Cambridge IGCSE Mathematics (9-1) (UK only) 0626 — 2019 Oct/Nov Paper 2 · Variant 1

This document consists of 12 printed pages. DC (SC/SW) 170853/2 © UCLES 2019 [Turn over * 0 0 1 5 5 9 1 2 0 1 * MATHEMATICS 0626/02 Paper 2 (Extended) October/November 2019 1 hour 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 60. Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education (9–1) This syllabus is regulated for use in England as a Cambridge International Level 1/Level 2 (9–1) Certificate.

2 0626/02/O/N/19 © UCLES 2019 1 Solve. x 7 16 3 + = x = … [2] 2 Change 5 m3 into cm3. …cm3 [1] 3 Find the highest common factor (HCF) of 315 and 225. … [2] 4 A bus travels at a constant speed of 90 kilometres per hour. Calculate the distance the bus travels in 22 seconds. … km [3]

3 0626/02/O/N/19 © UCLES 2019 [Turn over 5 Adele and Pierre both walked their family dog on 1 January. After that, Adele walks the dog every 8th day and Pierre walks the dog every 12th day. After 1 January, how many times do Adele and Pierre both walk the dog on the same day during this year (365 days)? … [3] 6 (a) Here are the first four terms of a sequence. 2 9 16 23 Find the nth term of this sequence. … [2] (b) Here are the first four terms of a different sequence. 1 8 27 64 (i) Find the next term of this sequence. … [1] (ii) 42 875 is a term in this sequence. Work out the term number of 42 875. … [1]

4 0626/02/O/N/19 © UCLES 2019 7 Simplify. x x y 4 8 2 7 6 … [2] 8 The diagram shows two right-angled triangles, ABC and BCD. 23 m 11 m 9 m D C A B NOT TO SCALE Show that AC is 18.1 m correct to 1 decimal place. [4]

5 0626/02/O/N/19 © UCLES 2019 [Turn over 9 The diagram shows two circles. x° O A B E D C NOT TO SCALE Points D and E lie on the large circle, centre O. Points O, B and C lie on the small circle, centre A. BOD is a straight line and angle ° BDE x = . Find, in terms of x, an expression for (a) angle BOC, Angle BOC = … [1] (b) reflex angle BAC. Reflex angle BAC = … [2]

6 0626/02/O/N/19 © UCLES 2019 10 The area of a rectangular garden is 1677 m2 correct to the nearest m2. The length of the garden is 68.4 m correct to 3 significant figures. Calculate the upper bound for the width of the garden. Give your answer correct to 4 significant figures. … m [3]

7 0626/02/O/N/19 © UCLES 2019 [Turn over 11 C NOT TO SCALE A B D ABCD is a cyclic quadrilateral. Its angles are in the ratio angle A : angle B : angle C : angle D = 3 : 6 : 7 : x. Work out the size of angle D. State any geometrical reason you use. Angle D = … [4]

8 0626/02/O/N/19 © UCLES 2019 12 Cassie and Ben each have a fair 6-sided dice. They both throw their dice at the same time. (a) Cassie says: The probability that the score on my dice is less than the score on Ben’s dice is 12 5 . Show that Cassie is correct. [2] (b) Cassie and Ben both throw their dice 60 times. Work out the expected number of times that Cassie’s score is less than Ben’s score. … [1] (c) Cassie and Ben each have 150 counters. If the score on Cassie’s dice is less than the score on Ben’s dice, Cassie gives Ben 3 counters. Otherwise, Ben gives Cassie 4 counters. Work out the expected number of counters they will each have after they have both thrown their dice 60 times. Cassie …counters Ben …counters [3]

9 0626/02/O/N/19 © UCLES 2019 [Turn over 13 a b 3 4 2 1 4 3 5 18 19 17 - - - = - - e e e o o o Find the value of a and the value of b. a = … b = … [3] 14 (a) Express x x 6 4 2 - + in the form x a b 2 + + ` j . … [3] (b) Write down the co-ordinates of the minimum point on the graph of y x x 6 4 2 = - + . (… , …) [2]

10 0626/02/O/N/19 © UCLES 2019 15 (a) Solve the simultaneous equations. You must show your working. x y y x 20 2 10 2 2 + = = + … [5] (b) Explain what your answer to part (a) tells you about the graphs of x y 20 2 2 + = and y x 2 10 = + . … … [1]

11 0626/02/O/N/19 © UCLES 2019 [Turn over 16 C O N NOT TO SCALE A M B a OA = and b OB = . M is the midpoint of AB. C is the midpoint of OB. ON OM 4 3 = . (a) Write the following vectors in terms of a and b. Give your answers in their simplest form. (i) AC AC = … [1] (ii) OM OM = … [2] (iii) AN AN = … [2] (b) Do the points A, N and C lie on the same straight line? Justify your answer using vectors. … [1] Question 17 is printed on the next page.

