Cambridge IGCSE Mathematics (with coursework) 0581 — 2010 Oct/Nov Paper 2 · Variant 3

This document consists of 12 printed pages. IB10 11_0581_23/FP © UCLES 2010 [Turn over *4403424656* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0581/23 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 0581/23/O/N/10 For Examiner's Use 1 Write down the number which is 3.6 less than – 4.7 . Answer [1] 2 A plane took 1 hour and 10 minutes to fly from Riyadh to Jeddah. The plane arrived in Jeddah at 23 05. At what time did the plane depart from Riyadh? Answer [1] 3 Calculate 2 2 3 2.35 1.09 − . Give your answer correct to 4 decimal places. Answer [2] 4 Shade the required region on each Venn diagram. A B A ∩ B' (P ∪ Q) ∩ R' P Q R [2]

3 © UCLES 2010 0581/23/O/N/10 [Turn over For Examiner's Use 5 Show that 3 3 4 + 1 1 3 = . 12 1 5 Write down all the steps in your working. Answer [2] 6 Write the following in order of size, smallest first. 20 41 80 161 0.492 4.93% Answer I I I [2] 7 In France, the cost of one kilogram of apricots is €3.38 . In the UK, the cost of one kilogram of apricots is £4.39 . £1 = €1.04 . Calculate the difference between these prices. Give your answer in pounds (£). Answer £ [2] 8 A large rectangular card measures 80 centimetres by 90 centimetres. Maria uses all this card to make small rectangular cards measuring 40 millimetres by 15 millimetres. Calculate the number of small cards. Answer [2]

4 © UCLES 2010 0581/23/O/N/10 For Examiner's Use 9 A B P Q C 8 cm 10 cm 12 cm NOT TO SCALE APB and AQC are straight lines. PQ is parallel to BC. AP = 8 cm, PQ = 10 cm and BC = 12 cm. Calculate the length of AB. Answer AB = cm [2] 10 Nikhil invests $200 for 2 years at 4% per year compound interest. Calculate the exact amount Nikhil has after 2 years. Answer $ [2] 11 In a group of 24 students, 21 like football and 15 like swimming. One student does not like football and does not like swimming. Find the number of students who like both football and swimming. Answer [2]

5 © UCLES 2010 0581/23/O/N/10 [Turn over For Examiner's Use 12 The side of a square is 6.3 cm, correct to the nearest millimetre. The lower bound of the perimeter of the square is u cm and the upper bound of the perimeter is v cm. Calculate the value of (a) u, Answer(a) u = [1] (b) v – u. Answer(b) v – u = [1] 13 a × 107 + b × 106 = c × 106 Find c in terms of a and b. Give your answer in its simplest form. Answer c = [2] 14 Priyantha completes a 10 km run in 55 minutes 20 seconds. Calculate Priyantha’s average speed in km/h. Answer km/h [3]

6 © UCLES 2010 0581/23/O/N/10 For Examiner's Use 15 Find the equation of the straight line which passes through the points (0, 8) and (3, 2). Answer [3] 16 i h g = 2 Find i in terms of g and h. Answer i = [3] 17 Solve the simultaneous equations. 5x – y = – 10 x + 2y = 9 Answer x = y = [3]

7 © UCLES 2010 0581/23/O/N/10 [Turn over For Examiner's Use 18 x° 8 cm NOT TO SCALE The diagram shows a sector of a circle of radius 8 cm. The angle of the sector is x°. The perimeter of the sector is (16 + 14π) cm. Find the value of x. Answer x = [3] 19 A model of a car is made to a scale of 1 : 40. The volume of the model is 45 cm3. Calculate the volume of the car. Give your answer in m3. Answer m3 [3]

8 © UCLES 2010 0581/23/O/N/10 For Examiner's Use 20 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 x y 9 8 7 6 5 4 3 2 1 M L K The triangle KLM is shown on the grid. (a) Calculate angle KML. Answer(a) Angle KML = [2] (b) On the grid, draw the shear of triangle KLM, with a shear factor of 3 and the x-axis invariant. [2]

9 © UCLES 2010 0581/23/O/N/10 [Turn over For Examiner's Use 21 20 18 16 14 12 10 8 6 4 2 0 10 20 30 40 Speed (m / s) Time (seconds) The graph shows 40 seconds of a car journey. The car travelled at a constant speed of 20 m/s, decelerated to 8 m/s then accelerated back to 20 m/s. Calculate (a) the deceleration of the car, Answer(a) m/s2 [1] (b) the total distance travelled by the car during the 40 seconds. Answer(b) m [3]

10 © UCLES 2010 0581/23/O/N/10 For Examiner's Use 22 y x –6 –5 –4 –3 –2 –1 –1 1 2 3 4 0 9 8 7 6 5 4 3 2 1 Find the three inequalities which define the shaded triangle in the diagram. Answer [5]

