Cambridge IGCSE Mathematics - International 0607 — 2013 May/June Paper 3 · Variant 2

This document consists of 16 printed pages. IB13 06_0607_32/4RP © UCLES 2013 [Turn over *7157903421* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) May/June 2013 1 hour 45 minutes Candidates answer on the Question Paper. Additional Materials: Geometrical Instruments Graphics Calculator READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. Do not use staples, paper clips, highlighters, glue or correction fluid. You may use a pencil for any diagrams or graphs. DO NOT WRITE IN ANY BARCODES. Answer all the questions. Unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. Answers in degrees should be given to one decimal place. For π, use your calculator value. You must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 96. www.XtremePapers.com

2 © UCLES 2013 0607/32/M/J/13 Formula List Area, A, of triangle, base b, height h. A = 1 2 bh Area, A, of circle, radius r. A = πr2 Circumference, C, of circle, radius r. C = 2πr Curved surface area, A, of cylinder of radius r, height h. A = 2πrh Curved surface area, A, of cone of radius r, sloping edge l. A = πrl Curved surface area, A, of sphere of radius r. A = 4πr2 Volume, V, of prism, cross-sectional area A, length l. V =Al Volume, V, of pyramid, base area A, height h. V= 1 3 Ah Volume, V, of cylinder of radius r, height h. V = πr2h Volume, V, of cone of radius r, height h. V = 1 3 πr2h Volume, V, of sphere of radius r. V = 4 3 πr3

3 © UCLES 2013 0607/32/M/J/13 [Turn over For Examiner's Use Answer all the questions. 1 A jar is filled with 120 cream toffees, 90 liquorice toffees and 60 chocolate toffees. (a) How many more cream toffees are there than liquorice toffees? Answer(a) [1] (b) Find the total number of toffees in the jar. Answer(b) [1] (c) One toffee is chosen at random. Find the probability that it is (i) a liquorice toffee, Answer(c)(i) [1] (ii) not a cream toffee, Answer(c)(ii) [1] (iii) a mint toffee. Answer(c)(iii) [1] (d) Sid is 14 years old, Ren is 15 years old and Tarrik is 16 years old. They share all the toffees in the ratio of their ages. Calculate the number of toffees that Ren receives. Answer(d) [2]

4 © UCLES 2013 0607/32/M/J/13 For Examiner's Use 2 Fifteen children were each given a different number of equations to solve. The number of equations solved and the time taken to solve them, to the nearest second, are shown in the table. Number of equations 3 4 6 9 10 11 12 14 15 17 20 21 22 25 30 Time (seconds) 8 11 12 20 21 34 28 40 41 45 60 58 61 70 82 5 10 15 Number of equations 20 25 30 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0 Time (seconds) (a) Complete the scatter diagram. The first eleven points have been plotted for you. [2]

5 © UCLES 2013 0607/32/M/J/13 [Turn over For Examiner's Use (b) Describe the type of correlation. Answer(b) [1] (c) (i) Find the mean number of equations solved. Answer(c)(i) [1] (ii) Find the mean time taken. Answer(c)(ii) s [1] (iii) On the diagram, plot the mean point. [1] (d) On the diagram, draw the line of best fit by eye. [2] (e) Use your line of best fit to estimate the time taken to solve 8 equations. Answer(e) s [1]

6 © UCLES 2013 0607/32/M/J/13 For Examiner's Use 3 Yana and Jelle are arranging a party. The cost of one packet of crisps is $ c and the cost of one bottle of juice is $ j. Yana spends a total of $10 on 12 packets of crisps and 5 bottles of juice. Jelle spends a total of $11 on 6 packets of crisps and 10 bottles of juice. (a) Write down two equations in c and j to show this information. Answer(a) [2] (b) Find the cost of one packet of crisps and the cost of one bottle of juice. Answer(b) crisps $ juice $ [3] 4 A bean plant grows at a constant rate. The table shows its height above the ground each day. Day 1 2 3 4 5 Height above ground (h cm) 1 3 5 (a) Complete the table. [2] (b) Find an expression, in terms of n, for the height of the bean plant after n days. Answer(b) [2] (c) Calculate the number of days it takes for the bean plant to reach a height of 83 cm. Answer(c) days [2]

7 © UCLES 2013 0607/32/M/J/13 [Turn over For Examiner's Use 5 y x 7 6 5 4 3 2 1 –1 –2 –3 –4 –5 0 1 –1 –2 –3 –4 –5 –6 –7 2 3 4 5 The diagram shows the graph of y = f(x). (a) Write down the zeros of y = f(x). Answer(a) and [2] (b) On the same diagram, sketch the graphs of y = f(x) – 3, and y = f(x + 2). [2]

