Cambridge IGCSE Mathematics - International 0607 — 2014 May/June Paper 2 · Variant 3

This document consists of 8 printed pages. IB14 06_0607_23/2RP © UCLES 2014 [Turn over *8932327307* Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/23 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 0607/23/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 0607/23/M/J/14 [Turn over Answer all the questions. 1 The price of a book was $7.00 . It is reduced by 20%. Find the new price of the book. Answer $ [2] 2 (a) Write 0.0063 in standard form. Answer(a) [1] (b) 5.7 × 109 + 2.4 × 108 = k × 109 Find the value of k. Answer(b) k = [2] 3 Find the next term in each of these sequences. (a) 3, 5, 8, 12, 17, ………………… [1] (b) 100, 91, 80, 67, 52, ………………… [1] (c) 4, 12, 36, 108, 324, ………………… [1]

4 © UCLES 2014 0607/23/M/J/14 4 2y 6x A small square of side 2y is inside a larger square of side 6x. (a) Find an expression for the shaded area, A, in terms of x and y. Answer(a) A = [2] (b) Rearrange your answer to part (a) to write x in terms of y and A. Answer(b) x = [3] 5 (a) Find 1250 . Answer(a) [1] (b) Simplify 3 27 27y . Answer(b) [2]

5 © UCLES 2014 0607/23/M/J/14 [Turn over 6 (a) D C B A x° y° 50° 98° NOT TO SCALE A, B, C and D lie on the circumference of a circle. Angle ABC = 98° and angle ACB = 50°. Find the value of x and the value of y. Answer(a) x = [1] y = [1] (b) O P T S R Q w° v° NOT TO SCALE 65° P, Q, R and S lie on the circumference of a circle, centre O. TP is a tangent to the circle at P and PR is a diameter. Find the value of v and the value of w. Answer(b) v = [1] w = [1]

6 © UCLES 2014 0607/23/M/J/14 7 y varies directly as the square of x. When x = 8, y = 40. Find y when x =12. Answer [3] 8 (a) Simplify )1 2 2 )( 2 2 3 ( + − . Answer(a) [3] (b) Rationalise the denominator of 5 10 . Answer(b) [2]

7 © UCLES 2014 0607/23/M/J/14 [Turn over 9 (a) y x 2 1 –1 –2 0 –4 –3 –2 –1 1 2 3 4 The diagram shows the graph of y = f(x). On the same diagram, sketch the graph of y = 2f(x). [1] (b) y x 2 1 –1 –2 0 –4 –3 –2 –1 1 2 3 4 The diagram shows the graph of y = f(x). On the same diagram, sketch the graph of y = f(x + 1). [1] 10 3 1 x Find the exact value of cos x. Answer [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 0607/23/M/J/14 11 U P R Q a b c d e The Venn diagram shows the sets P, Q and R. Complete the following statements using set notation. (a) P …….. R = {a, b, c, d, e} [1] (b) Q …….. R = ∅ [1] (c) e …….. R [1] (d) P …….. Q = P [1] 12 f(x) = x + 3 and g(x) = x 12 , 0 ≠ x Find (a) g(f (1)), Answer(a) [2] (b) g –1(x). Answer(b) [1]

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2014 series 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/23 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 23 © Cambridge International Examinations 2014 1 5.6[0] 2 M1 for 7 × 0.8 oe 2 (a) (b) 3 10 3.6 − × 5.94 1 2 B1 for 0.24 × 109 or 57 × 108 or figures 594 seen 3 (a) (b) (c) 23 35 972 1 1 1 4 (a) (b) 2 2 4 36 y x − oe 36 4 2 y A + or 2 (2y) A 6 1 + oe 2 3 B1 for 36x2 or 4y2 M1 for correct division by 36 or 6 M1 for correct re-arrangement M1 for correct square root 5 (a) (b) 1 9 3y 1 2 B1 for ky9 or 3yk, k ≠0 6 (a) (b) [x=] 32 [y=] 32 [v=] 25 [w=] 65 1 1FT 1 1 FT their x FT (90 – their v) 7 90 3 B2 for 2 8 5 x × oe or 2 8 12 40       = y or M1 for y = kx2 , k ≠0, 1 8 (a) (b) 2 10 − 5 2 3 2 B2 for 2 2 3 2 4 12 − + − or better or B1 if three of these terms correct M1 for 5 5 × or 5 5 2 × 9 (a) (b) Good sketch of stretch factor 2, x-axis invariant Good sketch of translation      − 0 1 1 1

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0607 23 © Cambridge International Examinations 2014 10 3 2 2 or 3 8 3 B2 for 2 2 1 3 − or better or B1 for k2 + 12 = 32 or better 11 (a) (b) (c) (d) ∪ ∩ ∈ or ⊂ } {e ∪ 1 1 1 1 12 (a) (b) 3 x 12 2 1 B1 for [ f (1) = ]4