NCERT Class 12 Syllabus for Mathematics

CLASS XII

(Total Periods 180)

UNIT I: RELATIONS AND FUNCTIONS

1. Relations and Functions (Periods 10)
Types of relations: Reflexive, symmetric, transitive and equivalence relations. One to one and onto
functions, composite functions, inverse of a function. Binary operations.

2. Inverse Trigonometric Functions (Periods 12)
Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions.
Elementary properties of inverse trigonometric functions.

UNIT II: ALGEBRA

1. Matrices (Periods 18)
Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric
and skew symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple
properties of addition, multiplication and scalar multiplication. Non-commutativity of multiplication
of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square
matrices of order 2). Concept of elementary row and column operations. Invertible matrices and
proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

2. Determinants (Periods 20)
Determinant of a square matrix (up to 3 × 3 matrices), 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 (having unique solution) using inverse of
a matrix.

UNIT III: CALCULUS

1. Continuity and Differentiability (Periods 18)
Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse
trigonometric functions, derivative of implicit function. Concepts of exponential, logarithmic functions.
Derivatives of logex and ex. Logarithmic differentiation. Derivative of functions expressed in parametric
forms. Second order derivatives. Rolle’s and Lagrange’s Mean Value Theorems (without proof)
and their geometric interpretations.

2. Applications of Derivatives (Periods 10)
Applications of derivatives: Rate of change, increasing/decreasing functions, tangents and normals,
approximation, maxima and minima (first derivative test motivated geometrically and second derivative
test given as a provable tool). Simple problems (that illustrate basic principles and understanding of
the subject as well as real-life situations).

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