Cambridge IGCSE Mathematics (9-1) (UK only) 0626 — 2019 Oct/Nov Paper 4 · Variant 1

This document consists of 15 printed pages and 1 blank page. DC (SC/SW) 170855/3 © UCLES 2019 [Turn over * 5 2 4 1 9 9 4 2 8 0 * MATHEMATICS 0626/04 Paper 4 (Extended) October/November 2019 1 hour 30 minutes 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 or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. CALCULATORS MAY NOT BE USED IN THIS PAPER. 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. 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 84. 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 0626/04/O/N/19 © UCLES 2019 1 Find the reciprocal of 2 4 3 . … [2] 2 The bearing of a lighthouse from a boat is 153°. Work out the bearing of the boat from the lighthouse. … [2] 3 Marcia goes to the supermarket. She buys • 1.6 kg of apples at 2k pence per kilogram • 0.8 kg of bananas at ( ) k 5 + pence per kilogram. (a) Write down an expression, in terms of k, for the cost in pence of Marcia’s shopping. Give your answer in its simplest form. …pence [2] (b) The total cost of Marcia’s shopping is £2.44. Find the value of k. k = … [2] (c) Find the cost of 1 kilogram of bananas. …pence [1]

3 0626/04/O/N/19 © UCLES 2019 [Turn over 4 Work out. 5 9 7 12 11 3 2 # - Give your answer as a mixed number. … [3] 5 (a) Write 0.0567 in standard form. … [1] (b) Work out . . 7 3 10 2 4 10 14 12 # # + . Give your answer in standard form. … [2] 6 X Enlarge this shape by scale factor 3 1 from the centre of enlargement X. [2]

4 0626/04/O/N/19 © UCLES 2019 7 Here is a description of triangle DEF. • Side DE = 8 cm • Angle EDF = 42° • Side EF = 6 cm Two different triangles can be constructed using this description. Construct accurately these two triangles. [4]

5 0626/04/O/N/19 © UCLES 2019 [Turn over 8 Find five positive integers which satisfy all four of the following conditions. • mode = 5 • median = 5 • mean = 6 • range = 7 … , … , … , … , … [3] 9 Simplify. (a) ( ) ( ) x x x x 3 3 - - + … [2] (b) x5 2 ` j … [1] (c) x36 … [1]

6 0626/04/O/N/19 © UCLES 2019 10 (a) Change 8 3 into a decimal. … [2] (b) Change the recurring decimal .0 14o into a fraction. … [2] 11 (a) Factorise x y 4 2 2 - . … [2] (b) Use your answer to part (a) to evaluate 4 343 314 2 2 # - . … [2]

7 0626/04/O/N/19 © UCLES 2019 [Turn over 12 Work out. (a) .0 642 1 … [1] (b) 8 3 2 - … [2] 13 Here are two sets. A = {4, 8, 12, 16, 20, 24} B = {8, 16, 24} Use set notation to complete this statement. B … A [1]

8 0626/04/O/N/19 © UCLES 2019 14 Cylinder P has radius 5 cm and height 4 cm. (a) Calculate the volume of cylinder P. Give your answer as a multiple of r. …cm3 [2] (b) Cylinder Q is mathematically similar to cylinder P. The surface area of cylinder Q is 9 times the surface area of cylinder P. Find the volume of cylinder Q. Give your answer as a multiple of r. …cm3 [3]

9 0626/04/O/N/19 © UCLES 2019 [Turn over 15 These two triangles are mathematically similar. 8 cm 3 cm 6 cm NOT TO SCALE v cm w cm ( ) 4 2 3 cm + (a) Find the value of v. Give your answer in the form a b 3 + , where a and b are integers. v = … [2] (b) Find the value of w. Give your answer in the form c d 3 + , where c and d are integers. w = … [4]

10 0626/04/O/N/19 © UCLES 2019 16 Expand and simplify. ( )( )( ) x x x 4 4 2 + - + … [3]

