Cambridge IGCSE Mathematics - International 0607 — 2020 Oct/Nov Paper 3 · Variant 1

Cambridge IGCSE™ This document has 20 pages. Blank pages are indicated. DC (ST/CT) 183466/2 © UCLES 2020 [Turn over * 4 7 9 2 5 8 0 8 8 8 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) October/November 2020 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 0607/31/O/N/20 © UCLES 2020 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/20 © UCLES 2020 [Turn over Answer all the questions. 1 (a) Write down the fraction of the shape that is shaded. … [1] (b) Shade 30% of this shape. [1] (c) Write as a decimal. (i) 60% … [1] (ii) 4 3 … [1] (d) Work out. (i) 63 … [1] (ii) . . . 5 9 3 3 2 3 ' + Give your answer correct to 2 decimal places. … [2]

4 0607/31/O/N/20 © UCLES 2020 2 (a) (i) Write down the mathematical name of this shape. … [1] (ii) Write down the number of lines of symmetry of the shape. … [1] (iii) Write down the order of rotational symmetry of the shape. … [1] (iv) On the shape, draw one line to divide it into two congruent triangles. [1]

5 0607/31/O/N/20 © UCLES 2020 [Turn over (b) x y – 3 – 2 – 1 – 1 1 2 3 – 2 – 3 1 2 3 0 A B C (i) Write down the coordinates of (a) point A, ( … , …) [1] (b) point B, ( … , …) [1] (c) point C. ( … , …) [1] (ii) The shape is drawn on a 1cm2 grid. Find the area of the shape. … cm2 [2]

6 0607/31/O/N/20 © UCLES 2020 3 (a) Sonny’s old car is for sale at $5500. Paula pays him 3 2 of this price. Work out how much Paula pays. Give your answer correct to the nearest dollar. $ … [2] (b) Sonny buys a new car in a sale. The original price of the car is $18 000. In the sale, this price is reduced by 12%. Work out the sale price of the car. $ … [2] (c) Sonny does some research about his new car. (i) The car has a mass of 1.4 tonnes. Work out the total mass of 8 of these cars. … t [1] (ii) It took 4 2 1 years to develop the design of the car. Change 4 2 1 years into months. … months [1] (iii) The car can travel 2 km in 1 minute 24 seconds. Change 1 minute 24 seconds into seconds. … seconds [1]

7 0607/31/O/N/20 © UCLES 2020 [Turn over 4 (a) Here are the first three patterns in a sequence of dots. Pattern 1 Pattern 2 Pattern 3 Pattern 4 (i) In the space above, draw Pattern 4. [1] (ii) Complete the table. Pattern number 1 2 3 4 Number of dots 4 [1] (iii) Write down the rule for continuing the sequence of dots. … [1] (iv) Find the number of dots in Pattern 9. … [1] (b) The nth term of another sequence is n n 2 2 - . Find the first three terms of this sequence. … , … , … [2] (c) These are the first five terms of a different sequence. 3 7 11 15 19 Find the nth term of this sequence. … [2]

8 0607/31/O/N/20 © UCLES 2020 5 (a) (i) NOT TO SCALE 52° y° Work out the value of y. y = … [1] (ii) For any right-angled triangle, explain why none of the angles can be obtuse. … … [1] (b) a° c° b° 65° 80° NOT TO SCALE B E C A D In the diagram, ACE is a straight line. Find the value of a, the value of b and the value of c. a = … b = … c = … [3]

9 0607/31/O/N/20 © UCLES 2020 [Turn over (c) Work out the size of one exterior angle of a regular hexagon. … [2] 6 This word formula can be used to work out the total number of points scored by a hockey team during one season. Total number of points = 3 × number of games won plus 1 × number of games drawn (a) One team had won 17 games and drawn 7 games. Work out the total number of points scored by this team. … [2] (b) Another team scored a total of 44 points. This team had drawn 5 games. Work out how many games this team had won. … [2] (c) A different team scored a total of 36 points. This team had won and drawn exactly the same number of games. Work out how many games this team had won. … [2]

10 0607/31/O/N/20 © UCLES 2020 7 (a) The diagram shows the path of a boat that sails from A to B to C. The scale of the diagram is 1 cm represents 20 km. North A C B Scale: 1 cm to 20 km (i) Find the actual distance from A to B. … km [2] (ii) The boat travels from A to B in 4 hours. Work out the speed of the boat in kilometres per hour. … km/h [2] (iii) Measure the bearing of C from B. … [1]

