I.COM Business Mathematics Definitions
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.ProportionWhen two ratios are equal, the
resulting equation is called proportion. What are the different
types of Proportion?1. Direct proportion2. Inverse proportion3.
Continued proportion4. Compound proportionDirect ProportionWhen 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 ProportionWhen 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
PercentageRatio of any number with a standard 100 is called
Percentage.CommissionThe amount paid to an agent for his services
is called commission.BrokerageA 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 discount2. Cash discount3. Commodity discount4.
Retail discountTrade DiscountTrade 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 DiscountIt 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 discountInstead 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 PriceIt is the price marked on the article
on which the retailer is agrees to sale the article to general
public.
Define ProductThe result obtained by multiplying numbers is
called the product.Define quotient.The result obtain by division is
called quotientDefine InterestInterest is the amount of money paid
each year at a stated rate as a free from the use of borrowed
capital or investment.AnnuityA 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
Annuity1. Ordinary annuity2. Annuity due3. PerpetuityOrdinary
annuityIf the payments are made at the end of the payment period
then it is called ordinary annuity,Annuity DueIf the payments are
made at beginning of each period, the annuity is called annuity
due.PerpetuityWhen the payments start on a certain date and
continue for indefinite period it is said to be perpetuity.Payment
PeriodThe time between two successive payment dates is called
payment periodFunction 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 VariableThe variable to which values are
assigned arbitrarily is called independent variable.Dependent
VariableThe values, which are determined from independent variable,
are called dependent variable.VariableA symbol, which can assume
more than one numerical values throughout the discussion, is called
variable.ConstantA symbol which does not change its numerical value
throughout the discussion is called constant.Absolute ConstantA
symbol that represents the same value in all discussion is called
absolute constant.Arbitrary ConstantA symbol that represents the
same value throughout a given discussion but may represent another
discussion is called arbitrary constant.Linear FunctionFunction 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
FunctionIf y = g(x) = ax2 + bx +c where a, b IR , a 0, is called
Quadratic functionParabolaGraph of quadratic function is called
parabola.Explicit FunctionA function in which dependent variable y
is expressed in terms of independent variable x is called explicit
function. e.g., Y = X2 +4 Implicit FunctionA 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 FunctionAn 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)3Rectangular pointsLet 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.DomainThe set of all input values to which the rule applies
and make is domain.RangeThe set of all possible output values is
called the range.Even or Odd functionA function f(x) is called ani.
Even function if f(-x) = f(x)ii. Odd function if f(-x) = -
f(x)EquationAn open stance formed by the sign of equality ( = ) is
called an equation. Linear EquationWhen the highest degree of
variable in an equation is one, then equation is called linear
equation.e.g. 3x 7 = 0RootAll the values of variable that make the
equation true are called roots or solutions of the
equation.Quadratic EquationWhen highest power of unknown variable
in equation is two, then it is called quadratic equation.Standard
form of quadratic equation is ax2 + bx +c = 0Simultaneous
EquationMore than one equation, that is to be satisfied by the same
value of the variable involved, is called simultaneous
equations.Extraneous rootIf 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
SystemThe number system with base 2 is known as binary system, that
two digits are 0 and 1.Decimal Number SystemThe number system with
base 10 is known as Decimal number system. HexadecimalNumber
system, which consists of sixteen digits, etc.OctalNumber system,
which consists of eight digits, etcMatrixA rectangle array (or
table) of number enclosed by a pair of brackets and subject to a
certain rules is called a matrix.Order of MatrixThe number of rows
and number of columns in a matrix is called order of the
matrix.Types of MatrixSquare MatrixIf number of rows is equal to
the number of columns, then the matrix is called square matrix.Row
MatrixA matrix having only one row is called row matrix.Column
MatrixA matrix which having only one column is called column
matrix.Equal MatricesTwo matrices A and B are said to be equal if
and only if I. A and B have same orderII. Every element of A is
equal to the corresponding elements of B.Null or Zero MatrixThe
matrix in which all elements are zero is called null or zero matrix
and it is denoted by O.Diagonal MatrixA 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 MatrixA square matrix whose principal
diagonal elements are scalar (say) k and all other elements are
zero, then it is called scalar matrix.Identity MatrixA 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 MatrixA 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 MatricesTwo 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
MatrixLet 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
MatrixIf 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 MatrixIf determinant of a square matrix is
equal to zero than it is called singular matrix.Inverse of MatrixI
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-1.5Al-Hamd
Science & Commerce Academy Murad Pur | Prepared by : Tahsin
Raza
