MATHEMATICS (SYLLABUS D) 4024/11

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1 Cambridge International Examinations Cambridge Ordinary Level * * MATHEMATICS (SYLLABUS D) 4024/11 Paper 1 May/June hours Candidates answer on the Question Paper. Additional Materials: Geometrical instruments READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80. This document consists of 20 printed pages. DC (LK/SG) /3 [Turn over

2 2 ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. 1 (a) Evaluate 12-6 ' (b) Evaluate 0. 3 # Answer... [1] Answer... [1] 2 (a) Evaluate (b) Evaluate 1 7 ', giving your answer as a fraction in its lowest terms. 3 9 Answer... [1] Answer... [1] 4024/11/M/J/16

3 3 (a) An aircraft leaves at on a flight that takes 3 hours and 50 minutes. Find the time when the aircraft arrives. 3 (b) The aircraft flies a distance of 3200 km, correct to the nearest 100 km. Write down the lower bound for the distance. Answer... [1] Answer... km [1] 4 A bottle full of liquid has a total mass of 1.27 kg. When the bottle is half-full of liquid the total mass is 900 grams. Calculate the mass of the bottle. Answer... grams [2] 4024/11/M/J/16 [Turn over

4 4 5 Stella walks to a park. For 4 minutes she walks at a rate of 80 steps per minute. For 1 minute she walks at a rate of 120 steps per minute. Find the mean number of steps per minute she takes. Answer... [2] 6 (a) Write the number # 10-3 in standard form. (b) Arrange the following numbers in order, starting with the smallest # # # 10-5 Answer... [1] Answer...,...,... [1] smallest 4024/11/M/J/16

5 5 7 By writing each number correct to 1 significant figure, estimate the value of # Answer... [2] 8 (a) Complete the diagram to make a quadrilateral ABCD which has AC as its line of symmetry. A B C (b) Complete the diagram to make a quadrilateral PQRS which has rotational symmetry of order 2. [1] P Q R [1] 4024/11/M/J/16 [Turn over

6 6 9 y x The shaded region in the diagram is defined by three inequalities. 1 One of these is y H x Write down the other two inequalities. Answer [2] 10 Factorise completely 3xy x - 12y. Answer... [2] 4024/11/M/J/16

7 11 f( x) 3 (a) Find f c- m. 4 7 = 2x - 9 Answer... [1] (b) Find f 1 (3). Answer... [2] 12 A map is drawn to a scale of 2 cm to 5 km. (a) Two towers are 9 km apart. Calculate the distance between them on the map. Answer... cm [1] (b) On the map, a town covers an area of 4 cm 2. Calculate its actual area. Answer... km 2 [1] (c) Express the scale of the map in the form 1 : n. Answer 1 :... [1] 4024/11/M/J/16 [Turn over

8 8 13 Solve the simultaneous equations. 3x = 4y 1 + 5x = 6y Answer x =... y =... [3] 4024/11/M/J/16

9 [The volume of a sphere is r r ] [The volume of a cone is r r h] 3 3 A cone is removed from a solid wooden hemisphere of radius 3 cm. The cone has radius 3 cm and height 2 cm. The volume of wood remaining is kr cm Find k. Answer k =... [3] 15 (a) y is directly proportional to the square of x. Given that y = 8 when x = 4, find y when x = 3. Answer y =... [2] (b) p is inversely proportional to q. It is known that p = 15 for a particular value of q. Write down the value of p when this value of q is doubled. Answer p =... [1] 4024/11/M/J/16 [Turn over

10 10 16 E D C A 160 B P Q R In the diagram, AB, BC, CD and DE are four sides of a regular polygon. Each interior angle of the polygon is 160. ABPQR, DCP and EDQ are straight lines. (a) Find CAB t. (b) Find CBP t. Answer CAB t =... [1] (c) Find DQ t R. Answer CBP t =... [1] Answer DQ t R =... [1] 4024/11/M/J/16

11 17 A sequence of diagrams is made using counters. 11 Diagram 1 Diagram 2 Diagram 3 Diagram 4 (a) Complete the table. Diagram number Number of counters [1] (b) Find an expression, in terms of n, for the number of counters in Diagram n. (c) In this sequence, Diagram p has 200 counters. Find the value of p. Answer... [1] Answer p =... [2] 4024/11/M/J/16 [Turn over

12 12 18 Henri did a survey of the lengths of the leaves on a plant. The results are summarised in the table. Length (x cm) 1 1 x G x G x G x G 8 Frequency (a) When asked to draw a histogram to illustrate the results, Henri drew the following diagram Frequency Length (x cm) Explain why this diagram is incorrect [1] (b) On the grid below, draw a correct histogram for Henri s results Length (x cm) [3] 4024/11/M/J/16

