MINISTRY OF EDUCATION MALAYSIAIntegrated Curriculum for Secondary SchoolsCurriculum SpecificationsMATHEMATICSForm 3Curricu...
Integrated Curriculum for Secondary SchoolsCurriculum SpecificationsMATHEMATICSFORM 3Curriculum Development CentreMinistry...
Copyright © 2003 Curriculum Development CentreMinistry of Education MalaysiaPersiaran Duta50604 Kuala LumpurFirst publishe...
iiiCONTENTSPageRUKUNEGARA vNATIONAL PHILOSOPHY OF EDUCATION viiPREFACE ixINTRODUCTION 1LINES AND ANGLES II 10POLYGONS II 1...
vRUKUNEGARADECLARATIONOUR NATION, MALAYSIA, being dedicatedto achieving a greater unity of all her peoples;to maintaining ...
viiNATIONAL PHILOSOPHY OF EDUCATIONEducation in Malaysia is an on-going effort towards developing the potential of individ...
ixof English assisted by ICT will provide greateropportunities for pupils to enhance their knowledge andskills because the...
iiiCONTENTSPageRUKUNEGARA vNATIONAL PHILOSOPHY OF EDUCATION viiPREFACE ixINTRODUCTION 1LINES AND ANGLES II 10POLYGONS II 1...
vRUKUNEGARADECLARATIONOUR NATION, MALAYSIA, being dedicatedto achieving a greater unity of all her peoples;to maintaining ...
viiNATIONAL PHILOSOPHY OF EDUCATIONEducation in Malaysia is an on-going effort towards developing the potential of individ...
ixof English assisted by ICT will provide greateropportunities for pupils to enhance their knowledge andskills because the...
Form310LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form311LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form312LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form313Students will be taught to: Students will be able to:2.2 Understand anduse theknowledge ofexterior andinterior angl...
Form314LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form315LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form316LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form317LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form318LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form319LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form320LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form321LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form322LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form323LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form324LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form325LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form326LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form327LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form328LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form329LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form330LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form331LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form332LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form333LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form334LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form335LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form336LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form337LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form338LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form339LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form340LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form341LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form342LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form343LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form344LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form345LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form346LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form347LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form348LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form349LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form350LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form351LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form352LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form353LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form354LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form355LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form356LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form357LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form358LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form359LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form360LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form361LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will...
Form362CONTRIBUTORSAdvisor Dr. Sharifah Maimunah Syed Zin DirectorCurriculum Development CentreDr. Rohani Abdul Hamid Depu...
Form363WRITERSRusnani Mohd SirinCurriculum Development CentreAbdul Wahab IbrahimCurriculum Development CentreRosita Mat Za...
Form364LAYOUT AND ILLUSTRATIONRosita Mat ZainCurriculum Development CentreMohd Razif HashimCurriculum Development Centre
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Hsp maths f3

  1. 1. MINISTRY OF EDUCATION MALAYSIAIntegrated Curriculum for Secondary SchoolsCurriculum SpecificationsMATHEMATICSForm 3Curriculum Development CentreMinistry of Education Malaysia2003
  2. 2. Integrated Curriculum for Secondary SchoolsCurriculum SpecificationsMATHEMATICSFORM 3Curriculum Development CentreMinistry of Education Malaysia2003
  3. 3. Copyright © 2003 Curriculum Development CentreMinistry of Education MalaysiaPersiaran Duta50604 Kuala LumpurFirst published 2003Copyright reserved. Except for use in a review, the reproductionor utilization of this work in any form or by any electronic,mechanical, or other means, now known or hereafter invented,including photocopying, and recording is forbidden without priorwritten permission from the Director of the CurriculumDevelopment Centre, Ministry of Education Malaysia.
  4. 4. iiiCONTENTSPageRUKUNEGARA vNATIONAL PHILOSOPHY OF EDUCATION viiPREFACE ixINTRODUCTION 1LINES AND ANGLES II 10POLYGONS II 12CIRCLES II 15STATISTICS II 19INDICES 21ALGEBRAIC EXPRESSIONS III 27ALGEBRAIC FORMULAE 32SOLID GEOMETRY III 34SCALE DRAWINGS 40TRANSFORMATIONS II 42LINEAR EQUATIONS II 45LINEAR INEQUALITIES 47GRAPHS OF FUNCTIONS 53RATIO, RATE AND PROPORTION II 55TRIGONOMETRY 58CONTRIBUTORS 62
  5. 5. vRUKUNEGARADECLARATIONOUR NATION, MALAYSIA, being dedicatedto achieving a greater unity of all her peoples;to maintaining a democratic way of life;to creating a just society in which the wealth of the nation shall be equitably shared;to ensuring a liberal approach to her rich and diverse cultural traditions;to building a progressive society which shall be oriented to modern science and technology;WE, her peoples, pledge our united efforts to attain these ends guided by these principles:BELIEF IN GODLOYALTY TO KING AND COUNTRYUPHOLDING THE CONSTITUTIONRULE OF LAWGOOD BEHAVIOUR AND MORALITY
  6. 6. viiNATIONAL PHILOSOPHY OF EDUCATIONEducation in Malaysia is an on-going effort towards developing the potential of individualsin a holistic and integrated manner, so as to produce individuals who are intellectually,spiritually, emotionally and physically balanced and harmonious based on a firm belief inand devotion to God. Such an effort is designed to produce Malaysian citizens who areknowledgeableandcompetent,whopossesshighmoralstandardsandwhoareresponsibleand capable of achieving a high level of personal well being as well as being able tocontribute to the harmony and betterment of the family, society and the nation at large.