11 0626/04/O/N/19 © UCLES 2019 [Turn over 17 NOT TO SCALE 8 cm 75° 60° F G E The diagram shows triangle EFG. Find FG. Give your answer in the form a b , where a and b are integers. FG = … cm [5]

12 0626/04/O/N/19 © UCLES 2019 18 w is inversely proportional to the square root of y. When , y w 25 22 = = . Find y when w 10 = . y = … [3] 19 ° tan45 1 = Use the information above to solve the equation tanx 1 =- for x between 0° and 360°. x = … or x = … [2]

13 0626/04/O/N/19 © UCLES 2019 [Turn over 20 ( )x ax b f = + where a and b are numbers. (a) Show that ( )x a x ab b ff 2 = + + . [1] (b) a x ab b x 2 + + = (i) Find the value of b when a 1 = . b = … [1] (ii) Comment on the value of b when a 1 =- . … [1] 21 Rearrange w y x 7 5 4 3 = - to make x the subject of the formula. … [4]

14 0626/04/O/N/19 © UCLES 2019 22 (a) Describe fully the single transformation represented by the matrix 0 1 1 0 - - e o. … … [2] (b) y x 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 C D Sosuke says the enlargement that maps triangle C onto triangle D is represented by the matrix 2 0 0 2 e o . Give two reasons why he is not correct. 1. … 2. … [2] (c) Matrix A represents a rotation about the origin and A A 1 = - . Find matrix A. f p [2]

15 0626/04/O/N/19 © UCLES 2019 23 A bag contains n marbles. There are w white marbles in the bag. Two marbles are selected at random from the bag. (a) p1 is the probability of selecting 2 white marbles from the bag with replacement. Find an expression, in terms of n and w, for p1. p1 = … [1] (b) p2 is the probability of selecting 2 white marbles from the bag without replacement. Find an expression, in terms of n and w, for p2. p2 = … [1] (c) p p 20 21 1 2 # = Show that n w w 21 20 = - . [3] (d) Complete this statement. The largest possible number of white marbles in the bag is … and this occurs when there is a total of … marbles in the bag. [2]

16 0626/04/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 6 printed pages. © UCLES 2019 [Turn over Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education (9–1) MATHEMATICS 0626/04 Paper 4 October/November 2019 MARK SCHEME Maximum Mark: 84 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.

0626/04 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2019 © UCLES 2019 Page 2 of 6 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.

0626/04 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2019 © UCLES 2019 Page 3 of 6 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 4 11 2 M1 for 11 4 or for 1 3 2 4 oe or for 4 1 1 their 2 333 2 M1 for 153 + 180 oe seen or a correct sketch diagram shown 3(a) 4 4 k + or ( ) 4 1 k + final answer 2 M1 for ( ) 2 1.6 0.8 5 k k × + × + oe or B1 for 3.2k seen or for 0.8 4 k + seen or for answer 4 k c + 3(b) 60 2 M1FT their( ) 4 4 244 k + = oe soi 3(c) 65 1 FT their (b) + 5

