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Intermediate Algebra



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The Sullivan/Struve/Mazzarella Algebra programis designed to motivate students to "do the math"- at home or in the lab-and supports a variety of learning environments. The text is known for its two-column example format that provides annotations to the left of the algebra. These annotations explain what the authors are about to do in each step (instead of what was just done), just as an instructor would do.

Author Biography

Michael Sullivan, III is a full-time professor of mathematics at Joliet Jr. College. His training is in mathematics, statistics, and economics and he has more than 18 years experience as an instructor. His publications with Pearson cover developmental math, precalculus, and introductory statistics. Most recently, Mike has been highly involved in Course Redesign at Joliet Junior College. His experience in course redesign and writing texts for the college-level math and statistics courses gives him a unique insight into where students are headed after the developmental math track, and what they need to do to be successful. Mike is the father of three children and an avid golfer.

Katherine Struve is a full-time instructor with Columbus State Community College and has more than 30 years experience in the classroom. She is in tune with the challenges of teaching mathematics at a large, urban community college. She has served as the Lead Instructor of Developmental Mathematics and has been involved in the recent course redesign effort at Columbus State.


Janet Mazzarella is a full-time instructor at Southwestern College and has more than 18 years experience teaching a wide range of courses from arithmetic through calculus. She helped develop the self-paced developmental math program and spent two years serving as its director. Along with Mike and Kathy, Janet has also been active in the course redesign initiative at her institution.

Table of Contents

R. Real Numbers and Algebraic Expressions

R.1 Success in Mathematics

R.2 Sets and Classification of Numbers

R.3 Operations on Signed Numbers; Properties of Real Numbers

R.4 Order of Operations

R.5 Algebraic Expressions


1. Linear Equations and Inequalities

Part I: Linear Equations and Inequalities in One Variable

1.1 Linear Equations in One Variable

1.2 An Introduction to Problem Solving

1.3 Using Formulas to Solve Problems

1.4 Linear Inequalities in One Variable

            Putting the Concepts Together (Sections 1.1–1.4)


Part II: Linear Equations and Inequalities in Two Variables

1.5 Rectangular Coordinates and Graphs of Equations

1.6 Linear Equations in Two Variables

1.7 Parallel and Perpendicular Lines

1.8 Linear Inequalities in Two Variables

            Chapter 1 Activity: Pass the Paper

            Chapter 1 Review

            Chapter 1 Test

            Cumulative Review Chapters R–1


2. Relations, Functions, and More Inequalities

2.1 Relations

2.2 An Introduction to Functions

2.3 Functions and Their Graphs

            Putting the Concepts Together (Sections 2.1–2.4)

2.4 Linear Functions and Models

2.5 Compound Inequalities

2.6 Absolute Value Equations and Inequalities

            Chapter 2 Activity: Shifting Discovery?

            Chapter 2 Review

            Chapter 2 Test


3. Systems of Linear Equations and Inequalities

3.1 Systems of Linear Equations in Two Variables

3.2 Problem Solving: Systems of Two Linear Equations Containing Two Unknowns

3.3 Systems of Linear Equations in Three Variables

            Putting the Concepts Together (Sections 3.1–3.3)

3.4 Using Matrices to Solve Systems

3.5 Determinants and Cramer's Rule

3.6 Systems of Linear Inequalities

            Chapter 3 Activity: Find the Numbers

            Chapter 3 Review

            Chapter 3 Test

            Cumulative Review Chapters R–3


Getting Ready for Chapter 4: Laws of Exponents and Scientific Notation


4. Polynomial and Polynomial Functions

4.1 Adding and Subtracting Polynomials

4.2 Multiplying Polynomials

4.3 Dividing Polynomials; Synthetic Division

            Putting the Concepts Together (Sections 4.1–4.3)

4.4 Greatest Common Factor; Factoring by Grouping

4.5 Factoring Trinomials

4.6 Factoring Special Products

4.7 Factoring: A General Strategy

4.8 Polynomial Equations

            Chapter 4 Activity: What Is the Question?

            Chapter 4 Review

            Chapter 4 Test


Getting Ready for Chapter 5: A Review of Operations on Rational Numbers (54)


5. Rational Expressions and Rational Functions

5.1 Multiplying and Dividing Rational Expressions

5.2 Adding and Subtracting Rational Expressions

5.3 Complex Rational Expressions

            Putting the Concepts Together (Sections 5.1–5.3)

5.4 Rational Equations

5.5 Rational Inequalities

5.6 Models Involving Rational Expressions

5.7 Variation

            Chapter 5 Activity: Correct the Quiz

            Chapter 5 Review

            Chapter 5 Test

            Cumulative Review Chapters R–5


Getting Ready for Chapter 6: Square Roots


6. Radicals and Rational Exponents

6.1 nth Roots and Rational Exponents

6.2 Simplify Expressions Using the Law of Exponents

6.3 Simplify Radical Expressions Using Properties of Radicals

6.4 Adding, Subtracting, and Multiplying Radical Expressions

6.5 Rationalizing Radical Expressions

            Putting the Concepts Together (Sections 6.1–6.5)

6.6 Functions Involving Radicals

6.7 Radical Equations and Their Applications

6.8 The Complex Number System

            Chapter 6 Activity: Which One Does Not Belong?

            Chapter 6 Review

            Chapter 6 Test


7. Quadratic Equations and Functions

7.1 Solving Quadratic Equations by Completing the Square

7.2 Solving Quadratic Equations by the Quadratic Formula

7.3 Solving Equations Quadratic in Form

            Putting the Concepts Together (Sections 7.1–7.3)

7.4 Graphing Quadratic Functions Using Transformations

7.5 Graphing Quadratic Functions Using Properties

7.6 Polynomial Inequalities

            Chapter 7 Activity: Presidential Decision Making

            Chapter 7 Review

            Chapter 7 Test

            Cumulative Review Chapters R–7


8. Exponential and Logarithmic Functions

8.1 Composite Functions and Inverse Functions

8.2 Exponential Functions

8.3 Logarithmic Functions

            Putting the Concepts Together (Sections 8.1–8.3)

8.4 Properties of Logarithms

8.5 Exponential and Logarithmic Equations

            Chapter 8 Activity: Correct the Quiz

            Chapter 8 Review

            Chapter 8 Test


9. Conics

9.1 Distance and Midpoint Formulas

9.2 Circles

9.3 Parabolas

9.4 Ellipses

9.5 Hyperbolas

            Putting the Concepts Together (Sections 9.1–9.5)

9.6 Systems of Nonlinear Equations

            Chapter 9 Activity: How Do You Know That...?

            Chapter 9 Review

            Chapter 9 Test

            Cumulative Review Chapters R–9


10. Sequences, Series, and the Binomial Theorem

10.1 Sequences

10.2 Arithmetic Sequences

10.3 Geometric Sequences and Series

            Putting the Concepts Together (Sections 10.1–10.3)

10.4 The Binomial Theorem

            Chapter 10 Activity: Discover the Relation

            Chapter 10 Review

            Chapter 10 Test


Answers to Selected Exercises

Graphing Answer Sections

Application Index

Subject Index

Photo Credits

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