Cambridge IGCSE Mathematics 0580 — 2007 May/June Paper 1 · Variant 1

Location Entry Codes From the June 2007 session, as part of CIE’s continual commitment to maintaining best practice in assessment, CIE has begun to use different variants of some question papers for our most popular assessments with extremely 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 are 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 Examiner’s Reports. 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 www.XtremePapers.com

This document consists of 11 printed pages and 1 blank page. IB07 06_0580_01/8RP © UCLES 2007 [Turn over *9556778355* For Examiner's Use P UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0580/01, 0581/01 Paper 1 (Core) May/June 2007 1 hour Candidates answer on the Question Paper. Additional Materials: Electronic Calculator Mathematical tables (optional) Geometrical Instruments 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 56. First variant Question Paper

2 © UCLES 2007 0580/01/J/07 For Examiner's Use 1 Work out the value of _ 9 3×7 3×2 . Answer [1] 2 Write the following in order, with the smallest first. 3 5 0.58 62% Answer < < [1] 3 Jamal arrived at work at 09 20 and left at 17 15. How long, in hours and minutes, did he spend at work? Answer h min [1] 4 NOT TO SCALE 150 cm A piece of wood is 150 centimetres long. It has to be cut into equal lengths of 6 4 1 centimetres. How many of these lengths can be cut from this piece of wood? Answer [1] First variant Question Paper

3 © UCLES 2007 0580/01/J/07 [Turn over For Examiner's Use 5 Daniel plots a scatter diagram of speed against time taken. As the time taken increases, speed decreases. Which one of the following types of correlation will his scatter graph show? Positive Negative Zero Answer [1] 6 The average temperatures in Moscow for each month are shown in the table below. Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Temperature °C −10.2 −8.9 −4.0 4.5 12.2 16.3 18.5 16.6 10.9 4.3 −2.0 −7.5 (a) Which month has the lowest average temperature? Answer(a) [1] (b) Find the difference between the average temperatures in July and December. Answer(b) °C [1] 7 145° North P L NOT TO SCALE North The bearing of a lighthouse, L, from a port, P, is 145°. Find the bearing of P from L. Answer [2] First variant Question Paper

4 © UCLES 2007 0580/01/J/07 For Examiner's Use 8 The points A and B are marked on the diagram. y x –4 –3 –2 –1 1 2 3 4 0 4 3 2 1 –1 –2 –3 –4 A B (a) Write AB as a column vector. Answer(a) AB = [1] (b) BC = 3 2           − − . Write down the co-ordinates of C. Answer(b) ( , ) [1] 9 Expand the brackets and simplify 3x2 – x(x−3y). Answer [2] First variant Question Paper

5 © UCLES 2007 0580/01/J/07 [Turn over For Examiner's Use 10 NOT TO SCALE 25° 130° A B E F C D In the diagram, AB, CD and EF are parallel lines. Angle ABC = 25° and angle CEF = 130°. Calculate angle BCE. Answer Angle BCE = [2] 11 The net of a solid is drawn accurately below. Write down the special name for (a) the triangles shown on the net, Answer(a) [1] (b) the solid. Answer(b) [1] First variant Question Paper

6 © UCLES 2007 0580/01/J/07 For Examiner's Use 12 Write down the equation of the straight line through (0, −1) which is parallel to y = 3x + 5. Answer y = [2] 13 (a) 4p × 45 = 415. Find the value of p. Answer(a) p = [1] (b) 27 ÷ 2q = 24. Find the value of q. Answer(b) q = [1] (c) 5r = 1 25 . Find the value of r. Answer(c) r = [1] 14 (a) Alex changed $250 into euros (€) when the rate was €1 = $1.19886. How many euros did he receive? Answer(a) € [2] (b) Write 1.19886 correct to 3 significant figures. Answer(b) [1] First variant Question Paper

7 © UCLES 2007 0580/01/J/07 [Turn over For Examiner's Use 15 The diagram shows a regular hexagon and a square. x° y° NOT TO SCALE Calculate the values of x and y. Answer x = y = [3] 16 Aminata bought 20 metres of cloth at a cost of $80. She sold 15 metres of the cloth at $5.40 per metre and 5 metres at $3 per metre. (a) Calculate the profit she made. Answer(a) $ [2] (b) Calculate this profit as a percentage of the original cost. Answer(b) % [1] First variant Question Paper

