Cambridge IGCSE Mathematics - International 0607 — 2014 May/June Paper 3 · Variant 2

This document consists of 16 printed pages. IB14 06_0607_32/3RP © UCLES 2014 [Turn over *6364749909* Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) May/June 2014 1 hour 45 minutes Candidates answer on the Question Paper. Additional Materials: Geometrical Instruments Graphics Calculator READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. Do not use staples, paper clips, glue or correction fluid. You may use an HB pencil for any diagrams or graphs. DO NOT WRITE IN ANY BARCODES. Answer all the questions. Unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. Answers in degrees should be given to one decimal place. For 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.

2 © UCLES 2014 0607/32/M/J/14 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 2014 0607/32/M/J/14 [Turn over Answer all the questions. 1 (a) Round 245 to the nearest hundred. Answer(a) [1] (b) Write down a square number between 40 and 60. Answer(b) [1] (c) Write 0.01 as a percentage. Answer(c) [1] (d) Write down all the factors of 18. Answer(d) [2] (e) Write down the lowest common multiple of 8 and 12. Answer(e) [1] (f) Write 21 14 as a fraction in its lowest terms. Answer(f) [1] (g) Work out 35% of 48. Answer(g) [2] (h) Write down a prime number between 10 and 20. Answer(h) [1]

4 © UCLES 2014 0607/32/M/J/14 2 A B C (a) Write down the mathematical name of shape A, shape B and shape C. Answer(a) A B C [3] (b) On each shape, draw any lines of symmetry. [3] (c) For each shape, write down the order of rotational symmetry. Answer(c) A B C [3]

5 © UCLES 2014 0607/32/M/J/14 [Turn over 3 (a) q° p° r° s° 58° 39° NOT TO SCALE Three straight lines cross at a point. Find the values of p, q, r and s. Answer(a) p = q = r = s = [4] (b) d ° e° c° 114° NOT TO SCALE A straight line intersects three parallel lines. Find the values of c, d and e. Answer(b) c = d = e = [3]

6 © UCLES 2014 0607/32/M/J/14 4 (a) Find the value of 3p – 2q when p = 1.5 and q = –1.2 . Answer(a) [2] (b) Solve the equation. 3 x = 6 Answer(b) x = [1] (c) Solve the simultaneous equations. x – y = 10 2x + y = 2 Answer(c) x = y = [2]

7 © UCLES 2014 0607/32/M/J/14 [Turn over 5 P y x 8 7 6 5 4 3 2 1 –1 –2 –3 –4 –5 –6 –7 –8 –6 –5 –8 –7 –4 –3 –2 –1 2 3 1 0 4 5 6 7 8 The diagram shows a kite, P. (a) Reflect P in the x-axis. Label the image A. [1] (b) Rotate P through 90° anticlockwise about the origin. Label the image B. [2] (c) Translate P by the vector       − − 7 6 . Label the image C. [2]

8 © UCLES 2014 0607/32/M/J/14 6 Jin owns a Chinese restaurant. The table shows the number of orders in one day for rice and noodles. Cost ($) Number of orders Plain rice 1.60 20 Fried rice 1.75 35 Noodles 1.60 25 Chinese noodles 1.85 15 (a) Write down the ratio 20 : 35 : 25 : 15 in its simplest form. Answer(a) : : : [2] (b) The table shows the cost of rice and noodles. Calculate the total income from the orders of rice and noodles. Answer(b) $ [3] (c) The total income for that day was $1500. Work out the income from the rice and noodles as a percentage of the total income. Answer(c) % [1]

9 © UCLES 2014 0607/32/M/J/14 [Turn over 7 Ibrahim ran 12 km for charity. For each kilometre he received $8.25 . (a) Find how much money Ibrahim raised for charity. Answer(a) $ [1] (b) Ibrahim took 90 minutes to run the 12 km. Find his speed in kilometres per hour. Answer(b) km/h [2] 8 These are the first four numbers in a sequence. 12 19 26 33 (a) Write down the next two numbers in this sequence. Answer(a) , [2] (b) Find the nth term of this sequence. Answer(b) [2]

