Cambridge IGCSE Mathematics - International 0607 — 2022 May/June Paper 3 · Variant 3

This document has 20 pages. Any blank pages are indicated. [Turn over Cambridge IGCSE™ * 3 4 4 5 8 2 7 7 8 9 * DC (CE/SG) 303913/2 © UCLES 2022 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 Paper 3 (Core) May/June 2022 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 0607/33/M/J/22 © UCLES 2022 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/22 © UCLES 2022 [Turn over Answer all the questions. 1 (a) Write sixteen thousand and twenty-four in numbers. … [1] (b) Write 8 5 2 as a decimal. … [1] (c) Write down the square number between 10 and 20. … [1] (d) Work out . . . 2 6 5 8 3 2 + . Give your answer correct to 5 significant figures. … [2] (e) Find the value of .4 234. Give your answer correct to 1 decimal place. … [2] (f) Kelly buys candy bars that cost $0.72 each. He buys the greatest number of candy bars he can with $8. (i) Work out the number of candy bars that he buys. … [2] (ii) Work out how much change he receives. $ … [1]

4 0607/33/M/J/22 © UCLES 2022 2 The table shows the type of doughnut and the number of doughnuts sold in a shop on one day. Type Sugar Raisin Cream Jam Iced Number 2000 2500 1500 1250 750 (a) Find the total number of doughnuts sold. … [1] (b) Write down the most popular type of doughnut. … [1] (c) Work out how many more jam doughnuts were sold than iced doughnuts. … [1] (d) Work out the fraction of the doughnuts sold that were jam doughnuts. Give your answer as a fraction in its simplest form. … [2] (e) Write the ratio 1500 : 1250 : 750 in its simplest form. … : … : … [2]

5 0607/33/M/J/22 © UCLES 2022 [Turn over (f) On the grid below, complete the bar chart to show the information in the table. 0 500 1000 1500 2000 2500 3000 Number of doughnuts sold Sugar Raisin Cream Type of doughnut Jam Iced [2] (g) Sugar doughnuts cost $1.25 each. Raisin doughnuts cost $1.50 each. Work out the total cost of 5 sugar doughnuts and 3 raisin doughnuts. $ … [2]

6 0607/33/M/J/22 © UCLES 2022 3 (a) This shape is drawn on a 1cm2 grid. Work out the perimeter and the area of the shape. Give the units of each answer. Perimeter … … Area … … [3] (b) Add one more square to the shape above so that the shape has rotational symmetry of order 2. [1]

7 0607/33/M/J/22 © UCLES 2022 [Turn over (c) (i) Add one more square to the shape above so that the shape has line symmetry. [1] (ii) On your shape, draw the line of symmetry. [1]

8 0607/33/M/J/22 © UCLES 2022 4 – 4 – 3 – 2 – 1 1 2 3 4 5 6 0 – 1 1 2 3 4 5 6 7 – 2 – 3 – 4 – 5 – 6 – 7 y x C A B D The diagram shows quadrilateral ABCD drawn on a 1cm2 grid. (a) Write down the coordinates of points A, B and C. A (… , …) B (… , …) C (… , …) [3] (b) Write down the mathematical name of (i) quadrilateral ABCD, … [1] (ii) triangle BCD. … [1]

9 0607/33/M/J/22 © UCLES 2022 [Turn over (c) Use Pythagoras’ Theorem to calculate the length of AD. AD = … cm [2] (d) Use trigonometry to calculate angle DCB. Angle DCB = … [2] (e) Reflect quadrilateral ABCD in the y-axis. [1]

10 0607/33/M/J/22 © UCLES 2022 5 To hire a van, a company charges $2.50 for each kilometre travelled plus a fixed charge of $800. (a) The total cost is T dollars when the distance travelled is k kilometres. Write an equation for T in terms of k. … [2] (b) Kiera hires a van and travels 324 kilometres. Find the total amount she has to pay. $ … [2] (c) Misty hires a van and pays $1045. Find how many kilometres she travels. … km [2]

