## CBSE Class 11 Maths Syllabus - Free PDF Download

CBSE Syllabus 2024-25 Class 11: The CBSE Class 11 Maths Syllabus for the examination year 2024-25 has been released by the Central Board of Secondary Education, CBSE. The board will hold the final examination at the end of the year following the annual assessment scheme, which has led to the release of the syllabus. The 2024-25 CBSE Class 11 Maths Board Exam will entirely be based on the most recent syllabus. Therefore, students must thoroughly understand the new CBSE syllabus to prepare for their annual exam properly.

The detailed CBSE Class 11 Maths Syllabus for 2024-25 is below.

## CBSE Class 11 Mathematics Revised Syllabus

CBSE Class 11 Mathematics and their Unit wise marks distribution

### CBSE Class 11 Mathematics Course Structure 2024-25 With Marking Scheme

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## Syllabus

### CBSE Class 11 Mathematics Syllabus for Chapter 1: Sets and Functions

- Sets and Their Representations
- Roster or Tabular method or List method
- Set-Builder or Rule Method

- Types of Sets
- Empty Set (Null or Void Set)

- Finite and Infinite Sets

- Equal Sets

- Subsets
- Subsets of set of real numbers
- Intervals as subsets of R

- Power Set

- Universal Set

- Venn Diagrams
- Operations on Sets
- Intrdouction of Operations on Sets

- Union of Sets
- Union of sets
- Some Properties of the Operation of Union

- Intersection of Sets
- Intersection of sets
- Some Properties of Operation of Intersection

- Difference of Sets
- Difference of sets

- Disjoint Sets

- Complement of a Set
- De Morgan's Law
- Some Properties of Complement Sets

- Practical Problems on Union and Intersection of Two Sets
- Proper and Improper Subset
- Open and Close Intervals
- Element Count Set

- Cartesian Product of Sets
- Number of Elements in the Cartesian Product of Two Finite Sets
- Cartesian Product of set of the Reals with Itself

- Concept of Relation
- Definition of Relation
- Domain
- Co-domain and Range of a Relation

- Pictorial Diagrams

- Pictorial Representation of a Function
Domain, Co-domain and Range of a function

- Concept of Functions
- Function, Domain, Co-domain, Range
- Types of function

1. One-one or One to one or Injective function

2. Onto or Surjective function - Representation of Function
- Graph of a function
- Value of funcation
- Some Basic Functions - Constant Function, Identity function, Power Functions, Polynomial Function, Radical Function, Rational Function, Exponential Function, Logarithmic Function, Trigonometric function

- Exponential Function
Domain and range of this function

- Logarithmic Functions
Concept of Logarithmic Functions

Domain and range of this function

- Some Functions and Their Graphs
- Identity function - Domain and range of this function
- Constant function - Domain and range of this function
- Polynomial function -Domain and range of this function
- Rational functions - Domain and range of this function
- The Modulus function - Domain and range of this function
- Signum function - Domain and range of this function
- Greatest integer function

- Algebra of Real Functions
- Sum, Difference,Product and Quotient of Function
- Addition of two real functions
- Subtraction of a real function from another
- Multiplication by a scalar
- Multiplication of two real functions
- Quotient of two real functions

- Sets
- Ordered Pairs

- Equality of Ordered Pairs

- Graph of Function
- Brief Review of Cartesian System of Rectanglar Co-ordinates

- Concept of Angle
- Part of Angle - Initial Side,Terminal Side,Vertex
- Types of Angle - Positive and Negative Angles
- Measuring Angles in Radian
- Measuring Angles in Degrees
- initial side, terminal side, vertex,positive angle, negative angle
- Degree measure
- Radian measure
- Relation between radian and real numbers
- Relation between degree and radian

- Introduction of Trigonometric Functions
- Trigonometric Functions with the Help of Unit Circle

- Signs of Trigonometric Functions
- Domain and Range of Trigonometric Functions
- Domain and Range of Trignometric Functions and Their Graphs

- Trigonometric Functions of Sum and Difference of Two Angles
- Identities Related to Sin 2x, Cos2x, Tan 2x, Sin3x, Cos3x and Tan3x.
- Deducing the Identities
- Deducing the identities like the following:-

`tan(x+-y)=(tanx+-tany)/(1+-tanxtany)", "cot(x+-y)=(cotxcoty+-1)/(coty+-cotx)`

`sinalpha+-sinbeta=2"sin"1/2(alpha+-beta)"cos"1/2(alpha+-beta)`

`cosalpha+cosbeta=2"cos"1/2(alpha+beta)"cos"1/2(alpha-beta)`

`cosalpha-cosbeta=-2"sin"1/2(alpha+beta)"sin"1/2(alpha-beta)`

- Trigonometric Equations
- Trigonometric Functions
- Truth of the Identity
sin

^{2}x+cos^{2}x=1, for All X.

