Cambridge IGCSE Mathematics (9-1) (UK only) 0626 — 2017 Oct/Nov Paper 2 · Variant 1

This document consists of 14 printed pages and 2 blank pages. DC (NF/SG) 133930/2 © UCLES 2017 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education (9–1) * 7 6 5 9 6 8 8 1 0 4 * MATHEMATICS 0626/02 Paper 2 (Extended) October/November 2017 1 hour Candidates answer on the Question Paper. Additional Materials: Geometrical instruments Tracing paper (optional) 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. You may use an HB pencil for any diagrams and graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. Electronic calculators should be used. If working is required for any question it must be shown below that question. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 60. This syllabus is regulated for use in England as a Cambridge International Level 1/Level 2 (9–1) Certificate.

2 0626/02/O/N/17 © UCLES 2017 1 3 cm 5 cm NOT TO SCALE Work out the volume of this cylinder. … cm3 [2] 2 (a) Solve the inequality. x 7 2 19 G - … [2] (b) Represent your solution on the number line. –5 –4 –3 –2 –1 0 1 2 3 5 4 x [1]

3 0626/02/O/N/17 © UCLES 2017 [Turn over 3 Solve the equation. 7(8 − 2x) = 35 x = … [3] 4 Jess carries out a survey to find out if Year 11 students in her school want to have a summer ball. There are 360 students in Year 11. She selects a systematic sample of 20 of these students to survey. Explain clearly how she selects these 20 students. … … … [2]

4 0626/02/O/N/17 © UCLES 2017 5 10.1 m 15.2 m 4.9 m 10.1 m 10.1 m NOT TO SCALE The diagram shows a netball court. It consists of three identical rectangles with two semi-circles. Each rectangle is 15.2 m long and 10.1 m wide. Each semi-circle has radius 4.9 m. The Wing Attack player can move anywhere in the shaded area. What percentage of the whole court can the Wing Attack player move in? … % [4]

5 0626/02/O/N/17 © UCLES 2017 [Turn over 6 Simplify. 7x2 y3 × 2x5 y … [2] 7 Make c the subject of this formula. S = cd + 3dh … [2]

6 0626/02/O/N/17 © UCLES 2017 8 7 22 and 3 7 1 5 3 + c m can both be used as approximations for π. The actual value of π is 3.141 59 correct to 5 decimal places. Show that 3 7 1 5 3 + c m is the better approximation for π. [3] 9 A purple case contains x red cartons. Each red carton contains y green boxes. Each green box contains z counters. x y z 1 2 2 2 Altogether there are 455 counters in the purple case. Find the values of x, y and z. x = … , y = … , z = … [3]

7 0626/02/O/N/17 © UCLES 2017 [Turn over 10 Harry bought his car a year ago. The value of his car has fallen by 12% since he bought it. The car is now worth £14 520. What was the price of his car when he bought it? £ … [3] 11 This is a sector of a circle, radius 6 cm. 35° NOT TO SCALE Calculate the perimeter of this sector. … cm [3]

8 0626/02/O/N/17 © UCLES 2017 12 The table shows information about the salaries of the employees in a company. Salary Greatest £86 000 Least £15 000 Median £32 000 Lower Quartile £24 000 Upper Quartile £46 000 (a) Complete this box plot. 0 20 40 60 Salary (£ thousands) 80 100 [2] (b) Complete the following. (i) The inter-quartile range is £ … . [1] (ii) Three quarters of the employees earn at least £ … . [1]

9 0626/02/O/N/17 © UCLES 2017 [Turn over 13 x x 4 3 f 7 | - x x g 2 7 | (a) Find f −1(x). f −1(x) = … [2] (b) Archie is asked to find fg(x). (i) This is his solution. f(x) = 4x − 3 So fg(x) = (4x − 3)2 Archie has made an error. Explain his error. … … [1] (ii) Find fg(x). fg(x) = … [1]

10 0626/02/O/N/17 © UCLES 2017 14 y x y = 2x – 3 A (4, 5) O NOT TO SCALE The line y = 2x − 3 passes through the point A with coordinates (4, 5). Find the equation of the straight line that passes through A and is perpendicular to y = 2x − 3. … [3]

11 0626/02/O/N/17 © UCLES 2017 [Turn over 15 A C O B NOT TO SCALE An equilateral triangle, ABC, is inscribed in a circle with centre O and radius 5 cm. (a) Work out the length of the line BC. BC = … cm [4] (b) Work out the area of triangle ABC. … cm2 [2]

12 0626/02/O/N/17 © UCLES 2017 16 (a) Show that x2 − 5x + 3 = 0 can be written as x x 5 3 = - . [2] (b) Find an approximate solution, correct to 2 decimal places, to x2 − 5x + 3 = 0. Use the iteration formula x x 5 3 n n 1 = - + with x1 = 4. Show the result of each iteration. x = … [3]

13 0626/02/O/N/17 © UCLES 2017 [Turn over 17 (a) Show that x2 − 4x + 7 = (x − 2)2 + 3. [1] (b) Explain why the equation x2 − 4x + 7 = 0 has no solutions. … … [1] (c) Write down the co-ordinates of the turning point of y = x2 − 4x + 7. ( … , … ) [1] (d) Sketch the graph of y = x2 − 4x + 7 on the grid. y x O [2]

14 0626/02/O/N/17 © UCLES 2017 18 Jackie is a javelin thrower. She must throw over 55 metres in at least one of 3 throws to qualify for an athletics event. The probability of her throwing over 55 metres in any one throw is p. The probability of her not qualifying for the athletics event is 343 125 . Find the value of p. p = … [3]

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16 0626/02/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 syllabus is regulated for use in England as a Cambridge International Level 1/Level 2 (9–1) Certificate. This document consists of 5 printed pages. © UCLES 2017 [Turn over Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education (9–1) MATHEMATICS 0626/02 Paper 2 October/November 2017 MARK SCHEME Maximum Mark: 60 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.

