Cambridge IGCSE Mathematics (9-1) (UK only) 0626 — 2019 Oct/Nov Paper 6 · Variant 1

This document consists of 19 printed pages and 1 blank page. DC (SC/SW) 164777/3 © UCLES 2019 [Turn over Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education (9–1) * 3 8 0 4 0 4 9 3 0 8 * MATHEMATICS 0626/06 Paper 6 (Extended) October/November 2019 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 r, 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/19 © UCLES 2019 1 In this question all lengths are in centimetres. x + 4 x – 1 x NOT TO SCALE The area of this trapezium is 108 cm2. (a) Show that x2 + x - 110 = 0. [4]

3 0626/06/O/N/19 © UCLES 2019 [Turn over (b) Solve by factorisation x2 + x - 110 = 0. x = … or x = … [3] (c) Work out the perpendicular height of the trapezium. … cm [1]

4 0626/06/O/N/19 © UCLES 2019 2 NOT TO SCALE y x L P 0 10 4 The diagram shows a straight line L. The line crosses the axes at (10, 0) and (0, 4). (a) Find the equation of line L. … [3]

5 0626/06/O/N/19 © UCLES 2019 [Turn over (b) (i) Calculate the size of the acute angle that line L makes with the x-axis. … [2] (ii) The point P has co-ordinates (3, 0). Calculate the shortest distance from point P to line L. … [3]

6 0626/06/O/N/19 © UCLES 2019 3 (a) Vladimir invested some money at a rate of 3% per year simple interest. After one year he has £642.72. Work out how much money he invested. £ … [3] (b) On January 1st 2016 Maike changed £1000 to euros (€). On January 1st 2017 she changed these euros (€) back to pounds (£). The exchange rate on January 1st 2016 was £1 = €1.360. The exchange rate on January 1st 2017 was £1 = €1.174. Calculate the percentage increase in the value of her money for the year. Give your answer correct to 1 decimal place. …% [4] (c) Albert invests £400 at a rate of 2% per year compound interest. On the same day, Ximena invests £390 at a rate of 2.5% per year compound interest. Work out the number of whole years needed for the value of Ximena’s investment to be greater than the value of Albert’s investment. You must show working to support your answer. … [4]

7 0626/06/O/N/19 © UCLES 2019 [Turn over (d) Johan invests in an account that pays a rate of 4% compound interest per year. The account has a yearly charge of £20, which is deducted at the end of each year. (i) The iterative formula ur+1 = 1.04 # ur - 20 can be used to calculate the value of Johan’s investment in pounds at the end of each year. ur is the value of Johan’s investment at the end of year r. Given that u0 = 600, find u3. Give your answer correct to the nearest penny. u3 = … [3] (ii) Complete this statement. A person should not invest less than £ … in this account because … … [2]

8 0626/06/O/N/19 © UCLES 2019 4 (a) Kuda constructs a regular polygon with exterior angles of 12°. How many sides does Kuda’s polygon have? … [2] (b) Use a straight edge and compasses only for this question. You must show all your construction arcs. (i) Here are two sides of a parallelogram. Construct the parallelogram. [2]

9 0626/06/O/N/19 © UCLES 2019 [Turn over (ii) Line L is the perpendicular bisector of FG. Construct the circle that passes through the points F, G and H. F H L G [3]

10 0626/06/O/N/19 © UCLES 2019 5 (a) Some children are asked which vegetables they like from leeks (L), beans (B) and carrots (C). • 11 children like both leeks and beans • 9 children like leeks but do not like carrots • n(L) = 17 • 4 1 of the children asked like carrots (i) Complete the Venn diagram. 2 … … … … C B L 7 11 0 [3] (ii) Work out the number of children who like at least two of the vegetables. … [1] (iii) Find ( ( )) L B C n k j l . … [1]

11 0626/06/O/N/19 © UCLES 2019 [Turn over (b) Use set notation to describe the shaded region in each Venn diagram. (i) F G … [1] (ii) P Q R … [1]

