Cambridge IGCSE Mathematics - International 0607 — 2016 Oct/Nov Paper 4 · Variant 3

This document consists of 19 printed pages and 1 blank page. DC (RW/JG) 117017/3 © UCLES 2016 [Turn over * 9 0 9 3 7 0 0 0 3 3 * CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/43 Paper 4 (Extended) October/November 2016 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 0607/43/O/N/16 © UCLES 2016 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 0607/43/O/N/16 © UCLES 2016 [Turn over Answer all the questions. 1 (a) Work out. (i) 79507 3 … [1] (ii) . . 3 6 0 63 1 2 + … [1] (b) . p 5 62 105 # = . q 6 83 10 3 # = - Work out, giving your answers in standard form. (i) p2 … [2] (ii) q p … [2]

4 0607/43/O/N/16 © UCLES 2016 2 Gennaro has $276 480 in his Pension Fund. (a) Gennaro has two options. Option A Receive 25% of the $276 480 now plus 5.5% of the remaining 75% each year. Option B Receive 5.5% of the whole $276 480 each year. (i) Show that the total amount Gennaro will have received at the end of 10 years, if he chooses option A, is $183 168. [3] (ii) After how many whole years will the total amount received using option B become more than the total amount received under option A? … [4] (b) The $276 480 is 8% more than the amount the Pension Fund was worth one year ago. Calculate how much it was worth one year ago. $ … [3]

5 0607/43/O/N/16 © UCLES 2016 [Turn over 3 y x 0 6 5 4 3 2 1 –1 –1 –2 –3 –4 –5 –6 –7 –8 –2 –3 –4 –5 1 B D C 2 3 4 5 6 7 A Describe fully the single transformation that maps (a) triangle A onto triangle B, … … [2] (b) triangle A onto triangle C, … … [3] (c) triangle A onto triangle D. … … [3]

6 0607/43/O/N/16 © UCLES 2016 4 NOT TO SCALE V C B N A D O The diagram shows a solid, square-based pyramid VABCD. O is the centre of the base ABCD and VO is perpendicular to the base. N is the midpoint of AB. AB = 6 cm and VO = 8 cm. (a) Calculate (i) the volume of the pyramid, … cm3 [2] (ii) the length of VN. … cm [2]

7 0607/43/O/N/16 © UCLES 2016 [Turn over (b) The similar pyramid VPQRS is removed from the original pyramid to leave the solid below. NOT TO SCALE C B R Q P S A D The height of this solid is half the height of the pyramid VABCD. (i) Find the volume of this solid. … cm3 [3] (ii) Find the total surface area of this solid. … cm2 [5]

8 0607/43/O/N/16 © UCLES 2016 5 –3 –10 25 y x 3 0 x x x 4 6 f 3 = - + ^ h (a) On the diagram, sketch the graph of y x f = ^ h for x 3 3 G G - . [2] (b) Solve the equation x x 2 3 f = + ^ h . x = … or x = … or x = … [3] (c) (i) Find the co-ordinates of the local maximum point and the local minimum point. Maximum (… , …) Minimum (… , …) [3] (ii) Find the range of values of k for which x k f = ^ h has only one solution. … [1] (d) Describe fully the symmetry of the graph of y x f = ^ h. … … [3]

9 0607/43/O/N/16 © UCLES 2016 [Turn over 6 y x 0 × B × C × A NOT TO SCALE The diagram shows the points A (-1, -1), B (1, 3) and C (6, 3). (a) The points A, B, C and D are the vertices of a parallelogram. Write down the co-ordinates of the three possible positions of D. (… , …) (… , …) (… , …) [3] (b) E is a point such that C is the midpoint of the line AE. Find the co-ordinates of the point E. (… , …) [2] (c) The line L is perpendicular to the line AC and goes through A. Find the equation of the line L. … [4]

