Cambridge IGCSE Mathematics 0580 — 2008 Oct/Nov Paper 2 · Variant 0

Location Entry Codes As part of CIE’s continual commitment to maintaining best practice in assessment, CIE uses different variants of some question papers for our most popular assessments with large and widespread candidature. The question papers are closely related and the relationships between them have been thoroughly established using our assessment expertise. All versions of the paper give assessment of equal standard. The content assessed by the examination papers and the type of questions is unchanged. This change means that for this component there are now two variant Question Papers, Mark Schemes and Principal Examiner’s Reports where previously there was only one. For any individual country, it is intended that only one variant is used. This document contains both variants which will give all Centres access to even more past examination material than is usually the case. The diagram shows the relationship between the Question Papers, Mark Schemes and Principal Examiners’ Reports that are available. Question Paper Mark Scheme Principal Examiner’s Report Introduction Introduction Introduction First variant Question Paper First variant Mark Scheme First variant Principal Examiner’s Report Second variant Question Paper Second variant Mark Scheme Second variant Principal Examiner’s Report Who can I contact for further information on these changes? Please direct any questions about this to CIE’s Customer Services team at: international@cie.org.uk The titles for the variant items should correspond with the table above, so that at the top of the first page of the relevant part of the document and on the header, it has the words: • First variant Question Paper / Mark Scheme / Principal Examiner’s Report or • Second variant Question Paper / Mark Scheme / Principal Examiner’s Report as appropriate. www.XtremePapers.com

This document consists of 12 printed pages. IB08 11_0580_02/4RP © UCLES 2008 [Turn over *7999036037* For Examiner's Use UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0580/21, 0581/21 Paper 2 (Extended) October/November 2008 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 THE BARCODE 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. First Variant Question Paper

2 © UCLES 2008 0580/21/O/N/08 For Examiner's Use 1 For this diagram, write down (a) the order of rotational symmetry, Answer(a) [1] (b) the number of lines of symmetry. Answer(b) [1] 2 _2 1 1 0 5 6 3 4 8 7 1 1 3 3 The answer to this matrix multiplication is of order a × b. Find the values of a and b. Answer a = b = [2] 3 Work out the value of 1 + 2 4 3 + 5 + 6 . Answer [2]

3 © UCLES 2008 0580/21/O/N/08 [Turn over For Examiner's Use 4 A light on a computer comes on for 26 700 microseconds. One microsecond is 10-6 seconds. Work out the length of time, in seconds, that the light is on (a) in standard form, Answer(a) s [1] (b) as a decimal. Answer(b) s [1] 5 A B D C ABCD is a square. It is rotated through 90° clockwise about B. Draw accurately the locus of the point D. [2]

4 © UCLES 2008 0580/21/O/N/08 For Examiner's Use 6 sin x ° = 0.86603 and 0 Y x Y 180. Find the two values of x. Answer x = or x = [2] 7 A rectangle has sides of length 6.1 cm and 8.1 cm correct to 1 decimal place. Calculate the upper bound for the area of the rectangle as accurately as possible. Answer cm2 [2] 8 (a) Factorise ax 2 + bx 2. Answer(a) [1] (b) Make x the subject of the formula ax 2 + bx 2 – d 2 = p 2. Answer(b) x = [2]

5 © UCLES 2008 0580/21/O/N/08 [Turn over For Examiner's Use 9 y x y = 2x + 3 A C O B NOT TO SCALE The distance AB is 7 units. (a) Write down the equation of the line through B which is parallel to y = 2x + 3. Answer(a) [2] (b) Find the co-ordinates of the point C where this line crosses the x axis. Answer(b) ( , ) [1] 10 Solve these simultaneous equations. x + 2y – 18 = 0 3x – 4y – 4 = 0 Answer x = y = [3]

6 © UCLES 2008 0580/21/O/N/08 For Examiner's Use 11 Write as a single fraction in its simplest form 4 2 _ _ 2 +3 3 x x . Answer [3] 12 Solve the inequality _ 2 5 2 < . 7 5 x Answer [3] 13 The quantity p varies inversely as the square of (q + 2). p = 5 when q = 3. Find p when q = 8. Answer p = [3]

