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Notes Mark Scheme Syllabus IGCSE EXAMINATIONS JUNE 003 0580/058 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. b.o.d. c.a.o. e.e.o. o.e. SC s.o.i. ww www Anything rounding to Benefit of the doubt has been given to the candidate Correct answer only (i.e. no follow through ) Each error or omission Or equivalent Special case Seen or implied Without working Without wrong working Work followed through after an error: no further error made Work followed through and another error found

June 003 INTERNATIONAL GCSE MARK SCHEME MAXIMUM MARK: 56 SYLLABUS/COMPONENT: 0580/0, 058/0 MATHEMATICS Paper (Core)

Page Mark Scheme Syllabus Paper IGCSE EXAMINATIONS JUNE 003 0580/058 * indicates that it is necessary to look in the working following a wrong answer. (a) 9.5549(345) 9.55 (a) 3.3 to 3.7 3-0.9 33 (a) 67% 0.68 50 7 5 Allow negative values.6 - I(a)I Allow 0.66, 0.67, 0.68 o.e. 4 4 * M 7 5 78000 * M for 550 000 x.4 6 366 * M for "97.60" x 3.75 7 4 9 8 (a) - 30 c.a.o. 9 v(4u 3) * M for 4 9 or 0.44..., 4, 3, 3 c.a.o. 3* M 6 3x M x + 3x = 6 4 0 (a) 0.004 4 x 0-3 * M figs : 500000 or figs 4 in answer a = 3, b = - 3* M adding or x nd equation by 3 and subtracting A A o.e. (Rearrange and substitute scores M) (a) 88 c.a.o. 85.5, 86.5 3 (a) 0 05 (i) 0.4 (ii) 4, * Working essential if only one answer is correct Not 88.0 B both correct and reversed Allow 0:05, 8.05pm. Not 0.5 or 0h5m M 30 75 (i) 60 University of Cambridge Local Examinations Syndicate 003 9Dwebsite.tk

Page Mark Scheme Syllabus Paper IGCSE EXAMINATIONS JUNE 003 0580/058 4 (a) 3 4 6 = 6 7 * M for first term o.e. 6 7 x = 5 4 0 * M for improper fractions 5 (a) (i) 8 (ii) 76 pyramid 6 (a) 90 7.7 (c) 3 7 (a) 9.59 * * * * M for ½ x 8 x 7 M for 4 x (i) + 8 A M sin40 = PB/ or = PB sin(a) sin40 M x 6 M 8.3 + 4.8 0 8 (a) (i) 35 (ii) 5 3* 4.8 M tan x = M 80 + x at P 8.3 If sin or cos used then allow from (a). NO marks for scale drawing 60 (i) similar (c) (.0) * M 6.6 = CX o.e. Not. 8.3 5.5 6.6 CX or M for = sin0 sin35 TOTAL 56 University of Cambridge Local Examinations Syndicate 003 9Dwebsite.tk

November 003 INTERNATIONAL GCSE MARK SCHEME MAXIMUM MARK: 56 SYLLABUS/COMPONENT: 0580/0, 058/0 MATHEMATICS Paper (Core)

Page Mark Scheme Syllabus Paper IGCSE EXAMINATIONS NOVEMBER 003 0580/058 Question Part Mark Scheme Details Number Mark 400 (grams) 5 ($).7(0) M for 8 o.e. 00 85 SC for 8 = 5. 3 00 3 (a) Accept equivalent fractions, 5 decimals, percentages (with sign) 0 0 0 accept, do not accept, 5 k none, not but condone it with 0 4 (a) 6 o 44 40(%) M for 00 o.e. 360 3 5.7(0 ) M for 5 sin 0 o or 5 cos70 or.7 6 60 6 M for,, 6 or 0 0 7 44 o ( 0 4) 90 3 M for or 0 ( 0 ) 80 or 0 360 80. 0 6 60 3 After 0, SC for answer 36 o 8 50 r.l. < 350 + SC if reversed 9 (a) 0x 5xy B for one term correct 6x (x + ) M for 6(x + x) or x(6x + ) or (3x + 6x) or x(3x + 6) or 3(x + 4x) or 3x(x + 4) 0 (a) 87 o 4 8 o (c) 6 o f.t. is (90 y) 3 University of Cambridge Local Examinations Syndicate 003 9Dwebsite.tk

Page Mark Scheme Syllabus Paper IGCSE EXAMINATIONS NOVEMBER 003 0580/058 Lines may be freehand but must go completely through the shape Any line through the centre 3 x = 4, y = 3 M for attempting to eliminate one unknown by a correct method A for one correct value (x or y) 3 3 (a) (i).4096 (ii).4 f.t. from (i) 9.3 or 9.3(6 ) B for.68 seen or implied by 9. 4 4 (a) Monday, Tuesday and Saturday All three and no extras -o 3 B for 4 seen + M for (their 4) 7 4 5 (a) (i) 0.8 (ii) 0.75 (iii) 0.857 or 0.86 4 75 000, 8%, 7 or equivalent f.t. from (a) 6 (a) 4.58(m) M for 66.4o or 66.3o 66.45o 5 s.o.i. e.g. 4 M for cos - o.e. incl 5 University of Cambridge Local Examinations Syndicate 003 9Dwebsite.tk

Page 3 Mark Scheme Syllabus Paper IGCSE EXAMINATIONS NOVEMBER 003 0580/058 7 (a) 3 0 8 etc. penalise once only -4 accept 04 (c) 0 4 (d) - 8 (a) 0.4 or.6 B for one correct SC if (0.4,0) (.6,0) (i) 0 (ii) Correct line from x = - to x = 4 Must be ruled 6 (c) (0,), (4,5) B for one correct f.t. from (ii) University of Cambridge Local Examinations Syndicate 003 9Dwebsite.tk

June 004 INTERNATIONAL GCSE MARK SCHEME MAXIMUM MARK: 56 SYLLABUS/COMPONENT: 0580/0, 058/0 MATHEMATICS Paper (Core)

