Questions and Answers
What does the Distance Formula calculate?
What is the Point-Slope Formula?
y - y1 = m(x - x1)
What is slope represented by in a formula?
m
What is the general form of the equation of a line?
Signup and view all the answers
What do you do when multiplying monomials?
Signup and view all the answers
What do you do when dividing monomials?
Signup and view all the answers
What do you do with exponents in the Power to Power rule?
Signup and view all the answers
A number raised to the zero power equals 1.
Signup and view all the answers
What is the result of a negative exponent?
Signup and view all the answers
What is the formula for the volume of a sphere?
Signup and view all the answers
What is the formula for the volume of a cylinder?
Signup and view all the answers
What is the formula for the volume of a cone?
Signup and view all the answers
What is the Midpoint formula?
Signup and view all the answers
What does the Pythagorean's Theorem state?
Signup and view all the answers
What is the formula for the area of a circle?
Signup and view all the answers
What is the formula for the circumference of a circle?
Signup and view all the answers
Rational numbers can be written as fractions.
Signup and view all the answers
Irrational numbers can be expressed as fractions.
Signup and view all the answers
What is the Triangle Sum?
Signup and view all the answers
What does translation in geometry mean?
Signup and view all the answers
Study Notes
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
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.