  7. 7. ixof English assisted by ICT will provide greateropportunities for pupils to enhance their knowledge andskills because they are able to source the variousrepositories of mathematical knowledge written inEnglish whether in electronic or print forms. Pupils willbe able to communicate mathematically in English notonly in the immediate environment but also with pupilsfrom other countries thus increasing their overallEnglish proficiency and mathematical competence inthe process.The development of this Curriculum Specificationsaccompanying the syllabus is the work of manyindividuals expert in the field. To those who havecontributed in one way or another to this effort, on behalfof the Ministry of Education, I would like to express mydeepest gratitude and appreciation.(Dr. SHARIFAH MAIMUNAH SYED ZIN)DirectorCurriculum Development CentreMinistry of Education MalaysiaPREFACEScience and technology plays a critical role in meetingMalaysia’s aspiration to achieve developed nationstatus. Since mathematics is instrumental indeveloping scientific and technological knowledge, theprovision of quality mathematics education from anearly age in the education process is important.The secondary school Mathematics curriculum asoutlined in the syllabus has been designed to provideopportunities for pupils to acquire mathematicalknowledge and skills and develop the higher orderproblem solving and decision making skills that theycan apply in their everyday lives. But, moreimportantly, together with the other subjects in thesecondary school curriculum, the mathematicscurriculum seeks to inculcate noble values and lovefor the nation towards the final aim of developing thewholistic person who is capable of contributing to theharmony and prosperity of the nation and its people.Beginning in 2003, science and mathematics will betaught in English following a phased implementationschedule which will be completed by 2008.Mathematics education in English makes use of ICTin its delivery. Studying mathematics in the medium
  8. 8. iiiCONTENTSPageRUKUNEGARA vNATIONAL PHILOSOPHY OF EDUCATION viiPREFACE ixINTRODUCTION 1LINES AND ANGLES II 10POLYGONS II 12CIRCLES II 15STATISTICS II 19INDICES 21ALGEBRAIC EXPRESSIONS III 27ALGEBRAIC FORMULAE 32SOLID GEOMETRY III 34SCALE DRAWINGS 40TRANSFORMATIONS II 42LINEAR EQUATIONS II 45LINEAR INEQUALITIES 47GRAPHS OF FUNCTIONS 53RATIO, RATE AND PROPORTION II 55TRIGONOMETRY 58CONTRIBUTORS 62
  9. 9. vRUKUNEGARADECLARATIONOUR NATION, MALAYSIA, being dedicatedto achieving a greater unity of all her peoples;to maintaining a democratic way of life;to creating a just society in which the wealth of the nation shall be equitably shared;to ensuring a liberal approach to her rich and diverse cultural traditions;to building a progressive society which shall be oriented to modern science and technology;WE, her peoples, pledge our united efforts to attain these ends guided by these principles:BELIEF IN GODLOYALTY TO KING AND COUNTRYUPHOLDING THE CONSTITUTIONRULE OF LAWGOOD BEHAVIOUR AND MORALITY
  10. 10. viiNATIONAL PHILOSOPHY OF EDUCATIONEducation in Malaysia is an on-going effort towards developing the potential of individualsin a holistic and integrated manner, so as to produce individuals who are intellectually,spiritually, emotionally and physically balanced and harmonious based on a firm belief inand devotion to God. Such an effort is designed to produce Malaysian citizens who areknowledgeableandcompetent,whopossesshighmoralstandardsandwhoareresponsibleand capable of achieving a high level of personal well being as well as being able tocontribute to the harmony and betterment of the family, society and the nation at large.
  11. 11. ixof English assisted by ICT will provide greateropportunities for pupils to enhance their knowledge andskills because they are able to source the variousrepositories of mathematical knowledge written inEnglish whether in electronic or print forms. Pupils willbe able to communicate mathematically in English notonly in the immediate environment but also with pupilsfrom other countries thus increasing their overallEnglish proficiency and mathematical competence inthe process.The development of this Curriculum Specificationsaccompanying the syllabus is the work of manyindividuals expert in the field. To those who havecontributed in one way or another to this effort, on behalfof the Ministry of Education, I would like to express mydeepest gratitude and appreciation.(Dr. SHARIFAH MAIMUNAH SYED ZIN)DirectorCurriculum Development CentreMinistry of Education MalaysiaPREFACEScience and technology plays a critical role in meetingMalaysia’s aspiration to achieve developed nationstatus. Since mathematics is instrumental indeveloping scientific and technological knowledge, theprovision of quality mathematics education from anearly age in the education process is important.The secondary school Mathematics curriculum asoutlined in the syllabus has been designed to provideopportunities for pupils to acquire mathematicalknowledge and skills and develop the higher orderproblem solving and decision making skills that theycan apply in their everyday lives. But, moreimportantly, together with the other subjects in thesecondary school curriculum, the mathematicscurriculum seeks to inculcate noble values and lovefor the nation towards the final aim of developing thewholistic person who is capable of contributing to theharmony and prosperity of the nation and its people.Beginning in 2003, science and mathematics will betaught in English following a phased implementationschedule which will be completed by 2008.Mathematics education in English makes use of ICTin its delivery. Studying mathematics in the medium
