Cambridge IGCSE Mathematics - International 0607 — 2022 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 2022 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 0 8 9 8 4 6 6 2 3 * DC (CJ/SG) 304968/2 © UCLES 2022

2 0607/31/M/J/22 © UCLES 2022 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/22 © UCLES 2022 [Turn over Answer all the questions. 1 (a) Write the number 20 202 in words. … [1] (b) Work out. . . . 1 75 6 27 2 48 + … [1] (c) Write down all the factors of 42. … [2] (d) Write down a prime number between 15 and 20. … [1] (e) Write 7832.948 (i) correct to 2 decimal places, … [1] (ii) correct to 4 significant figures, … [1] (iii) correct to the nearest 100. … [1] (f) Insert the symbols ( ), , , # + - so that the following statement is correct. 5 3 4 1 = 9 [1] (g) Jeffrey invests $550 for 3 years at a rate of 3.2% per year simple interest. Work out the interest he receives. $ … [2]

4 0607/31/M/J/22 © UCLES 2022 2 Wim measures the amount of rain, in mm, each day for 31 days. The bar chart shows his results. Amount of rain (mm) Number of days 0 0 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 (a) Write down the mode. … mm [1] (b) Write down the number of days that had no rain. … [1] (c) Work out the mean amount of rain per day. … mm [2] (d) Wim picks one of these days at random. Find the probability that, on that day, the amount of rain was 3 mm or more. … [1]

5 0607/31//M/J/22 © UCLES 2022 [Turn over 3 4.2 cm A O B E C D NOT TO SCALE The diagram shows a circle, centre O, radius 4.2 cm. A, B and C are points on the circle. The line DE touches the circle at C. (a) Write down the mathematical name for each of these straight lines. AC is a … DE is a … AB is a … [3] (b) Work out (i) the circumference of the circle, … cm [2] (ii) the area of the circle. … cm2 [2] (c) Angle AOB = 110°. Calculate the area of sector AOB. … cm2 [2]

6 0607/31/M/J/22 © UCLES 2022 4 10 9 8 7 6 5 4 3 2 1 0 – 1 – 2 – 1 1 2 3 4 5 6 7 – 2 – 3 x y A C The diagram shows point A and point C plotted on a 1 cm2 grid. (a) Plot point ( , ) B 5 7 and point ( , ) D 1 7 - and draw the quadrilateral ABCD. [2] (b) (i) Find the length of AC. AC = … cm [1] (ii) Use Pythagoras’ Theorem to find the length of AB. AB = … cm [2] (c) Write down the mathematical name for quadrilateral ABCD. … [1] (d) Reflect quadrilateral ABCD in the line y 4 = . [2]

7 0607/31//M/J/22 © UCLES 2022 [Turn over 5 (a) Solve. (i) x 6 96 = x = … [1] (ii) x 7 6 13 - =- x = … [2] (b) Simplify. (i) r r r 5 2 - - … [1] (ii) a b a b 4 3 7 2 - - + … [2] (c) T m n 4 2 = + Find (i) the value of T when . m 1 8 = and . n 0 3 =- , T = … [2] (ii) the value of n when T 26 = and . m 3 4 = . n = … [2]

8 0607/31/M/J/22 © UCLES 2022 6 30 members of a sports club were asked what their favourite game was. They could choose from tennis (T), squash (S) or badminton (B). These are the results. B T S S T S B B T S S S S T T T S S B T B T S S T T B S S T (a) Complete the frequency table. Game Frequency Tennis (T) Squash (S) Badminton (B) [2] (b) Find how many more members chose tennis than badminton. … [1] (c) One of the 30 members is chosen at random. Write down the probability that this member chose squash. … [1]

9 0607/31//M/J/22 © UCLES 2022 [Turn over (d) Shadana begins to draw a pie chart to show the results. (i) Show that the sector angle for tennis is 132°. [2] (ii) Complete the pie chart for Shadana. [3]

10 0607/31/M/J/22 © UCLES 2022 7 Gheza wants to know if the number of weeks that a song is Number One in the charts is related to the length of the song, in minutes. The table shows the results for one year. Number of weeks at Number One 3 2 1 5 4 11 7 4 3 3 9 Length of song (minutes) 3.5 3.9 4.2 3.1 3.2 2.5 2.9 3.0 3.4 3.7 2.9 (a) Complete the scatter diagram. The first 6 points have been plotted for you. 0 1 2 3 4 5 0 1 2 3 4 5 6 Number of weeks at Number One 7 8 9 10 11 Length of song (minutes) [2] (b) What type of correlation is shown in the diagram? … [1]