12 0626/02/O/N/19 © UCLES 2019 17 y x – 2 – 3 – 1 1 2 3 4 5 6 7 8 9 – 1 – 2 – 3 – 4 – 5 – 6 – 7 – 8 – 9 – 10 0 1 2 P The graph of y x 3 1 4 = - - is drawn on the grid. (a) P is the point where the graph intersects the y-axis. Work out the co-ordinates of P. (… , …) [1] (b) Write down the equations of the asymptotes of the graph. … [2] 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.

This syllabus is regulated for use in England as a Cambridge International Level 1/Level 2 (9–1) Certificate. This document consists of 5 printed pages. © UCLES 2019 [Turn over Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education (9–1) MATHEMATICS 0626/02 Paper 2 October/November 2019 MARK SCHEME Maximum Mark: 60 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.

0626/02 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2019 © UCLES 2019 Page 2 of 5 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.

0626/02 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2019 © UCLES 2019 Page 3 of 5 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 Question Answer Marks Partial Marks 1 5 2 M1 for 16 3 7 x + = × oe 2 5 000 000 or 5 6 10 × 1 3 45 2 B1 for answer 3, 5, 9 or 15 or for [315 =] 3 × 3 × 5 × 7 or for [225 =] 3 × 3 × 5 × 5 4 [0].55 3 M1 for conversion between hours and seconds soi M1 for use of speed × time soi 5 15 3 B1 for 24 M1 for 365 24k soi by e.g. 15.2 If 0 scored SC2 for final answer of 16 6(a) 7n − 5 oe final answer 2 B1 for 7n + c or kn − 5 k ≠ 0 6(b)(i) 125 1

0626/02 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2019 © UCLES 2019 Page 4 of 5 Question Answer Marks Partial Marks 6(b)(ii) 35 1 7 5 6 2x y final answer 2 B1 for 5 6 kx y or 6 2 kx y or 5 2 k x y 8 2 2 2 11 9 BC   = +   M1 2 2 2 23 AC theirBC = − M2 M1 for 2 2 2 23 AC theirBC = + AC = 18.08… A1 9(a) 2x 1 9(b) 360 – 4x 2 FT their 9(a) B1 for obtuse angle BAC = 2 × their 2x 10 24.54 3 B1 for one of 1677.5 or 1676.5 and one of 68.35 or 68.45 seen M1 for [ ]1677.5 UB 68.35 = or for x y where 1677 1678 x < < and 68.3 68.4 y < < 11 Opposite angles of a cyclic quadrilateral sum to 180° 1 72° 3 M1 for 3 + 7 parts is 180 soi M1 for x is 4 parts soi or for [angle B =]6 1 8 their × or for 16 1 8 their × 12(a) A complete sample space or 15 correct combinations seen M1 15 36 seen A1 12(b) 25 1 12(c) Cassie 215 Ben 85 3 FT their 25 M1 for 3 × 25 and 4 × (60 – 25) seen M1 for ± (3 × 25 – 4 × (60 – 25)) soi by ±65 counters 13 2, 16 a b = − = 3 M1 for 16 18 a − + = − soi by 2 a = − M1 for 12 2a b − =

0626/02 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2019 © UCLES 2019 Page 5 of 5 Question Answer Marks Partial Marks 14(a) ( ) 2 3 5 x − − 3 B1 for ( ) 2 3 x − seen M1 for ( ) 2 2 3 ( 3) 4 x − −± + OR B2 for 3 and 5 = − = − a b or B1 for 3 or 5 = − = − a b 14(b) (3, –5) 2FT FT their 14(a) B1 for each co-ordinate correct 15(a) ( ) 2 2 2 10 20 x x + + = M1 Correct substitution ( ) 2 2 2 10 4 20 20 100 x x x x + = + + + M1 Expansion of bracket Allow one error in expansion 2 5 40 80 0 x x + + = M1 Rearranging to a 3 term quadratic Allow one further error in collecting terms ( )( ) 4 4 kx k x + + M1 Correct factorisation or solution 4, 2 x y = − = A1 15(b) Line is a tangent to the curve oe 1 Strict FT their 15(a) 16(a)(i) 1 2 −+ a b 1 16(a)(ii) 1 1 2 2 + a b or ( ) 1 2 + a b 2 M1 for a correct route e.g. 1 2 OM OB BA = + JJJJG JJJG JJJG e.g. ( ) 1 2 + −+ b b a 16(a)(iii) 5 3 8 8 − + a b or ( ) 1 5 3 8 − + a b 2 M1 for a correct route e.g. 3 1 ( ) 4 2 AN AO OB BA = + + JJJG JJJG JJJG JJJJG or 3 4 AN AO OM = + JJJG JJJG JJJJG or ( ) 3 1 4 2 AN   = −+ + −+     a b b a JJJG or FT ( ) 3 4 AN their = −+ a 16(a)(ii) JJJG 16(b) No, AC JJJG is not a multiple of AN JJJG 1FT FT their 16(a)(i) and their 16(a)(iii) 17(a) (0, 1 4 3 − ) 1 17(b) x = 3 4 y = − 2 B1 for each