Cambridge IGCSE Mathematics - International 0607 — 2023 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 2023 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 7 7 8 6 9 6 3 3 3 * DC (PQ/CB) 311915/2 © UCLES 2023

2 0607/33/M/J/23 © UCLES 2023 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/23 © UCLES 2023 [Turn over Answer all the questions. 1 (a) Work out. (i) 3 2 5 2 # … [1] (ii) 5 2 3 4 - … [2] (b) Write 80 as a product of its prime factors. … [2] (c) Work out . 4500000000 5 8 107 # - . Give your answer in standard form. … [2] (d) Write .3 9 10 4 # - as an ordinary number. … [1]

4 0607/33/M/J/23 © UCLES 2023 2 (a) These are the highest temperatures, in °C, each day during one month. 5 4 3 1 2 4 6 6 7 7 5 8 9 8 10 9 10 10 9 10 9 8 8 9 8 7 7 9 10 9 (i) Complete the frequency table. Temperature (°C) 1 2 3 4 5 6 7 8 9 10 Frequency 1 1 1 5 [2] (ii) Find how many days there are in this month. … [1] (iii) What is the most common highest temperature this month? … °C [1] (iv) Find how many more days have a highest temperature of 9 °C than have a highest temperature of 6 °C. … [1] (v) Complete the bar chart to show the information in the table. 0 1 2 3 4 5 Temperature (°C) Frequency 6 7 8 9 10 1 2 3 4 5 6 7 8 [2]

5 0607/33/M/J/23 © UCLES 2023 [Turn over (b) These are the amounts of rainfall, in mm, measured during one week. 13 6 7 11 4 6 9 (i) Work out the range. … mm [1] (ii) Work out the mean. … mm [1] (iii) Work out the median. … mm [2]

6 0607/33/M/J/23 © UCLES 2023 3 (a) These are the first three patterns in a sequence of grey tiles and black tiles. Pattern 1 Pattern 2 Pattern 3 (i) On the grid below, draw Pattern 4 in the sequence of grey and black tiles. [1] (ii) Complete the table. Pattern number 1 2 3 4 5 Number of black tiles 1 2 3 4 5 Number of grey tiles 4 [2] (iii) One of the patterns in this sequence has 16 grey tiles. Work out how many black tiles there are in this pattern. … [1] (iv) One of the patterns in this sequence has 10 black tiles. Work out how many grey tiles there are in this pattern. … [1] (b) (i) Find the first term and the sixth term of this sequence of numbers. … 3 9 15 21 … [2] (ii) Write down the rule for continuing this sequence. … [1] (iii) Find the nth term of this sequence. … [2]

7 0607/33/M/J/23 © UCLES 2023 [Turn over 4 (a) (i) Find the value of y y 5 10 2 - when y 3 = . … [2] (ii) Factorise completely. y y 5 10 2 - … [2] (b) Solve. (i) x 4 9 - = x = … [1] (ii) x 3 5 7 - = x = … [2]

8 0607/33/M/J/23 © UCLES 2023 5 (a) This pentagon has one line of symmetry, shown dashed in the diagram. NOT TO SCALE 80° 75° x° Work out the value of x. x = … [4]

9 0607/33/M/J/23 © UCLES 2023 [Turn over (b) NOT TO SCALE 128° 32° y° x° S R Q O P P, Q, R and S are points on the circle, centre O. POR is a straight line. (i) Give a reason why triangle OPQ is isosceles. … … [1] (ii) Work out the value of x. x = … [2] (iii) Work out the value of y. y = … [2]

10 0607/33/M/J/23 © UCLES 2023 6 (a) At a fast food restaurant, a burger costs $6.40 and a milkshake costs $2.50 . (i) Work out the total cost of 4 burgers and 3 milkshakes. $ … [2] (ii) Toby buys one burger and one milkshake. Work out how much change he gets from $10. $ … [2] (iii) Some friends buy 2 burgers and a number of milkshakes. They pay a total of $30.30 . Work out how many milkshakes they buy. … [3]

