Cambridge IGCSE Mathematics - International 0607 — 2020 Oct/Nov Paper 4 · Variant 2

This document has 20 pages. Blank pages are indicated. DC (RW/SW) 187924/1 © UCLES 2020 [Turn over * 3 5 9 1 5 2 7 4 2 9 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/42 Paper 4 (Extended) October/November 2020 2 hours 15 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 120. ● The number of marks for each question or part question is shown in brackets [ ]. Cambridge IGCSE™

2 0607/42/O/N/20 © UCLES 2020 Formula List For the equation ax bx c 0 2 + + = x a b b ac 2 4 2 ! = - - Curved surface area, A, of cylinder of radius r, height h. r A rh 2 = Curved surface area, A, of cone of radius r, sloping edge l. r A rl = Curved surface area, A, of sphere of radius r. r A r 4 2 = Volume, V, of pyramid, base area A, height h. V Ah 3 1 = Volume, V, of cylinder of radius r, height h. r V r h 2 = Volume, V, of cone of radius r, height h. r V r h 3 1 2 = Volume, V, of sphere of radius r. r V r 3 4 3 = sin sin sin A a B b C c = = cos a b c bc A 2 2 2 2 = + - sin bc A 2 1 Area = A C B c b a

3 0607/42/O/N/20 © UCLES 2020 [Turn over Answer all the questions. 1 Asif buys a one-year old car. He pays $19 975 which is 15% less than its price when it was new. (a) Calculate the price when it was new. $ … [2] (b) Option 1 Pay 10% of the $19 975 and then pay $345 per month for 5 years. Option 2 Borrow $19 975 and pay this back at the end of 5 years at a rate of 2.5% per year compound interest. Asif can pay for the car using Option 1 or Option 2. (i) Using Option 1, find how much Asif would pay in total for the car. $ … [3] (ii) By how much is Option 2 cheaper than Option 1? $ … [4]

4 0607/42/O/N/20 © UCLES 2020 2 – 1 1 2 3 4 5 0 – 2 – 3 – 4 – 5 – 5 – 4 – 3 – 2 – 1 1 2 3 4 5 6 7 y x E A B (a) Describe fully the single transformation that maps triangle A onto triangle B. … … [2] (b) Reflect triangle A in the line y x =- . Label the image C. [2] (c) Rotate triangle A through 90° clockwise about centre (1, 1 - ). Label the image D. [2] (d) Describe fully the single transformation that maps triangle C onto triangle D. … … [2] (e) Describe fully the single transformation that maps triangle A onto triangle E. … … [3]

5 0607/42/O/N/20 © UCLES 2020 [Turn over 3 The table shows the engine capacity, x litres, and the fuel consumption, y kilometres per litre, for each of nine cars. Engine capacity (x litres) 1 1.3 1.5 1.8 2 2.5 3 3.5 4 Fuel consumption (y km/l) 16.6 15.6 13.8 14.4 13.2 11.0 11.5 9.2 7.4 (a) Complete the scatter diagram. The first five points have been plotted for you. 6 1 1.5 2 2.5 Engine capacity (litres) Fuel consumption (km / l) 3 3.5 4 7 8 9 10 11 12 13 14 15 16 17 18 y x [2] (b) What type of correlation is shown in your scatter diagram? … [1] (c) Find the equation of the regression line for y in terms of x. y = … [2] (d) Use your answer to part (c) to estimate the fuel consumption for a car with engine capacity 2.8 litres. …km/l [1]

6 0607/42/O/N/20 © UCLES 2020 4 0 y x – 3 – 10 15 3 ( ) f x x x 5 3 3 = - + for x 3 3 G G - (a) On the diagram, sketch the graph of ( ) f y x = . [2] (b) Find the coordinates of the local minimum point. ( … , … ) [2] (c) Describe fully the symmetry of the diagram. … … [3] (d) ( ) g x x 2 1 = - (i) Solve ( ) ( ) f g x x = for x 3 3 G G - . … , … , … [3] (ii) Use your answers to part(i) to solve ( ) ( ) f g x x 2 . … [2]