8 © UCLES 2013 0607/32/M/J/13 For Examiner's Use 6 R T U P Q V S e° f ° d ° b ° c° a° 40° 51° NOT TO SCALE PQ, RS and TU are parallel lines and UV is a straight line. Find the values of a, b, c, d, e and f. Answer a = b = c = d = e = f = [6]

9 © UCLES 2013 0607/32/M/J/13 [Turn over For Examiner's Use 7 12 10 8 6 4 2 –2 –4 –4 –2 0 2 4 6 8 10 12 y x (a) On the grid, plot the points A(1, 9) and B(7, –3). [2] (b) Write down in component form. Answer(b)         [1] (c) Find the co-ordinates of the midpoint of AB. Answer(c) ( , ) [1] (d) Calculate the length of AB. Answer(d) [2] (e) Calculate the gradient of AB. Answer(e) [2] (f) Find the equation of the line passing through the points A and B. Give your answer in the form y = mx + c. Answer(f) y = [2]

10 © UCLES 2013 0607/32/M/J/13 For Examiner's Use 8 CLASSICAL COUNTRY RAP JAZZ POPULAR x° 42° 78° 84° 54° NOT TO SCALE Rita asked 60 students what type of music they liked best. The pie chart shows her results. (a) Find the value of x. Answer(a) [1] (b) Calculate the number of students who like rap best. Answer(b) [2] (c) One of the students is chosen at random. Find the probability that this student liked jazz best. Answer(c) [1]

11 © UCLES 2013 0607/32/M/J/13 [Turn over For Examiner's Use 9 U = {a, b, c, d, e, f, g, h} A = {c, e, g} B = {f, g, h} (a) Complete the Venn diagram. U A B [2] (b) List the elements of the following sets. (i) A ∪ B Answer(b)(i) [1] (ii) B′ Answer(b)(ii) [1] (iii) A ∩ B Answer(b)(iii) [1] (iv) A ∪ B′ Answer(b)(iv) [1] (c) Write down n(A ∪ B). Answer(c) [1]

12 © UCLES 2013 0607/32/M/J/13 For Examiner's Use 10 B A C D 500 cm 50 cm 300 cm NOT TO SCALE The diagram shows the side view of a child’s slide, ABCD. (a) Calculate CD. Answer(a) cm [3] (b) Use trigonometry to find the size of angle CDA. Answer(b) [2] (c) Tayaab takes 3 seconds to slide from C to D. Calculate his speed in metres per minute. Answer(c) m/min [3]

13 © UCLES 2013 0607/32/M/J/13 [Turn over For Examiner's Use 11 40 –40 –3 7 y x 0 (a) On the diagram, sketch the graph of y = x3 – 5x2 – 8x + 12. [2] (b) Find the co-ordinates of the local maximum and the local minimum points. Answer(b) ( , ) ( , ) [2] (c) On the same diagram sketch the graph of y = 2x + 3. [1] (d) Find the x co-ordinates of the points where the two graphs intersect. Answer(d) x = or x = or x = [3]

14 © UCLES 2013 0607/32/M/J/13 For Examiner's Use 12 NOT TO SCALE 30 cm 30 cm A closed cylinder has a diameter of 30 cm and a height of 30 cm. (a) (i) Find the total surface area of the cylinder. Answer(a)(i) cm2 [3] (ii) Find the volume of the cylinder. Answer(a)(ii) cm3 [2]

15 © UCLES 2013 0607/32/M/J/13 [Turn over For Examiner's Use (b) The cylinder contains a sphere of radius 15 cm. NOT TO SCALE 15 cm (i) Find the volume of this sphere. Answer(b)(i) cm3 [2] (ii) Find the percentage of the volume of the cylinder that is not taken up by the sphere. Answer(b)(ii) % [3] Question 13 is printed on the next page.

16 Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright 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. © UCLES 2013 0607/32/M/J/13 For Examiner's Use 13 (a) Expand and simplify. (x – 2)(2x + 3) Answer(a) [2] (b) Factorise completely. 10x2 – 15x Answer(b) [2] (c) Simplify fully the following expressions. (i) y xy 2 8 2 Answer(c)(i) [2] (ii) t t s 10 3 5 9 ÷ Answer(c)(ii) [2] (iii) 3 2 4 3 p p − Answer(c)(iii) [2] (iv) (2y2)3 Answer(c)(iv) [2]

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2013 series 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core), maximum raw mark 96 This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2013 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components. www.XtremePapers.com

