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

This document has 20 pages. Any blank pages are indicated. [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 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 [ ]. * 7 4 3 1 2 7 2 0 3 3 * DC (KS) 342061 © UCLES 2024

2 0607/33/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 0607/33/M/J/24 © UCLES 2024 [Turn over Answer all the questions. 1 (a) Write the number 27 964 in words. … … [1] (b) Write 27 964 (i) correct to the nearest thousand … [1] (ii) correct to 1 significant figure. … [1] (c) Write down (i) a multiple of 15 … [1] (ii) a factor of 12. … [1] (d) Find the value of (i) 81 … [1] (ii) 73. … [1]

4 0607/33/M/J/24 © UCLES 2024 2 These are the numbers of days each student in a class was absent during one month. 1 5 2 2 1 3 1 0 2 4 3 7 2 1 0 7 (a) Complete the frequency table. The frequencies for 0 and 1 days have been completed for you. Number of days absent 0 1 2 3 4 5 6 7 Frequency 2 4 [2] (b) Find how many students are in the class. … [1] (c) Find how many more students were absent for 1 day than for 7 days. … [1] (d) One of these students is chosen at random. Find the probability that this student was absent for 0 days. … [1] (e) Complete the bar chart to show the information in the table. Frequency 6 5 4 3 2 1 0 1 0 3 2 4 6 5 7 Number of days absent [2]

5 0607/33/M/J/24 © UCLES 2024 [Turn over 3 (a) 28° 130° y° x° S P Q R NOT TO SCALE In the diagram, PQR is a straight line. (i) Write down the mathematical name for an angle of 130°. … [1] (ii) Work out the value of x and the value of y. Give a geometrical reason for each answer. x = … because … … y = … because … … [4] (b) 94° p° C B A NOT TO SCALE (i) Write down the mathematical name for triangle ABC. … [1] (ii) Work out the value of p. p = … [2]

6 0607/33/M/J/24 © UCLES 2024 4 (a) Write 0.40 as a percentage. … % [1] (b) Write 8 7 as a decimal. … [1] (c) Write 20 11 as a percentage. … % [1] (d) Write 12% as a fraction in its simplest form. … [2] (e) Work out 6% of 2500. … [1] (f) Work out. 5 3 4 3 # Give your answer as a fraction. … [1]

7 0607/33/M/J/24 © UCLES 2024 [Turn over 5 (a) These are the first four terms of a sequence. 19 15 11 7 (i) Work out the next three terms. … … … [2] (ii) Write down the rule for continuing this sequence. … [1] (b) This is the rule for continuing a different sequence. Add 6 to the previous term. The 5th term of this sequence is 31. Find the 1st term of this sequence. … [2] (c) The nth term of another sequence is n 4 2 + . Find the first three terms of this sequence. … … … [2] (d) These are the first four terms of a different sequence. 19 21 23 25 Find an expression for the nth term. … [2]

8 0607/33/M/J/24 © UCLES 2024 6 The table shows the marks obtained by each of 10 students in a science exam and in a technology exam. Science mark 30 48 59 37 42 56 53 47 63 25 Technology mark 45 51 60 41 48 66 56 56 67 40 (a) Complete the scatter diagram. The first five points have been plotted for you. 20 20 30 40 50 60 70 80 30 40 50 Science mark Technology mark 60 70 80 [2] (b) What type of correlation is shown in the scatter diagram? … [1]

9 0607/33/M/J/24 © UCLES 2024 [Turn over (c) (i) Work out the mean science mark and the mean technology mark. Mean science mark = … Mean technology mark = … [2] (ii) On the scatter diagram, draw a line of best fit. [2] (d) Toby scored 35 marks in the science exam but missed the technology exam. Use your line of best fit to estimate a mark for Toby in the technology exam. … [1]

10 0607/33/M/J/24 © UCLES 2024 7 (a) Solve. (i) x 3 9 = x = … [1] (ii) x 5 4 11 - = x = … [2] (b) Expand. ( ) x 4 3 + … [1] (c) Factorise. y y 2 2 - … [1]

11 0607/33/M/J/24 © UCLES 2024 [Turn over (d) 3x 2x NOT TO SCALE The diagram shows a rectangle. All lengths are in centimetres. (i) Find an expression, in terms of x, for the area of the rectangle. Give your answer in its simplest form. … cm2 [1] (ii) The area of the rectangle is 54 cm2. Write down an equation in terms of x and solve it to find the length and the width of the rectangle. Show all your working. Length = … cm Width = … cm [4]

