Elementary & Intermediate Algebra for College Students

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Allen Angel received his BS and MS in mathematics from SUNY at New Paltz. He completed additional graduate work at Rutgers University. He taught at Sullivan County Community College and Monroe Community College, where he served as chairperson of the Mathematics Department. He served as Assistant Director of the National Science Foundation at Rutgers University for the summers of 1967 - 1970. He was President of The New York State Mathematics Association of Two Year Colleges (NYSMATYC). He also served as Northeast Vice President of the American Mathematics Association of Two Year Colleges (AMATYC). Allen lives in Palm Harbor, Florida but spends his summers in Penfield, New York. He enjoys playing tennis and watching sports. He also enjoys traveling with his wife Kathy.

Dennis Runde received his BS and MS in mathematics from the University of Wisconsin–Platteville and Milwaukee, respectively. He has a PhD in Mathematics Education from the University of South Florida. He has been teaching for twenty-seven years at State College of Florida-Manatee-Sarasota. His interests include reading, history, fishing, trivia contests, and cooking. He and his wife Kristin are the proud parents of their three sons - Alex, Nick, and Max.

Preface

To the Student

1. Real Numbers

1.1 Study Skills for Success in Mathematics

1.2 Problem Solving

1.3 Fractions

1.4 The Real Number System

1.5 Inequalities

Mid-Chapter Test: Sections 1.1—1.5

1.6 Addition of Real Numbers

1.7 Subtraction of Real Numbers

1.8 Multiplication and Division of Real Numbers

1.9 Exponents, Parentheses, and the Order of Operations

1.10 Properties of the Real Number System

Chapter 1 Summary

Chapter 1 Review Exercises

Chapter 1 Practice Test

2. Solving Linear Equations and Inequalities

2.1 Combining Like Terms

2.2 The Addition Property of Equality

2.3 The Multiplication Property of Equality

2.4 Solving Linear Equations with a Variable on Only One Side of the Equation

Mid-Chapter Test: Sections 2.1—2.4

2.5 Solving Linear Equations with the Variable on Both Sides of the Equation

2.6 Formulas

2.7 Ratios and Proportions

2.8 Inequalities in One Variable

Chapter 2 Summary

Chapter 2 Review Exercises

Chapter 2 Practice Test

Cumulative Review Test

3. Applications of Algebra

3.1 Changing Application Problems into Equations

3.2 Solving Application Problems

Mid-Chapter Test: Sections 3.1—3.2

3.3 Geometric Problems

3.4 Motion, Money, and Mixture Problems

Chapter 3 Summary

Chapter 3 Review Exercises

Chapter 3 Practice Test

Cumulative Review Test

4. Graphing Linear Equations

4.1 The Cartesian Coordinate System and Linear Equations in Two Variables

4.2 Graphing Linear Equations

4.3 Slope of a Line

Mid-Chapter Test: Sections 4.1—4.3

4.4 Slope-Intercept and Point-Slope Forms of a Linear Equation

Chapter 4 Summary

Chapter 4 Review Exercises

Chapter 4 Practice Test

Cumulative Review Test

5. Exponents and Polynomials

5.1 Exponents

5.2 Negative Exponents

5.3 Scientific Notation

Mid-Chapter Test: Sections 5.1—5.3

5.4 Addition and Subtraction of Polynomials

5.5 Multiplication of Polynomials

5.6 Division of Polynomials

Chapter 5 Summary

Chapter 5 Review Exercises

Chapter 5 Practice Test

Cumulative Review Test

6. Factoring

6.1 Factoring a Monomial from a Polynomial

6.2 Factoring by Grouping

6.3 Factoring Trinomials of the Form ax ² + bx + c, a = 1

6.4 Factoring Trinomials of the Form ax ² + bx + c, a ≠ 1

Mid-Chapter Test: Sections 6.1—6.4

6.5 Special Factoring Formulas and a General Review of Factoring

6.6 Solving Quadratic Equations Using Factoring

6.7 Applications of Quadratic Equations

Chapter 6 Summary

Chapter 6 Review Exercises

Chapter 6 Practice Test

Cumulative Review Test

7. Rational Expressions and Equations

7.1 Simplifying Rational Expressions

7.2 Multiplication and Division of Rational Expressions