11 © UCLES 2010 0581/23/O/N/10 [Turn over For Examiner's Use 23 30° 86° 50° B C D A O NOT TO SCALE The points A, B, C and D lie on the circumference of the circle, centre O. Angle ABD = 30°, angle CAD = 50° and angle BOC = 86°. (a) Give the reason why angle DBC = 50°. Answer(a) [1] (b) Find (i) angle ADC, Answer(b)(i) Angle ADC = [1] (ii) angle BDC, Answer(b)(ii) Angle BDC = [1] (iii) angle OBD. Answer(b)(iii) Angle OBD = [2] Questions 24 and 25 are 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 0581/23/O/N/10 For Examiner's Use 24 (a) Write 1 2 y x − as a single fraction in its lowest terms. Answer(a) [2] (b) Write 2 3 3 x x x + + in its lowest terms. Answer(b) [3] 25 f : 2 7 x x → − g : 1 x x → Find (a) fg 1 2       , Answer(a) [2] (b) gf (x), Answer(b) gf (x) = [1] (c) f –1 (x). Answer(c) f–1 (x) = [2]

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 0581/23 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 23 © 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 –8.3 1 Allow –810 3 2 21 55 1 Allow 9.55 pm 3 1.6305 cao 2 B1 4.33(44…) seen or answer 1.63, 1.630, 1.6304…. 4 1, 1 5 Correct working 2 M1 4 15 + 3 4 = 12 16 12 45 + M1 12 1 5 12 61 = 6 4.93% < 41 20 < 0.492 < 161 80 2 Allow decimal equivalents in answer space M1 decimals 0.48(78..), 0.496(8..), 0.0493 7 1.14 2 M1 3.38 ÷ 1.04 (= 3.25) or M1 4.39 × 1.04 8 1200 2 M1 figs 8 ÷ 40 × figs 9 ÷ 15 or M1 (figs 8 × figs 9) ÷ (40 × 15) 9 9.6 cao 2 M1 10 12 8 = x oe 10 216.32 cao 2 M1 200 × (1 + (4/100))2 oe 11 13 2 M1 21 + 15 – 23 or M1 15 – x + x + 21 – x + 1 = 24 oe 12 (a) 25 (b) 0.4 1 1 If zero scored SC1 for 250 and 4 or 6.25 and 6.35 13 10a + b or a × 101 + b (× 100) 2 M1 [a × 107 + b × 106] ÷ 106

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2010 0581 23 © UCLES 2010 14 10.8 or 10 83 70 3 M1 figs 10 ÷ time M1 10 ÷ 0.92r, 0.922 or 83/90 15 y = –2x + 8 cao oe 3 M1 (m =) 3 0 2 8 − − oe B1 c = 8 or y = mx + 8 or subst. correct point in y = “m” x + c 16 2 4 g h or 2 2       g h 3 M1 squaring correctly M1 clearing denominator correctly M1 dividing by coefficient of i or SC2 for correct unsimplified expression 17 x = –1, y = 5 3 M1 consistent multiplication and either add or subtract A1 for one correct after M1 18 315 3 M1 360 x × 2 × π × 8 oe M1 360 x × 2 × π × 8 (+ 16) = (16 +) 14π 19 2.88 3 M1 403 oe seen A1 2 880 000 B1ft their 2 880 000 ÷ 1003 or B1 0.000045 M1 403 A1 cao or M1 0.43 M1 45 × 0.43 A1 20 (a) 63.4 2 M1 tan(M) = 2 4 oe (b) Vertices at (4, 1), (8, 1) and (10, 3) 2 B1 two vertices correct 21 (a) 2.4 oe (b) 680 1 3 M1 an area found M1 40 × 20 – 2 1 × 20 × 12 oe 22 y [ 1, x Y 3, y Y x + 5 oe 5 B1 y R 1 B1 x R 3 B2 y R x + 5 or B1 y R – x + 5 where R is any inequality B1 all 3 inequalities correct 23 (a) (Angles in) same segment (b) (i) 100 (ii) 43 1 1 1 Allow (angles on) the same arc (iii) 3 2 B1 OBC or OCB = 2 1 (180 – 86) (= 47)

Page 4 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – October/November 2010 0581 23 © UCLES 2010 24 (a) xy y x 2 − 2 B1 correct numerator B1 correct denominator (b) 3 x www 3 M1 x(x + 1) M1 3(x + 1) 25 (a) –3 2 B1 g( 2 1 ) = 2 or fg(x) = x 2 – 7 oe (b) 7 2 1 − x 1 (c) 2 7 + x 2 M1 for y + 7 = 2x or x = 2y – 7