=  and angle \u00b0 cab 90= .  (a) show that   \u00b0 tan152 3 =- . [3]  (b) find the exact length of bc. [2]",
            "7": "7 0606/21/o/n/20 \u00a9 ucles 2020 [turn over 7 do not use a calculator in this question.     ()pxx xx 23 23 1232=- + -  (a) find the value of p21bl. [1]  (b) write ()px as the product of three linear factors and hence solve   ()px 0=. [5]",
            "8": "8 0606/21/o/n/20 \u00a9 ucles 2020 8 the population p, in millions, of a country is given by   pa bt#= ,   where t is the number of years  after january 2000 and a and b are constants. in january 2010 the population was 40  million and had  increased to 45 million by january 2013.  (a) show that . b 104=  to 2 decimal places and find a to the nearest integer.  [4]  (b) find the population in january 2020, giving your answer to the nearest million.  [1]  (c) in january of which year will the population be over 100 million for the first time?  [3]",
            "9": "9 0606/21/o/n/20 \u00a9 ucles 2020 [turn over 9 a particle moves in a straight line such that, t seconds after passing a fixed point o, its displacement  from o is s m, where   ee st 10 12 9tt2=- -+ .  (a) find expressions for the velocity and acceleration at time t. [3]  (b) find the time when the particle is instantaneously at rest.  [3]  (c) find the acceleration at this time.  [2]",
            "10": "10 0606/21/o/n/20 \u00a9 ucles 2020 10 the gradient of the normal to a curve at the point ( x, y) is given by   xx 1+ .  (a) given that the curve passes through the point (1, 4), show that its equation is    ln yx x 5=- -.  [5]",
            "11": "11 0606/21/o/n/20 \u00a9 ucles 2020 [turn over  (b) find, in the form ym xc=+ , the equation of the tangent to the curve at the point where x3=.  [3]",
            "12": "12 0606/21/o/n/20 \u00a9 ucles 2020 11 the equation of a curve is   yx x 162=-    for x04gg .  (a) find the exact coordinates of the stationary point of the curve.  [6]",
            "13": "13 0606/21/o/n/20 \u00a9 ucles 2020 [turn over  (b) find   dd xx 16223 - `j  and hence evaluate the area enclosed by the curve   yx x 162=-  and the   lines , yx 01==  and x3=. [5]",
            "14": "14 0606/21/o/n/20 \u00a9 ucles 2020 12  4 cm b a5 cm3 cmc d  the diagram shows a shape consisting of two circles of radius 3  cm and 4  cm with centres a and b  which are 5  cm apart. the circles intersect at c and d as shown. the lines ac and bc are tangents to  the circles, centres b and a respectively. find  (a) the angle cab  in radians,  [2]",
            "15": "15 0606/21/o/n/20 \u00a9 ucles 2020  (b) the perimeter of the whole shape,  [4]  (c) the area of the whole shape.  [4]",
            "16": "16 0606/21/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"
        },
        "0606_w20_qp_22.pdf": {
            "1": "cambridge igcse\u2122dc (lk/sg) 187993/3 \u00a9 ucles 2020  [turn overthis document has 16 pages. blank pages are indicated.additional mathematics  0606/22 paper 2  october/november  2020  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ]. *6696758013*",
            "2": "2 0606/22/o/n/20 \u00a9 ucles 2020 mathematical formulae 1. algebra quadratic equation  for the equation ax bx c02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o  where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ -  () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=-  ()() srarr111nn ! =--  () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/22/o/n/20 \u00a9 ucles 2020 [turn over 1 solve the inequality   () () xx81 03 52 -- . [4] 2 find the value of x such that   2432 8xx 11 x 3 31 # =-+  . [4]",
            "4": "4 0606/22/o/n/20 \u00a9 ucles 2020 3 (a) find the equation of the perpendicular bisector of the line joining the points (12, 1) and (4,  3),  giving your answer in the form ym xc=+ . [5]  (b) the perpendicular bisector cuts the axes at points a and b. find the length of ab. [3]",
            "5": "5 0606/22/o/n/20 \u00a9 ucles 2020 [turn over 4 solve the simultaneous equations.     () () ()log logl ogxy xy2 21 23 33+= += + [6]",
            "6": "6 0606/22/o/n/20 \u00a9 ucles 2020 5 do not use a calculator in this question.  (a) find the equation of the tangent to the curve   yx xx63 1032=- ++    at the point where x1=.  [4]  (b) find the coordinates of the point where this tangent meets the curve again.  [5]",
            "7": "7 0606/22/o/n/20 \u00a9 ucles 2020 [turn over 6 find the exact value of ()dxxx1 22 24+y . [6]",
            "8": "8 0606/22/o/n/20 \u00a9 ucles 2020 7 a geometric progression has a first term of 3 and a second term of 2.4. for this progression, find  (a) the sum of the first 8 terms,  [3]  (b) the sum to infinity,  [1]  (c) the least number of terms for which the sum is greater than 95% of the sum to infinity.  [4]",
            "9": "9 0606/22/o/n/20 \u00a9 ucles 2020 [turn over 8 do not use a calculator in this question.  in this question lengths are in centimetres.  23 1+ 30\u00b0 ab c you may use the following  trigonometric ratios. sin3021\u00b0= cos3023\u00b0= tan3031\u00b0=  (a) given that the area of the triangle abc  is 5.5  cm2, find the exact length of ac. write your answer  in the form ab 3+ , where a and b are integers.  [4]  (b) show that   bc cd 32=+ ,   where c and d are integers to be found.  [4]",
            "10": "10 0606/22/o/n/20 \u00a9 ucles 2020 9 a 3a2b bp q o srx  in the diagram b op 2= , s a o 3= , rb s= and a pq=. the lines or and qs intersect at x.  (a) find oq in terms of a and b. [1]  (b) find sq in terms of a and b. [1]  (c) given that  s qx qn= , find ox in terms of a, b and n. [1]  (d) given that r ox om= , find ox in terms of a, b and m.  [1]",
            "11": "11 0606/22/o/n/20 \u00a9 ucles 2020 [turn over  (e) find the value of m and of n. [3]  (f) find the value of xqx s . [1]  (g) find the value of oxor . [1]",
            "12": "12 0606/22/o/n/20 \u00a9 ucles 2020 10 the number, b, of bacteria in a sample is given by   e pqbt2=+ ,   where p and q are constants and t is  time in weeks. initially there are 500 bacteria which increase to 600 after 1 week.   (a) find the value of p and of q. [4]",
            "13": "13 0606/22/o/n/20 \u00a9 ucles 2020 [turn over  (b) find the number of bacteria present after 2 weeks.  [1]  (c) find the first week in which the number of bacteria is greater than 1  000 000. [3]",
            "14": "14 0606/22/o/n/20 \u00a9 ucles 2020 11 (a) show that     cossintansecxxxx11-=+ . [4]",
            "15": "15 0606/22/o/n/20 \u00a9 ucles 2020  (b) solve the equation   tanc ot sec xx x 53 2 -=    for \u00b0\u00b0x 0 360 gg . [6]",
            "16": "16 0606/22/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"
        },
        "0606_w20_qp_23.pdf": {
            "1": "cambridge igcse\u2122dc (lk/sg) 187992/4 \u00a9 ucles 2020  [turn overthis document has 16 pages. blank pages are indicated.additional mathematics  0606/23 paper 2  october/november  2020  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ]. *4908419373*",
            "2": "2 0606/23/o/n/20 \u00a9 ucles 2020 mathematical formulae 1. algebra quadratic equation  for the equation ax bx c02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o  where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ -  () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=-  ()() srarr111nn ! =--  () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/23/o/n/20 \u00a9 ucles 2020 [turn over 1 solve   xx32 4=+- . [3] 2 solve the simultaneous equations.       y xx xy34 25 42+= +=  [5]",
            "4": "4 0606/23/o/n/20 \u00a9 ucles 2020 3 find the values of k for which the equation   () xk x99 02++ +=    has two distinct real roots.  [4] 4 it is given that   ()ln sin yx 1=+    for x 011 r.  (a) find dd xy. [2]",
            "5": "5 0606/23/o/n/20 \u00a9 ucles 2020 [turn over  (b) find the value of  dd xy when x6r=, giving your answer in the form  a1, where a is an integer.  [2]  (c) find the values of x for which ddtanxyx = . [5]",
            "6": "6 0606/23/o/n/20 \u00a9 ucles 2020 5 solve the following simultaneous equations.     39 243xy 1# =-     82422 yx21 21 # =-+  [5]",
            "7": "7 0606/23/o/n/20 \u00a9 ucles 2020 [turn over 6 a 4-digit code is to be formed using 4 different numbers selected from 1, 2, 3, 4, 5, 6, 7, 8 and 9. find  how many different codes can be formed if  (a) there are no restrictions,  [1]  (b) only prime numbers are used,  [1]  (c) two even numbers are followed by two odd numbers,  [2]  (d) the code forms an even number.  [2]",
            "8": "8 0606/23/o/n/20 \u00a9 ucles 2020 7 a curve has equation    cos yx x = .  (a) find dd xy. [2]  (b) find the equation of the normal to the curve at the point where xr=, giving your answer in the  form ym xc=+ . [4]",
            "9": "9 0606/23/o/n/20 \u00a9 ucles 2020 [turn over  (c) using your answer to part (a) , find the exact value of   0sindxx xr 6y . [5]",
            "10": "10 0606/23/o/n/20 \u00a9 ucles 2020 8 do not use a calculator in this question.     () ()logl og logl ogyx xy13 22222 22+= += +-  (a) show that   xx63 2032+- =. [4]",
            "11": "11 0606/23/o/n/20 \u00a9 ucles 2020 [turn over  (b) find the roots of   xx63 2032+- =. [4]  (c) give a reason why only one root is a valid solution of the logarithmic equations. find the value of  y corresponding to this root.  [2]",
            "12": "12 0606/23/o/n/20 \u00a9 ucles 2020 9 x m 300  m 400  mb c d e a  the rectangle abcde  represents a ploughed field where m ab 300=  and m ae 400= . joseph needs  to walk from a to d in the least possible time. he can walk at .ms 091- on the ploughed field and at  .ms 151- on any part of the path bcd  along the edge of the field. he walks from a to c and then from  c to d. the distance mx bc= .  (a) find, in terms of x, the total time, t s, joseph takes for the journey.  [3]",
            "13": "13 0606/23/o/n/20 \u00a9 ucles 2020 [turn over  (b) given that x can vary, find the value of x for which t is a minimum and hence find the minimum  value of t. [6]",
            "14": "14 0606/23/o/n/20 \u00a9 ucles 2020 10 (a) the sum of the first 4 terms of an arithmetic progression is 38 and the sum of the next 4 terms is  86. find the first term and the common difference.  [5]",
            "15": "15 0606/23/o/n/20 \u00a9 ucles 2020 [turn over  (b) the third term of a geometric progression is 12 and the sixth term is 96-. find the sum of the first  10 terms of this progression.  [6] question 11 is printed on the next page.",
            "16": "16 0606/23/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 do not use a calculator in this question.  solve the quadratic equation   xx 72 47 202-- ++ = `` jj ,   giving each of your answers in the form  ab 7+ , where a and b are constants.  [7]"
        }
    },
    "2021": {
        "0606_m21_qp_12.pdf": {
            "1": "this document has 16 pages. cambridge igcse\u2122 dc (ce/sw) 202024/2 \u00a9 ucles 2021  [turn overadditional mathematics  0606/12 paper 1  february/march  2021  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ]. *3251633375*",
            "2": "2 0606/12/f/m/21 \u00a9 ucles 2021 mathematical formulaemathematical formulae 1. algebra quadratic equation for the equation ax bx c 02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ - () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=- ()() srarr111nn ! =-- () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/12/f/m/21 \u00a9 ucles 2021 [turn over 1 find the exact solutions of the equation  . ln ln xx 35 25 102+- = `j  [4]",
            "4": "4 0606/12/f/m/21 \u00a9 ucles 2021 2 y x 2r- r- r 2r 01234567 y = a sin bx + c  the diagram shows the graph of sin ya bx c =+   where x is in radians and  x 22ggrr- , where a, b  and c are positive constants. find the value of each of a, b and c. [3]",
            "5": "5 0606/12/f/m/21 \u00a9 ucles 2021 [turn over 3 the line ab is such that the points a and b have coordinates (, ) 46-  and (2, 14) respectively.  (a) the point c, with coordinates (7, a) lies on the perpendicular bisector of ab. find the value of a.    [4]  (b) given that the point d also lies on the perpendicular bisector of ab, find the coordinates of d such  that the line ab bisects the line cd. [2]",
            "6": "6 0606/12/f/m/21 \u00a9 ucles 2021 4 (a) show that  xx25 32+-   can be written in the form ax bc2++`j , where a, b and c are constants.  [3]  (b) hence write down the coordinates of the stationary point on the curve with equation  yx x 25 32=+ -. [2]  (c) on the axes below, sketch the graph of   yx x 25 32=+ -,   stating the coordinates of the intercepts  with the axes.  [3] y x o  (d) write down the value of k for which the equation   xx k 25 32+- =   has exactly 3 distinct  solutions.  [1]",
            "7": "7 0606/12/f/m/21 \u00a9 ucles 2021 [turn over 5 in this question all lengths are in kilometres and time is in hours.  boat a sails, with constant velocity, from a point o with position vector 0 0eo. after 3 hours a is at the  point with position vector 12 9-eo .  (a) find the position vector, op, of a at time t. [1]  at the same time as a sails from o, boat b sails from a point with position vector  12 6eo, with constant  velocity  5 8-eo .  (b) find the position vector,  oq, of b at time t. [1]  (c) show that at time t   pq tt26 36 1802=+ +2. [3]  (d) hence show that a and b do not collide.  [2]",
            "8": "8 0606/12/f/m/21 \u00a9 ucles 2021 6 (a) a geometric progression has first term 10 and sum to infinity 6.   (i) find the common ratio of this progression.  [2]   (ii) hence find the sum of the first 7 terms, giving your answer correct to 2 decimal places.  [2]",
            "9": "9 0606/12/f/m/21 \u00a9 ucles 2021 [turn over  (b) the first three terms of an arithmetic progression are    log3x,  () log3x2,  () log3x3.   (i) find the common difference of this progression.  [1]   (ii) find, in terms of n and log3x, the sum to n terms of this progression. simplify your answer.  [2]   (iii) given that the sum to n terms is log 3081 3x, find the value of n. [2]   (iv) hence, given that the sum to n terms is also equal to 1027, find the value of x. [2]",
            "10": "10 0606/12/f/m/21 \u00a9 ucles 2021 7 do not use a calculator in this question  in this question all lengths are in centimetres. 17 1- 17 4+17 1+b ca d e  the diagram shows a trapezium abcde  such that ab is parallel to ec and abcd  is a rectangle. it is  given that bc 17 1 =+ , ed 17 1 =-  and . dc 17 4 =+  (a) find the perimeter of the trapezium, giving your answer in the form ab 17+ , where a and b are  integers.  [3]  (b) find the area of the trapezium, giving your answer in the form cd 17+ , where c and d are  integers.  [2]",
