Pre Algebra Formulas Flashcards

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Questions and Answers

What does the Distance Formula calculate?

The area of a triangle

The slope of a line

The distance between two points in a plane (correct)

The circumference of a circle

What is the Point-Slope Formula?

y - y1 = m(x - x1)

What is slope represented by in a formula?

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

y = mx + b Signup and view all the answers

What do you do when multiplying monomials?

Add exponents Signup and view all the answers

What do you do when dividing monomials?

Subtract exponents Signup and view all the answers

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

Multiply exponents Signup and view all the answers

A number raised to the zero power equals 1.

True Signup and view all the answers

What is the result of a negative exponent?

Change places Signup and view all the answers

What is the formula for the volume of a sphere?

V = \frac{4}{3} \pi r^3 Signup and view all the answers

What is the formula for the volume of a cylinder?

V = \pi r^2 h Signup and view all the answers

What is the formula for the volume of a cone?

V = \frac{1}{3} \pi r^2 h Signup and view all the answers

What is the Midpoint formula?

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

What does the Pythagorean's Theorem state?

a^2 + b^2 = c^2 Signup and view all the answers

What is the formula for the area of a circle?

πr^2 Signup and view all the answers

What is the formula for the circumference of a circle?

πd Signup and view all the answers

Rational numbers can be written as fractions.

True Signup and view all the answers

Irrational numbers can be expressed as fractions.

False Signup and view all the answers

What is the Triangle Sum?

180º Signup and view all the answers

What does translation in geometry mean?

Slide 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.

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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.