Cambridge IGCSE Mathematics - International 0607 — 2022 May/June Paper 5 · Variant 2

This document has 8 pages. [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/52 Paper 5 Investigation (Core) May/June 2022 1 hour 10 minutes You must answer on the question paper. No additional materials are needed. INSTRUCTIONS ● Answer all questions. ● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs. ● Write your name, centre number and candidate number in the boxes at the top of the page. ● Write your answer to each question in the space provided. ● Do not use an erasable pen or correction fluid. ● Do not write on any bar codes. ● You should use a graphic display calculator where appropriate. ● You may use tracing paper. ● You must show all necessary working clearly, including sketches, to gain full marks for correct methods. ● In this paper you will be awarded marks for providing full reasons, examples and steps in your working to communicate your mathematics clearly and precisely. INFORMATION ● The total mark for this paper is 36. ● The number of marks for each question or part question is shown in brackets [ ]. * 7 3 9 0 7 3 9 1 8 8 * DC (LK/SG) 219350/1 © UCLES 2022

2 0607/52/M/J/22 © UCLES 2022 Answer all the questions. INVESTIGATION OPPOSITE CORNERS This investigation is about the difference between the products of the numbers in the opposite corners of a square window on a grid. To calculate the opposite difference for any window: • multiply the numbers in the opposite corners • subtract the smaller answer from the larger answer. 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 Consecutive even numbers fill a grid of width 10 as shown. The grid continues downwards. A 2 by 2 window moves on the grid. Example This is the first window. 2 4 22 24 22 4 88 # = 2 24 48 # = 88 48 40 - = The opposite difference is 40.

3 0607/52/M/J/22 © UCLES 2022 [Turn over 1 (a) Use the grid to complete each window and find the opposite difference. 14 34 36 34 # … = … 14 # 36 = … … - … = … Opposite difference = … 66 86 68 … 150 152 … [4] (b) What do you notice about the opposite difference for each of these windows on this grid? … [1]

4 0607/52/M/J/22 © UCLES 2022 2 A 3 by 3 window moves on the same grid. (a) Complete the corner squares in the first window. 2 6 [1] (b) Complete the opposite difference calculations for this window. … # 6 = … 2 # … = … … - … = … [2] (c) Complete the corner squares for each window and find the opposite difference. 44 4 … 54 10 … 174 … [4]

5 0607/52/M/J/22 © UCLES 2022 [Turn over 3 A 4 by 4 window moves on the grid on page 2. (a) Complete the corner squares in the first window. 2 8 [2] (b) Complete the opposite difference calculations for this window. … # 8 = … 2 # … = … … - … = … [2] (c) Complete the corner squares for each window and find the opposite difference. 64 … 20 … [3]

6 0607/52/M/J/22 © UCLES 2022 4 (a) Copy the opposite differences that you have found and complete the table. Size of window Opposite difference 2 by 2 ( ) 2 1 2 - = 1 3 by 3 ( ) 1 3 2 - = 4 4 by 4 ( ) 1 4 2 - = 9 5 by 5 w by w 40( ) [4] (b) Find the greatest possible opposite difference for a square window on the grid on page 2. … [3] (c) Can a square window on this grid have an opposite difference of 1400? Show how you decide. [2]

7 0607/52/M/J/22 © UCLES 2022 [Turn over 5 Another grid of consecutive even numbers has width 5. The diagram shows the start of the grid. 2 4 6 8 10 12 The diagram shows a 2 by 2 window on the grid. n is the first number in the window. n 2 + n (a) Complete the window using expressions in terms of n. [2] (b) Use your expressions to show that the opposite difference for a 2 by 2 window is 20. [3] Question 6 is printed on the next page.

8 0607/52/M/J/22 © UCLES 2022 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 Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge. 6 A square window moves on the grid of width 5 with squares numbered 2, 4, 6, … . The opposite difference for this window is 180. Find the size of the window. … [3]

This document consists of 6 printed pages. © UCLES 2022 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/52 Paper 5 (Core) May/June 2022 MARK SCHEME Maximum Mark: 36 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 2022 series for most Cambridge IGCSE, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

0607/52 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 2 of 6 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. Maths-Specific Marking Principles 1 Unless a particular method has been specified in the question, full marks may be awarded for any correct method. However, if a calculation is required then no marks will be awarded for a scale drawing.