8 © UCLES 2007 0580/01/J/07 For Examiner's Use 17 (a) The surface area of the earth is approximately 510 000 000 square kilometres. Write this number in standard form. Answer(a) km2 [2] (b) 29.4% of the surface area of the earth is land. Calculate the area of land. Answer(b) km2 [2] 18 O N M 1200 m 900 m NOT TO SCALE A hot air balloon, M, is 900 metres vertically above a point N on the ground. A boy stands at a point O, 1200 metres horizontally from N. (a) Calculate the distance, OM, of the boy from the balloon. Answer(a) OM = m [2] (b) Calculate angle MON. Answer(b) Angle MON = [2] First variant Question Paper

9 © UCLES 2007 0580/01/J/07 [Turn over For Examiner's Use 19 In triangle ABC, AB = 110 mm, AC = 65 mm and BC = 88 mm. (a) Calculate the perimeter of the triangle ABC. Answer(a) mm [1] (b) Construct the triangle ABC, leaving in your construction arcs. The side AB is drawn for you. A 110 mm B [2] (c) The side AB is 110 mm, correct to the nearest millimetre. Write down the shortest possible length of AB. Answer(c) mm [1] First variant Question Paper

10 © UCLES 2007 0580/01/J/07 For Examiner's Use 20 15 students estimated the area of the rectangle shown below. Their estimates, in square centimetres, were 45 44 50 50 48 24 50 46 43 50 48 20 45 49 47 (a) Work out (i) the mode, Answer(a)(i) cm2 [1] (ii) the mean, Answer(a)(ii) cm2 [2] (iii) the median. Answer(a)(iii) cm2 [2] (b) Explain why the mean is not a suitable average to represent this data. Answer(b) [1] First variant Question Paper

11 © UCLES 2007 0580/01/J/07 For Examiner's Use 21 1400 1200 1000 800 600 400 200 0 50 100 150 200 Time (seconds) 250 300 350 400 Home Work Distance (metres) A B C D A B C D E The graph shows the distance travelled by a cyclist on a journey from Home to Work. (a) The cyclist stopped twice at traffic lights. For how many seconds did the cyclist wait altogether? Answer(a) s [2] (b) For which part of the journey did the cyclist travel fastest? Answer(b) [1] (c) (i) How far did the cyclist travel from Home to Work? Answer(c)(i) m [1] (ii) Calculate the cyclist’s average speed for the whole journey. Answer(c)(ii) m/s [3] First variant Question Paper

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 2007 0580/01/J/07 BLANK PAGE First variant Question Paper

This document consists of 11 printed pages and 1 blank page. IB07 06_0580_01_TZ/RP © UCLES 2007 [Turn over *0089378030* For Examiner's Use Q UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0580/01, 0581/01 Paper 1 (Core) May/June 2007 1 hour Candidates answer on the Question Paper. Additional Materials: Electronic Calculator Mathematical tables (optional) Geometrical Instruments 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 56. Second variant Question Paper

2 © UCLES 2007 0580/01/M/J/07 For Examiner's Use 1 Work out the value of 6-3×12 3×2 . Answer [1] 2 Write the following in order, with the smallest first. 4 5 0.79 81% Answer < < [1] 3 Jamal arrived at work at 09 40 and left at 17 25. How long, in hours and minutes, did he spend at work? Answer h min [1] 4 NOT TO SCALE 150 cm A piece of wood is 150 centimetres long. It has to be cut into equal lengths of 6 4 1 centimetres. How many of these lengths can be cut from this piece of wood? Answer [1] Second variant Question Paper

3 © UCLES 2007 0580/01/M/J/07 [Turn over For Examiner's Use 5 Daniel plots a scatter diagram of speed against time taken. As the time taken increases, speed decreases. Which one of the following types of correlation will his scatter graph show? Positive Negative Zero Answer [1] 6 The average temperatures in Moscow for each month are shown in the table below. Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Temperature °C −10.2 −8.9 −4.0 4.5 12.2 16.3 18.5 16.6 10.9 4.3 −2.0 −7.5 (a) Which month has the lowest average temperature? Answer(a) [1] (b) Find the difference between the average temperatures in February and October. Answer(b) °C [1] 7 125° North P L NOT TO SCALE North The bearing of a lighthouse, L, from a port, P, is 125°. Find the bearing of P from L. Answer [2] Second variant Question Paper

4 © UCLES 2007 0580/01/M/J/07 For Examiner's Use 8 The points A and B are marked on the diagram. y x –4 –3 –2 –1 1 2 3 4 0 4 3 2 1 –1 –2 –3 –4 A B (a) Write AB as a column vector. Answer(a) AB = [1] (b) BC = _3 _2           . Write down the co-ordinates of C. Answer(b) ( , ) [1] 9 Expand the brackets and simplify 4x2 – x(x −2y). Answer [2] Second variant Question Paper