            "11": "11 0606/12/f/m/21 \u00a9 ucles 2021 [turn over  (c) find tanaed , giving your answer in the form ef 17 8+, where e and f are integers.  [2]  (d) hence show that secaed81 917 322=+. [2]",
            "12": "12 0606/12/f/m/21 \u00a9 ucles 2021 8 (a) (i) show that   . sint an coss ec xx xx+=  [3]   (ii) hence solve the equation  sint an cos22 24ii i+=    for r 04ggi , where i is in radians.  [4]",
            "13": "13 0606/12/f/m/21 \u00a9 ucles 2021 [turn over  (b) solve the equation   (\u00b0 ) coty38 3 +=    for \u00b0\u00b0y 0 360 gg . [3]",
            "14": "14 0606/12/f/m/21 \u00a9 ucles 2021 9 the polynomial  ()xx xx 23 1 p32=- -+    has a factor x21-.  (a) find ()xp in the form () () xx21 q- , where ()xq is a quadratic factor.  [2] y x obayx1= yx x 23 12=- ++  the diagram shows the graph of   yx1=   for x02, and the graph of   yx x 23 12=- ++ .   the curves  intersect at the points a and b.  (b) using your answer to part (a) , find the exact x-coordinate of a and of b. [4]",
            "15": "15 0606/12/f/m/21 \u00a9 ucles 2021 [turn over  (c) find the exact area of the shaded region.  [6] question 10 is printed on the next page.",
            "16": "16 0606/12/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.10 a curve has equation   yx x21 0 12 23 =+ -`j    for x12.  (a) show that xy dd can be written in the form   (x xax bxc21 0 12 221 2+ -++ )` `jj , where a, b and c are  integers.  [5]  (b) show that, for x12, the curve has exactly one stationary point. find the value of x at this  stationary point.  [4]"
        },
        "0606_m21_qp_22.pdf": {
            "1": "this document has 16 pages. cambridge igcse\u2122 dc (ce/sw) 202023/5 \u00a9 ucles 2021  [turn over *2436662856* additional mathematics  0606/22 paper 2  february/march  2021  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].",
            "2": "2 0606/22/f/m/21 \u00a9 ucles 2021 mathematical formulae 1. algebra quadratic equation  for the equation ax bx c02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o  where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ -  () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=-  ()() srarr111nn ! =--  () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/22/f/m/21 \u00a9 ucles 2021 [turn over 1 solve the equation   xx49 65 += -  . [3]  2 find the values of the constant k for which the equation   () kx kx31 25 02-+ +=    has equal roots.   [4]",
            "4": "4 0606/22/f/m/21 \u00a9 ucles 2021 3 y x \u2013 1012 \u2013 2\u2013 1 1 2 \u2013 2  the diagram shows the graph of  () yx f= , where () () () xa xb xc f2=+ + and a, b and c are integers.  (a) find the value of each of a, b and c. [2]  (b) hence solve the inequality   ()x 1 fg-. [3]",
            "5": "5 0606/22/f/m/21 \u00a9 ucles 2021 [turn over 4 the curve   xy4 45122+=    and the line   xy20+=    intersect at two points. find the exact distance  between these points.  [6]",
            "6": "6 0606/22/f/m/21 \u00a9 ucles 2021 5 a cube of side x cm has surface area scm2. the volume, vcm3, of the cube is increasing at a rate of  480cms31-. find, at the instant when v = 512,  (a) the rate of increase of x, [4]  (b) the rate of increase of s. [2]",
            "7": "7 0606/22/f/m/21 \u00a9 ucles 2021 [turn over 6 b c 7.5 cm16 cma orad2 7r  aob  is a sector of a circle with centre o and radius 16  cm. angle aob  is 72r radians. the point c lies  on ob such that oc is of length 7.5  cm and ac is a straight line.  (a) find the perimeter of the shaded region.  [3]  (b) find the area of the shaded region.  [3]",
            "8": "8 0606/22/f/m/21 \u00a9 ucles 2021 7 a curve has equation () yx p= , where   ()xx xx46 1 p32=- +- .  (a) find the equation of the tangent to the curve at the point (3, 8). give your answer in the form  ym xc=+ . [5]  (b) (i) given that p1- exists, write down the gradient of the tangent to the curve () yx p1=- at the  point (8, 3).  [1]   (ii) find the coordinates of the point of intersection of these two tangents.  [2]",
            "9": "9 0606/22/f/m/21 \u00a9 ucles 2021 [turn over 8 a photographer takes 12 different photographs. there are 3 of sunsets, 4 of oceans, and 5 of mountains.  (a) the photographs are arranged in a line on a wall.   (i) how many possible arrangements are there if there are no restrictions?  [1]   (ii) how many possible arrangements are there if the first photograph is of a sunset and the last  photograph is of an ocean?  [2]   (iii) how many possible arrangements are there if all the photographs of mountains are next to  each other?  [2]  (b) three of the photographs are to be selected for a competition.   (i) find the number of different possible selections if no photograph of a sunset is chosen.  [2]   (ii) find the number of different possible selections if one photograph of each type (sunset,  ocean, mountain) is chosen.  [2]",
            "10": "10 0606/22/f/m/21 \u00a9 ucles 2021 9 (a) in the expansion of   kkx25 -bl ,   where k is a constant, the coefficient of x2 is 160. find the value  of k. [3]  (b) (i) find, in ascending powers of x, the first 3 terms in the expansion of   x 136+`j ,   simplifying  the coefficient of each term.  [2]",
            "11": "11 0606/22/f/m/21 \u00a9 ucles 2021 [turn over   (ii) when   xa x 132 6++`` jj   is written in ascending powers of x, the first three terms are    xb x 46 82++ , where a and b are constants. find the value of a and of b. [3]",
            "12": "12 0606/22/f/m/21 \u00a9 ucles 2021 10 the function f is defined by   ()xx x41 2f2 =-  for .. x 05 15 gg .  the diagram shows a sketch of () yx f= . y x 00.5 1.5yx x41 22 =-  (a) (i) it is given that f1- exists. find the domain and range of f1-. [3]",
            "13": "13 0606/22/f/m/21 \u00a9 ucles 2021 [turn over   (ii) find an expression for ()x f1-. [3]  (b) the function g is defined by ()xgex2=  for all real x. show that ()xgfebxa12=-eo, where a and b  are integers.  [2]",
            "14": "14 0606/22/f/m/21 \u00a9 ucles 2021 11 (a) (i) find    xx 10 11d6-c edd`j . [2]    (ii) find   xxx25d32+ c edd`j  . [3]",
            "15": "15 0606/22/f/m/21 \u00a9 ucles 2021 [turn over  (b) (i) differentiate   ()tan yx 31 =+    with respect to x. [2]   (ii) hence find   () secsinxxx231d2 rr 1210 +-c eddeo  . [4] question 12 is printed on the next page.",
            "16": "16 0606/22/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.12 a particle p travels in a straight line so that, t seconds after passing through a fixed point o, its velocity,   vms1-, is given by     vt 2e=  for  t02gg ,     vet 2=-  for  t22 .  given that, after leaving o, particle p is never at rest, find the distance it travels between t = 1 and  t = 3. [6]"
        },
        "0606_s21_qp_11.pdf": {
            "1": "this document has 16 pages. any blank pages are indicated. cambridge igcse\u2122 *2172618678* additional mathematics  0606/11 paper 1  may/june  2021  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ]. dc (lk/fc) 202078/4 \u00a9 ucles 2021  [turn over",
            "2": "2 0606/11/m/j/21 \u00a9 ucles 2021 mathematical formulae 1. algebra quadratic equation for the equation ax bx c 02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ - () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=- ()() srarr111nn ! =-- () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/11/m/j/21 \u00a9 ucles 2021 [turn over 1 (a) on the axes, sketch the graph of   () () () yx xx 51 32 2 =+ -- ,   stating the intercepts with the  coordinate axes.  [3] y ox  (b) hence find the values of x for which () () () xx x 51 32 202 +- - . [2] 2 find   ()dx xx11 11 235 ---eoy ,   giving your answer in the form  lnab+ , where a and b are rational  numbers.  [5]",
            "4": "4 0606/11/m/j/21 \u00a9 ucles 2021 3 the polynomial   ()pxa xx bx 9632=- +- , where a and b are constants, has a factor of x2-. the  polynomial has a remainder of 66 when divided by  x3-.  (a) find the value of a and of b. [4]  (b) using your values of a and b, show that () () () pqxx x 2 =- , where ()qx is a quadratic factor to be  found.  [2]  (c) hence show that the equation ()px 0= has only one real solution.  [2]",
            "5": "5 0606/11/m/j/21 \u00a9 ucles 2021 [turn over 4 the first 3 terms in the expansion of   axx1335 +-` bj l,   in ascending powers of x, can be written in the   form bx cx 272++ , where a, b and c are integers. find the values of a, b and c. [8]",
            "6": "6 0606/11/m/j/21 \u00a9 ucles 2021 5 the functions f and g are defined as follows. )(fxx x42=+    for  xr! ()gex 1x2=+    for  xr!  (a) find the range of f.  [2]  (b) write down the range of g.  [1]  (c) find the exact solution of the equation  )(fgx 21= , giving your answer as a single logarithm.  [4]",
            "7": "7 0606/11/m/j/21 \u00a9 ucles 2021 [turn over 6 (a) (i) find how many different 5-digit numbers can be formed using the digits  1,  3,  5,  6,  8 and 9.    no digit may be used more than once in any 5-digit number.  [1]   (ii) how many of these 5-digit numbers are odd?  [1]   (iii) how many of these 5-digit numbers are odd and greater than 60  000?  [3]  (b) given that   () cc n 45 1nn 41 5##=++,  find the value of n. [4]",
            "8": "8 0606/11/m/j/21 \u00a9 ucles 2021 7 (a) in this question, all lengths are in metres and time, t, is in seconds. \u20131001020304050displacement time 10 20 30 40   the diagram shows the displacement\u2013time graph for a runner, for t04 0 gg .    (i) find the distance the runner has travelled when t40= . [1]   (ii) on the axes, draw the corresponding velocity\u2013time graph for the runner, for t04 0 gg . [2] \u201310246velocity time1 \u20132 \u20133 \u2013 4 \u20135 \u2013635 10 20 30 40",
            "9": "9 0606/11/m/j/21 \u00a9 ucles 2021 [turn over  (b) a particle, p, moves in a straight line such that its displacement from a fixed point at time t is s.   the acceleration of p is given by  t2421 +-`j , for  t02.   (i)  given that p has a velocity of 9 when t6=, find the velocity of p at time t. [3]   (ii) given that s31= when t6=, find the displacement of p at time t. [3]",
            "10": "10 0606/11/m/j/21 \u00a9 ucles 2021 8 do not use a calculator in this question.  a curve has equation   yx x 23 12=- +- `j .   the x-coordinate of a point a on the curve is   3 231 -+.  (a) show that the coordinates of a can be written in the form , pq rs33++`j , where p, q, r and s  are integers.  [5]",
            "11": "11 0606/11/m/j/21 \u00a9 ucles 2021 [turn over  (b) find the x-coordinate of the stationary point on the curve, giving your answer in the form ab 3+  ,  where a and b are rational numbers.  [3]",
            "12": "12 0606/11/m/j/21 \u00a9 ucles 2021 9 (a) (i) write   xyyx63 42 +++    in the form () () ax bcyd++ , where a, b, c and d are positive  integers.  [1]   (ii) hence solve the equation   sincos coss in 63 42 0 ii ii ++ +=    for \u00b0\u00b00 36011i . [4]",
            "13": "13 0606/11/m/j/21 \u00a9 ucles 2021 [turn over  (b) solve the equation   rsec21 4231z+= bl    for rr11z - , where z is in radians. give your   answers in terms of r. [5]",
            "14": "14 0606/11/m/j/21 \u00a9 ucles 2021 10 in this question all lengths are in centimetres. o a b c251510  the diagram shows a shaded shape. the arc ab is the major arc of a circle, centre o, radius 10. the line  ab is of length 15, the line oc is of length 25 and the lengths of ac and bc are equal.  (a) show that the angle aob  is 1.70 radians correct to 2 decimal places.  [2]  (b) find the perimeter of the shaded shape.  [4]",
            "15": "15 0606/11/m/j/21 \u00a9 ucles 2021  (c) find the area of the shaded shape.  [5]",
            "16": "16 0606/11/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.blank page"
        },
        "0606_s21_qp_12.pdf": {
            "1": "this document has 16 pages. cambridge igcse\u2122 *3617765859* additional mathematics  0606/12 paper 1  may/june  2021  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ]. dc (lk/fc) 202077/1 \u00a9 ucles 2021  [turn over",
            "2": "2 0606/12/m/j/21 \u00a9 ucles 2021 mathematical formulae 1. algebra quadratic equation for the equation ax bx c 02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ - () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=- ()() srarr111nn ! =-- () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/12/m/j/21 \u00a9 ucles 2021 [turn over 1 write   () pr qpqr r 213231 -- `j   in the form  pq rab c, where a, b and c are constants.  [3]",
            "4": "4 0606/12/m/j/21 \u00a9 ucles 2021 2 (a) on the axes, sketch the graph of   yx 43=- ,   stating the intercepts with the coordinate axes.  [2] y ox  (b) solve the inequality   x 43 7h- . [3]",
            "5": "5 0606/12/m/j/21 \u00a9 ucles 2021 [turn over 3 opba ccba  the diagram shows the quadrilateral oabc  such that a oa=, b ob= and c oc=. the lines ob and  ac intersect at the point p, such that ::appc 32= .  (a) find op in terms of a and c. [3]  (b) given also that ::oppb 23= , show that bc a 23 2 =+ . [2]",
            "6": "6 0606/12/m/j/21 \u00a9 ucles 2021 4 a curve is such that   -()dd xyx3222 31 =+ .   the curve has gradient 4 at the point (2,  6.2). find the equation  of the curve.  [6]",
            "7": "7 0606/12/m/j/21 \u00a9 ucles 2021 [turn over 5 (a) given that   logl og logl og p 54 20aa aa+- = ,   find the value of p. [2]  (b) solve the equation   () 38 33 0xx21+- =+. [3]  (c) solve the equation   2 4log 2 log 4.y y+=   [3]",
            "8": "8 0606/12/m/j/21 \u00a9 ucles 2021 6 do not use a calculator in this question.  a curve has equation   yx x 35 85 602=+ -+ `j .  (a) find the x-coordinate of the stationary point on the curve, giving your answer in the form ab 5+ ,  where a and b are integers.  [4]",
            "9": "9 0606/12/m/j/21 \u00a9 ucles 2021 [turn over  (b) hence find the y-coordinate of this stationary point, giving your answer in the form c5, where c  is an integer.  [3]",
            "10": "10 0606/12/m/j/21 \u00a9 ucles 2021 7 (a) a six-character password is to be made from the following eight characters.    digits   1 3 5 8 9    symbols   * $ #   no character may be used more than once in a password.   find the number of different passwords that can be chosen if   (i) there are no restrictions,  [1]   (ii) the password starts with a digit and finishes with a digit,  [2]   (iii) the password starts with three symbols.  [2]  (b) the number of combinations of 5 objects selected from n objects is six times the number of  combinations of 4 objects selected from n1- objects. find the value of n. [3]",
