Cambridge IGCSE Mathematics - International 0607 — 2017 Oct/Nov Paper 4 · Variant 1

* 7 2 3 4 0 8 3 0 0 9 * This document consists of 19 printed pages and 1 blank page. DC (NF/SW) 134061/2 © UCLES 2017 [Turn over CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/41 Paper 4 (Extended) October/November 2017 2 hours 15 minutes Candidates answer on the Question Paper. Additional Materials: Geometrical Instruments Graphics Calculator READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. Do not use staples, paper clips, glue or correction fluid. You may use an HB pencil for any diagrams or graphs. DO NOT WRITE IN ANY BARCODES. Answer all the questions. Unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. Answers in degrees should be given to one decimal place. For r, use your calculator value. You must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 120. Cambridge International Examinations Cambridge International General Certificate of Secondary Education

2 0607/41/O/N/17 © UCLES 2017 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/17 © UCLES 2017 [Turn over Answer all the questions. 1 These are 12 of Stefan’s recent homework scores. 10 16 18 11 18 15 8 18 13 9 12 11 (a) Find (i) the mode, … [1] (ii) the range, … [1] (iii) the median, … [1] (iv) the mean, … [1] (v) the interquartile range. … [2] (b) The teacher wants to compare Stefan’s scores with those of another student in the class. Explain why the mode is not the best value to use to represent Stefan’s scores. … … [1]

4 0607/41/O/N/17 © UCLES 2017 2 Two banks pay interest in the following ways. Bank A Simple interest at a rate of 2.5% per year for the first year and then compound interest at a rate of 1.5% per year for each year after that. Bank B Simple interest at 1.6% per year. (a) Cherie invested $3000 in Bank A on 1st January 2016. Find how much the investment will be worth on 1st January 2019. $ … [3] (b) Dieter invested $3000 in Bank B on 1st January 2016. Find how much the investment will be worth on 1st January 2019. $ … [3] (c) Show that Cherie’s investment will be the first to be worth $3500. [4]

5 0607/41/O/N/17 © UCLES 2017 [Turn over 3 (a) The nth term of a sequence is n2 + 3n. Find the first four terms of this sequence. … , … , … , … [2] (b) These are the first four terms of another sequence. 5 7 9 11 (i) Write down the next two terms. … , … [1] (ii) Find the nth term of this sequence. … [2] (c) Using the sequences in part (a) and part (b), or otherwise, find the nth term of this sequence. 14, 24, 36, 50, … Write your answer as simply as possible. … [2]

6 0607/41/O/N/17 © UCLES 2017 4 The table shows the distance that each of 12 students lives from school and the time they each take to get to school. Distance (x km) 0.8 1.1 1.2 1.6 1.8 2.4 2.8 3.1 3.5 4.2 4.7 5.1 Time (t minutes) 15 18 15 24 23 35 37 35 45 48 52 63 (a) Complete the scatter diagram. The first six points have been plotted for you. 1 0 2 3 4 5 6 x t Time (minutes) Distance (km) 10 0 20 30 40 50 60 70 [2] (b) What type of correlation is shown by the scatter diagram? … [1]

7 0607/41/O/N/17 © UCLES 2017 [Turn over (c) (i) Find the equation of the regression line in the form t = mx + c. t = … [2] (ii) Use your answer to part (c)(i) to estimate the time taken to get to school for a student who lives 2.2 km from school. … min [1] (iii) Why would it not be sensible to use your answer to part (c)(i) to estimate the time taken to get to school for a student who lives 10 km from school? … … [1]

8 0607/41/O/N/17 © UCLES 2017 5 The diagram shows a paper cup. NOT TO SCALE The curved surface of the cup is made from a sector of a circle with a smaller sector cut from it, as shown below. NOT TO SCALE 45° 32.5 cm 22.5 cm The small sector has radius 22.5 cm and the large sector has radius 32.5 cm. The sectors have the same centre and both have sector angle 45°. (a) Show that the radius of the base of the cup is 2.81 cm, correct to 2 decimal places. [3]

9 0607/41/O/N/17 © UCLES 2017 [Turn over (b) Find the total area of the paper that makes the cup, including the circular base. … cm2 [5] (c) A mathematically similar cup holds 8 times as much liquid as this cup. Find the total area of the paper that makes the larger cup. … cm2 [2]

