Cambridge IGCSE Mathematics - International 0607 — 2014 Oct/Nov Paper 2 · Variant 2

This document consists of 8 printed pages. IB14 11_0607_22/RP © UCLES 2014 [Turn over *7601043393* Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/22 Paper 2 (Extended) October/November 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 0607/22/O/N/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 0607/22/O/N/14 [Turn over Answer all the questions. 1 3 2 = − x Find the values of x. Answer [2] 2 Find the nth term of this sequence. – 1, 0, 3, 8, 15, …... Answer [3] 3 Find the value of 2 3 9 16 −     . Answer [2]

4 © UCLES 2014 0607/22/O/N/14 4 b a + = + 2 1 2 3 Find the values of a and b. Answer a = b = [3] 5 (a) 7 24 x NOT TO SCALE Find x. Answer(a) x = [2] (b) y 8 NOT TO SCALE α sin 5 3 = α cos 5 4 = α tan 4 3 = α Find y. Answer(b) y = [2]

5 © UCLES 2014 0607/22/O/N/14 [Turn over 6 Factorise. (a) x2 – 5x – 24 Answer(a) [2] (b) pq + p – tq – t Answer(b) [2] 7 The bag contains 5 white beads and 3 black beads. Two beads are taken from the bag at random, without replacement. Find the probability that the two beads are different colours. Answer [3]

6 © UCLES 2014 0607/22/O/N/14 8 y varies inversely as the square root of x. When x = 4, y = 3. Find (a) y in terms of x, Answer(a) y = [2] (b) y when x = 9, Answer(b) [1] (c) x in terms of y. Answer(c) x = [2] 9 (a) Find the value of     9 1 log3 . Answer(a) [1] (b) 3 log logq p = Find q in terms of p. Answer(b) q = [2]

7 © UCLES 2014 0607/22/O/N/14 [Turn over 10 y x O A B l M NOT TO SCALE The equation of the line l is 3x + 4y = 12. The line cuts the x-axis at A and the y-axis at B. The midpoint of AB is M. (a) Find the co-ordinates of (i) A, Answer(a)(i) ( , ) [1] (ii) B, Answer(a)(ii) ( , ) [1] (iii) M. Answer(a)(iii) ( , ) [1] (b) Find the equation of the line through the origin which is perpendicular to the line l. Answer(b) [3] Questions 11 and 12 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 0607/22/O/N/14 11 1 0 2 3 4 5 6 4 3 2 1 y x Draw the stretch of the shaded triangle with the y-axis invariant and factor 2. [2] 12 0 y x 4 2 NOT TO SCALE The diagram shows the graph of y = ax2 + bx + c. The graph passes through (0, 0) and has a maximum point (2, 4). Find the values of a, b and c. Answer a = b = c = [3]

® IGCSE is the registered trademark of Cambridge International Examinations. CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the October/November 2014 series 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/22 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 October/November 2014 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

Page 2 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2014 0607 22 © Cambridge International Examinations 2014 1 – 1, 5 2 B1 each 2 n2 – 2n oe 3 B2 for n2 + kn or (n – 1)2 + k or M1 for second differences equal or any other quadratic expression 3 64 27 2 B1 for 27 or 64 in answer or M1 for 3 9 16 1       oe or better 4 a = 3, b = – 3 3 M1 for × 1 2 1 2 − − or b b a a + + + = 2 2 2 3 A1 for one correct 5 (a) 25 2 M1 for 72 + 242 (b) 4.8 oe 2 M1 for 8 sin y = α oe 6 (a) (x – 8)(x + 3) 2 SC1 for (x + a)(x + b) where ab = –24 or a + b = –5 (b) (q + 1)(p – t) 2 B1 for p(q + 1) – t(q + 1) or q(p – t) + p – t 7 56 30 oe 3 M2 for 7 5 8 3 7 3 8 5 × + × oe or M1 for one of these products 8 (a) x y 6 = 2 M1 for x k y = or for 4 1 1 3 x y = (b) 2 1FT (c) 2 6       y oe 2FT FT their (a) only if x k y = or x k y = or 2 x k y = M1 for correct multiplication and division M1 for correct squaring 9 (a) –2 1 (b) 3p 2 B1 for log3 q or p log 3 seen or SC1 for answer 10 p log 3

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2014 0607 22 © Cambridge International Examinations 2014 10 (a) (i) (4, 0) 1 (ii) (0, 3) 1 (iii) (2, 1.5) 1FT FT their (i), (ii) but can recover (b) x y 3 4 = oe 3 M1 FT for gradient of l = 4 3 − M1 for gradient = l of gradient 1 − If 0 scored, SC1 for answer in form y = kx oe, k > 0 11 Triangle vertices (2, 1), (2, 2), 6, 1) 2 SC1 for stretch factor 2 with x-axis invariant 12 a = – 1, b = 4, c = 0 3 B2 for a(x – 2)2 + 4 or B2 for x(4 – x) or x(x – 4) or M1 for c = 0 and 4a + 2b = 4 and 16a + 4b = 0 and M1 for eliminating a or b or M1 for 0a + 0b + c = 0 4a + 2b + c = 4 16a + 4b + c = 0 and M1 for eliminating two of a, b, c