            "11": "11 0606/12/m/j/21 \u00a9 ucles 2021 [turn over 8 variables x and y are such that ya xb= , where a and b are constants. when lgy is plotted against lgx,  a straight line graph passing through the points (0.61, 0.57) and (5.36, 4.37) is obtained.  (a) find the value of a and of b. [5]  using your values of a and b, find  (b) the value of y when x3=, [2]  (c) the value of x when y3=. [2]",
            "12": "12 0606/12/m/j/21 \u00a9 ucles 2021 9 (a) the first three terms of an arithmetic progression are ,,48 20 - . find the smallest number of terms  for which the sum of this arithmetic progression is greater than 2000.  [4]",
            "13": "13 0606/12/m/j/21 \u00a9 ucles 2021 [turn over  (b) the 7th and 9th terms of a geometric progression are 27 and 243 respectively. given  that the  geometric progression has a positive common ratio, find   (i) this common ratio,  [2]   (ii) the 30th term, giving your answer as a power of 3.  [2]  (c) explain why the geometric progression   1, sini, sin2i, \u2026   for rr 2211i - , where i is in  radians, has a sum to infinity.  [2]",
            "14": "14 0606/12/m/j/21 \u00a9 ucles 2021 10 (a) solve the equation   sinc osec cossec 022aa aa+=    for rr11a - , where a is in radians.  [4]",
            "15": "15 0606/12/m/j/21 \u00a9 ucles 2021 [turn over  (b) (i) show that   sincos cossinsec112ii iii-+-= . [4]   (ii) hence solve the equation   sincos cossin 133 3134zz zz -+-=   for  \u00b0\u00b00 180 ggz . [4] question 11 is printed on the next page.",
            "16": "16 0606/12/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.11 the normal to the curve   lnyxx 2322 =-+`j    at the point where x2= meets the y-axis at the point p.   find the coordinates of p. [7]"
        },
        "0606_s21_qp_13.pdf": {
            "1": "this document has 16 pages. any blank pages are indicated. cambridge igcse\u2122 *2445269796* additional mathematics  0606/13 paper 1  may/june  2021  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ]. dc (lk/fc) 202076/2 \u00a9 ucles 2021  [turn over",
            "2": "2 0606/13/m/j/21 \u00a9 ucles 2021 mathematical formulae 1. algebra quadratic equation for the equation ax bx c 02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ - () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=- ()() srarr111nn ! =-- () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/13/m/j/21 \u00a9 ucles 2021 [turn over 1 find the possible values of the constant k such that the equation   kx kx k 43 102++ +=    has two  different real roots.  [4]",
            "4": "4 0606/13/m/j/21 \u00a9 ucles 2021 2 (a) find   ddexxx 23`j . [3]  (b) (i) find    dd xx342 31 + `j . [2]   (ii) hence find    dx xx342 0232 +- `jy . [3]",
            "5": "5 0606/13/m/j/21 \u00a9 ucles 2021 [turn over 3 solve the equation   cose cc ot cot 22 922ii i += +,   where i is in radians and rr 2211i - . [5]",
            "6": "6 0606/13/m/j/21 \u00a9 ucles 2021 4 (a) find the first three non-zero terms in the expansion of x2426 -eo  in ascending powers of x. simplify  each term.  [3]  (b)  hence find the term independent of x in the expansion of x x243126 22 - - e eo o. [3]",
            "7": "7 0606/13/m/j/21 \u00a9 ucles 2021 [turn over 5 when ey is plotted against x2 a straight line graph passing through the points (2.24,  5) and (4.74,  10) is  obtained. find y in terms of x. [5]",
            "8": "8 0606/13/m/j/21 \u00a9 ucles 2021 6  o d c a2aaa b  the diagram shows a circle, centre o, radius 2 a. the points a and b lie on the circumference of the  circle. the points c and d are the mid-points of the lines ob and oa respectively. the arc dc is part of  a circle centre o. the chord ab is of length 2 a.  (a) find angle aob , giving your answer in radians in terms of r. [1]  (b) find, in terms of a and r, the perimeter of the shaded region abcd . [2]  (c) find, in terms of a and r, the area of the shaded region abcd . [3]",
            "9": "9 0606/13/m/j/21 \u00a9 ucles 2021 [turn over 7 (a) a committee of 8 people is to be formed from 5 teachers, 4 doctors and 3 police officers. find the  number of different committees that could be chosen if   (i) all 4 doctors are on the committee,  [2]   (ii) there are at least 2 teachers on the committee.  [3]  (b) given that   p 6 pnn 51 4#=-, find the value of n. [3]",
            "10": "10 0606/13/m/j/21 \u00a9 ucles 2021 8 y x 03 p qrcos ya bx c =+ 65r  the graph shows the curve   cos ya bx c =+ ,   for .x 02 8 gg , where a, b and c are constants and x is   in radians. the curve meets the y-axis at (0, 3) and the x-axis at the point p and point , r650rbl .  the curve has a minimum at point q. the period of  cosab xc+ is r radians.  (a) find the value of each of a, b and c. [4]  (b) find the coordinates of p. [1]  (c) find the coordinates of q. [2]",
            "11": "11 0606/13/m/j/21 \u00a9 ucles 2021 [turn over 9 (a) show that the equation of the curve   yx x422=- - ` `j j   can be written as   yx ax bx 832=+ ++ ,   where a and b are integers. hence find the exact coordinates of the stationary points on the curve.  [4]  (b) on the axes, sketch the graph of   yx x422=- - ` `j j,   stating the intercepts with the coordinate  axes.  [4] y ox  (c) find the possible values of the constant k for which xx k 422-- = ` `j j  has exactly 4 different  solutions.  [2]",
            "12": "12 0606/13/m/j/21 \u00a9 ucles 2021 10 oa ca b d ce  the diagram shows the parallelogram oabc , such that a oa= and c oc=. the point d lies on cb  such that ::cddb 31= . when extended, the lines ab and od meet at the point e. it is given that  oe hod=  and be kab= , where h and k are constants.  (a) find de in terms of a, c and h. [4]",
            "13": "13 0606/13/m/j/21 \u00a9 ucles 2021 [turn over  (b) find de in terms of a, c and k. [1]  (c) hence find the value of h and of k. [4]",
            "14": "14 0606/13/m/j/21 \u00a9 ucles 2021 11 the line   xy21 0 +=    intersects the two lines satisfying the equation   xy 2 +=    at the points a and  b.  (a) show that the point (, ) c 520-  lies on the perpendicular bisector of the line ab. [8]",
            "15": "15 0606/13/m/j/21 \u00a9 ucles 2021  (b) the point d also lies on this perpendicular bisector. m is the mid-point of ab. the distance cd is  three times the distance of cm. find the possible coordinates of d. [4]",
            "16": "16 0606/13/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.blank page"
        },
        "0606_s21_qp_21.pdf": {
            "1": "this document has 16 pages. any blank pages are indicated. dc (rw/sg) 202074/2 \u00a9 ucles 2021  [turn over *9726863048* additional mathematics  0606/21 paper 2  may/june  2021  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].cambridge igcse\u2122",
            "2": "2 0606/21/m/j/21 \u00a9 ucles 2021 mathematical formulae 1. algebra quadratic equation for the equation ax bx c 02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ - () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=- ()() srarr111nn ! =-- () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/21/m/j/21 \u00a9 ucles 2021 [turn over 1 (a) write the expression    xx612-+    in the form ()xa b2++ , where a and b are constants.  [2]  (b) hence write down the coordinates of the minimum point on the curve   yx x612=- +. [1] 2 variables x and y are such that, when lny is plotted against lnx, a straight line graph passing through  the points (6, 5) and (8, 9) is obtained. show that yxepq=   where p and q are integers.  [4]",
            "4": "4 0606/21/m/j/21 \u00a9 ucles 2021 3 (a) solve the inequality   x41 92- . [3]  (b) solve the equation   xx21 11 20 -+ =. [3]",
            "5": "5 0606/21/m/j/21 \u00a9 ucles 2021 [turn over 4 the graph of   tan ya bx 2=+ ,   where a and b are constants, passes through the point (0, 4-) and has  period 480\u00b0.  (a) find the value of a and of b. [3]  (b) on the axes, sketch the graph of y for values of x between 0\u00b0 and 480\u00b0.  [2] xy 0 480\u00b0",
            "6": "6 0606/21/m/j/21 \u00a9 ucles 2021 5 the curves   yx2=    and   yx 272=    intersect at o(0, 0) and at the point a. find the equation of the  perpendicular bisector of the line oa. [8]",
            "7": "7 0606/21/m/j/21 \u00a9 ucles 2021 [turn over 6 variables x and y are such that    cos y xx 2 ex 2=+ , where x is in radians. use differentiation to find the  approximate change in y as x increases from 1 to h1+, where h is small.  [6]",
            "8": "8 0606/21/m/j/21 \u00a9 ucles 2021 7 find the exact values of the constant k for which the line   yx21=+    is a tangent to the curve  yx kx k 422=+ +- . [6]",
            "9": "9 0606/21/m/j/21 \u00a9 ucles 2021 [turn over 8 in this question, a, b, c and d are positive constants.  (a) (i) it is given that   () () logl og yx x 32 1aa=+ +- .   explain why x must be greater than 21. [1]   (ii) find the exact solution of the equation   () loglog y36 2 aa +=. [3]  (b) write the expression   () () logl og log ba 99aa b+    in the form log cd 9a+ , where c and d are  integers.  [4]",
            "10": "10 0606/21/m/j/21 \u00a9 ucles 2021 9 a curve is such that    rsinxyx62 dd 22 =- bl .   given that  xy 21 dd= at the point rr,41 213bl  on the curve, find  the equation of the curve.  [7]",
            "11": "11 0606/21/m/j/21 \u00a9 ucles 2021 [turn over 10 relative to an origin o, the position vectors of the points a, b, c and d are oa6 5=-eo ,  ob10 3=eo,  ocx y=eo and od12 7=eo.  (a) find the unit vector in the direction of ab. [3]  (b) the point a is the mid\u2011point of bc. find the value of x and of y. [2]  (c) the point e lies on od such that oe : od is 1 : 1m+. find the value of m such that be is parallel  to the x\u2011axis.  [3]",
            "12": "12 0606/21/m/j/21 \u00a9 ucles 2021 11 the 2nd, 8th and 44th terms of an arithmetic progression form the first three terms of a geometric  progression. in the arithmetic progression, the first term is 1 and the common difference is positive.  (a) (i) show that the common difference of the arithmetic progression is 5.  [5]   (ii) find the sum of the first 20 terms of the arithmetic progression.  [2]",
            "13": "13 0606/21/m/j/21 \u00a9 ucles 2021 [turn over  (b) (i) find the 5th term of the geometric progression.  [2]   (ii) explain whether or not the sum to infinity of this geometric progression exists.  [1]",
            "14": "14 0606/21/m/j/21 \u00a9 ucles 2021 12 x b a oy () () yx x 93=- - yk 3=-(, ) ckk 3-  the diagram shows part of the curve () () yx x 93=- - and the line yk 3=- , where k32. the line  through the maximum point of the curve, parallel to the y\u2011axis, meets the x\u2011axis at a. the curve meets  the x\u2011axis at b, and the line yk 3=-  meets the curve at the point c(k, k3-). find the area of the  shaded region.  [9]",
            "15": "15 0606/21/m/j/21 \u00a9 ucles 2021 continuation of working space for question 12.",
            "16": "16 0606/21/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.blank page"
        },
        "0606_s21_qp_22.pdf": {
            "1": "this document has 16 pages. dc (rw/sg) 202073/2 \u00a9 ucles 2021  [turn over *4371182274* additional mathematics  0606/22 paper 2  may/june  2021  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].cambridge igcse\u2122",
            "2": "2 0606/22/m/j/21 \u00a9 ucles 2021 mathematical formulae 1. algebra quadratic equation for the equation ax bx c 02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ - () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=- ()() srarr111nn ! =-- () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/22/m/j/21 \u00a9 ucles 2021 [turn over 1 using the binomial theorem, expand   ()1ex24+ , simplifying each term.  [2] 2 on the axes, sketch the graph of     () () () y xxx3 312 =--+    stating the intercepts with the coordinate  axes.  [3] y x o",
            "4": "4 0606/22/m/j/21 \u00a9 ucles 2021 3 find the values of the constant k for which    ()kx xk 21 61 02-+ ++ =    has real roots.  [5]",
            "5": "5 0606/22/m/j/21 \u00a9 ucles 2021 [turn over 4 the polynomial   ()pxm xxx n 29 3932=- ++ ,   where m and n are constants, has a factor x31-, and  remainder 6 when divided by x1-. show that x2- is a factor of ()px. [6]",
            "6": "6 0606/22/m/j/21 \u00a9 ucles 2021 5 the function f is defined, for \u00b0\u00b0x 0 810 gg , by   ()fc os xx232=-+ .  (a) write down the amplitude of f.  [1]  (b) find the period of f.  [2]  (c) on the axes, sketch the graph of ()f yx= . [2] 00\u00b0 90\u00b0 180\u00b0 270\u00b0 360\u00b0 450\u00b0 540\u00b0 630\u00b0 720\u00b0 810\u00b0xy 5 \u2013 5",
            "7": "7 0606/22/m/j/21 \u00a9 ucles 2021 [turn over 6 the points a(5, 4-) and c(11, 6) are such that ac is the diagonal of a square, abcd .  (a) find the length of the line ac. [2]  (b) (i) the coordinates of the centre, e, of the square are (8, y). find the value of y. [1]   (ii) find the equation of the diagonal bd. [3]   (iii) given that the x\u2011coordinate of b is less than the x\u2011coordinate of d, write eb and ed as  column vectors.  [2]",
            "8": "8 0606/22/m/j/21 \u00a9 ucles 2021 7 97rrada18 cm c db  dab  is a sector of a circle, centre a, radius 18  cm. the lines cb and cd are tangents to the circle.  angle dab  is r 97 radians.  (a) find the perimeter of the shaded region.  [3]  (b) find the area of the shaded region.  [3]",
            "9": "9 0606/22/m/j/21 \u00a9 ucles 2021 [turn over 8 a particle moves in a straight line so that, t seconds after passing through a fixed point o, its velocity,  v ms1-, is given by   vt t 33 07 22=- +.  (a) find the distance between the particle\u2019s two positions of instantaneous rest.  [6]  (b) find the acceleration of the particle when t2=. [2]",
            "10": "10 0606/22/m/j/21 \u00a9 ucles 2021 9 solve the following simultaneous equations.     xx yy xy43 8 4022++ = +=  [6]",
            "11": "11 0606/22/m/j/21 \u00a9 ucles 2021 [turn over 10 (a) find   () x edx13+y . [2]  (b) (i) differentiate, with respect to x,   sin yx x4 = . [2]    (ii) hence show that   rcosxx x 4483 1 6drr 3 4=- y . [4]",
            "12": "12 0606/22/m/j/21 \u00a9 ucles 2021 11 in this question all lengths are in centimetres.  the volume and surface area of a sphere of radius r are  rr34 3  and  rr42  respectively. x y  the diagram shows a solid object made from a hemisphere of radius x and a cylinder of radius x and  height y. the volume of the object is 500  cm3.  (a) find an expression for y in terms of x and show that the surface area, s, of the object is given by  r sxx 35 1000 2=+ . [4]",
