Elementary & Intermediate Algebra for College Students

Allen R. Angel received his AAS in Electrical Technology from New York City Community College. He then received his BS in Physics and his MS in Mathematics from SUNY at New Paltz, and he took additional graduate work at Rutgers University. He is Professor Emeritus at Monroe Community College in Rochester, New York where he served for many years as the chair of the Mathematics Department. He also served as the Assistant Director of the National Science Foundation Summer Institutes at Rutgers University from 1967–73. He served as the President of the New York State Mathematics Association of Two Year Colleges (NYSMATYC) and the Northeast Vice President of the American Mathematics Association of Two Year Colleges (AMATYC). He is the recipient of many awards including a number of NISOD Excellence in Teaching Awards, NYSMATYC's Outstanding Contributions to Mathematics Education Award, and AMATYC's President Award. Allen enjoy tennis, worldwide travel, and visiting with his children and granddaughter.   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 years at State College of Florida, Manatee, and Sarasota Counties and for ten years at Saint Stephen's Episcopal School. Besides coaching little league baseball, his other interests include history, politics, fishing, canoeing, and cooking. He and his wife Kristin stay busy keeping up with 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

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

            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 ax2 + bx + c, a = 1

6.4 Factoring Trinomials of the Form ax2 + 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 and Other 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