Cambridge IGCSE Mathematics (with coursework) 0581 — 2007 May/June Paper 2 · Variant 1

This document consists of 12 printed pages. IB07 06_0580_02/6RP © UCLES 2007 [Turn over *3354131474* For Examiner's Use UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0580/02, 0581/02 Paper 2 (Extended) May/June 2007 1 hour 30 minutes Candidates answer on the Question Paper. Additional Materials: Electronic calculator Mathematical tables (optional) Geometrical instruments Tracing paper (optional) 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. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown below that question. Electronic calculators should be used. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for the paper is 70. www.XtremePapers.com

2 © UCLES 2007 0580/02/J/07 For Examiner's Use 1 For the diagram above write down (a) the order of rotational symmetry, Answer(a) [1] (b) the number of lines of symmetry. Answer(b) [1] 2 (a) Use your calculator to work out 2 1 (tan 40 ) ) 2(tan 40 − o o . Answer(a) [1] (b) Write your answer to part (a) in standard form. Answer(b) [1] 3 Xsara throws a ball three times at a target. Each time she throws the ball, the probability that she hits the target is 0.2. Calculate the probability that she does not hit the target in any of the three throws. Answer [2]

3 © UCLES 2007 0580/02/J/07 [Turn over For Examiner's Use 4 Write the following in order of size, smallest first. cos100° sin100° tan100° Answer < < [2] 5 A tin of soup has the following information on the label. 200 grams of soup contains Protein Carbohydrate Fat 4 g 8.7 g 5.8 g (a) What fraction of the soup is Protein? Give your answer in its simplest form. Answer(a) [1] (b) What percentage of the soup is Carbohydrate? Answer(b) % [1] 6 Carmen spends 5 minutes, correct to the nearest minute, preparing one meal. She spends a total time of T minutes preparing 30 meals. Between what limits does T lie? Answer T < [2] 7 M = 1 1 1 2 M2 = 2 3 3 5 M3 = 5 8 8 13 Find M4. Answer M4 = [2]

4 © UCLES 2007 0580/02/J/07 For Examiner's Use 8 On the Venn diagrams shade the regions (a) A′ ∩ C′, A B C [1] (b) (A ∪ C ) ∩ B. A B C [1] 9 Write down (a) an irrational number, Answer(a) [1] (b) a prime number between 60 and 70. Answer(b) [1] 10 Write as a fraction in its simplest form 3 4 4 3 −+ − x x . Answer [3]

5 © UCLES 2007 0580/02/J/07 [Turn over For Examiner's Use 11 A = 8 2 x x . (a) Find │A│, the determinant of A, in terms of x. Answer(a) [1] (b) Find the values of x when │A│= 9. Answer(b) x = or x = [2] 12 1 2 3 4 5 6 7 7 6 5 4 3 2 1 0 y x By shading the unwanted parts of the grid above, find and label the region R which satisfies the following three inequalities y 3, y 5x and x + y 6. [3] 13 The quantity y varies as the cube of (x + 2). y = 32 when x = 0. Find y when x = 1. Answer y = [3]

6 © UCLES 2007 0580/02/J/07 For Examiner's Use 14 70o A B C NOT TO SCALE The diagram shows three touching circles. A is the centre of a circle of radius x centimetres. B and C are the centres of circles of radius 3.8 centimetres. Angle ABC = 70°. Find the value of x. Answer x = [3] 15 Two unbiased spinners are used in a game. One spinner is numbered from 1 to 6 and the other is numbered from 1 to 3. The scores on each spinner are multiplied together. The table below shows the possible outcomes. First Spinner 1 2 3 4 5 6 1 1 2 3 4 5 6 2 2 4 6 8 10 12 Second Spinner 3 3 6 9 12 15 18 (a) Find the probability that the outcome is even. Answer(a) [1] (b) When the outcome is even, find the probability that it is also greater than 11. Answer(b) [2]

