Cambridge IGCSE Mathematics - International 0607 — 2023 May/June Paper 3 · Variant 1

This document has 16 pages. [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 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 [ ]. * 3 0 8 0 3 0 9 7 3 3 * DC (CJ/FC) 311895/2 © UCLES 2023

2 0607/31/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 0607/31/M/J/23 © UCLES 2023 [Turn over Answer all the questions. 1 (a) The points A, B, and C are drawn on a 1 cm square grid. – 4 – 3 – 2 – 1 0 1 2 3 4 y x 1 – 1 – 2 – 3 – 4 4 3 2 A B C (i) Write down the coordinates of point A and point C. A = ( … , … ) C = ( … , … ) [2] (ii) ABCD is a rectangle. Plot point D on the grid. Write down the coordinates of point D. D = ( … , … ) [2] (iii) Draw rectangle ABCD and find its area and perimeter. Area … cm2 Perimeter … cm [2] (b) On the rectangle below, draw all the lines of symmetry. [2]

4 0607/31/M/J/23 © UCLES 2023 2 (a) Tilda and Kim sell bottles of salad dressing. At the beginning of Monday, they have 200 bottles of salad dressing for sale. During Monday, Tilda sells half of the 200 bottles and Kim sells 10% of the 200 bottles. Work out how many of the 200 bottles are left at the end of Monday. … [3] (b) A bottle of salad dressing costs $3.25 . Work out the greatest number of bottles of salad dressing that can be bought with $20 and how much change there is. … bottles with $ … change [3]

5 0607/31/M/J/23 © UCLES 2023 [Turn over (c) Salad dressing is made by mixing oil and vinegar in this ratio. oil : vinegar = 5 : 3 Work out how much oil and how much vinegar is needed to make 1 litre of salad dressing. Give your answers in millilitres. Oil … ml Vinegar … ml [3] (d) Kim invests $5000 at 4% per year simple interest. Work out how much the investment is worth at the end of 3 years. $ … [3]

6 0607/31/M/J/23 © UCLES 2023 3 (a) Some students take a test. Their scores are shown in the stem-and-leaf diagram. 0 8 1 2 5 7 2 1 1 1 2 3 6 9 3 2 2 5 4 0 Key : 4 | 0 means 40 (i) Find how many students take the test. … [1] (ii) Find the range. … [1] (iii) Find the mode. … [1] (iv) Find the median. … [1] (v) One of the students is chosen at random. Find the probability that this student scored more than 20. … [2]

7 0607/31/M/J/23 © UCLES 2023 [Turn over (b) Ten students take a different test. These are their scores. 18 29 32 36 40 30 27 9 39 40 (i) Find the mean of these ten scores. … [1] (ii) Complete a stem-and-leaf diagram for these ten scores. 0 1 2 3 4 Key : 4 | 0 means 40 [2] (iii) One of these students scored 32 out of 40. Write 40 32 as a fraction in its simplest form. … [1] (iv) One of these students scored 36 out of 40. Write 40 36 as a percentage. … % [1]

8 0607/31/M/J/23 © UCLES 2023 4 (a) X 48° 52° p° r° q° A Y Z B NOT TO SCALE In the diagram, XYZ is a straight line. YB is parallel to XA. Find the value of p, the value of q and the value of r. Give a geometrical reason for each of your answers. p = … because … … q = … because … … r = … because … … [6] (b) Find the size of one exterior angle of a regular polygon with 15 sides. … [2]

9 0607/31/M/J/23 © UCLES 2023 [Turn over 5 (a) Write these decimals in order of size, starting with the smallest. 0.6 0.63 0.069 0.608 … … … … [2] smallest (b) Find the value of 29. Write your answer correct to 3 significant figures. … [2] (c) (i) Write 0.000 035 in standard form. … [1] (ii) Work out 8 10 4 10 2 6 # # - . Give your answer in standard form. … [2]