13 13 19 B A 40 P R Q D C In the diagram, the two circles intersect at P and Q. The line AB is a tangent to the circles at A and B. AD and BC are diameters. BD intersects the larger circle at R. DBC t = 40. (a) Find CPR t. Answer CPR t =... [1] (b) Find CQR t. Answer CQR t =... [1] (c) Find ABD t. Answer ABD t =... [1] (d) Find ADB t. Answer ADB t =... [1] 4024/11/M/J/16 [Turn over

14 20 The number of goals scored in each of 50 football matches was recorded. The results are given in the table. 14 Number of goals scored Frequency For these results, find (a) the mode, (b) the median, Answer... [1] (c) the mean. Answer... [1] Answer... [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 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. 4024/11/M/J/16

15 15 21 (a) Express 500 as the product of its prime factors. Answer... [1] 4 2 (b) M = 2 # 3 2 N = 2 # 3 Find the values of p and q when (i) M # N = 2 # 3, p q (ii) M ' N = 2 # 3, p q Answer p =... q =... [1] 2 (iii) N = 2 # 3. p q Answer p =... q =... [1] Answer p =... q =... [1] 4024/11/M/J/16 [Turn over

16 16 22 The diagram shows triangle ABC. C A B (a) Measure ABC t. Answer ABC t =... [1] (b) On the diagram, construct the locus of points, inside triangle ABC, that are (i) 4 cm from B, [1] (ii) 2 cm from AC. [1] (c) The point P is 4 cm from B, 2 cm from AC, and nearer to A than to C. Label the position of P on the diagram and find the length of AP. Answer AP =... cm [1] 4024/11/M/J/16

17 17 23 (a) In the Venn diagram, shade the region which represents the subset ( P, Q) l + R. P Q R [1] (b) = { x : x is an integer and 22 G x G 33 } E = { x : x is an even number } T = { x : x is a multiple of 3 } F = { x : x is a multiple of 4 } (i) List the members of T + F. Answer... [1] (ii) Find n( E, T ). (iii) Given that y! Fl + E, find one possible value of y. Answer... [1] Answer y =... [1] 4024/11/M/J/16 [Turn over

18 18 24 The diagram shows the speed-time graph of a train which slows down from 20 m/s to a stop in T seconds. Speed (m/s) Time (t seconds) T (a) (i) Find an expression, in terms of T, for the retardation of the train. 3 (ii) Find the speed of the train when t = T. 4 Answer... m/s 2 [1] (b) The distance travelled by the train between t = 0 and t = T is 150 m. (i) Find T. Answer... m/s [1] (ii) On the diagram, sketch the distance time graph of the train. Answer T =... [1] 150 Distance (metres) 0 0 Time (t seconds) T [1] 4024/11/M/J/16

19 19 25 p Y A q X Z C B In the diagram, 1 X is the point on AB where AX = AB, 4 1 Y is the point on AC where AY = AC, 3 Z is the point on BC produced where CZ = 2BC. AY = p and AX = q. (a) Express, as simply as possible, in terms of p and q, (i) XY, Answer XY =... [1] (ii) BC, Answer BC =... [1] (iii) XZ. Answer XZ =... [2] (b) Hence find XY : YZ. Answer... :... [1] Question 26 is printed on the next page 4024/11/M/J/16 [Turn over

20 20 26 Box 1 Box 2 Box 1 contains 2 white balls. Box 2 contains 4 white balls and 3 black balls. (a) Ann chooses, at random, one ball from each box. (i) Find the probability that these balls are both black. (ii) Find the probability that these balls have different colours. Answer... [1] Answer... [1] (b) From the original contents of Box 2, Belle chooses, at random, two balls without replacement. Find the probability that these balls are both white. Answer... [1] (c) Carla chooses one of the boxes at random. With the original box contents, she then chooses, at random, one ball from this box. Find the probability that the ball is white. Answer... [2] 4024/11/M/J/16

21 Cambridge International Examinations Cambridge Ordinary Level * * MATHEMATICS (SYLLABUS D) 4024/12 Paper 1 May/June hours Candidates answer on the Question Paper. Additional Materials: Geometrical instruments READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80. This document consists of 20 printed pages. DC (RW/AR) /2 [Turn over

22 2 ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. 1 (a) Evaluate ^ h # (b) Evaluate Answer... [1] Answer [1] 2 (a) Complete this description. A rectangle has rotational symmetry of order and lines of symmetry. [1] (b) Shade 4 more small squares in the shape below to make a pattern with rotational symmetry of order 4. [1] 4024/12/M/J/16

