Cambridge IGCSE Mathematics - International 0607 — 2017 May/June Paper 6 · Variant 1

This document consists of 12 printed pages. DC (KN/SW) 136671/3 © UCLES 2017 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 6 8 0 2 5 5 0 8 7 5 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/61 Paper 6 (Extended) May/June 2017 1 hour 30 minutes 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 both parts A and B. You must show all the 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 40.

2 0607/61/M/J/17 © UCLES 2017 Answer all the questions. A INVESTIGATION VIRUS (20 marks) You are advised to spend no more than 45 minutes on this part. 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) Complete this table. Day (n) Total number of plants that are infected or dead (t) 1 1 2 3 3 5 4 5

3 0607/61/M/J/17 © UCLES 2017 [Turn over (b) Find a formula for t in terms of n. … (c) On which day are there a total of 97 plants that are infected or dead? … 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. On Day 1, one of the plants is infected with a virus (V). The virus infects all the plants next to it. V On Day 2 that plant is dead (D) and the plants next to it are infected. D V V V V On Day 3 there are 5 dead plants and 8 infected plants. D D V V D D V D V V V V V

4 0607/61/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.

5 0607/61/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) Find a formula for t in terms of n. …

6 0607/61/M/J/17 © UCLES 2017 (f) Show that your formula works when n = 6. (g) On which day are exactly 221 plants infected or dead? …

7 0607/61/M/J/17 © UCLES 2017 [Turn over 3 In another field on Day 1 eight plants, in the arrangement below, are infected. V V V V V V V V On Day 2 these plants are dead and the plants next to them are infected. (a) Show that the number of plants that are infected on Day n, where n 2 H , is n 4 3 + . (b) Find an expression for the total number of plants that are infected or dead on Day n, where n 2 H . …

8 0607/61/M/J/17 © UCLES 2017 B MODELLING SCOUT’S PACE (20 marks) You are advised to spend no more than 45 minutes on this part. This task investigates a way of travelling long distances on foot using a mixture of walking and jogging. 1 Explain why multiplying by 60 1000 changes km/h into metres per minute. … … 2 (a) A scout walks at 5 km/h. Show that 5 km/h is approximately 83.3 metres per minute. (b) When walking at 5 km/h, the scout takes 120 paces in one minute. How many metres does the scout walk in 30 paces? … (c) When jogging at 10 km/h, the scout takes 150 paces in one minute. How many metres does the scout jog in 30 paces? …

9 0607/61/M/J/17 © UCLES 2017 [Turn over 3 Scout’s Pace means to walk for 30 paces then to jog for 30 paces and to keep repeating this. (a) Show that the scout takes 27 seconds to walk 30 paces then to jog 30 paces. (b) Find the average speed, in m/s, of the scout when using Scout’s Pace. … (c) Change your answer in part (b) into km/h. …

10 0607/61/M/J/17 © UCLES 2017 4 To find a model for average speed using Scout’s Pace assume that, at different speeds, the scout always takes • 120 paces per minute when walking and • 150 paces per minute when jogging. The scout walks at x km/h and jogs at y km/h. (a) Show that an expression for the distance travelled by the scout when walking 30 paces is x 6 25 metres. (b) The distance travelled by the scout when jogging 30 paces is y 3 10 metres. Show that a model for the average speed, S km/h, using Scout’s Pace is S x y 9 5 4 = + .

11 0607/61/M/J/17 © UCLES 2017 [Turn over (c) Find the average speed using Scout’s Pace when the jogging speed, y km/h, is twice the walking speed, x km/h. Give your answer, in terms of x, in its simplest form. … (d) Find y in terms of x when the average speed is 1.5x km/h. … (e) The average speed is 7 km/h. The jogging speed is 10 km/h. Find the walking speed. … Question 5 is printed on the next page.

12 0607/61/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. 5 The scout now walks at 150 paces per minute and jogs at 180 paces per minute. Change the model in question 4(b) for the average speed using Scout’s Pace. Give your answer in its simplest form. …

® IGCSE is a registered trademark. This document consists of 7 printed pages. © UCLES 2017 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/61 Paper 6 (Extended) May/June 2017 MARK SCHEME Maximum Mark: 40 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.

0607/61 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2017 © UCLES 2017 Page 2 of 7 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

0607/61 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2017 © UCLES 2017 Page 3 of 7 Question Answer Marks Part Marks A INVESTIGATION VIRUS 1(a) 7, 9 1 1(b) 2 1 n − oe 1 C opportunity 1(c) 49 1 C opportunity 2(a) V V D V V D D D V V D D D D D V V D D D V V D V V 1 2(b) 12, 16 2 B1 for each C opportunity 2(c) [p =] 4n – 4 oe 2 M1 for 4n seen C opportunity 2(d) 25, 41 1 2(e) [ ] 2 2 2 1 t n n = − + oe 2 M1 for 2 2n soi 2(f) Substitution leading to 61 and correct diagram or continued sequence of 25, 41, 61 with differences of 16, 20 seen 2 B1 for each 2(g) 11 2 M1 for 11 and – 10 or for continuation of the sequence from 61 as 85, 113, 145, 181, 221 C opportunity

