Cambridge IGCSE Mathematics - International 0607 — 2016 May/June Paper 3 · Variant 1

This document consists of 16 printed pages. DC (LK/CGW) 115323/3 © UCLES 2016 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 0 0 1 1 9 8 9 2 0 8 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) May/June 2016 1 hour 45 minutes Candidates answer on the Question Paper. Additional Materials: Geometrical Instruments Graphics Calculator READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. Do not use staples, paper clips, glue or correction fluid. You may use an HB pencil for any diagrams or graphs. DO NOT WRITE IN ANY BARCODES. Answer all the questions. Unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. Answers in degrees should be given to one decimal place. For r, use your calculator value. You must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 96.

2 0607/31/M/J/16 © UCLES 2016 Formula List Area, A, of triangle, base b, height h. A = bh 2 1 Area, A, of circle, radius r. A = rr2 Circumference, C, of circle, radius r. C = 2rr Curved surface area, A, of cylinder of radius r, height h. A = 2rrh Curved surface area, A, of cone of radius r, sloping edge l. A = rrl Curved surface area, A, of sphere of radius r. A = 4rr2 Volume, V, of prism, cross-sectional area A, length l. V = Al Volume, V, of pyramid, base area A, height h. V= Ah 3 1 Volume, V, of cylinder of radius r, height h. V = rr2h Volume, V, of cone of radius r, height h. V = r h 3 1 2 r Volume, V, of sphere of radius r. V = r 3 4 3 r

3 0607/31/M/J/16 © UCLES 2016 [Turn over Answer all the questions. 1 (a) Write 356.31 (i) correct to 1 decimal place, … [1] (ii) correct to 2 significant figures, … [1] (iii) correct to the nearest 100, … [1] (iv) in standard form. … [1] (b) (i) Calculate . . 16 8 9 61 2 - . Write down all the figures shown on your calculator, giving your answer as a decimal. … [1] (ii) Myrto estimates that the answer to part (b)(i) is 300. (a) Find the difference between Myrto’s estimate and your answer to part (b)(i). … [1] (b) Write this difference as a percentage of your answer to part (b)(i). … % [1]

4 0607/31/M/J/16 © UCLES 2016 2 (a) Write 4 × 4 × 4 × 4 × 4 × 4 (i) as a power of 4, … [1] (ii) as an integer. … [1] (b) Find the value of (i) 4 4 4 2 + , … [1] (ii) 4 4 4 0 - . … [1] (c) Write 4 4 2 10 as a power of 4. … [1]

5 0607/31/M/J/16 © UCLES 2016 [Turn over 3 Tingwei buys 2 kg of cheese. The cheese costs $13.50 for one kilogram. (a) Work out how much Tingwei pays for the 2 kg of cheese. $ … [1] (b) He uses all the cheese to make 200 cheese balls. Find the mass, in grams, of one cheese ball. … g [1] (c) (i) He sells all these cheese balls at a school fair for $0.25 each. Work out how much money he received. $ … [1] (ii) The profit goes to the school charity. Work out how much money goes to the school charity. $ … [1] (d) The school fair makes a total profit of $460. Write the profit that Tingwei made as a fraction of $460. Give your answer in its simplest form. … [2]

6 0607/31/M/J/16 © UCLES 2016 4 The number of strawberries in each of 20 boxes is listed below. 32 28 27 32 33 28 34 28 29 29 28 28 33 31 33 33 30 29 29 26 (a) Complete the frequency table. Number of strawberries 26 27 28 29 30 31 32 33 34 Frequency 1 1 1 [2] (b) Find (i) the range, … [1] (ii) the mode, … [1] (iii) the median, … [1] (iv) the mean. … [1] (c) One of these boxes of strawberries is chosen at random. Find the probability that it contains (i) exactly 33 strawberries, … [1] (ii) fewer than 30 strawberries. … [1]

