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

This document consists of 8 printed pages. DC (LK/SG) 114971/1 © UCLES 2016 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 5 2 9 4 0 0 2 5 2 1 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/22 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 0607/22/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 0607/22/M/J/16 © UCLES 2016 [Turn over Answer all the questions. 1 Work out 1 3 2 1 3 1 + . … [2] 2 Increase 1 h 30 min by 10%. … h … min [2] 3 42° D C A B NOT TO SCALE In the diagram, DC is parallel to AB and AC = AB. Work out angle ACB. Angle ACB = … [2]

4 0607/22/M/J/16 © UCLES 2016 4 t p 1 2 = Rearrange the formula to write p in terms of t. p = … [2] 5 A biased die, that has six faces, is numbered 1 to 6. The table shows the results when the die is rolled 60 times. Number 1 2 3 4 5 6 Frequency 3 12 8 16 7 14 (a) Jose rolls the die. Find the probability that the number shown is even. … [1] (b) Jose rolls the die 1200 times. Find the expected number of times that the number shown on the die is even. … [1] 6 Solve the simultaneous equations. 3x – 2y = 7 5x + 2y = 1 x = … y = … [2]

5 0607/22/M/J/16 © UCLES 2016 [Turn over 7 Work out 5 10 8 10 12 7 # # - . Give your answer in standard form. … [2] 8 Solve the inequality. x x 9 6 2 2 - + … [2] 9 (a) x x x p 3 5 ' = Find the value of p. p = … [1] (b) Work out. (i) 6 2 ^ h … [1] (ii) 8 1 3 1 - … [2]

6 0607/22/M/J/16 © UCLES 2016 10 The line 2x + 3y = 36 intersects the x-axis at P and the y-axis at Q. M is the midpoint of PQ. Find the column vector OM where O is the origin. ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ [4] 11 Factorise completely. p q xp xq 2 2 - + - … [2] 12 Rationalise the denominator. 1 2 5 + … [2]

7 0607/22/M/J/16 © UCLES 2016 [Turn over 13 The area of a semicircle is 32π cm2. Work out the perimeter of the semicircle. Give your answer in terms of π. … cm [3] 14 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 x 10 20 30 Frequency density Complete the frequency table using the information in the histogram. Class interval Frequency x 0 20 1 G x 20 30 1 G [2] Questions 15, 16 and 17 are printed on the next page

8 0607/22/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. 15 y x 1 \ When x = 4, y = 3. Find y in terms of x. y = … [2] 16 log log log log y 2 3 3 2 6 = + - Find the value of y. y = … [3] 17 Describe fully the single transformation that maps the graph of y = cosx onto the graph of y = 3cosx. … … [2]

® IGCSE is the registered trademark of Cambridge International Examinations. This document consists of 3 printed pages. © UCLES 2016 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/22 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 22 © 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 5 6 4 2 M1 for 3 2 6 6 4 + + or 9 20 6 6 + oe 2 1 [h] 39 [min] 2 M1 for 90 × 1.1 oe 3 69 2 M1 for 0.5(180 42) − 4 1 [ ] ± t oe 2 M1 for 2 1 = tp or 1 = t p or better 5 (a) 42 60 oe 1 (b) 840 1FT FT their (a) × 1200 6 [x = ] 1 [y = ] – 2 1 1 If 0 scored SC1 for correct substitution and evaluation of other variable 7 19 1.6 10 × 2 B1 for 1.6 × 10n or k × 1019 or correct answer not in SF 8 x < 1 or 1 > x 2 M1 for 9 – 2 > x + 6x oe or answer of 1 with incorrect inequality 9 (a) – 2 1 (b) (i) 8 1 (ii) 2 2 M1 for 1 38 or 1 2 1 oe If 0 scored then SC1 for answer 1 2

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2016 0607 22 © Cambridge International Examinations 2016 Question Answer Mark Part Marks 10 9 6    4 B3 for (9, 6) or B1 for (0, 12) soi B1 for (18, 0) soi M1 for (0.5 their 18, 0.5 their 12) 11 (2 )(1 ) − + p q x 2 B1 for 2 (2 ) − + − p q x p q or 2 (1 ) (1 ) + − + p x q x 12 5( 2 1) − or 5 2 5 − 2 M1 for 2 1 2 1 − × − 13 8 16 π + oe 3 B1 for radius = 8 and M1 for radius their π× or their curved length + 2 × their radius or if 0 scored SC2 for final answer 32( 2) π + oe 14 32 13 1 1 15 6 x oe 2 M1 for = k y x or M1 for k = 6 with no correct equation seen 16 12 3 B1 for 2log3 log9 = or 3log2 log8 = and M1 for correct use of log log log + = a b ab or log log log  − =     a a b b 17 Stretch x-axis invariant, factor 3 1 1