Cambridge IGCSE Mathematics - International 0607 — 2015 May/June Paper 3 · Variant 2

This document consists of 16 printed pages. DC (LEG/FD) 99288/5 © UCLES 2015 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 8 0 2 2 0 9 9 5 2 5 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 Paper 3 (Core) May/June 2015 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 0607/32/M/J/15 © UCLES 2015 Formula List Area, A, of triangle, base b, height h. A = bh 2 1 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= Ah 3 1 Volume, V, of cylinder of radius r, height h. V = πr2h 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 0607/32/M/J/15 © UCLES 2015 [Turn over Answer all the questions. 1 (a) Write 32 652 (i) correct to the nearest 10, Answer(a)(i) … [1] (ii) correct to the nearest 100. Answer(a)(ii) … [1] (b) Write 62.584 correct to 1 decimal place. Answer(b) … [1] (c) Calculate 4.84. Answer(c) … [1] (d) Find 216 3 . Answer(d) … [1] (e) Find the highest common factor (HCF) of 18 and 45. Answer(e) … [1] (f) Find the lowest common multiple (LCM) of 6 and 8. Answer(f) … [1] (g) Divide 442 in the ratio 8 : 9. Answer(g) … : …[2] (h) Sem buys 7 hamburgers each costing $1.20 . Find how much change he receives from $10. Answer(h) $ … [2]

4 0607/32/M/J/15 © UCLES 2015 2 (a) Write 0.75 as a fraction. Answer(a) … [1] (b) Write 3 2 as a percentage, giving your answer correct to 4 significant figures. Answer(b) …% [2] (c) Write 48% as a fraction in its lowest terms. Answer(c) … [2] (d) Find 8% of 72. Answer(d) … [1] (e) The price of a jacket is $96. The price is reduced by 20%. Find the new price of the jacket. Answer(e) $ … [2] (f) $800 is invested for 5 years at 3% per year simple interest. Find the total interest received at the end of the 5 years. Answer(f) $ … [2]

5 0607/32/M/J/15 © UCLES 2015 [Turn over 3 A special die has 10 faces numbered 1 to 10. When the die is rolled it is equally likely to land on any face. Find the probability that the die lands on (a) an even number, Answer(a) … [1] (b) a prime number, Answer(b) … [1] (c) 11, Answer(c) … [1] (d) a square number less than 5. Answer(d) … [1]

6 0607/32/M/J/15 © UCLES 2015 4 Jacinta asks some students in her class which colour they prefer. The results are in the table. Colour Number of students Brown 1 Green 4 Black 8 Pink 12 Blue 15 (a) Calculate the total number of students. Answer(a) … [1] (b) Write down the most popular colour. Answer(b) … [1]

7 0607/32/M/J/15 © UCLES 2015 [Turn over (c) Jacinta wants to draw a pie chart for these results. Colour Number of students Sector angle in pie chart Brown 1 Green 4 Black 8 Pink 12 108° Blue 15 135° (i) Complete the table. [2] (ii) Complete the pie chart to show this information. Two sectors have been drawn for you. Blue Pink [2]

8 0607/32/M/J/15 © UCLES 2015 5 HanRa asked 30 students if they ate cereal (C ) or toast (T ) for breakfast. The information is shown in the Venn diagram. U C 18 6 5 T 1 Write down the number of students in (a) C T + , Answer(a) … [1] (b) C, Answer(b) … [1] (c) C T , l ^ h , Answer(c) … [1] (d) T C , l. Answer(d) … [1]

9 0607/32/M/J/15 © UCLES 2015 [Turn over 6 10 cm 10 cm 10 cm 5 cm NOT TO SCALE A trophy is in the shape of a cube of side 10 cm with a sphere of radius 5 cm on top. (a) Find the surface area of the cube. Answer(a) … cm2 [2] (b) Find the surface area of the sphere. Answer(b) … cm2 [2] (c) Find the total volume of the trophy. Answer(c) … cm3 [4] The trophy is made from metal that costs 4 cents per cm3. (d) Find the cost of the metal used to make the trophy. Give your answer in dollars. Answer(d) $ … [2]

