F3 scheme of work 2013 maths
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  • 1. 1. LEARNING AREA: LINES AND ANGLES IIWEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY12/1 –4/1Students will be taught to:1.1 Understand and useproperties of anglesassociated withtransversal and parallellines.• Explore the properties of anglesassociated with transversal usingdynamic geometry software,geometry sets, acetate oerlaysor tracing paper.• Discuss when alternate andcorresponding angles are notequal.• Discuss when all anglesassociated with transversals areequal and the implication on itsconverse.Students will be able to:i. Identify:a) transversalsb) corresponding anglesc) alternate anglesd) interior anglesii. Determine that for parallel lines:a) corresponding angles areequalb) alternate angles are equalc) sum of interior angles is 180˚ .iii. Find the values of:a) corresponding anglesb) alternate anglesc) interior angles associatedwith parallel lines.iv. Determine if two given lines areparallel based on the properties ofangles associated withtransversals.v. Solve problems involvingproperties of angles associatedwith transversals.The interior angles on thesame side of thetransversal aresupplementary.Limit to transversalintersecting parallel lines.parallel linestransversalalternate angleIiterior angleassociated correspondangleintersecting linessupplementary - 180˚acetate overlay1SEKOLAH MENENGAH KEBANGSAAN RAJA PEREMPUAN, IPOH.SCHEME OF WORK MATHEMATICS FORM 3 YEAR 2010
  • 2. 2. LEARNING AREA: POLYGONS IIWEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY27/1-11/1Students will be taught to:2.1 Understand the concept ofregular polygons.• Use models of polygons andsurroundings to identify regularpolygons.• Explore properties of polygonsusing rulers, compasses,protractors, grid papers,templates, geo-boards, flashcards and dynamic geometrysoftware.• Include examples of non-regular polygons developedthrough activities such asfolding papers in the shape ofpolygons.• Relate to applications inarchitecture.Students will be able to:i. Determine if a given polygon is aregular polygon.ii. Find:a) the axes of symmetryb) the number of axes ofsymmetry of a polygon.iii. Sketch regular polygons.iv. Draw regular polygons by dividingequally the angle at the centre.v. Construct equilateral triangles,squares and regular hexagons.Limit to polygons with amaximum of 10 sides.Construct usingstraightedges andcompasses.Emphasise on the accuracyof drawings.polygonregular polygonconvex polygonaxes of symmetrystraightedges angleequilateral trianglesquareregular hexagon2
  • 3. 2. LEARNING AREA: POLYGONS IIWEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to:2.2 Understand and use theknowledge of exterior andinterior angles of polygons.• Explore angles of differentpolygons through activities suchas drawing, cutting and pasting,measuring angles and usingdynamic geometry software.• Investigate the number oftriangles formed by dividing apolygon into several triangles byjoining one chosen vertex of thepolygon to the other vertices.• Include examples from everydaysituations.Students will be able to:i. Identify the interior angles andexterior angles of a polygon.ii. Find the size of an exterior anglewhen the interior angle of apolygon is given and vice versa.iii. Determine the sum of the interiorangles of polygons.iv. Determine the sum of theexterior angles of polygons.v. Find:a) the size of an interior angleof a regular polygon giventhe number of sides.b) the size of an exterior angleof a regular polygon giventhe number of sides.vi. Solve problems involving anglesand sides of polygons.Interior angleExterior angleComplementaryAnglesum3
  • 4. 3. LEARNING AREA: CIRCLES IIWEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY314/1 –18/1Students will be taught to:3.1 Understand and useproperties of circles involvingsymmetry, chords and arcs.• Explore through activities such astracing, folding, drawing andmeasuring using compasses,rulers, threads, protractors, filterpapers and dynamic geometrysoftware.Students will be able to:i. Identify a diameter of a circle asan axis of symmetry.ii. Determine that:a) a radius that is perpendicularto a chord divides the chordinto two equal parts and viceversa.b) perpendicular bisectors oftwo chords intersect at thecentre.c) two chords that are equal inlength are equidistant fromthe centre and vice versa.d) chords of the same lengthcut arcs of the same length.iii. Solve problems involvingsymmetry, chords and arcs ofcircles.Diameteraxis of symmetrychordperpendicularbisectorintersectequidistantarcsymmetrycentreradiusperpendicular4
