4024 MATHEMATICS (SYLLABUS D)

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1 CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge dinary 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) 30 B f [0] seen M f oe (b) 6.5[0] final answer B f 0.5[0] seen M f oe w = 4.65 x = [0].5 y = 40.5[0] z = B f [w = ] 4.65 B f [x = ] [0].5 B f [y = ] 40.5[0] M f 3.4[0] 0.8 oe Bft f 3.35 (a) (i) 9.[ ] 3 4 M f [AB = ] + 5 better (ii) 8.6 to their M f tan θ = 5 A f 38.6 to 38. Bft f [ (b) 44.8[ ] 3 M f oe AB ˆ C = ] their θ + 90 Alternative method M f complete method using cosine rule f cos ABC using their 9. M f sin sin 65 = oe sin x (a) (i) B f one row one column crect (ii) oe isw B f det = 4 soi f 3 (b) oe B f one row one column crect M f C = 4 oe 0 3 f C = 0 3 Cambridge International Examinations 05

3 PagP ge 3 MarM k Schemee Cambridgee O Level October/November 055 Syllabus 404 Paper Question Answers Markk Partt marks (i)) B f elements crect in i a 3 by matrix all 3 values crect inn dollars M f (ii)) Amount [inn cents] f each week ( iii) ) 85.5 cao 4 (a) A B C (b) E ( (D F F) (DD F ) E E D' F ' (i)) P Q B f 8 9 numbers crectly placed o f 0 numbers cc rrectly placed with onee additional number f, 3, 4,, 5,, 9 seen crc rectly positionedd and no numberss positionedd increctlyy (ii)) ft ( iii) ) 3 00 oe ft B f their 3 seen as numerat of a fraction soi 5 (a) 3xx y( y 5x) 5 B f 3x (y 3y(x y x y( ( 6 y 5 5x) ) 3xy( ( xy x ) 5 5x ) 5xyy ) 3xx y(aa 5x) 3xx y(y B) Cambridgee International Examinationss 055

4 Page 4 Mark Scheme Syllabus Paper Cambridge O Level October/November (b) x = ±.63[...] ± 8 4( x + ) + x 3 M f = 3 soi 3 x( x + ) Mdep f 4x x = 3x + 6x better (i) Crect region shaded with 4 crect lines 3 B f 3 4 crect lines B f crect lines (ii) oe B f (3, 3) (, 4) soi 6 (a) (i) a =, b = 3 B f one crect (ii) 5.38 to M f 5 + (b) (i) b a ( b a) (ii) b + a ( a 4b) final answer + final answer (iii) λ : 3 λ dep Bdep f b + 4 a seen n(b + 4 a ) seen k = OF = OE oe Cambridge International Examinations 05

5 Page 5 Mark Scheme Syllabus Paper Cambridge O Level October/November SECTION B (a) A crect shape with one of diagonal lines as line of symmetry (b) Crect shape B f three additional triangles drawn round M, at least two crect SC f (i) C at (3, ) (3, 3) (4, 3) B f either vertical hizontal crect f two vertices crect and crect ientation (ii) y = x oe (iii) Translation 3 B f translation 3 M f D seen at (, 3), (3, 3), (3, 4) (iv) (a) (, 0) (4, 0) (4, ) (b) Rotation, 90 o clockwise, (0,0) oe B f two crect from: Rotation, 90 clockwise oe, (0, 0) oe (a) πr + πr (r + 4) with crect wking leading to 6r(r + ) M f πr + πr (r + 4) πr (r + r + 4) (b) 48, 90 Crect shape curve through crect points Bft f at least 5 crect points plotted (d) [h = ] 8 r + 6 r + 4 [h = ] ( r + 4) r better M f (r + 4) = r + h better (e) 6 M f 8r + 6 = 44 oe Cambridge International Examinations 05

6 Page 6 Mark Scheme Syllabus Paper Cambridge O Level October/November (f) (i) 4.8 to 4.95 (ii) 8 cao B f.[ ] M f substituting their f(i) into 9 (a) (i) 4 [minutes] 8 [seconds] ( r + 4) r (ii) [minute] 0 [seconds] B f attempt to read at.5 and 3.5 (b) 0,, 3, 5, B f 3 crect [minutes] 30 [seconds] B f three times only seen including 6, 5:30 and time in range 5:30 < t 6 (d) (i) 3 (ii) 0.4 Bft f their + their 5 seen 50 time = 5 [mins] seen SC f answer 50 oe (e) 4 a 49 oe M f a where a < B f and seen SC f answer oe answer oe (a) (i) (x + 5)(x 3) = 5 M equivalent equation f area Crect expansion leading to x + x 95 = 0 www A (ii) 9. cao 3 B f 9.9[8 ] 9.[0] seen OR B f 4 95 soi ± their94 And B f (iii).3 M f AD their 9. = 38.0 oe BC their 9. = 38.0 oe SC f answer [BC = ] 6.5 oe Cambridge International Examinations 05

7 Page Mark Scheme Syllabus Paper Cambridge O Level October/November (b) (i) B f LM ˆ N = 08 seen (ii) 4 3 M f 6 : their soi B f 6 seen SC f answer 4 (a) (i) 9.9[ ] M f 4 6 sin 50 (ii) 83 to 84 ft ft 0 their 9.9 (iii) 30 to ft ft 9 + their 9.9 B3 f [8 ] M f cos 50 M f cosine fmula with one err AND M f 0 ( their4.60) + their9.9 oe (b).3[ ] 4 B f crect change of units soi M f use of π r 0. = M f r = soi 0. π Cambridge International Examinations 05

MARK SCHEME for the October/November 2015 series 0580 MATHEMATICS

MARK SCHEME for the October/November 2015 series 0580 MATHEMATICS CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME f the October/November 05 series 0580 MATHEMATICS 0580/4 Paper 4 (Extended), maximum