Cambridge IGCSE Mathematics (with coursework) 0581 — 2010 Oct/Nov Paper 2 · Variant 1

This document consists of 12 printed pages. IB10 11_0581_21/FP © UCLES 2010 [Turn over *5063398122* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0581/21 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 0581/21/O/N/10 For Examiner's Use 1 Write each number correct to 1 significant figure and estimate the value of the calculation. You must show your working. 2.65 × 4.1758 + 7.917 Answer [2] 2 Use a calculator to work out the exact value of 1 + 5 1 + 2 5 1       + 3 5 1       + 4 5 1       . Answer [2] 3 Expand the brackets and simplify. 2 1 (6x – 2) – 3(x – 1) Answer [2] 4 Write the following in order of size, smallest first. 0.9 3 0.9 0.92 0.93 Answer I I I [2]

3 © UCLES 2010 0581/21/O/N/10 [Turn over For Examiner's Use 5 (a) This cuboid has a square cross-section. Write down the number of planes of symmetry. Answer(a) [1] (b) axis This cuboid has a rectangular cross-section. The axis shown passes through the centre of two opposite faces. Write down the order of rotational symmetry of the cuboid about this axis. Answer(b) [1]

4 © UCLES 2010 0581/21/O/N/10 For Examiner's Use 6 Work out 6 2 10 5 240 × . Give your answer in standard form. Answer [2] 7 Write as a single fraction in its simplest form. 2 1 2 1 2 + + x x Answer [2] 8 The length of a side of a regular hexagon is 6.8 cm, correct to one decimal place. Find the smallest possible perimeter of the hexagon. Answer cm [2]

5 © UCLES 2010 0581/21/O/N/10 [Turn over For Examiner's Use 9 Johan invested $600 for 3 years at 4% per year compound interest. Calculate the final amount he had after three years. Answer $ [3] 10 Solve the simultaneous equations 2x + y = 5 and 2y = x – 10. Answer x = y = [3]

6 © UCLES 2010 0581/21/O/N/10 For Examiner's Use 11 ABCD is a rectangle with AB = 10 cm and BC = 6 cm. MN is the perpendicular bisector of BC. AP is the bisector of angle BAD. O is the midpoint of AB and also the centre of the semicircle, radius 5 cm. D A C P B M N O Write the letter R in the region which satisfies all three of the following conditions. • nearer to AB than to AD • nearer to C than to B • less than 5 cm from O [3] 12 Make x the subject of 5 3) ( 2 + = x y . Answer x = [3]

7 © UCLES 2010 0581/21/O/N/10 [Turn over For Examiner's Use 13 Solve the inequality. 2x + 5 I 4 1 − x Answer [3] 14 Find the value of n in the following equations. (a) 2n = 1024 Answer(a) n = [1] (b) 42n – 3 = 16 Answer(b) n = [2] 15 NOT TO SCALE 8 cm 6 cm 6 cm A semicircle of diameter 6 cm is cut from a rectangle with sides 6 cm and 8 cm. Calculate the perimeter of the shaded shape, correct to 1 decimal place. Answer cm [3]

8 © UCLES 2010 0581/21/O/N/10 For Examiner's Use 16 Simplify this fraction. 4 6 5 2 2 − + − x x x Answer [4] 17 A =       −2 2 2 2 Work out (a) A2, Answer(a)             [2] (b) A–1, the inverse of A. Answer(b)             [2]

9 © UCLES 2010 0581/21/O/N/10 [Turn over For Examiner's Use 18 0 5 10 15 20 25 30 35 60 50 40 30 20 10 Speed (m / s) Time (seconds) t The graph shows the speed of a sports car after t seconds. It starts from rest and accelerates to its maximum speed in 12 seconds. (a) (i) Draw a tangent to the graph at t = 7. [1] (ii) Find the acceleration of the car at t = 7. Answer(a)(ii) m/s2 [2] (b) The car travels at its maximum speed for 13 seconds. Find the distance travelled by the car at its maximum speed. Answer(b) m [2]

10 © UCLES 2010 0581/21/O/N/10 For Examiner's Use 19 Reina went on holiday to New Zealand. (a) She travelled the 65 km from Tokyo to Narita Airport by taxi. The taxi journey cost 300 yen (¥) per kilometre plus a fixed charge of ¥ 700. Calculate the cost of the taxi journey. Answer(a) ¥ [2] (b) At Narita Airport, Reina changed ¥ 71 190 into New Zealand dollars (NZ$). The exchange rate was NZ$1 = ¥ 56.5. How many New Zealand dollars did she receive? Answer(b) NZ$ [2] 20 Solve the equation. x2 – 8x + 6 = 0 Show all your working and give your answers correct to 2 decimal places. Answer x = or x = [4]