10 © UCLES 2014 0607/32/M/J/14 9 René has 6 oranges and 5 plums in a bag. He picks out a fruit at random and eats it. (a) Find the probability that the fruit is an orange. Answer(a) [1] (b) René picks out a second fruit at random and eats it. Complete the tree diagram. Orange First fruit Second fruit Plum Orange Plum Plum Orange … … … … … … [3] (c) Find the probability that René eats two oranges. Answer(c) [2]

11 © UCLES 2014 0607/32/M/J/14 [Turn over 10 y x 10 –12 –2 4 0 f(x) = 2x2 – 5x – 8 (a) On the diagram, sketch the graph of y = f(x) between x = –2 and x = 4 . [2] (b) Find the zeros of f(x). Answer(b) , [2] (c) Find the co-ordinates of the local minimum point. Answer(c) ( , ) [2] (d) g(x) = –2x – 3 On the diagram, sketch the graph of y = g(x). [2] (e) Solve f(x) = g(x). Answer(e) x = or x = [2]

12 © UCLES 2014 0607/32/M/J/14 11 15 cm 15 cm 18 cm 18 cm 18 cm NOT TO SCALE The diagram shows the front of a bird box. A circular hole of radius 2.1 cm is cut out from the front. Show that the area of the front is 418 cm2, correct to 3 significant figures. [6]

13 © UCLES 2014 0607/32/M/J/14 [Turn over 12 (a) Ayako invests $50 000 at a rate of 3.4% per year simple interest. Calculate the total amount that Ayako has at the end of 6 years. Answer(a) $ [3] (b) Mayumi invests $48 000 at a rate of 3.25% per year compound interest. Calculate the total amount that Mayumi has at the end of 6 years. Give your answer correct to the nearest dollar. Answer(b) $ [3] 13 U Soccer Tennis Seven children, A, B, C, D, E, F and G, are asked whether they play soccer or tennis. A, E and G play soccer. A, B and C play tennis. D and F do not play soccer or tennis. (a) Complete the Venn diagram. [2] (b) One of the children is chosen at random. Find the probability that (i) the child plays both soccer and tennis, Answer(b)(i) [1] (ii) the child does not play soccer or tennis. Answer(b)(ii) [1]

14 © UCLES 2014 0607/32/M/J/14 14 The frequency table shows the masses, in kilograms, of 30 dogs. Mass (x kg) Frequency 0 < x Y 10 6 10 < x Y 20 8 20 < x Y 30 7 30 < x Y 40 6 40 < x Y 50 3 (a) Write down the mid-value of the interval 0 < x Y 10 . Answer(a) [1] (b) Calculate an estimate of the mean mass of the 30 dogs. Answer(b) kg [2] (c) Complete the cumulative frequency table. Mass (x kg) Cumulative frequency x Y 10 6 x Y 20 x Y 30 x Y 40 x Y 50 30 [1]

15 © UCLES 2014 0607/32/M/J/14 [Turn over (d) Use your answer to part (c) to complete the cumulative frequency curve. 30 25 20 15 10 5 10 20 Mass (kg) 30 40 50 0 x Cumulative frequency [3] (e) Use your graph to find (i) the median, Answer(e)(i) kg [1] (ii) the lower quartile, Answer(e)(ii) kg [1] (iii) the upper quartile. Answer(e)(iii) kg [1] Question 15 is printed on the next page.

