MyMaths MyLife

Factorial is defined for any positive integer. It is denoted by !. Thus “Factorial n” is written as n!. n! is defined as the product of all the integers from 1 to n.

Thus n! = 1.2.3.. ... (n-1),n.

Example 5! = 1*2*3*4*5 = 120

0! is defined to be equal to 1.
Therefore 0! = 1 and 1! = 1

An equation which has the unknown quantity raised only to powers which are whole numbers and the highest power being the square of the unknown quantity, is called a quadratic equation.
The most general form of a quadratic equation is ax^2 + bx + c = 0.
There are two values of x that satisfy such a quadratic equation. These values are called the roots of the quadratic equation.

The roots of the above quadratic equation are given by (-b±√(b^2-4ac))/2a

For ax^2 + bx + c = 0, sum of the roots = -b/a; Product of the roots = c/a

In the previous post we have discussed little bit about algebra. Here take a look about variables and constants.

In arithmetic, the numbers used have definite values. These values do not change. But the letters used in algebra have no particular value and may have any value assigned to them.

Consider,
The perimeter 'p' of a rectangle of length 'l' and breadth 'b' is p = 2(l+b). Here '2' is a fixed number. The letters p, l and b have no fixed value. They can take any positive value depending upon the size of the rectangle.

So, a letter symbol which can take any value of a certain set is called a variable. Above p, l and b are variables. Quantities which have only one fixed value are called constants. Above 2 is a constant.

Algebra is my favorite part in maths because it is easy. You will not find any difficulty when comparing with other parts.

Algebra is the part of the maths. In algebra, letters are used to represent numbers. The letters which are used to represent numbers are called literal numbers or literals. Using of literals in place of numerals helps us to think in more general terms and obtain a rule.

Consider 5*6 = 6*5 , -2*3 = 3*-2 , (1/2)*(3/4) = (3/4)*(1/2)
We can generalize the fact by the statement that the product of two rational numbers remains same in whichever order they are multiplied.
This can further be simplified by using symbols as, a*b = b*a , where a and b are any two rational numbers.

Permutations and combinations is one of the important areas in many exams because of two reasons. The first is that solving questions in this area is a measure of students reasoning ability. Secondly, solving problems in areas like probability requires through knowledge of permutations and combinations.

If one operation can be performed in 'm' ways and, a second operation then can be performed in 'n' ways, the number of ways of performing the two operations will be m*n.

Permutations:
The different arrangements of a given number of things by taking some or all at a time,are called permutations.
eg:- All permutations( or arrangements)made with the letters
a,b,c by taking two at a time are (ab,ba,ac,ca,bc,cb).

ombinations:
Each of the group or selections which can be made by taking some or all of a number of items is called a combination.
eg:- All permutations( or arrangements)made with the letters
a,b,c by taking two at a time are (ab,bc,ca).

Probability is nothing but chances of occurrences. I go to my college by bus. I find my college bus for every 5 buses. So the Probability of getting my bus is 1 out of 5.

Probability is an important topic for the entrance exams. This is a topic that you will be requiring in your management courses also. Hence the basic concepts that we are going to learn should be understood thoroughly. Because their usefulness goes beyond the entrance exams.

The word Probability is used, in a broad sense, to indicate a vague possibility that something might happen.

Terms we use in Probability are
Experiment:
An operation which can produce some well-defined outcome is called an experiment.

Random Experiment:
An experiment in which all possible out comes are known and the exact output cannot be predicted in advance is called a random experiment.

Basic Mathematical Symbols:

+ Plus

- Minus

× Multiply

÷ Divide

= Equal

% percent

: Ratio

> Greater than

< Less than

.∙. Therefore

∙.∙ Because

± Plus- minus sign

≠ Not equal to

≤ Less than or equal to

≥ Greater than or equal to

∞ Infinity

≈ Almost equal to