12 0626/06/O/N/19 © UCLES 2019 6 Nathan bakes x chocolate cakes and y fruit cakes. He wants to bake • at least 4 chocolate cakes • at least 2 fruit cakes • a total of at least 9 cakes. (a) This information can be represented by three inequalities. Write down these inequalities. The first one has been done for you. x H 4 … … … [2] (b) A chocolate cake uses 400 g of flour. A fruit cake uses 700 g of flour. Nathan has 5600 g of flour. Write down another inequality in x and y to show this information. … [1]

13 0626/06/O/N/19 © UCLES 2019 [Turn over (c) Draw four lines on the grid to show your inequalities and shade the unwanted regions. 0 2 4 6 8 10 12 2 4 6 8 10 12 14 16 y x [6] (d) Find the greatest number of cakes Nathan can bake. … [1] (e) Nathan makes a profit of £1.50 for each chocolate cake and £4 for each fruit cake he bakes. He wants to maximise his profit. Find the number of each type of cake he should bake and the profit he makes. Nathan should bake … chocolate cakes and … fruit cakes. Nathan’s maximum profit is £ … [2]

14 0626/06/O/N/19 © UCLES 2019 7 64° NOT TO SCALE 25 cm B C O A The diagram shows two intersecting circles. The large circle has centre O and passes through points B and C. The small circle has centre A, radius 25 cm and passes through points B, C and O. Angle BAC = 64°. Triangles OAB and OAC are congruent. (a) For the small circle, calculate the area of sector ABC. …cm2 [2]

15 0626/06/O/N/19 © UCLES 2019 [Turn over (b) Calculate OB, the radius of the large circle. OB = … cm [4] (c) Calculate the area of triangle AOB. …cm2 [2] (d) Calculate the area of the shaded region. …cm2 [4]

16 0626/06/O/N/19 © UCLES 2019 8 In a survey, 250 commuters were asked how much money they spent on public transport in 2018. (a) The data was collected at a train station one Monday between 1 pm and 7 pm. Give two limitations in the way the data was collected and suggest an improvement for each. 1. Limitation … Improvement … 2. Limitation … Improvement … [2] (b) The results from the survey are shown in the histogram. 0 0 500 Frequency density Money spent in 2018 (£c) 1000 1500 2000 2500 3000 3500 There were 40 commuters who spent between £2500 and £3500. Complete the table. Money spent in 2018 (£c) Frequency 250 G c 1 500 500 G c 1 1000 1000 G c 1 1500 1500 G c 1 2500 2500 G c 1 3500 40 Total 250 [2]

17 0626/06/O/N/19 © UCLES 2019 [Turn over (c) Calculate an estimate for the mean amount of money spent on public transport by these commuters. £ … [4] (d) (i) On the grid, draw a cumulative frequency diagram to show the data from the survey. 0 500 Money spent in 2018 (£c) 1000 1500 2000 2500 3000 3500 0 100 200 300 Cumulative frequency [4] (ii) Use your cumulative frequency diagram to estimate the inter-quartile range. £ … [2]

18 0626/06/O/N/19 © UCLES 2019 9 A curve has equation y = x3 - 3x2. (a) Find x y d d . x y d d = … [2] (b) (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]

19 0626/06/O/N/19 © UCLES 2019 (c) Work out the exact values of x where the curve has gradient 6. Give your answers in their simplest form. x = … and x = … [3]

20 0626/06/O/N/19 © UCLES 2019 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 syllabus is regulated for use in England as a Cambridge International Level 1/Level 2 (9–1) Certificate. This document consists of 9 printed pages. © UCLES 2019 [Turn over Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education (9–1) MATHEMATICS 0626/06 Paper 6 October/November 2019 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 2019 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 2019 © UCLES 2019 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.