10 0607/32/M/J/15 © UCLES 2015 7 45° 12 cm 36 cm 18 cm 31 cm B C D G E F A NOT TO SCALE The diagram shows a triangle ABC and a trapezium CDEF. BCGD is a straight line and angle FCD = 45°. AB = 36 cm, BC = 12 cm, CD = 31 cm and ED = 18 cm. (a) Find the size of angle CFE. Answer(a) Angle CFE = … [1] (b) Use trigonometry to calculate the size of angle BCA. Answer(b) Angle BCA = … [2] (c) Use Pythagoras’ Theorem to find the length of AC. Answer(c) AC = … cm [2]

11 0607/32/M/J/15 © UCLES 2015 [Turn over (d) Use trigonometry to calculate the length of CF. Answer(d) CF = … cm [3] (e) (i) Explain why EF = 13 cm. [2] (ii) Find the total perimeter of the shape. Answer(e)(ii) … cm [1] (f) Calculate the total area of the shape. Answer(f) …cm2 [3]

12 0607/32/M/J/15 © UCLES 2015 8 The table shows the number of shirts and the number of jackets owned by 12 students. Shirts 3 6 2 8 8 10 6 5 9 8 4 12 Jackets 5 4 2 4 6 8 5 4 6 5 4 7 (a) Complete the scatter diagram. The first 6 points have been plotted for you. 0 1 2 3 4 5 6 7 8 9 10 2 1 4 6 8 10 3 5 7 9 11 12 Number of shirts Number of jackets [2] (b) Write down the type of correlation shown by the scatter diagram. Answer(b) … [1] (c) (i) Find the mean number of shirts. Answer(c)(i) … [1] (ii) Find the mean number of jackets. Answer(c)(ii) … [1] (iii) On the diagram, plot the mean point. [1]

13 0607/32/M/J/15 © UCLES 2015 [Turn over (d) On the diagram, draw a line of best fit by eye. [2] (e) Use your line of best fit to estimate the number of jackets for a student who has 7 shirts. Answer(e) … [1]

14 0607/32/M/J/15 © UCLES 2015 9 –3 – 6 1 0 x 10 y f x x x 6 5 3 2 = - - ^ h (a) On the diagram, sketch the graph of f y x = ^ h for x 3 1 G G - . [2] (b) Write down the y co-ordinate of the point where the graph crosses the y-axis. Answer(b) y = … [1] (c) Write down the x co-ordinates of the points where the graph crosses the x-axis. Answer(c) x = … and x = …[2] (d) Find the co-ordinates of the local maximum point. Answer(d) ( … , …) [1] (e) g x x 2 4 = + ^ h On the same diagram, sketch the graph of g y x = ^ h. [2] (f) Find the co-ordinates of the points of intersection of f(x) and g(x). Answer(f) (… , …) and (… , …) [2]

15 0607/32/M/J/15 © UCLES 2015 [Turn over 10 (a) Solve. (i) x 5 6 4 + =- Answer(a)(i) … [2] (ii) x 6 3 21 1 + Answer(a)(ii) … [2] (b) Simplify. (i) s s 3 4 # Answer(b)(i) … [1] (ii) t2 4 ^ h Answer(b)(ii) … [1] (iii) r r 18 3 3 ' Answer(b)(iii) … [2] (c) Expand and simplify. x x 4 3 3 2 1 - + + ^ ^ h h Answer(c) … [2] (d) Factorise completely. y y 15 3 2 - Answer(d) … [2] Question 11 is printed on the next page.