16 Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright 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. © UCLES 2014 0607/32/M/J/14 15 y x 3 2 1 –1 –2 –3 –4 –5 –6 0 –1 1 2 3 4 5 –2 –3 –4 –5 (a) Plot and label the points A(–1, –5) and B(3, 1). [2] (b) Find the gradient of AB. Answer(b) [2] (c) Find the equation of the line parallel to AB passing through the point (0, 0). Answer(c) [1]

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2014 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 2014 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

Page 2 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0607 32 © Cambridge International Examinations 2014 1 (a) 200 1 (b) 49 1 (c) 1% 1 (d) 1, 2, 3, 6, 9, 18 2 B1 for 1 and 18 B1 for all the other factors (e) 24 1 (f) 3 2 1 (g) 16.8 2 M1 for 35 × 48 (h) 11 or 13 or 17 or 19 1 2 (a) Square Parallelogram Isosceles Triangle 1 1 1 (b) 4 correct lines drawn no lines 1 correct line 1 1 1 (c) 4 2 1 1 1 1 3 (a) 39 83 58 83 1 1 1 1 (b) 66 114 66 1 1 1FT FT from their 66. 4 (a) 6.9 2 M1 for 4.5 or 2.4 seen. soi by 2.1 (b) 18 1 (c) [x =] 4 [y =] –6 1 1 If 0 scored M1 for correct elimination of one variable

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0607 32 © Cambridge International Examinations 2014 5 (a) Vertices at (4, –1), (2, –5), (6, –5) and (4, –7) 1 (b) Vertices at (–1, 4), (–5, 2), (–5, 6) and (–7, 4) 2 B1 for 90° clockwise rotation about the origin or 90° anticlockwise rotation about another point (c) Vertices at (–2, –6), (–4, –2), (0, –2) and (–2, 0) 2 B1 for correct translation of      − k 6 or       −7 k 6 (a) 4 : 7 : 5 : 3 2 B1 for 2 correct terms (b) 161 3 M2 for 20 × 1.60 + 35 × 1.75 + 25 × 1.60 + 15 × 1.85 soi or M1 for 2 correct products seen. (c) 10.7 or [10.73…] 1FT FT from answer to (b) 7 (a) 99 1 (b) 8 2 M1 for 90 12 or 60 90 oe seen 8 (a) 40 47 1 1FT (their 40) + 7 (b) 5 7 + n 2 M1 for k n + 7 9 (a) 11 6 1 (b) 11 5 11 6 10 5 10 5 10 4 10 6 1 1 1 1 mark for each pair (c) 110 30 oe isw 2FT M1 for multiplying their 11 6 by their 10 5

Page 4 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0607 32 © Cambridge International Examinations 2014 10 (a) 2 B1 for a parabola with vertex downwards (b) –1.11 or –1.108… , 3.61 or 3.608… 1 1 (c) (1.25, –11.125) 1, 1 (d) 2 B1 for a line with negative gradient cutting the curve twice B1 for line within tolerance (e) –1 2.5 1 1 11 M2 for 2 2 9 15 − M1 for 0.5 × 18 × their h M1 for 182 M1 for 21.2 × π A1 for 418.1… 6 or M1 for 2 2 2 15 9 = + h 12 (a) 60 200 3 M2 for 50 000 × 0.034 × 6 + 50 000 or M1 for 50 000 × 0.034 × 6 (b) art 58154 www 3 3 M2 for 48 000(1 + 0.0325)6 or M1 for 48 000(1 + 0.0325)k

Page 5 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0607 32 © Cambridge International Examinations 2014 13 (a) 2 B1 for A correctly placed (b) (i) 7 1 1FT FT from Venn diagram (ii) 7 2 1 14 (a) 5 1 (b) 22.3 or 22.33… 2 M1 for multiplying 1 correct mid- value by frequency (c) 14, 21, 27 1 (d) 3FT B2FT for plotting 4 points correctly or B1FT for plotting 2 or 3 points correctly B1 for smooth increasing curve (e) (i) 21.5 ±1 1FT dependent on increasing curve (ii) 12 ±1 1FT dependent on increasing curve (iii) 32.5 ±1 1FT dependent. on increasing curve 15 (a) Points correctly plotted 1 , 1 (b) 4 6 oe 2 M1 for run rise (c) x y 4 6 = oe 1FT FT their 4 6 if positive Tennis Soccer G E C B A F D