Cambridge IGCSE Mathematics - International 0607 — 2020 May/June Paper 3 · Variant 1

Cambridge IGCSE™ This document has 16 pages. Blank pages are indicated. DC (CE/FC) 183470/2 © UCLES 2020 [Turn over * 8 4 7 0 7 7 7 3 6 0 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) May/June 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/M/J/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/M/J/20 © UCLES 2020 [Turn over Answer all the questions. 1 24 people take part in a cookie-eating competition. The number of cookies eaten by each person in two minutes is recorded. 11 12 13 8 12 8 12 10 9 11 8 13 11 10 12 9 9 10 10 9 10 9 9 12 (a) Complete the frequency table. Number of cookies 8 9 10 11 12 13 Frequency 3 [2] (b) Find (i) the mode, … [1] (ii) the range, … [1] (iii) the median, … [1] (iv) the mean, … [1] (v) the interquartile range. … [2] (c) Complete the bar chart. 0 1 8 9 10 Number of cookies Frequency 11 12 13 2 3 4 5 6 7 [2]

4 0607/31/M/J/20 © UCLES 2020 2 (a) 1 2 3 4 5 6 7 8 9 10 From this list of numbers, write down (i) a square number, … [1] (ii) a triangle number, … [1] (iii) a prime number, … [1] (iv) a factor of 13, … [1] (v) a multiple of 6. … [1] (b) Work out 65% of 34. … [2] (c) Write 9876.543 (i) correct to 2 decimal places, … [1] (ii) correct to 4 significant figures, … [1] (iii) correct to the nearest hundred. … [1] (d) Write your answer to part (c)(iii) in standard form. … [1]

5 0607/31/M/J/20 © UCLES 2020 [Turn over (e) Work out. Give each answer as a fraction in its simplest form. (i) 5 2 3 1 + … [1] (ii) 8 5 4 1 - … [1] (iii) 3 10 3 6 5 # … [1]

6 0607/31/M/J/20 © UCLES 2020 3 (a) Write down the rule for continuing each sequence. (i) 86, 78, 70, 62, … … [1] (ii) 4, 12, 36, 108, … … [1] (iii) 80, 40, 20, 10, … … [1] (b) The nth term of a sequence is n 2 1 2 + . Work out the first two terms of this sequence. … , … [2] (c) These are the first four terms of another sequence. 8 19 30 41 (i) Find the next two terms of this sequence. … , … [2] (ii) Find the nth term of this sequence. … [2] (iii) Use your expression from part (ii) to find the 30th term. … [1]

7 0607/31/M/J/20 © UCLES 2020 [Turn over 4 23 cm 18 cm A B NOT TO SCALE C D 52° E 18 cm ABCD is a rectangle and EDC is a straight line. DE = BC = 18 cm, AB = 23 cm and angle BCA = 52°. Find (a) angle BAC, Angle BAC = … [1] (b) angle AED, Angle AED = … [1] (c) angle EAC, Angle EAC = … [2] (d) AE, AE = … cm [2] (e) the total perimeter of the shape ABCE. … cm [1]

8 0607/31/M/J/20 © UCLES 2020 5 (a) Cinzia goes to the zoo with her mother. Cinzia is 12 years old. The entrance fee is $25 for each adult and $14 for each child under the age of 16 years. Work out the total entrance fee for Cinzia and her mother and how much change they receive from $50. Total entrance fee $ … Change $ … [2] (b) Cinzia and her mother arrive at the zoo at 11 35 and leave at 15 45. Find the time, in hours and minutes, that they are at the zoo. … h … min [1] (c) Cinzia sees this notice. Monkeys 500 metres Cinzia can walk at 5 km/h. Find how many minutes it takes Cinzia to walk to the monkeys. … min [3]

9 0607/31/M/J/20 © UCLES 2020 [Turn over 6 50 cm 24 cm 4 m NOT TO SCALE The diagram shows a cylindrical pipe. The external radius is 50 cm and the internal radius is 24 cm. (a) Find the shaded area. … cm2 [3] (b) The pipe is 4 metres long. (i) Change 4 metres into centimetres. … cm [1] (ii) Find the volume of the pipe. … cm3 [1] (c) Work out the area of the outside curved surface of the pipe. … cm2 [2]

10 0607/31/M/J/20 © UCLES 2020 7 (a) Solve. (i) x x 4 6 8 14 = - + x = … [2] (ii) ( ) x 2 3 11 + = x = … [2] (b) C M N 2 3 = + (i) Find C when M = 1.8 and N = 1.3 . C = … [2] (ii) Find M when C = 8.4 and N = 0.6 . M = … [2] (iii) Rearrange the formula to make N the subject. N = … [2]