            "13": "13 0606/22/m/j/21 \u00a9 ucles 2021 [turn over  (b) given that x can vary and that s has a minimum value, find the value of x for which s is a minimum.  [4]",
            "14": "14 0606/22/m/j/21 \u00a9 ucles 2021 12 do not use a calculator in this question. y a o bc xyx211=+ yx51=-  the diagram shows part of the curve   yx211=+  and part of the line    yx51=- .  the curve meets the y\u2011axis at point a. the line meets the x\u2011axis at point b. the line and curve intersect  at point c.  (a) (i) find the coordinates of a and b. [1]   (ii) verify that the x\u2011coordinate of c is 2.  [2]",
            "15": "15 0606/22/m/j/21 \u00a9 ucles 2021 [turn over  (b) find the exact area of the shaded region.  [5] question 13 is printed on the next page.",
            "16": "16 0606/22/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.13 the functions f and g are defined, for x02, by     ()fxxx 3212 =-,     ()gxx1=.  (a) find and simplify an expression for ()fgx. [2]  (b) (i) given that f1- exists, write down the range of f1-. [1]   (ii) show that ()fxpx qx r 412 =++- , where p, q and r are integers.  [4]"
        },
        "0606_s21_qp_23.pdf": {
            "1": "this document has 16 pages. any blank pages are indicated. dc (rw/sg) 202072/3 \u00a9 ucles 2021  [turn over *2417627705* additional mathematics  0606/23 paper 2  may/june  2021  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].cambridge igcse\u2122",
            "2": "2 0606/23/m/j/21 \u00a9 ucles 2021 mathematical formulae 1. algebra quadratic equation for the equation ax bx c 02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ - () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=- ()() srarr111nn ! =-- () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/23/m/j/21 \u00a9 ucles 2021 [turn over 1 do not use a calculator in this question.  write   73 545 --   with a rational denominator, simplifying your answer.  [3] 2 given that   () () y27 37 19xx21=- ++,   find the value of x when y30= . [4]",
            "4": "4 0606/23/m/j/21 \u00a9 ucles 2021 3 (a) write   () yxx y 8127 5 4335    in the form xy3abc##   where a, b and c are constants.  [3]  (b) (i) find the value of a such that    log2823 a=. [2]   (ii) write   log a3()a2   as a single logarithm to base a. [2]",
            "5": "5 0606/23/m/j/21 \u00a9 ucles 2021 [turn over 4 variables x and y are such that    cossinyxx=  .   using differentiation, find the approximate change in y as  x increases from r 4- to rh4-, where h is small.  [4] 5 (a) solve the inequality   xx21 72 102g -+ . [3]  (b) hence find the area enclosed between the curve   yx x 21 72 12=- +   and the x\u2011axis.  [3]",
            "6": "6 0606/23/m/j/21 \u00a9 ucles 2021 6 the polynomial p is given by   ()pxx xx 36 15 2132=- -+ .  (a) show that . x 025 =-  is a root of the equation ()px 0=. [1]  (b) show that the equation ()px 0= has a repeated root.  [4]",
            "7": "7 0606/23/m/j/21 \u00a9 ucles 2021 [turn over 7 (a) sketch the graph of the curve  ()ln yx 43=-   on the axes, stating the intercept with the x\u2011axis.  [2] \u2013 1 3xy 0  (b) find the equation of the tangent to the curve   ()ln yx 43=-   at the point where x2=. [5]",
            "8": "8 0606/23/m/j/21 \u00a9 ucles 2021 8 (a) (i) find rsin3dzz+eo y . [2]   (ii) find   ()sinc os 55 d22ii i + y . [2]  (b) show that     1e xx 11131dee2 +- =-ebl o y . [4]",
            "9": "9 0606/23/m/j/21 \u00a9 ucles 2021 [turn over 9 (a) the function f is defined, for all real x, by    ()fxx x 13 422=- - .   (i) write ()fx in the form () ab xc2++ , where a, b and c are constants.  [3]   (ii) hence write down the range of f.  [1]  (b) the function g is defined, for x1h, by   ()gxx x212=+ -.   (i) given that  ()x g1- exists, write down the domain and range of g1-. [2]   (ii) show that ()xp xq 1 g12=-++- , where p and q are integers.  [4]",
            "10": "10 0606/23/m/j/21 \u00a9 ucles 2021 10 in this question all lengths are in centimetres.  the volume and curved surface area of a cone of base radius r, height h and sloping edge l are rrh31 2  and rrl respectively. y xxy22+  the diagram shows a cone of base radius x, height y and sloping edge xy22+ .  the volume of the  cone is 10 r.  (a) find an expression for y in terms of x and show that the curved surface area, s, of the cone is given  by   rsxx9006 =+. [3]",
            "11": "11 0606/23/m/j/21 \u00a9 ucles 2021 [turn over  (b) given that x can vary and that s has a minimum value, find the exact value of x for which s is a  minimum.  [5]",
            "12": "12 0606/23/m/j/21 \u00a9 ucles 2021 11 (a) the first three terms of an arithmetic progression are  p1 , q1 , q1- .   (i) show that the common difference can be written as p32-  . [3]   (ii) the 10th term of the progression is pk, where k is a constant. find the value of k. [2]",
            "13": "13 0606/23/m/j/21 \u00a9 ucles 2021 [turn over  (b) the sum to infinity of a geometric progression is 8. the second term of the progression is 23. find  the two possible values of the common ratio.  [5]",
            "14": "14 0606/23/m/j/21 \u00a9 ucles 2021 12 a particle moves in a straight line such that its displacement, s metres, from a fixed point o at time  t seconds, is given by    cos st t 22=+ - ,   for t0h.  (a) find the displacement of the particle from o at the time when it first comes to instantaneous rest.  [5]",
            "15": "15 0606/23/m/j/21 \u00a9 ucles 2021  (b) find the time when the particle next comes to rest.  [1]  (c) find the distance travelled by the particle for rt023gg . [2]",
            "16": "16 0606/23/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"
        },
        "0606_w21_qp_11.pdf": {
            "1": "this document has 16 pages. cambridge igcse\u2122additional mathematics  0606/11 paper 1  october/november  2021  2 hours 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 calculator where appropriate.   \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.   \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ]. *7876434750* dc (cj/fc) 212434/2 \u00a9 ucles 2021  [turn over",
            "2": "2 0606/11/o/n/21 \u00a9 ucles 2021 mathematical formulae 1. algebra quadratic equation  for the equation ax bx c02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o  where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ -  () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=-  ()() srarr111nn ! =--  () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/11/o/n/21 \u00a9 ucles 2021 [turn over 1 - 90\u00b0 - 690\u00b0 180\u00b0 270\u00b0 360\u00b0xy - 180\u00b0 - 270\u00b0 - 360\u00b0 - 4- 20 2  the diagram shows the graph of   sin yabxc =+    for , x 360 360 \u00b0\u00b0gg -  where a, b and c are integers.    (a) write down the period of . sinabxc+ [1]  (b) find the value of a, of b and of c. [3]",
            "4": "4 0606/11/o/n/21 \u00a9 ucles 2021 2 points a and c have coordinates (, )46-  and (, ) 218 respectively. the point b lies on the line ac such  that   . ab ac32=  (a) find the coordinates of b. [2]  (b) find the equation of the line l, which is perpendicular to ac and passes through b. [2]  (c) find the area enclosed by the line l and the coordinate axes.  [2]",
            "5": "5 0606/11/o/n/21 \u00a9 ucles 2021 [turn over 3 (a) find the vector which has magnitude 39 and is in the same direction as 512 -bl .  [2]  (b) given that   a12=-bl    and   b54=-bl ,  find the constants m and n such that ab564mn+=eo . [4]",
            "6": "6 0606/11/o/n/21 \u00a9 ucles 2021 4 (a) given that    rqp r pqpqrab c 32 3=- -`j,   find the value of each of the constants a, b and c. [3]  (b) solve the equation   xx38 5054 52-+ =. [4]",
            "7": "7 0606/11/o/n/21 \u00a9 ucles 2021 [turn over 5 the polynomial   ()p ax bx x x 6432=+ ++ ,   where a and b are integers, is divisible by x2-. when  ()pxl is divided by x1+ the remainder is 7-.   (a) find the value of a and of b. [5]  (b) using your answers to part (a) , find the remainder when ()pxll is divided by x. [2]",
            "8": "8 0606/11/o/n/21 \u00a9 ucles 2021 6 a curve with equation ()f yx=  is such that   ddexyx4 6x 22 3=+ .   the curve has a gradient of 5 at the  point ,035bl . find ()fx. [7]",
            "9": "9 0606/11/o/n/21 \u00a9 ucles 2021 [turn over 7 the first three terms, in ascending powers of x, in the expansion of   ax2n+`j    can be written as  bx cx 642++ ,  where n, a, b and c are constants.  (a) find the value of n. [1]  (b) show that bc5 7682= .  [4]  (c) given that b12= , find the exact value of a and of c. [2]",
            "10": "10 0606/11/o/n/21 \u00a9 ucles 2021 8 od bca 6 cm 5 cm  the diagram shows a circle, centre o, radius 5  cm. the lines aob  and cod  are diameters of this circle.  the line ac has length 6  cm.  (a) show that angle aoc  = 1.287 radians, correct to 3 decimal places.  [2]  (b) find the perimeter of the shaded region.  [2]",
            "11": "11 0606/11/o/n/21 \u00a9 ucles 2021 [turn over  (c) find the area of the shaded region.  [3]",
            "12": "12 0606/11/o/n/21 \u00a9 ucles 2021 9 (a) find the coordinates of the stationary points on the curve   yx x 21 32=+ - `` jj .   give your answers  in exact form.  [4]",
            "13": "13 0606/11/o/n/21 \u00a9 ucles 2021 [turn over  (b) on the axes below, sketch the graph of   yx x 21 32=+ - `` jj ,   stating the coordinates of the  points where the curve meets the axes.  [4] oy x  (c) hence write down the value of the constant k such that   xx k 21 32+- = `` jj    has exactly  3 distinct solutions.  [1]",
            "14": "14 0606/11/o/n/21 \u00a9 ucles 2021 10 (a)  jess runs on 5 days each week to prepare for a race.     in week 1, every run is 2  km.   in week 2, every run is 2.5  km.   in week 3, every run is 3  km.   jess increases the distance of the run by 0.5  km every week.   (i) find the week in which jess runs 16  km on each of the 5 days.  [2]   (ii) find the total distance jess will have run by the end of week 8.  [3]",
            "15": "15 0606/11/o/n/21 \u00a9 ucles 2021 [turn over  (b) kyle also runs on 5 days each week to prepare for a race.   in week 1, every run is 2  km.   in week 2, every run is 2.5  km.   in week 3, every run is 3.125  km.   the distances he runs each week form a geometric progression.   (i) find the common ratio of the geometric progression.  [1]   (ii) find the first week in which kyle will run more than 16  km on each of the 5 days.  [3]   (iii) find the total distance kyle will have run by the end of week 8.  [3] question 11 is printed on the next page.",
            "16": "16 0606/11/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.11 (a) solve the equation   cose cc ot 35 52ii-=    for \u00b0\u00b00 180 ggi .  [4]  (b)  solve the equation   rsin321z+= - bl ,   where z is in radians and rrggz - . give your answers  in terms of r.  [4]"
        },
        "0606_w21_qp_12.pdf": {
            "1": "this document has 16 pages. any blank pages are indicated. cambridge igcse\u2122 dc (ce/cb) 212422/4 \u00a9 ucles 2021  [turn overadditional mathematics  0606/12 paper 1  october/november  2021  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ]. *5982126712*",
            "2": "2 0606/12/o/n/21 \u00a9 ucles 2021 mathematical formulae 1. algebra quadratic equation  for the equation ax bx c02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o  where n is a positive integer and () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ -  () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=-  ()() srarr111nn ! =--  () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/12/o/n/21 \u00a9 ucles 2021 [turn over 1 x 0y - 3 - 51 5  the diagram shows the graph of the cubic function () yx f= . the intercepts of the curve with the axes  are all integers.  (a) find the set of values of x for which ()x 0 f1. [1]  (b) find an expression for ()xf. [3]",
            "4": "4 0606/12/o/n/21 \u00a9 ucles 2021 2 (a) given that   xy xz zzy xyzab c3 32 =-`` jj ,   find the exact values of the constants a, b and c. [3]  (b) solve the equation   () () 52 1723 0pp21-+ =+. [4]",
            "5": "5 0606/12/o/n/21 \u00a9 ucles 2021 [turn over 3 (a) write   lg lg ab 32 4 +-    as a single logarithm to base 10.  [4]  (b) solve the equation   logl oga 34 27a 4+= . [5]",
            "6": "6 0606/12/o/n/21 \u00a9 ucles 2021 4 solve the equation   , cotx2330r+- = bl    where x11rr-  radians. give your answers in terms  of r. [4] 5 find the possible values of the constant c for which the line yc= is a tangent to the curve . sin yx534 =+  [3]",
            "7": "7 0606/12/o/n/21 \u00a9 ucles 2021 [turn over 6 do not use a calculator in this question.  the polynomial   ()xx ax xb 10 10 p32=+ -+ ,   where a and b are integers, is divisible by   x21+.  when ()xp is divided by  x1+,  the remainder is 24-.  (a) find the value of a and of b. [4]  (b) find an expression for ()xp as the product of three linear factors.  [4]  (c) write down the remainder when ()xp is divided by x. [1]",
            "8": "8 0606/12/o/n/21 \u00a9 ucles 2021 7 (a) oa b ca b c   the diagram shows triangle oac , where oa a=, ob b= and oc c=. the point b lies on the  line ac such that ::abbc mn= , where m and n are constants.   (i) write down ab in terms of a and b. [1]   (ii) write down bc in terms of b and c. [1]   (iii) hence show that () nm mn ac b += + . [2]  (b) given that   () ()2 114 714 2mn m +--=+-ee e oo o,   find the value of each of the constants m and n.  [4]",
            "9": "9 0606/12/o/n/21 \u00a9 ucles 2021 [turn over 8 (a) a 5-digit number is made using the digits   0, 1, 4, 5, 6, 7 and 9. no digit may be used more  than once in any 5-digit number. find how many such 5-digit numbers are even and greater than  50 000. [3]  (b) the number of combinations of n objects taken 4 at a time is equal to 6 times the number of  combinations of n objects taken 2 at a time. calculate the value of n. [5]",
            "10": "10 0606/12/o/n/21 \u00a9 ucles 2021 9 m a ob d c n6 cm 4 cm 12 cm  the diagram shows a circle, centre o, radius 12  cm, and a rectangle abcd . the diagonals ac and  bd intersect at o. the sides ab and ad of the rectangle have lengths 6  cm and 4  cm respectively. the  points m and n lie on the circumference of the circle such that mac  and ndb  are straight lines.  (a) show that angle aod  is 1.176 radians correct to 3 decimal places.  [2]  (b) find the perimeter of the shaded region.  [4]",