  • 5. 3. LEARNING AREA: CIRCLES IIWEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to:3.2 Understand and useproperties of angles incircles.• Explore roperties of angles in acircle by drawing, cutting andpasting, and using dynamicgeometry software.Students will be able to:i. Identify angles subtended byan arc at the centre and at thecircumference of a circle.ii. Determine that angles subtendedat the circumference by the samearc are equal.iii. Determine that angles subtended:a) at the circumferenceb) at the centre by arcs of thesame length are equal.iv. Determine the relationshipbetween angle at the centre andangle at the circumferencesubtended by an arc.v. Determine the size of an anglesubtended at the circumferencein a semicircle.vi. Solve problems involving anglessubtended at the centre andangles at the circumference ofcircles.Include reflex anglesSubtended at the centre.Angle subtended by an arcis the same as anglesubtended by thecorresponding chord.anglesubtendedsemicirclecircumferencearcchordreflex anglecentre5
  • 6. 3. LEARNING AREA: CIRCLES IIWEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY421/1-25/124/1Students will be taught to:3.3 Understand and use theconcept of cyclicquadrilaterals.CUTI MAULIDUR RASUL• Explore properties of cyclicquadrilaterals by drawing, cuttingand pasting and using dynamicgeometry software.Students will be able to:i. Identify cyclic quadrilaterals.ii. Identify the interior oppositeangles of cyclic quadrilaterals.iii. Determine the relationshipbetween interior opposite anglesof cyclic quadrilaterals.iv. Identify exterior angles and thecorresponding interior oppositeangle of cyclic quadrilaterals.v. Determine the relationshipbetween exterior angles andthe corresponding interioropposite angle of cyclicquadrilaterals.vi. Solve problems involving anglesof cyclic quadrilaterals.vii. Solve problems involving circles.6
  • 7. 4. LEARNING AREA: STATISTICS IIWEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY528/1 –29/1Students will be taught to:4.1 Represent and interpret datain pie charts to solveproblems.• Use everyday examples fromsources such as newspapers,magazines, reports and theinternet.• Use calculators and computersoftware in constructing pie charts.Students will be able to:i. Obtain and interpret informationfrom pie charts.ii. Constuct pie charts to representdata.iii. Solve problems involving piecharts.iv. Determine suitable representationof data.Relate the quantities of thedata to the size of angles ofthe sectors.A complete pie chart shouldinclude:i. The titleii. Appropriate labels forthe groups of data.Pie charts are mainlysuitable for categoricaldata.Include pictograms, barcharts, line graphs and piechart.Discuss that representationof data depends on the typeof data.sectorpie chartanglesuitablerepresentationconstructsize of sectorquantitydatasize of anglelabeltitlepictogramsbar chartpie chart7
  • 8. 4. LEARNING AREA: STATISTICS IIWEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY630/1-1/2Students will be taught to:4.2 Understand and use theconcept of mode, medianand mean to solve problems.PRA USBF 1• Use sets of data from everydaysituations to evaluate and toforecast.• Discuss appropriate measurementin different situations.• Use calculators to calculate themean for large sets of data.• Discuss appropriate use of mode,median and mean in certainsituations.Students will be able to:i. Determine the mode of:a) sets of datab) data given in frequencytables.ii. Determine the mode and therespective frequency frompictographs, bar charts, linegraphs and pie charts.iii. Determine the median for setsof data.iv. Determine the median of datain frequency tables.v. Calculate the mean of:a) sets of datab) data in frequency tablesvi. Solve problems involving mode,median and mean.Involve data with more thanone mode.Limit to cases with discretedata only.Emphasise that moderefers to the category orscore and not to thefrequency.Include change in thenumber and value of data.datamodediscretefrequencymedianarrangeoddevenmiddlefrequency tablemean8
