Act Math Formulas to Put in Calculator

This guide provides essential ACT Math formulas that you can directly input into your calculator. Whether you're preparing for the ACT or just need a quick reference, these formulas will help you solve problems efficiently during the test.

Basic ACT Math Formulas

These are fundamental formulas that appear frequently on the ACT Math section. Make sure you know how to use them with your calculator.

Percentage Formula

Percentage = (Part / Whole) × 100

Example: What is 20% of 50?
(20 / 100) × 50 = 10

Simple Interest Formula

Interest = Principal × Rate × Time

Example: Calculate the interest on $1000 at 5% for 3 years.
1000 × 0.05 × 3 = $150

Compound Interest Formula

A = P(1 + r/n)^(nt)

Where:
A = amount of money accumulated after n years, including interest.
P = principal amount (the initial amount of money)
r = annual interest rate (decimal)
n = number of times that interest is compounded per year
t = time the money is invested for, in years

Algebra Formulas

Algebra is a significant part of the ACT Math section. These formulas will help you solve equations and work with functions.

Quadratic Formula

x = [-b ± √(b² - 4ac)] / (2a)

Example: Solve 2x² + 4x - 6 = 0
a=2, b=4, c=-6
x = [-4 ± √(16 + 48)] / 4 = [-4 ± √64]/4 = [-4 ± 8]/4
Solutions: x = 1 and x = -3

Slope Formula

Slope (m) = (y₂ - y₁) / (x₂ - x₁)

Example: Find the slope between (2,4) and (4,8)
m = (8 - 4) / (4 - 2) = 4 / 2 = 2

Distance Formula

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Example: Find the distance between (1,2) and (4,6)
Distance = √[(4-1)² + (6-2)²] = √[9 + 16] = √25 = 5

Geometry Formulas

Geometry problems are common on the ACT. These formulas will help you calculate areas, volumes, and other geometric properties.

Area of a Rectangle

Area = Length × Width

Example: Find the area of a rectangle with length 5 and width 3
Area = 5 × 3 = 15

Area of a Triangle

Area = (Base × Height) / 2

Example: Find the area of a triangle with base 6 and height 4
Area = (6 × 4) / 2 = 12

Volume of a Cylinder

Volume = π × Radius² × Height

Example: Find the volume of a cylinder with radius 3 and height 5
Volume ≈ 3.1416 × 9 × 5 ≈ 141.37

Trigonometry Formulas

Trigonometry is another important topic on the ACT. These formulas will help you solve right triangle problems and work with trigonometric functions.

Pythagorean Theorem

a² + b² = c²

Example: Find the hypotenuse of a right triangle with legs 3 and 4
c = √(3² + 4²) = √(9 + 16) = √25 = 5

Sine, Cosine, Tangent

sinθ = opposite/hypotenuse
cosθ = adjacent/hypotenuse
tanθ = opposite/adjacent

Example: In a right triangle with sides 3, 4, 5:
sinθ = 3/5 = 0.6
cosθ = 4/5 = 0.8
tanθ = 3/4 = 0.75

Law of Cosines

c² = a² + b² - 2ab cosC

Example: Find side c in a triangle with sides a=5, b=7, and angle C=60°
c² = 25 + 49 - 2×5×7×cos60° ≈ 74 - 35 = 39
c ≈ √39 ≈ 6.24

Calculator Tips for ACT Math

Using your calculator effectively can save you time and prevent mistakes on the ACT. Here are some tips to help you use your calculator more efficiently.

Basic Calculator Operations

Use the memory functions (M+, M-, MR, MC) to store intermediate results
Take advantage of the exponent and square root functions
Use the percentage function for quick percentage calculations

Handling Fractions

Convert fractions to decimals for easier calculations
Use the fraction function to convert decimals back to fractions
Simplify fractions before performing operations

Graphing Functions

Use the graphing feature to visualize functions and equations
Set appropriate window settings to see the relevant portion of the graph
Use the trace function to find specific points on the graph

Remember that the ACT allows the use of graphing calculators, but you must be able to perform calculations without one as well. Practice using both methods to prepare thoroughly.

Frequently Asked Questions

What formulas are most important for the ACT Math section?: The most important formulas typically include those for percentages, interest calculations, quadratic equations, geometry, and basic trigonometry. These formulas appear frequently on the test.
Can I use my calculator for all ACT Math problems?: Yes, you can use your calculator for all ACT Math problems. The test allows the use of graphing calculators, but you should also be prepared to solve problems without one.
How should I organize my formulas for the ACT?: Organize your formulas by topic (algebra, geometry, trigonometry) and keep them in a notebook or digital document. Review them regularly to prepare for the test.
Are there any formulas I should avoid using on the ACT?: There are no formulas you should avoid, but you should focus on mastering the most common ones. Spend more time on formulas that appear frequently in practice problems.
How can I practice using these formulas with my calculator?: Practice solving problems using your calculator, then check your work by hand. This will help you understand the formulas better and improve your calculation speed.