0607 CAMBRIDGE INTERNATIONAL MATHEMATICS
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1 CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Seconary Eucation MARK SCHEME for the May/June 03 series 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/4 Paper 4 (Extene), maximum raw mar 0 This mar scheme is publishe as an ai to teachers an caniates, to inicate the requirements of the examination. It shows the basis on which Examiners were instructe to awar mars. It oes not inicate the etails of the iscussions that too place at an Examiners meeting before maring began, which woul have consiere the acceptability of alternative answers. Mar schemes shoul be rea in conjunction with the question paper an the Principal Examiner Report for Teachers. Cambrige will not enter into iscussions about these mar schemes. Cambrige is publishing the mar schemes for the May/June 03 series for most IGCSE, GCE Avance Level an Avance Subsiiary Level components an some Orinary Level components.
2 Page Mar Scheme Syllabus Paper IGCSE May/June (a) (i) $ M for o.e. or M for 5840 = 88% seen (ii) $0 800 or 0790 to M for or their (i) or M for 5840 (or 8000) 0.88 n, n > (iii) 00 M for multiplying by 0.88, 3 more times or n = 5000 o.e. soi by 9.0 or 500 to 504 or 440 to 443 or SC for 0. (b) 8. or (8.5 to 8.6) 4 M3 for ( ) 5840 soi by figs 859 to 86 M for (876 to 877) M for (906 to 907) (a) Reflection y = x o.e. Secon transformation loses all mars Inepenent (b) (i) Triangle vertices (3, ), (5, ), (5, ) B for vertices correct or rotation 80 about other centre (ii) Triangle vertices (0, ), (4, ), (4, 4) FT B FT for vertices correct or enlargement s.f. correct orientation (iii) Enlargement s.f. centre (, 0) Secon transformation loses all mars All inepenent Cambrige International Examinations 03
3 Page 3 Mar Scheme Syllabus Paper IGCSE May/June (a) B for correct cubic shape B for max on x = 0 an +ve x- intercepts (b) 0.73 or 0.73 to 0.730,,.73 or.73 B for any one solution (c) (i) (0, ), (, ) B for each (ii) < < FT FT (c)(i) Allow < an > full mars SC for or better or in wors () Setch of line Inication that it only cuts curve once 4 (a) 30/cos65 = (Answer Given) M for cos 65 = 30/QC o.e. If using Pythagoras must reach their PC + 30 (b) ( or 8.48 to cos5) M A Allow correct use of cosine rule in other triangles for M or M M for ( cos5) If 0 score SC for answer in range without Cosine rule (c) 457 or to FT FT their (b). () 64.3 or 64.4 or to M for tan 65 = x/30 o.e. (M mar may be seen earlier) (e) 790 or 800 or 790 to 796 www FT FT for o.e. [their ()(i)]² sin 0 M FT for [their ()(i)]² sin 0 o.e. Cambrige International Examinations 03
4 Page 4 Mar Scheme Syllabus Paper IGCSE May/June (a) Line from (0, 5) to (6, 0) (if extene) x = 4 rawn Line from (0, ) to (, 0) (if extene) Region R clearly ientifie cao Lines must be long enough to efine region B for line through either point with negative graient. (b) (i) 7 cao (ii) 9 cao 6 (a) 89.7 or to M for (50 π 3²).5 or π 3.5 or M for π 3² or (b) 7.7 or 7.8 or 7.7 to 7.76 FT FT for their (b) 0.8 (c) 55 or 55. to M for o.e. (horizontal rectangles) (35) M for.5 5 (vertical rectangles) (5) M for 0 5 π 3² o.e. or better (front face) (35.86 or 7.7) M for π 6.5 o.e. (arch) (3.56) Cambrige International Examinations 03
5 Page 5 Mar Scheme Syllabus Paper IGCSE May/June (a) (i) 38 (ii) 3 M for clear reaing off at 35 an 05 (b) (i) 33, 53, 85, 5 B FT for any (ii) 8 points plotte Joine by smooth curve FT FT B FT for 5 or more correct All mars epen on frequencies increasing (iii) Comparison of spees or spreas (ranges) Justification referring to meian or inter-quartile range SC for comparison of spees an spreas without reasons Mar the best provie there is no contraiction (iv) 59. or M for at least two mipoints (5, 35, 4.5, 47.5, 55, 70, 90) soi at least correct proucts (50, 40, 637.5, 950, 760, 00, 50) or total (v) Bars of correct with Bars correct heights 3, 4, 3.,.5 an.5 3 Allow freehan B for 4 correct or B for correct SC3 for correct but interval 40 to 45 an 45 to 50 combine with height of (a) 4 or or to o.e. 99 In all parts accept ecimal / % to 3sf but not ratios or wors etc. 7 6 M for o.e. 3 3 (b) (c) or or o.e. 3 M for + o.e or M for one of above proucts 490 or 0.87 or to o.e M for o.e. 5 4 M for omitte prouct in or for alone 5 4 Cambrige International Examinations 03
6 Page 6 Mar Scheme Syllabus Paper IGCSE May/June (a) (i) 0. R = o.e. 3 coul be evaluate in part (ii) M for R = o.e. M for substituting 0.8, 0.5 into R = or R = ² or R = (ii) 0.05 FT FT R = o.e. with incorrect only (iii) 0.4 or 0.36 cao M for substituting R= 4 into R = or R = ² or R = with numerical (b) 0.5 M for R 4 o.e. 0 (a) (b) (, 0) 3 Goo setch with no overlaps of asymptotes an no eparting from asymptotes. Must have positive x intercept. B for left han branch to left of x = 3 an above y = (approx.) B for right han branch to right of x = 3 an below y = (approx.) (c) x = 3 y = () 3 f(x) Accept y, x etc. Conone B for either inequality or 3 < f(x) (e) Setch of 5 x or formula after x + x + 4 o.e. 4.4 or or.586 to.585 M B B Allow other correct setch for o.e. B max if no setch or metho shown (f) Correct setch B for translation in x irection B for asymptote at x = 0 Cambrige International Examinations 03
7 Page 7 Mar Scheme Syllabus Paper IGCSE May/June (a) Any of ABO = CDO (alt angles) BAO = DCO (alt angles) AOB = COD (vert opp angles) + B for any pairs of angles ientifie without a reason (b) 0 M for CD/6 = 5/3 o.e. (c) (i) (ii) (iii) 3 o.e. 5 9 o.e. 5 9 o.e or (a) 5500 x (b) 5500 x their x x + 60 = o.e. B MFT FT their expressions 5500(x + 60) 5500x = ½x(x + 60) o.e. or better MFT Only FT their 5500 x = x or 30 o.e. or for common enominator or LHS resolve to a single fraction an equate to (allow sign x + 60x = 0 E error) Establishe without any errors or omissions (c) 60 ± 60 4()( ) Or parabola setche with one +ve an one ve root M B B If B0 then SC for correct but both not roune to nearest whole number 78.9 to 78.96, 84.9 to () 4 or 4 3 M for 5500 their +ve x 5500 B for 0540 or their x [in hrs mins] 4 Cambrige International Examinations 03
0607 CAMBRIDGE INTERNATIONAL MATHEMATICS
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