- Expressing Sin (X±Y) and Cos (X±Y) in Terms of Sinx, Siny, Cosx and Cosy and Their Simple Applications

- Truth of the Identity
- Negative Function Or Trigonometric Functions of Negative Angles
- 90 Degree Plusminus X Function
- Conversion from One Measure to Another
- 180 Degree Plusminus X Function
- 2X Function
- 3X Function
- Graphs of Trigonometric Functions
- Transformation Formulae
4.3.1 Transformation of the products into sum or difference

4.3.2 Transformation of sum or difference into product

- Values of Trigonometric Functions at Multiples and Submultiples of an Angle
- Sine and Cosine Formulae and Their Applications

### CBSE Class 11 Mathematics Syllabus for Chapter 2: Algebra

- Concept of Complex Numbers
- Imaginary number
- Complex Number

- Algebra of Complex Numbers - Equality
Equality of Complex number

- Algebraic Properties of Complex Numbers

- Need for Complex Numbers
Need for complex numbers, especially √−1, to be motivated by inability to solve some of the quardratic equations

- Square Root of a Complex Number

- Algebraic Operations of Complex Numbers
- Equality of two Complex Numbers
- Conjugate of a Complex Number
- Properties of `barz`
- Addition of complex numbers - Properties of addition, Scalar Multiplication
- Subtraction of complex numbers - Properties of Subtraction
- Multiplication of complex numbers - Properties of Multiplication
- Powers of i in the complex number
- Division of complex number - Properties of Division
- The square roots of a negative real number
- Identities

- The Modulus and the Conjugate of a Complex Number
- Modulus of Complex Number
- Conjugate of Complex Number

- Argand Plane and Polar Representation
- Quadratic Equations
- Quadratic equations in real and complex number system and their solutions Relations between roots and co-efficient

- Inequalities - Introduction
- Algebraic Solutions of Linear Inequalities in One Variable and Their Graphical Representation
- Graphical Solution of Linear Inequalities in Two Variables
Linear Inequalities - Graphical Representation of Linear Inequalities in Two Variables

- Solution of System of Linear Inequalities in Two Variables

- Fundamental Principles of Counting
- Tree Diagram
- Addition Principle
- Multiplication principle

- Permutations
- Permutation
- Permutation of repeated things
- Permutations when all the objects are not distinct
- Number of Permutations Under Certain Restricted Conditions
- Circular Permutations

- Combination
^{n}C_{r},^{n}C_{n}=1,^{n}C_{0}= 1,^{n}C_{r}=^{n}C_{n–r},^{n}C_{x}=^{n}C_{y}, then x + y = n or x = y,^{n+1}C_{r}=^{n}C_{r-1}+^{n}C_{r}- When all things are different
- When all things are not different.
- Mixed problems on permutation and combinations.

- Introduction of Permutations and Combinations
- Permutation Formula to Rescue and Type of Permutation
- Without repetition
- With repetition

- Smaller Set from Bigger Set
- Derivation of Formulae and Their Connections
Derivation of formulae for

^{n}P_{r }and^{n}C_{r}and their connections - Simple Applications of Permutations and Combinations
- Factorial N (N!) Permutations and Combinations

- Motivation
- Motivating the Application of the Method by Looking at Natural Numbers as the Least Inductive Subset of Real Numbers

- Principle of Mathematical Induction

- Introduction of Binomial Theorem
- History of Binomial Theorem

- Binomial Theorem for Positive Integral Indices
- Statement and Proof of the Binomial Theorem for Positive Integral Indices
- Proof of Binomial Therom by Induction
- Special Case in Binomial Therom
- Pascal's Triangle
- Binomial theorem for any positive integer n
- Some special cases-(In the expansion of (a + b)
^{n})

- General and Middle Terms
- Proof of Binomial Therom by Pattern
- Proof of Binomial Therom by Combination
- Rth Term from End
- Binomial Theorem
- Simple Applications of Binomial Theorem

- Concept of Sequences
- Finite sequence
- Infinite sequence
- Progression

- Concept of Series
- Arithmetic Progression (A.P.)
- Geometric Progression (G. P.)
- N
^{th}Term of Geometric Progression (G.P.) - General Term of a Geometric Progression (G.P.)
- Sum of First N Terms of a Geometric Progression (G.P.)
- Sum of infinite terms of a G.P.
- Geometric Mean (G.M.)

- N
- Relationship Between A.M. and G.M.
- Relation Between Arithematic Mean (A.M.) and Geometric Mean (G.M.)

