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 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 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. Cambridge will not enter into discussions or correspondence in connection with these mark schemes. Cambridge is publishing the mark schemes for the May/June 0 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 0 0580 4 Abbreviations cao correct answer only cso correct solution only dep dependent ft follow through after error isw ignore subsequent working oe or equivalent SC Special Case www without wrong working art anything rounding to soi seen or implied Qu. Answers Mark Part Marks (a) 4 504 M for ( + 7 + 8) soi by answer of 0 or B for 7 or 4 or 94 or 6 seen 9 (b) (i) 468.7 M for 504 oe soi by 468.7 or 469 00 7 or M for 504 (implied by 5.8) 00 64.68 84 M for 00 77 or M for (00 )% = 64.68 (c) 6.9 cao M for 50.06 oe implied by answer 6. or better or M for 50.06 n oe n > seen (d).5% 4 88 M for 00 88 4 6 or M for 00 (.5) or (0.5) 88 88 (a) 0.9 or 0.9 www 4 4 M for 4 + 9 4 9 cos 08 If M0, M for correct implicit statement A for 9.49...(which can be www) (b) (i) 5.6 or 5.6.. www M for 9 cos 55 oe in correct triangle (0)5 B SC for answer If M0, B for 55 or 5 in correct position soi University of Cambridge International Examinations 0
Page Mark Scheme: Teachers version Syllabus Paper IGCSE May/June 0 0580 4 (a) 0.98(4) 0 0.98(4) B B for 4 correct, B for correct (b) 9 points plotted smooth curve Pft C B for 7 or 8 points correct B for 5 or 6 points correct correct cubic shape through 8 or more points from to (c) (i) y = 0.8 drawn B Accept good freehand To make the three possible intersections (otherwise the line must be from to ). to., 0.4 to 0. 5,.55 to.65,, (d) correct tangent drawn at x =.5 4 to 5.5 T B Allow slight daylight dep on T M for evidence rise/run with correct scales dep on T 4 (a) 90 B (b) tan(acb) = 7 0 oe 4.9(9...) M A Any longer method must reach equivalent stage (c) same segment B Allow same arc oe (d) (i).9 or.8(9...) www M for 7 sin 77 sin 5 or M for implicit form 8.6 (8.58 to 8.6) www M for 0.5 7 their (d)(i) sin(80 77 5) oe Allow 68.00 to 68.0 for 68 (e) 8.69 or 8.7(0) or 8.685 to 8.700. cao www M for 0..9 their or M for 0.9 or reciprocal seen their 5 (a) (i).8 cao accept (h) 48, not.48.8 cao accept (h) 48 not.48 (iii).8 cao ft ft their (a) accept (h) 48 and.48 (b) 6 (c) (i) 9, 4, 4 B for correct University of Cambridge International Examinations 0
Page 4 Mark Scheme: Teachers version Syllabus Paper IGCSE May/June 0 0580 4.5.5 4.5 5.5 7 M At least 5 correct mid-values seen 0 + 5.5 + 8.5 + their 9 4.5 + their 4 5.5 + their 4 7 (= 6) M fx where x is in the correct interval (0 + 6.5 + 6 + 40.5 + + 8) 80 M Dependent on second method mark.95 cao A Allow www 4 (d) Axes suitably numbered or horizontal axis suitably numbered and area scale stated e.g. 4cm = 0 6 columns with correct relative widths no gaps, but condone reasonable freehand heights: 0 5, 8, their 9, their 4 their 4 if vertical axis not labelled use correct relative heights 6 (a) (i) ( 4x 7)(x ) = 8x 4x 4x + 7 4x 9x + = 0 M B E or ( 4x 7)(x ) = 0 only allow 8x and/or + 6 = 0 or = 6 at least one more line e.g. 8x 8x + 6 = 0 with no errors or omissions seen ( 9) ± ( x = ) ( 9) 4 (x = ) 0.4,.84 cao 4(4)() B B,B B for ( 9) 4(4)() or better seen ( ) B for p = ( 9) and r = 4 or better as long as p + or q in the form r After B0B0, SC for 0.4 or 0.406(99...) and.8 or.84(070...) (iii) 0.6 or 0.70 to 0.74 or 0.7 Bft ft their value to give positive ( 4x 7) (b) (i) ( x 4)( x + 4) B (x + )( x + 4) + ( x + 40) = ( x 6) oe x + 8x + x + or x + x x 48 x = 7 www 4 M B A fractions cleared or could all still be over ( x 6) or (x + )( x 6) + ( x + 40)( x 4) = ( x 4)( x 6) Condone sign slips University of Cambridge International Examinations 0
Page 5 Mark Scheme: Teachers version Syllabus Paper IGCSE May/June 0 0580 4 7 In any part of part (a) all marks are independent but mention of a second transformation scores 0 out of (a) (i) Rotation (centre/about) origin (O) (0,0) 80 accept R SC for all of enlargement, sf, (0, 0) Enlargement (centre/about) (0, ) SF accept E (iii) Enlargement (centre/about) (0, 6) SF accept E (b) (i) image at ( 4, ) (, ) and (, 0) 4 SC for translation by k image at (, ) ( 4, ) and ( 5, 5) SC for reflection in y = or k, k 0 5 (c) (i) image at (0, ) (4, ) and (6, 5) SC for stretch sf with x-axis invariant ie at (0,6) (,6) (,0) 0 0 ft ft ft their stretch factor only SC for correct left hand column ft or 0 0 ft 8 (a) 4 6 8 (b) x SC any other ( x + a)( x + b) where a b = 6 or a + b = (c) (i) ( 4)( x 9) 4 9 B ft ft or can recover (d) E E 6 8 4 9 5 7 G F Must have all 9 numbers on diagram and no extras SC for 5 or more correct elements (e) (i) or { } cao cao (iii) cao University of Cambridge International Examinations 0
Page 6 Mark Scheme: Teachers version Syllabus Paper IGCSE May/June 0 0580 4 9 (a) (i) 4 x M for 7 ( x ) (iii) 5x 8 final answer (b) 7 x oe 7 y M for x = 7 y, x = oe or x = 7 y, y = 7 x oe i.e one step from answer (c) 9x + 0x + 7 M for ( x + 5) 8 seen B for 9x + 0x + 5 (d) 7 cao M for (x + 5) + 5 = 8 or better or B for (x + 5) + 5 oe (e) x < oe cao 8 M for (x + 5) < 7 x oe B for 8x * or 8x * Do not accept 8 0 (a) 00 or 040 or 04 to 06. ( ) ( V = ) π 9 4 Accept 648π for marks if final answer (b) (upper radius =) (vol cut off =) π their 8 their (a) their 75.9 958 to 964.(...) (c) 960 = 5 π r 5 soi B M M dep E M accept 8 9 oe 4 (= 75.6 to 75.4) their r must be less than 9 [ alternate method M for ratio sides : M ratio vols : 7 M their (a) 6 7 ] 64π implies B M or M must see a figure after decimal point if 960 r = 960 π 5 5 M implied by 8.8... their 8.8.88 to.89 M E dep on M M SC for 5 π.9 5 = 980 to 98 University of Cambridge International Examinations 0