Cambridge IGCSE Mathematics - International 0607 — 2015 May/June Paper 2 · Variant 1

This document consists of 8 printed pages. DC (LEG/SW) 99284/5 © UCLES 2015 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 1 6 4 3 4 4 6 5 9 5 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/21 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 0607/21/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 0607/21/M/J/15 © UCLES 2015 [Turn over Answer all the questions. 1 (a) Write 4725.6 correct to two significant figures. Answer(a) … [1] (b) Write 0.01026 correct to three decimal places. Answer(b) … [1] 2 Expand and simplify. (a) x x x 3 2 3 7 2 - - - - ^ ^ h h Answer(a) … [2] (b) x y y x 5 3 2 5 - - ^ ^h h Answer(b) … [3]

4 0607/21/M/J/15 © UCLES 2015 3 Find the exact value of 27 3 1 - . Answer … [2] 4 Simplify x y 16 8 2 2 1 ^ h . Answer … [2] 5 (a) Simplify. 27 147 + Answer(a) … [2] (b) Rationalise the denominator. 3 5 3 5 + - Answer(b) … [3]

5 0607/21/M/J/15 © UCLES 2015 [Turn over 6 Solve. log log log log x 5 25 10 + - = Answer x= … [3] 7 There are 400 students at a school. 5 2 of the students are boys. 70% of the girls can swim. The ratio of boys that cannot swim to girls that cannot swim is 2 : 3. Complete the table. Boys Girls Total Can swim Cannot swim Total 400 [4]

6 0607/21/M/J/15 © UCLES 2015 8 y° 30° x cm 2 cm 1 cm NOT TO SCALE (a) Write down the value of x. Answer(a) x = …[1] (b) Find the value of y. Answer(b) y = … [2] 9 f x x 3 2 1 = - ^ h (a) Find f 4 ^ h. Answer(a) … [1] (b) Solve f x 4 1 = ^ h . Answer(b) … [2] (c) Find f x 1 - ^ h. Answer(c) … [3]

7 0607/21/M/J/15 © UCLES 2015 [Turn over 10 NOT TO SCALE N M D C B A ABCD is a trapezium. AB = 2DC, DM = 2MC and AN = 3NB. p AB = and A q D = . (a) Write MC in terms of p. Answer(a) … [2] (b) Find MN in terms of p and q. Answer(b) … [2] Question 11 is printed on the next page.

8 0607/21/M/J/15 © UCLES 2015 11 The point A has co-ordinates (2, 8) and the point B has co-ordinates (6, 6). Find the equation of the perpendicular bisector of the line AB. Answer … [4] 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 May/June 2015 series 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/21 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 21 © 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) 4700 1 (b) [0].010 1 2 (a) –6x + 7 2 B1 for 2 3 6 x x + − or 7 3 2 + −x (b) 2 2 6 25 25 y x xy − − 3 B2 for xy y x xy 15 6 25 10 2 2 + − − or B1 for 1 error in above 3 3 1 2 B1 for 3 seen or for 3 27 1 4 y x4 4 2 B1 for y kx4 or y xk 4 or k y x4 4 5 (a) 3 10 2 M1 for 3 3 or 3 7 (b) 2 5 3 7 − or 4 5 6 14 − 3 M1 for 5 3 5 3 − − × M1 for 4 5 b a − a,b ≠ 0 oe 6 50 3 M2 for [ ] [ ] 10 log 25 5 log =      x oe or M1 for a correct use of logs 7 Boys Girls Total Can 112 168 280 Cannot 48 72 120 Total 160 240 4 B1 for 240 B1 for 72 M1 for 72 3 2 their ×

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2015 0607 21 © Cambridge International Examinations 2015 8 (a) 1 1 (b) 45° 2 M1 for 1 45 tan = or M1 for tan y their = (a) or M1 for (180 90) 2 − 9 (a) 10 1 oe 1 (b) 2 2 M1 for 4 2 3 = − x (c)       + 2 1 3 1 x oe 3 M1 for one correct step M1 for ‘swapping’ x and y 10 (a) 6 1 p 2 B1 for 1 2 DC = p soi (b) 5 12 p – q 2 M1 for p q 4 3 + − seen 11 1 2 − = x y oe 4 B1 for [mid-point =] (4, 7) B1 for [gradient =] –0.5 M1 for grad of perp = ) 5.0 ( 1 − − their