Cambridge IGCSE Mathematics - International 0607 — 2009 May/June Paper 2 · Variant 1

This document consists of 8 printed pages. IB09 06_0607_02/5RP © UCLES 2009 [Turn over *6634783498* 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 2009 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 of the marks for this paper is 40. www.XtremePapers.com

2 © UCLES 2009 0607/02/M/J/09 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 2009 0607/02/M/J/09 [Turn over For Examiner's Use Answer all the questions. 1 The distance from the Earth to the Moon is 3.8 × 105 km. A spacecraft travels this distance four times. Calculate the total distance travelled. Give your answer in standard form. Answer km [2] 2 For the function f(x) = 2sin 3x write down (a) the amplitude, Answer (a) [1] (b) the period. Answer (b) [1] 3 O D A z° y° B C 20° x° NOT TO SCALE A, B, C and D lie on a circle, centre O. AC is a diameter and angle ACD = 20°. AB = BC. Find the values of x, y and z. Answer x = [1] y = [1] z = [1]

4 © UCLES 2009 0607/02/M/J/09 For Examiner's Use 4 Write the following as algebraic expressions. (a) One-third of the sum of p and q. Answer (a) [1] (b) The square root of the product of x and y. Answer (b) [1] 5 List the elements of the following sets. (a) A = {x | x∈w, – 4 < x Y1} Answer (a) [1] (b) B = {prime numbers between 25 and 35} Answer (b) [1] (c) C = {x | x∈o, | x | = 4} Answer (c) [1] 6 (a) Write as a single logarithm. log6 + log3 – log2 Answer (a) [1] (b) Simplify. _ 98 50 + 8 Answer (b) [2]

5 © UCLES 2009 0607/02/M/J/09 [Turn over For Examiner's Use 7 The first five terms of a sequence are 0, 3, 8, 15, 24. (a) Write down the next two terms of the sequence. Answer (a) , [1] (b) Find the nth term of the sequence. Answer (b) [2] 8 y x –3 –4 –2 –1 1 2 3 4 3 2 1 –1 –2 –3 0 F The diagram shows a flag F. (a) Translate flag F by       2 _ 3 . Label the image P. [2] (b) Reflect flag F in the line x = 1. Label the image Q. [2]

6 © UCLES 2009 0607/02/M/J/09 For Examiner's Use 9 Solve the simultaneous equations. 2x + 3y = 7 5x – 4y = –17 Answer x = y = [4] 10 Make t the subject of the formula. = _ 2 a y t Answer t = [3]

7 © UCLES 2009 0607/02/M/J/09 [Turn over For Examiner's Use 11 The points A(−3, 5) and B(3, 2) are shown on the diagram below. y x 0 A B NOT TO SCALE (a) (i) Write down the vector AB in component form. Answer (a)(i)           [1] (ii) Find AB  leaving your answer in surd form. Answer (a)(ii) [2] (b) Calculate the gradient of the line AB. Answer (b) [2] (c) Calculate the co-ordinates of the midpoint of the line AB. Answer (c) ( , ) [1] (d) Find the equation of the perpendicular bisector of the line AB. Answer (d) [2] Question 12 is 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. 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 2009 0607/02/M/J/09 For Examiner's Use 12 Find the value of the following. (a) 2 3 16 Answer (a) [1] (b) (cos 30°)2 Answer (b) [2]

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2009 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 2009 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 2009 0607 02 © UCLES 2009 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. Abbreviations cao correct answer only cso correct solution only ft follow through oe or equivalent soi seen or implied ww without working www without wrong working 1 (a) 4 × 3.8 × 105 1.52(0…) × 106 M1 A1 If zero scored SC1 for 1.5 × 106 ww. www 2 [2] 2 (a) (b) 2 120 B1 B1 Accept 3 2π [2] 3 x = 45 y = 40 z = 70 B1 B1 B1 Answers on the diagram can be accepted on the diagram unless contradicted in the answer spaces. [3] 4 (a) (b) ) ( 3 1 q p + oe xy or any unambiguous equivalent B1 B1 Accept ± , –, + Not √ xy [2] 5 (a) (b) (c) −3, −2, −1, 0, 1 29, 31 −4, 4 B1 B1 B1 [3] 6 (a) (b) log 9 4 2 or 2 8 or 32 B1 B2 Accept 2 log 3 B1 for two of 7 2 or 5 2 or 2 2 seen [3] 7 (a) (b) 35, 48 n2 – 1 oe B1 B2 B1 for n2 , or n2 + c seen, or n = n2 – 1 or M1 for difference method seen as far as third line (all 2’s) [3]

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2009 0607 02 © UCLES 2009 8 (a) (b) Correct translation. Top of flag at (2,1) Correct reflection. Top of flag at (3,3) D2 D2 D1 any other translation. Ignore labels D1 Reflection y = 1, or reflecting their P in x = 1 [4] 9 Attempt to get 2 equations for elimination Correct addition/subtractions of their equations x = −1 y = 3 OR Equation x = or y = from one equation Substitute their expression into other equation correctly x = −1 y = 3 www 4 M1 M1 A1 A1 OR M1 M1 A1 A1 Condone 1 slip Condone 1 further slip (dep on first M1) Condone 1 slip No further slips (dep on first M1) [4] 10 For correct multiplication by t −2 For a correct division by y For adding 2 or 2y correctly as appropriate Leading to t = y y a 2 + or t = 2 + y a www 3 M1 M1 M1 Can be in any order Final answer must be correct to score M3 [3] 11 (a) (i) (ii) (b) (c) (d)       −3 6 cao 62 + 32 = 45 or 3 5 Gradient = 6 3 − oe Midpoint = (0, 2 7 ) oe cao Gradient of perpendicular = 2 or ) ( 1 b their − y = mx + 2 7 oe (indep) B1 M1 A1ft B2 B1 B1ft B1 Only if (a)(i) is in non zero integer form If B0 then B1ft for Gradient = x their in change y their in change B1 for negative gradient (indep) If still B0 SC1 for x 6 3 − oe Implied by (y =) 2x c ± [8] 12 (a) (b) 64 4 3 or 0.75 B1 B2 If B0, then B1 for 2) 2 3 ( seen [3]