Class 12 Mathematics Notes

Types of relations, equivalence relations, one-one and onto functions, and composition and invertibility.

Principal value branches, graphs and elementary properties of inverse trigonometric functions.

Types of matrices, operations, transpose, symmetric and skew-symmetric matrices and invertibility.

Determinants up to order 3, area of a triangle, minors, cofactors, adjoint, inverse and solving equations.

Continuity, chain rule, implicit, inverse-trigonometric, exponential and logarithmic differentiation.

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

Integration as anti-derivative, substitution, partial fractions, by parts and definite integrals.

Area under simple curves such as lines, circles, parabolas and ellipses.

Order and degree, general and particular solutions, separable, homogeneous and linear equations.

Vectors, components, section formula, and scalar (dot) and vector (cross) products.

Direction cosines and ratios, equations of a line, angle between lines and shortest distance.

Formulating LPP, the graphical method, feasible region and optimal solutions.

Conditional probability, multiplication theorem, independent events and Bayes’ theorem.