LCM × GCF = Product of the two numbers

Percent change = (New − Old) / Old × 100

a^m × aⁿ = a^m+n ; (a^m)ⁿ = a^mn

Negative exponent: a⁻ⁿ = 1/aⁿ

Order of operations: PEMDAS (Parentheses, Exponents, Multiply/Divide, Add/Subtract)

Solving equations: do the same operation to both sides

Slope = (y₂ − y₁) / (x₂ − x₁) = rise/run

Slope-intercept form: y = mx + b (m = slope, b = y-intercept)

FOIL: (a+b)(c+d) = ac + ad + bc + bd

Quadratic: ax² + bx + c = 0 → x = (−b ± √(b²−4ac)) / 2a

Triangle angles sum = 180°; Quadrilateral = 360°

Pythagorean theorem: a² + b² = c²

Common triples: 3-4-5, 5-12-13, 8-15-17

Circle: C = 2πr, A = πr²

Volume of rectangular prism: V = l × w × h

Mean = sum of values ÷ number of values

Median = middle value (sorted list); if even number of values, average the two middle ones

Mode = most frequently occurring value

Probability = favorable outcomes ÷ total outcomes

P(A or B) = P(A) + P(B) − P(A and B)

Rate problems: D = R × T (Distance = Rate × Time)

Work problems: if A does a job in n days, rate = 1/n per day

Ratio: if ratio is a:b, parts are a/(a+b) and b/(a+b) of total

Mixture problems: use weighted average concept

Age problems: set up equations for present/future ages