Welcome to our

Business mathematics Presentation

Special Thanks To Kazi Md.Nasir Uddin Assistant Professor Department of AIS Faculty Of Business

Studies Jagannath University

Name Roll(merit) Nabanita Chakrabarty 447Md.Sakib Hossain Rabbi

446

Jasim Uddin 449Md.Ashrafur Rahman 450Md.Badruzzam 451Raihan Ahamed 452Md.Shariful Haque 453Zahidul Islam 455

Group member

Presentation Topic

“Business mathematics is a very powerful tool and analytical process that results in and

offers an optimal solution , in spite of its limitations”

WHAT IS MATHEMATICS? Mathematics is a language, it is the

transmission of knowledge.

Limitations of Mathematics

RigiditySo expensive to use tools for

compulsionDelicacy or coarseness

Presenter Nabanita Chakrabarty Merit:447 Presentation Topic Mathematics Of Finance

Mathematics of FinanceAnnuity A regular periodic payment made by an insurance

company to a policyholder for a specified period of time.

Types of Annuity Annuity Certaini. Annuity Dueii. Annuity Immediate Annuity Contingent

Present value Present value describes how much a future sum of money is worth today. The formula for present value is: PV = CF/(1+r)n

Future value Refers to a method of calculating how much the present value (PV) of

an asset or cash will be worth at a specific time in the future

Simple Interest A quick method of calculating the interest charge on a loan. Simple

interest is determined by multiplying the interest rate by the principal by the number of periods.

Compound Interest Interest which is calculated not only on the initial principal but

also the accumulated interest of prior periods. Compound interest differs from simple interest in that simple interest is calculated solely as a percentage of the principal sum.

Depreciation The principle value is diminished every year by a certain constant amount,

and in the subsequent period the diminished value becomes the principle value

Presenter MD.Ashrafur Rahman Merit:450

Presentation Topic LOGARITHM

Logarithms – making complex calculations easyJohn Napier

John Wallis

Jost Burgi

Johann Bernoulli

Logarithms

102 = 100“10 raised to the power 2 gives 100”

Base

IndexPower

ExponentLogarithm

“The power to which the base 10 must be raised to give 100 is 2”

“The logarithm to the base 10 of 100 is 2”

Log10100 = 2

Number

Logarithms

102 = 100Base

Logarithm

Log10100 = 2

Number

Logarithm

Num

ber

Base

y = bx

Logby = x

23 = 8 Log28 = 3

34 = 81 Log381 = 4

Log525 =2 52 = 25

Log93 = 1/2 91/2 = 3

logby = xis the inverse of

y = bx

Presenter MD.Jasim Uddin Merit:449

Presentation Topic NUMBER SYSTEM

Number System Number theory is one of the oldest branches of pure mathematics

and focuses on the study of natural numbers. Arithmetic is taught in schools where children begin with learning numbers and number operations. The first set of numbers encountered by children is the set of counting numbers or natural numbers.

In mathematics, a number system is a set of numbers. As mentioned earlier, children begin by studying the natural numbers: 1,2,3, ... with the four basic operations of addition, subtraction, multiplication and division. Later, whole numbers 0,1,2, .... are introduced, followed by integers including the negative numbers. 

Flow Chart of Number System

Examples

Presenter Zahidul Islam Merit:455

Presentation Topic EQUATION

Equation: • Equation is a mathematical statement that

uses the equal sign to show that the two expressions are equal. The equity is true only for certain value or values symbolized generally by x,y,z etc. for example:

The equation: 3x+5=2x+7 is true for x=2 but not for x=3.

Classification:

Linear equation Non- linear equation

Classification:• Linear equation: A

linear equation is an equation for a straight line. It is made up of two expressions equal to each other. For example,

• “y=2x+1”

• Non-linear equation: Equation whose graph doesn’t form a straight line is called a non-linear equation the variables are either of degree greater than 1 or less than 1 but never 1. For example,

• x2-x-1=0

Degree of equation:

The degree of equation is denoted by the highest index of the variable in any equation.