23 3 It is given that 100 dollars ($) is equivalent to 56 pounds ( ). (a) Use this information to draw a conversion graph between pounds and dollars on the grid below Pounds ( ) Dollars ($) [1] (b) Use your graph to convert $64 to pounds. Answer... [1] 4024/12/M/J/16 [Turn over

24 4 4 Complete the table. Fraction Decimal Percentage 1 2 = 0.5 = 50% 3 20 =... = =... = 62.5% [2] 5 The table shows some information about the temperatures in a city. Date Maximum temperature Minimum temperature 1 February 10 C T C 1 March 4 C 5 C (a) Find the difference between the maximum and minimum temperatures on 1 March. Answer... C [1] (b) The minimum temperature, T C, on 1 February was 13 degrees lower than the minimum temperature on 1 March. Find T. Answer T =... [1] 4024/12/M/J/16

25 6 (a) Express 96 as a product of its prime factors. 5 Answer... [1] (b) 24 is a common factor of 96 and the integer n. Given that n is less than 96, find the largest possible value of n. Answer... [1] 7 The table shows information about some flights from Dubai to Mumbai. Departs Dubai (local time) Arrives Mumbai (local time) Flight duration 3 hours 10 minutes 2 hours 55 minutes 3 hours 5 minutes (a) Work out the time difference between Dubai and Mumbai. (b) Work out the local time in Mumbai when the flight arrives. Answer... [1] Answer... [1] 4024/12/M/J/16 [Turn over

26 6 8 y is directly proportional to the square of x. When x = 10, y = 20. Find the value of y when x = 6. Answer y =... [2] 9 50 students are asked what type of movie they like to watch. Of these students, 26 like comedy, 15 like both action and comedy and 8 like neither action nor comedy. Using a Venn diagram, or otherwise, find the number of students who like action but not comedy. Answer... [2] 4024/12/M/J/16

27 7 10 Solve the simultaneous equations. 6x + y = 1 4x - y = 4 Answer x =... y =... [2] 11 Simplify (a) 7 5x y x y, (b) t c 4 m. v Answer... [1] Answer... [1] 4024/12/M/J/16 [Turn over

28 8 12 The diagram below shows triangle ABC. C A B (a) On the diagram construct the locus of points inside the triangle that are (i) 3.5 cm from A, [1] (ii) equidistant from AC and BC. [1] (b) On the diagram, shade the region inside the triangle containing the points that are more than 3.5 cm from A and closer to AC than to BC. [1] 4024/12/M/J/16

29 13 (a) Write these values in order of size, starting with the smallest (b) Write down one possible value of x that satisfies each inequality. Answer...,...,...,... [1] smallest (i) 2 1 x 1 3 Answer x =... [1] (ii) x 1 0 Answer x =... [1] 14 The coordinates of the midpoint of the line AB are (1, 2). The length of the line AB is 10 units. (a) If the gradient of AB is 0, find the coordinates of A and B. (b) If the gradient of AB is 4 3, find the coordinates of A and B. Answer A = (...,...) B = (...,...) [1] Answer A = (...,...) B = (...,...) [2] 4024/12/M/J/16 [Turn over

30 10 15 The diagram shows the lines x + y = 8 and 2y = x + 4. y x (a) The shaded region on the diagram is defined by three inequalities. Write down these three inequalities. Answer [2] (b) Another region, R, is defined by the inequalities x + y G 8, 2y G x + 4 and y H a, where a is an integer. This region contains 5 points with integer coordinates. Write down the value of a. Answer a =... [1] 4024/12/M/J/16

31 16 Anil has some sweets with a mass of 600 g, correct to the nearest 10 grams. 11 (a) Write down the lower bound of the mass of sweets. (b) Anil sells the sweets in small portions. Each portion has a mass of 25 g, correct to the nearest gram. He sells 10 portions of the sweets. Calculate the lower bound of the mass of sweets remaining. Answer... g [1] Answer... g [2] 17 In the diagram, the bearing of B from A is 170. The bearing of A from C is 060. The bearing of C from B is x. North North A 170 C 060 North B x Given that triangle ABC is isosceles, find the three possible values of x. Answer x =... or... or... [3] 4024/12/M/J/16 [Turn over

32 18 The diagram is the speed-time graph for part of a car s journey. 12 Speed (m/s) v Time (t seconds) The retardation of the car between t = 8 and t = 12 is 4 m/s 2. (a) Find v. (b) Find the total distance travelled by the car in the 12 seconds. Answer v =... [1] Answer... m [2] 4024/12/M/J/16

33 13 19 A P O Q B AB is a diameter of the circle, centre O. PA and QB are tangents to the circle at A and B respectively. Prove that triangle PAO is congruent to triangle QBO. Give a reason for each statement you make [3] 4024/12/M/J/16 [Turn over

