Cambridge IGCSE Mathematics - International 0607 — 2018 May/June Paper 3 · Variant 1

* 6 8 4 7 1 4 8 8 2 5 * This document consists of 15 printed pages and 1 blank page. DC (ST/SW) 153516/2 © UCLES 2018 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) May/June 2018 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/18 © UCLES 2018 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/18 © UCLES 2018 [Turn over Answer all the questions. 1 (a) Work out. (i) . . 16 4 23 8 - … [1] (ii) . . 5 2 3 4 1 # - … [1] (b) (i) Work out . 14 2 . … [1] (ii) Write 64% as a fraction in its lowest terms. … [2] (c) Write the following in order of size, starting with the smallest. 9 5 0.55 55.5% … 1 … 1 … [1] smallest (d) (i) Write 2076 in words. … [1] (ii) Write two million, five hundred and fifty thousand and two as a number. … [1]

4 0607/31/M/J/18 © UCLES 2018 2 (a) A pack of 200 cards is 80 mm thick. Find the thickness of 1 card. …mm [1] (b) Write 358.297 (i) correct to 1 decimal place, … [1] (ii) correct to 3 significant figures, … [1] (iii) correct to the nearest 10. … [1] (c) Work out 59% of $348. $ … [2] (d) Divide 630 in the ratio 8 : 13. … : … [2]

5 0607/31/M/J/18 © UCLES 2018 [Turn over 3 Food Number of calories 1 bread roll 78 1 bagel 69 1 tomato 3 1 slice of chicken 60 1 slice of cheese 69 1 lettuce leaf 1 1 apple 53 (a) For lunch, Clint has 1 bread roll, 1 lettuce leaf, 1 tomato, 2 slices of chicken and 1 apple. Work out the total number of calories in Clint’s lunch. … [2] (b) Work out your answer to part (a) as a percentage of 2500. …% [1] (c) A bagel costs $0.65 . Find the greatest number of these bagels that Clint can buy with $10. How much change does he receive? … bagels change = $ … [3]

6 0607/31/M/J/18 © UCLES 2018 4 (a) Find the lowest common multiple (LCM) of 7 and 8. … [2] (b) Find the highest common factor (HCF) of 18 and 48. … [2] (c) Jovana invested some money at a rate of 3% per year simple interest. At the end of 4 years the interest is $78. Work out the amount that she invested. $ … [3] (d) Isabelle invests $800 at a rate of 3.2% per year compound interest. Work out the value of the investment at the end of 2 years. $ … [3] (e) Change 8 kilometres per hour to metres per minute. … metres per minute [2]

7 0607/31/M/J/18 © UCLES 2018 [Turn over 5 Merel counts the number of three-letter words on every page of a book. Her results are shown in the table. Number of three-letter words on a page 5 7 8 12 13 16 Number of pages (frequency) 10 16 15 13 9 6 (a) Find the total number of pages in the book. … [1] (b) Write down the mode. … [1] (c) Find the median. … [1] (d) Find the mean. … [2] (e) Use the information in the table to complete the bar chart. 5 7 8 12 13 16 0 2 4 6 8 10 12 14 16 Number of three-letter words on a page Number of pages [2]

8 0607/31/M/J/18 © UCLES 2018 6 P M O N R 48° NOT TO SCALE S P, R and S lie on a circle, centre O. MPN is a tangent to the circle at P and angle RPN = 48°. (a) Find the size of (i) angle OPR, Angle OPR = … [1] (ii) angle ORP, Angle ORP = … [1] (iii) angle POR, Angle POR = … [1] (iv) angle SOR, Angle SOR = … [1] (v) angle SRP, Angle SRP = … [1] (vi) angle OSR. Angle OSR = … [2]

9 0607/31/M/J/18 © UCLES 2018 [Turn over (b) OP = 3 cm. Find (i) the circumference of the circle, … cm [2] (ii) the length of the minor arc SR, … cm [2] (iii) the area of the circle, … cm2 [2] (iv) the area of the minor sector SOR. … cm2 [2]