12 0607/33/M/J/24 © UCLES 2024 8 (a) 6 cm 6 cm 30 cm NOT TO SCALE The diagram shows a solid cuboid. Find the total surface area of the cuboid. Give the units of your answer. … … [4] (b) 25 cm 8 cm NOT TO SCALE The diagram shows a cylinder of height 25 cm and diameter 8 cm. Find the volume of the cylinder. … cm3 [2]

13 0607/33/M/J/24 © UCLES 2024 [Turn over (c) NOT TO SCALE O P Q R (i) The straight line RPQ touches the circle, centre O, at P. Complete this statement. Angle ° OPQ 90 = because … … [1] (ii) PQ 7cm = and OP 4cm = . (a) Work out OQ. OQ = … cm [2] (b) Work out angle OQP. Angle OQP = … [2]

14 0607/33/M/J/24 © UCLES 2024 9 The table shows the population and land area of Denmark and of Sweden. Denmark Sweden Population .5 8 106 # . 10 1 1 7 # Land area ( ) km2 . 10 4 2 4 # . 10 4 5 5 # (a) Write the population of Denmark as an ordinary number. … [1] (b) Work out the total land area of Denmark and Sweden. Give your answer in standard form. … km2 [2] (c) Work out how much greater the population of Sweden is than the population of Denmark. … [1] (d) Population density Land area Population = Work out the population density of Denmark. Give your answer correct to the nearest integer. … people/km2 [2] (e) The population of Denmark is 0.53 times the population of Sweden. Write 0.53 in standard form. … [1]

15 0607/33/M/J/24 © UCLES 2024 [Turn over 10 y x 5 4 3 2 1 1 2 3 4 5 – 5 – 4 – 3 – 2 – 1 0 – 1 – 2 – 3 – 4 – 5 P (a) (i) Reflect triangle P in the x-axis. Label the image X. [1] (ii) Reflect triangle P in the y-axis. Label the image Y. [1] (iii) Describe fully the single transformation which maps triangle Y onto triangle X. … … [3] (b) Translate triangle P by 2 4 - e o. Label the image Z. [2]

16 0607/33/M/J/24 © UCLES 2024 11 Ali collects the prices, in $, of cars advertised in two newspapers, The Globe and The Herald. The cumulative frequency curves show the data he collected. 100 90 80 70 60 0 2000 4000 6000 Price of car ($) Cumulative frequency 8000 10 000 KEY The Globe The Herald 40 50 30 20 10 0 (a) Work out how many more cars costing $6000 were advertised in The Globe than in The Herald. … [2] (b) Work out how many cars advertised in The Herald cost at least $8000. … [2]

17 0607/33/M/J/24 © UCLES 2024 [Turn over (c) For cars advertised in The Globe, find (i) the median price $ … [1] (ii) the interquartile range. $ … [2] (d) Ali has $2000 to buy a car. Is The Globe or The Herald more useful to help Ali find a car? Give a reason for your choice. … because … … [1]

18 0607/33/M/J/24 © UCLES 2024 12 60 0 6 y x – 4 – 10 (a) (i) On the diagram, sketch the graph of y x x 2 6 2 = - for x 4 6 G G - . [2] (ii) Find the x-coordinate of the local minimum. x = … [1] (b) On the diagram, sketch the graph of y x x 4 15 2 = - + for x 4 6 G G - . [2] (c) Find the x-coordinate of each point of intersection of y x x 2 6 2 = - and y x x 4 15 2 = - + . x = … and x = … [2]

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20 0607/33/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 7 printed pages. © Cambridge University Press & Assessment 2024 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 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.

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 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.