7 0607/42/O/N/20 © UCLES 2020 [Turn over 5 Naomi flies non-stop from London, England, to Perth, Australia. The flight takes 16 hours 45 minutes. The distance is 14 498 km. (a) Find the average speed of the plane in km/h. … km/h [2] (b) The plane leaves London at 13 15. The time in Perth is 8 hours ahead of the time in London. Find the time in Perth when the plane lands. … [3] (c) The cost, in pounds (£), of the flight is £827.75 . The exchange rate is 1 Australian dollar = £0.55 . Calculate the cost of the flight in Australian dollars. … Australian dollars [2]

8 0607/42/O/N/20 © UCLES 2020 6 75° A B C NOT TO SCALE D 44 m 74 m 62 m North 95 m The diagram shows a field ABCD with a straight path from A to C. The bearing of B from A is 075° and angle ° ADC 90 = . (a) Show that angle . ° BAC 31 6 = , correct to 1 decimal place. [3]

9 0607/42/O/N/20 © UCLES 2020 [Turn over (b) Find the bearing of D from A. … [3] (c) Find the shortest distance from B to AC. … m [2] (d) Find the total area of the field ABCD. … m2 [3]

10 0607/42/O/N/20 © UCLES 2020 7 A O B NOT TO SCALE y x A is the point (3, 2) and B is the point (9, 5). (a) Find the length AB. AB = … [3] (b) Find the equation of the line AB. Give your answer in the form y mx c = + . y = … [3] (c) C is the point (8, 2). Find the equation of the line perpendicular to AB which passes through C. Give your answer in the form y mx c = + . y = … [3]

11 0607/42/O/N/20 © UCLES 2020 [Turn over (d) Find the coordinates of the point where the line in part (c) intersects AB. ( … , … ) [2] (e) D is the reflection of C in the line AB. (i) Find the coordinates of D. ( … , … ) [2] (ii) What is the special name of quadrilateral ACBD? … [1] (f) Find the area of the quadrilateral ACBD. … [3]

12 0607/42/O/N/20 © UCLES 2020 8 Bag A Bag B Bag A contains 5 black balls and 2 white balls. Bag B contains 4 black balls and 5 white balls. (a) Gustav picks one ball at random from bag A and replaces it. Write down the probability that the ball Gustav picks is black. … [1] (b) Sharia picks one ball at random from bag A, notes its colour, and places it in bag B. She then picks a ball at random from bag B. Find the probability that (i) both balls are white, … [2] (ii) one ball is black and the other ball is white. … [3]

13 0607/42/O/N/20 © UCLES 2020 [Turn over (c) The balls are returned to their original bags. Jean picks a ball at random from bag A. He then replaces the ball. He continues to do this until he gets a white ball. Find the probability that the first time he gets a white ball is on the 5th pick. … [2] (d) The balls are returned to their original bags. Leanne picks a ball at random from bag B. She continues to do this without replacement until she gets a white ball. The probability that she picks the first white ball on her nth attempt is 126 5 . Find the value of n. … [3]

14 0607/42/O/N/20 © UCLES 2020 9 The cumulative frequency curve shows the marks of 120 students in an examination. 0 0 20 40 60 Marks Cumulative frequency 80 100 10 30 50 70 90 10 20 30 40 50 60 70 80 90 100 110 120 (a) Use the graph to estimate (i) the median, … [1] (ii) the interquartile range. … [2] (b) The top 15% of the students gained a grade A in the examination. Estimate the minimum mark for a grade A. … [3]

15 0607/42/O/N/20 © UCLES 2020 [Turn over 10 y is inversely proportional to the square root of x. When x 25 = , y 4 = . (a) Find y in terms of x. y = … [2] (b) Find y when . x 0 25 = . y = … [1] (c) Find x when y 5 = . x = … [2] (d) z is proportional to y 2 + . When x 4 = , z 84 = . Find z in terms of x. z = … [3]

16 0607/42/O/N/20 © UCLES 2020 11 ( ) f x x 5 3 = - ( ) g x x 2 7 = + (a) Solve ( ) ( ) x x f g = . … [2] (b) Find and simplify ( ( )) g f x . … [2] (c) (i) Find ( ) ( ) f g x x 2 2 + simplifying your answer. … [2] (ii) Find ( ( ) ( )) f g x x 2 + giving your answer in the form ax bx c 2 + + . … [3]

