CBSE Class 12 Maths Syllabus - Free PDF Download
CBSE Syllabus 2026-27 Class 12: The CBSE Class 12 Maths Syllabus for the examination year 2026-27 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 2026-27 CBSE Class 12 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 12 Maths Syllabus for 2026-27 is below.
Academic year:
CBSE Class 12 Mathematics Revised Syllabus
CBSE Class 12 Mathematics Course Structure 2026-27 With Marking Scheme
| # | Unit/Topic | Weightage |
|---|---|---|
| 1 | Relations and Functions | |
| 1 | Relations and Functions | |
| 2 | Inverse Trigonometric Functions | |
| 2 | Algebra | |
| 3 | Matrices | |
| 4 | Determinants | |
| 3 | Calculus | |
| 5 | Continuity and Differentiability | |
| 6 | Applications of Derivatives | |
| 7 | Integrals | |
| 8 | Applications of the Integrals | |
| 9 | Differential Equations | |
| 4 | Vectors and Three-dimensional Geometry | |
| 10 | Vectors | |
| 11 | Three - Dimensional Geometry | |
| 5 | Linear Programming | |
| 12 | Linear Programming | |
| 6 | Probability | |
| 13 | Probability | |
| 7 | Sets | |
| Total | - |
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Syllabus
1: Relations and Functions [Revision]
CBSE Class 12 Mathematics Syllabus
1 Relations and Functions [Revision]
- Fundamental Concepts of Ordered Pairs and Relations
- Definition of Relation
- Domain
- Co-domain and Range of a Relation
- Types of Relations
- Empty Relation
- Universal Relation
- Trivial Relations
- Identity relation
- Symmetric relation
- Transitive relation
- Equivalence Relation
- Antisymmetric relation
- Inverse relation
- One-One Relation (Injective)
- Many-one relation
- Into relation
- Onto relation (Surjective)
- Types of Functions
- Types of Function based on Elements:
1) One One Function (or injective)
2) Many One Function
3) Onto Function (or surjective)
4) One One and Onto Function (or bijective)
5) Into Function
6) Constant Function - Types of Function based on Equation:
1) Identity Function
2) Linear Function
3) Quadratic Function
4) Cubic Function
5) Polynomial Functions - Types of Function based on the Range:
1) Modulus Function
2) Rational Function
3) Signum Function
4) Even and Odd Functions
5) Periodic Functions
6) Greatest Integer Function
7) Inverse Function
8) Composite Functions - Types of Function based on the Domain:
1) Algebraic Functions
2) Trigonometric Functions
3) Logarithmic Functions - Explicit and Implicit Functions
- Value of a Function
- Equal Functions
- Types of Function based on Elements:
- Invertible Functions
- Concept of Binary Operations
- Commutative Binary Operations
- Associative Binary Operations
- Identity Binary Operation,
- Invertible Binary Operation
- Inverse of a Function
- Overview of Relations and Functions
2 Inverse Trigonometric Functions [Revision]
- Inverse Trigonometric Functions
- Introduction of Inverse Trigonometric Functions
- Graphs of Inverse Trigonometric Functions
- Inverse Trigonometric Functions (Simplification and Examples)
- Properties of Inverse Trigonometric Functions
Inverse of Sin, Inverse of cosin, Inverse of tan, Inverse of cot, Inverse of Sec, Inverse of Cosec
- Overview of Inverse Trigonometric Functions
2: Algebra [Revision]
CBSE Class 12 Mathematics Syllabus
3 Matrices [Revision]
- Concept of Matrices
- Matrices
- Determinants
- Cramer’s Rule
- Application in Economics
- Proof of the Uniqueness of Inverse
- Types of Matrices
- Row Matrix
- Column Matrix
- Zero or Null matrix
- Square Matrix
- Diagonal Matrix
- Scalar Matrix
- Unit or Identity Matrix
- Upper Triangular Matrix
- Lower Triangular Matrix
- Triangular Matrix
- Symmetric Matrix
- Skew-Symmetric Matrix
- Determinant of a Matrix
- Singular Matrix
- Transpose of a Matrix
- Equality of Matrices
- Determine equality of two matrices
- Properties of Matrix Addition
- Commutative Law
- Associative Law
- Existence of additive identity
- The existence of additive inverse