5 © UCLES 2007 0580/01/M/J/07 [Turn over For Examiner's Use 10 NOT TO SCALE 35° 135° A B E F C D In the diagram, AB, CD and EF are parallel lines. Angle ABC = 35° and angle CEF = 135°. Calculate angle BCE. Answer Angle BCE = [2] 11 The net of a solid is drawn accurately below. Write down the special name for (a) the triangles shown on the net, Answer(a) [1] (b) the solid. Answer(b) [1] Second variant Question Paper

6 © UCLES 2007 0580/01/M/J/07 For Examiner's Use 12 Write down the equation of the straight line through (0, −3) which is parallel to y = 2x + 3. Answer y = [2] 13 (a) 3p × 35 = 314. Find the value of p. Answer(a) p = [1] (b) 28 ÷ 2q = 23. Find the value of q. Answer(b) q = [1] (c) 6 r = 1 36 . Find the value of r. Answer(c) r = [1] 14 (a) Alex changed $270 into euros (€) when the rate was €1 = $1.19886. How many euros did he receive? Answer(a) € [2] (b) Write 1.19886 correct to 3 significant figures. Answer(b) [1] Second variant Question Paper

7 © UCLES 2007 0580/01/M/J/07 [Turn over For Examiner's Use 15 The diagram shows a regular hexagon and a square. x° y° NOT TO SCALE Calculate the values of x and y. Answer x = y = [3] 16 Aminata bought 20 metres of cloth at a cost of $90. She sold 15 metres of the cloth at $5.80 per metre and 5 metres at $3 per metre. (a) Calculate the profit she made. Answer (a)$ [2] (b) Calculate this profit as a percentage of her original cost. Answer (b) % [1] Second variant Question Paper

8 © UCLES 2007 0580/01/M/J/07 For Examiner's Use 17 (a) The surface area of the earth is approximately 510 000 000 square kilometres. Write this number in standard form. Answer(a) km2 [2] (b) 29.4% of the surface area of the earth is land. Calculate the area of land. Answer(b) km2 [2] 18 A C B 1100 m 800 m NOT TO SCALE A hot air balloon, B, is 800 metres vertically above a point C on the ground. A girl stands at a point A, 1100 metres horizontally from C. (a) Calculate the distance, AB, of the girl from the balloon. Answer(a) AB = m[2] (b) Calculate the angle BAC. Answer(b) Angle BAC = [2] Second variant Question Paper

9 © UCLES 2007 0580/01/M/J/07 [Turn over For Examiner's Use 19 In triangle LMN, LM = 120 mm, LN = 70 mm and MN = 86 mm. (a) Calculate the perimeter of the triangle LMN. Answer(a) mm [1] (b) Construct the triangle LMN, leaving in your construction arcs. The side LM is drawn for you. L 120 mm M [2] (c) The side LM is 120 mm, correct to the nearest millimetre. Write down the shortest possible length of LM. Answer(c) mm [1] Second variant Question Paper

10 © UCLES 2007 0580/01/M/J/07 For Examiner's Use 20 15 students estimated the area of the rectangle shown below. Their estimates, in square centimetres were 45 44 50 50 51 21 50 46 43 50 48 22 45 49 48 (a) Work out (i) the mode, Answer(a)(i) cm2 [1] (ii) the mean, Answer(a)(ii) cm2 [2] (iii) the median. Answer(a)(iii) cm2 [2] (b) Explain why the mean is not a suitable average to represent this data. Answer(b) [1] Second variant Question Paper

11 © UCLES 2007 0580/01/M/J/07 For Examiner's Use 21 1400 1200 1000 800 600 400 200 0 50 100 150 200 Time (seconds) 250 300 350 400 Home Work Distance (metres) A B C D A B C D E The graph shows the distance travelled by a cyclist on a journey from Home to Work. (a) The cyclist stopped twice at traffic lights. For how many seconds did the cyclist wait altogether? Answer (a) s [2] (b) For which part of the journey did the cyclist travel fastest? Answer (b) [1] (c) (i) How far did the cyclist travel from Home to Work? Answer (c)(i) m [1] (ii) Calculate the cyclist’s average speed for the whole journey. Answer(c)(ii) m/s [3] Second variant Question Paper

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 2007 0580/01/M/J/07 BLANK PAGE Second variant Question Paper

