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Basic EducationDepartment:REPUBLIC OF SOUTH AFRICAbasic educationMATHEMATICSCurriculum and AssessmentPolicy StatementFurth...
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Fet   mathematics   gr 10-12 _ web#1133
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  1. 1. Basic EducationDepartment:REPUBLIC OF SOUTH AFRICAbasic educationMATHEMATICSCurriculum and AssessmentPolicy StatementFurther Education and Training PhaseGrades 10-12National Curriculum Statement (NCS)
  2. 2. CAPSCurriculum and Assessment Policy StatementGRADES 10-12MATHEMATICS
  3. 3. MATHEMATICS GRADES 10-12CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)Department of Basic Education222 Struben StreetPrivate Bag X895Pretoria 0001South AfricaTel: +27 12 357 3000Fax: +27 12 323 0601120 Plein Street Private Bag X9023Cape Town 8000South AfricaTel: +27 21 465 1701Fax: +27 21 461 8110Website: http://www.education.gov.za© 2011 Department of Basic EducationIsbn: 978-1-4315-0573-9Design and Layout by: Ndabase Printing SolutionPrinted by: Government Printing Works
  4. 4. MATHEMATICS GRADES 10-12CAPSAGRICULTURAL MANAGEMENT PRACTICES GRADES 10-12CAPSFOREWORD by thE ministEROur national curriculum is the culmination of our efforts over a period of seventeenyears to transform the curriculum bequeathed to us by apartheid. From the start ofdemocracy we have built our curriculum on the values that inspired our Constitution(Act 108 of 1996). the Preamble to the Constitution states that the aims of theConstitution are to:• heal the divisions of the past and establish a society based on democratic values, social justice and fundamental human rights;• improve the quality of life of all citizens and free the potential of each person;• lay the foundations for a democratic and open society in which government is based on the will of the people and every citizen is equally protected by law; and• build a united and democratic South Africa able to take its rightful place as a sovereign state in the family of nations.Education and the curriculum have an important role to play in realising these aims.in 1997 we introduced outcomes-based education to overcome the curricular divisions of the past, but the experienceof implementation prompted a review in 2000. This led to the first curriculum revision: the Revised National CurriculumStatement Grades R-9 and the National Curriculum Statement Grades 10-12 (2002).Ongoing implementation challenges resulted in another review in 2009 and we revised the Revised NationalCurriculum Statement (2002) to produce this document.From 2012 the two 2002 curricula, for Grades R-9 and Grades 10-12 respectively, are combined in a single documentand will simply be known as the National Curriculum Statement Grades R-12. the National Curriculum Statement forGrades R-12 builds on the previous curriculum but also updates it and aims to provide clearer specification of what is to be taught and learnt on a term-by-term basis.the National Curriculum Statement Grades R-12 accordingly replaces the subject statements, Learning ProgrammeGuidelines and subject Assessment Guidelines with the(a) Curriculum and Assessment Policy statements (CAPs) for all approved subjects listed in this document;(b) National policy pertaining to the programme and promotion requirements of the National Curriculum StatementGrades R-12; and(c) National Protocol for Assessment Grades R-12.MRS ANGIE MOTSHEKGA, MPMINISTER OF BASIC EDUCATION
  5. 5. MATHEMATICS GRADES 10-12CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
  6. 6. MATHEMATICS GRADES 10-121CAPScontentsSection 1: INTRODUCTION TO THE CURRICULUM AND ASSESSMENT POLICY STATEMENTS... 31.1 Background .....................................................................................................................................................31.2 Overview...........................................................................................................................................................31.3 General aims of the South African Curriculum.............................................................................................41.4 Time allocation.................................................................................................................................................6 1.4.1 Foundation Phase....................................................................................................................................6 1.4.2 Intermediate Phase..................................................................................................................................6 1.4.3 Senior Phase...........................................................................................................................................7 1.4.4 Grades 10-12...........................................................................................................................................7SECTION 2: INTRODUCTION TO MATHEMATICS...................................................................................82.1 What is Mathematics?.....................................................................................................................................82.2 Specific Aims....................................................................................................................................................82.3 Specific Skills...................................................................................................................................................82.4 Focus of Content Areas...................................................................................................................................92.5 Weighting of Content Areas............................................................................................................................92.6 Mathematics in the FET.................................................................................................................................10SECTION 3: OVERVIEW OF TOPICS PER TERM AND ANNUAL TEACHING PLANS........................ 113.1 Specification of content to show Progression............................................................................................11 3.1.1 Overview of topics..................................................................................................................................123.2 Content clarification with teaching guidelines............................................................................................16 3.2.1 Allocation of teaching time.....................................................................................................................16 3.2.2 Sequencing and pacing of topics...........................................................................................................18 3.2.3 Topic allocation per term........................................................................................................................21 Grade 10 Term: 1...................................................................................................................................21 Grade 10 Term: 2...................................................................................................................................24 Grade 10 Term: 3...................................................................................................................................26 Grade 10 Term: 4...................................................................................................................................29 Grade 11 Term: 1...................................................................................................................................30 Grade 11 Term: 2...................................................................................................................................32 Grade 11 Term: 3...................................................................................................................................34
  7. 7. MATHEMATICS GRADES 10-122 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS) Grade 11 Term: 4...................................................................................................................................39 Grade 12 Term:1....................................................................................................................................40 Grade 12 Term: 2...................................................................................................................................44 Grade 12 Term: 3...................................................................................................................................48 Grade 12 Term: 4...................................................................................................................................50SECTION 4: ASSESSMENT IN MATHEMATICS.....................................................................................514.1. Introduction....................................................................................................................................................514.2. Informal or Daily Assessment.......................................................................................................................514.3. Formal Assessment.......................................................................................................................................524.4. Programme of Assessment...........................................................................................................................534.5. Recording and reporting...............................................................................................................................554.6. Moderation of Assessment...........................................................................................................................564.7. General............................................................................................................................................................56
  8. 8. MATHEMATICS GRADES 10-123CAPSsECTION 1INTRODUCTION TO THE Curriculum and Assessment Policy StatementS forMATHEMATICS gradeS 10-121.1 BackgroundThe National Curriculum Statement Grades R-12 (NCS) stipulates policy on curriculum and assessment in theschooling sector.To improve implementation, the National Curriculum Statement was amended, with the amendments coming intoeffect in January 2012. A single comprehensive Curriculum and Assessment Policy document was developed foreach subject to replace Subject Statements, Learning Programme Guidelines and Subject Assessment Guidelinesin Grades R-12.1.2 Overview(a) The National Curriculum Statement Grades R-12 (January 2012) represents a policy statement for learningand teaching in South African schools and comprises the following:(i) Curriculum and Assessment Policy Statements for each approved school subject;(ii) The policy document, National policy pertaining to the programme and promotion requirements of theNational Curriculum Statement Grades R-12; and(iii) The policy document, National Protocol for Assessment Grades R-12 (January 2012).(b) The National Curriculum Statement Grades R-12 (January 2012) replaces the two current national curriculastatements, namely the(i) Revised National Curriculum Statement Grades R-9, Government Gazette No. 23406 of 31 May 2002,and(ii) National Curriculum Statement Grades 10-12 Government Gazettes, No. 25545 of 6 October 2003 andNo. 27594 of 17 May 2005.(c) The national curriculum statements contemplated in subparagraphs b(i) and (ii) comprise the following policydocuments which will be incrementally repealed by the National Curriculum Statement Grades R-12 (January2012) during the period 2012-2014:(i) The Learning Area/Subject Statements, Learning Programme Guidelines and Subject AssessmentGuidelines for Grades R-9 and Grades 10-12;(ii) The policy document, National Policy on assessment and qualifications for schools in the GeneralEducation and Training Band, promulgated in Government Notice No. 124 in Government Gazette No.29626 of 12 February 2007;(iii) The policy document, the National Senior Certificate: A qualification at Level 4 on the NationalQualifications Framework (NQF), promulgated in Government Gazette No.27819 of 20 July 2005;
  9. 9. MATHEMATICS GRADES 10-124 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)(iv) The policy document, An addendum to the policy document, the National Senior Certificate: Aqualification at Level 4 on the National Qualifications Framework (NQF), regarding learners with specialneeds, published in Government Gazette, No.29466 of 11 December 2006, is incorporated in the policydocument, National policy pertaining to the programme and promotion requirements of the NationalCurriculum Statement Grades R-12; and(v) The policy document, An addendum to the policy document, the National Senior Certificate: Aqualification at Level 4 on the National Qualifications Framework (NQF), regarding the National Protocolfor Assessment (Grades R-12), promulgated in Government Notice No.1267 in Government GazetteNo. 29467 of 11 December 2006.(d) The policy document, National policy pertaining to the programme and promotion requirements of theNational Curriculum Statement Grades R-12, and the sections on the Curriculum and Assessment Policy ascontemplated in Chapters 2, 3 and 4 of this document constitute the norms and standards of the NationalCurriculum Statement Grades R-12. It will therefore, in terms of section 6A of the South African Schools Act,1996 (Act No. 84 of 1996,) form the basis for the Minister of Basic Education to determine minimum outcomesand standards, as well as the processes and procedures for the assessment of learner achievement to beapplicable to public and independent schools.1.3 General aims of the South African Curriculum(a) The National Curriculum Statement Grades R-12 gives expression to the knowledge, skills and values worthlearning in South African schools. This curriculum aims to ensure that children acquire and apply knowledgeand skills in ways that are meaningful to their own lives. In this regard, the curriculum promotes knowledge inlocal contexts, while being sensitive to global imperatives.(b) The National Curriculum Statement Grades R-12 serves the purposes of:• equipping learners, irrespective of their socio-economic background, race, gender, physical ability orintellectual ability, with the knowledge, skills and values necessary for self-fulfilment, and meaningfulparticipation in society as citizens of a free country;• providing access to higher education;• facilitating the transition of learners from education institutions to the workplace; and• providing employers with a sufficient profile of a learner’s competences.(c) The National Curriculum Statement Grades R-12 is based on the following principles:• Social transformation: ensuring that the educational imbalances of the past are redressed, and that equaleducational opportunities are provided for all sections of the population;• Active and critical learning: encouraging an active and critical approach to learning, rather than rote anduncritical learning of given truths;• High knowledge and high skills: the minimum standards of knowledge and skills to be achieved at eachgrade are specified and set high, achievable standards in all subjects;• Progression: content and context of each grade shows progression from simple to complex;
  10. 10. MATHEMATICS GRADES 10-125CAPS• Human rights, inclusivity, environmental and social justice: infusing the principles and practices of social andenvironmental justice and human rights as defined in the Constitution of the Republic of South Africa. TheNational Curriculum Statement Grades R-12 is sensitive to issues of diversity such as poverty, inequality,race, gender, language, age, disability and other factors;• Valuing indigenous knowledge systems: acknowledging the rich history and heritage of this country asimportant contributors to nurturing the values contained in the Constitution; and• Credibility, quality and efficiency: providing an education that is comparable in quality, breadth and depth tothose of other countries.(d) The National Curriculum Statement Grades R-12 aims to produce learners that are able to:• identify and solve problems and make decisions using critical and creative thinking;• work effectively as individuals and with others as members of a team;• organise and manage themselves and their activities responsibly and effectively;• collect, analyse, organise and critically evaluate information;• communicate effectively using visual, symbolic and/or language skills in various modes;• use science and technology effectively and critically showing responsibility towards the environment andthe health of others; and• demonstrate an understanding of the world as a set of related systems by recognising that problem solvingcontexts do not exist in isolation.(e) Inclusivity should become a central part of the organisation, planning and teaching at each school. This canonly happen if all teachers have a sound understanding of how to recognise and address barriers to learning,and how to plan for diversity. The key to managing inclusivity is ensuring that barriers are identified and addressed by all the relevant supportstructures within the school community, including teachers, District-Based Support Teams, Institutional-LevelSupport Teams, parents and Special Schools as Resource Centres. To address barriers in the classroom,teachers should use various curriculum differentiation strategies such as those included in the Department ofBasic Education’s Guidelines for Inclusive Teaching and Learning (2010).
