ACT Algebra and Functions

Master algebra and function concepts tested on the ACT Math section.

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ACT: Algebra and Functions

Linear Equations

Slope-Intercept Form

y=mx+by = mx + b

Point-Slope Form

yy1=m(xx1)y - y_1 = m(x - x_1)

Systems of Equations

Use substitution or elimination.

Quadratics

x=b±b24ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Factoring

x2+5x+6=(x+2)(x+3)x^2 + 5x + 6 = (x+2)(x+3)

Vertex

(b2a,f(b2a))\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)

Functions

Domain and Range

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

Composition

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

Exponents

aman=am+na^m \cdot a^n = a^{m+n} aman=amn\frac{a^m}{a^n} = a^{m-n} (am)n=amn(a^m)^n = a^{mn}

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

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