  • 9. 5 LEARNING AREA: INDICESWEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY74/2 –8/210/2-11/2Students will be taught to:5.1 Understand the conceptof indices.CUTI TAHUN BARU CINA• Explore indices using calculatorsand spreadsheets.Students will be able to:i. Express repeated multiplicationas aⁿ and vice versa.ii. Find the value of aⁿ .iii. Express numbers in indexnotation.Begin with squares andcubes.‘a’ is a real number.Include algebraic terms.Emphasise base andIndex.a x a x …. a = aⁿn factorsa is the base, n is theindex.Involve fractions andDecimals.Limit n to positive integers.indicesbaseindexpower ofindex notationindex formexpressvaluereal numbersrepeated multiplicationfactor9
  • 10. 5. LEARNING AREA: INDICESWEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY812/2-15/2Students will be taught to:5.2 Perform computationsinvolving multiplication ofnumbers in index notation.5.3 Perform computationInvolving division of numbersIn index notation.• Explore laws of indices usingrepeated multiplication andcalcul tors.Students will be able to:i. Verify amx aⁿ = am+nii. Simplify multiplication of:a) numbersαb) algebraic termsexpressed in index notationwith the same base.iii. Simplify multiplication of:a) numbersb) algebraic termsexpressed in index notation withdifferent bases.i. Verify am÷ an= am-nii. Simplify division of:a) numbersb) algebraic termsexpressed in index notation withthe same base.Limit algebraic terms to oneunknown.Emphasise a° = 1multiplicationsimplifybasealgebraic termverifyindex notationindiceslaw of indicesunknown10
  • 11. 5. LEARNING AREA: INDICESWEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY918/2-22/2Students will be taught to:5.4 Perform computationsinvolving raising numbersand algebraic terms in indexnotation to a power.Students will be able to:i. Derive ( am)ⁿ = amnii. Simplify:a) numbersb) algebraic termsexpressed in index notationraised to a power.iii. Simplify multiplication and divisionof:a) numbersb) algebraic termsexpressed in index notation withdifferent bases raised to a power.iv. Perform combined operationsinvolving multiplication, division,and raised to a power on:a) numbersb) algebraic terms(am)ⁿ = amnm and n are positiveintegers.Limit algebraic terms to oneunknown.Emphasise:(amx bⁿ )p= ampx bⁿpam= ampbnbnpraised to a powerbase11
  • 12. 5. LEARNING AREA: INDICESStudents will be taught to:5.5 Perform computationsinvolving negative indices.• Explore using repeatedmultiplications and the law ofindices.Students will be able to:i. Verify a -ⁿ = 1aⁿii. State a -ⁿ as 1 and vice versaaⁿiii. Perform combined operations ofmultiplication, division andraising to a power involvingnegative indices on:a) numbersb) algebraic terms1i. Verify a ⁿ = ⁿ √ a .1ii. State a ⁿ as ⁿ √ a and viceversa.1iii. Find the value of a ⁿ .miv. State a ⁿ as:1 1a) ( am) ⁿ or ( a ⁿ )m.b) ⁿ √ a or ( ⁿ √ a ) mn is a positive integer..Begin with n = 1.a and n are positiveintegers.Begin with n = 2verify12
  • 13. Students will be taught to:5.6 Perform computationinvolving laws of indices.Students will be able to:v. Perform combined operationsof multiplications, division andraising to a power involvingfractional indices ona) numbersb) algebraic termsmvi. Find the value of a ⁿi. Perform multiplication, division,raised to a power or combinationof these operations on severalnumbers expressed in indexnotation.ii. Perform combined operations ofmultiplication, division and raisedto a power involving positive,negative and fractional indices.Limit to positive integralroots.13
  • 14. 6. LEARNING AREA: ALGEBRAIC EXPRESSIONS IIIWEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY1025/2-8/3115/3-7/3Students will be taught to:6.1 Understand and use theconcept of expandingbrackets.USBF 1• Relate to concrete examples.• Explore using computer software.Students will be able to:i. Expand single brackets.ii. Expand two brackets.Begin with linear algebraicterms.Limit to linear expressions.Emphasise:(a ± b) (a ± b)= (a ± b)²Include:(a + b) (a + b)(a – b) (a – b)(a + b) (a – b)(a – b) (a + b)linear algebraic termslike termsunlike termsexpansionexpandsingle bracketstwo bracketsmultiply6. LEARNING AREA: ALGEBRAIC EXPRESSIONS III14
  • 15. WEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY1211/3-15/3Students will be taught to:6.2 Understand and use theconcept of factorisation ofalgebraic expression tosolve problems.• Explore using concrete materialsand computer software.Students will be able to:i. State factors of an algebraic term.ii. State common factors and the aHCFfor several algebraic terms.iii. Factorise algebraic expression:a) using common factorb) the difference of two squaresEmphasise the relationshipbetween expansion andfactorisation.Note that “1” is a factor forall algebraic terms.The difference of twosquares means:a² - b²= (a ± b) (a ± b) .Limit to four algebraicterms.ab – ac = a(b – c)e² - f² = (e + f) (e – f)x + 2xy + y² = (x + y)²Limit answers to(ax + by)²ab + ac + bd + cd= (b + c) (a + d)factorisationsquarecommon factortermhighest common factor(HCF)difference of twosquares6. LEARNING AREA: ALGEBRAIC EXPRESSIONS III15
