Cambridge IGCSE Mathematics - International 0607 — 2015 May/June Paper 5 · Variant 2

This document consists of 7 printed pages and 1 blank page. DC (LK/CGW) 100449/3 © UCLES 2015 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 1 1 6 3 7 9 9 3 0 9 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/52 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 0607/52/M/J/15 © UCLES 2015 Answer all the questions. INVESTIGATION MOLECULES This investigation looks at the structure of models of molecules. Molecules called alkanes contain carbon atoms (C) and hydrogen atoms (H) arranged in a pattern. 1 These diagrams show the first three alkanes. H C H H H H C H H C H H H H C H H C H H C H H H (a) Draw a diagram to show the next alkane which contains four carbon atoms.

3 0607/52/M/J/15 © UCLES 2015 [Turn over (b) (i) Complete this table to show the number of hydrogen atoms (h) for different numbers of carbon atoms (c). c h 1 4 2 6 3 4 5 6 (ii) What is the value of h when c is 12? … (iii) Find a formula for h in terms of c. h = … (iv) What is the value of c when h is 100? …

4 0607/52/M/J/15 © UCLES 2015 2 Alkanes can be made into alcohols by adding one oxygen atom (O). For example H C H H C H H O H (a) Complete the table below for an alcohol with 3 carbon atoms. Number of carbon atoms c Number of hydrogen atoms h Number of oxygen atoms o Total number of atoms t 1 4 1 6 2 6 1 9 3 (b) Find a formula for t in terms of c. t = …

5 0607/52/M/J/15 © UCLES 2015 [Turn over 3 Chemists use small spheres and rods to make models of molecules. These diagrams show a sequence of molecules of height 1. Molecule 1 Molecule 2 Molecule 3 (a) Draw the next two molecules in this sequence. (b) Complete this table for molecules of height 1. Molecule m Number of spheres s Number of rods r 1 1 0 2 2 1 3 3 2 4 5 6 (c) Write down a formula for s in terms of m. s = … (d) A molecule of height 1 has 97 spheres. How many rods does this molecule have? …

6 0607/52/M/J/15 © UCLES 2015 4 These diagrams show a sequence of molecules of height 2. Molecule 1 Molecule 2 Molecule 3 Molecule 4 (a) Complete this table for molecules of height 2. Molecule m Number of spheres s Number of rods r 1 2 1 2 4 4 3 6 7 4 5 6 (b) Find, in terms of m, a formula for (i) s, s = … (ii) r. r = … (c) A molecule of height 2 has 100 spheres. How many rods does this molecule have? …

7 0607/52/M/J/15 © UCLES 2015 5 (a) Use your answers to questions 3(c) and 4(b) to help you complete the table for molecules of height h. Height (h) Number of spheres (s) in terms of m Number of rods (r) in terms of m 1 m − 1 2 3 3m 5m − 3 4 5 5m 9m − 5 6 (b) Find, in terms of m and h, a formula for (i) s, s = … (ii) r. r = …

8 0607/52/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. BLANK PAGE

® 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 0607/52 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 52 © 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) 1 (b) (i) 8, 10, 12, 14 1 (ii) 26 1 (iii) 2c + 2 2 B1 for 2c C opportunity (iv) 49 1FT FT their (b)(iii) providing linear formula C opportunity 2 (a) c h o t 3 8 1 12 1 (b) 3c + 3 oe 2 B1 for 3c C opportunity 3 (a) 1 Both diagrams correct (b) 4 3 5 4 6 5 1 (c)
1 (d) 96 1 H  C  C  C  C  Η H  H  H  H   H  H  H  H

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – May/June 2015 0607 52 © Cambridge International Examinations 2015 4 (a) 8 10 10 13 12 16 1 (b) (i) 2m oe 1 (ii) 3m – 2 oe 2 B1 for 3m oe C opportunity (c) 148 2FT B1 FT for their 50 soi FT their 50 in their formula for r C opportunity 5 (a) h s r 1 m m – 1 2 2m 3m –2 3 3m 5m – 3 4 4m 7m –4 5 5m 9m – 5 6 6m 11m – 6 2 B1 for row 4 or 6 correct or either column correct (b) (i) hm oe 1 (ii) (2h – 1)m – h oe isw 1 oe Communication seen in two of 1(b)(iii), 1(b)(iv), 2(b), 4(b)(ii), 4(c) 1