Class 12 Mathematics

Below is an overview of the key units and topics typically included in the Class 12 Mathematics syllabus:

1. Relations and Functions

• Types of Relations: Definition, types (reflexive, symmetric, transitive, equivalence).
• Functions: Definition, types of functions (one-to-one, onto, inverse functions).
• Composition of Functions: Understanding composition and its properties.

2. Inverse Trigonometric Functions

• Definition and Range: Introduction to inverse trigonometric functions and their properties.
• Graphing: Graphs of inverse trigonometric functions.
• Applications: Solving trigonometric equations using inverse functions.

3. Matrices and Determinants

• Matrices: Definition, types, and operations (addition, multiplication).
• Determinants: Calculation of determinants and properties.
• Applications: Solving systems of linear equations using matrices and determinants.

4. Continuity and Differentiability

• Continuity: Definition and types of discontinuities.
• Differentiability: Rules of differentiation, derivatives of functions, and applications.
• Mean Value Theorem: Understanding and applying the Mean Value Theorem.

5. Applications of Derivatives

• Rate of Change: Understanding and calculating rates of change in real-life contexts.
• Tangent and Normal: Finding equations of tangent and normal to curves.
• Maxima and Minima: Identifying local maxima and minima using the first and second derivative tests.

6. Integrals

• Indefinite Integrals: Basic rules of integration and standard integrals.
• Definite Integrals: Properties and applications of definite integrals.
• Area Under Curves: Calculating areas using definite integrals.

7. Differential Equations

• Introduction: Definition and order of a differential equation.
• Solving Differential Equations: Methods for solving first-order differential equations.
• Applications: Real-life applications of differential equations.

8. Vector Algebra

• Vectors: Definition, types (position vector, zero vector), and operations (addition, scalar multiplication).
• Dot and Cross Products: Understanding and calculating dot and cross products of vectors.
• Applications: Geometric interpretations and applications in physics.

9. Three-Dimensional Geometry

• Coordinates in Space: Understanding three-dimensional coordinates.
• Distance Formula: Calculating distance between points in 3D space.
• Direction Cosines: Concept of direction cosines and angles between lines.

10. Linear Programming

• Introduction: Basic concepts of linear programming and real-life applications.
• Graphical Method: Solving linear programming problems using graphical methods.
• Feasible Region: Identifying and interpreting feasible regions.

11. Probability

• Probability Theory: Basic concepts and definitions.
• Conditional Probability: Understanding and calculating conditional probabilities.
• Bayes’ Theorem: Application of Bayes' theorem in solving problems.

12. Statistics

• Measures of Central Tendency: Mean, median, mode, and their applications.
• Measures of Dispersion: Range, variance, and standard deviation.
• Probability Distributions: Introduction to random variables and probability distributions.