0607/52 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 3 of 6 2 Unless specified in the question, answers may be given as fractions, decimals or in standard form. Ignore superfluous zeros, provided that the degree of accuracy is not affected. 3 Allow alternative conventions for notation if used consistently throughout the paper, e.g. commas being used as decimal points. 4 Unless otherwise indicated, marks once gained cannot subsequently be lost, e.g. wrong working following a correct form of answer is ignored (isw). 5 Where a candidate has misread a number in the question and used that value consistently throughout, provided that number does not alter the difficulty or the method required, award all marks earned and deduct just 1 mark for the misread. 6 Recovery within working is allowed, e.g. a notation error in the working where the following line of working makes the candidate’s intent clear. 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

0607/52 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 4 of 6 Question Answer Marks Partial Marks 1(a) 16 88 170 172 40 40 40 3 B1 for 16 and 88 B1 for 170 and 172 B1 for 40 seen three times One set of calculations for an opposite difference for the second or third grid C1 86 × 68 – 66  their 88 or their 170  152  150  their 172 1(b) The same or It’s 40 or It’s always 40 oe 1 2(a) 42 and 46 1 2(b) 42 ( 6 =) 252 (2 ) 46 (=) 92 252 – 92 2 For 2 marks FT their 42, their 46 B1 for correct with one multiplication error (in 252 or 92) For B1 FT their 42 and 46 here 2(c) 8 14 134 138 48 50 178 160 160 160 3 B2 for four from 8, 48, 14, 50, 134, 138 and 178 or B1 for two from 8, 48, 14, 50, 134, 138 and 178 If 0 scored SC1 for 160 seen 3 times One complete correct set of calculations for a difference C1 FT 44  their 8 – 4  their 48 or their 50  their 14  10  54 or 174  their 138  their 134  their 178 3(a) 62 and 68 2 B1 for each 3(b) 62 (× 8 =) 496 (2 ×) 68 (=) 136 496 – 136 2 For 2 marks FT their 62, their 68 B1FT for correct with one multiplication error (in 496 or 136) 3(c) 4 10 14 70 74 80 360 360 2 B1 for three from 4, 10, 70, 14, 74, 80 If 0 scored SC1 for 360 seen twice One complete correct set of calculations for a difference C1 64  their 10 – their 4  their 70 or their 74  20 – their 14  their 80

0607/52 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 5 of 6 Question Answer Marks Partial Marks 4(a) Size of window Working Difference 2 by 2 (2 – 1)2 = 1 40 3 by 3 (3 – 1)2 = 4 160 4 by 4 (4 – 1)2 = 9 360 5 by 5 (5 – 1)2 = 16 640 w by w (w – 1)2 isw 40(w – 1)2 isw 3 B1 for (5 – 1)2 and 16 B1 for 640 or B1 for (w – 1)2 seen once Differences of 120, 200 and 280 seen or two multiplications by 40 or 5 by 5 window from grid to support 640 seen C1 4(b) 3240 1 Correct substitution of 10 in their 40(w – 1)2 or complete correct calculation from grid C2 C1 for 40  92 or 10 identified (without substitution) or incomplete correct calculation from grid 4(c) 1400 35 40        and No oe with valid reason e.g. 35 is not a square number or 52  40 [=] 1000 and 62  40 [=] 1440 or [40] (6 – 1)2 [=] 1000 and [40] (7 – 1)2 [=] 1440 (table form) or correct calculations using correct grid numbers for 6 by 6 and 7 by 7 windows 2 B1 for 35 seen OR either 52  40 [=] 1000 or 62  40 [=] 1440 seen OR either (6 – 1)2 [=] 1000 or (7 – 1)2 [=] 1440 (table form) OR correct calculations using correct grid numbers for 6 by 6 or 7 by 7 window 5(a) n + 10 and n + 12 2 B1 for each 5(b) (n + 10)  (n + 2) = n2 + 12n + 20 M2 FT their (n + 10) M1 for one error n2 + 12n + 20 – n2  12n leading to 20 or = 20 M1 If 0 scored SC1 for n = 2, 4, 6 or 8 explicitly stated and correctly substituted into all four correct expressions and complete correct calculations leading to 20

0607/52 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 6 of 6 Question Answer Marks Partial Marks 6 4 [by 4] 1 A correct trial with a 4 by 4 window and full working OR Reference to difference for 2 by 2 being halved from 10 wide grid and testing with another sized window on 5 wide grid OR 20(w – 1)2 = 180 (w – 1)2 = 9 (w – 1) = 3 C2 C1 for a correct trial with a 3 by 3 window or a 5 by 5 window with full working or incomplete trial with a 4 by 4 window OR Reference to difference for 2 by 2 being halved from 10 wide grid OR 20(w – 1)2 =180 soi by working