Add Maths Form 4 YLP 2012
10
SEKOLAH MENENGAH SETIABUDI YEARLY LESSON PLAN 2012 ADDITIONAL MATHEMATICS FORM 4 WEEK TOPIC LEARNING OBJECTIVES STRATEGIES/ACTIVITIES TEACHING AIDS HOMEWORKS 1 (JAN) ORIENTATION WEEK 2 (JAN) 1 Functions 1.1 Concept of Relations (a) Represent a relation by using arrow diagrams, ordered pairs and graphs. (b) Identify domain, codomain, object, image and range of a relation. (c) Classify a relation as one‐to‐one, many‐to‐one, one‐to‐many or many‐to‐many Real‐life investigation on concept of relations. Calculator and computer explorations: object image Responding to open‐ended questions. Whiteboard Manipulative Top 1 Pelangi Analysis Series (10 questions minimum) 1.2 Concept of Functions (a) Recognize functions as a special relation. (b) Express functions using function notation. (c) Determine the domain, object, image and range of function. (d) Determine the image of function given the object and vice versa. Apply the understanding from real‐life situations into numbers, figures and patterns. Write functions from given information or questions. Solving problems by using functions notation (include H.O.T.S.) Whiteboard Manipulative Scientific Calculator Top 1 Pelangi Analysis Series (10 questions minimum) 3 (JAN) 1.4 Inverse Functions (a) Find the object by inverse mapping given its image and function. (b) Determine the inverse function using algebra (c) State the condition for the existence of an inverse function. Guided Learning Do‐now exercise Use graph sketches and arrow diagrams to show the relationship between a function and its inverse. (state inverse function as reverse function. Top 1 Pelangi Analysis Series (15 questions minimum) 4 (JAN) 1.3 Composite Functions (a) Determine a composite function of two functions. (b) Determine the image of a composite function given the object and vice versa. (c) Determine one of the functions in a given composite function, given the other function. Collaborative group work. State composite functions as combined functions. Exploring with manipulatives and real‐life situations to represent composite functions Top 1 Pelangi Analysis Series (15 questions minimum)
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Transcript of 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
Top1 PelangiAnalysisSeries(10questionsminimum)
3(JAN)
1.4 InverseFunctions (a)Findtheobjectbyinversemappinggivenitsimageandfunction.
(b)Determinetheinversefunctionusingalgebra
(c) Statetheconditionfortheexistenceofaninversefunction.
GuidedLearningDo‐nowexerciseUsegraphsketchesandarrowdiagramstoshowtherelationshipbetweenafunctionanditsinverse.(stateinversefunctionasreversefunction.
Top1 PelangiAnalysisSeries(15questionsminimum)
4(JAN)
1.3CompositeFunctions (a)Determineacompositefunctionoftwofunctions.
(b)Determinetheimageofacompositefunctiongiventheobjectandviceversa.
(c) Determineoneofthefunctionsinagivencompositefunction,giventheotherfunction.
Collaborativegroupwork.Statecompositefunctionsascombinedfunctions.Exploringwithmanipulativesandreal‐lifesituationstorepresentcompositefunctions
Top1 PelangiAnalysisSeries(15questionsminimum)
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
Top1 PelangiAnalysisSeries(10questionsminimum)
5&6(FEB)
2.2QuadraticEquation (a)Determinetherootsofaquadraticequationbyfactorization,completingthesquareandquadraticformula.
(b)Formaquadraticequationfromgivenroots.
Guidedlearninganddo‐nowexercise.Tellthestudentstheyneedtoknowonly3methodstofindrootsDemonstrateonallthe3methods.Studentsdotheanalysiswhethertheanswersdifferornot.Introducetheanddemonstrateformula. . . . andexplainwhentouseit
Top1 PelangiAnalysisSeries(15questionsminimum)
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
WEEK TOPIC LEARNINGOBJECTIVES STRATEGIES/ACTIVITIES TEACHINGAIDS HOMEWORKS
12(MAR)
3 QuadraticFunctions3.1QuadraticFunctions
andtheirgraphs
(a) Recognizequadraticfunctions(b) Plotquadraticfunctiongraphs(c) Recognizeshapesofgraphsof
quadraticfunctions(d) Relatethepositionofquadratic
functiongraphswiththetypeofrootsoftheequation 0.
Exploreandinvestigateonshapesofgraphsforcaseswhere 0and 0for
GeometersSketchpad
EfofexGraph Autograph PhETSimulator
ScientificCalculator
TopicalModule
Top1 PelangiAnalysisSeries(15questionsminimum)
13(MAR)
3.2Maximumandminimumvaluesofquadraticfunction
(a)Determinethemaximumorminimumvalueofquadraticfunctionbyusingthecompletingthesquaremethod
Do‐nowexerciseInvestigateandanalyzethepositionofmaximumandminimumvalueonvarioustypeofquadraticgraphs.