10 0607/41/O/N/17 © UCLES 2017 6 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 –1 –2 –3 –4 x y A C B (a) Describe fully the single transformation that maps triangle A onto triangle B. … … [2] (b) On the grid, draw the image of triangle A after a stretch with scale factor 3 and invariant line the x-axis. [2] (c) Triangle A can be mapped onto triangle C by a rotation followed by a reflection. Complete the following to fully describe the two transformations. Rotation … Reflection … [3]

11 0607/41/O/N/17 © UCLES 2017 [Turn over 7 Javier starts a journey at 22 50. (a) For the first part of the journey he drives for 2 hours 45 minutes at 70 km/h. Find the distance he travels. … km [3] (b) Javier then stops for 30 minutes. He then drives the remaining 180 km of his journey at 85 km/h. (i) Find his average speed for the whole journey. … km/h [4] (ii) Find the time he arrives at his destination. … [2]

12 0607/41/O/N/17 © UCLES 2017 8 ABC and ACD are two triangular fields. NOT TO SCALE North 60 m 55° 63° 76° 30° A D C B (a) Find the bearing of B from C. … [3] (b) Calculate AC and show that it rounds to 104.6 m, correct to 1 decimal place. [3]

13 0607/41/O/N/17 © UCLES 2017 [Turn over (c) Calculate the total area of the two fields. … m2 [6] (d) Maria walks in a straight line from D towards A. She stops when she is at her closest point to C. Calculate her distance from C. … m [2]

14 0607/41/O/N/17 © UCLES 2017 9 Two bags each contain white balls and black balls only. Bag A Bag B Bag A contains 3 white balls and 5 black balls. Bag B contains 6 white balls and 3 black balls. A ball is picked at random from the 8 balls in Bag A. • If it is white, the ball is not replaced and a second ball is picked at random from Bag A. • If it is black, a second ball is picked at random from the 9 balls in Bag B. (a) Complete the tree diagram. White Black White 1st ball 2nd ball Black White Black [3]

15 0607/41/O/N/17 © UCLES 2017 [Turn over (b) Find the probability that (i) both balls are white, … [2] (ii) exactly one of the two balls is black. … [3]

16 0607/41/O/N/17 © UCLES 2017 10 (a) Make y the subject of 3x + y = 8. y = … [1] (b) The line 3x + y = 8 intersects the curve x2 + y2 = 25 at two points. (i) Use substitution to show that 10x2 − 48x + 39 = 0. [3] (ii) Solve the equation 10x2 − 48x + 39 = 0 and find the co-ordinates of the two points of intersection. Show all your working. ( … , …) ( … , …) [5]

17 0607/41/O/N/17 © UCLES 2017 [Turn over 11 x 6 –6 –6 0 12 y x x x x x 2 3 2 3 f 2 = + - + ^ ^ ^ h h h (a) On the diagram, sketch the graph of y = f(x) for values of x between −6 and 6. [3] (b) Find the co-ordinates of the local minimum. ( … , …) [2] (c) Find the equations of the two asymptotes that are parallel to the y-axis. … and … [2] (d) g(x) = 3x + 2 Solve. (i) f(x) = g(x) … [3] (ii) x x f g 2 ^ ^ h h … [3]

18 0607/41/O/N/17 © UCLES 2017 12 f(x) = 5 − 3x g(x) = 2x + 3 (a) Solve f(x) = 11. x = … [2] (b) Find f −1(x). f −1(x) = … [2] (c) Solve f(x) × g(x) = 0. … [2] (d) Simplify. (i) g−1(g(x)) … [1] (ii) f(f(x)) + g(x) … [3] (iii) x x 2 4 f g + ^ ^ h h … [3]

19 0607/41/O/N/17 © UCLES 2017 13 NOT TO SCALE A B Q C O c a P OABC is a parallelogram and OPQ is a straight line. P divides AC in the ratio 1 : 2. P divides OQ in the ratio 1 : 2. OA a = and OC c = . (a) Find these vectors in terms of a and/or c. Give each answer in its simplest form. (i) AC … [1] (ii) OP … [2] (iii) CQ … [2] (b) Use your answer to part(a)(iii) to complete the statement. The points C, B and Q are … [1]

