# CBSE Class 11 Mathematics Syllabus 2022-23

CBSE Class 11 Mathematics Syllabus 2022-23 includes Sets and Functions, Coordinate Geometry, Statistics and Probability, Calculus etc for the session 2022 – 2023. Here is the detailed syllabus. To download class 11 Mathematics CBSE latest sample question papers for the 2023 exams, please install the myCBSEguide App which is the best mobile app for CBSE students. The myCBSEguide app not only provides you the CBSE class 11 Mathematics model question papers but it also provides class 11 Mathematics chapter-wise test papers, class 11 Mathematics best revision notes and other study material for class 11 Mathematics students.

CBSE Class – 11
Mathematics (Code No. 041)
Syllabus (2022-23)

Time: 3 Hours
Max. Marks: 80

S.no.UnitsNo. of PeriodsMarks
I.Sets and Functions6023
II.Algebra5025
III.Coordinate Geometry5012
IV.Calculus4008
V.Statistics and Probability4012
Total24080
Internal Assessment20

## Unit-I: Sets and Functions

1. Sets (20 Periods)
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.Difference of sets. Complement of a set. Properties of Complement.
2. Relations & Functions (20 Periods)
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 (upto R x R x R).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. Sum, difference, product and quotients of functions.
3. Trigonometric Functions (20 Periods)
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 sin 2x + cos 2x = 1, for all x. Signs of trigonometric functions. Domain and range of trigonometric functions and their graphs. Expressing sin (x {tex}\pm{/tex} y) and cos (x {tex}\pm{/tex} y) in terms of sinx, siny, cosx & cosy and their simple applications. Deducing identities like the following:
tan(x {tex}\pm{/tex} y) = {tex}\frac{\tan x \pm \tan y}{1 \mp \tan x \tan y}{/tex}, cot(x {tex}\pm{/tex} y) = {tex}\frac{\cot x \cot y \mp 1}{\cot y \pm \cot x}{/tex}
sin{tex}\alpha \pm{/tex} sin{tex}\beta{/tex} = 2sin{tex}\frac 12({\alpha \pm \beta}){/tex} cos{tex}\frac 12({\alpha \mp \beta}){/tex}
cos{tex}\alpha{/tex} + cos{tex}\beta{/tex} = 2cos{tex}\frac 12({\alpha + \beta}){/tex} cos{tex}\frac 12({\alpha – \beta}){/tex}
cos{tex}\alpha{/tex} – cos{tex}\beta{/tex} = -2sin{tex}\frac 12({\alpha + \beta}){/tex} sin{tex}\frac 12({\alpha – \beta}){/tex}
Identities related to sin2x, cos2x, tan2 x, sin3x, cos3x and tan3x.

## Unit-II: Algebra

1. Complex Numbers and Quadratic Equations (10) Periods
Need for complex numbers, especially {tex}\sqrt {-1}{/tex}, to be motivated by inability to solve some of the quadratic equations. Algebraic properties of complex numbers. Argand plane
2. Linear Inequalities (10) Periods
Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line.
3. Permutations and Combinations (10) Periods
Fundamental principle of counting. Factorial n. (n!) Permutations and combinations, derivation of Formulae for nPr and nCr and their connections, simple applications.
4. Binomial Theorem (10) Periods
Historical perspective, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, simple applications.
5. Sequence and Series (10) Periods
Sequence and Series. 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 (15 Periods)
Brief recall of two dimensional geometry from earlier classes. Shifting of origin. 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.Equation of family of lines passing through the point of intersection of two lines.Distance of a point from a line.
2. Conic Sections (25 Periods)
Sections of a cone: circles, ellipse, parabola, hyperbola, a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse and hyperbola.Standard equation of a circle.
3. Introduction to Three-dimensional Geometry (10 Periods)
Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula.

## Unit-IV: Calculus

1. Limits and Derivatives (40 Periods)
Derivative introduced as rate of change both as that of distance function and geometrically. Intuitive idea of limit. Limits of polynomials and rational functions trigonometric, exponential and logarithmic functions. 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. Statistics (20 Periods)
Measures of Dispersion: Range, Mean deviation, variance and standard deviation of ungrouped/grouped data.
2. Probability (20 Periods)
Events; occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic) probability, connections with other theories of earlier classes. Probability of an event, probability of ‘not’, ‘and’ and ‘or’ events.

## Question Paper Design

S.No.Typology of QuestionsTotal Marks% Weightage
1.Remembering: Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers.4455
Understanding: Demonstrate understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating main ideas
2Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way.2025
3Analysing: Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations1620
Evaluating: Present and defend opinions by making judgments about information, validity of ideas, or quality of work based on a set of criteria.
Creating: Compile information together in a different way by combining elements in a new pattern or proposing alternative solutions
Total80100
1. No chapter wise weightage. Care to be taken to cover all the chapters.
2. Suitable internal variations may be made for generating various templates keeping the overall weightage to different form of questions and typology of questions same.

Choice (s):
There will be no overall choice in the question paper.
However, 33% internal choices will be given in all the sections.

Internal Assessment20 Marks
Periodic Tests (Best 2 out of 3 tests conducted)10 Marks
Mathematics Activities10 Marks

## Prescribed Books:

1. Mathematics Textbook for Class XI, NCERT Publications  