Cambridge IGCSE Mathematics - International 0607 — 2011 May/June Paper 2 · Variant 1

This document consists of 8 printed pages. IB11 06_0607_21/4RP © UCLES 2011 [Turn over *4380945812* 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 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 0607/21/M/J/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 0607/21/M/J/11 [Turn over For Examiner's Use Answer all the questions. 1 (a) Simplify 75 . Answer(a) [1] (b) Simplify 2 5 3 − by rationalising the denominator. Answer(b) [2] 2 The first four terms of a sequence are 0, 3, 8, 15. (a) Write down the next two terms of this sequence. Answer(a) , [1] (b) Find an expression for the nth term of this sequence. Answer(b) [2] 3 Solve the equation 17 – 2x = 4x – 7. Answer x = [2]

4 © UCLES 2011 0607/21/M/J/11 For Examiner's Use 4 p = 2 3    q = 4 3 −       (a) Find 2p – 3q. Answer(a)           [2] (b) Calculate │q│. Answer(b) [2] 5 (a) Factorise x2 – 3x – 4. Answer(a) [2] (b) Solve for x. 10 I 2(6 – x) Answer(b) [2]

5 © UCLES 2011 0607/21/M/J/11 [Turn over For Examiner's Use 6 Using set notation describe the regions shaded on the Venn diagrams. (a) U A B Answer(a) [1] (b) U A B Answer(b) [1] 7 F varies inversely as the square of d. When F = 9, d = 2. (a) Find F in terms of d. Answer(a) F = [2] (b) Find the value of F when d is 3. Answer(b) F = [1]

6 © UCLES 2011 0607/21/M/J/11 For Examiner's Use 8 Simplify. (a) log 9 + 3 log 2 – 2 log 6 Answer(a) [3] (b) 3 4 81 16 −       Answer(b) [2] 9 d x c x c d + = − Find x in terms of c and d. Answer x = [3]

7 © UCLES 2011 0607/21/M/J/11 [Turn over For Examiner's Use 10 All the students in a class of 20 took tests in Mathematics and Chemistry. The following table shows the results of these two tests. Pass Fail Mathematics 12 8 Chemistry 11 9 M is the set of students who passed the Mathematics test. C is the set of students who passed the Chemistry test. x is the number of students who passed both tests. (a) Write 3 expressions in terms of x to complete the Venn diagram. U M x … … … C [3] (b) Two pupils failed both Mathematics and Chemistry. Find the value of x, the number of students who passed both tests. Answer(b) x = [2] 11 For 0° I x I 360° find the values of x that satisfy the equation cos x = – 1 2 . Answer x = and x = [2]

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 0607/21/M/J/11 For Examiner's Use 12 y x 3 2 1 –1 –2 –3 0 –180° –90° 90° 180° 270° 360° (a) Write down the equation of the graph. Answer(a) [2] (b) On the same axes above sketch the graph of y = 2 sin x for −180° Y x Y 360°. [2]

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2011 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 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 – May/June 2011 0607 21 © University of Cambridge International Examinations 2011 1 (a) 5 3 B1 (b) 11 3 5 + or 22 ) 3 5 ( 2 + oe Final Answer B2 Only allow denominators of 11 or 22. If B0 give M1 for intention of multiplying by 3 5 3 5 + + [3] 2 (a) (b) Both 24 and 35 n2 – 1 oe B1 B2 If B0 give B1 for n2 seen but no n term. i.e. n2 + k where k is an integer. [3] 3 (a) 4 B2 If B0 give B1 for either ±6x or ±24 seen [2] 4 (a)       −3 16 B2 Give B1 for each correct number (b) 5 B2 Not ±5 If B0 give M1 for (±4)2 + 32 [condone no brackets] which can be implied by ±5 or 25. [4] 5 (a) (b) (x – 4)(x + 1) oe x < 1 B2 B2 ISW for any solutions once correct factors seen, but any solutions without working score 0. If B0 give SC1 for signs reversed. Still ISW for any solutions. Condone ≤ used throughout. If B0 give M1 for 12 – 2x or 5 < 6 – x or 5 = 6 – x seen. (x =) 1 ww is M0. [4] 6 (a) (b) A ∩ B B ∩ A′ oe B1 B1 E.g. (A ∪ B) ∩ A′ (A ∪ B′)′ [2] 7 (a) 2 36 d [Condone k/d2 with k = 36 stated] Final Answer B2 If B0 give B1 for (F =) 2 d k or (F =) 2 1 kd seen [k ≠ 1] (b) 4 B1ft Ft only from answers in the form 2 d k or kd2 or d k [k ≠ 1] [3]

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2011 0607 21 © University of Cambridge International Examinations 2011 8 (a) For correct use of nlog a = log an For correct use log a + log b = log ab or log a – log b = log b a log 2 www3 M1 M1 A1 E.g. log 23 or log 8 or log 62 or log 36. Using their figures (b) 27 8 or 3 3 2       Final Answer B2 If B0 give B1 for answers with numerator 8 or denominator 27 OR SC1 for answers of 8 27 or ( ) 8 / 27 1 or 3 2 3 ±       [5] 9 Clearing both denominators correctly to get d2 = (x + c)(x – c) or better. Making x2 the subject of an equation with no denominators. Finding the square root of an equation having x2 as the subject. (±)√(c2 + d2) as final answer www3 M1 M1 M1 Condone d(x – c) as denominator on both sides. Condone missing ± Their final answer must be correct and www to score M3 [3] 10 (a) (b) 12 – x, 11 – x, x – 3 oe 5 B1B1B1 B2 SC1 for Venn diagram with 7, 6 and 2 seen If B0 scored give M1 for their (x − 3) = 2 or their (12 – x) + x + their (11 – x ) + 2 = 20 seen. [5] 11 120 and 240 B1B1 [2] 12 (a) (b) y = 3sin2x Final Answer Correct sketch B2 B2 If B0 give B1 for 3sin(f(x)) or ksin2x If B0 give SC1 for either correct amplitude (2) or correct period (360°). [4]