Syllabus CBSE Class 12th
Mathematics
Units & Marks:
- RELATIONS AND FUNCTIONS - 10 Marks
- ALGEBRA - 13 Marks
- CALCULUS - 44 Marks
- VECTORS AND THREE - DIMENSIONAL GEOMETRY - 17 Marks
- LINEAR PROGRAMMING - 06 Marks
- PROBABILITY - 10 Marks
Total : 100 Marks
UNIT I. RELATIONS AND FUNCTIONS
1. Relations and Functions : (10) Periods
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: (12) Periods
Definition, range, domain, principal value branches. Graphs of inverse
trigonometric functions. Elementary properties of inverse trigonometric
functions.
UNIT-II: ALGEBRA
1. Matrices: (18) Period
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: (20) Periods
Determinant of a square matrix (up to 3 x 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.