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

This document consists of 12 printed pages. IB12 06_0581_11/FP © UCLES 2012 [Turn over *5283208917* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0581/11 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 0581/11/M/J/12 For Examiner's Use 1 Kyle scores 84 marks out of 96 in an examination. Work out his percentage mark. Answer % [1] 2 The lengths of each side of this triangle are the same. (a) Write down the mathematical name for this triangle. Answer(a) [1] (b) Write down the number of lines of symmetry for the triangle. Answer(b) [1] 3 Work out the number of minutes from 18 27 on Tuesday to 03 19 on Wednesday. Answer min [2]

3 © UCLES 2012 0581/11/M/J/12 [Turn over For Examiner's Use 4 Gregor changes $700 into euros (€) when the rate is €1 = $1.4131 . Calculate the amount he receives. Answer € [2] 5 w = 3a – 5b Calculate w when a = 2 and b = –3. Answer w = [2] 6 One bracelet costs 85 cents and one necklace costs $7.50 . Write down an expression, in dollars, for the total cost of b bracelets and n necklaces. Answer $ [2]

4 © UCLES 2012 0581/11/M/J/12 For Examiner's Use 7 (a) A quadrilateral has four sides of equal length and two pairs of equal angles. Write down the mathematical name for this quadrilateral. Answer(a) [1] (b) 74° 92° 63° NOT TO SCALE Three of the angles in a quadrilateral are 63°, 74° and 92°. Work out the size of the fourth angle. Answer(b) [1] 8 Solve the equation 4x – 2 = 7 . Answer x = [2] 9 The temperature at the top of a mountain is –12°C. The temperature at the bottom of the mountain is 18°C. (a) Work out the difference in these temperatures. Answer(a) °C [1] (b) 18°C is given correct to the nearest degree. Write down the upper bound for this temperature. Answer(b) °C [1]

5 © UCLES 2012 0581/11/M/J/12 [Turn over For Examiner's Use 10 x cm 29 cm 53.2° NOT TO SCALE Calculate the value of x. Answer x = [2] 11 (a) Write down all the factors of 15. Answer(a) [1] (b) Factorise completely. 15p2 + 24pt Answer(b) [2] 12 Triangle ABC has sides AB = 40 m, BC = 25 m and AC = 35 m. Using a scale of 1 cm to represent 5 m, construct triangle ABC. The construction must be completed using a ruler and compasses only. All construction arcs must be clearly shown. Answer A B [3]

6 © UCLES 2012 0581/11/M/J/12 For Examiner's Use 13 Shania invests $750 at a rate of 2 2 1 % per year simple interest. Calculate the total amount Shania has after 5 years. Answer $ [3] 14 Without using your calculator, work out 1 6 5 + 10 9 . You must show your working and give your answer as a mixed number in its simplest form. Answer [3]

7 © UCLES 2012 0581/11/M/J/12 [Turn over For Examiner's Use 15 (a) Find the value of x. x° 51° NOT TO SCALE Answer(a) x = [1] (b) EF is a diameter of the circle. Find the value of y. y° 63° E F NOT TO SCALE Answer(b) y = [1] (c) Find the value of z in this isosceles triangle. z° 48° NOT TO SCALE Answer(c) z = [1]

8 © UCLES 2012 0581/11/M/J/12 For Examiner's Use 16 Solve the simultaneous equations. 3x + 5y = 24 x + 7y = 56 Answer x = y = [3]

9 © UCLES 2012 0581/11/M/J/12 [Turn over For Examiner's Use 17 y x 7 6 5 4 3 2 1 –1 –2 –3 –4 –5 –4 –3 –2 –1 0 1 2 3 4 5 A B (a) Write down the co-ordinates of point A. Answer(a) ( , ) [1] (b) Write as a column vector. Answer(b) =           [1] (c) =       3 2 Write down the co-ordinates of C. Answer(c) ( , ) [1]

