Cambridge IGCSE Mathematics - International 0607 — 2025 Oct/Nov Paper 3 · Variant 1

This document has 12 pages. [Turn over Cambridge IGCSE™ * 6 7 7 1 8 8 3 8 2 8 * DC (CE/SG) 342429/7 © UCLES 2025 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 Calculator (Core) October/November 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 [ ]. ,










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2 0607/31/O/N/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/O/N/25 © UCLES 2025 [Turn over 1 Work out. (a) . . . 2 5 19 4 3 8 + … [1] (b) . 29 791 3 … [1] 2 Work out 76% of 67.42 . Give your answer correct to 2 decimal places. … [2] 3 (a) Write these numbers in order of size, starting with the smallest. 43.9% 0.44 7 3 … , … , … [1] smallest (b) Write down a number between 0.6 and 0.7 . … [1] 4 (a) Write 13 708 in words. … [1] (b) Write twenty million, seven hundred and forty thousand in figures. … [1] * 0000800000003 * ,










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4 0607/31/O/N/25 © UCLES 2025 5 (a) Complete the mathematical name for each angle. … angle … angle [2] (b) A B C 67.3° 54.1° 57.6° NOT TO SCALE Show that ABC is not a straight line. [2] 6 Show the inequality x 3 1 1 G - on the number line. -5 -4 -3 -2 -1 0 1 2 x [2] * 0000800000004 * ,










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5 0607/31/O/N/25 © UCLES 2025 [Turn over 7 (a) On the diagram, draw the line of symmetry. [1] (b) The diagram has 12 small identical triangles. Shade 6 small triangles to make a pattern with rotational symmetry of order 6. [1] 8 (a) A rectangle has length 4.5 cm and width 2.8 cm. Work out the area of the rectangle. Give the units of your answer. … … [2] (b) The perimeter of an equilateral triangle is 18.3 cm. Work out the length of one side of the triangle. … cm [1] * 0000800000005 * ,










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6 0607/31/O/N/25 © UCLES 2025 9 The bar chart shows the favourite sport of each student in a sports group. Number of students Football Running Swimming Key: Boys Girls 12 16 20 24 28 8 4 0 (a) Work out the difference between the total number of boys and the total number of girls. … [2] (b) One of these students is chosen at random. Work out the probability that this student’s favourite sport is football. … [2] 10 Expand and simplify. ( ) ( ) x x 4 7 1 3 5 4 + + + … [2] 11 A is the point ( , ) 3 6 - and B is the point (2, 8). Find the coordinates of the midpoint of AB. ( … , … ) [2] * 0000800000006 * ,










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7 0607/31/O/N/25 © UCLES 2025 [Turn over 12 (a) There are 80 students in year 10. 9 students study both French (F ) and German (G ). 35 students study French only. 2 students do not study French and do not study German. (i) Complete the Venn diagram. G F … … … … U [2] (ii) Find n(G ). … [1] (b) Shade the region indicated for each Venn diagram. B A U D C U A B k C D j l ` j [2] 13 A square spinner is numbered 1, 2, 3, 4. The table shows the probability of the spinner landing on each number. Number 1 2 3 4 Probability 0.37 0.1 0.26 Complete the table. [2] * 0000800000007 * ,










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8 0607/31/O/N/25 © UCLES 2025 14 x° 7 m 4.2 m NOT TO SCALE Work out the value of x. x = … [2] 15 8 cm 8 cm 5 cm B C A NOT TO SCALE ABC is an isosceles triangle. AB = BC = 8 cm and AC = 5 cm. Use Pythagoras’ theorem to calculate the height of the triangle. … cm [3] * 0000800000008 * ,










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9 0607/31/O/N/25 © UCLES 2025 [Turn over 16 Output Input 4 # 15 - (a) The input is 10. Work out the output. … [1] (b) The output is 19. Work out the input. … [1] (c) The input is x. (i) Write an expression for the output. … [1] (ii) The input is the same as the output. Work out the input. … [2] * 0000800000009 * ,










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10 0607/31/O/N/25 © UCLES 2025 17 NOT TO SCALE 2.5 cm 5 cm w cm The cuboid has volume cm 0 9 3. Work out the value of w. w = … [2] 18 (a) Write 0.000 09 in standard form. … [1] (b) Work out ( . ) ( . ) 4 1 10 3 7 10 3 5 # # # . Give your answer in standard form. … [2] * 0000800000010 * ,










