Cambridge IGCSE Mathematics - International 0607 — 2021 Oct/Nov Paper 3 · Variant 1

This document has 20 pages. Any blank pages are indicated. Cambridge IGCSE™ DC (CE/CGW) 199833/2 © UCLES 2021 [Turn over CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) October/November 2021 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 [ ]. * 2 4 4 0 4 5 9 1 4 5 *

2 0607/31/O/N/21 © UCLES 2021 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/O/N/21 © UCLES 2021 [Turn over Answer all the questions. 1 (a) Write sixty thousand and three in figures. … [1] (b) Work out 729. … [1] (c) Work out. . . . 3 21 4 73 6 89 + … [1] (d) Write down all the factors of 10. … [2] (e) Write 965.384 correct to (i) 1 decimal place, … [1] (ii) 3 significant figures, … [1] (iii) the nearest ten. … [1]

4 0607/31/O/N/21 © UCLES 2021 2 (a) These are the first four terms of a sequence. 23 27 31 35 (i) Write down the next two terms of this sequence. … , … [2] (ii) Write down the rule for continuing this sequence. … [1] (b) Here is a list of numbers. -2 3 0.24 9 3 1 - Write down one of the numbers from the list to complete each statement. You must use a different number in each statement. … is a natural number (N). … is an integer (Z). … is a rational number (Q). [3]

5 0607/31/O/N/21 © UCLES 2021 [Turn over 3 (a) Kate works part-time in a supermarket. She is paid $14 per hour. One month, Kate works 64 hours. Work out how much she is paid that month. $ … [1] (b) Kate invests $560 at a rate of 1.6% per year simple interest. Calculate the total interest she receives at the end of 8 years. $ … [2] (c) Ruth invests $800 at a rate of 2.1% per year compound interest. Work out the value of her investment at the end of 4 years. $ … [3]

6 0607/31/O/N/21 © UCLES 2021 4 (a) Decorations $5 for a packet of 3 decorations $9 for a packet of 6 decorations (i) Paul buys 5 packets of 3 decorations and 2 packets of 6 decorations. (a) Work out the total number of decorations he buys. … [1] (b) Work out the total amount he pays for these decorations. $ … [2] (ii) Vasek buys 15 decorations. Work out the least amount that he pays for 15 decorations. $ … [2]

7 0607/31/O/N/21 © UCLES 2021 [Turn over (b) Vasek buys 12 praline balls. (i) One praline ball costs $0.83 . Work out the cost of the 12 praline balls. $ … [1] (ii) Vasek pays with $10. Work out how much change he receives. $ … [1] (iii) Vasek shares the 12 praline balls with his friend, Paul, in the ratio Vasek : Paul = 2 : 1. Work out how many praline balls they each receive. Vasek … Paul … [2]

8 0607/31/O/N/21 © UCLES 2021 5 (a) A taxi company charges a fixed amount of $3 and then $1.50 for each kilometre travelled. (i) Write a formula for the cost, $C, for travelling n kilometres. … [2] (ii) Menno travels 15 kilometres in a taxi from this company. Work out the cost of Menno’s taxi journey. $ … [2] (iii) Weston pays $37.50 for a taxi journey with this company. Work out how many kilometres the taxi travels. … km [2]

9 0607/31/O/N/21 © UCLES 2021 [Turn over (b) The table shows the number of customers for some taxi companies on Monday. There is a total of 875 customers on Monday. Taxi company A B C D E Number of customers 200 150 225 125 175 (i) Complete the bar chart to show this information. 50 0 100 150 Number of customers Taxi company 200 250 A B C E D [2] (ii) Write down the company that had the most customers. … [1] (iii) One of the 875 customers is chosen at random. Find the probability that this customer used company E. … [1]

10 0607/31/O/N/21 © UCLES 2021 6 33° 46° x° y° m° t° z° NOT TO SCALE A B D E C ABCD is a trapezium with angle ADB = 33° and angle BCD = 46°. AB is parallel to DC and AD = AB. DCE is a straight line. (a) Write down the mathematical name for triangle ABD. … [1] (b) Find the value of each of x, y, z, m and t. x = … y = … z = … m = … t = … [5]

11 0607/31/O/N/21 © UCLES 2021 [Turn over 7 A bag contains 30 pieces of fruit. There are 16 grapes and 14 cherries. Fumi takes one piece of fruit at random from the bag and eats it. (a) Find the probability that she takes a grape. … [1] (b) Fumi takes a second piece of fruit at random from the bag. (i) Complete the tree diagram. Second piece of fruit First piece of fruit … … Grape Cherry … … Grape Cherry … … Grape Cherry [3] (ii) Work out the probability that Fumi takes 2 cherries. … [2]

