6 Math Formulas to Know Before Taking the ACT

Dec 9, 2021

Are you preparing for the ACT and feeling uncertain about the math section? Don't worry, we've got you covered! In this guide, we will provide you with the essential math formulas that you need to know to ace the ACT. Whether you're aiming for a perfect score or simply looking to improve your math skills, these formulas will be your secret weapon.

1. Quadratic Formula

One of the fundamental formulas you must know for the ACT is the quadratic formula. It can help you find the solutions (roots) of quadratic equations, which frequently appear in the math section. The quadratic formula is:

x = (-b ± √(b2 - 4ac)) / 2a

This formula allows you to solve equations of the form ax2 + bx + c = 0. Knowing how to apply the quadratic formula efficiently will save you valuable time during the ACT.

2. Distance Formula

The distance formula is a vital tool for solving problems that involve finding the distance between two points in a coordinate plane. It is especially useful for questions related to geometry or coordinate geometry. The distance formula can be written as:

d = √((x2 - x1)2 + (y2 - y1)2)

By mastering the distance formula, you will be able to solve distance-based problems with ease, demonstrating your strong math skills to ACT graders.

3. Pythagorean Theorem

When it comes to geometry, the Pythagorean theorem is a game-changer. It relates to right triangles and enables you to find the length of one side of a triangle if you know the lengths of the other two sides. The Pythagorean theorem can be stated as follows:

a2 + b2 = c2

Mastering this formula is crucial for tackling geometry questions involving right triangles, which frequently appear on the ACT.

4. Slope Formula

The slope formula is essential for solving problems related to lines and their slopes. It helps you determine how steep a line is by finding the ratio between the change in the y-coordinates and the change in the x-coordinates. The slope formula can be written as:

m = (y2 - y1) / (x2 - x1)

Understanding the slope formula allows you to analyze the characteristics and behavior of lines, aiding you in solving various types of ACT math problems.

5. Arithmetic and Geometric Series Formulas

The ACT often includes questions involving arithmetic and geometric sequences or series. To tackle such problems efficiently, it is crucial to be familiar with their respective formulas.

For an arithmetic sequence, the formula to find the nth term is:

an = a1 + (n - 1)d

where a1 is the first term, n is the position of the term, and d is the common difference.

For a geometric sequence, the formula to find the nth term is:

an = a1 × r(n - 1)

where a1 is the first term, n is the position of the term, and r is the common ratio.

Having a solid understanding of these series formulas will give you an advantage in solving related ACT math questions swiftly and accurately.

6. Exponential Growth and Decay Formulas

Last but not least, understanding exponential growth and decay is important for the ACT math section. These concepts often appear in word problems and require the use of specific formulas.

The exponential growth formula is:

P = P0 × (1 + r)t

where P is the population after time t, P0 is the initial population, and r is the growth rate.

On the other hand, the exponential decay formula is:

P = P0 × (1 - r)t

where P is the population after time t, P0 is the initial population, and r is the decay rate.

Knowing these formulas will equip you with the necessary tools to confidently approach exponential growth and decay problems on the ACT.

By mastering these six essential math formulas, you will have a solid foundation for tackling the math section of the ACT. Practice applying these formulas in a variety of contexts, and you'll be well-prepared to excel on test day.

Remember, understanding these formulas is just one aspect of achieving a high score on the ACT. Make sure to practice regularly, review various math topics, and familiarize yourself with the structure and format of the test. Good luck on your ACT journey!

Connector User
Great article! These math formulas are a must-know for anyone preparing for the ACT. Knowing the quadratic formula and other essential formulas will definitely help improve math skills and boost test scores. Thanks for sharing this valuable resource!
Nov 11, 2023