Cambridge IGCSE Mathematics - International 0607 — 2025 May/June Paper 3 · Variant 1

This document has 12 pages. [Turn over Cambridge IGCSE™ * 6 7 0 5 9 9 3 9 0 5 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 Calculator (Core) May/June 2025 1 hour 15 minutes You must answer on the question paper. You will need: Geometrical instruments 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. You will be given marks for correct methods, including sketches, even if your answer is incorrect. ● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. ● For r, use either your calculator value or 3.142. INFORMATION ● The total mark for this paper is 60. ● The number of marks for each question or part question is shown in brackets [ ]. DC (DE/SG) 341829/3 © UCLES 2025 ,










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2 0607/31/M/J/25 © UCLES 2025 List of formulas Area, A, of triangle, base b, height h. A = bh 2 1 Area, A, of circle of radius r. A = r2 r Circumference, C, of circle of radius r. C = 2rr Curved surface area, A, of cylinder of radius r, height h. A = 2rrh Curved surface area, A, of cone of radius r, sloping edge l. A = rrl Surface area, A, of sphere of radius r. A = r 4 2 r Volume, V, of prism, cross-sectional area A, length l. V = Al Volume, V, of pyramid, base area A, height h. V = Ah 3 1 Volume, V, of cylinder of radius r, height h. V = r h 2 r Volume, V, of cone of radius r, height h. V = r h 3 1 2 r Volume, V, of sphere of radius r. V = r 3 4 3 r * 0000800000002 * ,










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3 0607/31/M/J/25 © UCLES 2025 [Turn over 1 Coaches are used to take 105 children to an event. Each coach has places for 32 children. Explain why 4 is the minimum number of coaches that are needed. … [2] 2 Calculate. (a) 29791 3 … [1] (b) . . . 11 23 9 38 7 45 - Give your answer correct to 2 decimal places. … [2] 3 (a) Write the time 18 42 as a 12-hour clock time. … [1] (b) A film begins at 19 45. The film lasts for 123 minutes. Work out the time that the film ends. … [1] * 0000800000003 * ,










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4 0607/31/M/J/25 © UCLES 2025 4 These are the numbers of students entered for an examination from each of 15 schools. 81 87 61 68 73 76 95 62 62 73 84 78 92 74 60 (a) Complete an ordered stem-and-leaf diagram, including the key, to show this information. 6 7 8 9 Key …|… represents … [3] (b) Find the range. … [1] (c) Find the median. … [1] 5 Write down the reciprocal of 5 2 giving your answer as a fraction. … [1] 6 Ella climbs a mountain. The greater the height she climbs the lower the temperature. What is the type of correlation between height and temperature? … [1] * 0000800000004 * ,










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5 0607/31/M/J/25 © UCLES 2025 [Turn over 7 Abuja 3438 Cairo 8356 5222 Kathmandu 5649 2758 2766 Muscat The table shows the distances, in km, an aircraft flies when travelling between cities. For example, the aircraft flies 8356 km between Abuja and Kathmandu. (a) Write down the distance the aircraft flies between Cairo and Muscat. … km [1] (b) Naji wants to fly from Abuja to Kathmandu. He has two possible routes. Route 1: Abuja to Cairo then Cairo to Kathmandu Route 2: Abuja to Muscat then Muscat to Kathmandu Use information from the table to help you complete the sentence. You must show your working. Route 1 is longer than Route 2 by … km [3] * 0000800000005 * ,










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6 0607/31/M/J/25 © UCLES 2025 8 NOT TO SCALE 125° 73° A D C B x° y° The diagram shows 4 straight lines. BC and AD are parallel. (a) Write down the mathematical name of the quadrilateral ABCD. … [1] (b) Work out the value of x. x = … [1] (c) Write down value of y. y = … [1] * 0000800000006 * ,










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7 0607/31/M/J/25 © UCLES 2025 [Turn over 9 (a) These are the first 4 terms of a sequence. 5 11 17 23 Write down the rule for continuing this sequence. … [1] (b) These are the first 4 terms of another sequence. 51 48 45 42 Find an expression for the nth term of this sequence. … [2] (c) The expression for the nth term of a different sequence is n 5 4 2 + . Work out the first 2 terms of this sequence. …,… [2] 10 66° x° NOT TO SCALE The diagram shows an isosceles triangle. Find the value of x. x = … [3] * 0000800000007 * ,










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8 0607/31/M/J/25 © UCLES 2025 11 A shop has 90 bowls and 72 jugs. (a) Write the ratio number of bowls : number of jugs in its simplest form. … : … [1] (b) Some of the bowls are sold but none of the jugs are sold. The ratio number of bowls : number of jugs is now 2 : 3. Work out how many bowls are sold. … [3] 12 The price of a ticket is $280. The exchange rate between euros (€) and dollars ($) is €1 = $1.297 . Work out the price of the ticket in euros. € … [1] * 0000800000008 * ,










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9 0607/31/M/J/25 © UCLES 2025 [Turn over 13 The diagram shows a right-angled triangle. y cm 2.1 cm 2.9 cm x° NOT TO SCALE (a) Use trigonometry to work out the value of x. x = … [2] (b) Use Pythagoras’ theorem to find the value of y. y = … cm [3] 14 A cyclist rides 200 m. The cyclist rides at a constant speed of 45 km/h. Work out how many seconds it takes the cyclist to ride 200 m. … s [3] * 0000800000009 * ,