10 0607/43/O/N/16 © UCLES 2016 7 A farmer measured the milk yield of each of his 120 cows over a one-year period. The results are shown in the frequency table. Milk yield (m litres) Frequency Milk yield (m litres) Cumulative frequency m 5000 6000 1 G 6 m 6000 G 6 m 6000 6500 1 G 12 m 6500 G m 6500 7000 1 G 22 m 7000 G m 7000 7500 1 G 37 m 7500 G m 7500 8000 1 G 20 m 8000 G m 8 00 9000 0 1 G 17 m 9000 G m 9000 10000 1 G 6 m 10000 G 120 (a) (i) Complete the cumulative frequency table. [1] (ii) Complete the cumulative frequency curve. m 5000 0 10 20 30 40 50 60 70 80 Cumulative frequency Milk yield (litres) 90 100 110 120 6000 7000 8000 9000 10 000 [3]

11 0607/43/O/N/16 © UCLES 2016 [Turn over (iii) Use your graph to estimate the median. … litres [1] (iv) Use your graph to estimate the inter-quartile range. … litres [2] (v) The farmer sells the cows with a milk yield of less than 6200 litres. Use your graph to estimate the number of cows he sells. … [1] (b) On the grid below, complete the histogram to represent the data in the first table. m 5000 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Frequency density Milk yield (litres) 6000 7000 8000 9000 10 000 [4]

12 0607/43/O/N/16 © UCLES 2016 8 A ship sails on the following course. • 60 km on a bearing of 025° from A to B • 80 km on a bearing of 115° from B to C • 75 km on a bearing of 195° from C to D The diagram shows the course. A C B D NOT TO SCALE North North North 195° 115° 25° (a) Show that angle ABC = 90°. [1] (b) Calculate angle BCA. Angle BCA = … [2] (c) Calculate the distance AC. AC = … km [2]

13 0607/43/O/N/16 © UCLES 2016 [Turn over (d) Calculate the distance AD. AD = … km [4] (e) Calculate the bearing of D from A. … [4]

14 0607/43/O/N/16 © UCLES 2016 9 Justine travels 760 km in her car. (a) Justine’s average speed for the journey is 77 km/h. Calculate the time Justine takes to complete the journey. Give your answer in hours and minutes correct to the nearest minute. … h … min [3] (b) Justine travels 270 km on main roads and 490 km on autoroutes. On main roads her car travels x km on each litre of fuel. On autoroutes her car travels x 4 + ^ h km on each litre of fuel. (i) Write down an expression, in terms of x, for the fuel that Justine’s car uses on main roads on this journey. … litres [1] (ii) Altogether Justine’s car uses 62 litres of fuel for the whole journey. Write down an equation in x and show that it simplifies to x x 31 256 540 0 2 - - = . [3]

15 0607/43/O/N/16 © UCLES 2016 [Turn over (iii) Solve the equation x x 31 256 540 0 2 - - = to find the distance Justine’s car travels on 1 litre of fuel on autoroutes. … km [4]

16 0607/43/O/N/16 © UCLES 2016 10 (a) (i) Factorise. x x 2 3 1 2 - + … [2] (ii) Show that x x 2 1 2 3 + + - can be written as x x x 2 2 1 1 - - - ^ ^ ^ h h h . [3] (b) –3 –10 20 y x 5 0 x x x x 2 2 1 1 f - - - = ^ ^ ^ ^ h h h h (i) On the diagram, sketch the graph of y x f = ^ h for values of x between -3 and 5. [2]

17 0607/43/O/N/16 © UCLES 2016 [Turn over (ii) On the same diagram, sketch the graph of y x 2 1 = + . [2] (iii) Write down the equations of the asymptotes to the graph of y x f = ^ h. … … [2] (iv) Solve x 0 f = ^ h . x = … or x = … [2]

18 0607/43/O/N/16 © UCLES 2016 11 The 50 members of an activities group either go walking or cycling. The table shows the choices of the males and females. Walking Cycling Total Male 16 29 Female Total 22 50 (a) Complete the table. [2] (b) Two of the 50 members are chosen at random. Calculate the probability that they both go cycling. … [2] (c) Two of those who go walking are chosen at random. Calculate the probability that one is a male and the other is a female. … [3]

