# CBSE Class 12-humanities Syllabus

• ## Mathematics

• ### Relations and Functions

• Introduction to Relations
• Introduction to Functions
• Problems on Functions
• Composition of Functions
• Problems on Composition
• Binary Operations

### Inverse Trigonometric Functions

• Introduction: Inverse Trigonometry
• Properties of Inverse Trigonometry

### Matrices

• Introduction to Matrices
• Matrix Operations
• Transpose of A Matrix
• Elementary Operations

### Determinants

• Introduction to Determinants
• Properties of Determinants
• Properties and Applications of Determinants
• Minors and Co-factors
• Solving Simultaneous Equations

### Continuity and Differentiability

• Continuity
• Differentiability and Chain Rule
• Differentiation: Implicit Functions
• Differentiation of Exponential Functions
• Logarithmic Functions
• Differentiation of Parametric Functions
• Second Order Derivatives
• Mean Value Theorems

### Applications of Derivatives

• Rate of Change and Approximations
• Increasing and Decreasing Functions
• Tangents and Normals
• Maxima - Minima - I Derivative Test
• Maxima - Minima - II Derivative Test

### Integrals

• Introduction to Integration
• Integration by Substitution
• Integrals of Special Functions
• Integrals of Trigonometric Identities
• Integration by Partial Fractions
• Integration by Parts
• More Problems on Integration
• Limit of A Sum
• Properties of Definite Integrals
• Evaluating Definite Integrals
• Problems on Definite Integrals

### Applications of Integrals

• Area Between A Curve and A Line
• Area Between Two Curves

### Differential Equations

• Intro: Differential Equations
• Variable Separable Form
• Homogenous Differential Equations
• Linear Differential Equations

### Vector Algebra

• Introduction to Vector Algebra
• Properties of Vectors
• Scalar Product of Two Vectors
• Cross Product

### Three Dimensional Geometry

• Introduction to 3-D Geometry
• Cartesian Equation of A Line
• Skew Lines
• Equation of Plane
• Intercept Form and Family of Planes
• Distance of A Point From A Plane

### Linear Programming

• Introduction to Linear Programming
• Optimal Solution
• Solution of Linear Programming Problems

### Probability

• Introduction to Conditional Probability
• Independent Events
• Bayes' Theorem
• Distribution of Random Variables
• Mean and Variance of A Random Variable
• Binomial Distribution