MARK SCHEME for the October/November 2013 series 0580 MATHEMATICS

Transcription

1 CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 03 series 0580 MATHEMATICS 0580/4 Paper 4 (Extended), maximum raw mark 30 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 October/November 03 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

2 Page Mark Scheme Syllabus Paper IGCSE October/November Abbreviations cao correct answer only cso correct solution only dep dependent ft follow through after error isw ignore subsequent working oe or equivalent SC Special Case www without wrong working art anything rounding to soi seen or implied (a) (i) cao 5 (ii) 3 : cao (b) (i). M for (ii).3 [0] nfww 3 M for.56. oe or M for.56 = 0% soi (c) 33.6[0] M for ( ) 0.5 oe (a) 3 correct lines on grid (0, 0) to (40, 5) (40, 5) to (00, 5) (00, 5) to (0, 0) Allow good freehand SCFT for lines correct, FT from an incorrect line (b) 5 oe 40 (c) M for oe [450] or M for evidence of a relevant area = distance and Mdep their area (or distance) 0 Cambridge International Examinations 03

3 Page 3 Mark Scheme Syllabus Paper IGCSE October/November (a) (i) 04 or 04. to 04.3 M for π 5 3 implied by answer in range 04. to 04.3 (ii) cao 3 M for 3 5 or states 5,, 3 triangle or M for 3 = 5 + h or better (iii) 34 or 34. to 34. M for 5 3 answer in range 34 to 34.3 FT FT their (a) (iii) 00 3 correctly evaluated and (iv) or 3.4 to given in standard form to 3 sig figs or better or M FT for their (a) (iii) 00 3 or SC for conversion of their m 3 into standard form only if negative power (b) 38 or 38.3 to π M3 for 360 oe or 6π π 5 3ortheir(a) (i) 360 oe π 3 or M for a correct fraction without 360 or M for π 3 oe [8.6 to 8.8] seen or π 3 oe [530.6 to 53.] seen 4 (a) 45.[0] or 45.0 to 45.0 nfww 4 M for cos 40 or M for correct implicit equation A for 06.. (b) 84.9 or to for angle BDC = 40 soi 70sin ( their 40) M for sin 3 or M for correct implicit equation (c) (i) 4060 or 4063 to 4064 nfww 3 M for ( sin 40) + ( 70 ( b)sin (80 their 40 3) ) their oe or M for correct method for one of the triangle areas (ii) 00 or 05 to 06 FT FT their (c) (i) 4 oe correctly evaluated or M their (c) (i) figs 4 oe (d) 35.4 or nfww M for sin 40 = distance or better 55 or for (55 70 sin 40) = (70 distance) or better Cambridge International Examinations 03

4 Page 4 Mark Scheme Syllabus Paper IGCSE October/November (a) (i) Correct reflection to (4, 8) (, 9) (4, 9) SC for reflection in line x = 5 or reflection in y = k Ignore additional triangles (ii) Correct rotation to (4, ), (4, 3) (6, 3) (iii) Shear, x-axis oe invariant, [factor] SC for rotation 80 with incorrect centre Ignore additional triangles 3 each (independent) (iv) 0 FT FT their shear factor FT for one correct column or row in by matrix but not identity matrix 0 or SCFT for (b) (i) p + s final answer M for recognising OQ as position vector soi (ii) s + p final answer for s + kp or ks + p or correct route (k 0) (c) parallel and OQ = SR oe 6 (a) (i).4 to.6 (ii).5 to.5 (iii) (iv).5 to. 0.9 to to.35 3 B for correct or for one correct or for y = x drawn ruled to cut curve 3 times (b) (i) 5 for [h(3) =] 8 seen or M for (x ) or better (ii) x or x oe final answer M for x = y or x = y or better (iii), 3 M for x = 3 or better for one answer (iv) 3 M for 8x = or 8x = 0 oe nfww 8 or M for (3x) [= x] Cambridge International Examinations 03

5 Page 5 Mark Scheme Syllabus Paper IGCSE October/November (a) 4.7 or 4.66 to M for midpoints soi (condone error or omission) (5, 5, 5, 35, 45, 55) and M for use of fx with x in correct interval including both boundaries (condone further error or omission) and M (dependent on second M) for fx 0 (b) (i) 50, 90, 4 for correct (ii) Correct curve or ruled polygon 3 Ignore section to left of t = 0 for 6 correct horizontal plots and FT for 6 correct vertical plots If 0 scored SC for 5 out of 6 correct plots and FT for curve or polygon through at least 5 of their points dep on an increasing curve/polygon that reaches 0 vertically (iii).5 to 3 5 to to 6 4 B or for 7 or 7.6 seen (c) (i) 50, 30 each (ii) Correct histogram 3FT for blocks of widths 0 0, (no gaps) FT for block of height.5 or their 50 0 and FT for block of height or their Cambridge International Examinations 03

6 Page 6 Mark Scheme Syllabus Paper IGCSE October/November (a) ( ) 4( 8)( ) or better p = ( ), r = (8) or better Seen anywhere or for x 6 Must be in the form p + r q or p r q or for ,.05 final answers SC for 0.7 or 0.67 to 0.67 and.0 or.046 to.047 or answers 0.67 and.05 (b) 3 3 M for y = k x oe or x = ky oe A for k = 6 oe or better or for k = to 0.67 [k = 6 implies MA] oe (c) 0 with supporting algebraic working 6 B for x = 9 oe x x 4.5 or for or.5. 5 Mdep on B for first completed correct move to clear both fractions M for second completed correct move to collect terms in x to a single term M for third completed correct move to collect numeric term[s] leading to ax = b SC for 0 with no algebraic working 9 (a) y = oe y = x oe y = x + 5 oe (b) y oe y x oe M for y = kx, k 0 or gradient soi M for gradient ½ soi or y = kx + 5oe or x + y = k k 0 oe If L and L 3 both correct but interchanged then SC3 y x + 5 oe 3 for each correct inequality, allow in any order After 0 scored, SC for all inequalities reversed (c) (i) 4 [bushes], 3 [trees] M for any correct trial using integer coordinates in region or 30x + 00y = 70 seen (ii) [bushes], 4 [trees] 860 M for any correct trial using integer coordinates in region Cambridge International Examinations 03

7 Page 7 Mark Scheme Syllabus Paper IGCSE October/November (a) (i) = 5 (ii) Correct substitution equating to sum ( + ) e.g. = 3 and k = stated k with no errors seen M for using a value of n in ( + ) e.g. = 3 k or for a verification using k = ( + ) e.g. = 3 ( n + ) n k (iii) 830 (iv) 30 M for n( n + ) = 465 or better (v) n 8 (b) (i) 5, 5 either (ii) n ( n + ) 4 oe (iii) 3600 M for 9 ( 9 + ) 4 oe or 90 Cambridge International Examinations 03