<ul><li> 1. http://samacheerkalvi.net/X Std. SYLLABUSTransactional Expected Learning No. ofTopicContentTeachingOutcomesPeriods Strategyi. Introduction Torevisethebasiccon-Use Vennii. Properties of operations oncepts on Set operations diagrams for all sets Tounderstandtheproper- illustrationsiii.DeMorganslaws-verifi-ties of operations of sets cation using example Venn - commutative, associative, diagram anddistributiverestrictedGive examples tothreesets. I. Sets and Functionsiv. Formula forof functions fromv. Functions Tounderstandthelawsofeconomics, medi- complementation of sets.cine, science etc. TounderstandDeMor- gans laws and demonstrat- ingthembyVenndiagram26 as well. Tosolvewordproblems usingtheformulaaswell as Venn diagram. Tounderstandthedefini- tion,typesandrepresenta- tion of functions. Tounderstandthetypes offunctionswithsimple examples.i. Introduction TounderstandtoidentifyUse pattern ap-ii. SequencesanArithmeticProgressionproachiii.ArithmeticProgression and a Geometric Progres-II. Sequences and Series of (A.P) sion. Use dot pattern asiv. Geometric Progression AbletoapplytofindtheteachingaidRealNumbers (G.P) nthtermofanArithmeticv. SeriesProgression and a Geomet- Use patterns to ric Progression.derive formulae27 Todeterminethesumof ntermsofanArithmetic Examplestobe Progression and a Geomet- given from real ric Progression.life situations Todeterminethesumof somefiniteseries.i. Solving linear equations Tounderstandtheideaabout Illustrativeii. Polynomials pair of linear equations in examples iii.Syntheticdivisiontwo unknowns. Solving aiv. Greatest common divisorpair of linear equations in Usechartsas III.Algebra (GCD) twovariablesbyelimination teachingaidsand Least common mul-methodandcrossmultipli- tiple (LCM) cationmethod.Recall GCD andv. Rational expressions Tounderstandtherelation- LCMofnumbersvi. Square rootshipbetweenzerosandco-initiallyvii. Quadratic Equations efficientsofapolynomial withparticularreferenceto quadraticpolynomials. (v)</li></ul><p> 2. http://samacheerkalvi.net/ Todeterminetheremain-Comparewithderandthequotientofoperations onthegivenpolynomial fractionsusingSyntheticDivisionMethod. TodeterminethefactorsofthegivenpolynomialusingSyntheticDivisionMethod. Abletounderstandthedif-ferencebetweenGCDandComparewiththeLCM, of rational expres-square root opera-sion. tion on numerals. Abletosimplifyrationalexpressions(SimpleProb- Help studentsvisualizethelems), III.Algebranature of roots Tounderstandsquarealgebraicallyandroots.graphically. Tounderstandthestandard 40form of a quadratic equa-tion . Tosolvequadraticequa-tions(onlyrealroot)-byfactorization,bycomplet-ingthesquareandbyusingquadratic formula. Abletosolvewordprob-lemsbasedonquadraticequations. Abletocorrelaterelation-shipbetweendiscriminantand nature of roots. AbletoFormquadraticequationwhentherootsare given. i. Introduction Abletoidentifytheorder Using of rect- ii. Typesofmatrices and formation of matrices angulararrayof iii.Additionandsubtraction Abletorecognizethetypesnumbers. iv. Multiplication of matrices v. Matrix equation Abletoaddandsubtract Using real lifethegivenmatrices. situations. TomultiplyamatrixbyaIV. Matricesscalar,andthetransposeof Arithmeticopera-a matrix. tionstobeused 16 Tomultiplythegivenmatrices (2x2; 2x3; 3x2Matrices). Usingmatrixmethodsolvetheequationsoftwovari-ables.(vi) 3. http://samacheerkalvi.net/i. Introduction Torecallthedistance Simple geometri-ii. Revision:Distancebe- betweentwopoints,andcal result related tween two points locatethemidpointoftwoto triangle andiii. Section formula, Mid given points. quadrilaterals to point formula, Centroid Todeterminethepoint beverifiedasap- formulaof division using section plications.iv. Area of a triangle andformula (internal). quadrilateral Tocalculatetheareaofa theformv. Straightline triangle.y = mx + ctobe V.CoordinateGeometry Todeterminetheslopeoftakenasthestart-alinewhentwopointsare ing pointgiven, equation is given. 