10 0607/31/M/J/18 © UCLES 2018 7 (a) Complete the mathematical name of each of these angles. … angle … angle … angle [3] (b) NOT TO SCALE 110° 160° x° 95° 110° 135° The diagram shows a hexagon. Find the value of x. x = … [3]

11 0607/31/M/J/18 © UCLES 2018 [Turn over 8 (a) On any day, the probability that the sun will shine is 0.64 . If the sun is shining, the probability that Mees goes to the beach is 0.82 . If the sun is not shining, the probability that Mees goes to the beach is 0.15 . (i) Complete the tree diagram. sun is shining sun is not shining … … 0.64 … … … goes to the beach does not go to the beach goes to the beach does not go to the beach [3] (ii) Find the probability that the sun is shining and Mees does not go to the beach. … [2] (b) On any day in June, the probability that it does not rain is 0.7 . There are 30 days in June. Find the number of days that it is expected to rain in June. … [2]

12 0607/31/M/J/18 © UCLES 2018 9 A scientist measures the temperature at seven different heights above sea level. The table shows her results. Height above sea level (h metres) 0 500 1000 1500 2500 3000 5000 Temperature (t °C) 15 11 8.5 5 -1 -5 -17 (a) Complete the scatter diagram. The first three points have been plotted for you. 0 –2 –4 –6 –8 –10 –12 –14 –16 –18 1000 2000 3000 4000 5000 h t 2 4 6 8 10 12 14 16 [2]

13 0607/31/M/J/18 © UCLES 2018 [Turn over (b) What type of correlation is shown in the scatter diagram? … [1] (c) Find (i) the mean height, … m [1] (ii) the mean temperature. …°C [1] (d) (i) Plot the mean point on the scatter diagram. [1] (ii) On the scatter diagram, draw a line of best fit. [2] (iii) Use your line of best fit to estimate the temperature at a height of 4000 m. …°C [1]

14 0607/31/M/J/18 © UCLES 2018 10 (a) (i) Solve. x 2 3 15 1 - … [2] (ii) Show your answer to part (a)(i) on this number line. 10 9 8 7 6 5 4 3 2 1 0 –1 –2 x [1] (b) Solve. x x 3 5 4 3 + = - x = … [2] (c) Expand the brackets and simplify. ( )( ) x x 2 1 3 - + … [2] (d) Simplify fully. (i) r r 2 3 # … [1] (ii) r r 2 8 … [1]

15 0607/31/M/J/18 © UCLES 2018 11 –10 10 0 6 x y ( ) x x x 2 12 10 f 2 =- + - (a) On the diagram, sketch the graph of ( ) y x f = for x 0 6 G G . [2] (b) Find the co-ordinates of the points where the graph crosses the x-axis. ( … , … ) and ( … , … ) [2] (c) Find the co-ordinates of the local maximum. ( … , … ) [1] (d) (i) On the same diagram, draw the line y x 2 = - . [2] (ii) Solve. x x x 2 12 10 2 2 - + - = - x = … or x = … [2]

16 0607/31/M/J/18 © UCLES 2018 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 7 printed pages. © UCLES 2018 [Turn over Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) May/June 2018 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 2018 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 2018 © UCLES 2018 Page 2 of 7 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 2018 © UCLES 2018 Page 3 of 7 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 2018 © UCLES 2018 Page 4 of 7 Question Answer Marks Partial Marks 1(a)(i) 7.4 − 1 1(a)(ii) 7.1 − 1 1(b)(i) 3.77 or 3.768… 1 1(b)(ii) 16 25 2 M1 for a fraction not in its lowest terms 1(c) 5 0.55, 55.5%, 9 1 1(d)(i) Two thousand and seventy six 1 1(d)(ii) 2 550 002 1 2(a) 0.4 1 2(b)(i) 358.3 1 2(b)(ii) 358 cao 1 2(b)(iii) 360 1 2(c) 205.32 2 M1 for 59 348 100 × soi 205 2(d) 240 : 390 2 M1 for 630 soi 30 8 13 + 3(a) 255 2 M1 for 78 + 1 + 3 + 2 × 60 + 53 If 0 scored, SC1 for 195 as final answer 3(b) 10.2 1 FT their (a) 3(c) 15 [bagels] 2 10 for oe 0.65 M1 0.25 1 FT 10 – their 15 × 0.65 4(a) 56 2 M1 for a correct common multiple 4(b) 6 2 M1 for any correct common factor, except 1 4(c) 650 3 M2 for 3 4 78 100 p× × = or better or M1 for 78 3 4 or 4 p× ×

