Cambridge IGCSE Mathematics (with coursework) 0581 — 2006 May/June Paper 1 · Variant 1

This document consists of 8 printed pages. IB06 06_0580_01/3RP  UCLES 2006 [Turn over UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS Paper 1 (Core) 0580/01 0581/01 Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments May/June 2006 Mathematical tables (optional) Tracing paper (optional) 1hour 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 THE BARCODE. DO NOT WRITE IN THE GREY AREAS BETWEEN THE PAGES. Answer all questions. If working is needed for any question it must be shown below that question. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 56. 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. Candidate Name Centre Number Candidate Number *051001* For Examiner's Use www.XtremePapers.com

2 © UCLES 2006 0580/01 0581/01 For Examiner's Use 1 The temperature at noon at an Antarctic weather centre was –15 °C. At midnight it had fallen by 12 °C. What was the temperature at midnight? Answer oC [1] 2 0.09 90% 1000 9 9% 0.9 100 9 900% Write down the three numbers from the list above which have the same value. Answer [1] 3 Write down the number of square centimetres in one square metre. Answer [1] 4 (a) Write down a number, other than 1, which is a factor of both 14 and 35. Answer(a) [1] (b) Write down a number which is a multiple of both 14 and 35. Answer(b) [1] 5 l m l m l m NOT TO SCALE A cube of side l metres has a volume of 20 cubic metres. Calculate the value of l. Answer l = [2]

3 © UCLES 2006 0580/01 0581/01 [Turn over For Examiner's Use 6 (a) Work out 7.52 8 0.063 12.48 + × . Write down all the figures on your calculator display. Answer(a) [1] (b) Write your answer to part (a) correct to 2 significant figures. Answer(b) [1] 7 The population of a city is 350 000 correct to the nearest ten thousand. Complete the statement about the limits of the population. population < Answer [2] 8 Factorise completely 2x2 – 6xy. Answer [2] 9 (a) A bowl of fruit contains 3 apples, 4 bananas, 2 pears and 1 orange. Aminata chooses one piece of fruit at random. What is the probability that she chooses (i) a banana, Answer(a)(i) [1] (ii) a mango? Answer(a)(ii) [1] (b) The probability that it will rain in Switzerland on 1st September is 12 5 . State the probability that it will not rain in Switzerland on 1st September. Answer(b) [1] 10 Simplify (a) p2 × p3, Answer(a) [1] (b) q3 ÷ q−4, Answer(b) [1] (c) (r2)3. Answer(c) [1]

4 © UCLES 2006 0580/01 0581/01 For Examiner's Use 11 Rodriguez puts $500 into a bank account. The bank pays 5% compound interest per year. (a) How much is the interest after one year? Answer(a) $ [1] (b) Work out the total amount he has in his bank account after two years. Answer(b) $ [2] 12 (a) Draw all the lines of symmetry on the following shapes. (Shape B is a regular polygon.) Shape A Shape B [2] (b) Write down the order of rotational symmetry of shape A. Answer(b) [1] 13 Solve the simultaneous equations 3x − y = 18, 2x + y = 7. Answer x = y = [3] 14 (a) Pierre arrives at school at 08 40 and leaves at 15 30. How long, in hours and minutes, is he in school? h Answer(a) min [1] (b) Each day, Pierre gets up at 07 00 and goes to bed at 22 00. What percentage of each day is he in bed? Answer(b) % [2]

5 © UCLES 2006 0580/01 0581/01 [Turn over For Examiner's Use 15 =      − 4 1 and = 3 . (a) Write as a column vector. Answer(a) =       [1] (b) Make two statements about the relationship between the lines AB and CD. Statement 1 Statement 2 [2] 16 Yousef asked 24 students to choose their favourite sport. He recorded the information in the table below so that he could draw a pie chart. (a) Complete the table. Sport Volleyball Football Hockey Cricket Number of students 6 9 7 2 Angle on pie chart 90o 135o [2] (b) Complete the pie chart accurately to show this data. Volleyball Football [1] (c) Which is the modal sport? Answer(c) [1]

6 © UCLES 2006 0580/01 0581/01 For Examiner's Use 17 NOT TO SCALE 90 m (a) The diagram shows the plan for a new soccer field. The length of the pitch is 90 metres. The ratio length : width is 5 : 3. Calculate the width of the pitch. Answer(a) m [2] (b) The centre circle has a circumference of 57.5 metres. Calculate the radius. Answer(b) m [2]

7 © UCLES 2006 0580/01 0581/01 [Turn over For Examiner's Use 18 3 cm 2 cm 4 cm NOT TO SCALE The solid shown is a cuboid with length 4 cm, width 2 cm and height 3 cm. (a) Draw an accurate net of the cuboid on the grid below. [2] (b) Using your net, calculate the total surface area of the cuboid. Answer(b) cm2 [2]