11 0607/31//M/J/22 © UCLES 2022 [Turn over (c) Find (i) the mean number of weeks at Number One, … [1] (ii) the mean length of a song. … min [1] (d) On the scatter diagram, draw a line of best fit. [2]

12 0607/31/M/J/22 © UCLES 2022 8 (a) The nth term of a sequence is n 2 3 2 + . Write down the first three terms of this sequence. … , … , … [2] (b) These are the first four terms of a different sequence. 5 3 - 11 - 19 - (i) Find the next two terms of the sequence. … , … [2] (ii) Find the nth term of the sequence. … [2] (iii) Sanjay says that 101 - is a term of the sequence. Show that he is not correct. [2]

13 0607/31//M/J/22 © UCLES 2022 [Turn over 9 C B A 7 6 5 4 3 2 1 0 – 1 – 2 – 3 – 4 – 1 1 2 3 4 5 6 7 – 2 – 3 – 4 x y (a) Describe fully the single transformation that maps shape A onto shape B. … … [3] (b) Describe fully the single transformation that maps shape A onto shape C. … … [2] (c) Rotate shape A 90° clockwise about (0, 0). [2]

14 0607/31/M/J/22 © UCLES 2022 10 NOT TO SCALE 16 0 – 12 3 – 4 x y The diagram shows a sketch of the graph of . . y x x x 0 5 0 65 2 2 3 2 = + - + for x 4 3 G G - . (a) Find the coordinates of the point where the graph crosses the y-axis. ( … , … ) [1] (b) Find the coordinates of the point where the graph crosses the x-axis. ( … , … ) [1] (c) Find the coordinates of the local maximum. ( … , … ) [2] (d) Find the coordinates of the local minimum. ( … , … ) [2] (e) On the diagram, sketch the graph of y 8 = . [1] (f) Solve this equation. . . x x x 0 5 0 65 2 2 8 3 2 + - + = . x = … [1]

15 0607/31//M/J/22 © UCLES 2022 [Turn over 11 x° y° A B O 14 cm NOT TO SCALE The diagram shows a regular hexagon with centre and cm O OA OB 14 = = . (a) Work out the size of angle x and the size of angle y. x = … y = … [2] (b) Write down the length of AB. AB = … cm [1] (c) Work out the area of triangle AOB. … cm2 [3] The regular hexagon is the cross-section of a prism. The length of the prism is 5 cm. (d) Work out the volume of the prism. … cm3 [2] Question 12 is printed on the next page.

16 0607/31/M/J/22 © UCLES 2022 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. 12 Ruben’s house is 1.3 km from the supermarket. (a) He walks to the supermarket at a speed of 5 km / h. Work out how long it takes him. Give your answer in minutes and seconds. … min … s [3] (b) On another day, Ruben cycles to the supermarket in a time of 5 minutes 12 seconds. (i) Show that 12 seconds = 0.2 minutes. [1] (ii) Work out Ruben’s average speed when cycling to the supermarket. Give your answer in km / h. … km / h [2]

This document consists of 7 printed pages. © UCLES 2022 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) May/June 2022 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 2022 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 2022 © UCLES 2022 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 2022 © UCLES 2022 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 2022 © UCLES 2022 Page 4 of 7 Question Answer Marks Partial Marks 1(a) Twenty thousand, two hundred [and] two 1 1(b) 5 1 1(c) 1, 2, 3, 6, 7, 14, 21, 42 2 B1 for 4 to 7 correct factors with no incorrect or 8 correct factors with one extra 1(d) 17 or 19 1 1(e)(i) 7832.95 1 1(e)(ii) 7833 1 1(e)(iii) 7800 1 1(f) (5 3) 4 1 9    1 1(g) 52.8[0] 2 M1 for 3.2 550 [ 3] 100   implied by 17.6[0] 2(a) 2 1 2(b) 7 1 2(c) 1.90 or 1.903… 2 M1 for [7 0 ]6 1 9 2 4 3 2 4 3 5       soi by 59 2(d) 9 31 1 3(a) [AC is a] diameter [DE is a] tangent [AB is a] chord 3 B1 for each 3(b)(i) 26.4 or 26.38 to 26.39 2 M1 for 2 4.2  oe 3(b)(ii) 55.4 or 55.41 to 55.43 2 2 1 for 4.2  M 3(c) 16.9 or 16.92 to 16.93 2  110 1 for b ii 360 their  M 4(a) Both points correctly plotted 2 B1 for each 4(b)(i) 4 1 4(b)(ii) [AB =] 4.47 or 4.472… 2 M1 for their 22 + their 42 oe 4(c) kite 1 FT their shape if a closed shape and a special quadrilateral

