Download - Add Maths Form 4 YLP 2012

SEKOLAHMENENGAHSETIABUDIYEARLYLESSONPLAN2012

ADDITIONALMATHEMATICSFORM4

WEEK TOPIC LEARNINGOBJECTIVES STRATEGIES/ACTIVITIES TEACHINGAIDS HOMEWORKS1

(JAN) ORIENTATIONWEEK

2(JAN)

1Functions1.1ConceptofRelations

(a) Representarelationbyusing

arrowdiagrams,orderedpairsandgraphs.

(b) Identifydomain,codomain,object,imageandrangeofarelation.

(c) Classifyarelationasone‐to‐one,many‐to‐one,one‐to‐manyormany‐to‐many

Real‐lifeinvestigationonconceptofrelations.Calculatorandcomputerexplorations: object image

Respondingtoopen‐endedquestions.

Whiteboard Manipulative

Top1 PelangiAnalysisSeries(10questionsminimum)

1.2ConceptofFunctions (a)Recognizefunctionsasaspecialrelation.

(b)Expressfunctionsusingfunctionnotation.

(c) Determinethedomain,object,imageandrangeoffunction.

(d)Determinetheimageoffunctiongiventheobjectandviceversa.

Applytheunderstandingfromreal‐lifesituationsintonumbers,figuresandpatterns.Writefunctionsfromgiveninformationorquestions.Solvingproblemsbyusingfunctionsnotation(includeH.O.T.S.)

Whiteboard Manipulative ScientificCalculator


3(JAN)

1.4 InverseFunctions (a)Findtheobjectbyinversemappinggivenitsimageandfunction.

(b)Determinetheinversefunctionusingalgebra

(c) Statetheconditionfortheexistenceofaninversefunction.

GuidedLearningDo‐nowexerciseUsegraphsketchesandarrowdiagramstoshowtherelationshipbetweenafunctionanditsinverse.(stateinversefunctionasreversefunction.


4(JAN)

1.3CompositeFunctions (a)Determineacompositefunctionoftwofunctions.

(b)Determinetheimageofacompositefunctiongiventheobjectandviceversa.

(c) Determineoneofthefunctionsinagivencompositefunction,giventheotherfunction.

Collaborativegroupwork.Statecompositefunctionsascombinedfunctions.Exploringwithmanipulativesandreal‐lifesituationstorepresentcompositefunctions


WEEK TOPIC LEARNINGOBJECTIVES STRATEGIES/ACTIVITIES TEACHINGAIDS HOMEWORKS

5(FEB)

2 QuadraticEquations2.1QuadraticEquationand

itsroots

(a) Recognizeaquadraticequation

andexpressitinageneralform.(b) Determinewhetheragiven

valueistherootofquadraticequationbysubstitution.

Usingdynamicandinteractivesoftware GeometersSketchpad. Autograph.

Identifyquadraticequationsfromphysicalappearance.Exploreandinvestigatethatrootisaspecialvalueof ,whichgivesthevalueofquadraticequationzero.

GeometersSketchpad

EfofexGraph Autograph PhETSimulator

ScientificCalculator


5&6(FEB)

2.2QuadraticEquation (a)Determinetherootsofaquadraticequationbyfactorization,completingthesquareandquadraticformula.

(b)Formaquadraticequationfromgivenroots.

Guidedlearninganddo‐nowexercise.Tellthestudentstheyneedtoknowonly3methodstofindrootsDemonstrateonallthe3methods.Studentsdotheanalysiswhethertheanswersdifferornot.Introducetheanddemonstrateformula. . . . andexplainwhentouseit


6&7(FEB)

2.3TypesofQuadraticEquations

(a)Determinethetypeofrootsfromthevaluesof 4

(b)Solveproblemsinvolving4 inquadraticequations

tofind: (i) unknownvalue (ii) derivearelation

RemindthestudentsthattheformulaISNOTthesameasquadraticformula.Determinetypesofrootsofquadraticequationsfromthevalueof 4 :

4 0 twodiff.roots4 0 twoequalroots4 0 noroot

Respondingtoopen‐endedquestions

Top1 PelangiAnalysisSeries(8questionsminimumoneachskill)

8(FEB) CHECK&BALANCE

9&10(MAR) TEST1

11(MAR) MID‐SEMESTERBREAK


12(MAR)

3 QuadraticFunctions3.1QuadraticFunctions

andtheirgraphs

(a) Recognizequadraticfunctions(b) Plotquadraticfunctiongraphs(c) Recognizeshapesofgraphsof

quadraticfunctions(d) Relatethepositionofquadratic

functiongraphswiththetypeofrootsoftheequation 0.

