Cambridge IGCSE Mathematics - International 0607 — 2021 May/June Paper 3 · Variant 1

This document has 16 pages. Cambridge IGCSE™ DC (CE/CGW) 199831/2 © UCLES 2021 [Turn over CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) May/June 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 [ ]. * 8 6 3 9 1 8 8 8 2 3 *

2 0607/31/M/J/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/M/J/21 © UCLES 2021 [Turn over Answer all the questions. 1 (a) Work out. (i) 36 … [1] (ii) 73 … [1] (b) (i) 4 # 4 # 4 # 4 # 4 # 4 = 4n Write down the value of n. n = … [1] (ii) Write down the value of 40. … [1] (c) Work out. 2 17 1 2 + Give your answer correct to 3 decimal places. … [2] (d) (i) Write 0.000 082 in standard form. … [1] (ii) Work out. ( . ) ( . ) 7 3 10 1 8 10 9 4 # # # - Give your answer in standard form. … [2]

4 0607/31/M/J/21 © UCLES 2021 2 0 x 2 3 4 5 – 3 – 2 – 5 – 4 – 1 – 1 – 2 – 3 – 4 – 5 3 4 5 2 1 y A B 1 C Points A, B and C are plotted on a 1 cm2 grid. (a) Write down the coordinates of (i) point B, ( … , …) [1] (ii) point A. ( … , …) [1] (b) On the grid, plot the point (-3, -1) and label it D. [1] (c) Join A, B, C and D to form a quadrilateral. Write down the mathematical name of quadrilateral ABCD. … [1]

5 0607/31/M/J/21 © UCLES 2021 [Turn over (d) Work out the area of quadrilateral ABCD. … cm2 [2] (e) On the grid, draw the reflection of quadrilateral ABCD in the x-axis. [2]

6 0607/31/M/J/21 © UCLES 2021 3 Ralf records the number of people in each car entering the school car park. The results are shown in the table. Number of people in the car Number of cars 1 8 2 13 3 6 4 3 5 2 (a) Work out the total number of cars that Ralf records. … [1] (b) Work out the total number of people in these cars. … [2] (c) On the grid, draw and label a bar chart to show the information in the table. Number of people in the car Number of cars [4]

7 0607/31/M/J/21 © UCLES 2021 [Turn over 4 (a) Ana is 28 years 3 months old. Change 28 years 3 months into months. … months [2] (b) Ana has three children. The ages of the children are 7 years 11 months 5 years 4 months 2 years 6 months. For these three ages, work out (i) the range, … years … months [1] (ii) the mean. … years … months [3] (c) Jon has a watch that records the number of calories he uses when he goes for a walk. He uses 0.05 calories for each step he takes. He takes 1250 steps for every kilometre he walks. One day he uses 300 calories on a walk. Work out how far he has walked. … km [2]

8 0607/31/M/J/21 © UCLES 2021 5 (a) Complete this sequence of patterns by drawing Pattern 1 and Pattern 5. Pattern 1 Pattern 2 Pattern 3 Pattern 4 Pattern 5 x x x x x x x x x x x x x x x x x x [2] (b) These are the first four terms of a sequence. 4 7 10 13 For this sequence, write down (i) the next term, … [1] (ii) the rule for continuing the sequence. … [1] (c) The nth term of another sequence is 3n2. Work out the first two terms of this sequence. … and … [2] (d) These are the first five terms of a different sequence. 7 15 23 31 39 Find the nth term of this sequence. … [2]

9 0607/31/M/J/21 © UCLES 2021 [Turn over 6 (a) Simplify. y y y 3 4 + - … [1] (b) Solve. (i) x 6 20 + = x = … [1] (ii) x 4 8 = x = … [1] (iii) ( ) x 2 3 14 - = x = … [2] (c) On the number line, show the inequality x 4 H . 0 1 2 3 4 5 6 x [1] (d) Factorise. 5x + 20 … [1] (e) Multiply out the brackets and simplify. ( )( ) x x 6 5 3 + - … [2]

10 0607/31/M/J/21 © UCLES 2021 7 (a) 48° 84° NOT TO SCALE C A B What type of triangle is ABC ? Show how you decide. [2] (b) Work out the size of one exterior angle of a regular pentagon. … [2]