Page Mark Scheme Syllabus Paper MATHEMATICS JUNE 004 0580/058 39 84 Ignore any or no units after answer. Allow 8400cm. 3 (a) 3 4 final answer 7 00 final answer 4 (a) 49 3 5 4.5(0) M for 8 x 5 or 450 or 4m 50cm seen (8:450 and 8:4.5 also indicate M) 6 4 or 9 or 8 4 or 4 9 4 M for 4 x () seen. Allow SC for 4.5 or 4 oe seen with incomplete or decimal working.( 9 4 or oe or.5 0.5) () Answer only, no working, is 0. 7 4.5, 4.5 for each answer SC for both values correct but wrong way round. 8 x( y 3z) M for ( xy 3xz) or x( 4y 6z ) or x(wrong expression) Allow omitted last bracket. 9 90.48 or 90.47 or 90 M for 00.05, implied by 90.(..) Not allow 90.5 or 90.4 or 90.00 for marks 0 (a) 0 (a) and reversed no marks 8 (a) 0 B for Q = 35 s.o.i.(can be on diagram) 70 seen implies B. (a) 3 0 3 (a)(i) 00 40 (a)(ii) 5f.t. Only f.t. for simple mental calculation. E.g. 0 40 = 5.5 or 00 30 = 6 or 7 or 6 3 or 6.6 or 6.66 etc 5.6 4 B or nd dependent on M, M 3 M for a correct method for bottle, implied by figs 65 or 65 seen or figs 65 or 53 seen. M(dep) for a complete correct method with consistent units. (Implied by a correct pair of values seen. Alt. Method completely correct is M 5.65 or.649(.) 3 M for sin 3 = h 5 M (dep) for h = 5sin 3 (.6. implies M provided no obvious scale drawing, which is zero) Other methods can be split similarly. From grads.409 or radians.757 implies M 3 University of Cambridge International Examinations 004 9Dwebsite.tk

Page Mark Scheme Syllabus Paper MATHEMATICS JUNE 004 0580/058 6 (a) 3 M for 3 + 6 seen y a or y a oe M for a correct step, for clearly dividing by b or y a seen. b b b Allow a y b 7 Bar Chart 4 S correct scale and equal width bars. (Lost for vertical lines drawn) B all bars correct height or B for any bars correct height. Dots or line graph is B0. L correct labels. 8 (a) $4.5(0) M for 50 x ( 0.5 or 5) or $.5(0) or 50 seen, or 0.5 8 50 = (0.09) or 5 800 50 = ( 9) * 56.5 or 56 or 56.3 or 56. f.t. M for their (a)/8 x 00 or their profit for orange 00 their cost for orange 9 (a) 86 to 88 or 830 M for π x 30 or π 0.3 and method not spoilt. * 6.(080) to 6.(40) or 6.(4 ) f.t. M for his (a) 80 s.o.i. or correct f.t. answer seen in cubic centimetres. 6 0 (a) 9 M for 3 + 5 or 3 5 or x.5 = 7.75 4 4 M for 4y 0 = 36 or y 5 = 9 or better. (a) 00 5 or 5am Ignore am added to 00 5 (i) * 7 h 30min f.t. f.t. their (a) Allow 7 or 7.5 hours Allow a clear time in words. E.g. 5 minutes after midnight. Not 5 or 4 5 (ii) * 749.(33.) f.t. 3f.t. B for their 7.5 or 7 or their 450 minutes and (finally) multiplied by 60 used. M for 560/their time (independent of B) (f.t. dependent on B and M) [Watch for 560 7.3 = 769.(86 ) implies B0 M.] 9 University of Cambridge International Examinations 004 9Dwebsite.tk

November 004 INTERNATIONAL GCSE MARK SCHEME MAXIMUM MARK: 56 SYLLABUS/COMPONENT: 0580/0, 058/0 MATHEMATICS Paper (Core)

Page Mark Scheme Syllabus Paper IGCSE EXAMINATIONS NOVEMBER 004 0580/058 Number Answers Mark Notes 7 Not -7 (0-5) x (9 + 3) Ignore omission of final bracket only 3 0.56 B for 5 9 or digits 55 (.) or digits 56 Common answer for B is 0.55 4 (a) 00 400 5.5 (0...) 5 M for x 3.6 (4 + 3 + 5) SC for. or 0.9 (ie. Wrong ingredient) 6 (a) 70 (0)45 7 Obtuse Reflex 8 5 + One mark each component. If 0 only number 5 in bracket allow mark. If 0 scored SC for or 4 4 0 seen, or 5 Ignore a line between Components 9 3 0 x 5 7 M Only acceptable method. 30 6 = or 35 7 3 6 = 7 7 E University of Cambridge International Examinations 005 9Dwebsite.tk

Page Mark Scheme Syllabus Paper IGCSE EXAMINATIONS NOVEMBER 004 0580/058 0 (a) a 7 b Allow b (a) < = (a) 3 Ignore any added words 3 Net of the pyramid. A square with 4 equal isosceles triangles correctly positioned. for a square for all 4 triangles, isosceles or equilateral. Reasonable accuracy by eye. Ignore any tabs shown. 4 6.66 cao 3 M for 0.5 x 9.60 (implied by.94 seen) M for 9.60 his.94 (allow if.94 is rounded to.90, method only) or M for 0.85 x 9.60 [allow for ( 0.5) x 9.60] Answer 666 marks, 670 mark ww. 6.7(0) implies M 5 4500 3 M for 350 x 350 x 00 or 3.5 x 3.5 x soi A for 4500000 or 4.5 seen B for his volume correctly converted to litres. 6 (a) (i) (base) = 7.5 (ii) (height) = 5.5 0.6 (5) or 0.6 or 0.6 (3) f.t. 7 (a) 08 89.38 final answer ft. Allow marks for correct answers reversed. Allow mark for one of the answers seen in either (i) or (ii). A correct calculation of the area using his values of base and height regardless of his values. M for his (a) x 8.78 soi or SC for answer in cents. University of Cambridge International Examinations 005 9Dwebsite.tk

Page 3 Mark Scheme Syllabus Paper IGCSE EXAMINATIONS NOVEMBER 004 0580/058 8 (a),,3,5,6,0,5,30 cao or x 30, x 5, 3 x 0, 5 x 6 cao,3,5 or x 3 x 5 9 (a) 6 (hours) 45 (minutes) 6 rounds to 5.6 or 5 7 0 (a) 0 35 4 oe or 0.4 (...) or.4% (a).34 x 0 3.6 x 0 6 (a) diameter (i) rounds to 30.8 or 30.9 (ii) rounds to 56.5 or 56.6 f.t. 3f.t. B for 4 correct factors, none incorrect. All the correct primes from his part (a), and at least one prime and no non-primes. B for 6.75 or 6 4 3 oe used or his time correctly converted to hours. M for 355 his time. (any form) (55.0 or 0.87.ww implies M) A f.t. provided his (a) correctly converted to hours. M for 7 x 35 3 M for - + soi or 7 5 [35 - (his (a) + 5 3 x 35] 35 0. or % seen imply M SC for figs 34 seen or.3 x 0 3 SC for figs 6 seen or.3 x 0 6 M for 0.5 x π x or + π x (implied by rounding to8.8 or 8.9 or 49.7 seen) M for using π x 6 (implied by 3 (. ) seen University of Cambridge International Examinations 005 9Dwebsite.tk

