Cambridge IGCSE Mathematics (9-1) (UK only) 0626 — 2017 Oct/Nov Paper 4 · Variant 1

This document consists of 15 printed pages and 1 blank page. DC (NH/JG) 133828/3 © UCLES 2017 [Turn over * 0 6 3 1 1 9 5 2 3 1 * MATHEMATICS 0626/04 Paper 4 (Extended) October/November 2017 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/17 © UCLES 2017 1 A straight line passes through the point (0, 3) and the point (2, 11). (a) Work out the gradient of this line. … [2] (b) Write down the equation of this line. y = … [1] 2 One of the angles in a triangle is twice as big as the smallest angle. The third angle in the triangle is 40° bigger than the smallest angle. Work out the sizes of the three angles in the triangle. …°, …°, …° [4]

3 0626/04/O/N/17 © UCLES 2017 [Turn over 3 Construct the bisector of this acute angle. Use a straight edge and compasses only. Leave in all your construction arcs. [2] 4 Q 2 1 n = - (a) Work out the value of Q when n = 3. Q = … [1] (b) Q is a prime number for some values of n. Find the values of Q that are prime when n = 2, 3, 4 or 5. … [2] (c) When n = 6, Q is not a prime number. Explain how you know this value of Q is not prime. … … [1]

4 0626/04/O/N/17 © UCLES 2017 5 Ewan travels to work by car. He goes through two sets of traffic lights on his journey. The probability that he stops at the first set of traffic lights is 5 3 . The probability that he stops at the second set of traffic lights is 7 4 . These probabilities are independent. (a) Complete the tree diagram. 3 5 stops does not stop stops does not stop stops does not stop … … … … … First set Second set [2] (b) Work out the probability that Ewan stops at neither set of traffic lights. … [2] 6 (a) Factorise x x 3 18 2 - - . … [2] (b) Solve x x 3 18 0 2 - - = . x = … or x = … [1]

5 0626/04/O/N/17 © UCLES 2017 [Turn over 7 Sophie drives 125 miles from Adton to Berham at an average speed of 50 miles per hour. She then drives 90 miles from Berham to Chand. She does not stop and her whole journey takes 4 hours. What is her average speed driving from Berham to Chand? …mph [4] 8 Show that x x x x 7 4 3 1 + - + - ^ ^ ^ h h h simplifies to x 4 7 2 - ^ h. [3]

6 0626/04/O/N/17 © UCLES 2017 9 10 20 30 40 50 60 70 80 90 100 110 120 0 10 20 30 40 Waiting time (minutes) Cumulative frequency This cumulative frequency diagram summarises the waiting times of 120 patients in a doctor’s surgery. (a) Use the diagram to estimate (i) the median waiting time, … minutes [1] (ii) the inter-quartile range. … minutes [2]

7 0626/04/O/N/17 © UCLES 2017 [Turn over (b) Use the diagram to estimate the percentage of patients who waited longer than 30 minutes. …% [3] 10 (a) Simplify. k k 9 3 2 5 ' - … [1] (b) Evaluate. 25 4 2 1 - c m … [2] (c) 27 3 x = Find the value of x. x = … [1]

8 0626/04/O/N/17 © UCLES 2017 11 In this question all lengths are in centimetres. 2x 5x NOT TO SCALE A solid shape consists of a cube with a pyramid on top. The cube has sides of length 2x. The base of the pyramid is a square with sides of length 2x. The vertex at the top of the pyramid is 5x above the base of the cube. Find an expression, in terms of x, for the volume of the solid. Give your answer in its simplest form. [The volume, V, of a pyramid with base area A and height h is Ah V 3 1 = .] …cm3 [4]

9 0626/04/O/N/17 © UCLES 2017 [Turn over 12 NOT TO SCALE 9 cm 6 cm A B These are two mathematically similar hexagonal prisms. Prism A has length 6 cm and volume 80 cm3. Prism B has length 9 cm. Calculate the volume of prism B. …cm3 [3] 13 Express .0 78 o o as a fraction in its simplest form. … [3]

