Cambridge IGCSE Mathematics (9-1) (UK only) 0626 — 2017 Oct/Nov Paper 6 · Variant 1

This document consists of 16 printed pages. DC (NF/SG) 133752/4 © UCLES 2017 [Turn over Cambridge International Examinations Cambridge International General Certificate of Secondary Education (9–1) * 9 7 6 1 5 0 9 6 5 6 * MATHEMATICS 0626/06 Paper 6 (Extended) October/November 2017 2 hours Candidates answer on the Question Paper. Additional Materials: Geometrical instruments Tracing paper (optional) 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. You may use an HB pencil for any diagrams and graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. Electronic calculators should be used. If working is required for any question it must be shown below that question. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 96. This syllabus is regulated for use in England as a Cambridge International Level 1/Level 2 (9–1) Certificate.

2 0626/06/O/N/17 © UCLES 2017 1 The Newbold family are going on holiday to Switzerland. They travel by ferry from Dover in England to Calais in France. (a) The bearing of Calais from Dover is 118°. Work out the bearing of Dover from Calais. …° [2] (b) (i) The shop on the ferry sells different sized bottles of the same perfume. The bottles are priced in euros (€). €5.80 for 18 ml €9.10 for 29 ml €12.25 for 37 ml Which bottle is the best buy? Show your working. … [3]

3 0626/06/O/N/17 © UCLES 2017 [Turn over (ii) A gold watch costs €1000 on the ferry. The same watch can be bought in Switzerland for 1040 Swiss francs (CHF). The exchange rate on the ferry is £1 = €1.358. The exchange rate in Switzerland is 1 CHF = £0.679. Calculate the difference in the cost of the watch on the ferry and in Switzerland. Give your answer in pounds, correct to the nearest penny. £ … [4] (c) The ratio of the number of child passengers : adult passengers : crew members = 11 : 16 : 3. (i) There are 340 more adult passengers than child passengers. Work out the number of crew members. … [2] (ii) Write down the ratio of total passengers : crew in its simplest form. … : … [1] (d) The ferry has a mass of 47 600 tonnes, correct to the nearest 50 tonnes. (i) Write down the lower bound for the mass of the ferry. … tonnes [1] (ii) Write 47 600 in standard form. … [1]

4 0626/06/O/N/17 © UCLES 2017 2 (a) C B S 23 4 60 pupils are asked which activities they like from Swimming (S), Bowling (B) and the Cinema (C). • 5 pupils do not like any of the activities • 3 pupils only like Swimming • 13 pupils like Swimming but not Bowling • 7 pupils like Cinema and Bowling but not Swimming • 40 pupils like Bowling (i) Complete the Venn diagram. [3] (ii) Work out the number of pupils who like at least 2 of the activities. … [1] (b) Use set notation to describe the shaded regions in each Venn diagram. (i) A B … [1] (ii) A B … [1]

5 0626/06/O/N/17 © UCLES 2017 [Turn over 3 In this question, all lengths are in centimetres. NOT TO SCALE 2x + 1 4x 4x – 2 The diagram shows a rectangle. The diagonal has length 4x. (a) Write down an expression for the perimeter of the rectangle. Give your answer in its simplest form. … [2] (b) (i) Show that 4x2 − 12x + 5 = 0. [3] (ii) Find the length of the diagonal. … cm [4]

6 0626/06/O/N/17 © UCLES 2017 4 (a) Sammy invests £6000. The value of his investment decreases exponentially by 4% each year. (i) Work out the value of his investment after 2 years. £ … [2] (ii) Write down an expression for the value of his investment after k years. … [1] (b) Teresa invests £3000 at the same time as Sammy invests his money. The value of Teresa’s investment increases exponentially by 4% each year. Write down an expression for the value of Teresa’s investment after k years. … [1] (c) (i) After n years, the value of Sammy’s investment is equal to the value of Teresa’s investment. Show that 12 13 2 n = c m . [2]