June 005 IGCSE MARK SCHEME MAXIMUM MARK: 56 SYLLABUS/COMPONENT: 0580/0, 058/0 MATHEMATICS Paper (Core)

Page Mark Scheme Syllabus Paper IGCSE JUNE 005 0580/058 Question Answers Mark Notes 393000 Allow 393000.0 or.393 0 6 9 or 3 30 0 or 0.3 or 30% isw isw only for incorrect cancelling 3 40 4 35 : 8 ignore consistent units 5 64 B for 4 3 or 4 6 (a) only 3 only M for 3500 or 0.8 seen. SC Reversed SC for : 8 or 4 3 35 : ( :) or 35k : 8k 35 8 8 (decimal form for SC correct to 3sf) () 3 or (±) 64 seen. decimal form only B0 7 63 M for 8 4 x 9 (can be implied by 4 63.64 or 63.63 implies M 8 9 www B for 7 or (+)8 seen 9 55 weight < 65 mark for each. Allow 55.0 and 65.0 SC for fully correct but reversed 0 3.3 or 3.308 or 3.307(.) 7 M for sin6 (implied by 0.8 or better) Grads.98. implies M. 3.3ww no marks 900 M for (5000 x 3 x 6) 00 oe or B for 300 seen SC for 5900 (s =) (p + q)/t or p + q oe t 3 (a) similar 45 5 ) B for p + q seen or correct by t or p/t = s q/t or (p q)/t SC for p + q/t or p/t + q 4 rounds to 40 isw (isw only for incorrect rounding eg 43 = 4) M for π 5 (or π.5 0. ) SC if π 30 calculated correctly (rounds to 5650 or 5660) (allow 3(.0)used).4 cm 3 is marks,.4 or 5.65 implies M 5 (a) multiple of 4 4 6 (a) 3 isw 43 (c) 4n + 3 oe final answer ft 4 ignore extras if lowest correct M for a correct attempt at two equivalent fractions (e.g.. 5 8 3 6 48 and 48 seen or better) ww. and decimals alone zero ignore extras even if incorrect their (a) + 0 allow any unsimplified form e.g. 7 + (n ) 4 or 7 + 4n 4 University of Cambridge International Examinations 005 9Dwebsite.tk

Page Mark Scheme Syllabus Paper IGCSE JUNE 005 0580/058 7 (a) 4x + 7 final answer x (5x 7) B for 3x + or 4x or +7 seen (+7 strictly www) condone missing final bracket 8.45 3 B for.0 or.35 seen. (or 0 or 35) M for 5 their (.5 0.8 + 3 0.45) or 500 their (.5 80 + 3 45) 9 (a) (i) 9 3 3 (ii) (equals).0 ft allow slip of denominator as 3.0 or 3.00 (not allow zeros in other figures) their (a)(i) provided order of operation is as seen and both (a)(i) and (a)(ii) are to a maximum of dp apart from zeros 0 (a) Panama, (Guyana), Colombia, Brazil 5 (a) 5.6(0) oe (allow 5 3 5 ) (a) 0.4(0) oe www (allow 5 ) 0 (c) on the graph (d) (allow 0 < time < 5) (allow from calculation) 3 (a) 90 65 (c) 5 ft 5 ft ft ft 0 allow figures if correct M for (.4 0 6 ) (.5 0 5 ) implied by figs 53(0 ) M for 35 00 6 SC for $0.40 $8 their (a) if positive result from their (a) allow saving calculated from comparing costs or savings M for use of distance time with figures. 5/0.5, 5/30, 5/6, 5/0.30 only. Not 5/8.00, 5/0.3 ruled single line from 8.00 am home continued to school, km line. Ignore beyond km line must cross within square ft their intended single straight line (need not be ruled) and within a square, not on the boundary unless actually on a boundary M for 80 5 their (a) [55 their (a)] ft. 90 their B for angle DEB = 90 used or B for angle CEB = 65 seen University of Cambridge International Examinations 005 9Dwebsite.tk

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the November 005 question papers 0580/058 MATHEMATICS 0580/0, 058/0 Paper (Core), maximum raw mark 56 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 initially instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners meeting before marking began. Any substantial changes to the mark scheme that arose from these discussions will be recorded in the published Report on the Examination. 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 discussion or correspondence in connection with these mark schemes. The minimum marks in these components needed for various grades were previously published with these mark schemes, but are now instead included in the Report on the Examination for this session. CIE is publishing the mark schemes for the November 005 question papers for most IGCSE and GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

Page Mark Scheme Syllabus Paper IGCSE NOVEMBER 005 0580/058 Question Answers Mark Notes.0(00) x 0 4 x(3y ) 3 6950 4 5 5 5x = 8 + 7 or better seen. M (Correct first step) (x = ) 3 A 6 SC correct method seen or better. 8 7 (a) 0 (allow 0) 8 P b = a M P b A oe 9 (a) 7 Allow 0.07 or 7% 00 7% 7 Allow 0.7 or 00 (c) 0.07 and 7.% In this form. [5] 0 (a) (c) 6 or 67 63 64 (a) 5 mark for each correct component. Correct Vector Drawn height M (alt. method) 00 seen B sin = oe or better. C s 00 sin o M 430 (.0...) A f.t. 0.43(0 ) 430(.0.) A Bft 3 (Decrease) 00 000 B 500000 (alt. method) x 00 or 9.5 B 700000 subtract answer from 00 M Their 00 000 M 00 700 000 4 (a) (c) 7.4 or 7.40(7.) A > < < [5] University of Cambridge International Examinations 005 9Dwebsite.tk

Page Mark Scheme Syllabus Paper IGCSE NOVEMBER 005 0580/058 Question Answers Mark Notes 5 (a) (i) (ii) 0.5 not 0.50 0 6 x c s 0.5 = 7 7.0908 f.t. 6 (a) (c) 7 (a) 3r 3s or 3(r s) q or q p 4 A clear attempt to multiply each by 3 and add, or equivalent. 60 9 M A f.t. 8 (a) 60 Their (a) π 50.9(..) or 5 M A 9 (a) (c) 9.5 or 9. or 9.3 8 Their (a).0 4 M A [6] 0 (a) 35 00 900 M =35 A (Payments) 70 B Deposit + Payments 900 M 35 A f.t. (a) 6 (c)(i) Ruled line through (0, 0) and (, 6) B Through and further than (5, 80) B (ii) 5 f.t. [0] Only f.t. c s (a) if it is 0.4 (0) or 0.50 or 0 Allow 7.6 or 8 from 0.4 Must be a clear use of Dalila s intended total from (a) subtract Implied by 3.3 or 3. (...) seen Implied by 035 seen No follow through for negative answer Dependent Intersection of their line with the given line. University of Cambridge International Examinations 005 9Dwebsite.tk