0607/61 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2017 © UCLES 2017 Page 4 of 7 Question Answer Marks Part Marks 3(a) [8,] 11, 15, 19 with supporting diagram(s) seen and 4(2) + 3 = 11, 4(3) + 3 = 15, 4(4) + 3 = 19 soi or solving 4n + 3 = 11, 4n + 3 = 15, 4n + 3 = 19 to obtain n = 2, 3, 4 or differences of 4 implying 4n + k and substituting at least one of n = 2, 3, 4, … to find k 2 B1 for each or B1 for any two correct values found from diagrams and verified by calculation 3(b) 2 2 5 1 n n + + oe 2 M1 for 19, 34, 53 seen C opportunity Communication: Seen in three of the following questions 1 1b or 2c or 2e At least 3 differences of 2 seen; may be in table in 1(a) At least 3 differences of 4 seen ; may be in table in 2(b) For 2 rows of differences with at least 3 differences in the 2nd row; may be in table in 2(d) 1c 97 = (2 1) their n − seen oe or algebraic change of subject of their t = 2n – 1 seen and then 97 1 2 n + = or continuation of sequence (need not be term by term) 2b At least one more correct diagram drawn 2g Attempt at correct method to solve their 3-term quadratic equation in n e.g. if correct, (2 22)( 10) 0 n n − + = or( 11)( 10) 0 n n − + = 2 ( 2) ( 2) 4 2 220 2(2) n −− ± − − × × − = or 2 ( 1) ( 1) 4 1 110 2 n −− ± − − × × − = or sketch of relevant graphs 3b For 19, 34, 53, 76, [103] seen and two rows of differences

0607/61 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2017 © UCLES 2017 Page 5 of 7 Question Answer Marks Part Marks A MODELLING SCOUT’S PACE 1 1 km = 1000 m oe and 1 h = 60 min or 1 min = 1 60 h oe 1 2(a) 5 1000 60 × oe seen 1 2(b) awrt 20.8 or 5 20 6 isw 1 C opportunity 2(c) awrt 33.3 or 1 333 isw 1 C opportunity 3(a) 30 30 + ×60 120 150       oe or 60 60 5 4 + oe or 5 1 20 33 6 3 60 1 2 83 166 3 3     + ×       oe or Walking: 120 2 60 = 30 15 2 = Jogging: 150 2.5 60 = 30 12 2.5 = 15 + 12 = 27 1 3(b) 2[.00] to 2.01 nfww 1 FT (20.8 + 33.3) 27 their C opportunity 3(c) 7.2[0] to 7.236 1 FT their (b) × 3.6 C opportunity 4(a) 30 1000 120 60 x × oe or 5 20 1000 6 1 60 833 x × leading to 25 6 x 1

0607/61 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2017 © UCLES 2017 Page 6 of 7 Question Answer Marks Part Marks 4(b) 25 10 6 3 27 x y + oe M1 Allow this mark for total dist / time attempt i.e. for correct numerator over a constant; ignore units for this mark 2 25 10 60 6 3 27 1000 x y their   +   ×     oe M1 Allow × 3.6 Correct simplification to 5 4 9 x y + A1 Note: Answer is given so evidence must be seen; must have at least one interim step after 2 25 10 60 6 3 27 1000 x y   +   ×     seen Alternative method using ratios and the approach 1 1 2 2 1 2 speed time speed time time time × + × + 15 12 3600 3600 27 3600 x y + or 240 300 3 400 x y + oe M1 Or two times given as a ratio a : b equivalent to 5 : 4 or b : a equivalent to 4 : 5 e.g. 15 : 12 or 12 : 15 or 0.2 : 0.25 15 12 27 x y + or 5 4 1200 1200 9 1200 x y + DM1 ax by a b + + with correct values of a and b completion to given answer 5 4 9 x y + A1 If 0 scored, SC1 for 15 12 5 4 27 9 x y x y + + = only 4(c) 13 9 x oe isw 2 M1 for 5 4 2 oe 9 x x + × or 5 8 9 x x + C opportunity 4(d) 17 8 x oe or 2.125x isw 2 M1 for 5 4 1.5 9 x y x + = 4(e) 4.6 oe or 3 45 2 M1 for 5 4 10 7 9 x + × = oe C opportunity

0607/61 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2017 © UCLES 2017 Page 7 of 7 Question Answer Marks Part Marks 5 [ ] 6 5 11 x y S + = 2 M1 for 25 9 y oe or 22 seen or 12 and 10 seen or 1 5 and 1 6 oe seen or 1 300 and 1 360 oe seen C opportunity Communication: Seen in three of the following questions 1 2b for 83.3 4 or 5 1000 4 60 × × oe; may be in steps or e.g. 120 : 83.3 and 30: x compared or e.g. 120 30 83.3 x = 2c for 10 1000 60 5 × × or 83.3 2 5 × oe or e.g. 150 : 166.6 and 30 : x compared or e.g. 150 30 166.6 x = 3b for (20.8 33.3) 27 their + or e.g. (54.1) 27 their seen or for comparison of ratios e.g. 54.1 to 27 x to 1 3c for multiplying by a correct conversion factor e.g. ( 2.01) 60 60 1000 their × × or ( 2.01) 3600 1000 their × or ( 2.01) 3.6 their × seen Note: Division by 1000 may be implied by sight of m / h and km / h etc. 4c for correct units seen e.g. 13 9 x km/h 4e for correct units e.g. 4.6 km / h 5 for showing how to get 22 e.g. 30 30 60 150 180   + ×     or for showing how to get 10 e.g. 30 60 180 × ; may be in steps or for a correct step in simplification of 2 10 25 60 3 9 22 1000 x y their   +   ×     towards answer