  12. 12. Form310LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:1.1 Understand anduse properties ofangles associatedwith transversaland parallel lines.• Explore the properties of anglesassociated with transversal usingdynamic geometry software,geometry sets, acetate overlaysor tracing paper.• Discuss when alternate andcorresponding angles are notequal.• Discuss when all anglesassociated with transversals areequal and the implication on itsconverse.i. Identify:a) transversalsb) corresponding anglesc) alternate anglesd) interior angles.ii. Determine that for parallellines:a) corresponding anglesare equalb) alternate angles areequalc) sum of interior angles is180°.iii. Find the values of:a) corresponding anglesb) alternate anglesc) interior anglesassociated with parallel lines.The interior angles onthe same side of thetransversal aresupplementary.parallel linestransversalalternate angleinterior angleassociatedcorrespondingangleintersectinglinessupplementaryangleacetate overlayLEARNING AREA:LLIINNEESS AANNDD AANNGGLLEESS IIII1
  13. 13. Form311LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:iv. Determine if two given linesare parallel based on theproperties of anglesassociated with transversals.v. Solve problems involvingproperties of anglesassociated with transversals.Limit to transversalintersecting parallellines.LEARNING AREA:LLIINNEESS AANNDD AANNGGLLEESS IIII1
  14. 14. Form312LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:2.1 Understand theconcepts of regularpolygons.• Use models of polygons andsurroundings to identify regularpolygons.• Explore properties of polygonsusing rulers, compasses,protractors, grid papers, templates,geo-boards, flash cards anddynamic geometry software.• Include examples of non-regularpolygons developed throughactivities such as folding papers inthe shape of polygons.• Relate to applications inarchitecture.i. Determine if a given polygonis a regular polygon.ii. Find:a) the axes of symmetryb) the number of axes ofsymmetryof a polygon.iii. Sketch regular polygons.iv. Draw regular polygons bydividing equally the angle atthe centre.v. Construct equilateraltriangles, squares andregular hexagons.Limit to polygons witha maximum of 10sides.Construct usingstraightedges andcompasses.Emphasise on theaccuracy of drawings.polygonregularpolygonconvexpolygonaxes ofsymmetrystraightedgesangleequilateraltrianglesquareregularhexagonLEARNING AREA:PPOOLLYYGGOONNSS IIII2
  15. 15. Form313Students will be taught to: Students will be able to:2.2 Understand anduse theknowledge ofexterior andinterior angles ofpolygons.• Explore angles of differentpolygons through activities such asdrawing, cutting and pasting,measuring angles and usingdynamic geometry software.• Investigate the number of trianglesformed by dividing a polygon intoseveral triangles by joining onechosen vertex of the polygon to theother vertices.i. Identify the interior angles andexterior angles of a polygon.ii. Find the size of an exteriorangle when the interior angleof a polygon is given and viceversa.iii. Determine the sum of theinterior angles of polygons.iv. Determine the sum of theexterior angles of polygons.interior angleexterior anglecomplementaryanglesumLEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYLEARNING AREA:PPOOLLYYGGOONNSS IIII2
  16. 16. Form314LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:• Include examples from everydaysituations.v. Find:a) the size of an interiorangle of a regularpolygon given thenumber of sides.b) the size of an exteriorangle of a regularpolygon given thenumber of sides.c) the number of sides of aregular polygon given thesize of the interior orexterior angle.vi. Solve problems involvingangles and sides ofpolygons.LEARNING AREA:PPOOLLYYGGOONNSS IIII2
  17. 17. Form315LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:3.1 Understand anduse properties ofcircles involvingsymmetry, chordsand arcs.• Explore through activities such astracing, folding, drawing andmeasuring using compasses,rulers, threads, protractor, filterpapers and dynamic geometrysoftware.i. Identify a diameter of a circleas an axis of symmetry.ii. Determine that:a) a radius that isperpendicular to a chorddivides the chord into twoequal parts and viceversa.b) perpendicular bisectorsof two chords intersect atthe centre.c) two chords that are equalin length are equidistantfrom the centre and viceversa.d) chords of the samelength cut arcs of thesame length.iii. Solve problems involvingsymmetry, chords and arcs ofcircles.diameteraxis ofsymmetrychordperpendicularbisectorintersectequidistantarcsymmetrycentreradiusperpendicularLEARNING AREA:CCIIRRCCLLEESS IIII3
  18. 18. Form316LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:3.2 Understand anduse properties ofangles in circles.• Explore properties of angles in acircle by drawing, cutting andpasting, and using dynamicgeometry software.i. Identify angles subtended byan arc at the centre and atthe circumference of a circle.ii. Determine that anglessubtended at thecircumference by the samearc are equal.iii. Determine that anglessubtended:a) at the circumferenceb) at the centreby arcs of the same lengthare equal.iv. Determine the relationshipbetween angle at the centreand angle at thecircumference subtended byan arc.v. Determine the size of anangle subtended at thecircumference in asemicircle.Include reflex anglessubtended at thecentre.Angle subtended byan arc is the same asangle subtended bythe correspondingchord.anglesubtendedsemicirclecircumferencearcchordreflex anglecentreLEARNING AREA:CCIIRRCCLLEESS IIII3
  19. 19. Form317LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:vi. Solve problems involvingangles subtended at thecentre and angles at thecircumference of circles.3.3 Understand anduse the conceptsof cyclicquadrilaterals.• Explore properties of cyclicquadrilaterals by drawing, cuttingand pasting and using dynamicgeometry software.i. Identify cyclic quadrilaterals.ii. Identify interior oppositeangles of cyclicquadrilaterals.iii. Determine the relationshipbetween interior oppositeangles of cyclicquadrilaterals.iv. Identify exterior angles andthe corresponding interioropposite angles of cyclicquadrilaterals.cyclicquadrilateralinterioroppositeangleexterior angleLEARNING AREA:CCIIRRCCLLEESS IIII3