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 006 question paper 0580 and 058 MATHEMATICS 0580/0 and 058/0 Paper, maximum raw mark 56 These mark schemes are published as an aid to teachers and students, to indicate the requirements of the examination. They show the basis on which Examiners were initially instructed to award marks. They do not indicate the details of the discussions that took place at an Examiners meeting before marking began. Any substantial changes to the mark scheme that arose from these discussions will be recorded in the published Report on the Examination. 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 minimum marks in these components needed for various grades were previously published with these mark schemes, but are now instead included in the Report on the Examination for this session. CIE will not enter into discussion or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the May/June 006 question papers for most IGCSE and GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

Page Mark Scheme Syllabus Paper IGCSE May/June 006 0580 and 058 0 7 0.09 9% 9 00 3 0000 or x 0 4 oe. 4 (a) 7 Any multiple of 70 (e.g. 490) 5.7(4.) M for attempt at cube root of 0 6 (a) 0.075976(.) 0.076 f.t. f.t. candidates (a) 7 345000 355000, 8 x(x 3y) M for (x 3xy) or x(x 6y) or x( ) 9 (a) (i) 4 oe. 0 (ii) 0 7 o.e. 0 (a) p 5 q 7 (c) r 6 9 University of Cambridge International Examinations 006 9Dwebsite.tk

Page Mark Scheme Syllabus Paper IGCSE May/June 006 0580 and 058 0 (a) ($) 5 ($) 55.5 M for 500 x.05 or (c s (a) + 500) x.05 (a) A- correct lines and B-6 correct lines, Allow not ruled and small inaccuracies. 3 (x=) 5, (y=) 3 3 M correct method to eliminate y or x. (add equations or correct multiply and subtract) 4 (a) 6 (h) 50 (min) A, A ww allow SC for correct answer. ww both correct, full marks. 37.5 (%) B for 9 (hours) seen or M for c s 9 4 x 00 5 (a) 3 Parallel oe. CD is 3 times as long as AB oe. 6 (a) (hockey) 05, (cricket) 30 mark each correct entry. Correct line on pie chart to divide hockey and cricket. (30 ± ) degrees to left of vertical oe. ft ft only if the angles in (a) total 35 (c) Football 9 University of Cambridge International Examinations 006 9Dwebsite.tk

Page 3 Mark Scheme Syllabus Paper IGCSE May/June 006 0580 and 058 0 7 (a) 54 M for 90 5 x 3 9.5(.) M for 57.5 (π) or SC for 57.5 π. (implied by 8.3 ) 8 (a) Net of the cuboid M for a net with 6 correct size rectangles. A for a fully correct net. 5 ft M for 5 or 6 areas calculated and added or SC for answer of 6. ft only if 5 or 6 rectangles are shown in part (a). 9 (Joseph $) 7.5(0) M for 30 x 7. (Maria $) 9 M for 30 00 x 30. (Rebecca $) 3.50 ft 30 c s Joseph c s Maria. 0 (a).3 x 0 6 M for 000 x 565 seen or B for figs 3 4.4(.) x 0 3 M for 5 565 soi and B for figs 44(.) 8 0 Total 56 University of Cambridge International Examinations 006 9Dwebsite.tk

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 006 question paper 0580, 058 MATHEMATICS 0580/0, 058/0 Paper (Core), maximum raw mark 56 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 006 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

Page 3 Mark Scheme Syllabus Paper IGCSE - OCT/NOV 006 0580, 058 Question Answers Mark Notes 3. ( 3 4 ) + 5 = 3 & no other brackets 3 Negative (allow ve) Not allow N or n or No 4 8 5.09 or. Not.0 6 a( ab 3 ) final answer. SC for ( a b 3a ) or a( ab 6 ) or a( ab + 3 ) or a( ab 6 ) final answer. 7 (a) 0.056 (Answers may be in standard form) 5300 8 3x 6 y 3 or 3(x y) 3 SC for x 6 or y 3 seen in final answer 9 (a) 79507 80000 0 6 0 33 50 ft ft provided (a) > 500 and not a multiple of 000. SC for reverse order. 3 M- at least fractions correctly compared in the same form. (decimal, percentage or common denominator) 5 (x = ) 5 6 oe isw M for - + 8 = 0x 5x oe or better. B (and) D, Either way round. - each extra letter. 3 3.5 0 B for figures 35 seen 4 5.55 ( length < ) 5.65 mark for each. SC for fully correct but reversed. 5 (a) 3. 384 ft their (a) 0. 6 (a) 3 or 3 = 8 SC for 3 and 3 in the answer spaces 4 or 3 4 = 8 7 (a) art 34 A A oe M for seen 4π 4π 8 (a)(i) 30 (ii) Straight line from ( 00, 0) to ( 45, 80) Correct horizontal line Correct return journey line Ignore all beyond ( 45, 80) Horizontal line @ 80, 4 units long. Line to (4 30, 0) 9 UCLES 006

Page 4 Mark Scheme Syllabus Paper IGCSE - OCT/NOV 006 0580, 058 9 (a) 5.(0) 83.7() 7.8(0) (c) art 36.4 allow ve. Accept 36www 0 (a) correct lines on H correct line on W ft ft 60 their ($3.48 5) M for ((their 83.7 5 3.55)/their 83.7) 00 or 00 ((5 3.55)/their 83.7) 00 Ruled not essential in either. Judge by eye. No extraneous lines on either. Allow 0 or indication of no rotational symmetry. (a) 0 Final ans 4 30 Final ans 4 Ignore fraction lines in (a) and Allow coordinate form mark for each correct component. mark for each correct component. (a) 0 + 0 5 (0 0) SC for 3 or 4 of the numbers given to significant figure. 0 cao. (c) 9.49 cao. 7 B for 9.485(5) to 9.493 seen. (Allows for 3 rounded to 3sf) If zero, SC for 9.5www as final answer (Not 9.50 but check for possible B) 3 3 (a) (i) 36 oe isw Fraction, decimal or percentage only. (ii) 0 Final ans 0 6, 0 36, 0% or zero. Not allow no, none, 0 7 or 0/0. (iii) 6 36 Allow 6 or 36 or 00%. 7 99 isw If decimal, allow art 0.7 (c) Piero s Can be indicated by 0 5 Total for the paper is 56 marks UCLES 006

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 007 question paper 0580/058 MATHEMATICS 0580/0 and 058/0 Paper (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 007 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

