Cambridge IGCSE Mathematics - International 0607 — 2019 May/June Paper 5 · Variant 1

This document consists of 7 printed pages and 1 blank page. DC (LEG) 170700/2 © UCLES 2019 [Turn over * 0 0 7 8 4 7 8 1 1 4 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/51 Paper 5 (Core) May/June 2019 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 Assessment International Education Cambridge International General Certificate of Secondary Education

2 0607/51/M/J/19 © UCLES 2019 Answer all the questions. INVESTIGATION GAMES IN A COMPETITION This investigation looks at games played in a competition. In a competition every team must play each of the other teams once. Example There are three teams, A, B and C in the competition. Three different games are played. These are: A against B A against C B against C These are written as: AB AC BC Note that AB is the same as BA. 1 (a) (i) There are now four teams A, B, C and D in the competition. Write down the 6 different games played by these four teams. … (ii) There are now five teams A, B, C, D and E in the competition. Write down all the different games played by these five teams. …

3 0607/51/M/J/19 © UCLES 2019 [Turn over (b) Complete the table. Use your answer to part (a)(ii) to help you. Number of teams (n) 2 3 4 5 6 7 Number of games (g) 1 3 6 (c) (i) The numbers of games in the second row of the table form a sequence. Write down the mathematical name for this sequence. … (ii) Write down the rule to find further terms in this sequence. … …

4 0607/51/M/J/19 © UCLES 2019 (d) When there are n teams in the competition the number of games played is g, where g n kn 2 1 2 = + . Find the value of k. … (e) Using your value of k, show that the formula in part (d) is correct for 8 teams. (f) Find the number of games played when there are 20 teams in the competition. …

5 0607/51/M/J/19 © UCLES 2019 [Turn over 2 There are now 8 teams in the competition, A, B, C, D, E, F, G and H. Every team plays one game each week. Note that AB is the same as BA. (a) Complete the table to show the games for the first three weeks. There are many ways of doing this. You only need to show one way. Game 1 Game 2 Game 3 Game 4 Week 1 AB DG CH Week 2 AC Week 3 (b) Write down the total number of weeks it will take to play all the games. …

6 0607/51/M/J/19 © UCLES 2019 (c) Points are awarded to each of the 8 teams in the competition every time they play one of their 7 games. A team gets • 3 points for a win • 1 point for a draw (when the score for each team is the same) • 0 points for a loss. A team plays all 7 games. (i) Find the highest number of points that this team can get. … (ii) Write down the smallest number of points that this team can get. … (iii) The team wins two games, loses two games and draws the rest. Calculate the number of points that this team gets. …

7 0607/51/M/J/19 © UCLES 2019 (iv) Can this team finish the competition with 20 points? Show how you decide. (v) Find all the different ways that this team could score 9 points. One way is 1 win and 6 draws.

8 0607/51/M/J/19 © UCLES 2019 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 Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge. BLANK PAGE

This document consists of 5 printed pages. © UCLES 2019 [Turn over Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/51 Paper 5 (Core) May/June 2019 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 International will not enter into discussions about these mark schemes. Cambridge International is publishing the mark schemes for the May/June 2019 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 2019 © UCLES 2019 Page 2 of 5 Generic Marking Principles These general marking principles must be applied by all examiners when marking candidate answers. They should be applied alongside the specific content of the mark scheme or generic level descriptors for a question. Each question paper and mark scheme will also comply with these marking principles. GENERIC MARKING PRINCIPLE 1: Marks must be awarded in line with: • the specific content of the mark scheme or the generic level descriptors for the question • the specific skills defined in the mark scheme or in the generic level descriptors for the question • the standard of response required by a candidate as exemplified by the standardisation scripts. GENERIC MARKING PRINCIPLE 2: Marks awarded are always whole marks (not half marks, or other fractions). GENERIC MARKING PRINCIPLE 3: Marks must be awarded positively: • marks are awarded for correct/valid answers, as defined in the mark scheme. However, credit is given for valid answers which go beyond the scope of the syllabus and mark scheme, referring to your Team Leader as appropriate • marks are awarded when candidates clearly demonstrate what they know and can do • marks are not deducted for errors • marks are not deducted for omissions • answers should only be judged on the quality of spelling, punctuation and grammar when these features are specifically assessed by the question as indicated by the mark scheme. The meaning, however, should be unambiguous. GENERIC MARKING PRINCIPLE 4: Rules must be applied consistently e.g. in situations where candidates have not followed instructions or in the application of generic level descriptors. GENERIC MARKING PRINCIPLE 5: Marks should be awarded using the full range of marks defined in the mark scheme for the question (however; the use of the full mark range may be limited according to the quality of the candidate responses seen). GENERIC MARKING PRINCIPLE 6: Marks awarded are based solely on the requirements as defined in the mark scheme. Marks should not be awarded with grade thresholds or grade descriptors in mind.

0607/51 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2019 © UCLES 2019 Page 3 of 5 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 2019 © UCLES 2019 Page 4 of 5 Question Answer Marks Partial Marks 1(a)(i) AB BC CD AC BD AD 2 B1 for 4 or 5 correct, ignore repeats 1(a)(ii) AB BC CD DE AC BD CE AD BE AE 3 B2 for 8 or 9 correct, ignore repeats or B1 for 6 or 7 correct, ignore repeats 1(b) No of teams 2 3 4 5 6 7 No of games 1 3 6 10 15 21 2 B1 for one correct C opportunity 1(c)(i) Triangle [Numbers] 1 1(c)(ii) Add the previous number of games to the previous number of teams oe 1 1(d) − 1 2 oe 2 FT M1 for correct substitution of one pair of n and g 1(e) 2 1 1 8 8 2 2 × − × [= 28] oe www 1 continuing the sequence of games or AB BC CD DE EF FG GH AC BD CE DF EG FH AD BE CF DG EH AE BF CG DH AF BG CH AG BH AH 1 If 0 scored SC1 for ( ) 2 1 8 8 2 their k × + × correctly evaluated 1(f) 190 1FT FT their k as seen in 1(d) C opportunity 2(a) Correct completion of table 2 B1 for EF and correct week 2 B1 for correct week 3 2(b) 7 1 2(c)(i) 21 1 2(c)(ii) 0 1

0607/51 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2019 © UCLES 2019 Page 5 of 5 Question Answer Marks Partial Marks 2(c)(iii) 9 1 C opportunity 2(c)(iv) No oe and 7 [wins] × 3 = 21 [points] oe 6 [wins] × 3 + 1 [draw] × 1 = 19 oe 2 B1 for each row Maximum 1 mark if ‘No’ missing or incorrect 2(c)(v) 3 wins [+ 0 draws + 4 losses] 2 wins + 3 draws [+ 2 losses] and no others 1 Extras score 0 Communication: seen in one of the following questions 1 1(b) list for 6 teams (A to F) or list for 7 teams (A to G), or minimum 3 first differences seen or description of how the sequence increases in calculations (minimum of 3) or words 1(f) 2 1 20 2 × + their 1 20 2   − ×     oe seen or continuation of table correct to at least (15, 105) 2(c)(iii) 2 × 3 and (7 – 4) or 3 × 1 seen