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.  

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

1.5 Exponents

1.6 Scientific Notation

 

2. Equations and Inequalities

2.1 Solving Linear Equations

2.2 Problem Solving and Using Formulas

2.3 Applications of Algebra

2.4 Additional Application Problems

2.5 Solving Linear Inequalities

2.6 Solving Equations and Inequalities Containing Absolute Values

 

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

3.5 The Point-Slope Form of a Linear Equation

3.6 The Algebra of Functions

3.7 Graphing Linear Inequalities

 

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

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

 

5. Polynomials and Polynomial Equations

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

5.5 Factoring Trinomials

5.6 Special Factoring Formulas

5.7 A General Review of Factoring

5.8 Polynomial Equations

 

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

6.5 Rational Equations: Applications and Problem Solving

6.6 Variation

 

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

7.5 Dividing Radicals

7.6 Solving Radical Equations

7.7 Complex Numbers

 

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

8.4 Writing Equations in Quadratic Form

8.5 Graphing Quadratic Functions

8.6 Quadratic and Other Inequalities in One Variable

 

9. Exponential and Logarithmic Functions

9.1 Composite and Inverse Functions

9.2 Exponential Functions

9.3 Logarithmic Functions

9.4 Properties of Logarithms

9.5 Common Logarithms

9.6 Exponential and Logarithmic Equations

9.7 Natural Exponential and natural Logarithmic Functions

 

10. Conic Sections

10.1 The Parabola and the Circle

10.2 The Ellipse

10.3 The Hyperbola

10.4 Nonlinear Systems of Equations and Their Applications

 

11. Sequences, Series, and the Binomial Theorem

11.1 Sequences and Series

11.2 Arithmetic Sequences and Series

11.3 Geometric Sequences and Series

11.4 The Binomial Theorem

 

Appendix: Geometric Formulas