Cambridge IGCSE Mathematics (with coursework) 0581 — 2010 May/June Paper 2 · Variant 3

This document consists of 12 printed pages. IB10 06_0581_23/FP © UCLES 2010 [Turn over *6417528597* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0581/23 Paper 2 (Extended) May/June 2010 1 hour 30 minutes Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Mathematical tables (optional) 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 of the marks for this paper is 70. www.XtremePapers.com

2 © UCLES 2010 0581/23/M/J/10 For Examiner's Use 1 During one week in April, in Quebec, the daily minimum temperatures were –5°C, –1°C, 3°C, 2°C, –2°C, 0°C, 6°C. Write down (a) the lowest of these temperatures, Answer(a) °C [1] (b) the range of these temperatures. Answer(b) °C [1] 2 23 48% 4.80 11 53 Write the numbers in order of size with the largest first. Answer K= K K [2] 3 Ricardo changed $600 into pounds (£) when the exchange rate was $1 = £0.60. He later changed all the pounds back into dollars when the exchange rate was $1 = £0.72. How many dollars did he receive? Answer $ [2] 4 The maximum speed of a car is 252 km/h. Change this speed into metres per second. Answer m/s [2]

3 © UCLES 2010 0581/23/M/J/10 [Turn over For Examiner's Use 5 Amalie makes a profit of 20% when she sells a shirt for $21.60. Calculate how much Amalie paid for the shirt. Answer $ [2] 6 3x × 94 = 3n. Find n in terms of x. Answer n = [2] 7 Shade the required regions in the Venn diagrams below. A B C A B C [2] 8 Write as a single fraction in its simplest form 1 3 2 x x − + . Answer [2]

4 © UCLES 2010 0581/23/M/J/10 For Examiner's Use 9 1 second = 106 microseconds. Change 3 × 1013 microseconds into minutes. Give your answer in standard form. Answer min [2] 10 The length of each side of an equilateral triangle is 74 mm, correct to the nearest millimetre. Calculate the smallest possible perimeter of the triangle. Answer mm [2] 11 P F A beach cliff 55 m NOT TO SCALE The diagram shows a point P at the top of a cliff. The point F is on the beach and vertically below P. The point A is 55m from F, along the horizontal beach. The angle of elevation of P from A is 17°. Calculate PF, the height of the cliff. Answer PF = m [3]

5 © UCLES 2010 0581/23/M/J/10 [Turn over For Examiner's Use 12 Expand and simplify 2(x – 3)2 – (2x – 3)2. Answer [3] 13 (a) Write down the number of lines of symmetry for the diagram below. Answer(a) [1] (b) Write down the order of rotational symmetry for the diagram below. Answer(b) [1] (c) The diagram shows a cuboid which has no square faces. Draw one of the planes of symmetry of the cuboid on the diagram. [1]

6 © UCLES 2010 0581/23/M/J/10 For Examiner's Use 14 Solve the equation 9 2 ) 4 ( 3 = + − y y . Answer y = [3] 15 G O H N g h NOT TO SCALE In triangle OGH, the ratio GN : NH = 3 : 1. = g and = h. Find the following in terms of g and h, giving your answers in their simplest form. (a) Answer(a) = [1] (b) Answer(b) = [2]

7 © UCLES 2010 0581/23/M/J/10 [Turn over For Examiner's Use 16 Make y the subject of the formula. 5 ) 2 ( + = y r A Answer y = [3] 17 40° O L K 5.6 cm NOT TO SCALE OKL is a sector of a circle, centre O, radius 5.6 cm. Angle KOL = 40°. Calculate (a) the area of the sector, Answer(a) cm2 [2] (b) the perimeter of the sector. Answer(b) cm [2]

8 © UCLES 2010 0581/23/M/J/10 For Examiner's Use 18 f(x) = x2 + 2 g(x) = (x + 2)2 h(x) = 3x – 5 Find (a) gf(–2), Answer(a) [2] (b) h –1(22) . Answer(b) [2] 19 v t 3 4 15 Time (seconds) Speed (m / s) 0 NOT TO SCALE The diagram shows the speed-time graph for 15 seconds of the journey of a cyclist. (a) Calculate the acceleration of the cyclist during the first 4 seconds. Answer(a) m/s2 [1] (b) Calculate the average speed for the first 15 seconds. Answer(b) m/s [3]

9 © UCLES 2010 0581/23/M/J/10 [Turn over For Examiner's Use 20 y x 4 3 2 1 0 1 2 3 4 Find the three inequalities which define the shaded region on the grid. Answer [5]

