Class 10 Cbse Maths Syllabus 2012
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The document outlines the mathematics curriculum for Class X, detailing the units of study including Number Systems, Algebra, Geometry, Trigonometry, Statistics, and Probability, with specified periods assigned for each topic. It includes information on concepts to be taught, proofs to be demonstrated, and problems to be solved, along with recommended textbooks for reference. The total assessment marks for the curriculum is 80, divided among various mathematical topics.
Class 10 Cbse Maths Syllabus 2012
- 1. w w w .edurite.com 105 CLASS X FirstTerm Marks : 80 UNITS MARKS I. NUMBER SYSTEMS 10 II. ALGEBRA 20 III. GEOMETRY 15 IV TRIGONOMETRY 20 V STATISTICS 15 TOTAL 80 UNIT I : NUMBER SYSTEMS 1. REAL NUMBERS (15) Periods Euclid'sdivisionlemma, FundamentalTheoremofArithmetic-statementsafterreviewingworkdoneearlier andafterillustratingandmotivatingthroughexamples,Proofsofresults-irrationalityof√2,√3,√5,decimal expansionsofrationalnumbersintermsofterminating/non-terminatingrecurringdecimals. UNIT II : ALGEBRA 1. POLYNOMIALS (7) Periods Zerosofapolynomial.Relationshipbetweenzerosandcoefficientsofquadraticpolynomials.Statementand simpleproblemsondivisionalgorithmforpolynomialswithrealcoefficients. 2. PAIR OFLINEAR EQUATIONS IN TWO VARIABLES (15) Periods Pair of linear equations in two variables and their graphical solution. Geometric representation of different possibilitiesofsolutions/inconsistency.
- 2. w w w .edurite.com 106 Algebraicconditionsfornumberofsolutions.Solutionofpairoflinearequationsintwovariablesalgebraically -bysubstitution,byeliminationandbycrossmultiplication.Simplesituationalproblemsmustbeincluded. Simpleproblemsonequationsreducibletolinearequationsmaybeincluded. UNIT III : GEOMETRY 1. TRIANGLES (15) Periods Definitions,examples,counterexamplesofsimilartriangles. 1. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. 2. (Motivate)Ifalinedividestwosidesofatriangleinthesame ratio,thelineisparalleltothethirdside. 3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportionalandthetrianglesaresimilar. 4. (Motivate)Ifthecorrespondingsidesoftwotrianglesareproportional,theircorrespondinganglesare equalandthetwotrianglesaresimilar. 5. (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including theseanglesareproportional,thetwotrianglesaresimilar. 6. (Motivate) If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse,thetrianglesoneachsideoftheperpendiculararesimilartothewholetriangleandtoeach other. 7. (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares on their correspondingsides. 8. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. 9. (Prove)Inatriangle,ifthesquareononesideisequaltosumofthesquaresontheothertwosides,the anglesoppositetothefirstsideisarighttraingle. UNIT IV : TRIGONOMETRY 1. INTRODUCTION TO TRIGONOMETRY (10) Periods Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios, whichever are defined at 0o & 90o .Values (with proofs) of the trigonometric ratios of 30o , 45o & 60o . Relationships between the ratios. 2. TRIGONOMETRIC IDENTITIES (15) Periods Proof and applications of the identity sin2 A + cos2 A= 1. Only simple identities to be given.Trigonometric ratiosofcomplementaryangles.
- 3. w w w .edurite.com 107 UNIT VII : STATISTICS AND PROBABILITY 1. STATISTICS (18) Periods Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph. SecondTerm Marks : 80 UNITS MARKS II. ALGEBRA(Contd.) 20 III. GEOMETRY(Contd.) 16 IV. TRIGONOMETRY(Contd.) 08 V. PROBABILITY 06 VI. COORDINATE GEOMETRY 10 VII. MENSU RATION 20 TOTAL 80 UNIT II : ALGEBRA (Contd.) 3. QUADRATIC EQUATIONS (15) Periods Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solution of the quadratic equations (only real roots) by factorization, by completing the square and by using quadratic formula. Relationship betweendiscriminantandnatureofroots. Problems related to day to day activities to be incorporated. 4. ARITHMETIC PROGRESSIONS (8) Periods MotivationforstudyingAP.Derivationofstandardresultsoffindingthenth termandsumoffirstnterms. UNIT III : GEOMETRY (Contd.) 2. CIRCLES (8) Periods Tangents to a circle motivated by chords drawn from points coming closer and closer to the point. 1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact. 2. (Prove) The lengths of tangents drawn from an external point to circle are equal.
- 4. w w w .edurite.com 108 3. CONSTRUCTIONS (8) Periods 1. Divisionofalinesegmentinagivenratio(internally) 2. Tangent to a circle from a point outside it. 3. Constructionofatrianglesimilartoagiventriangle. UNIT IV : TRIGONOMETRY 3. HEIGHTSAND DISTANCES (8) Periods Simpleandbelievableproblemsonheightsanddistances.Problemsshouldnotinvolvemorethantworight triangles.Angles of elevation / depression should be only 30o , 45o , 60o . UNIT V : STATISTICS AND PROBABILITY 2. PROBABILITY (10) Periods Classical definition of probability. Connection with probability as given in Class IX. Simple problems on singleevents,notusingsetnotation. UNIT VI : COORDINATE GEOMETRY 1. LINES (In two-dimensions) (14) Periods Reviewtheconceptsofcoordinategeometrydoneearlierincludinggraphsoflinearequations.Awarenessof geometrical representation of quadratic polynomials. Distance between two points and section formula (internal).Areaofatriangle. UNIT VII : MENSURATION 1. AREAS RELATED TO CIRCLES (12) Periods Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas and perimeter/circumferenceoftheabovesaidplanefigures.(Incalculatingareaofsegmentofacircle,problems should be restricted to central angle of 60o , 90o & 120o only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.) 2. SURFACEAREASAND VOLUMES (12) Periods (i) Problems on finding surface areas and volumes of combinations of any two of the following: cubes, cuboids,spheres,hemispheresandrightcircularcylinders/cones.Frustumofacone. (ii) Problemsinvolvingconvertingonetypeofmetallicsolidintoanotherandothermixedproblems.(Problems withcombinationofnotmorethantwodifferentsolidsbetaken.)
- 5. w w w .edurite.com 109 RECOMMENDED BOOKS 1. Mathematics -Textbook for class IX - NCERTPublication 2. Mathematics -Textbook for class X - NCERTPublication 3. GuidelinesforMathematicslaboratoryinschools,classIX-CBSEPublication 4. GuidelinesforMathematicslaboratoryinschools,classX-CBSEPublication 5. Ahandbookfordesigningmathematicslaboratoryinschools-NCERTPublication 6. Laboratory manual - Mathematics, secondary stage - NCERTPublication.