Formula Master

x = (-b ± √(b²-4ac)) / 2a

Solves ax² + bx + c = 0

a² + b² = c²

Right triangle: hypotenuse squared equals sum of squares of other sides

A = πr²

Area of a circle with radius r

C = 2πr

Circumference of a circle with radius r

d = √((x₂-x₁)² + (y₂-y₁)²)

Distance between two points in a plane

m = (y₂-y₁) / (x₂-x₁)

Slope of a line through two points

F = ma

Force equals mass times acceleration

KE = ½mv²

Energy of an object in motion

c = 3 × 10⁸ m/s

Speed of light in vacuum

V = IR

Voltage equals current times resistance

F = G(m₁m₂/r²)

Gravitational attraction between two masses

v = fλ

Wave speed = frequency × wavelength

PV = nRT

Pressure × Volume = moles × gas constant × temperature

M = mol/L

Concentration: moles of solute per liter of solution

pH = -log[H⁺]

Measure of hydrogen ion concentration

V = (4/3)πr³

Volume of a sphere with radius r

A = 4πr²

Surface area of a sphere

x̄ = Σxᵢ / n

Average of all values

σ = √(Σ(xᵢ-x̄)² / n)

Measure of spread in a dataset