Basics

Basic Equations

Sample Problem:	x + 9 = 18 - 2x
Solution:	x = 3

Basic Proportions

Sample Problem:	4 8 - = -- x 20
Solution:	x = 10

Consecutive Integer Word Problems

Sample Problem:	What are two consecutive even integers that have a sum of 26?
Solution:	12, 14

Simplifying

Simplifying and Solving Equations with Multiple Signs

Sample Problem:	- -16 - x = 13
Solution:	x = 3

Simplifying and Solving Equations by Combining Like Terms

Sample Problem:	6x - 2 + 2x = -2 + 4x + 8
Solution:	x = 2

Multiplication

Two Single Terms

Sample Problem:	11s * 12s3
Solution:	132s4

Distributive Property

Sample Problem:	2(4 + 9x)
Solution:	8 + 18x

FOIL Method

Sample Problem:	(1 + x)(3 + 2x)
Solution:	3 + 5x + 2x2

Exponents

Of Numbers

Sample Problem:	52
Solution:	25

Of Variables

Sample Problem:	(k2m3)2
Solution:	k4m6

Of Polynomials (Parentheses)

Sample Problem:	(2y + 9)2
Solution:	4y2 + 36y + 81

Advanced Simplifying

Order of Operations

Sample Problem:	3 + 2 * 5x(y + 1)
Solution:	3 + 10xy + 10x

Negative Exponents

Negative Exponents of Numbers

Sample Problem:	2-3
Solution:	1/8

Negative Exponents of Variables

Sample Problem:	j-3
Solution:	1/j3

Negative Exponents in Fractions

Sample Problem:	a-2b/a
Solution:	b/a3

Substitution

Substitution Introduction

Sample Problem:	Evaluate: b + x2, where b = -2 and x = p + 1.
Solution:	p2 - 2p - 1

Factoring

Factoring Numbers

Sample Problem:	15
Solution:	1, 3, 5, 15

Finding a Greatest Common Factor (GCF) of Two Numbers

Sample Problem:	42, 98
Solution:	14

Finding a Greatest Common Factor (GCF) of Two Terms

Sample Problem:	21x2y, 7xy3
Solution:	3xy

Factoring a GCF From an Expression

Sample Problem:	5x2 + 15x3
Solution:	5x2(1 + 3x)

Factoring a Difference Between Two Squares

Sample Problem:	x2 - 49
Solution:	(x + 7)(x - 7)

Factoring a Trinomial

Sample Problem:	5u2 + -11uv + 6v2
Solution:	(5u - 6v)(u - v)

Factoring Completely

Sample Problem:	x4 + 7x3 + 12x2
Solution:	x2(x + 3)(x + 4)

Equations - Advanced

Solve By Factoring

Sample Problem:	x2 - 12x + 27 = 0
Solution:	x = 3, 9

Completing the Square

Sample Problem:	x2 + x - 3.75 = 0
Solution:	x = -2.5, 1.5

Solve Using the Quadratic Formula

Sample Problem:	x2 + x - 3.75 = 0
Solution:	x = -2.5, 1.5

Graphing

Graphing Points

Sample Problem:	(1, 5), (-1, 3)
Solution:

Reading the Coordinates of Points on a Graph

Sample Problem:
Solution:	(3, 3)

Graphing Linear Equations by Graphing Two Points

Sample Problem:	y = 3x; points where x = -1 and x = 1
Solution:

Determining the Slope of a Line

Sample Problem:
Solution:	slope: 1.5

Determining x and y Intercepts of a Line

Sample Problem:
Solution:	y intercept: 1

Graphing Linear Equations Using Slope-Intercept Form

Sample Problem:	y = x + 2
Solution:

Determining a Linear Equation From the Graph of a Line

Sample Problem:
Solution:	y = x + 1

Determining a Linear Equation From Two Points (Using the two-point formula)

Sample Problem:	(5, 13) and (10, 23)
Solution:	y = 2x + 3