11 0607/31/M/J/20 © UCLES 2020 [Turn over 8 A boat sails 300 m on a bearing of 060° from A to B. It then changes course and sails 220 m on a bearing of 150° from B to C. The boat then returns directly to A. (a) On the diagram, sketch the path of the boat. Show the distances and bearings that you have been given. NOT TO SCALE North A [4] (b) Angle ABC = 90°. (i) Calculate angle BAC. Angle BAC = … [2] (ii) Find the bearing of C from A. … [1]

12 0607/31/M/J/20 © UCLES 2020 9 8 –1 0 3.5 x y – 4 The diagram shows the graph of y x x 2 5 3 2 =- + + for . x 1 3 5 G G - . (a) Use your calculator to find (i) the coordinates of the point of intersection of the graph with the y-axis, ( … , …) [1] (ii) the coordinates of the points of intersection of the graph with the x-axis, ( … , …) and ( … , …) [2] (iii) the coordinates of the local maximum. ( … , …) [2] (b) On the diagram, sketch the graph of y x 2 1 = + . [2] (c) Find the coordinates of the points of intersection of y x x 2 5 3 2 =- + + and y x 2 1 = + . ( … , …) and ( … , …) [2]

13 0607/31/M/J/20 © UCLES 2020 [Turn over 10 B A C 1 2 3 4 5 6 7 8 9 10 x y –10 –9 –8 –7 – 6 –5 – 4 –3 –2 –10 –9 –8 –7 – 6 –5 – 4 –3 –2 –1 1 2 3 4 5 6 7 8 9 10 0 –1 (a) Reflect shape A in the y-axis. [1] (b) Describe fully the single transformation that maps shape A onto shape B. … … [3] (c) Describe fully the single transformation that maps shape A onto shape C. … … [2] (d) Enlarge shape A with centre (0, 0) and scale factor 2 - . [2]

14 0607/31/M/J/20 © UCLES 2020 11 (a) In a class of 24 students • 10 students wear glasses (G ) • 12 students have black hair (B ) • 5 students do not wear glasses and do not have black hair. (i) Complete the Venn diagram. G U B … … … … [2] (ii) Describe in words the set G B + . Students who … [1] (iii) One of the 24 students is chosen at random. Write down the probability that this student wears glasses but does not have black hair. … [1] (iv) On the Venn diagram below, shade the region G B + l . G U B [1]

15 0607/31/M/J/20 © UCLES 2020 (b) Another class has 20 students. In this class • 5 students wear glasses and have black hair • 8 students wear glasses and do not have black hair • all the students either wear glasses or have black hair or both. (i) Complete the Venn diagram. G … … … U B [2] (ii) Write down the number of students in this class who have black hair. … [1]

16 0607/31/M/J/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) May/June 2020 MARK SCHEME Maximum Mark: 96 Published Students did not sit exam papers in the June 2020 series due to the Covid-19 global pandemic. This mark scheme is published to support teachers and students and should be read together with the question paper. It shows the requirements of the exam. The answer column of the mark scheme shows the proposed basis on which Examiners would award marks for this exam. Where appropriate, this column also provides the most likely acceptable alternative responses expected from students. Examiners usually review the mark scheme after they have seen student responses and update the mark scheme if appropriate. In the June series, Examiners were unable to consider the acceptability of alternative responses, as there were no student responses to consider. Mark schemes should usually be read together with the Principal Examiner Report for Teachers. However, because students did not sit exam papers, there is no Principal Examiner Report for Teachers for the June 2020 series. Cambridge International will not enter into discussions about these mark schemes. Cambridge International is publishing the mark schemes for the June 2020 series for most Cambridge IGCSE™ and Cambridge International A & AS Level components, and some Cambridge O Level components.