  • 16. WEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to:• Explore using computer software.Students will be able to:iv. Factorise and simplify algebraicfractions.Begin with one-termexpressions for thenumerator anddenominator.Limit to factorisationinvolving common factorsand difference of twosquares.numeratordenominatoralgebraic fractionfactorisation6. LEARNING AREA: ALGEBRAIC EXPRESSIONS III16
  • 17. WEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to:6.3 Perform addition andsubtraction on algebraicfractions.• Explore using computer software.• Relate to real-life situations.Students will be able to:i. Add or subtract two algebraicfractions with the samedenominator.ii. Add or subtract two algebraicfractions with one denominatoras a multiple of the otherdenominator.iii. Add or subtract two algebraicfractions with denominators:a) without any common factorb) with a common factorThe concept of LCM maybe used.Limit denominators to onealgebraic term.common factorlowest commonmultiple (LCM)multipledenominator6. LEARNING AREA: ALGEBRAIC EXPRESSIONS III17
  • 18. WEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to:6.4 Perform multiplication anddivision on algebraicfractions.• Explore using computer software.Students will be able to:i. Multiply two algebraic fractionsinvolving denominator with:a) one termb) two termsii. Divide two algebraic fractionsinvolving denominator with:a) one termb) two termsiii. Perform multiplication and divisionof two algebraic fractions usingfactorisation involving commonfactors and the different of twosquares.Begin multiplication anddivision withoutsimplification followed bymultiplication and divisionwith simplification.simplification7. LEARNING AREA: ALGEBRAIC FORMULAE18
  • 19. WEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY1318/3-22/3Students will be taught to:7.1 Understand the concept ofvariables and constants.7.2 Understand the concept offormulae to solve problems.• Use example of everydaysituations to explain variablesand constants.Students will be able to:i. Determine if a quantity in a givensituation is a variable or aconstant.ii. Determine the variable in agiven situation and represent itwith a letter symbol.iii. Determine the possible values ofa variable in a given situation.Students will be able to:i. Write a formula based on agiven:a) statementb) situation.ii. Identify the subject of a givenformula.Variables include integers,fractions and decimals.quantityvariableconstantpossible valueformulavalueletter symbolformulae7. LEARNING AREA: ALGEBRAIC FORMULAE19
  • 20. WEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY23/3-31/3Students will be taught to:CUTI PENGGAL 1iii. Express a specified variable asthe subject of a formulainvolving:a) one of the basic operations:+, -, x, ÷b) powers or rootsc) combination of the basicoperations and powers orroots.iv. Find the value of a variable whenit is:a) the subject of the formulab) not the subject of the formulav. Solve problems involvingformulae.Symbols representing aquantity in a formula mustbe clearly stated.Involve scientific formulae.subject of a formulastatementpowerrootsformulae20
  • 21. 8. LEARNING AREA: SOLID GEOMETRY IIIWEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY141/4-5/4Students will be taught to:Understand and use the conceptof volume of right prisms andright circular cylinders tosolve problems.• Use concrete models to derive theformula.• Relate the volume of right prismsto right circular cylinders.Students will be able to:i. Derive the formula for volume of:a) prismsb) cylinders.ii. Calculate the volume of a rightprism in cubic units given theheight and:a) the area of the baseb) dimensions of the base.iii. Calculate the height of a prismgiven the volume and the area ofthe base.iv. Calculate the area of the base ofa prism given the volume andthe height.Prisms and cylinders referto right prisms and rightcircular cylindersrespectively.Limit the bases to shapesof triangles andquadrilaterals.deriveprismcylinderright circular cylindercircularbaseradiusvolumeareacubic unitsrectangletriangledimensionheight21
