Cambridge IGCSE Mathematics - International 0607 — 2017 Oct/Nov Paper 3 · Variant 1

This document consists of 15 printed pages and 1 blank page. DC (LK/CGW) 133482/3 © UCLES 2017 [Turn over * 4 6 1 0 5 8 8 2 5 0 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) October/November 2017 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 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. Cambridge International Examinations Cambridge International General Certificate of Secondary Education

2 0607/31/O/N/17 © UCLES 2017 Formula List Area, A, of triangle, base b, height h. A = 2 1 bh 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 = 3 1 Ah Volume, V, of cylinder of radius r, height h. V = rr2h Volume, V, of cone of radius r, height h. V = 3 1 rr2h Volume, V, of sphere of radius r. V = 3 4 rr3

3 0607/31/O/N/17 © UCLES 2017 [Turn over Answer all the questions. 1 (a) Bijul and Samar work in a restaurant on Saturdays. (i) One Saturday Bijul sells 280 hamburgers at $1.50 each and 330 bags of fries at $1.10 each. Calculate the total amount of money Bijul receives. $ … [2] (ii) Samar is paid $12 per hour. Work out how much she is paid for working 8 hours. $ … [1] (iii) Bijul is paid $15 per hour. Work out Samar’s pay per hour as a percentage of Bijul’s pay per hour. … % [1] (b) Bijul has $15 to spend on cards. Cards cost $1.20 per packet. Find the greatest number of packets Bijul can buy and how much change she receives. … packets of cards and $ … change [3] (c) Samar invests $600 at a rate of 4% simple interest per year. Calculate how much interest she will receive at the end of 5 years. $ … [2]

4 0607/31/O/N/17 © UCLES 2017 2 (a) (i) The mean number of sweets in 9 bags is 35. Show that the total number of sweets in all 9 bags is 315. [1] (ii) Another bag has 45 sweets. Find the mean number of sweets in all 10 bags. … [2] (b) Ad, Ben and Gal share 72 sweets. They share the sweets in the ratio Ad : Ben : Gal = 5 : 4 : 3. Work out the number of sweets that Ben receives. … [2]

5 0607/31/O/N/17 © UCLES 2017 [Turn over 3 (a) Write 3562.845 (i) correct to 2 decimal places, … [1] (ii) correct to 3 significant figures, … [1] (iii) correct to the nearest hundred. … [1] (b) Work out 14 284 632 - . Write your answer correct to the nearest whole number. … [2] (c) Find the value of . 156 25. … [1] (d) Write 38% as a fraction in its simplest form. … [2] (e) Complete the list of factors of 63. 1, … , … , … , … , 63 [2] (f) Write the following in order of size, starting with the smallest. 5 3 55% 0.59 0.52 … 1 … 1 … 1 … [2] smallest

6 0607/31/O/N/17 © UCLES 2017 4 Lucy plays a game with the cards below. –2.7 1 1 3 5 6 8 9 27 5.8 –5 – 7 9 (a) From these numbers, write down (i) a positive integer, … [1] (ii) a square number, … [1] (iii) a prime number. … [1] (b) The 10 cards are turned over to hide the numbers and one card is chosen at random. Find the probability that the number is (i) negative, … [1] (ii) even, … [1] (iii) less than 1. … [1]

7 0607/31/O/N/17 © UCLES 2017 [Turn over 5 24 students each recorded the number of hours of voluntary service they completed during one year. The results are shown in the table. Number of hours 30 40 50 60 70 80 Number of students 9 5 4 1 2 3 (a) For the number of hours completed, find (i) the range, … hours [1] (ii) the mode. … hours [1] (b) Find the mean number of hours completed by a student. … hours [2] (c) Complete the bar chart. 30 0 1 2 3 4 5 Number of students Number of hours 6 40 50 60 70 80 7 8 9 [2]

8 0607/31/O/N/17 © UCLES 2017 6 Here is a pattern of shapes. Pattern 1 Pattern 2 Pattern 3 Pattern 4 (a) In the space above, draw Pattern 4. [1] (b) Complete the table. Pattern number 1 2 3 4 5 Number of dots 1 3 [2] (c) Find an expression for the number of dots in Pattern n. … [2] (d) Use your expression in part (c) to find the number of dots in Pattern 18. … [2]

9 0607/31/O/N/17 © UCLES 2017 [Turn over 7 A C F E D G 103° s° 42° NOT TO SCALE 30° p° r° t° q° B ABC, GD and FE are parallel lines. AGF and CDE are also parallel lines. Find the values of p, q, r, s and t. p = … q = … r = … s = … t = … [5]

