Introductory Algebra

Table of Contents



R. Prealgebra Review
R.1 Fractions
R.2 Decimals and Percents
Study Skills Using Your Math Text



The Real Number System

1.1 Exponents, Order of Operations, and Inequality

Study Skills Taking Lecture Notes


1.2 Variables, Expressions, and Equations

Study Skills Reading Your Math Text


1.3 Real Numbers and the Number Line

Study Skills Using Study Cards


1.4 Adding Real Numbers
1.5 Subtracting Real Numbers

Study Skills Completing Your Homework


1.6 Multiplying and Dividing Real Numbers

Summary Exercises Performing Operations with Real Numbers


1.7 Properties of Real Numbers
1.8 Simplifying Expressions

Study Skills Reviewing a Chapter




Equations, Inequalities, and Applications

2.1 The Addition Property of Equality

Study Skills Managing Your Time


2.2 The Multiplication Property of Equality
2.3 More on Solving Linear Equations

Study Skills Using Study Cards Revisited
Summary Exercises Applying Methods for Solving Linear Equations


2.4 An Introduction to Applications of Linear Equations
2.5 Formulas and Additional Applications from Geometry
2.6 Ratio, Proportion, and Percent

Summary Exercises Applying Problem-Solving Techniques


2.7 Solving Linear Inequalities

Study Skills Taking Math Tests




Graphs of Linear Equations and Inequalities in Two Variables

3.1 Linear Equations and Rectangular Coordinates

Study Skills Analyzing Your Test Results


3.2 Graphing Linear Equations in Two Variables
3.3 The Slope of a Line

Study Skills Preparing for Your Math Final Exam


3.4 Slope-Intercept Form of a Linear Equation
3.5 Point-Slope Form of a Linear Equation and Modeling

Summary Exercises Applying Graphing and
Equation-Writing Techniques for Lines


3.6 Graphing Linear Inequalities in Two Variables


Systems of Linear Equations and Inequalities

4.1 Solving Systems of Linear Equations by Graphing
4.2 Solving Systems of Linear Equations by Substitution
4.3 Solving Systems of Linear Equations by Elimination

Summary Exercises Applying Techniques for Solving Systems of Linear Equations


4.4 Applications of Linear Systems
4.5 Solving Systems of Linear Inequalities


Exponents and Polynomials

5.1 The Product Rule and Power Rules for Exponents
5.2 Integer Exponents and the Quotient Rule

Summary Exercises Applying the Rules for Exponents


5.3 An Application of Exponents: Scientific Notation
5.4 Adding and Subtracting Polynomials
5.5 Multiplying Polynomials
5.6 Special Products
5.7 Dividing a Polynomial by a Monomial
5.8 Dividing a Polynomial by a Polynomial


Factoring and Applications

6.1 Greatest Common Factors; Factor by Grouping
6.2 Factoring Trinomials
6.3 Factoring Trinomials by Grouping
6.4 Factoring Trinomials Using the FOIL Method
6.5 Special Factoring Techniques

Summary Exercises Recognizing and Applying Factoring Strategies


6.6 Solving Quadratic Equations Using the Zero-Factor Property
6.7 Applications of Quadratic Equations


Rational Expressions and Applications

7.1 The Fundamental Property of Rational Expressions
7.2 Multiplying and Dividing Rational Expressions
7.3 Least Common Denominators
7.4 Adding and Subtracting Rational Expressions
7.5 Complex Fractions
7.6 Solving Equations with Rational Expressions

Summary Exercises Simplifying Rational Expressions vs. Solving Rational Equations


7.7 Applications of Rational Expressions
7.8 Variation


Roots and Radicals

8.1 Evaluating Roots
8.2 Multiplying, Dividing, and Simplifying Radicals
8.3 Adding and Subtracting Radicals
8.4 Rationalizing the Denominator
8.5 More Simplifying and Operations with Radicals

Summary Exercises Applying Operations with Radicals


8.6 Solving Equations with Radicals


Quadratic Equations

9.1 Solving Quadratic Equations by the Square Root Property
9.2 Solving Quadratic Equations by Completing the Square
9.3 Solving Quadratic Equations by the Quadratic Formula

Summary Exercises Applying Methods for Solving Quadratic Equations


9.4 Graphing Quadratic Equations
9.5 Introduction to Functions



Appendix: Factoring Sums and Differences of Cubes