20 0607/41/O/N/17 © UCLES 2017 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 International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. BLANK PAGE

® IGCSE is a registered trademark. This document consists of 7 printed pages. © UCLES 2017 [Turn over Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/41 Paper 4 (Extended) October/November 2017 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 2017 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 2017 © UCLES 2017 Page 2 of 7 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 2017 © UCLES 2017 Page 3 of 7 Question Answer Marks Partial Marks 1(a)(i) 18 1 1(a)(ii) 10 1 1(a)(iii) 12.5 cao 1 1(a)(iv) 13.25 1 1(a)(v) 6.5 nfww 2 B1 for 17 or 10.5 seen 1(b) It is the largest oe 1 2(a) 3167.94 3 M2 for 3000 × 1.025 × 1.0152 oe or M1 for 3000 × 1.025 [× kn] soi by 3075 or for 3000 × 0.025 soi by 75 2(b) 3144 3 M2 for 3000 × 0.016 × 3 + 3000 oe or M1 for 3000 × 0.016 × 3 soi by 144 or for 3000 × 0.016 × n + 3000, n > 1 2(c) log ( 3500 ) 3000 1.025 × ÷ log 1.015 oe M2 or M1 for 3000 × 1.025 × 1.015n = 3500 implied by at least two correct attempts with n > 2, n integer 3000 × 0.016 × n + 3000 = 3500 oe or 3000 × 0.016 × n = 500 oe M1 9.7[0] or 9.695... and 10.4 or 10.41 to 10.42 oe A1 A1 depends on corresponding years 3(a) 4, 10, 18, 28 2 B1 for any 2 in correct position or 0, 4, 10, 18 3(b)(i) 13, 15 1 3(b)(ii) 2n + 3 oe 2 B1 for 2n [+ c], or kn + 3, k ≠ 0 3(c) n2 + 7n + 6 or (n + 6) (n + 1) 2 M1 for 2 their (2n + 3) + n2 + 3n or 2nd differences = 2, 2, [2] and quadratic or correct unsimplified 4(a) 6 points correctly plotted 2 ± small square, B1 for 4 or 5 points correct. 4(b) Positive 1 4(c)(i) 10.6x + 5.7[0] 2 or a = 10.57..., b = 5.702... B1 for y = ax + b with either a or b correct. SC1 for 11x + 5.7 4(c)(ii) 29[.0] or 28.95 to 29.02 1 Strict FT (their 10.6 × 2.2) + their 5.7 4(c)(iii) [Too far] outside range of data oe 1

0607/41 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 4 of 7 Question Answer Marks Partial Marks 5(a) 45 360 × 2π × 22.5 = 2πr or 2 45 22.5 22.5 360 r × π× = π× × M2 or M1 for 45 360 × 2π × 22.5 or 2 45 22.5 360 × π× 2.812 to 2.813 A1 5(b) 241 or 240.7 to 241.0... 5 M3 for 45 360 × π (32.52 – 22.52) oe or M2 for 45 360 × π × 32.52 or 45 360 × π × 22.52 and M1 for π × 2.812 5(c) 963 or 964 or 962.8 to 963.6 2 FT their (b) × 4 B1 for length scale factor = 2, 3 8 , 1 2 soi, or area factor = 22 oe 6(a) Translation 5 6 −       2 B1 for each 6(b) Triangle at (2, 6), (3, 6), (2, 12) 2 B1 for any stretch with x-axis invariant or stretch with scale factor 3 and y = k invariant or stretch with y-axis invariant, s.f. = 3 6(c) 90° [anti-clockwise] or 270° clockwise Centre (a, a + 1) x = a + 3 OR 90° clockwise or 270° [anticlockwise] Centre (b +5, b ) y = b + 3 3 B1 for each Dep on 90° anti-clockwise or 270° clockwise Dep on previous mark If 0 scored, SC1 for centre (a, a + 1) and x = a + 3 OR B1 for each Dep on 90° clockwise or 270° anti- clockwise Dep on previous mark If 0 scored, SC1 for centre (b + 5, b ) and y = b + 3 7(a) 192.5 3 B1 for 2.75 oe M1 for 70 × their 2.75