11 0607/33/M/J/22 © UCLES 2022 [Turn over 6 The cumulative frequency curve shows the heights, in cm, of 100 adult Emperor penguins. 0 100 105 110 115 Height (cm) 120 125 130 10 20 30 40 50 60 70 80 90 100 Cumulative frequency Use the curve to estimate (a) the median, … cm [1] (b) the lower quartile, … cm [1] (c) the interquartile range, … cm [1] (d) the number of Emperor penguins that have a height of 120 cm or more. … [2]

12 0607/33/M/J/22 © UCLES 2022 7 Greta joins a gym for one year. (a) She can pay her membership every week, every month or in one payment for the whole year. Payment type Cost Weekly $5.95 Monthly $25.00 Yearly $297.75 Work out which payment type is the cheapest. Show all your working. … [3] (b) On the cycle machine, Greta cycles a distance of 3.2 km in 10 minutes. Work out her average speed in km/h. … km/h [2] (c) On the treadmill, Greta walks at 6.3 km/h. (i) Work out the distance she walks in 27 minutes. Give your answer in kilometres. … km [2] (ii) Change 6.3 km/h to m/min. … m/min [2]

13 0607/33/M/J/22 © UCLES 2022 [Turn over 8 C 5 cm B 136° NOT TO SCALE D A O The diagram shows a circle, centre O, radius 5 cm. Angle AOB = 136° and CBD is a tangent to the circle at B. (a) Find the size of (i) angle OBC, Angle OBC = … [1] (ii) angle OAB, Angle OAB = … [2] (iii) angle ABD. Angle ABD = … [1] (b) Show that the area of the minor sector AOB is 29.7 cm2, correct to 1 decimal place. [2] (c) Work out the length of the minor arc AB. … cm [2]

14 0607/33/M/J/22 © UCLES 2022 9 (a) Solve. (i) x 6 42 = x = … [1] (ii) x 4 2 2 - = x = … [2] (b) Factorise completely. b b 7 14 2 - … [2] (c) Expand. ( ) a 4 2 5 - … [2] (d) Solve the simultaneous equations. Show all your working. a b a b 5 2 12 6 11 - = + = a = … b = … [3]

15 0607/33/M/J/22 © UCLES 2022 [Turn over (e) Find the value of x in each of the following. (i) a a ax 2 6 = x = … [1] (ii) a a a x 3 15 # = x = … [1] (f) Write as a single fraction in its simplest form. (i) x x 3 5 2 + … [2] (ii) mn m n 5 15 2 2 ' … [3]

16 0607/33/M/J/22 © UCLES 2022 10 y x 10 – 10 – 2 2 0 (a) On the diagram, sketch the graph of y x x 1 3 = + for values of x between 2 - and 2. [2] (b) Write down the equation of the vertical asymptote. … [1] (c) Find the coordinates of the local minimum. (… , …) [2] (d) On the same diagram, sketch the graph of y x 5 = for x 2 2 G G - . [2] (e) Solve the equation x x x 1 5 3 + = for values of x between 2 - and 2. … and … [2]

17 0607/33/M/J/22 © UCLES 2022 11 The probability that it snows on any day in February is 10 6 . If it snows, the probability that Maud goes for a walk is 5 2. If it does not snow, the probability that Maud goes for a walk is 7 5. (a) Complete the tree diagram to show this information. … … … … … snows goes for a walk does not go for a walk goes for a walk does not go for a walk does not snow 10 6 [3] (b) One day in February is chosen at random. Find the probability that it snows and Maud does not go for a walk. … [2]

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20 0607/33/M/J/22 © UCLES 2022 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 Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge. BLANK PAGE

This document consists of 8 printed pages. © UCLES 2022 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 Paper 3 (Core) May/June 2022 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 2022 series for most Cambridge IGCSE, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 2 of 8 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.

