Cambridge IGCSE Mathematics - International 0607 — 2012 May/June Paper 5 · Variant 1

This document consists of 5 printed pages and 3 blank pages. IB12 06_0607_05/4RP © UCLES 2012 [Turn over *7158128086* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/05 Paper 5 (Core) May/June 2012 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, highlighters, glue or correction fluid. You may use a 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. www.XtremePapers.com

2 © UCLES 2012 0607/05/M/J/12 For Examiner's Use Answer all the questions. INVESTIGATION ADDITION TRIPLES An addition triple has three different numbers. The numbers (8, 10, 18) form an addition triple because 8 + 10 = 18. Some other addition triples are (10, 11, 21) and (21, 24, 45). This investigation explores patterns with addition triples. 1 Nine addition triples can be found from the list of integers 1, 2, 3, 4, 5, 6, 7. One of these triples is (3, 4, 7). Write down the other eight addition triples in the spaces provided. [Note that (3, 4, 7) and (4, 3, 7) are the same addition triple.] ( , , ) ( , , ) ( , , ) ( , , ) ( , , ) ( , , ) ( , , ) ( , , ) ( 3 , 4 , 7 )

3 © UCLES 2012 0607/05/M/J/12 [Turn over For Examiner's Use 2 Complete the table, showing the addition triples for each list of integers. In the last column write the total number of triples. Number of integers List of integers Addition triples Total number of addition triples 3 1, 2, 3 (1, 2, 3) 1 4 1, 2, 3, 4 2 5 1, 2, 3, 4, 5 6 1, 2, 3, 4, 5, 6 7 1, 2, 3, 4, 5, 6, 7 Leave this blank – do not write your answer to question 1 again. 9 8 1, 2, 3, 4, 5, 6, 7, 8 12

4 © UCLES 2012 0607/05/M/J/12 For Examiner's Use 3 Look at the pattern in the last column in the table on page 3. Use it to complete the following table. Number of integers 3 4 5 6 7 8 9 10 11 12 13 14 15 Number of addition triples 1 2 9 12 16 20 30 36 4 Using Question 3, complete the following table. Number of integers 3 5 7 9 11 13 15 17 Number of addition triples 1 = 12 9 = 32 16 = 42 36 = 62 5 How many integers are in the list when there are 100 addition triples?

5 © UCLES 2012 0607/05/M/J/12 For Examiner's Use 6 (a) Is it possible to have 225 addition triples? Explain your answer. (b) Explain why it is not possible to have 900 000 addition triples. 7 (a) The numbers in the second row of the table in Question 4 form a sequence. Find the number of addition triples when there are 99 integers in the list. Show how you do this. (b) The numbers in the second row of the table in Question 3 form a sequence. Find the number of addition triples when there are 100 integers in the list. Show how you do this.

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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2012 question paper for the guidance of teachers 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/05 Paper 5 (Core), maximum raw mark 24 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 must be read in conjunction with the question papers and the report on the examination. • Cambridge will not enter into discussions or correspondence in connection with these mark schemes. Cambridge is publishing the mark schemes for the May/June 2012 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses. www.XtremePapers.com

Page 2 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2012 0607 05 © University of Cambridge International Examinations 2012 Qu. Answer Mark Notes Comments 1 (1, 2, 3) (1, 3, 4) (1, 4, 5) (2, 3, 5) (1, 5, 6) (2, 4, 6) (1, 6, 7) (2, 5, 7) 3 B1 for 4 or 5 B2 for 6 or 7 First two numbers can be swapped (1, 2, 3) (1, 3, 4) 1 cao (1, 2, 3) (1, 3, 4) (1, 4, 5) (2, 3, 5) 2 cao B1 for any 3 (1, 2, 3) (1, 3, 4) (1, 4, 5) (2, 3, 5) (1, 5, 6) (2, 4, 6) 2 cao B1 for any 5 2 (1, 2, 3) (1, 3, 4) (1, 4, 5) (2, 3, 5) (1, 5, 6) (2, 4, 6) (1, 6, 7) (2, 5, 7) (3, 4, 7) (1, 7, 8) (2, 6, 8) (3, 5, 8) 2 B1 for any 10 Communication for systematic setting: ascending order within each triple and first or last numbers in order (after repeating previous set) 3 4 5 6 7 8 9 10 11 12 13 14 15 2 4 6 9 12 16 20 25 30 36 42 49 2 B1 for 3 ft the numbers from their table unless wrongly counted. 4 3 5 7 9 11 13 15 17 1 = 12 [4=] 22 32 42 [25=]52 36 = 62 [49=]72 [64=]82 2 B1 for 3 5 21 2 B1 10² soi Communication: Table extension OR √100 = 10 oe and 10 × 2 = 20 OR 10 + 11 = 21

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2012 0607 05 © University of Cambridge International Examinations 2012 6 (a) (b) Yes, 152 = 225 soi Is not a square 1 2 M1 948.6... SC1 √900000 does not exist OR does not have a square root oe Accept Yes, 31 [integers] OR Yes, √225 is a whole number OR Yes, 225 is a square Accept √900 000 is a not whole number OR 900 000 is not 3002 and not 30002 OR does not have an exact square root OR is a decimal OR 900000 is in between 898704 = 948² and 900601 = 949² 7 (a) (b) 2401 2450 cao 2 2 M1 for 49 or 49.5 soi M1 502 – 50 oe soi OR 492 + 49 OR their 2401 + 49 Accept 492 Communication: 98/2 = 49 or 99/2 = 49.5 and 49² = 2401 OR correct table extension! Communication 1 Communication seen in questions 2, 5 or 7(a)