Cambridge IGCSE Mathematics (with coursework) 0581 — 2011 May/June Paper 1 · Variant 1

This document consists of 10 printed pages and 2 blank pages. IB11 06_0581_11/FP © UCLES 2011 [Turn over *9403466071* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0581/11 Paper 1 (Core) May/June 2011 1 hour 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 56. www.XtremePapers.com

2 © UCLES 2011 0581/11/M/J/11 For Examiner's Use 1 A concert hall has 1540 seats. Calculate the number of people in the hall when 55% of the seats are occupied. Answer [1] 2 (a) Write down in figures the number twenty thousand three hundred and seventy six. Answer(a) [1] (b) Write your answer to part (a) correct to the nearest hundred. Answer(b) [1] 3 For an equilateral triangle, write down (a) the number of lines of symmetry, Answer(a) [1] (b) the order of rotational symmetry. Answer(b) [1] 4 A B Write down the geometrical name for (a) shape A, Answer(a) [1] (b) shape B. Answer(b) [1]

3 © UCLES 2011 0581/11/M/J/11 [Turn over For Examiner's Use 5 Mark and Naomi share $600 in the ratio Mark : Naomi = 5 : 1. Calculate how much money Naomi receives. Answer $ [2] 6 Calculate the area of a circle with radius 6.28 centimetres. Answer cm2 [2] 7 The scale on a map is 1 : 20 000. Calculate the actual distance between two points which are 2.7 cm apart on the map. Give your answer in kilometres. Answer km [2] 8 (a) Find m when 4m × 42 = 412. Answer(a) m = [1] (b) Find p when 6 p ÷ 67 = 62. Answer(b) p = [1]

4 © UCLES 2011 0581/11/M/J/11 For Examiner's Use 9 A B C D 2x° 5x° x° NOT TO SCALE AB is parallel to CD. Calculate the value of x. Answer x = [3] 10 Solve the simultaneous equations. 3x + y = 30 2x – 3y = 53 Answer x = y = [3] 11 Without using your calculator, and leaving your answer as a fraction, work out 2 6 1 – 12 7 . You must show all your working. Answer [3]

5 © UCLES 2011 0581/11/M/J/11 [Turn over For Examiner's Use 12 (a) Write 1738.279 correct to 1 decimal place. Answer(a) [1] (b) Write 28 700 in standard form. Answer(b) [1] (c) The mass of a ten-pin bowling ball is 7 kg to the nearest kilogram. Write down the lower bound of the mass of the ball. Answer(c) kg [1] 13 Paulo invests $3000 at a rate of 4% per year compound interest. Calculate the total amount Paulo has after 2 years. Give your answer correct to the nearest dollar. Answer $ [3] 14 A train leaves Barcelona at 21 28 and takes 10 hours and 33 minutes to reach Paris. (a) Calculate the time the next day when the train arrives in Paris. Answer(a) [1] (b) The distance from Barcelona to Paris is 827 km. Calculate the average speed of the train in kilometres per hour. Answer(b) km/h [3]

6 © UCLES 2011 0581/11/M/J/11 For Examiner's Use 15 (a) The table shows part of a railway timetable. arrival time 12 58 13 56 14 54 15 52 Peartree Station departure time 13 07 14 05 15 03 16 01 (i) Each train waits the same number of minutes at Peartree Station. Write down how many minutes each train waits. Answer(a)(i) min [1] (ii) Janine is at Peartree Station at 3 pm. At what time does the next train depart? Answer(a)(ii) [1] (b) The average temperature each month in Moscow and Helsinki is recorded. The table shows this information from January to June. January February March April May June Temperature in Moscow (°C) −16 −14 −8 1 8 11 Temperature in Helsinki (°C) −9 −10 −7 −1 4 10 (i) Find the difference in temperature between Moscow and Helsinki in January. Answer(b)(i) °C [1] (ii) Find the increase in temperature in Helsinki from March to June. Answer(b)(ii) °C [1]

7 © UCLES 2011 0581/11/M/J/11 [Turn over For Examiner's Use 16 96° 60° 120° Blue Red Yellow Green NOT TO SCALE In a survey a number of people chose their favourite colour. The results are shown in the pie chart. (a) Calculate the size of the sector angle for green. Answer(a) [1] (b) The number of people who chose red is 16. Calculate the number who chose yellow. Answer(b) [1] (c) Calculate the total number of people in the survey. Answer(c) [1] (d) Write down the fraction who chose red. Answer(d) [1]

