Cambridge IGCSE Mathematics - International 0607 — 2019 May/June Paper 3 · Variant 1

This document consists of 18 printed pages and 2 blank pages. DC (LK/FC) 168251/2 © UCLES 2019 [Turn over * 7 3 1 4 2 0 0 0 7 8 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) May/June 2019 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. Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education

2 0607/31/M/J/19 © UCLES 2019 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/19 © UCLES 2019 [Turn over Answer all the questions. 1 (a) Write in words the number 6015. … [1] (b) Find the value of (i) 43, … [1] (ii) ( ) 3 16 2 3 9 # + , … [1] (iii) 3 52 # , … [1] (iv) 40 10 2 # - . … [1] (c) Find (i) 81, … [1] (ii) a prime number between 20 and 30, … [1] (iii) 60 as a product of prime factors. … [2]

4 0607/31/M/J/19 © UCLES 2019 2 This shape is drawn on a 1 cm2 grid. (a) (i) Work out the area and the perimeter of the shape. Give the units of each answer. Area = … … Perimeter = … … [4] (ii) The shape is enlarged by a scale factor of 3. Find the perimeter of the enlarged shape. Give your answer in metres. … m [3] (b) Write down the order of rotational symmetry of the shape. … [1] (c) On the diagram, draw all the lines of symmetry. [2]

5 0607/31/M/J/19 © UCLES 2019 [Turn over (d) Work out the sum of all the interior angles of the shape. … [3] (e) –2 –3 –2 –1 1 2 3 4 5 –1 0 1 A B x y 4 5 6 2 3 Write down the co-ordinates of point A and point B. A ( … , … ) B ( … , … ) [2]

6 0607/31/M/J/19 © UCLES 2019 3 (a) A packet of cereal costs $2.80 . Work out the largest number of these packets that can be bought with $20. How much change would you get? … packets and $ … change [3] (b) A packet originally contained 450 g of cereal. The mass of cereal in the packet is increased by 15%. Work out how much extra cereal is added to the packet. … g [2] (c) 51 out of 300 people said they would buy the heavier packet of cereal. Work out 51 as a percentage of 300. … % [1]

7 0607/31/M/J/19 © UCLES 2019 [Turn over 4 This formula can be used to change a temperature in degrees Celsius, C, to a temperature in degrees Fahrenheit, F. F C 2 30 = + (a) Find the value of F when (i) C 0 = , … [1] (ii) C 120 = . … [1] (b) Find the value of C when F 350 = . … [2] (c) Find the value of C when F C = . … [2] (d) Rearrange the formula to make C the subject. F C 2 30 = + C = … [2]

8 0607/31/M/J/19 © UCLES 2019 5 Henri records the number of people in each car passing through his village. The results are shown in the table. Number of people Number of cars 1 35 2 25 3 20 4 10 5 10 (a) Complete the bar chart to show this information. 0 1 2 3 4 Number of people Number of cars 5 5 10 15 20 25 30 35 40 [2]

9 0607/31/M/J/19 © UCLES 2019 [Turn over (b) Find the total number of cars that Henri recorded. … [1] (c) Using the results in the table, work out (i) the mode, … [1] (ii) the median, … [1] (iii) the mean. … [2] (d) One of the cars is chosen at random. Work out the probability that it contains (i) 4 people, … [1] (ii) 1 or 2 people. Give your answer as a fraction in its simplest form. … [2]

10 0607/31/M/J/19 © UCLES 2019 6 (a) These are the first four terms of a sequence. 11 18 25 32 (i) Write down the rule for continuing this sequence. … [1] (ii) Find an expression for the nth term of this sequence. … [2] (b) Here are the first four terms of another sequence. 23 18 13 8 Find the next two terms of this sequence. … , … [2]

11 0607/31/M/J/19 © UCLES 2019 [Turn over 7 (a) On the grid, draw the image of the shape after a translation by vector 4 2 - e o. [2] (b) On the grid, draw the image of the shape after a rotation of 90° anticlockwise about the point O. O [2]

12 0607/31/M/J/19 © UCLES 2019 8 (a) Simplify. a a a 4 2 3 + - … [1] (b) Solve. (i) x 17 4 - = x = … [1] (ii) x 5 4 = x = … [1] (iii) x 2 3 1 44 + = ` j x = … [3] (c) Factorise fully. x 12 30 - … [2]

13 0607/31/M/J/19 © UCLES 2019 [Turn over (d) Simplify fully. (i) x x x 7 4 3 # … [2] (ii) y y 3 15 2 6 … [2]

