Cambridge IGCSE Mathematics - International 0607 — 2011 Oct/Nov Paper 5 · Variant 1

This document consists of 6 printed pages and 2 blank pages. IB11 11_0607_05/2RP © UCLES 2011 [Turn over *4924094545* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/05 Paper 5 (Core) October/November 2011 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 2011 0607/05/O/N/11 For Examiner's Use Answer all questions. INVESTIGATION MAXIMISING THE PERIMETER Identical shapes can be joined to make larger shapes. 1 Squares of side 1 cm may be joined edge to edge, for example but not like this. (a) The diagram below shows a shape made of 3 squares and a shape made of 4 squares. Draw a different shape made of 3 squares and a different shape made of 4 squares. (b) (i) The diagram below shows a shape, made of 5 squares, with a perimeter of 10 cm. Draw two different shapes each made of 5 squares and each with a perimeter greater than 10 cm.

3 © UCLES 2011 0607/05/O/N/11 [Turn over For Examiner's Use (ii) The diagram below shows a shape, made of 6 squares, with a perimeter of 12 cm. Draw two different shapes each made of 6 squares and each with a perimeter greater than 12 cm. (c) Find the greatest perimeter for shapes made of (i) 4 squares, cm (ii) 5 squares, cm (iii) 6 squares. cm You may use the grid below to draw your shapes.

4 © UCLES 2011 0607/05/O/N/11 For Examiner's Use (d) (i) Complete this table. Number of squares 2 3 4 5 6 7 8 9 10 Greatest perimeter (cm) 6 16 22 (ii) Write down the greatest perimeter for a shape made of 17 squares. cm (iii) How many squares make the shape when the greatest perimeter is 32 cm? (e) Look at your table to help you complete the following statements. (i) To find the greatest perimeter for a shape made of 2 squares, multiply 2 by 2, then add (ii) To find the greatest perimeter for a shape made of 7 squares, multiply 7 by , then add (f) Write down an expression, in terms of x, for the greatest perimeter for a shape made of x squares.

5 © UCLES 2011 0607/05/O/N/11 [Turn over For Examiner's Use 2 Equilateral triangles of side 1 cm may be joined edge to edge, for example but not like this. (a) Find the greatest perimeter for a shape made of 6 equilateral triangles. cm You may use the grid below to help you. (b) (i) Complete this table. Number of equilateral triangles 2 3 4 5 6 7 8 Greatest perimeter (cm) 4 10 (ii) Write down the greatest perimeter for a shape made of 10 equilateral triangles. cm (iii) How many equilateral triangles make the shape when the greatest perimeter is 18 cm? (c) Write down an expression, in terms of x, for the greatest perimeter for a shape made of x equilateral triangles.

6 © UCLES 2011 0607/05/O/N/11 For Examiner's Use 3 Find an expression, in terms of x, for the greatest perimeter for a shape made of x regular hexagons.

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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 2011 question paper for the guidance of teachers 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 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 October/November 2011 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 – October/November 2011 0607 05 © University of Cambridge International Examinations 2011 INVESTIGATION MAXIMISING THE PERIMETER 1 (a) e.g. 3 squares 4 squares or or or 1 1 Shapes may not be rotations or reflections of those given (b) (i) 2 arrangements required with perimeter > 10 (= 12). e.g. or or 1 1 Shapes may not be rotations or reflections of those given or of each other (ii) 2 arrangements required with perimeter > 12 (= 14). e.g. or or or or 1 1 Shapes may not be rotations or reflections of those given or of each other (c) (i) 10 (cm) (ii) 12 (cm) (iii) 14 (cm) 1 1 1 C opportunity for shapes drawn on grid (d) (i) Number of square 2 3 4 5 6 7 8 9 10 Greatest perimeter (cm) 6 8 10 12 14 16 18 20 22 2 –1 eeoo (ii) 36 (cm) 1 (iii) 15 (squares) 1 (e) (i) (then add) 2 1 (ii) (by) 2, (then add) 2 1

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2011 0607 05 © University of Cambridge International Examinations 2011 (f) 2x + 2 oe 1 2 (a) 8 (cm) 1 C opportunity for shapes drawn on grid (b) (i) Number of equilateral triangles 2 3 4 5 6 7 8 Greatest perimeter (cm) 4 5 6 7 8 9 10 2 –1 eeoo (ii) 12 (cm) 1 (iii) 16 1 (c) x + 2 1 3 4x + 2 2 1 for 4x + k C opportunity for attempt to explain C2 C2 for 3 C opportunities seen C1 for 1 or 2 C opportunities seen [Total: 26 scaled to 24]