Cambridge IGCSE Mathematics (with coursework) 0581 — 2011 Oct/Nov Paper 2 · Variant 2

This document consists of 12 printed pages. IB11 11_0581_22/FP © UCLES 2011 [Turn over *3815120679* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0581/22 Paper 2 (Extended) October/November 2011 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 2011 0581/22/O/N/11 For Examiner's Use 1 A bus leaves a port every 15 minutes, starting at 09 00. The last bus leaves at 17 30. How many times does a bus leave the port during one day? Answer [2] 2 Factorise completely ax + bx + ay + by. Answer [2] 3 Use your calculator to find the value of (a) 30 × 2.52, Answer(a) [1] (b) 2.5 – 2. Answer(b) [1] 4 The cost of making a chair is $28 correct to the nearest dollar. Calculate the lower and upper bounds for the cost of making 450 chairs. Answer lower bound $ upper bound $ [2]

3 © UCLES 2011 0581/22/O/N/11 [Turn over For Examiner's Use 5 Jiwan incorrectly wrote 1 + 2 1 + 3 1 + 4 1 = 1 9 3 . Show the correct working and write down the answer as a mixed number. Answer [3] 6 The force, F, between two magnets varies inversely as the square of the distance, d, between them. F = 150 when d = 2. Calculate F when d = 4. Answer F = [3]

4 © UCLES 2011 0581/22/O/N/11 For Examiner's Use 7       4 3 _ 2 0       b a =       25 8 Find the value of a and the value of b. Answer a = b = [3] 8 A cruise ship travels at 22 knots. [1 knot is 1.852 kilometres per hour.] Convert this speed into metres per second. Answer m/s [3]

5 © UCLES 2011 0581/22/O/N/11 [Turn over For Examiner's Use 9 A sequence is given by u1 = 1 , u2 = 3 , u3 = 5 , u4 = 7 , … (a) Find a formula for un , the nth term. Answer(a) un = [2] (b) Find u29 . Answer(b) u29 = [1] 10 Write as a single fraction in its simplest form. 10 3 + x O 4 1 + x Answer [3]

6 © UCLES 2011 0581/22/O/N/11 For Examiner's Use 11 Find the values of m and n. (a) 2m = 0.125 Answer(a) m = [2] (b) 24n × 22n = 512 Answer(b) n = [2] 12 40 30 20 10 0 1 2 3 4 5 Time (seconds) 6 7 8 9 10 Speed (m / s) Small car Large car A small car accelerates from 0 m/s to 40 m/s in 6 seconds and then travels at this constant speed. A large car accelerates from 0 m/s to 40 m/s in 10 seconds. Calculate how much further the small car travels in the first 10 seconds. Answer m [4]

7 © UCLES 2011 0581/22/O/N/11 [Turn over For Examiner's Use 13 76° O A B T C P North NOT TO SCALE AOC is a diameter of the circle, centre O. AT is a straight line that cuts the circle at B. PT is the tangent to the circle at C. Angle COB = 76°. (a) Calculate angle ATC. Answer(a) Angle ATC = [2] (b) T is due north of C. Calculate the bearing of B from C. Answer(b) [2]

8 © UCLES 2011 0581/22/O/N/11 For Examiner's Use 14 R 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 y x The region R is bounded by three lines. Write down the three inequalities which define the region R. Answer [4]

9 © UCLES 2011 0581/22/O/N/11 [Turn over For Examiner's Use 15 6 5 4 3 2 1 0 1 2 3 4 5 6 y x A B The points A(1, 2) and B(5, 5) are shown on the diagram . (a) Work out the co-ordinates of the midpoint of AB. Answer(a) ( , ) [1] (b) Write down the column vector . Answer(b) =           [1] (c) Using a straight edge and compasses only, draw the locus of points which are equidistant from A and from B. [2]

10 © UCLES 2011 0581/22/O/N/11 For Examiner's Use 16 In a survey of 60 cars, the type of fuel that they use is recorded in the table below. Each car only uses one type of fuel. Petrol Diesel Liquid Hydrogen Electricity 40 12 2 6 (a) Write down the mode. Answer(a) [1] (b) Olav drew a pie chart to illustrate these figures. Calculate the angle of the sector for Diesel. Answer(b) [2] (c) Calculate the probability that a car chosen at random uses Electricity. Write your answer as a fraction in its simplest form. Answer(c) [2]

