Cambridge IGCSE Mathematics (with coursework) 0581 — 2012 May/June Paper 1 · Variant 3

This document consists of 10 printed pages and 2 blank pages. IB12 06_0581_13/FP © UCLES 2012 [Turn over *6852261746* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0581/13 Paper 1 (Core) May/June 2012 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 2012 0581/13/M/J/12 For Examiner's Use 1 Write 5 2 as a percentage. Answer %[1] 2 Change 5.2 square metres into square centimetres. Answer cm2 [1] 3 Mohinder changes $240 into Rupees. The exchange rate is $1 = 46.2875 Rupees. Calculate how many Rupees he receives. Answer Rupees [1] 4 (a) Write down the next prime number after 47. Answer(a) [1] (b) Write down the next square number after 49. Answer(b) [1]

3 © UCLES 2012 0581/13/M/J/12 [Turn over For Examiner's Use 5 I K = Choose one of these symbols to make each statement correct. (a) −15 −5 [1] (b) (−5)2 25 [1] 6 Hans invests $750 for 8 years at a rate of 2% per year simple interest. Calculate the interest Hans receives. Answer $ [2] 7 B C D E A 120° 82° 73° x° NOT TO SCALE The diagram shows a quadrilateral ABCD. CDE is a straight line. Calculate the value of x. Answer x = [2]

4 © UCLES 2012 0581/13/M/J/12 For Examiner's Use 8 Work out (a)       3 5 −       −2 6 , Answer(a)           [1] (b) 5       −4 3 . Answer(b)           [1] 9 Simplify (a) a0 , Answer(a) [1] (b) b3 × b-5 . Answer(b) [1] 10 During her holiday, Hannah rents a bike. She pays a fixed cost of $8 and then a cost of $4.50 per day. Hannah pays with a $50 note and receives $10.50 change. Calculate for how many days Hannah rents the bike. Answer days [3]

5 © UCLES 2012 0581/13/M/J/12 [Turn over For Examiner's Use 11 E D F A C B a° b° 52° NOT TO SCALE In the diagram lines AC and DF are parallel and AE = EB. Angle AEB = 52°. (a) Write down the mathematical name for triangle AEB. Answer(a) [1] (b) Work out the value of a. Answer(b) a = [1] (c) Explain why a = b. Answer(c) [1] 12 Solve the simultaneous equations. 4x + y = 18 5x + 3y = 19 Answer x = y = [3]

6 © UCLES 2012 0581/13/M/J/12 For Examiner's Use 13 (a) Write 0.000 64 in standard form. Answer(a) [1] (b) Calculate, writing the answer in standard form. 4 7 10 5.84 10 8.18 × × Answer(b) [2] 14 7 3 8 2 5 1 5 3 4 6 2 3 For the numbers above work out the (a) mode, Answer(a) [1] (b) median, Answer(b) [2] (c) range. Answer(c) [1]

7 © UCLES 2012 0581/13/M/J/12 [Turn over For Examiner's Use 15 Without using your calculator, work out the following. Show all the steps of your working and give each answer as a fraction in its simplest form. (a) 12 11 − 3 1 Answer(a) [2] (b) 4 1 ÷ 13 11 Answer(b) [2] 16 (a) Solve the equation 5(x − 3) = 21 . Answer(a) x = [2] (b) Make x the subject of the equation y = 3x − 2 . Answer(b) x = [2]

8 © UCLES 2012 0581/13/M/J/12 For Examiner's Use 17 12 cm 12 cm 34 cm 4 cm 18 cm 18 cm NOT TO SCALE For the shape above, work out (a) the perimeter, Answer(a) cm [2] (b) the area. Answer(b) cm2 [2] 18 (a) Find the value of 7p – 3q when p = 8 and q = O5 . Answer(a) [2] (b) Factorise completely. 3uv + 9vw Answer(b) [2]

9 © UCLES 2012 0581/13/M/J/12 [Turn over For Examiner's Use 19 28° North North A B C 74 km 26 km NOT TO SCALE (a) Work out the bearing of A from C. Answer(a) [2] (b) Calculate the distance AB. Answer(b) km [2]

10 © UCLES 2012 0581/13/M/J/12 For Examiner's Use 20 (a) Colin has some seeds. The probability a seed will grow is 0.85 . Find the probability that a seed will not grow. Answer(a) [1] (b) Richard grows flowers. Some of his flowers are chosen at random. The colours are recorded in the table below. Colour of flower Frequency Relative Frequency Red 20 0.16 Blue 15 Yellow 35 Other 55 (i) Complete the table to show the relative frequency of each colour. [2] (ii) Richard grows 800 flowers in total. Estimate how many of these flowers are red. Answer(b)(ii) [2]

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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 0581/13 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 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 13 © 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 40 1 2 52 000 1 3 11 109 1 4 (a) (b) 53 64 1 1 5 (a) (b) < = 1 1 6 120 2 M1 for 100 8 2 750 × × oe seen or SC1 870 as final answer 7 95 2 B1 for 85 seen or M1 x = 180 – ‘their angle ADC’, if it is clearly seen 8 (a) (b)      − 5 1       −20 15 1 1 9 (a) (b) 1 b–2 1 1 accept 21 b 10 7 cao 3 B1 for 39.5(0) or 31.5(0) or 42 M1 for (their 39.5 – 8) ÷ 4.5 or (their 42 – 10.5) ÷ 4.5 11 (a) (b) (c) isosceles 64 alternate (angle) 1 1 1 accept z angle

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2012 0581 13 © University of Cambridge International Examinations 2012 12 [x =] 5, [y =] –2 3 M1 for consistent multiply and add/subtract as appropriate. Allow computational errors. Other methods allowed. A1 for correct x or y. 13 (a) (b) 6.4 × 10–4 1.4 × 103 1 2 M1 for 1400 or answer rounding to 1401 or 1.4 × 10k 14 (a) (b) (c) 3 3.5 7 1 2 1 M1 for at least 7 numbers in order and an attempt to find the middle number 15 (a) (b) 12 4 12 11 − oe 12 7 cao ww 0 11 13 4 1 × oe 44 13 cao ww 0 2 2 M1 correct use of a common denominator A1 M1 inversion and operation change A1 16 (a) (b) 7.2 oe [x =] 3 2 + y 2 2 M1 for 5x – 15 = 21 or x – 3 = 5 21 M1 for 3x = y + 2 or – 3x = –2 – y 17 (a) (b) 112 564 2 2 M1 Attempt to add 6 given and their 2 sides M1 for 18 × 34 – 12 × 4 : (612 – 48) or (18 × 12) + (14 × 12) + (10 × 18) or (4 × 12) + (10 × 4) + (34 × 14) 18 (a) (b) 71 3v (u + 3w) final answer 2 2 M1 for 7×8 – 3×–5 or B1 56 and –15 B1 for 3(uv + 3vw) or v (3u + 9w) As final answer 19 (a) (b) 332 78.4 2 2 M1 for BCA = 28. Or 360 – 28 or 152 marked correctly at C or 180 + 152 M1 for AB2 = 742 + 262 or better 20 (a) (b) [0].15 oe (i) 0.12, 0.28, 0.44 oe (ii) 128 1 2 2 M1 for division of 15, 35 or 55 by their 125 Or B1 for 1 correct M1 for 800 × [0].16