Cambridge IGCSE Mathematics - International 0607 — 2014 May/June Paper 2 · Variant 1

This document consists of 8 printed pages. IB14 06_0607_21/RP © UCLES 2014 [Turn over *3698974700* Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/21 Paper 2 (Extended) May/June 2014 45 minutes Candidates answer on the Question Paper. Additional Materials: Geometrical Instruments 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. CALCULATORS MUST NOT BE USED IN THIS PAPER. All answers should be given in their simplest form. You must show all the relevant working to gain full marks and you will be given marks for correct methods 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 40.

2 © UCLES 2014 0607/21/M/J/14 Formula List For the equation ax2 + bx + c = 0 x = 2 _ ± 4 2 _ b b ac a Curved surface area, A, of cylinder of radius r, height h. A = 2πrh Curved surface area, A, of cone of radius r, sloping edge l. A = πrl Curved surface area, A, of sphere of radius r. A = 4πr2 Volume, V, of pyramid, base area A, height h. V= 1 3 Ah Volume, V, of cylinder of radius r, height h. V = πr2h Volume, V, of cone of radius r, height h. V = 1 3 πr2h Volume, V, of sphere of radius r. V = 4 3 πr3 = = sin sin sin a b c A B C a2 = b2 + c2 – 2bc cos A Area = 1 2 bc sin A A a B C b c

3 © UCLES 2014 0607/21/M/J/14 [Turn over Answer all the questions. 1 (a) Factorise. x2 – y2 Answer(a) [1] (b) Work out. 1642 – 362 Answer(b) [1] 2 (a) Simplify. 12 Answer(a) [1] (b) Solve the equation. cos x = 2 3 for 0° Y x Y 90° Answer(b) x = [1] (c) Solve the equation. cos x = 4 12 − for –180° Y x Y 180° Answer(c) x = or x = [2]

4 © UCLES 2014 0607/21/M/J/14 3 Find the highest common factor (HCF) in each list. (a) 24 56 72 Answer(a) [1] (b) x3y4 x2y5 x4y2 Answer(b) [2] 4 A manufacturer made a profit of 60% when he sold a chair for $20. Find the cost of making the chair. Answer $ [3]

5 © UCLES 2014 0607/21/M/J/14 [Turn over 5 A travel agent displays the following exchange rates. £1 = $1.55 £1 = ¥ 9.3 (a) Change £200 into dollars ($). Answer(a) $ [1] (b) Find the number of Chinese yuan (¥) received in exchange for $1. Answer(b) ¥ [2] 6 (a) Simplify. 27 75 − Answer(a) [2] (b) Rationalise the denominator. 2 5 7 − Answer(b) [2]

6 © UCLES 2014 0607/21/M/J/14 7 y x 0 2 4 6 8 10 12 12 10 8 6 4 2 (a) On the grid, draw the following lines. x = 1 y = 12 – 2x for 0 Y x Y 6 4y + 3x = 36 for 0 Y x Y 12 [5] (b) On the grid, label the region R containing the points which satisfy these three inequalities. x [ 1 y Y 12 – 2x 4y + 3x [ 36 [1] (c) (i) Find the minimum value of x + y in the region R. Answer(c)(i) [1] (ii) Find the co-ordinates of the point corresponding to this minimum value. Answer(c)(ii) ( , ) [1]

7 © UCLES 2014 0607/21/M/J/14 [Turn over 8 A bag contains 10 discs, 7 are red and 3 are green. A disc is picked at random and not replaced. A second disc is then picked at random. (a) Complete the tree diagram. One probability is shown on the diagram. Red Green Red Green Green Red … … … … … 3 10 [2] (b) Find the probability that (i) both discs are red, Answer(b)(i) [2] (ii) at least one disc is red. Answer(b)(ii) [3] Questions 9 and 10 are printed on the next page.

8 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. 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. © UCLES 2014 0607/21/M/J/14 9 In one month there were 120 new cars sold in a town. The table shows how many cars of each colour were sold. Colour Red Blue White Green Silver Black Yellow Number 17 20 24 x 28 17 x (a) Find the value of x. Answer(a) [1] (b) Find the relative frequency of white cars, giving your answer as a fraction in its lowest terms. Answer(b) [2] 10 Solve the equation. 7 )3 4 ( + x = )3 4 ( 7 + x Answer [3]

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2014 series 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/21 Paper 2 (Extended), maximum raw mark 40 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 May/June 2014 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

Page 2 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0607 21 © Cambridge International Examinations 2014 1 (a) (b) ( )( ) y x y x − + 25 600 1 1 2 (a) (b) (c) 3 2 30 150, –150 1 1 2 B1 for 1 correct answer –1 for extra answer(s) in range 3 (a) (b) 8 2 2y x 1 2 B1 for 1 correct term 4 12.5 3 M2 for 6.1 20 oe or M1 for 160% = 20 5 (a) (b) 310 6 1 2 M1 for 55 .1 3.9 6 (a) (b) 3 2 ( ) 23 2 5 7 + 2 2 B1 for 3 5 or 3 3 Accept other correct alternate numerators, but must see 23. M1 for ( ) ( ) 2 5 2 5 + + ×

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0607 21 © Cambridge International Examinations 2014 7 (a) (b) (c) (i) (ii) 1 = x x y 2 12 − = 36 3 4 = + x y R in correct region 9.25 or 9.1 to 9.4 (1, 8.25 ) or (1, 8.1 to 8.4) 1 2 2 1 1 1 Answers on the diagram B1 for ruled line with correct gradient, or B1 for correct intercept on either axis B1 for ruled line with correct gradient, or B1 for correct intercept on either axis

Page 4 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0607 21 © Cambridge International Examinations 2014 8 (a) (b) (i) (ii) , 10 7 , 9 6 , 9 3 , 9 7 9 2 correctly placed 15 7 oe 15 14 oe 2 2 3 B1 3 probs correct M1 FT for their10 7 × their 9 6 M2 for      −15 1 1 , or two of           × +       × +       × 10 7 10 3 9 3 10 7 9 6 10 7 seen or M2 for       × − 9 2 10 3 1 their or two of           × + × + × 9 7 10 3 9 3 10 7 9 6 10 7 their their their their their or M1 for 10 3 × their 9 2 or 2 of their products correct. 9 (a) (b) 7 5 1 1 2 B1 for 120 24 oe 10 1, – 2.5 oe cao 3 M1 Correct multiplication eliminating fractions M1 Correct simplification leading to 4  3  7 or M1 Correct multiplication eliminating fractions M1 Correct simplification leading to quadratic equation 16
 24 40  0 If M0 then SC1 for x = 1 only.