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 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. 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

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2024 © Cambridge University Press & Assessment 2024 Page 4 of 7 Question Answer Marks Partial Marks 1(a) Twenty seven thousand nine hundred [and] sixty four 1 1(b)(i) 28 000 1 1(b)(ii) 30 000 1 1(c)(i) One of 15, 30, 45 etc. 1 1(c)(ii) One of 1, 2, 3, 4, 6, 12 1 1(d)(i) 9 1 1(d)(ii) 343 1 2(a) [2 4] 4 2 1 1 0 2 2 B1 for 3, 4 or 5 correct 2(b) 16 1 2(c) 2 1 FT their table 2(d) 2 16 oe 1 FT their (b) 2(e) Correct bar chart 2 FT their table M1 for 3, 4 or 5 bars with correct width and height or for all heights correct but incorrect widths 3(a)(i) obtuse 1 3(a)(ii) [x=] 22 1 [Angles in a] triangle [add to] 180 1 [y=] 50 1 [Angles on a] line [add to] 180 1 3(b)(i) isosceles 1 3(b)(ii) 43 2 M1 for 180 94 2  4(a) 40 1 4(b) [0].875 cao 1 4(c) 55 1 4(d) 3 25 cao 2 B1 for 12 100 or better

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2024 © Cambridge University Press & Assessment 2024 Page 5 of 7 Question Answer Marks Partial Marks 4(e) 150 1 4(f) 9 20 cao 1 5(a)(i) 3, −1, −5 2 B1 for 3 5(a)(ii) − 4 oe 1 5(b) 7 2 M1 for subtracting 6 at least once soi or for 31 ‒ 6×4 5(c) 5, 8, 13 2 B1 for two correct in correct positions If 0 scored, SC1 for 4, 5, 8 5(d) 2n + 17 oe 2 B1 for 2n + k , any k 6(a) 5 points correctly plotted 2 B1 for 3or 4 points correctly plotted 6(b) positive 1 6(c)(i) [science] = 46 [technology] = 53 2 B1 for each If 0 scored, SC1 for correct answers reversed 6(c)(ii) Ruled line through mean and within tolerance 2 B1 for ruled line through mean but not within tolerance or for ruled line not through mean but within tolerance 6(d) 42 to 46 1 FT their ruled line with positive gradient 7(a)(i) 27 1 7(a)(ii) 3 2 M1 for 5x = 11 + 4 or better 7(b) 4x + 12 final answer 1 7(c) y(y – 2) final answer 1 7(d)(i) 6x2 1 7(d)(ii) 6x2 = 54 M1 FT their((d)(i) in x) = 54 x2 = 9 M1 FT their equation simplified to x2 = … or x = … x = 3 A1 [Length=] 9 [Width=] 6 B1 For both values, either order

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2024 © Cambridge University Press & Assessment 2024 Page 6 of 7 Question Answer Marks Partial Marks 8(a) 792 3 M2 for 2(6 × 6) + 4(6 × 30) oe or M1 for 6 × 6 and 6 × 30 seen cm2 1 8(b) 1260 or 1256 to 1257 2 M1 for π × 42 × 25 8(c)(i) Tangent [perp. to] radius 1 8(c)(ii)(a) 8.06 or 8.062… 2 M1 for 72 + 42 8(c)(ii)(b) 29.59 to 30.21 2 M1 for tan and 4 7 or sin and 4 their OQ or cos and 7 their OQ 9(a) 5 800 000 cao 1 9(b) 4.92 × 105 cao 2 B1 for 492 000 seen 9(c) 5 200 000 or 5.2 × 106 1 9(d) 138 cao 2 B1 for 138.1 or 138.095… 9(e) 5.3 × 10–1 cao 1 10(a)(i) Correct image labelled X (1, –2) (2, –2) (2, –4) 1 10(a)(ii) Correct image labelled Y (–1, 2) (–2, 2) (–2, 4) 1 If 0 scored in (i) and (ii), SC1 for correct images with incorrect or no labels 10(a)(iii) Rotation 180 About (0, 0) oe 3 B1 for each 10(b) Correct image (4, 0) (4, –2) (3, –2) 2 M1 for either correct horizontal move of 2 or for correct vertical move of –4 11(a) 30 2 B1 for 90 or 60 soi 11(b) 12 2 B1 for 88 11(c)(i) 2800 1 11(c)(ii) 2000 2 B1 for 1800 or 3800 11(d) Globe, more cars in price range oe 1

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2024 © Cambridge University Press & Assessment 2024 Page 7 of 7 Question Answer Marks Partial Marks 12(a)(i) Correct quadratic sketch 2 B1 for correct shape crossing x-axis twice 12(a)(ii) 1.5 oe 1 12(b) Correct quadratic sketch 2 B1 for correct shape not crossing x-axis 12(c) −3 and 5 2 B1 for each If 0 scored, SC1 for both x values correct in coordinates