            "11": "11 0606/12/o/n/21 \u00a9 ucles 2021 [turn over  (c) find the area of the shaded region.  [3]",
            "12": "12 0606/12/o/n/21 \u00a9 ucles 2021 10 xa by - 1 2 0()yx213 2=++()x2+  the diagram shows the graph of the curve   y x213 2= ++ ()x2+ `j   for x 22-. the points a and b lie  on the curve such that the x-coordinates of a and of b are -1 and 2 respectively.  (a) find the exact y-coordinates of a and of b. [2]  (b) find the area of the shaded region enclosed by the line ab and the curve, giving your answer in the   form lnqpr- , where p, q and r are integers.  [6]",
            "13": "13 0606/12/o/n/21 \u00a9 ucles 2021 [turn over additional working space for question 10(b).",
            "14": "14 0606/12/o/n/21 \u00a9 ucles 2021 11 (a) t sv ms-1 60 30 10 0 25 35 55   the diagram shows the velocity\u2013time graph for a particle p, travelling in a straight line with  velocity vms1- at a time t seconds. p accelerates at a constant rate for the first 10  s of its motion,  and then travels at constant velocity, 30ms1-, for another 15  s. p then accelerates at a constant  rate for a further 10  s and reaches a velocity of  06ms1-. p then decelerates at a constant rate and  comes to rest when t55= .   (i) find the acceleration when t12= . [1]   (ii) find the acceleration when t50= . [1]   (iii) find the total distance travelled by the particle p. [2]",
            "15": "15 0606/12/o/n/21 \u00a9 ucles 2021  (b) a particle q travels in a straight line such that its velocity, vms1-, at time t s after passing through  a fixed point o is given by cos vt43 4 =- .   (i) find the speed of q when t95r= . [2]   (ii) find the smallest positive value of t for which the acceleration of q is zero.  [3]   (iii) find an expression for the displacement of q from o at time t. [2]",
            "16": "16 0606/12/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.blank page"
        },
        "0606_w21_qp_13.pdf": {
            "1": "this document has 16 pages. any blank pages are indicated. cambridge igcse\u2122 dc (pq/sg) 212423/2 \u00a9 ucles 2021  [turn over *2709190526* additional mathematics  0606/13 paper 1  october/november  2021  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].",
            "2": "2 0606/13/o/n/21 \u00a9 ucles 2021 mathematical formulae 1. algebra quadratic equation for the equation ax bx c 02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ - () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=- ()() srarr111nn ! =-- () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/13/o/n/21 \u00a9 ucles 2021 [turn over 1 on the axes below, sketch the graph of   () () () y xxx412 134 =- +- +   stating the intercepts with the  coordinate axes.  [3] 0y x 2 a particle moves in a straight line such that its velocity, vms1-, at time t seconds after passing through  a fixed point o, is given by v 25 et3=- . find the speed of the particle when t1=. [2]",
            "4": "4 0606/13/o/n/21 \u00a9 ucles 2021 3 solve the equation   cotx2331 2 r-=bl ,   where x is in radians and x01g r. [5]",
            "5": "5 0606/13/o/n/21 \u00a9 ucles 2021 [turn over 4 (a) find the first three terms, in ascending powers of x2, in the expansion of   x21 3228 -eo .   write your  coefficients as rational numbers.  [3]  (b) find the coefficient of x2 in the expansion of   xxx 21 3221 282 -+e bo l. [3]",
            "6": "6 0606/13/o/n/21 \u00a9 ucles 2021 5 a geometric progression is such that its sum to 4 terms is 17 times its sum to 2 terms. it is given that the  common ratio of this geometric progression is positive and not equal to 1.  (a) find the common ratio of this geometric progression.  [3]  (b) given that the 6th term of the geometric progression is 64, find the first term.  [2]  (c) explain why this geometric progression does not have a sum to infinity.  [1]",
            "7": "7 0606/13/o/n/21 \u00a9 ucles 2021 [turn over 6 (a) a 5-digit number is made using the digits   0,  1,  2,  3,  4,  5,  6,  7,  8 and 9.  no digit may be used  more than once in any 5-digit number. find how many such 5-digit numbers are odd and greater  than 70  000. [3]  (b) the number of combinations of n objects taken 3 at a time is 2 times the number of combinations  of n objects taken 2 at a time. find the value of n. [4]",
            "8": "8 0606/13/o/n/21 \u00a9 ucles 2021 7 p b ao q  the diagram shows a circle, centre o, radius 10  cm. the points a, b and p lie on the circumference of  the circle. the chord ab is of length 14  cm. the point q lies on ab and the line poq  is perpendicular to  ab.  (a) show that angle  poa  is 2.366 radians, correct to 3 decimal places.  [2]  (b) find the area of the shaded region.  [3]",
            "9": "9 0606/13/o/n/21 \u00a9 ucles 2021 [turn over  (c) find the perimeter of the shaded region.  [5]",
            "10": "10 0606/13/o/n/21 \u00a9 ucles 2021 8 the curves   yx x12=+ -   and   yx x 26 22=+ -   intersect at the points a and b.  (a) show that the mid-point of the line ab is (2, 9).  [5]  the line  l is the perpendicular bisector of ab.  (b) show that the point c (12, 7) lies on the line l. [3]",
            "11": "11 0606/13/o/n/21 \u00a9 ucles 2021 [turn over  (c) the point d also lies on l, such that the distance of d from ab is two times the distance of c from  ab. find the coordinates of the two possible positions of d. [4]",
            "12": "12 0606/13/o/n/21 \u00a9 ucles 2021 9 when ey2 is plotted against x2, a straight line graph passing through the points (4, 7.96) and (2, 3.76) is  obtained.  (a) find y in terms of x. [5]  (b) find y when x1=.  [2]  (c) using your equation from part (a) , find the positive values of  x for which the straight line exists.  [3]",
            "13": "13 0606/13/o/n/21 \u00a9 ucles 2021 [turn over 10 a curve with equation () yx f=  is such that   dd xyx23 522 21 =+ +-`j    for x02.   the curve has gradient  10 at the point ,3219bl .   (a) show that, when x11= , xy52dd= .  [5]  (b) find ()xf. [4]",
            "14": "14 0606/13/o/n/21 \u00a9 ucles 2021 11  a curve has equation   yxx 152 31 =+-`j    for x 12-.  (a) show that   xy xxax bxc 31 5dd 222 32 = +-++ ` `j j   where a, b and c are integers.  [6]",
            "15": "15 0606/13/o/n/21 \u00a9 ucles 2021  (b) find the x-coordinate of the stationary point on the curve.  [2]  (c) explain how you could determine the nature of this stationary point.  [2]   [you are not required to find the nature of this stationary point.]",
            "16": "16 0606/13/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"
        },
        "0606_w21_qp_21.pdf": {
            "1": "this document has 16 pages. any blank pages are indicated. cambridge igcse\u2122 dc (pq/fc) 212424/3 \u00a9 ucles 2021  [turn over *7116278869* additional mathematics  0606/21 paper 2  october/november  2021  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].",
            "2": "2 0606/21/o/n/21 \u00a9 ucles 2021 mathematical formulae 1. algebra quadratic equation  for the equation ax bx c02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o  where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ -  () {( )} sn an an d l21 2121n=+ =+ - geometric series  ua rnn1=-  ()() srarr111nn ! =--  () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/21/o/n/21 \u00a9 ucles 2021 [turn over 1 solve the inequality   () () xx x 52 362 +- +. [3] 2 solve the following simultaneous equations. xy x 152+=  yx31 1 +=  [5]",
            "4": "4 0606/21/o/n/21 \u00a9 ucles 2021 3 a curve has equation   sinyxx 123=++.   (a) show that the exact value of dd xy at the point where x6r= can be written as   k 612r+bl ,   where k  is an integer.  [5]  (b) find the equation of the normal to the curve at the point where x0=. [4]",
            "5": "5 0606/21/o/n/21 \u00a9 ucles 2021 [turn over 4 find rational values a and b such that   ab 52 521++-=. [5]",
            "6": "6 0606/21/o/n/21 \u00a9 ucles 2021 5 it is given that tan yx 32=  for \u00b0 \u00b0x 0 36011 .  (a) show that   ddtansecxymx x2=    where m is an integer to be found.  [2]  (b) find all values of x such that   ddseccosecxyxx 3= . [5]",
            "7": "7 0606/21/o/n/21 \u00a9 ucles 2021 [turn over 6 find the values of m for which the line   yxm 2 =-    does not touch or cut the curve  ()yx x m 18 12=+ ++ .  [6]",
            "8": "8 0606/21/o/n/21 \u00a9 ucles 2021 7 (a) use logarithms to solve the following equation, giving your answer correct to 1 decimal place.  53 2xx22 3#=-+ [4]  (b) solve the equation   () () logl og yy 11 2132 3+- =- . [5]",
            "9": "9 0606/21/o/n/21 \u00a9 ucles 2021 [turn over 8 marc chooses 5 people from 4 men, 4 women and 2 children.  find the number of ways that marc can do this  (a) if there are no restrictions,  [1]  (b) if at least 2 men are chosen,  [3]  (c) if at least 1 man, at least 1 woman and at least 1 child are chosen.  [3]",
            "10": "10 0606/21/o/n/21 \u00a9 ucles 2021 9 the following functions are defined for x12.  f()xxx 13=+ -          g()xx 12=+  (a) find f( )xg. [2]  (b) find ()x g1-. [2]",
            "11": "11 0606/21/o/n/21 \u00a9 ucles 2021 [turn over  (c) do not use a calculator in this part of the question.   solve the equation   f()g () xx= . [5]",
            "12": "12 0606/21/o/n/21 \u00a9 ucles 2021 10  y x oyxxx5 2+-=  the diagram shows part of the curve   yxxx5 2=+ -.  (a) find, in the form ym xc=+ , the equation of the tangent to the curve at the point where x1=.  [5]",
            "13": "13 0606/21/o/n/21 \u00a9 ucles 2021 [turn over  (b) find the exact area enclosed by the curve, the x-axis, and the lines x1= and x3=. [4]",
            "14": "14 0606/21/o/n/21 \u00a9 ucles 2021 11 the volume, v, of a cone with base radius r and vertical height h is given by rh31 2r .  the curved surface area of a cone with base radius r and slant height l is given by rlr.   a cone has base radius r cm, vertical height h cm and volume v cm3. the curved surface area of the  cone is r4cm2.  (a) show that   hrr16 2 22=- . [4]  (b) show that   vr r31626 r=- . [2]",
            "15": "15 0606/21/o/n/21 \u00a9 ucles 2021  (c) given that r can vary and that v has a maximum value, find the value of r that gives the maximum  volume.  [5]",
            "16": "16 0606/21/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"
        },
        "0606_w21_qp_22.pdf": {
            "1": "this document has 16 pages. any blank pages are indicated. cambridge igcse\u2122additional mathematics  0606/22 paper 2  october/november  2021  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ]. *8550153025* dc (lk/fc) 212425/3 \u00a9 ucles 2021  [turn over",
            "2": "2 0606/22/o/n/21 \u00a9 ucles 2021 mathematical formulae 1. algebra quadratic equation  for the equation ax bx c02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o  where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ -  () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=-  ()() srarr111nn ! =--  () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/22/o/n/21 \u00a9 ucles 2021 [turn over 1  - 6- 5- 4- 3- 2- 10y x1 2 3 4 5 65101520  (a) on the axes, draw the graphs of   yx53 2 =+ -   and   yx11=- . [4]  (b) using the graphs, or otherwise, solve the inequality   xx 11 53 2 1-+ -. [2]",
            "4": "4 0606/22/o/n/21 \u00a9 ucles 2021 2 (a) expand   () x 234- , evaluating all of the coefficients.  [4]  (b) the sum of the first three terms in ascending powers of x in the expansion of   () xxa23 14-+ bl   is   xbc x32++ , where a, b and c are integers. find the values of each of a, b and c. [4]",
            "5": "5 0606/22/o/n/21 \u00a9 ucles 2021 [turn over 3 (a) show that   secs eccotcosecxxxx11 112-++= . [4]  (b) hence solve the equation   secs ecsecxxx11 113-++=    for   x 0 360 \u00b0\u00b011 . [4]",
            "6": "6 0606/22/o/n/21 \u00a9 ucles 2021 4 (a) find the x-coordinates of the stationary points on the curve   ln yx xx 372=+ -, where x02.  [5]  (b) determine the nature of each of these stationary points.  [3]",
            "7": "7 0606/22/o/n/21 \u00a9 ucles 2021 [turn over 5 (a) solve the following simultaneous equations.      ee23 8 -=ee 5xy xy+=  [5]  (b) solve the equation   ee 5() () tt21 53=--. [4] ",
            "8": "8 0606/22/o/n/21 \u00a9 ucles 2021 6 do not use a calculator in this question.  all lengths in this question are in centimetres.  you may use the following  trigonometrical ratios. \u00b0 \u00b0sin cos6023 6021 3= = \u00b0 tan60=a c b60\u00b0 62\u2013 62+  the diagram shows triangle abc  with ac 62=- , ab 62=+    and angle \u00b0 cab 60= .  (a) find the exact length of bc. [3]  (b) show that   sinacb6 42=+. [2]  (c) show that the perpendicular distance from a to the line bc is 1.  [2]",
            "9": "9 0606/22/o/n/21 \u00a9 ucles 2021 [turn over 7 it is given that   () ddexy x11 x 22 2 2=++   for   x 12-.  (a) find an expression for dd xy given that   dd xy2=   when x0=. [3]  (b) find an expression for y given that   y4=   when   x0=. [3]",
            "10": "10 0606/22/o/n/21 \u00a9 ucles 2021 8 variables x and y are such that when y is plotted against () logx12+, where x 12-, a straight line is  obtained which passes through (, .) 2104 and (, .) 4154.  (a) find y in terms of () logx12+. [4]  (b) find the value of y when x15= . [1]",
            "11": "11 0606/22/o/n/21 \u00a9 ucles 2021 [turn over  (c) find the value of x when y25= . [3]",
            "12": "12 0606/22/o/n/21 \u00a9 ucles 2021 9 (a) find the equation of the normal to the curve   yx xx4632=+ -+    at the point (, ) 14. [5]",
            "13": "13 0606/22/o/n/21 \u00a9 ucles 2021 [turn over  (b) do not use a calculator in this part of the question.   find the exact x-coordinate of each of the two points where the normal cuts the curve again.  [5]",
            "14": "14 0606/22/o/n/21 \u00a9 ucles 2021 10 (a) the first three terms of an arithmetic progression are x, x54- and x82+. find x and the common  difference.  [4]",
            "15": "15 0606/22/o/n/21 \u00a9 ucles 2021  (b) the first three terms of a geometric progression are y, y54- and y82+.   (i) find the two possible values of y. [4]   (ii) for each of these values of y, find the corresponding value of the common ratio.  [2]",
            "16": "16 0606/22/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"
        },
        "0606_w21_qp_23.pdf": {
