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
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 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 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
Page 3 Mark Scheme: Teachers version Syllabus Paper IGCSE May/June 009 0580, 058 (a) 63 (7 8 5 9) their63 63 oe final answer M Aft ft their (a) (a) (z =) 3 (x =) z + y oe final answer z y M for z + y = x or = x or x = z y ± z± y SC for answer of form ± 3 (a) Correct ruled line with correct arcs and at 30 to 34 to the line AB. W W 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. 05(m) to.5(m) ft 5 their DB (±mm) 4 (a) 8 64 87 (d) 73 5 (a) 5p 4 final answer W for 5p n (n 0) or kp 4 (k 0) 3q 5 final answer W for 3q n (n 0) or kq 5 (k 0) 6.45 to.6 www 4 M 0 0 or 00 M indep π r where r is 5, 4.4 or 4.5 M dep Subtraction of the two areas. Dependent on both first two M s or Alternative method Alt. M r r where r is 5, 4.4 or 4.5 M ind 4 π r where r is 5, 4.4 or 4.5 M dep 4 subtraction of the two areas. Dependent on both first two M s Follow one method only. or W3 art 36.4 or art 39. www UCLES 009
Page 4 Mark Scheme: Teachers version Syllabus Paper IGCSE May/June 009 0580, 058 7 (a) D plotted at (3, 7) Within mm by eye. 4 4 ft mark for each component if in working, no brackets 3 3 SC Both and correct but written as coordinates. 8 (a) (i) Isosceles (ii) Equilateral or two Allow order (=) Correct horizontal and vertical ruled lines. By eye and to or beyond the edges of the plan., SC Both freehand and correct accuracy by eye to or beyond edge of the plan or both short of the full figure. for each additional line. 9 (a) 4 M for 350 4 00 or M for 350 (350 96 00) (i) 335 M Attempt at sum of the 5 values 5 (ii) (iii) 334 5 SC for mean and median correct but reversed UCLES 009
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) 0.0053(48.) or 0.00535 or.53(4 ) 0 3 or.535 0 3 5.84 0 3 7 M for 3500 00 or 3.5 0. 4 30 M for a + 5a = 80 or 6a = 80 or 5a + 5a + a + a =360 or better 5 8.999. to 9 M for 58.5 or 67.499 to 67.5 seen 6 (a) 3 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 9.64 or 9.643(6 ) or 9.644 M for 7 4 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) 3c d www M for 0c d 7c or better or W for 3c or d seen as terms in final answer m(m n) www UCLES 009
Page 3 Mark Scheme: Teachers version Syllabus Paper IGCSE May/June 009 0580, 058 (a) 63 (7 8 5 9) their63 63 oe final answer M Aft ft their (a) (a) (z =) 3 (x =) z + y oe final answer z y M for z + y = x or = x or x = z y ± z± y SC for answer of form ± 3 (a) Correct ruled line with correct arcs and at 30 to 34 to the line AB. W W 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. 05(m) to.5(m) ft 5 their DB (±mm) 4 (a) 8 64 87 (d) 73 5 (a) 4d 5 final answer W for 4d n (n 0) or kd 5 (k 0) 4t 7 final answer W for 4t n (n 0) or kt 7 (k 0) 6.45 to.6 www 4 M 0 0 or 00 M indep π r where r is 5, 4.4 or 4.5 M dep Subtraction of the two areas. Dependent on both first two M s or Alternative method M r r where r is 5, 4.4 or 4.5 M ind 4 π r where r is 5, 4.4 or 4.5 M dep 4 subtraction of the two areas. Dependent on both first two M s Follow one method only. or W3 art 36.4 or art 39. www UCLES 009
Page 4 Mark Scheme: Teachers version Syllabus Paper IGCSE May/June 009 0580, 058 7 (a) D plotted at (3, 7) Within mm by eye. 4 4 ft mark for each component if in working, no brackets 3 3 SC Both and correct but written as coordinates. 8 (a) (i) Isosceles (ii) Equilateral or two Allow order (=) Correct horizontal and vertical ruled lines. By eye and to or beyond the edges of the plan., SC Both freehand and correct accuracy by eye to or beyond edge of the plan or both short of the full figure. for each additional line. 9 (a) 8 M for 360 5 00 or M for 360 (360 95 00) (i) 335 M Attempt at sum of the 5 values 5 (ii) (iii) 334 5 SC for mean and median correct but reversed UCLES 009