0580 S12 Ms 42 - Cienotes

wwapePmetr.XwUNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONSfor the guidance of teachers0580 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 must be read in conjunction with the question papers and the report on theexamination. Cambridge will not enter into discussions or correspondence in connection with these mark schemes.Cambridge is publishing the mark schemes for the May/June 2012 question papers for most IGCSE,GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Levelsyllabuses.om.cMARK SCHEME for the May/June 2012 question paperserInternational General Certificate of Secondary Education

Page 2Mark Scheme: Teachers’ versionIGCSE – May/June 2012Syllabus0580Paper42Abbreviationscaocorrect answer onlycsocorrect solution onlydepdependentftfollow through after erroriswignore subsequent workingoeor equivalentSCSpecial Casewww without wrong workingartanything rounding tosoiseen or impliedQu.AnswersMark1 (a) (i) 6 correct plots2(ii) Positive1(iii) Line of best fit1(iv) English (integer) value on line atM 22(b)(26 39 35 28 9 37 45 33 16 12) 10(c)46 cao www 32 (a)445 final answer(b)Part MarksP1 for 4 or 5 correct plots.Ruled line at least from x 5 to x 48, with atleast 3 points on each side and cuts axes between(5, 0) and (0, 20)1ftStrict ft from their single ruled line 5 ø x ø 48.M2M1 for 26 39 35 28 9 37 45 33 16 12, condone one slipor SC1, for at least 2 valueseg (26 39 ) 103M2 for (31 12 – 28 10) 2 soi by 92 2or M1 for 31 12 soi by 372 or 923M2 for 351.55 (1 – 0.21) oeor M1 for 351.55 (100 – 21) (%)640 or 46404622.5 or 622.522M1 for 4000 0.08 2 oeM1 for 4000 (1.075) 2 oeor 4000 0.075 ( 300) and (4000 their 300) 0.075 and total interest the sum of their 2interests.Alex by 17.5(0) cao final answerwww 62M1 for S I amount – C I amount or reverseor simple interest – compound interest or reversewww 3 University of Cambridge International Examinations 2012

Page 3Mark Scheme: Teachers’ versionIGCSE – May/June 20123 (a) (i) x 41(ii) y 91(iii) x y 201(b)5x 10y 170 seen(c) (i) x 4 ruledy 9 ruledSyllabus0580Paper42111Each line long enough to enclose their regionCondone good freehand or dottedy 9 must be between 8.8 and 9.2x y 20 ruled2B1 for gradient – 1 or y intercept 20 orx intercept 20. Exclude lines parallel to eitheraxis.x 2y 34 ruled2B1 for y intercept 17 or x intercept 34.Exclude lines parallel to either axis.Correct region indicated cao1Dependent on all 6 marks for the 4 lines.(ii) 145 cao (from 11, 9) www 22M1 for using 5x 10y when x y 20and integers (x, y) is in their region University of Cambridge International Examinations 2012

Page 4Mark Scheme: Teachers’ versionIGCSE – May/June 2012Syllabus0580Paper42In all parts of (a) candidates may refer to anglesmarked in diagram. Allow if clear even if reason ismore complicated as long as it is full.Reasons dependent on correct answers4(a) (i) 42Alternate oe11Not alternate segment(ii) 90semicircle oe11Allow diameter(iii) 42same segment oe11same arc(iv) 138cyclic quad oe11key words must not be spoiled3M2 for 12 2 5 2 oe i.e explicit(b)10.9 (10.90 to 10.91) www 3or M1 for 12 2 5 2 PQ 2 oe i.e implicitAllow full marks for 119 as final answerUse of trig method must be complete to explicitexpression for possible M2(c) (i) AD CD and DE DG(Angle) CDG (angle)ADE(Sides of) square or 90 angle ADGoe(ii) Congruent11R1Extra pair of sides loses this mark.Extra pair of angles loses this markAs in (a), for all 3 marks allow references todiagram if completely clear.R mark dep on at least one pair of sides stated orpair of angles stated1 University of Cambridge International Examinations 2012

Page 55 (a)(b)Mark Scheme: Teachers’ versionIGCSE – May/June 20122M1 for 34.95 1.17 implied by 29.87 or 29.9or SC1 for 2.77 or 2.78 or 2.775154 days 4 hours cao3M1 for 4.07 1012 (1.1 109) implied by figs 37or 154. ( .)A1 for 3700 seen or 3.7 103 seen or 154 16 oe or154 rem 41(ii) Lower 51.3375 final answerUpper 52.8275 final answer(x ) 64 www 3(b) (i) –1n 2 oe5n oen 2 5n oeFinal answerx 4cao www 42x 1(5, 3)7 (a)(c)3B2 for x 2 x x 360 114 10 or betteror M1 for x 2 x 114 x 10 3602M1 for their n 2 5n 500 or 20 and 25 seen4B1 for (x – 4)(x 4)B2 for (2x – 1)(x 4)or SC1 for (2x a)(x b) where eithera 2b 7 or ab – 4121c or12(6a c )(iii) a c(iv)After 0 scoredSC1 for answers reversed or 9.35 and 5.65 seenor 51.3375 and 52.8275 seen1(b) (i) 3a c(ii) 3a 111111(ii) 20(c)Paper42( ) 2.37 or 2.371 to 2.372 www 2(c) (i) 9.256 (a)Syllabus05802M1 for OM oe e.g OA AM or correctunsimplified answer1311a c or (3a c)222(CD) parallel (to OB) oe cao1CD OB oe cao2213M1 for – c their (iii) or a their (iii) or22correct unsimplified answer or any correct routee.g. CE ED1depPart (c) dependent on simplified (i) and (iv)Dep on (i) k (iv)1depDep on (i) 2 (iv) must be scalars University of Cambridge International Examinations 2012