7 0607/31/M/J/16 © UCLES 2016 [Turn over 5 (a) A B C D 5 2 2 1 = - - (i) Find the value of A when B = 2, C = 3 and D = 6. … [2] (ii) Find the value of B when A = 12, C = 1 and D = 4. … [3] (b) Find the value of 7p − 4q when p = −3 and q = –2. … [2] (c) Rearrange 2y = 3x − 9 to make x the subject. x = … [2] (d) The mass of 1 pomegranate and 2 kiwi fruit is 480 g. The mass of 1 pomegranate and 6 kiwi fruit is 840 g. Find the mass of 1 pomegranate and the mass of 1 kiwi fruit. Show all your working. 1 pomegranate = … g 1 kiwi fruit = … g [4]

8 0607/31/M/J/16 © UCLES 2016 6 30 people were asked where they were going on holiday. The results are to be shown in a pie chart. Country India Spain South Africa United States Australia Number of people 5 12 3 6 4 Sector angle 60° 48° (a) Calculate the sector angle for Spain. … [2] (b) Complete the pie chart. Label each sector. Australia India [3]

9 0607/31/M/J/16 © UCLES 2016 [Turn over 7 (a) F E A C B 105° NOT TO SCALE D G H AFB and CGD are parallel lines. EFGH is a straight line and angle AFE = 105°. Find (i) angle EFB, Angle EFB = … [1] (ii) angle CGF. Angle CGF = … [1] (b) NOT TO SCALE A O D C B r° s° p° 70° q° AOB and COD are diameters of a circle, centre O. The lines AD and CB are parallel and angle CAB = 70°. Find the values of p, q, r and s. p = … q = … r = … s = … [4]

10 0607/31/M/J/16 © UCLES 2016 8 NOT TO SCALE 2.5 km 40° H C S B The diagram shows four straight cycle tracks HB, HC, BC and CS. BC = CS and HC = 2.5 km. Angle HBC = 90° and angle BHC = 40°. (a) Abimela cycles from home, H, to school, S, each day along cycle track HC and CS. (i) Use trigonometry to find the distance BC. … km [2] (ii) Find the distance Abimela cycles to school. … km [1] (b) One day track HC is blocked and she has to cycle along tracks HB, BC and CS. Find the distance HB. … km [2] (c) Find the extra distance that Abimela now has to cycle to school. … km [1]

11 0607/31/M/J/16 © UCLES 2016 [Turn over 9 1 0 2 1 2 3 4 5 6 7 8 3 4 5 6 7 8 9 y x (a) On the grid, plot the points A(2, 3) and B(5, 7). Draw the line AB. [2] (b) Write down the co-ordinates of the midpoint of AB. ( … , … ) [1] (c) Find the gradient of AB. … [2] (d) Find the equation of the line parallel to AB that passes through the point (0, 4). … [2]

12 0607/31/M/J/16 © UCLES 2016 10 15 cm 12 cm 4 cm NOT TO SCALE The diagram shows 12 solid cylinders packed into a box. Each cylinder has radius 1 cm and length 15 cm. (a) (i) Find the volume of one cylinder. … cm3 [1] (ii) Work out the volume of 12 cylinders. … cm3 [1] (b) The box measures 15 cm by 12 cm by 4 cm. Find the volume of the box. … cm3 [1] (c) Find the volume of the box not taken up by the cylinders. … cm3 [1] (d) Write your answer to part (c) as a percentage of the total volume of the box. … % [1]

13 0607/31/M/J/16 © UCLES 2016 [Turn over 11 2 2 −2 −4 −6 4 6 8 10 y 4 6 −6 −4 −2 0 8 10 x P The diagram shows a pentagon, P. (a) Draw the image of P after a reflection in the y-axis. Label this image Q. [1] (b) Draw the image of P after a translation by the vector 2 6 - J L KK N P OO . Label this image R. [2] (c) Draw the image of P after an enlargement, scale factor 3, centre (0, 0). Label this image S. [2] (d) Find the ratio length of horizontal side of S : length of horizontal side of P. … : … [1] (e) Congruent Regular Similar Choose a word from the list to complete the statement. P and S are ……………..……… shapes. [1]

