Cambridge IGCSE Mathematics - International 0607 — 2021 Oct/Nov Paper 4 · Variant 1

DC (NF/SG) 215048/2 © UCLES 2021 [Turn over This document has 20 pages. * 4 0 5 5 5 9 5 3 9 5 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/41 Paper 4 (Extended) October/November 2021 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 0607/41/O/N/21 © UCLES 2021 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 0607/41/O/N/21 © UCLES 2021 [Turn over Answer all the questions. 1 Amir, Bibi and Caitlyn are each given $1500 to invest. (a) Amir invests his $1500 in an account which pays compound interest. The interest rate is 3% per year for 5 years, after which it is 2% per year. Find the value of Amir’s investment at the end of 11 years. $ … [3] (b) Bibi invests her $1500 in an account which pays r % per year simple interest. At the end of 11 years, the investment is worth $1962. Calculate the value of r. r = … [3] (c) Caitlyn invests her $1500 in an account which pays t % per year compound interest. At the end of 11 years, the investment is worth $1968.13 . Calculate the value of t. t = … [3]

4 0607/41/O/N/21 © UCLES 2021 2 (a) In part (a) enlargements and stretches have scale factors greater than 1. (i) A transformation maps triangle A onto triangle B. Triangle A is congruent to triangle B. Tick all the possible transformations it could be. Transformation Tick (✓) Rotation Reflection Translation Enlargement Stretch [1] (ii) A transformation maps triangle C onto triangle D. The angles of triangle C are the same as the corresponding angles of triangle D. Tick all the possible transformations it could be. Transformation Tick (✓) Rotation Reflection Translation Enlargement Stretch [1] (iii) A transformation maps triangle E onto triangle F. Triangle F has a larger area than triangle E. Tick all the possible transformations it could be. Transformation Tick (✓) Rotation Reflection Translation Enlargement Stretch [1]

5 0607/41/O/N/21 © UCLES 2021 [Turn over (b) y x 1 0 – 1 – 2 – 3 – 4 2 3 4 5 6 7 8 – 1 – 2 –3 – 4 – 5 1 2 3 4 5 6 Q P (i) Describe fully the single transformation that maps triangle P onto triangle Q. … … [3] (ii) Stretch triangle P with the x-axis invariant and scale factor 2. [2]

6 0607/41/O/N/21 © UCLES 2021 3 The table shows the number of days, d, since planting and the heights, h cm, of some plants. Number of days (d) 20 20 42 76 90 24 86 98 10 56 Height (h cm) 34 66 80 76 100 50 86 94 40 54 (a) Complete the scatter diagram. The first five points have been plotted for you. h d 10 0 0 20 30 40 50 Number of days 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 Height (cm) [2] (b) What type of correlation is shown in the scatter diagram? … [1] (c) Find the equation of the regression line for h in terms of d. h = … [2]

7 0607/41/O/N/21 © UCLES 2021 [Turn over (d) Use your regression line to estimate the height of a plant that was planted 28 days ago. … cm [1] (e) A plant was planted 140 days ago. Explain why you should not use the equation of the regression line to estimate the height of this plant. … [1]

8 0607/41/O/N/21 © UCLES 2021 4 The table shows a set of data. x Frequency 5 16 6 18 7 25 8 11 9 6 10 4 Total 80 (a) When x represents the number of emails Essa receives each day, find (i) the median, … [1] (ii) the range, … [1] (iii) the upper quartile, … [1] (iv) the mean. … [2] (b) When x represents the height of a seedling, correct to the nearest centimetre, explain why you cannot work out the range of the heights. … … [1]

9 0607/41/O/N/21 © UCLES 2021 [Turn over 5 y x 7 – 7 – 7 7 0 ( ) ( )( ) ( ) x x x x 1 2 2 3 f 2 = + - + for x 7 7 G G - (a) On the diagram, sketch the graph of ( ). y x f = [3] (b) Write down the equation of each asymptote parallel to the y-axis. … [2] (c) Write down the coordinates of the local minimum. ( … , …) [2] (d) Find the range of values of x for which the gradient of ( )x f is negative. … [3] (e) Solve ( ) . x x f =- x = … [1]