Page 6Mark Scheme: Teachers’ versionIGCSE – May/June 20128Syllabus0580Paper42Throughout question, penalise non-reducedfraction only once; isw any conversion and allowdecimals in working and on branches but not finalanswers if fractions not seen.(a) (i)(ii)2311 2 2 3 1 5, , , , ,3 3 5 5 6 6correctly placed2B1 for1235andandor correctly placed3356For method marks in (b) and (c), ft tree with eachprobability 0 p 1(b)(c)94cao www 3914cao www 345332512 or 3633121321 or 353536125 M1 for33612 13 2 , or two of ,35 35 3M2 for 1 –161added613214 12 or their – 35369 351321or from aM1 for one of 3536maximum of two products added.M2 forAccurate ruled perp. bisector withcorrect intersecting arcs2B1 for accurate with no/wrong arcsor M1 for correct intersecting arcsIgnore one extra perp. bisectorAccurate ruled angle bisector withcorrect intersecting arcs2B1 for accurate with no/wrong arcsor M1 for correct intersecting arcsIgnore one extra angle bisectorCompass drawn arc centre F radius5.5 cm long enough to enclose region2M1 for compass drawn arc centre FCorrect region indicated cao1Accept dotty lines but not freehand for all three University of Cambridge International Examinations 2012

Page 7Mark Scheme: Teachers’ versionIGCSE – May/June 20126 910 (a) (i) 8x y final answer(ii)6x 2 11xy – 10y 2 final answer(b)(c) (i)(d)11 (a)(b)1x2oe but notoe final answer33x 2VrV πr 3 oe but not tripleor2222πr2πrfractions final answer23Syllabus0580Paper42B1 for any two of 8, x 6 , y 9 in a single term inanswer31or 3 x 2 oras answer2x3x 21x6or B1 foroe as answer orseen27273x6or SC1 for 3 or x 2 or x – 2 seen in answerB2 for3B2 for 3 of 6x 2 – 4xy 15xy – 10y 2 (11xy implies2 terms)or B1 for 2 of 6x 2 – 4xy 15xy – 10y 22M1 for correct subtraction or correct division by2πr 2 seen V h or h 3 2B1 for V 3h or5xfinal answer1226x 20x 21x10x,,oe implied by12 121224ie 2 with common denominator at least 6452 or 452.1 to 452.4 2M1 for π 12 2 Allow full marks for 144π asfinal answer59.9 or 59.86 to 59.91 cao www 55M1 for π 24 7 (soi by 527 to 528) oe or22 π 24 oe (soi by 4.60 to 4.61)36022 π 24 7 (soi by 32.2 toand M1 dep for36032.3)22 their (a) oe may restart (soi byand M1 for36027.6 to 27.7)2V3 B1 for 2 ofand M1 dep on M3 for adding two areas(c)2V2(ii)final answer311 cos50 soi by 17.(11 ) oe(their AC) 2 312 –2 their AC 31cos100art 37.9 cao www 6M2M2A211oe i.e. implicitACM1 for implicit cos ruleA1 for 1433 to 1443M1 for cos 50 University of Cambridge International Examinations 2012

Page 812 (a)Mark Scheme: Teachers’ versionIGCSE – May/June 201210x 4y 10.7 oe8x 6y 10.1 oeSyllabus0580Paper4211Multiplying or dividing equation(s) bynumber(s) suitable for eliminationM1Allow one arithmetic error. If substitution,correctly making one variable the subject of oneequation.Elimination of one variableM1Allow one arithmetic error. If substitution methodthen M is for the actual substitution.x 0.85 caoy 0.55 caoA1A1SC1 for correct fractionsAfter M0, SC2 for both correct answersIf working in cents, likely mark is 0 for equations,M2 for method, A2 if answers converted todollars, A1 if left in cents(b) 5 ( 5)2 4.2. 8B2B1 for2.2B1 for( 5)2 4.2. 8p rorand r 2 2 or 4p r( 89 )with p – – 5 or 5 Completing the square B1 for x 25B1 for 4 163.61 or –1.11 final answerB1B125 and4 After B0 B0 for answers,SC1 for 3.6 or 3.608 and – 1.1 or – 1.108or 3.61 and –1.11 seenCorrect answers without working score max 2 University of Cambridge International Examinations 2012

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 the examination. It shows the basis on wh