0580 MATHEMATICS. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers.

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Valentine McLaughlin
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1 CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 0 series 0580 MATHEMATICS 0580/4 Paper 4 (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 ds 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 May/June 0 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

2 Page Mark Scheme Syllabus Paper IGCSE May/June Abbreviations cao correct answer only cso correct solution only dep dependent ft follow through after error isw ignore subsequent working or equivalent SC Special Case www without wrong working art anything rounding to soi seen or implied Qu Answers Mark Part Marks (a) (i) [= 40] Accept of used instead of M for 560 ( ) 0 (b) 90 M for 40 8 (i) 960 final answer M for their(a) 75 + (560 their (a)) [0] final answer M for or M for ( )[%] = 98 seen (d) 84[...] M for or M for 00 or [7.5] 9.5 used implied by answer 84. or SC for final answer 84[...] (e) 69.4 and 69[.0] cao SC for one correct or both correct but reversed M for two of 0.85, 0.95,.65 or.75 seen or ( ) + 4(0.05) or ( ) 4(0.05) Cambridge International Examinations 0

3 Page Mark Scheme Syllabus Paper IGCSE May/June (a) (i) Translation, 5, Brackets needed for vector Not ( 5, 8), ( 5 8) 8 correct trapezium at (, ) (4, ) (4, 5) (, 5) SC for reflection in x = or vertices only (iii) (b) (i) correct trapezium at (4, ) (5, 4) (7, 4) (7, ) Shear x axis () invariant M for 4 correct vertices on grid or in working or M for or SC for vertices correct or complete shape in correct orientation but wrong position rectangle at (, ) (, ) (, 8) (, 8) SC for all vertices only or correct orientation and size, wrong position (a) 0,, 0, B for correct or B for correct (b) Correct curve B4 BFT for 8 points BFT for 7 or 6 points BFT for 5 or 4 points y = indicated x =. to.4 and 4. to 4. B B e.g. Could be mark[s] on curve isw other lines if not clearly used (d) (i) line drawn from (0, ) to touch curve M No daylight at point of contact If short, must cross at (0, ) within ½ small square when extended (.5 to.75, to.4) A rise/run e.g. (their y )/their x M dep on attempt at a tangent from (0, ) in (d)(i) and uses scales correctly Can be implied from answer check on tangent for their rise for a run of (½ small square) 0.4 to 0.48 A ww dep on attempt at a tangent from (0, ) in (d)(i) Cambridge International Examinations 0

4 Page 4 Mark Scheme Syllabus Paper IGCSE May/June (a) 7 or 6.95 to 7.0 M for (b) 5.5 π [0] to 9.0[] their b M for sin [MOB]= 8.5 Dep on their b < 8.5 (d) 0. or 0. or 0.4 to M for π a or M for π where 0 < a < 60 Implied by 5.78 to 5.79 or.5 to.6 or.4 to.5 or. or. or 4.8 to 4.84 or 4.8 (e) AB = BC TA = TC TB = TB isw comments or reasons If 0 scored SC for all three sides the same [SSS] and no mention of angles 5 (a) 7 final answer x (b) 5 x final answer = x x M FT their (b) 4 = their (a) must be eqn in x ( x ) = 7( x ) 5x 4x M 5 7 FT + 4 = only for nd and rd x x M mark If all on one side then condone omission of = 0 4x + 7x 5x 8x 54[ = 0] Mdep Dep on nd M Must see brackets expanded before this award and terms on one side of eqn x x 7 = 0 without error seen A Must see 4x 6x 54 = 0 first (d), 4.5 B for ( x 9)( x + ) or SC for ( x + a)( x + b) (e) 6 cao integers and a + b= or ab = 7 where a and b are Cambridge International Examinations 0

5 Page 5 Mark Scheme Syllabus Paper IGCSE May/June (a) (i) to 44.4 M A M for 5² = ² + ² -..cosm A for [cos =] 0.74 or 0.74 to 0.74 or or 88.5 to 88.9 M for 0.5 sin (44.4) (b) 7.74 or 7.76 to www 4 B for 55 soi 6.4 M sin8 sin( their R) or M for 6.4 PR sin( theirr ) = sin8 7 (a) (i) 5 not possible (iii) () final answer M for 0 8 (iv) (v) B for one correct row or column 0 (b) 4 or better isw 4 B for k seen or implied a b or seen c d 8 (a) hat scarf 5, mark per pair in correct place (b) (i) FT 5 FT their correctly evaluated M FT from their tree FT 5 FT their correctly evaluated 8 5 M FT from their tree 8 Cambridge International Examinations 0

6 Page 6 Mark Scheme Syllabus Paper IGCSE May/June (iii) cao M for their + their (b) soi or or or cao M for FT their tree or or M for [ wears all = ] 5 7 FT their tree seen (a) 7 or M for ( 6 4 ) + ( sin 60) or M for area of or hexagons or M for area of one relevant triangle or trapezium or rectangle within hexagon If 0 scored SC for 88 shown (b) (i) 740 or 74.6 to M for ( π 0.74 ) 4 or SC for figs 74[..] or 74[4..] or B for π 0.74 seen [.7..] or B for 000 / 4 soi by cao www 5 5 B4 for 87.9 to 87.4 figs or M for [r=] π figs 5 figs or M for [ r =] = π figs 5 or M for figs = π r figs5 5 8x x 0 (a) (i) final answer M for or better seen x + 5x + 9 B for x + 6x x soi final answer ( x + ) x or x + 9 seen and B for denom ( + ) (b) x = or or to y = M for correct method to eliminate one variable A for x = or or to or y = Cambridge International Examinations 0

7 Page 7 Mark Scheme Syllabus Paper IGCSE May/June final answer 7 x + www 4 B for 7 ( x + ) in numerator and B for ( + )( x + ) x in denominator or SC for ( x + a)( x + b) where a and b are integers and a + b= 9 or ab = 9 After B scored, SC for final answer 7.5 or x +.5 x +. ( ) 5 (a) + Ignore attempt to evaluate 0 (b) (i) 0 final answer 0 final answer 0 M for their 0 or ( 0 ) 0 their + implied by. seen 00 9 or isw conversion 7 7 or.7[0] to.7[04] M for or for [ OP ] 4 = n or for their (b) where n is or 4 n 0 where n is or (d) (i) M for tan [P OP ] = 8.4[ ] (iii) 0 SC for 9 or M for [... ] Cambridge International Examinations 0

MARK SCHEME for the May/June 2012 question paper for the guidance of teachers 0580 MATHEMATICS

MARK SCHEME for the May/June 2012 question paper for the guidance of teachers 0580 MATHEMATICS UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 0 question paper for the guidance of teachers 0580 MATHEMATICS 0580/4