Quadratic equation: • A quadratic equation is one that can be

written in the standard form of ax2+bx+c=0. Where a,b and c are real number and a is not equal to zero. And the highest power of quadratic equation is 2. For example,

• 7x2+9x+2=0

Cubic equation:• An equation of third is called cubic

equation. The general degree form of a cubic equation is x3+bx2+cx+d=0. A cubic equation has three possible values of its variable and at least one of them is real number. For example,

• X3 +6x2+12x+7=0

Bio-quadratic equation:

• Bio-quadratic equation is a type of equation which relates to the fourth degree of power and does not contain any terms of the third or first power. for example,

• x4+5x2+4=0• x4-4=x2-1

•Identity: An identity is true any value of the variable. For example,

a2+2ab+b2= (a+b)2

• Variable: A variable is a symbol for number we don’t know. Generally it is written as x,y,z etc.

Inequality:•An inequality is a mathematical sentence in which two expressions are joined by relations symbols such as (not equal to), > (greater than), < (less than), (greater than or equal to), (less than or equal to). Examples of inequalities are,

•

• a>b : a is greater than b• a<b : a is less than b•

Presenter Md.Badruzzaman Merit:451

Presentation Topic Indices

Indices• Definition• In all cases a factor which multiplies is called the base and

the number of time multiplied is called the power or the index.

power

• Example: a*a=a2

base

Laws of indices

Fractional Indice In a positive fractional index the numerator represents

the power and the denominator the root.For example:

Presenter MD.Shariful Haque Merit:453

Presentation Topic Sequence&Progressions

SequenceWhat is a Sequence?A set of a real number in a definite order formed according to some law is cale a sequence

A Sequence is a list of things (usually numbers) that are in order.

Arithmetic Progression• An arithmetic progression is a sequence

whose terms increase or decrease by a constant number.

Geometric Progression• Arithmetic progression is a sequence whose

terms increase or decrease by a constant ratio.

PresenterMD.Sakib Hossain Rabbi Merit:446

Presentation Topic SET THEORY

Set theoryWhat is set? A set is collection of well-defined and well distinguished

objects .

For example, the items you wear: shoes, socks, hat, shirt, pants, and so on.

Types of Set Finite set When the elements of a set can be counted by a finite number of elements then the set is called finite

set.Example:A={1,2,3,4,5,6} B={1,2,3,4,5……,500} Infinite Set If the elements of a set cannot be counted by a finite number , the set is called infinite set.Example:A={1,2,3…..} B={x| x is an odd number}

Singleton Set A set containing only one element.Example: A={1} Empty set Which has no elementExample: The set of people who have travelled from the earth to the sun is an

empty set.

Equal Set Two sets A & B ,if every element of A is also an element of B ,and every element of B also in an element A.Example: A={3,5,5,9} B={9,5,3}Singleton Set A set containing only one element.Example: A={1}Empty set Which has no elementExample: The set of people who have travelled from the earth to the sun is an empty set. Subset If every element of set A is also an element of a set B then set A is called subset of B.

Equivalent Set• If the elements of one set can be put in to one to

one correspondence with the elements of another set , the the two sets are called equivalent.

• Example: A={a,b,c,d}• B={1,2,3,4} Proper subset• If B is a proper subset of A , then all elements of B are in A

but A contains at least one element that is not in B . Venn Diagram A venn diagram is a pictorial representation. It was named

after English logician John Venn.

Presenter Raihan Ahamed Merit:452

Presentation TopicPermutations&combinations

Permutations All possible arrangements of a collection of

things, where the order is important.

Example: You want to visit the homes of three friends Alex ("a"), Betty ("b") and Chandra ("c"), but haven't decided in what order. What choices do you have?

Answer: {a,b,c} {a,c,b} {b,a,c} {b,c,a} {c,a,b} {c,b,a} 

Combinations• A collection of things, in which the order does not matter.

Example: You are making a sandwich. How many different combinations of 2 ingredients can you make with cheese, mayo and ham?

Answer: {cheese, mayo}, {cheese, ham} or {mayo, ham}

Formulas of Permutations & combinations