ACT Math Formulas Flashcards

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Questions and Answers

What is the Distance Formula?

d=√(x₁-x₂)² + (y₁-y₂)²

Select the correct formula for Slope.

Slope = Rise/Run

Slope = (y₂-y₁)/(x₂-x₁)

Both A and B (correct)

None of the above

What is the equation for Slope Intercept?

y=mx+b

How is the Midpoint Formula calculated?

( (x₁+x₂)/2 , (y₁+y₂)/2 ) Signup and view all the answers

What does PEDMAS stand for?

Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction Signup and view all the answers

What is the standard form of a Quadratic Equation?

ax²+bx+c=0 Signup and view all the answers

What is the Quadratic Formula?

x = -b ± √(b² - 4ac) / 2a Signup and view all the answers

How do you calculate Percent?

Part = Percent × Whole Signup and view all the answers

What is the rule for multiplying powers with the same base?

Add exponents and keep the same base Signup and view all the answers

What happens when dividing powers with the same base?

Subtract exponents and keep the same base Signup and view all the answers

What is the rule for raising a power to another power?

Multiply the exponents Signup and view all the answers

What does a Negative Exponent represent?

X⁻ⁿ = 1/Xⁿ Signup and view all the answers

What does a Rational Exponent signify?

ⁿ√x Signup and view all the answers

What is the Absolute Value of -3?

3 Signup and view all the answers

What does FOIL stand for in algebra?

First, Outside, Inside, Last Signup and view all the answers

What is the formula for the Area of a Triangle?

area = ½ (base)(height) Signup and view all the answers

What is the Pythagorean Theorem for right triangles?

(leg₁)² + (leg₂)² = (hypotenuse)² Signup and view all the answers

What is the formula for the Area of a Rectangle?

area = length × width Signup and view all the answers

What is the formula for the Area of a Parallelogram?

area = base × height Signup and view all the answers

What is the formula for the Area of a Square?

area = (side)² Signup and view all the answers

What is the formula for the Circumference of a Circle?

circumference = 2πr Signup and view all the answers

What is the formula for the Area of a Circle?

area = πr² Signup and view all the answers

Study Notes

Distance Formula

Formula: ( d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2} )
Used to calculate distance between two points on a coordinate plane.

Slope

Formula: ( \text{Slope} = \frac{\text{Rise}}{\text{Run}} = \frac{y_2 - y_1}{x_2 - x_1} )
Indicates the steepness of a line; positive slope rises, negative slope falls.

Slope Intercept Form

Equation: ( y = mx + b )
( m ) represents slope, and ( b ) is the y-intercept.

Midpoint Formula

Formula: ( \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) )
Provides the midpoint between two points in a coordinate system.

PEDMAS

Acronym representing the order of operations: Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
Essential for solving mathematical expressions correctly.

Quadratic Equation

Standard form: ( ax^2 + bx + c = 0 )
Represents a parabolic function; can have two, one, or no real solutions.

Quadratic Formula

Formula: ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} )
Used to find roots of a quadratic equation; handles cases when factors are not obvious.

Percent Formula

Formula: ( \text{Part} = \text{Percent} \times \text{Whole} )
Facilitates calculation of percentage values in various scenarios.

Multiplication of Power Exponents

Rule: ( x^m \cdot x^n = x^{m+n} )
You add exponents when multiplying like bases.

Dividing Power Exponents

Rule: ( \frac{x^m}{x^n} = x^{m-n} )
You subtract exponents when dividing like bases.

Raising Power to Powers

Rule: ( (x^m)^n = x^{m \cdot n} )
You multiply exponents when raising a power to another power.

Negative Exponent

Definition: ( x^{-n} = \frac{1}{x^n} )
Indicates the reciprocal of the base raised to a positive exponent.

Rational Exponent

Notation: ( \sqrt[n]{x} )
Represents the nth root of ( x ).

Absolute Value

Definition: ( |x| ) represents the distance of ( x ) from zero on a number line.
Example: ( |-3| = 3 )

FOIL Method

Technique for multiplying binomials: First, Outside, Inside, Last.
Example: ((x - 3)(x + 5) = x^2 + 2x - 15)

Factoring Difference of Squares

Formula: ( a^2 - b^2 = (a - b)(a + b) )
Useful for simplifying expressions and solving equations.

Area of a Triangle

Formula: ( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} )
Represents the space contained within a triangle.

Pythagorean Theorem

Formula: ( a^2 + b^2 = c^2 )
Applies to right triangles; ( a ) and ( b ) are legs, ( c ) is the hypotenuse.
Notable special triangles: 3-4-5, 30-60-90, 5-12-13, 45-45-90.

Area Formulas

Rectangle: ( \text{Area} = \text{length} \times \text{width} )
Parallelogram: ( \text{Area} = \text{base} \times \text{height} )
Square: ( \text{Area} = (\text{side})^2 )

Circumference of a Circle

Formula: ( \text{Circumference} = 2\pi r )
Represents the distance around the circle.

Area of a Circle

Formula: ( \text{Area} = \pi r^2 )
Represents the space contained within the circle.

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Description

This quiz features essential math formulas for the ACT, including the Distance Formula, Slope, and Slope Intercept. Each card provides a definition along with an example to help you master the key concepts. Use these flashcards to prepare effectively for the math section of the ACT exam.