Cambridge IGCSE Mathematics (with coursework) 0581 — 2009 May/June Paper 1 · Variant 1

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 11 printed pages and 1 blank page. IB09 06_0580_01/2RP © UCLES 2009 [Turn over *5862600330* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0580/11, 0581/11 Paper 1 (Core) May/June 2009 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 2009 0580/11/M/J/09 For Examiner's Use 1 [ < > = Y Choose one of the above symbols to make a correct statement in the answer space. Answer 0.4 4 9 [1] 2 (a) Calculate 0.0763 1.85 + 4.7×8 . Answer(a) [1] (b) Write 0.0763 in standard form. Answer(b) [1] 3 How many glasses, each holding 200 cm3, can be filled completely from a full 4.5 litre bottle of water? Answer [2]

3 © UCLES 2009 0580/11/M/J/09 [Turn over For Examiner's Use 4 In the diagram AB is parallel to CD. Calculate the value of a. A B C D a° 5a° NOT TO SCALE Answer a = [2] 5 Hakim and Bashira measure their heights. Hakim’s height is 157 cm and Bashira’s height is 163 cm, both correct to the nearest centimetre. Find the greatest possible difference between their heights. Answer cm [2] 6 (a) Write down the gradient of the line y = 3x – 4. Answer(a) [1] (b) Write down the equation of a line through (0, 0) parallel to y = 3x – 4. Answer(b) [1]

4 © UCLES 2009 0580/11/M/J/09 For Examiner's Use 7 A and B are two points marked on a map. By measuring a suitable angle, find the bearing of A from B. North A B North Answer [2] 8 Town E is 13 kilometres due east of D. Town F is due south of E, and DF = 16 kilometres. Calculate the distance from E to F. D E F 13 km 16 km North NOT TO SCALE Answer km [2]

5 © UCLES 2009 0580/11/M/J/09 [Turn over For Examiner's Use 9 In 2007 Klaus paid 350 euros (€) for a flight from Berlin to Nairobi. The return flight from Nairobi to Berlin cost him 30 700 Kenyan Shillings (KES). The exchange rate at the time of the return flight was €1 = 79.6 KES. Calculate the difference, in euros, between the costs of the two flights. Give your answer correct to 2 decimal places. Answer € [2] 10 (a) Expand and simplify 5(3c – 4d) – 8c. Answer(a) [2] (b) Factorise pq – q2. Answer(b) [1] 11 (a) Find the lowest common multiple of 7 and 9. Answer(a) [1] (b) Without using a calculator, work out 8 5 _ 9 7 , leaving your answer as a fraction. You must show all your working. Answer(b) [2]

6 © UCLES 2009 0580/11/M/J/09 For Examiner's Use 12 z = 2x – y (a) Find z when x = –3 and y = 7. Answer(a) z = [1] (b) Make x the subject of the formula. Answer(b) x = [2] 13 The diagram shows an accurate drawing of a triangular field. 1 centimetre represents 15 metres. Florentina walks along a straight path from A to the side BC. The path is always the same distance from AB and AC. C A B (a) Using a straight edge and compasses only, construct the line of the path. You must show your construction arcs clearly. [2] (b) The path meets BC at D. How far, in metres, is Florentina from B when she reaches D? Answer(b) m [1]

7 © UCLES 2009 0580/11/M/J/09 [Turn over For Examiner's Use 14 x is an integer between 60 and 90. Write down the value of x when it is (a) an odd square number, Answer(a) x = [1] (b) 43, Answer(b) x = [1] (c) a multiple of 29, Answer(c) x = [1] (d) a prime factor of 146. Answer(d) x = [1] 15 Simplify (a) 3p × 5p3, Answer(a) [2] (b) 24q2 ÷ 8q –3. Answer(b) [2]

8 © UCLES 2009 0580/11/M/J/09 For Examiner's Use 16 The diagram shows a square tile of side 10 centimetres with 4 identical quarter circles shaded. 10 cm 10 cm Calculate the area of the unshaded region. Answer cm2 [4]