  20. 20. Form318LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:v. Determine the relationshipbetween exterior angles andthe corresponding interioropposite angles of cyclicquadrilaterals.vi. Solve problems involvingangles of cyclic quadrilaterals.vii. Solve problems involvingcircles.LEARNING AREA:CCIIRRCCLLEESS IIII3
  21. 21. Form319LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:4.1 Represent andinterpret data in piecharts to solveproblems.• Use everyday examples fromsources such as newspapers,magazines, reports and theInternet.• Use calculators and computersoftware in constructing pie charts.i. Obtain and interpretinformation from pie charts.ii. Construct pie charts torepresent data.iii. Solve problems involving piecharts.iv. Determine suitablerepresentation of data.Relate the quantitiesof the data to the sizeof angles of thesectors.A complete pie chartshould include:i) The titleii) Appropriate labelsfor the groups ofdata.Pie charts are mainlysuitable forcategorical data.Include pictograms,bar charts, line graphsand pie charts.Discuss thatrepresentation of datadepends on the typeof data.sectorpie chartanglesuitablerepresentationconstructsize of sectorquantitydatasize of anglelabeltitlepictogramsbar chartpie chartLEARNING AREA:SSTTAATTIISSTTIICCSS IIII4
  22. 22. Form320LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:4.2 Understand anduse the conceptsof mode, medianand mean to solveproblems.• Use sets of data from everydaysituations to evaluate and toforecast.• Discuss appropriatemeasurement in differentsituations.• Use calculators to calculate themean for large sets of data.• Discuss appropriate use of mode,median and mean in certainsituations.i. Determine the mode of:a) sets of data.b) data given in frequencytables.ii. Determine the mode and therespective frequency frompictographs, bar charts, linegraphs and pie charts.iii. Determine the median forsets of data.iv. Determine the median ofdata in frequency tables.v. Calculate the mean of:a) sets of datab) data in frequency tablesvi. Solve problems involvingmode, median and mean.Involve data withmore than one mode.Limit to cases withdiscrete data only.Emphasise that moderefers to the categoryor score and not tothe frequency.Include change in thenumber and value ofdata.datamodediscretefrequencymedianarrangeoddevenmiddlefrequencytablemeanLEARNING AREA:SSTTAATTIISSTTIICCSS IIII4
  23. 23. Form321LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:5.1 Understand theconcepts ofindices.• Explore indices using calculatorsand spreadsheets.i. Express repeatedmultiplication as anand viceversa.ii. Find the value of an.iii. Express numbers in indexnotation.Begin with squaresand cubes.‘a ’ is a real number.Include algebraicterms.Emphasise base andindex.a x a x …a = ann factorsa is the base, n is theindex.Involve fractions anddecimals.Limit n to positiveintegers.indicesbaseindexpower ofindex notationindex formexpressvaluereal numbersrepeatedmultiplicationfactorLEARNING AREA:IINNDDIICCEESS5
  24. 24. Form322LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:5.2 Performcomputationsinvolvingmultiplication ofnumbers in indexnotation.• Explore laws of indices usingrepeated multiplication andcalculators.i. Verify amx an= am+ nii. Simplify multiplication of:a) numbersb) algebraic termsexpressed in index notationwith the same base.iii. Simplify multiplication of:a) numbersb) algebraic termsexpressed in index notationwith different bases.Limit algebraic termsto one unknown.5.3 Performcomputationinvolving divisionof numbers inindex notation.i. Verify am÷ am= am – nii. Simplify division of:a) numbersb) algebraic termsexpressed in index notationwith the same base.Emphasise a0= 1.multiplicationsimplifybasealgebraic termverifyindex notationindiceslaw of indicesunknownLEARNING AREA:IINNDDIICCEESS5
  25. 25. Form323LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:5.4 Performcomputationsinvolving raisingnumbers andalgebraic terms inindex notation toa power.i. Derive (am)n= amn.ii. Simplify:a) numbersb) algebraic termsexpressed in index notationraised to a power.iii. Simplify multiplication anddivision of:a) numbersb) algebraic termsexpressed in index notationwith different bases raised toa power.iv. Perform combinedoperations involvingmultiplication, division, andraised to a power on:a) numbersb) algebraic terms.( am)n= amnm and n are positiveintegers.Limit algebraic termsto one unknown.Emphasise:(amx bn)p= ampx bnppnmba= npmpbaraised to apowerbaseLEARNING AREA:IINNDDIICCEESS5
  26. 26. Form324LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:5.5 Performcomputationsinvolving negativeindices.• Explore using repeatedmultiplications and the law ofindices.i. Verify a- n= n1a.ii. State a- nas n1aand viceversa.iii. Perform combined operationsof multiplication, division andraising to a power involvingnegative indices on:a) numbersb) algebraic terms.n is a positive integer.Begin with n = 1.5.6 Performcomputationsinvolvingfractional indices.i. Verify a n1= na .ii. State a n1as na and viceversa.a and n are positiveintegers.Begin with n = 2.verifyLEARNING AREA:IINNDDIICCEESS5
  27. 27. Form325LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:iii. Find the value of a n1.iv. State a nmas:a) (a m) n1or (a n1) mb)n ma or ( na )mv. Perform combinedoperations of multiplication,division and raising to apower involving fractionalindices on:a) numbersb) algebraic terms.vi. Find the value of nma . Limit to positiveintegral roots.LEARNING AREA:IINNDDIICCEESS5
  28. 28. Form326LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:5.7 Performcomputationinvolving laws ofindices.i. Perform multiplication,division, raised to a power orcombination of theseoperations on severalnumbers expressed in indexnotation.ii. Perform combined operationsof multiplication, division andraised to a power involvingpositive, negative andfractional indices.LEARNING AREA:IINNDDIICCEESS5
