Cambridge IGCSE Mathematics - International 0607 — 2025 Feb/March Paper 5 · Variant 2

This document has 12 pages. Any blank pages are indicated. [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/52 Paper 5 Investigation (Core) February/March 2025 1 hour 15 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 40. ● The number of marks for each question or part question is shown in brackets [ ]. * 6 9 3 6 4 4 7 8 8 0 * DC (PQ/CT) 346895/3 © UCLES 2025 ,










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2 0607/52/F/M/25 © UCLES 2025 INVESTIGATION REGULAR POLYGONS In this task you will investigate fitting regular polygons together at a point. All the polygons have sides of the same length. The polygons fit together exactly with one corner from each polygon meeting at a point with no gaps or overlaps. 1 The diagram shows 4 squares fitting together at a point. Complete the sentences. Each interior angle of a square is … The sum of the angles at the point where the squares meet is … + … + … + … = … The sum of the angles at a point is … [2] 2 (a) The diagram shows an equilateral triangle. Complete the diagram to show that equilateral triangles fit together at a point. [1] * 0000800000002 * ,










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3 0607/52/F/M/25 © UCLES 2025 [Turn over (b) The diagram shows a regular hexagon. Complete the diagram to show that regular hexagons fit together at a point. [1] (c) Show how 2 equilateral triangles and 2 regular hexagons can fit together at a point. [1] * 0000800000003 * ,










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4 0607/52/F/M/25 © UCLES 2025 3 The rest of this investigation is about 3 regular polygons fitting together at a point. The diagram shows a square and 2 congruent polygons fitting together at a point. B B Write down the mathematical name for polygon B. … [1] 4 This is the formula for the size of each interior angle of a regular polygon. ) ( ° 180 360 Interior angle ° number of sides ' = - (a) Use the formula to show that the size of each interior angle of polygon B is 135°. [1] (b) Complete the sentences to explain why the 3 polygons fit together at a point. Each interior angle of polygon B is 135°. Each interior angle of a square is … The sum of angles at a point is … The 3 polygons fit together at a point because ° ° 135 135 + + … = … [2] * 0000800000004 * ,










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5 0607/52/F/M/25 © UCLES 2025 [Turn over 5 Use the formula in Question 4 to complete the table. Number of sides 5 6 8 9 10 12 18 20 Interior angle in degrees 108 135 144 150 162 [4] * 0000800000005 * ,










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6 0607/52/F/M/25 © UCLES 2025 6 The diagram shows regular polygons P and Q and part of regular polygon R. NOT TO SCALE Q R P x° P is an equilateral triangle. Q is a regular decagon. R is a different regular polygon. (a) Write down the number of sides in a regular decagon. … [1] (b) Write down the size of each angle in an equilateral triangle. … [1] (c) Work out the size of angle x. Use the table in Question 5 to help you. … [2] (d) This is the formula for the number of sides, n, of a regular polygon with interior angle A°. ° n A 180 360 = - Work out the number of sides in polygon R. … [2] * 0000800000006 * ,










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7 0607/52/F/M/25 © UCLES 2025 [Turn over 7 The diagram shows 2 regular polygons with 5 sides and part of another regular polygon. NOT TO SCALE Calculate the number of sides of the other regular polygon. … [3] 8 Tom uses a regular 5-sided polygon and a regular 8-sided polygon. Show that Tom cannot fit these 2 polygons and a third regular polygon together at a point. [3] * 0000800000007 * ,










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8 0607/52/F/M/25 © UCLES 2025 9 The diagram shows an equilateral triangle and parts of 2 congruent regular polygons. NOT TO SCALE Show that each of the 2 congruent regular polygons has 12 sides. [3] * 0000800000008 * ,










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9 0607/52/F/M/25 © UCLES 2025 [Turn over 10 Samira wants to find all the ways to fit 3 regular polygons together at a point. In this question one of the polygons is always an equilateral triangle. (a) Samira uses an equilateral triangle and a regular hexagon. Give reasons why these 2 polygons and a third regular polygon cannot fit together at a point. … … [2] (b) Complete the table. Use your answers from Question 5 and Question 6(d) to help you. Number of sides of first polygon Number of sides of second polygon Number of sides of third polygon 3 7 42 3 8 3 9 3 10 3 12 12 [5] * 0000800000009 * ,










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10 0607/52/F/M/25 © UCLES 2025 11 Find all the possible ways where one of the 3 polygons is a square. Use the table from Question 5 to help you. … [5] * 0000800000010 * ,










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12 0607/52/F/M/25 © UCLES 2025 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 * 0000800000012 * ,









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This document consists of 8 printed pages. © Cambridge University Press & Assessment 2025 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/52 Paper 5 (Core) February/March 2025 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 International will not enter into discussions about these mark schemes. Cambridge International is publishing the mark schemes for the February/March 2025 series for most Cambridge IGCSE, Cambridge International A and AS Level components, and some Cambridge O Level components.