0626/04 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2019 © UCLES 2019 Page 4 of 6 Question Answer Marks Partial Marks 4 1 5 6 or 5 6 k k 3 B1 for 11 18 k k seen M1 for [5]14 11 18 18 k k their k k − oe where denominators are both the same. If 0 scored SC2 for answer 3 13 54 k k or SC1 for 175 36 oe seen 5(a) 2 5.67 10− × cao 1 5(b) 14 7.324 10 × cao 2 M1 for 14 14 7.3 10 0.024 10 × + × or 12 12 730 10 2.4 10 × + × or answer figs 7324 6 Correct enlargement drawn 2 B1 for enlargement correct size and orientation but in the wrong position or for 4 or 5 vertices plotted correctly 7 Two different accurately constructed triangles 4 B3 for one triangle DEF accurately drawn or B2 for a triangle satisfying two conditions or B1 for a triangle satisfying one condition or for an incomplete triangle satisfying two conditions. 8 4,5,5,5,11 or 3,5,5,7,10 3 B1 for five numbers with mode = 5 and median = 5 B1 for five numbers that total 30 B1 for five numbers with range = 7 Maximum 2 marks if answer not correct. 9(a) 6x − 2 M1 for 2 3 x x − or 2 3 x x − − or ( ) ( ) 3 3 x x x −− + 9(b) 10 x 1 9(c) 18 x 1 10(a) [0].375 2 M1 for attempt at 3 8 ÷ or for [0].125 seen 10(b) 13 90 2 M1 for 10 1.4444 0.1444 x x − = …− … or better or 1 4 10 90 + 11(a) ( )( ) 2 2 x y x y − + 2 M1 for ( )( ) ax by cx dy + + where 4 and 1 ac bd = = −

0626/04 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2019 © UCLES 2019 Page 5 of 6 Question Answer Marks Partial Marks 11(b) 372 000 from use of correct factorisation 2 M1 for ( ) 343 314 their a theirb × − × ( ) 343 314 their c their d × × + × 12(a) 0.8 oe 1 12(b) 1 4 oe 2 B1 for ( ) 1 3 64 − or 2 2− or 2 3 1 8 or better 13 ∩ 1 14(a) 100π final answer 2 M1 for [ ] 5 5 4 π× × × oe 14(b) 2700π final answer 3 B2 for volume factor = 27 or M2 for ( ) 3 9 100π ×their or M1 for length scale factor is 9 soi 15(a) 2 3 + 2 M1 for 6 3 4 2 3 v = + oe 15(b) 48 24 3 − 4 M1 for 6 4 2 3 + ×8 or 3 8 their v × M1 for 4 2 3 4 2 3 4 2 3 k − × + − or ( ) ( ) 3 3 their a b k their v their a b − × − M1 for ( ) 4 2 3 16 4 3 k − −× or ( ) ( ) ( ) 2 2 3 3 k their a b their a b − − 16 3 2 2 16 32 x x x + − − 3 B1 for expanding and simplifying two sets of brackets correctly M1 for expanding their quadratic and final factor 17 4 6 5 B1 for angle EGF = 45 B1 for 3 sin60 2 = or 1 sin 45 2 = oe M2 for 8 sin 60 sin 45 × = FG or M1 for sin 45 sin60 8 = FG

0626/04 Cambridge IGCSE (9–1) – Mark Scheme PUBLISHED October/November 2019 © UCLES 2019 Page 6 of 6 Question Answer Marks Partial Marks 18 121 3 M2 for 10 22 25 y = oe or for 110 w y = or M1 for k w y = or 22 25 or k=110 19 135, 315 2 B1 for each or for a sketch of y = tanx 20(a) ( ) a ax b b + + 2 a x ab b = + + 1 20(b)(i) 0 b = nfww 1 20(b)(ii) b can take any value oe 1 21 2 3 7 4 5 w y x + = oe final answer 4 M1 for squaring both sides M1 for eliminating fraction M1 for isolating 3x M1 for cube rooting both sides Maximum of 3 marks if answer incorrect 22(a) Reflection y x = − oe 2 B1 for each 22(b) centre of enlargement is (0,1) or is not (0,0) oe scale factor from C to D is 1 2 or is not 2 oe 2 B1 for each 22(c) 1 0 0 1 −     −   2 B1 for a matrix satisfying 1 − = A A or for a rotation matrix or for a complete description: rotation 180 about origin 23(a) w w n n × oe 1 23(b) 1 1 w w n n − × − oe 1 23(c) For their p1 = 21 20 their p2 Elimination of denominator or use of common denominator Correct completion to 20 21 w n w = − M1 M1 A1 23(d) 20, 400 2 B1 for each