Page Mark Scheme Syllabus Paper IGCSE May/June 007 0580/058 0 B 0.58 < 5 3 < 6(%) B Accept answer in alternative form provided equivalence is clear. 3 7 (h) 55 (min) B 4 4 B 5 Negative B 6 (a) Jan B Not just 0. but ignore if included. 6(.0) 7 45 + 80 or 360 their acute angle at L 35 B M A Allow 6 Must be clearly indicated in working or diagram. 8 (a) 3 (, ) B B [9] SC for both answers with components of (a) and coordinates of reversed. 3 i.e. for (a) and (, ) for 9 x + 3xy or x(x + 3y) B B for 3x x + 3xy or x(3x x + 3y) seen. SC for answer x 3xy oe or x seen in final answer of terms. 0 75 B B for 5 or 50 seen on diagram or clear in working that angle BCD is 5 or angle DCE is 50. Minimum - arc seen in diagram. (a) Equilateral (Triangular) prism B B Not equal If qualified must be triangular (or triangle). [8] UCLES 007

Page 3 Mark Scheme Syllabus Paper IGCSE May/June 007 0580/058 0 (y =) 3x B B for mx or 3x + c where m and c are integers with m 0 and c 5. 3 (a) (c) 0 3 B B B SC for 4 0, 3 and 5. SC for two of the above 4 (a) 50.9886 M Allow division by.9 to. 08 to 0.084.. A.0 B One and only one zero is essential 5 360 80 6 (x =) 0 (y =) 50 M A Bft Alt. ( 6 4) 90 6 oe 360 (90 + their x) ft if positive ww. reversed answers marks. 6 (a) 5 5.40 + 5 3 80 6 M A 360 Alt. (y first) + 90 M 50 A 6 (x=) 0 Bft 0 Bft ft their (a) 80 00 (provided profit >0) If 0 scored in parts (a) and allow SC for 96 seen [4] UCLES 007

Page 4 Mark Scheme Syllabus Paper IGCSE May/June 007 0580/058 0 7 (a) 5. 0 8 9.4 their (a)/ 00 art.5 0 8 oe B M Acao B for 5. 0 n where n is an integer greater than Calculator form; penalise mark each form. May revert to given value. Answer does not need to be in standard form. (e.g. 49940000) If M0, SC for 3.6 0 8 8 (a) (AB = ) 00 + 900 500 tan (=) 900/00 oe art 36.9 M A M Acao Indicated by 50000 seen Allow art 500 if sin or cos used and done before (a). For sin or cos method allow their (a) for M only. 9 (a) (c) 63 Correct construction with arcs 09.5 B B B B without arcs, accuracy mm SC for correct mirror image with arcs. 0 (a) (i) (a) (ii) (a) (iii) 50 Sum divided by 5 43.9(3.) Attempt to order estimates 47 (Low) Extreme values oe B M A M A B 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. [] (a) (c) (i) (c) (ii) 30 + 60 (seconds) 90 (seconds) D to E 80(m) 400 used their (c)(i) divided by 400 (only) 3. M A B B B M Aft SC for 30 or 60 seen. Any clear indication of section Allow 70 to 80 Also indicated by 30 or (400 their (a)). ft correct to 3 significant figures. [3] UCLES 007

Page 5 Mark Scheme Syllabus Paper IGCSE May/June 007 0580/058 0 5 B 0.79 < 5 4 < 8% B Accept answer in alternative form provided equivalence is clear. 3 7 (h) 45 (min) B 4 4 B 5 Negative B 6 (a) Jan B Not just 0. but ignore if included. 3. 7 5 + 80 or 360 their acute angle at L 305 B M A Allow 3. Must be clearly indicated in working or diagram. 8 (a) 3 (, ) B B [9] SC for both answers with components of (a) and co-ordinates of reversed. 3 i.e. for (a) and (, ) for 9 3x + xy or x(3x + y) B B for 4x x + xy or x(4x x + y)seen. SC for answer 3x xy oe or 3x seen in final answer of terms. 0 80 B B 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. (a) Equilateral (Triangular) prism B B Not equal. If qualified must be triangular (or triangle). [8] UCLES 007

Page 6 Mark Scheme Syllabus Paper IGCSE May/June 007 0580/058 0 (y =) x 3 oe B B for mx 3 or x + c where m and c are integers with m 0 and c 3 3 (a) (c) 9 5 B B B SC for 3 9, 5 and 6. SC for two of the above 4 (a) 70.9886 M Allow division by.9 to. 5 to 6.89 A.0 B One and only one zero is essential. 5 360 80 6 (x =) 0 (y =) 50 M A Bft Alt. ( 6 4) 90 6 360 (90 + their x) ft if positive ww. reversed answers marks. 360 Alt. (y first) + 90 M 50 A 6 (x=) 0 Bft 6 (a) 5 5.80 + 5 3 90 3(.3..) M A Bft ft their (a) 90 00 (provided profit >0) If 0 scored in parts (a) and allow SC for 0 seen. [4] UCLES 007

Page 7 Mark Scheme Syllabus Paper IGCSE May/June 007 0580/058 0 7 (a) 5. 0 8 9.4 their (a)/ 00 art.5 0 8 oe B M Acao B for 5. 0 n where n is an integer greater than. Calculator form; penalise mark each form. May revert to given value. Answer does not need to be in standard form. (e.g. 49940000) If M0, SC for 3.6 0 8 8 (a) (AB = ) 00 + 800 art 360 tan (=) (800/00) oe 36 to 36.03 M A M Acao Indicated by 850000 seen. For sin or cos method allow their (a) for M only. 9 (a) (c) 76 Correct construction with arcs 9.5 B B B B without arcs, accuracy mm SC for correct mirror image with arcs. 0 (a) (i) (a) (ii) (a)(iii) 50 Sum divided by 5 44.(3..) Attempt to order estimates 48 (Low) Extreme values oe B M A M A B Indicated by answer of 43 to 45 or calculation shown. (Total = 66) Must be at least 7 values [] Two very low values etc. Must not refer to extreme high values. (a) (c) (i) (c) (ii) 30 + 60 (seconds) 90 (seconds) D to E 80 (m) 400 used their (c)(i) divided by 400(only) 3. M A B B B M Aft SC for 30 or 60 seen. Any clear indication of section. Allow 70 to 80 Also indicated by 30 or (400 their (a)). ft correct to 3 significant figures. [3] UCLES 007

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 007 question paper 0580 and 058 MATHEMATICS 0580/0 and 058/0 Paper (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 October/November 007 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