  11. 11. MATHEMATICS GRADES 10-126 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)1.4 Time Allocation1.4.1 Foundation Phase(a) The instructional time in the Foundation Phase is as follows:SUBJECTGRADE R(HOURS)GRADES 1-2(HOURS)GRADE 3(HOURS)Home Language 10 8/7 8/7First Additional Language 2/3 3/4Mathematics 7 7 7Life Skills• Beginning Knowledge• Creative Arts• Physical Education• Personal and Social Well-being6(1)(2)(2)(1)6(1)(2)(2)(1)7(2)(2)(2)(1)TOTAL 23 23 25(b) Instructional time for Grades R, 1 and 2 is 23 hours and for Grade 3 is 25 hours.(c) Ten hours are allocated for languages in Grades R-2 and 11 hours in Grade 3. A maximum of 8 hours and aminimum of 7 hours are allocated for Home Language and a minimum of 2 hours and a maximum of 3 hours forAdditional Language in Grades 1-2. In Grade 3 a maximum of 8 hours and a minimum of 7 hours are allocatedfor Home Language and a minimum of 3 hours and a maximum of 4 hours for First Additional Language.(d) In Life Skills Beginning Knowledge is allocated 1 hour in Grades R-2 and 2 hours as indicated by the hours inbrackets for Grade 3.1.4.2 Intermediate Phase(a) The instructional time in the Intermediate Phase is as follows:SUBJECT HOURSHome Language 6First Additional Language 5Mathematics 6Natural Sciences and Technology 3,5Social Sciences 3Life Skills• Creative Arts• Physical Education• Personal and Social Well-being4(1,5)(1)(1,5)TOTAL 27,5
  12. 12. MATHEMATICS GRADES 10-127CAPS1.4.3 Senior Phase(a) The instructional time in the Senior Phase is as follows:SUBJECT HOURSHome Language 5First Additional Language 4Mathematics 4,5Natural Sciences 3Social Sciences 3Technology 2Economic Management Sciences 2Life Orientation 2Creative Arts 2TOTAL 27,51.4.4 Grades 10-12(a) The instructional time in Grades 10-12 is as follows:Subject Time allocation per week (hours)Home Language 4.5First Additional Language 4.5Mathematics 4.5Life Orientation 2A minimum of any three subjects selected from Group BAnnexure B, Tables B1-B8 of the policy document, National policypertaining to the programme and promotion requirements ofthe National Curriculum Statement Grades R-12, subject to theprovisos stipulated in paragraph 28 of the said policy document.12 (3x4h)TOTAL 27,5 The allocated time per week may be utilised only for the minimum required NCS subjects as specified above,and may not be used for any additional subjects added to the list of minimum subjects. Should a learner wishto offer additional subjects, additional time must be allocated for the offering of these subjects
  13. 13. MATHEMATICS GRADES 10-128 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)sECTION 2IntroductionIn Chapter 2, the Further Education and Training (FET) Phase Mathematics CAPS provides teachers with a definitionof mathematics, specific aims, specific skills, focus of content areas and the weighting of content areas.2.1 What is Mathematics?Mathematics is a language that makes use of symbols and notations for describing numerical, geometric andgraphical relationships. It is a human activity that involves observing, representing and investigating patterns andqualitative relationships in physical and social phenomena and between mathematical objects themselves. It helps todevelop mental processes that enhance logical and critical thinking, accuracy and problem solving that will contributein decision-making.Mathematical problem solving enables us to understand the world (physical, social and economic)around us, and, most of all, to teach us to think creatively.2.2 Specific Aims1. To develop fluency in computation skills without relying on the usage of calculators.2. Mathematical modeling is an important focal point of the curriculum. Real life problems should be incorporatedintoallsectionswheneverappropriate.Examplesusedshouldberealisticandnotcontrived.Contextualproblemsshould include issues relating to health, social, economic, cultural, scientific, political and environmental issueswhenever possible.3. To provide the opportunity to develop in learners the ability to be methodical, to generalize, make conjecturesand try to justify or prove them.4. To be able to understand and work with number system.5. To show Mathematics as a human creation by including the history of Mathematics.6. To promote accessibility of Mathematical content to all learners. It could be achieved by catering for learnerswith different needs.7. To develop problem-solving and cognitive skills. Teaching should not be limited to “how”but should ratherfeature the “when” and “why” of problem types. Learning procedures and proofs without a good understandingof why they are important will leave learners ill-equipped to use their knowledge in later life.8. To prepare the learners for further education and training as well as the world of work.2.3 Specific SkillsTo develop essential mathematical skills the learner should:• develop the correct use of the language of Mathematics;• collect, analyse and organise quantitative data to evaluate and critique conclusions;
  14. 14. MATHEMATICS GRADES 10-129CAPS• use mathematical process skills to identify, investigate and solve problems creatively and critically;• use spatial skills and properties of shapes and objects to identify, pose and solve problems creatively andcritically;• participate as responsible citizens in the life of local, national and global communities; and• communicate appropriately by using descriptions in words, graphs, symbols, tables and diagrams.2.4 Focus of Content AreasMathematics in the FET Phase covers ten main content areas. Each content area contributes towards the acquisitionof the specific skills. The table below shows the main topics in the FET Phase.The Main Topics in the FET Mathematics Curriculum1. Functions2. Number Patterns, Sequences, Series3. Finance, growth and decay4. Algebra5. Differential Calculus6. Probability7. Euclidean Geometry and Measurement8. Analytical Geometry9. Trigonometry10. Statistics2.5 Weighting of Content AreasThe weighting of mathematics content areas serves two primary purposes: firstly the weighting gives guidance onthe amount of time needed to address adequately the content within each content area; secondly the weighting givesguidance on the spread of content in the examination (especially end of the year summative assessment).
  15. 15. MATHEMATICS GRADES 10-1210 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)Weighting of Content AreasDescription Grade 10 Grade 11 Grade. 12PAPER 1 (Grades 12:bookwork: maximum 6 marks)Algebra and Equations (and inequalities) 30 ± 3 45 ± 3 25 ± 3Patterns and Sequences 15 ± 3 25 ± 3 25 ± 3Finance and Growth 10 ± 3Finance, growth and decay 15 ± 3 15 ± 3Functions and Graphs 30 ± 3 45 ± 3 35 ± 3Differential Calculus 35 ± 3Probability 15 ± 3 20 ± 3 15 ± 3TOTAL 100 150 150PAPER 2: Grades 11 and 12: theorems and/or trigonometric proofs: maximum 12 marksDescription Grade 10 Grade 11 Grade 12Statistics 15 ± 3 20 ± 3 20 ± 3Analytical Geometry 15 ± 3 30 ± 3 40 ± 3Trigonometry 40 ± 3 50 ± 3 40 ± 3Euclidean Geometry and Measurement 30 ± 3 50 ± 3 50 ± 3TOTAL 100 150 1502.6 Mathematics in the FETThe subject Mathematics in the Further Education and Training Phase forges the link between the Senior Phaseand the Higher/Tertiary Education band. All learners passing through this phase acquire a functioning knowledgeof the Mathematics that empowers them to make sense of society. It ensures access to an extended study of themathematical sciences and a variety of career paths.In the FET Phase, learners should be exposed to mathematical experiences that give them many opportunities todevelop their mathematical reasoning and creative skills in preparation for more abstract mathematics in Higher/Tertiary Education institutions.
  16. 16. MATHEMATICS GRADES 10-1211CAPSsECTION 3IntroductionChapter 3 provides teachers with:• specification of content to show progression;• clarification of content with teaching guidelines; and• allocation of time.3.1 Specification of Content to show ProgressionThe specification of content shows progression in terms of concepts and skills from Grade 10 to 12 for each contentarea. However, in certain topics the concepts and skills are similar in two or three successive grades. The clarificationof content gives guidelines on how progression should be addressed in these cases. The specification of contentshould therefore be read in conjunction with the clarification of content.
  17. 17. MATHEMATICS GRADES 10-1212 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)3.1.1 Overviewoftopics1.FUNCTIONSGrade10Grade11Grade12Workwithrelationshipsbetweenvariablesintermsofnumerical,graphical,verbalandsymbolicrepresentationsoffunctionsandconvertflexiblybetweentheserepresentations(tables,graphs,wordsandformulae).Includelinearandsomequadraticpolynomialfunctions,exponentialfunctions,somerationalfunctionsandtrigonometricfunctions.ExtendGrade10workontherelationshipsbetweenvariablesintermsofnumerical,graphical,verbalandsymbolicrepresentationsoffunctionsandconvertflexiblybetweentheserepresentations(tables,graphs,wordsandformulae).Includelinearandquadraticpolynomialfunctions,exponentialfunctions,somerationalfunctionsandtrigonometricfunctions.IntroduceamoreformaldefinitionofafunctionandextendGrade11workontherelationshipsbetweenvariablesintermsofnumerical,graphical,verbalandsymbolicrepresentationsoffunctionsandconvertflexiblybetweentheserepresentations(tables,graphs,wordsandformulae).Includelinear,quadraticandsomecubicpolynomialfunctions,exponentialandlogarithmicfunctions,andsomerationalfunctions.Generateasmanygraphsasnecessary,initiallybymeansofpoint-by-pointplotting,supportedbyavailabletechnology,tomakeandtestconjecturesandhencegeneralisetheeffectoftheparameterwhichresultsinaverticalshiftandthatwhichresultsinaverticalstretchand/orareflectionaboutthexaxis.Generateasmanygraphsasnecessary,initiallybymeansofpoint-by-pointplotting,supportedbyavailabletechnology,tomakeandtestconjecturesandhencegeneralisetheeffectsoftheparameterwhichresultsinahorizontalshiftandthatwhichresultsinahorizontalstretchand/orreflectionabouttheyaxis.Theinversesofprescribedfunctionsandbeawareofthefactthat,inthecaseofmany-to-onefunctions,thedomainhastoberestrictediftheinverseistobeafunction.Problemsolvingandgraphworkinvolvingtheprescribedfunctions.Problemsolvingandgraphworkinvolvingtheprescribedfunctions.Averagegradientbetweentwopoints.Problemsolvingandgraphworkinvolvingtheprescribedfunctions(includingthelogarithmicfunction).2.NUMBERPATTERNS,SEQUENCESANDSERIESInvestigatenumberpatternsleadingtothosewherethereisconstantdifferencebetweenconsecutiveterms,andthegeneraltermisthereforelinear.Investigatenumberpatternsleadingtothosewherethereisaconstantseconddifferencebetweenconsecutiveterms,andthegeneraltermisthereforequadratic.Identifyandsolveproblemsinvolvingnumberpatternsthatleadtoarithmeticandgeometricsequencesandseries,includinginfinitegeometricseries.3.FINANCE,GROWTHANDDECAYUsesimpleandcompoundgrowthformulaeandA=P(1+i)ntosolveproblems(includinginterest,hirepurchase,inflation,populationgrowthandotherreallifeproblems).UsesimpleandcompounddecayformulaeA=P(1+in)andA=P(1-i)ntosolveproblems(includingstraightlinedepreciationanddepreciationonareducingbalance).Linktoworkonfunctions.(a)Calculatethevalueofnintheformulae A=P(1+i)nandA=P(1-i)n(b) Applyknowledgeofgeometricseriestosolveannuityandbondrepaymentproblems.Theimplicationsoffluctuatingforeignexchangerates.Theeffectofdifferentperiodsofcompoundinggrowthanddecay(includingeffectiveandnominalinterestrates).Criticallyanalysedifferentloanoptions.
  18. 18. MATHEMATICS GRADES 10-1213CAPS4.ALGEBRA(a) Understandthatrealnumberscanbeirrationalorrational.Takenotethatthereexistnumbersotherthanthoseontherealnumberline,theso-callednon-realnumbers.Itispossibletosquarecertainnon-realnumbersandobtainnegativerealnumbersasanswers.Natureofroots.(a) Simplifyexpressionsusingthelawsofexponentsforrationalexponents.(b) Establishbetweenwhichtwointegersagivensimplesurdlies.(c)Roundrealnumberstoanappropriatedegreeofaccuracy(toagivennumberofdecimaldigits).(a)Applythelawsofexponentstoexpressionsinvolvingrationalexponents.(b)Add,subtract,multiplyanddividesimplesurds.Demonstrateanunderstandingofthedefinitionofalogarithmandanylawsneededtosolvereallifeproblems.Manipulatealgebraicexpressionsby:• multiplyingabinomialbyatrinomial;• factorisingtrinomials;• factorisingthedifferenceandsumsoftwocubes;• factorisingbygroupinginpairs;and• simplifying,addingandsubtractingalgebraicfractionswithdenominatorsofcubes(limitedtosumanddifferenceofcubes).Revisefactorisation.• Takenoteandunderstand,theRemainderandFactorTheoremsforpolynomialsuptothethirddegree.• Factorisethird-degreepolynomials(includingexampleswhichrequiretheFactorTheorem).Solve:• linearequations;• quadraticequations;• literalequations(changingthesubjectofaformula);• exponentialequations;• linearinequalities;• systemoflinearequations;and• wordproblems.Solve:• quadraticequations;• quadraticinequalitiesinonevariableandinterpretthesolutiongraphically;and• equationsintwounknowns,oneofwhichislineartheotherquadratic,algebraicallyorgraphically.