34 20 A bag contains 10 counters of which 8 are blue and 2 are white. Two counters are taken from the bag at random without replacement. (a) Complete the tree diagram to show the possible outcomes and their probabilities. 14 First counter Second counter 7 9 Blue 8 10 Blue... White... White... Blue (b) Find, as a fraction, the probability that (i) both counters are blue,... White [1] Answer... [1] (ii) one counter is blue and the other is white. Answer... [2] 4024/12/M/J/16

35 21 (a) The table shows the values of the function f^xh for some values of x. 15 x f^xh Express the function f^xh in terms of x. Answer f^xh =... [1] (b) 8 3x g ^xh = - 2 (i) Evaluate g^-2h. Answer... [1] (ii) Find - ^ x h. g 1 Answer - ^ x h =... [2] g /12/M/J/16 [Turn over

36 22 The table shows the populations, correct to 2 significant figures, of some African countries in Country Population Nigeria Sudan Chad Namibia (a) In 2014, the population of Nigeria was Complete the table with the population of Nigeria using standard form, correct to 2 significant figures. [2] (b) Complete the following. The population of Chad was... times the population of Namibia. [1] (c) The population density of a country is measured as the number of people per square kilometre. It can be found by dividing the population of the country by its area in km 2. The area of Sudan is square kilometres. Estimate the population density of Sudan. Give your answer correct to 1 significant figure. Answer...people / km 2 [2] 4024/12/M/J/16

37 23 The table and histogram show some information about the times taken by a group of students to travel to school one day. Time (t minutes) t G t G t G t G t G 120 Frequency m 6 5 Frequency density Time (t minutes) (a) Complete the histogram. [2] (b) Find the value of m. Answer m =... [1] (c) Work out the fraction of students who took more than half an hour to travel to school. Answer... [2] 4024/12/M/J/16 [Turn over

38 18 24 a r 3r The diagram shows a sector of a circle with radius 3r cm and angle a and a circle with radius r cm. The ratio of the area of the sector to the area of the circle with radius r cm is 8 : 1. (a) Find the value of a. (b) Find an expression, in terms of r and r, for the perimeter of the sector. Answer a =... [3] Answer... cm [2] 4024/12/M/J/16

39 19 25 (a) The nth term of a sequence is given by n 2-5n. (i) Find the 2nd term in the sequence. Answer... [1] (ii) The pth term in the sequence is 150. Find the value of p. Answer p =... [2] (b) The nth term of another sequence is given by 3n 2 - kn. The 5th term in this sequence is 55. Find the value of k. Answer k =... [2] Question 26 is printed on the next page 4024/12/M/J/16 [Turn over

40 20 p (a) Make p the subject of the formula t =. p - 4 (b) Simplify fully 2 4x x - 9x - 5. Answer p =... [3] Answer... [3] Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at 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. 4024/12/M/J/16

41 Cambridge International Examinations Cambridge Ordinary Level * * MATHEMATICS (SYLLABUS D) 4024/21 Paper 2 May/June hours 30 minutes Candidates answer on the Question Paper. Additional Materials: Geometrical instruments 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 a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Section A Answer all questions. Section B Answer any four questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100. This document consists of 23 printed pages and 1 blank page. DC (KN/SG) /3 [Turn over

42 2 Section A[52marks] Answerallquestionsinthissection. 1 Ashopkeeperbuyssomeplatesfromamanufacturerfor$12each. (a) Themanufacturermakesaprofitof60%. Calculatethecostofmanufacturingeachplate. (b) Theshopkeepersellseachplatefor$ Calculatethepercentageprofitmadebytheshopkeeper. Answer $... [2] (c) Inasale,eachplateisreducedfrom$17.40to$ Calculatethepercentagediscountgiven. Answer...%[2] Answer...%[2] 4024/21/M/J/16

43 (d) Theshopkeeperbuys100platesat$12each. Hesells60platesat$17.40eachandxplatesat$11.31each. Theshopkeepermakesaprofitofatleast10%. Findtheleastpossiblevalueofx. 3 Answer... [3] 4024/21/M/J/16 [Turn over

44 4 p 2 (a) Solvetheequation - 1 = p 1 J 6 9ab N 2 (b) SimplifyK a 3 b 2O. L P Answer... [2] Answer... [2] 4024/21/M/J/16

45 5 2 3 q - q (c) Simplify. 3-3q Answer... [2] (d) (i) Factorise4t t - 9. Answer... [2] (ii) Hencesolvetheequation4t t - 9 = 0. Answer... [1] 4024/21/M/J/16 [Turn over

