Maths Formula For Revision

We all know that formula is the shortest way to  achieve any result. In Maths either you can go through the long way or you can have the process in your mind and the shortest way remembered in your mind and it should be on your tongue . Your mathematics skill will depend how much you have memorized the formula and how you can apply the formula in the fastest way. I have tried here to note down all the formulas , which will be required for a candidate who takes preparation for competitive exams.

It is not exhaustive and it will be modified daily or else once in a week.

1. (a+b)²=a² +b²+2ab.                   =>   a²+b² = (a+b)²-2ab

2. (a-b)²=a²+b²-2ab.                      =>   a²+b² =  (a-b)² + 2ab

3. a. (a+b)³=a³+b³+3a²b+3ab².      =>   a³+b³ =   (a+b)³ - 3a²b -3ab²

    b. (a+b)³=a³+b³+3ab(a+b)         =>   a³+b³ =   (a+b)³ - 3ab(a+b)      

4. (a-b)³=a³-b³-3a²b+3ab².            =>   a³ - b³ =   (a-b)³ + 3a²b -3ab²

    (a-b)³=a³-b³-3ab(a-b)                        =>      a³- b³ =   (a-b)³ + 3ab(a-b)       

5. a²-b²=(a+b)(a-b)

6. a. (a+b)² + (a-b)² = 2 (a² + b²)
    b. (a+b)² - (a-b)² = 4ab
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Mensuration - Formulae.

1. Area of a triangle    - sqrt ( s * (s-a) * (s-b *(s-c ) ) where * denotes multiplication.

                                      ( For scalene triangle )

                                    - (1/2 ) * base * height  (For right angled triangle.)

                                    - (a * sqrt(3))/4              (For equilateral  triangle.)

2. Area of Rectangle           – Length x Breadth .

3. Area of Square                -  (Side)^{2
     Diagonal of Square           - Sqrt(2) * a where a= side.}

4. Area of Rhombus           - (1/2) x d1 x d2   where d1=diagonal1 and d2=diagonal2.

                                            - Base * Height

5. Area of Trapezium         - (1/2) x height x (sum of length of parallel sides )

6. Area of Parallelogram     - (1/2) x height x (sum of length of parallel sides )

7. Area of Circle                   - PI * r * r ( where PI=3.14 , r=radius )

    Circumference of circle    - 2 * PI * r
8. Area of Cuboid                -2*(l*b+b*h+l*h) , symbols have usual meanings.
9. Volume of Cuboid          -Length * Breadth * Height
10. Diagonal of Cuboid       -Sqrt(l*l + b*b + h*h ), where symbols have usual meanings.

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