10 0607/31/M/J/23 © UCLES 2023 6 (a) Tanvir works out his total pay using this word formula. Total pay = hourly rate # number of hours worked + bonus One week, Tanvir works for 40 hours. His hourly rate is $8.50 and his bonus is $20. Work out Tanvir’s total pay for this week. $ … [2] (b) Perry buys m kg of potatoes. (i) Perry’s shopping bag has a mass of 1.5 kg. Write down a formula for the total mass, W kg, of the bag and the potatoes. W = … [1] (ii) Potatoes cost 98 cents per kilogram. Write down a formula for the cost, $C, of m kg of potatoes. C = … [2] (c) ( ) P S B n # = - (i) Find P when , S B 9 4 = = and n 6 = . P = … [1] (ii) Find n when , P S 90 23 = = and B 8 = . n = … [2] (iii) Rearrange the formula ( ) P S B n # = - to make S the subject. S = … [2]

11 0607/31/M/J/23 © UCLES 2023 [Turn over 7 B A – 4 – 5 – 6 – 7 – 3 – 2 – 1 0 1 2 3 4 5 6 7 y x 1 – 1 – 2 –3 – 4 – 5 – 6 – 7 4 5 6 7 3 2 The grid shows two shapes, A and B. (a) Describe fully the single transformation that maps shape A onto shape B. … … [3] (b) Reflect shape A in the y-axis. Label the image P. [1] (c) Translate shape A by 8 5 - - e o. Label the image Q. [2] (d) Rotate shape A by 90° clockwise about (0, 0). Label the image R. [2]

12 0607/31/M/J/23 © UCLES 2023 8 (a) Simplify. x x x 5 4 3 + + … [1] (b) Expand. ( ) x x 5 9 - … [2] (c) Factorise completely. x xy 20 6 + … [2] (d) Solve. (i) ( ) x 4 2 3 28 - = x = … [3] (ii) x x 3 11 4 - = + x = … [2]

13 0607/31/M/J/23 © UCLES 2023 [Turn over 9 12 m 35 m x° NOT TO SCALE (a) Work out the area of the triangle. Give the units of your answer. … … [2] (b) Work out the perimeter of the triangle. … m [3] (c) Find the value of x. x = … [2]

14 0607/31/M/J/23 © UCLES 2023 10 120 students take part in a sponsored swim. The cumulative frequency table shows the amounts, in $, they raised. Amount raised ($A) A G 100 A G 200 A G 300 A G 400 A G 500 A G 600 Cumulative frequency 4 10 18 40 96 120 (a) On the grid, draw a cumulative frequency curve to show the information in the table. 0 0 50 100 150 200 250 300 Amount raised ($) Cumulative frequency A 350 400 450 500 550 600 10 20 30 40 50 60 70 80 90 100 110 120 [3]

15 0607/31/M/J/23 © UCLES 2023 [Turn over (b) Use your cumulative frequency curve to find (i) the median amount raised $ … [1] (ii) the interquartile range $ … [2] (iii) the number of students who raised more than $525. … [2] Question 11 is printed on the next page.

16 0607/31/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. 11 – 5 25 y x – 1 3 0 (a) (i) On the diagram, sketch the graph of y 3 2x # = for x 1 3 G G - . [2] (ii) Find the coordinates of the point where the graph crosses the y-axis. ( … , … ) [1] (b) On the diagram, sketch the graph of y x 4 3 = + for x 1 3 G G - . [2] (c) Find the x-coordinate of each point of intersection of y x 4 3 = + and y 3 2x # = . x = … and x = … [2]

This document consists of 7 printed pages. © UCLES 2023 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 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.

0607/31 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.

0607/31 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

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2023 © UCLES 2023 Page 4 of 7 Question Answer Marks Partial Marks 1(a)(i) [A =] (3, 2) [C =] (−1, −3) 2 B1 for each 1(a)(ii) D in correct position B1 (−1, 2) B1 FT their D 1(a)(iii) [Area =] 20 [Perimeter =] 18 2 B1 for each 1(b) 2 correct lines of symmetry only 2 B1 for one correct and none incorrect or for two correct and just one incorrect 2(a) 80 3 B1 for 100 B1 for 20 2(b) 6 with 0.5[0] change 3 M1 for 20 ÷ 3.25 oe A1 for 6 If 0 scored, SC1 for number of bottles less than 6 with correct change 2(c) [oil =] 625 [vinegar =] 375 3 B1 for 1000 soi M1 for 1000 5 3  their soi by figs125 2(d) 5600 3 B2 for 600 or M2 for 5000 4 3 100  + 500 or M1 for 5000 4 [3] 100  3(a)(i) 15 1 3(a)(ii) 32 1 3(a)(iii) 21 1 3(a)(iv) 22 1 3(a)(v) 11 15 oe isw 2 FT their(a)(i) for 2 marks B1 for 11 3(b)(i) 30 1 3(b)(ii) 0 9 1 8 2 7 9 3 0 2 6 9 4 0 0 2 B1 for correct leaves, unordered with 1error or omission 3(b)(iii) 4 5 cao 1

