Cambridge IGCSE Mathematics - International 0607 — 2024 May/June Paper 3 · Variant 1

This document has 20 pages. Any blank pages are indicated. [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) May/June 2024 1 hour 45 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 and 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 your calculator value. INFORMATION ● The total mark for this paper is 96. ● The number of marks for each question or part question is shown in brackets [ ]. * 4 7 4 9 7 9 0 6 7 4 * DC (LK/CT) 329123/5 © UCLES 2024

2 0607/31/M/J/24 © UCLES 2024 Formula List Area, A, of triangle, base b, height h. A = bh 2 1 Area, A, of circle, radius r. A = r2 r Circumference, C, of circle, 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 Curved 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

3 0607/31/M/J/24 © UCLES 2024 [Turn over Answer all the questions. 1 (a) Write fifty thousand and thirty-seven in figures. … [1] (b) Write 7 5 2 as a decimal. … [1] (c) Change $325 into Euros (€) when the exchange rate is $1 = €0.88 . € … [1] (d) Divide 3600 in the ratio 5 : 6 : 7. … , … , … [3] (e) Write down a prime number between 18 and 24. … [1] (f) The price of an e-bike is $2200. In a sale, this price is reduced by 33%. Work out the sale price of the e-bike. $ … [2] (g) Work out the value of . . 3 62 10 9 1 10 3 2 # # + . Give your answer in standard form. … [2]

4 0607/31/M/J/24 © UCLES 2024 2 Dagmar has a bag containing cards. Each card is blue, yellow, pink, green or purple. 21 students each pick one card at random from the bag and Dagmar records the colour. blue blue green yellow pink blue purple purple green blue yellow purple green blue blue green pink yellow blue purple green (a) Complete the frequency table. Colour Frequency blue yellow pink green purple [2] (b) Write down the colour that was picked the most. … [1] (c) Work out how many more purple cards were picked than yellow cards. … [1] (d) Write down the fraction of the 21 cards picked that were green. … [1] (e) Write down the probability of picking a red card from the bag. … [1]

5 0607/31/M/J/24 © UCLES 2024 [Turn over (f) Draw a bar chart to show the information in the table. 0 1 2 3 Frequency 4 5 6 7 8 Colour of card blue yellow pink green purple [2]

6 0607/31/M/J/24 © UCLES 2024 3 (a) Find 16% of 385. … [1] (b) Write these in order of size, starting with the smallest. 0.88 80% 8 7 … … … [1] smallest (c) Work out . 15 213. Give your answer correct to 2 decimal places. … [2] (d) Work out . . 2 3 4 7 2 + . Give your answer correct to 4 significant figures. … [2] (e) Write 54 15 as a fraction in its simplest form. … [1]

7 0607/31/M/J/24 © UCLES 2024 [Turn over (f) Si Jung walks 11 km to raise money. She receives $26.18 for each kilometre she walks. Work out how much money she raises. $ … [1] (g) One packet of football cards cost $21.95 . Work out the greatest number of these packets that Josh can buy with $100 and how much change he receives. … packets and $ … change [3] (h) Work out, giving each answer as a fraction. (i) 3 2 2 1 + … [1] (ii) 3 4 1 26 1 # … [1]

8 0607/31/M/J/24 © UCLES 2024 4 In this question, all lengths are in centimetres. A C B NOT TO SCALE h x 3 4 - x 3 4 - x 2 + ABC is an isosceles triangle. (a) cm AB AC 8 = = . Work out the value of x. x = … [2] (b) Work out the perimeter of the triangle. … cm [2] (c) The height of the triangle is h. Calculate the area of the triangle. … cm2 [4]

9 0607/31/M/J/24 © UCLES 2024 [Turn over 5 64° NOT TO SCALE O C B E D 4 cm The diagram shows a circle with centre O and radius 4 cm. C and B are points on the circumference and DE is a tangent at B. Angle ° COB 64 = . (a) Find (i) angle OBE Angle OBE = … [1] (ii) angle OCB Angle OCB = … [2] (iii) angle CBD Angle CBD = … [1] (iv) reflex angle COB. Reflex angle COB = … [1] (b) Work out the length of the minor arc CB. … cm [2]

10 0607/31/M/J/24 © UCLES 2024 6 The age and the height of each of 7 children are shown in the table. Age (years) 2 3 5 5 7 9 11 Height (cm) 92 98 112 118 128 140 152 (a) Complete the scatter diagram. The first three points have been plotted for you. 60 0 1 2 3 4 5 6 Age (years) Height (cm) 7 8 9 10 11 70 80 90 100 110 120 130 140 150 160 [2]

