Cambridge IGCSE Mathematics - International 0607 — 2013 May/June Paper 5 · Variant 1

This document consists of 5 printed pages and 3 blank pages. IB13 06_0607_05/RP © UCLES 2013 [Turn over *8732392529* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/05 Paper 5 (Core) May/June 2013 1 hour Candidates answer on the Question Paper. Additional Materials: Graphics Calculator 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. You must show all relevant working to gain full marks for correct methods, including sketches. In this paper you will also be assessed on your ability to provide full reasons and communicate your mathematics clearly and precisely. At the end of the examination, fasten all your work securely together. The total number of marks for this paper is 24. www.XtremePapers.com

2 © UCLES 2013 0607/05/M/J/13 For Examiner's Use Answer all the questions. INVESTIGATION DIAGONALS OF RECTANGLES Rectangles are drawn on a grid. The sides of each rectangle lie on gridlines and the length is greater than or equal to the width. This investigation looks for a method for calculating the number of small squares through which a diagonal passes. Example The diagram shows a rectangle with length 5 and width 3. Its diagonal passes through 7 small squares. 1 A B C D E F G I H

3 © UCLES 2013 0607/05/M/J/13 [Turn over For Examiner's Use (a) Complete the table for the rectangles A to I. Rectangle Length (x) Width (y) Number of squares passed through (S) Example 5 3 7 A B C D E F G H 9 4 12 I (b) Write down an equation connecting x + y and S. (c) Use this equation to find x and y for the three rectangles where the diagonal passes through 6 squares. x = y = x = y = x = y =

4 © UCLES 2013 0607/05/M/J/13 For Examiner's Use 2 When x and y do not have a common factor, the x by y rectangle is called a basic rectangle. In question 1, x and y did not have a common factor. In this question x and y do have a common factor. Example The diagram below shows a large rectangle with x = 10 and y = 6. x and y have a common factor of 2. The basic 5 by 3 rectangle has a diagonal passing through 7 squares. So the 10 by 6 rectangle has a diagonal passing through 2 × 7 = 14 squares. Complete the following table. Length (x) Width (y) Common factor Dimensions of the basic rectangle Calculation to find S 10 6 2 5 by 3 2 × 7 = 14 6 2 = 8 6 = 25 15 = 13 13 =

5 © UCLES 2013 0607/05/M/J/13 For Examiner's Use 3 A rectangle has an area of 18 squares. Use question 1 and question 2 to find the minimum and maximum values of S. minimum = maximum = 4 The diagonal of a rectangle passes through 4 squares. Use question 1 and question 2 to find the length and the width of each possible rectangle.

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CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2013 series 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/05 Paper 5 (Core), maximum raw mark 24 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 05 © Cambridge International Examinations 2013 1 (a) rectangle length (x) width (y) squares passed through (S) Example 5 3 7 A 3 1 3 B 3 2 4 C 5 4 8 D 7 2 8 E 7 3 9 F 6 5 10 G 7 4 10 H 9 4 12 I 8 5 12 8 x and y can be swapped in any or all rows. –1 per error or omission (b) x + y = S + 1 o.e. 1 Equation required (c) [x=] 6 [y=] 1 5 2 4 3 B2FT B1 for 2 correct Communication mark for x + y = their 7 OR 3 correct substitutions in their (b). Accept x and y reversed Correct answers OR follow-through their (b) 2 x y Calculation to find S 10 6 2 5 by 3 2 × 7 = 14 6 2 2 3 by 1 2 × 3 = 6 8 6 2 4 by 3 2 × 6 = 12 25 15 5 5 by 3 5 × 7 = 35 13 13 13 1 by 1 13 × 1 = 13 B1 B1 B2 FT B1FT 4 common factors 2, 2, 5, 13 3 or 4 basic rectangles 3 or 4 their factor × value for calculation OR B1 FT 1 or 2 their factor × value for calculation Strict FT except decimal answers. SC0 in this part for the same basic rectangle each time. All 4 multiplications SC1 in this part for 6, 12, 35, 13 without calculation and no error in table.

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2013 0607 05 © Cambridge International Examinations 2013 3 [minimum =] 6 [maximum =] 18 B2 B1 B1 1 by 18, 2 by 9, 3 by 6 OR B1 for any two soi (e.g. 3 + 6 1, etc.) Accept diagrams in the working space. 6 cao 18 cao Accept 6 or 18 in wrong answer space. Communication mark for showing numerical method to get 6. e.g. common factor = 3 soi and 3 × (2 + 1 – 1) o.e. Row as in the table. 4 [3 × 2] 4 × 1 4 × 2 4 × 4 B1 B1 B1 soi by diagrams in the answer space. 4 + 1 – 1 = 4 insufficient Deduct 1 for each extra incorrect rectangle but accept repeated rectangles. Communication mark for showing correct numerical method or statement once e.g. x + y – 1 = S, S = 4 x + y = 5 3 + 2 – 1 = 4 but not 3 + 2 = 5 – 1 = 4 Row as in the table. Communication 1 Seen in question 1(c), 3 or 4