Cambridge IGCSE Mathematics (9-1) (UK only) 0626 — 2018 Oct/Nov Paper 4 · Variant 0

* 2 8 4 9 9 5 2 5 6 6 * This document consists of 16 printed pages. DC (LK/SW) 153471/2 © UCLES 2018 [Turn over MATHEMATICS 0626/04 Paper 4 (Extended) October/November 2018 1 hour 30 minutes 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 or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. CALCULATORS MAY NOT BE USED IN THIS PAPER. 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. 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 84. This syllabus is regulated for use in England as a Cambridge International Level 1/Level 2 (9–1) Certificate. Cambridge International Examinations Cambridge International General Certificate of Secondary Education (9–1)

2 0626/04/O/N/18 © UCLES 2018 1 The probability that Marc drives to work on any day is 3 2 . The probability that it rains on any day is 5 1 . (a) Complete the tree diagram. 2 3 … … … … … Drives to work Does not drive to work Rains Does not rain Rains Does not rain [2] (b) Work out the probability that one day Marc drives to work and it does not rain. … [2]

3 0626/04/O/N/18 © UCLES 2018 [Turn over 2 Expand and simplify. ( ) ( ) r r 4 2 3 3 1 5 + + - … [2] 3 By rounding each number correct to 1 significant figure, estimate the value of . . . . 32 644 4 777 43 01 9 94 - + . … [2]

4 0626/04/O/N/18 © UCLES 2018 4 5 cm 6 cm NOT TO SCALE b cm The area of this trapezium is 39 cm2. Find the value of b. b = … [3] 5 The width, w cm, of an oven is 60 cm correct to the nearest centimetre. (a) Complete this statement about the value of w. … w 1 G … [2] (b) There is a gap between two cupboards in a kitchen. The width of the gap is 90 cm, correct to the nearest centimetre. The oven is placed in the gap. Work out the upper bound of the width of the remaining space. … cm [2]

5 0626/04/O/N/18 © UCLES 2018 [Turn over 6 Work out 64 2 3 ` j . … [2] 7 The interior angle of a regular polygon is 150°. Show that the polygon has 12 sides. [2]

6 0626/04/O/N/18 © UCLES 2018 8 (a) Solve ( )x 5 7 55 - = . x = … [3] (b) Rearrange the formula L r r = to make r the subject. r = … [2] 9 A travel company asked 60 people where they went on holiday last year. • 30 people went on holiday in the UK • 11 people went on holiday both in the UK and abroad • 6 people did not go on holiday K = {people who went on holiday in the UK} A = {people who went on holiday abroad} (a) Complete the Venn diagram to show this information. 11 K A [2] (b) Find ( ) n A K , . … [1]

7 0626/04/O/N/18 © UCLES 2018 [Turn over 10 Work out the magnitude of the vector 6 8 - e o. … [2] 11 (a) (i) Solve the inequality x 4 12 40 1 + . … [2] (ii) Show your solution to part (a)(i) on this number line. 0 1 2 3 4 5 6 7 8 9 10 x [1] (b) Write down all the integers that satisfy this inequality. x 2 3 1 G - … [2] 12 Simplify ( ) x 25 10 2 3 . … [2]

8 0626/04/O/N/18 © UCLES 2018 13 The surface area of a cube is 54 cm2. Find the volume of this cube. … cm3 [3] 14 NOT TO SCALE This shape is made from four straight edges and four arcs. Each straight edge has length 3 cm. Each arc is a quarter of the circumference of a circle of radius 5 cm. Find the perimeter of this shape. Give your answer in terms of r. … cm [3]

9 0626/04/O/N/18 © UCLES 2018 [Turn over 15 116° D C O NOT TO SCALE A B m A, B, C and D are points on a circle, centre O. Show that angle ° m 128 = . Give a reason for each step of your working. [3] 16 You are given that w is a 2-digit number and that w 2 # is an integer that is less than 10. Find the two possible values of w. w = … or w = … [3]

10 0626/04/O/N/18 © UCLES 2018 17 This table shows the distribution of marks in a literacy test taken by 60 students. Mark (m) Frequency m 40 50 1 G 8 m 0 0 5 6 1 G 12 m 0 0 6 7 1 G 14 m 0 0 7 8 1 G 12 m 0 0 8 9 1 G 9 m 0 0 9 10 1 G 5 (a) Draw a cumulative frequency diagram to represent this information. 40 0 10 20 30 40 50 60 50 60 70 Mark Cumulative frequency 80 90 100 m [4] (b) Three-quarters of the students pass the test. Use your diagram to find an estimate for the pass mark of the test. … [2]

11 0626/04/O/N/18 © UCLES 2018 [Turn over 18 –2 2 4 6 1 3 5 –2 0 –4 –6 –8 2 4 6 –1 –3 y x The graph of y x x 3 4 2 = - - is shown on the grid. By drawing a suitable straight line on the grid, solve the equation x x 5 0 2 - - = . … [3]

12 0626/04/O/N/18 © UCLES 2018 19 (a) ( ) f x x 5 3 = - Find and simplify an expression for ff(x). … [2] (b) A function g(x) is defined as self-inverse if ( ) ( ) g g x x 1 = - . ( ) h x x 2 = - Show that h(x) is self-inverse. [2] 20 Express x x 8 7 2 - - in the form ( ) x p q 2 + + where p and q are integers. … [2]

13 0626/04/O/N/18 © UCLES 2018 [Turn over 21 Given that x x x 3 2 4 3 - - + = , show that x x 11 28 0 2 - + = . [3] 22 (a) Write down the exact value of sin 60°. … [1] (b) 60° x 8 cm 6 cm NOT TO SCALE Find the exact value of sin x. Write your answer in the form a b 3 where a and b are integers. … [3]

14 0626/04/O/N/18 © UCLES 2018 23 (a) Given that y x x x 2 3 12 3 2 = + - , find d d x y. d d x y = … [2] (b) Find the co-ordinates of the two turning points of the curve y x x x 2 3 12 3 2 = + - . ( … , … ) and ( … , … ) [4]

15 0626/04/O/N/18 © UCLES 2018 [Turn over 24 In this question all lengths are in centimetres. NOT TO SCALE 2 1 1 7 This shape is made from two rectangles. Show that the fraction of the whole shape that is shaded is 3 2 7 4 - . [5] Question 25 is printed on the next page.

16 0626/04/O/N/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. 25 Solve cosx 2 1 0 - = for ° x 3 0 60° G G . … [3]