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

Cambridge IGCSE™ This document has 16 pages. Blank pages are indicated. DC (MB) 207017 © UCLES 2020 [Turn over * 7 3 2 6 2 4 8 9 0 0 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 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 0607/33/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 0607/33/O/N/20 © UCLES 2020 [Turn over Answer all the questions. 1 Ben was born on 25th March, 1936. (a) Write the number 1936 in words. … [1] (b) Work out how old Ben is on the 25th March, 2020. … [1] (c) Work out the year of Ben’s 99th birthday. … [1] (d) Find 1936 . … [1] (e) Write down 1936 (i) correct to the nearest 10, … [1] (ii) correct to 2 significant figures, … [1] (iii) in standard form. … [1] (f) Write down a multiple of 1936. … [1]

4 0607/33/O/N/20 © UCLES 2020 2 The number of seconds that it took each of 15 students to run 200 metres is shown below. 32 35 29 41 41 39 51 57 45 62 42 53 38 43 60 (a) Work out the mean. … s [1] (b) Complete the stem-and-leaf diagram to show this information. Key … | … represents … [3] (c) Find (i) the range, … s [1] (ii) the mode, … s [1] (iii) the median, … s [1] (iv) the interquartile range. … s [2]

5 0607/33/O/N/20 © UCLES 2020 [Turn over 3 A supermarket sells saving stamps for $0.10 each. These stamps are stuck onto pages in a special stamp book. (a) Each page of the stamp book has 35 stamps. Work out how much is paid for the stamps to fill one page. $ … [1] (b) It costs $49 to fill the book with stamps. Find the number of pages in the book. … [2] (c) Each full book of stamps can be used in the supermarket to pay for food costing $52. (i) Work out how much is saved by paying for food with a full book of stamps. $ … [1] (ii) Work out the answer to part (i) as a percentage of $49. … % [2] (d) Fred buys fruit and coffee for $49. The ratio cost of fruit : cost of coffee = 3 : 4. Find the cost of the coffee. $ … [2]

6 0607/33/O/N/20 © UCLES 2020 4 (a) Petra has a birthday party. The party starts at 19 30 and ends at 23 45. (i) Find how long the party lasts. … hours … minutes [1] (ii) The cost of hiring a band for the party is a total of $150. The cost of hiring a hall is $50 per hour. Petra hires the hall for 6 hours. Find the total cost of hiring the hall and the band. $ … [2] (b) Petra received $650 for her birthday. (i) She invests half of this in a bank at a rate of 3.1% per year compound interest. Work out the value of her investment at the end of 3 years. $ … [3] (ii) Petra invests the other half of her birthday money in a different bank at a rate of 3.5% per year simple interest. Work out the value of this investment at the end of 3 years. $ … [3]

7 0607/33/O/N/20 © UCLES 2020 [Turn over 5 NOT TO SCALE A D B O E C 31° The diagram shows a circle, centre O. The straight line ABC touches the circle at B. DOEC is a straight line, D and E lie on the circumference and angle OBD = 31°. (a) Using the letters in the diagram, write down (i) the diameter, … [1] (ii) a radius, … [1] (iii) a chord, … [1] (iv) the tangent. … [1] (b) Find (i) angle OBC, Angle OBC = … [1] (ii) angle ABD, Angle ABD = … [1] (iii) angle BOD, Angle BOD = … [2] (iv) angle BCO. Angle BCO = … [2]

8 0607/33/O/N/20 © UCLES 2020 6 (a) The diagram shows a shape drawn on a 1cm2 grid. x cm (i) Use Pythagoras’ theorem to calculate the value of x. x = … [2] (ii) Work out the perimeter of the shape. … cm [1] (b) Shade one small square so that the diagram has line symmetry. [1]

9 0607/33/O/N/20 © UCLES 2020 [Turn over (c) Shade one small square so that the diagram has rotational symmetry of order 2. [1] (d) A D E F B C NOT TO SCALE 7.5 cm 3 cm 2 cm x cm ABC and DEF are similar triangles. Find the value of x. x = … [2]