            "1": "this document has 16 pages. any blank pages are indicated. cambridge igcse\u2122 dc (ce/cb) 212426/3 \u00a9 ucles 2021  [turn overadditional mathematics  0606/23 paper 2  october/november  2021  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ]. *3772962579*",
            "2": "2 0606/23/o/n/21 \u00a9 ucles 2021 mathematical formulae 1. algebra quadratic equation  for the equation ax bx c02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o  where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ -  () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=-  ()() srarr111nn ! =--  () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/23/o/n/21 \u00a9 ucles 2021 [turn over 1 x 0 - 2- 1 1 2 3 4 5 6 7 8 - 2246810y  (a) on the axes draw the graphs of  yx 5 =-   and  yx62 7 =- -. [4]  (b) use your graphs to solve the inequality  xx56 272-- -. [2]",
            "4": "4 0606/23/o/n/21 \u00a9 ucles 2021 2 solve the following simultaneous equations. give your answers in the form ab 3+ , where a and b are  rational. xy xy3 23 5+= -= [5]",
            "5": "5 0606/23/o/n/21 \u00a9 ucles 2021 [turn over 3 012 - 1 - 2 - 3 - 4- r 2r r xy r 2-r 2r 23  (a) the curve has equation cos ya bx c =+  where a, b and c are integers. find the values of a, b  and c. [3]  (b) another curve has equation   sin yx 23 4 =+ .   write down   (i) the amplitude,  [1]   (ii) the period in radians.  [1]",
            "6": "6 0606/23/o/n/21 \u00a9 ucles 2021 4 (a) solve the equation   () logx2321 6-= .   give your answer in exact form.  [2]  (b) solve the equation   () ln lnuu24 1 -- =.   give your answer in exact form.  [3]  (c) solve the equation   2739vv 25=-. [3]",
            "7": "7 0606/23/o/n/21 \u00a9 ucles 2021 [turn over 5 (a) show that   cose cc osectansecxxxx11 112-++= . [4]  (b) hence solve the equation   cose cc oseccose cxxx11 115-++=    for \u00b0\u00b0x 0 36011 . [4]",
            "8": "8 0606/23/o/n/21 \u00a9 ucles 2021 6 it is given that  sec x 2 i =+    and   tan y 52i =+ .  (a) express y in terms of x. [2]  (b) find   xy dd in terms of x. [1]  (c) a curve has the equation found in part (a) . find the equation of the tangent to the curve when   r 3i= . [4]",
            "9": "9 0606/23/o/n/21 \u00a9 ucles 2021 [turn over 7 the vector p has magnitude 39 and is in the direction ij521-+ . the vector q has magnitude 34 and is  in the direction ij15 8-.  (a) write both p and q in terms of i and j. [4]  (b) find the magnitude of pq+ and the angle this vector makes with the positive x-axis.  [4]",
            "10": "10 0606/23/o/n/21 \u00a9 ucles 2021 8 x0y yx29= x4=yxx152 =-+  the diagram shows part of the curve  yxx152 =-+, and the straight lines x4= and yx29= .  (a) find the coordinates of the stationary point on the curve  yxx152 =-+. [5]",
            "11": "11 0606/23/o/n/21 \u00a9 ucles 2021 [turn over  (b) given that the curve and the line   yx29=    intersect at the point (2, 9), find the area of the shaded  region.  [5]",
            "12": "12 0606/23/o/n/21 \u00a9 ucles 2021 9 an arithmetic progression has first term a and common difference d. the third term is 13 and the tenth  term is 41.   (a) find the value of a and of d. [4]  (b) find the number of terms required to give a sum of 2555.  [4]",
            "13": "13 0606/23/o/n/21 \u00a9 ucles 2021 [turn over  (c) given that sn is the sum to n terms, show that   () ss kk31 2kk2-= + . [4]",
            "14": "14 0606/23/o/n/21 \u00a9 ucles 2021 10 (a) it is given that   ()xx xx 441 51 8 f32=- -+ .   find the equation of the normal to the curve  () yx f= at the point where  x1=. [5]",
            "15": "15 0606/23/o/n/21 \u00a9 ucles 2021  (b) do not use a calculator in this part of the question.   it is also given that xa+, where a is an integer, is a factor of ()xf. find a and hence solve the  equation ()x 0 f=. [6]",
            "16": "16 0606/23/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"
        }
    },
    "2022": {
        "0606_m22_qp_12.pdf": {
            "1": "this document has 16 pages. any blank pages are indicated.  [turn overcambridge igcse\u2122 *7011674582* dc (cj/cgw) 303740/2 \u00a9 ucles 2022additional mathematics  0606/12 paper 1  february/march  2022  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].",
            "2": "2 0606/12/f/m/22 \u00a9 ucles 2022 mathematical formulaemathematical formulae 1. algebra quadratic equation for the equation ax bx c 02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ - () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=- ()() srarr111nn ! =-- () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/12/f/m/22 \u00a9 ucles 2022 [turn over 1 find the values of k such that the line   yk x91=+    does not meet the curve   () . yk xx k 32 142=+ ++  [5]",
            "4": "4 0606/12/f/m/22 \u00a9 ucles 2022 2 do not use a calculator in this question.  solve the equation   () () xx 35 32 35 102-+ +- =,   giving your solutions in the form ab 3+ ,  where a and b are rational numbers.  [6]",
            "5": "5 0606/12/f/m/22 \u00a9 ucles 2022 [turn over 3 the curve with equation   sin ya bx c =+ ,   where a, b and c are constants, passes through the points    r(, ) 41 1 and r,345 -eo . it is given that   sinab xc+   has period r16.  (a) find the exact values of a, b and c. [4]  (b) using your answer to part (a) , find the coordinates of the minimum point on the curve for  r x01 6 gg . [4] ",
            "6": "6 0606/12/f/m/22 \u00a9 ucles 2022 4 (a) show that   () x x 211 214 2 -+-   can be written as   ()xx 2123 2-+. [1]  (b)  find  ()dxxx2123 225 -+y ,    giving your answer in the form n ab1+ , where a and b are constants.  [5]",
            "7": "7 0606/12/f/m/22 \u00a9 ucles 2022 [turn over 5 variables  x and y are such that   ()nyxx 1 3232 =-.  (a) find dd xy.  [3]  (b) hence find the approximate change in y when x increases from 2 to h2+, where h is small.  [2]  (c) at the instant when x2=, y is increasing at the rate of 4 units per second. find the corresponding  rate of increase in x. [2]",
            "8": "8 0606/12/f/m/22 \u00a9 ucles 2022 6 the normal to the curve  tan yx 13=+   at the point p with x-coordinate r 12, meets the x-axis at the  point q.  the line  rx12=   meets the x-axis at the point r. find the area of the triangle pqr .   [8]",
            "9": "9 0606/12/f/m/22 \u00a9 ucles 2022 [turn over 7 a curve ()f yx=  is such that  dd()xyx 2322 31=--.  the curve passes through the point (, .) 2102- . the  gradient of the tangent to the curve at  (, .) 2102-   is \u20136. find ()fx.  [8]",
            "10": "10 0606/12/f/m/22 \u00a9 ucles 2022 8 in this question, all lengths are in metres and all times are in seconds.  a particle a is moving in the direction  20 21-eo   with a speed of 58.  (a) find the velocity vector of a. [1]  (b) given that a is initially at the point with position vector 5 3-eo , write down the position vector of a  at time t. [1]   a particle b starts to move such that its position vector at time t is tt 44 235 4 --+eo .  (c) find the displacement vector ab at time t. [2]",
            "11": "11 0606/12/f/m/22 \u00a9 ucles 2022 [turn over  (d) hence find the distance ab, at time t, in the form pt qt r2++ , where p, q and r are constants.  [2]  (e) find the value of t when the distance ab is 6, giving your answer correct to 2 decimal places.  [2]",
            "12": "12 0606/12/f/m/22 \u00a9 ucles 2022 9 (a) the function f is such that   () n( ) fxx 15 2 =+ ,  for xa2, where a is as small as possible.     (i) write down the value of a. [1]   (ii) hence find the range of f.  [1]   (iii) find f1-()x, stating its domain.  [3]   (iv) on the axes, sketch the graphs of ()f yx=  and f y1=-()x, stating the exact values of the  intercepts of the curves with the coordinate axes.  [4] y o x",
            "13": "13 0606/12/f/m/22 \u00a9 ucles 2022 [turn over  (b) the function g is such that   gxx 4217| -, for x02. solve the equation g( )x 22=- .  [3]",
            "14": "14 0606/12/f/m/22 \u00a9 ucles 2022 10 (a) the first three terms of an arithmetic progression are   ,, sins in sin xx x 35 39 3.   find the exact  values of x, where  rx02gg ,  for which the sum to twenty terms is equal to 390.  [6]",
            "15": "15 0606/12/f/m/22 \u00a9 ucles 2022  (b) the first three terms of a geometric progression are ,, cosc os cos yy y 20 10 523.   (i) explain why this progression has a sum to infinity.  [2]   (ii) find the value of y, where y is in radians and y 0211 , for which the sum to infinity is 9.  give your answer correct to 2 decimal places.  [4]         ",
            "16": "16 0606/12/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.blank page"
        },
        "0606_m22_qp_22.pdf": {
            "1": "this document has 16 pages. any blank pages are indicated.  [turn overdc (rw/cgw) 303976/2 \u00a9 ucles 2022 *1704896938* additional mathematics  0606/22 paper 2  february/march  2022  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].cambridge igcse\u2122",
            "2": "2 0606/22/f/m/22 \u00a9 ucles 2022 mathematical formulae 1. algebra quadratic equation  for the equation ax bx c02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o  where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ -  () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=-  ()() srarr111nn ! =--  () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/22/f/m/22 \u00a9 ucles 2022 [turn over 1 a line, l,  has equation   xy45 9 += .   points a and b have coordinates ( 6-, 7) and (1, 9) respectively.  find the equation of the line parallel to l which passes through the mid\u2011point of ab. [3] 2 solve the equation   () logl og xx87 2255+- =. [3]",
            "4": "4 0606/22/f/m/22 \u00a9 ucles 2022 3 a group of students, 4  girls and  3 boys, stand in line.  (a) find the number of different ways the students can stand in line if there are no restrictions.  [1]  (b) find the number of different ways the students can stand in line if the 3  boys are next to each  other.  [2]  (c) cam and dea are 2 of the girls. find the number of ways the students can stand in line if cam and  dea are not next to each other.  [2]",
            "5": "5 0606/22/f/m/22 \u00a9 ucles 2022 [turn over 4 find the x\u2011coordinates of the points of intersection of the curves   x y 4912 2 +=    and   yx23= .      give your answers correct to 3  decimal places.  [5]",
            "6": "6 0606/22/f/m/22 \u00a9 ucles 2022 5 (a) y x4 0 4 1   the diagram shows the graph of ()f yx= , where ()fx is a quadratic function. write down the two  possible expressions for ()fx. [2]  (b) the three roots of ()px 0=, where   ()pxx ax bx 5232=+ +-    are    x51=,  xn= and  xn 1=+ ,      where a and b are positive integers and n is a negative integer. find ()px, simplifying your  coefficients.  [5]",
            "7": "7 0606/22/f/m/22 \u00a9 ucles 2022 [turn over 6 (a) (i) use the binomial theorem to expand   () x 137+    in ascending powers of x, as far as the term  in x3. simplify each term.  [2]   (ii) show that your expansion from part (i) gives the value of  .1037 as 1.23 to 2  decimal places.  [2]  (b) find the term independent of x in the expansion of    x x 22415 + eo . [2]",
            "8": "8 0606/22/f/m/22 \u00a9 ucles 2022 7 in this question, all angles are in radians.  (a) solve the equation   sect an 32ii=+    for  rr11i - . [5]  (b) show that, for r0211z ,     costansec 12zzz -= . [3]  (c) given that   cose cx817=-    and that    rr x232 11 ,    find the exact value of cotx. [2]",
            "9": "9 0606/22/f/m/22 \u00a9 ucles 2022 [turn over 8 15 cm a cm c oba rad6r  the diagram shows the sector aob  of a circle, centre  o and radius 15  cm. angle aob  is r 6 radians.  point  c lies on ob such that cb is a cm. ac is a straight line.  (a) find the exact value of a such that the area of triangle aoc  is equal to the area of the shaded  region acb . [4]  (b) for the value of a found in part (a), find the perimeter of the shaded region. give your answer  correct to 1 decimal place.  [3]",
            "10": "10 0606/22/f/m/22 \u00a9 ucles 2022 9 (a) a vehicle travels along a straight, horizontal road. at time t0= seconds, the vehicle, travelling at  a velocity of wms1-, passes point  o. the vehicle travels at this constant velocity for 12  seconds.  it then slows down, with constant deceleration, for 10  seconds until it reaches a velocity of  ()w14ms1--. it continues to travel at this velocity for 28  seconds until it reaches point  a, 458  m  from o.   find the value of w. [4]",
            "11": "11 0606/22/f/m/22 \u00a9 ucles 2022 [turn over  (b) a particle moves in a straight line. the velocity, vms1-, of the particle at time t seconds, where  t0h, is given by    () () vt t45=- -.   (i) find the value of t for which the acceleration of the particle is 0ms2-. [2]   (ii) find the set of values of t for which the velocity of the particle is negative.  [2]   (iii) find the distance travelled by the particle in the first 5  seconds of its motion.  [4]",
            "12": "12 0606/22/f/m/22 \u00a9 ucles 2022 10 relative to an origin  o, the position vector of point p is ij32- and the position vector of point q is  ij81 3+ .  (a) the point  r is such that  pq pr5= .  find the unit vector in the direction or. [5]  (b) the position vector of s relative to o is mj. given that rs is parallel to pq, find the value of m.   [3]",
            "13": "13 0606/22/f/m/22 \u00a9 ucles 2022 [turn over 11 y xa b 0 2e y64x \u2212 5=+  the diagram shows part of the graphs of   e y6x45=+-   and    x2=.   the line x2= meets the curve  at the point  b(2, b) and the line ab is parallel to the x\u2011axis. find the area of the shaded region.  [7]",
            "14": "14 0606/22/f/m/22 \u00a9 ucles 2022 12 in this question all lengths are in centimetres. o p a bq h12 8r c  the diagram shows a right triangular prism of height h inside a right pyramid.  the pyramid has a height of 12 and a base that is an equilateral triangle, abc , of side 8.  the base of the prism sits on the base of the pyramid.  points p, q and r lie on the edges oa, ob and oc, respectively, of the pyramid oabc .  pyramids oabc  and opqr  are similar.  (a) show that the volume, v, of the triangular prism is given by    () va hb hc h93 32=+ +    where a,  b and c are integers to be found.  [4]",
            "15": "15 0606/22/f/m/22 \u00a9 ucles 2022  (b) it is given that, as h varies, v has a maximum value. find the value of h that gives this maximum  value of v. [3]",
            "16": "16 0606/22/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.blank page"
        },
        "0606_s22_qp_11.pdf": {
