Cambridge IGCSE Mathematics (with coursework) 0581 — 2010 Oct/Nov Paper 2 · Variant 2

This document consists of 12 printed pages. IB10 11_0581_22/FP © UCLES 2010 [Turn over *3296081135* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0581/22 Paper 2 (Extended) October/November 2010 1 hour 30 minutes 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 70. www.XtremePapers.com

2 © UCLES 2010 0581/22/O/N/10 For Examiner's Use 1 For the diagram, write down (a) the order of rotational symmetry, Answer(a) [1] (b) the number of lines of symmetry. Answer(b) [1] 2 In a group of 30 students, 18 have visited Australia, 15 have visited Botswana and 5 have not visited either country. Work out the number of students who have visited Australia but not Botswana. Answer [2] 3 Rearrange the formula J = mv – mu to make m the subject. Answer m = [2]

3 © UCLES 2010 0581/22/O/N/10 [Turn over For Examiner's Use 4 O is the centre of the circle. DA is the tangent to the circle at A and DB is the tangent to the circle at C. AOB is a straight line. Angle COB = 50°. Calculate (a) angle CBO, Answer(a) Angle CBO = [1] (b) angle DOC. Answer(b) Angle DOC = [1] 5 JGR is a right-angled triangle. JR = 50m and JG = 20m. Calculate angle JRG. Answer Angle JRG = [2] 6 Write 0.00658 (a) in standard form, Answer(a) [1] (b) correct to 2 significant figures. Answer(b) [1] J G R 50 m 20 m NOT TO SCALE 50° O A D C B NOT TO SCALE

4 © UCLES 2010 0581/22/O/N/10 For Examiner's Use 7 = a + tb and = a + (3t – 5)b where t is a number. Find the value of t when = . Answer t = [2] 8 Show that 27 7 + 9 7 1 = 27 1 2 . Write down all the steps in your working. Answer [2] 9 When a car wheel turns once, the car travels 120 cm, correct to the nearest centimetre. Calculate the lower and upper bounds for the distance travelled by the car when the wheel turns 20 times. Answer lower bound cm upper bound cm [2]

5 © UCLES 2010 0581/22/O/N/10 [Turn over For Examiner's Use 10 140° 140° 140° A B C D E NOT TO SCALE The pentagon has three angles which are each 140°. The other two interior angles are equal. Calculate the size of one of these angles. Answer [3] 11 The resistance, R, of an object being towed through the water varies directly as the square of the speed, v. R = 50 when v = 10. Find R when v = 16. Answer R = [3] 12 Write as a single fraction, in its simplest form. 1 2 2 3 − − + x x Answer [3]

6 © UCLES 2010 0581/22/O/N/10 For Examiner's Use 13 NOT TO SCALE The diagram shows a circle of radius 5cm in a square of side 18cm. Calculate the shaded area. Answer cm2 [3] 14 Draw, accurately, the locus of all the points outside the triangle which are 3 centimetres away from the triangle. [3]

7 © UCLES 2010 0581/22/O/N/10 [Turn over For Examiner's Use 15 The air fare from Singapore to Stockholm can be paid for in Singapore dollars (S$) or Malaysian Ringitts (RM). One day the fare was S$740 or RM1900 and the exchange rate was S$1= RM2.448 . How much less would it cost to pay in Singapore dollars? Give your answer in Singapore dollars correct to the nearest Singapore dollar. Answer S$ [3] 16 Simplify (a) 2 1 16 81 16       x , Answer(a) [2] (b) 10 4 7 16 4 32 y y y − × . Answer(b) [2] 17 Boys Girls Total Asia 62 28 Europe 35 45 Africa 17 Total 255 For a small international school, the holiday destinations of the 255 students are shown in the table. (a) Complete the table. [3] (b) What is the probability that a student chosen at random is a girl going on holiday to Europe? Answer(b) [1]

8 © UCLES 2010 0581/22/O/N/10 For Examiner's Use 18 2 4 = 5 3         A 3 4 = 5 2 − −         B (a) Work out AB. Answer(a) [2] (b) Find | B |, the determinant of B. Answer(b) [1] (c) I is the (2 × 2) identity matrix. Find the matrix C, where C = A – 7I . Answer(c) [2]

9 © UCLES 2010 0581/22/O/N/10 [Turn over For Examiner's Use 19 M C B P D A 8 cm 10 cm 10 cm NOT TO SCALE The diagram represents a pyramid with a square base of side 10 cm. The diagonals AC and BD meet at M. P is vertically above M and PB = 8cm. (a) Calculate the length of BD. Answer(a) BD = cm [2] (b) Calculate MP, the height of the pyramid. Answer(b) MP = cm [3]

