Elementary and Intermediate Algebra for College Students + MyLab Math

Allen Angel received his BS and MS in mathematics from SUNY at New Paltz. He completed additional graduate work at Rutgers University. He taught at Sullivan County Community College and Monroe Community College, where he served as chairperson of the Mathematics Department. He served as Assistant Director of the National Science Foundation at Rutgers University for the summers of 1967 - 1970. He was President of The New York State Mathematics Association of Two Year Colleges (NYSMATYC). He also served as Northeast Vice President of the American Mathematics Association of Two Year Colleges (AMATYC). Allen lives in Palm Harbor, Florida but spends his summers in Penfield, New York. He enjoys playing tennis and watching sports. He also enjoys traveling with his wife Kathy. 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-seven years at State College of Florida-Manatee-Sarasota. His interests include reading, history, fishing, trivia contests, and cooking. He and his wife Kristin are the proud parents of their three sons - Alex, Nick, and Max.

Table of Contents

Preface
To the Student



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


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 2 Summary
Chapter 2 Review Exercises
Chapter 2 Practice Test
Cumulative Review Test


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


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


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


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


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


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


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


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


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


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, Polynomial, and Rational Inequalities in One Variable



Chapter 12 Summary
Chapter 12 Review Exercises
Chapter 12 Practice Test
Cumulative Review Test


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



Chapter 13 Summary
Chapter 13 Review Exercises
Chapter 13 Practice Test
Cumulative Review Test


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


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

Review of Decimals and Percent
Finding the Greatest Common Factor and Least Common Denominator
Geometry
Review of Exponents, Polynomials, and Factoring

Answers Applications Index Subject Index