10 0626/04/O/N/17 © UCLES 2017 14 A town planner uses this formula to predict the population, P, of a town after 2017. . P 36700 1 06n # = where n is the number of years after 2017 and n 0 5 G G . (a) For how many years is the formula used? … [1] (b) What is the population of the town in 2017? … [1] (c) By what percentage is the population expected to grow each year? …% [1] 15 A 4 6 3 7 = c m (a) Find 3A. f p [1] (b) Work out A . … [1] (c) Find A−1. f p [1]

11 0626/04/O/N/17 © UCLES 2017 [Turn over 16 This is a sketch of the graphs of y x 2 3 2 = - and y x 3 = + . O y = 2x2 – 3 y = x + 3 y x Work out the co-ordinates of the points of intersection of y x 2 3 2 = - and y x 3 = + . (… , …) and (… , …) [5]

12 0626/04/O/N/17 © UCLES 2017 17 Millie makes lemon cakes and chocolate cakes to sell. A lemon cake requires 250 g of flour and a chocolate cake requires 375 g of flour. Millie has 6 kg of flour. Millie makes x lemon cakes and y chocolate cakes. (a) Show that x y 2 3 48 G + . [2] (b) The maximum number of cakes that she can make is 20. She must make at least 3 chocolate cakes. Write down two further inequalities involving x and y. … … [2] (c) Represent the three inequalities on this grid. Shade the regions that do not satisfy the inequalities. 25 x y 20 15 10 5 0 5 10 15 20 25 30 [4]

13 0626/04/O/N/17 © UCLES 2017 [Turn over (d) Each lemon cake sells for a profit of £5. Each chocolate cake sells for a profit of £7. What is the greatest profit that Millie can make? £ … [2] 18 x g x x x x h 2 15 9 2 2 2 - + - = - + ^ ^ ^ ^ h h h h Find the value of g and the value of h. g = … h = … [4]

14 0626/04/O/N/17 © UCLES 2017 19 D A X B Y C 2p p 3q NOT TO SCALE ABCD is a parallelogram. , DC BC q p 3 2 = = and YB p = . X is the point on AB such that AX : XB = 2 : 1. (a) Find DX in terms of p and q. Give your answer in its simplest form. DX = … [3] (b) Show that DXY is a straight line. [2]

15 0626/04/O/N/17 © UCLES 2017 20 sin 63° = 0.89, correct to 2 decimal places. Use this result to solve . sinx 0 89 =- for ° ° x 0 360 G G . … [3] 21 Show that 27 2 3 1 + can be written as n m 3 , where m and n are integers to be found. [4]

16 0626/04/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 6 printed pages. © UCLES 2017 [Turn over Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education (9–1) MATHEMATICS 0626/04 Paper 4 October/November 2017 MARK SCHEME Maximum Mark: 84 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.

0626/04 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 2 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

0626/04 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 3 of 6 Question Answer Marks Partial Marks 1(a) 4 2 M1 for 11 3 2 0 − − oe soi 1(b) [y =] 4x + 3 oe 1 FT from their gradient 2 35, 70, 75 4 M1 for sum of angles in a triangle = 180 soi or for 3 angles that fit two of the conditions M1 for 2x and x + 40 oe M1 for x + 2x + x + 40 = 180 soi 3 Correct angle bisector with correct arcs shown 2 B1 for angle bisector or correct arcs 4(a) 7 1 4(b) 3, 7, 31 (with no extras) 2 B1 for two correct (with no extras) or for answer [n =] 2, 3, 5 only or M1 for 3, 7, 15, 31 seen 4(c) Valid reason 1 e.g. Because 63 is divisible by 3 or 7 or 9 or 21 e.g. because 63 has more than 2 factors 5(a) 2 , 5 4 7 , 3 7 , 4 7 , 3 7 correctly placed 2 B1 for 2 5 or 3 7 on a ‘does not stop’ branch 5(b) 6 35 oe 2 M1 for their 2 3 5 7 ×their 6(a) ( 3)( 6) + − x x 2 M1 for x(x – 6) + 3(x – 6) or x( x + 3) – 6 (x + 3) or for ( )( ) + + x a x b where a + b = −3 or ab = −18 6(b) 3, 6 x x = − = 1 FT their factors 7 60 4 M1 for time for A to B = 125 ÷ 50 soi M1 for time for B to C = 4 – their 2.5 M1 for 90 ÷ their 1.5 8 x2 + 7x – 4x – 28 M1 Must have at least 3 terms correct or 2 3 28 + − x x , must have at least 2 terms correct 3x2 – 3x B1 x2 + 7x – 4x – 28 + 3x2 – 3x = 4x2 – 28 = 4(x2 – 7) A1