16 0607/32/M/J/15 © UCLES 2015 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 (a) Ahmed cycles 15 kilometres in 50 minutes. Find his average speed in kilometres per hour. Answer(a) …km/h [3] (b) George runs 15 kilometres at an average speed of 12 kilometres per hour. Find how many minutes it takes George to run the 15 kilometres. Answer(b) …min [3]

® IGCSE is the registered trademark of Cambridge International Examinations. CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the May/June 2015 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 2015 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 2015 0607 32 © Cambridge International Examinations 2015 Abbreviations 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 1 (a) (i) 32 650 1 (ii) 32 700 1 (b) 62.6 1 (c) 530.8416 1 (d) 6 1 (e) 9 1 (f) 24 1 (g) 208 : 234 2 M1 for dividing by 17 soi (h) 1.6[0] 2 B1 for 8.4[0] 2 (a) 100 75 oe isw 1 (b) 66.67 2 B1 for correct answer to [ 2 sf (c) 25 12 2 B1 if correct fraction not in lowest terms (d) 5.76 1 (e) 76.8[0] 2 M1 for 0.8 × 96 oe (f) 120 2 M1 for 100 3 5 800 × × oe

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2015 0607 32 © Cambridge International Examinations 2015 3 (a) 10 5 oe 1 (b) 10 4 oe 1 (c) 10 0 1 (d) 10 2 oe 1 4 (a) 40 1 (b) blue 1 (c) (i) brown = 9 green = 36 black = 72 2 B1 for 1 correct angle (ii) 3 sectors correct 2 B1 for 1 sector correct 5 (a) 6 1 (b) 24 1 (c) 1 1 (d) 12 1 6 (a) 600 2 B1 for 100 (b) 314 or 314.1 to 314.2 2 M1 for 2 5 4 × ×π oe (c) 1520 or 1523 to 1524 4 M3 for 3 3 5 3 4 10 × × + π oe or M2 for 3 5 3 4 × ×π or M1 for 103 (d) 60.9 or 60.8 to 60.96 2 FT If 0 scored SC1 FT for 6090 or 6080 to 6096

Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2015 0607 32 © Cambridge International Examinations 2015 7 (a) 135 1 (b) 71.6 or 71.56 to 71.57 2 M1 for tan[C] = 12 36 (c) 37.9 or 37.94 to 37.95 2 M1 for 2 2 12 36 + or better (d) 25.5 or 25.45 to 25.46 3 M2 for 45 cos 18 or 45 sin 18 = CF or M1 for CF CF 18 45 cos or 18 45 sin = = If 0 scored SC2 for correct answer from Pythagoras (e) (i) [triangle CFG is] isosceles [CG = 18] 31 – 18 = 13 1 1 M1 for 31 – 18 oe Dep on isosceles (ii) 173 or 173.3 to 173.5 1 FT FT 110 + their (c) + their (d) (f) 612 3 M2 for 0.5×12×36 + 0.5×18 ×18 + 13 ×18 or better or M1 for 0.5×12×36 or 0.5×18×18 or 13×18 or better 8 (a) Points plotted correctly 2 B1 for 4 points correct (b) positive 1 (c) (i) 6.75 1 (ii) 5 1 (iii) Point plotted correctly 1 FT (d) Ruled line through mean within tolerance 2 B1 any line through mean point (e) 5 or 6 1 FT FT line with positive gradient 9 (a) 2 M1 for correct shape A1 for maximum in second quadrant and x intercepts approximately correct (b) 6 1

Page 5 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2015 0607 32 © Cambridge International Examinations 2015 (c) −2.47 or −2.475 to −2.474 0.808 or 0.8081… 1 1 (d) ( –0.833, 8.08) or (–0.833.., 8.083..) 1 (e) 2 B1 for positive gradient B1 for correct y-intercept at approximately 4 (f) (–2.59, –1.18) or (–2.591 to –2.590, –1.181…) (0.257 , 4.51) or (0.2573…, 4.514 to 4.515) 1 1 10 (a) (i) –2 2 M1 for subtracting 6 or dividing by 5 (ii) x < 3 2 M1 for subtracting 3 or dividing by 6 (b) (i) s7 1 (ii) t8 1 (iii) 6r2 2 B1 for kr2 or 6rk (k ≠ 0) (c) 10x – 9 final answer 2 M1 for( ) ( ) 3 6 or 12 4 + − x x (d) 3y(5 – y) final answer 2 B1 for ( ) ( ) y y y y 3 15 or 5 3 2 − − 11 (a) 18 3 M2 for 60 50 15 × oe or M1 for 60 50 or time 15 their (b) 75 3 M2 for 60 12 15 × or M1 for 60 12 or 12 15 or 5 min/km