17 0607/42/O/N/20 © UCLES 2020 [Turn over (d) Find ( ) f x 1 - . ( ) f x 1 = - … [2] (e) Write as a single fraction in its simplest form. ( ) ( ) f g x x 2 3 - … [3]

18 0607/42/O/N/20 © UCLES 2020 12 (a) The vector a 3 2 = e o and the vector b 2 1 = - e o. On the grid, draw and label these vectors. (i) 2a [1] (ii) b - [1] (iii) 2 a b - [2]

19 0607/42/O/N/20 © UCLES 2020 (b) p q 2 3 1 4 10 7 + - = - e e e o o o By solving a pair of simultaneous equations, find the value of p and the value of q. Show all your working. p = … q = … [4]

20 0607/42/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 9 printed pages. © UCLES 2020 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/42 Paper 4 (Extended) October/November 2020 MARK SCHEME Maximum Mark: 120 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.

0607/42 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 Page 2 of 9 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.

0607/42 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 Page 3 of 9 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

0607/42 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 Page 4 of 9 Question Answer Marks Partial Marks 1(a) 23 500 2 M1 for 100 15 19975 100 − × = x oe or better 1(b)(i) 22697.5[0] final answer 3 M1 for 19975 × 10 100 soi by 1997.5 M1 for 12 × 345 [× 5] 1(b)(ii) 97.62 4 M2 for 5 25 19975 1 100   +     or M1 for 25 19975 1 100 n   +     , n > 1 M1 for their 22 697.5 – their 22 599.88 2(a) Translation 4 0    2 B1 for each 2(b) Triangle at (–1, –1), (–2, –1), (–1, –3) 2 B1 for reflection in y = x 2(c) Triangle at (3, –1), (4, –1), (3, –3) 2 B1 for rotation 90° clockwise, wrong centre or rotation 90° anti-clockwise about (1, –1) 2(d) Reflection x = 1 2 B1 for each 2(e) Stretch x-axis invariant oe [factor] 2 3 B1 for each 3(a) 4 correct points 2 B1 for 2 or 3 correct points 3(b) Negative 1 3(c) [y =] –2.84x +19[.0] 2 2.844..., 19.03... B1 for –2.84x + b or ax +19[.0], a < 0 or –2.8x +19 3(d) 11[.0] or 11.1 or 11.04 to 11.08 1 FT their (c)

0607/42 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 Page 5 of 9 Question Answer Marks Partial Marks 4(a) Correct sketch 2 Cubic curve, crossing x-axis three times, with maximum in 2nd quadrant and minimum, in 4th quadrant B1 for any cubic (positive x3) 4(b) (1.29, –1.3[0]) 2 1.290 to 1.291, –1.303... B1 for each coordinate 4(c) Rotation [Order] 2 [centre] (0, 3) 3 B1 for each 4(d)(i) –2.9[0] or –2.895... 0.603 or 0.6027... 2.29 or 2.292... 3 B1 for each If three correct but seen in coordinate form, SC1. If 0 scored, SC1 for correct sketch of line (may be freehand but negative intersection with y-axis and crosses curve three times) 4(d)(ii) –2.9[0] < x < 0.603 x > 2.29 2 FT their (i) B1 for each 5(a) 866 or 865.5 to 865.6 2 M1 for 14 498 ÷ 16.75 5(b) 14 00 or 2 pm 3 B1 for 29h 60min or 30 h B1 for 06 00 OR B1 for 21 15 oe B1 for 38h or 37h 60min OR M1 for 13 15 + 8 + 16 45 or 13 15 + 16 45 + 8 M1 for a correct conversion to 24 hour clock 5(c) 1505 cao 2 M1 for 827.75 ÷ 0.55 f(x)=x^3-5x+3 -3 3 -5 5 10 15 x y