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2023 © UCLES 2023 Page 5 of 7 Question Answer Marks Partial Marks 3(b)(iv) 90 1 4(a) [p =] 52 alternate angles [q =] 48 corresponding angles [r =] 80 angles in a triangle sum to 180 or angles on a straight line must sum to 180. 6 B1 for each element FT their p or q for r 4(b) 24 2 M1 for 360 15 oe 5(a) 0.069 0.6 0.608 0.63 2 B1 for three in correct order when one is covered up 5(b) 5.39 cao 2 B1 for 5.385[1…] or for their answer to more than 3sf correctly rounded to 3sf 5(c)(i) 3.5 × 10−5 cao 1 5(c)(ii) 5.[0] × 107 cao 2 B1 for 50 000 000 or 0.5 × 108 6(a) 360 2 M1 for 40 × 8.5[0] soi by 340 6(b)(i) m + 1.5 oe 1 6(b)(ii) 0.98m oe 2 B1 for 98 [×] m 6(c)(i) 30 1 6(c)(ii) 6 2 M1 for 90 = (23 – 8) × n 6(c)(iii)  P B n or  P Bn n 2 M1 for P n = S – B or P = Sn − Bn 7(a) Enlargement Centre (0, 0) or Origin [scale factor] 1 2 oe 3 B1 for each 7(b) Correct reflection (–4, 0) (–4, 2) (–4, 4) (–6, 4) (–6, 2) 1 7(c) Correct translation (–4, –5) (–4, –3) (–4, –1) (–2, –1) (–2, –3) 2 B1 for either horizontal move correct or vertical move correct 7(d) Correct rotation (0, –4) (2, –4) (4, –4) (4, –6) (2, –6) 2 B1 for correct but 90° anticlockwise about (0,0) or for correct orientation, wrong position 8(a) 12x 1 8(b) 5x2 – 9x final answer 2 B1 for 5x2 or −9x

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2023 © UCLES 2023 Page 6 of 7 Question Answer Marks Partial Marks 8(c) 2x(10 + 3y) final answer 2 B1 for 2(10x + 3xy) or x(20 + 6y) 8(d)(i) 5 3 M1 for 8x – 12 = 28 or 2x – 3 = 7 M1 for 8x = 28 + their 12 or 2x = 3 + their 7 8(d)(ii) 1 7 2 or 7.5 or 15 2 2 M1 for 3x – x = 4 + 11 or better 9(a) 210 B1 m2 B1 9(b) 84 3 B2 for 37 or M1 for 122 + 352 soi by 1369 9(c) 71.1 or 71.07 to 71.08 2 M1 for tan[x =] 35 12 oe 10(a) Correct curve 3 M2 for 6 points correctly plotted or M1 for 4 or 5 points correctly plotted B1 for their 6 points correctly joined 10(b)(i) 430 to 450 1 FT their increasing curve 10(b)(ii) 110 to 145 2 FT their increasing curve B1 for UQ = 480 to 495 or LQ = 350 to 370 10(b)(iii) 12 to 18 2 FT their increasing curve B1 for 102 to 108 11(a)(i) correct sketch 2 B1 for increasing curve 11(a)(ii) (0, 3) 1

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2023 © UCLES 2023 Page 7 of 7 Question Answer Marks Partial Marks 11(b) correct straight line sketch 2 B1 for line with positive gradient or for line crossing y-axis above zero 11(c) 0 and 1.72 or 1.718 to 1.719 2 B1 for each