CBSE Class 12 Term Wise Syllabus 2021-22 Mathematics

MATHEMATICS (XI-XII)
(Code No. 041)
Session – 2021-22

The Syllabus in the subject of Mathematics has undergone changes from time to time in accordance with
growth of the subject and emerging needs of the society. Senior Secondary stage is a launching stage
from where the students go either for higher academic education in Mathematics or for professional
courses like Engineering, Physical and Biological science, Commerce or Computer Applications. The
present revised syllabus has been designed in accordance with National Curriculum Framework 2005 and
as per guidelines given in Focus Group on Teaching of Mathematics 2005 which is to meet the emerging
needs of all categories of students. Motivating the topics from real life situations and other subject areas,
greater emphasis has been laid on application of various concepts.

Objectives

The broad objectives of teaching Mathematics at senior school stage intend to help the students:

 to acquire knowledge and critical understanding, particularly by way of motivation and
visualization, of basic concepts, terms, principles, symbols and mastery of underlying processes
and skills.
 to feel the flow of reasons while proving a result or solving a problem.
 to apply the knowledge and skills acquired to solve problems and wherever possible, by more
than one method.
 to develop positive attitude to think, analyze and articulate logically.
 to develop interest in the subject by participating in related competitions.
 to acquaint students with different aspects of Mathematics used in daily life.
 to develop an interest in students to study Mathematics as a discipline.
 to develop awareness of the need for national integration, protection of environment,
observance of small family norms, removal of social barriers, elimination of gender biases.
 to develop reverence and respect towards great Mathematicians for their contributions to the
field of Mathematics.

COURSE STRUCTURE
CLASS XI (2021-22)
TERM - I

One Paper
90 Minutes Max Marks: 40
No. Units Marks
I. Sets and Functions 11
II. Algebra 13
III. Coordinate Geometry 6
IV. Calculus 4
V. Statistics and Probability 6
Total 40
Internal Assessment 10
Total 50
*No chapter-wise weightage. Care to be taken to cover all the chapters.

Unit-I: Sets and Functions

1. Sets

Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of a set
of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and
Intersection of sets.

2. Relations & Functions

Ordered pairs. Cartesian product of sets. Number of elements in the Cartesian product of two finite sets.
Cartesian product of the set of reals with itself ( R x R only).Definition of relation, pictorial diagrams, domain,
co-domain and range of a relation. Function as a special type of relation. Pictorial representation of a
function, domain, co-domain and range of a function. Real valued functions, domain and range of these
functions, constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest
integer functions, with their graphs.

Unit-II: Algebra

1. Complex Numbers and Quadratic Equations

Need for complex numbers, especially√−1, to be motivated by inability to solve some of the quardratic
equations. Algebraic properties of complex numbers. Argand plane. Statement of Fundamental Theorem
of Algebra, solution of quadratic equations (with real coefficients) in the complex number system.

2. Sequence and Series

Sequence and Series. Arithmetic Progression (A. P.). Arithmetic Mean (A.M.) Geometric Progression
(G.P.), general term of a G.P., sum of n terms of a G.P., infinite G.P. and its sum, geometric mean (G.M.),
relation between A.M. and G.M.

Unit-III: Coordinate Geometry

1. Straight Lines

Brief recall of two dimensional geometry from earlier classes. Slope of a line and angle between two lines.
Various forms of equations of a line: parallel to axis, point -slope form, slope-intercept form, two-point form,
intercept form and normal form. General equation of a line. Distance of a point from a line.

Unit-IV: Calculus
1. Limits
Intuitive idea of limit. Limits of polynomials and rational functions trigonometric, exponential and
logarithmic functions
Unit-V: Statistics and Probability
1. Statistics

Measures of Dispersion: Range, mean deviation, variance and standard deviation of ungrouped/grouped
data.

INTERNAL ASSESSMENT 10 MARKS
Periodic Test 5 Marks
Mathematics Activities: Activity file record +Term end assessment of one activity & Viva
5 Marks
Note: For activities NCERT Lab Manual may be referred

TERM - II

One Paper Max Marks: 40

No. Units Marks
I. Sets and Functions (Cont.) 8
II. Algebra (Cont.) 11
III. Coordinate Geometry (Cont.) 9
IV. Calculus (Cont.) 6
V. Statistics and Probability (Cont.) 6
Total 40
Internal Assessment 10
Total 50