8 © UCLES 2011 0581/11/M/J/11 For Examiner's Use 17 y x 4 3 2 1 –1 –2 –3 –3 –2 –1 1 0 2 3 4 5 6 7 B A (a) Write down the vector . Answer(a)           [1] (b) =      − 1 3 Mark the point C on the grid. [1] (c) Work out (i)      − 1 3 +       −4 7 , Answer(c)(i)           [1] (ii) 4 ×      − 1 3 . Answer(c)(ii)           [1]

9 © UCLES 2011 0581/11/M/J/11 [Turn over For Examiner's Use 18 C A B O T 24° NOT TO SCALE A, B and C are points on a circle, centre O. TA is a tangent to the circle at A and OBT is a straight line. AC is a diameter and angle OTA = 24°. Calculate (a) angle AOT, Answer(a) Angle AOT = [2] (b) angle BOC, Answer(b) Angle BOC = [1] (c) angle OCB. Answer(c) Angle OCB = [1]

10 © UCLES 2011 0581/11/M/J/11 For Examiner's Use 19 Piet, Rob and Sam collect model aeroplanes. Piet has x aeroplanes. Rob has 7 more aeroplanes than Piet. Sam has three times as many aeroplanes as Piet. (a) Write down an expression, in terms of x, for (i) the number of aeroplanes Rob has, Answer(a)(i) [1] (ii) the number of aeroplanes Sam has. Answer(a)(ii) [1] (b) The total number of aeroplanes is 32. (i) Use the information in part (a) to write down an equation in x. Answer(b)(i) [1] (ii) Solve your equation. Answer(b)(ii) x = [2] (c) Write down the number of aeroplanes Rob has. Answer(c) [1]

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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2011 question paper for the guidance of teachers 0581 MATHEMATICS 0581/11 Paper 1 (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. • Cambridge will not enter into discussions or correspondence in connection with these mark schemes. Cambridge is publishing the mark schemes for the May/June 2011 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 2011 0581 11 © University of Cambridge International Examinations 2011 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 Qu. Answers Mark Part Marks 1 847 1 2 (a) 20 376 (b) 20 400 1 1ft Their (a) to nearest 100 3 (a) 3 (b) 3 1cao 1 4 (a) Trapezium (b) Parallelogram 1 1 Do not allow Trapezoid 5 100 2 M1 for 1 5 600 + (×1) If zero, SC1 for answer of 500 6 124 or 123.8 or 123.83 to 123.92 2 M1 for π × 6.28 2 7 0.54 2 M1 for 100000 20000 7.2 × oe or SC1 for figs 54 in answer 8 (a) 10 (b) 9 1 1 9 22.5 oe 3 B2 for 180 = 5x + 2x + x oe or better B1 for 2x or 6x marked in the correct place on the diagram 10 x = 13 y = −9 3 M1 for consistent multiplication and addition/subtraction. A1 for x = 13 or A1 for y = –9 11 12 26 – 12 7 or 2 – 12 5 oe 112 7 or 12 19 oe M2 A1 M1 for 6 13 − 12 7 or 212 2 − 12 7 or 6 1 − 12 7 oe 12 (a) 1738.3 (b) 2.87 × 10 4 (c) 6.5 1 1 1

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2011 0581 11 © University of Cambridge International Examinations 2011 13 3245 3 M1 for 3000 × 1.04 2 A1 for 3244.8 If zero, SC2 for answer of 245 If zero, SC1 for their answer corrected to nearest dollar 14 (a) (0)8(.)01(am) (b) 78.4 or 78.38 to 78.39 1 3 Not 8.01 pm M2 for 827 ÷ 10.55 or M1 for figs 827 ÷ their time 15 (a) (i) 9 (ii) 15 03, 3.03pm (b) (i) 7 or −7 (ii) 17 1 1 1 1 16 (a) 84° (b) 10 (c) 60 (d) 360 96 or 60 16 1 1 1ft 1ft Check diagram ft their (b) × 6 where (b) is an integer ft their 16 (c) oe where (c) is an integer 17 (a)       2 6 (b) C marked at (1, 2) (c)       −3 4 (d)      − 4 12 1 1 1 1 18 (a) 66° (b) 114° (c) 33° 2 1ft 1ft M1 for 90° clearly identified as A 180 − their (a) 2 their 180 (b) − or 2 their (a) 19 (a) (i) x + 7 (ii) 3x (b) (i) x+their (a)(i)+their (a)(ii)=32 or better (ii) (x =) 5 (c) 12 1 1 1ft 2ft 1ft ft dependent on 2 algebraic expressions in (a) M1 for 5x = 32 − 7 oe ft their (b)(i) with M1 for ax = b and A1 if answer is an integer. ft their (b)(ii) substituted into their (a)(i) or their (b)(ii) + 7 evaluated correctly