Cambridge IGCSE Mathematics - International 0607 — 2016 May/June Paper 5 · Variant 1

This document consists of 8 printed pages. DC (NF/SG) 117229/2 © UCLES 2016 [Turn over * 7 2 3 5 9 6 1 3 1 1 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/51 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 0607/51/M/J/16 © UCLES 2016 Answer all the questions. INVESTIGATION DIVIDING RECTANGLES This investigation looks at the connections between the rectangles made by dividing one rectangle into two smaller rectangles. In this investigation •• the length of a rectangle is always longer than its width length length width width •• the length and width of a rectangle are always a whole number of units •• the scale factor of any enlargement is greater than 1. 1 In the diagrams below, rectangle B is an enlargement of rectangle A. (a) B A Write down the scale factor of this enlargement. …

3 0607/51/M/J/16 © UCLES 2016 [Turn over (b) B A Write down the scale factor of this enlargement. … (c) A B 4 NOT TO SCALE For this pair of rectangles, the scale factor is 10. Work out the length of rectangle B. … (d) A B 3 1 5 NOT TO SCALE Work out the length of rectangle B. …

4 0607/51/M/J/16 © UCLES 2016 2 A rectangle is cut into two smaller rectangles, A and B. A B When B is an enlargement of A, the original rectangle is called a scale-rectangle. A B width width length length A B width width length length Example A 4 by 10 rectangle is cut as shown. A B 4 10 2 8 4 A B 2 4 4 8 A B 2 4 4 8 NOT TO SCALE 4 8 2 length of A length of B = = and 2 4 2 width of A width of B = = So B is an enlargement of A with scale factor 2. This means that the rectangle with dimensions 4 by 10 is a scale-rectangle with a factor of 2.

5 0607/51/M/J/16 © UCLES 2016 [Turn over (a) A B The diagram shows a 3 by 10 rectangle. This is a scale-rectangle. Show that it has a factor of 3. (b) B A The diagram shows a 2 by 4 rectangle. Is this a scale-rectangle? Write Yes or No and give reasons for your answer. (c) A B 3 21 m A B 3 21 m NOT TO SCALE The diagram shows a scale-rectangle with a factor of 7. (i) Find m. … (ii) Write down the dimensions of the scale-rectangle. … by …

6 0607/51/M/J/16 © UCLES 2016 (d) A B 3 w 75 A B 3 w 75 NOT TO SCALE The diagram shows a scale-rectangle with a factor of 5. (i) Find w. … (ii) Write down the dimensions of the scale-rectangle. … by … 3 A B y x z The diagram shows a scale-rectangle with a factor of n. (a) When x = 2 and n = 6, (i) work out y, … (ii) find z, … (iii) complete this statement with a number, z = … × x (iv) write down the connection between your answer to part (iii) and the factor, n.

7 0607/51/M/J/16 © UCLES 2016 [Turn over (b) When x = 2 and z = 18, (i) find n, … (ii) work out the dimensions of this scale-rectangle. … by … (c) Use your answers to part (a) and part (b) to complete the second and third rows of the table. Complete the remaining rows of the table. n x y z Dimensions 2 2 4 8 4 by 10 6 2 … by … 2 18 … by … 5 7 … by … 1 4 16 4 by 17 5 20 … by … Question 4 is printed on the next page.

8 0607/51/M/J/16 © UCLES 2016 4 A B y x z The diagram shows a scale-rectangle with a factor of n. (a) Work out the dimensions of this scale-rectangle in terms of n and x. … by … (b) Show that, for any scale-rectangle, its dimensions are in the ratio width : length = n : n2 + 1. 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 0607/51 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 51 © 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 Question Answer Mark Part Marks 1 (a) 3 1 (b) 2 1 (c) 40 1 (d) 15 1 C opportunity 2 (a) 9 [ 3] 3 = and 3 [ 3] 1 = oe seen 1 (b) 3 2 or 1.5 and 2 1 or 2 oe and No oe 1 (c) (i) 147 1 C opportunity (ii) 21 by 150 or 150 by 21 1 FT their(i) (d) (i) 15 1 C opportunity (ii) 15 by 78 or 78 by 15 1 FT their(i) 3 (a) (i) 12 1 C opportunity (ii) 72 1 C opportunity (iii) 36 1 FT (ii) 2 their (iv) n2 oe 1 (b) (i) 3 1 C opportunity (ii) 6 by 20 or 20 by 6 1 C opportunity

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2016 0607 51 © Cambridge International Examinations 2016 Question Answer Mark Part Marks (c) n x y z Dimensions 2 2 4 8 4 by 10 6 2 their 12 their 72 12* by 74* their 3 2 their 6 18 their y by 20 5 7 35 175 35* by 182* 4 1 4 16 4 by 17 2 5 10 20 10* by 25 3 3 for all 8 cells *FT their y by (their z + 2) *FT their y by (their z + 7) *FT their y by 25 B2 for 6 or 7 cells correct or B1 for 4 or 5 cells correct 4 (a) nx [by] n2x + x oe 2 B1 for each C opportunity (b) 2 :( 1) nx n x + oe seen 1 Communication seen in at least 3 of 1(d), 2(c)(i), 2(d)(i), 3(a)(i), 3(a)(ii), 3(b)(i), 3(b)(ii) or 4(a) 2 C1 if seen in 2 of these