  29. 29. Form327LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:6.1 Understand anduse the concept ofexpandingbrackets.• Relate to concrete examples.• Explore using computer software.i. Expand single brackets.ii. Expand two brackets.Begin with linearalgebraic terms.Limit to linearexpressions.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 algebraictermslike termsunlike termsexpansionexpandsingle bracketstwo bracketsmultiplyLEARNING AREA:AALLGGEEBBRRAAIICC EEXXPPRREESSSSIIOONNSS IIIIII6
  30. 30. Form328LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:6.2 Understand anduse the conceptof factorisation ofalgebraicexpressions tosolve problems.• Explore using concrete materialsand computer software.i. State factors of an algebraicterm.ii. State common factors and theHCF for several algebraicterms.iii. Factorise algebraicexpressions:a) using common factorb) the difference of twosquares..Emphasise therelationship betweenexpansion andfactorisation.Note that “1”is a factor for allalgebraic terms.The difference of twosquares means:a2– b2= (a± b)(am b).Limit to four algebraicterms.ab – ac = a(b – c)e2– f 2= (e + f ) (e – f)x2+ 2xy + y2= (x + y)2limit answers to(ax + by)2ab + ac + bd + cd=(b + c)(a + d)factorisationsquarecommon factortermhighestcommon factor(HCF)difference oftwo squaresLEARNING AREA:AALLGGEEBBRRAAIICC EEXXPPRREESSSSIIOONNSS IIIIII6
  31. 31. Form329LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:• Explore using computer software. iv. Factorise and simplifyalgebraic fractions.Begin with one-termexpressions for thenumerator anddenominator.Limit to factorisationinvolving commonfactors and differenceof two squares.numeratordenominatoralgebraicfractionfactorisationLEARNING AREA:AALLGGEEBBRRAAIICC EEXXPPRREESSSSIIOONNSS IIIIII6
  32. 32. Form330LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:6.3 Perform additionand subtraction onalgebraic fractions.• Explore using computer software.• Relate to real-life situations.i. Add or subtract two algebraicfractions with the samedenominator.ii. Add or subtract two algebraicfractions with onedenominator as a multiple ofthe other denominator.iii. Add or subtract two algebraicfractions with denominators:a) without any commonfactorb) with a common factor.The concept of LCMmay be used.Limit denominators toone algebraic term.common factorlowestcommonmultiple (LCM)multipledenominatorLEARNING AREA:AALLGGEEBBRRAAIICC EEXXPPRREESSSSIIOONNSS IIIIII6
  33. 33. Form331LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:6.4 Performmultiplication anddivision onalgebraic fractions.• Explore using computer software. i. Multiply two algebraicfractions involvingdenominator with:a) one termb) two terms.ii. Divide two algebraic fractionsinvolving denominator with:a) one termb) two termsiii. Perform multiplication anddivision of two algebraicfractions using factorisationinvolving common factors andthe different of two squares.Begin multiplicationand division withoutsimplification followedby multiplication anddivision withsimplification.simplificationLEARNING AREA:AALLGGEEBBRRAAIICC EEXXPPRREESSSSIIOONNSS IIIIII6
  34. 34. Form332LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:7.1 Understand theconcepts ofvariables andconstants.• Use examples of everydaysituations to explain variables andconstants.i. Determine if a quantity in agiven situation is a variableor a constant.ii. Determine the variable in agiven situation and representit with a letter symbol.iii. Determine the possiblevalues of a variable in agiven situation.Variables includeintegers, fractions anddecimals.quantityvariableconstantpossible valueformulavalueletter symbolformulaeLEARNING AREA:AALLGGEEBBRRAAIICC FFOORRMMUULLAAEE7
  35. 35. Form333LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:7.2 Understand theconcepts offormulae to solveproblems.i. Write a formula based on agiven:a) statementb) situation.ii. Identify the subject of a givenformula.iii. Express a specified variableas the subject of a formulainvolving:a) one of the basicoperations: +, −, x, ÷b) powers or rootsc) combination of the basicoperations and powers orroots.iv. Find the value of a variablewhen it is:a) the subject of the formulab) not the subject of theformula.v. Solve problems involvingformulae.Symbols representinga quantity in a formulamust be clearlystated.Involve scientificformulae.subject of aformulastatementpowerrootsformulaeLEARNING AREA:AALLGGEEBBRRAAIICC FFOORRMMUULLAAEE7
  36. 36. Form334LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:8.1 Understand anduse the conceptsof volumes ofright prisms andright circularcylinders to solveproblems.• Use concrete models to derivethe formulae.• Relate the volume of right prismsto right circular cylinders.i. Derive the formula forvolume of:a) prismsb) cylinders.ii. Calculate the volume of aright prism in cubic unitsgiven the height and:a) the area of the baseb) dimensions of the base.iii. Calculate the height of aprism given the volume andthe area of the base.iv. Calculate the area of thebase of a prism given thevolume and the height.Prisms and cylindersrefer to right prismsand right circularcylinders respectively.Limit the bases toshapes of trianglesand quadrilaterals.deriveprismcylinderright circularcylindercircularbaseradiusvolumeareacubic unitssquarerectangletriangledimensionheightLEARNING AREA:SSOOLLIIDD GGEEOOMMEETTRRYY IIIIII8
  37. 37. Form335LEARNINGOBJECTIVESSUGGESTED 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 andthe heightof the cylinder.vi. Calculate the height of acylinder, given the volumeand the radius of the base.vii. Calculate the radius of thebase of a cylinder given thevolume and the height.viii. Convert volume in one metricunit to another:a) mm3, cm3and m3b) cm3, ml and l .cubic metrecubiccentimetrecubicmillimetremillilitrelitreconvertmetric unitLEARNING AREA:SSOOLLIIDD GGEEOOMMEETTRRYY IIIIII8
