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

* 4 8 4 2 4 1 2 9 0 3 * This document consists of 15 printed pages and 1 blank page. DC (LK/SG) 153467/1 © UCLES 2018 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education (9–1) MATHEMATICS 0626/04 Paper 4 (Extended) May/June 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 and 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.

2 0626/04/M/J/18 © UCLES 2018 1 (a) Write .6 25 10 3 # - as an ordinary number. … [1] (b) Work out . ( ) 0 03 2 106 # # . Give your answer in standard form. … [2] 2 (a) Write 231 as a product of prime factors. … [2] (b) Abby and Salma are racing in go-karts. Abby takes 75 seconds to complete each lap. Salma takes 100 seconds to complete each lap. At the start of the race, they line up together on the start line. How many minutes later do they next cross the start line together? … minutes [2]

3 0626/04/M/J/18 © UCLES 2018 [Turn over 3 Work out 5 3 1 1 4 3 # . Give your answer as a mixed number in its lowest terms. … [3] 4 The exterior angle of a regular polygon is 12°. The polygon has n sides. Find the value of n. n = … [2] 5 There are 300 marbles in a bag. Luna carries out an experiment to estimate how many of the marbles are red. She takes a marble out of the bag at random, records its colour and replaces it in the bag. Luna does this 50 times and she records a red marble 11 times. Estimate how many of the marbles in the bag are red. … [2]

4 0626/04/M/J/18 © UCLES 2018 6 Solve. (a) ( ) x x 7 2 3 6 1 - - = + x = … [3] (b) x x 4 0 2 - = x = … or x = … [2] 7 (a) Find the value of each of the following. (i) 100 … [1] (ii) 642 1 … [1] (iii) 12 12 5 3 ' … [2] (b) Harry writes: 1 x x 1 – = so 2 x x –2 = Is Harry correct? Explain how you know. … … [1]

5 0626/04/M/J/18 © UCLES 2018 [Turn over 8 (a) The nth term of a sequence is given by n 7 5 - . Which term in the sequence has the value –88? … [2] (b) Find an expression for the nth term of the following sequence. 3 24 81 192 375 … … [2] 9 y x 1 1 –1 –1 –2 –3 –4 –2 –3 –4 2 3 4 2 0 The diagram shows the graph of a straight line. Find the equation of this straight line. Give your answer in the form y mx c = + . y = … [3]

6 0626/04/M/J/18 © UCLES 2018 10 Use a straight edge and compasses only for this question. Leave in all your construction arcs. D A B C Construct and shade the region inside the quadrilateral ABCD which is • nearer to AB than AD and • nearer to C than D. [5] 11 By rounding each number correct to 1 significant figure, estimate the value of . . . 0 016 19 01 1 95 - . … [2]

7 0626/04/M/J/18 © UCLES 2018 [Turn over 12 (a) Show that .0 31o o can be written as 99 31 . [2] (b) Write 80 45 + in the form a 5, where a is an integer. … [2] 13 (a) Expand and simplify. ( )( ) x x 2 1 5 - - … [2] (b) Write as a single fraction in its simplest form. x x 3 2 5 1 7 - - + … [3]

8 0626/04/M/J/18 © UCLES 2018 14 A B y x 0 1 2 3 4 5 –6 –5 –4 –3 –2 –1 6 1 2 3 4 5 6 7 –1 –2 –3 –4 –5 –6 –7 (a) Describe fully the single transformation that maps triangle A onto triangle B. … … [3] (b) On the grid, draw the image of triangle A after the transformation represented by the matrix 1 0 0 1 - e o. [3]

9 0626/04/M/J/18 © UCLES 2018 [Turn over 15 The table shows information about the weekly wages earned by each of 100 part-time workers. Weekly wage (£w) Frequency w 20 50 1 G 15 w 0 0 5 6 1 G 35 w 0 6 75 1 G 30 w 75 100 1 G 20 On the grid, draw a histogram to represent this information. Frequency density 20 0 30 40 50 60 Weekly wage (£) 70 80 90 100 w [4]

10 0626/04/M/J/18 © UCLES 2018 16 B C D F A E NOT TO SCALE BC = EF and BCFE is a straight line. AB is parallel to ED and AC is parallel to FD. Show that triangle ABC is congruent to triangle DEF. Give reasons to support your statements. Statement Reason … … … … … … … … … … … … … … [3]

11 0626/04/M/J/18 © UCLES 2018 [Turn over 17 A circle has equation x y 25 2 2 + = . The points A(4, 3) and B(p, q) are the end points of a diameter of the circle. The circle has radius r. (a) Find the value of p, the value of q and the value of r. p = … q = … r = … [3] (b) Shania says: The line x y 4 3 25 + = is a tangent to the circle x y 25 2 2 + = because 4 3 3 4 1 #- =- and they meet at (4, 3). Show that Shania’s reasoning is correct. [3]

12 0626/04/M/J/18 © UCLES 2018 18 (a) y is inversely proportional to x. y = 10 when x = 4. (i) Find an equation connecting y and x. … [2] (ii) Find the value of x when y 8 5 = . x = … [2] (b) r is directly proportional to the cube root of V. Complete the statement. When r is multiplied by 2, V is multiplied by … [2]

13 0626/04/M/J/18 © UCLES 2018 [Turn over 19 Fifteen people go on an activity holiday. Of these 15 people: • 9 go canoeing • 4 go abseiling • 5 do not go canoeing or abseiling A person is chosen at random from those who go canoeing or abseiling or both. Find the probability that this person goes canoeing or abseiling but does not do both activities. You may use this diagram to help you. … [4]

14 0626/04/M/J/18 © UCLES 2018 20 A B C O D NOT TO SCALE In the diagram, • OBC is a straight line • a OA 2 = and b OB 3 = • OB : BC = 3 : 2 • AD AB 5 3 = . Find an expression, in terms of a and b, for DC. DC = … [4]

15 0626/04/M/J/18 © UCLES 2018 21 (a) On the grid, sketch the graph of cos y x = for ° ° x 0 360 G G . 90° 0 180° 270° 360° x –1 1 y [2] (b) Find all the solutions of the equation cosx 2 1 = for ° ° x 0 360 G G . … [2]

16 0626/04/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