Cambridge IGCSE Mathematics - International 0607 — 2018 May/June Paper 5 · Variant 2

* 5 1 7 4 3 9 9 7 3 7 * This document consists of 7 printed pages and 1 blank page. DC (CE/SW) 153512/2 © UCLES 2018 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/52 Paper 5 (Core) May/June 2018 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.

2 0607/52/M/J/18 © UCLES 2018 Answer all the questions. INVESTIGATION TILE PATTERNS This investigation looks at the number of grey tiles and the number of white tiles in a sequence of square patterns. All the tiles are the same size and each is a square. The grey tiles and white tiles make borders around a single grey tile. The single grey tile is the first grey border. The first white border is 8 white tiles surrounding the grey tile. The second grey border is 16 grey tiles surrounding the 8 white tiles. 1 (a) On this grid, complete the diagram to show the second white border.

3 0607/52/M/J/18 © UCLES 2018 [Turn over (b) On this grid, complete the diagram to show the third grey border. 2 This question looks at the patterns that finish with a white border. Pattern finishes with Number of white tiles in border Total number of white tiles in pattern 1st white border 8 8 2nd white border 32 3rd white border 72 4th white border 128 (a) Complete the table.

4 0607/52/M/J/18 © UCLES 2018 (b) The values in the last column are the first four terms of a sequence. (i) Write each term as a multiple of 8. 8 = 8 # … 32 = 8 # … 72 = 8 # … 128 = 8 # … (ii) The numbers that are multiplied by 8 also form a sequence. Write down the name for this sequence of numbers. … (iii) Write down an expression, in terms of n, for the total number of white tiles in the pattern that finishes with the nth white border. … (c) Here is the pattern that finishes with the first white border. There are 3 white tiles along one side. (i) Complete the table. Pattern finishes with Number of white tiles along one side 1st white border 3 2nd white border 3rd white border 4th white border

5 0607/52/M/J/18 © UCLES 2018 [Turn over (ii) The numbers of white tiles along one side form a sequence. Find an expression, in terms of n, for the number of white tiles along one side of the pattern that finishes with the nth white border. … (iii) Use your answer to part(c)(ii) to write down an expression, in terms of n, for the total number of all tiles in the pattern that finishes with the nth white border. … (d) Use your answers to part (c)(iii) and part (b)(iii) to show that an expression for the total number of grey tiles in the pattern that finishes with the nth white border is 8n2 – 8n + 1.

6 0607/52/M/J/18 © UCLES 2018 3 A workman uses the method of question 2 to cover a square floor completely with tiles. The first tile is grey and the final border is white. (a) The square floor measures 5.7 m by 5.7 m. Each tile measures 30 cm by 30 cm. (i) Work out the number of tiles along one side of the floor. … (ii) Use your result from question 2(c)(ii) to show that this is the 5th white border. (iii) Work out the number of white tiles and the number of grey tiles that the workman needs to cover the floor completely. number of white tiles = … number of grey tiles = … (iv) Tiles are sold in packs of 20 white tiles and packs of 20 grey tiles. Find the number of packs of white tiles and the number of packs of grey tiles that the workman needs. number of packs of white tiles = … number of packs of grey tiles = …

7 0607/52/M/J/18 © UCLES 2018 (b) The workman tiles a different square floor. He uses the same method of tiling, starting with a grey tile. He buys enough packs of 20 grey tiles and packs of 20 white tiles to cover the floor completely. Explain why the workman will have some grey tiles left over, whatever the size of the square floor. … … … …

8 0607/52/M/J/18 © UCLES 2018 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. BLANK PAGE

IGCSE™ is a registered trademark. This document consists of 5 printed pages. © UCLES 2018 [Turn over Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/52 Paper 5 (Core) May/June 2018 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 May/June 2018 series for most Cambridge IGCSE™, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