Exploreandinvestigateonshapesofgraphsforcaseswhere 0and 0for

GeometersSketchpad



TopicalModule


13(MAR)

3.2Maximumandminimumvaluesofquadraticfunction

(a)Determinethemaximumorminimumvalueofquadraticfunctionbyusingthecompletingthesquaremethod

Do‐nowexerciseInvestigateandanalyzethepositionofmaximumandminimumvalueonvarioustypeofquadraticgraphs.


14(APR)

3.3SketchgraphsofQuadraticFunctions

(a)Sketchquadraticfunctiongraphsbydeterminethemaximumorminimumpointandtwoanyotherpoints

Emphasizethemarkingofmaximumorminimumpointanddemonstratehowtofindanothertwopoints,axisofsymmetryand –interceptDetermineotherpointsbyfindingtheintersectionwiththe ‐axis(ifitexists)


3.4QuadraticInequalities (a)Determinetherangeofvaluesofthatsatisfiesquadraticinequalities

Demonstrateandemphasizeongraphssketchinganduseofnumberlineswhennecessary


15(APR)

4 SimultaneousEquations

4.1Simultaneousequationsintwounknowns

(a) Solvesimultaneousequations

usingsubstitutionmethod.(b) Solvesimultaneousequations

involvingreal‐lifesituations.

Do‐nowexerciseExploreandinvestigatetheconceptofsimultaneousequationsthroughcomputersoftwareandcalculatorInvestigateonreal‐lifesituationssuchasarea,perimeterandvolume.

GeometersSketchpad





16(APR)

5 Indices&Logarithms5.1 IndicesandLawof

Indices

(a) Findthevaluesofnumbers

givenintheformofintegerindicesandfractionalindices.

(b) Uselawsofindicestofindthevaluesofnumbersinindexformthataremultiplieddividedorraisedtopower.

(c) Uselawsofindicestosimplifythealgebraexpressions.

Real‐lifeinvestigationsDo‐nowexerciseDemonstrationonrulesofindices.


TopicalModule


5.2LogarithmsandLawsofLogarithms

(a)Expressanequationinindexformtologarithmformandviceversa.

(b)Findthelogarithmofanumber.(c) Simplifylogarithmicexpressions

tothesimplestform

Exploreandinvestigatedefinitionoflogarithm.

; with 0, 1.Emphasizethat:

1 0; 1.Emphasize: Logarithmofnegativenumbersisundefined

Logarithmofzeroisundefined

Discussoncaseswherethegivennumberisin: Indexform Numericalform

Discussonthelawsoflogarithms


17(APR)

5.3ChangethebaseofLogarithms

(a)Findthelogarithmofanumberbychangingthebaseofthelogarithmtoasuitablebase.

(b)Solveproblemsinvolvingchangeofbaseandlawsoflogarithms.

Discusson 1 loglog b

a

ab


5.4SolveEquationsInvolvingIndicesandLogarithms

(a)Solveequationsinvolvingindices.

(b)Solveequationsinvolvinglogarithms

Equationsthatinvolvedwithindicesandlogarithmsarelimitedtoequationswithsinglesolutiononly.Solveequationsinvolvingindicesby: Comparisonofindicesandbases, Usinglogarithms



18‐20(MAY) MIDTERMEXAMINATION

21(MAY) DISCUSSIONONEXAMPAPERS

22&23(JUNE) MIDTERMBREAK

24(JUNE)

6 CoordinateGeometry6.1DistanceBetweenTwo

Points

(a) Findthedistancebetween2

points.Do‐nowexerciseManipulatePythagoras’TheoremtofindtheformulafordistancebetweentwopointsCollaborativegroupwork

GeometersSketchpad



TopicalModule


6.2DivisionofaLineSegment

(a)Findthemidpointoftwogivenpoints.

(b)Findthecoordinatesofapointthatdividesalineaccordingtoagivenratio : .

Introduceanddemonstrateonformulaformidpointcoordinateandmanipulatetheformulatoderivetheformula

1 2 1 2,nx mx ny mym n m n

Limittocaseswhere and arepositive.Collaborativegroupwork.


25(JUNE)

6.3AreasofPolygons (a)Findtheareaoftrianglebasedontheareaofspecificgeometricshapes,andbyusingformula.

(b)Findtheareaofquadrilateralbyusingformula.

Limittonumericalvalues.Emphasizetherelationshipbetweenthesignofthevalueforareaobtainedwiththeorderoftheverticesused.Derivationoftheformulaisnotrequired.Emphasizethatwhentheareaofpolygoniszero,thegivenpointsarecollinear.



25&26(JUNE)

6.4EquationofStraightLines

(a)Determinethe interceptandinterceptofaline.

(b)Findthegradientofastraight

line.(c) Findthegradientandintercepts

ofastraightlinegivenitsequation.

(d)Changetheequationofastraightlinetothegeneralform.

