Class 12 Mathematics

Types of relations and functions, and one-one, onto and composite functions.

Domains, ranges and the properties of the inverse trigonometric functions.

Types of matrices, matrix algebra, and the transpose, symmetric and skew-symmetric matrices.

Properties of determinants, cofactors, the adjoint and inverse of a matrix, and solving linear equations.

Continuity, differentiability, the chain rule, and derivatives of implicit and inverse functions.

Rate of change, increasing and decreasing functions, maxima and minima, and approximations.

Integration as anti-differentiation, methods of integration, and definite integrals.

Using definite integrals to find the area under curves and between curves.

Order and degree, the general and particular solution, and solving first-order differential equations.

Vectors and scalars, the dot and cross product, and the scalar triple product.

Direction cosines and ratios, and the equations of a line and a plane in space.

Formulating and graphically solving linear programming problems.

Conditional probability, Bayes’ theorem, and random variables and their probability distributions.