0580 MATHEMATICS. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers.
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1 CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the March 05 series 0580 MATHEMATICS 0580/ Paper (Paper Extended), maximum raw mark 0 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 should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the March 05 series for most Cambridge IGCSE, components. IGCSE is the registered trademark of Cambridge International Examinations.
2 Page Mark Scheme Syllabus Paper Cambridge IGCSE March Abbreviations cao correct answer only dep dependent FT follow through after error isw ignore subsequent working oe or equivalent SC Special Case nfww not from wrong working soi seen or implied Qu. Answers Mark Part Marks.5 (a) oe Accept equivalent methods (b) 6000 M for 00 oe.5 or M for.5% associated with 6750 oe (c) 76.5 cao final answer B for.5 and 7.5 seen (d). M for 00 or seen oe (e) 58 M for 6 7 (f) 90 M for 000. A for to or 90.6 or 900 Bindep for their answer rounded to the nearest euro if possible (a) (i) 6 A B 8 B for 8 or 9 numbers correct B for 6 or 7 numbers correct 0 C cao {} or {} FT FT their intersection of all sets their diagram (iii) 5 FT FT their set B on diagram (b) (i) Cambridge International Examinations 05
3 Page Mark Scheme Syllabus Paper Cambridge IGCSE March X Y Z (a) 0 B for correct B for correct (b) smooth correct curve through correct points BFT for 8 or 9 correct plots BFT for 6 or 7 correct plots BFT for or 5 correct plots FT their table y ruled and.85 to to 0.95 (c) line = ( x + ) Line must be fit for purpose B for correct line and correct values or B for correct line and correct value or B for correct line or SC for no/wrong line and correct values or SC for no/wrong line and correct values (d) tangent ruled B No daylight between tangent and curve at point of contact. Consider point of contact as midpoint between two vertices of daylight, the midpoint must be between x =.85 and x =.65. to.5 (a) ( y m)( y + m) final answer B for y seen dep on B M for rise/run also dep on any tangent drawn or close attempt at tangent at any point Must see correct or implied calculation from a drawn tangent Accept M for answer in range. to.5 after B (b) x + 5x ( x 5)( x ) final answer B for denom ( 5)( x ) x oe isw and B for x + 6x 5x 0 soi Cambridge International Examinations 05
4 Page Mark Scheme Syllabus Paper Cambridge IGCSE March (c) ± ()( 7) B for ()( 7) or better seen p + or q and if in form r B for p = and r =.90. final answers x + + x + x + (d) (i) ( )( ) 5 = x + x + 6x + 6 = 0 or x + x + x + = 5 x + 5x = 0, M M A SC for.9,.896 or.897 and. or.0 or. and.90 final answers or.90 and. seen in working Allow ( x + 6)( x + ) = 5 Dep on st M With no errors or omissions.5 or, B for ( )( x + ) ( )( ) 5 ± 5 x or x + a x + b where a and b are or SC for ( )( ) integers and a + b = 5 or ab = or ( )( ) 5 or and r = p + or q where p = 5 r (iii) 6.5 or FT FT their pos root from (d) + 5 (a) 6 5. sin 6 oe 8... M A (b) 95.6 or 95.6 to sin 8 M for 8. or M for implicit form and Mdep for 80 8 their 6. Cambridge International Examinations 05
5 Page 5 Mark Scheme Syllabus Paper Cambridge IGCSE March (c) 86 or 85.7 to B for [Angle APB=] 8 M for cos their8 or M for implicit form and A for [AB =] 8676[...] After 0 scored, SC for ans to or 06.9 or 07 if 6 used in cos rule Or SC for cos 6 6 (a) 5 (b) 80 FT FT 00 their (a) (c) (i) 0 8 oe M for oe or M for M for oe 5 5 or M for or seen 5 5 (d) (i) 08 8 oe 0 5 M for oe oe or M for oe or oe or oe or oe M for + + oe or or M for equivalent of of above products added together oe or M for one correct relevant product oe 7 (a) (i) Rotation [centre] (0, 0) or origin 90 [anticlockwise] oe Cambridge International Examinations 05
6 Page 6 Mark Scheme Syllabus Paper Cambridge IGCSE March Enlargement [centre] (, ) [s.f.] (b) vertices at (, ) (, 5) (, 6) (, 6) SC for translation by k or k (c) vertices at (7, ) (7, ) (7, 5) (6, 5) SC for reflection in y = or reflection in any vertical line (d) reflection x-axis oe 8 (a) (i) 7.7 or 7.7 to 7.75 M for [arc =] 68 x or + + π = M for [x =] their arc 60 ( π ) 5 or 5. to M for r = or π their7.7 π ( π) 60 0 A for r =.8 or.8 to.8... or π (b) 9 or 9. to 9... nfww 5 M for 9 (a) 0 < h M for h = their r A for h =.8 or to.79 Mdep on M earned for V = π their h their r or M for π 8 + π π 8 8 and M for π and M for 8 added to at least one term with π (b).875 nfww M for at least correct mid-values soi M for fx where x is in the correct interval, allow one further error/omission M dep for 0 dependent on second method mark Cambridge International Examinations 05
7 Page 7 Mark Scheme Syllabus Paper Cambridge IGCSE March (c) correct blocks B for correct blocks B for correct blocks B for correct block or at least correct frequency densities (.,,, 0.65 ) 0 (a) x + 0y < 80 With no errors seen (b) y > x y 6 or y < 7 Accept 0 y 6 or 0 < y 6 or 0 y < 7 or 0 < y < 7 (c) ruled broken line through (5, 6) to (0,) B SC for correct only at (5, 6) or (0, ) ruled broken line y = x ruled solid line y = 6 or broken y = 7 B B Must be consistent with their (b) correct region indicated B (a) (d) 76 SC for (, 6 ) indicated or x + 0y evaluated for ( x, y ) in their region, x, y integers (b) 0 0 (c) ( n +) n oe B for an + bn + c a, b, c numeric a 0 (d) ( n ) n oe B for using ( an + bn + c ) oe in expression of form a 0 or kn ( n ) k 0 Cambridge International Examinations 05
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