7 © UCLES 2008 0580/21/O/N/08 [Turn over For Examiner's Use 14 A spacecraft made 58 376 orbits of the Earth and travelled a distance of 2.656 × 109 kilometres. (a) Calculate the distance travelled in 1 orbit correct to the nearest kilometre. Answer(a) km [2] (b) The orbit of the spacecraft is a circle. Calculate the radius of the orbit. Answer(b) km [2] 15 f(x) = cos x °, g(x) = 2x + 4. Find (a) f(60), Answer(a) [1] (b) fg(88), Answer(b) [2] (c) g-1(f(x)). Answer(c) [2]

8 © UCLES 2008 0580/21/O/N/08 For Examiner's Use 16 In an experiment, the number of bacteria, N, after x days, is N = 1000 × 1.4x. (a) Complete the table. x 0 1 2 3 4 N [2] (b) Draw a graph to show this information. 5000 4000 3000 2000 1000 0 1 2 3 4 N x [2] (c) How many days does it take for the number of bacteria to reach 3000? Give your answer correct to 1 decimal place. Answer(c) days [1]

9 © UCLES 2008 0580/21/O/N/08 [Turn over For Examiner's Use 17 A B C O q p O is the origin. Vectors p and q are shown in the diagram. (a) Write down, in terms of p and q, in their simplest form (i) the position vector of the point A, Answer(a)(i) [1] (ii) BC , Answer(a)(ii) [1] (iii) BC − AC. Answer(a)(iii) [2] (b) If | p | = 2, write down the value of | AB |. Answer(b) [1]

10 © UCLES 2008 0580/21/O/N/08 For Examiner's Use 18 20 10 30 0 180 160 200 140 120 100 80 60 40 20 Tanah Merah Expo Time (s) Speed (m / s) The graph shows the train journey between Tanah Merah and Expo in Singapore. Work out (a) the acceleration of the train when it leaves Tanah Merah, Answer(a) m/s2 [2] (b) the distance between Tanah Merah and Expo, Answer(b) m [3] (c) the average speed of the train for the journey. Answer(c) m/s [1]

11 © UCLES 2008 0580/21/O/N/08 [Turn over For Examiner's Use 19 P Q 30° O S R 12 cm 6 cm NOT TO SCALE OPQ is a sector of a circle, radius 12 cm, centre O. Angle POQ = 50°. ORS is a sector of a circle, radius 6 cm, also centre O. Angle ROS = 30°. (a) Calculate the shaded area. Answer(a) cm2 [3] (b) Calculate the perimeter of the shaded area, PORSOQP. Answer(b) cm [3] Question 20 is on page 12

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. 0580/21/O/N/08 For Examiner's Use 20 A new school has x day students and y boarding students. The fees for a day student are $600 a term. The fees for a boarding student are $1200 a term. The school needs at least $720 000 a term. (a) Show that this information can be written as x + 2y [ 1200. Answer (a) [1] (b) The school has a maximum of 900 students. Write down an inequality in x and y to show this information. Answer(b) [1] (c) Draw two lines on the grid below and write the letter R in the region which represents these two inequalities. y x 900 0 1200 Number of boarding students Number of day students [4] (d) What is the least number of boarding students at the school? Answer(d) [1]

This document consists of 12 printed pages. IB08 11_0580_22/3RP © UCLES 2008 [Turn over *2077738702* For Examiner's Use UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0580/22, 0581/22 Paper 2 (Extended) October/November 2008 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 THE BARCODE. 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. Second Variant Question Paper

2 © UCLES 2008 0580/22/O/N/08 For Examiner's Use 1 For this diagram, write down (a) the order of rotational symmetry, Answer(a) [1] (b) the number of lines of symmetry. Answer(b) [1] 2 –2 1 8 3 1 0 9 4 1 3 0 4 3 2 The answer to this matrix multiplication is of order a × b. Find the values of a and b. Answer a = b = [2] 3 Work out the value of 1 + 2 4 3 + 5 + 6 . Answer [2]

3 © UCLES 2008 0580/22/O/N/08 [Turn over For Examiner's Use 4 A light on a computer comes on for 38 500 microseconds. One microsecond is 10-6 seconds. Work out the length of time, in seconds, that the light is on (a) in standard form, Answer(a) s [1] (b) as a decimal. Answer(b) s [1] 5 A B D C ABCD is a square. It is rotated through 90° clockwise about B. Draw accurately the locus of the point D. [2]