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 3 of 8 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

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 4 of 8 Question Answer Marks Partial Marks 1(a) 16 024 1 1(b) 8.4 1 1(c) 16 1 1(d) 0.38095 cao 2 B1 for 0.380952… If 0 scored, SC1 for their value greater than 5 sf correctly rounded to 5sf. 1(e) 320.2 2 B1 for 320[.15…] If 0 scored, SC1 for their value greater than 1 dp correctly rounded to 1 dp 1(f)(i) 11 2 B1 for 8 0.72 soi by 11.11… or for a list (at least five correct) of 0.72, 1.44, 2.16, 2.88, 3.60, 4.32, 5.04, 5.76, 6.48, 7.20, 7.92 1(f)(ii) 0.08 1 FT an integer < 11 for their (f)(i) 2(a) 8000 1 2(b) Raisin 1 2(c) 500 1 2d) 5 32 cao 2 B1 for 1250 8000 their or 625 250 125 50 25 4000 1600 800 320 160 or or or or 2(e) 6 : 5 : 3 2 B1 for correct cancelation but not in its simplest form 2(f) Correct ruled bar chart 2 B1 for 3 correct height bars with equal widths or 4 correct height bars with unequal widths

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 5 of 8 Question Answer Marks Partial Marks 2(g) 10.75 2 M1 for 5 1.25  or 3 1.50  3(a) 10 cm 4 cm2 3 B1 for 10 B1 for 4 B1 for both cm and cm2 correct 3(b) Correct square added 1 3(c)(i) Correct square added 1 3(c)(ii) Correct line drawn 1 FT their diagram

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 6 of 8 Question Answer Marks Partial Marks 4(a) A(6,5) B(6,0) C(1, 3)  3 B1 for each 4(b)(i) Trapezium 1 4(b)(ii) Right-angled or scalene 1 4(c) 7.07 or 7.071… 2 M1 for 2 2 5 5  4(d) 59.0 or 59.03 to 59.04 2 M1 for 5 tan[...] 3  4(e) Correct reflection in y-axis ( 6,5),( 6,0),( 1, 3),( 1,0)     1 5(a) 2.5[0] 800 T k   oe 2 B1 for 2.5[0] 800 k  5(b) 1610 2 M1 for 324 2.5[0]  5(c) 98 2 B1 for correct substitution in their 800 2.5 T k   or 1045 – 800 6(a) 115 1 6(b) 112 1 6(c) 7 1 6(d) 20 2 B1 for 80 seen 7(a) 52 5.95 309.40   M1 12 25 300   M1 year A1 If only M1 scored, SC1 for their correct decision 7(b) 19.2 2 M1 for 3.2[ 60] 10  oe 7(c)(i) 2.835 2 M1 for 6.3 27 [60] oe 7(c)(ii) 105 2 M1 for 1000 60  oe 8(a)(i) 90 1

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 7 of 8 Question Answer Marks Partial Marks 8(a)(ii) 22 2 M1 for 180 136  oe 8(a)(iii) 68 1 FT 180 – their (i) – their (ii) 8(b) 136 360 π 25  M1 29.67… A1 8(c) 11.9 or 11.86 to 11.87 2 136 1 for 2 π 5 oe 360  M 9(a)(i) 7 1 9(a)(ii) 3 2 M1 for 2 2 4 x   or 4 2 2 2 x   9(b) 7 ( 2) b b  final answer 2 B1 for (7 14) b b  or 2 7( 2 ) b b  9(c) 8 20 a  final answer 2 B1 for any 8a or 20  9(d) 17 34 a  1 M1 for eliminating one variable (a or b) 2 1 a b   2 B1 for each If 0 scored, SC1 for correct substitution and evaluation to find the other variable or SC1 for correct answers with no working shown 9(e)(i) 4 1 9(e)(ii) 12 1 9(f)(i) 11 15 x cao 2 M1 for correct denominator 9(f)(ii) 3n m cao 3 M1 for 2 2 15 5 mn m n  M1 for correct partial cancellation 10(a) Correct sketch drawn 2 B1 for maximum and minimum in correct quadrants or for one correct branch

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 8 of 8 Question Answer Marks Partial Marks 10(b) 0 x  1 10(c) (0.76[0],1.75) or (0.7598...,1.754 to 1.755) 2 B1 for each If 0 scored, SC1 for (0.76,1.8) 10(d) Correct straight line drawn 2 B1 for positive slope B1 for passing through the origin 10(e) 0.457 or 0.4568 to 0.4569 0.457  or 0.4569  to 0.4568  2 B1 for each 11(a) Correct tree diagram 3 B2 for 3 or 4 correct probabilities correctly placed B1 for 2 correct probabilities correctly placed 11(b) 9 25 oe 2 M1 for 6 3 10 5 their 