10 © UCLES 2012 0581/11/M/J/12 For Examiner's Use 18 (a) Write 326.413 correct to 2 significant figures. Answer(a) [1] (b) Find the square root of one million. Answer(b) [2] (c) Calculate 3.65 5.2 7.465 64.3 − + . Answer(c) [1] 19 (a) Simplify 4p + 3q + 5p –7q. Answer(a) [2] (b) Make x the subject of this formula. g = 2x + y Answer(b) x = [2]

11 © UCLES 2012 0581/11/M/J/12 [Turn over For Examiner's Use 20 A B (a) Using a straight edge and compasses only, construct the perpendicular bisector of AB. Show all your construction arcs. [2] (b) Draw the locus of points that are 4 cm from A. [1] (c) Shade the region which is less than 4 cm from A and nearer to B than to A. [1] Question 21 is printed on the next page.

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. © UCLES 2012 0581/11/M/J/12 For Examiner's Use 21 13 17 13 17 19 13 31 21 29 (a) For the numbers above, find (i) the range, Answer(a)(i) [1] (ii) the median. Answer(a)(ii) [2] (b) Write down the only number in the list which is not a prime number. Answer(b) [1]

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 0581/11 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 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 11 © 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 87.5 1 2 (a) (b) Equilateral 3 1 1 3 532 2 M1 for 5(h)33(min) + 3(h)19(min) 4 495.36 2 M1 for 700 ÷ 1.4131 5 21 2 M1 for 2 × 3 – 5 × (–3) or better or B1 for 6 and –15 i.e. both terms evaluated 6 0.85b + 7.5n OR 100 750 85 n n + final answer 2 B1 for 0.85b OR 7.5n seen 7 (a) (b) Rhombus 131° 1 1 8 2.25 oe 2 M1 4x = 7 + 2 OR x – 4 2 = 4 7 or better 9 (a) (b) 30 18.5 1 1 10 23.2 2 M1 for sin 53.2 = 29 x implicit form or better 11 (a) (b) 1, 3, 5, 15 3p(5p + 8t) final answer 1 2 B1 for answer of 3(5p2 + 8pt) or p(15p + 24t) or SC1 for correct answer seen in working

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2012 0581 11 © University of Cambridge International Examinations 2012 12 Triangle drawn correctly with ruler and arcs 3 M1 for one side drawn to correct length and M1 for clear method of crossing arcs even if wrong scale or inaccurate 13 843.75 3 M2 for 750 100 5.2 5 750 + × × oe or M1 for 100 5.2 5 750 × × oe or SC2 for answer 93.75 14 30 27 30 55 + oe or 30 27 30 25 )1( + oe 30 82 oe or 30 52 )1( oe 15 11 2 M2 must be scored M1 M1 A1 for denominator of 30k for denominator of 30k dependent on previous M1 If M0 scored then SC1 for common denominator of 30k seen 15 (a) (b) (c) 51° 90° 66° 1 1 1 16 x = −7 y = 9 3 M1 for consistent multiplication and addition/ subtraction as appropriate. Allow computational errors A1 for x= –7 or y = 9 17 (a) (b) (c) (–1, 2)       −5 4 (1, 5) 1 1 1 18 (a) (b) (c) 330 1000 or 1 × 103 46.3 1 2 1 B1 for 1000000 or 1 × 106 or 106 seen

Page 4 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2012 0581 11 © University of Cambridge International Examinations 2012 19 (a) (b) 9p – 4q final answer 2 y g x − = oe 2 2 SC1 for answer of 9p ± jq OR ± kp – 4q j, k are integers or for continued work after correct answer M1 for correct first step i.e. either x y g 2 = − oe OR 2 2 y x g + = or SC1 for answer 2 g y x − = 20 (a) (b) (c) Perpendicular bisector drawn with 2 pairs of arcs and ruled Circle drawn radius 4cm Correct region shaded 2 1 1 SC1 for a ruled perpendicular without arcs or only one pair or 2 pairs of correct arcs with no line drawn Dependent on SC1 in (a) and an arc, radius 4cm in (b) to enclose correct area 21 (a) (i) (ii) (b) 18 17 21 1 2 1 M1 for clear attempt to find the middle number