12 0607/31/O/N/21 © UCLES 2021 8 (a) Solve. (i) x 7 3 = x = … [1] (ii) x 3 7 8 + =- x = … [2] (b) M Q P 2 3 = + Find the value of M when P = 2.13 and Q = 1.46 . M = … [2] (c) Simplify. a b a b 3 4 2 - + + … [2] (d) Simplify fully. ab a b 2 3 … [2] (e) Write as a single fraction in its simplest form. p p 5 4 8 3 # … [2]

13 0607/31/O/N/21 © UCLES 2021 [Turn over 9 15 cm 2 cm NOT TO SCALE 3 cm A solid metal disc is in the shape of a cylinder with a smaller cylinder removed from the centre. The radius of the larger cylinder is 15 cm and the radius of the smaller cylinder is 3 cm. The height of the disc is 2 cm. (a) Find the shaded area. … cm2 [3] (b) Find the volume of the disc. … cm3 [1] (c) A solid cube has the same volume as the disc. Find the length of one side of this cube. … cm [2]

14 0607/31/O/N/21 © UCLES 2021 10 NOT TO SCALE x° O D C B A E M The diagram shows a regular pentagon, ABCDE, inscribed in a circle, centre O. (a) Show that x = 72°. [1] (b) Show that angle OAB = 54°. [1]

15 0607/31/O/N/21 © UCLES 2021 [Turn over (c) The circle has radius 6 cm. M is the mid-point of BC. (i) Use trigonometry to calculate OM. … cm [2] (ii) Calculate BC. … cm [3] (iii) Calculate the area of the pentagon. … cm2 [2]

16 0607/31/O/N/21 © UCLES 2021 11 A farmer finds the mass, in kilograms, of each of 100 chickens. The results are shown in the table. Mass (w kg) Frequency 1 1 w G 1.5 8 1.5 1 w G 2 15 2 1 w G 2.5 32 2.5 1 w G 3 23 3 1 w G 3.5 16 3.5 1 w G 4 6 (a) Write down the modal class. … 1 w G … [1] (b) Complete the cumulative frequency table for this data. Mass (w kg) Cumulative frequency w G 1.5 w G 2 w G 2.5 w G 3 w G 3.5 w G 4 100 [2]

17 0607/31/O/N/21 © UCLES 2021 [Turn over (c) On the grid, draw a cumulative frequency curve. 0 0 10 20 30 40 50 60 70 80 90 100 1 2 3 w 4 Mass (kg) Cumulative frequency [3] (d) Use your curve to find an estimate for (i) the median, … kg [1] (ii) the interquartile range, … kg [2] (iii) the number of chickens with a mass greater than 3.25 kg. … [2]

18 0607/31/O/N/21 © UCLES 2021 12 0 y x – 2 2 – 8 8 (a) On the diagram, sketch the graph of y x3 = for x 2 2 G G - . [2] (b) Write down the coordinates of the point where the graph crosses the y-axis. ( … , …) [1] (c) On the same diagram, sketch the graph of y x 2 = for x 2 2 G G - . [2] (d) Find the x-coordinate of the points of intersection of y x3 = and y x 2 = . … , … , … [3]

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20 0607/31/O/N/21 © UCLES 2021 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 the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge. BLANK PAGE

This document consists of 7 printed pages. © UCLES 2021 [Turn over Cambridge IGCSE™ CAMBRIDGEINTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) October/November 2021 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 October/November 2021 series for most Cambridge IGCSE™, Cambridge International A and AS Level components and some Cambridge O Level components.

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 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 October/November 2021 © UCLES 2021 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 October/November 2021 © UCLES 2021 Page 4 of 7 Question Answer Marks Partial Marks 1(a) 60 003 1 1(b) 27 1 1(c) 0.868 or 0.8677 to 0.8678 1 1(d) 1, 2, 5, 10 2 B1 for 2 or 3 correct and none incorrect 1(e)(i) 965.4 1 1(e)(ii) 965 1 1(e)(iii) 970 1 2(a)(i) 39, 43 2 B1 for each 2(a)(ii) +4 1 2(b) 9 2 − 0.24 or 1 3 − 3 B1 for each 3(a) 896 1 3(b) 71.68 2 M1 for 560 [8] 1.6 100 × × 3(c) 869.35 3 M2 for 4 2.1 800 1 100   × +     oe or M1 for 2.1 800 1 100 n   × +     , n > 1 4(a)(i)(a) 27 1 4(a)(i)(b) 43 2 M1 for 5 5 × or 2 9 × 4(a)(ii) 23 2 B1 for 2 9 [1 ]5 × + × or for correct price but not the least amount, e.g. 24 or 25 4(b)(i) 9.96 1 4(b)(ii) 0.04 1 FT 10 – their (b)(i) 4(b)(iii) [Vasek] 8 [Paul] 4 2 B1 for correct but reversed or M1 for 12 1 2 +