10 © UCLES 2010 0581/23/M/J/10 For Examiner's Use 21 North North North 50 m 100 m Q R P 140° NOT TO SCALE The diagram shows three points P, Q and R on horizontal ground. PQ = 50 m, PR = 100 m and angle PQR = 140°. (a) Calculate angle PRQ. Answer(a) Angle PRQ = [3] (b) The bearing of R from Q is 100°. Find the bearing of P from R. Answer(b) [2]

11 © UCLES 2010 0581/23/M/J/10 [Turn over For Examiner's Use 22 A B C The diagram shows a farmer’s field ABC. The farmer decides to grow potatoes in the region of the field which is • nearer to A than to C and • nearer to AB than to AC. Using a straight edge and compasses only, construct two loci accurately and shade this region on the diagram. [5] Question 23 is printed 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 2010 0581/23/M/J/10 For Examiner's Use 23 A = ( ) 1 4 B = ( ) 3 1 2 2 − − Find (a) AB, Answer(a) AB = [2] (b) the inverse matrix B–1 , Answer(b) B–1 = [2] (c) BB–1. Answer(c) BB–1 = [1]

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 0581 MATHEMATICS 0581/23 Paper 23 (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, 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 0581 23 © UCLES 2010 Qu. Answers Mark Part Marks 1 (a) –5 (b) 11 1 1 2 % 48 23 80 .4 11 53 > > > 2 M1 for decimals seen 4.7958… 0.48 (4.80) 4.81(…) 3 500 2 M1 for 600 × 0.6 ÷ 0.72 seen 4 70 2 M1 for 252 × 1000 ÷ 60 ÷ 60 oe 5 18 2 M1 for 21.6 ÷ 1.2 oe 6 x + 8 2 M1 38 seen 7 2 B1 for one correct Venn diagram 8 6 3 5 − x 2 B1 for 5x – 3 seen SC1 6 3 6 5 − x on answer line 9 5(.00) × 105 2 SC1 for 5 × 10k or 500 000 on answer line 10 220.5 cao 2 M1 for 73.5 seen 11 16.8 3 M2 tan17 = 55 h or tan73 = h 55 or M1 tan17 = h 55 or tan73 = 55 h if angle seen in wrong place at P 12 9 – 2x2 3 B1 for x2 – 3x – 3x + 9 or 2x2 – 6x – 6x + 18 B1 for 4x2 – 6x – 6x + 9 or –4x2 + 6x + 6x – 9 13 (a) 0 (b) 2 (c) plane across centre of shape 1 1 1 Three possibilities 14 6 3 M1 for one correct first step which leads towards simplifying 9 2 12 3 = + − y y or 6(y – 4) + y = 18 or y – 4 + 6 y = 3 M1 correctly collecting their terms to py = q

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2010 0581 23 © UCLES 2010 15 (a) g – h 1 (b) 4 1 g + 4 3 h 2 M1 for OH + HN or h + 4 1 (a) OG + GN or g – 4 3 (a) 16 2 5 − r A or r r A 2 5 − 3 M1 for correctly multiplying by 5 M1 for correctly dividing by r M1 for correct subtraction in any order 17 (a) 10.9 2 M1 for 2 6.5 π 360 40 × × (b) 15.1 2 M1 for 6.5 2 π 360 40 × × × (= 3.91..) 18 (a) 64 2 B1 for evidence of f(–2) = 6 (b) 9 2 M1 for 3x – 5 = 22 or 3 5 + x seen 19 (a) 4 3 or 0.75 1 (b) 2.6 3 M1 for finding the area under the graph or M1 for their 39 ÷ 15 20 x [ 0 1 L1 x R 0 y [ 2 1 x oe 2 L1 y R 2 1 x x + y Y 4 oe 2 L1 x + y R 4 where R is any one of = < > Y [ B2 all inequalities correct or B1 2 correct 21 (a) 18.7 3 M2 for 100 140 sin 50 sin × = R (= 0.3219…) or M1 for 100 140 sin 50 sin = R oe (b) 261(.3) 2ft M1 360 – 80 – their (a) 22 Perpendicular bisector of AC Bisector of angle A Shaded region inside triangle and to left of perp bisector of AC and above bisector of angle A 2 2 1 B1 accurate line B1 two pairs of correct construction arcs B1 accurate line B1 two pairs of correct construction arcs B1 dep on first B1 being scored for both lines 23 (a) ( ) 7 5 − 2 B1 either correct in a (1 × 2) matrix (b)     3 2 1 2 4 1 oe 2 M1 for     3 2 1 2 seen or 2 × 3 – –1 × –2 ( = 4) (c)     1 0 0 1 or I cao 1