# 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