# CBSE Class 11 Mathematics Syllabus for 2022-23

2022-23 Reduced Syllabus

We have also provided the syllabus for the 2021-22 session that was previously restored so that you can compare the deleted and added topics.

2021-22 Reduced Syllabus

<red> Marked in red: <red> Topics<red> removed <red>for 2021-22

Units Unit Names Marks
Term I Term II
I Sets and Functions 11 08
II Algebra 13 11
III Coordinate Geometry 06 09
IV Calculus 04 06
V Mathematics Reasoning Deleted for 2021-22
VI Statistics and Probability 06 06
INTERNAL ASSESSMENT
(Periodic Test (05) + Activity File Record + Term-end Assessment + Viva (05))
10 10
TOTAL 100

### TERM I

#### 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. <red> Difference of sets. Complement of a set. Properties of Complement. <red>

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) <red> (upto R x R x R).<red> 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. <red> Sum, difference, product and quotients of functions. <red>

#### Unit II: Algebra

<red> 1. Principle of Mathematical Induction <red>

<red> Process of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers. The principle of mathematical induction and simple applications. <red>

2. Complex Numbers and Quadratic Equations

Need for complex numbers, especially√−1, to be motivated by inability to solve some of the quadratic equations. Algebraic properties of complex numbers.Argand plane and polar representation of complex numbers.Statement of Fundamental Theorem of Algebra, solution of quadratic equations (with real coefficients) in the complex number system. <red> Square root of a complex number. <red>

6. 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. <red> Formulae for the following special sums. <red>

#### Unit III: Coordinate Geometry

1. Straight Lines

Brief recall of two dimensional geometry from earlier classes. <red> Shifting of origin. <red> 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. <red> Equation of family of lines passing through the point of intersection of two lines. <red> 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 VI: Statistics and Probability

1. Statistics

Measures of Dispersion: Range, Mean deviation, variance and standard deviation of ungrouped/ grouped data. <red> Analysis of frequency distributions with equal means but different variances. <red>

### TERM II

#### Unit I: Sets and Functions

3. 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 ± y) = tan x ± tan y/ (1 ∓ tan x tan y), cot(x ± y) = cot x cot y ∓ 1/ (cot y ± cot x)

sinα ± sinβ = 2sin ½ (α ± β) cos ½ (α ∓ β)

cosα + cosβ = 2cos ½ (α + β) cos ½ (α − β)

cosα − cosβ = −2sin ½ (α + β) sin ½ (α − β)

Identities related to sin2x, cos2x, tan2x, sin3x, cos3x and tan3x. <red> General solution of trigonometric equations of the type sin y = sin a, cos y = cos a and tan y = tan a. <red>

#### Unit II: Algebra

3. 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 a system of linear inequalities in two variables.

4. Permutations and Combinations

Fundamental principle of counting. Factorial n. (n!) Permutations and combinations, <red> derivation of <red> Formulae for nPr and nCr <red> and their connections <red>, simple applications.

<red> 5. Binomial Theorem <red>

<red> Historical perspective, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, General and middle term in binomial expansion, simple applications. <red>

#### Unit III: Coordinate Geometry

2. Conic Sections

Sections of a cone: circles, ellipse, parabola, hyperbola, <red> a point, a straight line and a pair of intersecting lines as a degenerate case of a conic section. <red> Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle.

3. 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.

2. Probability

Random experiments; outcomes, sample spaces (set representation). Events; occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, <red> Axiomatic (set theoretic) probability, connections with other theories of earlier classes. <red> Probability of an event, probability of ‘not’, ‘and’ and ‘or’ events.