19 0607/43/O/N/16 © UCLES 2016 12 y is inversely proportional to the square root of x. When x = 25, y = 2. (a) Find y in terms of x. y = … [2] (b) Find the value of x when y = 3. … [2] (c) z = axn z is proportional to the cube of y. When x = 4, z = 500. Find the value of a and the value of n. a = … n = … [3]

20 0607/43/O/N/16 © UCLES 2016 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 the registered trademark of Cambridge International Examinations. This document consists of 6 printed pages. © UCLES 2016 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/43 Paper 4 (Extended) October/November 2016 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 will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the October/November 2016 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

Page 2 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2016 0607 43 © UCLES 2016 Abbreviations awrt answers which round to cao correct answer only dep dependent FT follow through after error isw ignore subsequent working oe or equivalent SC Special Case nfww not from wrong working soi seen or implied Question Answer Mark Part Marks 1 (a) (i) 43 1 (ii) 14.5 or14.54 to 14.55 1 (b) (i) 3.16 × 1011 or 3.158... × 1011 2 B1 for figs 316 or 3158... or k × 1011 where 1 < k < 10 (ii) 8.23 × 107 or 8.228... × 107 2 B1 for figs 823 or 8228... or k × 107 where 1 < k < 10 2 (a) (i) 276 480 × 0.25 oe 0.75× 276 480 × 0.055 × 10 oe adding with no errors M1 M1 M1 Dependent on M1 M1 (ii) 19 nfww 4 B3 for 18.2 or 18.18… or 18 (with correct working) or M2 for 0.055 × 276 480 × n = 0.25 × 276 480 + 0.055 × 0.75 × 276 480 × n oe or M1 for 0.055 × 276 480 × n or 0.25 × 276 480 + 0.055 × 0.75 × 276 480 × n (b) 256 000 3 M2 for 276 480 ÷ 1.08 oe or M1 for 108% = 276 480 3 (a) Reflection x = –2 1 1 In all three parts of (a) give 0 for any indication of second transformation. (b) Rotation 90° [anticlockwise] oe (5, 1) 1 1 1 (c) Stretch x-axis oe invariant [stretch factor] 3 1 1 1

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2016 0607 43 © UCLES 2016 Question Answer Mark Part Marks 4 (a) (i) 96 2 M1 for 3 1 × 6 × 6 × 8 (ii) 8.54 or 8.544... 2 M1 for 82 + 32 (b) (i) 84 3FT M2 for 8 7 × their (a)(i) oe or M1 for 96 × ( 2 1 )3 or 3 1 × 3 × 3 × 4 soi by 12 (ii) 122 or 121.8 to121.9 5 M3 for 4 × 4 3 × 2 1 × 6 × their (a)(ii) oe or 4 × 2 1 × (6 + 3) × 1 2 their (a)(ii) oe or M2 for 4 3 × 2 1 × 6 × their (a)(ii) oe or 2 1 × (6 + 3) × 1 2 their (a)(ii) oe or M1 for 2 1 × 6 × their (a)(ii) or 2 1 × 3 × 2 1 their (a)(ii) and M1 for 36 + 9 + 4 × their trapezium area oe 5 (a) Correct sketch f(x)=x^3 - 4x + 6 -3 -2 -1 1 2 3 -10 -5 5 10 15 20 25 x y 2 B1 for correct cubic shape with maximum on left of minimum (b) −2.67 or –2.669 ... 0.524 or 0.5239 to 0.5240 2.15 or 2.145... 1 1 1 (c) (i) Maximum (–1.15, 9.08) Minimum (1.15, 2.92) 3 or (–1.155 to –1.154, 9.079...) or (1.154 to 1.155, 2.920 to 2.921) B2 for either maximum or minimum or B1 for 1 correct value (ii) k < 2.92 and k > 9.08 1FT or above accuracy. (d) Rotational Order 2 (0, 6) 1 1 1

Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2016 0607 43 © UCLES 2016 Question Answer Mark Part Marks 6 (a) (4, –1), (–6, –1), (8, 7) 3 B1 for each (b) (13, 7) 2 B1 for each co-ordinate (c) y = – 4 7 x – 4 11 oe 4 isw correct 3 term equation B1 for 7 4 B1FT for – 4 7 M1 for correct method of finding 'c'. 7 (a) (i) [6], 18, 40, 77, 97, 114, [120] 1 (ii) Correct curve 3 All marks in (a) dependent on increasing cumulative frequencies B2FT for 6 points correctly plotted B1FT for 4 or 5 points correctly plotted If 0 scored SC1 for 'correct' curve translated consistently to left. (iii) 7100 to 7400 1FT FT their graph (iv) 750 to 1150 2 B1 for LQ = 6700 to 6900 or UQ = 7650 to 7850 (v) 9 or 10 or 11 1 (b) Correct graph 4 B3 for 6 correct heights or B2 for 4 or 5 correct heights or B1 for 2 or 3 correct heights B1 for correct widths If 0 scored B1 for correct frequency densities [0.006], 0.024, 0.044, 0.074, 0.04, 0.017, 0.006 8 (a) 360 – (155 + 115) oe 1 e.g. 25 + 65 with those angles marked on diagram (b) 36.9 or 36.86 to 36.87 2 M1 tan [C] = 80 60 oe (c) 100 or 99.93 to 100.04 2 M1 for 602 + 802 oe (d) 94.0 or 94.1 or 94.01 to 94.06 4 B1FT for ACD = 63.1 to 63.13 M1 for 752 + (their 100)2 – 2 ×75 × their 100 × cos their 63.1 A1 for 8838 to 8846

Page 5 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2016 0607 43 © UCLES 2016 Question Answer Mark Part Marks (e) 123 or 123.4 to 123.5 4 M2 for 75sin( 63.1) 94.1 their their or for [cos = ] )1. 94 ( ) 100 ( 2 75 )1. 94 ( ) 100 ( 2 2 2 their their their their × × − + or M1 for sin sin( 63.1) 75 94.1 = CAD their their 2 2 2 75 ( 100) ( 94.1) 2( 100) or ( r 9 ) o 4.1 f their their their their = + − A1 for 45.3 or 45.4 or 45.29 to 45.37 9 (a) 9 hours 52 mins 3 B2 for 9.870… or M1 for 760 ÷ 77 (b) (i) 270 x 1 (ii) x 270 + 4 + 490 x = 62 oe 270(x + 4) + 490x = 62x(x + 4) oe Completion with no errors M1 M1 A1 Could be over common denominator Must be at least one intermediate step (iii) (31x + 54)(x – 10) 10 and 54 31 − or 10 because x cannot be negative 14 cao M1 B2 B1 or correct substitution into formula or reasonable sketch or B1 for either 10 without support scores only the B1 10 (a) (i) (2x – 1)(x – 1) 2 SC1 for (2x + a)(x + b) where ab = 1 and a + 2b = –3 (ii) (2 1)( 2) 3 2 + − + − x x x oe 2 2 4 2 3 2 − + − + − x x x x 2 2 3 1 2 − + − x x x M1 A1 A1 Allow – 3x for – 4x + x (b) (i) Correct sketch f(x)=(2x-1)(x-1)/(x-2) f(x)=2x + 1 -3 -2 -1 1 2 3 4 5 -20 -10 10 20 x y 2 With no undue overlap at x = 2 or serious curving back B1 for either branch correct

Page 6 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2016 0607 43 © UCLES 2016 Question Answer Mark Part Marks (ii) Correct line 2 Not intersecting either branch B1 for line with positive gradient and positive y intercept (iii) y = 2x + 1 x = 2 1 1 (iv) 0.5 1 1 1 11 (a) Walking Cycling Total Male [16] 13 [29] Female 12 9 21 Total 28 [22] [50] 2 B1 for 3 or 4 correct (b) 2450 462 oe 2 M1 for 49 21 × 50 22 oe (c) 756 384 oe 3 M2 for 1 28 16 28 12 1 28 12 28 16 − × + − × their their their their their their oe or M1 for one of above products 12 (a) y = x 10 2 M1 for y = x k (b) 9 100 oe 2FT M1 for 3 x = their k (c) a = 4000, n = – 2 3 3 B2 for either or M1 for z = c 3       x k their oe