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.

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   Basic Concepts 1.1  Study Skills for Success in Mathematics, and Using a Calculator

1.2  Sets and Other Basic Concepts

1.3  Properties of and Operations with Real Numbers

1.4  Order of Operations

Mid-Chapter Test: Sections 1.1–1.4

1.5  Exponents

1.6  Scientific Notation

 

CHAPTER 2   Equations and Inequalities 2.1  Solving Linear Equations

2.2  Problem Solving and Using Formulas

2.3  Applications of Algebra

Mid-Chapter Test: Sections 2.1–2.3

2.4  Additional Application Problems

2.5  Solving Linear Inequalities

2.6  Solving Equations and Inequalities Containing Absolute Values

 

CHAPTER 3   Graphs and Functions 3.1  Graphs

3.2  Functions

3.3  Linear Functions:  Graphs and Applications

3.4  The Slope-Intercept Form of a Linear Equation

Mid-Chapter Test: Sections 3.1–3.4

3.5  The Point-Slope Form of a Linear Equation

3.6  The Algebra of Functions

3.7  Graphing Linear Inequalities

 

CHAPTER 4   Systems of Equations and Inequalities 4.1  Solving Systems of Linear Equations in Two Variables

4.2  Solving Systems of Linear Equations in Three Variables

4.3  Systems of Linear Equations:  Applications and Problem Solving

Mid-Chapter Test: Sections 4.1–4.3

4.4  Solving Systems of Equations Using Matrices

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

4.6  Solving Systems of Linear Inequalities

           

CHAPTER 5   Polynomials and Polynomial Functions 5.1  Addition and Subtraction of Polynomials

5.2  Multiplication of Polynomials

5.3  Division of Polynomials and Synthetic Division

5.4  Factoring a Monomial from a Polynomial and Factoring by Grouping

Mid-Chapter Test: Sections 5.1–5.4

5.5  Factoring Trinomials

5.6  Special Factoring Formulas

5.7  A General Review of Factoring

5.8  Polynomial Equations

 

CHAPTER 6   Rational Expressions and Equations 6.1  The Domains of Rational Functions and Multiplication and Division of Rational Expressions
6.2  Addition and Subtraction of Rational Expressions
6.3  Complex Fractions

6.4  Solving Rational Equations

Mid-Chapter Test: Sections 6.1–6.4

6.5  Rational Equations: Applications and Problem Solving
6.6  Variation

CHAPTER 7   Roots, Radicals, and Complex Numbers

7.1  Roots and Radicals

7.2  Rational Exponents

7.3  Simplifying Radicals

7.4  Adding, Subtracting, and Multiplying Radicals

Mid-Chapter Test: Sections 7.1–7.4

7.5  Dividing Radicals

7.6  Solving Radical Equations

7.7  Complex Numbers

 

CHAPTER 8   Quadratic Functions

8.1  Solving Quadratic Equations by Completing the Square

8.2  Solving Quadratic Equations by the Quadratic Formula

8.3  Quadratic Equations: Applications and Problem Solving

Mid-Chapter Test: Sections 8.1–8.3

8.4  Writing Equations in Quadratic Form

8.5  Graphing Quadratic Functions

8.6  Quadratic and Other Inequalities in One Variable

 

CHAPTER 9   Exponential and Logarithmic Functions

9.1  Composite and Inverse Functions

9.2  Exponential Functions

9.3  Logarithmic Functions

9.4  Properties of Logarithms

Mid-Chapter Test: Sections 9.1–9.4

9.5  Common Logarithms

9.6  Exponential and Logarithmic Equations

9.7  Natural Exponential and Natural Logarithmic Functions

 

CHAPTER 10   Conic Sections

10.1  The Parabola and the Circle

10.2  The Ellipse

Mid-Chapter Test: Sections 10.1–10.2

10.3  The Hyperbola

10.4  Nonlinear Systems of Equations and Their Applications

 

CHAPTER 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 Test: Sections 11.1–11.3

11.4  The Binomial Theorem

 

APPENDIX  Geometric Formulas  

Answers

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

Applications Index

Index

Photo Credits