Cambridge IGCSE Mathematics - International 0607 — 2015 Oct/Nov Paper 2 · Variant 3

This document consists of 8 printed pages. DC (ST/SW) 103948/3 © UCLES 2015 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 4 7 9 2 8 8 9 3 6 7 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/23 Paper 2 (Extended) October/November 2015 45 minutes Candidates answer on the Question Paper. Additional Materials: Geometrical Instruments 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. Do not use staples, paper clips, glue or correction fluid. You may use an HB pencil for any diagrams or graphs. DO NOT WRITE IN ANY BARCODES. Answer all the questions. CALCULATORS MUST NOT BE USED IN THIS PAPER. All answers should be given in their simplest form. You must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 40.

2 0607/23/O/N/15 © UCLES 2015 Formula List For the equation ax bx c 0 2 + + = x a b b ac 2 4 2 ! = - - Curved surface area, A, of cylinder of radius r, height h. r A rh 2 = Curved surface area, A, of cone of radius r, sloping edge l. r A rl = Curved surface area, A, of sphere of radius r. r A r 4 2 = Volume, V, of pyramid, base area A, height h. V Ah 3 1 = Volume, V, of cylinder of radius r, height h. r V r h 2 = Volume, V, of cone of radius r, height h. r V r h 3 1 2 = Volume, V, of sphere of radius r. r V r 3 4 3 = sin sin sin A a B b C c = = cos a b c bc A 2 2 2 2 = + - sin bc A 2 1 Area = A C B c b a

3 0607/23/O/N/15 © UCLES 2015 [Turn over Answer all the questions. 1 Find the highest common factor (HCF) of 60 and 90. Answer … [1] 2 Insert one pair of brackets to make the statement correct. 5 – 2 + 3 × 2 = – 5 [1] 3 p = 2 3 J L KK N P OO q = 1 6 J L KK N P OO Find 2p – 3q. Answer … [2] 4 Write 0.72 as a fraction in its lowest terms. Answer … [1] 5 The mean of a list of 9 numbers is 6. When a 10th number is included in the list the mean is 5.5 . Find the value of this 10th number. Answer … [2]

4 0607/23/O/N/15 © UCLES 2015 6 NOT TO SCALE cm cm 3 6 Find the length of the hypotenuse of the triangle. Answer … cm [2] 7 Solve the simultaneous equations. u w u w 9 3 19 - = + = Answer u = … w = … [2] 8 The scale of a map is 1 : 250 000 . Find the actual distance, in kilometres, between two cities which are 42 cm apart on the map. Answer … km [2]

5 0607/23/O/N/15 © UCLES 2015 [Turn over 9 | x | < 4 and x is an integer. Find the smallest possible value of x. Answer … [1] 10 The first 4 terms of a sequence are 20, 13, 6 and – 1. Find (a) the next term, Answer(a) … [1] (b) the nth term. Answer(b) … [2] 11 Make u the subject of the formula. v u as 2 2 2 = + Answer u = … [2] 12 Factorise completely. a b ax bx 2 2 - + - Answer … [2]

6 0607/23/O/N/15 © UCLES 2015 13 Find the exact value of (a) 3 3 - , Answer(a) … [1] (b) 4 3 16 , Answer(b) … [1] (c) cos 30°. Answer(c) … [1] 14 Simplify x 64 12 6 1 ^ h . Answer … [2] 15 On each Venn diagram, shade the region indicated. A (A B)' (C D) E ' U U B C D E [2]

7 0607/23/O/N/15 © UCLES 2015 [Turn over 16 Find the equation of the straight line passing through (– 2, – 4) and (2, 0). Answer … [3] 17 Rationalise the denominator. 5 3 2 + Answer … [2] 18 (a) Factorise y y 3 2 - . Answer(a) … [1] (b) Simplify y y y 9 3 2 2 - - . Answer(b) … [2] Questions 19 and 20 are printed on the next page.

8 0607/23/O/N/15 © UCLES 2015 19 Find the value of (a) log log 8 4 , Answer(a) … [2] (b) log 8 4 . Answer(b) … [1] 20 ( ) , g x x x x 1 2 1 1 ! = - + Solve the equation ( ) g x 2 1 = - . Answer x = … [1] 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.

® IGCSE is the registered trademark of Cambridge International Examinations. CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the October/November 2015 series 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/23 Paper 2 (Extended), maximum raw mark 40 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 will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the October/November 2015 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

Page 2 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2015 0607 23 © Cambridge International Examinations 2015 Abbreviations cao correct answer only dep dependent FT follow through after error isw ignore subsequent working oe or equivalent SC Special Case nfww not from wrong working soi seen or implied Question Answer Mark Part Marks 1 30 1 2 5 – (2 + 3) × 2 = –5 1 3       −12 1 2 B1 for each component 4 25 18 1 5 1 2 M1 for 10 × 5.5 – 9 × 6 6 3 2 M1 for ( ) ( ) 2 2 6 3 + 7 7 –2 1 1 If 0 scored SC1 for correct substitution and evaluation to find the other variable 8 105 2 M1 for 42 × 2.5 oe or SC1 for figs 105 9 –3 1 10 (a) (b) –8 –7n + 27 oe 1 2 SC1 for –7n + k or 27 + kn, k ≠0 11 as v 2 2 − 2 M1 for correct rearrangement for u term M1 for correct square root 12 ) 1 )( 2 ( x b a + − 2 M1 for ) 2 ( 2 b a x b a − + − or ) 1( ) 1( 2 x b x a + − + 13 (a) (b) (c) 27 1 8 2 3 1 1 1

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2015 0607 23 © Cambridge International Examinations 2015 14 2 2x 2 SC1 for 2 kx or kx 2 , 0 ≠ k 15 1 1 16 y = x – 2 oe 3 B2 for y = x + k oe or y = kx – 2 oe or M1 for gradient = 2 0 0 2 − − − or better or M1 for substituting co-ordinates of one point into their y = mx + c 17 ( ) 3 5 2 − oe 2 M1 for 2 5 2 5 − − × 18 (a) (b) y(3 – y) y y + 3 final answer 1 2FT FT only if (3 – y) or (3 + y) is cancelled B1 for 2 [9 ](3 )(3 ) y y y − = − + 19 (a) (b) 3 2 1.5 oe 2 1 M1 for 2 log 3 2 log 2 or 4 log8 20 5 1