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

This document has 16 pages. Any blank pages are indicated. Cambridge IGCSE™ DC (CE/CGW) 199829/2 © UCLES 2021 [Turn over CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 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 7 0 1 2 3 0 4 2 0 *

2 0607/33/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 0607/33/M/J/21 © UCLES 2021 [Turn over Answer all the questions. 1 (a) (i) Write in words 78 616. … [1] (ii) Write 78 616 correct to the nearest thousand. … [1] (iii) Write 78 616 correct to 3 significant figures. … [1] (b) Work out. (i) . . . . 4 25 3 53 2 45 1 474 - + … [1] (ii) 729 3 … [1] (iii) . . 2 43 1 65 2 2 + Give your answer correct to 2 decimal places. … [2] (c) (i) Write down all the factors of 12. … [2] (ii) Find the highest common factor (HCF) and the lowest common multiple (LCM) of 12 and 18. HCF … LCM … [3]

4 0607/33/M/J/21 © UCLES 2021 2 Owen carried out a survey of the weather in 2020. He randomly chose some days from each month and recorded the type of weather for each day. The results are shown in the table. Type of weather Tally Frequency Cloud IIII II Rain IIII III Sun IIII IIII IIII III Snow II Fog IIII (a) Complete the frequency column of the table. [1] (b) Work out the total number of days Owen chose in his survey. … [1] (c) Write down the most common type of weather in Owen’s survey. … [1] (d) On the grid, draw a bar chart to show the information in the table. Cloud 0 2 4 6 8 10 12 14 16 18 Rain Sun Type of weather Frequency Snow Fog 20 [2]

5 0607/33/M/J/21 © UCLES 2021 [Turn over (e) One of these days is chosen at random. Work out the probability that the type of weather on this day is Sun. … [1] (f) Use the information in the table to estimate how many days in one year (365 days) will have Rain. … [2] (g) Owen makes a pie chart using the information in the table. Work out the sector angle for Cloud. … [2]

6 0607/33/M/J/21 © UCLES 2021 3 (a) These are the first four terms of a sequence. 800 400 200 100 For this sequence, write down (i) the next two terms, … , … [2] (ii) the rule for continuing the sequence. … [1] (b) These are the first six terms of a different sequence. -5 -3 −1 1 3 5 Find the nth term of this sequence. … [2] (c) The nth term of another sequence is 6n + 5. (i) Work out the first three terms of this sequence. … , … , … [2] (ii) Rearrange the formula P = 6n + 5 to make n the subject. n = … [2]

7 0607/33/M/J/21 © UCLES 2021 [Turn over 4 (a) A packet of breakfast cereal costs $2.80 . (i) Work out the greatest number of these packets that can be bought with $20. … [2] (ii) Work out how much of the $20 is left. $ … [1] (b) The breakfast cereal contains only grain, fruit and nuts. The ratio, by mass, is grain : fruit : nuts = 16 : 7 : 2. Work out the mass of each ingredient in a box containing 500 g of cereal. Grain … g Fruit … g Nuts … g [3] (c) A box of the cereal normally contains 500 g. In a special offer, the mass of cereal in a box is increased by 12%. Work out the total mass of cereal in a special offer box. … g [2]

8 0607/33/M/J/21 © UCLES 2021 5 (a) 40° NOT TO SCALE B A C D y° x° ABC is an isosceles triangle and ACD is a straight line. (i) Find the value of x and the value of y. x = … y = … [2] (ii) Find the size of the reflex angle at B. … [1] (b) NOT TO SCALE z° 155° Find the value of z. z = … [3]

9 0607/33/M/J/21 © UCLES 2021 [Turn over 6 An examination consists of two papers, Paper 1 and Paper 2. The scores for each of nine candidates are shown below. Paper 1 75 73 68 60 60 55 47 33 15 Paper 2 29 34 26 31 25 19 20 17 6 (a) Complete the scatter diagram. The first five points have been plotted for you. 0 10 20 Paper 2 30 40 0 10 20 30 40 Paper 1 50 60 70 80 [2] (b) What type of correlation is shown in the scatter diagram? … [1] (c) (i) Work out the mean of the Paper 1 scores and the mean of the Paper 2 scores. Mean Paper 1 = … Mean Paper 2 = … [2] (ii) On the scatter diagram, draw a line of best fit. [2] (d) Sajid scored 22 on Paper 2. Use your line of best fit to estimate his score on Paper 1. … [1]

