0580 S14 Ms 42 - The Maths Mann
CAMBRIDGE INTERNATIONAL EXAMINATIONSInternational General Certificate of Secondary EducationMARK SCHEME for the May/June 2014 series0580 MATHEMATICS0580/42Paper 4 (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 May/June 2014 series for most IGCSE, GCEAdvanced Level and Advanced Subsidiary Level components and some Ordinary Level components.
Page 2Mark SchemeIGCSE – May/June 2014Syllabus0580Paper42Abbreviationscaocorrect answer onlydepdependentFTfollow through after erroriswignore subsequent workingoeor equivalentSCSpecial Casenfwwnot from wrong workingsoiseen or impliedQu1AnswersMark(a)240 (5 7) 7 [ 140] oe(b)2 : 3 final answerPart MarksM2M1 for 240 (5 7) or 240 72B1 for ratio of form 2x : 3x seenor SC1 for 3 : 2(c)1443M2 for 120 or M1 for(d)89.99 cao mark final answer3120 4 5oe100120 4 5100B2 for 89.9[8 ] shown but not spoiledor answer 90[ .0.] nfww3 104 or M1 for 80 oe 100 If M1 spoiled by adding 80 or subtracting 80then SC1 for answers 169.99 or 9.99(e)4.083M2 for200 r 2 200 1.042 – 200 oe100or M1 for 200 1.042 [216.3[2]] oeor200 r 2oe100 Cambridge International Examinations 2014
Page 3Qu2Mark SchemeIGCSE – May/June 2014Syllabus0580Paper42AnswersMarkPart Marks(a)3, 3, – 13B1 B1 B1(b)Complete correct curve5B3FT 11 pointsor B2FT for 9 or 10 points or B1FT for 7 or8 points6And B1indep two separate branches nottouching or crossing y-axis4203-2-1012-2-4(c)0.5 to 0.61(d)Correct line and 0.4 to 0.5or no line and 0.4 to 0.5 nfww3Must check line - not if wrong lineB2 for y 2x 3 ruled correctlyor SC1 for correct freehand lineor ruled line with either gradient 2 ory-intercept 3 but not y 3(e) (i)Tangent at x – 1.51No daylight at x –1.5. Consider point ofcontact as midpoint between two vertices ofdaylight, the midpoint must be between x –1.7 and –1.3– 2 to – 12Dependent on tangent mark awardedAllow integer/integer if in rangeOr M1 for rise/run also dep on any tangentdrawn or close attempt at tangent at any pointMust see correct or implied calculation from adrawn tangent(ii) Cambridge International Examinations 2014
Page 4Qu3Mark SchemeIGCSE – May/June 2014Answers(a)Syllabus0580Mark86.8 or 86.83 .3Paper42Part MarksM2 for80 sin 5580xor M1 for sin 49sin 49 sin 55oe(b)51.2 or 51.15 to 51.164M2 for [cos ]95 2 90 2 80 2oe2.95.90or M1 for80 2 95 2 90 2 2.90.95. cos BCD14310 725oretc. or 0.627 .A1 for22817 100(c)6700 or 6698 to 67033M2 for 0.5 80 their(a) sin(180-55-49) oe[3368 – 3370 ] [If AB used then AB 102.8to 103] 0.5 90 95 sin(their(b)) oe[3329 – 3332]or M1 for one of these triangle area methodsoe(d)2180 or 2176 to 21793FTFT their (c) 0.325 correctly evaluated to 33250sf or better M2 for their (c) 10 000or SC1 FT for figs 218 or figs 2176 to 2179 Cambridge International Examinations 2014
Page 5Qu4Mark SchemeIGCSE – May/June 2014AnswersSyllabus0580MarkPaper42Part Marks(a)Image at (–3, 2), (–5, 2), (–5, 4), (–3, 3)2SC1 reflection in y – 1 or x kor 4 correct points not joined(b) (i)Image at (–2, –4), (–6, –4), (–6, –8),(–2, –6)2SC1 other enlargement of scale factor -2,correct size and correct orientation or 4correct points not joined 2 0 0 2 2Image at (1, 4), (3, 4), (3, 8), (1, 6)2(ii) 1 0 0 2 2(iii)1 2 0 oe isw2 0 1 (ii)(c) (i)2FT k 0 , k may be algebraic orSC1 for 0 k numeric but not 0 or 1SC1 for trapezium with vertices at (1, 6) and(3, 8) or correct stretch with y-axis invariantor 4 correct points not joined 1 0 k may be algebraic orSC1 for 0 k 2 0 numeric but not 0 or 1 or for 0 1 FT inverse of their (c)(ii) (algebraic ornumeric)1 a c orB1FT their (c)(ii) for 2 b d 2 0 p 0 1 ie FT their correct fraction or their transposedmatrixFT for 2 and 1 mark dependent on det 0(iv)Stretch,1[factor ] ,2invariant [line] x-axis oe3B1 B1 B1 each independent cao Cambridge International Examinations 2014
