11thMat-1 Course Topics
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Unit-1 Basic Algebra |
Real Numbers - Revision : Rational, Irrational Numbers,
Expressing inequalities like or using
intervals; |
Absolute value of x; Exponents - Revision:
Properties of exponents, Converting radicals/surds to
exponents. Rationalizing fractions with surds;
Polynomials - Addition, multiplication and factorisation |
Method of
undetermined coefficients to find a polynomial of given
degree; Rational Expressions - Simplification of rational
expressions by factorization |
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Partial fractions: linear
and quadratic factors; Graphs - Graphical
representation of data, Interpreting a graph and
answering questions based on it |
Equations and simple
inequalitiesroots of Linear Equations, quadratic
equations, roots of a factored polynomial equation;
solving equations with radicals and absolute value; |
solving simple linear inequalities, graphical representation of equations and inequalities |
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Unit 2 :
Sets , Relations and Functions |
Sets - recalling: Definitions and Examples, types of sets,algebra of sets, De Morgan Laws, venn diagrams, practicalproblems; Intervals - open and closed intervals, other types of intervals, neighbourhood of a Point |
Cartesian product of sets - definition and examples; Relations -special relations: reflexive, symmetric, transitive, antisymmetric and equivalence relations |
Functions and
Graphs of Algebraic functions - functions as a formula,
real valued functions, identity function, polynomial
functions, rational functions, absolute value functions,
Signum functions, greatest integer functions |
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Algebra of
functions - addition, subtraction, multiplication and
quotient of functions, composition of functions, one to one
and onto functions, Inverse of a function |
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Unit 3 :
Trigonometry |
Basic concepts - angles, signs of an angle, degree and radian measures, trigonometric rations for all angles, basic trigonometric identities; Formulae for sum of angles and sum and products of trigonometric ratios |
formulae for sin (A+B) , cos(a+b), tan(A+B), sin2A, cos2A, tan2A, Sin3A, cos3A, tan3A, sum and product formulae: sinC +/- sinD, cosC+/- cosD sinAcosB, cosAcosB,sinAsinB; |
trigonometric equations - general solutons of the trigonometric equations; |
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Unit 3 : Trigonometry |
Properties of Triangles - sine and cosine rule: projection and area formulae, application to triangles; |
Inverse trigonometric functions - definitions, Identities and simple problems. |
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