10 0607/41/O/N/21 © UCLES 2021 6 The masses of 300 apples are shown in the table. Mass (m grams) m 0 25 1 G m 25 50 1 G m 0 5 5 7 1 G m 75 100 1 G m 100 125 1 G m 125 150 1 G Frequency 4 26 60 88 106 16 (a) Draw a cumulative frequency curve to show these results. m 10 0 0 20 30 40 50 Mass (grams) 60 70 80 90 100 110 120 130 140 150 50 100 150 200 250 300 Cumulative frequency [4] (b) Use your curve to find the interquartile range. … [2] (c) Apples with a mass below 80 g are used to make drinks. Find the percentage of the 300 apples that are used to make drinks. …% [2]

11 0607/41/O/N/21 © UCLES 2021 [Turn over 7 (a) The nth term of a sequence is ( )( ) . n n n 6 1 2 1 + + Find the first three terms of this sequence. … , … , … [2] (b) For each of the following sequences: • find the next two terms • find an expression for the nth term. (i) 11 8 5 2 Next two terms … , … nth term … [3] (ii) 2 - 2 - 0 4 10 18 Next two terms … , … nth term … [3] (iii) 3 5 9 17 33 Next two terms … , … nth term … [3]

12 0607/41/O/N/21 © UCLES 2021 8 NOT TO SCALE E B A F C D 4 cm 6 cm 11 cm The diagram shows a right-angled triangular prism. ABCD, ADFE and BCFE are rectangles. , cm AD 11 = cm DC 6 = and the height cm CF 4 = . (a) Calculate the volume of the prism. … cm3 [2] (b) Calculate the total surface area of the prism. … cm2 [4] (c) Calculate the length AF. AF = … cm [3]

13 0607/41/O/N/21 © UCLES 2021 [Turn over (d) Calculate angle FAC. Angle FAC = … [2] (e) The volume of a mathematically similar prism is . . cm 445 5 3 Calculate the total surface area of this similar prism. … cm2 [3]

14 0607/41/O/N/21 © UCLES 2021 9 NOT TO SCALE – 4 0 4 4 – 4 A B x y The equation of the circle is . x y 16 2 2 + = The equation of the straight line is . y x 3 1 = + The line crosses the circle at the points A and B. (a) Use substitution to show that the x-coordinates of the points A and B satisfy the equation . x x 10 6 15 0 2 + - = [3] (b) Solve the equation x x 10 6 15 0 2 + - = to find the coordinates of the points A and B. Show your working and give your answers correct to 2 decimal places. A ( … , …) B ( … , …) [4]

15 0607/41/O/N/21 © UCLES 2021 [Turn over 10 ( )x x 3 2 f = - ( ) ( ) x x 3 g 2 = - (a) Find ( ( )). 1 f g … [2] (b) Solve ( ) . x 25 g = x = … or x = … [2] (c) Find ( ). 4 f 1 - … [2] (d) Write down ( ( )). x f f 1 - … [1]

16 0607/41/O/N/21 © UCLES 2021 11 NOT TO SCALE North C B A 108 km 217 km 159 km A, B and C are three ports. (a) Show that angle . ° ABC 107 2 = correct to 1 decimal place. [3] (b) The bearing of B from A is °. 305 (i) Using the sine rule, show that angle . ° BAC 44 4 = correct to 1 decimal place. [3] (ii) Find the bearing of C from A. … [1]

17 0607/41/O/N/21 © UCLES 2021 [Turn over (c) A ship leaves A at 22 50 and sails at a constant speed of 24 km/h towards C. Calculate the time, correct to the nearest minute, when the ship is nearest to B. … [5]

18 0607/41/O/N/21 © UCLES 2021 12 (a) (i) For each Venn diagram, shade the given set. A B , l A B U A B U A B + l [2] (ii) Use set language to describe the shaded set. A B U … [1] (b) 40 people are asked which of 3 television programmes, P, Q and R, they watch. The results are shown in the Venn diagram. P R Q U 7 4 5 8 6 4 5 1

19 0607/41/O/N/21 © UCLES 2021 [Turn over (i) Two of the 40 people are chosen at random. Find the probability that they both watch exactly 2 of the 3 programmes. … [2] (ii) Two of the people who watch programme P are chosen at random. Find the probability that one of them watches both other programmes and one watches just one of the other programmes. … [3] (iii) Three of the 40 people are chosen at random. Find the probability that two of them watch only programme Q and one of them watches only programme R. … [3] Question 13 is printed on the next page.

