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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CBSE Grade 12 Mathematics
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