Elementary 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.

Note:  Each chapter concludes with Chapter Summary, Chapter Review Exercises, and Chapter Practice Test and after Chapter 1, Cumulative Review Test.

 

Preface

To the Student

CHAPTER 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 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 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 4   Exponents and Polynomials 4.1  Exponents

4.2  Negative Exponents

4.3  Scientific Notation

Mid-Chapter Test: Sections 4.1—4.3

4.4  Addition and Subtraction of Polynomials

4.5  Multiplication of Polynomials

4.6  Division of Polynomials

 

CHAPTER 5   Factoring

5.1  Factoring a Monomial from a Polynomial

5.2  Factoring by Grouping

5.3  Factoring Trinomials of the form ax² + bx + c, a = 1

5.4  Factoring Trinomials of the form ax² + bx + c, a ≠ 1

Mid-Chapter Test: Sections 5.1—5.4

5.5  Special Factoring Formulas and a General Review of Factoring

5.6  Solving Quadratic Equations Using Factoring

5.7  Applications of Quadratic Equations

 

CHAPTER 6   Rational Expressions and Equations 6.1   Simplifying Rational Expressions

6.2   Multiplication and Division of Rational Expressions

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

6.4   Addition and Subtraction of Rational Expressions

Mid-Chapter Test: Sections 6.1—6.4

6.5   Complex Fractions

6.6   Solving Rational Equations

6.7   Rational Equations: Applications and Problem Solving

6.8   Variation

 

CHAPTER 7   Graphing Linear Equations 7.1  The Cartesian Coordinate System and Linear Equations in Two Variables

7.2  Graphing Linear Equations

7.3  Slope of a Line

Mid-Chapter Test: Sections 7.1—7.3

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

7.5  Graphing Linear Inequalities

7.6  Functions

 

CHAPTER 8   Systems of Linear Equations 8.1  Solving Systems of Equations Graphically

8.2  Solving Systems of Equations by Substitution

8.3  Solving Systems of Equations by the Addition Method

Mid-Chapter Test: Sections 8.1—8.3

8.4  Systems of Equations: Applications and Problem Solving

8.5  Solving Systems of Linear Inequalities

 

CHAPTER 9   Roots and Radicals 9.1  Evaluating Square Roots

9.2  Simplifying Square Roots

9.3  Adding, Subtracting, and Multiplying Square Roots

9.4  Dividing Square Roots

Mid-Chapter Test: Sections 9.1—9.4

9.5  Solving Radical Equations

9.6  Radicals: Applications and Problem Solving

9.7  Higher Roots and Rational Exponents

 

CHAPTER  10   Quadratic Equations

10.1  The Square Root Property

10.2  Solving Quadratic Equations by Completing the Square

10.3  Solving Quadratic Equations by the Quadratic Formula

Mid-Chapter Test: Sections 10.1—10.3

10.4  Graphing Quadratic Equations

10.5  Complex Numbers

 

APPENDICES A   Review of Decimals and Percents

B   Finding the Greatest Common Factor and Least Common Denominator

C  Geometry

 

Answers

Graphing Answer Section *found only in the Annotated Instructor's Edition

Applications Index

Index

Photo Credits