  • 22. WEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:v. Calculate the volume of acylinder in cubic units given:a) area of the base and theheight.b) radius of the base and theheightof the cylinder.vi. Calculate the height of acylinder, given the volume andthe radius of the base.vii. Calculate the radius of the baseof a cylinder given the volumeand the height.viii. Convert volume in one metricunit to another:a) mm3, cm3and m3b) cm3, ml and lix. Calculate volume of liquid in acontainer.x. Solve problems involving volumeof prisms and cylinders.Limit the shape ofcontainers to right circularcylinder and right prisms.cubic metrecubic centimetrecubic milimetremililitrelitreconvertmetric unitliquidcontainer22
  • 23. 8. LEARNING AREA: SOLID GEOMETRY IIIWEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to:8.2 Understand and use theconcept of volume of rightpyramids and right circularcones to solve problems.• Use concrete models to derivethe formula.• Relate volume of pyramids toprisms and cones to cylinders.Students will be able to:i. Derive the formula for thevolume of:a) pyramidsb) cones.ii. Calculate the volume ofpyramids in mm3, cm3and m3,given the height and:a) area of the baseb) dimensions of base.iii. Calculate the height of a pyramidgiven the volume and thedimension of the base.iv. Calculate the area of the base ofa pyramid given the volume andthe height.v. Calculate the volume of a conein mm3, cm3and m3, given theheight and radius of the base.vi. Calculate the height of a cone,given the volume and the radiusof the base.vii. Calculate the radius of the baseof a cone given the volume andthe height.viii. Solve problems involving volumeof pyramids and cones.Inclue bases of differenttypes of polygons.pyramidconevolumebaseheightdimension8. LEARNING AREA: SOLID GEOMETRY III23
  • 24. WEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY158/4-15/41616/4-18/4Students will be taught to:8.3 Understand and use theconcept of volume of sphereto solve problems.8.4 Apple the concept of volumeto solve problems involvingcomposite solids.PRA PEPERIKSAANPERTENGAHAN TAHUN• Use concrete models to formcomposite solids.• Use examples from real-lifesituations.Students will be able to:i. Calculate the volume of a spheregiven the radius of the sphere.ii. Calculate the radius of a spheregiven the volume of the sphere.iii. Solve problems involving volumeof spheres.i. Calculate the volume ofcomposite solids.ii. Solve problems involvingvolumes of composite solids.Include hemisphereComposite solids arecombinations of geometricsolids.spherehemispheresolidcomposite solidcombinationvolumeradius24
  • 25. 9. LEARNING AREA: SCALE DRAWINGSWEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY1722/4-26/4Students will be taught to:9.1 Understand the concept ofscale drawings.• Explore scale drawings usingdynamic geometry software, gridpapers, geo-boards or graphpapers.• Relate to maps, graphics andarchitectural drawings.Students will be able to:i. Sketch shapes:a) of the same size as theobjectb) smaller than the objectc) larger than the objectusing grid papers.ii. Draw geometric shapesaccording to scale 1 : n , wheren = 1, 2, 3, 4, 5, 1 , 1 .2 10iii. Draw composite shapes,according to a given scale using:a) grid papersb) blank papers.iv. Redraw shapes on grids ofdifferent sizes.v. Solve problems involving scaledrawings.Limit objects to two-dimensional geometricshapes.Emphasise on the accuracyof the drawings.Include grids of differentsizes.Emphasise that gridsshould be drawn on theoriginal shapes.sketchdrawobjectsgrid paperssoftwarescalegeometrical shapescomposite shapessmallerlargeraccuratesizeredraw25
  • 26. 10. LEARNING AREA: TRANSFORMATIONS IIWEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY1829/4-3/5 Students will be taught to:10.1 Understand and use theconcept of similarity.10.2 Understand and use theconcept of enlargement.• Involve examples from everydaysituations.• Explore the concept ofenlargement using grid papers,concrete materials, drawings, geo-boards and dynamic geometrysoftware.Relate enlargement to similarity ofshapes.Students will be able to:i. Identify if given shapes aresimilar.ii. Calculate the lengths ofunknown sides of two similarshapes.i. Identify an enlargement.ii. Find the scale factor, given theobject and its image of anenlargement when:a) scale factor > 0b) scale factor <0iii. Determine the centre ofenlargement, given the objectand its image.iv. Determine the image of anobject given the centre ofenlargement and the scalefactor.v. Determine the properties ofenlargement.Emphasise that for atriangle, if thecorresponding angles areequal, then thecorresponding sides areproportional.Emphasise the case ofreduction.Emphasise the case whenscale factor = ± 1Emphasise that the centreof enlargement is aninvariant point.Emphasise the method ofconstructionshapesimilarsideangleproportioncentre of enlargementtransformationenlargementscale factorobjectimageinvariantreductionsizeorientationsimilarityproperties26
