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.   Judy Beecher has an undergraduate degree in mathematics from Indiana University and a graduate degree in mathematics from Purdue University. She has taught at both the high school and college levels with many years of developmental math and precalculus teaching experience at Indiana University–Purdue University Indianapolis. In addition to her career in textbook publishing, she spends time traveling, enjoying her grandchildren, and promoting charity projects for a children's camp.   Barbara Johnson has a BS in mathematics from Bob Jones University and a MS in math from Clemson University. She has taught high school and college math for 30  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.

Index of Applications

Preface

 

R. Review of Basic Algebra:

Part 1: Operations

R.1 The Set of Real Numbers

R.2 Operations with Real Numbers

R.3 Exponential Notation and Order of Operations

Part 2: Manipulations

R.4 Introduction to Algebraic Expressions

R.5 Equivalent Algebraic Expressions

R.6 Simplifying Algebraic Expressions

R.7 Properties of Exponents and Scientific Notation

            Summary and Review

            Test

 

1. Solving Linear Equations and Inequalities

1.1 Solving Equations

1.2 Formulas and Applications

1.3 Applications and Problem Solving

            Mid-Chapter Review

1.4 Sets, Inequalities, and Interval Notation

            Translating for Success

1.5 Intersections, Unions, and Compound Inequalities

1.6 Absolute-Value Equations and Inequalities

            Summary and Review

            Test

 

2. Graphs, Functions, and Applications

2.1 Graphs of Equations

2.2 Functions and Graphs

2.3 Finding Domain and Range

            Mid-Chapter Review

2.4 Linear Functions: Graphs and Slope

2.5 More on Graphing Linear Equations

Visualizing for Success

2.6 Finding Equations of Lines; Applications

            Summary and Review

            Test

            Cumulative Review

 

3. Systems of Equations

3.1 Systems of Equations in Two Variables

3.2 Solving by Substitution

3.3 Solving by Elimination

3.4 Solving Applied Problems: Two Equations

            Translating for Success

            Mid-Chapter Review

3.5 Systems of Equations in Three Variables

3.6 Solving Applied Problems: Three Equations

3.7 Systems of Inequalities in Two Variables

            Visualizing for Success

            Summary and Review

            Test

            Cumulative Review

 

4. Polynomials and Polynomial Functions

4.1 Introduction to Polynomials and Polynomial Functions

4.2 Multiplication of Polynomials

4.3 Introduction to Factoring

4.4 Factoring Trinomials: x2 + bx + c

            Mid-Chapter Review

4.5 Factoring Trinomials: ax2 + bx + c, a ≠ 1

4.6 Special Factoring

            Visualizing for Success

4.7 Factoring: A General Strategy

4.8 Applications of Polynomial Equations and Functions

Translating for Success

            Summary and Review

            Test

            Cumulative Review

 

5. Rational Expressions, Equations, and Functions

5.1 Rational Expressions and Functions: Multiplying, Dividing, and Simplifying

5.2 LCMs, LCDs, Addition, and Subtraction

5.3 Division of Polynomials

5.4 Complex Rational Expressions

            Mid-Chapter Review

5.5 Solving Rational Equations

5.6 Applications and Proportions

            Translating for Success

5.7 Formulas and Applications

5.8 Variation and Applications

            Summary and Review

            Test

            Cumulative Review

 

6. Radical Expressions, Equations, and Functions

6.1 Radical Expressions and Functions

6.2 Rational Numbers as Exponents

6.3 Simplifying Radical Expressions

6.4 Addition, Subtraction, and More Multiplication

            Mid-Chapter Review

6.5 More on Division of Radical Expressions

6.6 Solving Radical Equations

6.7 Applications Involving Powers and Roots

            Translating for Success

6.8 The Complex Numbers

            Summary and Review

            Test

            Cumulative Review

 

7. Quadratic Equations and Functions

7.1 The Basics of Solving Quadratic Equations

7.2 The Quadratic Formula

7.3 Applications Involving Quadratic Equations

            Translating for Success

7.4 More on Quadratic Equations

            Mid-Chapter Review

7.5 Graphing f(x) = a(x - h)2 + k

7.6 Graphing f(x) = ax2 + bx + c

            Visualizing for Success

7.7 Mathematical Modeling with Quadratic Functions

7.8 Polynomial Inequalities and Rational Inequalities

            Summary and Review

            Test

            Cumulative Review

 

8. Exponential Functions and Logarithmic Functions

8.1 Exponential Functions

8.2 Composite Functions and Inverse Functions

8.3 Logarithmic Functions

8.4 Properties of Logarithmic Functions

            Mid-Chapter Review

8.5 Natural Logarithmic Functions Visualizing for Success

8.6 Solving Exponential Equations and Logarithmic Equations

8.7 Mathematical Modeling with Exponential Functions and Logarithmic Functions

            Translating for Success

            Summary and Review

            Test

            Cumulative Review

 

9. Conic Sections

9.1 Parabolas and Circles

9.2 Ellipses

            Mid-Chapter Review

9.3 Hyperbolas

Visualizing for Success

9.4 Nonlinear Systems of Equations

            Summary and Review

            Test

            Cumulative Review

 

Appendices

A. Fraction Notation

B. Determinants and Cramer’s Rule

C. Elimination Using Matrices

D. The Algebra of Functions

 

Answers

Guided Solutions

Glossary

Index

Additional Instructor’s Answers