46 6 2 3 Thetablebelowisfor y = x + x - 3. x y (a) Usingascaleof2cmto1unitonthex-axisfor-3 G x G 2 andascaleof1cmto1unitonthey-axisfor- 4 G y G 4, plotthepointsfromthetableandjointhemwithasmoothcurve. y x [2] (b) (i) Useyourgraphtoestimatethesolutionsoftheequation x 2 + x - 3 = 0. Answer x=...or... [1] (ii) Useyourgraphtoestimatethesolutionsoftheequation x 2 + x - 5 = 0. Answer x=...or... [2] 4024/21/M/J/16

47 7 (c) Bydrawingatangent,estimatethegradientofthecurveat ^1, 1h. Answer... [2] (d) Theequation x 2 - x - 1 = 0canbesolvedbydrawingastraightlineonthegraphof 2 y = x + x - 3. (i) Findtheequationofthisstraightline. (ii) Drawthisstraightlineandhencesolve x 2 - x - 1 = 0. Answer... [2] Answer x=...or... [2] 4024/21/M/J/16 [Turn over

48 8 4 A N M B L C ANB,BLCandCMAarestraightlines.NMisparalleltoBCand LNisparalleltoCA. (a) ProvethattriangleANMissimilartotriangleNBL. Giveareasonforeachstatementyoumake [3] 4024/21/M/J/16

49 9 (b) AN:NB=2:3 (i) FindNM:BC. Answer... :...[2] (ii) FindareaANM:areaNBL. (iii) FindareaANM:areaNMCL. Answer... :...[1] Answer... :...[2] 4024/21/M/J/16 [Turn over

50 10 5 (a) A 31 C 115 B ABisverticalandCBishorizontal. AB=31mandCB=115m. CalculatetheangleofdepressionofCfromA. Answer... [3] 4024/21/M/J/16

51 11 (b) L J K JandKaretwopositionsatsea. ThebaseofalighthouseisatL. JisdueEastofLandKisdueSouthofL. KL=354mandKJ=1100m. (i) Calculate LJK t. Answer... [2] (ii) HencefindthebearingofKfromJ. Answer... [1] 4024/21/M/J/16 [Turn over

52 12 J4-1N J2 6 A = K OB = K L 1 3 P L 7 (a) Evaluate2A B. 0N O -5 P (b) FindA 2. Answer J K K L N O O [2] P Answer J K K L N O O [2] P 4024/21/M/J/16

53 13 (c) FindB 1. (d) A+Z=A Answer J K K L N O O [2] P FindZ. (e) M+2I=B,whereIisthe2 # 2identitymatrix. Answer J K K L N O O [1] P FindM. Answer J K K L N O O [2] P 4024/21/M/J/16 [Turn over

54 14 Section B[48marks] Answerfourquestionsinthissection. Eachquestioninthissectioncarries12marks. 7 (a) ACisadiameterofthecircle,centreO,radius5cm. ACB t =64. B Calculatethelengthoftheminorarc BC. A 5 O 64 C Answer... cm[4] (b) rim Abakingtrayisanopencylinderofradius15.5cmwitharim. Theouteredgeoftherimisacircleofradius16.5cm. 4024/21/M/J/16

55 15 (i) Calculatetheareaofthetopsurfaceoftherim. (ii) 44identicalcircularholesarecutoutofthebottomofthebakingtray. Theareaofthebottomthatremainsis650cm 2. Calculatetheradiusofeachcircularhole. Answer...cm 2 [2] Answer... cm[3] (iii) 15.5 cm d mm Tomakeapizza,thebakingtrayiscompletelyfilledwithdoughtoadepthofdmm. Theopencylinderholds500cm 3 ofdough. Calculatethedepthofthedough,dmm,givingyouranswercorrecttothenearestmillimetre. Answer... mm[3] 4024/21/M/J/16 [Turn over

56 16 8 (a) p 8 5q = - q (i) Findpwhenq=2.6. Answer... [1] (ii) Expressqintermsofp. Answer... [2] (b) x 2 H x + 3 Trapezium A x h Trapezium B x ThelengthsoftheparallelsidesoftrapeziumAarexcmand^x - 2hcm. ThelengthsoftheparallelsidesoftrapeziumBarexcmand^x + 3hcm. TheheightoftrapeziumAisHcmandtheheightoftrapeziumBishcm. Theareaofeachtrapeziumis15cm (i) ShowthatH = andh x = 2x + 3. [2] 4024/21/M/J/16

57 17 (ii) Findanexpressionintermsofxforthedifferenceinheight,H h,betweentrapeziumaand 75 trapeziumb,andshowthatitsimplifiesto ^ x - 1 h^2 x + 3h. [3] (iii) Thedifferenceinheightis1.5cm. (a) Showthat2x 2 + x - 53 = 0. [2] (b) Findx,givingyouranswercorrectto2decimalplaces. Answer x=... [2] 4024/21/M/J/16 [Turn over