14 0607/31/M/J/19 © UCLES 2019 9 Crystal carries out a survey of cars, vans and lorries that drive past her house. (a) She sees a total of 500 of these types of vehicle. The ratio cars : vans : lorries = 14 : 4 : 7. Work out how many of each type of vehicle she sees. Cars … Vans … Lorries … [3] (b) One car travels 2.5 km in 5 minutes. Work out the speed of this car in kilometres per hour. … km/h [2] (c) Crystal measures the speed of each of the 500 vehicles. Her results are shown in the table. Speed (s km/h) Frequency s 0 10 1 G 0 s 10 0 2 1 G 20 s 20 0 3 1 G 230 s 30 0 4 1 G 170 s 40 0 5 1 G 60 s 50 0 6 1 G 20

15 0607/31/M/J/19 © UCLES 2019 [Turn over (i) Complete the cumulative frequency table. Speed (s km/h) Cumulative Frequency s 10 G 0 s 20 G s 30 G s 40 G s 50 G s 60 G 500 [1] (ii) On the grid, draw a cumulative frequency curve for this information. 0 10 0 20 30 40 Speed (km/h) Cumulative frequency 50 60 s 100 200 300 400 500 [3] (iii) Use your cumulative frequency curve to estimate the number of cars travelling faster than 35 km/h. … [2]

16 0607/31/M/J/19 © UCLES 2019 10 7 cm h cm NOT TO SCALE A cylinder has radius 7 cm and height h cm. (a) Show that the area of the circular end of the cylinder is 154 cm2, correct to the nearest whole number. [2] (b) The volume of the cylinder is 2 litres. Work out the value of h. h = … [2] (c) A cube has side length x cm. It has the same volume as the cylinder. Find the value of x. x = … [3]

17 0607/31/M/J/19 © UCLES 2019 [Turn over 11 A vertical post, 1.75 m tall, stands on horizontal ground. One day, the post casts a shadow of length 3.28 m. x m 1.75 m NOT TO SCALE 3.28 m y° Sun (a) Find the value of x. x = … [2] (b) Find the value of y, the angle of elevation of the Sun. y = … [2]

18 0607/31/M/J/19 © UCLES 2019 12 x y –3 0 –3 20 5 The diagram shows the graph of y x 2 = + for x 3 5 G G - . (a) Find the co-ordinates of the y-intercept. ( … , … ) [1] (b) On the diagram, sketch the graph of y x x 1 2 = - - for x 3 5 G G - . [2] (c) Solve this equation. x x x 1 2 2 - - = + x = … or x = … [2]

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20 0607/31/M/J/19 © UCLES 2019 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 Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge. BLANK PAGE

This document consists of 6 printed pages. © UCLES 2019 [Turn over Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) May/June 2019 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 May/June 2019 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 2019 © UCLES 2019 Page 2 of 6 Generic Marking Principles These general marking principles must be applied by all examiners when marking candidate answers. They should be applied alongside the specific content of the mark scheme or generic level descriptors for a question. Each question paper and mark scheme will also comply with these marking principles. GENERIC MARKING PRINCIPLE 1: Marks must be awarded in line with: • the specific content of the mark scheme or the generic level descriptors for the question • the specific skills defined in the mark scheme or in the generic level descriptors for the question • the standard of response required by a candidate as exemplified by the standardisation scripts. GENERIC MARKING PRINCIPLE 2: Marks awarded are always whole marks (not half marks, or other fractions). GENERIC MARKING PRINCIPLE 3: Marks must be awarded positively: • marks are awarded for correct/valid answers, as defined in the mark scheme. However, credit is given for valid answers which go beyond the scope of the syllabus and mark scheme, referring to your Team Leader as appropriate • marks are awarded when candidates clearly demonstrate what they know and can do • marks are not deducted for errors • marks are not deducted for omissions • answers should only be judged on the quality of spelling, punctuation and grammar when these features are specifically assessed by the question as indicated by the mark scheme. The meaning, however, should be unambiguous. GENERIC MARKING PRINCIPLE 4: Rules must be applied consistently e.g. in situations where candidates have not followed instructions or in the application of generic level descriptors. GENERIC MARKING PRINCIPLE 5: Marks should be awarded using the full range of marks defined in the mark scheme for the question (however; the use of the full mark range may be limited according to the quality of the candidate responses seen). GENERIC MARKING PRINCIPLE 6: Marks awarded are based solely on the requirements as defined in the mark scheme. Marks should not be awarded with grade thresholds or grade descriptors in mind.