(e)Findtheintersectionpoint

Do‐nowexercises.CollaborativegroupworkAnswersforlearningoutcomes6.4(a)and6.4(b)mustbestatedinthesimplestform.Involvechangingtheequationintogradientandinterceptform.

GeometersSketchpad



TopicalModule


6.5ParallelandPerpendicularLines

(a)Determinewhethertwostraightlinesareparallelorperpendiculartoeachother,whengradientofbothlinesareknown,andviceversa.

(b)Solveproblemsinvolvingequationsofstraightlines.

Real‐lifeexplorationsandinvestigations,relatedtoparallelandperpendicularlines.Calculatorandmathsoftwareexplorations,relatedtoparallelandperpendicularlines.Demonstrateandemphasize: :parallellines 1:perpendicularlines


27(JUL)

6.6EquationofLocusInvolvingDistancebetweenTwoPoints

(a)Findtheequationofthelocusofamovingpointsuchthat:(i) itsdistancefromafixed

pointisconstant.(ii) theratioofitsdistancesfrom

twofixedpointsisconstant.

GuidedLearningReal‐lifeexplorationsandinvestigations,relatedtoequationoflocus,involvingdistancebetweentwopoints.Manipulatemathematicalsoftwaretoseeexploretheconceptofparallelandperpendicularlines.


28(JUL)

7 Statistics7.1MeasuresofCentral

Tendency

(a)Calculatethemean,modeand

medianofungrouped.Do‐nowexerciseConferencingongroupeddataandungroupeddata.(Involvecriticalthinking)

GeometersSketchpad

EfofexGraph PhETSimulator


TopicalModule

Top1 PelangiAnalysisSeries(Forungroupeddata:3questionsminimumforeachlearningobjective)

29(JUL)

(b) Determinethemodalclassofgroupeddatafromafrequencydistributiontable.

(c) Findmodefromhistogram.

Do‐nowexercisesCollaborativegroupwork

WEEK TOPIC LEARNINGOBJECTIVES STRATEGIES/ACTIVITIES TEACHINGAIDS HOMEWORKS(d) Calculatemeanandmedianof

groupeddata.(e) Estimatethemedianofgrouped

datafromanOgive.(f) Determinetheeffectsonthe

mode,medianandmeanofasetofdatawhen:(i) eachdataischanged

uniformly(ii)extremevalueexist(iii)certaindataisaddedor

removed(g) Determinethemostsuitable

measureofcentraltendencyforgivendata.

InvolveuniformclassintervalsonlyDerivationofthemedianformulaisnotrequiredEmphasizethatcomparisonbetweentwosetsofdatausingonlymeasuresofcentraltendencyisnotsufficient

(Forgroupeddata:5questionsminimumforeachlearningobjective)

30(JUL)

7.2MeasuresofDispersion (a)Findtherangeandinterquartilerangeforungroupedandgroupeddata.

(b)Determinethevarianceofgroupedandungroupeddata.

(c) Determinethestandarddeviationofgroupedandungroupeddata.

Exploreandinvestigatetheupperandlowerquartilesbyusingogiveandformula

Top1 PelangiAnalysisSeries(Forungroupeddata:3questionsminimumforeachlearningobjective)(Forgroupeddata:5questionsminimumforeachlearningobjective)

31&32(AUG) TEST2

33(AUG)

8 CircularMeasure8.1Conceptofradians

(a) Convertmeasurementsin

radianstodegreeandviceversaGuidedlearningConferencingonthedefinitionofoneradian.Includemeasurementsinradiansexpressedintermsof .




29(JUL)

WEEK TOPIC LEARNINGOBJECTIVES STRATEGIES/ACTIVITIES TEACHINGAIDS HOMEWORKS8.2LengthofArcofaCircle (a)Determine:

(i) lengthofarc(ii)radius(iii)anglesubtendedatthe

centerofacirclebasedongiveninformation

(b) Findtheperimeterofsegmentsofcircles.

(c) Solveproblemsinvolvinglengthofarcs.

Demonstrationandguidedlearningonformulae.Usingdynamicmathsoftwaretoexploreandinvestigatetheconceptofcircularmeasure.Real‐lifeexplorationandinvestigationrelatedtocircularmeasure.Usethestudents’priorknowledgeofForm3mathtoanswerquestions.

TopicalModule

Algodoo


34(AUG) MID‐SEMESTERSCHOOLHOLIDAY/AIDILFITRIBREAK

36&37(SEPT)

8.3AreaofSectorofaCircle

(a)Determine:(i) areaofsector(ii)radius(iii)anglesubtendedatthe

centerofacirclebasedongiveninformation

(d) Findtheareaofsegmentofacircle.

(e) Solveproblemsinvolvingareasofsectors.

Demonstrationandguidedlearningonformulae.Usingdynamicmathsoftwaretoexploreandinvestigatetheconceptofcircularmeasure.Real‐lifeexplorationandinvestigationrelatedtocircularmeasure.Usethestudents’priorknowledgeofForm3mathtoanswerquestions.