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 University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. 0580/01 0581/01 For Examiner's Use 19 Joseph, Maria and Rebecca each win a prize. Their total prize money is $30. Joseph wins 12 7 of the $30. Maria wins 30% of the $30. Rebecca wins the rest of the $30. Calculate the amount each receives. Answer Joseph $ [2] Maria $ [2] Rebecca $ [1] 20 There are 565 sheets of paper in a book. (a) How many sheets of paper are there in 2000 of these books? Give your answer in standard form. Answer(a) [2] (b) A pile of 565 sheets of paper is 25 millimetres high. Calculate the thickness of 1 sheet of paper. Give your answer in standard form. Answer(b) mm [3]

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2006 question paper 0580 and 0581 MATHEMATICS 0580/01 and 0581/01 Paper 1, maximum raw mark 56 These mark schemes are published as an aid to teachers and students, to indicate the requirements of the examination. They show the basis on which Examiners were initially instructed to award marks. They do not indicate the details of the discussions that took place at an Examiners’ meeting before marking began. Any substantial changes to the mark scheme that arose from these discussions will be recorded in the published Report on the Examination. All Examiners are instructed that alternative correct answers and unexpected approaches in candidates’ scripts must be given marks that fairly reflect the relevant knowledge and skills demonstrated. Mark schemes must be read in conjunction with the question papers and the Report on the Examination. The minimum marks in these components needed for various grades were previously published with these mark schemes, but are now instead included in the Report on the Examination for this session. • CIE will not enter into discussion or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the May/June 2006 question papers for most IGCSE and GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses. www.XtremePapers.com

Page 1 Mark Scheme Syllabus Paper IGCSE – May/June 2006 0580 and 0581 01 © University of Cambridge International Examinations 2006 1 –27 1 2 0.09 9% 100 9 1 3 10000 or 1 x 104 oe. 1 4 (a) 7 1 (b) Any multiple of 70 (e.g. 490) 1 5 2.71(4….) 2 M1 for attempt at cube root of 20 6 (a) 0.075976(….) 1 (b) 0.076 1 f.t. f.t. candidates (a) 7 345000 355000 1, 1 8 2x(x – 3y) 2 M1 for 2(x2 – 3xy) or x(2x – 6y) or 2x(……) 9 (a) (i) 10 4 oe. 1 (ii) 0 1 (b) 12 7 o.e. 1 10 (a) p5 1 (b) q7 1 (c) r6 1 19

Page 2 Mark Scheme Syllabus Paper IGCSE – May/June 2006 0580 and 0581 01 © University of Cambridge International Examinations 2006 11 (a) ($) 25 1 (b) ($) 551.25 2 M1 for 500 x 1.052 or (c’s (a) + 500) x 1.05 12 (a) A-2 correct lines and B-6 correct lines 1, 1 Allow not ruled and small inaccuracies. (b) 2 1 13 (x=) 5, (y=)–3 3 M1 correct method to eliminate y or x. (add equations or correct multiply and subtract) A1, A1 ww allow SC1 for 1 correct answer. ww both correct, full marks. 14 (a) 6 (h) 50 (min) 1 (b) 37.5 (%) 2 B1 for 9 (hours) seen or M1 for c’s 9 ÷ 24 x 100 15 (a)      − 12 3 1 (b) Parallel oe. 1 CD is 3 times as long as AB oe. 1 16 (a) (hockey) 105, (cricket) 30 2 1 mark each correct entry. (b) Correct line on pie chart to divide hockey and cricket. (30 ± 2) degrees to left of vertical oe. 1ft ft only if the angles in (a) total 135° (c) Football 1 19

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2006 0580 and 0581 01 © University of Cambridge International Examinations 2006 17 (a) 54 2 M1 for 90 ÷ 5 x 3 (b) 9.15(….) 2 M1 for 57.5 ÷ (2π) or SC1 for 57.5 ÷ π. (implied by 18.3…) 18 (a) Net of the cuboid 2 M1 for a net with 6 correct size rectangles. A1 for a fully correct net. (b) 52 2ft M1 for 5 or 6 areas calculated and added or SC1 for answer of 26. ft only if 5 or 6 rectangles are shown in part (a). 8 19 (Joseph $) 17.5(0) 2 M1 for 30 ÷ 12 x 7. (Maria $) 9 2 M1 for 30 ÷ 100 x 30. (Rebecca $) 3.50 1ft 30 – c’s Joseph – c’s Maria. 20 (a) 1.13 x 106 2 M1 for 2000 x 565 seen or B1 for figs 113 (b) 4.42(….) x 10–2 3 M1 for 25 ÷ 565 soi and B1 for figs 442(….) 10 Total 56