Ayush Agarwal Maths

Percentage -   According to mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted by using the percent sign, "%" .  Percentage formula -  Percentage = (Obtained marks/Total                                marks)×100 Example :-  3/5 ×100 = 0.60×100 = 60% =                                  60percent About Percentage - 1. 10% is equal to 1/10 fraction 2.  20% is equivalent to ⅕ fraction 3.  25% is equivalent to ¼ fraction 4.  50% is equivalent to ½ fraction 5.  75% is equivalent to ¾ fraction 6.  90% is equivalent to 9/10 fraction Points to remember :- 1. A percentage is a dimensionless number, it has no unit of measurement.  Practice Questions - Q1.   Convert as a fraction and as a decimal :  ...

Factorisation - The process of finding two or more expressions whose product is the given expression is called factorisarion. 

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...

Rational numbers :- The numbers of the form p/q , where p and q are integers and q is not equal to zero, q≠ 0 , are called rational numbers.  0 is neither positive nor negative.  Example-  Numbers 3/5 , -1/14 is a rational number.  - Every integer is a rational number.  - Every whole number is a rational number because every whole number can be expressed as a fraction. Positive rationals - A rational number is said to be positive if its numerator and denominator are either both positive or both negative.  Example - 3/7 or -6/11 are positive rationals.  Negative rationals - A rational number is said to be negative if its numerator and denominator are of opposite signs.  Example- -7/9, 4/-11 are negative rationals.  Some important facts :- 1. The product of a rational number and its reciprocal is 1. 2.  Zero '0' has no reciprocal.  3. The reciprocal of a positive rational number is positive.  4. The reciprocal of a neg...

                   CUBES AND CUBE ROOTS Cube number- A cube number is a number multiplied by itself twice, or we can say the cube of a number m is its third power.  For example- m³ =  m  ×  m 2  =  m  ×  m  ×  m . 8³ = 8 × 8 2  = 8  × 8  × 8 = 512 .  15³ = 15  ×  15 2  =  15  ×  15  ×  15 = 3375 .   Perfect cube - A natural number is said to be a perfect cube if it is the cube of some natural numbers.  Examples-   1 ³ = 1, 2³ = 8, 3³ = 27, 4³ = 64,  etc.            Thus 1, 8, 27, 64 etc.., are perfect cubes.  Facts About cube numbers:- 1. The cube of a number is that number raised to the power 3 .  2. The cube of an even natural number is even.  3. The cube of an odd natural number is odd.  4.  Numbers ending in 1, 2, 3, 4, 6, 7...