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 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 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