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

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

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

Algebra of functions - addition, subtraction, multiplication and quotient of functions, composition of functions, one to one and onto functions, Inverse of a function

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;

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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