Page 6Qu5Mark SchemeIGCSE – May/June 2014Answers(a) (i)(ii)Mark2412 to 2413. B22.41[0]B11 min 24 s(b)Syllabus05804Part MarksMust be at least 4 figures shownM1 for π 8 2 12 oeB3 for 83.76 to 83.8[0] or 84 or 1.396 to1.397 or 1.4 or1 min 23.76 to 1 min 23.8 seenor M2 for 13 π 4 2 10 2 [ 80/3 π ]or M1 for167.6]14(c)3Paper42M1 for1313π 4 2 10 [160/3 π or 167.5 to2410orπ 4 2 102410their cone vol from part (b)A1 for 14.3 to 14.4 .6[x ] 21, [y ] 422B1 B13.79 or 3.8[0] or 3.792 to 3.8022M1 for(b)404B3 for angle between HE and tangent 25or GFH 40or EGH 25 and angle EHG 115 (accept90 and 25 at H for 115)B2 for angle EGH 25or angle EHG 115 (accept 90 and 25 at Hfor 115)B1 for angle FEG 25or angle EFG 65(c)385B4 for angle ADC 104or M4 for x 14 20 x 70 180 or better(a) (i)(ii)3.31 8.23 oeTQ 9.43sin 21 or sin their x sin 117 oroeTQ9.43or B3 for angle OBA 20and angle OBC 56or angle CBA 76 or reflex angle AOC 208or B2 for angle OAB or OBA 20and angle ACB 70or obtuse angle AOC 152or angle BOC 68or B1 for angle OAB or OBA 20or angle ACB 70 Cambridge International Examinations 2014
Page 7Qu7Mark SchemeIGCSE – May/June 2014Answers(a) (i)(ii)Syllabus0580MarkPaper42Part Marks24 39 oe78(100 – 70) 0.4 [ 12] or better1Accept60.9 or 60.89 nfww5B1 for 3 or 4 correct extra frequencies 3, 6,10, 8 soiM1 for at least 4 of mid-interval values 15,40, 55, 65, 85 soiM1 for Σfx where x is any value in eachinterval allow their frequencies providedintegers and they must be shown[3 15 6 40 10 55 8 65 12 85] [2375]M1 (dependent on second M1) for 39or (3 6 10 8 12)8(b)60.53M2 for 20 70 – 19 70.5 oeor M1 for either 20 70 or 19 70.5(a) (i)600x1Not x 600x600x 11Not x 600x 1(ii)(b) (i)600600– 20 oex 1xM1FTFT their (a)(i) – their (a)(ii) 20 oeIf M0, SC1FT fortheir(a)(ii) – their (a)(i) 20 oe600( x 1) 600 x 20 x( x 1) or betterA1May still be over common denominator andcan be implied by third line. Allow recovery ifbracket omitted600 x 600 600 x 20 x 2 20 x0 20 x 2 20 x 600x 2 x 30 0A1Dep on M1A1 and conclusion reached with atleast one of the interim lines and without anyerrors or omissions Cambridge International Examinations 2014
Page 8QuMark SchemeIGCSE – May/June 2014Answers(ii)x 5Syllabus0580MarkB3Part MarksB2 for ( x 6)( x 5) [ 0] oeor SC1 for ( x a )( x b) where ab – 30 ora b 1or B2 foror or x 9B1FT(a)1 9 1 2, , ,4 10 3 33(b)451(c)3oe40(d)101oe120(e)781oe1024 1 or 12 4.1. 302.1 1 30 2 or B1 for100Paper422 12 1 or qor 12 4.1 302 .11 2 2FT 600 (their x 1) if x 0 correctlyevaluatedB1 for1912B1 forB1 for and341032M1 for3 1 oe4 103M2 for2 3 M1 for 1 oe 4 3 9 1 2 only4 10 4 31 1or 1 their (c) only4 31 23 9or or M1 for 4 104 31 1or their (c) 4 35 Cambridge International Examinations 2014
Page 9Qu10Mark SchemeIGCSE – May/June 2014AnswersSyllabus0580MarkPaper42Part Marks(a)221 1 1B1 for g soi or [fg ]1 x 2 2(b)1–x1Accept equivalents e.g. –(x – 1)(c)x 2 2x 23M1 for (1 x ) 2 1(d)(e)[]B1 for (1 x ) 1 x x x 2 or better–621( 3) 4(1)(1) or betterB13 or for x 2 p ( 3) and r 2 1 oeB1Must see22p qp qoror bothrr2or for0.38, 2.62(f)f(x) and g(x)B1B113 3 or 12 2 SC1 for answers 0.4 and 2.6 or 0.3819 to0.3820 and 2.618 or 0.38 and 2.62 seen in workingor for –0.38 and –2.62 as final ansAccept f and g or 1/x and 1 – x Cambridge International Examinations 2014
Page 10Mark SchemeIGCSE – May/June 2014Syllabus0580MarkPaper42QuAnswersPart Marks1113172oe3601142162M1 for [X 6 ] 0.5 l2 sin60or [X 6 ] 0.5 l2 sin120Or recognition that the area of the obtuseangled triangle shaded is equal to the area ofone of the 6 equilateral triangles from thecentreπ 22or 1 or 0.363 or 0.3630 toππ0.36354If fraction given as answer, check if it fallsinto range1B1 for [sector ] πr 2 oe41B1 for [triangle ] r 2 oe2their sector their triangleM1dep fordeptheir sectoron B1B1 earnedAllow equivalent decimal throughout(3sf or better where necessary)2 1 M1 for or (2)2 or 12 : 22 or 22 : 12 oe seen 2 Cambridge International Examinations 2014
0580 MATHEMATICS 0580/42 Paper 4 (Extended), maximum raw mark 130 This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of . 21, [y ] 42 2 B1 B1 (ii) 3.79 or 3.8[0] or 3.792 to 3.802 2 M1
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MARK SCHEME for the June 2004 question papers 0580/0581 MATHEMATICS 0580/01, 0581/01 Paper 1 (Core), maximum raw mark 56 0580/02, 0581/02 Paper 2 (Extended), maximum raw mark 70 0580/03, 0581/03 Paper 3 (Core), maximum raw mark 104 0580/04, 0581/04 Paper 4 (Extended), maximum raw mark 130
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