Top1 PelangiAnalysisSeries(15questionsminimum)
14(APR)
3.3SketchgraphsofQuadraticFunctions
(a)Sketchquadraticfunctiongraphsbydeterminethemaximumorminimumpointandtwoanyotherpoints
Emphasizethemarkingofmaximumorminimumpointanddemonstratehowtofindanothertwopoints,axisofsymmetryand –interceptDetermineotherpointsbyfindingtheintersectionwiththe ‐axis(ifitexists)
Top1 PelangiAnalysisSeries(12questionsminimum)
3.4QuadraticInequalities (a)Determinetherangeofvaluesofthatsatisfiesquadraticinequalities
Demonstrateandemphasizeongraphssketchinganduseofnumberlineswhennecessary
Top1 PelangiAnalysisSeries(15questionsminimum)
15(APR)
4 SimultaneousEquations
4.1Simultaneousequationsintwounknowns
(a) Solvesimultaneousequations
usingsubstitutionmethod.(b) Solvesimultaneousequations
involvingreal‐lifesituations.
Do‐nowexerciseExploreandinvestigatetheconceptofsimultaneousequationsthroughcomputersoftwareandcalculatorInvestigateonreal‐lifesituationssuchasarea,perimeterandvolume.
GeometersSketchpad
EfofexGraph Autograph PhETSimulator
ScientificCalculator
Top1 PelangiAnalysisSeries(12questionsminimum)
WEEK TOPIC LEARNINGOBJECTIVES STRATEGIES/ACTIVITIES TEACHINGAIDS HOMEWORKS
16(APR)
5 Indices&Logarithms5.1 IndicesandLawof
Indices
(a) Findthevaluesofnumbers
givenintheformofintegerindicesandfractionalindices.
(b) Uselawsofindicestofindthevaluesofnumbersinindexformthataremultiplieddividedorraisedtopower.
(c) Uselawsofindicestosimplifythealgebraexpressions.
Real‐lifeinvestigationsDo‐nowexerciseDemonstrationonrulesofindices.
ScientificCalculator
TopicalModule
Top1 PelangiAnalysisSeries(10questionsminimum)
5.2LogarithmsandLawsofLogarithms
(a)Expressanequationinindexformtologarithmformandviceversa.
(b)Findthelogarithmofanumber.(c) Simplifylogarithmicexpressions
tothesimplestform
Exploreandinvestigatedefinitionoflogarithm.
; with 0, 1.Emphasizethat:
1 0; 1.Emphasize: Logarithmofnegativenumbersisundefined
Logarithmofzeroisundefined
Discussoncaseswherethegivennumberisin: Indexform Numericalform
Discussonthelawsoflogarithms
Top1 PelangiAnalysisSeries(20questionsminimum)
17(APR)
5.3ChangethebaseofLogarithms
(a)Findthelogarithmofanumberbychangingthebaseofthelogarithmtoasuitablebase.
(b)Solveproblemsinvolvingchangeofbaseandlawsoflogarithms.
Discusson 1 loglog b
a
ab
Top1 PelangiAnalysisSeries(8questionsminimum)
5.4SolveEquationsInvolvingIndicesandLogarithms
(a)Solveequationsinvolvingindices.
(b)Solveequationsinvolvinglogarithms
Equationsthatinvolvedwithindicesandlogarithmsarelimitedtoequationswithsinglesolutiononly.Solveequationsinvolvingindicesby: Comparisonofindicesandbases, Usinglogarithms
Top1 PelangiAnalysisSeries(20questionsminimum)
WEEK TOPIC LEARNINGOBJECTIVES STRATEGIES/ACTIVITIES TEACHINGAIDS HOMEWORKS
18‐20(MAY) MIDTERMEXAMINATION
21(MAY) DISCUSSIONONEXAMPAPERS
22&23(JUNE) MIDTERMBREAK
24(JUNE)
6 CoordinateGeometry6.1DistanceBetweenTwo
Points
(a) Findthedistancebetween2
points.Do‐nowexerciseManipulatePythagoras’TheoremtofindtheformulafordistancebetweentwopointsCollaborativegroupwork
GeometersSketchpad
EfofexGraph Autograph PhETSimulator
ScientificCalculator
TopicalModule
Top1 PelangiAnalysisSeries(8questionsminimum)
6.2DivisionofaLineSegment
(a)Findthemidpointoftwogivenpoints.
(b)Findthecoordinatesofapointthatdividesalineaccordingtoagivenratio : .
