Important Math Formulas on the ACT

You won’t see a formula sheet on the ACT Math section, so there are a few math formulas you need to memorize and recall when you take the ACT test.

Often, knowledge of these key formulas can help you solve problems faster and more accurately. Below, you’ll find a list of ACT math formulas to know from every content area in the Math section: Numbers and Quantity, Algebra and Functions, Statistics and Probability, and Geometry.

At the end of the post, you can find a downloadable ACT formula sheet in PDF format.

Number and Quantity

Percents

Calculating percents:

or, change the words to an algebraic equation and solve:

Example: 40% of what is 20?

Complex Numbers

Use the conjugate to eliminate the imaginary:

Arithmetic Sequences

Each term (t) is the previous term plus a common difference (d) to find the nth term

Geometric Sequences

Each term (t) is the previous term times a common ratio (r) to find the nth term

Statistics and Probability

Median

The middle value when items are arranged from least to greatest

Range

The difference between the max value and min value

Mode

The value that occurs the most in a set

Standard Deviation

Shows how spread the data points are.

Low standard deviation:

Data points are closer to the mean

High standard deviation:

Data is spread over a wider range

Fundamental Counting Principle

Pick 1 from each group, multiply the number of options in each group

Permutation

A combination of events occurring when order matters and the items cannot be repeated

Combination

A combination of events occurring when the order does not matter

Domain

Set of possible values of x

Range

Set of possible values of y

Algebra and Functions

Lines

The slope of a line:

Parallel lines:

Have the same slope

Perpendicular lines:

Have slopes that are negative reciprocals

Direct Variation

y=kx where k is the constant of variation

Indirect Variation

yx=k where k is the constant of variation

To find the solutions: Set y equal to 0, and solve for x by factoring or use the Quadratic Formula:

To find the vertex:  x = -b/2a, plug value back into the equation to find the y-coordinate

The vertex is (h, k ).

x-intercepts/solutions/zeros are x=p & x=q

Exponential Functions

Shows growth if b>1or decay if 0<b<1

Growth/Decay when r  is a percent:

Change to decimal, add to 1 if growth, subtract from 1 if decay

Geometry

Triangles

Degrees sum to 180°

Sides

No side can be greater than the sum or less than the difference in length of the other two. Side lengths are in the same ratio as opposite angle measures.

Angles

Complementary angles sum to 90°

Supplementary angles sum to 180°

Exterior angles for ANY polygon sum to 360°.

Interior angles for a polygon sum to 180° (n-2) where n is the number of sides in the polygon.

Trigonometric Ratios

Remember these ratios with the acronym “SOH-CAH-TOA”

Circles

Vertex Form of a Circle

(h, k) is the center and r is the radius