0607/42 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 Page 6 of 9 Question Answer Marks Partial Marks 6(a) [ ] 2 2 2 44 95 62 cos 2 44 95 + − = × × M2 M1 for 622 = 442 + 952 – 2 × 44 × 95cos[...] 31.64... A1 6(b) 145 or 145.4 to 145.5 3 B2 for [angle DAC =] 38.8 or 38.83 to 38.84 or M1 for cos [DAC] = 74 95 oe 6(c) 23.1 or 23.05 to 23.09 2 M1 for sin31.6 44 distance = oe 6(d) 3300 or 3296 to 3302 3 M1 for 0.5 × 95 × their(c) oe M1 for 0.5 × 74 × 95 × sin(their 38.8) oe 7(a) 6.71 or 6.708... 3 M2 for (9 – 3)2 + (5 – 2)2 soi or M1 for 9 – 3 and 5 – 2 soi 7(b) [y =] 0.5x + 0.5 oe 3 M1 for gradient = 5 2 9 3 − − oe M1 for substituting (3, 2) or (9, 5) into their y = mx + c oe 7(c) [y =] –2x + 18 3 M1 for gradient = –1 ÷ their 0.5 M1 for substituting (8, 2) into their y = mx + c oe 7(d) (7, 4) 2 B1 for each coordinate or M1 for their (b) = their (c) 7(e)(i) (6, 6) 2 B1 for each coordinate 7(e)(ii) Kite 1

0607/42 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 Page 7 of 9 Question Answer Marks Partial Marks 7(f) 15 or 14.99 to 15.01 3 M2 for (8 3) (5 2) 2 2 − × − × OR M1 for ((their 6) – 8)2 + ((their 6) – 2)2 M1 for 0.5 × their (a) × their CD OR M2 for 24 – 6 – 2 × 1.5 oe or better or M1 for 6 4 0.5 3 4 2 0.5 1 3 × − × × −× × × 8(a) 5 7 oe 1 8(b)(i) 6 35 oe 2 M1 for seen 8(b)(ii) 33 70 oe 3 M2 for 5 5 2 4 7 10 7 10 × × × or M1 for one of above products 8(c) 1250 16807 2 M1 for 5 5 5 5 2 7 7 7 7 7 × × × × 8(d) 4 nfww 3 M2 for 4 3 2 5 9 8 7 6 × × × or M1 for a correct trial with black(s) then white 9(a)(i) 50 1 9(a)(ii) 24 2 B1 for [l.q. = ] 38 or [u.q. =] 62 seen but not as final answer 9(b) 68 or 69 3 M1 for 120 × 15 100 oe (18) M1 for reading at (120 – their 18) seen 10(a) [y =] 20 x oe 2 M1 for k x oe 10(b) 40 1 FT incorrect k only 10(c) 16 2 M1 their 20 = 5 x or better 6 10

0607/42 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 Page 8 of 9 Question Answer Marks Partial Marks 10(d) [ ] 20 7 2 z x   = +     oe final answer 3 M2 for 20 2 their z K x   = +     or for 20 84 2 4 their K   = +     oe or M1 for z = K(y + 2) oe 11(a) – 2 5 oe 2 M1 for 5 – 7 = 2x + 3x oe or better 11(b) 17 – 6x Final answer 2 M1 for 2(5 – 3x) + 7 seen 11(c)(i) 12 – x2 Final answer 2 M1 for 5 – 3x2 + 2x2 + 7 11(c)(ii) x2 – 24x + 144 Final answer 3 M1 for (5 – 3x + 2x + 7)2 oe B1 for three terms of 144 – 12x – 12x + x2 correct 11(d) 5 3 −x oe Final answer 2 M1 for x = 5 – 3y or y + 3x = 5 or y – 5 = –3x or 5 3 3 = − y x 11(e) ( )( ) 13 1 5 3 2 7 − − + x x x Final answer 3 M1 for 2(2x + 7) – 3(5 – 3x) or better seen M1 for common denominator (5 – 3x)(2x + 7) 12(a)(i) Vector 6 4    drawn 1 12(a)(ii) Vector 2 1 −       drawn 1 12(a)(iii) Vector 1 4 −       drawn 2 B1 for vector 1 k −       or vector 4    k drawn or 1 4 −       seen

0607/42 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 Page 9 of 9 Question Answer Marks Partial Marks 12(b) 2p – q = 10 3p + 4q = –7 B1 Equalising coefficients and adding or subtracting appropriately, or expression for one variable in terms of the other and correctly substituted, or rearranged equations seen and sketch of both lines intersecting. M1 p = 3, q = –4 A2 A1 for each If M0 A0 scored, SC1 for p = 3, q = –4 with no working or their answers satisfying one equation