  • 27. 10. LEARNING AREA: TRANSFORMATIONS IIWEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to:• Use grid papers and dynamicgeometry software to explore therelationship between the area ofthe image and its object.Students will be able to:vi. Calculate:a) the scale factorb) lengths of the side of theimagec) length of the side of theobjectof an enlargementvii. Determine the relationshipbetween the area of the imageand its object.viii. Calculate the:a) area of imageb) area of objectc) scale factorof an enlargementix. Solve problems involvingenlargement.Include negative scalefactors.area27
  • 28. 11. LEARNING AREA: LINEAR EQUATIONS IIWEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY196/5-10/52013/5-17/5Students will be taught to:11.1 Understand and use theconcept of linear equationsin two variables.11.2 Understand and use theconcept of twosimultaneous linearequations in two variablesto solve problems.PEPERIKSAAN PERTENGAHANTAHUN• Derive linear equations in twovariables relating to real-lifesituations.• Explore using graphic calculators,dynamic geometry software andspreadsheets to solve linearequations and simultaneous linearequations.• Use trial and improvementmethod.• Use examples from real-lifesituations.Students will be able to:i. Determine if an equation is alinear equation in two variables.ii. Wrtie linear equations in twovariables from given informationiii. Determine the value of a variablegiven the object variables.iv. Determine the possible solutionsfor a linear equation in twovariables.i. Determine if two given equationsare simultaneous linearequations.ii. Solve two simultaneous linearequations in two variables bya) substitutionb) eliminationiii. Solve problems involving twosimultaneous linear equations intwo variables.Include letter symbols otherthan x and y to representvariables.equationvariablelinear equationvaluepossible sollutionlinear equationvariablesimultaneous linearequationsolutionsubstitutionelimination28
  • 29. 12. LEARNING AREA: LINEAR INEQUALITIESWEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY2120/5-23/5Students will be taught to:12.1 Understand and use theconcept of inequalities.• Use everyday situations toillustrate the symbols and the useof “>” , “<” , “≥” and “≤”.Students will be able to:i. Identify the relationship:a) greater thanb) less thanbased on given situations.ii. Write the relationship betweentwo given numbers using thesymbol “>” or “<”.iii. Identify the relationship:a) greater than or equal tob) less than or equal tobased on given situations.Emphasise that a > b isequivalent to b < a.“>” read as “greater than”.“<” read as “less than”.“≥” read as “greater than orequal to”.“≤” read as “less than orequal to”.Inequalitygreaterlessgreater thanless thanequal toincludeequivalentsolution12. LEARNING AREA: LINEAR INEQUALITIES29
  • 30. WEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to:12.2 Understand and use theconcept of linearinequalities in oneunknown.Students will be able to:i. Determine if a given relationshipis a linear inequality.ii. Determine the possible solutionsfor a given linear inequality inone unknown:a) x > h;b) x < h;c) x ≥ h;d) x ≤ h.iii. Represent a linear inequality:a) x > h;b) x < h;c) x ≥ h;d) x ≤ h.on a number line and vice versa.h is a constant, x is aninterger.relationshiplinearunknownnumber line12. LEARNING AREA: LINEAR INEQUALITIES30
  • 31. WEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to:12.3 Perform computationsinvolving adding,subtraction, multiplicationand division on inequalities.• Involve examples from everydaysituations.Students will be able to:iv. Construct linear inequalitiesusing symbols:a) “>” or “<”b) “≥” or “≤”from given informationi. State a new inequality for agiven inequality when a numberis:a) added tob) subtracted fromboth sides of the inequalties.ii. State a new inequality for agiven inequality when both sidesof the inequalities are:a) multiplied by a numberb) divided by a number.Emphasise that thecondition of inequality isunchanged.Emphasise that when wemultiply or divide both sidesof an inequality by thesame negative number, theinequality is reversed.addadditionsubtractsubtractionmultiplymultiplicationdividedivision12. LEARNING AREA: LINEAR INEQUALITIES31