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2018 © UCLES 2018 Page 5 of 7 Question Answer Marks Partial Marks 4(d) 852.02 3 M2 for 2 3.2 800 1 100   +     or M1 for 3.2 800 100 × 4(e) 133 or 133.3… 2 M1 for 8 × 1000 or 1 60 5(a) 69 1 5(b) 7 1 5(c) 8 1 5(d) 9.43 or 9.434 to 9.435 2 M1 for dividing by their (a) 5(e) Correct bars drawn 2 B1 for 2 correct bars 6(a)(i) 42 1 6(a)(ii) 42 1 FT from (i) 6(a)(iii) 96 1 FT from (i) and (ii) 6(a)(iv) 84 1 FT from (iii) 6(a)(v) 90 1 6(a)(vi) 48 2 M1 for 180 2 their − (iv) or 180 – (their (i) + their (v)) 6(b)(i) 18.8 or 18.84 to 18.85 2 M1 for 2 3 × π× 6(b)(ii) 4.4[0] or 4.398 to 4.399 2 for 360 their their × (a)(iv) M1 (b)(i) 6(b)(iii) 28.3 or 28.27 to 28.28 2 for 3 3 π× × M1 6(b)(iv) 6.6[0] or 6.596 to 6.603… 2 for 360 their their × (a)(iv) M1 (b)(iii) 7(a) right reflex acute 3 B1 for each 7(b) 110 3 M1 for 110 + 135 + 110 + 95 + 160 M1 for 180 × 4 - their (110 + 135 + 110 + 95 + 160) 8(a)(i) Branch [0.64] and 0.36 Branch 0.82 and 0.18 Branch 0.15 and 0.85 3 B1 for each pair

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2018 © UCLES 2018 Page 6 of 7 Question Answer Marks Partial Marks 8(a)(ii) [0].1152 2 M1 for 0.64 × their 0.18 A1FT for 0.64 × their 0.18 correctly evaluated 8(b) 9 2 M1 for 1 – 0.7 soi 0.3 or × 30 9(a) Points plotted correctly 2 B1 for 2 or 3 points correctly plotted 9(b) negative 1 9(c)(i) 1930 or 1928 to 1929 1 9(c)(ii) 2.36 or 2.357... 1 9(d)(i) Point plotted correctly 1 FT from (c)(i) and (c)(ii) 9(d)(ii) Ruled line drawn correctly 2 B1 for ruled line through their mean or for ruled line with negative gradient 9(d)(iii) –11.5 to –10.5 1 FT from their ruled line with negative gradient 10(a)(i) x < 9 2 M1 for 2x < 18 If 0 scored, SC1 for x = 9 as final answer 10(a)(ii) Open circle at 9 and arrow in correct direction 1 FT their inequality from (a)(i) 10(b) 8 2 M1 for correct first step 10(c) 2 2 5 3 x x + − 2 [ ] [ ] 2 for any 3 of: 2 , 6 , 3 or x x x − − B1 10(d)(i) 5r 1 10(d)(ii) 6r 1 11(a) Correct graph 2 B1 for maximum in first quadrant B1 for axes intercepts approximately correct 11(b) (1, 0) (5, 0) 2 B1 for each 11(c) (3, 8) 1 11(d)(i) Correct line 2 B1 for y intercept at approximately –2 or B1 for correct gradient by eye

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2018 © UCLES 2018 Page 7 of 7 Question Answer Marks Partial Marks 11(d)(ii) 4.64 or 4.637… 0.863 or 0.8625… 2 B1 for each if 0 scored, SC1 for 4.6 and 0.86