11 © UCLES 2011 0581/22/O/N/11 [Turn over For Examiner's Use 17 O C B A a c M 4a O is the origin, = a, = c and = 4a. M is the midpoint of AB. (a) Find, in terms of a and c, in their simplest form (i) the vector , Answer(a)(i) = [2] (ii) the position vector of M. Answer(a)(ii) [2] (b) Mark the point D on the diagram where = 3a + c. [2] 18 w = LC 1 (a) Find w when L = 8 × 10 O3 and C = 2 × 10 O9. Give your answer in standard form. Answer(a) w = [3] (b) Rearrange the formula to make C the subject. Answer(b) C = [3] Question 19 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 2011 0581/22/O/N/11 For Examiner's Use 19 6 5 4 3 2 1 1 2 3 4 5 6 7 0 A B C y x A(1, 3), B(4, 1) and C(6, 4) are shown on the diagram. (a) Using a straight edge and compasses only, construct the angle bisector of angle ABC. [2] (b) Work out the equation of the line BC. Answer(b) [3] (c) ABC forms a right-angled isosceles triangle of area 6.5 cm2. Calculate the length of AB. Answer(c) AB = cm [2]

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 2011 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. • Cambridge will not enter into discussions or correspondence in connection with these mark schemes. Cambridge is publishing the mark schemes for the October/November 2011 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 2011 0581 22 © University of Cambridge International Examinations 2011 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 35 2 M1 for 4 × 8 + 3 or 4 × 4 3 8 or 4 × 2 1 8 + 1 or 15 525 or 15 510 + 1 SC1 for answer 34 2 (a + b)(x + y) 2 M1 x(a + b) + y(a + b) or M1 a(x + y) + b(x + y) 3 (a) 6.25 cao 1 (b) 0.16 cao 1 4 12375 cao 12825 cao 2 B1, B1 If no marks scored give M1 for 27.5 and 28.5 seen 5 212 1 cao with correct working 3 M1 (1+) 12 3 12 4 12 6 + + oe A1 (1)12 13 or 12 25 oe 6 37.5 3 M1 F = k/d 2 A1 k = 600 7 a = –3 b = 4 3 M1 –3a + 4b = 25 B1 one correct 8 11.3 3 M2 22 × 1.852 × 1000/3600 oe or M1 22 × figs 1852 or 22 × 1000/3600 9 (a) ( )1 2 − n 2 M1 ( ) k n + 2 or 2n – 1 (b) 57 or 7.55 1ft From their (a) 10 ( )( ) 4 10 2 2 + + + x x x oe 3 B1 common denominator (x + 10)(x + 4) oe seen B1 3(x + 4) – (x + 10) seen oe 11 (a) –3 2 M1 1/23 or 2–3 (b) 1.5 2 M1 26n or 6n = 9 12 80 www 4 M1 attempting area under the graph M1 large or small car area found correctly Dep M1 correct final area statement 13 (a) 52 2 M1 OAB or OBA = 38 or OCT = 90 (b) 322 2 M1 BCT = 38 or BCO = 52

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2011 0581 22 © University of Cambridge International Examinations 2011 14 y ≤ 5 x ≥ 2 y ≥ x 4 B1 each inequality but accept any of the four inequality symbols Final B1 all 3 symbols correct 15 (a) (3, 3½) 1 (b)       3 4 1 (c) Correct perpendicular bisector with arcs 2 B1 line through (3, 3½) perp to AB B1 two sets of correct arcs 16 (a) Petrol cao 1 (b) 72 2 M1 for 360 × 12 ÷ 60 (c) 10 1 2 B1 60 6 or 30 3 or 20 2 or 0.1 or 10% 17 (a) (i) 3a + c 2 B1 AO + OC + CB or –a + c + 4a (ii) 2 2 1 a + 2 1 c oe 2 M1 a + 2 1 their (a)(i) (b) D marked ¾ way along CB 2 B1 D on CB 18 (a) 2.5 × 105 3 B2 250000 oe or M1 correct part value seen (b) C = 1/(Lw2) 3 M1 each correct move 19 (a) correct bisector (through 3½, 3½) 2 B1 correct line B1 correct arcs (b) y = 1 2 1 x – 5 oe 3 B2 y = 1 2 1 x + k or y = kx – 5 k any number or B1 1 2 1 x + k or kx – 5 (c) 3.61 2 If O scored allow one each for m = 1 2 1 or c = –5 clearly identified in working M1 2 1 × L × L = 6.5 or M1 ( ) 2 2 2 3 +