20 0607/41/O/N/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. 13 (a) Rearrange y ex f ax b = + + to make x the subject. x = … [4] (b) ( ) ( )° x x 3 2 f sin = (i) Write down the amplitude and the period of ( ). x f Amplitude = … Period = … [2] (ii) The graph of ( ) y x f = is stretched with the x-axis invariant and scale factor 3 to give the graph of ( ). y x g = Find ( ). x g ( )x g = … [1] (iii) The graph of ( ) y x f = is translated through 90 0 - e o to give the graph of ( ). y x h = Find ( )x h , giving your answer in its simplest form. ( )x h = … [2]

This document consists of 9 printed pages. © UCLES 2021 [Turn over Cambridge IGCSE™ CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/41 Paper 4 (Extended) October/November 2021 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 2021 series for most Cambridge IGCSE™, Cambridge International A and AS Level components and some Cambridge O Level components.

0607/41 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 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.

0607/41 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 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

0607/41 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 4 of 9 Question Answer Marks Partial Marks 1(a) 1958.3[0] 3 M2 5 6 3 2 1500 1 1 100 100    + +       oe or M1 for 5 3 1 100   +     or 6 2 1 100   +     oe seen 1(b) 2.8 3 M2 for [ ] (1962 1500) 100 1500 11 − × × oe or 1962 100 100 1500   × −     oe or M1 for [1500 +] 1500 11 100 × × r or 1962 100 1500 × 1(c) 2.5 3 M2 for 111968.13 1500 oe M1 for ( ) 11 1500 k = 1968.13 2(a)(i) Rotation  Reflection  Translation  Enlargement Stretch 1 2(a)(ii) Rotation  Reflection  Translation  Enlargement  Stretch 1 2(a)(iii) Rotation Reflection Translation Enlargement  Stretch  1

0607/41 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 5 of 9 Question Answer Marks Partial Marks 2(b)(i) Rotation 90 [anticlockwise] oe (0, 0) oe 3 B1 for each 2(b)(ii) Triangle with vertices at (2, –4), (4, –4), (4, 4) 2 B1 for stretch, factor 2, y-axis invariant, or stretch, factor 2, y = c invariant 3(a) 5 points plotted correctly 2 B1 for 3 or 4 points plotted correctly 3(b) Positive 1 3(c) 0.587d + 37.4 2 0.5869 to 0.5870, 37.35 to 37.36 B1 for 0.587d + b or ad + 37.4, a > 0 or 0.59d + 37 3(d) 53.7 to 53.9 1 FT their (c) 3(e) Too far outside range of data oe 1 4(a)(i) 7 1 4(a)(ii) 5 1 4(a)(iii) 8 1 4(a)(iv) 6.81 or 6.812 to 6.813 2 M1 for 5 × 16 + 6 × 18 + 7 × 25 + 8 × 11 + 9 × 6 + 10 × 4 4(b) You do not actually know the biggest and the smallest oe 1 5(a) Correct Sketch f(x)=(2x^2+3)/((x+1)(2-x)) -7 7 -7 7 x y 3 B1 for each branch 5(b) x = – 1, x = 2 2 B1 for each 5(c) (0.208, 1.43) 2 0.2080 to 0.2081, 1.425 to 1.426 B1 for each coordinate 5(d) –1 < x < 0.208 B2 FT their 5(c) B1 for –1 < x or x < 0.208 x < –1 oe B1 5(e) 3.75 or 3.747... 1