10 0607/33/O/N/20 © UCLES 2020 7 One day, Mr Amir made a note of the number of employees who were on time for work and the number who were late for work. He asked each employee if they ate breakfast or not. The information is shown in the table. Number who ate breakfast Number who did not eat breakfast Total Number who were on time for work 12 a 17 Number who were late for work 2 c b Total 14 6 20 (a) Work out the value of each of a, b and c. a = … b = … c = … [3] (b) An employee is chosen at random. Find the probability that this employee (i) was on time, … [1] (ii) did not eat breakfast, … [1] (iii) ate breakfast and was late for work. … [1]

11 0607/33/O/N/20 © UCLES 2020 [Turn over 8 U = {F, R, A, C, T, I, O, N} X = {R, A, T, I, O} Y = {F, A, C, T} (a) Write down the elements in X Y + . … [1] (b) Complete the Venn diagram. X Y U [2] (c) Find ( ) X Y n , l. … [1] (d) On the Venn diagram below, shade the region X Y , l . X Y U [1]

12 0607/33/O/N/20 © UCLES 2020 9 (a) ( ) x x 2 1 f 2 = - (i) Find f(4). … [1] (ii) Find x when f(x) = 17. x = … or x = … [3] (b) Solve. (i) x 7 14 14 - = x = … [2] (ii) x x 5 3 3 7 - = + x = … [2] (c) Expand. ( ) x x 3 4 - … [2]

13 0607/33/O/N/20 © UCLES 2020 [Turn over (d) Simplify fully. r r 6 18 2 8 … [2] (e) (i) 3 3 3 m 6 18 # = Find the value of m. m = … [1] (ii) 8 8 8 n 3 2 = Find the value of n. n = … [1] (f) Solve the simultaneous equations. You must show all your working. x y 2 4 22 + = x y 2 3 15 - = x = … y = … [2]

14 0607/33/O/N/20 © UCLES 2020 10 12 x y 0 15 – 1 – 1 (a) (i) On the diagram, sketch the graph of . ( ) y 8 1 4 2 x # = + - for x 1 12 G G - . [2] (ii) Find the coordinates of the point where the graph crosses the y-axis. ( … , …) [1] (iii) Write down the equation of the horizontal asymptote. … [1] (b) On the same diagram, sketch the graph of y x 3 = + . [2] (c) Find the coordinates of the point of intersection of the graphs of . ( ) y 8 1 4 2 x # = + - and y x 3 = + . ( … , …) [2]

15 0607/33/O/N/20 © UCLES 2020 11 A C D B E y x 0 2 4 6 8 10 12 14 16 18 20 22 – 2 – 2 2 4 6 8 10 12 14 16 – 4 – 6 – 4 – 6 – 8 Describe fully the single transformation that maps (a) shape A onto shape B, … … [3] (b) shape A onto shape C, … … [2] (c) shape A onto shape D, … … [2] (d) shape A onto shape E. … … [3]

16 0607/33/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 8 printed pages. © UCLES 2020 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/33 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.

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 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 October/November 2020 © UCLES 2020 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 October/November 2020 © UCLES 2020 Page 4 of 8 Question Answer Marks Partial Marks 1(a) One thousand, nine hundred [and] thirty-six 1 1(b) 84 1 1(c) 2035 1 1(d) 44 1 1(e)(i) 1940 1 1(e)(ii) 1900 1 1(e)(iii) 1.936 × 103 1 1(f) Any multiple of 1936 1 2(a) 44.5 or 44.53… 1 2(b) 2 9 3 2 5 8 9 4 1 1 2 3 5 5 1 3 7 6 0 2 2 B1 for unordered diagram or 2 correct ordered rows Key 2 │9 = 29 1 dep must be consistent with their stem 2(c)(i) 33 1 2(c)(ii) 41 1 2(c)(iii) 42 1 2(c)(iv) 15 2 B1 for 53 or 38 seen 3(a) 3.5[0] 1 3(b) 14 2 M1 for 49 their (a) 3(c)(i) 3 1 3(c)(ii) 6.12 or 6.122… 2 M1 for 3 49 their 3(d) 28 2 M1 for 49 3 4 + 4(a)(i) 4 [hours] 15 [minutes] 1