11 0607/31/O/N/20 © UCLES 2020 [Turn over (b) 7 cm 25 cm x cm NOT TO SCALE Find the value of x. x = … [3]

12 0607/31/O/N/20 © UCLES 2020 8 (a) Solve. (i) x 3 8 + = x = … [1] (ii) ( ) x 3 2 5 12 - = x = … [3] (b) Multiply out and simplify. ( )( ) x x 7 4 + - … [2] (c) Simplify. y x y 20 4 # … [2]

13 0607/31/O/N/20 © UCLES 2020 [Turn over 9 0 40 – 10 – 6 4 y x (a) (i) On the diagram, sketch the graph of y x x 4 3 2 = + + for x 6 4 G G - . [2] (ii) Write down the coordinates of the local minimum. ( … , …) [1] (b) On the diagram, sketch the graph of y x x 2 15 2 =- - + for x 6 4 G G - . [2] (c) Find the x-coordinate of each point of intersection of y x x 4 3 2 = + + and y x x 2 15 2 =- + - . x = … and x = … [2]

14 0607/31/O/N/20 © UCLES 2020 10 (a) 6 cm 2 cm 10 cm NOT TO SCALE A toilet roll is a cylinder with radius 6 cm and height 10 cm. It has a hollow cylindrical centre of radius 2 cm. Work out the volume of paper in the toilet roll. … cm3 [3] (b) There are 325 million people in the USA. On average, each person uses 23.6 toilet rolls during one year. Calculate the total number of toilet rolls used in the USA in one year. Give your answer in standard form. … [2]

15 0607/31/O/N/20 © UCLES 2020 [Turn over (c) NOT TO SCALE 8 cm 12 cm 10 cm Toilet paper can also be bought in a box. The box is a cuboid. (i) Work out the volume of the box. … cm3 [2] (ii) The box is completely filled with individual sheets of toilet paper, one sheet on top of another. One sheet of toilet paper measures 12 cm by 10 cm and is .1 6 10 cm 2 # - thick. The box is 8 cm deep. Work out the largest number of sheets of toilet paper that can be placed in the box. … [2]

16 0607/31/O/N/20 © UCLES 2020 11 The time taken, t seconds, for the first points to be scored in each of 100 basketball games is shown in the table. Time (t seconds) Frequency 0 1 t G 20 1 20 1 t G 40 4 40 1 t G 60 22 60 1 t G 80 26 80 1 t G 100 31 100 1 t G 120 16 (a) Write down the time interval that is the mode. … 1 t G … [1] (b) One of these games is chosen at random. Work out the probability that the first points in this game were scored in the first 60 seconds. … [2] (c) Work out an estimate of the mean time. … s [2]

17 0607/31/O/N/20 © UCLES 2020 [Turn over (d) (i) Complete the cumulative frequency table. Time (t seconds) Cumulative frequency t G 20 1 t G 40 t G 60 t G 80 t G 100 84 t G 120 100 [2] (ii) Complete the cumulative frequency curve. 100 80 60 40 20 0 20 40 60 Time (seconds) 80 100 120 t 0 10 30 50 70 90 10 30 50 70 90 110 Cumulative frequency [3] (iii) Use your curve to find the median time. … s [1]

18 0607/31/O/N/20 © UCLES 2020 12 U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {2, 3, 4, 5} (a) Write down. (i) n(A) … [1] (ii) Al { … } [1] (b) Use a mathematical symbol to complete each of the following. (i) 2 … A [1] (ii) {3, 4} … A [1] (c) B = {7, 8, 9, 10} (i) List the elements of A B , . … [1] (ii) Find A B + . … [1] (d) U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {2, 3, 4, 5} B = {7, 8, 9, 10} Draw a Venn diagram to show this information. U [3]

