Cambridge IGCSE Mathematics - International 0607 — 2017 May/June Paper 3 · Variant 1

This document consists of 16 printed pages. DC (NF/SW) 133436/1 © UCLES 2017 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 9 8 9 1 3 4 8 0 2 2 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) May/June 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, 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/17 © UCLES 2017 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/17 © UCLES 2017 [Turn over Answer all the questions. 1 (a) What type of number is 7? Give two possible mathematical words to describe it. … and … [2] (b) (i) Write down a multiple of 7. … [1] (ii) Write 7% as a fraction. … [1] (iii) Work out. 7 + 72 + 73 … [1] (c) Write (i) 7 1 as a decimal, correct to 2 decimal places, … [2] (ii) 7 as a decimal, correct to 3 significant figures, … [2] (iii) 77 in standard form. … [2]

4 0607/31/M/J/17 © UCLES 2017 2 Rin asked some people how many pets they each have. The results are shown in the table. Number of pets 0 1 2 3 4 5 Number of people 14 45 18 11 7 5 (a) Find the number of people that Rin asked. … [1] (b) Find how many more people have 1 pet than have 2 pets. … [1] (c) One of the people is chosen at random. Work out the probability that this person has 1 pet. Give your answer as a fraction in its simplest form. … [2] (d) Complete the bar chart. 0 0 1 2 3 Number of pets Number of people 4 5 10 20 30 40 50 [2]

5 0607/31/M/J/17 © UCLES 2017 [Turn over 3 The price of a game of golf at each of two golf clubs is shown below. The Forest golf club Each game $13.50 The Valley golf club One game for $15 Buy 6 games and get the 7th game free (a) (i) Find how much it costs to play 7 games at The Forest golf club. $ … [1] (ii) Find how much it costs to play 7 games at The Valley golf club. $ … [1] (iii) Find which golf club is cheaper for 7 games, and by how much. … is cheaper by $… [1] (b) Jason is given $200 to spend playing golf at The Forest golf club. Find the greatest number of games he can play. Show all your working. … [3]

6 0607/31/M/J/17 © UCLES 2017 4 (a) Here are three angles on a straight line. 113° 38° NOT TO SCALE x Work out the size of angle x. x = … [1] (b) NOT TO SCALE y (i) Write down the mathematical name for this triangle. … [1] (ii) Find the size of angle y. y = … [2] (iii) Write down the number of lines of symmetry this triangle has. … [1]

7 0607/31/M/J/17 © UCLES 2017 [Turn over (c) NOT TO SCALE 24° z Work out the size of angle z. z = … [2] 5 Write each of these as a single power of x. (a) x7 × x4 … [1] (b) x x 2 10 … [1] (c) (x6)3 … [1]

8 0607/31/M/J/17 © UCLES 2017 6 (a) Here is a sequence of patterns using squares and crosses. Pattern 1 Pattern 2 Pattern 3 Pattern 4 (i) In the space above, draw Pattern 4. [1] (ii) Find the number of crosses in Pattern 5. … [1] (b) These are the first three terms of another sequence. 1 2 4 Find two different sequences that could have 1, 2 and 4 as their first three terms. In each case, write down the next three terms and the rule for continuing the sequence. 1 , 2 , 4 , … , … , … Rule … 1 , 2 , 4 , … , … , … Rule … [6]

9 0607/31/M/J/17 © UCLES 2017 [Turn over 7 NOT TO SCALE 27.5 cm A B 15 cm 16 cm 16 cm 4 cm 6.5 cm A company sells tissues in two different boxes, A and B. Each box is a cuboid. (a) Find the difference between the volumes of the two boxes. … cm3 [4] (b) The total surface area of box A is 1165 cm2. Show that the total surface area of box B is approximately 80% of the total surface area of box A. [5]