0607/52 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2018 © UCLES 2018 Page 2 of 5 Generic Marking Principles These general marking principles must be applied by all examiners when marking candidate answers. They should be applied alongside the specific content of the mark scheme or generic level descriptors for a question. Each question paper and mark scheme will also comply with these marking principles. GENERIC MARKING PRINCIPLE 1: Marks must be awarded in line with: • the specific content of the mark scheme or the generic level descriptors for the question • the specific skills defined in the mark scheme or in the generic level descriptors for the question • the standard of response required by a candidate as exemplified by the standardisation scripts. GENERIC MARKING PRINCIPLE 2: Marks awarded are always whole marks (not half marks, or other fractions). GENERIC MARKING PRINCIPLE 3: Marks must be awarded positively: • marks are awarded for correct/valid answers, as defined in the mark scheme. However, credit is given for valid answers which go beyond the scope of the syllabus and mark scheme, referring to your Team Leader as appropriate • marks are awarded when candidates clearly demonstrate what they know and can do • marks are not deducted for errors • marks are not deducted for omissions • answers should only be judged on the quality of spelling, punctuation and grammar when these features are specifically assessed by the question as indicated by the mark scheme. The meaning, however, should be unambiguous. GENERIC MARKING PRINCIPLE 4: Rules must be applied consistently e.g. in situations where candidates have not followed instructions or in the application of generic level descriptors. GENERIC MARKING PRINCIPLE 5: Marks should be awarded using the full range of marks defined in the mark scheme for the question (however; the use of the full mark range may be limited according to the quality of the candidate responses seen). GENERIC MARKING PRINCIPLE 6: Marks awarded are based solely on the requirements as defined in the mark scheme. Marks should not be awarded with grade thresholds or grade descriptors in mind.

0607/52 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2018 © UCLES 2018 Page 3 of 5 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 May/June 2018 © UCLES 2018 Page 4 of 5 Question Answer Marks Partial Marks TILE PATTERNS 1(a) Correct border 1 1(b) Correct border 1 2(a) Pattern finishes with Number of white tiles in border Total number of white tiles in pattern 1st white border 8 8 2nd white border 24 32 3rd white border 40 72 4th white border 56 128 2 B1 for any 2 correct C opportunity 2(b)(i) 8 = 8 × 1 32 = 8 × 4 72 = 8 × 9 128 = 8 × 16 1 2(b)(ii) square 1 2(b)(iii) 8n2 oe 1 2(c)(i) 7 11 15 2 B1 for any one correct 2(c)(ii) 4n – 1 oe 2 B1 for 4n or kn – 1 (k ≠ 0) C opportunity 2(c)(iii) (4n – 1)2 oe isw 1 FT their (4n − 1) 2(d) their (4n – 1)2 – their 8n2 M1 16n2 – 8n + 1 − 8n2 leading to given answer M1 answer given 3(a)(i) 19 1 C opportunity 3(a)(ii) 4 × 5 – 1 = 19 1 answer given

0607/52 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2018 © UCLES 2018 Page 5 of 5 Question Answer Marks Partial Marks 3(a)(iii) [number of white tiles =] 200 [number of grey tiles =] 161 3 FT their 2(b)(iii) M1 for use of their 8n2 for n = 5 or 8n2 – 8n + 1 for n = 5 or B1 for 361 or B1 for at least 4 terms of sequence:1 17 49 97 161 (grey) A1 for each correct answer C opportunity 3(a)(iv) [white =] 10 [grey =] 9 2 FT their (a)(iii) i.e.(a)(iii) ÷ 20 with B1 maximum if both are multiples of 20 B1 for each C opportunity 3(b) Number of grey tiles in pattern always odd oe or not a multiple of 20 oe 1 Communication: Seen in three of the following questions 2 1 for communication seen in two questions 2(a) for 128 − 72 = 56 2(c)(ii) for common differences shown oe might be seen in (c)(i) 3(a)(i) for 570 30 or 5.7/0.3 or 324900 900 or similar 3(a)(iii) further working to find second number of tiles 3(a)(iv) for 300 20 their or 161 20 their 3(a)(iv) Initial value for grey tiles seen before rounding up