25 Tofindanequationoflinewiththegiveninformation. Abletofindequationofa line in: slope-interceptform, point -slope form,two -point form, interceptform. Tofindtheequationofastraightlinepassingthroughapointwhichis(i)parallel (ii) perpendiculartoagivenstraightline.i.Basicproportionalitytheo- Tounderstandthetheo- Paper foldingrem(withproof)remsandapplythemto symmetryandii. Converse of Basic propor- solvesimpleproblemstransformationtionalitytheoremonly. techniquestobe(withproof) adopted.iii.AnglebisectortheoremFormal proof to(withproof-internalcase VI.Geometrybegivenonly)iv.ConverseofAnglebisec- Drawing of20tortheorem(withprooffigures-internalcaseonly)v.Similartriangles(theo- Stepbystepremswithoutproof) logicalproofwithdiagramstobeexplained anddiscussedi. Introduction Abletoidentifythe ByusingAlge-ii. Identities Trigonometricidentitiesbraicformulae VII.Trigonometryiii.Heightsanddistances andapplytheminsimple problems.Using trigonomet- Tounderstandtrigonomet- ric identities. 21 ricratiosandappliesthem tocalculateheightsandTheapproximate distances. nature of values (notmorethantworight tobeexplained triangles)(vii) 4. http://samacheerkalvi.net/ i. Introduction TodeterminevolumeandUse 3D models to ii. Surface Area and Volume surfaceareaofcylinder,createcombinedVIII. Mensuration ofCylinder,Cone,Sphere,cone,sphere,hemisphere,shapesHemisphere,Frustumfrustum iii. Surface area and volume VolumeandsurfaceareaUse models andofcombinedfiguresofcombinedfigures(onlypicturesadteach- iv. Invariant volumetwo). ing aids.24 Someproblemsrestricted to constant Volume. Chooseexamples from real life situ- ations. i. Introduction Abletoconstructtangents Tointroduce ii. Construction of tangentsto circles. algebraicverifica-to circles Abletoconstructtriangles, tionoflengthof IX.PracticalGeometry iii.ConstructionofTrianglesgivenitsbase,vertical tangent segments. iv. Constructionofcyclicangleattheoppositevertexquadrilateraland Recall related (a) medianproperties of (b)altitudeangles in a circle 15 (c)bisector. beforeconstruc- Abletoconstructacyclic tion. quadrilateral Recall relevant theoremsintheo- reticalgeometry i. Introduction AbletosolvequadraticInterpreting skills ii. Quadraticgraphs equationsthroughgraphsalsotobetaken iii.Somespecialgraphs Tosolvegraphicallythe careofgraphs X.Graphs equations of quadratics to . precedealgebraic Abletoapplygraphstotreatment. 10 solvewordproblems Real life situa- tionstobeintro- duced. i. Recall Measures of central TorecallMeanforgrouped Use real life situa-tendency and ungrouped data situa- tions like perfor- ii. Measures of dispersiontiontobeavoided).mance in exami-XI. Statistics iii.Coefficientofvariation Tounderstandtheconcept nation, sports, etc. ofDispersionandable16 tofindRange,Standard Deviation and Variance. Abletocalculatethecoef- ficientofvariation. i. Introduction TounderstandRandom Diagrams and ii. Probability-theoreticalap-experiments, Sample space investigationsproach andEventsMutuallyon coin tossing, XII.Probability iii.AdditionTheoremonExclusive, Complemen- diethrowingandProbabilitytary,certainandimpossible pickingupthe events. cards from a deck15 Tounderstandaddition ofcardsaretobe Theoremonprobability used. andapplyitinsolving somesimpleproblems. (viii) 5. http://samacheerkalvi.net/ CONTENTS1. SETS AND FUNCTIONS 1-33 1.1 Introduction1 1.2.Sets1 1.3.Operations on Sets3 1.4.Properties of Set Operations5 1.5.De Morgans Laws 12 1.6.Cardinality of Sets16 1.7.Relations19 1.8.Functions202. SEQUENCES AND SERIES OF REAL NUMBERS34-67 