Class 12 Mathematics Part 1

Relations, their types and equivalence, then functions, composition and invertible maps at the level of the CBSE Class 12 syllabus.

Principal value branches, graphs, complementary identities and simplification techniques for the six inverse trigonometric functions.

Matrix types, equality and the four operations, then transpose, symmetric and skew symmetric matrices and invertibility, with worked exercises.

Determinants of order two and three, their properties, area and collinearity, minors and cofactors, the adjoint and inverse, and solving linear systems by matrices.

Continuity and differentiability tests, the standard derivative rules, logarithmic differentiation, parametric curves and second order derivatives.

Related rates, increasing and decreasing functions, local and absolute extrema, tangents and normals, and optimisation word problems for the board exam.