Mathematics Formulae

1. CS Creations
By: Chirag Patil
Mathematics Formulae’s
1) (a+b)2
= a2
+2ab+b2
2) (a-b)2
= a2
-2ab+b2
3) (a+b)(a-b) = a2
-b2
4) (x+a)(x+b) = x2
+ax+bx+ab = x2
+(a+b)x+ab
5) (a+b)3
= a3
+3a2
b+3ab2
+b3
= a3
+b3
+3ab(a+b)
6) (a-b)3
= a3
-3a2
b+3ab2
-b3
= a3
-b3
-3ab(a-b)
7) (a+b+c)2
= a2
+b2
+c2
+2ab+2bc+2ac
8) a3
+b3
= (a+b)(a2
-ab+b2
)
9) a3
-b3
= (a+b)(a2
+ab+b2
)
10) Area of Circle = πr2
11) Circumference of Circle = 2πr
12) Perimeter of a Rectangle = 2(Length+Breadth)
13) Perimeter of a Square = 4*The Length of one side
14) Area of Rectangle = Length * Breadth
15) Area of Square = (Side)2
16) Mean =
𝐴𝑑𝑑𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑎𝑙𝑙 𝑁𝑢𝑚𝑏𝑒𝑟𝑠
𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟𝑠

2. CS Creations
By: Chirag Patil
17) Median = (
𝑛+1
2
)th
Number
18) Mode = Most frequent Number / Number has Greatest
Frequency
19) Area of base of a Cone = πr2
20) Curved surface Area of a Cone = πrl
21) Total surface Area of a Cone =πr(l+r)
22) Volume of a Cone =
1
3
*πr2
h
23) Volume of Hemisphere =
2
3
πr3
24) Total surface Area of Hemisphere = 2πr2
+πr2
= 3πr2
25) Trigonometry Formulas
Sin θ =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑆𝑖𝑑𝑒
𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
Cosec θ =
𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑆𝑖𝑑𝑒
Cos θ =
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑆𝑖𝑑𝑒
𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
Sec θ =
𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑆𝑖𝑑𝑒
Sin θ =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑆𝑖𝑑𝑒
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑆𝑖𝑑𝑒
Cot θ =
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑆𝑖𝑑𝑒
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑆𝑖𝑑𝑒
1
𝑆𝑖𝑛 𝜃
= Cosec θ Sin θ * Cosec θ = 1
1
𝐶𝑜𝑠 𝜃
= Sec θ Cos θ * Sec θ = 1
1
𝑇𝑎𝑛 𝜃
= Cot θ Tan θ * Cot θ = 1
Cot2
θ = 1 + Cosec2
θ Tan2
θ = 1 + Sec2
θ
Sin2
θ + Cos2
θ = 1

3. CS Creations
By: Chirag Patil
Trigonometric
Ratio
Angle
(θ)
00
300
450
600
900
Sin θ 0 ½ 1/√2 √3/2 1
Cos θ 1 √3/2 1/√2 ½ 0
Tan θ 0 1/√3 1 √3 ND
Cosec θ ND 2 √2 2/√3 1
Sec θ 1 2/√3 √2 2 ND
Cot θ ND √3 1 1/√3 0