CBSE Class 12 Maths Syllabus for Board Exam 2025, Download PDF

Units

No of Periods

Total Marks

Unit-I: Relations and Functions

1. Relations and Functions

Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions. 

2. Inverse Trigonometric Functions

Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions

15

15

08

Unit-II: Algebra 

1. Matrices

Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operations on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Noncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries). 

2. Determinants 

Determinant of a square matrix (up to 3 x 3 matrices), minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix. 

25

25

10

Unit-III: Calculus 

1. Continuity and Differentiability

Continuity and differentiability, chain rule, derivative of inverse trigonometric functions, 𝑙𝑖𝑘𝑒 sin-1x cos-1x tan-1x, derivative of implicit functions. Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives.

2. Applications of Derivatives

Applications of derivatives: rate of change of quantities, increasing/decreasing functions, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as reallife situations).

3. Integrals 

Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them. 

Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

4. Applications of the Integrals

Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only) 

5. Differential Equations

Definition, order and degree, general and particular solutions of a differential equation. Solution of differential equations by method of separation of variables, solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type:

20

10

20

15

15

35

Unit-IV: Vectors and Three-Dimensional Geometry

1. Vectors 

Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors.

2. Three - dimensional Geometry

Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, skew lines, shortest distance between two lines. Angle between two lines.

15

15

14

Unit-V: Linear Programming

1. Linear Programming

Introduction, related terminology such as constraints, objective function, optimization, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints). 

20

05 

Unit-VI: Probability

1. Probability 

Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean of random variable

30

08

CBSE Class 12 Mathematics Syllabus 2024-2025 PDF

Assessment Type

Marks

Theory Exam

80

Internal Assessment

• Periodic Tests
• Mathematics Activities

(10+10=20)

10 

10

100

IMPORTANT TOPICS SUBJECT-WISE

Physics

Chemistry

Mathematics

Mechanics

Atomic Mass of Elements

Pythagoras Theorem

Optics

Periodic Table

Prime Numbers

Thermodynamics

Balancing Chemical Equations

Probability

Electromagnetism

Benzene

Statistics

Unit Conversion

Organometallic Compounds

Fractions

Kirchhoff’s Law

Atomic Number and Mass Number

Relations and Functions

Faraday’s Law

How to Convert Celsius to Kelvin

Sequence and Series

Laws of Motion

Sulfuric Acid

Multiplication Tables

Refraction of Light

Homogenous Mixtures

Determinants and Matrices

Maxwell's Equation

Lewis Structure of Carbon Dioxide

Profit And Loss

Electrostatics

Valence Electrons

Polynomial Equations

Bernoulli's Principle

Carbonic Acid

Dividing Fractions

Projectile Motion

Elements and Compounds

Social Science

Electric Charge

Acids and Bases

Manufacturing Industries

Physics Symbols

Cathode and Anode

Sahara Desert

Difference Between Pound and Kilogram

Intensive and Extensive Properties

Amazon River

Velocity

Electron Configuration

Indian Tribes

Kinematics Equation

Atoms and Molecules

Mughal Dynasty

Gas Constant

Molar Mass Concept

Monuments of India List

Newton's 2nd Law

Domains of Earth

Judiciary

Tension

Carboxylic Acid

Autocratic Meaning

Ohm's Law

Baking Soda

Fundamental Rights of India

Force

Molecular Geometry

Union Territories of India

Relation Between Mass and Force

Bohr's Model

Capitals of Seven Sisters of India

Torque

Solutions

Biology

Frictional Force

Bases

Microbiology

Difference Between Series and Parallel Circuits

Electronegativity

Ecology

Electric Power

Heat Capacity

Photosynthesis

Law of Gravitation

Types of Mixtures

Magnetic Field

All About Sulfur

Avogadro’s Number

Enthalpy

Angular Velocity

Homogenous and Heterogenous Mixtures

Distance and Displacement

Hydroxides

Difference Between Conduction, Convection and Radiation

First 20 Elements

Types of Waves

Orbital Chemistry

Archimedes' Principle

Quantum Numbers

Kinetic Energy

Types of Chemical Reactions

Law of Conservation of Energy

Boyle's Law

Human Eye

Polarity

Law of Conservation of Mass

Amines

Ethanol