Cambridge IGCSE Mathematics - International 0607 — 2015 May/June Paper 2 · Variant 3

This document consists of 12 printed pages. DC (RW/SW) 99290/3 © UCLES 2015 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 4 2 1 2 2 9 3 3 0 7 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/23 Paper 2 (Extended) May/June 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/M/J/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/M/J/15 © UCLES 2015 [Turn over Answer all the questions. 1 Round these numbers to 3 significant figures. (a) 0.000 604 83 Answer(a) … [1] (b) 6 998 800 Answer(b) … [1] 2 By rounding each number to 1 significant figure, estimate the value of . . . . 1 82 10 43 0 583 311 6 # + . Show your working. Answer … [2]

4 0607/23/M/J/15 © UCLES 2015 3 a 2 3 5 3 2 # # = b 2 3 7 2 2 6 # # = (a) Find, giving each answer as the product of prime factors, (i) the highest common factor (HCF) of a and b, Answer(a)(i) … [1] (ii) b. Answer(a)(ii) … [1] (b) ap is a cube number. Find the smallest integer value of p. Answer(b) … [1]

5 0607/23/M/J/15 © UCLES 2015 [Turn over 4 3 cm 5 cm 8 cm 3 cm NOT TO SCALE The diagram shows a rectangle, two semicircles and two right-angled triangles. (a) Find the total area of the shape. Give your answer in the form r a b + . Answer(a) …cm2 [3] (b) Describe fully the symmetry of the shape. Answer(b) … … [2] 5 Solve. x x 5 2 2 4 7 1 + - ^ ^ h h Answer … [3]

6 0607/23/M/J/15 © UCLES 2015 6 François and George each ask a sample of students at their college how they travel to college. These are their results. Walk Cycle Bus Train Car Total number of students François 7 3 4 1 5 20 George 46 24 44 11 25 150 (a) Explain why George’s results will give the better estimates of the probabilities of the different types of travel. Answer(a) … [1] (b) A student is selected at random. (i) Use George’s results to estimate the probability that the student cycles to college. Answer(b)(i) … [1] (ii) There are 3000 students at the college. Use George’s results to estimate the number of students who cycle to college. Answer(b)(ii) … [1]

7 0607/23/M/J/15 © UCLES 2015 [Turn over 7 NOT TO SCALE 0 A x y The diagram shows the lines x 2 =- , y x 1 2 1 = + and x y 3 4 20 + = . (a) Use simultaneous equations to find the co-ordinates of the point A. Answer(a) ( … , … ) [3] (b) (i) P is a point in the region such that x 2 1- , y x 1 2 1 2 + and x y 3 4 20 1 + . On the diagram, mark and label a possible position of P. [1] (ii) Q is a point in the region such that x 2 2- , y x 1 2 1 = + and x y 3 4 20 1 + . On the diagram, mark and label a possible position of Q. [1]

8 0607/23/M/J/15 © UCLES 2015 8 NOT TO SCALE A B C 35° D E In the diagram, A, B, C, D and E are points on the circle. AD is a diameter and angle CAD 35° = . Find (a) angle ACD, Answer(a) … [1] (b) angle CBD, Answer(b) … [1] (c) angle AEC. Answer(c) … [2]

9 0607/23/M/J/15 © UCLES 2015 [Turn over 9 The sets P, Q and R are subsets of the universal set U. • P R k Q ! • Q is a subset of R • Q P k Q = Complete the Venn diagram to show the sets P, Q, and R. U [3]

10 0607/23/M/J/15 © UCLES 2015 10 (a) Factorise x x 3 10 2 - - . Answer(a) … [2] (b) Make x the subject of y a x 3 = . Answer(b) x = … [2]

11 0607/23/M/J/15 © UCLES 2015 [Turn over 11 (a) Find log 25 1 5 . Answer(a) … [1] (b) Find x when (i) log log log x 2 6 - = , Answer(b)(i) … [1] (ii) log 4 2 1 x = . Answer(b)(ii) … [1] Question 12 is printed on the next page.

12 0607/23/M/J/15 © UCLES 2015 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. 12 NOT TO SCALE y –3 0 2 (0, –12) x The diagram shows a sketch of the graph of y ax bx c 2 = + + . The graph goes through the points ,3 0 - ^ h, ,0 12 - ^ h and ,2 0 ^ h. Find the values a, b and c. Answer a = … b = … c = … [3]

® IGCSE is the registered trademark of Cambridge International Examinations. CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the May/June 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 May/June 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 – May/June 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 1 (a) 0.000 605 1 (b) 7 000 000 1 2 10 2 300 6.0 + × 15 M1 A1 At least 3 correct 3 (a) (i) 2² × 3 1 (ii) 2 × 3 × 7³ 1 (b) 45 1 4 (a) 64 + 6.25π 3 M1 for 8 × 5 + 2 × 1 2 × 8 × 3 oe M1 for 2 × 1 2 ×π × 2.5² oe (b) Rotational oe [Order] 2 1 1 5 x > 8 3 Accept 8 < x M1 for 5x + 10 < 8x – 14 M1FT for 10 + 24 < 8x – 5x oe or SC2 for [x =] 8 or x < 8 6 (a) Bigger sample oe 1 (b) (i) 150 24 oe 1 (ii) 480 1

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2015 0607 23 © Cambridge International Examinations 2015 7 (a) (3.2, 2.6) 3 B2 for one co-ordinate supported by algebra or M1 for 3x + 4( 1 2 x + 1) = 20 or other correct elimination of x or y (b) (i) P correct 1 × P (ii) Q correct 1 × Q 8 (a) 90 1 (b) 35 1 (c) 55 2 B1 for ABC = 90 + 35 or ADC = 55 9 R P Q 3 B1 for each criterion correct 10 (a) (x –5)(x + 2) 2 SC1 for (x + a)(x + b) where a + b = –3 or ab = –10 (b) [x =] (ay)3 oe 2 M1 for ay = 3 x or 3 3 = a x y 11 (a) –2 1 (b) (i) 12 1 (ii) 16 1 12 2, 2, –12 3 M2 for a(x + 3)(x – 2) or M1 for (x + 3)(x – 2) If 0 scored, B1 for c = –12