Cambridge IGCSE Mathematics (9-1) (UK only) 0626 — 2018 Oct/Nov Paper 6 · Variant 0

This document consists of 15 printed pages and 1 blank page. DC (LEG/CGW) 153472/2 © UCLES 2018 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education (9–1) * 5 9 5 2 5 9 3 3 5 1 * MATHEMATICS 0626/06 Paper 6 (Extended) October/November 2018 2 hours 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 96. This syllabus is regulated for use in England as a Cambridge International Level 1/Level 2 (9–1) Certificate.

2 0626/06/O/N/18 © UCLES 2018 1 (a) Use a straight edge and compasses only for this question. Leave in all your construction arcs. Here is a scale drawing of a park. A D C B Nick wants to plant a tree in the park that is • closer to D than it is to C and • the same distance from DA and DC. Construct and indicate clearly the locus of points where Nick can plant the tree. [5]

3 0626/06/O/N/18 © UCLES 2018 [Turn over (b) A lawn in the park is a rectangle with length 12 m and width 7 m. Part of the lawn is removed to make a flower bed in the shape of a semicircle of radius 4.2 m. 12 m 7 m NOT TO SCALE Calculate the area of lawn remaining. … m2 [3] (c) This table shows the distribution of heights of trees in the park. Height (h cm) Frequency h 100 110 1 G 7 h 1 0 1 0 1 2 1 G 11 h 1 0 1 0 2 3 1 G 23 h 1 0 1 0 3 4 1 G 35 h 1 0 1 0 4 5 1 G x h 1 0 1 0 5 6 1 G 25 Nick uses midpoints to calculate an estimate of the mean height of these trees. His estimated mean is 136 cm. Calculate x, the number of trees in the interval h 1 0 1 0 4 5 1 G . x = … [6]

4 0626/06/O/N/18 © UCLES 2018 2 (a) In April 2016 a company was valued at £79 000 000 000. (i) Write 79 000 000 000 in standard form. … [1] (ii) In April 2016 there were .7 1 109 # people on the Earth. If the £79 000 000 000 had been shared equally between every person on the Earth, how much money would each person have received? £ … [2] (b) On average, the company earns £1400 every second. At this rate, how much will the company earn in 7 days? Give your answer in standard form, correct to 2 significant figures. £ … [3]

5 0626/06/O/N/18 © UCLES 2018 [Turn over 3 (a) Complete the table of values for y = 3x2 – x – 1. x −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 y 13 7.25 0.25 –1 –0.75 1 9 [2] (b) On the grid, draw the graph of y = 3x2 – x – 1 for x 2 2 G G - . 2 −2 1.5 −1.5 0.5 −0.5 1 −1 0 −2 −1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 y x [3] (c) Use your graph to solve the equation 3x2 – x – 1 = 0. … [2]

6 0626/06/O/N/18 © UCLES 2018 4 (a) A yacht sails 8.3 km north, then x km west and then 14.1 km directly back to its starting point. Calculate the total distance the yacht has sailed. … km [4] (b) Another yacht sails at an average speed of 14 km/h. Calculate the time it takes this yacht to sail 45 km. Give your answer in hours and minutes, correct to the nearest minute. … hours … minutes [3]

7 0626/06/O/N/18 © UCLES 2018 [Turn over (c) This speed–time graph represents the 120 seconds of motion of a boat. 60 100 Time (s) 120 0 0 6 Speed (m/s) Calculate the total distance travelled by the boat. … m [3] (d) A motor boat travels on a triangular course PQR. 16 km North NOT TO SCALE 9 km 18 km R P Q Q is 9 km due north of P. QR = 16 km and RP = 18 km. Calculate the bearing of R from Q. … [5]

8 0626/06/O/N/18 © UCLES 2018 5 (a) A straight line, L, passes through point A (−2, −8) and point B (5, 6). (i) Find the length of the line segment AB. AB = … [3] (ii) Find the equation of the line L. Give your answer in the form y = mx + c. y = … [3] (b) Q is the midpoint of the line segment PR. P is the point (−1, 3) and Q is the point (5, 1). Find the coordinates of point R. R = (… , …) [2]

9 0626/06/O/N/18 © UCLES 2018 [Turn over 6 (a) The cost, £c, of a circular pizza is directly proportional to the square of its diameter, d inches. A pizza with diameter 10 inches costs £8. (i) Find a formula for c in terms of d. c = … [2] (ii) Work out the cost of a pizza with diameter 12 inches. £ … [1] (iii) Sketch the graph of c against d. c d O [1] (b) P is inversely proportional to V. When P = 8, V = 72. Find the value of P when P = V. P = … [3]

10 0626/06/O/N/18 © UCLES 2018 7 (a) Harry has a bag containing 7 black counters and 3 white counters. He chooses a counter at random, notes its colour and replaces it in the bag. He then chooses a second counter at random. Calculate the probability that Harry chooses at least one white counter. … [4]

11 0626/06/O/N/18 © UCLES 2018 [Turn over (b) Arlene has two bags containing coloured counters. Bag A has 4 green counters, 6 red counters and 2 yellow counters. Bag B has 3 green counters and 3 red counters. She takes a counter at random from Bag A and places it into Bag B. She then takes a counter at random from Bag B and places it into Bag A. Find the probability that, after these two moves, Bag A has 4 green counters, 6 red counters and 2 yellow counters. … [4]

12 0626/06/O/N/18 © UCLES 2018 8 (a) Sketch the graph of x2 + y2 = 25. O y x [2] (b) (i) Solve these simultaneous equations. x2 + y2 = 25 y = 3x – 2 You must show all your working. Give your answers correct to 2 decimal places. x = … y = … x = … y = … [7] (ii) What do your answers to part (i) tell you about the graphs x2 + y2 = 25 and y = 3x – 2? … [1]

13 0626/06/O/N/18 © UCLES 2018 [Turn over 9 (a) A regular pentagon has sides of length 4.2 cm correct to 1 decimal place. Find the lower bound of the perimeter of the pentagon. … cm [2] (b) h 8.4 cm NOT TO SCALE The length of the base of a right-angled triangle is 8.4 cm correct to 1 decimal place. The area of the triangle is 20.0 cm2 correct to 1 decimal place. Find the upper bound of the height, h, of the triangle. Show the values you have used in your calculation. … cm [3]

14 0626/06/O/N/18 © UCLES 2018 10 (a) A 3 4 1 2 7 5 2 4 28 29 + - = - c c m m Find A. A = f p [3] (b) B 2 2 32 2 x x 2 10 = c m The determinant of B is 0. Find the value of x. x = … [4]

15 0626/06/O/N/18 © UCLES 2018 11 Models of trains are made to different scales. (a) A model train that is made to a scale of 1 : 76.2 is called an OO model. (i) A piston rod on the real train is 1.4 m long. Show that the rod on the OO model is less than 2 cm long. [2] (ii) The water tank in the OO model has a capacity of 8 millilitres. Find the capacity of the water tank in the real train. Give your answer in litres. … litres [3] (b) Two other models of the same train are made to different scales. A TT model is made to a scale of 1 : 120. A ZO model is made to a scale of 1 : 60. The two models are painted with the same thickness of paint. Khadeeja says: I will need 100% more paint for the TT model than for the ZO model. Explain why Khadeeja is wrong and calculate the correct percentage. … … Correct percentage = … [4]

16 0626/06/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. BLANK PAGE