In Class 12 Mathematics, the syllabus typically covers a variety of topics divided into several chapters. Below is a list of chapters with their key topics for CBSE Class 12 Mathematics:
Chapter 1. Relations and Functions
- Types of relations (reflexive, symmetric, transitive, etc.)
- Functions: one-to-one, onto, bijective, and inverse functions
- Composition of functions
- Domain, co-domain, and range of functions
- Binary operations
Chapter 2. Inverse Trigonometric Functions
- Definition and properties of inverse trigonometric functions
- Graphs of inverse trigonometric functions
- Relations between trigonometric and inverse trigonometric functions
- Solving equations involving inverse trigonometric functions
Chapter 3. Matrices
- Types of matrices (square, rectangular, diagonal, identity, etc.)
- Operations on matrices (addition, multiplication, scalar multiplication)
- Determinants of matrices
- Adjoint and inverse of a matrix
- System of linear equations (using inverse matrices)
Chapter 4. Determinants
- Determinants of square matrices
- Properties of determinants
- Minors and cofactors
- Adjoint and inverse of a matrix using determinants
- Cramer’s rule for solving linear equations
Chapter 5. Continuity and Differentiability
- Continuity of functions at a point and in an interval
- Differentiability of functions
- Derivatives of composite and inverse functions
- Chain rule and implicit differentiation
- Differentiation of logarithmic, exponential, and trigonometric functions
- Applications of derivatives (tangents, normals, monotonicity, etc.)
Chapter 6. Application of Derivatives
- Rate of change of quantities
- Tangents and normals
- Increasing and decreasing functions
- Maxima and minima
- Approximations using differentials
Chapter 7. Integrals
- Indefinite integrals (basic integration formulas)
- Methods of integration: substitution, by parts, partial fractions, and integration using trigonometric identities
- Definite integrals and their properties
- Area under curves
- Application of integrals (area between curves, volumes of solids of revolution)
Chapter 8. Application of Integrals
- Area under the Curve
- Area between Two Curves
- Applications to Physics (Distance, Work, etc.)
- Volume of Solids of Revolution
- Area of Surface of Revolution
Chapter 9. Differential Equations
- Formation and solution of differential equations
- First order differential equations (separable, homogeneous, and linear)
- Solutions to linear differential equations
- Applications to real-life problems (growth and decay, motion of objects)
Chapter 10. Vector Algebra
- Vectors and their types (equal, zero, unit, and position vectors)
- Operations on vectors (addition, subtraction, scalar multiplication, dot product, cross product)
- Scalar and vector triple products
- Geometrical interpretations of vector operations
Chapter 11. Three-Dimensional Geometry
- Coordinates of a point in 3D
- Direction ratios and direction cosines
- Equation of a line and plane in 3D
- Angle between two lines, line and plane, and two planes
- Distance of a point from a plane
Chapter 12. Linear Programming
- Formulation of linear programming problems
- Graphical method of solution
- Feasible region and optimal solution
- Special cases of linear programming
Chapter 13. Probability
- Conditional probability and Bayes’ Theorem
- Random variables and their probability distributions
- Mean and variance of a probability distribution
- Binomial distribution and its properties
- Calculation of probabilities using distribution functions
These are the main chapters and topics covered in the CBSE Class 12 Mathematics syllabus. Depending on your school or board, the exact division of topics may vary slightly, but the core content remains the same.
