Cambridge IGCSE Mathematics - International 0607 — 2016 May/June Paper 5 · Variant 3

This document consists of 8 printed pages. DC (NH/SW) 115854/2 © UCLES 2016 [Turn over * 2 8 0 0 5 0 3 3 8 5 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/53 Paper 5 (Core) May/June 2016 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, glue or correction fluid. You may use an HB 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. Cambridge International Examinations Cambridge International General Certificate of Secondary Education

2 0607/53/M/J/16 © UCLES 2016 Answer all the questions. INVESTIGATION AREAS & PERIMETERS This investigation looks at the connection between the area and the perimeter of a rectangle. All diagrams are not to scale. The sides of all rectangles are whole numbers. 1 5 4 The area of this 4 by 5 rectangle is 20. (a) 10 3 Find the area of this rectangle. … Some rectangles have area 4. There are three ways to calculate their area. Area 4 1 × 4 2 × 2 4 × 1

3 0607/53/M/J/16 © UCLES 2016 [Turn over (b) Some rectangles have area 6. There are four ways to calculate their area. Complete the table below to show all four ways. The first one has been done for you. Area 6 1 × 6 … × … … × … … × … (c) Some rectangles have the same area. (i) There are exactly two ways to calculate their area. Complete the table when this area is a number between 6 and 15. Area … … × … … × … (ii) There are exactly three ways to calculate their area. Complete the table when this area is a number between 6 and 15. Area … … × … … × … … × …

4 0607/53/M/J/16 © UCLES 2016 (iii) There are more than four ways to calculate their area. Complete the table when the area is a number between 6 and 15. You may not need all the lines. Area … … × … … × … … × … … × … … × … … × … … × … … × …

5 0607/53/M/J/16 © UCLES 2016 [Turn over 2 Some rectangles have the same area. This area is between 1 and 20. (a) (i) List the areas that can be calculated in exactly two ways. … (ii) Write down the mathematical name for the numbers in your answer to part (a)(i). … (b) (i) List the areas that can be calculated in an odd number of ways. … (ii) Write down the mathematical name for the numbers in your answer to part (b)(i). … 3 Some rectangles have the same area. This area is between 150 and 200. Find an area that can be calculated in an odd number of ways. …

6 0607/53/M/J/16 © UCLES 2016 4 5 4 The perimeter of this 4 by 5 rectangle is 18. Find the perimeter of each of these rectangles. 10 3 … 9 2 …

7 0607/53/M/J/16 © UCLES 2016 [Turn over 5 The width of a rectangle is 3. Its area and its perimeter have the same value. (a) Find its length. … (b) Write down its perimeter. … 6 x 4 (a) Write down an expression for the area of this rectangle. … (b) Write down an expression for the perimeter of this rectangle. … (c) The area and the perimeter have the same value. Write down an equation and solve it to find x. Question 7 is printed on the next page.

8 0607/53/M/J/16 © UCLES 2016 7 A rectangle has width 2 and length x. Show that this rectangle cannot have the same value for its area as its perimeter. 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. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. 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.

® IGCSE is the registered trademark of Cambridge International Examinations. This document consists of 3 printed pages. © UCLES 2016 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/53 Paper 5 (Core) May/June 2016 MARK SCHEME Maximum Mark: 24 Published 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 2016 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

Page 2 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2016 0607 53 © Cambridge International Examinations 2016 Abbreviations awrt answers which round to cao correct answer only dep dependent FT follow through after error isw ignore subsequent working oe or equivalent SC Special Case nfww not from wrong working soi seen or implied Questions Answer Marks Part Marks 1 (a) 30 1 (b) 6 1 2 3 3 2 2 B1 for 1 row correct (c) (i) 7 or 11 or 13 1 7 1 11 1 13 7 1 11 1 13 1 2 B1 for top number B1 for both rows (ii) 9 1 9 9 1 3 3 2 B1 for 9 B1 for 3 correct rows (iii) 12 1 12 12 1 2 6 6 2 3 4 4 3 2 B1 for 12 B1 for rows Condone 1 missing row Ignore extras 2 (a) (i) 2, 3, 5, 7, 11, 13, 17, 19 1 C opportunity (ii) Prime 1dep dep on (a)(i) (b) (i) [1], 4, 9, 16 1 C opportunity (ii) Square 1dep dep on (b)(i) 3 169 or 196 1 C opportunity

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2016 0607 53 © Cambridge International Examinations 2016 Questions Answer Marks Part Marks 4 26 22 1 5 (a) 6 1 C opportunity (b) 18 1 6 (a) 4x 1 (b) 8 + 2x oe 1 (c) [ ] 8 2 4 4 x x x + = = oe 1 1 C opportunity 7 x 2 and 2x + 4 oe No solutions oe 1 1 Communication in two of 2(a)(i), 2(b)(i), 3, 5(a) and 6(c) 1