Location Entry Codes From the June 2007 session, as part of CIE’s continual commitment to maintaining best practice in assessment, CIE has begun to use different variants of some question papers for our most popular assessments with extremely 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 are 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 Examiner’s Reports. 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 www.XtremePapers.com

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2007 question paper 0580/0581 MATHEMATICS 0580/01 and 0581/01 Paper 1 (Core), maximum raw mark 56 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. 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. • CIE will not enter into discussions or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the May/June 2007 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

Page 2 Mark Scheme Syllabus Paper IGCSE – May/June 2007 0580/0581 01 © UCLES 2007 1 −2 B1 2 0.58 < 5 3 < 62(%) B1 Accept answer in alternative form provided equivalence is clear. 3 7 (h) 55 (min) B1 4 24 B1 5 Negative B1 6 (a) (b) Jan 26(.0) B1 B1 Not just –10.2 but ignore if included. Allow −26 7 145 + 180 or 360 − their acute angle at L 325 M1 A1 Must be clearly indicated in working or diagram. [9] 8 (a) (b)      − 3 1 (–2, –1) B1 B1 SC1 for both answers with components of (a) and coordinates of (b) reversed. i.e.       −1 3 for (a) and (–1, –2) for (b) 9 2x2+ 3xy or x(2x + 3y) B2 B1 for 3x2 − x2+ 3xy or x(3x – x + 3y) seen. SC1 for answer 2x2 − 3xy oe or 2x2 seen in final answer of 2 terms. 10 75° B2 B1 for 25° or 50° seen on diagram or clear in working that angle BCD is 25° or angle DCE is 50°. Minimum - arc seen in diagram. 11 (a) (b) Equilateral (Triangular) prism B1 B1 Not equal If qualified must be triangular (or triangle). [8] First variant Mark Scheme

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2007 0580/0581 01 © UCLES 2007 12 (y =) 3x − 1 B2 B1 for mx – 1 or 3x + c where m and c are integers with m ≠ 0 and c ≠ 5. 13 (a) (b) (c) 10 3 −2 B1 B1 B1 SC2 for 410, 23 and 5–2. SC1 for two of the above 14 (a) (b) 250 ÷ 1.19886 208 to 210.084….. 1.20 M1 A1 B1 Allow division by 1.19 to 1.2 One and only one zero is essential 15 180 – 6 360 (x =) 120 (y =) 150 M1 A1 B1ft Alt. (2 × 6 – 4) × 90 ÷ 6 oe 360 – (90 + their x) ft if positive ww. reversed answers 2 marks. Alt. (y first) 6 360 + 90 M1 150 A1 (x=) 120 B1ft 16 (a) (b) 15 × 5.40 + 5 × 3 − 80 16 20 M1 A1 B1ft ft their (a) ÷ 80 × 100 (provided profit >0) If 0 scored in parts (a) and (b) allow SC1 for 96 seen [14] First variant Mark Scheme

Page 4 Mark Scheme Syllabus Paper IGCSE – May/June 2007 0580/0581 01 © UCLES 2007 17 (a) (b) 5.1 ×108 29.4 × their (a)/ 100 art 1.5 × 108 oe B2 M1 A1cao B1 for 5.1 ×10n where n is an integer greater than 1 Calculator form; penalise 1 mark each form. May revert to given value. Answer does not need to be in standard form. (e.g. 149940000) If M0, SC1 for 3.6 × 108 18 (a) (b) (AB2 = ) 12002 + 9002 1500 tan (=) 900/1200 oe art 36.9 M1 A1 M1 A1cao Indicated by 2250000 seen Allow art 1500 if sin or cos used and (b) done before (a). For sin or cos method allow their (a) for M1 only. 19 (a) (b) (c) 263 Correct construction with arcs 109.5 B1 B2 B1 B1 without arcs, accuracy 2mm SC1 for ‘correct’ mirror image with arcs. [12] 20 (a) (i) (a) (ii) (a) (iii) (b) 50 Sum divided by 15 43.9(3…….) Attempt to order estimates 47 (Low) Extreme values oe B1 M1 A1 M1 A1 B1 Indicated by answer of 43 to 45 or calculation shown. (Total = 659) Must be at least 7 values Two very low values etc. Must not refer to extreme high values. 21 (a) (b) (c) (i) (c) (ii) 30 + 60 (seconds) 90 (seconds) D to E 1280(m) 400 used their (c)(i) divided by 400 (only) 3.2 M1 A1 B1 B1 B1 M1 A1ft SC1 for 30 or 60 seen. Any clear indication of section Allow 1270 to 1280 Also indicated by 310 or (400 – their (a)). ft correct to 3 significant figures. [13] First variant Mark Scheme

