Cambridge IGCSE Mathematics - International 0607 — 2013 Oct/Nov Paper 2 · Variant 1

This document consists of 8 printed pages. IB13 11_0607_02/2RP © UCLES 2013 [Turn over *3859409843* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/02 Paper 2 (Extended) October/November 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 0607/02/O/N/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 0607/02/O/N/13 [Turn over For Examiner's Use Answer all the questions. 1 Solve the simultaneous equations. 3g – 2h = 11 g – 2h = 5 Answer g = h = [2] 2 (a) U A B n(U) = 20, n(A ∪ B)' = 3, n(A) = 11, n(B) = 13. Find n(A ∩ B' ). Answer(a) [2] (b) On each Venn diagram, shade the region indicated. U P Q (P ∩ Q)' U S T S ∪ T ' [2] 3 Tiago buys a concert ticket and then sells it for $15. He makes a profit of 20%. Calculate how much Tiago paid for the ticket. Answer $ [3]

4 © UCLES 2013 0607/02/O/N/13 For Examiner's Use 4 36° 52° D C E P A B Q NOT TO SCALE ABCD is a parallelogram and BQPC is a rhombus. DCE is a straight line. Angle DAB = 52° and angle ECP = 36°. Find the size of angle BPC. Answer [3] 5 (a) Simplify 72 . Answer(a) [1] (b) 2 1 2 2 2 q p + = − + Find the values of p and q. Answer(b) p = q = [3]

5 © UCLES 2013 0607/02/O/N/13 [Turn over For Examiner's Use 6 Simplify the following. (a) 2y2 × 3y3 Answer(a) [2] (b) 3 27 27 p Answer(b) [2] 7 (a) Find the amplitude and period of the function f(x) = 4cos(4x). Answer(a) Amplitude = Period = [2] (b) g(x) = 4cos(4x) – 4 Describe fully the single transformation that maps the graph of y = f(x) onto the graph of y = g(x). Answer(b) [2]

6 © UCLES 2013 0607/02/O/N/13 For Examiner's Use 8 (a) Write down the value of 3 1 8 . Answer(a) [1] (b) Find the exact value of 2 3 4 −       . Answer(b) [2] 9 NOT TO SCALE x° The diagram shows a cube of side length 1. Find the value of tan x°. Answer [3]

7 © UCLES 2013 0607/02/O/N/13 [Turn over For Examiner's Use 10 x cm 12 cm 30° NOT TO SCALE Find the exact value of x. Answer x = [3] 11 NOT TO SCALE D C B A q p N M ABCD is a parallelogram. DM = MC and CN = 2NB. = p and = q. (a) Write down in terms of q. Answer(a) [1] (b) Find in terms of p and q. Answer(b) [1] 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 2013 0607/02/O/N/13 For Examiner's Use 12 f(x) = 3x – 1 g(x) = 12 – x Find (a) f(g(8)), Answer(a) [2] (b) f(g(x)), in its simplest form, Answer(b) [2] (c) g– 1(x). Answer(c) g– 1(x) = [1]

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 2013 series 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 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 October/November 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 – October/November 2013 0607 02 © Cambridge International Examinations 2013 1 3, – 1 1, 1 2 (a) 4 2 Allow on diagram if not spoiled B1 for 7 ) ( n = ∩B A (b) 1, 1 3 12.5[0] 3 M2 for 15 ÷ 1.2 oe or M1 for recognising 120% = 15 oe 4 44 3 M2 for angle BCP or BQP = 92 or angle CPQ or CBQ = 88 or M1 for angle DCB = 52 5 (a) 2 6 1 (b) 4, 3 3 M1 for 1 2 1 2 + + × or )1 2 )( 2 ( 2 2 − + = + q p A1 for 4, A1 for 3 6 (a) 5 6y 2 B1 for n y 6 or 5 ky (b) 9 3p 2 B1 for n p 3 or 9 kp 7 (a) 4, 90 1,1 (b) Translation,       −4 0 1,1 B1 for translation B1 for       −4 0 8 (a) 2 1 (b) 16 9 2 M1 for 9 16 or ( ) 2 3 4 1 oe or better 9 2 1 or 2 2 3 M1 for (diag of face)2 = 2 M1 for correct fraction = tan 10 3 6 3 M2 for 2 3 = 12 x or 2 2 2 6 12 − = x or B1 for cos30 = 2 3 or opp side = 6

Page 3 Mark Scheme Syllabus Paper IGCSE – October/November 2013 0607 02 © Cambridge International Examinations 2013 11 (a) – 3 2 q 1 (b) 2 1 p – 3 2 q 1FT FT 2 1 p + their (a) 12 (a) 11 2 B1 for [g(8)] = 4 (b) 35 – 3x oe 2 M1 for 1 ) 12 (3 − −x (c) 12 – x oe 1