CLASS-XII
MATHEMATICS (2021-22)
TERM - I
Unit-I: Relations and Functions
1. Relations and Functions
Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto
functions.
2. Inverse Trigonometric Functions
Definition, range, domain, principal value branch.
Unit-II: Algebra
1. Matrices
Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix,
symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and
multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Non-
commutativity of multiplication of matrices, Invertible matrices; (Here all matrices will have real entries)
2. Determinants
Determinant of a square matrix (up to 3 x 3 matrices), minors, co-factors and applications of
determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. 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
Continuity and differentiability, derivative of composite functions, chain rule, derivative of inverse
trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions.
Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions
expressed in parametric forms. Second order derivatives.
2. Applications of Derivatives
Applications of derivatives: increasing/decreasing functions, tangents and normals, 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).
Unit-V: Linear Programming
1. Linear Programming
Introduction, related terminology such as constraints, objective function, optimization, different types of
linear programming (L.P.) problems. Graphical method of solution for problems in two variables, feasible
and infeasible regions (bounded), feasible and infeasible solutions, optimal feasible solutions (up to
three non-trivial constraints).
TERM - II
Unit-III: Calculus
1. Integrals
Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by
partial fractions and by parts, Evaluation of simple integrals of the following types and problems based
on them.
Fundamental Theorem of Calculus (without proof).Basic properties of definite integrals and evaluation
of definite integrals.
2. Applications of the Integrals
Applications in finding the area under simple curves, especially lines, parabolas; area of circles /ellipses
(in standard form only) (the region should be clearly identifiable).
3. Differential Equations
Definition, order and degree, general and particular solutions of a differential equation. Solution of
differential equations by method of separation of variables, solutions of homogeneous differential
equations of first order and first degree of the type: ππ¦/ππ₯= π(y/x).
Solutions of linear differential equation
of the type:
dy/dx + py = q, where p and q are functions of x or constant.
Unit-IV: Vectors and Three-Dimensional Geometry
1. Vectors
Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a
vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point,
negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar,
position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation,
properties and application of scalar (dot) product of vectors, vector (cross) product of vectors.
2. Three - dimensional Geometry
Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation
of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation
of a plane. Distance of a point from a plane.
Unit-VI: Probability
1. Probability
Conditional probability, multiplication theorem on probability, independent events, total probability,
Bayesβ theorem, Random variable and its probability distribution.
Note: For activities NCERT Lab Manual may be referred
Assessment of Activity Work:
In first term any 4 activities and in second term any 4 activities shall be performed by the
student from the activities given in the NCERT Laboratory Manual for the respective class
(XI or XII) which is available on the link :
Record of the same may be kept by the
student. A term end test on the activity is to be conducted.
The weightage are as under:
ο· The activities performed by the student in each term and record keeping
: 3 marks
ο· Assessment of the activity performed during the term end test and Viva-voce
: 2 marks
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