公式参考

x = (-b ± √(b² - 4ac)) / 2a

Solves ax² + bx + c = 0

a² + b² = c²

Relationship in a right triangle

m = (y₂ - y₁) / (x₂ - x₁)

Slope between two points

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Distance between two points

M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

Midpoint between two points

(a + b)ⁿ = Σₖ C(n,k) aⁿ⁻ᵏ bᵏ

Expansion of (a+b)ⁿ

log_b(xy) = log_b(x) + log_b(y)

Product rule of logarithms

A = πr²

Area of a circle with radius r

C = 2πr

Circumference of a circle

A = ½bh

Area of a triangle

V = ⁴⁄₃πr³

Volume of a sphere

V = πr²h

Volume of a cylinder

V = ⅓πr²h

Volume of a cone

A = 4πr²

Surface area of a sphere

sin(A)/a = sin(B)/b = sin(C)/c

Triangle side/angle relationship

c² = a² + b² - 2ab cos(C)

Triangle side from angle

d/dx [xⁿ] = nxⁿ⁻¹

Derivative of power function

d/dx [fg] = f'g + fg'

Derivative of product

d/dx [f(g(x))] = f'(g(x)) · g'(x)

Derivative of composition

∫xⁿ dx = xⁿ⁺¹/(n+1) + C

Indefinite integral of power

∫ₐᵇ f(x) dx = F(b) - F(a)

Connects derivative and integral

d/dx [f/g] = (f'g - fg')/g²

Derivative of quotient

f'(x) = lim h→0 (f(x+h)-f(x))/h

Definition of derivative

F = ma

Force equals mass × acceleration

Eₖ = ½mv²

Energy of motion

Eₚ = mgh

Gravitational potential energy

E = mc²

Mass-energy equivalence

V = IR

Voltage = Current × Resistance

v = fλ

Wave speed = frequency × wavelength

F = G(m₁m₂)/r²

Newton's law of gravitation

P = F/A

Pressure = Force / Area

W = Fd cos(θ)

Work done by a force

P = W/t

Power = Work / time

PV = nRT

Pressure × Volume = moles × R × Temperature

M = n/V

Concentration = moles / volume (L)

pH = -log₁₀[H⁺]

Measure of acidity

ρ = m/V

Density = mass / volume

P₁V₁ = P₂V₂

Pressure-volume relationship (constant T)

q = mcΔT

Heat = mass × specific heat × temp change

1 mol = 6.022×10²³ particles

Number of particles per mole