CBSE CLASS 12 MATHEMATICS

📘 Class 12 Mathematics Syllabus

🔗 Unit I: Relations and Functions

Relations and Functions (15 Periods)

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

Inverse Trigonometric Functions (15 Periods)

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

🔣 Unit II: Algebra

Matrices (25 Periods)

• Concept, notation, order, equality, types of matrices
• Zero and identity matrix, transpose, symmetric and skew-symmetric matrices
• Operations: Addition, scalar multiplication, and matrix multiplication
• Properties and non-commutativity of matrix multiplication
• Invertible matrices and uniqueness of inverse (real entries only)

Determinants (25 Periods)

• Determinants of square matrices (up to 3×3), minors, cofactors
• Application: Area of triangle
• Adjoint and inverse of a square matrix
• Solving systems of linear equations using inverse of a matrix

📈 Unit III: Calculus

Continuity and Differentiability (20 Periods)

• Continuity, differentiability, chain rule
• Derivatives of inverse trigonometric and implicit functions
• Exponential and logarithmic functions
• Second order derivatives, parametric differentiation

Applications of Derivatives (10 Periods)

• Rate of change, increasing/decreasing functions
• Maxima and minima: First and second derivative tests

Integrals (20 Periods)

• Integration as the inverse process of differentiation
• Methods: substitution, partial fractions, by parts
• Standard integrals and applications
• Definite integrals and their basic properties

Applications of the Integrals (15 Periods)

• Area under simple curves, lines, circles, parabolas, ellipses (standard form)

Differential Equations (15 Periods)

• Definition, order, degree, general and particular solutions
• Methods: separation of variables, homogeneous equations, linear equations

🧭 Unit IV: Vectors and Three-Dimensional Geometry

Vectors (15 Periods)

• Vectors and scalars, magnitude and direction
• Direction cosines and direction ratios
• Types of vectors: equal, unit, zero, parallel, collinear
• Position vector, components, vector addition, scalar multiplication
• Dot product and cross product: properties and applications

Three-dimensional Geometry (15 Periods)

• Line joining two points: direction cosines and ratios
• Cartesian and vector equations of a line
• Skew lines and shortest distance between lines
• Angle between two lines

📊 Unit V: Linear Programming

Linear Programming (20 Periods)

• Introduction and terminology: constraints, objective function, optimization
• Graphical method for two-variable problems
• Feasible/infeasible regions and solutions, optimal solutions

🎲 Unit VI: Probability

Probability (30 Periods)

• Conditional probability and multiplication theorem
• Independent events and total probability
• Bayes’ Theorem
• Random variable and its probability distribution
• Mean of a random variable