4024 MATHEMATICS (SYLLABUS D)

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1 CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge Ordinary Level MARK SCHEME f the October/November 05 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 befe 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 Rept f Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes f the October/November 05 series f 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 O Level October/November (a) (i) (a) B f 360 seen 00 (b) 0 isw ft (ii) x x = oe 00 B f by figs 74 (b). 3 M f B f x x = 550 oe (a) 4 CA ( 7) oe SC f x (b) 0.8 ( 8 ( )) + (7 ) (c).8 ft B f [BC =] 5 soi (b) + theirbc + CA (d).8 ft tana = ( 7) (8 ( )) oe 3 (a) (i) Convincing explanation (ii) 8 B f O C D = 4 triangle COD isosceles soi (iii) 76 ft (b) (i) Convincing explanation B f a crect pair of equal angles stated (ii).5 3 B f 8.5 SR 8.5 QS seen and = 8. 5 SR 5 SR QS = QS Cambridge International Examinations 05

3 Page 3 Mark Scheme Syllabus Paper Cambridge O Level October/November (a) (i). 4 π r 3 = 0 soi 3 SC f (ii) 6.79 B f 3 3 oe = x 50 (b) 87 3 π(figs 5) oe and oe 4 π (figs 55) 50 their πr 5 (a) 5. AC + 40 = 65 oe AF (b).7 = sin5 oe (c) = cos30 oe and a further AG (AG = ) 35 cos30 oe 6 (a) (i) final answer B f one value SC f both 4.6 and.4 (ii) (B = ) 7 (C = ) 3 ( x + 7 ) = 4 5 and B f one crect value (b) x < isolating 3x and 6 soi (c) (x + 3y)(6 t) oe the crect extraction of a common fact at any stage (d) (a = ) 7 (b =) 6 4 equalising one set of coefficients substitution and a further eliminating one variable simplifying an equation in one variable and A f 7 and A f 6 After A0, SC f crect substitution into one of the iginal equations to find the other variable Cambridge International Examinations 05

4 Page 4 Mark Scheme Syllabus Paper Cambridge O Level October/November (a) Fully shown the area sine fmula (b) x 9x + 6 (= 0) crectly obtained 3 B f both x + and 4 + x 5 and x(x 5) = their( x + ) their(4 + x 5) 3 (c) (i) B f ( 9) 4 6 soi and B f ( 9) ± their33 soi and both real values of p ± r q (ii) 0.33 with reason (d) ft M f (BC =) c(i) + (c(i) 5) c(i) (c(i) 5) cos5 crect fmula with one err and A ft f crect evaluation from their M SC f x + (x 5) x(x 5)cos5 oe 5 8 (a) (i).6 π (ii) 7.85 π (b) (i) 39.3 ft (ii) ft B f (a)(i) and indep (a)(ii) (iii) 47 to 47 ft B f height = 5 and radius = soi 800 (c) (i) (h =) πr (ii) h is divided by 4 oe Cambridge International Examinations 05

5 Page 5 Mark Scheme Syllabus Paper Cambridge O Level October/November (a) 36 (b) Crect plots ft and curve P f 6 crect plots ft (c) (i) 4 < gradient < 6 ft B f tangent at t = 4 (ii) Speed oe (d) Their.5 ft B f their.8 and their 4.3 (e) (i) Their.65 towards Their 4.7 away from ft B f one crect ft (ii) t = oe isw t (iii) 3 cao 0 (a) Crect histogram 3 If 3 not sced, up to marks from: (b) 95 < t 00 (c) fx B f crect fd s (allow one err) B f crect column widths B f crect heights from their fd s B f division by 80 seen (d) (e) (i) 8 oe oe (ii) oe Cambridge International Examinations 05

6 Page 6 Mark Scheme Syllabus Paper Cambridge O Level October/November (a) (i) 6.08 (ii) AF = AH + HF oe 4 6 B f (iii) (a) (b) 4 7 GD = FH stated appropriate numerical vect statement dep (iv) (9.5, 3) ft (b) (i) Crect image (ii) Centre (4, 0) oe Scale fact oe B f either (iii) (5, ) (iv) Crect image B f either Stem of flag R on parallel to y = x Hypotenuse of flag parallel to y-axis. SC f crect clockwise rotation Cambridge International Examinations 05

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 Cambridge International General Certificate of Secondary Education MARK SCHEME f the May/June 205 series 0580 MATHEMATICS 0580/2 Paper 2 (Extended), maximum raw mark