Relations and Functions: This unit extends the concepts of relations and functions from class 11. It covers the topics such as types of relations, reflexive, symmetric, transitive and equivalence relations, one to one and onto functions, composite functions, inverse of a function, binary operations, inverse trigonometric functions and their properties.
Algebra: This unit extends the concepts of algebra from class 11. It covers the topics such as matrices and their types, operations on matrices, transpose of a matrix, symmetric and skew symmetric matrices, elementary operation on a matrix, inverse of a matrix, determinants and their properties, minors, cofactors and applications of determinants in finding the area of a triangle, adjoint and inverse of a square matrix, consistency and inconsistency of a system of linear equations, solution of linear equations in two or three variables using inverse of a matrix.
Calculus: This unit extends the concepts of calculus from class 11. It covers the topics such as continuity and differentiability of a function, derivative of composite functions, implicit functions, exponential and logarithmic functions, derivatives of inverse trigonometric functions, derivative of a function with respect to another function, derivative of a vector valued function, second order derivatives, Leibnitz’s theorem, mean value theorem, Taylor’s theorem, maxima and minima of a function in an interval and in a closed domain, indeterminate forms, L’Hospital’s rule, integration as inverse process of differentiation, integration of a variety of functions by substitution, by partial fractions and by parts, evaluation of simple integrals, fundamental theorem of calculus, basic properties of definite integrals and evaluation of definite integrals, application of integrals in finding the area under simple curves, area between two curves, volume of solids of revolution, differential equations and their formation, order and degree of a differential equation, general and particular solutions of a differential equation, methods of solving first order, first degree differential equations, homogeneous differential equations, linear differential equations, and differential equations with variable separable.
Vectors and Three-Dimensional Geometry: This unit introduces the concepts of vectors and three-dimensional geometry. It covers the topics such as vectors and scalars, magnitude and direction of a vector, types of vectors, equal vectors, unit vectors, zero vector, position vector, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio, scalar (dot) product of vectors, projection of a vector on a line, vector (cross) product of vectors, scalar triple product and vector triple product, direction cosines and direction ratios of a line, equation of a line in space, angle between two lines, shortest distance between two lines, equation of a plane, distance of a point from a plane, angle between two planes, angle between a line and a plane, and coplanarity of two lines.
Linear Programming: This unit introduces the concepts of linear programming and its applications. It covers the topics such as linear programming problems and their mathematical formulation, graphical method of solving linear programming problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions, and applications of linear programming in various areas.
Probability: This unit extends the concepts of probability from class 11. It covers the topics such as conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, random variable and its probability distribution, mean and variance of a random variable, repeated independent trials and Binomial distribution.