Page 2 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0607 32 © Cambridge International Examinations 2013 1 (a) (b) (c) (i) (ii) (iii) (d) 30 270 90/(their 270) o.e. 1/3, 0.333, 0.3333… their 150/(their 270) o.e. 5/9, 0.556 or 0.5555 to 0.5556 0 90 1 1 1 FT 1 FT 1 2 isw any cancelling or converting. No ratios or words. Condone 0.33 and 0.555. M1 for 45 15 seen or their 45 270 o.e. 2 (a) (b) (c) (i) (ii) (iii) (d) (e) (21, 58), (22, 61), (25, 70), (30, 82) plotted correctly. Positive cao 14.6 39.4 Mean point plotted on diagram 18 – 23 seconds 2 1 1 1 1 FT 2 1 B1 for 2 points correctly plotted. No alternatives accepted Line within template ( x y 9.2 = and 8.5 9.2 − = x y ) almost full domain (2.5 to 30) B1 for ruled line through (their 14.6, their 39.4) almost full domain (2.5 to 30) 3 (a) (b) 12c + 5j = 10 o.e. 6c + 10j = 11 o.e. c = 0.5[0] o.e. p = 0.8[0] o.e. 1 1 M1 B1 B1 M1 FT for eliminating one variable (allowing one numerical error) or sketch of both lines. Trial and improvement both correct 3. B1 for 0.5 and B1 for 0.8 No working, maximum 2 marks

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0607 32 © Cambridge International Examinations 2013 4 (a) (b) (c) 7 and 9 2n – 1 o.e. 42 1, 1 2 2 ft B1 for 2 seen. M1 for  2 1 83. FT a linear formula, if answer is an integer. 5 (a) (b) –3 and 1 1, 1 1 1 Accept (–3, 0) and (1, 0) Approx. 3 units down, vertex approx. ( – 1, – 5) Approx. 2 units to left , vertex approx. ( – 3, – 2) 6 a = 40 b = 50 c = 89 d = 90 e = 90 f = 140 1 1 1 1 1 1 7 (a) (b) (c) (d) (e) (f) (1, 9) and (7, – 3) correctly plotted  6 –12 (4, 3) 13.4 (13.41 – 13.42) 2 –2x + 11 1, 1 1 1 2 FT 2 2 FT Accept 6√5 M1 for 62 + 122. FT from part (b) M1 for rise/run e.g. 12/2, 2 etc. B1 for (their – 2)x + k or y = mx + 11 FT their gradient

Page 4 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0607 32 © Cambridge International Examinations 2013 8 (a) (b) (c) 102 14 360 54 o.e. 3/20 0.15 1 2 1 M1 for 84 360 × 60 o.e. isw cancelling etc. (as in question 1) 9 (a) (b) (i) (ii) (iii) (iv) (c) {c, e, f, g, h} {a, b, c, d, e} {g} {a, b, c, d, e, g} 5 2 1FT 1FT 1FT 1FT 1FT B1 for 5 correct. Ignore absence of brackets in parts (i) to (iv). FT (b)(i) 10 (a) (b) (c) 541 (540.8…) 33.7 (33.67 – 33.72) 108 (108.1 – 108.2) 3 2FT 3FT M2 for (500 – 50)2 + 3002 M1 for 500 – 50 M1 for tanD = 300/their (500 – ),   0 o.e. M1 for distance/time, M1 for converting their 541 to m and 3 seconds to minutes. 11 (a)(c) (b) (c) (d) (–2/3 or – 0.667 or – 0.6667 to – 0.6666, 14.8 or 14.81…..) and (4, –36) Line drawn as in diagram above –2.04 (–2.044….), 0.693 (0.6931…..) , 6.35 (6.351…..) 2 1, 1 1 1, 1, 1 B1 for smooth curve with maximum and minimum in approximately the correct place, B1 for cutting axes in approximately correct place. Condone – 0.666 and accept in either order Accept freehand isw y-coordinates A B c e f h g a b d

Page 5 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0607 32 © Cambridge International Examinations 2013 12 (a) (i) (ii) (b) (i) (ii) 4240 (4240 to 4242) 21200 – 21210 14100 (14130 – 14140) 33.3 – 33.52…. 3 2 2 3 FT Accept 1350π M1 for [2] × π × 152 and M1 for 2 × π × 15 × 30 Accept 6750 π M1 for.π × 152 × 30 Accept 4500  M1 for 4 3 × π × 153. M2 for (their 21206 – their 14137) /their 21206 [× 100] M1 for (their 21206 – their 14137) or their 14137 their 21206 13 (a) (b) (c) (i) (ii) (iii) (iv) 2x2 – x – 6 5x2x – 3 4xy 6s p 12 8y6 2 2 2 2 2 2 B1 for 3 correct terms from 6 3 4 2 2 − + − x x x . – x implies 2 terms correct. B1 for 52x2 – 3x or x (10x – 15) B1 for 4  or  . M1 for multiplying by 10t/3 o.e. M1 for finding common denominator. B1 for   or 8yk