10 0607/31/O/N/17 © UCLES 2017 8 400 students each took a mathematics test. The results are shown in the table below. Mark (x) Frequency x 10 20 1 G 10 x 0 0 2 3 1 G 30 x 0 0 3 4 1 G 40 x 0 0 4 5 1 G 60 x 0 0 5 6 1 G 120 x 0 0 6 7 1 G 60 x 0 0 7 8 1 G 30 x 0 0 8 9 1 G 30 x 0 0 9 10 1 G 20 (a) Complete the cumulative frequency table for this data. Mark (x) Cumulative frequency x G 20 10 x G 30 40 x G 40 x G 50 x G 60 x G 70 x G 80 350 x G 90 380 x G 100 400 [2]

11 0607/31/O/N/17 © UCLES 2017 [Turn over (b) Complete the cumulative frequency curve. 0 100 200 10 20 0 30 40 50 Mark (x) 60 70 80 90 100 300 400 Cumulative frequency [2] (c) Use your curve to find (i) the median mark, … [1] (ii) the inter-quartile range, … [2] (iii) the number of students with a mark greater than 75. … [2]

12 0607/31/O/N/17 © UCLES 2017 9 80 m 80 m NOT TO SCALE 220 m A path is made up of three straight lines and the arc of a semicircle. (a) Write down the length of the diameter of the semicircle. … m [1] (b) Find the length of the arc of the semicircle. … m [2] (c) Find the total length of the path. … m [1] (d) Kumi walks at an average speed of 4.5 km/h. Work out the time it takes him to walk the whole length of the path. … minutes [2] (e) Calculate the total area enclosed by the path. … m2 [3]

13 0607/31/O/N/17 © UCLES 2017 [Turn over 10 Daisuke is given the following directions. • Start at A. • Face North and then turn clockwise through 150°. • Walk 225 metres in a straight line to point B. • Face North and then turn 60° clockwise. • Walk 270 metres in a straight line to point C. (a) Draw a sketch to show this information. On the sketch, label B and C and mark the angles and distances. North A [4] (b) Angle ABC is a right angle. Use Pythagoras’ Theorem to calculate the distance AC. AC … m [2] (c) Use trigonometry to help you work out the bearing of C from A. … [3]

14 0607/31/O/N/17 © UCLES 2017 11 (a) Solve. x x 3 5 3 + = - x = … [2] (b) Expand the brackets and simplify. ( )( ) x x 1 3 - + … [2] (c) Factorise completely. x y xy 3 2 3 - … [2] (d) (i) a a a p 4 12 # = Find the value of p. p = … [1] (ii) b b b q 4 12 = Find the value of q. q = … [1] (e) Simplify. y y 3 2 5 3 - … [2]

15 0607/31/O/N/17 © UCLES 2017 12 –2.5 2.5 x y –10 15 0 ( ) . f x x x 3 1 5 9 2 = - - (a) On the diagram, sketch the graph of ( ) f y x = for . . x 2 5 2 5 G G - . [2] (b) Find the co-ordinates of the points where the graph cuts (i) the x-axis, ( … , … ) and ( … , … ) [2] (ii) the y-axis. ( … , … ) [1] (c) Find the co-ordinates of the local minimum point. ( … , … ) [2] (d) Find the x co-ordinates of the two points of intersection of the graph of ( ) f y x = and the line y 5 = . x = … and x = … [2]

16 0607/31/O/N/17 © UCLES 2017 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. BLANK PAGE

® IGCSE is a registered trademark. This document consists of 5 printed pages. © UCLES 2017 [Turn over Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) October/November 2017 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 International will not enter into discussions about these mark schemes. Cambridge International is publishing the mark schemes for the October/November 2017 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 2 of 5 MARK SCHEME NOTES The following notes are intended to aid interpretation of mark schemes in general, but individual mark schemes may include marks awarded for specific reasons outside the scope of these notes. Types of mark M Method marks, awarded for a valid method applied to the problem. A Accuracy mark, awarded for a correct answer or intermediate step correctly obtained. For accuracy marks to be given, the associated Method mark must be earned or implied. B Mark for a correct result or statement independent of Method marks. When a part of a question has two or more ‘method’ steps, the M marks are in principle independent unless the scheme specifically says otherwise; and similarly where there are several B marks allocated. The notation ‘dep’ is used to indicate that a particular M or B mark is dependent on an earlier mark in the scheme. Abbreviations awrt answers which round to cao correct answer only dep dependent FT follow through after error isw ignore subsequent working nfww not from wrong working oe or equivalent rot rounded or truncated SC Special Case soi seen or implied