58 18 9 (a) D 2 F 5 C A 15 E B ABCDrepresentstherectangularslopingsurfaceofatriangularprism. ABEFisahorizontalrectangle.CEandDFarevertical. CBE t =15,DC=5mandAD=2m. (i) CalculateAC. (ii) CalculateCE. Answer... m[2] Answer... m[2] 4024/21/M/J/16

59 19 (iii) Calculate FAE t. Answer... [4] (b) (i) 9 θ 6 10 Atrianglehassidesof10cm,9cmand6cm,andanangleofθ,asshowninthediagram. Calculateθ. Answer... [3] (ii) ThetriangleKGHhassidesofacm,bcmandccm asshowninthediagram. Itisgiventhat KGH t isanobtuseangle. K a c G b H Completethestatementbelowusingoneofthesymbols1 G = H c 2 ^a + b h [1] 4024/21/M/J/16 [Turn over

60 10 100electriclightbulbsofBrandAweretestedtofindhowlongeachbulblasted. Theresultsaresummarisedinthetablebelow. 20 Time (thours) tg tg tG tG tG tG tG350 Number ofbulbs (a) Completethecumulativefrequencytable. Time (thours) Cumulative frequency tg50 tg100 tg150 tg200 tg250 tg300 tg [1] (b) Onthegrid,drawasmoothcumulativefrequencycurvetorepresentthisinformation. LabelthiscurveBrandA. 100 Cumulative frequency Time (t hours) [2] 4024/21/M/J/16

61 (c) (i) Useyourgraphtoestimatethemedian. 21 Answer... hours[1] (ii) Useyourgraphtoestimatetheinterquartilerange. Answer... hours[2] (d) 100BrandBbulbsgavethefollowingresults. 4bulbslasted50hoursorless. Thelongesttimeanybulblastedwas300hours. Themedianis250hours. Theupperquartileis275hours. Theinterquartilerangeis75hours. Onthegrid,drawandlabelthecumulativefrequencycurvefortheBrandBbulbs. [4] (e) Usingyourgraph,estimatethenumberofBrandAbulbsthatlasted275hoursorless. Answer... [1] (f) Completethestatementbelow. Brand...had...morebulbsthatlastedlongerthan275hoursthanBrand... [1] 4024/21/M/J/16 [Turn over

62 11 (a) TriangleABChasverticesA(2,2),B(3,5)andC(4,1). Triangle AlBlC lhasvertices Al( 4,4), Bl( 3,7)andCl( 2,3). 22 WritedownthecolumnvectorofthetranslationthatmapstriangleABContotriangle AlBlC l. J N K O Answer K O [1] K O L P (b) PQRSisaparallelogram. J - 4N ThepositionvectorofPrelativetoOisgivenbyOP =K O. L 2 P J ThepositionvectorofQrelativetoOisgivenbyOQ= 4 N K O. L 6 P Q P R O (i) Express PQasacolumnvector. S (ii) Find RS. Answer J K K K L N O O O P [2] (iii) Find RS. Answer J K K K L N O O O P [1] Answer...units[2] 4024/21/M/J/16

63 23 10 (c) y 5 D x ThediagramshowstriangleD. (i) Anenlargementwithcentre(5,4),scalefactor2,mapstriangleDontotriangleE. DrawandlabeltriangleE. [2] (ii) Anenlargementwithcentre(5,4),scalefactor0.5,mapstriangleDontotriangleF. DrawandlabeltriangleF. [1] (iii) TriangleGhasvertices(5,4),(4,3)and(3,5). TriangleFcanbemappedontotriangleGusingasingleenlargement. TriangleFcanalsobemappedontotriangleGusingadifferent singletransformationt. DescribefullythesingletransformationT. Answer [3] 4024/21/M/J/16

64 24 BLANK PAGE Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at 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. 4024/21/M/J/16

65 Cambridge International Examinations Cambridge Ordinary Level * * MATHEMATICS (SYLLABUS D) 4024/22 Paper 2 May/June 2016 Candidates answer on the Question Paper. Additional Materials: Geometrical instruments Electronic calculator 2 hours 30 minutes READ THESE 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 a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Section A Answer all questions. Section B Answer any four questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100. This document consists of 19 printed pages and 1 blank page. DC (NF/SW) /2 [Turn over

66 2 Section A [52 marks] Answer all questions in this section. 1 (a) Each year the Reds play the Blues in a baseball match. In 2014, there were tickets sold for the match. In 2015, the number of tickets sold was 2.4% more than in Calculate the number of tickets sold for the match in (b) In 2015, the cost per ticket for the match was $ The cost per ticket for the match increased by 5% from 2014 to Calculate the cost per ticket for the match in Answer... [1] Answer $... [2] (c) Calculate the percentage increase, from 2014 to 2015, in the total money taken for the match. Answer... % [3] 4024/22/M/J/16

