Ayush Agarwal Maths

How to find Prime Numbers from 1 to 100 Easy Method......  Sieve of Eratosthenes. Round 1 : Cross out 1 because it is not a prime number. Round 2 : Encircle 2, cross out all the multiples of 2, other than 2 itself, i.e. 4, 6, 8 and so on. Round 3 : You will find that the next uncrossed number is 3. Encircle 3 and cross out all the multiples of 3, other than 3 itself. Round 4 : The next uncrossed number is 5. Encircle 5 and cross out all the multiples of 5 other than 5 itself. Round 5 : Continue this process till all the numbers in the list are either encircled or crossed out. All the encircled numbers are prime numbers. All the crossed out numbers, other than 1 are composite numbers. This method is called the Sieve of Eratosthenes.

     Important Terms in Mathematics  Perfect Number -  A number for which sum of all its factors is equal to twice the number is called a perfect number.  Prime Numbers -  The numbers other than 1 whose only factors are 1 and the number itself are called Prime numbers. Composite Numbers -  Numbers having more than two factors are called Composite numbers.

Algebra-  Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.  ALGEBRAIC EXPRESSIONS- A combination of constants and variables, connected by some or all of the operations +, -, ×, and  ÷ is known as an algebraic expression.                          Polynomials  Monomial  - Polynomial having one term.  Binomial  - Polynomial having two terms.  Trinomial  - Polynomial having three terms Zero Polynomial  - Polynomial having all its coefficient zero.  Constant Polynomial  - A polynomial having only a single term ( of real number).  Standard form  - Powers of x are either in increasing or decreasing order.  Addition of Algebraic expressions - In the addition of algebraic expression we collect the like terms and add them.  Practice Questions  1. Solve the following equation for P  : 2P/3 = 8 + 4P 2.If 8x + 5x + 2x + 4x = 114, then 7x + 8 = ?  3. If a = 3, then a 3 (a 3 -a)= ?  4. 5x + 2(x + 7) = 14x – 7. Find x ?  5.