  38. 38. Form336LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:ix. Calculate volume of liquid in acontainer.x. Solve problems involvingvolumes of prisms andcylinders.Limit the shape ofcontainers to rightcircular cylinders andright prisms.liquidcontainerLEARNING AREA:SSOOLLIIDD GGEEOOMMEETTRRYY IIIIII8
  39. 39. Form337LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:8.2 Understand anduse the conceptof volumes ofright pyramidsand right circularcones to solveproblems.• Use concrete models to derivethe formula.• Relate volumes of pyramids toprisms and volumes of cones tocylinders.i. Derive the formula for thevolume of:a) pyramidsb) cones.ii. Calculate the volume ofpyramids in mm3, cm3andm3, given the height and:a) area of the baseb) dimensions of base.iii. Calculate the height of apyramid given the volume andthe dimension of the base.iv. Calculate the area of the baseof a pyramid given the volumeand the height.Include bases ofdifferent types ofpolygons.pyramidconevolumebaseheightdimensionLEARNING AREA:SSOOLLIIDD GGEEOOMMEETTRRYY IIIIII8
  40. 40. Form338LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:v. Calculate the volume of acone in mm3, cm3and m3,given the height and radiusof the base.vi. Calculate the height of acone, given the volume andthe radius of the base.vii. Calculate the radius of thebase of a cone given thevolume and the height.viii. Solve problems involvingvolumes of pyramids andcones.heightdimensionLEARNING AREA:SSOOLLIIDD GGEEOOMMEETTRRYY IIIIII8
  41. 41. Form339LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:8.3 Understand anduse the conceptof volumes ofsphere to solveproblems.i. Calculate the volume of asphere given the radius of thesphere.ii. Calculate the radius of asphere given the volume ofthe sphere.iii. Solve problems involvingvolumes of spheres.Include hemisphere8.4 Apply the conceptof volumes tosolve problemsinvolvingcomposite solids.• Use concrete models to formcomposite solids.• Use examples from real-lifesituations.i. Calculate the volume of acomposite solid.ii. Solve problems involvingvolumes of composite solids.Composite solids arecombinations ofgeometric solids.spherehemispheresolidcompositesolidcombinationvolumeradiusLEARNING AREA:SSOOLLIIDD GGEEOOMMEETTRRYY IIIIII8
  42. 42. Form340LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:9.1 Understand theconcepts of scaledrawings.• Explore scale drawings usingdynamic geometry software, gridpapers, geo-boards or graphpapers.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,where n = 1, 2, 3, 4, 5 ,10121 , .iii. Draw composite shapes,according to a given scaleusing:a) grid papersb) blank papers.Limit objects to two-dimensionalgeometric shapes.Emphasise on theaccuracy of thedrawings.Include grids ofdifferent sizes.sketchdrawobjectsgrid papergeo-boardssoftwarescalegeometricalshapescompositeshapessmallerlargeraccuratesizeLEARNING AREA:SSCCAALLEE DDRRAAWWIINNGGSS IIIIII9
  43. 43. Form341LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:• Relate to maps, graphics andarchitectural drawings.iv. Redraw shapes on grids ofdifferent sizes.v. Solve problems involvingscale drawings.Emphasise that gridsshould be drawn onthe original shapes.redrawLEARNING AREA:SSCCAALLEE DDRRAAWWIINNGGSS IIIIII9
  44. 44. Form342LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:10.1 Understand anduse the conceptsof similarity.• Involve examples from everydaysituations.i. Identify if given shapes aresimilar.ii. Calculate the lengths ofunknown sides of two similarshapes.)Emphasise that for atriangle, if thecorresponding anglesare equal, then thecorresponding sidesare proportional.10.2 Understand anduse the conceptsof enlargement.• Explore the concepts ofenlargement using grid papers,concrete materials, drawings,geo-boards and dynamicgeometry software.• Relate enlargement to similarityof shapes.i. Identify an enlargement.ii. Find the scale factor, giventhe object and its image of anenlargement when:a) scale factor > 0b) scale factor < 0.iii. Determine the centre ofenlargement, given theobject and its image.Emphasise the caseof reduction.Emphasise the casewhenscale factor = ± 1Emphasise that thecentre of enlargementis an invariant point.shapesimilarsideangleproportioncentre ofenlargementtransformationenlargementscale factorobjectimageinvariantreductionsizeorientationsimilarityLEARNING AREA:TTRRAANNSSFFOORRMMAATTIIOONNSS IIII10
  45. 45. Form343LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:iv. Determine the image of anobject given the centre ofenlargement and the scalefactor.v. Determine the properties ofenlargement.vi. Calculate the:a) scale factorb) the lengths of sides of theimagec) the lengths of sides of theobjectof an enlargement.Emphasise themethod ofconstruction.propertiesLEARNING AREA:TTRRAANNSSFFOORRMMAATTIIOONNSS IIII10
  46. 46. Form344LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:• Use grid papers and dynamicgeometry software to explore therelationship between the area ofthe image and its object.vii. Determine the relationshipbetween the area of theimage and its object.viii. Calculate the:a) area of imageb) area of objectc) scale factorof an enlargement.ix. Solve problems involvingenlargement.Include negative scalefactors.areaLEARNING AREA:TTRRAANNSSFFOORRMMAATTIIOONNSS IIII10
  47. 47. Form345LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:11.1 Understand anduse the conceptsof linearequations in twovariables.• Derive linear equations in twovariables relating to real-lifesituations.• Explore using graphic calculators,dynamic geometry software andspreadsheets to solve linearequations and simultaneouslinear equations.i. Determine if an equation is alinear equation in twovariables.ii. Write linear equations in twovariables from giveninformation.iii. Determine the value of avariable given the othervariables.iv. Determine the possiblesolutions for a linear equationin two variables.equationvariablelinear equationvaluepossiblesolutionLEARNING AREA:LLIINNEEAARR EEQQUUAATTIIOONNSS IIII11
