ACT Math Reference Cheat Sheet

Key Facts

• The ACT Math section has $60$ questions in $60$ minutes, so the average pace is $1$ minute per question.
• Slope is $m = \frac{y_2 - y_1}{x_2 - x_1}$, and slope-intercept form is $y = mx + b$.
• The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ for equations in the form $ax^2 + bx + c = 0$.
• The distance between two points is $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$, and the midpoint is $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$.
• For right triangles, the Pythagorean theorem is $a^2 + b^2 = c^2$, and common triples include $3$-$4$-$5$ and $5$-$12$-$13$.
• Special right triangles have side ratios $45^{\circ}$-$45^{\circ}$-$90^{\circ}: x, x, x\sqrt{2}$ and $30^{\circ}$-$60^{\circ}$-$90^{\circ}: x, x\sqrt{3}, 2x$.
• Circle formulas include circumference $C = 2\pi r$, area $A = \pi r^2$, and arc length $s = \frac{\theta}{360^{\circ}} \cdot 2\pi r$.
• Probability is $P(E) = \frac{\text{favorable outcomes}}{\text{total outcomes}}$, and independent events multiply as $P(A \text{ and } B) = P(A)P(B)$.

Vocabulary

Slope

Slope measures the steepness of a line and is found using $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Intercept

An intercept is a point where a graph crosses an axis, such as the $y$-intercept $b$ in $y = mx + b$.

Discriminant

The discriminant is $b^2 - 4ac$ and tells how many real solutions a quadratic equation has.

Median

The median is the middle value in an ordered data set, or the average of the two middle values when there is an even number of values.

Function

A function is a rule that assigns each input exactly one output, often written as $f(x)$.

Complementary Probability

Complementary probability uses $P(\text{not } A) = 1 - P(A)$ to find the chance that an event does not happen.