0626/04 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 4 of 6 Question Answer Marks Partial Marks 9(a)(i) 18 1 9(a)(ii) 14 2 B1 for 26 or 12 or M1 for attempt at difference of quartiles 9(b) 15 3 B2 for answer 85 OR M1 for [t < 30] = 102 or [t > 30] = 18 seen M1 for 120 102 120 −their soi 10(a) 3k7 1 10(b) 5 2 oe 2 M1 for 2 5 seen or 1 2 25 4       10(c) 1 3 1 11 12x3 4 M1 for 2x × 2x × 2x M1 for 1 3 × 2x × 2x × (5x – 2x) M1 for their 8x3 − their 4x3 12 270 3 B2 for 3 9 6       or 3 6 9       oe soi or B1 for 9 6 or 6 9 oe soi 13 26 33 3 M2 for x = 78 99 or M1 for x = 0. . . 78 and 100x = 78. . . 78 soi 14(a) 5 1 14(b) 36 700 1 14(c) 6 1 15(a) 12 9 18 21       1 15(b) 10 1 15(c) 1 10 7 3 6 4 −     −   oe 1 FT from their determinant.

0626/04 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 5 of 6 Question Answer Marks Partial Marks 16 ( 1 12 − , 1 12 ), (2 , 5) 5 M1 for 2 2 3 3 − = + x x M1 for 2 2 6 0 − − = x x M1 for (2 3)( 2) 0 + − = x x A1 FT from their factorised quadratic, for x = 1 12 − or 2 After A0, SC1 for their x co-ordinates being +3 more than their y co-ordinates 17(a) Total of flour in grams is 250 375 + x y M1 250 375 6000 x + - → 2 3 48 + x y - A1 17(b) 20 + x y - oe y ≥ 3 oe 2 B1 for each or SC1 for x + y * 20 and y*3 where * can be an equals or any inequality sign. 17(c) Correct region clearly identified 4 B3 for three correct boundaries 2x + 3y = 48, x + y = 20, y = 3 or B2 for two correct boundaries or B1 for one correct boundary 17(d) 116 2 M1 for x =12 and y = 8 identified or for 5x + 7y for integer (x, y) in their region 18 g = 3 h = −5 4 B3 for one correct OR M1 for 3 2 2 2 2 15 15 − + − − + x gx x gx x g or (x – g)(2x – 5)(x + 3) M1 for 3 2 2 18 9 + − − x hx x h or (x – 3)(x + 3)(2x + h) 19(a) 2q – 2p oe 3 M1 for JJJG DA = −2p or JJJG AX = 2q or JJJG BX = −q M1 for JJJG DX = JJJG DA + JJJG AX oe soi 19(b) JJJG DY = 3q – 3p [= 3(q – p)] or JJJG XY = q – p M1 which is a multiple of JJJG DX and X is on DX and on DY oe A1

0626/04 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 6 of 6 Question Answer Marks Partial Marks 20 243 and 297 3 B2 for one correct or M1 for 180 + 63 or 360 – 63 oe or M1 for sketch of sine curve for 0° ⩽ x ⩽ 360° seen 21 2 2 27 3 3 = M1 2 3 27 27 3 + × 5 3 3 M1 2 3 27 81 + or numerator 2 3 27 + or better 5 5 3 3 3 3 3 3 × = × M1 2 3 3 3 9 + 5 3 9 A1 5 3 9