7 © UCLES 2007 0580/02/J/07 [Turn over For Examiner's Use 16 The function f(x) is given by f(x) = 3x – 1. Find, in its simplest form, (a) f-−1f(x), Answer(a) [1] (b) ff(x). Answer(b) [2] 17 (a) 32 = 2p. Find the value of p. Answer(a) p = [2] (b) 3 1 8 = 2q. Find the value of q. Answer(b) q = [2] 18 The equation of a straight line can be written in the form 3x + 2y – 8 = 0. (a) Rearrange this equation to make y the subject. Answer(a) y = [2] (b) Write down the gradient of the line. Answer(b) [1] (c) Write down the co-ordinates of the point where the line crosses the y axis. Answer(c) ( , ) [1]

8 © UCLES 2007 0580/02/J/07 For Examiner's Use 19 64° w° x° y° O P R S Q T NOT TO SCALE P, Q, R and S lie on a circle, centre O. TP and TQ are tangents to the circle. PR is a diameter and angle PSQ = 64°. (a) Work out the values of w and x. Answer(a) w = [1] x = [1] (b) Showing all your working, find the value of y. Answer(b) y = [2]

9 © UCLES 2007 0580/02/J/07 [Turn over For Examiner's Use 20 x x x x SEA A B D P LAND LAND The diagram shows a map of part of a coastline. 1 centimetre represents 40 metres. (a) A ferry leaves a port P and travels between two islands so that it is always equidistant from A and B. Using a straight edge and compasses only, draw this locus. [2] (b) For safety reasons the ferry must be at least 120 metres from a ship at D. Draw the locus of the points which form the boundary of safety around D. [1] (c) When the ferry is 120 metres from D it must change direction. How far is the ferry from the port P then? Answer(c) m [1]

10 © UCLES 2007 0580/02/J/07 For Examiner's Use 21 10 20 30 40 50 60 70 80 90 100 18 16 14 12 10 8 6 4 2 0 Time (s) Speed (m / s) The diagram shows part of a journey by a truck. (a) The truck accelerates from rest to 18 m/s in 30 seconds. Calculate the acceleration of the truck. Answer(a) m/s2 [1] (b) The truck then slows down in 10 seconds for some road works and travels through the road works at 12 m/s. At the end of the road works it accelerates back to a speed of 18 m/s in 10 seconds. Find the total distance travelled by the truck in the 100 seconds. Answer(b) m [3]

11 © UCLES 2007 0580/02/J/07 [Turn over For Examiner's Use 22 NORTH EASTERN BANK SAVINGS ACCOUNT 5% Per Year Simple Interest SOUTH WESTERN BANK SAVINGS ACCOUNT 4.9% Per Year Compound Interest Kalid and his brother have $2000 each to invest for 3 years. (a) North Eastern Bank advertises savings with simple interest at 5% per year. Kalid invests his money in this bank. How much money will he have at the end of 3 years? Answer(a)$ [2] (b) South Western Bank advertises savings with compound interest at 4.9% per year. Kalid’s brother invests his money in this bank. At the end of 3 years, how much more money will he have than Kalid? Answer(b)$ [3] Question 23 is on the next 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 2007 0580/02/J/07 For Examiner's Use 23 NOT TO SCALE A B 12 cm The largest possible circle is drawn inside a semicircle, as shown in the diagram. The distance AB is 12 centimetres. (a) Find the shaded area. Answer(a) cm2 [4] (b) Find the perimeter of the shaded area. Answer(b) cm [2]

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2007 question paper 0580 and 0581 MATHEMATICS 0580/02 and 0581/02 Paper 2 (Extended), maximum raw mark 70 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. All Examiners are instructed that alternative correct answers and unexpected approaches in candidates’ scripts must be given marks that fairly reflect the relevant knowledge and skills demonstrated. 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 2007 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 Syllabus Paper IGCSE – May/June 2007 0580 and 0581 2 © UCLES 2007

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2007 0580 and 0581 2 © UCLES 2007