Cambridge IGCSE Mathematics - International 0607 — 2018 May/June Paper 3 · Variant 2

* 4 0 8 0 5 2 4 4 3 7 * This document consists of 16 printed pages. DC (ST/SW) 153517/2 © UCLES 2018 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 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 0607/32/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 0607/32/M/J/18 © UCLES 2018 [Turn over Answer all the questions. 1 (a) Complete the statement. 6 weeks = …days [1] (b) Write in figures the number fifteen thousand and twenty seven. … [1] (c) Write (i) 144.1 correct to the nearest 10, … [1] (ii) 5.5349 correct to 2 decimal places, … [1] (iii) 50 617 correct to 2 significant figures. … [1] (d) Write 0.7 (i) as a fraction, … [1] (ii) as a percentage. …% [1] (e) Find the value of 0.73. … [1]

4 0607/32/M/J/18 © UCLES 2018 2 Tam recorded the number of hours of homework he did each night for 25 nights. His results, in hours, are shown below. 4 1 4 3 2 3 4 2 1 1 3 2 1 2 1 1 3 5 4 1 3 3 1 3 4 (a) Complete the frequency table. Number of hours Number of nights 1 2 3 4 5 [2] (b) Which number of hours is the mode? … hours [1] (c) Draw a bar chart to show this information. 0 1 2 3 Number of hours Number of nights 4 5 1 2 3 4 5 6 7 8 9 10 [2]

5 0607/32/M/J/18 © UCLES 2018 [Turn over (d) On one of the nights, Tam did mathematics homework, English homework and history homework. The pie chart shows the time he spent on each subject. 80° 130° Mathematics NOT TO SCALE History English (i) Work out the fraction of the total time he spent on mathematics homework. Give your answer in its simplest form. … [2] (ii) Tam spent 3 hours altogether on his homework that night. Work out the time, in minutes, Tam spent on English homework. …min [3]

6 0607/32/M/J/18 © UCLES 2018 3 –1 1 2 3 4 1 2 3 4 5 6 7 –2 –3 –1 0 –2 –3 x y p° T R (a) Write down the co-ordinates of (i) T, ( … , … ) [1] (ii) R. ( … , … ) [1] (b) On the grid, draw the line of symmetry of the quadrilateral. [1] (c) Measure the size of angle p. … [1]

7 0607/32/M/J/18 © UCLES 2018 [Turn over 4 In each part, give the mathematical name for the shape described. (a) A quadrilateral with each pair of opposite sides parallel. … [1] (b) A triangle with exactly two sides equal in length. … [1] (c) A polygon with 6 sides. … [1] (d) A quadrilateral with all sides of equal length but not all angles equal. … [1] (e) A solid shape with six faces. Four of the faces are identical rectangles and the other two faces are identical squares. … [1]

8 0607/32/M/J/18 © UCLES 2018 5 (a) A box contains 40 orange counters and 32 blue counters only. (i) Write the ratio orange counters : blue counters in its simplest form. … : … [2] (ii) Some of the orange counters are removed. The ratio orange counters : blue counters is now 1 : 2. Work out how many orange counters have been removed. … [2] (b) Another box contains 6 white counters, 3 black counters and 2 red counters only. (i) One of the 11 counters is chosen from the box at random. Write down the colour of the counter that is least likely to be chosen. … [1] (ii) One of the 11 counters is chosen from the box at random. Work out the probability that this counter is white. … [1] (iii) One white counter is removed from the box of 11 counters. A counter is now chosen from the box at random. Work out the probability that this counter is white. … [1]

9 0607/32/M/J/18 © UCLES 2018 [Turn over (c) A different box contains 180 counters. The counters are either yellow or green in the ratio yellow counters : green counters = 5 : 1. Work out the number of counters of each colour. yellow … green … [2] 6 John and Asif take part in a 30 km cycle race. (a) John starts his race at 10 15. He takes 1 2 1 hours to complete the race. (i) At what time does John complete the race? … [1] (ii) Work out John’s average speed, in km/h, for the 30 km race. …km/h [1] (b) Asif completes the 30 km race at a speed of 16 km/h. Work out the time, in hours and minutes, Asif takes to complete the race. … h … min [3]