  19. 19. MATHEMATICS GRADES 10-1214 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)5.DIFFERENTIALCALCULUS(a) Anintuitiveunderstandingoftheconceptofalimit.(b) Differentiationofspecifiedfunctionsfromfirstprinciples.(c) Useofthespecifiedrulesofdifferentiation.(d) Theequationsoftangentstographs.(e) Theabilitytosketchgraphsofcubicfunctions.(f) Practicalproblemsinvolvingoptimizationandratesofchange(includingthecalculusofmotion).6.PROBABILITY(a)Comparetherelativefrequencyofanexperimentaloutcomewiththetheoreticalprobabilityoftheoutcome.(b) Venndiagramsasanaidtosolvingprobabilityproblems.(c)Mutuallyexclusiveeventsandcomplementaryevents.(d) TheidentityforanytwoeventsAandB:P(AorB)=P(A)+(B)-P(AandB)(a)Dependentandindependentevents.(b)Venndiagramsorcontingencytablesandtreediagramsasaidstosolvingprobabilityproblems(whereeventsarenotnecessarilyindependent).(a)Generalisationofthefundamentalcountingprinciple.(b)Probabilityproblemsusingthefundamentalcountingprinciple.7.EuclideanGeometryandMeasurement(a)Revisebasicresultsestablishedinearliergrades.(b)Investigatelinesegmentsjoiningthemid-pointsoftwosidesofatriangle.(c)Propertiesofspecialquadrilaterals.(a)Investigateandprovetheoremsofthegeometryofcirclesassumingresultsfromearliergrades,togetherwithoneotherresultconcerningtangentsandradiiofcircles.(b)Solvecirclegeometryproblems,providingreasonsforstatementswhenrequired.(c)Proveriders.(a)Reviseearlier(Grade9)workonthenecessaryandsufficientconditionsforpolygonstobesimilar.(b)Prove(acceptingresultsestablishedinearliergrades):• thatalinedrawnparalleltoonesideofatriangledividestheothertwosidesproportionally(andtheMid-pointTheoremasaspecialcaseofthistheorem);• thatequiangulartrianglesaresimilar;• thattriangleswithsidesinproportionaresimilar;• thePythagoreanTheorembysimilartriangles;and• riders.
  20. 20. MATHEMATICS GRADES 10-1215CAPSSolveproblemsinvolvingvolumeandsurfaceareaofsolidsstudiedinearliergradesaswellasspheres,pyramidsandconesandcombinationsofthoseobjects.ReviseGrade10work.8.TRIGONOMETRY(a)Definitionsofthetrigonometricratiossinθ,cosθandtanθinaright-angledtriangles.(b)Extendthedefinitionsofsinθ,cosθandtanθto0o≤θ≤360o.(c) Deriveandusevaluesofthetrigonometricratios(withoutusingacalculatorforthespecialanglesθ∈{0o;30o;45o;60o;90o}(d)Definethereciprocalsoftrigonometricratios.(a) Deriveandusetheidentities:sinθcosθtanθ=andsin2θ+sin2θ=1.(b)Derivethereductionformulae.(c)Determinethegeneralsolutionand/orspecificsolutionsoftrigonometricequations.(d)Establishthesine,cosineandarearules.ProofanduseofthecompoundangleanddoubleangleidentitiesSoSolveproblemsintwodimensions.Solveproblemsin2-dimensions.Solveproblemsintwoandthreedimensions.9.ANALYTICALGEOMETRYRepresentgeometricfiguresinaCartesianco-ordinatesystem,andderiveandapply,foranytwopoints(x1;y1)and(x2;y2),aformulaforcalculating:• thedistancebetweenthetwopoints;• thegradientofthelinesegmentjoiningthepoints;• conditionsforparallelandperpendicularlines;and• theco-ordinatesofthemid-pointofthelinesegmentjoiningthepoints.UseaCartesianco-ordinatesystemtoderiveandapply:• theequationofalinethroughtwogivenpoints;• theequationofalinethroughonepointandparallelorperpendiculartoagivenline;and• theinclinationofaline.Useatwo-dimensionalCartesianco-ordinatesystemtoderiveandapply:• theequationofacircle(anycentre);and• theequationofatangenttoacircleatagivenpointonthecircle.10.STATISTICS(a) Collect,organiseandinterpretunivariatenumericaldatainordertodetermine:• measuresofcentraltendency;• fivenumbersummary;• boxandwhiskerdiagrams;and• measuresofdispersion.(a) Representmeasuresofcentraltendencyanddispersioninunivariatenumericaldataby:• usingogives;and• calculatingthevarianceandstandarddeviationofsetsofdatamanually(forsmallsetsofdata)andusingcalculators(forlargersetsofdata)andrepresentingresultsgraphically.(b)RepresentSkeweddatainboxandwhiskerdiagrams,andfrequencypolygons.Identifyoutliers.(a)Representbivariatenumericaldataasascatterplotandsuggestintuitivelyandbysimpleinvestigationwhetheralinear,quadraticorexponentialfunctionwouldbestfitthedata.(b)Useacalculatortocalculatethelinearregressionlinewhichbestfitsagivensetofbivariatenumericaldata.(c)Useacalculatortocalculatethecorrelationco-efficientofasetofbivariatenumericaldataandmakerelevantdeductions.
  21. 21. MATHEMATICS GRADES 10-1216 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)3.2 Content Clarification with teaching guidelinesIn Chapter 3, content clarification includes:• teaching guidelines;• sequencing of topics per term; and• pacing of topics over the year.• Each content area has been broken down into topics. The sequencing of topics within terms gives an idea ofhow content areas can be spread and re-visited throughout the year.• The examples discussed in the Clarification Column in the annual teaching plan which follows are by nomeans a complete representation of all the material to be covered in the curriculum. They only serve as anindication of some questions on the topic at different cognitive levels. Text books and other resources shouldbe consulted for a complete treatment of all the material.• The order of topics is not prescriptive, but ensure that part of trigonometry is taught in the first term and morethan six topics are covered / taught in the first two terms so that assessment is balanced between paper 1 and 2.
  22. 22. MATHEMATICS GRADES 10-1217CAPS3.2.1 Allocation of Teaching TimeTime allocation for Mathematics: 4 hours and 30 minutes, e.g. six forty five-minutes periods, per week in grades 10,11 and 12.Terms Grade 10 Grade 11 Grade 12No. ofweeksNo. ofweeksNo. ofweeksTerm 1Algebraic expressionsExponentsNumber patternsEquations andinequalitiesTrigonometry32123Exponents and surdsEquations andinequalitiesNumber patternsAnalytical Geometry3323Patterns, sequences andseriesFunctions and inversefunctionsExponential andlogarithmic functionsFinance, growth anddecayTrigonometry - compoundangles33122Term 2FunctionsTrigonometric functionsEuclidean GeometryMID-YEAR EXAMS4133FunctionsTrigonometry (reductionformulae, graphs,equations)MID-YEAR EXAMS443Trigonometry 2D and 3DPolynomial functionsDifferential calculusAnalytical GeometryMID-YEAR EXAMS21323Term 3Analytical GeometryFinance and growthStatisticsTrigonometryEuclidean GeometryMeasurement222211MeasurementEuclidean GeometryTrigonometry (sine,area,cosine rules)ProbabilityFinance, growth anddecay13222GeometryStatistics (regression andcorrelation)Counting and ProbabilityRevisionTRIAL EXAMS22213Term 4 ProbabilityRevisionEXAMS243StatisticsRevisionEXAMS333RevisionEXAMS36The detail which follows includes examples and numerical references to the Overview.
  23. 23. MATHEMATICS GRADES 10-1218 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)3.2.2 SequencingandPacingofTopicsMATHEMATICS:GRADE10PACESETTER1TERM1WeeksWEEK1WEEK2WEEK3WEEK4WEEK5WEEK6WEEK7WEEK8WEEK9WEEK10WEEK11TopicsAlgebraicexpressionsExponentsNumberpatternsEquationsandinequalitiesTrigonometryAssessmentInvestigationorprojectTestDatecompleted2TERM2WeeksWEEK1WEEK2WEEK3WEEK4WEEK5WEEK6WEEK7WEEK8WEEK9WEEK10WEEK11TopicsFunctionsTrigonometricfunctionsEuclideanGeometryAssessmentAssignment/TestMID-YEAREXAMINATIONDatecompleted3TERM3WeeksWEEK1WEEK2WEEK3WEEK4WEEK5WEEK6WEEK7WEEK8WEEK9WEEK10TopicsAnalyticalGeometryFinanceandgrowthStatisticsTrigonometryEuclideanGeometryMeasurementAssessmentTestTestDatecompleted4TERM4Paper1:2hoursPaper2:2hoursWeeksWEEK1WEEK2WEEK3WEEK4WEEK5WEEK6WEEK7WEEK8WEEK9WEEK10Algebraicexpressionsandequations(andinequalities)exponentsNumberPatternsFunctionsandgraphsFinanceandgrowthProbability3010301515EuclideangeometryandmeasurementAnalyticalgeometryTrigonometryStatistics20155015TopicsProbabilityRevisionAdminAssessmentTestExaminationsDatecompletedTotalmarks100Totalmarks100
  24. 24. MATHEMATICS GRADES 10-1219CAPSMATHEMATICS:GRADE11PACESETTER1TERM1WeeksWEEK1WEEK2WEEK3WEEK4WEEK5WEEK6WEEK7WEEK8WEEK9WEEK10WEEK11TopicsExponentsandsurdsEquationsandinequalitiesNumberpatternsAnalyticalGeometryAssessmentInvestigationorprojectTestDatecompleted2TERM2WeeksWEEK1WEEK2WEEK3WEEK4WEEK5WEEK6WEEK7WEEK8WEEK9WEEK10WEEK11TopicsFunctionsTrigonometry(reductionformulae,graphs,equations)AssessmentAssignment/TestMID-YEAREXAMINATIONDatecompleted3TERM3WeeksWEEK1WEEK2WEEK3WEEK4WEEK5WEEK6WEEK7WEEK8WEEK9WEEK10TopicsMeasurementEuclideanGeometryTrigonometry(sine,cosineandarearules)Finance,growthanddecayProbabilityAssessmentTestTestDatecompleted4TERM4Paper1:3hoursPaper2:3hoursWeeksWEEK1WEEK2WEEK3WEEK4WEEK5WEEK6WEEK7WEEK8WEEK9WEEK10Algebraicexpressionsandequations(andinequalities)NumberpatternsFunctionsandgraphsFinance,growthanddecayProbability4525451520EuclideanGeometryandmeasurementAnalyticalgeometryTrigonometryStatistics40306020TopicsStatisticsRevisionFINALEXAMINATIONAdminAssessmentTestDatecompletedTotalmarks150Totalmarks150
  25. 25. MATHEMATICS GRADES 10-1220 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)MATHEMATICS:GRADE12PACESETTER1TERM1WeeksWEEK1WEEK2WEEK3WEEK4WEEK5WEEK6WEEK7WEEK8WEEK9WEEK10WEEK11TopicsNumberpatterns,sequencesandseriesFunctions:Formaldefinition;inversesFunctions:exponentialandlogarithmicFinance,growthanddecayTrigonometryAssessmentTestInvestigationorprojectAssignmentDatecompleted2TERM2WeeksWEEK1WEEK2WEEK3WEEK4WEEK5WEEK6WEEK7WEEK8WEEK9WEEK10WEEK11TopicsTrigonometryFunctions:polynomialsDifferentialCalculusAnalyticalGeometryAssessmentTestMID-YEAREXAMINATIONDatecompleted3TERM3WeeksWEEK1WEEK2WEEK3WEEK4WEEK5WEEK6WEEK7WEEK8WEEK9WEEK10TopicsGeometryStatisticsCountingandProbabilityRevisionTRIALEXAMINATIONAssessmentTestDatecompleted4TERM4Paper1:3hoursPaper2:3hoursWeeksWEEK1WEEK2WEEK3WEEK4WEEK5WEEK6WEEK7WEEK8WEEK9WEEK10Algebraicexpressionsandequations(andinequalities)NumberpatternsFunctionsandgraphsFinance,growthanddecayDifferentialCalculusCountingandprobability252535153515EuclideanGeometryandmeasurementAnalyticalGeometryTrigonometryStatistics50404020TopicsRevisionFINALEXAMINATIONAdminAssessmentDatecompletedTotalmarks150Totalmarks150