11 0607/31/M/J/24 © UCLES 2024 [Turn over (b) What type of correlation is shown in the diagram? … [1] (c) Find (i) the mean age … years [1] (ii) the mean height. …cm [1] (d) On the diagram, draw a line of best fit. [2] (e) Use your line of best fit to estimate the height of a child of age 8 years. … cm [1]

12 0607/31/M/J/24 © UCLES 2024 7 (a) Complete the mapping diagram for ( ) g x x 3 2 = - . x g(x) 0 1 2 3 … … … … [2] (b) ( ) h x x 4 3 = - Find ( ) h 1 - . … [2] (c) – 2 – 1 0 1 2 3 4 5 x Write down the inequality represented on the number line. … [2]

13 0607/31/M/J/24 © UCLES 2024 [Turn over (d) – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 y x 1 – 1 – 2 –3 – 4 4 5 6 7 8 3 2 The diagram shows the sketch of ( ) f y x = . On the same diagram, draw the sketch of (i) ( ) f y x 2 = + [1] (ii) ( ) f y x 3 = + . [1]

14 0607/31/M/J/24 © UCLES 2024 8 B A – 4 – 5 – 3 – 2 – 1 0 1 2 3 4 5 6 y x 1 – 1 – 2 –3 – 4 4 5 6 7 8 10 9 3 2 (a) Describe fully the single transformation that maps shape A onto shape B. … … [3] (b) Rotate shape A 90° anticlockwise about (0, 0). Label the image C. [2] (c) Reflect shape A in the line y 1 =- . Label the image D. [2] (d) Translate shape A by the vector 4 3 - - e o. Label the image E. [2]

15 0607/31/M/J/24 © UCLES 2024 [Turn over 9 (a) Solve. (i) x 3 6 2- … [1] (ii) x 3 4 11 - = x = … [2] (b) Find each value of x. (i) 8 1 x = x = … [1] (ii) 2 2 2 x 5 = x = … [1] (c) Simplify fully. (i) x x 3 2 5 - … [2] (ii) xy x 2 4 ' … [2]

16 0607/31/M/J/24 © UCLES 2024 10 80 people climb a tower. The time each person takes is recorded. The table shows the results. Time (t minutes) Frequency t 2 4 1 G 6 t 4 6 1 G 24 t 6 8 1 G 30 t 8 10 1 G 16 t 10 12 1 G 4 (a) Write down the modal class. … t 1 G … [1] (b) (i) Find the mid-point of the interval t 2 4 1 G . … [1] (ii) Calculate an estimate for the mean time. … min [2]

17 0607/31/M/J/24 © UCLES 2024 [Turn over (c) The cumulative frequency curve shows the times taken to climb the tower. 0 0 2 4 6 Time (t minutes) Cumulative frequency 8 10 12 10 20 30 40 50 60 70 80 Use the cumulative frequency curve to find an estimate for (i) the median … min [1] (ii) the lower quartile … min [1] (iii) the number of people who took longer than 9 minutes to climb the tower. … [2]

18 0607/31/M/J/24 © UCLES 2024 11 0 12 y x 3 – 4 – 18 The diagram shows a sketch of the graph of y x x 2 3 2 = + - for x 4 3 G G - . (a) Draw this graph on your calculator and use it to find the coordinates of (i) the points where the graph crosses the x-axis ( … , … ) and ( … , … ) [2] (ii) the local minimum point. ( … , … ) [1] (b) On the same diagram, sketch the graph of y x x 2 2 =- + + for x 4 3 G G - . [2] (c) Find the x-coordinate of each point of intersection of y x x 2 3 2 = + - and y x x 2 2 =- + + . x = … and x = … [2]

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20 0607/31/M/J/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

This document consists of 8 printed pages. © Cambridge University Press & Assessment 2024 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) May/June 2024 MARK SCHEME Maximum Mark: 96 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 2024 series for most Cambridge IGCSE, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2024 © Cambridge University Press & Assessment 2024 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.