7 0626/06/O/N/17 © UCLES 2017 [Turn over (ii) Find the number of complete years it takes for the value of Teresa’s investment first to be greater than the value of Sammy’s investment. … years [2] (d) The sketch graph below shows how Teresa’s investment changes with time. On the same graph, show how Sammy’s investment changes with time. Amount (£) 3000 0 Time (years) [2]

8 0626/06/O/N/17 © UCLES 2017 5 (a) A B E C D NOT TO SCALE A, B, C and D are points on the circumference of a circle. The chords AC and BD meet at E. (i) Show that triangle ABE is similar to triangle DCE. Give a reason for each step of your working. [3] (ii) AB = 7.2 cm, BE = 4.8 cm and CD = 12 cm. Work out the length of CE. CE = … cm [2]

9 0626/06/O/N/17 © UCLES 2017 [Turn over (b) x° 61° 68° H F NOT TO SCALE E G F, G and H are points on the circumference of another circle. EF and EG are tangents to the circle at F and G. Work out the value of x. Give a reason for each step of your working. x = … [4]

10 0626/06/O/N/17 © UCLES 2017 6 (a) Rhona asked each of 50 pupils to guess the mass, m grams, of a marble. The results are recorded in the table. Mass of marble (m grams) Frequency m 20 30 1 G 5 m 30 40 1 G 7 m 40 60 1 G 16 m 60 80 1 G 12 m k 80 1 G 10 (i) Using mid-interval values, Rhona worked out an estimate of the mean as 61.2 grams. Work out the value of k which gives this estimate of the mean. k = … [5]

11 0626/06/O/N/17 © UCLES 2017 [Turn over (ii) Complete the histogram to show the information in the table. 0 20 40 60 80 100 120 140 160 Mass (m grams) [4] (b) A bag contains n marbles. There are 4 yellow marbles, the rest are green. Two marbles are taken out of the bag, at random, without replacement. The probability that both marbles are yellow is 6 1 . Work out the probability that both marbles are green. … [6]

12 0626/06/O/N/17 © UCLES 2017 7 y x (6, 2) NOT TO SCALE P O The diagram shows a circle, centre O, inside a rhombus. Each side of the rhombus is a tangent to the circle. Point P has co-ordinates (6, 2) and lies on the circle and on the rhombus. (a) Calculate OP. Give your answer as a surd. OP = … [2] (b) Write down the equation of the circle. … [2]

13 0626/06/O/N/17 © UCLES 2017 [Turn over (c) Show that the tangent to the circle at P has the equation y = −3x + 20. [3] (d) Work out the total area shaded on the diagram. … [6]

14 0626/06/O/N/17 © UCLES 2017 8 (a) 1 1 0 2 3 4 5 –1 –1 –2 –3 –4 –5 –6 –7 –8 –9 –2 –3 –4 –5 –6 –7 2 3 4 5 y x B A (i) Describe fully the single transformation that maps triangle A onto triangle B. … … [3] (ii) Write down the matrix that maps triangle A onto triangle B. f p [2]

15 0626/06/O/N/17 © UCLES 2017 [Turn over (b) (i) Describe fully the single transformation represented by the matrix 1 0 0 1 - c m . … … [2] (ii) Work out 1 0 0 1 1 0 0 1 - - c cm m . f p [1] (iii) Give a geometrical explanation of the result in part (b)(ii). … … [1] Question 9 is printed on the next page.

16 0626/06/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. 9 A curve has equation y = x3 − 6x2 + 9x. (a) Find x y d d . x y d d = … [2] (b) Find the gradient of the curve when x = 2. … [2] (c) (i) Find the co-ordinates of the two turning points of the curve. (… , …) and (… , …) [4] (ii) Determine whether each turning point is a maximum or a minimum. Show clearly how you decide. [3]

® IGCSE is a registered trademark. This syllabus is regulated for use in England as a Cambridge International Level 1/Level 2 (9–1) Certificate. This document consists of 8 printed pages. © UCLES 2017 [Turn over Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education (9–1) MATHEMATICS 0626/06 Paper 6 October/November 2017 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 2017 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

