Cambridge IGCSE Mathematics - International 0607 — 2024 Oct/Nov Paper 5 · Variant 3

This document has 8 pages. Any blank pages are indicated. [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/53 Paper 5 Investigation (Core) October/November 2024 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 [ ]. * 5 6 1 0 0 4 4 2 4 3 * DC (LO) 344631 © UCLES 2024 ,










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2 0607/53/O/N/24 © UCLES 2024 Answer all the questions. INVESTIGATION REVERSE DIFFERENCES This investigation looks at what happens when you reverse the digits of a number and then find the difference between the new number and the original number. This is called the reverse difference. STEP 1 Write down a 2-digit number. STEP 2 Reverse the digits of the number. STEP 3 Find the positive difference between the two numbers. Example 1 Example 2 STEP 1 Write a number 52 STEP 1 13 STEP 2 Reverse the digits 25 STEP 2 31 STEP 3 Find the difference 52 25 27 - = STEP 3 31 13 18 - = 1 (a) Complete the three steps for each 2-digit number in the table. STEP 1 12 13 14 15 16 17 18 STEP 2 21 31 41 51 STEP 3 18 45 63 [3] (b) Complete this table of 2-digit numbers and their reverse differences. Use part (a) and any patterns you notice to help you. Number Reverse difference Number Reverse difference Number Reverse difference Number Reverse difference 10 9 20 18 30 27 40 36 11 21 9 31 18 41 27 12 22 32 9 42 13 18 23 9 33 43 14 24 34 44 15 25 27 35 45 16 45 26 36 36 46 17 27 45 37 36 47 18 63 28 54 38 45 48 19 29 63 39 54 49 45 [4] * 0000800000002 * ,










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3 0607/53/O/N/24 © UCLES 2024 [Turn over (c) Find how many 2-digit numbers have a reverse difference of 0. … [2] (d) (i) Complete the statement with the largest number possible. The reverse difference is always a multiple of … [1] (ii) The table in part (b) is extended to the right. These two columns are part of the extended table. Number Reverse difference A 9 What is the value of the 2-digit number A? … [2] (iii) 64 has a reverse difference of 18. Show how you can use 6 and 4 to work out the reverse difference without using the STEPs. [1] * 0000800000003 * ,










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4 0607/53/O/N/24 © UCLES 2024 2 You can find reverse differences for 3-digit numbers using the same steps. Example STEP 1 Write a number 138 STEP 2 Reverse the digits 831 STEP 3 Find the difference 831 138 693 - = (a) Complete this table. You may use any patterns you notice to help you. Number Reverse difference Number Reverse difference Number Reverse difference Number Reverse difference 100 99 110 120 130 99 101 0 111 0 121 0 131 0 102 112 122 132 99 103 198 113 123 133 104 297 114 124 134 105 396 115 125 135 106 116 126 136 495 107 117 127 137 594 108 693 118 128 138 693 109 792 119 129 139 792 [3] (b) Complete the statement with the largest number possible. The reverse difference is always a multiple of … [1] * 0000800000004 * ,










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5 0607/53/O/N/24 © UCLES 2024 [Turn over (c) A 3-digit number abc has first digit a, second digit b and third digit c. In this part a c 2 . So the number 601 has a 6 = , b 0 = and c 1 = . (i) There is a relationship between a c - and the reverse difference. Investigate this relationship, giving three examples. Write down this relationship. … [3] (ii) Anna says that a is the hundreds digit, b is the tens digit and c is the units digit. She says the value of abc is a b c 100 10 + + . Anna writes the value of the reverse number cba. c b a 100 10 + + She writes the difference between the two numbers. ( ) ( ) a b c c b a 100 10 100 10 + + - + + Continue Anna’s working to show that the reverse difference is ( ) a c 99 - . [2] (iii) A 3-digit number has a 8 = and a reverse difference of 594. Find three possible 3-digit numbers. … [2] * 0000800000005 * ,










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6 0607/53/O/N/24 © UCLES 2024 3 Anna’s working in Question 2(c)(ii) is for the 3-digit number abc. Anna uses similar working for the 2-digit number ab where a b 2 . Use Anna’s working to show that your answer to Question 1(d)(i) is correct. [5] 4 A 4-digit number abcd, where a d 2 , has a value of a b c d 1000 100 10 + + + . (a) Find an expression, in terms of a, b, c and d, for the reverse difference. Your answer should have four terms. … [3] * 0000800000006 * ,










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7 0607/53/O/N/24 © UCLES 2024 (b) A 4-digit number has first digit 7 and last digit 5. Its reverse difference is 2178. Find the connection between the middle two digits of the 4-digit number. … [4] * 0000800000007 * ,










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8 0607/53/O/N/24 © UCLES 2024 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. BLANK PAGE * 0000800000008 * ,










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This document consists of 7 printed pages. © Cambridge University Press & Assessment 2024 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/53 Paper 5 (Core) October/November 2024 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 October/November 2024 series for most Cambridge IGCSE, Cambridge International A and AS Level components, and some Cambridge O Level components.