- Properties of Matrix Multiplication
- Transpose of a Matrix
- Symmetric and Skew Symmetric Matrices
- Define symmetric and skew symmetric matrix
- Invertible Matrices
- Overview of Matrices
- Negative of Matrix
- Operation on Matrices
- Elementary Transformations
- Interchange of any two rows or any two columns
- Multiplication of the elements of any row or column by a non-zero scalar
- Adding the scalar multiples of all the elements of any row (column) to corresponding elements of any other row (column)
4 Determinants [Revision]
- Determinants of Matrix of Order One and Two
- Determinant of a Matrix of Order 3 × 3
- 1st, 2nd and 3rd Row
- 1st, 2nd and 3rd Columns
- Expansion along the first Row (R1)
- Expansion along the second row (R2)
- Expansion along the first Column (C1)
- Minors and Co-factors
- Properties of Matrix Multiplication
- Applications of Determinants and Matrices
- Consistent System
- Inconsistent System
- Solution of a system of linear equations using the inverse of a matrix
- Elementary Transformations
- Interchange of any two rows or any two columns
- Multiplication of the elements of any row or column by a non-zero scalar
- Adding the scalar multiples of all the elements of any row (column) to corresponding elements of any other row (column)
- Properties of Determinants
- Property 1 - The value of the determinant remains unchanged if its rows are turned into columns and columns are turned into rows.
- Property 2 - If any two rows (or columns) of a determinant are interchanged then the value of the determinant changes only in sign.
- Property 3 - If any two rows ( or columns) of a determinant are identical then the value of the determinant is zero.
- Property 4 - If each element of a row (or column) of a determinant is multiplied by a constant k then the value of the new determinant is k times the value of the original determinant.
- Property 5 - If each element of a row (or column) is expressed as the sum of two numbers then the determinant can be expressed as the sum of two determinants
- Property 6 - If a constant multiple of all elements of any row (or column) is added to the corresponding elements of any other row (or column ) then the value of the new determinant so obtained is the same as that of the original determinant.
- Property 7 - (Triangle property) - If all the elements of a determinant above or below the diagonal are zero then the value of the determinant is equal to the product of its diagonal elements.
- Determinant of a Square Matrix
up to 3 x 3 matrices
- Rule A=KB
- Overview of Determinants
- Geometric Interpretation of the Area of a Triangle
3: Calculus [Revision]
CBSE Class 12 Mathematics Syllabus
5 Continuity and Differentiability [Revision]
- Concept of Continuity
- Algebra of Continuous Functions
- Concept of Differentiability
- Derivatives of Composite Functions - Chain Rule
- Derivatives of Implicit Functions
- Derivatives of Inverse Trigonometric Functions
- Exponential and Logarithmic Functions
- Logarithmic Differentiation
- Derivatives of Functions in Parametric Forms
- Second Order Derivative
- Derivative - Exponential and Log
- Proof Derivative X^n Sin Cos Tan
f(x) = xn
f(x) = sin x
f(x) = cos x
f(x) = tan x
- Infinite Series
- Higher Order Derivative
- Derivative of Functions Which Expressed in Higher Order Derivative Form
- Continuous Function of Point
Continuous left hand limit
Continuous right hand limit
- Mean Value Theorem
- Rolle’s Theorem
- Lagrange’s Mean Value Theorem
- Applications
- Overview of Continuity and Differentiability
6 Applications of Derivatives [Revision]
- Introduction to Applications of Derivatives
- Rate of Change of Bodies or Quantities
- Increasing and Decreasing Functions
- Maxima and Minima
- First and Second Derivative test
- Determine critical points of the function
- Find the point(s) of local maxima and local minima and corresponding local maximum and local minimum values