10 0607/32/M/J/18 © UCLES 2018 7 (a) Find the missing terms in each of these sequences. (i) … , 9, 17, 25, … [2] (ii) … , 8, 16, … , 64 [2] (iii) 35, 25, 16, 8, … , … [2] (iv) … , x 2 4 - , x 3 9 - , x 4 14 - , … [2] (b) The nth term of another sequence is n n 2 + . Find the first three terms of this sequence. … , … , … [2] (c) Find the nth term of this sequence. 1, 5, 9, 13, ... … [2]

11 0607/32/M/J/18 © UCLES 2018 [Turn over 8 (a) (i) Rearrange this formula to make d the subject. C d r = d = … [1] (ii) A circle has a circumference of 2 metres. Work out the diameter of this circle. Give your answer in centimetres, correct to the nearest whole number. … cm [3] (b) A CD is a ring with inner radius 0.8 cm and outer radius 6 cm. 0.8 cm 6 cm NOT TO SCALE Find the area of the CD, shown shaded. … cm2 [4]

12 0607/32/M/J/18 © UCLES 2018 9 (a) Factorise completely. x 12 16 + … [2] (b) Multiply out the brackets. ( ) x x 2 3 5 - … [2] (c) Solve. ( ) x 8 2 3 48 + = x = … [3]

13 0607/32/M/J/18 © UCLES 2018 [Turn over 10 A square has side 8 cm. A small square is drawn inside this larger square so that the corners of the small square touch the sides of the larger square. NOT TO SCALE 1 cm 1 cm 1 cm 1 cm 8 cm (a) (i) Calculate the area of the shaded triangle. …cm2 [2] (ii) Using your answer to part (a)(i), calculate the area of the small square. …cm2 [2] (b) Calculate the perimeter of the small square. … cm [3]

14 0607/32/M/J/18 © UCLES 2018 11 The cumulative frequency curve shows the heights, in cm, of 200 girls. 120 0 20 40 60 80 100 120 140 160 180 200 130 140 150 160 Height (cm) Cumulative frequency 170 180 190 (a) Find the median height. … cm [1] (b) Work out the inter-quartile range of the heights. … cm [2] (c) Find the number of girls with a height of 160 cm or less. … [1]

15 0607/32/M/J/18 © UCLES 2018 [Turn over 12 (a) NOT TO SCALE x° 3.5 m 5 m The diagram shows a ladder, 5 m long, leaning against a vertical wall. The bottom of the ladder is on horizontal ground, 3.5 m from the wall. Use trigonometry to find the value of x. x = … [2] (b) A different ladder leans against the same wall. This ladder makes an angle of 49° with the ground and touches the wall 4 m above the ground. Use trigonometry to find the length of this ladder. Include a labelled sketch in your working. …m [4] Questions 13 and 14 are printed on the next page.

16 0607/32/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. 13 A painting is valued at $2400. The value of the painting increases by 5% each year. Find the value of the painting at the end of 3 years. $ … [4] 14 A curve has equation y x x 6 2 = + - . (a) Find the co-ordinates of the points where this curve crosses (i) the y-axis, ( … , … ) [1] (ii) the x-axis. ( … , … ) and ( … , … ) [2] (b) Find the co-ordinates of the local minimum. ( … , … ) [2] (c) Find the equation of the line of symmetry of the curve. … [2]

IGCSE™ is a registered trademark. This document consists of 6 printed pages. © UCLES 2018 [Turn over Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/32 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.

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2018 © UCLES 2018 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.