4 © UCLES 2008 0580/22/O/N/08 For Examiner's Use 6 sin x ° = 0.707107 and 0 Y x Y 180. Find the two values of x. Answer x = or x = [2] 7 A rectangle has sides of length 2.4 cm and 6.4 cm correct to 1 decimal place. Calculate the upper bound for the area of the rectangle as accurately as possible. Answer cm2 [2] 8 (a) Factorise ax 2 + bx 2. Answer(a) [1] (b) Make x the subject of the formula ax 2 + bx 2 – d 2 = p 2. Answer(b) x = [2]

5 © UCLES 2008 0580/22/O/N/08 [Turn over For Examiner's Use 9 y x y = 2x + 5 A C O B NOT TO SCALE The distance AB is 11 units. (a) Write down the equation of the line through B which is parallel to y = 2x + 5. Answer(a) [2] (b) Find the co-ordinates of the point C where this line crosses the x axis. Answer(b) ( , ) [1] 10 Solve these simultaneous equations. x + 3y – 11 = 0 3x – 4y – 7 = 0 Answer x = y = [3]

6 © UCLES 2008 0580/22/O/N/08 For Examiner's Use 11 Write as a single fraction in its simplest form 5 2 _ _ 5 +1 2 3 x x . Answer [3] 12 Solve the inequality _ 2 5 2 < . 7 5 x Answer [3] 13 The quantity p varies inversely as the square of (q + 2). p = 4 when q = 2. Find p when q = 8. Answer p = [3]

7 © UCLES 2008 0580/22/O/N/08 [Turn over For Examiner's Use 14 A spacecraft made 58 376 orbits of the Earth and travelled a distance of 2.656 × 109 kilometres. (a) Calculate the distance travelled in 1 orbit correct to the nearest kilometre. Answer(a) km [2] (b) The orbit of the spacecraft is a circle. Calculate the radius of the orbit. Answer(b) km [2] 15 f(x) = tan x °, g(x) = 2x + 6. Find (a) f(45), Answer(a) [1] (b) fg(87), Answer(b) [2] (c) g-1(f(x)). Answer(c) [2]

8 © UCLES 2008 0580/22/O/N/08 For Examiner's Use 16 In an experiment, the number of bacteria, N, after x days, is N = 1000 × 1.4x. (a) Complete the table. x 0 1 2 3 4 N [2] (b) Draw a graph to show this information. 5000 4000 3000 2000 1000 0 1 2 3 4 N x [2] (c) How many days does it take for the number of bacteria to reach 3000? Give your answer correct to 1 decimal place. Answer(c) days [1]

9 © UCLES 2008 0580/22/O/N/08 [Turn over For Examiner's Use 17 A B C O q p O is the origin. Vectors p and q are shown in the diagram. (a) Write down, in terms of p and q, in their simplest form (i) the position vector of the point A, Answer(a)(i) [1] (ii) BC , Answer(a)(ii) [1] (iii) BC − AC. Answer(a)(iii) [2] (b) If | p | = 2, write down the value of | AB |. Answer(b) [1]

10 © UCLES 2008 0580/22/O/N/08 For Examiner's Use 18 20 10 30 0 180 160 200 140 120 100 80 60 40 20 Tanah Merah Expo Time (s) Speed (m / s) The graph shows the train journey between Tanah Merah and Expo in Singapore. Work out (a) the acceleration of the train when it leaves Tanah Merah, Answer(a) m/s2 [2] (b) the distance between Tanah Merah and Expo, Answer(b) m [3] (c) the average speed of the train for the journey. Answer(c) m/s [1]

11 © UCLES 2008 0580/22/O/N/08 [Turn over For Examiner's Use 19 P Q 30° O S R 10 cm 5 cm NOT TO SCALE OPQ is a sector of a circle, radius 10 cm, centre O. Angle POQ = 50°. ORS is a sector of a circle, radius 5 cm, also centre O. Angle ROS = 30°. (a) Calculate the shaded area. Answer(a) cm2 [3] (b) Calculate the perimeter of the shaded area, PORSOQP. Answer(b) cm [3] Question 20 is on page 12

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 2008 0580/22/O/N/08 For Examiner's Use 20 A new school has x day students and y boarding students. The fees for a day student are $600 a term. The fees for a boarding student are $1200 a term. The school needs at least $720 000 a term. (a) Show that this information can be written as x + 2y [ 1200. Answer (a) [1] (b) The school has a maximum of 900 students. Write down an inequality in x and y to show this information. Answer(b) [1] (c) Draw two lines on the grid below and write the letter R in the region which represents these two inequalities. y x 900 0 1200 Number of boarding students Number of day students [4] (d) What is the least number of boarding students at the school? Answer(d) [1]