Introduceanddemonstrateonformulaformidpointcoordinateandmanipulatetheformulatoderivetheformula
1 2 1 2,nx mx ny mym n m n
Limittocaseswhere and arepositive.Collaborativegroupwork.
Top1 PelangiAnalysisSeries(8questionsminimum)
25(JUNE)
6.3AreasofPolygons (a)Findtheareaoftrianglebasedontheareaofspecificgeometricshapes,andbyusingformula.
(b)Findtheareaofquadrilateralbyusingformula.
Limittonumericalvalues.Emphasizetherelationshipbetweenthesignofthevalueforareaobtainedwiththeorderoftheverticesused.Derivationoftheformulaisnotrequired.Emphasizethatwhentheareaofpolygoniszero,thegivenpointsarecollinear.
Top1 PelangiAnalysisSeries(8questionsminimum)
WEEK TOPIC LEARNINGOBJECTIVES STRATEGIES/ACTIVITIES TEACHINGAIDS HOMEWORKS
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
EfofexGraph Autograph PhETSimulator
ScientificCalculator
TopicalModule
Top1 PelangiAnalysisSeries(12questionsminimum)
6.5ParallelandPerpendicularLines
(a)Determinewhethertwostraightlinesareparallelorperpendiculartoeachother,whengradientofbothlinesareknown,andviceversa.
(b)Solveproblemsinvolvingequationsofstraightlines.
Real‐lifeexplorationsandinvestigations,relatedtoparallelandperpendicularlines.Calculatorandmathsoftwareexplorations,relatedtoparallelandperpendicularlines.Demonstrateandemphasize: :parallellines 1:perpendicularlines
Top1 PelangiAnalysisSeries(12questionsminimum)
27(JUL)
6.6EquationofLocusInvolvingDistancebetweenTwoPoints
(a)Findtheequationofthelocusofamovingpointsuchthat:(i) itsdistancefromafixed
pointisconstant.(ii) theratioofitsdistancesfrom
twofixedpointsisconstant.
GuidedLearningReal‐lifeexplorationsandinvestigations,relatedtoequationoflocus,involvingdistancebetweentwopoints.Manipulatemathematicalsoftwaretoseeexploretheconceptofparallelandperpendicularlines.
Top1 PelangiAnalysisSeries(10questionsminimum)
28(JUL)
7 Statistics7.1MeasuresofCentral
Tendency
(a)Calculatethemean,modeand
medianofungrouped.Do‐nowexerciseConferencingongroupeddataandungroupeddata.(Involvecriticalthinking)
GeometersSketchpad
EfofexGraph PhETSimulator
ScientificCalculator
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 .
EfofexGraph PhETSimulator
ScientificCalculator
Top1 PelangiAnalysisSeries(10questionsminimum)
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
Top1 PelangiAnalysisSeries(12questionsminimum)
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.
EfofexGraph PhETSimulator
Algodoo ScientificCalculator
TopicalModule
Top1 PelangiAnalysisSeries(12questionsminimum)
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
ScientificCalculator
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
ScientificCalculator
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
Top1 PelangiAnalysisSeries(10questionsminimum)
10.2 CosineRule (a) VerifyCosineRule.(b) Usetheruletofindunknown
sidesoranglesofatriangle.(c) SolveproblemsinvolvingCosine
Rule.(d) SolveproblemsinvolvingSine
andCosineRule.
UsedynamicandinteractivemathsoftwaretoexploretheCosineRule.Real‐lifeexplorationsandinvestigationsrelatedtotheCosineRule.Demonstrateoncasesrelatedtoobtuse‐angledtriangles.
Top1 PelangiAnalysisSeries(12questionsminimum)
10.3 FormulaofAreaofaTriangle
(a)Findareasoftrianglesusing
.formulaof1 sin2
ab C orits
equivalent.
Do‐now exercises.Demonstrateonformula.Respondtoopen‐endedquestions
Top1 PelangiAnalysisSeries(10questionsminimum)
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.
ScientificCalculator
TopicalModule
Top1 PelangiAnalysisSeries(10questionsminimum)
11.2 CompositeIndex (a)CalculateCompositeIndex.(b)FindIndexNumberorweightage
givenrelevantinformation.(c) SolveproblemsinvolvingIndex
NumberandCompositeIndex.
Real‐lifeexplorationsandinvestigationrelatedtoCompositeIndex.CollaborativegroupworkExplainweightageandCompositeIndex
Top1 PelangiAnalysisSeries(12questionsminimum)
42&43(OCT) FINALEXAMINATION
44&45(NOV) AFTEREXAMACTIVITIES
46–52(NOV/DEC)
ENDOFYEARHOLIDAYS
Preparedby:MohdZaidMohdIbrahimAdditionalMathematicsTeacher
Verifiedby:ZarinaAfandiVicePrincipal(Academic)