Page 3 Mark Scheme Syllabus Paper IGCSE October/November 007 0580/058 0 Question Answers Mark Notes 3 Not 3 ($) 0 M for 35 (5 + ) or better. SC for ($) 5 only or 5:0 or 5 and 0 in the answer space. 3 (x = ) M for 4 = x + x oe Not embedded unless x = seen. 4 60 M for 5.50 0.875. SC for answers 59.659 rot or 60.3448 rot (from rounding 0.875 to 0.88 or 0.87.) 5 x(y ) final answer SC for x(4y ) or (xy x) or x(y +) Or SC for x(y ) not as final answer. 6 art39.8 M for tan p = 5 30 oe 7 50 ( d <) 350 3 mark for each in correct order 8 (a) Two correct lines of symmetry, No extra lines Parallelogram 9 (a) 5 9 oe 0 (a) 30 5 = 7 oe 8 8 8 B E ft Lines must be a minimum of length and height of the figure. Eg 66 Allow 9 + 54 9 9 or better Must be finally reduced to 7 8 M for 360 either 30 or their (a) ft. answer only when calculation gives an integer > art38.3 3 M for d 50 = cos (80 40) oe soi Mdep. for ( d =) 50 cos (80 40) oe SC for 3. (distance east) UCLES 007

Page 4 Mark Scheme Syllabus Paper IGCSE October/November 007 0580/058 0 Question Answers Mark Notes (a) 3 (y =) 3x + 3 Final answer ft 3 (a) 55 or art 54.6 5 B for their (a)x or +3 as intercept seen in the equation. Not y = 3 M for 3 40( 00) implied by 54.5 M for 6.5 00 40 SC for answer 5 4 (a) art 5. www 5 (a) x 6 6 (Can be on diagram) (c) x 9 6 (a)(i) 8 000 (ii).8 0 4 0.056 7 (a) ($) 6.(0) ($) 6.3() or 6.3(0) 8 (a)(i) Vector KL drawn (ii) (0,) (, ) 9 (a)(i) 60 (m/min) (ii) 3.6 (km/h) 3 (km/h) 5 ft ft cao 5 M for π 8 or π 8 implied by answer of 5 M for 90 9 or 80 90 9 SC for angle Q = 90 soi M for ( 3 x ) or better. E.g. ( x 3 ) B if answer contains x as numerator or 3 (or 9) as denominator..7598 0 4 gets 0 B for 0.06 or 0.0565 or 0.05649 or 0.057 seen SC for final answer 0.0560(0) M for (00 4.05 )/00 SC for 6.(0) M for 00(.04) 00oe SC for 6.3(). SC for both 8.(00) and 8.3() seen If arrow shown, it must be correct. Only ft their point if labelled L. M for vector PS drawn or for 4 (PS =) SC Point S on diagram at (, ) M for their (a) 60 000 or. 0.33 or better M for total distance(figs 5) total time Values seen, but independent of units. UCLES 007

Page 5 Mark Scheme Syllabus Paper IGCSE October/November 007 0580/058 0 Question Answers Mark Notes Not ($) 5 M for 45 (4 + 5) or better SC for ($) 0 only or 0:5 or 5 and 0 in the answer space. 3 (x = ) M for 0 = x + 3x oe Not embedded unless x = seen. 4 80 M for 70.80 0.885 SC for answers 79.55 rot or 80.45 rot from rounding 0.885 to 0.89 or 0.88) 5 q(p ) final answer SC for q(p 4) or (pq q) or q(p + ) or SC for q(p ) not as final answer. 6 art34.5 M for tan p = 3 Grads 38.3 or rads 0.603 check for M A0 only. 7 8750 ( d <) 8850 3 mark for each in correct order SC for fully correct but reversed 8 (a) Two correct lines of symmetry. No extra lines. Parallelogram 9 (a) 5 7 oe 0 (a) 0 8 34 5 = 9 oe 4 4 4 B E ft Lines must be a minimum of length and height of the figure. Eg 68 48 Allow + 5 or better Must be finally reduced to 9 4 M for 360 either 0 or their (a) Ft answer only when calculation gives an integer > art34.6 www 3 M for d 40 = cos (80 50) oe soi Mdep for ( d =) 40 cos (80 50) oe SC for 0 (distance east) Grads 35.6 or rads 6.7 check M A0 only. UCLES 007

Page 6 Mark Scheme Syllabus Paper IGCSE October/November 007 0580/058 0 Question Answers Mark Notes (a) Allow and 4 or or 4 (y =) x + 4 ft B for their (a) x or +4 as intercept seen Final answer. in the equation. Not y = 4 3 (a) 48 or art 47.8 4 (a) art 40.8 or art 40.9 57 5 (a) y 8 (c) p 5 6 (a)(i) 6 000 (ii).6 0 4 0.0037 7 (a) ($) 48.4(0) ($) 49.4(4) or 49.4(0) 8 (a)(i) Vector KL drawn correctly (ii) (0, ) (, 0) 9 (a)(i) 45 (m/min) (ii).7 (km/h) 3. (km/h) 5 ft ft cao 5 M for 53 30 ( 00) M for 3.75 00 30 SC for answer 308 M for π 3 or π 3 implied by answer of 4 M for 90 33 or 80 90 33 SC for angle Q = 90 soi M for or better. E.g. ( p 5 () ) 5 p B if answer contains p as numerator or 5 (or 5) as denominator.5583 0 4 gets 0. B for 0.004 or 0.0037 or 0.00378 seen. SC final answer 0.00370(0) M for (400 6.05 )/00 SC for 448.4(0) M for 400(.06) 400 SC for 449.44 SC for 4 and 5.4(4) seen If arrow shown, it must be correct Allow L not labelled. Only ft their point if labelled L. M for vector PS drawn or for 6 (PS =) Ignore fraction line. 4 SC Point S on diagram at (, 0) M for their (a) 60 000 or 0.9 0.33 or better M for total distance(figs 6) total time Values seen, but independent of units. UCLES 007

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 008 question paper 0580, 058 MATHEMATICS 0580/, 058/ Paper (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 008 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

Page Mark Scheme Syllabus Paper IGCSE May/June 008 0580, 058 Abbreviations aro BOD CAO eeo NR o.e. SC www ft or dep Answer rounding to Benefit of the doubt is to be given to the candidate Correct answer only Each error or omission Answer space is completely blank or equivalent Special Case Without wrong working Work has been followed through after an error Dependent on the previous mark Qu Answer Mark Part Marks/Notes 3 (h) 6 (min) cao If not in the answer space units must be clear. E.g. Not :6 or.6. 3 96 4 0 5 33(%) < / 3 < 0.35 Accept the values in any form. / 3 must be to 3 or more s.f. 6 4 7 3.6 0 3 cao 8 (a) 9 ($)78 M 84 9 or 84 9 or better. 0.5 Ğ h <.5 + mark for each value in correct place. ($).40 or 40 cents M.45 (4 + 3) implied by 0.35. SC for answer 40. For answer in cents units must be stated. (a) 3 isw 4 isw 0 Ignore further attempts at cancelling in (a) and. Allow equivalent fractions in (a) and. SC Both correct but written as decimals or %. (Give mark in part ). 3 7.5 or 7½ M ½ 8 h = 5 6 or better. 30 5 Implied by or seen. 4