0626/06 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2019 © UCLES 2019 Page 3 of 9 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 2019 © UCLES 2019 Page 4 of 9 Question Answer Marks Partial Marks 1(a) ( )( ) 1 4 1 2 x x x + + − oe M1 ( )( ) 2 1 108 x x + − = or ( )( ) 2 4 1 216 x x + − = M1 2 2 1 2 108 x x x + − − = or 2 2 4 2 4 216 x x x + − − = M1 correct expansion of their brackets, allow one error or omission correct completion to 2 110 0 x x + − = A1 All correct with no errors seen 1(b) –11 and +10 with correct factorisation seen 3 M2 for ( )( ) 11 10 x x + − or M1 for ( )( ) x a x b + + where 110 ab = − or 1 a b + = After M1, SC1 for x their a = − and x their b = − If 0 scored, SC1 for both correct answers. 1(c) 9 1 FT provided 2 values of different signs are given for x in (b). 2(a) 2 5 20 x y + = or 2 4 5 y x − = + or equivalent 3 term equation 3 B1 for −4 10 M1 for 4 10 y x c = ± + or, e.g. ( ) ( ) 4 4 0 10 y x − = ± − 2(b)(i) 21.8 or 21.80… 2 M1 for [ ] 4 tan ... 10 = or [ ] 10 tan ... 4 = 2(b)(ii) 2.6[0] or 2.599… 3 B1 for using correct right-angled triangle soi, e.g. marked on diagram. M1FT for ( )( ) sin( b i ) 7 d their = oe 3(a) 624 3 M2 for 642.72 1.03 oe or M1 for 642.72 associated with 103[%]

0626/06 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2019 © UCLES 2019 Page 5 of 9 Question Answer Marks Partial Marks 3(b) 15.8 4 M3 for [ ] 1000 1.36 100 100 1000 1.174 × × − × oe soi by 116 or 115.8 or 15.8 or 15.84… or M2 for 1000 1.36 1.174 × soi by 1158 or 1160… or M1 for 1000 1.36 × 3(c) 6 with supporting evidence 4 M2 for calculating correctly either 400 1.02n × or 390 1.025n × for n ⩾ 3 oe or M1 if n = 2 calculated correctly for either or M1 for 400 1.02n × and 390 1.025n × both soi M1 for calculating correctly both investments for a value of n, n ⩾3 Alternative method: M2 for calculating correctly 1.025 1.02 n n for n ⩾ 3 oe or M1 if n = 2 calculated correctly or M1 for 1.025 1.02 n n and 400 390 both soi M1 for 1.0256[4…] 3(d)(i) 612.49 3 B1 for 604 and B1 for 608.16 3(d)(ii) 500 1 their investment will decrease oe 1 dep on their (d)(ii) ⩽ 500 4(a) 30 2 M1 for 360 12 4(b)(i) Parallelogram constructed with arcs 2 M1 for one pair of correct intersecting arcs drawn

0626/06 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2019 © UCLES 2019 Page 6 of 9 Question Answer Marks Partial Marks 4(b)(ii) Circle drawn with correct constructions shown 3 M2 for correct perpendicular bisector for 2 of the other points with correct arcs or M1 for correct perpendicular bisector with incorrect or no arcs or for 2 correct pairs of arcs seen. A1 for correct circle dependent on at least M1 If 0 scored SC1 for correct circle 5(a)(i) 3 B2 for three numbers correctly placed or B1 for two numbers correctly placed. 5(a)(ii) 12 1 FT 7 + their (4+1) 5(a)(iii) 13 1 5(b)(i) (F ∩ G) ' oe 1 5(b)(ii) ( P ∪Q) ∩ R oe 1 6(a) y ⩾ 2 oe x + y ⩾ 9oe 2 B1 for each 6(b) 400x + 700y ⩽ 5600 oe 1 6(c) 4 correct, continuous, ruled lines drawn and correct region left unshaded 6 B1 for 4 x = drawn B1FT for 2 their y = drawn dep on y k = B1FT for 9 their x y + = drawn dep on their x y k + = oe B2FT for 4 7 56 their x y + = drawn dep on 4 7 their x y k + = or SC1FT for line with negative gradient passing through one of their intercepts (14, 0) or (0, 8) 6(d) 12 1 [7] [0] 1 [2] [11] 4 5 10

