Slope = rise over run = change in y divided by change in x.

aˣ = b → x = log(b)/log(a) by the change of base formula. Or x = ln(b)/ln(a).

Negative exponent: a⁻ⁿ = 1/aⁿ. Example: 2⁻³ = 1/2³ = 1/8.

Sum of arithmetic series: Sₙ = n/2 × (first term + last term).

Power of a quotient: (a/b)ⁿ = aⁿ/bⁿ. The exponent applies to both numerator and denominator.

Remainder theorem: when polynomial f(x) is divided by (x-r), the remainder equals f(r).

Standard form: Ax + By = C, where A, B, and C are integers and A is non-negative.

Substitution: solve one equation for a variable, then substitute that expression into the other equation.

The quadratic formula is x = (-b ± √(b²-4ac)) / 2a. Note the negative b and the 2a in the denominator.

Rational exponent: a^(m/n) = (ⁿ√a)ᵐ. The denominator is the root; numerator is the power.

Axis of symmetry: x = -b/(2a). The parabola is symmetric about this vertical line.

Vertex form: y = a(x-h)² + k, where (h,k) is the vertex of the parabola.

Geometric sequence nth term: aₙ = a₁ × r^(n-1), where r is the common ratio.

Natural logarithm ln(x) = logₑ(x), where e ≈ 2.718. It is the inverse of eˣ.

|x| > a means x > a OR x < -a. The solution is two separate rays pointing outward.

Synthetic division efficiently divides a polynomial by a linear factor (x - r) using only coefficients.

Inverse variation: y = k/x. As x increases, y decreases. Their product xy = k is constant.

Factored form: y = a(x-r₁)(x-r₂), where r₁ and r₂ are the x-intercepts (roots/zeros).

Common difference d = any term minus the previous term: d = aₙ - aₙ₋₁.

Exponential function: f(x) = aˣ where a > 0 and a ≠ 1. The variable is in the exponent.