7.3 Addition and Subtraction of Rational Expressions with a Common Denominator and Finding the Least Common Denominator

7.4 Addition and Subtraction of Rational Expressions

Mid-Chapter Test: Sections 7.1—7.4

7.5 Complex Fractions

7.6 Solving Rational Equations

7.7 Rational Equations: Applications and Problem Solving

7.8 Variation

Chapter 7 Summary

Chapter 7 Review Exercises

Chapter 7 Practice Test

Cumulative Review Test

8. Functions and Their Graphs

8.1 More on Graphs

8.2 Functions

8.3 Linear Functions

Mid-Chapter Test: Sections 8.1—8.3

8.4 Slope, Modeling, and Linear Relationships

8.5 The Algebra of Functions

Chapter 8 Summary

Chapter 8 Review Exercises

Chapter 8 Practice Test

Cumulative Review Test

9. Systems of Linear Equations

9.1 Solving Systems of Equations Graphically

9.2 Solving Systems of Equations by Substitution

9.3 Solving Systems of Equations by the Addition Method

9.4 Solving Systems of Linear Equations in Three Variables

Mid-Chapter Test: Sections 9.1—9.4

9.5 Systems of Linear Equations: Applications and Problem Solving

9.6 Solving Systems of Equations Using Matrices

9.7 Solving Systems of Equations Using Determinants and Cramer’s Rule

Chapter 9 Summary

Chapter 9 Review Exercises

Chapter 9 Practice Test

Cumulative Review Test

10. Inequalities in One and Two Variables

10.1 Solving Linear Inequalities in One Variable

10.2 Solving Equations and Inequalities Containing Absolute Values

Mid-Chapter Test: Sections 10.1—10.2

10.3 Graphing Linear Inequalities in Two Variables and Systems of Linear Inequalities

Chapter 10 Summary

Chapter 10 Review Exercises

Chapter 10 Practice Test

Cumulative Review Test

11. Roots, Radicals, and Complex Numbers

11.1 Roots and Radicals

11.2 Rational Exponents

11.3 Simplifying Radicals

11.4 Adding, Subtracting, and Multiplying Radicals

Mid-Chapter Test: Sections 11.1—11.4

11.5 Dividing Radicals

11.6 Solving Radical Equations

11.7 Complex Numbers

Chapter 11 Summary

Chapter 11 Review Exercises

Chapter 11 Practice Test

Cumulative Review Test

12. Quadratic Functions

12.1 Solving Quadratic Equations by Completing the Square

12.2 Solving Quadratic Equations by the Quadratic Formula

12.3 Quadratic Equations: Applications and Problem Solving

Mid-Chapter Test: Sections 12.1—12.3

12.4 Factoring Expressions and Solving Equations That Are Quadratic in Form

12.5 Graphing Quadratic Functions

12.6 Quadratic, Polynomial, and Rational Inequalities in One Variable

Chapter 12 Summary

Chapter 12 Review Exercises

Chapter 12 Practice Test

Cumulative Review Test

13. Exponential and Logarithmic Functions

13.1 Composite and Inverse Functions

13.2 Exponential Functions

13.3 Logarithmic Functions

13.4 Properties of Logarithms

Mid-Chapter Test: Sections 13.1—13.4

13.5 Common Logarithms

13.6 Exponential and Logarithmic Equations

13.7 Natural Exponential and Natural Logarithmic Functions 818

Chapter 13 Summary 829

Chapter 13 Review Exercises 832

Chapter 13 Practice Test 835

Cumulative Review Test 836

14. Conic Sections

14.1 The Parabola and the Circle

14.2 The Ellipse

Mid-Chapter Test: Sections 14.1—14.2

14.3 The Hyperbola

14.4 Nonlinear Systems of Equations and Their Applications

Chapter 14 Summary

Chapter 14 Review Exercises

Chapter 14 Practice Test

Cumulative Review Test

15. Sequences, Series, and the Binomial Theorem

15.1 Sequences and Series

15.2 Arithmetic Sequences and Series

15.3 Geometric Sequences and Series

Mid-Chapter Test: Sections 15.1—15.3

15.4 The Binomial Theorem

Chapter 15 Summary

Chapter 15 Review Exercises

Chapter 15 Practice Test

Cumulative Review Test

Appendices

A. Review of Decimals and Percent

B. Finding the Greatest Common Factor and Least Common Denominator

C. Geometry

D. Review of Exponents, Polynomials, and Factoring

Answers

Applications Index

Subject Index     

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