Cambridge IGCSE Mathematics (with coursework) 0581 — 2012 May/June Paper 1 · Variant 2

This document consists of 11 printed pages and 1 blank page. IB12 06_0581_12/FP © UCLES 2012 [Turn over *5118361957* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0581/12 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 0581/12/M/J/12 For Examiner's Use 1 Work out the value of 4.6 3.5 19.1 48 × − . Answer [1] 2 Write the following in order of size, starting with the smallest. 0.83 6 5 82% 28 23 Answer < < < [2] 3 The ferry from Helsinki to Travemunde leaves Helsinki at 17 30 on a Tuesday. The journey takes 28 hours 45 minutes. Work out the day and time that the ferry arrives in Travemunde. Answer Day Time [2] 4 T R I G O N O M E T R Y From the above word, write down the letters which have (a) exactly two lines of symmetry, Answer(a) [1] (b) rotational symmetry of order 2. Answer(b) [1]

3 © UCLES 2012 0581/12/M/J/12 [Turn over For Examiner's Use 5 The table shows the average monthly temperatures in Beijing. Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Average temperature (°C) – 4.6 –2.2 4.5 13.1 19.8 24.0 25.8 24.4 19.4 12.4 4.1 –2.7 (a) Work out how many degrees higher the temperature is in December than in January. Answer(a) °C [1] (b) Find the range. Answer(b) °C [1] 6 a =       −3 5 b =      − 7 2 Work out 3a + b. Answer           [2] 7 1 2 1 + 3 1 + 4 1 = 12 p Work out the value of p. Show all your working. Answer p = [2]

4 © UCLES 2012 0581/12/M/J/12 For Examiner's Use 8 A lake has an area of 63 800 000 000 square metres. Write this area in square kilometres, correct to 2 significant figures. Answer km2 [2] 9 (a) Simplify a–3 × a8. Answer(a) [1] (b) Work out the value of 5–2. Answer(b) [1] 10 The number of people, n, who attended a concert was 12 600 to the nearest 100. Complete the statement about n. Answer Y n I= [2] 11 Keiko travels from Tokyo to London for the Olympic Games. On the internet, a flight costs £767. (a) Use the exchange rate £1 = 143 Japanese Yen to find the cost of the flight in Japanese Yen. Answer(a) Yen [1] (b) Write your answer to part (a) in standard form. Answer(b) [1]

5 © UCLES 2012 0581/12/M/J/12 [Turn over For Examiner's Use 12 8 cm 6 cm r NOT TO SCALE The perimeter of the rectangle is the same length as the circumference of the circle. Calculate the radius, r, of the circle. Answer r = cm [3] 13 (a) Factorise xy – y2. Answer(a) [1] (b) Solve 4x − 7 = 12. Answer(b) x = [2]

6 © UCLES 2012 0581/12/M/J/12 For Examiner's Use 14 Scatter diagrams are drawn to compare sets of data from each team in a hockey league during a year. Write down the type of correlation you would expect to see when the data recorded is (a) the number of games won and the total points scored, Answer(a) [1] (b) the number of games drawn and the average height of the team, Answer(b) [1] (c) the number of goals scored and the final position in the league. Answer(c) [1] 15 The diagram shows a quadrilateral drawn on a 1 cm square grid. (a) Write down the mathematical name of the quadrilateral. Answer(a) [1] (b) Find the area of the quadrilateral and give the units. Answer(b) [2]

7 © UCLES 2012 0581/12/M/J/12 [Turn over For Examiner's Use 16 The shirt colour of the teams in a football league are shown in the following table. Colour Frequency Red 8 White 3 Blue 7 Gold 2 The pie chart shows some of this information. The sectors for red shirts and white shirts have been drawn. Red White (a) Calculate the angle of the sector for blue shirts. Answer(a) [2] (b) Complete the pie chart. [1]

8 © UCLES 2012 0581/12/M/J/12 For Examiner's Use 17 Solve the simultaneous equations. 6x + 2y = 22 4x − y = 3 Answer x = y = [3] 18 The taxi fare in a city is $3 and then $0.40 for every kilometre travelled. (a) A taxi fare is $9. How far has the taxi travelled? Answer(a) km [2] (b) Taxi fares cost 30 % more at night. How much does a $9 daytime journey cost at night? Answer(b) $ [2]