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2019 © UCLES 2019 Page 3 of 6 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 2019 © UCLES 2019 Page 4 of 6 Question Answer Marks Partial Marks 1(a) Six thousand [and] fifteen 1 1(b)(i) 64 1 1(b)(ii) [0].5 oe 1 1(b)(iii) 75 1 1(b)(iv) 20 1 1(c)(i) 9 1 1(c)(ii) 23 or 29 1 1(c)(iii) 2 × 2 × 3 × 5 oe 2 B1 for any correct product equal to 60 or for 2, 3, 5 as final answer 2(a)(i) [A =] 9 cm2 [P =] 20 cm 4 B1 for each value and each unit 2(a)(ii) [0].6 3 FT P 3 100 their × B1 for their P × 3 M1 for ÷ 100 2(b) 2 1 2(c) Two correct ruled lines 2 B2 for 2 correct lines and no extra lines B1 for 2 correct lines and no more than 2 extra lines 2(d) 1800 3 M2 for 8 × 90 + 4 × 270 soi by 720 + 1080 or M1 for 8 × 90 or 4 × 270 soi by 720 or 1080 2(e) [A =] (1, 3) [B =] (4, –2) 2 B1 for each 3(a) 7 with [0].4[0] change 3 B2 for 7 or M1 for 20 ÷ 2.80 soi by 7.1… 3(b) 67.5 2 M1 for 450 × 0.15 oe soi 3(c) 17 1 4(a)(i) 30 1 4(a)(ii) 270 1 4(b) 160 2 B1 for 350 = 2C + 30 oe 4(c) –30 2 B1 for C = 2C + 30 4(d) 30 2 F − or 2 F − 15 2 B1 for F – 30 = 2C or for 2 F = C + 15

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2019 © UCLES 2019 Page 5 of 6 Question Answer Marks Partial Marks 5(a) Correct bar chart 2 B1 for 4 correct heights, unequal widths or for 3 correct heights, all equal widths 5(b) 100 1 5(c)(i) 1 1 5(c)(ii) 2 1 5(c)(iii) 2.35 2 M1 for 1 × 35 + 2 × 25 + 3 × 20 + 4 × 10 + 5 × 10 or for ÷ their100 5(d)(i) 10 100 oe 1 FT 10 1 00 their 5(d)(ii) 3 5 2 M1 for 60 1 00 their 6(a)(i) Add 7 oe 1 6(a)(ii) 7n + 4 2 B1 for 7n + x or for pn + 4 p ≠ 0 6(b) 3 –2 2 B1 for 3 or for their first value – 5 7(a) Correct image 2 B1 for 2     −   k or 4 k    7(b) Correct image 2 B1 for rotation 90° clockwise about O 8(a) 3a 1 8(b)(i) 13 1 8(b)(ii) 20 1 8(b)(iii) 7 3 M1 for 3x + 1 = 22 or 6x + 2 = 44 M1 for a correct FT next step 8(c) 6(2x – 5) 2 B1 for 3(4x – 10) or 2(6x – 15) If 0 scored, SC1 for 12(x – 2.5) 8(d)(i) x 0 or 1 2 B1 for 7 7 x x 8(d)(ii) 5y 4 2 B1 for 6 2 5y y or 4 15 3 y soi or 5y k or ky 4 9(a) [C] 280 [V] 80 [L] 140 3 B2 for one value correct or M1 for 500 14 4 7 + + soi by 20

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2019 © UCLES 2019 Page 6 of 6 Question Answer Marks Partial Marks 9(b) 30 2 M1 for 2.5 5 or 2.5 × 12 soi 9(c)(i) [0] 20 250 420 480 [500] 1 9(c)(ii) Correct curve 3 B2 for their 6 points correctly plotted and increasing or B1 for 4 or 5 of their points correctly plotted and increasing M1 for increasing curve through their points 9(c)(iii) 150 to 170 2 M1 for attempt to read y from using x = 35 FT their curve only if it is increasing 10(a) π × 72 M1 153.9… A1 10(b) 13[.0] 2 B1 for 2000 10(c) 12.6 or 12.59… 3 M2 for [ ] 1 3 2000 their or M1 for x 3 soi 11(a) 3.72 or 3.717 to 3.718 2 M1 for 3.282 + 1.752 11(b) 28.1 or 28.06 to 28.15 2 M1 for tan[ ] 1.75 3.28 or for sin[ ] ( ) 1.75 their a or for cos[ ] ( ) 3.28 their a 12(a) (0, 2) 1 12(b) Correct sketch 2 B1 for correct shape or for vertex in correct quadrant 12(c) –1 or 3 2 B1 for each