NCERT Class 11 Syllabus for Mathematics

CLASS XI
(Total Periods 180)

UNIT I: SETS AND FUNCTIONS

1. Sets (Periods 12)
Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of the
set of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union
and intersection of sets. Difference of sets. Complement of a set, Properties of Complement sets.

2. Relations and Functions (Periods 14)
Ordered pairs, Cartesian product of sets. Number of elements in the Cartesian product of two
finite sets. Cartesian product of the reals with itself (upto R × R × R).

Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Function as
a special kind of relation from one set to another. Pictorial representation of a function, domain,
co-domain and range of a function. Real valued function of the real variable, domain and range of
these functions, constant, identity, polynomial, rational, modulus, signum and greatest integer
functions with their graphs. Sum, difference, product and quotients of functions.

3. Trigonometric Functions (Periods 18)

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 and sketch of their
graphs. Expressing sin (x+ y) and cos (x + y) in terms of sin x, sin y,
cos x and cos y. Deducing the identities like following:

tan x ± tan y cot x cot y ∓ 1
tan (x + y) = 1 ∓ tan x × tan y , cot ( x ± y ) = cot y ± cot x

x+ y x− y x+ y x− y
sin x + sin y = 2 sin .cos , cos x + cos y = 2 cos cos
2 2 2 2

x+ y x− y x+ y x− y
sin x – sin y = 2 cos .sin , cos x − cos y = − 2 sin sin
2 2 2 2

Identities related to sin2x, cos2x, tan2x, sin3x, cos3x and tan3x. General solution of trigonometric
equations of the type sinθ = sin α, cosθ = cosα and tanθ = tan α. Proofs and simple applications
of sine and cosine formulae.

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