Pre Algebra Formulas Flashcards

What does the Distance Formula calculate?

What is the Point-Slope Formula?

What is slope represented by in a formula?

What is the general form of the equation of a line?

What do you do when multiplying monomials?

What do you do when dividing monomials?

What do you do with exponents in the Power to Power rule?

A number raised to the zero power equals 1.

What is the result of a negative exponent?

What is the formula for the volume of a sphere?

What is the formula for the volume of a cylinder?

What is the formula for the volume of a cone?

What is the Midpoint formula?

What does the Pythagorean's Theorem state?

What is the formula for the area of a circle?

What is the formula for the circumference of a circle?

Rational numbers can be written as fractions.

Irrational numbers can be expressed as fractions.

What is the Triangle Sum?

What does translation in geometry mean?

Distance and Line Formulas

Distance Formula: ( D = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2} )
Point-Slope Formula: ( y - y_1 = m(x - x_1) ) requires slope (m) and point (x1, y1).
Slope (m) calculation: ( m = \frac{y_2 - y_1}{x_2 - x_1} )
Equation of a Line: Standard form is ( y = mx + b ) where m is slope and b is y-intercept.

Monomial Operations

Multiplying Monomials: Sum the exponents of like bases.
Dividing Monomials: Subtract exponents of like bases.
Power to Power Rule: Multiply the exponents, e.g., ( (x^2)^4 = x^{2 \cdot 4} = x^8 ).

Exponents

Zero Power Rule: Any non-zero number raised to the power of zero equals 1, e.g., ( 4^0 = 1 ).
Negative Exponents: The reciprocal of the base raised to the positive exponent, e.g., ( 5^{-3} = \frac{1}{5^3} ).

Volume Formulas

Volume of a Sphere: ( V = \frac{4}{3} \pi r^3 )
Volume of a Cylinder: ( V = \pi r^2 h )
Volume of a Cone: ( V = \frac{1}{3} \pi r^2 h )

Geometry Measurements

Midpoint Formula: ( \left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} \right) )
Pythagorean Theorem: For a right triangle, ( a^2 + b^2 = c^2 ) where c is the hypotenuse.
Area of a Circle: ( A = \pi r^2 )
Circumference: Can be calculated via ( C = \pi d ) or ( C = 2\pi r ).

Number Types

Rational Numbers: Can be expressed as a fraction (e.g., ( \frac{a}{b} )).
Irrational Numbers: Cannot be expressed as fractions (e.g., ( \sqrt{2} )).

Triangle Properties

Triangle Angle Sum: The sum of angles in a triangle is always ( 180^\circ ).

Geometric Translations

Translation: A transformation that slides a figure to a different position without changing its shape or size.

Enhance your understanding of essential pre-algebra formulas with these flashcards. Each card provides key formulas like the Distance Formula, Point-Slope Formula, and more. Perfect for students looking to solidify their grasp of algebraic concepts.