2.1. Introduction34 2.2. Sequences 35 2.3. Arithmetic Sequence 38 2.4. Geometric Sequence43 2.5. Series493. ALGEBRA68-117 3.1 Introduction 68 3.2 System of Linear Equations in Two Unknowns 69 3.3 Quadratic Polynomials80 3.4 Synthetic Division 82 3.5 Greatest Common Divisor and Least Common Multiple86 3.6 Rational Expressions 93 3.7 Square Root97 3.8 Quadratic Equations 1014. MATRICES118-139 4.1 Introduction118 4.2 Formation of Matrices 119 4.3 Types of Matrices 121 4.4 Operation on Matrices 125 4.5 Properties of Matrix Addition 128 4.6 Multiplication of Matrices130 4.7 Properties of Matrix Multiplication 132 (ix) 6. http://samacheerkalvi.net/5.COORDINATE GEOMETRY140-1705.1 Introduction 1405.2 Section Formula1405.3 Area of a Triangle 1475.4 Collinearity of Three Points 1485.5 Area of a Quadrilateral1485.6 Straight Lines 1515.7 General form of Equation of a Straight Line1646.GEOMETRY 171-1956.1 Introduction 1716.2 Similar Triangles1826.3 Circles and Tangents 1897.TRIGONOMETRY 196-2187.1 Introduction 1967.2 Trigonometric Identities 1967.3 Heights and Distances2058.MENSURATION219-2488.1 Introduction 2198.2 Surface Area 2198.3 Volume 2308.4 Combination of Solids2409.PRACTICAL GEOMETRY249- 2669.1 Introduction 2499.2 Construction of Tangents to a Circle 2509.3 Construction of Triangles2549.4 Construction of Cyclic Quadrilaterals25910. GRAPHS 267-27810.1 Introduction26710.2 Quadratic Graphs26710.3 Some special Graphs 27511. STATISTICS 279-29811.1 Introduction27911.2 Measures of Dispersion28012. PROBABILITY 299 - 31612.1 Introduction 299 12.2 ClassicalDefinitionofProbability 30212.3 Addition theorem on Probability309(x) 7. http://samacheerkalvi.net/1SETS AND FUNCTIONSA set is Many that allows itself to be thought of as a One - Georg CantorIntroductionSets1.1Introduction The concept of set is one of the fundamental conceptsProperties of set operations in mathematics. The notation and terminology of set theoryDe Morgans Laws is useful in every part of mathematics. So, we may say thatFunctions set theory is the language of mathematics. This subject, which originated from the works of George Boole (1815-1864) and Georg Cantor (1845-1918) in the later part of 19th century, has had a profound influence on the development of all branches of mathematics in the 20th century. It has helped in unifying many disconnected ideas and thus facilitated the advancement of mathematics. In class IX, we have learnt the concept of set, some GeorGe Boole operations like union, intersection and difference of two sets. Here, we shall learn some more concepts relating to sets and(1815-1864)Englandanother important concept in mathematics namely, function. First let us recall basic definitions with some examples. WeBoole believed that there wasa close analogy between symbols that denote all positive integers (natural numbers) by N and allrepresent logical interactions and real numbers by R .algebraic symbols. 1.2 SetsHe used mathematical symbols Definitionto express logical relations. Althoughcomputers did not exist in hisA set is a collection of well-defined objects. The objectsday, Boole would be pleased toin a set are called elements or members of that set.know that his Boolean algebraHere, well-defined means that the criteria foris the basis of all computer arithmetic. deciding if an object belongs to the set or not, should be As the inventor of Booleandefined without confusion.logic-the basis of modern digitalFor example, the collection of all tall people incomputer logic - Boole is regarded in Chennai does not form a set, because here, the deciding criteriahindsight as a founder of the field of tall people is not clearly defined. Hence this collection doescomputer science. not define a set.</p>