Cambridge IGCSE Mathematics - International 0607 — 2011 Oct/Nov Paper 2 · Variant 1

This document consists of 8 printed pages. IB11 11_0607_02/3RP © UCLES 2011 [Turn over *0721467745* For Examiner's Use UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/02 Paper 2 (Extended) October/November 2011 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 2011 0607/02/O/N/11 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 2011 0607/02/O/N/11 [Turn over For Examiner's Use Answer all the questions. 1 (a) Write 375 × 1012 in standard form. Answer(a) [1] (b) Calculate 75% of $2.40. Answer(b) $ [2] (c) Solve the equation | x + 1 | = 2. Answer(c) x = or x = [2] 2 U A B (a) n(U) = 20, n(A) = 10, n(B) = 7, n(A ∪ B) = 13. Find (i) n(A ∪ B)', Answer(a)(i) [1] (ii) n(A ∩ B). Answer(a)(ii) [1] (b) On the Venn diagram, shade the region A ∪ B'. [1]

4 © UCLES 2011 0607/02/O/N/11 For Examiner's Use 3 The equation of a straight line is 3x + 4y = 12. Write the equation in the form y = mx + c. Answer y = [2] 4 The volume of a sphere of radius 3 cm is kπ cm3. Find the value of k. Answer k = [2] 5 (a) Simplify 125 . Answer(a) [1] (b) Simplify 1 6 3 − by rationalising the denominator. Answer(b) [2]

5 © UCLES 2011 0607/02/O/N/11 [Turn over For Examiner's Use 6 6, 12, 24, 48, 96, ... (a) Write down the next term in the sequence. Answer(a) [1] (b) Find the 8th term in the sequence. Answer(b) [1] (c) Find an expression for the nth term of the sequence. Answer(c) [2] 7 Factorise completely. (a) x2 – 2x – 24 Answer(a) [2] (b) xy2 – 4xz2 Answer(b) [2]

6 © UCLES 2011 0607/02/O/N/11 For Examiner's Use 8 q Q O P R p NOT TO SCALE The diagram shows the vectors = p and = q. R is on QP such that QR = 1 4 QP. Find the following vectors in terms of p and q. Give each answer in its simplest form. (a) Answer(a) = [1] (b) Answer(b) = [2] 9 0 6 1 The die in the diagram has a number on each face. The numbers are 0, 0, 1, 2, 4, 6. The die is rolled until it shows 0 on the top face. Find the probability that this happens for the first time on the third roll. Answer [2]

7 © UCLES 2011 0607/02/O/N/11 [Turn over For Examiner's Use 10 Solve the following equation. 2 1 1 9 3 2 x x + + + = Answer x = [3] 11 (a) 3 = log p 8 Write down the value of p. Answer(a) p = [2] (b) log12 + log9 = qlog2 + rlog3 Find the values of q and r. Answer(b) q = r = [3] Question 12 is printed 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 2011 0607/02/O/N/11 For Examiner's Use 12 An object moves in a circle with speed v. The force on the object is F. F varies directly as v2. When v = 5, F = 200. (a) Find a formula for F in terms of v. Answer(a) F = [2] (b) (i) Find F when v = 2. Answer(b)(i) F = [1] (ii) Find v when F = 968. Answer(b)(ii) v = [1]

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 2011 question paper for the guidance of teachers 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/02 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 October/November 2011 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 – October/November 2011 0607 02 © University of Cambridge International Examinations 2011 1 (a) 3.75 × 1014 1 (b) 1.8(0) 2 M1 for 0.75 × 2.4 or complete equivalent method (c) –3, 1 B1, B1 If B0, M1 for x + 1 = ±2 2 (a) (i) 7 1 (ii) 4 1 (b) 1 3 3 4 3 + − x o.e. 2 M1 for 4y = 12 – 3x or 4 12 4 3 = + y x 4 36 2 M1 for 3 4 π × 33 5 (a) 5 5 1 (b) 3 3 6 + o.e. 2 M1 for intention to × 3 6 3 6 + + 6 (a) 192 1 (b) 768 1 (c) 3 × 2n o.e. 6 × 2n–1, 2n+2–2n 2 M1 for power of 2 in terms of n in answer and not spoiled ∪ A B

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2011 0607 02 © University of Cambridge International Examinations 2011 7 (a) (x – 6)(x + 4) 2 SC1 for (x + a)(x + b) where ab = –24 or a + b = –2 (b) x(y – 2z)(y + 2z) 2 SC1 for x(y2 – 4z2) or (xy – 2xz)(y + 2z) or (y – 2z)(xy + 2xz) 8 (a) – p + q or q – p 1 (b) 4 1 p + 4 3 q o.e. (in simplest form) 2 M1 for QR OQ OR + = or PR OP + s.o.i. 9 27 4 o.e. 2 M1 for 6 2 6 4 6 4 × × o.e. 10 7 3 M1 for multiplying all three terms by 6 or all over 6 or left hand side over 6 = 9 A1 for 54 )1 ( 3 )1 2 ( 2 = + + + x x or 9 6 5 7 = + x 7 may be seen correctly embedded – accept 11 (a) 2 2 M1 for p3 = 8 (b) q = 2, r = 3 3 M1 for use of log ab = log a + log b or log ab = b log a M1 dep for log 12 and log 9 in terms of log2 and log3 only, or log22 + log33 seen, or 108 = 2q × 3r 12 (a) F = 8v2 2 M1 for 2 kv F = o.e. k ≠ 1 (b) (i) 32 1 ft ft their (a) only if kv2 k ≠ 1 (ii) 11 1 ft ft their (a) only if kv2 k ≠ 1