0626/06 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 2 of 8 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

0626/06 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 3 of 8 Question Answer Marks Partial Marks 1(a) 298 2 M1 for diagram with 118 correctly marked together with the relative positions of Calais and Dover or 118 + 180 or 62 seen. 1(b)(i) 29 ml with three correct consistent values worked out. 3 M2 for 3 correct consistent divisions soi or M1 for one correct division 1(b)(ii) 30.22 or 30.21 4 M1 for 1000 1.358 or better M1 for 1040 .679 × or better M1 for a correct, or correct ft, difference in a consistent currency e.g. their 736 706 −their 1(c)(i) 204 2 M1 for 340 16 11 − 1(c)(ii) 9 : 1 1 1(d)(i) 47 575 cao 1 1(d)(ii) 4.76 4 10 × cao 1 2(a)(i) 3 B2 for five numbers correct or for four numbers correct and a total of 60 or B1 for three or four numbers correctly placed. 2(a)(ii) 44 1 FT 23 + 4 + their (7 + 10) 2(b)(i) A ∩B oe 1 2(b)(ii) ( ∪ A B)' oe 1 3(a) 12 2 − x or ( ) 2 6 1 − x 2 M1 for ( ) ( ) 2 4 2 2 2 1 − + + x x oe or 8 4 x − or 4 2 + x or B1 for 12 + x k or 2 − kx [23] [4] 10 3 6 7 2 5

0626/06 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 4 of 8 Question Answer Marks Partial Marks 3(b)(i) ( ) ( ) ( ) 2 2 2 4 4 2 2 1 = − + + x x x oe M1 2 1 6 8 8 4 − − + x x x oe or 2 4 2 2 1 + + + x x x oe B1 2 2 2 16 16 16 4 4 4 1 = − + + + + x x x x x leading to 2 4 12 5 0 − + = x x A1 3(b)(ii) Correct working leading to answer of 10 only. 4 M1 for ( )( )[ ] 2 2 0 + + = x a x b where ab = 5 or a + b = −6 or ( )( )[ ] 4 0 + + = x c x d where cd = 5 or c + 4d = 12 − A1 for ( )( ) 2 1 2 5 [ − − x x =0] B1FT for 0.5 and 2.5 x their x their = = dep on M1 B1 for 10 only 4(a)(i) 5529.6[0] 2 M1 for [6000 ( ) 2 ] 0.96 × oe 4(a)(ii) 6000 ( ) 0.96 × k 1 4(b) 3000 ( ) 1.04 × k 1 4(c)(i) 3000 ( ) 1.04 × n =6000 ( ) 0.96 × n M1 FT their (a)(ii) provided of form 6000 n a 0 < a < 1 and their (b)(i) provided of form 3000bn b > 1 1.04 6000 3000 0.96 = n n leading to 13 2 12  =     n A1 A1 dep

0626/06 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 5 of 8 Question Answer Marks Partial Marks 4(c)(ii) 9 2 M1 for 8 13 12       = 1.89[7…] or 9 13 12       = 2.05[5…] or for at least 2 other trials correctly evaluated. If zero scored SC1 for answer of 8 or ‘8 to 9’ 4(d) Exponentially decreasing graph drawn from 6000 2 M1 for exponentially decreasing graph from y-axis or for decreasing graph starting from 6000 5(a)(i) Clear evidence with geometric reasons that , BAE CDE ∠ = ∠ ABE DCE ∠ = ∠ and BEA CED ∠ = ∠ therefore 3 equal angles, hence similar. 3 M2 for two of: , BAE CDE ∠ = ∠ angles in same segment are equal. ABE DCE ∠ = ∠ angles in same segment are equal BEA CED ∠ = ∠ vertically opposite or M1for one of the above. or for 3 pairs of angles and no, or incorrect, reasons. A1 for three of the above or two of the above and for clear statement that therefore that 3rd pair is equal and hence that ∆ABE and ∆DCE have 3 equal angles and are therefore similar. 5(a)(ii) 8 2 M1 for 12 7.2 oe or 4.8 7.2 oe or 12 4.8 7.2 = CE oe 5(b) 63 with at least 2 geometric reasons. 4 B1 for ∆EFG is isosceles triangle or equal tangents EF = EG B1 for FGE ∠ (or GFE ∠ ) = 56 B1 FHG EFG ∠ = ∠ (or EGF ∠ ) alternate segment theorem B1 for 63