9 © UCLES 2009 0580/11/M/J/09 [Turn over For Examiner's Use 17 A B C y x 10 8 6 4 2 0 2 4 6 8 10 Points A, B and C are shown on the grid. (a) Plot the point D on the grid above so that ABCD is a rhombus. [1] (b) Write BD as a column vector. Answer(b) BD =         [2] (c) M is the mid-point of AC. Write as a column vector. Answer(c) =         [1]

10 © UCLES 2009 0580/11/M/J/09 For Examiner's Use 18 The plan of a rectangular garden with 4 triangular flowerbeds is shown in the diagram. (a) Write down the name of the special triangles that are (i) shaded, Answer(a)(i) [1] (ii) unshaded. Answer(a)(ii) [1] (b) State the order of rotational symmetry of the plan. Answer(b) [1] (c) Draw the lines of symmetry on the plan. [2]

11 © UCLES 2009 0580/11/M/J/09 For Examiner's Use 19 A school has 350 students. (a) On the school sports day 96% of the students were present. Calculate how many students were absent. Answer(a) [2] (b) The table shows the number of students attending school in one week. Monday Tuesday Wednesday Thursday Friday 334 329 348 341 323 For these values, (i) calculate the mean, Answer(b)(i) [2] (ii) find the median, Answer(b)(ii) [1] (iii) find the range. Answer(b)(iii) [1]

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. 0580/11/M/J/09 BLANK PAGE

This document consists of 11 printed pages and 1 blank page. IB09 06_0580_12/RP © UCLES 2009 [Turn over *4608374430* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0580/12, 0581/12 Paper 1 (Core) May/June 2009 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 2009 0580/12/M/J/09 For Examiner's Use For Examiner's Use 1 [ < > = Y Choose one of the above symbols to make a correct statement in the answer space. Answer 7 9 0.7 [1] 2 (a) Calculate 0.0584 1.65 + 5.2×7 . Answer(a) [1] (b) Write 0.0584 in standard form. Answer(b) [1] 3 How many glasses, each holding 200 cm3, can be filled completely from a full 3.5 litre bottle of water? Answer [2]

3 © UCLES 2009 0580/12/M/J/09 [Turn over For Examiner's Use For Examiner's Use 4 In the diagram AB is parallel to CD. Calculate the value of a. A B C D a° 5a° NOT TO SCALE Answer a = [2] 5 Hakim and Bashira measure their heights. Hakim’s height is 159 cm and Bashira’s height is 167 cm, both correct to the nearest centimetre. Find the greatest possible difference between their heights. Answer cm [2] 6 (a) Write down the gradient of the line y = 3x – 4. Answer(a) [1] (b) Write down the equation of a line through (0, 0) parallel to y = 3x – 4. Answer(b) [1]

4 © UCLES 2009 0580/12/M/J/09 For Examiner's Use 7 A and B are two points marked on a map. By measuring a suitable angle, find the bearing of A from B. North A B North Answer [2] 8 Town E is 14 kilometres due east of D. Town F is due south of E, and DF = 17 kilometres. Calculate the distance from E to F. D E F 14 km 17 km North NOT TO SCALE Answer km [2]

5 © UCLES 2009 0580/12/M/J/09 [Turn over For Examiner's Use 9 In 2007 Klaus paid 350 euros (€) for a flight from Berlin to Nairobi. The return flight from Nairobi to Berlin cost him 30 700 Kenyan Shillings (KES). The exchange rate at the time of the return flight was €1 = 79.6 KES. Calculate the difference, in euros, between the costs of the two flights. Give your answer correct to 2 decimal places. Answer € [2] 10 (a) Expand and simplify 4(5c – 3d) – 7c. Answer(a) [2] (b) Factorise m2 – mn. Answer(b) [1] 11 (a) Find the lowest common multiple of 7 and 9. Answer(a) [1] (b) Without using a calculator, work out 8 5 _ 9 7 , leaving your answer as a fraction. You must show all your working. Answer(b) [2]

