Intended for a 2-semester sequence of Elementary and Intermediate Algebra where students get a solid foundation in algebra, including exposure to functions, which prepares them for success in College Algebra or their next math course.
Table of Contents:
Chapter 1 — Operations on Real Numbers and Algebraic Expressions
1.1 Success in Mathematics
1.2 The Number Systems and the Real Number Line
1.3 Adding, Subtracting, Multiplying, and Dividing Integers
1.4 Adding, Subtracting, Multiplying, and Dividing Rational Numbers Expressed as Fractions and Decimals
Putting the Concepts Together (Sections 1.1 — 1.4)
1.5 Properties of Real Numbers
1.6 Exponents and the Order of Operations
1.7 Simplifying Algebraic Expressions
Chapter 1 Activity
Chapter 1 Review
Chapter 1 Test
Chapter 2-Equations and Inequalities in One Variable
2.1 Linear Equations: The Addition and Multiplication Properties of Equality
2.2 Linear Equations: Using the Properties Together
2.3 Solving Linear Equations Involving Fractions and Decimals; Classifying Equations
2.4 Evaluating Formulas and Solving Formulas for a Variable
Putting the Concepts Together (Sections 2.1 — 2.4)
2.5 Introduction to Problem Solving: Direct Translation Problems
2.6 Problem Solving: Direct Translation Problems Involving Percent
2.7 Problem Solving: Geometry and Uniform Motion
2.8 Solving Inequalities in One Variable
Chapter 2 Activity
Chapter 2 Review
Chapter 2 Test
Chapter 3 — Introduction to Graphing and Equations of Lines
3.1 The Rectangular Coordinate System and Equations in Two Variables
3.2 Graphing Equations in Two Variables
3.3 Slope
3.4 Slope-Intercept Form of a Line
3.5 Point-Slope Form of a Line
3.6 Parallel and Perpendicular Lines
Putting the Concepts Together (Sections 3.1 — 3.6)
3.7 Variation
3.8 Linear Inequalities in Two Variables
Chapter 3 Activity
Chapter 3 Review
Chapter 3 Test
Cumulative Review Chapters 1-3
Chapter 4 — Systems of Linear Equations and Inequalities
4.1 Solving Systems of Linear Equations in Two Variables by Graphing
4.2 Solving Systems of Linear Equations in Two Variables Using Substitution
4.3 Solving Systems of Linear Equations in Two Variables Using Elimination
Putting the Concepts Together (Sections 4.1 — 4.3)
4.4 Solving Direct Translation, Geometry, and Uniform Motion Problems Using Systems of Linear Equations
4.5 Solving Mixture Problems Using Systems of Linear Equations
4.6 Systems of Linear Inequalities
Chapter 4 Activity
Chapter 4 Review
Chapter 4 Test
Chapter 5 — Exponents and Polynomials
5.1 Adding and Subtracting Polynomials
5.2 Multiplying Monomials: The Product and Power Rules
5.3 Multiplying Polynomials
5.4 Dividing Monomials: The Quotient Rule and Integer Exponents
Putting the Concepts Together (Sections 5.1 — 5.4)
5.5 Dividing Polynomials
5.6 Applying Exponent Rules: Scientific Notation
Chapter 5Activity
Chapter 5 Review
Chapter 5 Test
Cumulative Review Chapters 1-5
Chapter 6 - Factoring Polynomials
6.1 Greatest Common Factor and Factoring by Grouping
6.2 Factoring Trinomials of the Form x2 + bx + c
6.3 Factoring Trinomials of the Form ax2 + bx + c, a ¿ 1
6.4 Factoring Special Products
6.5 Summary of Factoring Techniques
Putting the Concepts Together (Sections 6.1 — 6.5)
6.6 Solving Polynomial Equations by Factoring
6.7 Modeling and Solving Problems with Quadratic Equations
Chapter 6 Activity
Chapter 6 Review
Chapter 6 Test
Getting Ready for Intermediate Algebra: A Cumulative Review of Chapters 1-6
Chapter 7 — Rational Expressions and Equations
7.1 Simplifying Rational Expressions
7.2 Multiplying and Dividing Rational Expressions
7.3 Adding and Subtracting Rational Expressions with a Common Denominators
7.4 Finding the Least Common Denominator and Forming Equivalent Rational Expressions
7.5 Adding and Subtracting Rational Expressions with Unlike Denominators
7.6 Complex Rational Expressions
Putting the Concepts Together (Sections 7.1 — 7.6)
7.7 Rational Equations
7.8 Models Involving Rational Expressions
Chapter 7 Activity
Chapter 7 Review
Chapter 7 Test
Getting Ready for Intermediate Algebra: A Cumulative Review of Chapters 1-7
Chapter 8— Graphs, Relations, and Functions
8.1 Graphs of Equations
8.2 Relations
Putting the Concepts Together (Section 8.1 — 8.2)
8.3 An Introduction to Functions
8.4 Functions and Their Graphs
8.5 Linear Functions
8.6 Compound Inequalities
8.7 Absolute Value Equations and Inequalities
Chapter 8 Activity
Chapter 8 Review
Chapter 8 Test
