Cambridge IGCSE Mathematics - International 0607 — 2016 May/June Paper 2 · Variant 1

This document consists of 11 printed pages and 1 blank page. DC (LK/AR) 115879/3 © UCLES 2016 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 9 9 8 9 7 3 9 1 8 6 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/21 Paper 2 (Extended) May/June 2016 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/16 © UCLES 2016 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/16 © UCLES 2016 [Turn over Answer all the questions. 1 Work out. (a) .0 04 8 … [1] (b) 5 4 4 1 -  [2] 2 (a) Shade two more squares so that this shape has exactly one line of symmetry. [1] (b) Shade two more triangles so that this shape has rotational symmetry of order 3. [1]

4 0607/21/M/J/16 © UCLES 2016 3 By rounding each number to 1 significant figure, estimate the value of this calculation. Show all your working. . . . 52 3 99 6 11 37 289 # + … [2] 4 a 2 3 7 5 2 3 # # = b 2 3 5 3 4 # # = Leaving your answer as the product of prime factors, find (a) b2, … [1] (b) the highest common factor (HCF) of a and b, . … [1] (c) the lowest common multiple (LCM) of a and b.  [2]

5 0607/21/M/J/16 © UCLES 2016 [Turn over 5 Luis has a large jar containing red, yellow, green and blue beads. He takes a bead at random from the jar, notes its colour and replaces it. He repeats this 200 times. The table shows his results. Colour Red Yellow Green Blue Number of beads 26 72 64 38 Relative frequency (a) Complete the table to show the relative frequencies. [2] (b) (i) There are 5000 beads in the jar altogether. Estimate the number of green beads in the jar. … [1] (ii) Explain why this is a good estimate. … … [1] 6 Solve. x x 2 3 1 2 - + = … [3]

6 0607/21/M/J/16 © UCLES 2016 7 U = {Integers from 1 to 18} F = {Factors of 12} M = {Multiples of 3} E = {Even numbers} (a) Complete the Venn diagram by putting the numbers 2, 3, 4, 8, 12, 15 and 18 in the correct subsets. F 1 6 9 10 14 16 E 5 13 7 11 17 M U [2] (b) List the members of (i) ( ) E F M , , l, … [1] (ii) E M F + + l l. … [1] 8 Solve. ( ) x x 2 3 2 3 1 2 + - … [3]

7 0607/21/M/J/16 © UCLES 2016 [Turn over 9 NOT TO SCALE 130° O C D A B A, B, C and D are points on the circle centre O. Angle BOD = 130°. (a) Find angle DCB. Angle DCB = … [1] (b) Find angle BAD. Angle BAD = … [1]

8 0607/21/M/J/16 © UCLES 2016 10 Factorise completely. (a) 12x2 – 27xy … [2] (b) 4a2 + 8ab – ac – 2bc  [2] 11 Rationalise the denominator. 7 1  [1]

9 0607/21/M/J/16 © UCLES 2016 [Turn over 12 q r b a p Write the vectors p, q and r in terms of a and b . p =  q = … r =  [3]

10 0607/21/M/J/16 © UCLES 2016 13 30 60 –30 –60 90 120 150 180 210 240 270 300 330 2 –2 y x° 0 The graph of y = asin (x + b)° is shown in the diagram. Find the value of a and the value of b. a = … b = … [2]

11 0607/21/M/J/16 © UCLES 2016 14 O P Q y x NOT TO SCALE The diagram shows a sketch of the graph of y = ax2 + bx O is the point (0, 0), P is the point (4, 0) and Q is the point (8, 96). Find the value of a and the value of b. a = … b =  [3]

12 0607/21/M/J/16 © UCLES 2016 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 the registered trademark of Cambridge International Examinations. This document consists of 4 printed pages. © UCLES 2016 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/21 Paper 2 (Extended) May/June 2016 MARK SCHEME Maximum Mark: 40 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 will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2016 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 2016 0607 21 © Cambridge International Examinations 2016 Abbreviations awrt answers which round to 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 (a) 200 1 (b) 11 20 oe 2 M1 for 20 a – 20 b with a = 16 or b = 5 2 (a) 1 (b) 1 3 10 300 50 100 × + 20 M1 A1 Accept any 3 from 4 4 (a) 26 × 38 × 52 1 (b) 23 × 32 1 (c) 25 × 34 × 5[1] × 73 2 B1 for 3 of 4 factors correct 5 (a) 0.13, 0.36, 0.32, 0.19 oe 2 B1 for 2 or 3 correct (b) (i) 1600 1 (ii) Sufficient trials oe 1 6 x = 14 3 M2 for 3x – 2x – 2 = 12 or M1 for 3 2( 1) 6 x x − + = 2 or better

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2016 0607 21 © Cambridge International Examinations 2016 Question Answer Mark Part Marks 7 (a) 2 B1 for 1 or 2 numbers omitted or misplaced (b) (i) 5, 7, 11, 13, 17 1FT (ii) 8, 10, 14, 16 1FT 8 x < 1.25 oe 3 With no wrong working seen M1 for 2x + 3 > 6x – 2 M1FT for 3 + 2 > 6x – 2x oe M1FT for b x a < from ax < b oe 9 (a) 65 1 (b) 115 1FT FT 180 – their (a) 10 (a) 3x(4x – 9y) final answer 2 B1 for ( ) 2 3 4 9 x xy − or ( ) 12 27 x x y − (b) (a + 2b)(4a – c) final answer 2 B1 for ( ) ( ) 4 2 2 a a b c a b + − + or ( ) ( ) 4 2 4 a a c b a c − + − 11 7 7 1 12 p = a + b oe q = 2a + b oe r = –2a + b oe 3 B1 for each 13 a = 2 b = 30 1 1

Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2016 0607 21 © Cambridge International Examinations 2016 Question Answer Mark Part Marks 14 [a =] 3 [b =] –12 3 M1 for kx(x – 4) M1 for substituting (8, 96) or b = –4a soi OR M1 for 2 0 4 4 a b = + or b = –4a soi M1 for 2 96 8 8 a b = + OR M1 for ( ) ( ) 2 [ ] 2 4 y a x = − − M1 for substituting (8, 96) or b = –4a soi If zero scored, SC1 for a = 3, or b = –12