Page 3 Mark Scheme Syllabus Paper IGCSE May/June 008 0580, 058 4 (a) 35.845(6 ) or 35.888 or 35.796 36 (cm) (Ignore trailing zeros) 5 Vertices (3,), (5,), (,4), (0,4) and ruled parallelogram drawn. ft π from calculator value or 3.4 or 3.4 respectively. 36 or follow through from their (a) but only if the answer to (a) is greater than. M 3 or 4 vertices correctly plotted. If M0, SC Correct reflection in y = 3. (3,5), (,5), (4,), (6,). 6 4.578 to 4.58 M.4 + 3.9 or better. Square root not essential for M. Implied by 0.97 or 5.76 + 5. seen. 7 ($).4 or 4 cents M 8 0.68.5 or 8 68 5. For answers in cents units must be stated. 8 3x( 3xy) final answer SC 3(x 3x y) or x(6 9xy) or 3x( + 3xy) as answers. 9 (a) (i) 7 (ii) 48 z Allow z. 0 (a) 4 or 8 or 9 (c) 64 or 8 (d) 4 or 3.7(4 ) (a) 5 43 (c) 3n + 0 oe final ans. SC 3n + k oe (k 0) as answer. (a) 0 (i) 0.83(3 ) or oe isw (ii) 49.8 to 50 ft ft 60 their (i) correct to 3sf. (c) 46 W for (CD = ) seen in working space, or answer line or between dotted lines at C and D.

Page 4 Mark Scheme Syllabus Paper IGCSE May/June 008 0580, 058 3 (a) ($)00 M for 4000 3 8.5 00 or SC for 500 final ans. ($)038.85 Allow 039 or 038.848 or 038.8 or 038.9 or 038.84 0 4 (a) (i) 4 3 M for 8 4000 + or better. 00 8 or M for 4000 + or better. 00 Alt. M for (4000 + 4000 0.08) 0.08. M dep for 4665.60 0.08. (NB Interest only method) mark for each component. 3 (ii) 4 4 Line segment from P to (, 6) mark for each component. W for (, 6) indicated or seen anywhere. 4 If zero, SC for line segment from P to (, k) or to (k, 6) or a line through P and (, 6).

Page Mark Scheme Syllabus Paper IGCSE May/June 008 0580, 058 Abbreviations aro BOD CAO eeo NR o.e. SC www ft or dep Answer rounding to Benefit of the doubt is to be given to the candidate Correct answer only Each error or omission Answer space is completely blank or equivalent Special case Without wrong working Work has been followed through after an error Dependent on the previous mark Qu Answer Mark Part Marks/Notes 9 3 (h) 9 (min) cao If not in the answer space units must be clear. E.g. Not 3:9 or 3.9. 3 96 4 0 5 33(%) < / 3 < 0.35 Accept the values in any form. / 3 must be to 3 or more s.f. 6 9 7 3.6 0 3 cao 8 (a) 9 ($)0 M 76 3 or 76 or better. 3 0.5 Ğ h <.5 + mark for each value in correct place. ($).5 or 5 cents M.5 (5 + 4) implied by 0.5. SC for answer 5. For answer in cents units must be stated. (a) 7 isw 9 3 isw 0 Ignore further attempts at cancelling in (a) and. Allow equivalent fractions in (a) and. SC Both correct but written as decimals or %. (Give mark in part ). 3 3.5 or 3½ M ½ 8 h = 6 9 or better. 54 7 Implied by or seen. 4

Page 3 Mark Scheme Syllabus Paper IGCSE May/June 008 0580, 058 4 (a) 3.6756(3 ) or 3.6768 or 3.656 33 (Ignore trailing zeros) 5 Vertices (3,), (5,), (,4), (0,4) and ruled parallelogram drawn. ft π from calculator value or 3.4 or 3.4 respectively. 33 or follow through from their (a) but only if the answer to (a) is greater than. M 3 or 4 vertices correctly plotted. SC Correct reflection in y = 3. (3,5), (,5), (4,), (6,). 6 4.4598 to 4.46 M.5 + 4. or better. Square root not essential for M. Implied by 9.89 or.5 + 7.64 seen. 7 ($).4 or 4 cents M 8 0.68.5 or 8 68 5. For answers in cents units must be stated. 8 3x( 3xy) final answer SC 3(x 3x y) or x(6 9xy) or 3x( + 3xy) as answers. 9 (a) (i) 64 (ii) 44 z Allow z. 0 (a) 4 or 8 or 9 (c) 64 or 8 (d) 4 or 3.7(4 ) (a) 5 43 (c) 3n + 0 oe final ans. SC 3n + k oe (k 0) as answer. (a) 0 (i) 0.83(3 ) or oe isw (ii) 49.8 to 50 ft ft 60 their (i) correct to 3sf. (c) 46 W for (CD = ) seen in working space, or answer line or between dotted lines at C and D.

Page 4 Mark Scheme Syllabus Paper IGCSE May/June 008 0580, 058 3 (a) 33 M for 6000 3 7.4 00 or SC for 733 final ans. 350.6 Allow 350 or 350.58 or 350.5 or 350. or 350.3 0 4 (a) (i) 4 7 3 M for 6000 + or better. 00 7 or M for 6000 + or better. 00 Alt. M for (6000 + 6000 0.07) 0.07. M dep for 6869.4 0.07. (NB Interest only method) mark for each component. 3 (ii) 4 4 Line segment from P to (, 6) mark for each component. W for (, 6) indicated or seen anywhere. 4 If zero, SC for line segment from P to (, k) or to (k, 6) or a line through P and (, 6).