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 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 May/June 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 May/June 2020 © UCLES 2020 Page 4 of 7 Question Answer Marks Partial Marks 1(a) [3] 6 5 3 5 2 2 B1 for 3 or 4 correct 1(b)(i) 9 1 1(b)(ii) 5 1 1(b)(iii) 10 1 1(b)(iv) 10.3 or 10.29… 1 1(b)(v) 3 2 B1 for 12 or 9 seen 1(c) Correct bar chart with heights at [3], 6, 5, 3, 5, 2 2 FT from their (a) B1 for 3 or 4 correct heights with equal widths or 5 correct heights and unequal widths. 2(a)(i) 1 or 4 or 9 1 2(a)(ii) 1 or 3 or 6 or 10 1 2(a)(iii) 2 or 3 or 5 or 7 1 2(a)(iv) 1 1 2(a)(v) 6 1 2(b) 22.1 2 M1 for 65 34 100 × 2(c)(i) 9876.54 1 2(c)(ii) 9877 1 2(c)(iii) 9900 1 2(d) 9.9[00] × 103 1 FT their (c)(iii) 2(e)(i) 11 15 1 2(e)(ii) 3 8 1 2(e)(iii) 11 4 or 3 2 4 1 3(a)(i) Subtract 8 oe 1 3(a)(ii) Multiply by 3 oe 1

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2020 © UCLES 2020 Page 5 of 7 Question Answer Marks Partial Marks 3(a)(iii) Divide by 2 or multiply by 1 2 oe 1 3(b) 3, 9 2 B1 for each If 0 scored, SC1 for 1 and 3 3(c)(i) 52, 63 2 B1 for 52 B1 for their 52 + 11 3(c)(ii) 11n – 3 2 B1 for 11n – j or kn – 3, k ≠ 0 3(c)(iii) 327 1 FT their (ii) 4(a) 38 1 4(b) 45 1 4(c) 97 2 BI for EAD = 45 or DAC = 52 4(d) 25.5 or 25.45 to 25.46 2 M1 for 182 + 182 or for [ ] 18 sin45 AE = oe 4(e) 107 or 107.4 to 107.5 1 FT their (d) 5(a) 39 11 2 B1 for 39 B1FT for 50 – their 39 correctly evaluated 5(b) 4 h 10 min 1 5(c) 6 3 M2 for 500 60 5 1000 × × oe or M1 for distance speed soi 500 5 6(a) 6040 or 6044 or 6044.4 to 6045.2… 3 M2 for π502 – π242 or M1 for π502 or π242 6(b)(i) 400 1 6(b)(ii) 2 420 000 or 2 416 000 to 2 420 000 1 6(c) 126 000 or 125 663 to 125 700 2 M1 for 2π × 50 × their 400 oe 7(a)(i) –5 2 M1 for 4x – 8x = 14 + 6 or better 7(a)(ii) 2.5 oe 2 M1 for 2x + 6 = 11 or x + 3 = 5.5 oe 7(b)(i) 7.5 or 1 7 2 2 M1 for 2 × 1.8 + 3 × 1.3 7(b)(ii) 3.3 2 M1 for 8.4 = 2M + 3 × 0.6

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2020 © UCLES 2020 Page 6 of 7 Question Answer Marks Partial Marks 7(b)(iii) 2 3 C M − or 2 3 3 C M − 2 M1 for C – 2M = 3N or 2 3 3 C M N = + 8(a) Correct sketch 4 B1 for 60 bearing approximately correct at A (0 to 90) B1 for 150 bearing approximately correct at B (90 to 180) B2 for all four labels marked in correct position or B1 for any two labels marked in correct position 8(b)(i) 36 or 36.3 or 36.25… 2 M1 for 220 tan 300 = oe 8(b)(ii) [0]96 or [0]96.3 or [0]96.25… 1 FT their (i) + 60 9(a)(i) (0, 3) 1 9(a)(ii) (–0.5, 0), (3, 0) 2 B1 for each 9(a)(iii) (1.25, 6.125) 2 B1 for each coordinate 9(b) Correct sketch with ruled line 2 B1 for correct y-intercept or positive slope 9(c) (–0.5, 0), (2, 5) 2 B1 for each 10(a) Correct reflection (–1, 2), (–4, 2), (–1, 4) and (–4, 4) 1 10(b) Rotation 90 clockwise oe About origin oe 3 B1 for each 10(c) Translation 3 4    2 B1 for each 10(d) Correct enlargement (–2, –4), (–2, –8), (–8, –4), (–8, –8) 2 B1 for correct enlargement, wrong centre or correct centre, wrong scale factor

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2020 © UCLES 2020 Page 7 of 7 Question Answer Marks Partial Marks 11(a)(i) Correct Venn diagram 2 B1 for 2 or 3 correct entries 11(a)(ii) wear glasses and have black hair. 1 11(a)(iii) 7 24 1 FT their 7 11(a)(iv) Correct region shaded 1 11(b)(i) Correct Venn diagram 2 B1 for 5, 8 or 7 seen in correct place 11(b)(ii) 12 1 FT their Venn diagram