            "1": "this document has 16 pages. any blank pages are indicated.  [turn overdc (rw/fc) 303927/3 \u00a9 ucles 2022 *6277213431* additional mathematics  0606/11 paper 1  may/june  2022  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].cambridge igcse\u2122",
            "2": "2 0606/11/m/j/22 \u00a9 ucles 2022 mathematical formulae 1. algebra quadratic equation for the equation ax bx c 02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ - () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=- ()() srarr111nn ! =-- () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/11/m/j/22 \u00a9 ucles 2022 [turn over 1 find constants a, b and c such that      pq rpqrpq rab c 121323 = --- `j. [3]",
            "4": "4 0606/11/m/j/22 \u00a9 ucles 2022 2 a particle moves in a straight line such that its displacement, s metres, from a fixed point, at time  t seconds, t0h, is given by   st 1321 =+-`j .  (a) find the exact speed of the particle when t1=. [3]  (b) show that the acceleration of the particle will never be zero.  [2]",
            "5": "5 0606/11/m/j/22 \u00a9 ucles 2022 [turn over 3 a function f is such that    () () fl n xx 21=+ ,  for x212-.  (a) write down the range of f.  [1]  a function g is such that   ()gxx 57=- ,    for xr!.  (b) find the exact solution of the equation   ()gfx 13= . [3]  (c) find the solution of the equation    () () fgxx1=-l . [6]",
            "6": "6 0606/11/m/j/22 \u00a9 ucles 2022 4 (a) y x\u2013 2 1 3 024   the diagram shows the graph of ()f yx= , where ()fx is a cubic. find the possible expressions  for ()fx. [3]  (b) (i) on the axes below, sketch the graph of   yx 21=+    and the graph of   () yx 41=- ,   stating the coordinates of the points where the graphs meet the coordinate axes.  [3] y xo",
            "7": "7 0606/11/m/j/22 \u00a9 ucles 2022 [turn over   (ii) find the exact solutions of the equation   () xx21 41 += - . [4]",
            "8": "8 0606/11/m/j/22 \u00a9 ucles 2022 5 (a) find the vector which is in the opposite direction to  15 8-eo  and has a magnitude of 8.5.  [2]  (b) find the values of a and b such that  a bab a532 1 262++=+ee e oo o. [3] 6 (a) write down the values of k for which the line yk= is a tangent to the curve rsin yx 4410 =+ + bl .   [2]",
            "9": "9 0606/11/m/j/22 \u00a9 ucles 2022 [turn over  (b) (i) show that () costan costan sinsin 11 11 21 2 ii ii ii -+++-=+ . [4]   (ii) hence solve the equation costan costan 11 113ii ii -+++-=,  for \u00b0\u00b00 360 ggi . [4]",
            "10": "10 0606/11/m/j/22 \u00a9 ucles 2022 7 (a) the first three terms of an arithmetic progression are    lg3,  lg33 ,  lg53 .  given that the sum to n  terms of this progression can be written as lg256 81, find the value of n. [5]",
            "11": "11 0606/11/m/j/22 \u00a9 ucles 2022 [turn over  (b) do not use a calculator in this part of the question.   the first three terms of a geometric progression are    ln256,  ln16,  ln4.   find the sum to infinity  of this progression, giving your answer in the form lnp2. [4]",
            "12": "12 0606/11/m/j/22 \u00a9 ucles 2022 8 do not use a calculator in this question.  (a) find the exact coordinates of the points of intersection of the curve   yx x25 202=+ -   and the  line yx35 10 =+ . [4]",
            "13": "13 0606/11/m/j/22 \u00a9 ucles 2022 [turn over  (b) it is given that   tan3 231i=+-,  for r0211i .   find cose c2i in the form ab 3+ , where a and  b are constants.  [5]",
            "14": "14 0606/11/m/j/22 \u00a9 ucles 2022 9 a circle, centre o and radius r cm, has a sector oab  of fixed area 10cm2. angle aob  is i radians and  the perimeter of the sector is p cm.  (a) find an expression for p in terms of r. [3]  (b) find the value of r for which p has a stationary value.  [3]  (c) determine the nature of this stationary value.  [2]  (d) find the value of i at this stationary value.  [1]",
            "15": "15 0606/11/m/j/22 \u00a9 ucles 2022 10 the normal to the curve   rtan yx 32=+ bl    at the point  p with coordinates ( p, 1-), where rp 061g,  meets the x\u2011axis at the point  a and the y\u2011axis at the point  b. find the exact coordinates of the mid\u2011point  of ab. [10]",
            "16": "16 0606/11/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"
        },
        "0606_s22_qp_12.pdf": {
            "1": "this document has 16 pages. any blank pages are indicated.  [turn overcambridge igcse\u2122additional mathematics  0606/12 paper 1  may/june  2022  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ]. *9896994444* dc (cj/fc) 303920/4 \u00a9 ucles 2022",
            "2": "2 0606/12/m/j/22 \u00a9 ucles 2022 mathematical formulae 1. algebra quadratic equation for the equation ax bx c 02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ - () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=- ()() srarr111nn ! =-- () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/12/m/j/22 \u00a9 ucles 2022 [turn over 1  y x 0 \u2013 82 180\u00b0 \u2013 180\u00b0  the diagram shows the graph of  sin ya bx c =+ ,  where a, b and c are integers, for   \u00b0\u00b0x 180 180 gg - .  find the values of a, b and c. [3]",
            "4": "4 0606/12/m/j/22 \u00a9 ucles 2022 2 given that  sec x2i =   and  cot y22i += ,  find y in terms of x. [4]",
            "5": "5 0606/12/m/j/22 \u00a9 ucles 2022 [turn over 3 variables x and y are such that, when   g( ) ly21+   is plotted against x2, a straight line graph passing  through the points (1, 1) and (2, 5) is obtained.  (a) find y in terms of x. [4]  (b) find the value of y when x23= . [1]  (c) find the value of x when y2=. [2]",
            "6": "6 0606/12/m/j/22 \u00a9 ucles 2022 4 (a) find the unit vector in the same direction as 15 8-eo . [2]  (b) given that  a b abba 2 5 341 242 -+-=+-e e e o o o,  find the values of a and b. [3]",
            "7": "7 0606/12/m/j/22 \u00a9 ucles 2022 [turn over 5 the first three terms, in ascending powers of x, in the expansion of   ()xx 1623123+-bl    can be written  in the form   px qx 82++ ,   where p and q are constants. find the values of p and q. [8]",
            "8": "8 0606/12/m/j/22 \u00a9 ucles 2022 6 the polynomial  p()xx ax xb 6632=+ ++ ,  where a and b are integers, is divisible by x21-. when  p()x is divided by x2-, the remainder is 120.  (a) find the values of a and b. [4]  (b) hence write down the remainder when p()x is divided by x. [1]  (c) find the value of p( )0ll. [2]",
            "9": "9 0606/12/m/j/22 \u00a9 ucles 2022 [turn over 7 (a) show that   () xx x 232 11 11 2 +--+-   can be written as   () () xxx 12 383 2-+-   . [2]  (b)  find  () ()dxxxx12 383a 22-+-y   where  a 22. give your answers in the form lncd+ , where c and d  are functions of a.   [6]",
            "10": "10 0606/12/m/j/22 \u00a9 ucles 2022 8 (a) a team of 6 people is to be chosen from 10 people. two of the people are sisters who must not be  separated. find the number of different teams that can be formed.  [3]  (b)  a 6-character password is to be chosen from the following characters.    digits  2 4 8    letters  x y z     symbols  * # !   no character may be used more than once in any password. find the number of different passwords  that may be chosen if    (i) there are no other restrictions,  [1]   (ii) the password starts with two letters and ends with two digits.  [3]",
            "11": "11 0606/12/m/j/22 \u00a9 ucles 2022 [turn over 9 the normal to the curve  ()lnyxx 1322 =++,  at the point a on the curve where x0=, meets the x-axis at  point b. point c has coordinates (, )ln 03 2. find the gradient of the line bc in terms of ln2. [9]",
            "12": "12 0606/12/m/j/22 \u00a9 ucles 2022 10 (a) given the simultaneous equations       g,ll g xy21+=      , xy31 32-=   (i) show that   xx13 30 02-- =. [4]   (ii) solve these simultaneous equations, giving your answers in exact form.  [2]",
            "13": "13 0606/12/m/j/22 \u00a9 ucles 2022 [turn over  (b) solve the equation  logl og xa34ax+= ,  where a is a positive constant, giving x in terms of a. [5]",
            "14": "14 0606/12/m/j/22 \u00a9 ucles 2022 11 in this question all lengths are in kilometres and time is in hours.  a particle p moves in a straight line such that its displacement, s, from a fixed point at time  t is given by     () () st t252=+ - , for t0h.  (a) find the values of t for which the velocity of p is zero.  [4]  (b) on the axes, draw the displacement\u2013time graph for p for t06gg , stating the coordinates of the  points where the graph meets the coordinate axes.  [2] s t 0 6 5 4 3 2 1",
            "15": "15 0606/12/m/j/22 \u00a9 ucles 2022  (c) on the axes below, draw the velocity\u2013time graph for p for t06gg , stating the coordinates of the  points where the graph meets the coordinate axes.  [2] velocity t 0 6 5 4 3 2 1  (d) (i) write down an expression for the acceleration of p at time  t.  [1]   (ii) hence, on the axes below, draw the acceleration\u2013time graph for  p for t06gg , stating the    coordinates of the points where the graph meets the coordinate axes.  [2] acceleration t 0 6 5 4 3 2 1",
            "16": "16 0606/12/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.blank page"
        },
        "0606_s22_qp_13.pdf": {
            "1": " [turn overdc (nf/fc) 303987/4 \u00a9 ucles 2022this document has 16 pages. any blank pages are indicated. *7338070369* additional mathematics  0606/13 paper 1  may/june  2022  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].cambridge igcse\u2122",
            "2": "2 0606/13/m/j/22 \u00a9 ucles 2022 mathematical formulae 1. algebra quadratic equation for the equation ax bx c 02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ - () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=- ()() srarr111nn ! =-- () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/13/m/j/22 \u00a9 ucles 2022 [turn over 1 (a) find the rational numbers a, b and c, such that the first three terms, in descending powers of x, in  the expansion of    xx391 25 - eo  can be written in the form   . ax bx cx10 74++  [3]  (b) hence find the coefficient of x4 in the expansion of    . xx x39111 25 32 -+ e eo o [3]",
            "4": "4 0606/13/m/j/22 \u00a9 ucles 2022 2 in this question, all lengths are in centimetres and all angles are in radians. b a co 810  the diagram shows a circle, centre o, radius 8. the points  a, b and c lie on the circumference of the  circle. the chord ab has length 10.  (a) show that angle boa  is 1.35 correct to 2 decimal places.  [2]  (b) given that the minor arc bc has a length of 18, find angle boc . [2]  (c) find the area of the minor sector aoc . [3]",
            "5": "5 0606/13/m/j/22 \u00a9 ucles 2022 [turn over 3 (a) find the exact solution of the equation   . 235 0 eexx63-- = [3]  (b) solve the following simultaneous equations.     1eeexx y 47 57 2' =-+     xy18 0 +=  [5]",
            "6": "6 0606/13/m/j/22 \u00a9 ucles 2022 4 variables  x and y are such that when ey4 is plotted against x, a straight line of gradient 52, passing  through (10,  2), is obtained.  (a) find y in terms of x. [3]  (b) find the value of y when x45= , giving your answer in the form lnp. [2]  (c) find the values of x for which y can be defined.  [1]",
            "7": "7 0606/13/m/j/22 \u00a9 ucles 2022 [turn over 5 the velocity, , vms1- of a particle moving in a straight line, t seconds after passing through a fixed  point o, is given by    . sin vt 63=  (a) find the time at which  the acceleration of the particle is first equal to . 9ms2-- [4]  (b) find the displacement of the particle from o when .. t56=  [4]",
            "8": "8 0606/13/m/j/22 \u00a9 ucles 2022 6 (a) it is given that  fxx 22\"|   for , x 0h     gxx21\"| +  for . x 0h   each of the expressions in the table can be written as one of the following. ff gg fg gf fg fg22 11--lm lm   complete the table. the first row has been completed for you.  [5] expression function notation 2 gl 0 x4 xx88 22++ x43+ x 21-",
            "9": "9 0606/13/m/j/22 \u00a9 ucles 2022 [turn over  (b) it is given that   () () xx 3 1 h2=+-  for . xah  the value of a is as small as possible such that h1-  exists.   (i)  write down the value of a. [1]   (ii) write down the range of h.  [1]   (iii) find ()x h1- and state its domain.  [3]",
            "10": "10 0606/13/m/j/22 \u00a9 ucles 2022 7 a curve has equation   ()yxx 52123 =++    for . x 0h  (a) show that     ()()() ,xy xxax b521 dd 221 =+++    where a and b are integers to be found.  [4]  (b) show that there are no stationary points on this curve.  [1]",
            "11": "11 0606/13/m/j/22 \u00a9 ucles 2022 [turn over  (c) find the approximate change in y when x increases from 1 to ,p 1+ where p is small.  [2]  (d) given that when x1= the rate of change in  x is 2.5 units per second, find the corresponding rate  of change in y. [2]",
            "12": "12 0606/13/m/j/22 \u00a9 ucles 2022 8 (a) a 6-digit number is formed from the digits  0,  1,  2,  5,  6,  7,  8,  9.  a number cannot start with 0  and each digit can be used at most once in any 6-digit number.   (i) find how many 6-digit numbers can be formed if there are no further restrictions.  [1]   (ii) find how many of these 6-digit numbers are divisible by 5.  [3]   (iii) find how many of these 6-digit numbers are greater than 850  000. [3]",
            "13": "13 0606/13/m/j/22 \u00a9 ucles 2022 [turn over  (b) a team of 8 people is to be chosen from 12 people. three of the people are brothers who must not  be separated. find the number of different teams that can be chosen.  [3]",
            "14": "14 0606/13/m/j/22 \u00a9 ucles 2022 9 (a) solve the equation   , cose c 32342 rz-= bl   for . 011 rz   give your solutions in terms of r.   [4]  (b) given that   cose c x212i -=    and   , tan y12i +=   find y in terms of x. [4]",
            "15": "15 0606/13/m/j/22 \u00a9 ucles 2022 10 (a) show that    ()x1+64 2 2 +-xx 23 1 ++   can be written as  .() ()xxx 23 114 10 2+++ [2]  (b) hence find the exact value of   () ().xxxx23 114 10d202 +++y    give your answer in the form , lnpq+   where p and q are rational numbers.  [6]",
            "16": "16 0606/13/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.blank page"
        },
        "0606_s22_qp_21.pdf": {
            "1": " [turn over*8556660969* dc (nf/cgw) 214154/2 \u00a9 ucles 2022this document has 12 pages.additional mathematics  0606/21 paper 2  may/june  2022  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].cambridge igcse\u2122",