- Sum to N Terms of Special Series
- Sequence and Series
- Introduction of Sequence and Series

### CBSE Class 11 Mathematics Syllabus for Chapter 3: Coordinate Geometry

- Slope of a Line
- Slope of a Line Or Gradient of a Line.
- Parallelism of Line
- Perpendicularity of Line in Term of Slope
- Collinearity of Points
- Slope of a line when coordinates of any two points on the line are given
- Conditions for parallelism and perpendicularity of lines in terms of their slopes
- Angle between two lines
- Collinearity of three points

- Various Forms of the Equation of a Line
- General Equation of a Line
- Different forms of Ax + By + C = 0 - Slope-intercept form, Intercept form, Normal form

- Distance of a Point from a Line
- Introduction of Distance of a Point from a Line
- Distance between two parallel lines

- Straight Lines
- Brief Recall of Two Dimensional Geometry from Earlier Classes

- Equation of Family of Lines Passing Through the Point of Intersection of Two Lines

- Shifting of Origin

- Sections of a Cone
- Concept of Circle
- Introduction of Parabola
- Parabola
- Standard Equations of Parabola

- Latus Rectum

- Introduction of Ellipse
- Ellipse
- Relationship Between Semi-major Axis, Semi-minor Axis and the Distance of the Focus from the Centre of the Ellipse

- Special Cases of an Ellipse

- Eccentricity

- Standard Equations of an Ellipse

- Latus Rectum
- Latus Rectum in Ellipse

- Introduction of Hyperbola
- Hyperbola
- Eccentricity

- Standard Equation of Hyperbola

- Latus Rectum

- Circle
- Standard Equation of a Circle

- Three - Dimensional Geometry
- Coordinate Axes and Coordinate planes
Coordinate Axes and Coordinate Planes in Three Dimensions

- Coordinates of a Point in Space

- Distance Between Two Points
- Distance Between Two Points in 3-D Space

- Section Formula

- Coordinate Axes and Coordinate planes
- Three Dimessional Space

### CBSE Class 11 Mathematics Syllabus for Chapter 4: Calculus

- Intuitive Idea of Derivatives
- Introduction of Limits
Left hand Limits

Right Hand Limis

- Introduction to Calculus
- Differential Calculus
- Integral calculus

- Concept of Limits
- Algebra of Limits

- Limits of Polynomials and Rational Functions

- Derivative Introduced as Rate of Change Both as that of Distance Function and Geometrically

- Limits of Logarithmic Functions

- Limits of Exponential Functions

- Limits of Trigonometric Functions
- Introduction of Derivatives
- The Concept of Derivative
- Algebra of Derivative of Functions

- Derivative of Polynomials and Trigonometric Functions

- Derivative of Slope of Tangent of the Curve

- Theorem for Any Positive Integer n
- Graphical Interpretation of Derivative
- Derive Derivation of x^n

`x^n`

### CBSE Class 11 Mathematics Syllabus for Chapter 5: Mathematical Reasoning

- Mathematically Acceptable Statements
- New Statements from Old
- Special Words Or Phrases
- Implications
- Contrapositive and Converse

- Introduction of Validating Statements
- Validating the Statements Involving the Connecting Words
- statement with
**“****and”** - Statements with
**“or”** **“Implies”****“Implied by”**- Statements with
**“If then”** - Statements with
**“if and only if”**

- Validation by Contradiction
- Mathematical Reasoning
- Difference Between Contradiction, Converse and Contrapositive

- Consolidating the Understanding
"if and only if (necessary and sufficient) condition", "implies", "and/or", "implied by'', "and", "or'', "there exists" and their use through variety of examples related to real life and Mathematics

### CBSE Class 11 Mathematics Syllabus for Chapter 6: Statistics and Probability

- Measures of Dispersion
- Concept of Range
- Measures of Dispersion - Range

- Mean Deviation
- Mean deviation for grouped data
- Mean deviation for ungrouped data

- Introduction of Variance and Standard Deviation
- Variance and Standard Deviation
- Standard Deviation

- Standard Deviation of a Discrete Frequency Distribution

- Standard Deviation of a Continuous Frequency Distribution

- Shortcut Method to Find Variance and Standard Deviation

- Introduction of Analysis of Frequency Distributions
- Analysis of Frequency Distributions
- Comparison of Two Frequency Distributions with Same Mean

- Statistics (Entrance Exam)
- Statistics Concept

- Measures of Dispersion - Quartile Deviation

- Central Tendency - Mean
- Central Tendency - Median
- Concept of Mode
- Standard Deviation - by Short Cut Method

- Random Experiments
- Introduction of Event
- Event
- Occurrence of an Event

- Types of Events
- Simple or elementary event
- Occurrence and non-occurrence of event
- Sure Event
- Impossible Event
- Complimentary Event

- Algebra of Events

- Exhaustive Events
- Types of Event - Exhaustive Events

- Mutually Exclusive Events
- Types of Event - Mutually Exclusive Events

- Axiomatic Approach to Probability
- Probability
- Probability of 'Not', 'And' and 'Or' Events