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

This document consists of 8 printed pages. IB10 06_0581_11/FP © UCLES 2010 [Turn over *3398247741* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0581/11 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 0581/11/M/J/10 For Examiner's Use 1 A ferry to Crete leaves at 07 30. The journey takes 2 hours and 48 minutes. Work out the time when the ferry arrives in Crete. Answer [1] 2 (a) Write the following in order, starting with the smallest. 0.43 9 4 41% Answer(a) < < [1] (b) Only one of the following statements is correct. sin 30° ≠ 0.5 42 > 16 0.3 < 3 1 Put a ring around the correct statement. [1] 3 In a group of 35 students, 14 go to school by bus. Write down the probability that a student, chosen at random, does not go to school by bus. Give your answer as a fraction in its lowest terms. Answer [2] 4 Write down the equation of the line, parallel to y = 4x + 1 , which passes through the point (0, −3). Answer [2]

3 © UCLES 2010 0581/11/M/J/10 [Turn over For Examiner's Use 5 North North 107° M P NOT TO SCALE The bearing of P from M is 107°. Work out the bearing of M from P. Answer [2] 6 Martin recorded the outside temperature every three hours. At 07 00 the temperature was − 2°C. (a) This was 5°C higher than the temperature at 04 00. Write down the temperature at 04 00. Answer(a) °C [1] (b) At 10 00 the temperature was 11°C. Write down the increase in temperature between 07 00 and 10 00. Answer(b) °C [1] 7 In a sale, the price of a car was reduced from $ 17 000 to $ 15 300. Calculate the reduction as a percentage of the original price. Answer % [2]

4 © UCLES 2010 0581/11/M/J/10 For Examiner's Use 8 2x – 7 x + 3 x NOT TO SCALE The lengths, in centimetres, of the sides of a triangle are x , x + 3 and 2x − 7. The perimeter of the triangle is 52 cm. (a) Use this information to write down an equation in x. Answer(a) [1] (b) Find the value of x. Answer(b) x = [2] 9 The area of a circle is 19.7 cm2. Calculate the radius of the circle. Answer cm [3] 10 Simplify (a) 3 4 p p × , Answer(a) [1] (b) 8 2 12 3 q q ÷ . Answer(b) [2]

5 © UCLES 2010 0581/11/M/J/10 [Turn over For Examiner's Use 11 160° 160° NOT TO SCALE The diagram shows part of a regular polygon. Each interior angle of the polygon is 160°. Calculate the number of sides of the polygon. Answer [3] 12 Write down the value of (a) 10-2, Answer(a) [1] (b) 40, Answer(b) [1] (c) 3 343 . Answer(c) [1] 13 Solve the simultaneous equations. 2x − y = 9 7x + 2y = 26 Answer x = y = [3]

6 © UCLES 2010 0581/11/M/J/10 For Examiner's Use 14 O C A B S T 54° NOT TO SCALE A, B and C lie on a circle, centre O. BC is a diameter and SCT is a tangent at C. Angle ACB = 54°. Find (a) angle BCT, Answer(a) Angle BCT = [1] (b) angle COA, Answer(b) Angle COA = [1] (c) angle CAB, Answer(c) Angle CAB = [1] (d) angle ABC. Answer(d) Angle ABC = [1] 15 d =       −5 3 e =      − 4 1 f =       7 0 Calculate (a) d – e, Answer(a)         [2] (b) 4f. Answer(b)         [2]

7 © UCLES 2010 0581/11/M/J/10 [Turn over For Examiner's Use 16 Complete the information about each shape. Shape Number of lines of symmetry Order of rotational symmetry [4] 17 3 2 1 0 City Distance (kilometres) Time (minutes) Port 0 15 30 45 60 (a) The travel graph shows the journey of a bus from a port to a city. Calculate the average speed of the bus (i) in kilometres per minute, Answer(a)(i) km/min [1] (ii) in kilometres per hour. Answer(a)(ii) km/h [1] (b) The bus waits in the city for 20 minutes and then returns to the port at an average speed of 12 km/h. Complete the travel graph. [2] Questions 18 and 19 are printed on the next page.

8 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 0581/11/M/J/10 For Examiner's Use 18 (a) Factorise 2 3 7 y xy − . Answer(a) [1] (b) Expand the brackets and simplify completely. ( ) ( ) 4 5 2 6 p p r r p r + + + Answer(b) [3] 19 Erica is tiling the floor of a rectangular room of length 3 metres and width 2.5 metres. She uses square tiles of side 25 centimetres. (a) Calculate (i) how many tiles will fit along the length of the room, Answer(a)(i) [1] (ii) how many tiles she will need altogether. Answer(a)(ii) [2] (b) Work out the area of one tile (i) in square centimetres, Answer(b)(i) cm2 [1] (ii) in square metres. Answer(b)(ii) m2 [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 0581/11 Paper 11 (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 11 © UCLES 2010 Qu. Answers Mark Part Marks 1 10 18 (am) 1 2 (a) 41% 0.43 9 4 1 accept decimals (b) 0.3 < 3 1 only 1 3 5 3 2 W1 for 35 21 M1 1 − 35 14 oe SC1 answer 5 2 4 y = 4x – 3 oe 2 W1 for y = 4x + j, or y = kx − 3 If zero, SC1 for 4x – 3 k ≠ 0 5 287° 2 W1 for 73 or 107 marked in correct position at P or M1 107 + 180 6 (a) –7 (b) 13 1 1 7 10 2 M1 for 17000 ) 15300 17000 ( their − W1 for 100 17000 15300 × or answer 90(%) 8 (a) x + x + 3 + 2x – 7 = 52 or better (b) 14 1 2ft W1 for 4x or 56 seen Follow through their (a) if linear and equal to 52 for 1 or 2 marks. 9 2.5(0) or 2.503…. to 2.504 3 M1 for πr2 = 19.7 soi M1 dep for 19.7 ÷ π 10 (a) p7 (b) 4q6 1 2 W1 for 4qn or kq6 k ≠ 0 11 18 3 M1 for exterior angle 180 − 160 implied by 20 (could be on diagram) M1 dep for 360 ÷ their 20 12 (a) 0.01 or 100 1 1 (b) 1 (c) 7 1 1

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2010 0581 11 © UCLES 2010 13 (x =) 4 (y =) − 1 3 M1 for multiplying and subtracting or adding as appropriate. (allow errors in arithmetic operations) or any other correct methods. A1 for one correct variable 14 (a) 90° (b) 72° (c) 90° (d) 36° 1 1 1 1 Ft 180 − (54 + their (c)) 15 (a)     −9 4 1, 1 (b)     28 0 1, 1 16 lines of symmetry 1 0 order rotational 1 4 1, 1 1, 1 17 (a) (i) 0.3 oe (ii) 18 (b) horizontal line to (30,3) line from (30,3) to (45,0) OR from their (x,3) to (their x + 15, 0) 1 1 1 1ft Follow through their (a)(i) × 60 18 (a) y(3y – 7x) final answer (b) 4p2 + 17pr + 2r2 final answer 1 3 W2 for 2 correct terms in answer. W1 for 1 correct term in answer. OR M1 for 4p2 + 5pr and M1 ind for 12pr + 2r2 19 (a) (i) 12 (ii) 120 ft (b) (i) 625 (ii) 0.0625 1 2 1 1ft M1 for attempt to multiply their (a)(i) by 10 soi. or their (b)(i) ÷ 10 000