Introductory Algebra: Concepts and Graphs is a traditional, one-semester, textbook for a first course in algebra. We cover graphing early. Systems of equations are covered in Chapter 7, but can easily be moved up to follow the chapter on graphing. The last chapter of the book is an introduction to both roots and radicals, and quadratic equations. Most books cover these topics in more detail in two separate chapters. If you prefer that treatment, we can put the two traditional, more detailed chapters online for you.
Features
Getting Ready for the Next Section
These problems appear at the end of every problem set. They are the exact problems that students will see when they read through the next section of the text. Students who consistently work these problems will be much better prepared for class than students who don't work these problems. The problems shown here are at the end of Problem Set 3.2. Section 3.3 covers graphing linear equations in two variables.
Anticipating Difficulties and Building Solutions into the Text
We try to anticipate problems students have and build features into the text that address these problems. For example, we know students don't always pay attention to instructions when they are doing their homework, and it gets them into trouble on tests and quizzes. So, we build problems into the text that require that they read instructions. The problems shown above appear in the problem set covering addition and subtraction with rational expressions.
Real-Data Application Problems
This book includes many new problems that use real-world applications for the mathematical subject, making the concepts easier to understand. Many times the charts and graphics in the text look like the types of charts and graphics students see in the media.
Blueprint for Problem Solving
These are detailed outlines of the steps needed to successfully solve application problems. Intended as a guide to problem solving in general, the Blueprint overlays the solution process to all the application problems early in the book. As students become more accomplished at problem solving, the steps are streamlined.
Using Technology
Scattered throughout the book are exercises that demonstrate how graphing calculators, spreadsheets and computer graphing programs can be used to enhance the topics being covered.
Facts from Geometry
This feature gives students a chance to see how topics from geometry are related to the algebra they are using.
Additional Resources Available Online
Videos
Every example in the book is done in videos available online at MathTV.com. Students can choose from a variety of instructors — including the book's author — and see and hear the examples done in both English and Spanish.
Online Homework
XYZHomework.com is provided free of charge to teachers and students using XYZ Textbook-published books. The system provides teachers with an online gradebook and students with numerous dynamically generated problems.
Online Textbooks
If students have Internet access, they have access to their textbook. An online version of the textbook is available to students as part of their purchase.
Additional Problems
In addition to an identical reproduction of their printed textbook, students also have access to additional resources such as Matched Problem sets, Multiple-choice questions and exercises where they must Find the Mistake.
Table of Contents
Downloadable formats: PDF | Word
- 1 The Basics
- 1.1 Notation and Symbols
- 1.2 Real Numbers
- 1.3 Addition with Real Numbers
- 1.4 Subtraction of Real Numbers
- 1.5 Properties of Real Numbers
- 1.6 Multiplication of Real Numbers
- 1.7 Division of Real Numbers
- 1.8 Subsets of the Real Numbers
- 1.9 Addition and Subtraction with Fractions
- 2 Linear Equations and Inequalities
- 2.1 Simplifying Expressions
- 2.2 Addition Property of Equality
- 2.3 Multiplication Property of Equality
- 2.4 Solving Linear Equations
- 2.5 Formulas
- 2.6 Applications
- 2.7 More Applications
- 2.8 Linear Inequalities
- 3 Graphing
- 3.1 Paired Data and Graphing Ordered Pairs
- 3.2 Solutions to Linear Equations in Two Variables
- 3.3 Graphing Linear Equations in Two Variables
- 3.4 More on Graphing: Intercepts
- 3.5 The Slope of a Line
- 3.6 Finding the Equation of a Line
- 3.7 Linear Inequalities in Two Variables
- 4 Exponents and Polynomials
- 4.1 Multiplication with Exponents
- 4.2 Division with Exponents
- 4.3 Operations with Monomials
- 4.4 Addition and Subtraction of Polynomials
- 4.5 Multiplication with Polynomials
- 4.6 Binomial Squares and Other Special Products
- 4.7 Dividing a Polynomial by a Monomial
- 4.8 Dividing a Polynomial by a Polynomial
- 5 Factoring
- 5.1 The Greatest Common Factor and Factoring by Grouping
- 5.2 Factoring Trinomials
- 5.3 More Trinomials to Factor
- 5.4 The Difference of Two Squares
- 5.5 The Sum and Difference of Two Cubes
- 5.6 Factoring: A General Review
- 5.7 Solving Equations by Factoring
- 5.8 Applications
- 6 Rational Expressions
- 6.1 Reducing Rational Expressions to Lowest Terms
- 6.2 Multiplication and Division of Rational Expressions
- 6.3 Addition and Subtraction of Rational Expressions
- 6.4 Equations involving Rational Expressions
- 6.5 Applications
- 6.6 Complex Fractions
- 6.7 Proportions
- 6.8 Variation
- 7 Systems of Equations
- 7.1 Solving Linear Systems by Graphing
- 7.2 The Elimination Method
- 7.3 The Substitution Method
- 7.4 Applications
- 8 Roots, Radicals, and more Quadratic Equations
- 8.1 Definitions and Common Roots
- 8.2 Properties of Radicals
- 8.3 Simplified Form for Radicals
- 8.4 More Quadratic Equations
- 8.5 Completing the Square
- 8.6 The Quadratic Formula
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