Act Equations to Put in Your Calculator

Essential ACT Math Equations

The ACT Math test includes both calculator and no-calculator sections. For the calculator section, you'll need to know which equations you can input directly and which you must memorize. Here are the most important formulas:

Algebra

• Quadratic Formula: \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)
• Distance Formula: \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)
• Midpoint Formula: \( M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \)
• Slope Formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} \)

Geometry

• Area of a Circle: \( A = \pi r^2 \)
• Volume of a Cylinder: \( V = \pi r^2 h \)
• Pythagorean Theorem: \( a^2 + b^2 = c^2 \)
• Surface Area of a Sphere: \( A = 4\pi r^2 \)

Trigonometry

• Pythagorean Identities: \( \sin^2 \theta + \cos^2 \theta = 1 \)
• Law of Cosines: \( c^2 = a^2 + b^2 - 2ab \cos C \)
• Law of Sines: \( \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \)

How to Input Equations in Your Calculator

Knowing how to properly input equations into your calculator is crucial for the ACT Math section. Here's a step-by-step guide:

1. Clear the calculator: Start with a clean screen to avoid errors from previous calculations.
2. Enter the formula: Type the equation exactly as it appears, using parentheses for grouping.
3. Substitute values: Replace variables with the given numbers in the problem.
4. Calculate: Press the equals button to get the result.
5. Check your work: Verify that you entered the equation correctly and that the result makes sense.

Example: Using the Quadratic Formula

Problem: Solve \( 2x^2 + 5x + 3 = 0 \) using the quadratic formula.

Step-by-step input:

1. Enter the quadratic formula: [ -5 ± √(5² - 4*2*3) ] / (2*2)
2. Calculate the discriminant: 25 - 24 = 1
3. Take the square root: √1 = 1
4. Calculate both solutions:
   • x = [-5 + 1]/4 = -1
   • x = [-5 - 1]/4 = -1.5

Common Mistakes to Avoid

Many students make mistakes when inputting equations into their calculators. Here are some common pitfalls to watch out for:

• Incorrect formula: Using the wrong formula for the problem type.
• Missing parentheses: Forgetting to group terms properly.
• Wrong order of operations: Not following PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).
• Incorrect variable substitution: Mixing up which values correspond to which variables.
• Not simplifying first: Trying to input complex expressions without simplifying them first.

Example Problems

Practice these example problems to reinforce your understanding of how to input equations into your calculator:

Problem 1: Quadratic Equation

Solve \( x^2 - 5x + 6 = 0 \) using the quadratic formula.

Problem 2: Distance Between Points

Find the distance between points (2, 3) and (5, 7).

Problem 3: Volume of a Cylinder

Calculate the volume of a cylinder with radius 4 cm and height 10 cm.

Problem 4: Trigonometry Problem

Given a right triangle with sides 3, 4, and 5, find the sine of the angle opposite the side of length 3.