10 0607/33/M/J/21 © UCLES 2021 7 (a) Simplify. 2x + 3y + 4x - y … [2] (b) Solve. 4x - 3 = 9 x = … [2] (c) Multiply out the brackets. ( ) x x x 3 2 5 2 - … [2] (d) Write as a single fraction in its simplest form. (i) y y 8 3 5 2 2 ' … [2] (ii) x x 7 4 3 + … [2]

11 0607/33/M/J/21 © UCLES 2021 [Turn over 8 – 6 – 4 – 2 2 6 0 4 8 2 3 A B 4 5 1 y x (a) Work out the coordinates of the mid-point of line AB. ( … , …) [2] (b) Find the equation of line AB. … [3] (c) (i) On the grid, draw the line y = 2. [1] (ii) Write down the coordinates of the point where the line y = 2 crosses line AB. ( … , …) [1]

12 0607/33/M/J/21 © UCLES 2021 9 18 m 24 m 31 m NOT TO SCALE 43 m y m The diagram shows a rectangle with a triangular corner cut off. (a) Work out the area of the shaded shape. Give the units of your answer. … … [5] (b) Use Pythagoras’ Theorem to work out the value of y. y = … [2] (c) Work out the perimeter of the shaded shape. … m [3]

13 0607/33/M/J/21 © UCLES 2021 [Turn over 10 0 x 2 C A B 3 4 5 6 7 – 3 – 2 – 5 – 4 – 1 – 1 – 2 – 3 – 4 3 4 5 2 7 8 9 6 1 y 1 (a) Describe fully the single transformation which maps triangle A onto triangle B. … … [2] (b) Describe fully the single transformation which maps triangle A onto triangle C. … … [3] (c) Reflect triangle A in the line x = 3. Label the image X. [2] (d) Rotate triangle A by 90° clockwise about (0, 0). Label the image Y. [2]

14 0607/33/M/J/21 © UCLES 2021 11 10 – 1 0 2 – 3 y x (a) (i) On the diagram, sketch the graph of y x x 2 1 2 = + + for x 3 2 G G - . [2] (ii) Find the coordinates of the local minimum. ( … , …) [1] (b) On the diagram, sketch the graph of y 2x = for x 3 2 G G - . [2] (c) Find the x-coordinate of each point of intersection of y x x 2 1 2 = + + and y 2x = . … and … [2]

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16 0607/33/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. BLANK PAGE

This document consists of 7 printed pages. © UCLES 2021 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 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.

0607/33 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. 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.

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2021 © UCLES 2021 Page 3 of 7 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

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2021 © UCLES 2021 Page 4 of 7 Question Answer Marks Partial Marks 1(a)(i) Seventy eight thousand six hundred [and] sixteen 1 1(a)(ii) 79 000 1 1(a)(iii) 78 600 1 1(b)(i) 5.45 1 1(b)(ii) 9 1 1(b)(iii) 2.94 2 B1 for 2.937… If 0 scored, SC1 for their answer of more than 2dp correctly rounded to 2dp 1(c)(i) 1, 2, 3, 4, 6, 12 2 B1 for 4 or 5 correct values 1(c)(ii) [HCF =] 6 [LCM=] 36 3 B1 for [HCF =] 6 B2 for [LCM=] 36 or B1 for 36k, k integer If 0 scored, SC1 for correct answers reversed or for 12 = 2 × 2 × 3 or 2 × 6 or 18 = 2 × 3 × 3 or 3 × 6 2(a) 7, 8, 18, 2, 5 1 2(b) 40 1 2(c) Sun 1 2(d) Correct diagram 2 B1 for 3 correct heights, bars equal widths or for 5 correct heights, bars unequal widths 2(e) 1 8 40 their their oe 1 2(f) 73 2 M1 for 8 40 their their 2(g) 63 2 M1 for 7 40 their their or 360 40 their 3(a)(i) 50, 25 2 B1 for each 3(a)(ii) ÷2 oe 1 3(b) 2n – 7 oe 2 B1 for 2n + k any k or for pn – 7 p ≠ 0

