# CBSE Grade 12 Mathematics

### Relations and Functions

1

Types of Relations

2

One to One and Onto Functions

3

Composite Functions

4

Inverse of a Function

### Inverse Trigonometric Functions

1

Definition, Range, Domain, Principal Value Branch

2

Graphs of Inverse Trigonometric Functions

3

Elementary Properties of Inverse Trigonometric Functions

### Matrices

1

Concept, Notation, Order, Equality

2

Types of Matrices, Zero and Identity Matrix

3

Transpose of a Matrix

4

Symmetric and Skew Symmetric Matrices

5

Operation on Matrices: Addition Multiplication and Multiplication with a Scalar

6

Simple Properties of Addition, Multiplication and Scalar Multiplication

7

Commutativity of Multiplication of Matrices

8

Existence of Non-Zero Matrices

9

Concept of Elementary Row and Column Operations

10

Invertible Matrices

11

Uniqueness of Inverse

### Determinants

1

Determinant of a Square Matrix

2

Properties of Determinants

3

Minors, Co-Factors

4

Applications of Determinants in Finding the Area of a Triangle

5

Adjoint and Inverse of a Square Matrix

6

Consistency, Inconsistency and Number of Solutions of System of Linear Equations

7

Solving System of Linear Equations in two or three Variables

### Continuity and Differentiability

1

Continuity and Differentiability

2

Derivative of Composite Functions

3

Chain Rule, Derivative of Inverse Trigonometric Functions

4

Derivative of Implicit Functions

5

Concept of Exponential and Logarithmic Functions

6

Derivatives of Logarithmic and Exponential Functions

7

Logarithmic Differentiation

8

Derivative of Functions Expressed in Parametric Forms

9

Second Order Derivatives

10

Rolle’s and Lagrange’s Mean Value Theorems

### Applications of Derivatives

1

Applications of Derivatives: Rate of Change of Bodies

2

Increasing/Decreasing Functions

3

Tangents and Normals

4

Use of Derivatives in Approximation

5

Maxima and Minima

6

Simple Real-Life Problems

### Integrals

1

Integration as Inverse Process of Differentiation

2

Integration of a Variety of Functions by Substitution

3

Integration by Partial Fractions

4

Integration by Parts

5

Evaluation of Simple Integrals

6

Definite Integrals as a Limit of a Sum

7

Fundamental Theorem of Calculus

8

Basic Properties of Definite Integrals and Evaluation of Definite Integrals

### Applications of the Integrals

1

Applications in Finding the Area Under Simple Curves

2

Area Between Curves

### Differential Equations

1

Definition, Order and Degree

2

General and Particular Solutions of a Differential Equation

3

Formation of Differential Equation Whose General Solution is Given

4

Solution of Differential Equations by Method of Separation of Variables

5

Solutions of Homogeneous Differential Equations of First Order and First Degree

6

Solutions of Linear Differential Equation

### Vectors

1

Vectors and Scalars

2

Magnitude and Direction of a Vector

3

Direction Cosines and Direction Ratios of a Vector

4

Types of Vectors

5

Position Vector of a Point, Negative of a Vector

6

Components of a Vector

7

Addition of Vectors, Multiplication of a Vector by a Scalar

8

Position Vector of a Point Dividing a Line Segment in a Given Ratio

9

Scalar Product of Vectors

10

Vector Product of Vectors

11

Scalar Triple Product of Vectors

### Three - Dimensional Geometry

1

Direction Cosines and Direction Ratios of a Line Joining two Points

2

Cartesian Equation and Vector Equation of a Line

3

Coplanar and Skew Lines, Shortest Distance Between two Lines

4

Cartesian and Vector Equation of a Plane

5

Angle Between : Two Lines, Two Planes, A Line and a Plane

6

Distance of a Point From a Plane

### Linear Programming

1

Introduction, Related Terminology

2

Different Types of Linear Programming (L.P.) Problems

3

Mathematical Formulation of L.P. Problems

4

Graphical Method of Solution for Problems in two Variables

5

Feasible and Infeasible Regions

6

Feasible and Infeasible Solutions

7

Optimal Feasible Solutions

### Probability

1

Conditional Probability

2

Multiplication Theorem on Probability

3

Independent Events

4

Total Probability

5

Bayes’ Theorem

6

Random Variable and its Probability Distribution

7

Mean and Variance of Random Variable

8

Binomial Probability Distribution

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