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11 0607/31/O/N/25 © UCLES 2025 [Turn over 19 y x 4 0 – 16 8 (a) On the diagram, sketch the graph of ( )( ) x x y 3 5 = - - for values of x between 0 and 8. [2] (b) Write down the x-coordinate of each point where the graph crosses the x-axis. x = … and x = … [2] (c) Find the coordinates of the point where the graph crosses the y-axis. ( … , … ) [1] (d) Find the coordinates of the local maximum. ( … , … ) [1] Question 20 is printed on the next page. * 0000800000011 * ,









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12 0607/31/O/N/25 © UCLES 2025 20 (a) Hannah invests $5350 at a rate of 2.6% per year compound interest. Calculate the value of Hannah’s investment at the end of 3 years. $ … [2] (b) Connor invests $1750 at a rate of x % per year simple interest. At the end of 4 years, the value of the investment is $1939. Find the value of x. x = … [3] 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) October/November 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 October/November 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 October/November 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 October/November 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 October/November 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 October/November 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 October/November 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 Question Answer Marks Partial Marks 1(a) 9.28 1 1(b) 3.1 1 2 51.24 cao 2 B1 for 51.239[2] If 0 scored, SC1 for their answer written in more than 2 d.p. and correctly rounded to 2 d.p. 3(a) 3 43.9% 0.44 7 1 3(b) Any number in range 0.6 < x < 0.7 1 4(a) Thirteen thousand seven hundred [and] eight 1 4(b) 20 740 000 1 5(a) Reflex Acute 2 B1 for each

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2025 © Cambridge University Press & Assessment 2025 Page 7 of 9 Question Answer Marks Partial Marks 5(b) 67.3 + 57.6 + 54.1 = 179 B1 Should be 180 [not straight line] oe B1 dep 6 Correct answer 2 B1 for a closed circle on 3 − and a line to the right or B1 for an open circle on 1 and a line to the left. or B1 for 2 correct circles with no line or wrong lines drawn or B1 open circle at –3 and closed circle at 1 joined with a line 7(a) Correct line of symmetry drawn 1 7(b) or 1 8(a) 12.6 1 cm2 1 8(b) 6.1 1 9(a) 6 2 B1 for 40 or 46 9(b) 30 86 oe isw 2 B1 for 30 n or 40 46 + n their their 10 43 16 + x final answer 2 B1 for answer 43 + x k or 16 + kx , k ≠ 0 or M1 for 28 4 or 15 12 + + x x 11 (–0.5 , 7) 2 B1 for each coordinate 12(a)(i) 2 B1 for three correct values 12(a)(ii) their 9 + their 34 1 12(b) 2 B1 for each

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2025 © Cambridge University Press & Assessment 2025 Page 8 of 9 Question Answer Marks Partial Marks 13 0.27 2 M1 for 1 – (0.37 + 0.1 + 0.26) oe 14 53.1[3…] 2 M1 for 4.2 cos 7 = x oe 15 7.6[0] 3 M2 for 2 2 5 8 2   −    or M1 for 2 2 2 5 8 2   + =     h 16(a) 25 1 16(b) 8.5 oe 1 16(c)(i) 4 15 − x final answer 1 16(c)(ii) 5 2 M1 for (4 15) = − x their x oe 17 7.2 2 M1 for 90 = 5 × 2.5 × w or better 18(a) 5 9 10−  1 18(b) 9 1.517 10  cao 2 B1 for 1 517 000 000 oe seen or 1.517 10 , 0   a a 19(a) Correct sketch 2 B1 for Correct shape and wrong position 19(b) 3 5 2 B1 for each 19(c) (0, 15) − 1 19(d) (4,1) 1 20(a) $5778.24 2 M1 for 3 2.6 5350 1 100    +     oe

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2025 © Cambridge University Press & Assessment 2025 Page 9 of 9 Question Answer Marks Partial Marks 20(b) 2.7 3 M2 for 1939 – 1750 = 1750 4 100 x oe or M1 for 1939 – 1750 = 189 oe or 1750 4 100  x SC1 for 27.7