  26. 26. MATHEMATICS GRADES 10-1221CAPS3.2.3 TopicallocationpertermGRADE10:TERM1NoofWeeksTopicCurriculumstatementClarificationWhereanexampleisgiven,thecognitivedemandissuggested:knowledge(K),routineprocedure(R),complexprocedure(C)orproblem-solving(P)3Algebraicexpressions1. Understandthatrealnumberscanberationalorirrational.2. Establishbetweenwhichtwointegersagivensimplesurdlies.3. Roundrealnumberstoanappropriatedegreeofaccuracy.4. Multiplicationofabinomialbyatrinomial.5. Factorisationtoincludetypestaughtingrade9and:• trinomials• groupinginpairs• sumanddifferenceoftwocubes6. Simplificationofalgebraicfractionsusingfactorizationwithdenominatorsofcubes(limitedtosumanddifferenceofcubes).Examplestoillustratethedifferentcognitivelevelsinvolvedinfactorisation:1. Factorisefully:1.1. m2-2m+1(revision)Learnersmustbeabletorecognisethesimplestperfectsquares.(R)1.2. 2x2-x-3 Thistypeisroutineandappearsinalltexts.(R)1.3.13y2+18-y22 Learnersarerequiredtoworkwithfractionsandidentify whenanexpressionhasbeen“fullyfactorised”.(R)2. Simplify(C)2Exponents1. ReviselawsofexponentslearntinGrade9where€x,y0and€m,€n  ∈Z:• €xm×xn=xm+n• €xm÷xn=xm−n• €(xm)n=xmn  • €xm×ym=(xy)mAlsobydefinition:• ,€x≠0  ,and• €x0=1,€x≠0  2. Usethelawsofexponentstosimplifyexpressionsandsolveequations,acceptingthattherulesalsoholdfor€m,€n  ∈Q.Examples:1.Simplify:(3x52)3-75Asimpletwo-stepprocedureisinvolved.(R)2.SimplifyAssumingthistypeofquestionhasnotbeentaught,spottingthatthenumeratorcanbefactorisedasadifferenceofsquaresrequiresinsight.(P)3.Solveforx:3.1125,02=x(R)3.2€2x32=54(R)3.3  (C)3.4  (C)
  27. 27. MATHEMATICS GRADES 10-1222 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)GRADE10:TERM1NoofWeeksTopicCurriculumstatementClarification1NumbersandpatternsPatterns:Investigatenumberpatternsleadingtothosewherethereisaconstantdifferencebetweenconsecutiveterms,andthegeneralterm(withoutusingaformula-seecontentoverview)isthereforelinear.Comment:• ArithmeticsequenceisdoneinGrade12,hence  isnotusedinGrade10.Examples:1. Determinethe5thandthenthtermsofthenumberpattern10;7;4;1;….Thereisanalgorithmicapproachtoansweringsuchquestions.(R)2. IfthepatternMATHSMATHSMATHS…iscontinuedinthisway,whatwillthe267thletterbe?Itisnotimmediatelyobvioushowoneshouldproceed,unlesssimilarquestionshavebeentackled.(P)2EquationsandInequalities1. Revisethesolutionoflinearequations.2. Solvequadraticequations(byfactorisation).3. Solvesimultaneouslinearequationsintwounknowns.4. Solvewordproblemsinvolvinglinear,quadraticorsimultaneouslinearequations.5. Solveliteralequations(changingthesubjectofaformula).6. Solvelinearinequalities(andshowsolutiongraphically).Intervalnotationmustbeknown.Examples:1. Solveforx:  (R)2. Solveform:2m2-m=1(R)3. Solveforxandy:x+2y=1;123=+yx(C)4. SolveforrintermsofV,∏andh:V=∏r2h(R)5. Solveforx:-1≤2-3x≤8(C)
  28. 28. MATHEMATICS GRADES 10-1223CAPSGRADE10:TERM1NoofWeeksTopicCurriculumstatementClarification3Trigonometry1. Definethetrigonometricratiossinθ,cosθandtanθ,usingright-angledtriangles.2.Extendthedefinitionsofsinθ,cosθandtanθfor00≤θ≤3600.3.Definethereciprocalsofthetrigonometricratioscosecθ,secθandcotθ,usingright-angledtriangles(thesethreereciprocalsshouldbeexaminedingrade10only).4.Derivevaluesofthetrigonometricratiosforthespecialcases(withoutusingacalculator)θ∈{00;300;450;600;900}.5. Solvetwo-dimensionalproblemsinvolvingright-angledtriangles.6. Solvesimpletrigonometricequationsforanglesbetween00and900.7. Usediagramstodeterminethenumericalvaluesofratiosforanglesfrom00to3600.Comment:Itisimportanttostressthat:• similarityoftrianglesisfundamentaltothetrigonometricratiossinθ,cosθandtanθ;• trigonometricratiosareindependentofthelengthsofthesidesofasimilarright-angledtriangleanddepend(uniquely)onlyontheangles,henceweconsiderthemasfunctionsoftheangles;• doublingaratiohasadifferenteffectfromdoublinganangle,forexample,generally2sinθ≠sin2θ;and• Solveequationoftheformcx=sin,orcx=cos2,orcx=2tan,wherecisaconstant.Examples:1. If5sinθ+4=0and00≤θ≤2700,calculatethevalueofsin2θ+cos2θwithoutusingacalculator.(R)2. LetABCDbearectangle,withAB=2cm.LetEbeonADsuchthatAEBˆˆ=E=450andBÊC=750.Determinetheareaoftherectangle.(P)3. Determinethelengthofthehypotenuseofaright-angledtriangleABC,whereEBˆˆ==900,DAˆˆ==300andAB=10cm(K)4. Solveforx:  for(C)AssessmentTerm1:1.Investigationorproject(onlyoneprojectperyear)(atleast50marks) Exampleofaninvestigation: Imagineacubeofwhitewoodwhichisdippedintoredpaintsothatthesurfaceisred,buttheinsidestillwhite.Ifonecutismade,paralleltoeachfaceofthecube(andthroughthecentreofthecube),thentherewillbe8smallercubes.Eachofthesmallercubeswillhave3redfacesand3whitefaces.Investigatethenumberofsmallercubeswhichwillhave3,2,1and0redfacesif2/3/4/…/nequallyspacedcutsaremadeparalleltoeachface.Thistaskprovidestheopportunitytoinvestigate,tabulateresults,makeconjecturesandjustifyorprovethem.2. Test(atleast50marksand1hour).Makesurealltopicsaretested. Careneedstobetakentosetquestionsonallfourcognitivelevels:approximately20%knowledge,approximately35%routineprocedures,30%complexproceduresand15%problem-solving.
  29. 29. MATHEMATICS GRADES 10-1224 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)GRADE10:TERM2WeeksTopicCurriculumstatementClarification(4+1)5Functions1. Theconceptofafunction,whereacertainquantity(outputvalue)uniquelydependsonanotherquantity(inputvalue).Workwithrelationshipsbetweenvariablesusingtables,graphs,wordsandformulae.Convertflexiblybetweentheserepresentations.Note:thatthegraphdefinedbyyx=shouldbeknownfromGrade9.2. Pointbypointplottingofbasicgraphsdefinedby2xy=,xy1=andxby=;0bandtodiscovershape,domain(inputvalues),range(outputvalues),asymptotes,axesofsymmetry,turningpointsandinterceptsontheaxes(whereapplicable).3. Investigatetheeffectofqxfay+=)(.andqxfay+=)(.onthegraphsdefinedbyqxfay+=)(.,wherexxf=)(,,)(2xxf=xxf1)(=and,)(xbxf=,0b4. Pointbypointplottingofbasicgraphsdefinedby,  andfor5.Studytheeffectofaandqxfay+=)(.onthegraphsdefinedby:;;andwhereqxfay+=)(.,qxfay+=)(.∈Qfor.6. Sketchgraphs,findtheequationsofgivengraphsandinterpretgraphs.Note:Sketchingofthegraphsmustbebasedontheobservationofnumber3and5.Comments:• AmoreformaldefinitionofafunctionfollowsinGrade12.Atthislevelitisenoughtoinvestigatetheway(unique)outputvaluesdependonhowinputvaluesvary.Thetermsindependent(input)anddependent(output)variablesmightbeuseful.• Aftersummarieshavebeencompiledaboutbasicfeaturesofprescribedgraphsandtheeffectsofparametersaandqhavebeeninvestigated:a:averticalstretch(and/orareflectionaboutthex-axis)andqaverticalshift.Thefollowingexamplesmightbeappropriate:• Rememberthatgraphsinsomepracticalapplicationsmaybeeitherdiscreteorcontinuous.Examples:1. Sketchedbelowaregraphsofqxaxf+=)(and.Thehorizontalasymptoteofbothgraphsistheliney=1.Determinethevaluesofa,b,n,qandt. (C)Oxy(1;-1)(2;0)2. Sketchthegraphdefinedby  for (R)
  30. 30. MATHEMATICS GRADES 10-1225CAPSGRADE10:TERM2WeeksTopicCurriculumstatementClarification3EuclideanGeometry1. Revisebasicresultsestablishedinearliergradesregardinglines,anglesandtriangles,especiallythesimilarityandcongruenceoftriangles.2. Investigatelinesegmentsjoiningthemid-pointsoftwosidesofatriangle.3. Definethefollowingspecialquadrilaterals:thekite,parallelogram,rectangle,rhombus,squareandtrapezium.Investigateandmakeconjecturesaboutthepropertiesofthesides,angles,diagonalsandareasofthesequadrilaterals.Provetheseconjectures.Comments:• Trianglesaresimilariftheircorrespondinganglesareequal,oriftheratiosoftheirsidesareequal:TrianglesABCandDEFaresimilarifDAˆˆ=,EBˆˆ=andFCˆˆ=.Theyarealsosimilarif.• Wecoulddefineaparallelogramasaquadrilateralwithtwopairsofoppositesidesparallel.Thenweinvestigateandprovethattheoppositesidesoftheparallelogramareequal,oppositeanglesofaparallelogramareequal,anddiagonalsofaparallelogrambisecteachother.• ItmustbeexplainedthatasinglecounterexamplecandisproveaConjecture,butnumerousspecificexamplessupportingaconjecturedonotconstituteageneralproof.Example:InquadrilateralKITE,KI=KEandIT=ET.ThediagonalsintersectatM.Provethat:1. IM=MEand(R)2. KTisperpendiculartoIE.(P)Asitisnotobvious,firstprovethat.3Mid-yearexaminationsAssessmentterm2:1.Assignment/test(atleast50marks)2.Mid-yearexamination(atleast100marks)Onepaperof2hours(100marks)orTwopapers-one,1hour(50marks)andtheother,1hour(50marks)
  31. 31. MATHEMATICS GRADES 10-1226 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)GRADE10:TERM3WeeksTopicCurriculumstatementClarification2AnalyticalGeometryRepresentgeometricfiguresonaCartesianco-ordinatesystem.Deriveandapplyforanytwopoints);(11yxand);(22yxtheformulaeforcalculatingthe:1. distancebetweenthetwopoints;2. gradientofthelinesegmentconnectingthetwopoints(andfromthatidentifyparallelandperpendicularlines);and3. coordinatesofthemid-pointofthelinesegmentjoiningthetwopoints.Example:Considerthepoints)5;2(PandintheCartesianplane.1.1. CalculatethedistancePQ. (K)1.2FindthecoordinatesofRifMisthemid-pointofPR. (R)1.3DeterminethecoordinatesofSifPQRSisaparallelogram. (C)1.4IsPQRSarectangle?Whyorwhynot? (R)2FinanceandgrowthUsethesimpleandcompoundgrowthformulaeandniPA)1(+=]tosolveproblems,includingannualinterest,hirepurchase,inflation,populationgrowthandotherreal-lifeproblems.Understandtheimplicationoffluctuatingforeignexchangerates(e.g.onthepetrolprice,imports,exports,overseastravel).
