Cambridge IGCSE Mathematics (with coursework) 0581 — 2010 May/June Paper 1 · Variant 3

This document consists of 11 printed pages and 1 blank page. IB10 06_0581_13/FP © UCLES 2010 [Turn over *8303224372* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0581/13 Paper 1 (Core) May/June 2010 1 hour 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 of the marks for this paper is 56. www.XtremePapers.com

2 © UCLES 2010 0581/13/M/J/10 For Examiner's Use 1 45° 26° x° NOT TO SCALE Find the value of x. Answer x = [1] 2 A train to Paris leaves at 06 30. The journey takes 3 hours and 56 minutes. Work out the time when the train arrives in Paris. Answer [1] 3 Write down the factors of 48 which are between 10 and 40. Answer [2]

3 © UCLES 2010 0581/13/M/J/10 [Turn over For Examiner's Use 4 I = K= For each part, choose a symbol from those above to make a correct statement. (a) 9 5 0.55 [1] (b) 66% 3 2 [1] 5 In a sale, the price of a boat was reduced from $21 000 to $16 800. Calculate the reduction as a percentage of the original price. Answer % [2] 6 Write down the equation of the line, parallel to y = 3x + 5 , which passes through the point (0, −2). Answer [2]

4 © UCLES 2010 0581/13/M/J/10 For Examiner's Use 7 Mrs Duval makes one litre of ice cream. She eats 1 8 litre and her children eat 3 5 litre. Without using your calculator, find what fraction of a litre of ice cream is left. Show all your working clearly. Answer [2] 8 (a) Use your calculator to work out 27.4 × (3.28 + 1.6 × 9.8) . Write down all the figures from your calculator display. Answer(a) [1] (b) Write your answer to part (a) correct to 3 significant figures. Answer(b) [1] 9 Calculate the area of a circle of radius 3.75 cm. Answer cm2 [2]

5 © UCLES 2010 0581/13/M/J/10 [Turn over For Examiner's Use 10 (a) Write down the order of rotational symmetry of the shape above. Answer(a) [1] (b) A M N O T X From the list, write down the letters which have only one line of symmetry. Answer(b) [2] 11 Simplify (a) 5 3 − × m m , Answer(a) [1] (b) 2 8 3 15 k k ÷ . Answer(b) [2]

6 © UCLES 2010 0581/13/M/J/10 For Examiner's Use 12 150° 150° NOT TO SCALE The diagram shows part of a regular polygon with each interior angle 150°. Calculate the number of sides of the polygon. Answer [3] 13 Expand the following expressions. (a) 5(3 – 4h) Answer(a) [1] (b) ) 2 2 6 ( 4 e d d + Answer(b) [2]

7 © UCLES 2010 0581/13/M/J/10 [Turn over For Examiner's Use 14 4 cm 2.3 cm 1.75 cm NOT TO SCALE The cuboid above has length 4 cm, width 2.3 cm and height 1.75 cm. Calculate the volume of the cuboid (a) in cubic centimetres, Answer(a) cm3 [2] (b) in cubic millimetres. Answer(b) mm3 [1] 15 Simplify the following expressions. (a) 6r + 2s + s – 4r Answer(a) [1] (b) 4f 2 – 3g + 4g – 9f 2 Answer(b) [2]

8 © UCLES 2010 0581/13/M/J/10 For Examiner's Use 16 4 cm 11 cm NOT TO SCALE A cylindrical can of beans has height 11 cm and radius 4 cm. A label covers the curved surface of the can completely. Calculate the area of the label. Answer cm2 [3] 17 Solve the simultaneous equations. 3x + y = 19 5x – y = 13 Answer x = y = [3]

9 © UCLES 2010 0581/13/M/J/10 [Turn over For Examiner's Use 18 P, Q and R lie on a circle, centre O. PR is a diameter and angle OQR = 55°. Find (a) angle PQR, Answer(a) Angle PQR = [1] (b) angle ROQ, Answer(b) Angle ROQ = [1] (c) angle OPQ. Answer(c) Angle OPQ = [1] 19 f = 6 0    g = 3 6 −       h = 2 2 −       Calculate (a) 3f, Answer(a)             [2] (b) g – h. Answer(b)             [2] 55° R O P Q NOT TO SCALE