9 © UCLES 2012 0581/12/M/J/12 [Turn over For Examiner's Use 19 O E A C B D 58° x° y° NOT TO SCALE AC is a diameter of a circle, centre O. BCD is a tangent to the circle and E is a point on the circumference. Angle ECD = 58°. Work out the value of (a) x, Answer(a) x = [2] (b) y. Answer(b) y = [2]

10 © UCLES 2012 0581/12/M/J/12 For Examiner's Use 20 C B A 34 cm 30 cm 16 cm NOT TO SCALE (a) Write down all your working to show that angle ABC is a right angle. Answer(a) [2] (b) Use trigonometry to calculate angle CAB. Answer(b) Angle CAB = [2]

11 © UCLES 2012 0581/12/M/J/12 For Examiner's Use 21 (a) Show that the sum of the interior angles of a regular pentagon is 540°. Answer(a) [2] (b) x° y° y° 76° B C D E A NOT TO SCALE The diagram shows a pentagon ABCDE. BC is parallel to AE and angle CDE is a right angle. Find the values of x and y. Answer(b) x = y = [3]

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 0581/12/M/J/12 BLANK PAGE

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 0581/12 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 12 © 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 16 1 2 82% < 28 23 < 0.83 < 6 5 2 M1 for correct conversion of both fractions to decimals or percentages. Minimum 3 sf. or B1 for correct but reverse order 3 Wednesday 22 15 or 10 15pm 2 B1 B1 4 (a) (b) I cao I N cao 1 1 5 (a) (b) 1.9 30.4 1 1 6       −2 13 2 B1 for one correct component 7 25 (correct working essential) 2 M1 for 18 + 4 + 3 with denominator 12 must be soi (oe is possible) 8 64 000 or 6.4 × 104 2 SC1 for 63800 or 6.38 × 104 or figs 64 or 6.4 × 10k in answer space. 9 (a) (b) a5 0.04 or 25 1 1 1 10 12 550 ø n < 12 650 2 B1 for one correct or both correct but reversed. 11 (a) (b) 109 681 final answer 1.09681 × 105 1 1ft Their part (a) in standard form 12 4.46 or 4.456 to 4.459 cao 3 B1 for 28 seen M1ft for π 2 28 their oe or better.

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2012 0581 12 © University of Cambridge International Examinations 2012 13 (a) (b) y(x – y) or y(–y + x) [x =] 4.75 oe 1 2 M1 for 4x = 12 + 7 or x – 4 7 = 4 12 or better 14 (a) (b) (c) Positive Zero oe Negative 1 1 1 15 (a) (b) Kite 14 cm2 1 1, 1 Independent marks 16 (a) (b) 126 Line dividing sector into 126° and 36° 2 1ft M1 for 7 ÷ (8 + 3 + 7 + 2) × 360 or for 54 ÷ 3 × 7 or 144 ÷ 8 × 7 Ft their angle for blue sector. 17 [x =] 2 [y =] 5 3 M1 for consistent multiply and add/subtract as appropriate. Allow computational errors. Other methods allowed. A1 for correct x or y. 18 (a) (b) 15 11.7(0) 2 2 M1 for 4.0 3 9 − oe M1 for 9 × 1.3 oe 19 (a) (b) [x =] 32 [y =] 58 2 2ft M1 for angle OCD = 90° soi (or angle OCB = 90°) M1 for angle AEC = 90° soi Follow through 90 – their (a) 20 (a) Pythagoras method 302 + 162 [ = 342] or 900 + 256 [ = 1156] 342 = 1156 or 1156 = 34 M1 E1dep Trig method Tan A = 16 30 and Sin C = 34 16 oe Angles 61.9 and 28.1 and statement to show that angle B = 90° M1 E1dep The two trig ratios used must involve all 3 sides of the triangle. (b) 61.9 or 61.92 to 61.93 2 M1 for tan [CAB =] 16 30 or sin [CAB =] 34 30 or cos [CAB =] 34 16 (or better)

Page 4 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2012 0581 12 © University of Cambridge International Examinations 2012 21 (a) Exterior angle method [Ext angle =] 360 ÷ 5 5 × (180 − 72) = 540 M1 E1dep Formula method (n – 2) × 180 or ( ) n n 180 2 × − (5 – 2) × 180 = 540 or ( ) 5 180 2 5 × − = 108 and 5 × 108 = 540 M1 E1dep Triangle methods Explanation or sketch to split pentagon into 3 or 5 triangles. 3 × 180 = 540 or 5 × 180 – 360 = 540 M1 E1dep (b) [x =] 104 [y =] 135 3ft B1 [x =] 104 M1 for 540 − (90 + 76 + their x)