Cambridge IGCSE Mathematics - International 0607 — 2012 May/June Paper 2 · Variant 1

This document consists of 8 printed pages. IB12 06_0607_21/4RP © UCLES 2012 [Turn over *6989037045* For Examiner's Use UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/21 Paper 2 (Extended) May/June 2012 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, highlighters, glue or correction fluid. You may use a 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. www.XtremePapers.com

2 © UCLES 2012 0607/21/M/J/12 Formula List For the equation ax2 + bx + c = 0 x = 2 _ ± 4 2 _ b b ac a Curved surface area, A, of cylinder of radius r, height h. A = 2πrh Curved surface area, A, of cone of radius r, sloping edge l. A = πrl Curved surface area, A, of sphere of radius r. A = 4πr2 Volume, V, of pyramid, base area A, height h. V= 1 3 Ah Volume, V, of cylinder of radius r, height h. V = πr2h Volume, V, of cone of radius r, height h. V = 1 3 πr2h Volume, V, of sphere of radius r. V = 4 3 πr3 = = sin sin sin a b c A B C a2 = b2 + c2 – 2bc cos A Area = 1 2 bc sin A A a B C b c

3 © UCLES 2012 0607/21/M/J/12 [Turn over For Examiner's Use Answer all the questions. 1 Solve the simultaneous equations. 7 2 = − y x 3 2 = + y x Answer x = Answer y = [2] 2 A bus leaves Afford at 07 55. It travels 15 km to Beetown at a speed of 50 km/h. Find the time the bus arrives in Beetown. Answer [3] 3 The area of a semicircle is given by the formula 2 2 r π A = . Make r the subject of the formula. Answer r = [3]

4 © UCLES 2012 0607/21/M/J/12 For Examiner's Use 4 (a) h 4 NOT TO SCALE 6 Find the exact value of h. Answer(a) [2] (b) g 12 θ NOT TO SCALE sin 3 2 = θ , cos 3 5 = θ , tan 5 2 = θ . Find the exact value of g. Answer(b) [2] 5 0 y x The sketch shows the graph of y = f(x). Using the same axes, sketch the graph of y = 2f(x). [2]

5 © UCLES 2012 0607/21/M/J/12 [Turn over For Examiner's Use 6 (a) Find the two possible values of y x + when 4 2 = x and 1 = y . Answer(a) , [2] (b) Expand and simplify ( )( ) 1 2 3 1 2 − + . Answer(b) [2] 7 Sara records some information about the number of cars in a car park. U = {cars in the car park} F = {5-door cars} S = {silver cars} F S U You may use the Venn diagram to help you answer the following questions. (a) n(U) = 12, n(F) = 7, 2 ) n( = ∩S F , 11 ) n( = ∪S F . Find (i) n(S), Answer(a)(i) [1] (ii) ) n( F S ′ ∪ . Answer(a)(ii) [1] (b) Sara chooses a car from the car park at random. Find the probability that it is a 5-door car. Answer(b) [1] (c) Sara chooses a silver car at random. Find the probability that it is a 5-door car. Answer(c) [1]

6 © UCLES 2012 0607/21/M/J/12 For Examiner's Use 8 Factorise completely. (a) 48 2 2 − + x x Answer(a) [2] (b) z y xz xy 6 3 2 − − + Answer(b) [2] 9 x y 1 ∝ When x = 4, y = 3. Find y when x = 25. Answer [3]

7 © UCLES 2012 0607/21/M/J/12 [Turn over For Examiner's Use 10 The first five terms of a sequence are – 2, 1, 6, 13, 22. (a) Write down the next term in the sequence. Answer(a) [1] (b) Find an expression, in terms of n, for the nth term of the sequence. Answer(b) [3] 11 Two mathematically similar containers have heights of 3 cm and 6 cm. The larger container, when full, can hold 320 ml of water. Calculate how much water the smaller container can hold when full. Answer ml [2] Question 12 is on the next page.

8 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. University of 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. © UCLES 2012 0607/21/M/J/12 For Examiner's Use 12 (a) (i) 81 3 = p Write down the value of p. Answer(a)(i) [1] (ii) 8 1 2 = q Write down the value of q. Answer(a)(ii) [1] (b) 2 log 5 3 log 2 log + = y Find the value of y. Answer(b) [3]

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2012 question paper for the guidance of teachers 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 must be read in conjunction with the question papers and the report on the examination. • Cambridge will not enter into discussions or correspondence in connection with these mark schemes. Cambridge is publishing the mark schemes for the May/June 2012 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses. www.XtremePapers.com

Page 2 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2012 0607 21 © University of Cambridge International Examinations 2012 1 (x) = 5, (y) = –1 2 B1 each, or M1 for attempt to eliminate x or y (allow 1 numerical slip) [2] 2 08 13 oe 3 M1 for distance/speed seen (implied by 0.3) A1 for 18 minutes [3] 3 π A 2 ) (± 3 M1 for × 2 correctly M1 for ÷ π correctly M1 for correctly All independent, in any order [3] 4 (a) 13 2 or 52 as final answer 2 M1 for 42 + 62 (b) 5 4 or 3 5 12 or 80 2 M1 for 12 cos g = θ or better [4] 5 2 B1 for parabola with vertex twice as high B1 for cutting x-axis in same places as y = f(x) (Ignore curve below the x axis) [2] 6 (a) 1, 3 2 B1 each (b) 2 2 5 + 2 M1 for 1 2 3 2 2 2 3 − + − or better [4] 7 (a) (i) 6 1 (ii) 7 1 (b) 12 7 oe 1 (c) 6 2 oe 1 ft If 6 2 not seen, then ft their part (a)(i) [4] 8 (a) (x + 8)(x – 6) 2 SC1 for any pairs of brackets giving two correct terms when multiplied out. (b) (y + 2z)(x – 3) 2 M1 for x(y + 2z) – 3(y + 2z) or y(x – 3) + z(2x – 6) (or better) [4] 9 (±)1.2 oe 3 M2 for x y 6 = oe or M2 for 4 1 25 1 3 = y oe (M1 for x k y = oe, where k ≠ 1, then dep M1 for 25 their k y = ) [3]

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2012 0607 21 © University of Cambridge International Examinations 2012 10 (a) 33 1 Ignore extra terms (b) n2 – 3 3 M1 for reaching second differences same M1 for an2 + bn + c (implies first M) a ≠ 0 [4] 11 40 2 M1 for 3 3 6       or 3 6 3       seen [2] 12 (a) (i) 4 1 (ii) –3 1 (b) 288 3 M1 for a log b = log ba correctly used once (Implied by 32 or 25 seen) M1 for log p + log q = log pq correctly used (Implied by y = 32 × 25 but can be seen to be correctly used with incorrect values of p, q.) Note log 288 scores 2/3 [5]