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20 0607/31/O/N/20 © UCLES 2020 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 2020 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) October/November 2020 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 2020 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 October/November 2020 © UCLES 2020 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 2020 © UCLES 2020 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 2020 © UCLES 2020 Page 4 of 7 Question Answer Marks Partial Marks 1(a) 4 9 1 1(b) 3 squares shaded 1 1(c)(i) 0.6[0] 1 1(c)(ii) 0.75 1 1(d)(i) 216 1 1(d)(ii) 7.33 2 B1 for 7.334… If 0 scored, SC1 for their answer greater than 2 d.p. correctly rounded to 2 d.p. 2(a)(i) Parallelogram 1 2(a)(ii) 0 oe 1 2(a)(iii) 2 1 2(a)(iv) One diagonal line drawn 1 2(b)(i)(a) (1, 2) 1 2(b)(i)(b) (–2, 0) 1 2(b)(i)(c) (–1, –2) 1 2(b)(ii) 8 2 B1 for 7 to 9 or M1 for 1 2 × 4 × 2 [× 2] soi 3(a) 3667 2 B1 for 3666.66… or M1 for 2 3 × 5500 If 0 scored, SC1 for rounding their decimal to the nearest whole number 3(b) 15 840 2 M1 for 18 000 × 12 100 oe soi by 2160 3(c)(i) 11.2 1 3(c)(ii) 54 1 3(c)(iii) 84 1 4(a)(i) Correct pattern 1 4(a)(ii) [4] 7 10 their 13 1 FT their (i) 4(a)(iii) Add 3 oe 1

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 Page 5 of 7 Question Answer Marks Partial Marks 4(a)(iv) 28 1 4(b) –1 0 3 2 B1 for two of these 4(c) 4n – 1 oe 2 B1 for 4n + k any k or jn – 1 j ≠ 0 5(a)(i) 38 1 5(a)(ii) All angles are 90 or less Obtuse is greater than 90 oe 1 5(b) [a =] 65 [b =] 80 [c =] 35 3 B1 for each 5(c) 60 2 B1 for hexagon has 6 sides soi 6(a) 58 2 B1 for 17 × 3 soi by 51 6(b) 13 2 M1 for 44 – 1 × 5 soi by 39 6(c) 9 2 M1 for 36 4 soi or for three or more correct trials with ‘win = draw’ 7(a)(i) 100 2 B1 for 5 7(a)(ii) 25 2 FT their (i) M1 for 4 their (i) 7(a)(iii) 138 1 7(b) 24 3 M2 for 252 − 72 or M1 for 72 + x2 = 252 8(a)(i) 5 1 8(a)(ii) 1 4 2 or 4.5 or 9 2 3 M1 for 6x – 15 = 12 or 2x – 5 = 4 M1 for correct FT second step to achieve ax = b 8(b) x2 + 3x – 28 final answer 2 B1 for three of x2, [+]7x, −4x, −28 8(c) 5x final answer 2 M1 for cancelling y or numbers 9(a)(i) 2 B1 for correct shape or for minimum in correct quadrant

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 Page 6 of 7 Question Answer Marks Partial Marks 9(a)(ii) (–2, –1) 1 9(b) 2 B1 for correct shape or for maximum in correct quadrant 9(c) –4.37 or 1.37 2 B1 for each If 0 scored, SC1 for –4.4 and 1.4 or giving both coordinates correctly 10(a) 1010 or 1005. … 3 M2 for π × 62 × 10 and π × 22 × 10 or M1 for π × 62 × 10 or π × 22 × 10 10(b) 7.67 × 109 2 B1 for figs 767 10(c)(i) 960 2 M1 for 10 × 12 × 8 soi 10(c)(ii) 500 2 M1 for [ ] [ ] 10 12 8 10 12 0.016 × × × × soi 11(a) [ ] 80 100 t < ≤ 1 11(b) 27 100 oe 2 M1 for 100 n or 27 n 11(c) 76 2 M1 for 10 × 1 + 30 × 4 + 50 × 22 + … at least three of these soi by 7600 11(d)(i) [1] 5 27 53 [84] [100] 2 B1 for two correct 11(d)(ii) Correct curve 3 B2 for their 3 points correctly plotted or B1 for 2 of their points correctly plotted and M1 for curve through their 6 ascending points. 11(d)(iii) 76 to 79 1 FT their ascending curve 12(a)(i) 4 1 12(a)(ii) 0, 1, 6, 7, 8, 9, 10 1 12(b)(i) . . … ∈… 1 12(b)(ii) . … ⊂…. 1 12(c)(i) 2, 3, 4, 5, 7, 8, 9, 10 1 12(c)(ii) ∅ or { } 1

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 Page 7 of 7 Question Answer Marks Partial Marks 12(d) 3 B1for two circles labelled and B1 for elements in two of A, B, ( ) A B ′ ∪ correct 2 3 4 5 7 8 9 10 1 6 A B