11 © UCLES 2010 0581/21/O/N/10 [Turn over For Examiner's Use 21 8 7 6 5 4 3 2 1 0 –1 –2 –3 –4 1 2 3 4 5 6 7 y x A B (a) Using a straight edge and compasses only, construct the perpendicular bisector of AB on the diagram above. [2] (b) Write down the co-ordinates of the midpoint of the line segment joining A(1, 8) to B(7, –4). Answer(b) ( , ) [1] (c) Find the equation of the line AB. Answer(c) [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 0581/21/O/N/10 For Examiner's Use 22 In a survey of 60 cars, 25 use diesel, 20 use liquid hydrogen and 22 use electricity. No cars use all three fuels and 14 cars use both diesel and electricity. There are 8 cars which use diesel only, 15 cars which use liquid hydrogen only and 6 cars which use electricity only. In the Venn diagram below = {cars in the survey}, D = {cars which use diesel}, L = {cars which use liquid hydrogen}, E = {cars which use electricity}. 8 6 15 … … … … … D E L (a) Use the information above to fill in the five missing numbers in the Venn diagram. [4] (b) Find the number of cars which use diesel but not electricity. Answer(b) [1] (c) Find n(D'∩ (E ∪ L)). Answer(c) [1]

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 0581/21 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 21 © 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 20 (but 3, 4 and 8 must be seen www) 2 M1 3, 4 and 8 seen www 2 1.2496 cao 2 Allow 1 625 156 M1 1 + 0.2 + 0.04 + 0.008 + 0.0016 3 2 2 M1 3x – 1 – 3x + 3 4 0.93 0.92 9.0 3 9.0 2 M1 0.94(8683…) 0.96(5489….) 0.8(1) 0.7(29) 5 (a) 5 (b) 2 1 1 6 1.15(2) × 10–2 2 M1 figs 115(2) 7 x x 2 5 + 2 M1 4 + 1 + x seen or M1 x x 4 2 10 + oe 8 40.5 2 M1 6.75 seen or 6 × their LB 9 $674.92, 674.9(0) or 675 3 M2 600 × (1 + (4/100))3 or better oe or M1 600 × 1.042 oe 10 x = 4 y = –3 3 M1 consistent mult and sub/add A1 one correct value but M must be scored 11 D P C 1 2 3 A O B 0 2 2 1 1 3 Marks allocated for R in one of the regions shown 12 x = +/- √(5y) – 3 or x = +/- y 5 – 3 3 M1 correct move of the 5 completed M1 correct move of the square completed M1 correct move of the 3 completed

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2010 0581 21 © UCLES 2010 13 x < –3 3 M1 correct move M1 correct move M1 correct move 14 (a) 10(.0) 1 (b) 2 2 1 , 2.5(0) 2 M1 2n – 3 = 2 15 31.4 cao 3 M1 2 1 × 2 × π × 3 oe M1 6 + 8 + 6 + 1 + 1 + k π 16 2 3 + − x x 4 B2 (x – 3)(x – 2) or B1 (x + a)(x + b) where ab = 6 or a + b = –5 B1 (x – 2)(x + 2) 17 (a)     8 0 0 8 oe 2 B1 for one column (or row) correct (b)         −4 1 4 1 4 1 4 1 oe 2 B1 for –1/8     d b c a or B1 for     − − − 2 2 2 2 seen 18 (a) (i) Tangent (ii) 4.4 to 6 (b) 780 1 2 2 Correct tangent drawn dep M1 attempting to find gradient of their tangent M1 evidence of finding the area under the graph ONLY from t = 12 to t = 25 19 (a) 20200 (b) 1260 2 2 M1 65 × 300 + 700 M1 71190 / 56.5 20 x = 0.84 or 7.16 4 B1 2 8 k ± B1 √(82 – 4 × 1 × 6) or better A1 A1 21 (a) Bisector (b) (4, 2) (c) y = –2x + 10 oe 2 1 3 B1 accurate line B1 two sets of correct arcs B1 correct m B1 correct c M1 correct use of y = mx + c oe on answer line 22 (a) D 14 0 3 2 12 L E 4 B1 0 and 14 in correct place B1 2 in correct place B1 3 in correct place B1 12 in correct place (b) 11 (c) 23 1ft 1ft B1ft 8 + their 3 B1ft 21 + their 2