11 0607/31/M/J/21 © UCLES 2021 [Turn over (c) 126° x° 57° 34° NOT TO SCALE A D E C B In the diagram, ADE is a straight line. (i) Find the value of x. x = … [2] (ii) Show that ABCD is not a trapezium. [2]

12 0607/31/M/J/21 © UCLES 2021 8 Here are three unbiased spinners made from regular polygons. 1 4 6 4 5 3 5 6 2 3 1 5 4 6 1 Spinner B Spinner C Spinner A 6 6 3 5 5 6 1 2 (a) (i) For Spinner A work out the probability of getting 6. … [1] (ii) Spinner A is spun twice. Work out the probability of getting 6 each time. … [2] (b) Show that, of the three spinners, Spinner C has the greatest probability of getting 6 on one spin. [4]

13 0607/31/M/J/21 © UCLES 2021 [Turn over 9 (a) Amir has car insurance, home insurance and health insurance. In one year he spends a total of $5775 on insurance in the ratio car : home : health = 2 : 3 : 6. Work out how much he spends on each type of insurance. Car $ … Home $ … Health $ … [3] (b) A company offers Samal health insurance for $850 when it is not bought online. The company offers a 15% reduction when this insurance is bought online. Work out how much this insurance will cost Samal if she buys it online. $ … [2] (c) Terry’s car insurance increases from $900 to $1100. Work out the percentage increase. … % [3]

14 0607/31/M/J/21 © UCLES 2021 10 (a) The line with equation y = mx + 1 passes through the point (3, 19). Work out the value of m. m = … [3] (b) 0 B 8 A NOT TO SCALE y x – 4 In the diagram, the line meets the x-axis at A (-4, 0) and the y-axis at B (0, 8). (i) Find the coordinates of the mid-point of AB. ( … , …) [2] (ii) Find the equation of the line AB. … [3]

15 0607/31/M/J/21 © UCLES 2021 [Turn over 11 In this question, all lengths are in metres. 2.5 2 2 3 NOT TO SCALE x° h The diagram shows a shed in the shape of a prism. (a) Use Pythagoras’ Theorem to show that h = 1.5 . [2] (b) Use trigonometry to find the value of x. x = … [2] (c) (i) The end of the shed is shaded. Calculate this area. … m2 [2] (ii) Work out the volume of the shed. Give the units of your answer. … … [2] Question 12 is printed on the next page.

16 0607/31/M/J/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. 12 0 y x – 3 2 – 10 25 (a) (i) On the diagram, sketch the graph of y x x 3 3 2 = + for x 3 2 G G - . [2] (ii) Find the coordinates of the local minimum. ( … , …) [1] (iii) Find the coordinates of the local maximum. ( … , …) [1] (b) On the diagram, sketch the graph of y x 3 5 2 = - for x 3 2 G G - . [2] (c) Find the coordinates of the point of intersection of the graphs of y x x 3 3 2 = + and y x 3 5 2 = - . ( … , …) [2]

This document consists of 7 printed pages. © UCLES 2021 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/31 Paper 3 (Core) May/June 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 May/June 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 May/June 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 May/June 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 May/June 2021 © UCLES 2021 Page 4 of 7 Question Answer Marks Partial Marks 1(a)(i) 6 1 1(a)(ii) 343 1 1(b)(i) 6 1 1(b)(ii) 1 1 1(c) 0.123 2 B1 for 0.1231… If 0 scored, SC1 for their answer to more than 3dp correctly rounded to 3dp 1(d)(i) 8.2 × 10−5 1 1(d)(ii) 1.314 × 106 2 B1 for 1 314 000 oe 2(a)(i) (4, 3) 1 2(a)(ii) (−2, 3) 1 2(b) (−3, −1) plotted 1 2(c) Parallelogram 1 2(d) 24 2 M1 for 6 × 4 or other correct and complete method 2(e) Correct reflection 2 FT their quadrilateral B1 for two points correctly reflected in x-axis or for correct reflection in the y-axis 3(a) 32 1 3(b) 74 2 M1 for two of 1 × 8, 2 × 13, 3 × 6, 4 × 3, 5 × 2 soi 3(c) Correct, complete bar chart 4 M1 for correct x ‘scale’ M1 for correct linear y scale M2 for 5 bars correct height and equal width or M1 for 3 bars correct height and equal width or for 5 bars correct height but unequal width 4(a) 339 2 M1 for 12 months in one year soi 4(b)(i) 5 years 5 months 1

