4024 MATHEMATICS (SYLLABUS D)

Transcription

1 CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level MARK SCHEME for the May/June 04 series 404 MATHEMATICS (SYLLABUS D) 404/ Paper, maximum raw mark 00 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 04 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

2 Page Mark Scheme Syllabus Paper GCE O LEVEL May/June (a) 8 to 40 (b) D marked at intersection of correct arcs B for a correctly positioned D with one correct construction arc or no correct arcs Or, provided D to the west of AB B for D on one correct arc or radii 5 cm and 6 cm reversed with arcs Or, provided D to the east of AB B for D on intersection of two correct construction arcs (c) 0 Tolerance ± (d) (i) P and Q marked at intersection of perpendicular bisector and circle B for perpendicular bisector of AC minimum cm long B for arcs radius 4.5 cm centre B, minimum cm long cumulatively B for P and Q at correct positions 49 Tolerance ± (a) (i) 97 4 f + d ( c = ± ) M for 4f = 6c d or better 6 (b) x cao B for final answer {+ or } x * {+ or }, where * can be wrong inequality or equals (c) ( + 5x)( 5x) oe Must be integers (d) (8p q)(x y) oe seen isw M for x(8p q) oe or y(8p q) oe Or 8p(x y) oe or q(x y) oe Cambridge International Examinations 04

3 Page Mark Scheme Syllabus Paper GCE O LEVEL May/June (e). and. final answer 4 B for one correct solution or x =. to. and -. to -. p ± ( or + or ) q If in the form r B for p = 6 and r = 0 And B for q = 96 or q = 7... (a) (i) 5.9(0) to 54 M for M for [= 64] M for their SC for an answer of 8.75, 8.7, 8.8, 5,.7,.8 or [0] or 40 or 40 M for 7 ( ) 4 (a) (i) 5 numbers completed correctly After 0+0 allow B for /6 and 4/6 Or 0. and 0.66 or better (a) 8 oe isw 0 (b) 8 oe isw 0 After for (b), If all 6 used B for 8/6 and 0/6 If 5 used, B for 8/5 and 9/5 5 (a) 78. to 78. M for 64 cos 5 = or better AB (b) 7.9 to 8 M for or () cos 5 M for AD = cos 5 (c) 4. to 4. M for M for sin ADC sin5 = oe 64 their8 64 sin5 sin ADC = their8 (d) 900 M for 0.5 ( ) 40 Cambridge International Examinations 04

4 Page 4 Mark Scheme Syllabus Paper GCE O LEVEL May/June (a) 6n cao B for 6n soi 4, 0, 8, 8 B for correct terms seen and 4 4 n + n M for = 6 or better 5n M for n 7n + 7 = 0 B for either or 4 7 (a) (i) 9600 cao 60 M for 600 oe 60 cao 60 (iii) 440 cao (44 90) M for their oe 40. M for M for division by their ( ) Correct histogram B for 5 bars correct width and position B for at least correct heights k (.4,.6, 4.5,.65,.) B for 5 correct heights (iii) 8 or 9 or 40 or 4 8 (a) (i) (0) to 6.4 or 4 cao (iii) y =.5x + 7 oe B for gradient =.5 or y-intercept = +7 soi in a final equation (iv) (, 8) B for one value correct (a) b a (b) a cao (c) 4(b a) (a) : 4 B for correct unsimplified CD or for (b a) (b) : 5 Cambridge International Examinations 04

5 Page 5 Mark Scheme Syllabus Paper GCE O LEVEL May/June (a) = 6.5(5...) Must be shown to at least d.p. (b) 47 to 49 M for π 6 6. soi by 05.4 M for π 6 soi by. (c) 565 to 566 M for π 6 5 or better (d) 6 to 7 FT FT their (c) 0.56 evaluated B for figs 6( ) or 7( ) or their (c) figs 56 evaluated (e) (i) 8.89 to 8.9 M for or.5 seen oe 66 to 665 M for or.58 seen oe (a) [L =] (x + ) or x + x x or x + x + + x x B for 50 seen x (b) 4.5 to 4.6, 45 B for one correct (c) Correct smooth curve through the eight given points correctly plotted on correctly scaled axes ± half a small square B for seven or eight of the given points correctly plotted on their axes or B for six of the given points correctly plotted on their axes (d).8 to. < x < 6.8 to 7. B B M for attempt to read off two x values at y = 40 (e) (i) 7.5 < answer < 8.5 7, 7 cao (f) 0, 0 cao Cambridge International Examinations 04

6 Page 6 Mark Scheme Syllabus Paper GCE O LEVEL May/June (a) (i) EC = BE or AC = FE and AEC = FBE or ECA = BEF Two correct reasons for their choices Third statement, leading to correct congruence condition i.e. RHS, SAS, SSA B B B Statements and reasons: EC = BE; radii AC = FE; diameters AEC = FBE [= 90 ]; angle in semicircle ECA = BEF [= 60 ]; equilateral triangle BFD (iii) EBF = DFB = 90 Cointerior/interior/supplementary/allied angles [sum to 80] OR BEF = EFD = 60 Alternate angles [are equal] dep OR dep Both 90 could be marked on diagram Both 60 could be marked on diagram (iv) 0 0 could be marked on diagram 6.6 to 6. M for 4 4 sin 0 Or PQ perpendicular height (numerical) 8. to 8. (60 0) M for 60 0 or π 4 soi by π 4 soi by. And M for their major sector area + their triangle area Or for their circle area their minor sector area + their triangle area Cambridge International Examinations 04