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 01 series 0580 MATHEMATICS 0580/4 Paper 4 (Extended), maximum raw mark 10 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 ds 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 01 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 or equivalent SC Special Case www without wrong working art anything rounding to soi seen or implied Correct answer Mark Part marks 1 (a) (i) 16 Final answer M1 for ( ) 0.4 (ii) 107 Final answer FT FT (18900 their (a)(i)) 1 correctly evaluated M1 for (18900 their (a)(i)) 1 (b) 4.5[%] nfww [ 18900] M1 for or (c) A by 1.05 or 1.04 to 1.05 or 1.[0] 1.1[0] 5 M1 for /100 [+ 1500] M1 for [ 1500] A1 for or or 165[.45..] or 15[.45..] and M1dep for subtraction of their amounts or their interests (a) 6.9 or 6.86 to 6.87 M1 for tan[dbc] = 1.8/.4 (b) (i) 1.8² +.4² leading to 9 M1 for 1.8² +.4² or better (ii) [cosabd) =] or 16.8 M A M1 for correct cos rule but implicit version A1 for After 0 scored, SC nfww for answer 17 or 16.8 to from other methods or no working shown (c) 9.6 or 9.7 or 9.59 to 9.68 M for ½ ( ) Or M1 for ( ) soi by 9.9 to 9.9 Cambridge International Examinations 01

3 Page Mark Scheme Syllabus Paper IGCSE October/November (a) 4x 7 10 final answer nfww 5(x 1) (x + 1) M for 5 5(x 1) (x + 1) or 5 5 or M1 for attempt to convert to common denominator of 10 or multiple of 10 with one error in numerator (b) x² + 9 final answer nfww 4 B for 4x² 6x 6x + 9 x² +1x or correct answer given and then spoilt or for 4x² 6x 6x + 9 seen and for x² +1x or (x² 1x) seen (c) (i) (x 1)(x + ) isw solving M1 for (x + a)(x + b) where ab = or b + a = 5 with integers a and b (ii) x 1 x 1 or ( x ) x 6 final answer nfww M for (x + )(x ) or (x 6)(x + ) or (x + 6)(x ) seen or M1 for (x² 9) seen 4 (a) (i) 90 (4/60 π 8 ) o.e..86 to.87 M A1 M for 4/60 π 8 h = 90 or M1 for 4/60 π 8 (ii) 11 or to 10.9 nfww 5 M for 4/60 π 8.84 [.48 to.5] or M1 for 4/60 π 8 soi [5.86 to 5.87] and M1 for (8.84) [61.7 to 61.44] and M1 for (4/60 π 8 ) [46.88 to 47] (b).4 or.416 to.419 M for.84 or M1 for.84 or h = or or h = seen.5 Cambridge International Examinations 01

4 Page 4 Mark Scheme Syllabus Paper IGCSE October/November (a) 7, 11.5, 4.5 1,1,1 (b) Correct curve cao 5 BFT for 10 correct plots, on correct vertical grid line and within correct mm square vertically Or BFT for 8 or 9 correct plots Or FT for 6 or 7 correct plots and indep for two separate branches on either side of y-axis (c) (i) 0.69 < x < (ii). < x <. 0.8 < x < < x < 0.5 for each correct After 0 scored, allow SC1 for drawing line y = 7.5 long enough to cross curve at least once (d) (i) y = 10 x ruled correctly B long enough to cross curve twice. for ruled line gradient or y intercept at 10 but not y = 10 Or for correct but freehand 0.55 < x < < x < 0.45 dep dep Dependent on at least scored for line After 0 scored, SC for 0.5 and 0.4 [from solving equation] (ii) 10 1 or 10 1 B for x 10x [= 0] 1 Or for 10 = 0 Correctly x x eliminating x Or for x x = 10x x Correctly clearing fractions Cambridge International Examinations 01

5 Page 5 Mark Scheme Syllabus Paper IGCSE October/November (a) (i) M1 for 1 1 (ii) M1 for (iii) FT FT their (a)(ii) + correctly evaluated 1 or M1 their (a)(ii) + (b) (i) M1 for (ii) M1 for (iii) M4 for or M for or Or 8 M1 for seen and M1 for seen Cambridge International Examinations 01

6 Page 6 Mark Scheme Syllabus Paper IGCSE October/November (a) or 10 pm final answer M1 for (0)8 10 or answer 14 hours and 10 minutes or answer 10 [am] (b) 5 hours 45 minutes cao M1 for 45 [mins] seen or for 805 /7 or 5.75 seen (c) (i) 798 or 798. to M1 for 1071 / 5 1 or (ii) or to B for or to seen or M for /59 or M1 for figs 1071/figs 59 soi by figs 18 or figs 1815 to 1816 and FT for their number of litres correctly converted to standard form rounded to sf or better (d) 8600 M for or M1 for associated with 118[%] 8 (a) (i) 6 1 (ii).75 M1 for [g(x) =] 0.5 or 7/ Or + 5 x + 1 x + 1 (b) x 4 or 4 x 4 Final answer M1 for y = 4x or better or x = 4y + or better or 4 y = 4 + x or flowchart with then 4 (c) (i) 5 M1 for 4x = or x + 4 = 4 or better (ii) x² + 5x 7 = 0 May be implied by correct values in formula 5 ± 5 4(1)( 7) (1) for 5 4(1)( 7) or better [5] p + q p q If in form or, for 5 and r r (1) or better No recovery of full line unless seen 1.14 and 6.14 final answers Or SC1 for 1.1 or and 6.1 or Or answers 1.14 and 6.14 Cambridge International Examinations 01

7 Page 7 Mark Scheme Syllabus Paper IGCSE October/November (a) (i) Reflection x = for either (ii) Translation 7 for either (iii) Stretch x-axis invariant [factor] for each (b) (i) Triangle with coords at (8, ) (7, ) and (7, 5) (ii) Triangle with coords at (, 5) ( 6, 5) and ( 8, 7) (iii) Triangle with coords at (1, 1) (4, 6) and (, 5) for rotation about (6, 0) but 90 anticlockwise Or for rotation 90 clockwise around any point for correct points or for enlargement of SF any centre for correct points or coordinates of points shown (c) for one row or one column correct but not identity matrix. 1 Or SC1 for (a) 48 and 57, 9n + 1 for 9n + k (b) 56 and 50, 86 6n 1 for k 6n (c) 15 and 16, n 1 1 (d) 10 and n + n 1 1FT FT their (c) + n dep on expression in n in (c) Cambridge International Examinations 01