  32. 32. MATHEMATICS GRADES 10-1227CAPSGRADE10:TERM3WeeksTopicCurriculumstatementClarification2Statistics1.Revisemeasuresofcentraltendencyinungroupeddata.2.Measuresofcentraltendencyingroupeddata: calculationofmeanestimateofgroupedandungroupeddataandidentificationofmodalintervalandintervalinwhichthemedianlies.3. Revisionofrangeasameasureofdispersionandextensiontoincludepercentiles,quartiles,interquartileandsemiinterquartilerange.4. Fivenumbersummary(maximum,minimumandquartiles)andboxandwhiskerdiagram.5. Usethestatisticalsummaries(measuresofcentraltendencyanddispersion),andgraphstoanalyseandmakemeaningfulcommentsonthecontextassociatedwiththegivendata.Comment:Ingrade10,theintervalsofgroupeddatashouldbegivenusinginequalities,thatis,intheform0≤x20ratherthanintheform0-19,20-29,…Example:Themathematicsmarksof200grade10learnersataschoolcanbesummarisedasfollows:PercentageobtainedNumberofcandidates0≤x20420≤x301030≤x403740≤x504350≤x603660≤x702670≤x802480≤x100201. Calculatetheapproximatemeanmarkfortheexamination.(R)2. Identifytheintervalinwhicheachofthefollowingdataitemslies:2.1. themedian; (R)2.2. thelowerquartile; (R)2.3. theupperquartile;and (R)2.4.thethirtiethpercentile. (R)
  33. 33. MATHEMATICS GRADES 10-1228 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)GRADE10:TERM3WeeksTopicCurriculumstatementClarification2TrigonometryProblemsintwodimensions.Example:Twoflagpolesare30mapart.Theonehasheight10m,whiletheotherhasheight15m.Twotightropesconnectthetopofeachpoletothefootoftheother.Atwhatheightabovethegrounddothetworopesintersect?Whatifthepoleswereatdifferentdistanceapart?(P)1EuclideanGeometrySolveproblemsandproveridersusingthepropertiesofparallellines,trianglesandquadrilaterals.Comment:Usecongruencyandpropertiesofquads,esp.parallelograms.Example:EFGHisaparallelogram.ProvethatMFNHisaparallelogram.NMHEFG(C)2Measurement1. Revisethevolumeandsurfaceareasofright-prismsandcylinders.2. Studytheeffectonvolumeandsurfaceareawhenmultiplyinganydimensionbyaconstantfactork.3. Calculatethevolumeandsurfaceareasofspheres,rightpyramidsandrightcones.Example:Theheightofacylinderis10cm,andtheradiusofthecircularbaseis2cm.Ahemisphereisattachedtooneendofthecylinderandaconeofheight2cmtotheotherend.Calculatethevolumeandsurfaceareaofthesolid,correcttothenearestcm3andcm2,respectively.(R)Comments:• Incaseofpyramids,basesmusteitherbeanequilateraltriangleorasquare.• Problemtypesmustincludecompositefigure.Assessmentterm3:Two(2)Tests(atleast50marksand1hour)coveringalltopicsinapproximatelytheratiooftheallocatedteachingtime.
  34. 34. MATHEMATICS GRADES 10-1229CAPSGRADE10:TERM4NoofWeeksTopicCurriculumstatementClarification2Probability1.Theuseofprobabilitymodelstocomparetherelativefrequencyofeventswiththetheoreticalprobability.2.TheuseofVenndiagramstosolveprobabilityproblems,derivingandapplyingthefollowingforanytwoeventsAandBinasamplespaceS:AP(orand);BAandBaremutuallyexclusiveifAP(and;0)=BAandBarecomplementaryiftheyaremutuallyexclusive;and.1)()(=+BPAPThen()(PBP=not.Comment:• Itgenerallytakesaverylargenumberoftrialsbeforetherelativefrequencyofacoinfallingheadsupwhentossedapproaches0,5.Example:Inasurvey80peoplewerequestionedtofindouthowmanyreadnewspaperSorDorboth.Thesurveyrevealedthat45readD,30readSand10readneither.UseaVenndiagramtofindhowmanyread1. Sonly;(C)2. Donly;and(C)3. bothDandS.(C)4RevisionComment:Thevalueofworkingthroughpastpaperscannotbeoveremphasised.3ExaminationsAssessmentterm41.Test(atleast50marks)2.ExaminationPaper1:2hours(100marksmadeupasfollows:15±3onnumberpatterns,30±3onalgebraicexpressions,equationsandinequalities,30±3onfunctions,10±3onfinanceandgrowthand15±3onprobability.Paper2:2hours(100marksmadeupasfollows:40±3ontrigonometry,15±3onAnalyticalGeometry,30±3onEuclideanGeometryandMeasurement,and15±3onStatistics
  35. 35. MATHEMATICS GRADES 10-1230 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)GRADE11:TERM1NofWeeksTopicCurriculumstatementClarificationWhereanexampleisgiven,thecognitivedemandissuggested:knowledge(K),routineprocedure(R),complexprocedure(C)orproblemsolving(P)3Exponentsandsurds1. Simplifyexpressionsandsolveequationsusingthelawsofexponentsforrationalexponentswhere;qpqpxx=0;0qx.2. Add,subtract,multiplyanddividesimplesurds.3. Solvesimpleequationsinvolvingsurds.Example:1. Determinethevalueof239.(R)2. Simplify:(R)3. Solveforx:  .(P)3EquationsandInequalities1. Completethesquare.2. Quadraticequations(byfactorisationandbyusingthequadraticformula).3. Quadraticinequalitiesinoneunknown(Interpretsolutionsgraphically).NB:Itisrecommendedthatthesolvingofequationsintwounknownsisimportanttobeusedinotherequationslikehyperbola-straightlineasthisisnormalinthecaseofgraphs.4. Equationsintwounknowns,oneofwhichislinearandtheotherquadratic.5. Natureofroots.Example:1. Ihave12metresoffencing.WhatarethedimensionsofthelargestrectangularareaIcanenclosewiththisfencingbyusinganexistingwallasoneside?Hint:letthelengthoftheequalsidesoftherectanglebexmetresandformulateanexpressionfortheareaoftherectangle.(C)(Withoutthehintthiswouldprobablybeproblemsolving.)2.1.Showthattherootsof  areirrational.(R)2.2.Showthat012=++xxhasnorealroots.(R)3. Solveforx:.(R)4. Solveforx:  .(R)5. Twomachines,workingtogether,take2hours24minutestocompleteajob.Workingonitsown,onemachinetakes2hourslongerthantheothertocompletethejob.Howlongdoestheslowermachinetakeonitsown?(P)2NumberpatternsPatterns:Investigatenumberpatternsleadingtothosewherethereisaconstantseconddifferencebetweenconsecutiveterms,andthegeneraltermisthereforequadratic.Example:InthefirststageoftheWorldCupSoccerFinalsthereareteamsfromfourdifferentcountriesineachgroup.Eachcountryinagroupplayseveryothercountryinthegrouponce.Howmanymatchesarethereforeachgroupinthefirststageofthefinals?Howmanygameswouldtherebeiftherewerefiveteamsineachgroup?Sixteams?nteams?(P)
  36. 36. MATHEMATICS GRADES 10-1231CAPSGRADE11:TERM1NofWeeksTopicCurriculumstatementClarification3AnalyticalGeometryDeriveandapply:1. theequationofalinethoughtwogivenpoints;2. theequationofalinethroughonepointandparallelorperpendiculartoagivenline;and3. theinclination(θ)ofaline,whereisthegradientofthelineExample:GiventhepointsA(2;5);B(-3;-4)andC(4;-2)determine:1. theequationofthelineAB;and(R)2. thesizeofCABˆ.(C)AssessmentTerm1:1. AnInvestigationoraproject(amaximumofoneprojectinayear)(atleast50marks)Noticethatanassignmentisgenerallyanextendedpieceofworkundertakenathome.Linearprogrammingquestionscanbeusedasprojects.Exampleofanassignment:Ratiosandequationsintwovariables.(Thisassignmentbringsinanelementofhistorywhichcouldbeextendedtoincludeoneortwoancientpaintingsandexamplesofarchitecturewhichareintheshapeofarectanglewiththeratioofsidesequaltothegoldenratio.)Task1If2x2-3xy+y2=0then(2x-y)(x-y)=0so2yx=oryx=.Hencetheratio21=yxor11=yx.Inthesamewayfindthepossiblevaluesoftheratioyxifitisgiventhat2x2-5xy+y2=0TaskMostpaperiscuttointernationallyagreedsizes:A0,A1,A2,…,A7withthepropertythattheA1sheetishalfthesizeoftheA0sheetandsimilartotheA0sheet,theA2sheetishalfthesizeoftheA1sheetandsimilartotheA1sheet,etc.Findtheratioofthelengthyx=tothebreadthyx=ofA0,A1,A2,…,A7paper(insimplestsurdform).Task3Thegoldenrectanglehasbeenrecognisedthroughtheagesasbeingaestheticallypleasing.ItcanbeseeninthearchitectureoftheGreeks,insculpturesandinRenaissancepaintings.Anygoldenrectanglewithlengthxandbreadthyhasthepropertythatwhenasquarethelengthoftheshorterside(y)iscutfromit,anotherrectanglesimilartoitisleft.Theprocesscanbecontinuedindefinitely,producingsmallerandsmallerrectangles.Usingthisinformation,calculatetheratiox:yinsurdform.Exampleofproject:Collecttheheightsofatleast50sixteen-year-oldgirlsandatleast50sixteen-year-oldboys.Groupyourdataappropriatelyandusethesetwosetsofgroupeddatatodrawfrequencypolygonsoftherelativeheightsofboysandofgirls,indifferentcolours,onthesamesheetofgraphpaper.Identifythemodalintervals,theintervalsinwhichthemedianslieandtheapproximatemeansascalculatedfromthefrequenciesofthegroupeddata.Byhowmuchdoestheapproximatemeanheightofyoursampleofsixteen-year-oldgirlsdifferfromtheactualmean?Commentonthesymmetryofthetwofrequencypolygonsandanyotheraspectsofthedatawhichareillustratedbythefrequencypolygons.2. Test(atleast50marksand1hour).Makesurealltopicsaretested.Careneedstobetakentoaskquestionsonallfourcognitivelevels:approximately20%knowledge,approximately35%routineprocedures,30%complexproceduresand15%problem-solving.
  37. 37. MATHEMATICS GRADES 10-1232 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)GRADE11:TERM2NoofWeeksTopicCurriculumstatementClarification4Functions1. Revisetheeffectoftheparametersaandqandinvestigatetheeffectofponthegraphsofthefunctionsdefinedby:1.1.qpxaxfy++==2)()( 1.2.qpxaxfy++==)(1.3.qbaxfypx+==+.)(where b0,b≠12. Investigatenumericallytheaveragegradientbetweentwopointsonacurveanddevelopanintuitiveunderstandingoftheconceptofthegradientofacurveatapoint.3. Pointbypointplottingofbasicgraphsdefinedby,  andfor€θ∈[−360°;360°]  4. Investigatetheeffectoftheparameterkonthegraphsofthefunctionsdefinedby€y=sin(kx),  and.5. Investigatetheeffectoftheparameterponthegraphsofthefunctionsdefinedby),sin(pxy+=,),cos(pxy+=and),tan(pxy+=.6. Drawsketchgraphsdefinedby:𝑦=𝑎 𝑠𝑖𝑛 𝑘 (𝑥+𝑝),𝑦=𝑎 𝑐𝑜𝑠 𝑘 (𝑥+𝑝)and𝑦=𝑎 𝑡𝑎𝑛 𝑘 (𝑥+𝑝)atmosttwoparametersatatime.Comment:• Oncetheeffectsoftheparametershavebeenestablished,variousproblemsneedtobeset:drawingsketchgraphs,determiningthedefiningequationsoffunctionsfromsufficientdata,makingdeductionsfromgraphs.Reallifeapplicationsoftheprescribedfunctionsshouldbestudied.• Twoparametersatatimecanbevariedintestsorexaminations.Example:Sketchthegraphsdefinedbyand€f(x)=cos(2x−120°)  onthesamesetofaxes,where  .(C)
  38. 38. MATHEMATICS GRADES 10-1233CAPSGRADE11:TERM2NoofWeeksTopicCurriculumstatementClarification4Trigonometry1. Deriveandusetheidentitieskanoddinteger;and  .2. Deriveandusereductionformulaetosimplifythefollowingexpressions:2.1.;2.2.  2.3. and2.4.  .3. Determineforwhichvaluesofavariableanidentityholds.4. Determinethegeneralsolutionsoftrigonometricequations.Also,determinesolutionsinspecificintervals.Comment:• Teachersshouldexplainwherereductionformulaecomefrom.Examples:1. Provethat  . (R)2. Forwhichvaluesofis  undefined? (R)3. Simplify€cos180°−x()sinx−90°()−1tan2540°+x()sin90°+x()cos−x()   (R)4. Determinethegeneralsolutionsof. (C)3Mid-yearexaminationsAssessmentterm2:1. Assignment(atleast50marks)2. Mid-yearexamination:Paper1:2hours(100marksmadeupasfollows:generalalgebra(25±3)equationsandinequalities(35±3);numberpatterns(15±3);functions(25±3)Paper2:2hours(100marksmadeupasfollows:analyticalgeometry(30±3)andtrigonometry(70±3)).