Chapter 9- Radicals and Rational Exponents
9.1 Square Roots
9.2 nth Roots andRational Exponents
9.3 Simplify Expressions Using the Laws of Exponents
9.4 Simplifying Radical Expressions
9.5 Adding, Subtracting, and Multiplying Radical Expressions
9.6 Rationalizing Radical Expressions
Putting the Concepts Together (Sections 9.1 — 9.6)
9.7 Functions Involving Radicals
9.8 Radical Equations and Their Applications
9.9 The Complex Number System
Chapter 9 Activity
Chapter 9 Review
Chapter 9 Test
Chapter 10- Quadratic Equations and Functions
10.1 Solving Quadratic Equations by Completing the Square
10.2 Solving Quadratic Equations by the Quadratic Formula
10.3 Solving Equations Quadratic in Form
Putting the Concepts Together (Sections 10.1 — 10.3)
10.4 Graphing Quadratic Functions Using Transformations
10.5 Graphing Quadratic Functions Using Properties
10.6 Quadratic Inequalities
10.7 Rational Inequalities
Chapter 10 Activity
Chapter 10 Review
Chapter 10 Test
Cumulative Review Chapters 1-10
Chapter 11- Exponential and Logarithmic Functions
11.1 Composite Functions and Inverse Functions
11.2 Exponential Functions
11.3 Logarithmic Functions
Putting the Concepts Together (Sections 11.1 — 11.3)
11.4 Properties of Logarithms
11.5 Exponential and Logarithmic Equations
Chapter 11 Activity
Chapter 11 Review
Chapter 11 Test
Chapter 12- Conics
12.1 Distance and Midpoint Formulas
12.2 Circles
12.3 Parabolas
Putting the Concepts Together (Sections 12.1 — 12.3)
12.4 Ellipses
12.5 Hyperbolas
12.6 Nonlinear Systems of Equations
Chapter 12 Activity
Chapter 12 Review
Chapter 12 Test
Cumulative Review Chapters 1-12
Chapter 13- Sequences, Series, and The Binomial Theorem
13.1 Sequences
13.2 Arithmetic Sequences
13.3 Geometric Sequences and Series
Putting the Concepts Together (Section 13.1 — 13.3)
13.4 The Binomial Theorem
Chapter 13 Activity
Chapter 13 Review
Chapter 13 Test
Appendix A: Review of Fractions, Decimals, and Percents
A.1 Fractions
A.2 Decimals and Percents
Appendix B: Division of Polynomials; Synthetic Division
Appendix C: The Library of Functions
Appendix D: Geometry
Appendix E: More on Systems of Equations
E.1 Systems of Linear Equations in Three Variables
E.2 Using Matrices to Solve Systems
E.3 Determinants and Cramer’s Rule
About the Author :
Michael Sullivan, III, Joliet Junior College
With training in mathematics, statistics, and economics, Michael Sullivan, III has a varied teaching background that includes 15 years of instruction in both high school and college-level mathematics. He is currently a full-time professor of mathematics at Joliet Junior College. Michael has numerous textbooks in publication, including an Introductory Statistics series, and a Precalculus series, which he writes with his father, Michael Sullivan. Michael believes that his experiences writing texts for college-level math and statistics courses give him a unique perspective as to where students are headed once they leave the developmental mathematics tract. This experience is reflected in the philosophy and presentation of his developmental text series. When not in the classroom or writing, Michael enjoys spending time with his three children, Michael, Kevin, and Marissa, and playing golf. Now that his two sons are getting older, he has the opportunity to do both at the same time!
Kathy Struve, Columbus State Community College
Kathy Struve has been a classroom teacher for nearly 25 years, first at the high school level, and, for the past 13 years, at Columbus State Community College. Kathy emphasizes classroom diversity: diversity of age, learning styles, and previous learning success. She is aware of the challenges of teaching mathematics at a large, urban community college, where students have varied mathematics backgrounds, and may enter college with a high level of mathematics anxiety. Kathy served as Lead Instructor of the Developmental Algebra sequence at Columbus State where she developed curriculum and provided leadership to adjunct faculty in implementing graphing calculator technology in the classroom. She has authored classroom activities at the Elementary Algebra, Intermediate Algebra, and College Algebra levels and conducted workshops at local, state, and national conferences on both integrating graphing calculator applications into the curriculum and developing varied forms of assessment. This textbook incorporates her 25 years of experience in addressing the individual needs of students.
