math formulas

area of a square

s²

area of a circle

πr²

area of a trapezoid

(b₁+b₂)/2 * h

area of a triangle

(bh)/2

area of equilateral triangle

(√3)/4 * s²

area of polygon inscribed in a circle

(1/2)*nr²sin(2π)/n

surface area of a cube

6s²

surface area of a cylinder

2πrh + 2πr²

surface area of a sphere

4πr²

volume of a sphere

(4/3)πr³

volume of a cylinder

πr²*h

volume of a cone

πr²*h(1/3)

volume of a pyramid

lw*h(1/3)

standard quadratic formula

ax² + bx + c = 0

vertex form of quadratic equation

a(x - h)² + k

sum of roots of quadratic

-b/a

product of roots of quadratic

c/a

standard equation of a circle

(x - h)² + (y - k)² = r ²

equation of a hyperbola

ax² + by² + cx + dy + e = 0 [where either a or b is +]

permutation probability

nPr = n!/(n-r)!

combination probability

n!/[(n-r)!r!]

round table permutation

(n-1)!

simple interest

A = P(1 + rt)

compound interest

A = P(1 + [r/k])^kt

F → C

C = (F-32)*5/9

C → F

F = C * 9/5 - 32

STP temperature

273K

STP pressure

760mmHg/1atm

series circuit

R_T = R₁ + R₂ + R₃ …

parallel circuit

1/R_T = 1/R₁ + 1/R₂ + 1/R₃ …

mirrors

1/f = 1/d_i + 1/d_o

magnification

-d_i/d_o

arithmetic sequence difference

a₂ - a₁ = a₃ - a₂

artithmetic sequence term

a_n = a_x + d(n-x)

arithmetic sequence sum

S_n = n(a₁ + a_n)/2

geometric series ratio

r₂/r₁ = r₃/r₂

geometric series term

a_n = a_x * r^(n-x)

geometric series sum (finite)

S_n = [a(1-rⁿ)]/(1-r)

geometric series sum (infinite)

S_n = a/(1-r)

rational roots theorem

factors of constant/leadingcoefficient = possible factors of polynomial

area of a kite

(d₁*d₂)/2

tangent secant theorem

√[(length of full secant)(length of secant chord)] = length of tangent from same point

slope intercept formula

y = mx + b

point slope formula

(y - y1) = m(x - x1)