Overview

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Description

Relations and Functions

Types of relations: Reflexive, symmetric, transitive and equivalence relations
Binomial theorem
Inverse Trigonometric Functions
Definition, range, domain, principal value branches
Graphs of inverse trigonometric functions
Elementary properties of inverse trigonometric functions

Algebra

Matrices: Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric and skew symmetric matrices
Addition multiplication & properties of matrices
Determinants, properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle
Adjoint and inverse of a square matrix
Consistency, inconsistency and number of solutions of system of linear equations by examples
Solving system of linear equations in two or three variables using inverse of a matrix

Calculus

Continuity and Differentiability
Derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function
Concepts of exponential, logarithmic functions
Integrals, definite integrals as a limit of a sum
Fundamental Theorem of Calculus (without proof)
Applications in finding the area under simple curves, especially lines, arcs of circles/parabolas/ellipses
Differential Equations
Definition, order and degree, general and particular solutions of a differential equation
Formation of differential equation whose general solution is given

Vectors and three-dimensional geometry

Vectors and scalars
Magnitude and direction of a vector
Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point
Three-dimensional Geometry
Linear Programming

Probability

Multiplications theorem on probability. Conditional probability, independent events, total probability
Baye’s theorem
Random variable and its probability distribution, mean and variance of haphazard variable
Repeated independent (Bernoulli) trials and Binomial distribution