Cambridge IGCSE Mathematics - International 0607 — 2017 Oct/Nov Paper 5 · Variant 2

This document consists of 8 printed pages. DC (ST/FC) 134792/2 © UCLES 2017 [Turn over * 2 6 1 6 3 0 9 7 6 4 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/52 Paper 5 (Core) October/November 2017 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 to 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 0607/52/O/N/17 © UCLES 2017 Answer all the questions. INVESTIGATION NUMBER WALLS This investigation looks at what happens when you place numbers on a Number Wall. You make a Number Wall like this. • Integers are put on the bottom row of bricks. • The number on a brick is the sum of the numbers on the two bricks below. Examples Total = 1 4 5 Total = –5 7 2 Total = 1 2 3 5 8 3 1 (a) Complete this Number Wall. Total = 1 3 2 (b) In part (a), the number 3 is on the middle brick of the bottom row. In the example, the number 3 is on the end brick of the bottom row. Explain why putting the number 3 on the middle brick of the bottom row increases the total. … …

3 0607/52/O/N/17 © UCLES 2017 [Turn over 2 (a) Complete this Number Wall. Total = 1 2 3 4 (b) Put the numbers 1, 2, 3 and 4 on the bottom row and complete this Number Wall so that the total is bigger than the total in part (a). Total = (c) Complete this Number Wall. You may use negative numbers. Total = 31 10 4 7 4

4 0607/52/O/N/17 © UCLES 2017 3 This Number Wall is 3 bricks high. (a) Complete each brick using expressions in terms of a, b and c. Write each expression in its simplest form. b c a (b) Use the expression for the total you found in part (a) to find the value of b. b 7 7 4 …

5 0607/52/O/N/17 © UCLES 2017 [Turn over 4 (a) This Number Wall is 4 bricks high. Complete each brick using expressions in terms of a, b, c and d. Write each expression in its simplest form. b a a + b d c (b) In another wall that is 4 bricks high, the total is 34 and the values of a, b, c and d are all the same. Use the expression for the total you found in part (a) to show that the value of a cannot be an integer.

6 0607/52/O/N/17 © UCLES 2017 (c) In this Number Wall that is 5 bricks high, only integers greater than 0 are used. Find one set of possible values for a, b, c, d and e. b a d e c 43 14 9 6 a = … b = … c = … d = … e = … 5 In 1653 a French mathematician, Blaise Pascal, wrote about a triangle of numbers similar to the one shown below. It is made in the same way as Number Walls but • the number on a brick is the sum of the numbers on the two bricks above and • the number on the first and last brick in each row is always 1. 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 Row 1 Row 2 Row 3 Row 4 Row 5 Row 6 6 15 20 15 6 1

7 0607/52/O/N/17 © UCLES 2017 [Turn over (a) The wall in question 4(a) is 4 bricks high. Show clearly how your expression for the total in question 4(a) connects to the numbers in one row of this triangle. Write down which row this is. Row … (b) A wall that is 5 bricks high has a, b, c, d and e, in that order, along the bottom row. Write down an expression in terms of a, b, c, d and e for the total. … (c) Use your expression from part (b) to check that the set of values you found for a, b, c, d and e in question 4(c) gives a total of 43. Question 5(d) is printed on the next page.

8 0607/52/O/N/17 © UCLES 2017 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. (d) A wall that is 5 bricks high has the number 2017 on each brick of the bottom row. Find the total. …

® IGCSE is a registered trademark. This document consists of 4 printed pages. © UCLES 2017 [Turn over Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/52 Paper 5 (Core) October/November 2017 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 International will not enter into discussions about these mark schemes. Cambridge International is publishing the mark schemes for the October/November 2017 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

0607/52 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 2 of 4 MARK SCHEME NOTES The following notes are intended to aid interpretation of mark schemes in general, but individual mark schemes may include marks awarded for specific reasons outside the scope of these notes. Types of mark M Method marks, awarded for a valid method applied to the problem. A Accuracy mark, awarded for a correct answer or intermediate step correctly obtained. For accuracy marks to be given, the associated Method mark must be earned or implied. B Mark for a correct result or statement independent of Method marks. When a part of a question has two or more ‘method’ steps, the M marks are in principle independent unless the scheme specifically says otherwise; and similarly where there are several B marks allocated. The notation ‘dep’ is used to indicate that a particular M or B mark is dependent on an earlier mark in the scheme. Abbreviations awrt answers which round to cao correct answer only dep dependent FT follow through after error isw ignore subsequent working nfww not from wrong working oe or equivalent rot rounded or truncated SC Special Case soi seen or implied

0607/52 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 3 of 4 Question Answer Marks Partial Marks 1(a) 9 4 5 1 1(b) 3 is added two times oe or 1 is added to 3 and not 2 oe 1 2(a) 20 8 12 3 5 7 2 B1 for 3 5 7 or for top three numbers correct following one error 2(b) A correct number wall with total > their 20 2 B1 for a number wall with (2 and 4) or (3 and 4) in middle of bottom row 2(c) 14 17 7 −3 3 3 B1 for each row 3(a) a + 2b + c a + b b + c 2 B1 for each row 3(b) −2 1 C opportunity 4(a) a + 3b + 3c + d a + 2b + c b + 2c + d b + c c + d 2 B1 for 3 cells correct, may be unsimplified 4(b) their (a + 3b + 3c + d) = 34 oe M1 C opportunity 4.25 or 34 8 is not an integer oe M1 4(c) 3 5 1 2 6 or 4 4 2 1 7 2 B1 for c = 1 and d = 2 or c = 2 and d = 1 C opportunity 5(a) Row gives the coefficients of a, b, c and d 3 2 B1 for each 5(b) [1]a + 4b + 6c + 4d + [1]e oe 1 5(c) [1] × 3 + 4 × 5 + 6 × 1 + 4 × 2 + [1] × 6 [= 43] or [1] × 4 + 4 × 4 + 6 × 2 + 4 × 1 + [1] × 7 [= 43] 1 FT their correct 5(b) only 5(d) 32272 1 C opportunity

0607/52 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 4 of 4 Question Answer Marks Partial Marks Communication: seen in one of the following questions 1 3(b) their (a + 2b +c) = 7 4(b) 8x = 34 or x + 3x + 3x + x = 34 or 34 ÷ 8 4(c) Completing all empty bricks with 23, 20, 11, 8, 3, 8 or showing working with equations 5(d) Relevant working 1 + 4 + 6 + 4 + 1 or 16 × 2017 or completing the number wall