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2021 © UCLES 2021 Page 5 of 7 Question Answer Marks Partial Marks 4(b)(ii) 5 years 3 months 3 M2 for 7 12 11 5 12 4 2 12 6 3 × + + × + + × + oe or M1 for 3 sumof ages 4(c) 4.8 2 M1 for 300 0.05 soi by 6000 or for 1250 × 0.05 soi by 62.5 or for 1250 their number of steps 5(a) Pattern 1: 6 by 5 Pattern 5: 2 by 1 2 B1 for each 5(b)(i) 16 1 5(b)(ii) +3 oe 1 5(c) 3 12 2 B1 for each If 0 scored, SC1 for answer 0, 3 5(d) 8n – 1 oe 2 B1 for 8n + k any k or for kn – 1 any k ≠ 0 6(a) 6y 1 6(b)(i) 14 1 6(b)(ii) 32 1 6(b)(iii) 10 2 M1 for x – 3 = 7 or for 2x – 6 = 14 6(c) Filled circle at 4 with arrow to right 1 6(d) 5(x + 4) 1 6(e) 6x2 – 13x – 15 2 B1 for three of 6x2, –18x, (+)5x, – 15 7(a) C = 48 Isosceles 2 B1 for each If 0 scored, SC1 for ‘scalene’ with a value of C ≠ 48 7(b) 72 2 B1 for 5 seen 7(c)(i) 37 2 M1 for 360 – (126 + 34 + 57) soi by 143 7(c)(ii) x ≠ 34 or 126 + 57 ≠ 180 oe and BC not parallel to AD 2 B1 for each 8(a)(i) 1 5 oe 1

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2021 © UCLES 2021 Page 6 of 7 Question Answer Marks Partial Marks 8(a)(ii) 1 25 oe 2 FT their (a)(i) M1 for their 1 5 × their 1 5 oe 8(b) P(B) = 2 8 oe or P(C) = 3 10 oe M1 0.25, 0.2, 0.3 or 25%, 20%, 30% or 10 40 , 8 40 , 12 40 or 90°, 72°, 108° A2 A1 for two of the three values in the same form 3 10 > 2 8 and 3 10 > 1 5 oe A1 Correct comparisons 9(a) [Car] 1050 [Home] 1575 [Health] 3150 3 B2 for one value correct or M1 for 5775 2 3 6 + + soi by 525 9(b) 722.5[0] 2 M1 for 0.15 × 850 oe or for 0.85 × 850 oe 9(c) 22.2 or 22.22… 3 M2 for 1100 900 900 − oe or 1100 900 × 100 oe or M1 for 1100 – 900 or 1100 900 10(a) 6 3 B1 for 19 = 3m + 1 M1 for correct first step in solving their equation 10(b)(i) (−2, 4) 2 B1 for each 10(b)(ii) y = 2x + 8 oe 3 B2 for 2x + 8 oe or y = kx + 8 oe or M1 for 8 4 oe or kx + 8 oe 11(a) 2 2 2.5 2 − [= 1.5] M2 M1 for 2.52 = 22 + h2 oe 11(b) 36.9 or 36.86 to 36.87 2 M1 for cos = 2 2.5 or sin = 1.5 2.5 or tan = 1.5 2 11(c)(i) 5.5 2 M1 for 2 × 2 or 1 2 1.5 2 × × soi 11(c)(ii) 16.5 1 FT 3 × their (c)(i) m3 1

0607/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2021 © UCLES 2021 Page 7 of 7 Question Answer Marks Partial Marks 12(a)(i) Correct sketch 2 B1 for correct shape 12(a)(ii) (0, 0) 1 12(a)(iii) (−2, 4) 1 12(b) Correct sketch 2 B1 for correct shape or for minimum on y-axis 12(c) (−1.71, 3.77) 2 B1 for each If 0 scored, SC1 for (−1.7, 3.8)