  39. 39. MATHEMATICS GRADES 10-1234 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)GRADE11:TERM3No.ofweeksTopicCurriculumStatementClarification1Measurement1. RevisetheGrade10work.3EuclideanGeometryAcceptresultsestablishedinearliergradesasaxiomsandalsothatatangenttoacircleisperpendiculartotheradius,drawntothepointofcontact.Theninvestigateandprovethetheoremsofthegeometryofcircles:• Thelinedrawnfromthecentreofacircleperpendiculartoachordbisectsthechord;• Theperpendicularbisectorofachordpassesthroughthecentreofthecircle;• Theanglesubtendedbyanarcatthecentreofacircleisdoublethesizeoftheanglesubtendedbythesamearcatthecircle(onthesamesideofthechordasthecentre);• Anglessubtendedbyachordofthecircle,onthesamesideofthechord,areequal;• Theoppositeanglesofacyclicquadrilateralaresupplementary;• Twotangentsdrawntoacirclefromthesamepointoutsidethecircleareequalinlength;• Theanglebetweenthetangenttoacircleandthechorddrawnfromthepointofcontactisequaltotheangleinthealternatesegment.Usetheabovetheoremsandtheirconverses,wheretheyexist,tosolveriders.Comments:Proofsoftheoremscanbeaskedinexaminations,buttheirconverses(wherevertheyhold)cannotbeasked.Example:1. ABandCDaretwochordsofacirclewithcentreO.MisonABandNisonCDsuchthatOM⊥ABandON⊥CD.Also,AB=50mm,OM=40mmandON=20mm.DeterminetheradiusofthecircleandthelengthofCD.(C)2. OisthecentreofthecirclebelowandxO2ˆ1=.2.1. Determine2ˆOandMˆintermsofx.(R)2.2. Determine1ˆKand2ˆKintermsofx.(R)2.3. DetermineMKˆˆ1+.Whatdoyounotice?(R)2.4.Writedownyourobservationregardingthemeasuresof2ˆKandMˆ.(R)
  40. 40. MATHEMATICS GRADES 10-1235CAPSGRADE11:TERM3No.ofweeksTopicCurriculumStatementClarification3. OisthecentreofthecircleaboveandMPTisatangent.Also,  .Determine,withreasons,yx,andz.(C)  2  y  3  z  O  B  T  M  A  P  x  4.Given:,and22ˆˆBA=..Provethat:4.1 PALisatangenttocircleABC;(P)4.2ABisatangenttocircleADP.(P)
  41. 41. MATHEMATICS GRADES 10-1236 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)GRADE11:TERM3No.ofweeksTopicCurriculumStatementClarification5.Intheaccompanyingfigure,twocirclesintersectatFandD.BFTisatangenttothesmallercircleatF.StraightlineAFEisdrawnsuchthatFD=FE.CDEisastraightlineandchordACandBFcutatK.Provethat:5.1 BT//CE(C)5.2 BCEFisaparallelogram(P)5.3 AC=BF(P)
  42. 42. MATHEMATICS GRADES 10-1237CAPSGRADE11:TERM3No.ofweeksTopicCurriculumStatementClarification2Trigonometry1. Proveandapplythesine,cosineandarearules.2. Solveproblemsintwodimensionsusingthesine,cosineandarearules.Comment:• Theproofsofthesine,cosineandarearulesareexaminable.Example:InDisonBC,ADC=θ,DA=DC=r,bd=2r,AC=k,and  . Showthat  .(P)2Finance,growthanddecay1. Usesimpleandcompounddecayformulae:A=P(1-in)andA=P(1-i)ntosolveproblems(includingstraightlinedepreciationanddepreciationonareducingbalance).2. Theeffectofdifferentperiodsofcompoundgrowthanddecay,includingnominalandeffectiveinterestrates.Examples:1. ThevalueofapieceofequipmentdepreciatesfromR10000toR5000infouryears.Whatistherateofdepreciationifcalculatedonthe:1.1straightlinemethod;and(R)1.2reducingbalance?(C)2. Whichisthebetterinvestmentoverayearorlonger:10,5%p.a.compoundeddailyor10,55%p.a.compoundedmonthly?(R)3. R50000isinvestedinanaccountwhichoffers8%p.a.interestcompoundedquarterlyforthefirst18months.Theinterestthenchangesto6%p.a.compoundedmonthly.Twoyearsafterthemoneyisinvested,R10000iswithdrawn.Howmuchwillbeintheaccountafter4years?(C)Comment:• Theuseofatimelinetosolveproblemsisausefultechnique.• Stresstheimportanceofnotworkingwithroundedanswers,butofusingthemaximumaccuracyaffordedbythecalculatorrighttothefinalanswerwhenroundingmightbeappropriate.
  43. 43. MATHEMATICS GRADES 10-1238 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)GRADE11:TERM3No.ofweeksTopicCurriculumStatementClarification2Probability1.Revisetheadditionruleformutuallyexclusiveevents:𝑃(𝐴 𝑜𝑟 𝐵)=𝑃𝐴+𝑃(𝐵), thecomplementaryrule:𝑃(𝑛𝑜𝑡 𝐴)=1−𝑃(𝐴) andtheidentityP(AorB)=P(A)+P(B)-P(AandB)2.Identifydependentandindependenteventsandtheproductruleforindependentevents:𝑃(𝐴 𝑎𝑛𝑑 𝐵)=𝑃(𝐴)×𝑃(𝐵).3.TheuseofVenndiagramstosolveprobabilityproblems,derivingandapplyingformulaeforanythreeeventsA,BandCinasamplespaceS.4.Usetreediagramsfortheprobabilityofconsecutiveorsimultaneouseventswhicharenotnecessarilyindependent.Comment:• VennDiagramsorContingencytablescanbeusedtostudydependentandindependentevents.Examples:1. P(A)=0,45,P(B)=0,3andP(AorB)=0,615.AretheeventsAandBmutuallyexclusive,independentorneithermutuallyexclusivenorindependent? (R)2. Whatistheprobabilityofthrowingatleastonesixinfourrollsofaregularsixsideddie?(C)3. Inagroupof50learners,35takeMathematicsand30takeHistory,while12takeneitherofthetwo.Ifalearnerischosenatrandomfromthisgroup,whatistheprobabilitythathe/shetakesbothMathematicsandHistory?(C)4. Astudywasdonetotesthoweffectivethreedifferentdrugs,A,BandCwereinrelievingheadaches.Overtheperiodcoveredbythestudy,80patientsweregiventheopportunitytousealltwodrugs.Thefollowingresultswereobtained:fromatleastoneofthedrugs?(R)40reportedrelieffromdrugA35reportedrelieffromdrugB40reportedrelieffromdrugC21reportedrelieffrombothdrugsAandC18reportedrelieffromdrugsBandC68reportedrelieffromatleastoneofthedrugs7reportedrelieffromallthreedrugs.4.1RecordthisinformationinaVenndiagram.(C)4.2Howmanysubjectsgotnorelieffromanyofthedrugs?(K)4.3HowmanysubjectsgotrelieffromdrugsAandB,butnotC?(R)4.4Whatistheprobabilitythatarandomlychosensubjectgotrelieffromatleastoneofthedrugs?(R)
  44. 44. MATHEMATICS GRADES 10-1239CAPSGRADE11:TERM4No.ofweeksTopicCurriculumStatementClarification3Statistics1. Histograms2. Frequencypolygons3. Ogives(cumulativefrequencycurves)4. Varianceandstandarddeviationofungroupeddata5. Symmetricandskeweddata6. IdentificationofoutliersComments:• Varianceandstandarddeviationmaybecalculatedusingcalculators.• Problemsshouldcovertopicsrelatedtohealth,social,economic,cultural,politicalandenvironmentalissues.• Identificationofoutliersshouldbedoneinthecontextofascatterplotaswellastheboxandwhiskerdiagrams.3Revision3ExaminationsAssessmentterm4:1. Test(atleast50marks)2. Examination(300marks)Paper1:3hours(150marksmadeupasfollows:(25±3)onnumberpatterns,on(45±3)exponentsandsurds,equationsandinequalities,(45±3)onfunctions,(15±3)onfinancegrowthanddecay,(20±3)onprobability).Paper2:3hours(150marksmadeupasfollows:(50±3)ontrigonometry,(30±3)onAnalyticalGeometry,(50±3)onEuclideanGeometryandMeasurement,(20±3)onStatistics.
  45. 45. MATHEMATICS GRADES 10-1240 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)GRADE12:TERM1No.ofWeeksTopicCurriculumstatementClarification3Patterns,sequences,series1. Numberpatterns,includingarithmeticandgeometricsequencesandseries2. Sigmanotation3. Derivationandapplicationoftheformulaeforthesumofarithmeticandgeometricseries:3.1;;3.2;and3.3,Comment:Derivationoftheformulaeisexaminable.Examples:1.Writedownthefirstfivetermsofthesequencewithgeneralterm  .(K)2.Calculate.(R)3.Determinethe5thtermofthegeometricsequenceofwhichthe8thtermis6andthe12thtermis14.(C)4.Determinethelargestvalueofnsuchthat  .(R)5.Showthat19999,0.=.(P)3Functions1. Definitionofafunction.2. Generalconceptoftheinverseofafunctionandhowthedomainofthefunctionmayneedtoberestricted(inordertoobtainaone-to-onefunction)toensurethattheinverseisafunction.3. Determineandsketchgraphsoftheinversesofthefunctionsdefinedby    Focusonthefollowingcharacteristics:domainandrange,interceptswiththeaxes,turningpoints,minima,maxima,asymptotes(horizontalandvertical),shapeandsymmetry,averagegradient(averagerateofchange),intervalsonwhichthefunctionincreases/decreases.Examples:1. Considerthefunctionfwhere.1.1 Writedownthedomainandrangeoff.(K)1.2 Showthatfisaone-to-onerelation.(R)1.3 Determinetheinversefunction  .(R)1.4Sketchthegraphsofthefunctionsf,  andxy=lineonthesamesetofaxes.Whatdoyounotice?(R)2. RepeatQuestion1forthefunction  and  .(C)Caution:1.Donotconfusetheinversefunction  withthereciprocal)(1xf.Forexample,forthefunctionwherexxf=)(,thereciprocalisx1,whilefor€x≥0  .2.Notethatthenotation  isusedonlyforone-to-onerelationandmustnotbeusedforinversesofmany-to-onerelations,sinceinthesecasestheinversesarenotfunctions.