0626/06 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 6 of 8 Question Answer Marks Partial Marks 6(a)(i) 130 5 B1 for at least 3 correct midpoints seen 25, 35, 50, 70 B1 for 50 × 61.2 or 3060 seen M1FT for 25 × 5 + 35 × 7 + 50 × 16 + 70 × 12 + ‘x’ × 10 = 50 × 61.2 A1 ‘x’ = 105 6(a)(ii) 3 correct bars drawn and frequency density axis correctly labelled 4 FT their k M1FT for at least 3 correct frequency densities soi 0.5, 0.7, 0.8, 0.6, their 0.2 A1 for a correct bar drawn. A1 for 3 bars correct. B1 for vertical axis labelled ‘frequency density’ and correct scale plotted. 6(b) 5 18 oe 6 M1 for 4 n and 3 1 − n or 4 n and 3 n seen M1FT dep for 4 n × 3 1 − n or 4 n × 3 n A1 for 4 n × 3 1 1 6 = − n oe or n(n–1) = 72 A1 for n = 9 M1FT for ( ) ( ) ( ) 4 5 1 − − × − their n their n their n their n , 7(a) 40 or 2 10 2 M1 for 62 + 22 7(b) x2 + y2 = 40 2 FT their 40 B1 for x2 + y2 = k, where k > 0 7(c) gradient OP = 2 6 oe M1 perpendicular gradient 3 = − M1 Dependent on first M1 2 3 6 = −× + c and 20 = c A1

0626/06 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 7 of 8 Question Answer Marks Partial Marks 7(d) 141 or 140.9 to 141.0… 6 M1 for π × their ( ) 2 40 B1 for 20 and 20 3 oe seen M1 for 20 20 3 × × k where k = 0.5, 1 or 2 A1 for 800 3 M1 for their 800 3 −their 40π 8(a)(i) Enlargement [Scale factor] −2 Centre O oe 3 B1 for each 8(a)(ii) 2 0 0 2 −     −   2 M1 for 0 0 k k −     −   or 2 0 0 2       8(b)(i) Reflection y -axis or 0 = x 2 B1 for each 8(b)(ii) 1 0 0 1       1 8(b)(iii) Two reflections in y-axis are equivalent to the identity transformation. oe 1 9(a) 2 3 12 9 − + x x 2 M1 for one correct term 9(b) 3 − 2 M1 for 2 = x substituted into their d d y x 9(c)(i) (3,0) , (1,4) 4 M1 for their ( ) 2 3 12 9 0 − + = x x M1FTdep for [3]( ( )[ ] ) 0 + + = x a x b where 3 = ab or 4 + = − a b or for ( )( )[ ] 3 0 + + = x c x d where 9 = cd or 3 12 + = − c d or for correct use of quadratic formula, allow one error A1 for 3 = x and 1 = x A1 (3, 0) and (1, 4)

0626/06 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2017 © UCLES 2017 Page 8 of 8 Question Answer Marks Partial Marks 9(c)(ii) (1,4) is a max correctly justified and ( ) 3,0 is a min correctly justified 3 M1FT for 2 2 d 6 12 d = − y x x A1 for 1 = x , 2 2 d 6 0 d = −< y x max A1 for 3, = x 2 2 d 6 0 d = > y x min Alternative method M1FT for considering d d y x both sides of 1 = x or 3 = x A1 for 1 = x is a max with valid points tested correctly A1 for 3 = x is a min with valid points tested correctly