Cambridge IGCSE Mathematics - International 0607 — 2016 May/June Paper 2 · Variant 3

This document consists of 8 printed pages. DC (NH/SW) 115871/2 © UCLES 2016 [Turn over * 5 4 7 0 2 7 1 6 0 9 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/23 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. Cambridge International Examinations Cambridge International General Certificate of Secondary Education

2 0607/23/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 0607/23/M/J/16 © UCLES 2016 [Turn over Answer all the questions. 1 Alex drives 40 km to work at a speed of 50 km/h. He leaves home at 07 45. Find the time he arrives at work. … [3] 2 Alexis and Bertrand share a sum of money in the ratio 3 : 5. Alexis receives $36. Work out how much Bertrand receives. $ … [2] 3 11 16 8 9 14 6 20 16 12 10 Find the median of these ten numbers. … [2]

4 0607/23/M/J/16 © UCLES 2016 4 (a) A regular polygon has 12 sides. Work out the sum of the interior angles of the polygon. … [2] (b) The interior angle of a regular polygon is 165°. Find the number of sides of this polygon. … [2] 5 The total cost of 2 kg of apples and 1.5 kg of pears is $9.70 . Apples cost $2.60 per kilogram. Find the cost of 1 kg of pears. $ … [3]

5 0607/23/M/J/16 © UCLES 2016 [Turn over 6 Find the next term in each of these sequences. (a) 81, 77, 72, 66, 59, … [1] (b) 3, –6, 12, –24, 48, … [1] (c) 16, 8, 4, 2, 1, … [1] 7 Work out, giving your answer in standard form. (a) 7.5 10 4 10 4 6 # # + - - ^ ^ h h … [2] (b) 7.5 10 4 10 4 6 # # # - - ^ ^ h h … [2]

6 0607/23/M/J/16 © UCLES 2016 8 Expand the brackets. 7 x x 2 3 - ^ h  [2] 9 Write this list of numbers in order starting with the smallest. 3 2 65% 0.7 0.069 0.62 … < … < … < … < … [2] smallest 10 Expand the brackets and simplify. 2 3 4 3 2 3 x x - - - ^ ^ h h … [2]

7 0607/23/M/J/16 © UCLES 2016 [Turn over 11 (a) Simplify. 3 4 12 7 3 - ^ h … [2] (b) Rationalise the denominator. 3 2 7 - … [2] 12 Solve the simultaneous equations. You must show all your working. 3 2 5 2 5 3 x y x y + =- - = x = … y = … [4] Question 13 is printed on the next page.

8 0607/23/M/J/16 © UCLES 2016 13 (a) Sketch the graph of 2 y x3 = + . Give the co-ordinates of the point where the graph crosses the y-axis. 0 y x ( … , … ) [2] (b) Sketch the graph of 2cos y x = for 180° 180° x G G - . Give the co-ordinates of the point where the graph crosses the y-axis. 0 –180 180 y x ( … , … ) [3] 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. This document consists of 3 printed pages. © UCLES 2016 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/23 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 23 © 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 [0]8 33 3 M2 for 40 60 50 × oe or M1 for 40 50 soi 2 60 2 M1 for 36 3 3 11.5 2 M1 for re-ordering list of at least 6 4 (a) 1800 2 M1 for 360 180 12 − or for (12 – 2) ×180 soi (b) 24 2 B1 for 360 180 165 − 5 3 3 M2 for 9.7 2 2.6 1.5 −× or M1 for 9.70 – 2 ×2.6 6 (a) 51 1 (b) –96 1 (c) 0.5 oe 1 7 (a) 4 7.54 10− × 2 M1 for 0.000 75 + 0.000 004 or 6 750 10− × or 4 0.04 10− × or figs 754 (b) 9 3 10− × 2 B1 for 10 30 10− × or answer 0.000 000 003 8 5 2 7 − x x final answer 2 B1 for each 9 2 2 0.069 0.6 65% 0.7 3 2 B1 for one in wrong place 10 1 2 B1 for 6 8 − x or 6 9 − + x If 0 scored SC1 for 1 + kx

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2016 0607 23 © Cambridge International Examinations 2016 Question Answer Mark Part Marks 11 (a) 3 2 B1 for 4 36 oe or 7 9 oe soi (b) 3 2 + final answer 2 M1 for 3 2 3 2 + × + 12 Correctly equating one set of coefficients Correct method to eliminate one variable 1 = − x 1 = − y M1 M1 B1 B1 Equation x = or y = from one equation Correct substitution into other equation If 0 scored SC1 for correct substitution into one of original equations and evaluation to find other variable 13 (a) Correct graph 2 B1 for 3 = y x shape B1 for cubic graph through (0, 2), with 2 marked or (0, 2) on answer line (b) Correct graph 3 B1 for cos graph, max at (0, k) approx B1 for graph through (0, 2), with 2 marked or (0, 2) on answer line B1 for range as 2 to –2 approx