  46. 46. MATHEMATICS GRADES 10-1241CAPSGRADE12:TERM1No.ofWeeksTopicCurriculumstatementClarification1Functions:exponentialandlogarithmic1. Revisionoftheexponentialfunctionandtheexponentiallawsandgraphofthefunctiondefinedbywhereand2. Understandthedefinitionofalogarithm:,whereand.3.Thegraphofthefunctiondefinexyblog=forboththecases10band1b.Comment:Thefourlogarithmiclawsthatwillbeapplied,onlyinthecontextofreal-lifeproblemsrelatedtofinance,growthanddecay,are:;;  ;and BAABlogloglog=.Theyfollowfromthebasicexponentiallaws(term1ofgrade10).• Manipulationinvolvingthelogarithmiclawswillnotbeexamined.Caution:1.Makesurelearnersknowthedifferencebetweenthetwofunctionsdefinedbyxyb=andbyx=wherebisapositive(constant)realnumber.2.Manipulationinvolvingthelogarithmiclawswillnotbeexamined.Examples:1.Solveforx:  (R)2.Letxaxf=)(,.0a2.1Determineaifthegraphoffgoesthroughthepoint(R)2.2Determinethefunction  .(R)2.3Forwhichvaluesofxis  ?(C)2.4Determinethefunctionhifthegraphofhisthereflectionofthegraphoffthroughthey-axis.(C)2.5Determinethefunctionkifthegraphofkisthereflectionofthegraphoffthroughthex-axis.(C)2.6Determinethefunctionpifthegraphofpisobtainedbyshiftingthegraphofftwounitstotheleft.(C)2.7Writedownthedomainandrangeforeachofthefunctions  ,kandp.(R)2.8Representallthesefunctionsgraphically.(R)
  47. 47. MATHEMATICS GRADES 10-1242 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)GRADE12:TERM1No.ofWeeksTopicCurriculumstatementClarification2Finance,growthanddecay1. Solveproblemsinvolvingpresentvalueandfuturevalueannuities.2. Makeuseoflogarithmstocalculatethevalueofn,thetimeperiod,intheequationsniPA)1(+=or.3. Criticallyanalyseinvestmentandloanoptionsandmakeinformeddecisionsastobestoption(s)(includingpyramid).Comment:Derivationoftheformulaeforpresentandfuturevaluesusingthegeometricseriesformula,shouldbepartoftheteachingprocesstoensurethatthelearnersunderstandwheretheformulaecomefrom.Thetwoannuityformulae:€F=x[(1+i)n−1]iandholdonlywhenpaymentcommencesoneperiodfromthepresentandendsafternperiods.Comment: Theuseofatimelinetoanalyseproblemsisausefultechnique.Examples:Giventhatapopulationincreasedfrom120000to214000in10years,atwhatannual(compound)ratedidthepopulationgrow?(R)1. Inordertobuyacar,JohntakesoutaloanofR25000fromthebank.Thebankchargesanannualinterestrateof11%,compoundedmonthly.Theinstalmentsstartamonthafterhehasreceivedthemoneyfromthebank.1.1Calculatehismonthlyinstalmentsifhehastopaybacktheloanoveraperiodof5years.(R)1.2Calculatetheoutstandingbalanceofhisloanaftertwoyears(immediatelyafterthe24thinstalment).(C)2TrigonometryCompoundangleidentities:  ;;;;;and  .2.Accepting,derivetheothercompoundangleidentities.(C)3.Determinethegeneralsolutionof0cos2sin=+xx.(R)4.Provethat.(C)
  48. 48. MATHEMATICS GRADES 10-1243CAPSGRADE12:TERM1No.ofWeeksTopicCurriculumstatementClarificationAssessmentTerm1:1.Investigationorproject.(atleast50marks)Onlyoneinvestigationorprojectperyearisrequired.• Exampleofaninvestigationwhichrevisesthesine,cosineandarearules:Grade12Investigation:Polygonswith12Matches • Howmanydifferenttrianglescanbemadewithaperimeterof12matches?• Whichofthesetriangleshasthegreatestarea?• Whatregularpolygonscanbemadeusingall12matches?• Investigatetheareasofpolygonswithaperimeterof12matchesinanefforttoestablishthemaximumareathatcanbeenclosedbythematches.Anyextensionsorgeneralisationsthatcanbemade,basedonthistask,willenhanceyourinvestigation.Butyouneedtostriveforquality,ratherthansimplyproducingalargenumberoftrivialobservations.Assessment:Thefocusofthistaskisonmathematicalprocesses.Someoftheseprocessesare:specialising,classifying,comparing,inferring,estimating,generalising,makingconjectures,validating,provingandcommunicatingmathematicalideas.2.AssignmentorTest.(atleast50marks)3.Test.(atleast50marks)
  49. 49. MATHEMATICS GRADES 10-1244 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)GRADE12:TERM2No.ofWeeksTopicCurriculumstatementClarification2Trigonometrycontinued1. Solveproblemsintwoandthreedimensions.Examples:a150°yxPQRT1.  isatower.Itsfoot,P,andthepointsQandRareonthesamehorizontalplane.FromQtheangleofelevationtothetopofthebuildingisx.Furthermore,,  yandthedistancebetweenPandRisametres.Provethat  (C)2.In,  .Provethat:2.1 BcCbacoscos+=where  and  .(R)2.2 (onconditionthat  ).(P)2.3  (onconditionthat  ).(P)2.4 CbaBacAcbcbacos)(cos)(cos)(+++++=++.(P)1Functions:polynomialsFactorisethird-degreepolynomials.ApplytheRemainderandFactorTheoremstopolynomialsofdegreeatmost3(noproofsrequired).AnymethodmaybeusedtofactorisethirddegreepolynomialsbutitshouldincludeexampleswhichrequiretheFactorTheorem.Examples:1.Solvefor:x  (R)2.If  isdividedby,theremainderis  .Determinethevalueofp.(P)
  50. 50. MATHEMATICS GRADES 10-1245CAPSGRADE12:TERM2No.ofWeeksTopicCurriculumstatementClarification3DifferentialCalculus1. Anintuitiveunderstandingofthelimitconcept,inthecontextofapproximatingtherateofchangeorgradientofafunctionatapoint.2. Uselimitstodefinethederivativeofafunctionfatanyx:.Generalisetofindthederivativeoffatanypointxinthedomainoff,i.e.,definethederivativefunction)(xfofthefunction)(xf.Understandintuitivelythat)(afisthegradientofthetangenttothegraphoffatthepointwithx-coordinatea.3. Usingthedefinition(firstprinciple),findthederivative,)(xffora,bandcconstants:3.1 3.2 ;3.3 xaxf=)(;and3.3 cxf=)(.Comment:Differentiationfromfirstprincipleswillbeexaminedonanyofthetypesdescribedin3.1,3.2and3.3.Examples:1. Ineachofthefollowingcases,findthederivativeof)(xfatthepointwhere,usingthedefinitionofthederivative:1.1 2)(2+=xxf(R)1.2 (R)1.3  (R)1.4 (C)Caution:Careshouldbetakennottoapplythesumrulefordifferentiation4.1inasimilarwaytoproducts.• Determine.• Determine.• Writedownyourobservation.2.Usedifferentiationrulestodothefollowing:2.1 Determine)(xfif  (R)2.2 Determine)(xfifxxxf3)2()(+=(C)(P)
  51. 51. MATHEMATICS GRADES 10-1246 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)GRADE12:TERM2No.ofWeeksTopicCurriculumstatementClarification4. Usetheformula  (foranyrealnumbern)togetherwiththerules4.1and4.2(kaconstant)5. Findequationsoftangentstographsoffunctions.6. Introducethesecondderivativeof)(xfandhowitdeterminestheconcavityofafunction.7. Sketchgraphsofcubicpolynomialfunctionsusingdifferentiationtodeterminetheco-ordinateofstationarypoints,andpointsofinflection(whereconcavitychanges).Also,determinethex-interceptsofthegraphusingthefactortheoremandothertechniques.8. Solvepracticalproblemsconcerningoptimisationandrateofchange,includingcalculusofmotion.2.3 Determineif   (R)2.4 Determineif(C)3. Determinetheequationofthetangenttothegraphdefinedby)2()12(2++=xxywhere43=x.(C)4. Sketchthegraphdefinedbyby:4.1 findingtheinterceptswiththeaxes;(C)4.2 findingmaxima,minimaandtheco-ordinateofthepointofinflection;(R)4.3 lookingatthebehaviourofyas  andas  .(P)(Remember:Tounderstandpointsofinflection,anunderstandingofconcavityisnecessary.Thisiswherethesecondderivativeplaysarole.)5. Theradiusofthebaseofacircularcylindricalcanisxcm,anditsvolumeis430cm3.5.1 Determinetheheightofthecanintermsofx.(R)5.2 Determinetheareaofthematerialneededtomanufacturethecan(thatis,determinethetotalsurfaceareaofthecan)intermsofx.(C)5.3 Determinethevalueofxforwhichtheleastamountofmaterialisneededtomanufacturesuchacan.(C)5.4 IfthecostofthematerialisR500perm2,whatisthecostofthecheapestcan(labourexcluded)?(P)
  52. 52. MATHEMATICS GRADES 10-1247CAPSGRADE12:TERM2No.ofWeeksTopicCurriculumstatementClarification2AnalyticalGeometry1. Theequationdefinesacirclewithradiusrandcentre);(ba.2. Determinationoftheequationofatangenttoagivencircle.Examples:1. Determinetheequationofthecirclewithcentre  andradius6(K)2. Determinetheequationofthecirclewhichhasthelinesegmentwithendpoints)3;5(and  asdiameter.(R)3. Determinetheequationofacirclewitharadiusof6units,whichintersectsthex-axisat  andthey-axisat)3;0(.Howmanysuchcirclesarethere?(P)4. Determinetheequationofthetangentthattouchesthecircledefinedby  atthepoint.(C)5. Thelinewiththeequation2+=xyintersectsthecircledefinedbyatAandB.5.1 Determinetheco-ordinatesofAandB.(R)5.2 Determinethelengthofchord.(K)5.3 Determinetheco-ordinatesof,Mthemidpointof.(K)5.4 Showthat,whereOistheorigin.(C)5.5DeterminetheequationsofthetangentstothecircleatthepointsAandB.(C)5.6Determinetheco-ordinatesofthepointCwherethetwotangentsin5.5intersect.(C)5.7 Verifythat.(R)5.8 Determinetheequationsofthetwotangentstothecircle,bothparalleltothelinewiththeequation  .(P)3Mid-YearExaminationsAssessmentterm2:1.Assignment(atleast50marks)2.Examination(300marks)
  53. 53. MATHEMATICS GRADES 10-1248 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)GRADE12TERM3No.ofWeeksTopicCurriculumstatementClarification2EuclideanGeometry1.Reviseearlierworkonthenecessaryandsufficientconditionsforpolygonstobesimilar.2.Prove(acceptingresultsestablishedinearliergrades):• thatalinedrawnparalleltoonesideofatriangledividestheothertwosidesproportionally(andtheMid-pointTheoremasaspecialcaseofthistheorem);• thatequiangulartrianglesaresimilar;• thattriangleswithsidesinproportionaresimilar;and• thePythagoreanTheorembysimilartriangles.Example:ConsiderarighttriangleABCwith.Letand.LetDbeonsuchthat.Determinethelengthof  intermsofaandc.(P)1Statistics(regressionandcorrelation)1.Revisesymmetricandskeweddata.2. Usestatisticalsummaries,scatterplots,regression(inparticulartheleastsquaresregressionline)andcorrelationtoanalyseandmakemeaningfulcommentsonthecontextassociatedwithgivenbivariatedata,includinginterpolation,extrapolationanddiscussionsonskewness.Example:Thefollowingtablesummarisesthenumberofrevolutionsx(perminute)andthecorrespondingpoweroutputy(horsepower)ofaDieselengine:x400500600700750y58010301420188021001.Findtheleastsquaresregressionline  (K)2.Usethislinetoestimatethepoweroutputwhentheenginerunsat800m.(R)3.Roughlyhowfastistheenginerunningwhenithasanoutputof1200horsepower?(R)
  54. 54. MATHEMATICS GRADES 10-1249CAPSGRADE12TERM3No.ofWeeksTopicCurriculumstatementClarification2Countingandprobability1.Revise:• dependentandindependentevents;• theproductruleforindependentevents:P(AandB)=P(A)×P(B).• thesumruleformutuallyexclusiveeventsAandB:AP(or)()()BPAPB+=• theidentity:AP(or  and)B• thecomplementaryrule:(Pnot2.probabilityproblemsusingVenndiagrams,trees,two-waycontingencytablesandothertechniques(likethefundamentalcountingprinciple)tosolveprobabilityproblems(whereeventsarenotnecessarilyindependent).3.Applythefundamentalcountingprincipletosolveprobabilityproblems.Examples:1.Howmanythree-charactercodescanbeformedifthefirstcharactermustbealetterandthesecondtwocharactersmustbedigits?(K)2.WhatistheprobabilitythatarandomarrangementofthelettersBAFANAstartsandendswithan‘A’?(R)3.Adrawercontainstwentyenvelopes.Eightoftheenvelopeseachcontainfiveblueandthreeredsheetsofpaper.Theothertwelveenvelopeseachcontainsixblueandtworedsheetsofpaper.Oneenvelopeischosenatrandom.Asheetofpaperischosenatrandomfromit.Whatistheprobabilitythatthissheetofpaperisred?(C)4.Assumingthatitisequallylikelytobeborninanyofthe12monthsoftheyear,whatistheprobabilitythatinagroupofsix,atleasttwopeoplehavebirthdaysinthesamemonth?(P)3Examinations/RevisionAssessmentTerm3:1.Test(atleast50marks)2.Preliminaryexaminations(300marks)Important:Takenotethatatleastoneoftheexaminationsinterms2and3mustconsistoftwothree-hourpaperswiththesameorverysimilarstructuretothefinalNSCpapers.Theotherexaminationcanbereplacedbytestsonrelevantsections.