- Find the absolute maximum and absolute minimum value of a function
- Maximum and Minimum Values of a Function in a Closed Interval
- Simple Problems on Applications of Derivatives
Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations)
- Graph of Maxima and Minima
- Approximations
- Tangents and Normals
- Overview of Applications of Derivatives
7 Integrals [Revision]
- Introduction of Integrals
- Integration as an Inverse Process of Differentiation
Derivatives Integrals
(Anti derivatives)`d/(dx) (x^(n+1)/(n+1)) = x^n` `int x^n dx = x^(n+1)/(n+1) + "C"`, n ≠ –1 `d/(dx)`(x) = 1 `int dx` = x + C `d/(dx)`(sin x) = cos x `int` cos x dx = sin x +C `d/(dx)` (-cos x) = sin x `int`sin x dx = -cos x +C `d/(dx)` (tan x) = sec2x `int sec^2 x` dx = tanx + C `d/(dx)`(-cot x) = `cosec^2x ` `int cosec^2x` dx = -cot x +C `d/(dx)` (sec x) = sec x tan x `int` sec x tan x dx = sec x +C `d/(dx)` (-cosecx) = cosec x cot x `int` cosec x cot x dx = -cosec x +C `d/(dx) (sin^-1) = 1/(sqrt(1-x^2))` `int (dx)/(sqrt(1-x^2))= sin^(-1) x +C ` `d/(dx) (-cos^(-1)) = 1/(sqrt (1-x^2))` `int (dx)/(sqrt (1-x^2))= -cos^(-1) x + C ` `d/(dx) (tan^(-1) x) = 1/(1+x^2)` `int (dx)/(1+x^2)= tan^(-1) x + C ` `d/(dx) (-cot^(-1) x) = 1/(1+x^2)` `int (dx)/(1+x^2)= -cot^(-1) x + C ` `d/(dx) (sec^(-1) x) = 1/(x sqrt (x^2 - 1))` `int (dx)/(x sqrt (x^2 - 1))`= `sec^(-1)` x + C `d/(dx) (-cosec^(-1) x) = 1/(x sqrt (x^2 - 1))` `int (dx)/(x sqrt (x^2 - 1))=-cosec^(-1) x + C ` `d/(dx)(e^x) = e^x` `int e^x dx = e^x + C` `d/(dx) (log|x|) = 1/x` `int 1/x dx = log|x| +C` `d/(dx) ((a^x)/(log a)) = a^x` `int a^x dx = a^x/log a` +C - Some Properties of Indefinite Integral
- Methods of Integration: Integration by Substitution
- Integration Using Trigonometric Identities
- Integrals of Some Particular Functions
1) `int (dx)/(x^2 - a^2) = 1/(2a) log |(x - a)/(x + a)| + C`
2) `int (dx)/(a^2 - x^2) = 1/(2a) log |(a + x)/(a - x)| + C`
3) `int (dx)/(x^2 - a^2) = 1/a tan^(-1) (x/a) + C`
4) `int (dx)/sqrt (x^2 - a^2) = log |x + sqrt (x^2-a^2)| + C`
5) `int (dx)/sqrt (a^2 - x^2) = sin ^(-1) (x/a) +C`
6) `int (dx)/sqrt (x^2 + a^2) = log |x + sqrt (x^2 + a^2)| + C`
7) To find the integral `int (dx)/(ax^2 + bx + c)`
8) To find the integral of the type `int (dx)/sqrt(ax^2 + bx + c)`
9) To find the integral of the type `int (px + q)/(ax^2 + bx + c) dx`
10) For the evaluation of the integral of the type `int (px + q)/sqrt(ax^2 + bx + c) dx`
- Methods of Integration: Integration Using Partial Fractions
- Methods of Integration: Integration by Parts
- Fundamental Theorem of Calculus
Area function, First fundamental theorem of integral calculus and Second fundamental theorem of integral calculus
- Evaluation of Definite Integrals by Substitution
- Properties of Definite Integrals
- Definite Integrals
- Indefinite Integral Problems
- Comparison Between Differentiation and Integration
- Integration
- Indefinite Integral by Inspection
- Definite Integral as the Limit of a Sum
- Evaluation of Simple Integrals of the Following Types and Problems
- Overview of Integrals
8 Applications of the Integrals [Revision]
- Area of the Region Bounded by a Curve and a Line
- Area of the Region Bounded by a Curve & X-axis Between two Ordinates
- Area of the Region Bounded by a Curve & Y-axis Between two Abscissa
- Circle-line, elipse-line, parabola-line
- Area Between Two Curves
- Area Under Simple Curves
- Simple curves: lines, parabolas, polynomial functions
- Overview of Applications of Integrals
9 Differential Equations [Revision]
- Differential Equations
- Order and Degree of a Differential Equation
- General and Particular Solutions of a Differential Equation
- Methods of Solving First Order, First Degree Differential Equations
- Solutions of Linear Differential Equation
- Solutions of linear differential equation of the type:
- `dy/dx` + py = q, where p and q are functions of x or constants.