11 0607/33/M/J/23 © UCLES 2023 [Turn over (b) Toby notices that 80% of all customers in this fast food restaurant order fries. (i) Complete this tree diagram for the next two customers at the restaurant. First customer Fries No fries Fries No fries Fries No fries 0.80 … … … … … Second customer [2] (ii) Find the probability that both customers do not order fries. … [2]

12 0607/33/M/J/23 © UCLES 2023 7 (a) The diagram shows a prism. All measurements are in centimetres. NOT TO SCALE 6 8 2 2 3 4 5 (i) Find the total number of faces of this prism. … [1] (ii) Work out the perimeter and area of the shaded face. Give the units of each answer. Perimeter = … … Area = … … [4] (iii) Work out the volume of the prism. … cm3 [1]

13 0607/33/M/J/23 © UCLES 2023 [Turn over (b) NOT TO SCALE 17 m 15 m Work out the area of this triangle. … m2 [5]

14 0607/33/M/J/23 © UCLES 2023 8 (a) Atif and Faiza share $5000 in this ratio. Atif : Faiza = 3 : 7 Work out how much they each receive. Atif $ … Faiza $ … [2] (b) Atif earns $2200 each month. Each month he gives 8 1 of his earnings to charity. Work out how much Atif has left each month after giving to charity. $ … [2] (c) Faiza gives $40 to charity each month. She increases this amount by 14%. Work out how much Faiza now gives to charity each month. $ … [2]

15 0607/33/M/J/23 © UCLES 2023 [Turn over 9 y 0 x A B – 1 1 2 3 4 5 6 – 1 1 2 3 4 5 6 7 8 – 2 – 3 – 4 – 5 – 6 – 7 – 8 – 2 – 3 – 4 – 5 – 6 (a) Reflect triangle A in the y-axis. Label the image X. [1] (b) Rotate triangle A by 90° clockwise about (0, 0). Label the image Y. [2] (c) Describe fully the single transformation which maps triangle Y onto triangle B. … … [2] (d) Enlarge triangle A by scale factor 2 from centre (1, 1). Label the image Z. [2]

16 0607/33/M/J/23 © UCLES 2023 10 Jonah draws a line of best fit on a scatter diagram. y x 0 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 (a) What type of correlation is shown in the diagram? … [1] (b) Use the line of best fit to find y when . x 5 6 = . y = … [1] (c) Find the equation of the line of best fit. Give your answer in the form y mx c = + . y = … [3]

17 0607/33/M/J/23 © UCLES 2023 [Turn over (d) Jonah finds information for two more points for his scatter diagram. x 6.8 9 y 8 9.4 (i) Plot these points on the scatter diagram. [1] (ii) How should Jonah now alter his line of best fit? … [1]

18 0607/33/M/J/23 © UCLES 2023 11 y x 0 – 15 30 – 8 3 (a) (i) On the diagram, sketch the graph of y x x 7 2 = + for x 8 3 G G - . [2] (ii) Find the coordinates of the local minimum. ( … , …) [2] (b) On the diagram, sketch the graph of y x 36 = for values of x between 8 - and 3. [2] (c) Find the x-coordinate of each point of intersection of y x x 7 2 = + and y x 36 = . x = … and x = … and x = … [3]

