Cambridge IGCSE Mathematics - International 0607 — 2012 May/June Paper 1 · Variant 3

This document consists of 9 printed pages and 3 blank pages. IB12 06_0607_13/RP © UCLES 2012 [Turn over *8151451650* For Examiner's Use UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/13 Paper 1 (Core) May/June 2012 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 2012 0607/13/M/J/12 Formula List Area, A, of triangle, base b, height h. A = 1 2 bh Area, A, of circle, radius r. A = πr2 Circumference, C, of circle, radius r. C = 2πr 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 prism, cross-sectional area A, length l. V =Al 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

3 © UCLES 2012 0607/13/M/J/12 [Turn over For Examiner's Use Answer all the questions 1 (a) Work out 0.2 × 0.4 . Answer (a) [1] (b) Write these in order, smallest first. 0.85 89% 0.9 0.745 Answer (b) < < < [1] 2 Work out 15% of $160 . Answer $ [2] 3 (a) Write 0.007582 correct to 3 significant figures. Answer (a) [1] (b) Write 20 9 as a decimal. Answer (b) [1]

4 © UCLES 2012 0607/13/M/J/12 For Examiner's Use 4 Work out. 2 4 3 + 3 3 2 Answer [3] 5 (a) Find the value of 70 . Answer (a) [1] (b) Simplify. 7x2 × 3x5 Answer (b) [2]

5 © UCLES 2012 0607/13/M/J/12 [Turn over For Examiner's Use 6 (a) Factorise. 3a – a2 Answer (a) [1] (b) Expand and simplify. (x – 5)(x + 1) Answer (b) [2] 7 Under each shape write the correct letter from the table. L Line symmetry only R Rotational symmetry only B Both line and rotational symmetry N No symmetry ≠ θ P § ☺ [3]

6 © UCLES 2012 0607/13/M/J/12 For Examiner's Use 8 f(x) = 3x + 2 (a) Find f(5) . Answer (a) [1] (b) Find x when f(x) = 14 . Answer (b) [2] 9 A class of 21 students took a mathematics test. Here are their results. 29 34 18 28 43 49 8 29 45 32 28 17 46 32 26 17 42 39 21 38 47 Draw an ordered stem-and-leaf diagram to show these results. 0 1 2 3 4 Key:  means [3]

7 © UCLES 2012 0607/13/M/J/12 [Turn over For Examiner's Use 10 (a) Solve. 5x – 2 < 3x + 5 Answer (a) [2] (b) Simplify. xy 7 ÷ y x 2 3 Answer (b) [2]

8 © UCLES 2012 0607/13/M/J/12 For Examiner's Use 11 U = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} P = {prime numbers} F = {factors of 6} (a) Complete the Venn diagram to show this information. U P F [3] (b) A number is chosen at random from the 14 elements in U. Write down the probability that this number is an element of (i) (P ∩ F ), Answer (b)(i) [1] (ii) (P ∪ F )V. Answer (b)(ii) [1]

9 © UCLES 2012 0607/13/M/J/12 For Examiner's Use 12 NOT TO SCALE M (1, –1) A (–5, –4) B The diagram shows three points A(– 5, – 4), M (1, –1) and B. M is the midpoint of the line AB. (a) Find the co-ordinates of B. Answer (a) ( , ) [2] (b) Find the gradient of the line AB. Answer (b) [2] (c) 0 4 1 1 5 y x NOT TO SCALE C D Find the length of the line CD. Answer (c) [3]

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12 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 2012 0607/13/M/J/12 BLANK PAGE

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2012 question paper for the guidance of teachers 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/13 Paper 1 (Core), 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 2012 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 2012 0607 13 © University of Cambridge International Examinations 2012 1 (a) 0.08 1 (b) 0.745, 0.85, 89%, 0.9 1 [2] 2 24 2 M1 for 160 × 0.15 oe or 10% = 16 and 5% = 8 [2] 3 (a) 0.00758 1 (b) 0.45 1 [2] 4 612 5 3 M2 for 5 + 12 9 + 12 8 or 12 19 + 12 44 Or M1 for common denominator 12 [3] 5 (a) 1 1 (b) 21x7 2 B1 for kx7 or 21xk k ¸ 0 [3] 6 (a) a(3 – a) 1 (b) x2 – 4x – 5 2 B1 for 3 terms correct in x2 + x – 5x – 5 [3] 7 R L B N R L 3 B2 for 4 or 5 correct Or B1 for 2 or 3 correct [3] 8 (a) 17 1 (b) 4 2 M1 for 3x = 12 oe (e.g. –3x = –12) [3] 9 0 8 1 7 7 8 2 1 6 8 8 9 9 3 2 2 4 8 9 4 2 3 5 6 7 9 Key e.g. 1
7 = 17 2 1 –1 for up to 3 errors (1 misplaced is 1 error) [3] 10 (a) x < 3.5 2 M1 for 5x – 3x < 5 + 2 oe or better (b) 2 3 14 x 2 M1 for x y xy 3 2 7 × or better soi [4] 11 (a) P F U 5 7 11 13 3 2 6 4 8 9 10 12 14 15 3 B2 if 1 or 2 elements misplaced B1 if 3 or 4 elements misplaced (b) (i) 14 2 oe 1 ft (ii) 14 7 oe 1 ft [5]

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2012 0607 13 © University of Cambridge International Examinations 2012 12 (a) (7, 2) 2 B1 for each. If 0 scored SC1 for (2, 7) (b) 2 1 oe 2 M1 for either riser or run correct or 2 or 1 2 − or x 2 1 (c) 5 3 M2 2 2 4 3 + M1 for attempt to use c2 = a2 + b2 [7]