10 © UCLES 2010 0581/22/O/N/10 For Examiner's Use 20 0 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 y x (a) Draw the lines y = 2, x + y = 6 and y = 2x on the grid above. [4] (b) Label the region R which satisfies the three inequalities x + y [ 6, y [ 2 and y Y 2x. [1]

11 © UCLES 2010 0581/22/O/N/10 [Turn over For Examiner's Use 21 An animal starts from rest and accelerates to its top speed in 7 seconds. It continues at this speed for 9 seconds and then slows to a stop in a further 4 seconds. The graph shows this information. 14 12 10 8 6 4 2 0 2 4 6 8 10 12 14 16 18 20 Speed (m / s) Time (seconds) (a) Calculate its acceleration during the first seven seconds. Answer(a) m/s2 [1] (b) Write down its speed 18 seconds after the start. Answer(b) m/s [1] (c) Calculate the total distance that the animal travelled. Answer(c) m [3] Question 22 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 2010 0581/22/O/N/10 For Examiner's Use 22 (a) The line y = 2x + 7 meets the y-axis at A. Write down the co-ordinates of A. Answer(a) A = ( , ) [1] (b) A line parallel to y = 2x + 7 passes through B(0, 3). (i) Find the equation of this line. Answer(b)(i) [2] (ii) C is the point on the line y = 2x + 1 where x = 2. Find the co-ordinates of the midpoint of BC. Answer(b)(ii) ( , ) [3]

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 2010 question paper for the guidance of teachers 0581 MATHEMATICS 0581/22 Paper 2 (Extended), maximum raw mark 70 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. • CIE will not enter into discussions or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the October/November 2010 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 – October/November 2010 0581 22 © UCLES 2010 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 (a) 5 (b) 0 1 1 2 10 2 M1 33 – 25 or 38 – 30 M1 30 – 15 – 5 oe with no further working 3 u v J m − = 2 M1 m(v – u) seen 4 (a) 40 (b) 65 1 1 5 23.6 2 M1 sin R = 20/50 or 90 sin 50 sin 20 = R 6 (a) 6.58 × 10–3 (b) 0.0066 cao 1 1 × and 10 essential Allow 6.6 × 10–3 7 t = 2 2 1 2 M1 (b)t = (b)(3t – 5) 8 Answer given so only working scores marks 2 M1 7/27 + 48/27 or 7/27 + (1)21/27 M1 completely correct finish 9 2390 2410 2 M1 119.5 and 120.5 or B1 for one correct answer 10 60 3 B1 540 used M1 [their 540 – 3 × 140]/2 11 128 3 M1 R = kv2 A1 k = 2 1 12 ) 2 )( 1 ( 7 + − − x x x 3 M1 3(x – 1) – 2(x + 2) seen B1 denominator correct seen A1 all correct

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2010 0581 22 © UCLES 2010 13 245 or 246 3 M1 π × 52 M1 182 – their kπ 14 3 M1 2 lines correct length M1 2 compass arcs correct length A1 complete accurate drawing with all lines and arcs solid 15 36 cao 3 M1 1900/2.448 (= 776.14) A1 “776.(14…)” – 740 (= 36.14…) 16 (a) 9 4 x8 2 B1 9 4 B1 x8 (b) 2y–1 2 B1 2 B1 y–1 17 (a) Boys Girls Total Asia 62 28 90 Europe 35 45 80 Africa 68 17 85 Total 165 90 255 3 B1 two or three correct or B2 four or five correct (b) 17 3 or 0.176(47…) 1 Allow 255 45 , 85 15 , 51 9 18 (a)     − − 14 0 0 14 2 B1 two or three correct answers (b) –14 1 (c)     − − 4 5 4 5 2 B1 two or three terms correct 19 (a) 14.1 (b) 3.74 or 3.78 2 3 M1 (BD2) = 102 + 102 or sin45 = 10/CD M1 (a)/2 M1 (their (a)/2)2 + PM2 = 82 20 (a) R (b) 4 1 B1 y = 2 single line thro B1 (6, 0) and B1 (0,6) B1 y = 2x Correct R cao

Page 4 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2010 0581 22 © UCLES 2010 21 (a) 2 (b) 6.7 to 7.3 (c) 203 1 1 3 M1 intention to find area under the graph M1 2 1 × 7 × 14 + 9 × 14 + 2 1 × 4 × 14 oe 22 (a) (0, 7) (b) (i) y = 2x + 3 1 2 B1 y = 2x + c, c ≠ 7 or B1 y = kx + 3, k ≠ 0 (ii) (1, 4) 3 B1 y = 5 M1       + + 2 " 5 " 3 , 2 2 0 A1 (1, ft4)