Cambridge IGCSE Mathematics (with coursework) 0581 — 2012 May/June Paper 2 · Variant 1

This document consists of 12 printed pages. IB12 06_0581_21/FP © UCLES 2012 [Turn over *9178372827* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0581/21 Paper 2 (Extended) May/June 2012 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 2012 0581/21/M/J/12 For Examiner's Use 1 The price of a ticket for a football match is $124 . (a) Calculate the amount received when 76 500 tickets are sold. Answer(a) $ [1] (b) Write your answer to part (a) in standard form. Answer(b) $ [1] 2 Gregor changes $700 into euros (€) when the rate is €1 = $1.4131 . Calculate the amount he receives. Answer € [2] 3 Factorise completely. 15p2 + 24pt Answer [2] 4 Write the following in order of size, smallest first. 0.47 17 8 0.22 tan 25° Answer < < < [2]

3 © UCLES 2012 0581/21/M/J/12 [Turn over For Examiner's Use 5 x cm 29 cm 53.2° NOT TO SCALE Calculate the value of x. Answer x = [2] 6 Leon scores the following marks in 5 tests. 8 4 8 y 9 His mean mark is 7.2. Calculate the value of y. Answer y = [2] 7 The sides of a rectangle are 6.3 cm and 4.8 cm, each correct to 1 decimal place. Calculate the upper bound for the area of the rectangle. Answer cm2 [2]

4 © UCLES 2012 0581/21/M/J/12 For Examiner's Use 8 Find r when (5) 3 r = 125 . Answer r = [2] 9 A B D (a) The point C lies on AD and angle ABC = 67°. Draw accurately the line BC. [1] (b) Using a straight edge and compasses only, construct the perpendicular bisector of AB. Show clearly all your construction arcs. [2]

5 © UCLES 2012 0581/21/M/J/12 [Turn over For Examiner's Use 10 Shania invests $750 at a rate of 2 2 1 % per year simple interest. Calculate the total amount Shania has after 5 years. Answer $ [3] 11 Solve the simultaneous equations. 3x + 5y = 24 x + 7y = 56 Answer x = y = [3]

6 © UCLES 2012 0581/21/M/J/12 For Examiner's Use 12 Without using your calculator, work out 1 6 5 + 10 9 . You must show your working and give your answer as a mixed number in its simplest form. Answer [3] 13 y is inversely proportional to x2. When x = 4, y = 3. Find y when x = 5. Answer y = [3]

7 © UCLES 2012 0581/21/M/J/12 [Turn over For Examiner's Use 14 y x 7 6 5 4 3 2 1 –1 0 –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 The region R contains points which satisfy the inequalities y Y 2 1 x + 4, y [ 3 and x + y [ 6. On the grid, label with the letter R the region which satisfies these inequalities. You must shade the unwanted regions. [3] 15 The scale of a map is 1 : 500 000 . (a) The actual distance between two towns is 172 km. Calculate the distance, in centimetres, between the towns on the map. Answer(a) cm [2] (b) The area of a lake on the map is 12 cm2. Calculate the actual area of the lake in km2. Answer(b) km2 [2]

8 © UCLES 2012 0581/21/M/J/12 For Examiner's Use 16 M =       − 4 3 2 5 N =       − − 6 2 2 1 Calculate (a) MN, Answer(a) MN = [2] (b) M−1, the inverse of M. Answer(b) M–1 = [2] 17 Make w the subject of the formula. c = 3 4 + + w w Answer w = [4]

9 © UCLES 2012 0581/21/M/J/12 [Turn over For Examiner's Use 18 20 15 10 5 0 10 20 30 40 50 60 70 80 90 100 110 120 Speed (m / s) Time (s) The diagram shows the speed-time graph for the first 120 seconds of a car journey. (a) Calculate the acceleration of the car during the first 25 seconds. Answer(a) m/s2 [1] (b) Calculate the distance travelled by the car in the first 120 seconds. Answer(b) m [4]

10 © UCLES 2012 0581/21/M/J/12 For Examiner's Use 19 O T P Q R S t p O is the origin and OPQRST is a regular hexagon. = p and = t. Find, in terms of p and t, in their simplest forms, (a) , Answer(a) = [1] (b) , Answer(b) = [2] (c) the position vector of R. Answer(c) [2]