14 0607/31/M/J/16 © UCLES 2016 12 The masses of 200 meerkats are recorded in the frequency table. Mass (x grams) Frequency x 200 300 1 G 5 x 00 00 3 4 1 G 10 x 00 00 4 5 1 G 26 x 00 00 5 6 1 G 34 x 00 00 6 7 1 G 40 x 00 00 7 8 1 G 62 x 00 00 8 9 1 G 18 x 00 00 9 10 1 G 5 Total 200 (a) Write down the modal group. … x 1 G … [1] (b) (i) Show that the midpoint of the first group is 250. [1] (ii) Find an estimate of the mean mass of these 200 meerkats. … g [2] (c) Complete the cumulative frequency table. Mass (x grams) Cumulative frequency x 300 G 5 x 400 G x 500 G x 00 6 G x 00 7 G x 00 8 G x 900 G 195 x 1000 G 200 [2]

15 0607/31/M/J/16 © UCLES 2016 [Turn over (d) Complete the cumulative frequency curve. 20 100 200 300 400 500 Mass (grams) 600 700 800 900 1000 40 60 80 0 100 120 Cumulative frequency 140 160 180 200 x [3] (e) Use your graph to find (i) the median, … g [1] (ii) the inter-quartile range, … g [2] (iii) the number of meerkats with a mass of more than 850 g. … [2] Question 13 is printed on the next page.

16 0607/31/M/J/16 © UCLES 2016 Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. 13 0 −3 3 10 y x −10 ( ) f x x x 2 2 = + (a) On the diagram, sketch the graph of y = f(x) from x = −3 to x = 3. [4] (b) Write down the equation of the vertical asymptote for this graph. … [1] (c) Find the co-ordinates of the local minimum point. ( … , … ) [1] (d) Write down the number of solutions of y = f(x) when y = 6. … [1]

® IGCSE is the registered trademark of Cambridge International Examinations. This document consists of 6 printed pages. © UCLES 2016 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) May/June 2016 MARK SCHEME Maximum Mark: 96 Published 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 2016 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

Page 2 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2016 0607 31 © Cambridge International Examinations 2016 Abbreviations awrt answers which round to cao correct answer only dep dependent FT follow through after error isw ignore subsequent working oe or equivalent SC Special Case nfww not from wrong working soi seen or implied Question Answer Mark Part Marks 1 (a) (i) 356.3 1 (ii) 360 1 (iii) 400 1 (iv) 3.56[31] × 102 1 (b) (i) 279.14 1 (ii) (a) 20.86 1FT FT 300 – their (b)(i) (b) 7.47 or 7.472 to 7.473 1FT FT their (b)(ii) ÷ their (b)(i) × 100 2 (a) (i) 46 1 (ii) 4096 1 (b) (i) 272 1 (ii) 255 1 (c) 48 1 3 (a) 27 1 (b) 10 1 (c) (i) 50 1 (ii) 23 1 FT FT their 50 – their 27 (d) 1 20 2 B1 FT for 23 460 their

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2016 0607 31 © Cambridge International Examinations 2016 Question Answer Mark Part Marks 4 (a) 26 27 28 29 30 31 32 33 34 1 1 5 4 1 1 2 4 1 2 B1 for 4 correct entries (b) (i) 8 1 (ii) 28 1 (iii) 29 1 (iv) 30 1 (c) (i) 4 20 oe isw 1FT FT 4 20 their (ii) 11 20 oe isw 1FT FT 2 5 4 20 + + their their 5 (a) (i) 1 2 M1 for 1 2 5 2 2 3 6 × −× −× or better (ii) 3.2 3 M2 for 5B = 12 + 2 + 2 or better (Allow 1 sign error e.g. –5B) or M1 for ( ) 1 12 5 2(1) 4 2 = − − B or better (b) −13 2 M1 for 7 × −3 − 4 ×−2 or better (c) 2 9 3 + y oe final answer 2 M1 for correct first step (d) 6 kiwi – 2 kiwi = 840 – 480 oe kiwi =90 pomegranate + 2 × their 90 = 480 oe pomegranate = 300 M1 A1 M1 A1 FT OR M1 for setting up two equations M1 for eliminating one variable A1 kiwi = 90 A1 pomegranate = 300 second A1 is FT If no working shown SC1 for both answers correct 6 (a) 144 2 M1 for [ ] 12 360 30 × seen or 48 × 3 or 60 12 5 × (b) Fully correct answer 3 B2 for correct sectors but no labels or B1 for 1 correct sector or B1for correct 3 labels according to size

Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2016 0607 31 © Cambridge International Examinations 2016 Question Answer Mark Part Marks 7 (a) (i) 75 1 (ii) 105 1 (b) [p = ] 70 1 [q = ] 20 1 [r = ] 20 1FT FT their q or 90 − their p [s = ] 140 1FT FT 70 + their p or 180 − 2 × their r 8 (a) (i) 1.61 or 1.606 to 1.607 2 M1 for sin 40 2.5 = BC or better (ii) 4.11 or 4.106 to 4.107 1FT FT 2.5 + their (a)(i) (b) 1.92 or 1.915… 2 M1 for cos40 2.5 HB = or better or M1 for 2.52 – their 1.612 (c) 1.02 or 1.016 or 1.02 to 1.03 1FT FT 2 × their (a)(i) + their (b) − their (a)(ii) 9 (a) Correct points plotted (2, 3) and (5, 7) 2 B1 for each correct point (b) (3.5, 5) 1 (c) 4 3 2 M1 for rise run or B1 for 1.3 (d) 4 4 3 y x = + oe final answer 2 FT FT (c) 4 y their x = + oe B1 for 4 3 y their x k = + or 4 = + y kx 10 (a) (i) 47.1 or 47.12 to 47.13 1 (ii) 565 to 566 1 FT FT their (a)(i) × 12 (b) 720 1 (c) 154 to 155 1 FT FT their (b) − their (a)(ii) (d) 21.39 to 21.53 1 FT FT their (c) ÷ their (b) × 100

Page 5 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2016 0607 31 © Cambridge International Examinations 2016 Question Answer Mark Part Marks 11 (a) (0, 2), (–1, 1), (–2, 1), (–3, 2), (–2, 3) 1 (b) (2, –4), (3, –5), (4, –5), (5, –4), (4, –3) 2 B1 for translation of 6 k     −   or 2    k or B1 for 6 2 −       (c) (0, 6), (3, 3), (6, 3), (9, 6), (6, 9) 2 B1 for any enlargement centre (0, 0) or correct shape, wrong position (d) 3 : 1 1 (e) similar 1 12 (a) [ ] 700 800 x <
1 (b) (i) ( ) [ ] 200 300 250 2 + = oe 1 (ii) 638.5 2 M1 for multiplying midpoints by frequencies (and adding) – implied by 127700 (c) x < 300 5 x < 400 15 x < 500 41 x < 600 75 x < 700 115 x < 800 177 x < 900 195 x < 1000 200 2 B1FT for 2 correct entries (d) Fully correct curve or ruled polygon 3FT FT only if increasing B2FT for their 4 or 5 points plotted correctly or B1FT for their 3 points plotted correctly

Page 6 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2016 0607 31 © Cambridge International Examinations 2016 Question Answer Mark Part Marks (e) (i) 662 (660 to 680) 1FT FT as long as it is an increasing curve (ii) 230 (230 to 260) 2FT B1 for one correct quartile seen ( ) 756 5 or 526 5 ± ± FT as long as it is an increasing curve (iii) 12 (8 to 16) 2FT B1 for 188 ± 4 seen or M1 for clear method seen on graph FT as long as it is an increasing curve 13 (a) Fully correct sketch 4 B1 for minimum in first quadrant B1 for crossing x-axis approximately between –1 and –2 B1 for not crossing y-axis B1 for correct overall shape (b) x = 0 1 (c) (1, 3) 1 (d) 3 1FT FT their graph