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Ratio
When two quantities or numbers m and n are compared by division the quotient
“r” is called a ratio between m and n and written as m/n = m : n.
Proportion
When two ratios are equal, the resulting equation is called proportion.
What are the different types of Proportion?
1. Direct proportion
2. Inverse proportion
3. Continued proportion
4. Compound proportion
Direct Proportion
When two quantities are so related that an increase (or decrease) in one quantity
causes a corresponding increase (or decrease) in other quantity. They are said to
be directly proportional to each other e.g.,

1) Less the number of telephone calls, less the amount of bills.
2) Faster the speed of a car, the greater the distance covered.
Inverse Proportion
When two quantities are so related with one another that an increase in one
quantity results in a corresponding decrease in other quantity or decrease in one
quantity causes a corresponding increase in other one, then they are called inverse
of each other, e.g.
1) The greater the speed of a car, the less time is required to cover the distance.
2) Smaller the body, greater the acceleration.
Define Break even point.
Level of production and sales where the sales revenue is just equal to total cost. If
C represent the total cost and R represent the total revenue then at break even
point C = R.
Net Price
It is obtained by deduction the amount of trade discount as well as amount of cash
discount from the bill on the basis of list price.

Define Percentage
Ratio of any number with a standard 100 is called Percentage.
Commission
The amount paid to an agent for his services is called commission.
Brokerage
A broker is an agent who brings the prospective buyers and seller together and
negotiates the sale. His commission is called brokerage.
What are different types of discount?
1. Trade discount
2. Cash discount
3. Commodity discount
4. Retail discount
Trade Discount
Trade discount is the reduction offered by the manufacturer to the wholesaler or
by the wholesaler to the retailer on the list price of goods is called trade discount.
Cash Discount
It is the reduction on the amount of the bill, offered by the manufacturer to the
wholesaler or wholesaler to retailer, for ready cash payment, or if the payment is
made within a specified time.
Commodity discount
Instead of offering a reduction in price, the seller may give more goods than
quantity charged, for such benefit is called commodity discount.
Retail Discount
A reduction in the selling price of an article offered by the retailer to the general
public is known as retail discount.
Defined Marked Price
It is the price marked on the article on which the retailer is agrees to sale the
article to general public.

Define Product
The result obtained by multiplying numbers is called the product.

Define quotient.
The result obtain by division is called quotient
Define Interest
Interest is the amount of money paid each year at a stated rate as a free from the
use of borrowed capital or investment.
Annuity
A series of payments, which are made at regular intervals of time such as weekly,
monthly quarterly, semi annually is known as annuity.
What are the different types of Annuity
1. Ordinary annuity
2. Annuity due
3. Perpetuity
Ordinary annuity
If the payments are made at the end of the payment period then it is called
ordinary annuity,
Annuity Due
If the payments are made at beginning of each period, the annuity is called annuity
due.
Perpetuity
When the payments start on a certain date and continue for indefinite period it is
said to be perpetuity.
Payment Period
The time between two successive payment dates is called payment period
Function
If two variables are so related that for each value that may be assigned to one of
the variables, there corresponds exactly one value of the second, variable, then the
second variable is called function of the first variable.
Independent Variable
The variable to which values are assigned arbitrarily is called independent
variable.

Dependent Variable
The values, which are determined from independent variable, are called dependent
variable.
Variable
A symbol, which can assume more than one numerical values throughout the
discussion, is called variable.
Constant
A symbol which does not change its numerical value throughout the discussion is
called constant.
Absolute Constant
A symbol that represents the same value in all discussion is called absolute
constant.
Arbitrary Constant
A symbol that represents the same value throughout a given discussion but may
represent another discussion is called arbitrary constant.
Linear Function
Function of the type y = f(x) = ax + b where a, b ∈ IR , a ≠ 0, is called linear
function. Graph of linear is always straight line.
Quadratic Function
If y = g(x) = ax2 + bx +c where a, b ∈ IR , a ≠ 0, is called Quadratic function
Parabola
Graph of quadratic function is called parabola.
Explicit Function
A function in which dependent variable y is expressed in terms of independent
variable x is called explicit function. e.g., Y = X2 +4
Implicit Function
A function where variable y is not expressed in terms of independent variable x is
called implicit function. In such types of functions y and x and both appear
together in an equation.
e.g. XY +6Y2 + X2 + 4 = 0