10 © UCLES 2010 0581/13/M/J/10 For Examiner's Use 20 100 90 80 70 60 50 40 30 20 10 0 0 1 2 3 4 5 6 7 8 9 Distance (kilometres) Garage Café Factory Time (hours) The travel graph shows part of the journey of a truck driver. The driver leaves a factory to deliver tyres to a garage. After unloading the tyres, the driver returns to the factory, but stops at a café for 1 hour. He then completes the journey at an average speed of 80 km/h. (a) Calculate the average speed of the truck on its journey from the factory to the garage. Answer(a) km/h [1] (b) Write down the length of time the truck stays at the garage. Answer(b) hours [1] (c) Complete the travel graph. [2]

11 © UCLES 2010 0581/13/M/J/10 For Examiner's Use 21 24° 9 cm 16 cm B D A C NOT TO SCALE The diagram shows a quadrilateral ABCD. AB = 16 cm, BD = 9 cm and angle BDC = 24°. Angle ADB = 90° = angle BCD. Calculate the length of (a) AD, Answer(a) AD = cm [3] (b) CD. Answer(b) CD = cm [2]

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. 0581/13/M/J/10 BLANK PAGE

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 0581/13 Paper 13 (Core), maximum raw mark 56 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 13 © UCLES 2010 Qu. Answers Mark Part Marks 1 109 1 2 10 26 (am), 10:26, 10.26 1 3 12, 16, 24 2 W1 for any 2 correct out of their 2 or 3 answers in the range or W1 for all 3 with other factors outside the range. 4 (a) > (b) < 1 1 5 20 2 M1 for 21000 ) 16800 21000 ( their − or 21000 4200 6 y = 3x – 2 oe final answer 2 W1 for 3x + j, j ≠ 5 or W1 for kx − 2, k ≠ 0 7 40 11 or equivalent fraction isw www Condone if followed by 0.275 or 27.5% 2 cao M1 for 5 8 1 5 8 5 8 3 × × + × × or 40 24 40 5 + or 0.6 + 0.125 or 40 24 40 5 1 − − or 1 − 0.6 − 0.125 or 600 + 125 or 60 + 12.5 or 1000 − 600 − 125 seen If M0, then SC1 for 40 11 with no, incomplete or wrong working. 8 (a) 519.504 (b) 520 1 1ft Only ft if their (a) is 4 figs or more 9 44.2 or 44.15 to 44.19 2 M1 for 3.752 × π 10 (a) 2 (b) A M T 1 2 W1 for 4 letters listed, 3 of them correct or W1 for 2 and only 2 correct 11 (a) m–2, 2 1 m o.e. 1 (b) 5k6 2 W1 for 5kn (n ≠ 0) or mk6 (m ≠ 0). 12 12 3 M1 for exterior angle 180 − 150 implied by 30 (could be on the diagram) and M1 dep for 360 ÷ their 30 13 (a) 15 – 20h final answer (b) 24d3 + 4de2 final answer 1 2 W1 for 24d3 or (+)4de2 seen 14 (a) 16.1 (b) 16100 2 1ft M1 for 4 × 2.3 × 1.75, or better 1000 × their (a)

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2010 0581 13 © UCLES 2010 15 (a) 2r + 3s final answer (b) g – 5f 2 final answer 1 2 W1 for g or for – 5f 2 seen 16 276 or 276.3 to 276.5 3 M2 for 2π × 4 × 11, or better, seen or M1 for 2π × 4 SC1 for 4 × π × 11 or 138…., seen 17 (x =) 4 (y =) 7 www 3 M1 for adding or multiplying and subtracting (allow errors in arithmetic operations) or any other correct methods A1 for one correct variable. 18 (a) 90° (b) 70° (c) 35° 1 1 1ft ft their (b) ÷ 2 only 19 (a)     0 18 1, 1 (b)    − 8 5 1, 1 20 (a) 45 (b) 1.5 o.e. (c) horizontal line from (5.5, 40) to (6.5, 40) diagonal line from their (x, 40) to (x + ½ , 0) 1 1 1 1ft Allow 1 h(our) 30(min) or 1:30 Independent 21 (a) 13.2 or 13.22 to 13.23 3 M2 for √(162 – 92) or √175 or M1 for 162 = x2 + 92 or better (b) 8.22 to 8.23 2 M1 for cos 24 = 9 CD or better