0607/41 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 6 of 9 Question Answer Marks Partial Marks 6(a) Correct cumulative frequency curve 4 Through (25,4), (50, 30), (75,90), (100, 178), (125, 284), (150, 300) B3 for one plotting error OR B1 for 4, 30, 90, 178, 284, 300 soi B1FT for CF diagram at correct heights B1FT for CF plotting at RH end of interval FT dependent on increasing curve. 6(b) 36 to 44 2 FT their CF diagram B1 FT for LQ = 68 to 72 or UQ = 108 to 112 6(c) 33.3 or 33.33... to 36.7 or 36.66 to 36.67 2 B1 for 100 to 110 or M1 for correct percentage calculated from their reading. 7(a) 1, 5, 14, 2 B1 for 2 correct 7(b)(i) –1, –4 B1 14 – 3n oe final answer B2 B1 for k – 3n oe or 14 + cn, c ≠ 0 or correct answer spoiled 7(b)(ii) 28, 40 B1 n² – 3n oe final answer B2 B1 for any quadratic or M1 for common second differences = 2 7(b)(iii) 65, 129 B1 2n + 1 oe final answer B2 B1 for 2n seen 8(a) 132 2 M1 for 1 6 4 2 × × 8(b) 213 or 213.3... 4 M1 for 62 + 42 M2 for 2 × their ( 1 6 4 2 × × ) + 6 × 11 + 4 × 11 + their 7.211 × 11 or M1 for correct area of at least 3 faces 8(c) 13.2 or 13.15... 3 M2 for 62 + 42 + 112 oe e.g. 112 + (their DF)2 or M1 for 62 + 42 or 42 + 112 or 62 + 112 8(d) 17.6 or 17.7 or 17.63... to 17.71 2 M1 for sin = 4 theirAF oe

0607/41 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 7 of 9 Question Answer Marks Partial Marks 8(e) 479 to 480 3 M1 for 3 445.5 ( ) their a oe soi by 1.5 oe or 2 3 oe M1 for (their 1.5)2 oe or for 2 3 445.5 ( ) ( )     =         area their a their b oe 9(a) x2 + (3x + 1)2 = 16 M1 9x2 + 3x + 3x + 1 or 9x2 + 6x + 1 B1 Completion to 10x2 + 6x – 15 = 0 with no errors A1 9(b) 2 6 (6) 4(10)( 15) 2 10 −± − − × or sketch of parabola (+ve x²) with x intercepts opposite sign M2 M1 for 6 2 10 −± × D or 2 (6) 4(10)( 15) ± − − p q or sketch of any U shaped parabola (–1.56, –3.68) (0.96, 3.88) A2 A marks depend on M2 A1 for both x-values correct or one coordinate pair correct or both y-values correct FT their x If M0 scored, SC1 for correct answers with wrong or no working. 10(a) 10 2 B1 for g(1) = 4 soi 10(b) 8, –2 2 B1 for each 10(c) 2 2 B1 for 3x – 2 = 4 or 2 3 + x 10(d) x cao 1 11(a) [cos =] 2 2 2 159 108 217 2 159 108 + − × × M2 M1 for 2172 = 1592 + 1082 – 2 × 159 × 108 × cos[ABC] 107.17 to 107.18 A1 11(b)(i) 159sin107.2 217 M2 M1 for sin sin107.2 159 217 = BAC 44.42 to 44.43 A1 11(b)(ii) 261 or 260.5 to 260.6 1

0607/41 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 8 of 9 Question Answer Marks Partial Marks 11(c) 02 03 5 B4 for 3h 13 mins or 3.215 to 3.22 hours OR M2 for 108 cos 44.4 or M1 for [ ] cos44.4 108 = AN M1 for their 77.2 ÷ 24 If 0 scored, SC1 for converting their time in hours to hours and minutes or minutes only 12(a)(i) 2 B1 for each 12(a)(ii) ( ) ( ) A B A B ′ ′ ∩ ∪ ∩ oe 1 12(b)(i) 7 60 oe 2 M1 for 14 13 40 39 × 12(b)(ii) 50 231 oe 3 M2 for 5 10 22 21 × or 10 5 22 21 × oe or M1 for 22 21 × a b or 5 10 1 × − k k oe 12(b)(iii) 2 247 oe 3 M2 for [k ×] 5 4 8 40 39 38 × × oe or M1 for 1 40 39 38 − × × a a b oe any integer k oe 13(a) − − b fy ey a or − − fy b a ey final answer 4 M1 for y(ex + f) = ax + b M1FT for eyx + fy = ax + b M1FT for eyx – ax = b – fy M1FT for factorise and divide correctly Max of 3 marks if answer incorrect 13(b)(i) [Amplitude] 3 [Period] 180 2 B1 for each 13(b)(ii) 9 sin(2x) 1

0607/41 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 9 of 9 Question Answer Marks Partial Marks 13(b)(iii) –3 sin(2x) cao 2 B1 for 3 sin(2(x ± 90)) oe