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2024 © Cambridge University Press & Assessment 2024 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. 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 2024 © Cambridge University Press & Assessment 2024 Page 4 of 8 Question Answer Marks Partial Marks 1(a) 50 037 1 1(b) 7.4 cao 1 1(c) 286 1 1(d) 1000 : 1200 : 1400 3 M2 for 3600 5 or 6 or 7 5 6 7   soi by 1000 or 1200 or 1400 or M1 for 3600 5 6 7   soi by 200 1(e) 19 or 23 1 1(f) 1474 2 B1 for 726 seen M1 for 33 2200 oe 100  100 33 or 2200 100   oe 1(g) 4.53[0] 3 10  cao 2 B1 for 4530 seen 2(a) blue 7 yellow 3 pink 2 green 5 purple 4 2 B1 for 3 or 4 values correct or only tally marks 2(b) blue 1 FT their values 2(c) 1 1 FT their values 2(d) 5 21 1 FT their 5 2(e) 0 1 2(f) Correct bar chart 2 FT their values B1 for 3 or 4 bars correct or all correct heights but different widths 3(a) 61.6 1

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2024 © Cambridge University Press & Assessment 2024 Page 5 of 8 Question Answer Marks Partial Marks 3(b) 7 80% 0.88 8 1 3(c) 3518.74 cao 2 B1 for 3518.743… or their answer to more than 2 decimal places correctly rounded to 2 decimal places. 3(d) 7.458 cao 2 B1 for 7.4579… or their answer to more than 4 significant figures correctly rounded to 4 significant figures. 3(e) 5 18 1 3(f) 287.98 1 3(g) 4 and 12.2[0] change 3 M1 for 100 21.95 or 4 M1 for 100 – their 4  21.95 or their 100 4 21.95 21.95         oe 3(h)(i) 7 6 or 1 16 1 3(h)(ii) 1 8 oe 1 4(a) 4 2 M1 for 3 4 8   x or better 4(b) 22 2 B1 for 2 4 their 4(c) 22.2 or 22.24 to 22.25 4 M2 for 2 2 2 2 8 2 x h their             soi by 7.416… or M1 for 2 2 2 2 8 2 x h their          AND M1 for 1 2   their BC their h 5(a)(i) 90 1 5(a)(ii) 58 2 M1 for 180 64 2 

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2024 © Cambridge University Press & Assessment 2024 Page 6 of 8 Question Answer Marks Partial Marks 5(a)(iii) 32 1 FT 90 – their (a)(ii) 5(a)(iv) 296 1 5(b) 4.47 or 4.468 to 4.469 2 M1 for 64 2π 4 360   6(a) Points plotted correctly 2 B1 for 2 or 3 correct 6(b) Positive 1 6(c)(i) 6 1 6(c)(ii) 120 1 6(d) Correct ruled line drawn 2 B1 for ruled line through mean but not in tolerance or in tolerance but not through the mean 6(e) 130 135  1 FT their increasing ruled line 7(a) 3 1 –1 –3 2 B1 for 2 or 3 correct 7(b) 5 2 B1 for   3 4 1  7(c) 1 4   x 2 B1 for 1 or for 4  7(d)(i) Correct sketch 1

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2024 © Cambridge University Press & Assessment 2024 Page 7 of 8 Question Answer Marks Partial Marks 7(d)(ii) Correct sketch 1 8(a) Enlargement [Scale factor] 3 [Centre] (0, 0) 3 B1 for each 8(b) Correct rotation (–1, 1), (–2, 2), (–2, 3), (–1, 3) 2 B1 for correct orientation wrong position 8(c) Correct reflection (1, –3), (3, –3), (3, –4), (2, –4) 2 B1 for reflection in  y k 8(d) Correct translation      3, 2 , 1, 2 , 1, 1 , 2, 1      2 B1 for vertical or horizontal translation correct 9(a)(i) 2  x 1 9(a)(ii) 5 2 M1 for 3 11 4   x oe 9(b)(i) 0 1 9(b)(ii) 6 1 9(c)(i) 7 15 x final answer 2 M1 for denominator 15k 9(c)(ii) 2y final answer 2 M1 for 2 xy  4 x or better 10(a)   6 8  t 1 10(b)(i) 3 1 10(b)(ii) 6.7 2 M1 for 3 6 5 24 7 30 9 16 11 4        their soi by 536 10(c)(i) 6.6 to 6.8 1 10(c)(ii) 5.1 to 5.3 1 10(c)(iii) 11 or 12 2 B1 for 69 or 68 seen

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2024 © Cambridge University Press & Assessment 2024 Page 8 of 8 Question Answer Marks Partial Marks 11(a)(i)   3, 0    1, 0 2 B1 for each 11(a)(ii)   1, 4   1 11(b) Correct parabola drawn 2 B1 for correct shape B1 for curves crossing in the correct quadrants 11(c) 1.35 or 1 .350 to 1 .351 1.85 or 1.851 to 1.850    2 B1 for each If 0 scored, SC1 for 1.4 and 1.9 