0626/02 Cambridge IGCSE (9–1) – 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

0626/02 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 3 of 5 Question Answer Marks Partial Marks 1 141 or 141.3 to 141.4 2 M1 for π × 32 × 5 soi 2(a) x ⩽ 3 final answer 2 M1 for 7x ≤ 9 + 2 M1 for x ≤b a after ax ≤ b seen max 1 mark if answer incorrect If 0 scored, SC1 for answer 3 or x 3 with any incorrect equality or inequality symbol or answer 7 × 3 – 2 ≤ 19 2(b) 1 FT their inequality in (a) 3 1.5 oe 3 M1 for 8 – 2x = 5 or 56 – 14x = 35 M1 for collecting their like terms M1 for x = b a after ax = b seen max 2 marks if answer incorrect 4 Number (order) each student from 1 to 360 Choose every 18th student 2 B1 for incomplete explanation or 18 seen If 0 scored, SC1 for details of how to select a random sample 5 58.4 to 58.5 4 M1 for π × 4.92 [÷ 2] M1 for 2 × 10.1 × 15.2 or 3 × 10.1 × 15.2 M1 for their shaded area ÷ their total area 6 14x7y4 final answer 2 B1 for x7 or y4 seen in answer 7 3 S dh c d − = final answer or 3 S c h d = − final answer 2 M1 for 3 S dh cd − = or 3 S c h d = + or for 3 S dh d − or 3 S h d − 8 Correct comparison of the correct values with 3.14159[…] 22 7 – π = 0.00126[...] or 0.00127 and 7 3 1 3 5 ( ) + – π = 0.00003[…] 3 B2 for 0.00003[…] and 0.00126[…] oe seen or B1 for one of the values 0.00003[…] or 0.00126[…] oe or for 22 7 = 3.14285[…] or 3.14286 and 7 3 1 3 5 ( ) + = 3.14162[…] seen 9 x = 13 y = 7 z = 5 3 B2 for correct figures in wrong order or two correct answers or 5 × 7 × 13 seen or B1 for 5, 7 or 13 seen on answer line or xyz [= 455] seen or M1 for attempt to divide 455 by an integer n > 2 3

0626/02 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 4 of 5 Question Answer Marks Partial Marks 10 16500 3 M2 for 14520 ÷ (1 – 0.12) or 165 (is 1%) oe seen or B1 for 88[%] oe seen 11 15.7 or 15.66 to 15.67 3 M2 for 35 × 12 × 6 6 360 π + + oe or M1 for 35 × 12 × 360 π oe 12(a) Correct Box Plot 2 M1 for median and quartiles plotted correctly with an appropriate vertical line or box with 2 values correct 12(b)(i) 22000 1 12(b)(ii) 24000 1 13(a) 3 4 x + final answer oe 2 M1 for 3 4 y x + = or 3 4 4 y x = − or 4 3 x y = − If 0 scored, SC1 for 3 4 y + 13(b)(i) Valid explanation 1 e.g. He has found gf(x) 13(b)(ii) 4x2 – 3 1 14 1 7 2 y x = − + oe 3 B1 for gradient = 1 2 − oe M1 for substituting x = 4 and y = 5 in their linear equation oe 15(a) 8.66 or 8.660[…] 4 M3 for 2 2 5 5 2 5 5 cos120 + −× × × or 5 sin120 sin30 × or M2 for 2 2 5 5 2 5 5 cos120 + − × × × or 5 sin120 sin30 BC = oe or M1 for identifying angle OBC = 30 or angle BOC = 120 oe Alternative Method If X is such that OX is perpendicular to BC M3 for 2 × 5cos30 or 2 × 5sin60 or M2 for [BX] = 5cos30 or 5sin60 or M1 for identifying angle OBC = 30 or angle BOX = 60 oe 15(b) 32.5 or 32.47 to 32.48 2 M1 for 0.5 × theirBC × theirBC × sin60 or 0.5 × 5 × 5 × sin120 × 3 or 0.5 × theirBC × (5 + 5sin30) or 0.5 × theirBC × 2.5 × 3

0626/02 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 5 of 5 Question Answer Marks Partial Marks 16(a) Correct completion to 5 3 x x = − (Answer Given) 2 M1 for correct first step x2 = 5x – 3 or 2 5 3 0 x x x − + = oe 16(b) Iteration leading to 4.30 3 B1 for x2 = 4.25 M1 for x3 = 4.294[…] and x4 = 4.301[...] using their x2 and x3 17(a) x2 – 4x + 4 + 3 or (x – 2)2 – 4 + 7 1 Answer Given 17(b) Valid Explanation 1 e.g. As (x – 2)2 ≥ 0, (x – 2)2 + 3 > 0 so (x – 2)2 + 3 cannot equal 0. oe e.g. b2 – 4ac = 16 – 28 = –12 < 0 17(c) (2, 3) 1 17(d) Correct sketch of quadratic with minimum at (2, 3) indicated 2 FT from their (c), if y co-ordinate > 0 B1 for any symmetrical U-shaped quadratic 18 2 7 3 M1 for (1 – p)3 = 125 343 soi M1 for 1 3 125 343 ( ) soi