0626/06 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2019 © UCLES 2019 Page 7 of 9 Question Answer Marks Partial Marks 6(e) 5, 5 27.5[0] 2 B1 for 5,5 or for 27.5[0] If 0 scored SC1 for clear use of [ ]1.5 4 P x y = + for a point in their region. 7(a) 349 or 349.0 to 349.11… 2 M1 for 2 64 π 25 360   × ×     7(b) 48.1 or 48.06… 4 B1 for 148° or 74° or 16° seen on diagram or used. M2 for 25sin148 sin16 or M1 for sin16 sin148 oe 25 x = OR M2 for 2 2 25 25 2 25 25cos148 + − × × or M1 for 2 2 25 25 2 25 25cos148 + −× × OR M2 for 2 25 sin74 × × oe or M1 for sin74 25 x = oe 7(c) 166 or 165.5 to 165.6 2 M1 for 1 25 25 sin148 2 × × × or for ( ) 1 25 7 sin16 2 their b × × × 7(d) 35.2 or 35.17 to 35.3 4 M3 for their 7(a) + ( ) 2 their c × − ( ) 2 32 π 7 360 their b × × or M2 for ( ) 2 32 π 7 360 their b × × or for two of the M1 cases or M1 for their 7(a) + ( ) 2 their c × or ( ) 2 π 7 k their b × × or BOC = 32° 8(a) Two correct limitations with improvement 2 B1 for each 8(b) 20, 60, 50, 80 2 B1 for two correct

0626/06 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2019 © UCLES 2019 Page 8 of 9 Question Answer Marks Partial Marks 8(c) 1580 4 M1 for midpoints soi (375, 750, 1250, 2000, 3000) M1 for use of fx ∑ with x in correct interval including both boundaries 20 375 60 750 50 1250 × + × + × + 80 2000 40 3000 × + × M1 (dep on 2nd M1) for fx ∑ ÷ 250 8(d)(i) Correct graph 4 B1 for 6 points plotted at upper ends of intervals B1FT from their frequency table for heights of 0, 20, 80, 130, 210, 250 B1FT for increasing curve or polygon through 5 or 6 points 8(d)(ii) 1350 – 1400 2 FT their cumulative frequency diagram M1 for correct UQ or LQ for their cumulative frequency diagram 9(a) 2 3 6 x x − 2 M1 for 2 ax bx − or B1 for 2 3x or 6x − 9(b)(i) (0, 0) (2, −4) 4 M1 for 2 0 their ax bx − = M1 for 0 x = and theirb x theira = or ( ) 0 x ax b − = A1 for 0 x = and 2 x = or (0, 0) dep on first M1 seen or(2, −4) dep on first M1 seen

0626/06 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2019 © UCLES 2019 Page 9 of 9 Question Answer Marks Partial Marks 9(b)(ii) (0, 0) maximum (2, −4) minimum with supporting evidence 3 M1FT for 2 2 d 6 6 d y x x   = −     or 2 their ax b − A1 for 0 x = 2 2 d 6 d y x   = −     0 < therefore maximum A1 for 2 x = 2 2 d 6 d y x   =     0 > therefore minimum Alternative method M1FT for considering d d y x both sides of 0 x = or 2 x = A1 for 0 x = is a maximum with valid points tested correctly A1 for 2 x = is a minimum with valid points tested correctly 9(c) 1 3 ± 3 M1FT for 2 3 6 6 x x − = or their d 6 d y x = , dep on their d d y x being a function of x. M1FT for ( ) ( ) 2 6 6 4 3 6 2 3 + − − × × − × or ( ) ( ) 2 6 6 4 3 6 2 3 − − − × × − × or better, dep on their d d y x being quadratic