Cambridge IGCSE Mathematics - International 0607 — 2017 May/June Paper 5 · Variant 1

* 6 6 1 1 3 8 1 1 4 4 * This document consists of 8 printed pages. DC (AL/AR) 136864/1 © UCLES 2017 [Turn over CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/51 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. Cambridge International Examinations Cambridge International General Certificate of Secondary Education

2 0607/51/M/J/17 © UCLES 2017 Answer all the questions. INVESTIGATION VIRUS This investigation looks at the way a virus spreads in plants in a field. 1 In a field there are a large number of plants in a straight line. The diagram shows the plants near the middle of the field. On Day 1, one of the plants is infected with a virus (V). V On Day 2, that plant is dead (D) and the virus infects the plants next to it. D V V This continues from day to day so this is the pattern on Day 3. D D V V D The diagram shows that the virus infects two more plants on day 3. So the total number of plants that are infected or dead is five. (a) Draw the pattern for Day 4. (b) Complete this table. Day (n) Total number of plants that are infected or dead (t) 1 1 2 3 3 5 4 5

3 0607/51/M/J/17 © UCLES 2017 [Turn over (c) What is the name of the numbers in the t column in part (b)? … (d) Find the total number of plants that are infected or dead on Day 9. … (e) Find a formula for t in terms of n. … (f) On which day are there a total of 97 plants that are infected or dead? …

4 0607/51/M/J/17 © UCLES 2017 2 In another field there are a large number of plants in equally spaced rows and columns. The diagram shows the plants near the middle of the field. One of the plants is infected with the virus (V). V On Day 2, that plant is dead (D) and the virus infects the plants next to it. These plants form a cross. D V V V V On Day 3, the virus spreads along the arms of the cross. D D V V D D V D V This continues from day to day. (a) Draw the pattern for Day 4.

5 0607/51/M/J/17 © UCLES 2017 [Turn over (b) Complete this table. Day (n) Total number of plants that are infected or dead (t) 1 1 2 5 3 9 4 5 (c) Find a formula for t in terms of n. … 3 In another field, one of the plants is infected with a different virus (Z). This virus affects all the plants next to it. Z On Day 2 that plant is dead (D) and the plants next to it are infected. D Z Z Z Z On Day 3 there are 5 dead plants and 8 infected plants. D D Z Z D D Z D Z Z Z Z Z

6 0607/51/M/J/17 © UCLES 2017 (a) Draw the pattern for Day 4. (b) Complete this table to show the number of infected plants each day. Day (n) Number of infected plants (p) 1 1 2 4 3 8 4 5 You may use this grid to help you.

7 0607/51/M/J/17 © UCLES 2017 [Turn over (c) Work out a formula for the number of infected plants (p) in terms of the day (n) for n 2 H . … (d) Complete this table to show the total number of infected or dead plants each day. Day (n) Total number of infected or dead plants (t) 1 1 2 5 3 13 4 5 (e) The formula for t in terms of n is t n bn c 2 2 = + + . Find the value of b and the value of c. b = … c = … Question 3(f) is printed on the next page.

8 0607/51/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. (f) Show that your formula works when n = 6.

® 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 0607/51 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.

0607/51 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

0607/51 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2017 © UCLES 2017 Page 3 of 4 Question Answer Marks Part Marks 1(a) V D D D D D V 1 1(b) 7 9 1 1(c) Odd 1 1(d) 17 1 C opportunity 1(e) [t =] 2n – 1 oe 2 M1 for 2n oe C opportunity 1(f) 49 1 C opportunity 2(a) V D D V D D D D D V D D V 1 2(b) 13 17 1 2(c) [t =] 4n – 3 oe 2 M1 for 4n oe C opportunity 3(a) Z Z D Z Z D D D Z Z D D D D D Z Z D D D Z Z D Z Z 1 3(b) 12 16 2 B1 for each in correct row C opportunity 3(c) [p =] 4n – 4 oe 2 M1 for 4n oe C opportunity 3(d) 25 41 2 B1 for each in correct row

0607/51 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2017 © UCLES 2017 Page 4 of 4 Question Answer Marks Part Marks 3(e) [b =] –2 [c =] 1 2 B1 for each C opportunity 3(f) Substitution leading to 61 and correct diagram or continued sequence 2 B1 for each 25 16 41 20 61 Communication: Seen in three of the following questions (maximum of one difference method) 2 1 for communication seen in one question 1(d) Continuing sequence at least to 15 or substitution into 2n – 1 1(f) their = 97 (2n – 1) oe or trial and improvement – minimum of 2 substitutions for their n or correctly deduced from a continued sequence 3(b) Correct diagram for day 5 3(e) Substitution and attempt to solve equations simultaneously or difference method - with 4 first differences and 3 second differences 1(e) At least 3 differences of 2 seen 2(c) At least 3 differences of 4 seen 3(c) At least 3 differences of 4 seen