Intermediate Algebra

Marvin Bittinger has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University Purdue University Indianapolis, and is now professor emeritus of mathematics education. Professor Bittinger has authored over 190 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." His hobbies include hiking in Utah, baseball, golf, and bowling. In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters.   David Ellenbogen has taught math at the college level for nearly 30 years, spending most of that time in the Massachusetts and Vermont community college systems, where he has served on both curriculum and developmental math committees. He has taught at St. Michael's College and The University of Vermont. Professor Ellenbogen has been active in the American Mathematical Association of Two Year Colleges (AMATYC) since 1985, having served on its Developmental Mathematics Committee and as a delegate. He has been a member of the Mathematical Association of America (MAA) since 1979. He has authored dozens of texts on topics ranging from prealgebra to calculus and has delivered lectures on the use of language in mathematics. Professor Ellenbogen received his bachelor's degree in mathematics from Bates College and his master’s degree in community college mathematics education from The University of Massachusetts—Amherst. In his spare time, he enjoys playing piano, biking, hiking, skiing and volunteer work. He currently serves on the boards of the Vermont Sierra Club and the Vermont Bicycle Pedestrian Coalition. He has two sons, Monroe and Zachary.   Barbara Johnson has a B.S. in mathematics from Bob Jones University and a M.S. in math from Clemson University. She has taught high school and college math for 25 years, and enjoys the challenge of helping each student grow in appreciation for and understanding of mathematics.  As a Purdue Master Gardener, she also enjoys helping others learn gardening skills.  Believing that the best teacher is always learning, she recently earned a black belt in karate.

Preface

 

1. Basics of Algebra and Graphing

1.1 Some Basics of Algebra

1.2 Operations with Real Numbers

1.3 Equivalent Algebraic Expressions

1.4 Exponential Notation and Scientific Notation

            Mid-Chapter Review

1.5 Graphs

1.6 Solving Equations and Formulas

1.7 Introduction to Problem Solving and Models

            Summary and Review

            Test

 

2. Functions, Linear Equations, and Models

2.1 Functions

2.2 Linear Functions: Slope, Graphs, and Models

2.3 Another Look at Linear Graphs

2.4 Introduction to Curve Fitting: Point-Slope Form

            Mid-Chapter Review

2.5 The Algebra of Functions

            Summary and Review

            Test

 

3. Systems of Linear Equations and Problem Solving

3.1 Systems of Equations in Two Variables

3.2 Solving by Substitution or Elimination

3.3 Solving Applications: Systems of Two Equations

            Mid-Chapter Review

3.4 Systems of Equations in Three Variables

3.5 Solving Applications: Systems of Three Equations

3.6 Elimination Using Matrices

3.7 Determinants and Cramer's Rule

3.8 Business and Economics Applications

            Summary and Review

            Test

 

Cumulative Review: Chapters 1—3

 

4. Inequalities

4.1 Inequalities and Applications

4.2 Solving Equations and Inequalities by Graphing

4.3 Intersections, Unions, and Compound Inequalities

4.4 Absolute-Value Equations and Inequalities

            Mid-Chapter Review

4.5 Inequalities in Two Variables

            Summary and Review

            Test

 

5. Polynomials and Polynomial Functions

5.1 Introduction to Polynomials and Polynomial Functions

5.2 Multiplication of Polynomials

5.3 Polynomial Equations and Factoring

5.4 Trinomials of the Type x2 + bx + c

5.5 Trinomials of the Type ax2 + bx + c

5.6 Perfect-Square Trinomials and Differences of Squares

5.7 Sums or Differences of Cubes

            Mid-Chapter Review

5.8 Applications of Polynomial Equations

            Summary and Review

            Test

 

6. Rational Expressions, Equations, and Functions

6.1 Rational Expressions and Functions: Multiplying and Dividing

6.2 Rational Expressions and Functions: Adding and Subtracting

6.3 Complex Rational Expressions

            Mid-Chapter Review

6.4 Rational Equations

6.5 Applications Using Rational Equations

6.6 Division of Polynomials

6.7 Synthetic Division

6.8 Formulas, Applications, and Variation

            Summary and Review

            Test

 

Cumulative Review: Chapters 1—6

 

7. Exponents and Radical Functions

7.1 Radical Expressions, Functions, and Models

7.2 Rational Numbers as Exponents

7.3 Multiplying Radical Expressions

7.4 Dividing Radical Expressions

7.5 Expressions Containing Several Radical Terms

            Mid-Chapter Review

7.6 Solving Radical Equations

7.7 The Distance Formula, the Midpoint Formula, and Other Applications

7.8 The Complex Numbers

            Summary and Review

            Test

 

8. Quadratic Functions and Equations

8.1 Quadratic Equations

8.2 The Quadratic Formula

8.3 Studying Solutions of Quadratic Equations

8.4 Studying Solutions of Quadratic Equations

8.5 Equations Reducible to Quadratic

            Mid-Chapter Review

8.6 Quadratic Functions and Their Graphs

8.7 More About Graphing Quadratic Functions

8.8 Problem Solving and Quadratic Functions

8.9 Polynomial Inequalities and Rational Inequalities

            Summary and Review

            Test

 

9. Exponential Functions and Logarithmic Functions

9.1 Composite Functions and Inverse Functions

9.2 Exponential Functions

9.3 Logarithmic Functions

9.4 Properties of Logarithmic Functions

            Mid-Chapter Review

9.5 Natural Logarithms and Changing Bases

9.6 Solving Exponential and Logarithmic Equations

9.7 Applications of Exponential and Logarithmic Functions

            Summary and Review

            Test

 

Cumulative Review: Chapters 1—9

 

10. Conic Sections

10.1 Conic Sections: Parabolas and Circles

10.2 Conic Sections: Ellipses

10.3 Conic Sections: Hyperbolas

            Mid-Chapter Review

10.4 Nonlinear Systems of Equations

            Summary and Review

            Test

 

11. Sequences, Series, and the Binomial Theorem

11.1 Sequences and Series

11.2 Arithmetic Sequences and Series

11.3 Geometric Sequences and Series

            Mid-Chapter Review

11.4 The Binomial Theorem

            Summary and Review

            Test

 

Cumulative Review: Chapters 1-11

 

Answers

Glossary

Photo Credits

Index

Index of Applications