Unit-I: Sets and Functions

1. Trigonometric Functions

Positive and negative angles. Measuring angles in radians and in degrees and conversion from one
measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity
sin2x + cos2x = 1, for all x. Signs of trigonometric functions. Domain and range of trigonometric functions
and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple
applications. Deducing identities like the following:

tan x ± tan y cot x cot y ∓ 1
tan(x ± y) = , cot(x ± y) =
1 ∓ tan x tan y cot y ± cot x
1 1
sinα ± sinβ = 2sin (α ± β)cos (α ∓ β)
2 2
1 1
cosα + cosβ = 2cos (α + β)cos (α − β)
2 2
1 1
𝑐𝑜𝑠𝛼 − 𝑐𝑜𝑠𝛽 = −2𝑠𝑖𝑛 (𝛼 + 𝛽)𝑠𝑖𝑛 (𝛼 − 𝛽)
2 2

Identities related to sin2x, cos2x, tan2 x, sin3x, cos3x and tan3x.

Unit-II: Algebra
1. Linear Inequalities
Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the
number line. Graphical solution of linear inequalities in two variables. Graphical method of finding a solution
of system of linear inequalities in two variables.

2. Permutations and Combinations
Fundamental principle of counting. Factorial n. (n!) Permutations and combinations, formula
for nPr and nCr, simple applications.

Unit-III: Coordinate Geometry
1. Conic Sections
Sections of a cone: circles, ellipse, parabola, hyperbola. Standard equations and simple properties of
parabola, ellipse and hyperbola. Standard equation of a circle.

2. Introduction to Three-dimensional Geometry
Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two
points and section formula.
Unit-IV: Calculus
1. Derivatives
Derivative introduced as rate of change both as that of distance function and geometrically. Definition of
Derivative, relate it to scope of tangent of the curve, derivative of sum, difference, product and quotient of
functions. Derivatives of polynomial and trigonometric functions.

Unit-V: Statistics and Probability
1. Probability

Random experiments; outcomes, sample spaces (set representation). Events; occurrence of events, ‘not’,
‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Probability of an event, probability of
‘not’, ‘and’ and ‘or’ events.

INTERNAL ASSESSMENT 10 MARKS
Periodic Test 5 Marks
Mathematics Activities: Activity file record +Term end assessment of one activity & Viva
5 Marks
Note: For activities NCERT Lab Manual may be referred
 Please refer the guidelines given under XII Mathematics Syllabus:

CLASS-XII
MATHEMATICS (2021-22)
TERM - I

One Paper
90 minutes Max Marks: 40
No. Units Marks
I. Relations and Functions 08
II. Algebra
10
III. Calculus
17
V. Linear Programming
05
Total
40
Internal Assessment
10
Total 50

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).

INTERNAL ASSESSMENT 10 MARKS
Periodic Test 5 Marks
Mathematics Activities: Activity file record +Term end assessment of one activity & Viva
5 Marks
Note: For activities NCERT Lab Manual may be referred

TERM - II

One Paper
Max Marks: 40

No. Units Marks
III. Calculus
18
IV. Vectors and Three-Dimensional Geometry
14
VI. Probability
8
Total
40
Internal Assessment
10
Total 50
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.
dx dx dx dx dx
∫ 2 2,
∫ ,∫ ,∫ 2 ,∫
x ±a √x 2 ± a2 √a2 − x 2 ax + bx + c √ax 2+bx+c
px + q px + q
∫ dx, ∫ dx, ∫ √a2 ± x 2 dx, ∫ √x 2 − a2 dx
ax 2 + bx + c √ax 2+ bx + c

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
𝑑𝑦
equations of first order and first degree of the type: 𝑑𝑥 = 𝑓(y/x). Solutions of linear differential equation

of the type:
dy
+ py = q, where p and q are functions of x or constant.
dx

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,
Bayes’ theorem, Random variable and its probability distribution.

INTERNAL ASSESSMENT 10 MARKS
Periodic Test 5 Marks
Mathematics Activities: Activity file record +Term end assessment of one activity & Viva
5 Marks

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 :
http://www.ncert.nic.in/exemplar/labmanuals.htmla 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:
 The activities performed by the student in each term and record keeping
: 3 marks
 Assessment of the activity performed during the term end test and Viva-voce
: 2 marks

Prescribed Books:

1) Mathematics Textbook for Class XI, NCERT Publications
2) Mathematics Part I - Textbook for Class XII, NCERT Publication
3) Mathematics Part II - Textbook for Class XII, NCERT Publication
4) Mathematics Exemplar Problem for Class XI, Published by NCERT
5) Mathematics Exemplar Problem for Class XII, Published by NCERT
6) Mathematics Lab Manual class XI, published by NCERT
7) Mathematics Lab Manual class XII, published by NCERT