Cambridge IGCSE Mathematics - International 0607 — 2010 May/June Paper 1 · Variant 1

This document consists of 8 printed pages. IB10 06_0607_01/2RP © UCLES 2010 [Turn over *9521008140* For Examiner's Use UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/01 Paper 1 (Core) May/June 2010 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 2010 0607/01/M/J/10 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 2010 0607/01/M/J/10 [Turn over For Examiner's Use Answer all the questions. 1 Write down the value of (a) 23, Answer(a) [1] (b) 20. Answer(b) [1] 2 Simplify 4 8 4 8 + × . Give your answer as a fraction in its lowest terms. Answer [2] 3 p = 2 × 105 Find the value of 6p, giving your answer in standard form. Answer [2]

4 © UCLES 2010 0607/01/M/J/10 For Examiner's Use 4 The heights of 20 buildings are measured. (a) State whether the data is discrete or continuous. Answer(a) [1] (b) The heights, correct to the nearest metre, are shown below. 12 10 15 18 8 9 23 26 14 21 11 16 20 21 22 13 22 25 17 19 Draw an ordered stem-and-leaf diagram to show this information. [3] (c) Work out the range of the heights. Answer(c) m [1]

5 © UCLES 2010 0607/01/M/J/10 [Turn over For Examiner's Use 5 (a) Simplify 5p2 × 3p3. Answer(a) [2] (b) Factorise completely 2x2 + 6xy. Answer(b) [2] 6 (a) Plot the points A(−1, 5) and B(3, 7) on the grid. y x 8 7 6 5 4 3 2 1 –1 –2 –1 –2 1 0 2 3 4 5 6 7 8 [2] (b) Write down the coordinates of the midpoint of the line joining A and B. Answer(b) ( , ) [1]

6 © UCLES 2010 0607/01/M/J/10 For Examiner's Use 7 All measurements in this question are in centimetres. Three rectangles are placed together to form the shape below. 2 2 3 4 6 NOT TO SCALE (a) Calculate the area of this shape. Answer(a) cm2 [2] (b) The shape is projected onto a screen and the enlargement is shown below. 24 x NOT TO SCALE Find the value of x. Answer(b) x = cm [2]

7 © UCLES 2010 0607/01/M/J/10 [Turn over For Examiner's Use 8 The probability that it is windy is 0.3 . (a) Write down the probability that it is not windy. Answer(a) [1] (b) Anita plans to go sailing. If it is windy, the probability that she will go sailing is 0.8 . If it is not windy, the probability that she will go sailing is 0.1 . (i) Complete the tree diagram. 0.3 … 0.8 … windy not windy sailing not sailing 0.1 … sailing not sailing [2] (ii) Find the probability that it is windy and Anita goes sailing. Answer(b)(ii) [2] 9 (a) Solve the inequality 3(x – 1) < 6. Answer(a) [2] (b) Show your solution on the number line below. –4 –3 –2 –1 0 1 2 3 4 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 2010 0607/01/M/J/10 For Examiner's Use 10 The Venn diagram shows the numbers 1 to 9 placed in different regions. U A B 5 7 9 4 8 3 6 1 2 Complete the following statements. (a) n(A) = [1] (b) A∩B = { } [1] (c) (A∪B)' = { } [1] (d) A number in the Venn diagram is chosen at random. Find the probability that the number is in A. Answer(d) [1] 11 −2, 1, 4, 7, 10, ….. (a) Write down the next term of the sequence. Answer(a) [1] (b) Find the nth term of the sequence. Answer(b) [2] (c) Is the number 296 a term of the sequence? You must show your working. [2]

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2010 question paper for the guidance of teachers 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/01 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. • CIE will not enter into discussions or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the May/June 2010 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 2010 0607 01 © UCLES 2010 • M marks are given for a correct method. • A marks are given for an accurate answer following a correct method. • B marks are given for a correct statement or step. • D marks are given for a clear and appropriately accurate drawing. • P marks are given for accurate plotting of points. • E marks are given for correctly explaining or establishing a given result. • ft follow through • oe or equivalent • soi seen or implied • www without wrong working 1 (a) (b) 8 1 B1 B1 [2] 2 8 3 B2 Final answer B1 for 32 12 or any correct fraction not in lowest terms seen [2] 3 1.2 × 106 B2 After B0, B1 for 1.2 seen or SC1 for 12 × 105 or 1200000 [2] 4 (a) (b) (c) Continuous 0 | 8 9 1 | 0 1 2 3 4 5 6 7 8 9 2 | 0 1 1 2 2 3 5 6 Key 1| 2 means 12(m) oe 18 B1 B3 B1 B1 for Key B2 for correct numbers in the correct order. After B0 award B1 for at most two errors or omissions or M1 for correct unordered stem-and-leaf. [5] 5 (a) (b) 15p5 2x(x + 3y) B2 B2 [4] B1 for 15 seen or for p5 seen B1 for 2x identified as a factor or for 2(x2 + 3xy) or for x(2x + 6y) [4] 6 (a) (b) Points plotted correctly (1, 6) P1P1 B1ft [3] 7 (a) 18 B2 After B0 award M1 for finding the area of any appropriate rectangle. (b) 6 2 24 x = oe or for scale factor 12 soi M1 x = 72 A1 [4]

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2010 0607 01 © UCLES 2010 8 (a) (b) (i) (ii) 0.7 0.7, 0.2, 0.9 0.24 B1 B2ft B2 Accept equivalent fractions or percentages in all parts. Do not accept ratios or words. B1 if 2 correct ft from their (a) B1 for 0.3 × 0.8 seen [5] 9 (a) 3x – 3 < 6 or 3 6 1< − x M1 For correct multiplication of brackets or dividing by 3. x < 3 A1 (b) -4 -3 -2 -1 4 3 2 1 0 B2ft After B0 B1 for an appropriate arrow from their 3 or B1 for appropriate circle. Follow through from their inequality. [4] 10 (a) (b) (c) 4 { 1 , 2 } { 5, 7, 9 } B1 B1 B1 Correct answer or ft from their (a). (d) 9 4 B1ft Accept 0.44 or 44% or better but not a ratio or word(s). [4] 11 (a) (b) (c) 13 3n – 5 oe as final answer Their 3n – 5 = 296 B1 B2 M1 Ignore extra terms. Award B1 for 3n soi. Alternative Method A correct method leading to consecutive terms in the sequence and which includes either 295 or 298 earns M1. An appropriate correct conclusion indicating that 296 is not a term earns A1. n = 3 301 which is not a whole number oe and indicating that 296 is not a term. A1 [5]