CBSE Class 12 Mathematics Syllabus (2025-26) - Detailed Breakdown

CBSE Class XII Mathematics Syllabus 2025-26 - Complete Curriculum Guide

Course Overview

Theory Paper

Marks

Internal Assessment

Marks

Duration

Hours

Total Units

Units

Key Learning Objectives

Acquire knowledge and critical understanding of basic mathematical concepts, terms and principles
Feel the flow of reasons while proving a result or solving a problem
Apply knowledge and skills acquired to solve problems (preferably in multiple ways)
Develop positive attitude to think, analyze and articulate logically
Develop interest in Mathematics and participate in related competitions
Acquaint students with different aspects of Mathematics used in daily life
Develop awareness of the need for national integration and environmental protection
Develop reverence and respect towards great Mathematicians for their contributions

Unit-wise Marks Distribution

Unit No.	Unit Name	Marks	Percentage
I	Relations and Functions	08	10%
II	Algebra	10	12.5%
III	Calculus	35	43.75%
IV	Vectors and Three-Dimensional Geometry	14	17.5%
V	Linear Programming	05	6.25%
VI	Probability	08	10%
Total Theory		80	100%
Internal Assessment		20	-

Note: Calculus carries the highest weightage (35 marks - 43.75%)

Unit I: Relations and Functions (08 Marks)

Relations and Functions

Types of relations: reflexive, symmetric, transitive
Equivalence relations
One to one functions (injective)
Onto functions (surjective)
Bijective functions
Composition of functions
Invertible functions

Inverse Trigonometric Functions

Definition and concept
Range and domain determination
Principal value branch
Graphs of inverse trigonometric functions
Properties and identities
sin⁻¹x, cos⁻¹x, tan⁻¹x
sec⁻¹x, cosec⁻¹x, cot⁻¹x

Unit II: Algebra (10 Marks)

Matrices

Concept, notation, order, equality
Types of matrices (zero, identity, diagonal, scalar)
Transpose of a matrix
Symmetric and skew symmetric matrices
Addition and scalar multiplication
Matrix multiplication
Non-commutativity of multiplication
Invertible matrices and uniqueness of inverse

Determinants

Determinant of square matrix (up to 3×3)
Minors and co-factors
Applications in finding area of triangle
Adjoint and inverse of square matrix
Consistency and inconsistency
Number of solutions of linear equations
Solving systems using matrix inverse
Cramer's rule applications

Unit III: Calculus (35 Marks)

HIGHEST WEIGHTAGE UNIT - 43.75% of Total Marks

Continuity and Differentiability

Continuity and differentiability concepts
Chain rule for differentiation
Derivative of composite functions
Derivatives of inverse trigonometric functions
Derivative of implicit functions
Exponential and logarithmic functions
Logarithmic differentiation
Parametric form derivatives
Second order derivatives

Applications of Derivatives

Rate of change of quantities
Increasing and decreasing functions
Maxima and minima problems
First derivative test (geometrical)
Second derivative test
Real-life optimization problems
Tangent and normal equations
Motion problems

Integrals

Integration as inverse of differentiation
Integration by substitution method
Integration by partial fractions
Integration by parts
Standard integral formulas
Fundamental Theorem of Calculus
Properties of definite integrals
Evaluation of definite integrals

Applications of Integrals

Area under simple curves
Area between curves and lines
Area of circles in standard form
Area of parabolas in standard form
Area of ellipses in standard form
Area between two curves
Real-life applications

Differential Equations

Definition, order and degree
General and particular solutions
Separation of variables method
Homogeneous differential equations
Linear differential equations (first order)
dy/dx + py = q type equations
dx/dy + px = q type equations
Applications in real-life problems

Unit IV: Vectors and Three-Dimensional Geometry (14 Marks)

Vectors

Vectors and scalars concepts
Magnitude and direction of vectors
Direction cosines and direction ratios
Types of vectors (equal, unit, zero, parallel, collinear)
Position vector of a point
Components of a vector
Addition of vectors
Scalar multiplication of vectors
Scalar (dot) product of vectors
Vector (cross) product of vectors
Properties and applications

Three-Dimensional Geometry

Direction cosines and ratios of line
Line joining two points
Cartesian equation of a line
Vector equation of a line
Skew lines concept
Shortest distance between two lines
Angle between two lines
Coplanar and non-coplanar lines

Unit V: Linear Programming (05 Marks)

Linear Programming Problem

Introduction to Linear Programming
Related terminology and concepts
Constraints and objective function
Optimization problems
Graphical method of solution
Problems in two variables
Feasible and infeasible regions
Bounded and unbounded regions
Feasible and infeasible solutions
Optimal feasible solutions
Problems with up to three non-trivial constraints

Unit VI: Probability (08 Marks)

Advanced Probability

Conditional probability concepts
Multiplication theorem on probability
Independent events
Dependent events
Total probability theorem
Bayes' theorem
Applications of Bayes' theorem
Real-life probability problems
Mutually exclusive events
Exhaustive events

Examination Pattern

Typology of Questions	Marks	Percentage
Remembering & Understanding: Exhibit memory of previously learned material by recalling facts, terms, basic concepts. Demonstrate understanding by organizing, comparing, translating, interpreting, giving descriptions.	44	55%
Applying & Analysing: Solve problems in new situations by applying acquired knowledge, facts, techniques and rules. Examine and break information into parts by identifying motives or causes.	20	25%
Evaluating & Creating: Make judgments about information, validity of ideas based on criteria. Compile information in a different way by combining elements in new patterns.	16	20%
Total	80	100%

Important Examination Features

No overall choice in the question paper, but 33% internal choices will be given in all sections

No chapter-wise weightage - Care to be taken to cover all chapters

Time Duration: 3 Hours | Maximum Marks: 80

Internal Assessment (20 Marks)

Periodic Tests

Best 2 out of 3 tests conducted throughout the year

10 Marks

Mathematics Activities

Based on NCERT Laboratory Manual activities