  • 32. WEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:iii. Construct inequalitiesa) x + k > m + kb) x – k > m - kc) kx > kmd) x > mk kfrom given information.Information given from real-life situations.Include also <, ≤ and ≥.relationequivalentaddingsubtractingsimplestcollectisolatesolve12. LEARNING AREA: LINEAR INEQUALITIES32
  • 33. WEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to:12.4 Perform computations tosolve inequalities in onevariable.• Explore using dynamic geometrysoftware and graphic calculators.Students will be able to:i. Solve a linear inequality by:a) adding a numberb) subtracting a numberon both sides of the inequality.ii. Solve a linear inequality bya) multiplying a numberb) dividing a numberon both sides of the inequalityiii. Solve linear inequalities in onevariable using a combination ofoperations.Emphasise that for asolution, the variable iswritten on the left side ofthe inequalities.addsubtractmultiplydivide12. LEARNING AREA: LINEAR INEQUALITIES33
  • 34. WEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY24/5-9/6Students will be taught to:12.5 Understand the concept ofsimultaneous linearinequalities in one variableCUTI PERTENGAHAN TAHUNStudents will be able to:i. Represent the common values oftwo simultaneous linearinequalities on a number line.ii. Determine the equivalentinequalities for two given linearinequalties.iii. Solve two simultaneous linearinequalities.Emphasise the meaning ofinequalities such as:i. a < x < bii. a ≤ x ≤ biii. a ≤ x < biv. a < x ≤ bEmphasise that forms suchas:i. a > x < bii. a < x ≥ biii. a < x > bare not accepted.determinecommon valuesimultaneouscombininglinear inequalitynumber lineequivalent13. LEARNING AREA: GRAPH OF FUNCTIONS34
  • 35. WEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY2210/6-14/6Students will be taught to:13.1 Understand and use theconcept of functions.13.2 Draw and use graphs offunctions.• Explore using “function machines”.Students will be able to:i. State the relationship betweentwo variables based on the giveninformation.ii. Identify the dependent andindependent variables in a givenrelationship involving twovariables.iii. Calculate the value of thedependent variables, given thevalue of the independentvariable.i. Construct tables of values forgiven functions.ii. Draw graphs of functions usinggiven scale.iii. Determine from graph the valueof y, given value of x and viceversa.iv. Solve problems involving graphsof functions.Involve functions such as:i. y = 2x + 3ii. p = 3q2+ 4q – 5iii. A = B3iv. W = 1ZLimit to linear, quadraticand cubic functions.Include cases when scalesare not givenfunctionrelationshipvariabledependent variableindependent variableordered pairscoordinate planetable of valuesorigingraphx-coordinatey-coordinatex-axisy-axisscale14. LEARNING AREA: RATIOS, RATES AND PROPORTIONS II35
  • 36. WEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to:13.1 Understand the concept ofrate and performcomputations involvingrates.• Use real-life situations that involverates.Students will be able to:i. Determine the rates involved ingiven situations and identifythe two quantities involved.ii. Calculate the rate given twodifferent quantities.iii. Calculate a certain quantitygiven the rate and the otherquantity.iv. Convert rates from one unit ofmeasurement to another.v. Solve problems involving rates.Emphasise the units in thecalculations.ratequantityunit of measurement14. LEARNING AREA: RATIOS, RATES AND PROPORTIONS II36
  • 37. WEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY2317/6-21/6Students will be taught to:13.2 Understand and use theconcept of speed.• Use examples from everydaysituations.Students will be able to:i. Identify the two quantitiesinvolved in speed.ii. Calculate and interpret speed.iii. Calculate:a) the distance, given thespeed and the timeb) the time, given the speedand the distance.iv. Convert speed from one unit ofmeasurement to another.v. Differentiate between uniformspeed and non-uniform speed.Moral values related totraffic rules should beincorporated.Include the use of graphs.speeddistancetimeuniformnon-uniformdifferentiate14. LEARNING AREA: RATIOS, RATES AND PROPORTIONS II37