6 © UCLES 2009 0580/12/M/J/09 For Examiner's Use 12 z = 2x – y (a) Find z when x = –3 and y = 7. Answer(a) z = [1] (b) Make x the subject of the formula. Answer(b) x = [2] 13 The diagram shows an accurate drawing of a triangular field. 1 centimetre represents 15 metres. Florentina walks along a straight path from A to the side BC. The path is always the same distance from AB and AC. C A B (a) Using a straight edge and compasses only, construct the line of the path. You must show your construction arcs clearly. [2] (b) The path meets BC at D. How far, in metres, is Florentina from B when she reaches D? Answer(b) m [1]

7 © UCLES 2009 0580/12/M/J/09 [Turn over For Examiner's Use 14 x is an integer between 60 and 90. Write down the value of x when it is (a) an odd square number, Answer(a) x = [1] (b) 43, Answer(b) x = [1] (c) a multiple of 29, Answer(c) x = [1] (d) a prime factor of 146. Answer(d) x = [1] 15 Simplify (a) 4d × 6d 4, Answer(a) [2] (b) 28t3 ÷ 7t –4. Answer(b) [2]

8 © UCLES 2009 0580/12/M/J/09 For Examiner's Use 16 The diagram shows a square tile of side 10 centimetres with 4 identical quarter circles shaded. 10 cm 10 cm Calculate the area of the unshaded region. Answer cm2 [4]

9 © UCLES 2009 0580/12/M/J/09 [Turn over For Examiner's Use 17 A B C y x 10 8 6 4 2 0 2 4 6 8 10 Points A, B and C are shown on the grid. (a) Plot the point D on the grid above so that ABCD is a rhombus. [1] (b) Write BD as a column vector. Answer(b) BD =         [2] (c) M is the mid-point of AC. Write as a column vector. Answer(c) =         [1]

10 © UCLES 2009 0580/12/M/J/09 For Examiner's Use 18 The plan of a rectangular garden with 4 triangular flowerbeds is shown in the diagram. (a) Write down the name of the special triangles that are (i) shaded, Answer(a)(i) [1] (ii) unshaded. Answer(a)(ii) [1] (b) State the order of rotational symmetry of the plan. Answer(b) [1] (c) Draw the lines of symmetry on the plan. [2]

11 © UCLES 2009 0580/12/M/J/09 For Examiner's Use 19 A school has 360 students. (a) On the school sports day 95% of the students were present. Calculate how many students were absent. Answer(a) [2] (b) The table shows the number of students attending school in one week. Monday Tuesday Wednesday Thursday Friday 334 329 348 341 323 For these values, (i) calculate the mean, Answer(b)(i) [2] (ii) find the median, Answer(b)(ii) [1] (iii) find the range. Answer(b)(iii) [1]

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. 0580/12/M/J/09 BLANK PAGE

Location Entry Codes 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 2009 question paper for the guidance of teachers 0580, 0581 MATHEMATICS 0580/11, 0581/11 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, 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 May/June 2009 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses. First variant Mark Scheme

