Cambridge IGCSE Mathematics - International 0607 — 2010 May/June Paper 2 · Variant 1

This document consists of 10 printed pages and 2 blank pages. IB10 06_0607_02/2RP © UCLES 2010 [Turn over *0414909462* For Examiner's Use UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/02 Paper 2 (Extended) May/June 2010 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, highlighters, glue or correction fluid. You may use a 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. www.XtremePapers.com

2 © UCLES 2010 0607/02/M/J/10 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 2010 0607/02/M/J/10 [Turn over For Examiner's Use Answer all the questions. 1 Write 36 000 in standard form. Answer [1] 2 (a) Find the value of (i) 30, Answer(a)(i) [1] (ii) 1 2 36 . Answer(a)(ii) [1] (b) 28 ÷ 2 = 2x Find the value of x. Answer(b) x = [1] 3 Factorise completely 3x2y – 12y3. Answer [2]

4 © UCLES 2010 0607/02/M/J/10 For Examiner's Use 4 4 3 2 1 –1 –2 –3 –4 0 –90° 90° 180° 270° 360° –180° y x The diagram shows the graph of y = f(x), where f(x) = asin(bx). Find the values of a and b. Answer a = [1] Answer b = [1]

5 © UCLES 2010 0607/02/M/J/10 [Turn over For Examiner's Use 5 (a) Factorise 2x2 + x – 6. Answer(a) [2] (b) Solve the equation. 2x2 = 6 – x Answer(b) x = or x = [2] 6 (a) 3log2 + 2log3 = logk Find the value of k. Answer(a) k = [2] (b) Find the value of log 25 log5 . Answer(b) [1]

6 © UCLES 2010 0607/02/M/J/10 For Examiner's Use 7 p = 5 1    and q = 4 2 −       (a) Write 2p − 1 2 q as a column vector. Answer(a)           [2] (b) Find │q│ leaving your answer in surd form. Answer(b) [2] 8 (a) Simplify 72 50 − . Answer(a) [2] (b) Write 1 2 3 − in its simplest form by rationalising the denominator. Answer(b) [2]

7 © UCLES 2010 0607/02/M/J/10 [Turn over For Examiner's Use 9 B A 8 6 4 2 –2 –4 –6 –8 0 y x –2 2 4 6 8 –4 –6 –8 (a) Describe fully the single transformation which maps shape A onto shape B. [3] (b) Draw the image of shape A after a stretch, with y-axis invariant and scale factor 2. [2]

8 © UCLES 2010 0607/02/M/J/10 For Examiner's Use 10 B O C E D A 55° 20° NOT TO SCALE The points A, B, C and D lie on a circle, centre O. AB is a diameter, angle BAD = 55° and angle BDC = 20°. ABE and DCE are straight lines. Find (a) angle ABD, Answer(a) [1] (b) angle BCD, Answer(b) [1] (c) angle AED. Answer(c) [1]

9 © UCLES 2010 0607/02/M/J/10 [Turn over For Examiner's Use 11 0 y x P Q l NOT TO SCALE The diagram shows a line, l, which passes through the points P(0, 4) and Q(2, 0). (a) Find the equation of the line l. Answer(a) [2] (b) Find the equation of the line which is perpendicular to l and passes through the midpoint of PQ. Answer(b) [4]

10 © UCLES 2010 0607/02/M/J/10 For Examiner's Use 12 700 600 500 400 300 200 100 0 10 20 30 40 50 y x The graph shows the result of an experiment measuring x and y. It is known that y is directly proportional to the square of x. Find the equation connecting y and x. Answer [3]

11 © UCLES 2010 0607/02/M/J/10 BLANK PAGE

12 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. University of 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 2010 0607/02/M/J/10 BLANK PAGE

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2010 question paper for the guidance of teachers 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/02 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 must be read in conjunction with the question papers and the report on the examination. • CIE will not enter into discussions or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the May/June 2010 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses. www.XtremePapers.com

Page 2 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2010 0607 02 © UCLES 2010 • M marks are given for a correct method. • A marks are given for an accurate answer following a correct method. • B marks are given for a correct statement or step. • D marks are given for a clear and appropriately accurate drawing. • P marks are given for accurate plotting of points. • E marks are given for correctly explaining or establishing a given result. • ft follow through • oe or equivalent • soi seen or implied • www without wrong working 1 3.6(0) × 104 B1 [1] 2 (a) (i) (ii) (b) 1 6 7 B1 B1 B1 Accept –6 or ±6 [3] 3 3y(x – 2y)(x + 2y) B2 M1 for 3y(x2 – 4y2), (x – 2y)(3xy + 6y2), (x + 2y)(3xy – 6y2) or better seen [2] 4 a = 4, b = 2 B1 B1 After B0 B0 award B1 for 4sin2x seen and not spoilt. [2] 5 (a) (b) (2x – 3)(x + 2) oe x = 3/2 or x = –2 oe B2 B1ft B1ft If B0 award SC1 for signs reversed ft dependent on (a) in the form (ax + b)(cx + d) with a, b, c, d all non- zero [4] 6 (a) (b) 72 2 B2 B1 If B0 award M1 for log(23 × 32 ) or log23 + log32 or better seen e.g. log72 [3] 7 (a)     1 12 B1 B1 If B0 B0 award M1 for 2     1 5 –    − 2 4 2 1 or better (b) 20 or 2 5 seen B2 If B0 award M1 for (±4)2 + 22 or better seen [4] 8 (a) 2 B2 If B0 award B1 for 6 2 or 5 2 seen (b) 2 + 3 or 1 3 2 + B2 If B0 then M1 for 3 2 3 2 + + × seen [4]

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2010 0607 02 © UCLES 2010 9 (a) (b) rotation, centre (0, 0) oe 90° anticlockwise oe 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 B1 B1 B1 P2 Award B0 if more than one transformation given. If P0 award P1 for stretch y-axis invariant line scale factor k > 0 (k ≠ 1) , or for stretch x-axis invariant line scale factor 2, or for any horizontal translation of the correct solution. [5] 10 (a) (b) (c) 35o 125o 15o B1 B1 B1 [3] 11 (a) y = –2x + 4 oe B2 After B0 award B1 for y = mx + 4 (m ≠ 0) or for y = –2x + c or award (b) gradient of perp = 2 1 B1 ft mid point = (1, 2) B1 2 = 2 1 × 1 + c M1 For substituting correctly into the equation of a line formula. M1 can imply B1, B1 if correct. y = 2 1 x + 2 3 or any correct equivalent A1 [6] 12 100 = k × 202 or any other correct point used M2 If M0 award M1 for y = kx2 (k ≠ 1) or y α x2 y = 4 1 x2 oe A1 [3]