40 ACT Math Formulas You Must Know

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Reviewed by:

Mary Banks

Former Admissions Committee Member, Columbia University

Reviewed: 11/06/23

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If you’re taking the ACT, you need to know ACT math formulas. This article will go over the key terms and formulas you need to brush up on.  

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ACT prep can be demanding, particularly when grappling with numerous math formulas included in the test. However, understanding and practicing these formulas beforehand can be the key to boosting your ACT math score. 

By mastering these formulas, you're not only preparing for the ACT but also equipping yourself with problem-solving skills that extend beyond the test. So, let’s get into the key formulas you need to know and how to set yourself up for success. 

Breakdown of ACT Math Formulas to Know

Let's get right to it. This section is all about breaking down the math formulas you need to know. These formulas are the foundation for tackling the ACT math test. We'll go through them one by one, making sure you're well-prepared to tackle the math questions on test day.

Arithmetic Formulas

• Order of Operations (PEMDAS/BODMAS): This rule dictates the sequence for solving math expressions, starting with parentheses or brackets, then exponents, followed by multiplication and division (left to right), and finally addition and subtraction (left to right).
• Percentage: This formula converts a part of a whole into a percentage, commonly used for proportions, discounts, and relative values.
• Ratio and Proportion: Ratios compare quantities using a colon (":"), while proportions assert that two ratios are equal. They're handy for problems involving direct and inverse variation.
• Simple Interest: This formula calculates interest on a principal amount over time at a constant interest rate, used in finance and investment calculations.
• Compound Interest: Compound interest factors in both the initial principal and compounding frequency. It helps determine the growth of an investment or the cost of a loan, considering compounding effects.

Algebraic Formulas

• Linear Equations: They make straight lines on graphs. 'm' controls steepness, 'b' is where it crosses the y-axis. Used a lot in math and real life.
• Quadratic Formula: Solves quadratic equations, super handy for real-world problems. It finds 'x' by using 'a,' 'b,' and 'c.'
• Exponents: Rules for making math with tiny numbers (exponents) easier. Like multiplying tiny numbers with the same base.
• Factoring: A way to break complex math expressions into simpler parts. Helps solve quadratic problems and simplify math.
• Polynomial Operations: Basic building blocks of math. You add, subtract, and multiply these a lot in algebra.
• Quadratic Vertex Form: Describes parabolas. 'a' says if it's up or down, 'h' and 'k' move it around.
• Quadratic Discriminant: Helps you figure out what kind of answers you'll get when solving quadratic equations. Positive means two real answers, zero means one real answer repeated, and negative means two complex answers.

Geometry Formulas

• Pythagorean Theorem: It's the go-to tool for finding distances and angles in right triangles.
• Area of a Triangle: Helps find the space inside triangles using their base and height.
• Area of a Rectangle: Multiply length and width to find how much space a rectangle covers. Used in construction and engineering.
• Area of a Circle: Calculates the space inside a circle using 'π' and the radius. Important for circular objects.
• Circumference of a Circle: Measures the circle's perimeter using 'r' and '2π'. Helpful for things that go in circles.
• Volume of a Cylinder: Finds how much stuff can fit in a cylinder, useful in engineering and science.
• Volume of a Sphere: Measures how much space is inside a sphere, used in physics and engineering.
• Area of a Parallelogram: Calculates the space inside parallelograms using base and height. Useful for various shapes.
• Area of a Trapezoid: Helps find the area of trapezoids, which have two parallel sides. Useful in geometry and practical situations.
• Volume of a Cone: Calculates how much stuff can fit in a cone-shaped container, common in geometry and engineering.
• Volume of a Rectangular Prism (Box): Finds the space inside rectangular boxes by multiplying length, width, and height.
• Surface Area of a Rectangular Prism (Box): Adds up the areas of all sides of a rectangular box. Useful for packaging and construction.

Trigonometric Formulas

• Sine (sin), Cosine (cos), and Tangent (tan): These trigonometric functions relate the ratios of the sides of a right triangle to the angles within the triangle. Understanding these ratios is fundamental for solving problems involving angles and distances.
• Trigonometric Identities: Trigonometric identities are equations involving trigonometric functions that are always true. They include the Pythagorean identity, which relates sine and cosine, and reciprocal and quotient identities, which express one trigonometric function in terms of others.
• Inverse Trigonometric Functions: Inverse trigonometric functions allow you to find angles associated with specific trigonometric ratios. For example, 'arcsin(x)' gives the angle whose sine is 'x,' helping you find angles in problems involving angles of elevation, depression, and more.

Coordinate Geometry Formulas

• Distance Between Two Points: Calculates the distance between two points in a 2D plane using the Pythagorean theorem, useful for various distance calculations.
• Midpoint Formula: Finds the midpoint's coordinates between two given points, useful for determining the center of line segments and geometric shapes.
• Slope-Intercept Form: A common linear equation form ('y = mx + b') where 'm' is the slope and 'b' is the y-intercept, widely used for representing lines.
• Distance Between Two Points in 3D: Extends distance calculation to three-dimensional space, applicable in geometry and 3D problems.
• Equation of a Circle (Center-Radius Form): Describes a circle's position and size in a 2D plane using the center coordinates ('(h, k)') and radius ('r').
• Point-Slope Form: Represents a line's equation using a known point ('(x₁, y₁)') and the slope ('m'), particularly useful for linear equations and graphing lines.

Statistics and Probability Formulas

• Mean (Average): Calculated by adding all values in a dataset and dividing by the total count, it represents the dataset's average value.
• Median: The middle value when data is arranged; it's less influenced by extreme values than the mean.
• Mode: The most frequently occurring value in a dataset, highlighting the most common data point.
• Range: Found by subtracting the minimum from the maximum, it measures data spread or variability.
• Probability: A measure of event likelihood, computed as favorable outcomes divided by total possible outcomes.
• Combinations: Determines ways to choose 'r' items from 'n' items without regard to order, used in counting and probability.
• Permutations: Computes arrangements of 'r' items from 'n' items in a specific order, applicable in counting and arrangement problems.

Final Thoughts

We've covered the essential ACT Math formulas you need to succeed. From basic math to more complex concepts, we've got you covered.

But knowing the formulas isn't enough; you need to understand and remember them. Practice and helpful memory aids are your allies. Now, get ready to conquer your ACT prep with confidence and ace that test.