Math formulas by topic

Linear equations & lines

Slope
m = (y₂ − y₁) / (x₂ − x₁)
Slope-intercept form
y = mx + b, where b is the y-intercept
Point-slope form
y − y₁ = m(x − x₁)
Parallel lines
same slope (m₁ = m₂)
Perpendicular lines
slopes are negative reciprocals (m₁ · m₂ = −1)

Quadratics

Standard form
y = ax² + bx + c
Quadratic formula
x = (−b ± √(b² − 4ac)) / 2a
Vertex x-coordinate
x = −b / 2a
Vertex form
y = a(x − h)² + k, vertex at (h, k)
Discriminant
b² − 4ac: positive → 2 real roots, zero → 1, negative → 0
Factoring a difference of squares
a² − b² = (a − b)(a + b)

Exponents & radicals

Product of powers
aᵐ · aⁿ = aᵐ⁺ⁿ
Quotient of powers
aᵐ / aⁿ = aᵐ⁻ⁿ
Power of a power
(aᵐ)ⁿ = aᵐⁿ
Negative exponent
a⁻ⁿ = 1 / aⁿ
Fractional exponent
a^(m/n) = ⁿ√(aᵐ)
Zero exponent
a⁰ = 1 (a ≠ 0)

Geometry — area & volume

Triangle area
A = ½ · base · height
Circle area
A = πr²
Circle circumference
C = 2πr
Rectangle area
A = length · width
Trapezoid area
A = ½(b₁ + b₂) · height
Rectangular prism volume
V = length · width · height
Cylinder volume
V = πr²h
Sphere volume
V = (4/3)πr³
Cone volume
V = (1/3)πr²h

Geometry — triangles & circles

Pythagorean theorem
a² + b² = c² (right triangles)
Special right triangle — 45-45-90
legs : legs : hypotenuse = x : x : x√2
Special right triangle — 30-60-90
sides = x : x√3 : 2x
Sum of interior angles
(n − 2) · 180°, for an n-sided polygon
Triangle angle sum
the three interior angles sum to 180°
Arc length
s = r θ (θ in radians), or (angle/360°) · 2πr

Statistics & probability

Mean
sum of values ÷ number of values
Median
the middle value once sorted (average the two middles if even count)
Probability
P(event) = favorable outcomes ÷ total outcomes
Independent events
P(A and B) = P(A) · P(B)