MyMaths MyLife

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

I am a big fan of cricket, i rate cricketers on the basis of their averages. Average is nothing but consistency.

Average is very simple but effective way of representing an entire group by a single value.

Average of any number of quantities will always be higher than the lowest value and lower than the highest value of items whose average is being taken.

1.Average = Sum of quantities/Number of quantities.

2.Suppose a man covers a certain distance at x kmph and an equal distance at y kmph,then the average speed during the whole journey is (2xy/x+y) kmph.

Sometimes it so happens that the borrower and the lender agree to fix up a certain unit of time ,say yearly or half-yearly or quarterly to settle the previous account.
In such cases ,the amount after the first unit of time becomes the principal for the 2nd unit ,the amount after second unit becomes the principal for the 3rd unit and so
on. After a specified period ,the difference between the amount and the money borrowed is called Compound Interest for that period.

Formulae:
As we discussed in the simple interest
Let principal=p,Rate=R% per annum Time=nyears

1.When interest is compounded Annually, Amount=P[1+(R/100)]n
2.When interest is compounded Half-yearly, Amount=P[1+((R/2)100)]2n
3.When interest is compounded Quarterly, Amount=P[1+((R/4)100)]4n
4.When interest is compounded Annually,but time in fractions
say 3 2/5 yrs Amount=P[1+(R/100)]3[1+((2R/5)/100)]
5.When rates are different for different years R1%,R2%,R3%
for 1st ,2nd ,3rd yrs respectively Amount=P[1+(R1/100)][1+(R2/100)][1+(R3/100)]
6.Present Worth of Rs.X due n years hence is given by
Present Worth=X/[1+(R/100)]n

When you borrow money from some one he will give you money for interest. Usually money lender calculates simple interest and gives you money.

The interest is calculated only on the principal through out the loan period, it is called simple interest.

Principal or Sum:- The money borrowed or lent out for a certain period is called Principal or the Sum.

Interest:- Extra money paid for using others money is called Interest.

Simple Interest:- If the interest on a sum borrowed for a certain period is reckoned uniformly,then it is called Simple Interest.

Formulae:
Principal = P
Rate = R% per year
Time = T years. Then,

(i)Simple Interest(S.I)= (P*T*R)/100

(ii) Principal(P) = (100*S.I)/(R*T)
Rate(R) = (100*S.I)/(P*T)
Time(T) = (100*S.I)/(P*R)