Page 5 Mark Scheme Syllabus Paper IGCSE – May/June 2007 0580/0581 01 © UCLES 2007 1 −5 B1 2 0.79 < 5 4 < 81% B1 Accept answer in alternative form provided equivalence is clear. 3 7 (h) 45 (min) B1 4 24 B1 5 Negative B1 6 (a) (b) Jan 13.2 B1 B1 Not just –10.2 but ignore if included. Allow −13.2 7 125 + 180 or 360 − their acute angle at L 305 M1 A1 Must be clearly indicated in working or diagram. [9] 8 (a) (b)      − 3 1 (–2, –1) B1 B1 SC1 for both answers with components of (a) and co-ordinates of (b) reversed. i.e.       −1 3 for (a) and (–1, –2) for (b) 9 3x2+ 2xy or x(3x + 2y) B2 B1 for 4x2 − x2 + 2xy or x(4x – x + 2y)seen. SC1 for answer 3x2− 2xy oe or 3x2 seen in final answer of 2 terms. 10 80° B2 B1 for 35° or 45° seen on diagram or clear in working that angle BCD is 35º or angle DCE is 45°. Minimum - arc seen in diagram. 11 (a) (b) Equilateral (Triangular) prism B1 B1 Not equal. If qualified must be triangular (or triangle). [8] Second variant Mark Scheme

Page 6 Mark Scheme Syllabus Paper IGCSE – May/June 2007 0580/0581 01 © UCLES 2007 12 (y =) 2x − 3 oe B2 B1 for mx – 3 or 2x + c where m and c are integers with m ≠ 0 and c ≠ 3 13 (a) (b) (c) 9 5 −2 B1 B1 B1 SC2 for 39, 25 and 6–2. SC1 for two of the above 14 (a) (b) 270 ÷ 1.19886 225 to 226.891 1.20 M1 A1 B1 Allow division by 1.19 to 1.2 One and only one zero is essential. 15 180 – 6 360 (x =) 120 (y =) 150 M1 A1 B1ft Alt. (2 × 6 – 4) × 90 ÷ 6 360 – (90 + their x) ft if positive ww. reversed answers 2 marks. Alt. (y first) 6 360 + 90 M1 150 A1 (x=) 120 B1ft 16 (a) (b) 15 × 5.80 + 5 × 3 − 90 12 13(.3…..) M1 A1 B1ft ft their (a) ÷ 90 × 100 (provided profit >0) If 0 scored in parts (a) and (b) allow SC1 for 102 seen. [14] Second variant Mark Scheme

Page 7 Mark Scheme Syllabus Paper IGCSE – May/June 2007 0580/0581 01 © UCLES 2007 17 (a) (b) 5.1 ×108 29.4 × their (a)/ 100 art 1.5 × 108oe B2 M1 A1cao B1 for 5.1 ×10n where n is an integer greater than 1. Calculator form; penalise 1 mark each form. May revert to given value. Answer does not need to be in standard form. (e.g. 149940000) If M0, SC1 for 3.6 × 108 18 (a) (b) (AB2 = ) 11002 + 8002 art 1360 tan (=) (800/1100) oe 36 to 36.03 M1 A1 M1 A1cao Indicated by 1850000 seen. For sin or cos method allow their (a) for M1 only. 19 (a) (b) (c) 276 Correct construction with arcs 119.5 B1 B2 B1 B1 without arcs, accuracy 2mm SC1 for ‘correct’ mirror image with arcs. [12] 20 (a) (i) (a) (ii) (a)(iii) (b) 50 Sum divided by 15 44.1(3…..) Attempt to order estimates 48 (Low) Extreme values oe B1 M1 A1 M1 A1 B1 Indicated by answer of 43 to 45 or calculation shown. (Total = 662) Must be at least 7 values Two very low values etc. Must not refer to extreme high values. 21 (a) (b) (c) (i) (c) (ii) 30 + 60 (seconds) 90 (seconds) D to E 1280 (m) 400 used their (c)(i) divided by 400(only) 3.2 M1 A1 B1 B1 B1 M1 A1ft SC1 for 30 or 60 seen. Any clear indication of section. Allow 1270 to 1280 Also indicated by 310 or (400 – their (a)). ft correct to 3 significant figures. [13] Second variant Mark Scheme