Cambridge IGCSE Mathematics - International 0607 — 2017 May/June Paper 5 · Variant 2

* 6 9 4 0 7 4 7 8 7 1 * This document consists of 7 printed pages and 1 blank page. DC (ST) 133977/1 © UCLES 2017 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/52 Paper 5 (Core) May/June 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 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/17 © UCLES 2017 Answer all the questions. INVESTIGATION NUMBER STEMS This investigation is about finding numbers that have the same Number Stem. The possible Number Stems are the nine integers from 1 to 9. Here is how to calculate the Number Stem of a number. Step 1 Add the digits of the number to get a total. Step 2 If the total is 9 or less, STOP. Otherwise, add the digits of the total. Step 3 Repeat Step 2. Examples Number 124 Number 893 Step 1 1 + 2 + 4 = 7 Step 1 8 + 9 + 3 = 20 Step 2 STOP Step 2 2 + 0 = 2 Number Stem is 7. Step 3 STOP Number Stem is 2. 1 (a) Complete the tables to show the Number Stems for these multiples of 3, 12, 21 and 30. Multiple of 3 3 6 9 12 15 18 21 24 27 30 Number Stem 3 6 9 3 9 3 6 9 3 Multiple of 12 12 24 36 48 60 72 84 96 108 120 Number Stem 3 6 9 9 9 3 Multiple of 21 21 42 63 84 105 126 147 168 189 210 Number Stem 3 9 3 6 9 3 Multiple of 30 30 60 90 120 150 180 210 240 270 300 Number Stem 3 9 3 6 9 3

3 0607/52/M/J/17 © UCLES 2017 [Turn over (b) Complete this statement. The numbers in the table that have a Number Stem of 9 are all … of 9. (c) Complete this table. 3 ÷ 9 = 0 remainder 3 12 ÷ 9 = 1 remainder 3 21 ÷ … = 2 remainder 3 … ÷ 9 = 3 remainder 3 39 ÷ 9 = … remainder … (d) Complete the statement. A number that has a … of 3 when divided by 9 has a Number Stem of … .

4 0607/52/M/J/17 © UCLES 2017 (e) The only one-digit number with a Number Stem of 3 is 3. This sequence shows the first four numbers greater than 3 with a Number Stem of 3. 12, 21, 30, 39, ... (i) Write down the rule for continuing this sequence. … (ii) Find the nth term of this sequence. … (iii) Find the 87th number greater than 3 that has a Number Stem of 3. …

5 0607/52/M/J/17 © UCLES 2017 [Turn over 2 (a) Complete the tables to show the Number Stems for different multiples of 2 and 11. Multiple of 2 2 4 6 8 10 12 14 16 18 20 22 24 Number Stem 2 4 6 8 2 4 6 Multiple of 11 11 22 33 44 55 66 77 88 99 Number Stem 2 4 6 8 2 4 6 (b) The sequence shows the first three numbers greater than 2 with a Number Stem of 2. 11, 20, 29, ... (i) Write down the next two numbers of the sequence. … , … (ii) Find the nth term of this sequence. … (iii) Show that 1352 is the 150th number greater than 2 that has a Number Stem of 2.

6 0607/52/M/J/17 © UCLES 2017 3 (a) Write down the first four numbers greater than 8 with a Number Stem of 8. … , … , … , … (b) Find the nth term of this sequence. … (c) Using your answer to part (b), find the number closest to 10 000 that has a Number Stem of 8. …

7 0607/52/M/J/17 © UCLES 2017 4 The integer k is a Number Stem. (a) Write down, in terms of k, expressions for the first four numbers greater than k with a Number Stem of k. … , … , … , … (b) Write down, in terms of n and k, the nth term for the sequence of numbers greater than k with a Number Stem of k. …

8 0607/52/M/J/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. BLANK PAGE

® IGCSE is a registered trademark. This document consists of 4 printed pages. © UCLES 2017 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/52 Paper 5 (Core) May/June 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 will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2017 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 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 May/June 2017 © UCLES 2017 Page 3 of 4 Question Answer Mark Part Marks 1(a) ×3 3 6 9 12 15 18 21 24 27 30 NS 3 6 9 3 6 9 3 6 9 3 ×12 12 24 36 48 60 72 84 96 108 120 NS 3 6 9 3 6 9 3 6 9 3 ×21 21 42 63 84 105 126 147 168 189 210 NS 3 6 9 3 6 9 3 6 9 3 ×30 30 60 90 120 150 180 210 240 270 300 NS 3 6 9 3 6 9 3 6 9 3 2 B1 for at most 2 errors 1(b) multiples oe 1 1(c) 3 ÷ 9 = 0 remainder 3 12 ÷ 9 = 1 remainder 3 21 ÷ 9 = 2 remainder 3 30 ÷ 9 = 3 remainder 3 39 ÷ 9 = 4 remainder 3 2 B1 for 3 correct 1(d) …remainder … 3 1 1(e)(i) Add 9 oe 1 1(e)(ii) 9n + 3 oe 2 B1 for 9n + a oe (a may = 0) 1(e)(iii) 786 1 FT their (9n + 3) C opportunity 2(a) ×2 2 4 6 8 10 12 14 16 18 20 22 24 NS 2 4 6 8 1 3 5 7 9 2 4 6 ×11 11 22 33 44 55 66 77 88 99 110 121 132 NS 2 4 6 8 1 3 5 7 9 2 4 6 2 B1 for at most 2 errors 2(b)(i) 38, 47 2 B1 for each 2(b)(ii) 9n + 2 oe 1 C opportunity

0607/52 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2017 © UCLES 2017 Page 4 of 4 Question Answer Mark Part Marks 2(b)(iii) 9 × 150 + 2 [ = 1352] oe 1 or n = 1352 2[ 150] 9 − = oe 3(a) 17, 26, 35, 44 2 B1 for any three correct 3(b) 9n + 8 oe 1 C opportunity FT their answer to 3(a) 3(c) 9998 2 FT their (9n + 8) B1 for 1110[.….] C opportunity 4(a) k + 9, k + 18, k + 27, k + 36 1 4(b) 9n + k oe 1 SC1for 9n + k – 9 oe from an answer of k, k + 9, k + 18, k + 27 in (a) Communication: Seen in two of the following questions 1 1(e)(iii) for their (9 × 87 + 3) seen 2(b)(ii) for two differences of 9 seen or for saying e.g. the sequence is one less than the previous sequence 3(b) for three correct differences FT seen 3(c) for their (9n + 8) * 10 000, where * is = or any inequality sign or for 2 trials close to 10 000 and number stems calculated or substitution for n then stem checked and checked for closest