IMPORTANT MATHEMATICS CONCEPTS

IMPORTANT MATHEMATICS CONCEPTS

SIMPLE INTEREST:-

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

 Interest:- Extra money paid for using other’s money is called interest.

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

Let,
Principal = P 
Rate = R% 
per annum (p.a.) 
and Time = T years, 
Then,

(i)S.I. = [P * R * T / 100]
(ii) P = [100 * S.I. / R * T]
(iii)R = [100 * S.I / P * T] and
(iv)T = [100 * S.I. / P * R]



Numbers:-
 Natural Numbers:- Counting numbers 1, 2, 3, 4, 5,..... are called natural numbers.

 Whole Numbers:- All counting numbers together with zero form the set of whole numbers. Thus, (i) 0 is the only whole number which is not a natural number. (ii) Every natural number is a whole number

 Integers:- All natural numbers, 0 and negatives of counting numbers
 i.e., {…, - 3, - 2, - 1, 0, 1, 2, 3,...} together form the set of integers.

(i) Positive Integers:- {1, 2, 3, 4, …} is the set of all positive integers.

(ii) Negative Integers:- {- 1, - 2, - 3,…} is the set of all negative integers.

(iii) Non-Positive and Non-Negative Integers:- 0 is neither positive nor negative. So, {0, 1, 2, 3,….} represents the set of non-negative integers, while {0, - 1 , - 2 , - 3 ,…..} represents the set of non-positive integers.

•  Even Numbers:- A number divisible by 2 is called an even number, e.g., 2, 4, 6, 8, 10, etc.

•  Odd Numbers:- A number not divisible by 2 is called an odd number. e.g., 1, 3, 5, 7, 9, 11, etc.

•  Prime Numbers:- A number greater than 1 is called a prime number, if it has exactly two factors, namely 1 and the number itself.

Prime numbers upto 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.

•  Composite Numbers:- Numbers greater than 1 which are not prime are known as composite numbers, e.g., 4, 6, 8, 9, 10, 12.

Noticable point:-

(i) 1 is neither prime nor composite.
(ii) 2 is the only even number which is prime.
(iii) There are 25 prime numbers between 1 and 100.
 (iv)Co-primes : Two numbers a and b are said to be co-primes, if their H.C.F. is 1. e.g., (2, 3), (4, 5), (7, 9), (8, 11), etc. are co-primes.

 ( 1 + 2 + 3 + .....+ n) = n (n + 1 ) / 2
 (1 2 + 22 + 32 + ..... + n2) = n ( n + 1 ) (2n + 1) / 6

 (1 3 + 23 + 33 + ..... + n3) = n2 (n + 1)2 / 4