  48. 48. Form346LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:11.2 Understand anduse the conceptsof twosimultaneouslinear equationsin two variablesto solveproblems.• Use trial and improvementmethod.• Use examples from real-lifesituations.i. Determine if two givenequations are simultaneouslinear equations.ii. Solve two simultaneouslinear equations in twovariables bya) substitutionb) eliminationiii. Solve problems involving twosimultaneous linearequations in two variables.Include letter symbolsother than x and y torepresent variables.linear equationvariablesimultaneouslinearequationsolutionsubstitutioneliminationLEARNING AREA:LLIINNEEAARR EEQQUUAATTIIOONNSS IIII11
  49. 49. Form347LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:12.1 Understand anduse the conceptsof inequalities.• Use everyday situations to illustratethe symbols and the use of “ > ” ,“ < ” , “ ≥ “ and “ ≤ “.i. Identify the relationship:a) greater thanb) less thanbased on given situations.ii. Write the relationshipbetween two given numbersusing the symbol “>” or “<”.iii. Identify the relationship:a) greater than or equal tob) less than or equal tobased on given situations.Emphasise that a > bis equivalent to b < a.“ > “ read as “greaterthan”.“ < “ read as “lessthan”.“ ≥ “ read as “greaterthan or equal to”.“ ≤ “ read as “ lessthan or equal to”.inequalitygreaterlessgreater thanless thanequal toincludeequivalentsolutionLEARNING AREA:LLIINNEEAARR IINNEEQQUUAALLIITTIIEESS12
  50. 50. Form348LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:12.2 Understand anduse theconcepts oflinearinequalities inone unknown.i. Determine if a givenrelationship is a linearinequality.ii. Determine the possiblesolutions for a given linearinequality in one 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 viceversa.h is a constant, x is aninteger.relationshiplinearunknownnumber lineLEARNING AREA:LLIINNEEAARR IINNEEQQUUAALLIITTIIEESS12
  51. 51. Form349LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:• Involve examples from everydaysituations.iv. Construct linear inequalitiesusing symbols:a) “ > “ or “ < “b) “ ≥ “ or “ ≤ “from given information.12.3 Performcomputationsinvolvingaddition,subtraction,multiplicationand division onlinearinequalities.i. State a new inequality for agiven inequality when anumber is:a) added tob) subtracted fromboth sides of the inequalities.ii. State a new inequality for agiven inequality when bothsides of the inequality are:a) multiplied by a numberb) divided by a number.Emphasise that thecondition of inequalityis unchanged.Emphasise that whenwe multiply or divideboth sides of aninequality by the samenegative number, theinequality is reversed.addadditionsubtractsubtractionmultiplymultiplicationdividedivisionLEARNING AREA:LLIINNEEAARR IINNEEQQUUAALLIITTIIEESS12
  52. 52. Form350LEARNINGOBJECTIVESSUGGESTED 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)kx>kmfrom given information.Information given fromreal-life situations.Include also <, ≥ and≤.relationequivalentaddingsubtractingsimplestcollectisolatesolveLEARNING AREA:LLIINNEEAARR IINNEEQQUUAALLIITTIIEESS12
  53. 53. Form351LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:12.4 Performcomputations tosolve inequalitiesin one variable.• Explore using dynamic geometrysoftware and graphic calculators.i. Solve a linear inequality by:a) adding a numberb) subtracting a numberon both sides of theinequality.ii. Solve a linear inequality bya) multiplying a numberb) dividing a numberon both sides of theinequality.iii. Solve linear inequalities inone variable using acombination of operations.Emphasise that for asolution, the variableis written on the leftside of theinequalities.addsubtractmultiplydivideLEARNING AREA:LLIINNEEAARR IINNEEQQUUAALLIITTIIEESS12
  54. 54. Form352LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:12.5 Understand theconcepts ofsimultaneouslinearinequalities inone variable.i. Represent the commonvalues of two simultaneouslinear inequalities on anumber line.ii. Determine the equivalentinequalities for two givenlinear inequalities.iii. Solve two simultaneous linearinequalities.Emphasise themeaning ofinequalities such as:i. bxa <<ii. bxa ≤≤iii. bxa <≤iv. bxa ≤<Emphasise that formssuch as:i. bxa <>ii. bxa ≥<iii. bxa ><are not accepted.determinecommon valuesimultaneouscombininglinearinequalitynumber lineequivalentLEARNING AREA:LLIINNEEAARR IINNEEQQUUAALLIITTIIEESS12
  55. 55. Form353LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:13.1Understand anduse the conceptsof functions.• Explore using “functionmachines”.i. State the relationship betweentwo variables based on giveninformation.ii. Identify the dependent andindependent variables in agiven relationship involvingtwo variables.iii. Calculate the value of thedependent variable, given thevalue of the independentvariable.Involve functions suchas:i. y = 2x + 3ii. p = 3q2+ 4q – 5iii. A = B3iv. W =Z1functionrelationshipvariabledependentvariableindependentvariableordered pairsLEARNING AREA:GGRRAAPPHHSS OOFF FFUUNNCCTTIIOONNSS13
  56. 56. Form354LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:13.2 Draw and usegraphs offunctions.i. Construct tables of values forgiven functions.ii. Draw graphs of functionsusing given scale.iii. Determine from a graph thevalue of y, given the value ofx and vice versa.iv. Solve problems involvinggraphs of functions.Limit to linear,quadratic and cubicfunctions.Include cases whenscales are not given.coordinateplanetable of valuesorigingraphx-coordinatey-coordinatex-axisy-axisscaleLEARNING AREA:GGRRAAPPHHSS OOFF FFUUNNCCTTIIOONNSS13
  57. 57. Form355LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:14.1 Understand theconcepts of ratesand performcomputationsinvolving rate.• Use real-life situations thatinvolve rate.i. Determine the rate involvedin given situations andidentify the two quantitiesinvolved.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 rate.Emphasise the unitsin the calculation.ratequantityunit ofmeasurementLEARNING AREA:RRAATTIIOO,, RRAATTEE AANNDD PPRROOPPOORRTTIIOONN IIII14