0607/53 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 2 of 7 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 descriptions 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.

0607/53 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 3 of 7 Mathematics-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. 2 Unless specified in the question, non-integer 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 or sign 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 A or B 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.

0607/53 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 4 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 Question Answer Marks Partial Marks 1(a) 12 14 15 16 17 18 61 71 81 9 27 36 54 3 B2 for 4 correct or B1 for 3 correct

0607/53 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 5 of 7 Question Answer Marks Partial Marks 1(b) N D N D N D N D 10 9 20 18 30 27 40 36 11 0 21 9 31 18 41 27 12 9 22 0 32 9 42 18 13 18 23 9 33 0 43 9 14 27 24 18 34 9 44 0 15 36 25 27 35 18 45 9 16 45 26 36 36 27 46 18 17 54 27 45 37 36 47 27 18 63 28 54 38 45 48 36 19 72 29 63 39 54 49 45 3 B2 for 5 correct rows or B1 for 2 correct rows One correct subtraction seen or 3 differences of 9 C1 1(c) 9 1 [11, 22, 33, 44,] 55, 66, 77, 88, 99 or comment that the digits must be the same. C1 1(d)(i) 9 1 1(d)(ii) 80 1 In 2nd column three from 72, 63, 54, 45, 36, 27, 18, 9, 0 leading to 9 in the bottom row or [72, 63, 54, 45,] 36, 27, 18 (bottom row) or 89 in bottom left cell and 98 – 89 = 9 or 12, 23, 34, 45, … or difference in digits is 1 C1 1(d)(iii) (6 – 4)  9 oe 1

0607/53 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 6 of 7 Question Answer Marks Partial Marks 2(a) N D N D N D N D 100 99 110 99 120 99 130 99 101 0 111 0 121 0 131 0 102 99 112 99 122 99 132 99 103 198 113 198 123 198 133 198 104 297 114 297 124 297 134 297 105 396 115 396 125 396 135 396 106 495 116 495 126 495 136 495 107 594 117 594 127 594 137 594 108 693 118 693 128 693 138 693 109 792 119 792 129 792 139 792 2 B1 for first D column correct One correct subtraction seen or three differences of 99 C1 2(b) 99 1 2(c)(i) Three examples, each with three calculations showing the rule e.g. 601 – 106 = 495 6 – 1 = 5 5  99 = 495 oe or 500 – 5 = 495 2 B1 for two examples, each with two or three calculations from e.g. 601 – 106 = 495 6 – 1 = 5 5  99 = 495 oe (a – c)  99 = reverse difference oe isw 1 Dependent on one example with three calculations 2(c)(ii) 100a + 10b + c – 100c – 10b – a 1 99a – 99c = 99(a – c) 1 2(c)(iii) 594  99 or difference [between a and c] = 6 or 99c = 99×8 – 594 or three correct trials with a = 8 C1 Three numbers of the form 8 ... 2 1

0607/53 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 7 of 7 Question Answer Marks Partial Marks 3 (10a + b) – (10b + a) M3 M1 for 10a + b M1FT for their (10a + b) reversed 9a – 9b 1 Dependent on M2 or M3 awarded 9(a – b) 1 4(a) 1000d + 100c + 10b + a C1 999a + 90b − 90c − 999d 2 B1 for two terms correct 4(b) Second digit minus third digit is 2 oe or b – c = 2 1 AND One correct calculation with b – c = 2 e.g. 7 3 1 5 − 5 1 3 7 2 1 7 8 C2 C1 for 7 . . 5 − 5 . . 7 2 1 7 8 or 7 b c 5 − 5 c b 7 Two further correct calculations with b – c = 2 C1 OR Substitution of a = 7 and d = 5 e.g. 999 × 7 + 90b – 90c – 999 × 5 = 2178 C2 FT their four-term expression C1 for a = 7 and d = 5 Collection of terms 90b – 90c = 2178 – 6993 + 4995 or better C1 OR 7 – 5 = 2 C1 2178 – 2  999 C1 180  90 = 2 C1