Page 2 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2009 0580, 0581 11 © UCLES 2009 Abbreviations cao correct answer only ft work has been followed through after an error isw ignore subsequent working oe or equivalent SC Special Case soi seen or implied ww without working Qu. Answers Mark Part Marks 1 < 1 ( accept ≤ or both symbols) 2 (a) (b) 0.00193(4….) or 1.93(4…) × 10–3 7.63 × 10–2 1 1cao 3 22 2 M1 for 4500 ÷ 200 or 4.5 ÷ 0.2 4 30 2 M1 for a + 5a = 180 or 6a = 180 or 5a + 5a + a + a =360 or better 5 6.999…. to 7 2 M1 for 156.5 or 163.499… to 163.5 seen 6 (a) (b) 3 y = 3x oe 1cao 1ft Allow y = 3x + 0 or y = 3x − 0 Must be an equation. i.e. y = ….. 7 328 ± 2 (ie 326 to 330) 2 W1 for angle of 32 ± 2 or 58 ± 2 or 148 ± 2 seen on diagram or in working or in the answer space. 8 9.33 or 9.327(…) 2 M1 for 162 − 132 as chosen method. Alt. Trig must be complete correct method for M1. 9 35.68 2cao M1 30700 ÷ 79.6 SC1 for 2840(KES). Units need to be seen in the working or on answer line. 10 (a) (b) 7c − 20d www final answer q(p − q) www 2 1 M1 for 15c − 20d − 8c or better or W1 for 7c or − 20d seen as terms in final answer First variant Mark Scheme

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2009 0580, 0581 11 © UCLES 2009 11 (a) (b) 63 63 ) 9 5 8 7 ( their × − × oe 63 11 final answer 1 M1 A1ft ft their (a) 12 (a) (b) (z =) − 13 (x =) 2 y z + oe final answer 1cao 2 M1 for z + y = 2x or 2 z = x − 2 y or –2x = –z – y SC1 for answer of form 2 ± ± ± y z 13 (a) (b) Correct ruled line with correct arcs and at 30° to 34° to the line AB. 105(m) to 112.5(m) W2 1ft W1 for correct ruled line, 30° to 34° to AB (i) with correct arcs but short of BC or (ii) reaching BC with wrong or absent arcs. 15 × their DB (±2mm) 14 (a) (b) (c) (d) 81 64 87 73 1cao 1cao 1cao 1cao 15 (a) (b) 15p4 final answer 3q5 final answer 2 2 W1 for 15pn (n ≠ 0) or kp4 (k ≠ 0) W1 for 3qn (n ≠ 0) or kq5 (k ≠ 0) 16 21.45 to 21.6 www 4 M1 10 × 10 or 100 M1 indep π × r2 where r is 5, 4.4 or 4.5 M1 dep Subtraction of the two areas. Dependent on both first two M1’s or Alternative method Alt. M1 r × r where r is 5, 4.4 or 4.5 M1 ind 4 1 π × r2 where r is 5, 4.4 or 4.5 M1 dep 4 × subtraction of the two areas. Dependent on both first two M1’s Follow one method only. or W3 art 36.4 or art 39.2 www First variant Mark Scheme

Page 4 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2009 0580, 0581 11 © UCLES 2009 17 (a) (b) (c) D plotted at (3, 7)      − 4 4       3 3 1 2ft 1cao Within 1 mm by eye. 1 mark for each component −1 if in working, no brackets SC1 Both (b) and (c) correct but written as coordinates. 18 (a) (i) (ii) (b) (c) Isosceles Equilateral 2 or two Correct horizontal and vertical ruled lines. By eye and to or beyond the edges of the plan. 1 1 1 1, 1 Allow order (=) 2 SC1 Both freehand and ‘correct’ accuracy by eye to or beyond edge of the plan or both short of the full figure. −1 for each additional line. 19 (a) × × × (b) (i) (ii) (iii) 14× × 335× 334 25 ×2× × ×2× 1cao 1cao M1 for 350 × 4 ÷ 100 or M1 for 350 − (350 × 96 ÷ 100) M1 Attempt at sum of the 5 values ÷ 5 SC1 for mean and median correct but reversed First variant Mark Scheme

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2009 question paper for the guidance of teachers 0580, 0581 MATHEMATICS 0580/12, 0581/12 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, 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 May/June 2009 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses. Second variant Mark Scheme

