Cambridge IGCSE Mathematics 0580 — 2006 Oct/Nov Paper 2 · Variant 1

This document consists of 11 printed pages and 1 blank page. IB06 11_0580_02/5RP  UCLES 2006 [Turn over UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS Paper 2 (Extended) 0580/02 0581/02 Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments October/November 2006 Mathematical tables (optional) Tracing paper (optional) 1hour 30 minutes 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 in the spaces provided on the Question Paper. 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 THE BARCODE. DO NOT WRITE IN THE GREY AREAS BETWEEN THE PAGES. 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. Given answers in degrees to one decimal place. For π , use either your calculator value or 3.142. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 70. Candidate Name Centre Number Candidate Number *058002* For Examiner's Use www.XtremePapers.com

2 © UCLES 2006 0580/02/N/06 For Examiner's Use 1 Two quantities c and d are connected by the formula c = 2d + 30. Find c when d = −100. Answer [1] 2 (a) . 2 6 5 3 2 x = + Find the value of x. Answer(a) x= [1] (b) 3 5 ÷ . 9 40 3 = y Find the value of y. Answer(b) y= [1] 3 Use your calculator to work out (a) √(7 + 6 × 2430.2), Answer(a) [1] (b) 2 – tan30° × tan60°. Answer(b) [1] 4 Angharad sleeps for 8 hours each night, correct to the nearest 10 minutes. The total time she sleeps in the month of November (30 nights) is T hours. Between what limits does T lie? T < Answer [2]

3 © UCLES 2006 0580/02/N/06 [Turn Over For Examiner's Use 5 The picture shows the Sky Tower in Auckland. Alongside the tower is a boat. The boat is 33 metres long. Use the length of the boat to estimate the height of the Sky Tower. Answer m [2] 6 0.0008 8 × 10−5 0.8% 000 125 1 Write the numbers above in order, smallest first. < < < Answer [2] 7 Find the value of n in each of the following statements. (a) 32n =1 Answer(a) n = [1] (b) 32n = 2 Answer(b) n = [1] (c) 32n = 8 Answer(c) n = [1] 33 m

4 © UCLES 2006 0580/02/N/06 For Examiner's Use 8 The Canadian Maple Leaf train timetable from Toronto to Buffalo is shown below. Toronto 10 30 Oakville 10 52 Aldershot 11 07 Grimsby 11 41 St Catharines 11 59 Niagra Falls 12 24 Buffalo 13 25 (a) How long does the journey take from Toronto to Buffalo? h Answer(a) min [1] (b) This journey is 154 kilometres. Calculate the average speed of the train. Answer(b) km/h [2] 9 For each of the following sequences, write down the next term. (a) 2, 3, 5, 8, 13, … Answer(a) [1] (b) x6, 6x5, 30x4, 120x3, … Answer(b) [1] (c) 2, 6, 18, 54, 162, ... Answer(c) [1]

5 © UCLES 2006 0580/02/N/06 [Turn Over For Examiner's Use 10 150 cm 24x cm 7x cm NOT TO SCALE The right-angled triangle in the diagram has sides of length 7x cm, 24x cm and 150 cm. (a) Show that x2 = 36. [2] (b) Calculate the perimeter of the triangle. Answer(b) cm [1] 11 (a) Shade the region A ∩ B. A B [1] (b) Shade the region (A ∪ B)′. A B [1] (c) Shade the complement of set B. A B [1]

6 © UCLES 2006 0580/02/N/06 For Examiner's Use 12 P Q R S T 38º 38º NOT TO SCALE In the diagram PT and QR are parallel. TP and TR are tangents to the circle PQRS. Angle PTR = angle RPQ = 38°. (a) What is the special name of triangle TPR. Give a reason for your answer. Answer(a) name reason [1] (b) Calculate (i) angle PQR, Answer(b)(i) Angle PQR = [1] (ii) angle PSR. Answer(b)(ii)Angle PSR = [1] 13 A statue two metres high has a volume of five cubic metres. A similar model of the statue has a height of four centimetres. (a) Calculate the volume of the model statue in cubic centimetres. Answer(a) cm3 [2] (b) Write your answer to part (a) in cubic metres. Answer(b) m3 [1]