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 Page 5 of 8 Question Answer Marks Partial Marks 4(a)(ii) 450 2 M1 for 6 × 50 + 150 4(b)(i) 356.17 or 356.172 to 356.173 3 M2 for 3 650 3.1 1 2 100   × +     oe or M1 for 650 3.1 1 , 1 2 100 k k   × + >     oe If 0 scored, SC1 for $712[.34] (from using 650) 4(b)(ii) 359.13 3 M2 for 650 3.5 3 650 2 2 100 × × + oe or M1 for 650 3.5 3 2 100 × × oe If 0 scored, SC1 for $718[.25] (from using 650) 5(a)(i) DE 1 5(a)(ii) OD, OB or OE 1 5(a)(iii) DB 1 5(a)(iv) AC 1 5(b)(i) 90 1 5(b)(ii) 59 1 FT 180 – 31 – their (b)(i) 5(b)(iii) 118 2 M1 for recognising BDO = 31 5(b)(iv) 28 2 B1 for BOC = 62 or DBC = 90 + 31 oe 6(a)(i) 1.41 or 1.414… 2 M1 for 12 + 12 6(a)(ii) 26.8 or 26.82 to 26.83 1 6(b) 1 6(c) 1

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 Page 6 of 8 Question Answer Marks Partial Marks 6(d) 5 2 M1 for 3 7.5 or 7.5 3 or 3 2 oe or 2 3 oe seen 7(a) [a =] 5 [b =] 3 [c =] 1 3 B1 for each 7(b)(i) 17 20 oe 1 7(b)(ii) 6 20 oe 1 7(b)(iii) 2 20 oe 1 8(a) A, T 1 8(b) 2 FT their (a) B1 for 2 or 3 of the 4 regions correct 8(c) 1 1 FT their (b) 8(d) 1 9(a)(i) 31 1 9(a)(ii) +3 and -3 3 M2 for x2 = 18 2 or better or M1 for 2x2 = 17 + 1 or 17 2 = x2 – 1 2 If 0 scored, SC1 for answer 3 seen. 9(b)(i) 4 2 M1 for 7x = 14 + 14 or x – 2 = 2 9(b)(ii) 5 2 M1 for 5x – 3x = 7 + 3 or better

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 Page 7 of 8 Question Answer Marks Partial Marks 9(c) 3ݔଶ−12ݔ final answer 2 M1 for 3x2 or – 12x 9(d) 3ݎ଺ final answer 2 B1 for 3 or r6 seen 9(e)(i) 12 1 9(e)(ii) 5 1 9(f) [x =] 9 [y =] 1 2 B1 for each If zero scored, SC1 for correct substitution and evaluation to find the other variable. or SC1 if no working shown but 2 correct answers given 10(a)(i) Correct sketch 2 B1 for approximately the correct shape B1 for crossing the y-axis at approximately 10 and not crossing the x-axis. 10(a)(ii) (0, 10) 1 10(a)(iii) y = 2 1 10(b) Correct sketch 2 B1 for straight line with positive gradient B1 for y-intercept at approximately 3 and not crossing the x-axis. 10(c) (2.48, 5.48) or (2.476…, 5.476…) 2 B1 for each If 0 scored, SC1 for (2.5, 5.5) or for (2.47, 5.47) 11(a) Rotation 90° [anticlockwise] oe about (0, 0) oe 3 B1 for each 11(b) Reflection x-axis or y = 0 2 B1 for each 11(c) Translation 10 7 −     −   2 B1 for each

0607/33 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 Page 8 of 8 Question Answer Marks Partial Marks 11(d) Enlargement [scale factor] 3 [centre] (0, 0) oe 3 B1 for each