67 3 2 2 (a) JK = J N K O L 5 P (i) Find JM. J 4N KL = K O L -2 P J 1 LM = - N K O L 3 P (ii) Calculate KL. Answer [1] Answer... [2] (b) O a A E D b B C In the diagram, OA = a and OB = b. C is the point such that OAC is a straight line and AC = 2OA. D is the midpoint of OB. E is the point such that EC = OD. (i) Express, as simply as possible, in terms of a and b, (a) AD, (b) EB. Answer... [1] (ii) Find EB : AD. Answer... [1] Answer... :... [1] 4024/22/M/J/16 [Turn over

68 3 Steven asked 25 women how many children they have. The results are summarised in the table below. (a) Find (i) the mean, Number of children 4 Frequency (ii) the median, Answer... [2] (iii) the mode. Answer... [1] (b) Steven says that the mode is the average that best represents the data. Explain why Steven is wrong. Answer... [1] Answer... [1] (c) Steven chooses two women at random from the group. Calculate the probability that both of them have just one child. Give your answer as a fraction in its simplest form. 4024/22/M/J/16 Answer... [2]

69 5 (d) Draw a bar chart to represent this data. Frequency Number of children [2] (e) Steven shows Frank the paper on which he recorded the data from his survey. Part of the paper has been torn Which five numbers are missing from the paper? Answer...,...,...,...,... [1] 4024/22/M/J/16 [Turn over

70 4 (a) Triangle ABC has sides AB = 8 cm, AC = 7 cm and BC = 12 cm. (i) Use a ruler and compasses to construct triangle ABC. Side AB has been drawn for you. 6 A B [2] (ii) Measure BAC t. (b) Calculate the interior angle of a regular 12-sided polygon. Answer... [1] Answer... [2] 4024/22/M/J/16

71 7 (c) 125 p 3p q The diagram shows a hexagon with two parallel sides and one horizontal line of symmetry. (i) Calculate p. (ii) Calculate q. Answer... [1] Answer... [2] (d) A B P Q D C S R Trapezium PQRS is similar to trapezium ABCD. AB is parallel to DC and ABC t = DC = 2AB, BC = AB and PQ = DC. 2 4 Given that BC = x cm, find an expression, in terms of x, for the area of PQRS. Answer... cm 2 [3] 4024/22/M/J/16 [Turn over

72 8 5 (a) Factorise fully 8x 2 y 12x 5. Answer... [1] (b) Solve 4x 2(x + 5) = 3. Answer... [2] (c) Solve 7 5y < 20. (d) A rectangle has length 2x cm, perimeter 18 cm and area 10 cm 2. (i) Show that 2x 2 9x + 5 = 0. Answer y... [2] 2x (ii) Solve 2x 2 9x + 5 = 0, giving your answers correct to 2 decimal places. [2] (iii) Find the difference between the length and the width of the rectangle. Answer x =... or... [3] Answer... cm [1] 4024/22/M/J/16

73 9 6 (a) = { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 } A = { x : x is a prime number } B = { x : x is an even number } C = { x : x is a multiple of 5 } (i) List the members of the subsets (a) B + C, Answer... [1] (b) ^A, B, Ch ', Answer... [1] (c) A + B'. Answer... [1] (ii) A number q is chosen at random from. Find the probability that q! A + B'. (b) Find J3 X = K L 2-1N O 0 P J 2 Y = K L - 1 2N O 1 P Answer... [1] (i) 2X + Y, (ii) Y 1. Answer J K K L N O O P [2] Answer J K K L N O O P [2] 4024/22/M/J/16 [Turn over

74 10 Section B [48 marks] Answer four questions in this section. Each question in this section carries 12 marks. 7 One day, garage A records the amount of petrol bought by the first 120 customers. The results are summarised in the table below. Petrol (k litres) Number of customers 0 < k < k < k < k < k < k < k < k (a) Complete the cumulative frequency table below. Petrol (k litres) Cumulative frequency k 10 k 20 k 30 k 40 k 50 k 60 k 70 k [1] (b) On the grid below, draw a cumulative frequency curve to represent this data. Cumulative frequency Petrol (k litres) 4024/22/M/J/ [3]