  55. 55. MATHEMATICS GRADES 10-1250 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)GRADE12:TERM4NoofWeeksTopicCurriculumstatementClarification3Revision6ExaminationsAssessmentTerm4:Finalexamination:Paper1:150marks:3hoursPaper2:150marks:3hoursPatternsandsequences(25±3)EuclideanGeometryandMeasurement(50±3)Finance,growthanddecay(15±3)AnalyticalGeometry(40±3)Functionsandgraphs(35±3)Statisticsandregression(20±3)Algebraandequations(25±3)Trigonometry(40±3)Calculus(35±3)Probability(15±3)
  56. 56. MATHEMATICS GRADES 10-1251CAPSsECTION 44.1 Introductionassessment is a continuous planned process of identifying, gathering and interpreting information about theperformance of learners, using various forms of assessment. It involves four steps: generating and collecting evidenceof achievement; evaluating this evidence; recording the findings and using this information to understand and assistin the learner’s development to improve the process of learning and teaching.Assessment should be both informal (Assessment for Learning) and formal (Assessment of Learning). In both casesregular feedback should be provided to learners to enhance the learning experience.Although assessment guidelines are included in the Annual Teaching Plan at the end of each term, the followinggeneral principles apply:1. Tests and examinations are assessed using a marking memorandum.2. Assignments are generally extended pieces of work completed at home. They can be collections of pastexamination questions, but should focus on the more demanding aspects as any resource material can beused, which is not the case when a task is done in class under strict supervision.3. At most one project or assignment should be set in a year. The assessment criteria need to be clearly indicatedon the project specification. The focus should be on the mathematics involved and not on duplicated picturesand regurgitation of facts from reference material. The collection and display of real data, followed by deductionsthat can be substantiated from the data, constitute good projects.4. Investigations are set to develop the skills of systematic investigation into special cases with a view to observinggeneral trends, making conjecures and proving them. To avoid having to assess work which is copied withoutunderstanding, it is recommended that while the initial investigation can be done at home, the final write upshould be done in class, under supervision, without access to any notes. Investigations are marked usingrubrics which can be specific to the task, or generic, listing the number of marks awarded for each skill:• 40% for communicating individual ideas and discoveries, assuming the reader has not come across the textbefore. The appropriate use of diagrams and tables will enhance the investigation.• 35% for the effective consideration of special cases;• 20% for generalising, making conjectures and proving or disproving these conjectures; and• 5% for presentation: neatness and visual impact.4.2 Informal or Daily Assessmentthe aim of assessment for learning is to collect continually information on a learner’s achievement that can be usedto improve individual] learning.Informal assessment involves daily monitoring of a learner’s progress. This can be done through observations,discussions, practical demonstrations, learner-teacher conferences, informal classroom interactions, etc. Althoughinformal assessment may be as simple as stopping during the lesson to observe learners or to discuss with learners
  57. 57. MATHEMATICS GRADES 10-1252 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)how learning is progressing. Informal assessment should be used to provide feedback to the learners and to informplanning for teaching, it need not be recorded. This should not be seen as separate from learning activities takingplace in the classroom. Learners or teachers can evaluate these tasks.Self assessment and peer assessment actively involve learners in assessment. Both are important as these allowlearners to learn from and reflect on their own performance. Results of the informal daily assessment activities arenot formally recorded, unless the teacher wishes to do so. The results of daily assessment tasks are not taken intoaccount for promotion and/or certification purposes.4.3 Formal AssessmentAll assessment tasks that make up a formal programme of assessment for the year are regarded as FormalAssessment. Formal assessment tasks are marked and formally recorded by the teacher for progress and certificationpurposes. All Formal Assessment tasks are subject to moderation for the purpose of quality assurance.Formal assessments provide teachers with a systematic way of evaluating how well learners are progressing in agrade and/or in a particular subject. Examples of formal assessments include tests, examinations, practical tasks,projects, oral presentations, demonstrations, performances, etc. Formal assessment tasks form part of a year-longformal Programme of Assessment in each grade and subject.Formal assessments in Mathematics include tests, aJune examination, a trial examination(for Grade 12), a project or an investigation.The forms of assessment used should be age- and developmental- level appropriate. The design of these tasksshould cover the content of the subject and include a variety of activities designed to achieve the objectives of thesubject.Formal assessments need to accommodate a range of cognitive levels and abilities of learners as shown below:
  58. 58. MATHEMATICS GRADES 10-1253CAPS4.4 ProgrammeofAssessmentThefourcognitivelevelsusedtoguideallassessmenttasksarebasedonthosesuggestedintheTIMSSstudyof1999.Descriptorsforeachlevelandtheapproximatepercentagesoftasks,testsandexaminationswhichshouldbeateachlevelaregivenbelow:CognitivelevelsDescriptionofskillstobedemonstratedExamplesKnowledge20%• Straightrecall• Identificationofcorrectformulaontheinformationsheet(nochangingofthesubject)Useofmathematicalfacts• Appropriateuseofmathematicalvocabulary1.Writedownthedomainofthefunction  (Grade10)2.TheangleˆAOBsubtendedbyarcABatthecentreOofacircle.......RoutineProcedures35%• Estimationandappropriateroundingofnumbers• Proofsofprescribedtheoremsandderivationofformulae• Identificationanddirectuseofcorrectformulaontheinformationsheet(nochangingofthesubject)• Performwellknownprocedures• Simpleapplicationsandcalculationswhichmightinvolvefewsteps• Derivationfromgiveninformationmaybeinvolved• Identificationanduse(afterchangingthesubject)ofcorrectformula• Generallysimilartothoseencounteredinclass1.Solvefor  (Grade10)2.Determinethegeneralsolutionoftheequation  (Grade11)2. ProvethattheangleˆAOBsubtendedbyarcABatthecentreOofacircleisdoublethesizeoftheangleˆACBwhichthesamearcsubtendsatthecircle.(Grade11)ComplexProcedures30%• Problemsinvolvecomplexcalculationsand/orhigherorderreasoning• Thereisoftennotanobviousroutetothesolution• Problemsneednotbebasedonarealworldcontext• Couldinvolvemakingsignificantconnectionsbetweendifferentrepresentations• Requireconceptualunderstanding1.Whatistheaveragespeedcoveredonaroundtriptoandfromadestinationiftheaveragespeedgoingtothedestinationisandtheaveragespeedforthereturnjourneyis(Grade11)2.Differentiatexx2)2(+withrespecttox.(Grade12)ProblemSolving15%• Non-routineproblems(whicharenotnecessarilydifficult)• Higherorderreasoningandprocessesareinvolved• MightrequiretheabilitytobreaktheproblemdownintoitsconstituentpartsSupposeapieceofwirecouldbetiedtightlyaroundtheearthattheequator.Imaginethatthiswireisthenlengthenedbyexactlyonemetreandheldsothatitisstillaroundtheearthattheequator.Wouldamousebeabletocrawlbetweenthewireandtheearth?Whyorwhynot?(Anygrade)TheProgrammeofAssessmentisdesignedtosetformalassessmenttasksinallsubjectsinaschoolthroughouttheyear.
  59. 59. MATHEMATICS GRADES 10-1254 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)a) NumberofAssessmentTasksandWeighting:Learnersareexpectedtohaveseven(7)formalassessmenttasksfortheirschool-basedassessment.Thenumberoftasksandtheirweightingarelistedbelow:GRADE10GRADE11GRADE12TASKSWEIGHT(%)TASKSWEIGHT(%)TASKSWEIGHT(%)School-basedAssessmentTerm1Project/InvestigationTest2010Project/InvestigationTest2010TestProject/InvestigationAssignment102010Term2Assignment/TestMid-YearExamination1030Assignment/TestMid-YearExamination1030TestMid-YearExamination1015Term3TestTest1010TestTest1010TestTrialExamination1025Term4Test10Test10School-basedAssessmentmark100100100School-basedAssessmentmark(as%ofpromotionmark)25%25%25%End-of-yearexaminations75%75%Promotionmark100%100%Note:• Althoughtheproject/investigationisindicatedinthefirstterm,itcouldbescheduledinterm2.OnlyONEproject/investigationshouldbesetperyear.• TestsshouldbeatleastONEhourlongandcountatleast50marks.• Projectorinvestigationmustcontribute25%ofterm1markswhilethetestmarkscontribute75%oftheterm1marks.Thecombination(25%and75%)ofthemarksmustappearinthelearner’sreport.• Nonegraphicandnoneprogrammablecalculatorsareallowed(forexample,tofactorise  ,ortofindrootsofequations)willbeallowed.Calculatorsshouldonlybeusedtoperformstandardnumericalcomputationsandtoverifycalculationsbyhand.• FormulasheetmustnotbeprovidedfortestsandforfinalexaminationsinGrades10and11.
  60. 60. MATHEMATICS GRADES 10-1255CAPSb) Examinations:In Grades 10, 11 and 12, 25% of the final promotion mark is a year mark and 75% is an examination mark.All assessments in Grade 10 and 11 are internal while in Grade 12 the 25% year mark assessment is internally setand marked but externally moderated and the 75% examination is externally set, marked and moderated.Mark distribution for Mathematics NCS end-of-year papers: Grades 10-12PAPER 1: Grades 12: bookwork: maximum 6 marksDescription Grade 10 Grade 11 Grade. 12Algebra and equations (and inequalities) 30 ± 3 45 ± 3 25 ± 3Patterns and sequences 15 ± 3 25 ± 3 25 ± 3Finance and growth 10 ± 3Finance, growth and decay 15 ± 3 15 ± 3Functions and graphs 30 ± 3 45 ± 3 35 ± 3Differential Calculus 35 ± 3Probability 15 ± 3 20 ± 3 15 ± 3TOTAL 100 150 150PAPER 2: Grades 11 and 12: theorems and/or trigonometric proofs: maximum 12 marksDescription Grade 10 Grade 11 Grade 12Statistics 15 ± 3 20 ± 3 20 ± 3Analytical Geometry 15 ± 3 30 ± 3 40 ± 3Trigonometry 40 ± 3 50 ± 3 40 ± 3Euclidean Geometry and Measurement 30 ± 3 50 ± 3 50 ± 3TOTAL 100 150 150Note:• Modelling as a process should be included in all papers, thus contextual questions can be set on any topic.• Questions will not necessarily be compartmentalised in sections, as this table indicates. Various topics can be integratedin the same question.• Formula sheet must not be provided for tests and for final examinations in Grades 10 and 11. 4.5 Recording and reporting• Recording is a process in which the teacher is able to document the level of a learner’s performance in aspecific assessment task.- It indicates learner progress towards the achievement of the knowledge as prescribed in theCurriculum and Assessment Policy Statements.- Records of learner performance should provide evidence of the learner’s conceptual progressionwithin a grade and her / his readiness to progress or to be promoted to the next grade.- Records of learner performance should also be used to monitor the progress made by teachers andlearners in the teaching and learning process.• Reporting is a process of communicating learner performance to learners, parents, schools and otherstakeholders. Learner performance can be reported in a number of ways.
  61. 61. MATHEMATICS GRADES 10-1256 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)-- These include report cards, parents’ meetings, school visitation days, parent-teacher conferences,phone calls, letters, class or school newsletters, etc.-- Teachers in all grades report percentages for the subject. Seven levels of competence have beendescribed for each subject listed for Grades R-12. The individual achievement levels and theircorresponding percentage bands are shown in the Table below.CODES AND PERCENTAGES FOR RECORDING AND REPORTINGRATING CODE DESCRIPTION OF COMPETENCE PERCENTAGE7 Outstanding achievement 80 – 1006 Meritorious achievement 70 – 795 Substantial achievement 60 – 694 Adequate achievement 50 – 593 Moderate achievement 40 – 492 Elementary achievement 30 – 391 Not achieved 0 - 29Note: The seven-point scale should have clear descriptors that give detailed information for each level.Teachers will record actual marks for the task on a record sheet; and indicate percentages for each subjecton the learners’ report cards.4.6 Moderation of AssessmentModeration refers to the process that ensures that the assessment tasks are fair, valid and reliable. Moderationshould be implemented at school, district, provincial and national levels. Comprehensive and appropriate moderationpractices must be in place to ensure quality assurance for all subject assessments.4.7 GeneralThis document should be read in conjunction with:4.7.1 National policy pertaining to the programme and promotion requirements of the National Curriculum StatementGrades R – 12; and4.7.2 The policy document, National Protocol for Assessment Grades R – 12.

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