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 3 of 5 Question Answer Marks Partial Marks 1(a)(i) 783 2 M1 for 280 × 1.50 or 330 × 1.10 soi by 420 or 363 1(a)(ii) 96 1 1(a)(iii) 80 1 1(b) 12 2 M1 for 15 1.2 oe soi by 12.5 [0].6[0] 1 1(c) 120 2 M1 for 600 × 0.04 [× 5] oe or [600 ×] 0.04 × 5 2(a)(i) 9 × 35 [= 315] 1 2(a)(ii) 36 2 M1 for 315 + 45 oe 2(b) 24 2 M1 for 72 5 4 3 + + soi by 6 3(a)(i) 3562.85 1 3(a)(ii) 3560 1 3(a)(iii) 3600 1 3(b) –25 2 B1 for –24.9 or –24.86 to –24.85 3(c) 12.5 1 3(d) 19 50 2 B1 for 38 100 3(e) 3, 7, 9, 21 2 B1 for 2 correct factors in any order 3(f) 0.52, 55%, 0.59, 3 5 oe 2 B1 for 3 in the correct order 4(a)(i) 1 or 7 or 9 or 27 1 4(a)(ii) 1 or 9 1 4(a)(iii) 7 1 4(b)(i) 3 10 oe 1 4(b)(ii) 0 1 4(b)(iii) 5 10 oe 1

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 4 of 5 Question Answer Marks Partial Marks 5(a)(i) 50 1 5(a)(ii) 30 1 5(b) 46.25 2 M1 for at least 2 of 30 × 9 + 40 × 5 + ... soi by 1110 5(c) Correct bars 2 B1 for 2 or 3 correct bars 6(a) Correct pattern 1 6(b) 5, 7, 9 2 B1 for 2 correct 6(c) 2n – 1 oe 2 M1 for 2n – k or kn – 1 6(d) 35 2 FT their (c) M1 for substituting 18 in their (c) 7 [p] = 48 1 [q] = 30 1 [r] = 29 1 [s] = 61 1 [t] = 47 1 8(a) 80 140 260 320 2 B1 for 2 or 3 correct 8(b) Correct curve drawn 2 FT from (a) but only if numbers are increasing B1FT for 2 points plotted correctly 8(c)(i) 54 to 56 1 FT their curve 8(c)(ii) 22 to 26 2 M1 for 66 to 68 or 42 to 44 seen 8(c)(iii) 400 – their cf value 2 FT B1 for their cf value 9(a) 220 1 9(b) 346 or 345.5 to 345.6… 2 M1 for π × 220 [÷ 2] soi 9(c) 726 or 725.5 to 725.6… 1 FT 380 + their(b) 9(d) 9.67 or 9.68 or 9.673 to 9.676 2 M1 for distance speed

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 5 of 5 Question Answer Marks Partial Marks 9(e) 36 600 to 36 610 3 M2 for 220 × 80 + 0.5 × π × (0.5 × 220)2 or M1 for 220 × 80 or 0.5 × π × (0.5 × 220)2 10(a) Correct sketch 4 B1 for 150° correct B1 for 225 m and B marked B1 for 60° correct B1 for 270 m and C marked 10(b) 351 or 351.4 to 351.5 2 M1 for 2252 + 2702 10(c) [0]99.8 or [0]99.80 to [0]99.81 3 M1 for tan[ ] = 270 225 oe M1 for subtracting answer from 150 11(a) – 4 2 M1 for correct first step 11(b) x2 + 2x – 3 final answer 2 M1 for x2 + 3x or – x – 3 11(c) xy(xy2 – 3) final answer 2 M1 for x(xy3 – 3y) or y(x2y2 – 3x) 11(d)(i) 8 1 11(d)(ii) 16 1 11(e) 15 y 2 M1 for both fractions written with denominator 15k or better 12(a) Correct sketch 2 M1 for correct shape 12(b)(i) (–1.5, 0) (2, 0) 2 B1 for each 12(b)(ii) (0, – 9) 1 12(c) (0.25, – 9.19) or (0.25, – 9.188 to – 9.187) 2 B1 for x co-ordinate B1 for y co-ordinate 12(d) –1.92 or –1.925 to –1.924 1 2.42 or 2.424 to 2.425 1