0580 MATHEMATICS. 0580/43 Paper 4 (Extended), maximum raw mark 130

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1 CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 04 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 04 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

2 Page Mark Scheme Syllabus Paper Abbreviations cao correct answer only dep dependent FT follow through after error isw ignore subsequent working or equivalent SC Special Case nfww not from wrong working soi seen or implied (a) 00[.00] Final answer B for 074[. 5] or 070 ( 900 M for or M for 4598 associated with 7 [%] (c) 04 M for (+4+) or (d) 4 M for or M for figs or 455 (e) 5545 M for (a) 0 < x 5 5 < x 0 0 < x 5 5 < x < x 0 9 [4] 5 5 correct B for or 4 correct or SC for all correct but in the form 0 to 5 or 0 5 B for 4 correct or B for correct ( 5.[0] or 5. to 5.4 nfww 4 M for mid-values soi, condone one error or omission soi and M for fx for any x in intervals including boundaries, but all fs must be integers, condone one further error or omission and M dep for fx 90 Dep on nd M mark earned Cambridge International Examinations 04

3 Page Mark Scheme Syllabus Paper (a) ( 7[.0] or 7.98 to 7.99 nfww 97 M for [sin P = ] 7 or M for implicit version (i. or.8 to.9 nfww 4 M for cos ( their 7) or M for implicit form and A for [XR =].8 to ( 7. or 7... nfww 4 M for [a =] 9.4 sin 7 cos 4 or [a = ] 9.4sin7/sin(90 4) or M for [a =] their height cos 4 a 9.4 or = sin 7 sin(90 4) or M for their height a = cos 4 or for [their height = ] 9.4 sin 7 or B for 48 correctly used or seen in correct position on diagram (c) (a) 0, 4.5,.[ ] B, B, B ( Complete correct curve with minimum below y = y 4 5 B FT for 9 points correctly plotted B FT for 7 or 8 points correctly plotted or B FT 5 or points correctly plotted x and B indep two separate branches not touching or cutting y-axis - (c) 0.5 to to to.9 if 0 SC for y = indicated (d) Correct line or no line and 0.7 to 0. nfww Must check line - not if wrong line B for y = x ruled correctly or SC for ruled line with either gradient or y-intercept but not line y = or correct freehand line Cambridge International Examinations 04

4 Page 4 Mark Scheme Syllabus Paper (e) tangent ruled at x = and 0. to 0.8 Accept integer/integer provided in range B for correct tangent drawn and M for change in y / change in x dep on any tangent or close attempt at tangent at any point Must see correct or implied calculation from a drawn tangent (f) x = x or + x = 0 = x or x = M M dep M x = A dep M 5 (a) ( 4 (i 5.8 to 5.8 M for + 5 seen ( ( p + q accept unsimplified (i PS = p +q or SP = p q B MS = p+ 4 q seen B or SM = p 4 q seen or RM = ( p + q) soi or MR = ( p q) soi or MQ = ( p + q) soi or QM = (p q) soi PM = p + RM or p MR or p + q + QM or p + q MQ [ = p + q ] M Any correct route for PM eg PR+ RM : nfww A After 0 scored, SC for : Cambridge International Examinations 04

5 Page 5 Mark Scheme Syllabus Paper (a) ( (i (ii 4 ( (c) 4 4 M + only 4 4 or M for one of or soi by M for only or M for denominators, 5, 4, soi in product of four fractions 7 (a) ( 48 (i B for 58 seen at A or seen at Y (ii 48 (iv) 0 nfww B for [sum of interior angles =] 70 and M for {(their 70) (p+q+t+90)} ( ( B for angle RPS = 7 or 90 at P or at S seen or stated (i 54 B for their x or or letter x at Q seen or state Cambridge International Examinations 04

6 Page Mark Scheme Syllabus Paper 8 (a) ( 7 + ( x )( x+ 4) = ( x+ 4) M Allow if bracket[s] omitted but recovers x + 8x x or better seen x + x = 0 B A with no errors seen and brackets correctly expanded on both sides and no omission of brackets (i () 4( ( ) ) p = and r = () or better B or x + 4 B Must see p+ r q or p r q or both Or + or and.4 cao BB SC for. and. final answer or.7 and.7 final answer or.4 and.4 seen in working or for -.4 and.4 as final ans ( π x + π x x M or M for π x x 4[] π x =[] π r M Dep on M x = r A with no errors seen 9 (a) 4 x final answer ( 9x 8 final answer M for 4 (4 x) seen (c) (d) (e) final answer M for soi by final answer to sf or better or M for [g( ) =] soi 4 x final answer M for a correct first step y 4 x= 4 y or x= 4 y or = x 4 or or. or better M for x 4 = 0 or better or M for (4 x) Cambridge International Examinations 04

7 Page 7 Mark Scheme Syllabus Paper 0 (a) [r =].0[9...] B for [r =]. or M for 4 tan 0 r or M for tan 0 4 = ( or.5 to. 4 M for sin 0 or M for sin 0 or M for their triangle area shown dep on used within their area of triangle method (c) ( 0 M for 0.4 or 0 4 or SC for figs (i.5 or.47 to.48[...] M forπ or SC for π. 4 soi by.5 or.47 to.48[ ] (ii 40[.0] or 40. or 40.0 to 40. nfww i M for00 00 i or 00 i or M for 00 their ( i or (a) 8 B for correct n SC for n 4 5 n or ( ( ( n ) 8 0 (i ( n ) or n- (c) 84 B for n = 8 Cambridge International Examinations 04

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

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