0607/41 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 5 of 7 Question Answer Marks Partial Marks 7(b)(i) 69.4 or 69.36 to 69.41 4 M1 for 180 ÷ 85 A1 for 2.12 or 2.117... or 36 17 oe M1dep for their total distance ÷ their total time (dependent on first M1) 7(b)(ii) 04 12[...] 2 M1 for correctly converting their total time to hours and minutes. or B1 for 02 05 seen or total time = 5h 22min or 322 min 8(a) 300° 3 B1 for ABN′ = 150 or ABS′ = 30 B1 for N′BC = 120 or CBS′ = 60 OR B1 for ACB = 35 B1 for N′CB = 60 8(b) 60 cos55 oe M2 or M1 for cos 55 = 60 AC oe 104.60 to 104.62 A1 8(c) 9780 or 9776 to 9782. ... 6 B1 for angle ADC = 41 M2 for[AD=] 104.6sin76 sin( 41) their (154.7...) or M1 for 104.6 sin( 41) sin76 = AD their M1 for 1 2 × 60 × 104.6 × sin 55 oe M1 for 1 2 × 104.6 × their AD × sin 63 oe 8(d) 93.2 or 93.16 to 93.23 2 M1 for 104.6 × sin 63 oe 9(a) 3 8 , 5 8 correctly placed 2 7 , 5 7 correctly placed 6 9 , 3 9 correctly placed 3 B1 for each pair 9(b)(i) 6 56 oe 2 M1 for their 3 8 × their 2 7 9(b)(ii) 115 168 oe 3 M2 for their 3 8 × their 5 7 + their 5 8 × their 6 9 oe or M1 for 1 of above products

0607/41 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 6 of 7 Question Answer Marks Partial Marks 10(a) 8 – 3x final answer 1 10(b)(i) x² + (their (8 – 3x))2 = 25 M1 64 – 24x – 24x + 9x2 B1 or their (8 – 3x)2 expanded correctly Completion to 10x2 – 48x + 39 = 0 A1 10(b)(ii) (1.04 or 1.036... , 4.88 to 4.89...) with working (3.76 or 3.763 to 3.764 ,–3.29.. to –3.28) with working 5 M1 for 2 48 ( 48) 4(10)(39) 2 10 ± − − × or sketch of parabola with both zeros > 0 or sketch of circle centre O with straight line B1 for each x co-ordinate B1 for each y co-ordinate or B1 , B1 for correct pairs reversed 11(a) Correct sketch 3 B1 for each branch 11(b) (–0.93[0], –0.252) or (–0.9303..., 0.2521...) 2 B1 for each co-ordinate 11(c) x = –2 final answer x = 3 final answer 2 B1 for each 11(d)(i) –2.12 or –2.117... –0.747 or –0.7465... 2.53 or 2.530 to 2.531 3 B1 for each 11(d)(ii) x < –2.12 –2 < x < –0.747 2.53 < x < 3 3 FT B1 for each only if three answers in (i) and asymptotes used 12(a) –2 2 M1 for –3x = 11 – 5 oe 12(b) 5 3 x − oe final answer 2 M1 for 3x = 5 – y or x = 5 – 3y or y – 5= –3x or 5 5 3 = − y x or better 12(c) 5 3 oe – 3 2 oe final answers 2 B1 for each -6 6 -6 -4 -2 2 4 6 8 10 x y

0607/41 Cambridge IGCSE – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 7 of 7 Question Answer Marks Partial Marks 12(d)(i) x 1 12(d)(ii) 11x – 7 3 M2 for 5 – 3(5 – 3x) + 2x + 3 or M1 for 5 – 3(5 – 3x) 12(d)(iii) 26 8 (5 3 )(2 3) x x x − − + final answer 3 M1 for 2(2 3) 4(5 3 ) + + − x x oe M1 for common denominator (5 – 3x)(2x + 3) 13(a)(i) c – a oe 1 13(a)(ii) 2 3 a + 1 3 c or 1 3 (2a + c) 2 B1 for correct unsimplified or correct route e.g. c + 2 3 JJJG CA or a + 1 3 their (i) 13(a)(iii) 2a 2 B1 for correct unsimplified or correct route e.g. –c + 3 × their (ii) 13(b) Collinear oe 1