MA098 Elementary Algebra Final Exam Review

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Questions and Answers

What is the formula for the perimeter of a square?

P = 4s

What is the formula for the perimeter of a rectangle?

P = 2L + 2w

What is the formula for the circumference of a circle?

C = 2πr

What is the formula for the area of a square?

A = s² Signup and view all the answers

What is the formula for the area of a rectangle?

A = length x width Signup and view all the answers

What is the formula for the area of a circle?

A = πr² Signup and view all the answers

What is the formula for the area of a parallelogram?

A = bh Signup and view all the answers

What is the formula for the area of a triangle?

A = 1/2 b h Signup and view all the answers

What is the formula for the volume of a box?

V = lwh Signup and view all the answers

What is the formula for the volume of a cylinder?

V = πr²h Signup and view all the answers

What does parallel lines refer to in terms of slope?

The same slope Signup and view all the answers

How do you find the slope of perpendicular lines?

Take the negative reciprocal of the slope Signup and view all the answers

What is the standard form of a linear equation?

Ax + By = C Signup and view all the answers

What is the slope of a line from the equation y = mx + b?

m Signup and view all the answers

What is the Pythagorean Theorem?

a² + b² = c² Signup and view all the answers

State the special product rule: (a + b)²

(a + b)² = a² + 2ab + b² Signup and view all the answers

State another special product rule: (a - b)²

(a - b)² = a² - 2ab + b² Signup and view all the answers

State the product of differences special rule: (a + b)(a - b)

(a + b)(a - b) = a² - b² Signup and view all the answers

State the special factor rule for a² + 2ab + b²

a² + 2ab + b² = (a + b)² Signup and view all the answers

State the special factor rule for a² - 2ab + b²

a² - 2ab + b² = (a - b)² Signup and view all the answers

State the special factor rule for a² - b²

a² - b² = (a + b)(a - b) Signup and view all the answers

Study Notes

Perimeter Formulas

Perimeter of a Square: ( P = 4s ) (s = side length)
Perimeter of a Rectangle: ( P = 2L + 2w ) (L = length, w = width)

Area Formulas

Area of a Square: ( A = s^2 )
Area of a Rectangle: ( A = length \times width ) (A = l x w)
Area of a Circle: ( A = \pi r^2 ) (r = radius)
Area of a Parallelogram: ( A = b h ) (b = base, h = height)
Area of a Triangle: ( A = \frac{1}{2} b h )

Volume Formulas

Volume of a Box: ( V = l \times w \times h )
Volume of a Cylinder: ( V = \pi r^2 h )

Line Formulas and Properties

Slope Formula: Used to determine the slope (m) of a line between two points.
Parallel Lines: Have the same slope (m).
Perpendicular Lines: Have slopes that are negative reciprocals of each other.
Standard Form: The equation of a line can be written in the form ( Ax + By = C ) where A, B, and C are constants.
Slope-Intercept Form: Represents the slope of a line as ( y = mx + b ) where m is the slope and b is the y-intercept.
Point-Slope Form: Used to write the equation of a line given a point and the slope.

Theorems and Special Rules

Pythagorean Theorem: ( a^2 + b^2 = c^2 ) relates the sides of a right triangle (a, b = legs; c = hypotenuse).
Quadratic Formula: Not provided but useful for solving quadratic equations.
Special Product Rules:
- ( (a+b)^2 = a^2 + 2ab + b^2 )
- ( (a-b)^2 = a^2 - 2ab + b^2 )
- ( (a+b)(a-b) = a^2 - b^2 )

Special Factor Rules

Factorization of Squares:
- ( a^2 + 2ab + b^2 = (a+b)^2 )
- ( a^2 - 2ab + b^2 = (a-b)^2 )
- ( a^2 - b^2 = (a+b)(a-b) )

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Description

This quiz focuses on essential formulas related to the geometric properties of shapes, including squares, rectangles, and circles. Review the definitions for perimeter and area as you prepare for your final exam in Elementary Algebra. Perfect for mastering key concepts in geometry.