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10 0607/31/M/J/25 © UCLES 2025 15 15 cm 16 cm NOT TO SCALE The diagram shows a square with a hole in the shape of a circle. The length of the side of the square is 16 cm. The diameter of the circle is 15 cm. (a) Show that the shaded area is . cm 79 3 2 correct to 3 significant figures. [3] (b) The shape in part (a) is the cross-section of a block. 12 cm NOT TO SCALE The block is a cuboid with a hole in the shape of a cylinder. The length of the block is 12 cm. Find the volume of the block. … cm3 [1] * 0000800000010 * ,










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11 0607/31/M/J/25 © UCLES 2025 [Turn over 16 The equation of line L is y x 3 12 - = . (a) Rearrange y x 3 12 - = to make y the subject. y = … [2] (b) Write down the equation of the line parallel to L, that passes through the point (0, 5). … [2] 17 The price of a game is $15. This price is increased by 12%. Find the new price. $ … [2] Question 18 is printed on the next page. * 0000800000011 * ,









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12 0607/31/M/J/25 © UCLES 2025 18 10 – 10 – 10 10 0 y x (a) On the diagram, sketch the graph of y x 2 7 = + for values of x between -10 and 10. [3] (b) Write down the coordinates of the point where the graph crosses the y-axis. ( … , … ) [1] (c) On the diagram, sketch the graph of y x 5 = for values of x between -10 and 10. [2] (d) Find the values of x when x x 2 7 5 + = . x = … or x = … [2] 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. * 0000800000012 * ,









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This document consists of 9 printed pages. © Cambridge University Press & Assessment 2025 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) May/June 2025 MARK SCHEME Maximum Mark: 60 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 2025 series for most Cambridge IGCSE, Cambridge International A and AS Level components, and some Cambridge O Level components.

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2025 © Cambridge University Press & Assessment 2025 Page 2 of 9 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.

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2025 © Cambridge University Press & Assessment 2025 Page 3 of 9 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.

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2025 © Cambridge University Press & Assessment 2025 Page 4 of 9 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 Independent mark awarded three Benefit of the doubt Communication mark Incorrect 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

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2025 © Cambridge University Press & Assessment 2025 Page 5 of 9 Annotation Meaning Method mark awarded three Misread Omission 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 Correct answer from incorrect working

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2025 © Cambridge University Press & Assessment 2025 Page 6 of 9 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

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2025 © Cambridge University Press & Assessment 2025 Page 7 of 9 Question Answer Marks Partial Marks 1 Relevant calculation e.g. 105 32  or repeated subtraction M1 Correct conclusion e.g. 3.3 is not enough because you can’t get 0.3 of a bus so you need 4 busses or repeated addition A1 2(a) 31 1 2(b) 4.03 cao 2 B1 for answer of 4.027… or M1 for their answer seen to more than 2 decimal places correctly rounded to 2 decimal places 3(a) 6 42 p.m. 1 3(b) 21 48 or 9 48 p.m. 1 4(a) 6 0 1 2 2 8 7 3 3 4 6 8 8 1 4 7 9 2 5 2 B1 for unordered diagram or 2 correct ordered rows Correct key e.g. 8 | 1 represents 81 1 4(b) 35 1 4(c) 74 1 5 5 2 cao 1 Accept 1 2 2 but not 2.5 6 negative 1 7(a) 2758 1 7(b) [Route 1] 3438 + 5222 = 8660 [Route 2] 5649 + 2766 = 8415 M2 B1 for 3 out of 4 correct values used or for Route 1 or Route 2 correct 245 A1 8(a) Trapezium 1 8(b) 55 1 8(c) 73 1 9(a) Add 6 oe 1

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2025 © Cambridge University Press & Assessment 2025 Page 8 of 9 Question Answer Marks Partial Marks 9(b) 54 – 3n oe final answer 2 B1 for k - 3n or 54 – jn for 0  j 9(c) 9 24 2 B1 for each 10 303 3 B2 for 57 OR M1 for 180 66 2 − M1 for 360 57 −their 11(a) 5 : 4 1 11(b) 42 3 M2 for 72 2 3  soi by 48 or M1 for 72 3 soi by 24 12 215.88 1 13(a) 43.6 or 43.60… 2 M1 for cos [ ] = 2.1 2.9 oe 13(b) Use Pythagoras’ Theorem leading to 2 3 M2 for 2 2 2.9 2.1 − or M1 for 2 2 2 2.1 2.9 + = x 14 16 3 M2 for 200 60 60 45000   oe or M1 for multiplication by 3600 or division by 1000 or for figs 2 figs 45 or B1 for 12.5 or 0.0125 oe or 1 225 oe 0.00444… seen 15(a) [Area of square] 16 16  or 2 16 M1 [Area of circle] 2 15 2       or 2 7.5  M1 Area of square – area of circle leading to 79.28… A1 15(b) 952 or 951.6 1 16(a)   4 3 = + x y or [ 12 ] 3 + = x y final answer 2 M1 for 3y = 12 + x or 12 3 3 − = x y oe

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2025 © Cambridge University Press & Assessment 2025 Page 9 of 9 Question Answer Marks Partial Marks 16(b) 5 3 = + x y oe 2 FT their gradient from (a) M1 for 5 3 + x or 3 = + x y k or 5 = + y kx 17 16.8[0] 2 M1 for 15 1.12  oe or B1 for 1.8 seen 18(a) Correct sketch 3 B1 for correct branch for y < 0 B1 for correct branch y > 0 B1 for intention of vertical asymptote 18(b) (0, 3.5) 1 18(c) Correct ruled line 2 B1 for positive gradient B1 for passing through (0, 0) 18(d) 5 –7 2 B1 for each If 0 scored, SC1 for (5, 1) and (–7, –1.4)