0607 CAMBRIDGE INTERNATIONAL MATHEMATICS

Transcription

1 CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the May/June 05 series 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/4 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 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 05 series for most Cambridge IGCSE, Cambridge International A and AS Level components and some Cambridge O Level components. IGCSE is the registered trademark of Cambridge International Examinations.

2 Page Mark Scheme Syllabus Paper Cambridge IGCSE May/June 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 (a) h 5 mins or h 4.8 to 5 mins M for A for.58 (b) [0]7 50 oe B for 50 or 7 0 or 5 50 (c) 85 or 85.0 to B for 8.08 hours or 8 60 oe M for 70 their 8.08 (a) (i) Triangle (, ), (, ) (, ) SC for rotation 90 clockwise about (0, 0) or rotation 90 anticlockwise about another point (ii) Triangle (, ), (, ), (, ) FT FT their (i) or SCFT for reflection in x = 0 (b) (iii) Reflection y = x Stretch [stretch factor] Invariant line x = 0 oe (a) (i) 74.4[0] M for oe or SC for 8.4[0] (ii).7 or.7 to.74 4 M for oe A for reduction = $4 MA implied by 70.4[0] or 4.4[0] M for their reduction (b) (i).5[0] M for (ii). or. FT M for (.4 their.5) oe Cambridge International Examinations 05

3 Page Mark Scheme Syllabus Paper Cambridge IGCSE May/June (a) ( 4, ), 6 or M for or SC for (8, ) (b) 7. or 7... or M for (c) y = x + 4 oe B for gradient = or SC for y = mx+ 4 (d) (, ) 5 (e) y = x oe M for grad = their gradient M for subs of their (d) into y = mx +c oe (f) Kite 5 (a) x(40 x)(0 x) 00 80x 60x + 4x² (b) or B for 40 x or 0 x indep B for any cubic curve ( +x³) with max & min (c).9 or or.80 to.8 (d).8 would produce negative width/length oe (e) 00 or 0 to or 8.68 to 8.69 or 8.7 or 8.68 to (a) (i) 4n B for 4n + k (ii) (4n ) 0 (n + ) (n + ) oe FT their (a) 0 (b) (i) 0 [], 0, 0, 0 5 B for correct or 0, 0, 0 [], 0 (ii) (n ) 0 (n ) B for n BFT for 0 (n ) or M for 0 FT dep on (a)(ii) in correct form (n + ) ( n) Cambridge International Examinations 05

4 Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE May/June AB 7 (a) 86 [.0] or 86.0 to M for = cos55 oe (b) 46 or 45.5 to M for [cos =] 0 50 or M for 5 = cosθ M for 5 + their0.6 (0.6) (c) 000 or 00 to 05 M for 50 their86 sin55 oe 0 50 sin ( theirdac ) + oe or M for of above areas soi by 58 to 585. or (a) 6.8 or 6800 M for clear evidence of midpoints used soi by figs 68 (b) Correct plotting 7 correct points and drawing smooth curve 5 All FTS dep on increasing curve B for correct cfs seen 8, 9, 60, 8, 9, 98, 00 or SC for correct cfs with error BFT for 7 corrects height plotted BFT for points plotted at 5, 6, 7, 8, 9, 0, B dep FT for smooth curve dependent on increasing and dependent on B for heights (c) (i) 0 FT B dep for 90 FT dependent on increasing curve (ii) 600 to 900 FT Bdep FT for 5.8 (or 5800) or 7.6 (or 7600) seen or answer.8 dependent on increasing curve 9 (a) (i) x 5 x + 40 = oe 0 0x = 5x oe Accept 600 for 40 5 (ii) or 0.9 or 5 65 M for (iii) 40. or 40.4 to 40.5 or 5 65 FT M for their (a)(i) oe 0 Cambridge International Examinations 05

5 Page 5 Mark Scheme Syllabus Paper Cambridge IGCSE May/June (b) (i) or to 8 75 M for π or M for either 0 60 π or 5 0 π 0 60 π 5 0 oe (ii) 540 or 59 to 54 4 MFT for π 0 (their (a)(ii) + their(a)(iii)) π 5 (their(a)(ii)) + π 5² or MFT for π 0 (their (a)(ii) + their(a)(iii)) π 5 (their(a)(ii)) or M for for π 0 (their (a)(ii) + their(a)(iii)) or π 5 (their(a)(ii)) 0 (a) 6 4, 0 0 4, 9, 9 oe correctly positioned twice 9 (b) (i) (ii) (iii) 8 6 oe M for oe M for or M for one of above products 64 4 oe M for their (b)(i) oe M for one of ,,, (a) M Basic shape A RH branch cuts both +ve axes A asymptotes approximately right with no overlap (b) x = y = (c) < y May be separate, B for either Cambridge International Examinations 05

6 Page 6 Mark Scheme Syllabus Paper Cambridge IGCSE May/June (d) Correct shape B for reflection of any part of (a) in x-axis (e) or. or. (a) (i) (ii) 7 FT (b) (i) 6 6x oe B for 4 (x ) (ii) (iii) 4 x or x ( x )( 4 x) x oe B for x = 4 y or x + y = 4 M for ( 4 x) ( x ) ( x )( 4 x) or B for 4 ( x) ( x ) 5 x or SC for ( x )( 4 x) or M for common denominator (x )(4 x) Cambridge International Examinations 05