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20 0607/33/M/J/23 © UCLES 2023 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. © UCLES 2023 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 Paper 3 (Core) May/June 2023 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 2023 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 2023 © UCLES 2023 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 descriptors 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 2023 © UCLES 2023 Page 3 of 7 Maths-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, 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 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 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 2023 © UCLES 2023 Page 4 of 7 Question Answer Marks Partial Marks 1(a)(i) 4 15 oe 1 1(a)(ii) 109 2 B1 for 125 or 16 1(b) 2 × 2 × 2 × 2 × 5 or 24 × 5 2 M1 for repeated division of 80 or for 2 and 5 seen as factors 1(c) 4.44 × 109 or 4.442 × 109 2 B1 for 4 442 000 000 1(d) 0.00 039 1 2(a)(i) [1, 1, 1] 2, 2, 2, 4, 5, 7, [5] 2 B1 for 4 or 5 correct 2(a)(ii) 30 1 2(a)(iii) 9 1 FT their table 2(a)(iv) 5 1 FT their table 2(a)(v) Correct bar chart 2 FT their table B1 for 4 or 5 correct bars 2(b)(i) 9 1 2(b)(ii) 8 1 2(b)(iii) 7 2 M1 for listing values in order 3(a)(i) Correct pattern 1 3(a)(ii) [4] 6, 8, 10, 12 2 B1 for 3 correct 3(a)(iii) 7 1 3(a)(iv) 22 1 3(b)(i) −3 and 27 2 B1 for each 3(b)(ii) +6 oe 1 3(b)(iii) 6n – 9 oe final answer 2 B1 for 6n  k 4(a)(i) 15 2 M1 for 5 × 32 – 10 × 3 or B1 for 45 4(a)(ii) 5y(y − 2) final answer 2 B1 for 5(y2 − 2y) or y(5y − 10) 4(b)(i) 13 1 4(b)(ii) 4 2 M1 for 3x = 7 + 5

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2023 © UCLES 2023 Page 5 of 7 Question Answer Marks Partial Marks 5(a) 155 4 B1 for 540 B1 for x, x, 80, 75, 75 M1 for [2x =] 540 – 80 – 75 – 75 OR B1 for 360 B1 for x, 75, 40, 90 M1 for[x =] 360 − 75 − 40 – 90 OR M1 for any correct equation in x 5(b)(i) [OP = OQ =] radius of circle 1 5(b)(ii) 26 2 M1 for 180 128 2  5(b)(iii) 58 2 B1 for PSR = 90° soi 6(a)(i) 33.1[0] 2 B1 for 25.6[0] or 7.5[0] 6(a)(ii) 1.1[0] 2 B1 for 8.9[0] 6(a)(iii) 7 3 M2 for 30.30 2 6.40 2.50  oe or M1 for 30.30 – 2 × 6.40 soi by 17.50 6(b)(i) Complete, correct diagram 2 M1 for 0.2[0] correctly placed once 6(b)(ii) 0.04 oe 2 M1 for their 0.2 × their 0.2 7(a)(i) 8 1 7(a)(ii) [Perimeter =] 22 [Area =] 18 B3 B1 for [Perimeter =] 22 B2 for [Area =] 18 or M1 for 5×2 or 4×2 or 6×2 or 3×2 cm cm2 B1

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2023 © UCLES 2023 Page 6 of 7 Question Answer Marks Partial Marks 7(a)(iii) 144 1 FT (their18) × 8 7(b) 60 5 B3 for height = 8 or M2 for 172 − 152 or M1 for 172 = h2 + 152 or better M1 for 15 height 2 their 8(a) [Atif =] 1500 [Faiza=] 3500 2 M1 for 5000 3 7  soi by 500 8(b) 1925 2 B1 for 275 8(c) 45.6[0] 2 M1 for 40 × 0.14 oe soi by 5.6[0] 9(a) Correct reflection (–2, 1) (–3, 1) (–2, 4) 1 9(b) Correct rotation (1, –2) (1, –3) (4, –2) 2 B1 for correct but 90 anticlockwise or for correct orientation, wrong position 9(c) Translation 5 1        2 B1 for each 9(d) Correct enlargement (3, 1) (3, 7) (5, 1) 2 B1 for two points correct or for correct size, wrong position 10(a) Positive 1 10(b) 5.8 1 10(c) [y =] 1 2 x + 3 3 B2 for [y =] 1 2 x + k or [ y =] mx + 3 k, m ≠ 0 or M1 for rise run for their triangle 10(d)(i) Two points correctly plotted 1 10(d)(ii) Steeper gradient oe 1

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2023 © UCLES 2023 Page 7 of 7 Question Answer Marks Partial Marks 11(a)(i) Correct diagram 2 B1 for correct shape or for vertex in correct quadrant 11(a)(ii) (−3.5[0], −12.25) 2 B1 for each 11(b) Correct diagram 2 B1 for two correct branches but joined or for one correct branch 11(c) −6, −3, 2 3 B1 for each