  58. 58. Form356LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:14.2 Understand anduse the conceptof speed.• Use examples from everydaysituations.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 unitof measurement to another.v. Differentiate between uniformspeed and non-uniformspeed.)Moral values relatedto traffic rules shouldbe incorporated.Include the use ofgraphs.speeddistancetimeuniformnon-uniformdifferentiateLEARNING AREA:RRAATTIIOO,, RRAATTEE AANNDD PPRROOPPOORRTTIIOONN IIII14
  59. 59. Form357LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:14.3 Understand anduse the conceptsof average speed.• Use examples from dailysituations.• Discuss the difference betweenaverage speed and mean speed.i. Calculate the average speedin various 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.14.4 Understand anduse the conceptsof acceleration.i. Identify the two quantitiesinvolved in acceleration.ii. Calculate and interpretacceleration.Include cases ofretardation.Retardation is alsoknown deceleration.average speeddistancetimeaccelerationretardationLEARNING AREA:RRAATTIIOO,, RRAATTEE AANNDD PPRROOPPOORRTTIIOONN IIII14
  60. 60. Form358LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:15.1 Understand anduse tangent of anacute angle in aright-angledtriangle.• Use right-angled triangles withreal measurements and developthrough activities.• Discuss the ratio of the oppositeside to the adjacent side whenthe angle approaches 90o.• Explore tangent of a given anglewhen:a) The size of the triangle variesproportionally.b) The size of angle varies.i. Identify the:a) hypotenuseb) the opposite side and theadjacent side with respectto one of the acuteangles.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.Tangentθ can bewritten as tan θ.Emphasise thattangent is a ratio.Limit to opposite andadjacent sides.Include cases thatrequire the use ofPythagoras’ Theorem.right-angledtriangleanglehypotenuseopposite sideadjacent sideratiotangentvaluelengthsizeLEARNING AREA:TTRRIIGGOONNOOMMEETTRRYY15
  61. 61. Form359LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:15.2 Understand anduse sine of anacute angle in aright-angledtriangle.• Explore sine of a given anglewhen:a) The size of the triangle variesproportionally.b) The size of the angle varies.i. Determine the sine of anangle.ii. Calculate the sine of anangle given the lengths ofsides of the triangle.iii. Calculate the lengths of sidesof a triangle given the valueof sine and the length ofanother side.Sineθ can be writtenas sinθ.Include cases thatrequire the use ofPythagoras’ Theorem.15.3 Understand anduse cosine of anacute angle in aright-angledtriangle.• Explore cosine of a given anglewhen:a) The size of the triangle variesproportionally.b) The size of the angle varies.i. Determine the cosine of anangle.ii. Calculate the cosine of anangle given the lengths ofsides of the triangle.iii. Calculate the lengths of sidesof a triangle given the value ofcosine and the length ofanother side.Cosineθ can bewritten as cosθ.Include cases thatrequire the use ofPythagoras’ Theorem.ratioright-angledtrianglelengthvaluehypotenuseopposite sidesizeconstantincreaseproportionLEARNING AREA:TTRRIIGGOONNOOMMEETTRRYY15
  62. 62. Form360LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:15.4 Use the values oftangent, sine andcosine to solveproblems.i. Calculate the values 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 30o, 45oand 60owithoutusing scientific calculator.iv. Find the value of:a) tangentb) sinec) cosineusing scientific calculator.Include anglesexpressed in:i) degreesii) degrees andminutesdegreeminutetangentsinecosineLEARNING AREA:TTRRIIGGOONNOOMMEETTRRYY15
  63. 63. Form361LEARNINGOBJECTIVESSUGGESTED TEACHING ANDLEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARYStudents will be taught to: Students will be able to:. v. Find the angles given thevalues of:a) tangentb) sinec) cosineusing scientific calculators.vi. Solve problems involvingtrigonometric ratios.angledegreeminutetangentsinecosineLEARNING AREA:TTRRIIGGOONNOOMMEETTRRYY15
  64. 64. Form362CONTRIBUTORSAdvisor Dr. Sharifah Maimunah Syed Zin DirectorCurriculum Development CentreDr. Rohani Abdul Hamid Deputy DirectorCurriculum Development CentreEditorial Ahmad Hozi H.A. Rahman Principal Assistant DirectorAdvisors (Science and Mathematics Department)Curriculum Development CentreRusnani Mohd Sirin Assistant Director(Head of Mathematics Unit)Curriculum Development CentreS. Sivagnanachelvi Assistant Director(Head of English Language Unit)Curriculum Development CentreEditor Rosita Mat Zain Assistant DirectorCurriculum Development Centre
  65. 65. Form363WRITERSRusnani Mohd SirinCurriculum Development CentreAbdul Wahab IbrahimCurriculum Development CentreRosita Mat ZainCurriculum Development CentreRohana IsmailCurriculum Development CentreSusilawati EhsanCurriculum Development CentreDr. Pumadevi a/p SivasubramaniamMaktab Perguruan Raja Melewar,Seremban, Negeri SembilanLau Choi FongSMK Hulu KelangHulu Kelang, SelangorProf. Dr. Nor Azlan ZanzaliUniversity Teknologi MalaysiaKrishen a/l GobalSMK Kg. Pasir PutehIpoh, PerakKumaravalu a/l RamasamyMaktab Perguruan Tengku AmpuanAfzan, Kuala LipisRaja Sulaiman Raja HassanSMK Puteri, Kota BharuKelantanNoor Aziah Abdul Rahman SafawiSMK Perempuan PuduKuala LumpurCik Bibi Kismete Kabul KhanSMK Dr. Megat KhasIpoh, PerakKrishnan a/l MunusamyJemaah Nazir SekolahIpoh, PerakMak Sai MooiSMK JenjaromSelangorAzizan Yeop ZaharieMaktab Perguruan Persekutuan PulauPinangAhmad Shubki OthmanSMK Dato’ Abdul Rahman YaakobBota, PerakZaini MahmoodSMK JabiPokok Sena, KedahLee Soon KuanSMK Tanah MerahPendang, KedahAhmad Zamri AzizSMK Wakaf BharuKelantan
  66. 66. Form364LAYOUT AND ILLUSTRATIONRosita Mat ZainCurriculum Development CentreMohd Razif HashimCurriculum Development Centre

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