0607 CAMBRIDGE INTERNATIONAL MATHEMATICS

Transcription

1 PAPA CAMBRIDGE CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Seconary Eucation MARK SCHEME for the May/June 0 series CAMBRIDGE INTERNATIONAL MATHEMATICS /4 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 0 series for most IGCSE, GCE Avance Level an Avance Subsiiary Level components an some Orinary Level components.

2 Page IGCSE May/June 0 4 $8 000 M for or M for 5840 = 88% seen $0 800 or 0790 to 0800 M for or their (i) or M for 5840 (or 8000) 0.88n, n > 00 M for multiplying by 0.88, more times or n = 5000 soi by 9.0 or 500 to 504 or 440 to 44 or SC for or (8.5 to 8.6) 4 M for ( ) 5840 soi by figs 859 to 86 M for (876 to 877) M for (906 to 907) Reflection y = x Secon transformation loses all mars Inepenent (i) Triangle vertices (, ), (5, ), (5, ) Triangle vertices (0, ), (4, ), (4, 4) FT B FT for vertices correct or enlargement s.f. correct orientation Enlargement s.f. centre (, 0) Secon transformation loses all mars All inepenent (a) (i) (a) Cambrige International Examinations 0 B for vertices correct or rotation 80 about other centre

3 Page IGCSE May/June 0 4 (a) B for correct cubic shape B for max on x = 0 an +ve x- intercepts 0.7 or 0.7 to 0.70,,.7 or.7 B for any one solution (i) (0, ), (, ) B for each < < FT FT (i) Allow < an > full mars SC for Y Y or better or in wors () Setch of line Inication that it only cuts curve once 4 (a) 0/cos65 = (Answer Given) M for cos 65 = 0/QC If using Pythagoras must reach their PC + 0 M 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 ( cos5) 8.5 or 8.48 to 8.50 A 457 or 457. to FT () 64. or 64.4 or 64. to 64.6 (e) 790 or 800 or 790 to 796 www FT FT.97 + their. M for tan 65 = x/0 (M mar may be seen earlier) FT for [their ()(i)]² sin 0 M FT for sin 0 Cambrige International Examinations 0 [their ()(i)]²

4 Page 4 IGCSE May/June 0 5 (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 (i) 7 cao 9 cao 89.7 or to (a) 7.7 or 7.8 or 7.7 to or 55. to 55. FT 5 Cambrige International Examinations 0 4 Lines must be long enough to efine region B for line through either point with negative graient. π ²).5 or π.5 or M for π ² or M for (50 FT for their 0.8 M for (horizontal rectangles) (5) M for.5 5 (vertical rectangles) (5) π ² M for 0 5 or better (front face) (5.86 or 7.7) M for π 6.5 (arch) (.56)

5 Page 5 IGCSE May/June (a) (i) 8 M for clear reaing off at 5 an 05, 5, 85, 5 B FT for any (i) 8 points plotte Joine by smooth curve FT FT B FT for 5 or more correct All mars epen on frequencies increasing 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, 5, 4.5, 47.5, 55, 70, 90) soi at least correct proucts (50, 40, 67.5, 950, 760, 00, 50) or total (v) Bars of correct with Bars correct heights, 4,.,.5 an.5 Allow freehan B for 4 correct or B for correct SC for correct but interval 40 to 45 an 45 to 50 combine with height of.5 8 (a) In all parts accept ecimal / % to sf but not ratios or wors etc. 6 7 M for 4 or 0.04 or 0.04 to or 0.66 or or M for one of above proucts 490 or 0.87 or to M for Cambrige International Examinations 0 M for M for omitte prouct in or for alone 4 5 4

6 Page 6 9 (a) (i) IGCSE May/June 0 R= FT 4 coul be evaluate in part M for R = M for substituting 0.8, 0.5 into R = or R = ² or R = FT R = with incorrect only 0.4 or 0.6 cao M for substituting R= 4 into R = or R = ² or R = with numerical 0.5 M for R 4 Goo setch with no overlaps of asymptotes an no eparting from asymptotes. Must have positive x intercept. 0 (a) B for left han branch to left of x = an above y = (approx.) B for right han branch to right of x = an below y = (approx.) (, 0) x = y = () =Y=f(x) I (e) Setch of 5 x or formula after x + x or or.586 to.585 (f) Correct setch Accept y, x etc. Conone 0. B for either inequality or < f(x) Y M B B Allow other correct setch for Cambrige International Examinations 0 B max if no setch or metho shown B for translation in x irection B for asymptote at x = 0

7 Page 7 IGCSE May/June 0 Any of ABO = CDO (alt angles) BAO = DCO (alt angles) AOB = COD (vert opp angles) (a) + 0 (i) x (a) () B for any pairs of angles ientifie without a reason M for CD/6 = 5/ 0.4 or x + 60 their = x x + 60 MFT FT their expressions (x + 60) x = ½x(x + 60) or better MFT Only FT their x + 60x = 0 4 B E = x + 60 x or 0 or for common enominator or LHS resolve to a single fraction an equate to (allow sign error) Establishe without any errors or omissions 60 ± 60 4()( ) Or parabola setche with one +ve an one ve root 78 M B 84 B 4 or 4 If B0 then SC for correct but both not roune to nearest whole number 78.9 to 78.96, 84.9 to M for their +ve x B for 0540 or their x [in hrs mins] 4 Cambrige International Examinations 0