75 11 (c) Use your graph to estimate (i) the median, Answer... litres [1] (ii) the 90th percentile of the distribution. Answer... litres [1] (d) On the same day, garage B also recorded the amount of petrol bought by its first 120 customers. The results are summarised below. 6 customers bought 10 litres or less. The most petrol bought by any customer was 60 litres. The median amount of petrol bought was 34 litres. The lower quartile of the distribution was 25 litres. The interquartile range of the distribution was 19 litres. Draw the cumulative frequency curve for garage B on the grid on the previous page. [3] (e) Petrol is priced at $2.60 per litre at both garages. Garage A offers a gift to customers who buy over 35 litres. Garage B offers a gift to customers who spend over $104. Use your graphs to estimate the number of these customers offered a gift at each garage and complete the sentence below. Show your working. Answer Garage... offers a gift to... more customers than garage... [3] 4024/22/M/J/16 [Turn over

76 1 8 The table below shows some values of x and the corresponding values of y for y = # 2 4 x. 12 x y (a) Complete the table. [1] 1 (b) On the grid below, draw the graph of y = # 2 4 x. y x [2] 4024/22/M/J/16

77 (c) By drawing a suitable line, find the gradient of your graph where x = Answer... [2] 1 (d) (i) Show that the line 2x + y = 6, together with the graph of y = # 2 4 x, can be used to solve the equation 2 x + 8x 24 = 0. (ii) Hence solve 2 x + 8x 24 = 0. [1] (e) The points P and Q are (2, 3) and (5, 4) respectively. (i) Find the gradient of PQ. Answer x =... [2] Answer... [1] 1 (ii) On the grid, draw the line l, parallel to PQ, that touches the curve y = # 2 4 x. [1] (iii) Write down the equation of l. Answer... [2] 4024/22/M/J/16 [Turn over

78 14 9 (a) A 30 C The diagram shows a vertical wind turbine with blades 30 m long. The blades are stationary with the point A being the maximum distance possible from the horizontal ground. The point B is such that the angle of elevation of A from B is 34 and the angle of elevation of the centre of the blades, C, from B is 25. Calculate the distance AB. B Answer... m [3] (b) A different wind turbine, shown in the diagram on the next page, has the centre of its blades, F, 75 m from the base of the turbine, D. Point E is on sloping ground, 180 m from F and 130 m from D. Calculate the angle of depression of E from F. 4024/22/M/J/16 Answer... [4]

79 15 F 75 D E (c) P is the point on a blade which is furthest from the centre of the blades. Each blade is 30 m long. (i) Calculate the distance travelled by P as the blade completes one revolution. (ii) The blade completes 15 revolutions per minute. Calculate the speed of P, giving your answer in kilometres per hour. Answer... m [1] Answer... km / h [2] (iii) A point Q lies on the straight line between P and the centre of the blades. Q travels 90 m as the blade completes one revolution. Calculate PQ. Answer... m [2] 4024/22/M/J/16 [Turn over

80 16 10 Triangles A, B, C and D are drawn on a centimetre square grid. y 6 5 B A x 1 D C 5 6 (a) The perimeter of triangle A is ^a + bh cm, where a and b are integers. Find a and b. (b) Triangle A is mapped onto triangle B by the translation T. Write down the column vector that represents T. Answer a =... b =... [2] Answer J K K L N O O P [1] (c) Describe fully the single transformation that maps triangle B onto triangle C. Answer [2] 4024/22/M/J/16

81 (d) Describe fully the single transformation that maps triangle B onto triangle D. 17 Answer [3] (e) Write down the matrix that represents the transformation which maps triangle D onto triangle A. Answer [1] (f) The transformation V is a reflection in the line y = 0. The transformation W is a rotation 90 clockwise about (0, 0). The single transformation X is equivalent to the transformation V followed by the transformation W. (i) The point (g, h) is mapped onto the point P by the transformation X. Find the coordinates of P. (ii) Describe fully the single transformation X. Answer (...,... ) [1] Answer [2] 4024/22/M/J/16 [Turn over

82 18 11 [ Volume of a cone = 3 1 πr 2 h ] (a) 3.5 r 20 Solid I Solid I is a cylinder with a small cylinder removed from its centre, as shown in the diagram. The height of each cylinder is 20 cm and the radius of the small cylinder is r cm. The radius of the large cylinder is 3.5 cm greater than the radius of the small cylinder. The volume of Solid I is 3000 cm 3. (i) Calculate r. Answer r =... [4] 4024/22/M/J/16

83 19 (ii) Solid II is a cone with volume of 3000 cm 3. The perpendicular height of the cone is twice its radius. Which solid is the taller and by how much? Solid II Answer Solid... is the taller by... cm [4] (b) The diagram shows a triangular prism of length 24 cm. Its cross-section is an equilateral triangle with sides 8 cm. 24 Calculate the total surface area of the prism. 8 Answer... cm 2 [4] 4024/22/M/J/16

84 20 BLANK PAGE Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at 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. 4024/22/M/J/16