  • 38. WEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to:14.3 Understand and use theconcept of average speed.14.4 Understand and use theconcept of acceleration.• Use examples from dailysituations.• Discuss the difference betweenaverage speed and mean speed.Students will be able to:i. Calculate the average speed invarious situations.ii. Calculate:a) the distance, given theaverage speed and thetime.b) the time, given theaverage speed and thedistance.iii. Solve problems involvingspeed and average speed.i. Identify the two quantitiesinvolved in acceleration.ii. Calculate and interpretacceleration.Include cases ofretardation.average speeddistancetimeaccelerationretardation38
  • 39. 15. LEARNING AREA: TRIGONOMETRYWEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY2424/6-28/6Students will be taught to:Understand and usetangent of an acute angel ina right-angled triangle.• Use right-angled triangles with realmeasurements and developthrough activities.• Discuss the ration of the oppositeside to the adjacent side when theangle approaches 90˚.• Explore tangent of a given anglewhen:a) The size of the triangle variesproportionally.b) The size of angle varies.Students will be able to:i. Identify the:a) hypotenuseb) the opposite side and theadjacent side with respectto one of the acute angles.ii. Determine the tangent of anangle.iii. Calculate the tangent of anangle given the lengths ofsides of the triangle.iv. Calculate the lengths of sidesof a triangle given the value oftangent and the length ofanother side.Use only right-angledtriangle.Tangent θ can be written astan θ.Emphasise that tangent is aratio.Limit to opposite andadjacent sides.Include cases that requirethe use of Pythagoras’Theorem.right-angled triangleanglehypotenenuseopposite sideadjacent sideratiotangentvaluelengthsize39
  • 40. 15. LEARNING AREA: TRIGONOMETRYWEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to:Understand and use sine ofan acute angle in a right-angled triangle.Understand and useconsine of an acute angle ina right-angled triangle.• Explore sine of a given anglewhen:a) The size of the trianglevaries proportionally.b) The size of the angle varies.• Explore cosine of a given anglewhen:a) The size of the trianglevaries proportionally.b) The size of the angle varies.Students will be able to:i. Determine the sine of an angle.ii. Calculate the sine of an anglegiven the lengths of sides of thetriangle.iii. Calculate the lengths of sides ofa triangle given the value of sineand the length of another side.i. Determine the cosine of anangle.ii. Calculate the cosine of an anglegiven the lengths of sides of thetriangle.iii. Calculate the lengths of sides ofa triangle given the value ofcosine and the length of anotherside.Sine θ can be written assin θ.Include cases that requirethe use of Pythagoras’Theorem.Cosine θ can be written ascos θ.Include cases that requirethe use of Pythagoras’Theorem.ratioright-angled trianglelengthvaluehypotenuseopposite sidesizeconstantincreaseproportion40
  • 41. 15. LEARNING AREA: TRIGONOMETRYWEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to:15.4 Use the values of tangent,sine and cosine to solveproblems.Students will be able to:i. Calculate the value of othertrigonometric ratios given thevalue of a trigonometric ratio.ii. Convert the measurement ofangles from:a) degrees to degrees andminutes.b) degrees and minutes todegrees.iii. Find the value of:a) tangentb) sinec) cosineof 30˚, 45˚ and 60˚ without usingscientific calculator.iv. Find the value of:a) tangentb) sinec) cosineusing scientific calculator.Include angles expressedin:i. Degreesii. Degrees and minutes.degreeminutetangentsinecosine41
  • 42. 15. LEARNING AREA : TRIGONOMETRYWEEK LEARNING OBJECTIVES SUGGESTED TEACHINGANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:v. Find the angles giventhe values of:a) tangentb) sinec) cosineusing scientificcalculators.vi.Solve problems involvingtrigonometric ratios.angledegreeminutetangentsinecosine251/7-8/7PMR Strategic Revision269/7-11/7PRA PEPERIKSAAN PERCUBAAN PMR27-2815/7-25/7PMR Strategic Revision2929/7-2/87/8-18/8PEPERIKSAAN PERCUBAAN PMRCUTI PERTENGAHAN PENGGAL 230-3219/8-5/9PMR Strategic Revision339/9-13/9PRA PMR34-3517/9-30/9PMR Strategic Revision1/10-8/10 PENILAIAN MENENGAH RENDAH9/10-15/11 PASCA PMR42
  • 43. Prepared by, Checked by, Verified by,…………………………......... ………………………… …………………………………….(PN. AIDA BT MAJID) (PN. WONG NYOOK NGOR) (PN NORLAILA BT ABD. GHANI)KETUA PANITA MATEMATIK GURU KANAN SAINS43