            "2": "2 0606/21/m/j/22 \u00a9 ucles 2022 mathematical formulae 1. algebra quadratic equation for the equation ax bx c 02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ - () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=- ()() srarr111nn ! =-- () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/21/m/j/22 \u00a9 ucles 2022 [turn over 1 (a) solve the equation   , 51 2w1=-   giving your answer correct to 2 decimal places.  [2]  (b) solve the equation   . xx 56 032 31-+ = [3] 2 (a) write   () lg lg lg xx26 3 -+ + `j    as a single logarithm to base 10.  [2]  (b) hence solve the equation   () . lg lg lg xx 26 30 -+ += `j  [4]",
            "4": "4 0606/21/m/j/22 \u00a9 ucles 2022 3 variables x and y are such that when y3 is plotted against ,x2 a straight line passing through the points  (9, 8) and (16,  1) is obtained. find y as a function of x. [4] 4 the polynomial   ()xm xx nx 17 6 p32=- ++     has a factor .x3- it has a remainder of 12- when  divided by .x1+ find the remainder when ()xp is divided by .x2- [6]",
            "5": "5 0606/21/m/j/22 \u00a9 ucles 2022 [turn over 5 (a) (i) write down, in ascending powers of x, the first three terms in the expansion of   () .x 14n+    simplify each term.  [2]   (ii) in the expansion of    () ()xx 14 14n+-    the coefficient of x2 is 6032. given that , n 02  find  the value of n. [3]  (b) find the term independent of x in the expansion of   .x x 28 410 -eo  [2]",
            "6": "6 0606/21/m/j/22 \u00a9 ucles 2022 6 (a) (i) a 5-digit number is to be formed from the seven digits 0, 1, 2, 3, 4, 5, 6. each digit can be  used at most once in any number and the number does not start with 0. find the number of  ways in which this can be done.  [2]   (ii) find how many of these 5-digit numbers are even.  [3]  (b) a team of 7 people is to be selected from a group of 9 women and 6 men. find the number of  different teams that can be selected which include at least one man.  [2]",
            "7": "7 0606/21/m/j/22 \u00a9 ucles 2022 [turn over  (c) (i) show that   () cc nn61 nn 323+= -    for . n 3h [5]   (ii) hence solve the equation   cc n4nn 32+=    where . n 3h [2]",
            "8": "8 0606/21/m/j/22 \u00a9 ucles 2022 7 variables x and y are such that   ().sinyxx 134 =+   use differentiation to find the approximate change  in y when x increases from 1.9 to .,h 19+ where h is small.  [6]",
            "9": "9 0606/21/m/j/22 \u00a9 ucles 2022 [turn over 8 in this question, i is a unit vector due east and j is a unit vector due north. distances are measured in  kilometres and time is measured in hours.  at 09  00, ship a leaves a point p with position vector   ij51 6+    relative to an origin o. it sails with a  constant speed of 63 on a bearing of 120\u00b0.  (a) show that the velocity vector of a is    . ij93 3-  [2]  (b) find the position vector of a at 12  00. [1]  (c) at 11  00 ship b leaves a point q with position vector   . ij29 16+    it sails with constant velocity  .j 12 3 -  write down the position vector of b, t hours after it starts sailing.  [1]  (d) find the distance between the two ships at 12  00. [3]",
            "10": "10 0606/21/m/j/22 \u00a9 ucles 2022 9 in this question all lengths are in metres. h 5x  the diagram shows a water container in the shape of a triangular prism. the depth of water in the  container is h. the container has length 5. the water in the container forms a prism with a uniform  cross-section that is an equilateral triangle of side x.  (a) show that the volume, v, of the water is given by   . vh 53 32 =  [4]  (b) water is pumped into the container at a rate of 0.5  m3 per minute. find the rate at which the depth  of the water is increasing when the depth of the water is 0.1  m. [4]",
            "11": "11 0606/21/m/j/22 \u00a9 ucles 2022 [turn over 10 (a) differentiate   lnxx x2-   with respect to x. simplify your answer.  [2]  (b) a curve is such that   .xy xx1 dd 22 2 =+eo    it is given that    xy 22dd ee2 =+     at the point ,.6eee32+ eo   using your answer to part (a) , find the exact equation of the curve.  [8] question 11 is printed on the next page.",
            "12": "12 0606/21/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.11  y a cd b o xcos yx 5 =x4r=eyx 2=  the diagram shows part of the curves    yex 2=    and   cos yx 5 =    and part of the line    . x4r=    the  curves intersect at a. the curve cos yx 5 =  cuts the x-axis at b. the line x4r= cuts the x-axis at c and  the curve yex 2=  at d. find the exact area of the shaded region, abcd . [7]"
        },
        "0606_s22_qp_22.pdf": {
            "1": "this document has 16 pages.  [turn overcambridge igcse\u2122 dc (kn/sw) 303758/3 \u00a9 ucles 2022 *1223544829* additional mathematics  0606/22 paper 2  may/june  2022  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].",
            "2": "2 0606/22/m/j/22 \u00a9 ucles 2022 mathematical formulae 1. algebra quadratic equation for the equation ax bx c 02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ - () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=- ()() srarr111nn ! =-- () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/22/m/j/22 \u00a9 ucles 2022 [turn over 1 do not use a calculator in this question.   a curve has equation   yxx 36=++   where x0h. find the exact value of y when x6=. give your  answer in the form ab c+ , where a, b and c are integers.  [3] 2 y x 0\u2013 11 2.55 y = g( x) y = g( x)f() yx=  the diagram shows the graphs of () yx f=  and ()g yx= , where ()f yx=  and ()g yx=  are straight  lines. solve the inequality   () () fxx gg . [5]",
            "4": "4 0606/22/m/j/22 \u00a9 ucles 2022 3 find the possible values of k for which the equation    () kx kx54 02++ -=    has real roots.  [5] 4 variables x and y are related by the equation   xy121 2 =+ +x   where x02. use differentiation to find  the approximate change in x when y increases from 4 by the small amount 0.01.  [5]",
            "5": "5 0606/22/m/j/22 \u00a9 ucles 2022 [turn over 5 (a) solve the equation    1256255xx 21 33 =- . [3]  (b) on the axes, sketch the graph of   y43ex=+    showing the values of any intercepts with the  coordinate axes.  [2] y x o",
            "6": "6 0606/22/m/j/22 \u00a9 ucles 2022 6  (a) in this question, i is a unit vector due east and j is a unit vector due north.    a cyclist rides at a speed of 4  ms\u22121 on a bearing of 015\u00b0. write the velocity vector of the cyclist in  the form xi + yj, where x and y are constants.  [2]   (b) a vector of magnitude 6 on a bearing of 300\u00b0 is added to a vector of magnitude 2 on a bearing of  230\u00b0 to give a vector v.  find the magnitude and bearing of v. [5]",
            "7": "7 0606/22/m/j/22 \u00a9 ucles 2022 [turn over 7 differentiate   lntanyxx ex4 =    with respect to x.  [4]",
            "8": "8 0606/22/m/j/22 \u00a9 ucles 2022 8 the function f is defined by   ()fs in cos xx x 322=-    for x24gg ,   where x is in radians.   (a) find the x-coordinate of the stationary point on the curve ()f yx= .  [5]",
            "9": "9 0606/22/m/j/22 \u00a9 ucles 2022 [turn over  (b) solve the equation   ()fc os xx 13=- . [5]",
            "10": "10 0606/22/m/j/22 \u00a9 ucles 2022 9 in this question all lengths are in centimetres. 2z radoap qt  the diagram shows a circle, centre o, radius a. the lines pt and qt are tangents to the circle at p and  q respectively. angle poq  is 2z radians.  (a) in the case when the area of the sector opq  is equal to the area of the shaded region, show that  tan2zz= . [4]",
            "11": "11 0606/22/m/j/22 \u00a9 ucles 2022 [turn over  (b) in the case when the perimeter of the sector opq  is equal to half the perimeter of the shaded  region, find an expression for tanz in terms of  z. [3] ",
            "12": "12 0606/22/m/j/22 \u00a9 ucles 2022 10 (a) a geometric progression has first term a and common ratio r, where r02. the second term of  this progression is 8. the sum of the third and fourth terms is 160.   (i) show that r satisfies the equation   rr 20 02+- =. [4]   (ii) find the value of a. [3]",
            "13": "13 0606/22/m/j/22 \u00a9 ucles 2022 [turn over  (b) an arithmetic progression has first term p and common difference 2. the qth term of this  progression is 14.    a different arithmetic progression has first term p and common difference 4. the sum of the first   q terms of this progression is 168.    find the values of p and q.  [6]",
            "14": "14 0606/22/m/j/22 \u00a9 ucles 2022 11 y p q b a ry = 1 y = 1 + cos  x x o  the diagram shows part of the line   y1=   and one complete period of the curve   cos yx1=+ ,   where  x is in radians. the line pq is a tangent to the curve at p and at q. the line qr is parallel to the y-axis.   area a is enclosed by the line y1= and the curve. area b is enclosed by the line y1=, the line pq  and the curve.  given that   area a : area b is 1 : k   find the exact value of k.  [9]",
            "15": "15 0606/22/m/j/22 \u00a9 ucles 2022 [turn over continuation of working space for question 11.  question 12 is printed on the next page.",
            "16": "16 0606/22/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.12 a curve is such that   xy x x1 dd 22 42 =+fp .   given that the gradient of the curve is 34 at the point (1, \u22121),  find the equation of the curve.  [7]"
        },
        "0606_s22_qp_23.pdf": {
            "1": "this document has 16 pages. any blank pages are indicated.  [turn overdc (rw/cgw) 214193/1 \u00a9 ucles 2022 *2585156821* additional mathematics  0606/23 paper 2  may/june  2022  2 hours 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 calculator where appropriate.  \u25cf you must show all necessary working clearly; no marks will be given for unsupported answers from a  calculator.  \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. information  \u25cf the total mark for this paper is 80.  \u25cf the number of marks for each question or part question is shown in brackets [  ].cambridge igcse\u2122",
            "2": "2 0606/23/m/j/22 \u00a9 ucles 2022 mathematical formulae 1. algebra quadratic equation for the equation ax bx c 02++ =, xabb ac 242!=-- binomial theorem ()ab aa ba ba bnn n rb12nn nn nr rn 12 2ff += ++ ++++-- -ee e oo o where n is a positive integer and  () !!! n r nr rn=-eo arithmetic series  () ua nd1n=+ - () {( )} sn al na nd21 2121n=+ =+ - geometric series  ua rnn1=- ()() srarr111nn ! =-- () srar111 =- 3 2. trigonometry identities sinc os aa 122+= sect an aa 122=+ eccosc ot aa 122=+ formulae for \u2206abc sins in sin aa bb cc== cos ab cb ca222 2=+ - sinbc a21t=",
            "3": "3 0606/23/m/j/22 \u00a9 ucles 2022 [turn over 1 solve the equation   x47 35 9 -- =. [3] 2 do not use a calculator in this question.  variables x and y are related by the equation   yk x2= .   when x12=+ , y12=- . find the value  of k, giving your answer in the form ab c+ , where a, b and c are integers.  [4]",
            "4": "4 0606/23/m/j/22 \u00a9 ucles 2022 3 the points a, b and c have coordinates (2, 6), (6, 1) and ( p, q) respectively. given that b is the mid\u2011point  of ac, find the equation of the line that passes through c and is perpendicular to ab. give your answer  in the form ax by c += , where a, b and c are integers.  [5] 4 (a) find the range of values of x satisfying the inequality   () () xx51 601 -- . [2]  (b) show that the equation   ()kx kx k 21 42 102+- +- =,    where k21!-,  has distinct, real roots.  [3]",
            "5": "5 0606/23/m/j/22 \u00a9 ucles 2022 [turn over 5 y 0 x 4r=(, ) p03 (, ) q27r x 4r=-x  the diagram shows part of the graph of    tan ya bx c =+ .   the graph has vertical asymptotes at  r x 4=-  and r x4=  and passes through the points p and q.  (a) write down the period of  tanab xc+. [1]  (b) find the values of a, b and c. [4]",
            "6": "6 0606/23/m/j/22 \u00a9 ucles 2022 6 the polynomial ()px is such that   ()pxx ax xb 65 232=+ -+ ,  where a and b are integers. it is given  that ()px is divisible by x23- and that ()p1 4= l .  (a) find the values of a and b. [5]  do not use a calculator in this part of the question.  (b) using your values of a and b, factorise ()px fully.  [3]",
            "7": "7 0606/23/m/j/22 \u00a9 ucles 2022 [turn over 7 (a) (i) write down the set of values of x for which   ()lgx53-   exists.  [1]   (ii) solve the equation   ()lgx53 1 -= . [1]  (b) it is given that    logl og log x42164 162yy y=+ + ,    where y02. find an expression for y in  terms of x. simplify your answer.  [5]",
            "8": "8 0606/23/m/j/22 \u00a9 ucles 2022 8 (a) differentiate   yx2ex4=    with respect to x. [2]  (b) hence find    xxedx4y . [4]",
            "9": "9 0606/23/m/j/22 \u00a9 ucles 2022 [turn over 9 (a) find the unit vector in the direction of   ij40 9-. [2]  (b) the position vectors of points p and q relative to an origin o are p and q respectively. the point r  lies on the line pq and is between p and q such that pqprk=.   (i) write down the set of all possible values of k. [1]   (ii) given that the position vector of r relative to o is   mnpq+    show that mn 1 += . [3]",
            "10": "10 0606/23/m/j/22 \u00a9 ucles 2022 10 y oa b c xyx x 322=+ -  the diagram shows part of the curve    yx x 322=+ -.  the point  a lies on the curve and has an  x\u2011coordinate of 1.5. the tangent to the curve at a meets the x\u2011axis at b. the curve meets the x\u2011axis at c.  find the area of the shaded region.  [10]",
            "11": "11 0606/23/m/j/22 \u00a9 ucles 2022 [turn over continuation of working space for question 10.",
            "12": "12 0606/23/m/j/22 \u00a9 ucles 2022 11 (a) the sum of the first 20 terms of an arithmetic progression is 1100. the sum of the first 70 terms is  14 350. find the 12th term.  [6]",
            "13": "13 0606/23/m/j/22 \u00a9 ucles 2022 [turn over  (b) the first three terms of a geometric progression are   x6+,   x9-,   ()x211+.   show that x  satisfies the equation   xx43 156 02-+ =.   hence show that a sum to infinity exists for each  possible value of x. [7]",
            "14": "14 0606/23/m/j/22 \u00a9 ucles 2022 12 in this question all lengths are in centimetres. x y  a container is a half\u2011cylinder, open as shown. it has length y and uniform cross\u2011section of radius x. the  volume of the container is 25  000. given that x and y can vary and that the outer surface area, s, of the  container has a minimum value, find this value.  [8]",
            "15": "15 0606/23/m/j/22 \u00a9 ucles 2022 blank page",
            "16": "16 0606/23/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.blank page"
        }
    },
    "Other Resources": {},
    "Specimen Papers": {}
}