10 0607/31/M/J/17 © UCLES 2017 8 (a) Work out the value of 5a − 4b when a = 3 and b = 2. … [2] (b) Factorise completely. 3x2 − 9x … [2] (c) Solve. (i) 4x + 5 = 13 … [2] (ii) 3(x − 4) = 15 … [2] (d) Rearrange this formula to make A the subject. F = 2A + B A = … [2]

11 0607/31/M/J/17 © UCLES 2017 [Turn over 9 –1 0 –2 –3 –4 –5 –5 5 4 3 2 1 –4 –3 –2 –1 1 2 3 4 5 x A B y (a) Describe fully the single transformation that maps triangle A onto triangle B. … … [3] (b) On the grid, translate triangle A by the vector 4 1 J L KK N P OO . Label the image C. [2] (c) On the grid, reflect triangle B in the line x = 1. Label the image D. [2]

12 0607/31/M/J/17 © UCLES 2017 10 Tariq sells cars. For each of ten days he records the number of cars sold and the number of hours of sunshine. His results are shown in the table. Number of hours of sunshine 6 5 2 10 11 4 8 2 5 7 Number of cars sold 3 6 11 2 0 7 2 12 7 5 (a) Complete the scatter diagram to show this information. The first 6 points have been plotted for you. 0 0 1 2 3 4 5 6 Number of cars sold 7 8 9 10 11 12 1 2 3 4 5 6 Number of hours of sunshine 7 8 9 10 11 12 [2] (b) What type of correlation is shown in your diagram? … [1]

13 0607/31/M/J/17 © UCLES 2017 [Turn over (c) Calculate (i) the mean number of hours of sunshine, … hours [1] (ii) the mean number of cars sold. … [1] (d) On the diagram, draw a line of best fit. [2] (e) Use your line of best fit to estimate the number of cars sold on a day when there are 3 hours of sunshine. … [1] (f) This table shows the number of cars Tariq sold each week for one year. Number of cars sold Number of weeks 0 to 20 12 21 to 40 17 41 to 60 15 61 to 80 7 81 to 100 1 (i) Write down the modal class of the number of cars sold. … to … [1] (ii) Find the largest possible range and the smallest possible range of the number of cars sold. Largest range … Smallest range … [2]

14 0607/31/M/J/17 © UCLES 2017 11 (a) Tammi travels 7 km at an average speed of 30 km / h. Find the number of minutes this journey takes. … minutes [2] (b) When the speed limit is 50 km / h, Tammi travels at a speed 8% below this limit. Find the speed at which Tammi travels. … km / h [2] (c) In a town, there are 208 roads. The speed limit on the roads is either 30 km / h or 50 km / h. The ratio number of 30 km / h roads : number of 50 km / h roads = 11 : 2. Calculate the number of 30 km / h roads. … [2]

15 0607/31/M/J/17 © UCLES 2017 [Turn over 12 The diagram shows a rectangular field. 54 m NOT TO SCALE B A x 85 m (a) Find how much further it is from A to B when walking along two sides of the field rather than straight across the field. … m [4] (b) Use trigonometry to calculate angle x. x = … [2] Question 13 is printed on the next page.

16 0607/31/M/J/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. 13 0 x y –4 –3 5 3 (a) On the diagram, sketch the graph of y = 2x − 3 for values of x from x = −3 to x = 3. [2] (b) On the diagram, sketch the graph of y = x 1 for values of x from x = −3 to x = 3. [2] (c) Find the x co-ordinates of the points of intersection of y = 2x − 3 and y = x 1 . x = … and x = … [2]

