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Introductory Algebra: University of Alabama

(For a list of materials used in the course, please see http://www.theNCAT.org/R2R/AcadPrac/CM/UA_IntroAlg_Mat.pdf.)

Introductory Algebra is a one-semester, no-credit course that covers the following topics:

The Real Number System

Fractions
Exponents, Order of Operations, and Inequality
Variables, Expressions, and Equations
Real Numbers and the Number Line
Addition and Subtractions of Real Numbers
Multiplication and Division of Real Numbers
Properties of Real Numbers
Simplifying Expressions

Linear Equations and Inequalities in One Variable

The Addition and Multiplication Properties of Equality
More on Solving Linear Equations
An Introduction to Applications of Linear Equations
Formulas and Applications from Geometry
Ratios and proportions
More About Problem Solving
The Addition and Multiplication Properties of Inequality

Linear Equations in Two Variables

Linear Equations in Two Variables
Graphing Linear Equations in Two Variables
The slope of a Line

Polynomials and Exponents

Addition and Subtraction of polynomials: Graphing Simple Polynomials
The Product Rule and Power Rules for Exponents
Multiplication of polynomials
Special Products
Integer Exponents and the Quotient Rule
Division of Polynomials
An Application of Exponents; Scientific Notation

Factoring and Applications

The Greatest Common Factor; Factoring by Grouping
Factoring Trinomials
More on Factoring Trinomials
Special Factoring Rules
Solving Quadratic Equations by Factoring
Applications of Quadratic Equations
Solving Quadratic Inequalities

Rational Expressions

The Fundamental property of Rational Expressions
Multiplication and Division of Rational Expressions
The Least Common Denominator
Addition and Subtraction of Rational Expressions
Complex Fractions
Solving Equations Involving Rational Expressions
Applications of Rational Expressions

Linear Systems

Solving Systems of Linear Equations by Graphing
Solving Systems of Linear Equations by Substitution
Solving Systems of Linear Equations by Elimination
Applications of Linear Systems
Solving Systems of Linear Inequalities

Roots and Radicals

Evaluating Roots
Multiplication and Division of Radicals
Addition and Subtraction of Radicals
Rationalizing the Denominator
Simplifying Radical Expressions
Solving Equations with Radicals
Fractional Exponents

Quadratic Equations

Solving Quadratic Equations by the Square Root Property
Solving Quadratic Equations by Completing the Square
Solving Quadratic Equations by the Quadratic Formula
Complex Numbers
More on Graphing Quadratic Equations: Quadratic Functions