CLASS - XII
SEMESTER – III
SUBJECT: MATHEMATICS ( MATH )
FULL MARKS: 40 CONTACT HOURS: 100 Hours
COURSE CODE : THEORY
CONTACT
UNIT No. TOPICS MARKS
HOURS
UNIT-I RELATIONS AND FUNCTIONS 20 7
1. Relations and Functions
Types of relations: Reflexive, symmetric, transitive and
10 4
equivalence relations. One-to-one and onto functions, composite
functions, inverse of a function.
2. Inverse Trigonometric Functions
Definition, range, domain, principal value branches. Graphs of
10 3
inverse trigonometric functions. Elementary properties of
inverse trigonometric functions.
UNIT- II ALGEBRA 25 10
1. Matrices
Concept, notation, order, equality, types of matrices, zero
matrix, identity matrix, transpose of a matrix, symmetric and
skew-symmetric matrices. Addition, multiplication and scalar
multiplication of matrices; properties of addition, multiplication
and scalar multiplication. Simple properties of addition, 15 6
multiplication and scalar multiplication. Non-commutativity of
multiplication of matrices. Existence of non-zero matrices whose
product is a zero matrix (restrict to square matrices of order 2).
Invertible matrices and proof of the uniqueness of inverse (if it
exists). (Here all matrices will have real entries).
2. Determinants
Determinant of a square matrix (upto 3 × 3 matrices), properties
of determinants, minors, cofactors and application of
determinants in finding the area of a triangle.
Adjoint and inverse of a square matrix. Consistency, 10 4
inconsistency and number of solutions of system of linear
equations by examples. Solutions of system of linear equations
in two or three variables (having unique solution) using inverse
of a matrix.
SEMESTER – III
SUBJECT: MATHEMATICS ( MATH )
FULL MARKS: 40 CONTACT HOURS: 100 Hours
COURSE CODE : THEORY
CONTACT
UNIT No. TOPICS MARKS
HOURS
UNIT-I RELATIONS AND FUNCTIONS 20 7
1. Relations and Functions
Types of relations: Reflexive, symmetric, transitive and
10 4
equivalence relations. One-to-one and onto functions, composite
functions, inverse of a function.
2. Inverse Trigonometric Functions
Definition, range, domain, principal value branches. Graphs of
10 3
inverse trigonometric functions. Elementary properties of
inverse trigonometric functions.
UNIT- II ALGEBRA 25 10
1. Matrices
Concept, notation, order, equality, types of matrices, zero
matrix, identity matrix, transpose of a matrix, symmetric and
skew-symmetric matrices. Addition, multiplication and scalar
multiplication of matrices; properties of addition, multiplication
and scalar multiplication. Simple properties of addition, 15 6
multiplication and scalar multiplication. Non-commutativity of
multiplication of matrices. Existence of non-zero matrices whose
product is a zero matrix (restrict to square matrices of order 2).
Invertible matrices and proof of the uniqueness of inverse (if it
exists). (Here all matrices will have real entries).
2. Determinants
Determinant of a square matrix (upto 3 × 3 matrices), properties
of determinants, minors, cofactors and application of
determinants in finding the area of a triangle.
Adjoint and inverse of a square matrix. Consistency, 10 4
inconsistency and number of solutions of system of linear
equations by examples. Solutions of system of linear equations
in two or three variables (having unique solution) using inverse
of a matrix.
