0580 M15 Ms 42

CAMBRIDGE INTERNATIONAL EXAMINATIONSCambridge International General Certificate of Secondary EducationMARK SCHEME for the March 2015 series0580 MATHEMATICS0580/42Paper 4 (Paper 42 – Extended), maximum raw mark 130This mark scheme is published as an aid to teachers and candidates, to indicate the requirements ofthe examination. It shows the basis on which Examiners were instructed to award marks. It does notindicate 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 ExaminerReport for Teachers.Cambridge will not enter into discussions about these mark schemes.Cambridge is publishing the mark schemes for the March 2015 series for most Cambridge IGCSE ,components. IGCSE is the registered trademark of Cambridge International Examinations.Visit https://boardedu.org/ for more support

Page 2Mark SchemeCambridge IGCSE – March 2015Syllabus0580Paper42Abbreviationscaocorrect answer onlydepdependentFTfollow through after erroriswignore subsequent workingoeor equivalentSCSpecial Casenfwwnot from wrong workingsoiseen or impliedQu.12AnswersMarkPart Marks(a)1.5 450 000 oe1001Accept equivalent methods(b)60003M2 for(c)376.25 cao2B1 for 21.5 and 17.5 seen(d)22.42M1 for 2002 or 22 seen oe(e)51842M1 for 12 16 27(f)90233M1 for 12000 1.33A1 for 9022.55 to 9022.56 or 9022.6 or 9020B1indep for their answer rounded to the nearesteuro if possible3B2 for 8 or 9 numbers correctfinal answer6750 100 oe112.5or M1 for 112.5% associated with 6750 oe(a) (i)A6421395 7BB1 for 6 or 7 numbers correct810C(ii)(iii)(b) (i) cao1{3}1FT or {}151FT 1FT their intersection of all 3 sets – theirdiagramFT their set B on diagram Cambridge International Examinations 2015Visit https://boardedu.org/ for more support

Page 3Mark SchemeCambridge IGCSE – March 2015Syllabus0580Paper421(ii)XYZ3(a)2 0 2 23B2 for 3 correctB1 for 2 correct(b)smooth correct curve through correctpoints4B3FT for 8 or 9 correct plotsB2FT for 6 or 7 correct plotsB1FT for 4 or 5 correct plotsFT their table1(x 1) ruled and2 2.85 to 2.95 10.85 to 0.954B3 for correct line and 2 correct valuesor B2 for correct line and 1 correct valueor B1 for correct lineor SC2 for no/wrong line and 3 correct valuesor SC1 for no/wrong line and 2 correct valuestangent ruledB1No daylight between tangent and curve at pointof contact. Consider point of contact asmidpoint between two vertices of daylight, themidpoint must be between x –1.85 andx –1.65 1.1 to 1.52dep on B1M1 for rise/run also dep on any tangent drawnor close attempt at tangent at any pointMust see correct or implied calculation from adrawn tangentAccept M1 for answer in range 1.1 to 1.5 afterB1(a)(11y m )(11y m ) final answer2B1 for 11y seen(b)3 x 2 5 x 14final answer(3x 5)(x 1)3B1 for denom (3x 5)(x 1) oe isw and(c)(d)4line y Line must be fit for purposeB1 for 3x 2 6 x 5 x 10 soi Cambridge International Examinations 2015Visit https://boardedu.org/ for more support

Page 4Mark SchemeCambridge IGCSE – March 2015 2 2 2 4(3)( 7 )2 3(c)2B1 forSyllabus0580Paper422 2 4(3)( 7 ) or better seenp or qrB1 for p –2 and r 2 3and if in form(d) (i)5(a)(b) 1.90 1.23 final answers1, 1SC1 for 1.9, 1.896 or 1.897and 1.2 or 1.230or 1.23 and 1.90 final answersor 1.90 and 1.23 seen in working1(x 4 3x 2)(x 1) 152M1Allow4 x 2 4 x 6 x 6 30or 2 x 2 2 x 3x 3 15M1Dep on 1st M12 x 2 5 x 12 0A1With no errors or omissions1(4 x 6)(x 1) 152 5 52 4(2 )( 12 )2 2or SC1 for (2 x a )(x b ) where a and b areintegers and a 2b 5 or ab 12 orp or qwhere p –552 4(2 )( 12 ) orrand r 2 2(ii)1.5 or3, 423B2 for (2 x 3)(x 4) or(iii)6.5 or1321FTFT 3 their pos root from (d)(ii) 212 16 5.4 sin 62 oeM138.14.A195.6 or 95.64 to 95.6546.7 sin 488.4or M1 for implicit formM2 forand M1dep for 180 48 their 36.4 Cambridge International Examinations 2015Visit https://boardedu.org/ for more support

