Class 12th Mathematics

Notes
Mathematics

RELATIONS AND FUNCTIONS

RELATIONS AND FUNCTIONS : A relation R between two non-empty sets A and B is a subset of their Cartesian product A × B.

Chapter 1

Inverse trigonometric functions

Inverse trigonometric functions : The domains and ranges (principal value branches) of inverse trigonometric functions are given in the following table:

Chapter 2

MATRICES

MATRICES : A matrix is an ordered rectangular array of numbers (real or complex) or functions or names or any type of data.

Chapter 3

DETERMINANTS

DETERMINANTS : To every square matrix A = [aij], a unique number (real or complex) called the determinant of the square matrix A can be associated.

Chapter 4

CONTINUITY & DIFFERENTIABILITY

CONTINUITY & DIFFERENTIABILITY : A real function f is said to be continuous if it is continuous at every point in the domain of f.

Chapter 5

Application of derivatives

Application of derivatives : If two variables x and y are varying with respect to another variable t, i.e., if x = f(t) and y =g(t) then by Chain Rule

Chapter 6

INTEGRALS

INTEGRALS : Integration is the inverse process of differentiation. The process of finding the function from its primitive

Chapter 7

Application of integrals

Application of integrals : Elementary area: The area is called elementary area which is located at any arbitary position within the region

Chapter 8

Differential equations

Differential equations : Differential Equation: An equation involving derivatives of the dependent variable with respect to independent variable (variables)

Chapter 9

VECTOR ALGEBRA

VECTOR ALGEBRA : A quantity which has magnitude as well as direction is called a vector. A directed line segment is called a vector.

Chapter 10

THREE DIMENSIONAL GEOMETRY

THREE DIMENSIONAL GEOMETRY : The coordinates of a point R which divides the line joining the points P(x1, y1, z1) and Q(x2, y2, z2 ) internally in ratio m : n

Chapter 11

LINEAR PROGRAMMING

LINEAR PROGRAMMING : Linear programming is the process of taking various linear inequalities relating to some situation and finding the best value

Chapter 12

PROBABILITY

PROBABILITY : In the experimental approach to probability, we find the probability of the occurrence of an event by actually performing the experiment

Chapter 13

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