Cambridge IGCSE Mathematics - International 0607 — 2013 May/June Paper 2 · Variant 2

This document consists of 8 printed pages. IB13 06_0607_22/RP © UCLES 2013 [Turn over *4727863751* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/22 Paper 2 (Extended) May/June 2013 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 2013 0607/22/M/J/13 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 2013 0607/22/M/J/13 [Turn over For Examiner's Use Answer all the questions. 1 U 3 3 1 5 6 4 7 1 B A C The Venn diagram shows the number of elements in each of the sets A, B and C, and n(U) = 30. (a) Find (i) n(A), Answer(a)(i) [1] (ii) n ) ( B C ′ ∪ . Answer(a)(ii) [1] (b) Shade the region C B A ∪ ∩ ) ( on the Venn diagram. [1] 2 P 65° Q B R A O NOT TO SCALE A, P, Q, B and R lie on a circle, centre O. Angle APB = 65°. Find (a) angle AQB, Answer(a) Angle AQB = [1] (b) angle AOB, Answer(b) Angle AOB = [1] (c) angle ARB. Answer(c) Angle ARB = [1]

4 © UCLES 2013 0607/22/M/J/13 For Examiner's Use 3 5 4 3 2 1 –1 –2 –3 –4 –5 –6 –7 –8 –9 –10 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9 10 y x P Q 0 (a) Enlarge shape P using centre (3, 4) and scale factor 3. [2] (b) Describe fully the single transformation that maps shape P onto shape Q. [3] 4 (a) Simplify. 16x16 ÷ 2x2 Answer(a) [2] (b) 2 1 8 = n Find the value of n. Answer(b) n = [2]

5 © UCLES 2013 0607/22/M/J/13 [Turn over For Examiner's Use 5 Rationalise the denominator in each of the following. (a) 3 2 Answer(a) [1] (b) 1 3 1 − Answer(b) [2] 6 (a) Find the value of ax3 when a = 1200 and x = 5. Give your answer in standard form. Answer(a) [2] (b) Make x the subject of the formula y = ax3. Answer(b) x = [2]

6 © UCLES 2013 0607/22/M/J/13 For Examiner's Use 7 (a) Write 2log(x + 1) – log(x – 1) as a single logarithm. Answer(a) [2] (b) log3 p = 4 where p is an integer. Find the value of p. Answer(b) p = [2] 8 These are the first five terms of a sequence. 2 6 12 20 30 (a) Find the next term. Answer(a) [1] (b) Find an expression for the nth term. Answer(b) [3]

7 © UCLES 2013 0607/22/M/J/13 [Turn over For Examiner's Use 9 f(x) = 3 + 2x Find (a) f(f(– 4)), Answer(a) [2] (b) f –1(x) . Answer(b) [2] 10 y varies inversely as x2. When x = 2, y = 24. Find a formula for y in terms of x. Answer y = [2] Question 11 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 2013 0607/22/M/J/13 For Examiner's Use 11 R r NOT TO SCALE The diagram shows a circle of radius r inside a circle of radius R. (a) Find an expression, in terms of π, r and R, for the shaded area. Factorise your expression completely. Answer(a) [2] (b) When R = r + 3, the shaded area is 24π. Find the value of r. Answer(b) r = [2]

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2013 series 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/22 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 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 2013 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components. www.XtremePapers.com

Page 2 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0607 22 © Cambridge International Examinations 2013 1 (a) (i) (ii) (b) 15 26 1 1 1 2 (a) (b) (c) 65 130 115 1 1 1 3 (a) Image at (–3, 1), (3, 1), (–3, –8) 2 B1 for correct shape and orientation but incorrect centre (b) Stretch [factor] 3 y-axis invariant 1 1 1 marks are independent 4 (a) 8x14 2 B1 for kx14 or 8xk, k ≠ 0 (b) 3 1 − o.e. 2 M1 for evidence of 23 = 8 5 (a) 3 3 2 1 (b) 2 1 3 + 2 M1 for 1 3 1 3 + + × 6 (a) 1.5 × 105 2 B1 for 150 000 (b) 3 a y 2 M1 for ÷ a correctly M1 for cube root correctly 7 (a) ( )       − + 1 1 log 2 x x 2 M1 for 2)1 log( + x or       −1 1 log x (b) 81 2 M1 for p = 34 8 (a) 42 1 (b) )1 ( + n n o.e. 3 M2 for c bn an + + 2 , a not zero and b, c not both zero or M1 for reaching differences of 2 or ‘as above’ with both b, c zero

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0607 22 © Cambridge International Examinations 2013 9 (a) –7 2 B1 for f(–4) = –5 (b) 2 3 − x 2 M1 for x = 3 + 2y or y – 3 = 2x or x y + = 2 3 2 10 2 96 x y = 2 M1 for 2 x k y = o.e. 11 (a) ) )( ( r R r R − + π 2 B1 for ) ( 2 2 r R − π or ) )( ( r R r R − π + π or ) )( ( r R r R + π − π (b) 2.5 o.e. 2 M1 for reaching π π 24 3 ) 3 2 ( = + r or better or for reaching R + r = 8 and R – r = 3