11 © UCLES 2012 0581/21/M/J/12 [Turn over For Examiner's Use 20 78° O R T P 5 cm NOT TO SCALE R and T are points on a circle, centre O, with radius 5 cm. PR and PT are tangents to the circle and angle POT = 78°. A thin rope goes from P to R, around the major arc RT and then from T to P. Calculate the length of the rope. Answer cm [6] Question 21 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 2012 0581/21/M/J/12 For Examiner's Use 21 In this question, give all your answers as fractions. A box contains 3 red pencils, 2 blue pencils and 4 green pencils. Raj chooses 2 pencils at random, without replacement. Calculate the probability that (a) they are both red, Answer(a) [2] (b) they are both the same colour, Answer(b) [3] (c) exactly one of the two pencils is green. Answer(c) [3]

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2012 question paper for the guidance of teachers 0581 MATHEMATICS 0581/21 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, 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. • Cambridge will not enter into discussions or correspondence in connection with these mark schemes. Cambridge is publishing the mark schemes for the May/June 2012 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 2012 0581 21 © University of Cambridge International Examinations 2012 Abbreviations cao correct answer only cso correct solution only dep dependent ft follow through after error isw ignore subsequent working oe or equivalent SC Special Case www without wrong working soi seen or implied Qu Answers Mark Part marks 1 (a) (b) 9486000 9.486 × 106 1 1ft 2 495.36 2 M1 for 700 ÷ 1.4131 3 3p(5p + 8t) final answer 2 B1 for answer of 3(5p2 + 8pt) or p(15p + 24t) or SC1 for correct answer seen in working 4 tan 25 < 22 0. < 0.47 < 17 8 2 M1 correct conversion to decimals 0.466, 0.469, 0.471 5 23.2 2 M1 for 29 2 53 sin x . = implicit form or better 6 7 2 M1 2 7 5 9 8 4 8 . y = + + + + oe 7 30.7975 cao 2 M1 6.35 and 4.85 seen 8 9 2 M1 3 5 125 = 9 (a) (b) angle of 67° at B perpendicular bisector of AB 1 2 B1 C marked on AD unless the line stops at AD and also correct ruled line B1 correct arcs B1 correct ruled line 10 843.75 3 M2 for 750 100 5.2 5 750 + × × oe or M1 for 100 5.2 5 750 × × oe or SC2 for answer 93.75

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2012 0581 21 © University of Cambridge International Examinations 2012 11 x = −7 y = 9 3 M1 for consistent multiplication and addition/ subtraction as appropriate. Allow computational errors A1 for x= –7 or y = 9 12 30 27 30 55 + oe or 30 27 30 25 )1( + oe 30 82 oe or 30 52 )1( oe 15 11 2 M2 must be scored M1 M1 A1 for denominator of 30k for denominator of 30k dependent on previous M1 If M0 scored then SC1 for common denominator of 30k seen 13 1.92 3 M1 2 x k y = oe B1 for k = 48 14 3 15 (a) (b) 34.4 300 2 2 SC1 figs 344 seen SC1 figs 3 seen 16 (a)      − 30 11 2 1 2 B1 any two entries correct (b)       − 5 3 2 4 26 1 oe 2 B1       d c b a 26 1 or       − 5 3 2 4 k 17 1 3 4 − − = c c w www 4 M1 clearing denominator and removing brackets M1 correctly collecting terms in w on one side only M1 factorising correctly M1 divide by coefficient of w 18 (a) (b) 0.8 1850 1 4 M1 for area = distance travelled M1 for two correct area statements M1 for complete correct area statement 2 1 3 1 2 0 2 R

Page 4 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2012 0581 21 © University of Cambridge International Examinations 2012 19 (a) (b) (c) −p + t p + 2t 2(p + t) or 2p + 2t 1 2 2ft M1 for a correct route from P to R or unsimplified answer M1 for OR or a correct route or ft p + their (b) unsimplified provided their (b) is a vector 20 64.8 to 64.9 6 M2 5 tan 78 soi by 23.5 or M1 tan 78 = 5 PT or 12 tan 5 or 12 sin 78 sin 5 M2 5 2 360 78 2 360 × × × × − π soi by 17.8 or M1 for 2π5 seen used M1 for their arc + 2 (their PT) 21 (a) 12 1 2 M1 1 9 2 4 2 3 3 − × + + ) (their (b) 18 5 3 M2 ( ) 72 1 2 72 3 4 their their their(a) × + × + or M1 72 3 4 their × or ( ) 72 1 2 their × (c) 9 5 3 M2 1 9 5 4 2 3 4 2 − × + + × ) (their or M1 1 9 5 4 2 3 4 − × + + ) (their