Cambridge IGCSE Mathematics - International 0607 — 2010 Oct/Nov Paper 2 · Variant 1

This document consists of 10 printed pages and 2 blank pages. IB10 11_0607_02/2RP © UCLES 2010 [Turn over *9648538625* For Examiner's Use UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/02 Paper 2 (Extended) October/November 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/O/N/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/O/N/10 [Turn over For Examiner's Use Answer all the questions. 1 (a) Simplify 75 . Answer(a) [2] (b) Find the value of log101000. Answer(b) [1] 2 Factorise completely. 2ac – 5bc + 6a – 15b Answer [2] 3 The gradient of the line joining the points (2, 1) and (6, a) is 3 2 . Find the value of a. Answer a = [3]

4 © UCLES 2010 0607/02/O/N/10 For Examiner's Use 4 The cumulative frequency curve shows the heights of 200 plants measured correct to the nearest centimetre. 200 190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 20 10 30 40 50 60 70 80 Height (cm) Cumulative frequency 0 (a) Use the graph to find (i) the median, Answer(a)(i) cm [1] (ii) the interquartile range. Answer(a)(ii) cm [2] (b) Find the percentage of plants with heights greater than 50 cm. Answer(b) % [2]

5 © UCLES 2010 0607/02/O/N/10 [Turn over For Examiner's Use 5 A cuboid has a square base of side x cm and a height of y cm. Find, in terms of x and y, (a) the volume of the cuboid, Answer(a) cm3 [1] (b) the total surface area of the cuboid. Answer(b) cm2 [2] 6 The distance between towns A and B is 50 km. The bearing of A from B is 210°. (a) Sketch the positions of A and B showing clearly the angle of 210°. North [1] (b) Calculate how far west A is from B. Answer(b) km [2]

6 © UCLES 2010 0607/02/O/N/10 For Examiner's Use 7 a = 3 2 −       b = 2 5 −       When 2a + kb = 2 16 −       find the value of k. Answer [3] 8 f(x) = 2x – 1 g(x) = 3x2 + 1 Find (a) g(2), Answer(a) [1] (b) g(f(x)), Answer(b) [2] (c) the inverse function f -1(x). Answer(c) [2]

7 © UCLES 2010 0607/02/O/N/10 [Turn over For Examiner's Use 9 The table shows the marks (x) gained by 100 students in an examination. Mark (x) 0 Y x I 10 10 Y x I 20 20 Y x I 40 40 Y x I 45 45 Y x I 60 Frequency 20 10 10 30 30 Use this information to draw a histogram on the grid below. 6 5 4 3 2 1 0 10 20 30 40 50 60 Frequency density Mark x [3]

8 © UCLES 2010 0607/02/O/N/10 For Examiner's Use 10 In Hurghada the probability that the sun will shine on any day is 0.8. If the sun shines, the probability Ahmed will go to the beach is 0.9. If the sun does not shine, the probability he will go to the beach is 0.5. (a) Complete the tree diagram. 0.8 … 0.9 … The sun shines The sun does not shine Goes to beach Does not go to beach … … Goes to beach Does not go to beach [2] (b) Find the probability that Ahmed will go to the beach on a given day. Answer(b) [2]

9 © UCLES 2010 0607/02/O/N/10 [Turn over For Examiner's Use 11 The diagram shows part of the graph of y = f(x), where f(x) = ax2 + bx – 6. y x 8 6 4 2 –2 –4 –6 –8 0 –3 –2 –1 1 2 3 4 Find the values of a and b. Answer a = b = [3]

10 © UCLES 2010 0607/02/O/N/10 For Examiner's Use 12 Which of the following functions are shown by the graphs below? In each case k > 1. Write the correct letter under each graph. A y = k x B y = | x + k | C y = kx D y = | x − k | E y = k−x F y = x k y x 0 … y x 0 … y x 0 … [3]

11 © UCLES 2010 0607/02/O/N/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/O/N/10 BLANK PAGE

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 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 October/November 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 – October/November 2010 0607 02 © UCLES 2010 1 (a) 3 5 B2 Award M1 for evidence of 3 25× (b) 3 B1 [3] 2 c(2a – 5b) + 3(2a – 5b) or 2a(c + 3) – 5b(c + 3) (2a – 5b)(c + 3) www2 M1 A1 [2] 3 2 6 1 − − a = 2 3 oe For correctly setting out the gradient M1 Alternative solution y = 2 2 3 − x 2a – 2 = 12 For a correct method to eliminate the fractions from a correct equation M1 a = 2 6 2 3 − × For substituting a and 6 correctly a = 7 www3 A1 a = 7 [3] 4 (a) (b) (c) 45 25 34 to 36 inclusive B1 B2 B2 If B0 award B1 for 30 or 55 seen and not spoilt by use of 150 and/or 50 If B0 award B1 for 128 to 132 inclusive seen [5] 5 (a) (b) x2y oe 4xy + 2x2 oe B1 B2 B1 for 2x2, B1 for 4xy [3] 6 (a) N B 210o A P1 A and B must be labelled correctly, with A between South and West (b) 50sin30 seen oe 25 ww2 M1 A1 Allow implicit form If scale drawing used then M0 [3]

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2010 0607 02 © UCLES 2010 7 2     −2 3 + k    − 5 2 =    − 16 2 oe M1 For setting up equation 6 – 2k = –2 or –4 + 5k = 16 k = 4 www3 M1 A1 Implies first M1 [3] 8 (a) (b) 13 3(2x – 1)2 + 1 isw B1 B2 isw attempts to expand/simplify only. If B0 award M1 for g(2x – 1) seen. (c) 2 1 + x B2 If B0 award M1 for x = 2y – 1 or 2 1 + y or 2 1 ) ( f + x [5] 9 For correct histogram with frequency density values of k(2, 1, 0.5, 6, 2) where k > 0 P3 Award P2 for one error, P1 for two errors, P0 otherwise, Or SC1 for correct frequency densities, Or SC2 for correct histogram with freq polygon superimposed. [3] 10 (a) beach sun no beach beach no sun 0.2 no beach B2 Award B1 for two correct values in correct positions, B0 otherwise (b) 0.8 × 0.9 + 0.2 × 0.5 0.82 www2 M1 A1 SC1 for 0.8 × 0.9 (= 0.72) or 0.2 × 0.5 (= 0.1) seen [4] 0.1 0.5 0.5

Page 4 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2010 0607 02 © UCLES 2010 11 Two correct simultaneous equations e.g. two of 9a + 3b = 6, a – b = 6, a + b = –2, 4a + 2b – 6 = –6 oe Correct method to eliminate one variable Condone one slip a = 2 and b = –4 www3 M1 M1dep A1 Alternative Solution (y =) a(x – –1)(x – 3) oe Correct substitution of values for x and y e.g. –6 = a × 1 × –3 a = 2 and b = –4 If M0 scored then SC2 for (x – –1)(x – 3) oe seen and, a = 2 or b = –4 [3] 12 D E A B1 B1 B1 [3]