详解数学答案

CAMBRIDGEINTERNATIONALEXAMINATIONS

InternationalGeneralCertificateofSecondaryEducation

MARKSCHEMEfortheNovember2004questionpaper

Thismarkschemeispublishedasanaidtoteachersandstudents,toindicatetherequirementsoftheexamination.ItshowsthebasisonwhichExaminerswereinitiallyinstructedtoawardmarks.ItdoesnotindicatethedetailsofthediscussionsthattookplaceatanExaminers’meetingbeforemarkingbegan.AnysubstantialchangestothemarkschemethatarosefromthesediscussionswillberecordedinthepublishedReportontheExamination.

AllExaminersareinstructedthatalternativecorrectanswersandunexpectedapproachesincandidates’scriptsmustbegivenmarksthatfairlyreflecttherelevantknowledgeandskillsdemonstrated.

MarkschemesmustbereadinconjunctionwiththequestionpapersandtheReportontheExamination.

•

CIEwillnotenterintodiscussionorcorrespondenceinconnectionwiththesemarkschemes.

CIEispublishingthemarkschemesfortheNovember2004questionpapersformostIGCSEandGCEAdvancedLevelsyllabuses.

0580/0581MATHEMATICS

0580/03,0581/03 Paper3(Core),maximumrawmark104

GradethresholdstakenforSyllabus0580/0581(Mathematics)intheNovember2004examination.

Thethreshold(minimummark)forBissethalfwaybetweenthoseforGradesAandC.Thethreshold(minimummark)forDissethalfwaybetweenthoseforGradesCandE.Thethreshold(minimummark)forGissetasmanymarksbelowtheFthresholdastheEthresholdisaboveit.

GradeA*doesnotexistatthelevelofanindividualcomponent.

maximummarkavailable

minimummarkrequiredforgrade:

A

C

E

F

Component3

104

N/A

78

55

45

TYPESOFMARK

Mostofthemarks(thosewithoutprefixes,and‘B’marks)aregivenforaccurateresults,drawingsorstatements.

•

•

•

Mmarksaregivenforacorrectmethod.

Bmarksaregivenforacorrectstatementorstep.

Amarksaregivenforanaccurateanswerfollowingacorrectmethod.

ABBREVIATIONS

a.r.t.

b.o.d.

c.a.o.

e.e.o.f.t.

o.e.SC

s.o.i.wwwww

Anythingroundingto

BenefitofthedoubthasbeengiventothecandidateCorrectansweronly(i.e.no‘followthrough’)

EacherrororomissionFollowthrough

OrequivalentSpecialcaseSeenorimpliedWithoutworking

Withoutwrongworking

Workfollowedthroughafteranerror:nofurthererrormade

November2004

INTERNATIONALGCSE

MARKSCHEME

MAXIMUMMARK:104

SYLLABUS/COMPONENT:0580/03,0581/03MATHEMATICS

Paper3

Questionnumber

1a)i)

PartMarks

1

QuestionTotal

MarkScheme

Notes

10

ii)

1

straightlinefrom(11,10)to(1130,10)

iii)

straightlinefrom

(1130,10)to(1245,16)

1√

allow+2mminlengthbyeyebutmustgothroughthecorrectpoints.f.t.fromtheir(1130,10)

iv)a)

1

15

allow¼hour

b)

1

Hatab

v)

1

32

b)i)

1

450

ii)

2

straightlineruledfrom(1,45)to(10,450)

SC1forfreehandorbrokenlineoranystraightlinethroughtheorigin±

½smallsquareatbothpoints

iii)a)

1

306±4

b)

1

11

1060to10.80

allow10.6etc.

2a)

1

translation

mustbesingletransformation

–6

–7

1

SC1forcorrectvectorinverted,or

1

–12

–14

,orforcorrectrow

vector,orco-ordinates.Condonemissingbrackets

b)

M1

rotation

mustbesingletransformation

A1

-90or90clockwiseo.e.

about(0,0)o.e.

A1

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MarkScheme

Syllabus

Paper

IGCSEEXAMINATIONS–NOVEMBER2004

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3

c)

(0,0)

1

1

1.5o.e.

not3:2etc.

d)i)

correcttriangledrawn

2

SC1forreflectionofAinanyverticallineor

iny=-1

o

ii)

2

correcttriangledrawn

SC1for180rotation

aboutanypointorSC1for

o

rotation±90about(-4,-3)

12

3

Inthisquestionalternativemethodsmustbecomplete

a)

8

1

b)

6

2

M1for 100−64o.e.mustshowsquareroot

c)

2

art53.1

M1forsinand8/10seeno.e.

d)

3

M1fortan40and6seen

+M1for6/tan40o.e.

art7.15

e)

13.15or13.2

1√

f.t.fortheirb)+d)to3s.f.orbetter

9

4a)i)

3

2fortwosidescorrect,witharcs

1fortwosidescorrectwithoutarcs

triangledrawnwiththreesidesthecorrectlength

±0.1cm

ii)

56±2c.a.o.

1

b)

inthispartofthequestiondeduct1onceforbrokenlines

i)

3

1foralinecorrectdistancefromPQ1forasemicircle

completelocusdrawn

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MarkScheme

Syllabus

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IGCSEEXAMINATIONS–NOVEMBER2004

0580/0581

3

ii)

correctlinedrawn

B1

±1mm,±

1o

correctarcs,radius>4cm

B1

iii)

correctareashaded

2

SC1forshadingonlefthandsideoftheir‘mediator’orinsidelinesdrawnfortheirb)i)

11

5a)i)

kite

1

ii)

correctlineBDdrawn

1

Allowbrokenline,onelineonly

360−140−80

iii)

70

2

M1for

o.e.

2

b)

(p=)90

1

(q=)50

1

(r=)50

f.t.fromtheirq,notstrictf.t.

360

1√

c)

128.6c.a.o.

4

M2for180-

5×180

or

7

o.e.

7

(maybeimpliedbyart129)

+A1for128.57

11

6a)

300

1,1,1

b)

7correctpointsplotted

P3√

P2√for5or6points±½sm.sq.

P1√for4points.notstrictf.t.

smoothcurvethroughallcorrectpoints

C1

incorrectlyplottedpointsshouldbeignoredforC1.Minimumcurved,notpointed

c)

-0.8to-0.7c.a.o.

1

ignoreanyyvalues

2.7to2.8c.a.o.

1

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MarkScheme

Syllabus

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IGCSEEXAMINATIONS–NOVEMBER2004

0580/0581

3

d)

40

1,1

e)

correctlinedrawnthrough(-4,8)and(4,0)

1

completeline

f)

-1.7to-1.4c.a.o.

1

ignoreanyyvalues

2.4to2.7c.a.o.

1

14

7a)i)

16

1

ii)

3x+8o.e.

2

M1for3x.allowninsteadofx.deduct1for‘=x’or‘=0’or=anynumber,butallowadifferentletter

b)

-9a

1

+5b

1

c)

3a(2–3a)

2

M1foranycorrectpartialfactorisation

v-u

d)

2

M1forv–useen

o.e.

a

(x=)2.5

e)

2

M1forcorrectmultiplicationofLHSofoneorbothequationstoequalisecoefficientsorforarecognisableattempttoeliminateonevariable

(y=)-3.5

2

M1forcorrectsubstitutionoftheirothervalueorM2correctmatrixmethod

13

8a)i)

22

1

67+87

ii)

2

M1