ACT Math Formulas Flashcards

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.