7 © UCLES 2006 0580/02/N/06 [Turn Over For Examiner's Use 14 The graph drawn below shows the conversion of temperatures in degrees Fahrenheit (°F) to temperatures in degrees Celsius (°C). ºC ºF 120 100 80 60 40 20 20 40 60 0 20 20 40 60 40 60 80 100 120 140 160 180 200 (a) The temperature of a room is 20 °C. What is the temperature in Fahrenheit? Answer(a) [1] (b) A liquid has a boiling point of 176 °F. What is the temperature in Celsius? Answer(b) [1] (c) Find T when T °C = T °F. Answer(c) T = [1] 15 f: x
5 − 3x. (a) Find f(−1). Answer(a) [1] (b) Find f −1(x). Answer(b) [2] (c) Find f f −1(8). Answer(c) [1]

8 © UCLES 2006 0580/02/N/06 For Examiner's Use 16 NOT TO SCALE 5x cm 13x cm yº A B C D 17x cm 12x cm ABCD is a trapezium. (a) Find the area of the trapezium in terms of x and simplify your answer. Answer(a) cm2 [2] (b) Angle BCD = y°. Calculate the value of y. Answer(b) y = [2] 17 Solve the equations (a) 0.2x – 3 = 0.5x, Answer(a) x = [2] (b) 2x2 – 11x + 12 = 0. or x = Answer(b) x = [3]

9 © UCLES 2006 0580/02/N/06 [Turn Over For Examiner's Use 18 E F G H The diagram shows a triangle EFG. The side EF is extended to H. (a) Using a straight edge and compasses only, showing your construction arcs, draw (i) the locus of points that are equidistant from E and G, [2] (ii) the locus of points that are equidistant from FG and FH. [2] (b) Measure accurately and write down the acute angle between the two lines drawn in part (a). Answer(b) [1] 19 (a) Find ( ) 4 3       2 5 . Answer(a) [2] (b) ) ( y x 3 7       =       18 42 12 8 2 . Find the values of x and y. Answer(b) x = y = [2] (c) Explain why       8 20 6 15 does not have an inverse. Answer(c) [1]

10 © UCLES 2006 0580/02/N/06 For Examiner's Use 20 (x + 4) cm (x + 12) cm (x + 2) cm R Q 4x cm NOT TO SCALE (a) (i) Write down an expression for the area of rectangle R. Answer(a) (i) cm2 [1] (ii) Show that the total area of rectangles R and Q is 5x2 + 30x + 24 square centimetres. [1] (b) The total area of rectangles R and Q is 64 cm2. Calculate the value of x correct to 1 decimal place. Answer(b) x = [4]

11 © UCLES 2006 0580/02/N/06 For Examiner's Use 21 y NOT TO SCALE C (4,3) B (1, 2) A 4x y = 6 2x + 3y = 17 x In the diagram, the line AC has equation 2x + 3y = 17 and the line AB has equation 4x – y = 6. The lines BC and AB intersect at B(1, −2). The lines AC and BC intersect at C(4, 3). (a) Use algebra to find the coordinates of the point A. Answer(a) [3] (b) Find the equation of the line BC. Answer(b) [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 University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. © UCLES 2006 0580/02/N/06 BLANK PAGE

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 2006 question paper 0580 and 0581 MATHEMATICS 0580/02 and 0581/02 Paper 2, maximum raw mark 70 This mark scheme is published as an aid to teachers and students, 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. All Examiners are instructed that alternative correct answers and unexpected approaches in candidates’ scripts must be given marks that fairly reflect the relevant knowledge and skills demonstrated. Mark schemes must be read in conjunction with the question papers and the report on the examination. The grade thresholds for various grades are published in the report on the examination for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses. • CIE will not enter into discussions or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the October/November 2006 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses. www.XtremePapers.com

TYPES OF MARK Most of the marks (those without prefixes, and ‘B’ marks) are given for accurate results, drawings or statements. • M marks are given for a correct method. • B marks are given for a correct statement or step. • A marks are given for an accurate answer following a correct method. ABBREVIATIONS a.r.t. Anything rounding to b.o.d. Benefit of the doubt has been given to the candidate c.a.o. Correct answer only (i.e. no ‘follow through’) e.e.o. Each error or omission f.t. Follow through i.s.w. Ignore subsequent working o.e. Or equivalent SC Special case s.o.i. Seen or implied ww Without working www Without wrong working > Work followed through after an error: no further error made=

Page 3 Mark Scheme Syllabus Paper IGCSE - OCT/NOV 2006 0580/0581 2 © UCLES 2006

Page 4 Mark Scheme Syllabus Paper IGCSE - OCT/NOV 2006 0580/0581 2 © UCLES 2006 3 5 , 3 5 − − − x x or 3 5 y −