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 008 question paper 0580 and 058 MATHEMATICS 0580/ and 058/ Paper (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 October/November 008 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

Page Mark Scheme Syllabus Paper IGCSE October/November 008 0580 and 058 Abbreviations cao ft isw oe SC soi ww correct answer only work has been followed through after an error ignore subsequent working or equivalent Special Case seen or implied without working Qu. Answers Mark Part Marks 8 3 3 4 6.5 5 3x cao final answer W for (+) or 3x seen anywhere 6.5 M for 4.6 figs 5 or W for figs 5 7 (a) > = 8 5.77 cao M for 0.685 or W for answers from 5 to 7 9 (x=) 0. or 0 5 isw M for (53 ) 5 soi 0 6650 L < 6750, mark for each value correctly placed. SC both correct but reversed (a) 4 (k=) 8 M for 0 = 4 k or better 3 (a) 5.78 0 0.0058 Accept 5.8 0 3 (c) 0.0 Accept 0 4 5 seen 4 W 5 4 their 8 5 6 M A Must be inversion of an improper fraction 5 ' 5 ' ' 0 ' Can be implied by =. 8 4 0 ww no marks UCLES 008

Page 3 Mark Scheme Syllabus Paper IGCSE October/November 008 0580 and 058 Qu. Answers Mark Part Marks 5 (a) Point marked at (3, ) (, ) (c) 0.5 or 6 (a) (c) q r 6 or 6 r Missing label not penalised. More than point seen, must be labelled By eye mm 7 (a) seen on diagram at A and B or 80 o 68 o = o. AND + 78 (= 90) 3 o Allow 68 o + o = 80 o only Allow 90 o 78 o = o or 90 o o = 78 o if the first condition is satisfied W for angle BAC (or angle BCA) = 45 o 8 (a) 083300 to 084000 or 080000 or 083000 Final answer Their (a) 0 6 evaluated ft M for π 50 38 or π 0.5.38 9 (a) 64 7 ft M for (0 + ) or + 0 + 4 + 6 + ( 4) + (0 6) M for ( 0) 6 8 or (40 0) + 8 4 or 4 6 + 4 0 (a) (i) (ii) (iii) 5 5(%) or 0.5 or 00 oe 4 oe cao 5 0 oe cao 5 0 or 5 0 cao isw for change of form or cancelling only in all parts. Not ratio. Allow 0.67 or 0.66(6.) or % form Minimum 3 significant figures Allow 0.667 or 0.666(6 ) or % form Minimum 3 significant figures Consistent use of wrong denominator in all of, once. Allow nil, none or zero only. No other denominator allowed. (a) (c) Similar 5 9 M for 0 8 or equivalent method M for 360 68 (a) 45 5 75 All sectors correct ± Correctly labelled ft ft Their 5 5 or 0 o 45 Ft provided angles total 360 Independent. Labelling of the other 3 sectors. UCLES 008

Page Mark Scheme Syllabus Paper IGCSE October/November 008 0580 and 058 Abbreviations cao ft isw oe SC soi ww correct answer only work has been followed through after an error ignore subsequent working or equivalent Special Case seen or implied without working Qu. Answers Mark Part Marks 36 3 3 4 7.4 5 0 7x cao final answer W for (+)0 or 7x seen anywhere 6 9.5 M for 3.8 figs 5 or W for figs 95 7 (a) > = 8 3.65 cao M for 30.685 or W for answers from 3 to 5 9 (x=) 0.6 or 0 5 3 isw M for (54 ) 5 soi 0 6650 Y L < 6750, mark for each value correctly placed. SC both correct but reversed (a) 4 (k=) 8 M for 0 = 4 k or better 3 (a) 6.56 0 0.0066 Accept 6.6 0 3 (c) 0.0 Accept 0 UCLES 008

Page 3 Mark Scheme Syllabus Paper IGCSE October/November 008 0580 and 058 Qu. Answers Mark Part Marks 4 0 W seen 3 5 (a) (c) 4 3 their 9 0 5 Point marked at (3, ) (, ) 0.5 or M A Must be inversion of an improper fraction 4 ' 0 ' ' ' Can be implied by = 9 3 80 ww no marks Missing label not penalised. More than point seen, must be labelled. By eye mm 6 (a) (c) q 8 r 8 or 8 r 7 (a) seen on diagram at A and B or 80 o 68 o = o. AND + 78 (= 90) 3 o Allow 68 o + o = 80 o Allow 90 o 78 o = o or 90 o o = 78 o If the first condition is satisfied W for angle BAC (or angle BCA) = 45 o 8 (a) 4586 to 45945 or 460000 or 459000 Final answer Their (a) 0 6 evaluated ft M for π 60 9 or π 0.6.9 9 (a) 64 7 ft M for (0 + ) or + 0 + 4 + 6 + ( 4) + (0 6) M for ( 0) 6 8 or (40 0) + 8 4 or 4 6 + 4 UCLES 008

Page 4 Mark Scheme Syllabus Paper IGCSE October/November 008 0580 and 058 Qu. Answers Mark Part Marks 0 (a) 5 5(%) or 0.5 or 00 oe isw for change of form or cancelling only in 4 all parts. Not ratio. (i) oe cao Allow 0.67 or 0.66(6.) or % form 5 0 Minimum 3 significant figures (ii) oe cao Allow 0.667 or 0.666(6 ) or % form 5 Minimum 3 significant figures Consistent use of wrong denominator in all of, once. (iii) 0 or 5 0 cao Allow nil, none or zero only. No other denominator allowed (a) (c) Similar 9.95 to 0.04 97 M for 9 5 or equivalent method M for 360 63 (a) 45 5 75 All sectors correct ± Correctly labelled ft ft Their 5 5 or 0 o 45 Ft provided angles total 360 Independent. Labelling of the other 3 sectors. UCLES 008

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 009 question paper for the guidance of teachers 0580, 058 MATHEMATICS 0580/, 058/ Paper (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 009 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

Page Mark Scheme: Teachers version Syllabus Paper IGCSE May/June 009 0580, 058 Abbreviations cao ft isw oe SC soi ww correct answer only work has been followed through after an error ignore subsequent working or equivalent Special Case seen or implied without working Qu. Answers Mark Part Marks < ( accept or both symbols) (a) 0.0093(4.) or.93(4 ) 0 3 7.63 0 cao 3 M for 4500 00 or 4.5 0. 4 30 M for a + 5a = 80 or 6a = 80 or 5a + 5a + a + a =360 or better 5 6.999. to 7 M for 56.5 or 63.499 to 63.5 seen 6 (a) 3 cao y = 3x oe ft Allow y = 3x + 0 or y = 3x 0 Must be an equation. i.e. y =.. 7 38 ± (ie 36 to 330) W for angle of 3 ± or 58 ± or 48 ± seen on diagram or in working or in the answer space. 8 9.33 or 9.37( ) M for 6 3 as chosen method. Alt. Trig must be complete correct method for M. 9 35.68 cao M 30700 79.6 SC for 840(KES). Units need to be seen in the working or on answer line. 0 (a) 7c 0d www final answer M for 5c 0d 8c or better or W for 7c or 0d seen as terms in final answer q(p q) www UCLES 009