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?
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What do you do when multiplying monomials?
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What do you do when dividing monomials?
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What do you do with exponents in the Power to Power rule?
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A number raised to the zero power equals 1.
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What is the result of a negative exponent?
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What is the formula for the volume of a sphere?
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What is the formula for the volume of a cylinder?
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What is the formula for the volume of a cone?
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What is the Midpoint formula?
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What does the Pythagorean's Theorem state?
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What is the formula for the area of a circle?
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What is the formula for the circumference of a circle?
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Rational numbers can be written as fractions.
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Irrational numbers can be expressed as fractions.
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What is the Triangle Sum?
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What does translation in geometry mean?
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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.
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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.
