Cambridge IGCSE Mathematics - International 0607 — 2013 May/June Paper 2 · Variant 3

This document consists of 8 printed pages. IB13 06_0607_23/3RP © UCLES 2013 [Turn over *4686246803* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/23 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 0607/23/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 0607/23/M/J/13 [Turn over For Examiner's Use Answer all the questions. 1 Work out (1.6 × 103) ÷ (4 × 105). Give your answer in standard form. Answer [2] 2 Solve the equations. (a) 2 – 3(1 – 2x) = 4(2 – x) Answer(a) x = [3] (b) sinx = 2 3 ± for 0° Y x Y 360° Answer(b) x = [3]

4 © UCLES 2013 0607/23/M/J/13 For Examiner's Use 3 Find the value of the following. (a) 40 Answer(a) [1] (b) 3 2 27 − Answer(b) [2] 4 (a) Simplify. 98 200 − Answer(a) [2] (b) Rationalise the denominator. 3 5 11 − Answer(b) [3]

5 © UCLES 2013 0607/23/M/J/13 [Turn over For Examiner's Use 5 The diagram shows the graph of y = f(x) for – 4 Y x Y 3. 3 2 1 –1 –2 –3 –4 –3 –2 –1 1 0 2 3 4 y x (a) On the diagram below, sketch the graph of y = |f(x)|. 3 2 1 –1 –2 –3 –4 –3 –2 –1 1 0 2 3 4 y x [3] (b) On the diagram below, sketch the graph of y = f(x – 1). 3 2 1 –1 –2 –3 –4 –3 –2 –1 1 0 2 3 4 y x [2]

6 © UCLES 2013 0607/23/M/J/13 For Examiner's Use 6 Make x the subject of the equation. x b x a = + 3 Answer x = [3] 7 O D E C B A 30° 70° x° y° z° NOT TO SCALE B, C, D and E lie on a circle, centre O. CE is a diameter, angle DAC = 30° and angle BOE = 70°. Find the values of x, y and z. Answer x = y = z = [3]

7 © UCLES 2013 0607/23/M/J/13 [Turn over For Examiner's Use 8 The points A (1, 9) and B (7, 1) are shown on the diagram below. 0 2 4 6 8 10 10 8 6 4 2 y x A B (a) Calculate the length AB. Answer(a) [2] (b) (i) Find the co-ordinates of the midpoint of the line AB. Answer(b)(i) ( , ) [1] (ii) Find the equation of the perpendicular bisector of the line AB. Answer(b)(ii) [3] Questions 9 and 10 are 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 0607/23/M/J/13 For Examiner's Use 9 Wendy walks 9 km in 2 1 1 hours. She then runs 9 km in 45 minutes. Find her average speed in km/h for the whole journey. Answer km/h [3] 10 Paulo goes to a supermarket. The probability that he buys orange juice is 0.65 . The probability that he does not buy milk is 0.30 . The probability that he buys milk but does not buy orange juice is 0.15 . (a) Complete the table of probabilities. Buys milk Does not buy milk Total Buys orange juice 0.65 Does not buy orange juice 0.15 Total 0.30 1.00 [2] (b) Find the probability that Paulo buys either orange juice or milk but not both. Answer(b) [2]

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2013 series 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/23 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 23 © Cambridge International Examinations 2013 1 3 10 4 − × 2 B1 2 10 4.0 − × o.e. 2 (a) (b) 0.9 o.e. cao 60, 120, 240, 300 3 3 M1 Correct expansion; condone 1 slip M1 Correct simplification of their equation into the form kx = a –1 for extra answer(s) in range, ignore answers out of range. B1 for 60 B1 for 120 B1 for 240 or 300 3 (a) (b) 1 9 1 1 2 B1 for 9 27 3 2 = soi 4 (a) (b) 2 3 2 3 5 + o.e. 2 3 B1 for either 2 10 or 2 7 seen M1 Multiplying by ( ) ( ) 3 5 3 5 + + M1 for 25 – 3 seen 5 (a) (b) Correct for 2 > x and 3 − < x Correct for 1 3 < < − x Correct curvature at 2 ,1 ,3 − = x Correct curve 1 1 1 2 Approx correct height of maxima B1 curve translated in x-direction 6 [ ] b a b x − = 3 www3 3 M1 Correct multiplication M1 Correct expansion and collection of terms M1 Correct factorisation and division by their ( ) b a − 7 x = 35 y = 55 z = 60 1 1 1 8 (a) (b) (i) (ii) 10 (4, 5) ( ) 4 4 3 5 − = − x y o.e. 2 1 3 M1 for 2 2 8 6 + B2 for k x y + = 4 3 B1 3 4 − seen B1FT their 4 3 o.e. seen

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0607 23 © Cambridge International Examinations 2013 9 8 3 B1 for 2.25 o.e. or 135 seen M1 ( ) 25 .2 18 their or 60 135 18 × 10 (a) (b) Buys Milk Does not buy Milk Total Buys Orange Juice 0.55 0.1 Does not buy orange juice 0.2 0.35 Total 0.7 0.25 o.e. 2 2 B1 for 3 entries correct M1 (their) 0.1 + 0.15