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2018 © UCLES 2018 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

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2018 © UCLES 2018 Page 4 of 6 Question Answer Marks Partial Marks 1(a) 42 1 1(b) 15 027 1 1(c)(i) 140 1 1(c)(ii) 5.53 1 1(c)(iii) 51 000 1 1(d)(i) 7 10 1 1(d)(ii) 70 1 1(e) 0.343 1 2(a) 8 4 7 5 1 2 B1 for 3 or 4 correct or SC1 for correct tally 2(b) 1 cao 1 2(c) Correct bar chart 2 FT their heights and equal widths B1 for 3 or 4 correct If 0 scored SC1 for their 5 correct heights and unequal widths 2(d)(i) 2 9 2 B1 for 80 360 or correct equivalent fraction 2(d)(ii) 75 3 M1 for 360 – (130 + 80) soi by 150 M1 for 150 180 360 their × 3(a)(i) (0, 2) 1 3(a)(ii) (5, –1) 1 3(b) Correct line of symmetry 1 3(c) 54 to 58 1 4(a) One of: Square, rectangle, parallelogram, rhombus 1 4(b) Isosceles 1 4(c) Hexagon 1 4(d) Rhombus 1

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2018 © UCLES 2018 Page 5 of 6 Question Answer Marks Partial Marks 4(e) Cuboid 1 5(a)(i) 5 : 4 2 B1 for 20 : 16 or 10 : 8 5(a)(ii) 24 2 B1 for answer 16 5(b)(i) red 1 5(b)(ii) 6 11 1 5(b)(iii) 5 10 oe 1 5(c) 150 30 2 M1 for 180 ÷ 6 soi 6(a)(i) 11 45 1 6(a)(ii) 20 1 6(b) 1 h 52.5 min 3 B2 for 1.875 or 112.5 or M1 for 30 ÷ 16 soi 7(a)(i) 1 , ……..….. , 33 2 B1 for 1 correct 7(a)(ii) 4 , ……. , 32 , … 2 B1 for 1 correct 7(a)(iii) ……….. , 1 , –5 2 B1 for 1 correct 7(a)(iv) x + 1 , …… , 5x – 19 2 B1 for 1 correct or for x … and 5x … or for … + 1 and … −19 7(b) 2 , 6 , 12 2 B1 for 2 correct 7(c) 4n – 3 2 B1 for 4n + c or kn – 3, k ≠ 0 8(a)(i) [d = ] c π 1 8(a)(ii) 64 3 B2 for 63.7 or better or M1 for 2[00] ÷ π soi 8(b) 111 or 111.0 to 111.1… 4 M3 for π × 62 – π × 0.82 or M1 for π × 62 or π × 0.82 and A1 for 113 or 2.01 9(a) 4(3x + 4) 2 B1 for 2(6x + 8) 9(b) 6x2 – 10x 2 B1 for 6x2 or –10x 9(c) 1 12 oe nfww 3 M1 for 16x + 24 = 48 or 2x + 3 = 6 M1 for a correct second step

0607/32 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2018 © UCLES 2018 Page 6 of 6 Question Answer Marks Partial Marks 10(a)(i) 3.5 oe 2 B1 for 7 seen 10(a)(ii) 8 × 8 – 4 × their(a)(i) M1 50 B1 10(b) 28.3 or 28.28… 3 M2 for 4× ( ) 2 2 1 7 + or 4 their × (a)(ii) or M1 for ( ) 2 2 1 7 + or their(a)(ii) 11(a) 156 to 157 1 11(b) 12 to 16 2 B1 for 147 to 149 or 161 to 163 11(c) 128 to 132 1 12(a) 45.6 or 45.57… 2 M1 for cos[=] 3.5 5 or better 12(b) 5.3[0] or 5.30... 4 B1 for diagram with 4 and 49 labelled correctly and M2 for [x =] 4 sin 49 or M1 for sin 49 = 4 x 13 2778.3[0] 4 M3 for 2400 × 3 5 1 100   +     oe or M2 for 2400 × 5 1 100   +     oe soi by 2520 or M1 for 2400 × 5 100 oe soi by 120 14(a)(i) (0, −6) 1 14(a)(ii) (−3, 0) and (2, 0) 2 B1 for one correct or for −3 and 2 seen 14(b) (−0.5, −6.25) oe 2 B1 for one part correct If 0 scored SC1 for co-ordinates reversed 14(c) x = −0.5 oe 2 FT their x co-ordinate in (b) B1 for −0.5 seen