- `dx/dy` + px = q, where p and q are functions of y or constants.
- Differential equations, order and degree.
- Solution of differential equations.
- Variable separable.
- Homogeneous equations
- Linear form `dy/dx` + Py = Q where P and Q are functions of x only. Similarly, for `dx/dy`.
- Formation of a Differential Equation Whose General Solution is Given
- Procedure to Form a Differential Equation that Will Represent a Given Family of Curves
- Overview of Differential Equations
4: Vectors and Three-dimensional Geometry [Revision]
CBSE Class 12 Mathematics Syllabus
10 Vectors [Revision]
- Vector Analysis
- Vector
- Definition: Vector
- Representation of vector
- Types of Vectors
- Examples of Vector Quantities
- Vector
- Basic Concepts of Vector Algebra
- Position Vector
- Direction Cosines and Direction Ratios of a Vector
- Direction Cosines
- Vector Operations>Addition and Subtraction of Vectors
- Statement
- Vector Addition: Parallel Vectors
- Vector Subtraction: Anti-Parallel Vectors
- Real-Life Applications
- Properties of Vector Addition
- Vector Operations>Multiplication of a Vector by a Scalar
- Introduction: Vector Operations
- Statement: Multiplication of a Vector by a Scalar
- Example
- Components of Vector
- Vector addition using components
- Components of a vector in two dimensions space
- Components of a vector in three-dimensional space
- Vector Joining Two Points
- Section Formula
- Formula
- Division of Line Segment
- Proof
- Examples
- Product of Two Vectors
- Geometrical Interpretation of Scalar
- Scalar Triple Product of Vectors
- Position Vector of a Point Dividing a Line Segment in a Given Ratio
- Magnitude and Direction of a Vector
- Vectors Examples and Solutions
- Introduction of Product of Two Vectors
- Overview of Vectors
11 Three - Dimensional Geometry [Revision]
- Introduction of Three Dimensional Geometry
- Direction Cosines and Direction Ratios of a Line
- Direction cosines of a line passing through two points.
- Relation Between Direction Ratio and Direction Cosines
- Equation of a Line in Space
- Equation of a line through a given point and parallel to a given vector `vec b`
- Equation of a line passing through two given points
- Angle Between Two Lines
- Shortest Distance Between Two Lines
- Coplanar
- Skew lines
- Distance between two skew lines
- Distance between parallel lines
- Three - Dimensional Geometry Examples and Solutions
- Equation of a Plane
- Forms of the Equation of a Straight Line
- y = mx+c
- Coplanarity of Two Lines
- Angle Between Line and a Plane
- Angle Between Two Planes
- Vector and Cartesian Equation of a Plane
- Distance of a Point from a Plane
- Overview of Three Dimensional Geometry
5: Linear Programming [Revision]
CBSE Class 12 Mathematics Syllabus
12 Linear Programming [Revision]
- Introduction of Linear Programming
- Definition of related terminology such as constraints, objective function, optimization.
- Mathematical Formulation of Linear Programming Problem
- Different Types of Linear Programming Problems
- Different types of linear programming (L.P.) problems
- Manufacturing problem
- Diet Problem
- Transportation problem
- Graphical Method of Solving Linear Programming Problems
- Graphical method of solution for problems in two variables
- Feasible and infeasible regions and bounded regions
- Feasible and infeasible solutions
- Optimum feasible solution
- Linear Programming Problem and Its Mathematical Formulation
- Overview of Linear Programming
6: Probability [Revision]
CBSE Class 12 Mathematics Syllabus
13 Probability [Revision]
