Chapter - Alzebra

(a + b)³     =  a³  +  b³ + 3a²b + 3b²a                                      

(a - b)³      = a³ - b³ - 3a²b  + 3b²a

a³ + b³      = (a + b)[a² - ab + b²]  

a³ -  b³      =(a -  b)[ a²   +   b²  +  ab]

(a + b)²     =   a²  +  2ab + b²   

(a - b)²     =   a² - 2ab  + b²

a² -  b²    =   (a + b)(a - b)

(a + b + c)²  = a² + b² + c² + 2ab + 2bc + 2ca

a² + b²       = (a +b)² - 2ab  

a²  + b²        =  (a + b)²  - 2ab

 

Chapter - Geometrical Formulas

Area of circle    =    πr²  ,    where r is the radius of the circle

Acute angle      =   Acute angle are those angle which are less than 90°                    

Obtuse angle    = obtuse angle are those angle which are greater than 90°

 Rectangle:-      =  Area :  Length x breadth        Perimeter :  2(length + breadth)

Square :-           =  Area :  (side)²                        Perimeter :   4(side)

Herons Formula :  s = (a + b + c) /2           where   a = first side

                                =√s(s-a)(s-b)(s-c)         b = second side

                                                                     c = third side

Chapter - Mensuration Formulas

Name of the solid	Lateral/Curved surface area	Total surface area	Volume
Cuboid	2h(l + b )	2(lb  + bh  + hl)	lbh
Cube	4a2	6a2	a3
Right Circular cylinder	2πrh	2πr(h + r )	π r2h
Right Circular cone	π rl	π r(l + r )	1/3 πr2h
Sphere	4 πr2	4 πr2	4/3 πr3
Hemisphere	2 πr2	3 πr2	2/3 πr3
Where    r : radius         h: height      l: Slant height