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

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 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 May/June 2017 © UCLES 2017 Page 3 of 5 Question Answer Marks Part Marks 1(a) Accept any two from: whole [number], prime [number], odd, integer, real [number], natural [number], rational [number], positive [number] 2 B1 for one correct 1(b)(i) Any multiple of 7 1 1(b)(ii) 7 100 1 1(b)(iii) 399 1 1(c)(i) 0.14 2 B1 for 0.143 or 0.1428 to 0.1429 1(c)(ii) 2.65 2 B1 for 2.645 to 2.646 1(c)(iii) 8.24 × 105 or 8.235… × 105 2 B1 for 823543 soi 2(a) 100 1 2(b) 27 1 2(c) 9 20 2 FT ( ) 45 a their correctly cancelled B1FT for 45 100 or ( ) 45 a their 2(d) Bars with heights at 45 and 18 2 B1 for one bar correct height 3(a)(i) 94.5[0] 1 3(a)(ii) 90 1 3(a)(iii) The Valley, 4.5[0] 1 FT their (a)(i) and (a)(ii) 3(b) 14 3 M1 for 200 ÷ 13.50 soi A1 for 14.8… 4(a) 29 1 4(b)(i) Equilateral 1 4(b)(ii) 60 2 M1 for 180÷3 4(b)(iii) 3 1 4(c) 78 2 M1 for (180 – 24) ÷ 2 soi 5(a) x11 1 5(b) x8 1 5(c) x18 1

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2017 © UCLES 2017 Page 4 of 5 Question Answer Marks Part Marks 6(a)(i) Correct diagram 1 6(a)(ii) 12 1 6(b) 8, 16, 32 2 B1 for two values Multiply by 2 oe 1 7, 11, 16 2 B1 for two values +1, +2, +3 oe 1 7(a) 14 4 M3 for 27.5 × 15 × 4 – 16 × 16 × 6.5 oe or M1 for 27.5 × 15 × 4 or 16 × 16 × 6.5 oe A1 for A = 1650 A1 for B = 1664 7(b) Area of 6 faces of B M2 M1 for area of 3 faces of B B = 928 A1 1165 their B [×100] M1 79.6 to 79.7 A1 8(a) 7 2 M1 for 5 × 3 – 4 × 2 or B1 for 15 or –8 seen 8(b) 3x(x – 3) 2 B1 for 3(x2 – 3x) or x(3x – 9) 8(c)(i) 2 2 M1 for 4x = 13 – 5 oe 8(c)(ii) 9 2 M1 for 3x – 12 = 15 or x – 4 = 5 8(d) 2 F B − oe final answer 2 M1 for F – B = 2A or 2 F = A + 2 B seen If 0 scored SC1 for answer 2 F – B or 2 F B − ÷ 9(a) Rotation 90 [anti-clockwise] or 270 clockwise [About] (0, 0) or Origin 3 B1 for each 9(b) Correct translation 2 M1 for translation 1 k    or 4 k    9(c) Correct reflection 2 M1 for correct reflection in any vertical line

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2017 © UCLES 2017 Page 5 of 5 Question Answer Marks Part Marks 10(a) 4 points correctly plotted 2 B1 for 2 or 3 points correctly plotted 10(b) Negative 1 10(c)(i) 6 1 10(c)(ii) 5.5 1 10(d) Ruled line of best fit through their mean point and within tolerance 2 M1 for ruled line within tolerance not through their mean point or for ruled line with negative gradient through their mean point 10(e) 9 1 FT their line with negative gradient 10(f)(i) 21 to 40 1 10(f)(ii) Largest 100 1 Smallest 61 1 11(a) 14 2 M1 for 7 ÷ 30 or 30 ÷ 60 11(b) 46 2 M1 for 50 × 0.08 oe or for 0.92 oe seen 11(c) 176 2 M1 for 208 ÷ (11 + 2) soi by 16 12(a) 38.3 or 38.29 to 38.30 4 B1 for 139 B2 for 100.7… or M1 for 852 + 542 12(b) 32.4 or 32.42 to 32.43 2 M1 for tan [...] = 54 85 oe FT their AB if using sine or cosine 13(a) Correct sketch 2 B1 for correct shape, wrong position 13(b) Correct sketch 2 B1 for correct shape but touching axes and/or with branches connected 13(c) 1.83 or 1.826 to 1.827 1 –0.442 or –0.4415 to –0.4419 1 If 0 scored SC1 for 1.8 and 0.44