ACT: Algebra and Functions

Linear Equations

Slope-Intercept Form

$y = mx + b$

Point-Slope Form

$y - y_1 = m(x - x_1)$

Systems of Equations

Use substitution or elimination.

Quadratics

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Factoring

$x^2 + 5x + 6 = (x+2)(x+3)$

Vertex

$\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$

Functions

Domain and Range

• Domain: all valid inputs
• Range: all possible outputs

Composition

$(f \circ g)(x) = f(g(x))$

Exponents

$a^m \cdot a^n = a^{m+n}$ $\frac{a^m}{a^n} = a^{m-n}$ $(a^m)^n = a^{mn}$

ACT Tip: The ACT Math section has 60 questions in 60 minutes. Speed matters.