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 5 of 7 Question Answer Marks Partial Marks 4(d) Correct reflection (1,3), (5,1), (1,-1), (-1,1) 2 B1 for 4 y  drawn or correct reflection in another horizontal or vertical line, provided it fits on the grid. FT wrong plotting if a closed shape and it fits on the grid. 5(a)(i) 16 1 5(a)(ii) 1  2 M1 for 7 13 6 x   or 6 13 7 7 x    5(b)(i) 2r final answer 1 5(b)(ii) 3 [1] a b   final answer 2 B1 for 3a  or [1]b  5(c)(i) 6.6 2 B1 for 4(1.8) 2( 0.3)   5(c)(ii) 6.2 2 M1 for 26 4(3.4) 2n   6(a) [T] 11 [S] 13 [B] 6 2 B1 for 2 correct 6(b) 5 1 FT their frequencies 6(c) 13 30 1 FT their 13 6(d)(i) 11 360 30  2 M1 for 11 30 or 360 30 oe seen 6(d)(ii) Correct pie chart with 2 angles within range drawn and labelled 3 B2 for correct pie chart with no labels or B1 for 1 correct angle drawn with correct label or 3 wrong angles (in correct proportion) with correct labels or 156 or 72 seen 7(a) Points correctly plotted 2 B1 for 3 or 4 points correctly plotted 7(b) Negative 1 7(c)(i) 4.73 or 4.727… 1 7(c)(ii) 3.3 1 7(d) Ruled line correctly drawn 2 B1 for ruled line in tolerance but not through the mean point or ruled line with negative gradient through the mean point but not in tolerance

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 6 of 7 Question Answer Marks Partial Marks 8(a) 5, 11, 21 2 B1 for two terms correctly placed If 0 scored, SC1 for 3, 5, 11 8(b)(i) 27 35   2 B1 for each 8(b)(ii) 13 8n  oe 2 B1 for 13 , 0 kn k   or 8 j n  8(b)(iii) 13 8 101 n   M1 FT their nth term equated to 101  or M1 for continuing the sequence correctly for a further 5 terms beyond 35  114 14.25 8 n   So, it is not a term of the sequence oe A1 or M1 for continuing until 99  or 107  followed by a suitable statement 9(a) Enlargement [Scale factor] 3 [Centre] (0, 0) oe 3 B1 for each 9(b) Translation 4 3         2 B1 for each 9(c) Correct rotation (0, 2),(1, 1),(1, 2),(2, 2),(2, 1)      2 B1 for correct rotation anticlockwise 10(a) (0,2) 1 10(b) ( 3.05,0)  or ( 3.045...,0)  1 10(c) ( 1.67,4.82)  or ( 1.666...,4.824...)  2 B1 for each If 0 scored, SC1 for ( 1.7,4.8)  10(d) (0.8,1.07) or (0.8,1.072) 2 B1 for each 10(e) Correct line drawn 1 10(f) 2.41 or 2.414… 1 11(a) 60, 60 2 B1 for each 11(b) 14 1 11(c) 84.9 or 84.87… 3 M1 for 14sin(60) or 2 2 14 14 2       M1 for 1 14 2  their height

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 7 of 7 Question Answer Marks Partial Marks 11(d) 2550 or 2546 to 2547 2 M1 for 6 5 their (c) 12(a) 15 [min] 36 [sec] 3 M2 for 1.3 60 5  oe, soi by 15.6 or M1 for 1.3 5 soi by 0.26 12(b)(i) 12 60 = 0.2 1 12(b)(ii) 15 2 M1 for 1.3 5.2 soi by 0.25 or 5.2 60 soi by 0.0866… oe