15 Most Important Mathematical Equations
1
Quadratic Formula
x =
−b ± √b2 − 4ac2a
−b ± √b2 − 4ac2a
(a ≠ 0)
2
Factorization Identity
a2 − b2 = (a − b)(a + b)
3
Arithmetic Progression (A.P.)
an = a + (n − 1)d
Sn = n2[2a + (n − 1)d]
4
Geometric Progression (G.P.)
an = arn−1
Sn = a(rn − 1)r − 1 (r ≠ 1)
(if r = 1, then Sn = na)
5
Binomial Theorem
(a + b)n =
nΣr=0
(nr)
an−rbr
nΣr=0
(nr)
an−rbr
(n is a non-negative integer)
6
Distance Formula
d = √(x2 − x1)2 + (y2 − y1)2
7
Slope of a Straight Line
m = y2 − y1x2 − x1
(x2 ≠ x1)
8
Trigonometric Ratios (Right Triangle)
sin θ = PH,
cos θ = BH,
tan θ = PB
cos θ = BH,
tan θ = PB
9
Pythagoras Theorem
c2 = a2 + b2
10
Trigonometric Identities
sin2θ + cos2θ = 1
1 + tan2θ = sec2θ
1 + cot2θ = cosec2θ
11
Area of a Triangle
A = 12bh
12
Area of a Circle
A = πr2
C = 2πr
13
Volume of a Cylinder
V = πr2h
14
Volume of a Cone
V = 13πr2h
15
Surface Area and Volume of a Sphere
S = 4πr2
V = 43πr3
