Cambridge IGCSE Mathematics - International 0607 — 2015 May/June Paper 5 · Variant 1

This document consists of 8 printed pages. DC (NF/SG) 101336/3 © UCLES 2015 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 2 9 7 7 7 4 4 3 7 5 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/51 Paper 5 (Core) May/June 2015 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 0607/51/M/J/15 © UCLES 2015 Answer all the questions. INVESTIGATION STAIRCASES This investigation looks at the number of cubes that make different types of staircase. 1 This is an UP staircase of height 3 made using 6 cubes. It is a 3-step UP staircase because it has a height of 3 cubes. (a) Write down the number of cubes that make an UP staircase of height 2. … (b) On the grid below draw an UP staircase of height 4.

3 0607/51/M/J/15 © UCLES 2015 [Turn over (c) Complete the table for the number of cubes that make these UP staircases. Height Number of cubes 1 2 3 1 6 4 5 6 (d) Find how many cubes make an UP staircase of height 10. … (e) (i) What is the height of the tallest UP staircase that can be made from 100 cubes? … (ii) Find how many cubes would be left over. …

4 0607/51/M/J/15 © UCLES 2015 2 This is an UP AND DOWN staircase of height 3 made using 9 cubes. It is a 3-step UP AND DOWN staircase because it has a height of 3 cubes. (a) Find how many cubes make an UP AND DOWN staircase of height 4. … (b) On the grid below draw an UP AND DOWN staircase of height 2.

5 0607/51/M/J/15 © UCLES 2015 [Turn over (c) Complete the table for the number of cubes that make these UP AND DOWN staircases. Height Number of cubes 1 2 3 1 9 4 5 6 (d) The numbers of cubes form a sequence. Write down the mathematical name of this sequence. … (e) Find how many cubes make an UP AND DOWN staircase of height 10. … (f) Find an expression, in terms of n, for the number of cubes that make an UP AND DOWN staircase of height n. …

6 0607/51/M/J/15 © UCLES 2015 3 This is a DOUBLE staircase of height 3 made using 12 cubes. It is a 3-step DOUBLE staircase because it has a height of 3 cubes. (a) Find how many cubes make a DOUBLE staircase of height 2. … (b) Complete the table for the number of cubes that make these DOUBLE staircases. Height Number of cubes 1 2 3 2 12 4 5 6

7 0607/51/M/J/15 © UCLES 2015 [Turn over (c) Find how many cubes make a DOUBLE staircase of height 10. … (d) (i) Find an expression, in terms of n, for the number of cubes that make a DOUBLE staircase of height n. … (ii) Find the height of a DOUBLE staircase made from 240 cubes. … (e) Write down the connection between the number of cubes that make a DOUBLE staircase and the number of cubes that make an UP AND DOWN staircase, when both staircases have the same height. … … Question 4 is printed on the next page.

8 0607/51/M/J/15 © UCLES 2015 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. 4 (a) Write down the connection between the number of cubes that make a DOUBLE staircase and the number of cubes that make an UP staircase, when both staircases have the same height. … … (b) Find an expression, in terms of n, for the number of cubes that make an UP staircase of height n. …

® IGCSE is the registered trademark of Cambridge International Examinations. CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the May/June 2015 series 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/51 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 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 2015 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 2015 0607 51 © Cambridge International Examinations 2015 Abbreviations 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 1 (a) 3 1 (b) 1 (c) Height 1 2 3 4 5 6 Cubes 1 3 6 10 15 21 2 B1 for 15 B1 for 21 (d) 55 1 C opportunity (e) (i) 13 1 C opportunity (ii) 9 1 FT their (i) if answer <13 2 (a) 16 1 (b) 1

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2015 0607 51 © Cambridge International Examinations 2015 (c) Height 1 2 3 4 5 6 Cubes 1 4 9 16 25 36 1 B1 for 25 and 36 (d) Square [numbers] 1 (e) 100 1 (f) n2 or n × n or 1n2 cao 1 3 (a) 6 1 (b) Height 1 2 3 4 5 6 Cubes 2 6 12 20 30 42 2 B1 for one of 20, 30, 42 FT double their 1(c) with no errors (c) 110 1 C opportunity (d) (i) n2 + n or n(n + 1) oe 2 If 0 scored B1 for kn2 (k ≠ 0) (ii) 15 1 (e) DOUBLE staircase = UP AND DOWN staircase + height (number of steps) oe 1 4 (a) Double staircase = 2 times UP staircase oe 1 (b) 2 1 1 2 2 n n + or 1 1 2 2 n n n × + oe 1FT FT 1 2 ×their 3(d)(i) Communication seen in two of 1(d), 1(e)(i), 3(c), 3(d)(ii) 1