Page 5Mark SchemeCambridge IGCSE – March 2015286 or 285.7 to 285.8(c)5Syllabus0580Paper42B1 for [Angle APB ] 83 M2 for180 2 2452 2 180 245 cos their 83or M1 for implicit formand A1 for [AB2 ] 81676[.1.]After 0 scored, SC2 for ans 406.87 to 406.88 or406.9 or 407 if 146 used in cos ruleOr SC1 for180 2 2452 2 180 245 cos 1466(a)4151(b)801FTFT 300 their (a)(c) (i)40oe2253M2 for3M2 for(ii) 8 45 1212255 4 2 oe15 155 4 or M1 for15 1511 11oe 15 15or M1 for(d) (i)108oe210 18 35 3M2 for114or 1 seen15156 9 9 6oe 15 14 15 146 99 6oe oroe 15 1415 146 56 4oe oroe or15 1415 14or M1 for(ii)148oe210 74 105 45 10 6 9 4 11oe 15 14 15 14 15 45 4 6 5 4 3or 1 15 14 15 14 15 14M3 foror M2 for equivalent of 2 of above productsadded together oeor M1 for one correct relevant product oe7(a) (i)Rotation[centre] (0, 0) or origin90 [anticlockwise] oe111 Cambridge International Examinations 2015Visit https://boardedu.org/ for more support

Page 6Syllabus0580Paper42Enlargement[centre] ( 2, 1)[s.f.] 2111(b)vertices at ( 3, 4) ( 3, 5) ( 3, 6)( 2, 6)2 2 k SC1 for translation by or k 1 (c)vertices at (7, 3) (7, 4) (7, 5) (6, 5)2SC1 for reflection in y 1 or reflection in anyvertical line(d)reflectionx-axis oe11(a) (i)47.7 or 47.74 to 47.753M1 for [arc ] 68 2 24x 2 π 24 68or 24 24 360M1 for [x ] their arc 360 (2 π 24)252 or 252.3 to 252.4.6M1 for r (ii)8Mark SchemeCambridge IGCSE – March 2015(ii)20or2π their 47.7 2 π 24 (2 π ) 360 A1 for r 3.18 or 3.182 to 3.183. or10πM1 for h 2 242 their r 2A1 for h 23.8 or 23.78. to 23.79M1dep on M1 earned for1V π their h their r 23(b)139 or 139.3 to 139.4. nfww5M4 for 8 2 or M1 for11 8 π 82 π 42 2 1π 824221 8 and M1 for π 2 2 2and M1 for 8 added to at least one term with π9(a)140 h 1441(b)144.875 nfww4M1 for at least 4 correct mid-values soiM1 for fx where x is in the correct interval,allow one further error/omissionM1 dep for 40dependent on second method mark Cambridge International Examinations 2015Visit https://boardedu.org/ for more support

Page 7(c)10 (a)(b)(c)(d)Mark SchemeCambridge IGCSE – March 2015Syllabus0580Paper424 correct blocks4B3 for 3 correct blocksB2 for 2 correct blocksB1 for 1 correct blockor at least 3 correct frequency densities(1.4, 1, 1, 0.65 )4 x 10 y 801With no errors seeny x1y 6 or y 71Accept 0 y 6 or 0 y 6 or 0 y 7or 0 y 7ruled broken line through (5, 6) to(10,4)B2SC1 for correct only at (5, 6) or (10, 4)ruled broken line y xruled solid line y 6 or broken y 7B1B1Must be consistent with their (b)correct region indicatedB1762SC1 for ( 4, 6 ) indicated or4 x 10 y evaluated for ( x, y ) in their region,x, y integers11 (a)1(b)301011(c)n(n 1) oe2(d)1n(n 1) oe22B1 for an 2 bn c a, b, c numeric a 0B1 for using(1oe in expression of form21an 2 bn c2 Cambridge International Examinations 2015)Visit https://boardedu.org/ for more supporta 0 or kn(n 1) k 0

0580 MATHEMATICS 0580/42 Paper 4 (Paper 42 – Extended), maximum raw mark 130 . 376.25 cao final answer 2 B1 for 21.5 and 17.5 seen (d) 22.4 2 M1 for 2002 or 22 seen oe (e) 5184 2 M1 for 12 16 27 (f) 9023 3 M1 for