Algodoo ScientificCalculator

TopicalModule


38&39(SEPT)

9 Progressions9.1ArithmeticProgressions

(a) Identifythecharacteristicsof

ArithmeticProgressions.(b) Determinewhetheragiven

sequenceisanArithmeticProgression.

(c) Determinespecifictermsandthenumberoftermsinarithmeticprogressionbyusingformula.

(d) Findthesumof terms,sumofaspecifiednumberofconsecutiveterms,andvalueof,giventhesumofthefirst termsofArithmeticProgressions.

Real‐lifeexplorationsandinvestigations,relatedtoArithmeticProgressions.UseinteractivemathsoftwaretoexploretheconceptofArithmeticProgression.BeginwithsequencestointroduceArithmeticorGeometricProgressions.Demonstrateexamplesinalgebraicexpressions.Demonstrateonformula

PhETSimulator


TopicalModule

Top1 PelangiAnalysisSeries(10questionsminimumrelatedtoSPMformat)

33(AUG)

WEEK TOPIC LEARNINGOBJECTIVES STRATEGIES/ACTIVITIES TEACHINGAIDS HOMEWORKS(e) Solveproblemsinvolving

ArithmeticProgressions.

39&40(SEPT/OCT)

9.2GeometricProgressions (a)IdentifycharacteristicsofGeometricProgressions.

(b)DeterminewhetheragivensequenceisaGeometricProgression.

(c) DeterminespecifictermandthenumberoftermsinGeometricProgressionsbyusingformula.

(d)Findsumofthefirst terms,sumofaspecifiednumberofconsecutiveterms,valueof giventhesumofthefirst terms,sumtoinfinityandfirsttermofcommonratio,giventhesumtoinfinityofgeometricprogressions.

Real‐lifeexplorationsandinvestigationsrelatedtotheconceptofGeometricProgressionsDemonstrateexamplesinalgebraicexpressions.Discuss: As → ∞, 0,then isreadas“sumtoinfinity”

PhETSimulator


TopicalModule

Top1 PelangiAnalysisSeries(10questionsminimumrelatedtoSPMformat)

40&41(OCT)

10 SolutionsofTriangles10.1 SineRule

(a) VerifySineRule.(b) Usetheruletofindunknown

sidesoranglesofatriangle.(c) Findunknownsidesandangles

ofatriangleinanambiguouscase.

(d) SolveproblemsinvolvingSineRule.

UsedynamicandinteractivemathsoftwaretoexploretheSineRule.Real‐lifeexplorationsandinvestigationsrelatedtotheSineRule.Demonstrateoncasesrelatedtoobtuse‐angledtriangles.

GeometersSketchpad

EfofexGraph ScientificCalculator

Manipulatives TopicalModule


10.2 CosineRule (a) VerifyCosineRule.(b) Usetheruletofindunknown

sidesoranglesofatriangle.(c) SolveproblemsinvolvingCosine

Rule.(d) SolveproblemsinvolvingSine

andCosineRule.

UsedynamicandinteractivemathsoftwaretoexploretheCosineRule.Real‐lifeexplorationsandinvestigationsrelatedtotheCosineRule.Demonstrateoncasesrelatedtoobtuse‐angledtriangles.


10.3 FormulaofAreaofaTriangle

(a)Findareasoftrianglesusing

.formulaof1 sin2

ab C orits

equivalent.

Do‐now exercises.Demonstrateonformula.Respondtoopen‐endedquestions


WEEK TOPIC LEARNINGOBJECTIVES STRATEGIES/ACTIVITIES TEACHINGAIDS HOMEWORKS(b)Solveproblemsinvolvingthree‐

dimensionalobjects.

40&41(OCT)

11 IndexNumbers11.1 IndexNumber

(a) CalculateIndexNumber.(b) CalculatePriceIndex.(c) Find or givenrelevant

information.

Real‐lifeexplorationsandinvestigationsrelatedtoIndexNumbers.Collaborativegroupwork.


TopicalModule


11.2 CompositeIndex (a)CalculateCompositeIndex.(b)FindIndexNumberorweightage

givenrelevantinformation.(c) SolveproblemsinvolvingIndex

NumberandCompositeIndex.

Real‐lifeexplorationsandinvestigationrelatedtoCompositeIndex.CollaborativegroupworkExplainweightageandCompositeIndex


42&43(OCT) FINALEXAMINATION

44&45(NOV) AFTEREXAMACTIVITIES

46–52(NOV/DEC)

ENDOFYEARHOLIDAYS

Preparedby:MohdZaidMohdIbrahimAdditionalMathematicsTeacher

Verifiedby:ZarinaAfandiVicePrincipal(Academic)