What is meant by Abscissa?
The x-coordinate of a point is called Abscissa.
Algebraic Function
An expression containing a finite number of terms involving powers and roots of
the variable connected by arithmetical operations is called algebraic function. for
example F(X) = (9X + 3)3
Rectangular points
Let us take any point P in the first quadrant and draw perpendiculars on x-axis
and y-axis from his point. The values of x and y at the points where the
perpendiculars meet these axes are called the rectangular points.
Domain
The set of all input values to which the rule applies and make is domain.
Range
The set of all possible output values is called the range.
Even or Odd function
A function f(x) is called an
i. Even function if f(-x) = f(x)
ii. Odd function if f(-x) = - f(x)
Equation
An open stance formed by the sign of equality ( = ) is called an equation.
Linear Equation
When the highest degree of variable in an equation is one, then equation is called
linear equation.
e.g. 3x – 7 = 0
Root
All the values of variable that make the equation true are called roots or solutions
of the equation.
Quadratic Equation
When highest power of unknown variable in equation is two, then it is called
quadratic equation.
Standard form of quadratic equation is ax2 + bx +c = 0

Simultaneous Equation
More than one equation, that is to be satisfied by the same value of the variable
involved, is called simultaneous equations.
Extraneous root
If any element of the solution of an equation reduced to quadratic form does not
satisfy the original equation. The such an element of the solution is called
extraneous root.
What is a reciprocal equation?
Equation of the form Ax4 + Bx3 + A = 0 is called reciprocal equation. In reciprocal
equation, the coefficient of the beginning and end are equal.
Binary Number System
The number system with base 2 is known as binary system, that two digits are 0
and 1.
Decimal Number System
The number system with base 10 is known as Decimal number system.
Hexadecimal
Number system, which consists of sixteen digits, etc.
Octal
Number system, which consists of eight digits, etc
Matrix
A rectangle array (or table) of number enclosed by a pair of brackets and subject to
a certain rules is called a matrix.
Order of Matrix
The number of rows and number of columns in a matrix is called order of the
matrix.
Types of Matrix
Square Matrix
If number of rows is equal to the number of columns, then the matrix is called
square matrix.
Row Matrix
A matrix having only one row is called row matrix.

Column Matrix
A matrix which having only one column is called column matrix.
Equal Matrices
Two matrices A and B are said to be equal if and only if
I. A and B have same order
II. Every element of A is equal to the corresponding elements of B.
Null or Zero Matrix
The matrix in which all elements are zero is called null or zero matrix and it is
denoted by O.
Diagonal Matrix
A square matrix A = [aij] or order m x n is called diagonal matrix. If aij = 0 (for all) i
≠ j and aij ≠ 0, when i = j.
Scalar Matrix
A square matrix whose principal diagonal elements are scalar (say) k and all other
elements are zero, then it is called scalar matrix.
Identity Matrix
A square matrix or order nxn in which principal diagonal elements are equal to 1
and all other elements are zero, then it is called identity or Unit matrix and it is
denoted by In.
Rectangular Matrix
A matrix in which number of rows is not equal to the number of columns is known
as rectangular matrix.
Additive Inverse
Let A be a matrix of order mxn, the matrix each of whose elements is additive
inverse of the corresponding element of A is called additive inverse of a matrix A
and is denoted by –A.
Multiplication of Matrices
Two matrices A and B are said to be conformable for multiplication “AB” if number
of columns in A is equal to the number of rows B.

Transpose of Matrix
Let A be a matrix of order mxn, if rows are changed into columns or columns into
rows of matrix A, the matrix so obtained is called transpose of matrix A and is
denoted by At.
Symmetric Matrix
If A = At If rows are changed into columns or columns into rows of matrix A and
the matrix remains same then matrix is called symmetric matrix.
Determinant
Let A be a square matrix or real numbers, then we can associate the matrix A with
a real number. This real number is called a determinant of the matrix A and
denoted by A .
Singular Matrix
If determinant of a square matrix is equal to zero than it is called singular matrix.
Inverse of Matrix

I A is a non-singular square matrix, then matrix Adj. of A / A  is said to be
inverse of the matrix A. It is denoted by A-1.

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