0607/52 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2025 © Cambridge University Press & Assessment 2025 Page 2 of 8 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.

0607/52 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2025 © Cambridge University Press & Assessment 2025 Page 3 of 8 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.

0607/52 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2025 © Cambridge University Press & Assessment 2025 Page 4 of 8 Annotations guidance for centres Examiners use a system of annotations as a shorthand for communicating their marking decisions to one another. Examiners are trained during the standardisation process on how and when to use annotations. The purpose of annotations is to inform the standardisation and monitoring processes and guide the supervising examiners when they are checking the work of examiners within their team. The meaning of annotations and how they are used is specific to each component and is understood by all examiners who mark the component. We publish annotations in our mark schemes to help centres understand the annotations they may see on copies of scripts. Note that there may not be a direct correlation between the number of annotations on a script and the mark awarded. Similarly, the use of an annotation may not be an indication of the quality of the response. The annotations listed below were available to examiners marking this component in this series. Annotations Annotation Meaning More information required Accuracy mark awarded zero Accuracy mark awarded one Accuracy mark awarded two Accuracy mark awarded three Independent mark awarded zero Independent mark awarded one Independent mark awarded two Benefit of the doubt Communication mark Incorrect point Follow through Highlighter Highlight a key point in the working Ignore subsequent work Method mark awarded zero Method mark awarded one Method mark awarded two Misread Omission

0607/52 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2025 © Cambridge University Press & Assessment 2025 Page 5 of 8 Annotation Meaning Off-page comment Allows comments to be entered at the bottom of the RM marking window and then displayed when the associated question item is navigated to. On-page comment Allows comments to be entered in speech bubbles on the candidate response. Premature rounding/approximation Special case Indicates that work/page has been seen Transcription error Correct point Not from wrong working 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 February/March 2025 © Cambridge University Press & Assessment 2025 Page 6 of 8 Question Answer Marks Partial Marks 1 90 90, 90, 90, 90, 360 360 2 B1 for any 90 or any 360 correctly placed 2(a) Correct diagram oe 1 2(b) Correct diagram oe 1 2(c) Correct diagram or 1 3 [regular] octagon 1 4(a) 180 360 8 135 − = 1 4(b) 90 and 360 135 + 135 + 90 = 360 2 B1 for each 5 5 6 8 9 10 12 18 20 108 120 135 140 144 150 160 162 3 B1 for each 180 – 360 ÷ (6 or 9 or 18) C1 6(a) 10 1 6(b) 60 1 6(c) 360 144 60 − − C1 FT their 6(b) 156 1

0607/52 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2025 © Cambridge University Press & Assessment 2025 Page 7 of 8 Question Answer Marks Partial Marks 6(d) 360 180 156 − C1 FT their 156 provided < 180 15 1 7 10 2 B1 for 144 360 108 108 − − C1 8 360 108 135 117 − − = 1 360 5.7... 180 117 = − which is not a positive integer oe or reference to 108 and 120 and number of sides between 5 and 6 from table 2 FT their 117 B1 for 360 180 117 −their or reference to 108 and 120 or 117 not an interior angle 9 360 60 2 − or 2x + 60 = 360 and 2x = 300 and x = 300 2 1 150 1 12 from calculation or reference to table 1 10(a) 360 – (120 + 60) = 180 soi 1 The third polygon has an interior angle of 180○, but this is a straight line oe 1 10(b) Number of sides of first polygon Number of sides of second polygon, Number of sides of third polygon 3 8 24 3 9 18 3 10 15 2 B1 for each 360 60 135 165 − − = or 360 60 140 160 − − = C2 C1 for identifying angles of 60 and either 135 or 140 360 180 165 − or 360 180 160 − C1 FT their 160 or 165 if answer positive

0607/52 Cambridge IGCSE – Mark Scheme PUBLISHED February/March 2025 © Cambridge University Press & Assessment 2025 Page 8 of 8 Question Answer Marks Partial Marks 11 [The sides are] [4,] 5, 20 [4,] 6, 12 [4,] 8, 8 and no others OR [The angles are] [90,] 108, 162 [90,] 120, 15 [90,] 135, 135 And no others 4 B3 for three correct and some incorrect or two correct and none incorrect or B2 for two correct and some incorrect or one correct and none incorrect or B1 for one correct set seen A correct calculation e.g. 360 – (90 + 108) = 162 or 108 + 162 = 270 C1