Page 2 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2009 0580, 0581 12 © UCLES 2009 Abbreviations cao correct answer only ft work has been followed through after an error isw ignore subsequent working oe or equivalent SC Special Case soi seen or implied ww without working Qu. Answers Mark Part Marks 1 > 1 ( accept ≥ or both symbols) 2 (a) (b) 0.00153(48….) or 0.001535 or 1.53(4…) × 10–3 or 1.535 × 10–3 5.84 × 10–2 1 1cao 3 17 2 M1 for 3500 ÷ 200 or 3.5 ÷ 0.2 4 30 2 M1 for a + 5a = 180 or 6a = 180 or 5a + 5a + a + a =360 or better 5 8.999…. to 9 2 M1 for 158.5 or 167.499… to 167.5 seen 6 (a) (b) 3 y = 3x oe 1cao 1ft Allow y = 3x + 0 or y = 3x − 0 Must be an equation. i.e. y = ….. 7 328 ± 2 (ie 326 to 330) 2 W1 for angle of 32 ± 2 or 58 ± 2 or 148 ± 2 seen on diagram or in working or in the answer space. 8 9.64 or 9.643(6…) or 9.644 2 M1 for 172 − 142 as chosen method. Alt. Trig must be complete correct method for M1. 9 35.68 2cao M1 30700 ÷ 79.6 SC1 for 2840(KES). Units need to be seen in the working or on answer line. 10 (a) (b) 13c − 12d www m(m − n) www 2 1 M1 for 20c − 12d − 7c or better or W1 for 13c or − 12d seen as terms in final answer Second variant Mark Scheme

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2009 0580, 0581 12 © UCLES 2009 11 (a) (b) 63 63 ) 9 5 8 7 ( their × − × oe 63 11 final answer 1 M1 A1ft ft their (a) 12 (a) (b) (z =) − 13 (x =) 2 y z + oe final answer 1cao 2 M1 for z + y = 2x or 2 z = x − 2 y or –2x = –z – y SC1 for answer of form 2 ± ± ± y z 13 (a) (b) Correct ruled line with correct arcs and at 30° to 34° to the line AB. 105(m) to 112.5(m) W2 1ft W1 for correct ruled line, 30° to 34° to AB (i) with correct arcs but short of BC or (ii) reaching BC with wrong or absent arcs. 15 × their DB (±2mm) 14 (a) (b) (c) (d) 81 64 87 73 1cao 1cao 1cao 1cao 15 (a) (b) 24d 5 final answer 4t 7 final answer 2 2 W1 for 24d n (n ≠ 0) or kd 5 (k ≠ 0) W1 for 4t n (n ≠ 0) or kt 7 (k ≠ 0) 16 21.45 to 21.6 www 4 M1 10 × 10 or 100 M1 indep π × r2 where r is 5, 4.4 or 4.5 M1 dep Subtraction of the two areas. Dependent on both first two M1’s or Alternative method M1 r × r where r is 5, 4.4 or 4.5 M1 ind 4 1 π × r2 where r is 5, 4.4 or 4.5 M1 dep 4 × subtraction of the two areas. Dependent on both first two M1’s Follow one method only. or W3 art 36.4 or art 39.2 www Second variant Mark Scheme

Page 4 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2009 0580, 0581 12 © UCLES 2009 17 (a) (b) (c) D plotted at (3, 7)      − 4 4       3 3 1 2ft 1cao Within 1 mm by eye. 1 mark for each component −1 if in working, no brackets SC1 Both (b) and (c) correct but written as coordinates. 18 (a) (i) (ii) (b) (c) Isosceles Equilateral 2 or two Correct horizontal and vertical ruled lines. By eye and to or beyond the edges of the plan. 1 1 1 1, 1 Allow order (=) 2 SC1 Both freehand and ‘correct’ accuracy by eye to or beyond edge of the plan or both short of the full figure. −1 for each additional line. 19 (a) × × × (b) (i) (ii) (iii) 18× × 335× 334 25 ×2× × ×2× 1cao 1cao M1 for 360 × 5 ÷ 100 or M1 for 360 − (360 × 95 ÷ 100) M1 Attempt at sum of the 5 values ÷ 5 SC1 for mean and median correct but reversed Second variant Mark Scheme