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2021 © UCLES 2021 Page 5 of 7 Question Answer Marks Partial Marks 3(c)(i) 11, 17, 23 2 B1 for two correct values in correct position If 0 scored, SC1 for 5, 11, 17 3(c)(ii) 5 6 − P or 6 P − 5 6 final answer 2 B1 for P – 5 = 6n or for 6 P = n + 5 6 4(a)(i) 7 2 M1 for 20 ÷ 2.8[0] soi by 7.14… 4(a)(ii) 0.4[0] 1 FT their (a)(i) 4(b) 320 140 40 3 B2 for one correct or M1 for 500 16 7 2 + + soi by 20 4(c) 560 2 M1 for 500 × 0.12 oe soi by 60 5(a)(i) [x =] 70 [y =] 110 2 B1 for each If 0 scored, SC1 for y = 180 – their x evaluated 5(a)(ii) 320 1 5(b) 115 3 M2 for 540 – (90 + 90 + 90 + 155) or B1 for 540 soi or (90 + 90 + 90 + 155) soi by 425 6(a) Four points correctly plotted 2 B1 for two or three points correctly plotted 6(b) Positive 1 6(c)(i) P1 = 54 P2 = 23 2 B1 for each 6(c)(ii) Ruled line through mean point and within tolerance 2 M1 for ruled line through mean point with positive gradient but not within tolerance or for ruled line within tolerance but not through mean point 6(d) 50 to 54 1 FT their line with positive gradient 7(a) 6x + 2y final answer 2 B1 for 6x or (+) 2y 7(b) 3 2 M1 for 4x = 9 + 3 soi or for x − 3 4 = 9 4 soi 7(c) 6x3 – 15x2 final answer 2 B1 for 6x3 or – 15x2

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2021 © UCLES 2021 Page 6 of 7 Question Answer Marks Partial Marks 7(d)(i) 15 16 y final answer 2 M1 for 2 3 8 y × 5 2y 7(d)(ii) 19 21 x final answer 2 M1 for correct common denominator 8(a) 1 2 ,1 2       2 B1 for each 8(b) y = 2x – 4 3 B2 for 2x – 4 oe or y = kx – 4 oe or B1 for 10 5 oe or kx – 4 oe 8(c)(i) Correct ruled line 1 8(c)(ii) (3, 2) 1 FT their(c)(i) 9(a) 1117 4 M3 for 1 43 31 24 18 2 × − × × oe OR M1 for 43 × 31 soi by 1333 M1 for 1 24 18 2 × × soi by 216 m2 1 9(b) 30 2 M1 for 242 + 182 soi 9(c) 136 3 M2 for 2 × (43 + 31) – (24 + 18) + their 30 oe or M1 for (43 – 24) or (31 – 18) soi by 19 or 13 10(a) Translation 7 5     −   2 B1 for each 10(b) Enlargement [scale factor] 3 [Centre] (−2, 0) 3 B1 for each 10(c) Correct reflection (5, 1) (8, 1) (8, 2) 2 B1 for correct reflection in any vertical line or for correct reflection in y = 3 10(d) Correct rotation (1, –1) (1, 2) (2, 2) 2 B1 for correct rotation 90 anticlockwise about (0, 0) or for correct orientation, wrong position

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2021 © UCLES 2021 Page 7 of 7 Question Answer Marks Partial Marks 11(a)(i) Correct quadratic sketch 2 B1 for correct shape or for minimum in correct quadrant 11(a)(ii) (−1, 0) 1 11(b) Correct exponential sketch 2 B1 for correct shape but crossing x-axis 11(c) 0 −1.58 or –1.579 to –1.578 2 B1 for each