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 5 of 7 Question Answer Marks Partial Marks 5(a)(i) 3 1.5[0] = + C n 2 B1 for 3, 0 + ≠ kn k or 1.5[0]n seen 5(a)(ii) 25.5[0] 2 M1 for [3 ]1.50 15 + × 5(a)(iii) 23 2 M1 for 37.50 – 3 soi by 34.5 5(b)(i) correct bar chart drawn 2 B1 for 3 correct bars of equal width or 4 correct height but different width 5(b)(ii) C 1 5(b)(iii) 175 875 oe 1 6(a) isosceles 1 6(b) [x =] 33 [y =] 114 [z =] 134 [m =] 33 [t =] 101 5 B1 for each FT m = their x 7(a) 16 30 oe 1 7(b)(i) correct tree diagram 3 FT their (a) B2 for 4 correct or B1 for 2 correct 7(b)(ii) 91 435 oe 2 M1 for 14 13 30 29 × their their

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 6 of 7 Question Answer Marks Partial Marks 8(a)(i) 21 1 8(a)(ii) 5 − 2 M1 for 3 8 7 = −− x or 7 8 3 3 − + = x or better 8(b) 8.64 2 M1 for 2 2.13 3 1.46 × + × or B1 for 4.26 or 4.38 seen 8(c) 4 2 − a b final answer 2 B1 for 4a or 2b − 8(d) 2 a b or 2 1 − a b final answer 2 B1 for any correct cancelling 8(e) 2 3 10 p final answer 2 B1 for 2 12 40 p oe or evidence of cancelling 4 and 8 9(a) 679 or 678.5 to 678.7… 3 M2 for 2 2 15 3 π π × − × or M1 for 2 15 π × or 23 π × 9(b) 1360 or 1357… 1 FT their (a) 2 × 9(c) 11.1 or 11.07 to 11.08 2 M1 for 3 their(b) or 3 = x their(b) soi 10(a) 360 5 1 10(b) 180 72 2 − oe 1 10(c)(i) 4.85 or 4.854… 2 M1 for sin (54) = 6 OM or cos (36) = 6 OM seen 10(c)(ii) 7.05 or 7.06 or 7.05 to 7.06… 3 B2 for BM = 3.52 to 3.54 or M2 for 2 6 cos54 × × or 2 6 sin36 × × or 2 2 2 6 4.85 × −their or M1 for 6 cos54 × or 6 sin36 × or 2 2 6 4.85 their − 10(c)(iii) 85.4 to 85.7 2 M1 for 1 2 ×their(c)(i) ×their(c)(ii)

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 7 of 7 Question Answer Marks Partial Marks 11(a) 2 < w ⩽ 2.5 1 11(b) 8 23 55 78 94 [100] 2 M1 for 3 or 4 correct 11(c) Correct cumulative frequency curve 3 M1 for horizontal plots correct M1FT for at least 4 vertical plots correct depending on increasing curve 11(d)(i) 2.4 1 FT their increasing curve 11(d)(ii) [0].9 2 FT their increasing curve B1 for 2.93 or 2.03 seen 11(d)(iii) 11 to 15 integer 2 FT their increasing curve B1 for 85 to 89 seen or correct non-integer value between 11 to 15 12(a) correct curve drawn 2 B1 for passing through (0, 0), B1 for correct shape 12(b) (0, 0) 1 12(c) correct line drawn 2 B1 for ruled line passing through (0, 0) or B1 for ruled line with positive gradient 12(d) 0 1.41 or 1.414… 1.41 − or 1.414... − 3 B1 for 0. B2 for 1.41 and 1.41 − or B1 for 1.41 or 1.41 − or 1.4 and 1.4 − If 0 scored, SC2 for 3 correct coordinates given or SC1 for 1 or 2 correct coordinates given