Mike Sullivan’s time-tested approach focuses students on the fundamental skills they need for the course: preparing for class, practicing with homework, and reviewing the concepts. In the Ninth Edition, College Algebra has evolved to meet today’s course needs, building on these hallmarks by integrating projects and other interactive learning tools for use in the classroom or online.
New Internet-based Chapter Projects apply skills to real-world problems and are accompanied by assignable MathXL exercises to make it easier to incorporate these projects into the course. In addition, a variety of new exercise types, Showcase Examples, and video tutorials for MathXL exercises give instructors even more flexibility, while helping students build their conceptual understanding.
Preparing for Class
- Just-in-time review begins all sections to prepare students for the topics ahead.
- Preparing for This Section lists previously learned concepts that will be useful in the section ahead. Page references are included for easy review.
- Now Work "Are You Prepared?" problems support the Preparing for This Section feature, allowing students to check that they are ready to proceed to the section ahead or if they need to turn back for further review. These problems appear at the start of each exercise set.
- Section-level guidance in each section helps students master the material and develop their problem-solving skills.
- NEW! Showcase Examples provide how-to instruction by offering a guided, step-by-step approach to solving a problem. Students can immediately see how each of the steps in a problem is employed. The two-column format describes the steps on the left and displays the algebra, complete with annotations, on the right.
- NEW! Model It examples are now highlighted, making it easy to identify which examples help students learn to build a mathematical model from verbal descriptions or from data. Model It exercises are also included so that instructors can assign these for homework or practice.
- "Now Work" Problems follow most examples, and point to a related exercise for immediate reinforcement of the skill or concept.
- Step-by-Step, Annotated Examples contain detailed intermediate steps with additional annotations to help students see specific nuances.
- Calculus icons appear next to information essential for the study of calculus. When the icon appears next to a definition, the notation used is consistent with that used in calculus.
- In Words provide alternative descriptions of select definitions and theorems, translating math into plain English.
- Warnings point out common mistakes and help students avoid them.
- Assess Your Understanding appears at the end of every section and contains a variety of problems for students to master the skills they need.
- "Are You Prepared?" Problems appear at the start of every exercise set and help students determine exactly what they need to review and where to review it. This feature is referenced from the Preparing for This Section feature. Answers appear at the end of the section.
- Concepts and Vocabulary questions are fill-in the-blank and true/false items that assess students’ understanding of key definitions and concepts. These have been written to serve as reading quizzes and are now assignable in MyMathLab® and MathXL®.
- Skill Building problems provide straightforward practice, are organized by difficulty, and are correlated to section examples.
- Graphical problems use graphs in a variety of ways, supplementing analytical understanding with graphical understanding.
- Now Work problems, marked by a yellow icon in the exercise set, correspond to a related example within the section. If students get stuck while doing their homework, they can look for the closest Now Work problem and refer back to the related example.
- NEW! Mixed Practice problems offer comprehensive assessment of the skills learned in the section by asking questions that relate to more than one concept or objective. These problems may also require students to utilize skills learned in previous sections, helping them to see how concepts are tied together.
- ENHANCED! Applications and Extensions allow students to apply their skills to real-world problems and to extend concepts learned in the section. These exercises have been updated and many new problems have been added involving sourced information and data sets to bring relevance and timeliness to these exercises. Model It exercises and examples are now highlighted, making it easy to identify which exercises ask students to build a mathematical model from verbal descriptions or from data.
- Explaining Concepts: Discussion and Writing problems are marked by red numbers. These support class discussion, verbalization of mathematical ideas, and writing and research projects.
Reviewing for Exams and Quizzes
- Chapter Reviews at the end of each chapter offer a variety of convenient tools for reference and review.
- "You Should be Able To…” is a list of every objective by section, with corresponding practice exercises. Doing the recommended exercises allows students to master the key concepts. If they get something wrong, they can easily review the examples and exposition and try again.
- Review Exercises provide comprehensive review and practice of key skills, matched to the Learning Objectives for each section. These problems combine exercises from all sections, giving students comprehensive review in one place.
- Chapter Tests contain about 15—20 problems that can help students prepare for in-class exams. For additional help, they can watch an instructor work out full solutions on the Chapter Test Prep Video on YouTube™, on DVD, or in MyMathLab.
- Cumulative Review problem sets appear at the end of every chapter after Chapter 1. They combine problems from previous chapters, providing an ongoing cumulative review.
- NEW! Internet-based Chapter Projects, with assignable exercises in MyMathLab, allow students the opportunity to experience mathematics firsthand in an active learning environment. By exploring and considering a variety of carefully guided “what-if” scenarios, they will develop a better understanding of the concepts presented in the section. Students will learn by doing and have fun in the process.
New to this Edition
- Internet-based Chapter Projects, with assignable exercises in MyMathLab, allow students to experience mathematics first hand in an active learning environment. By exploring and considering a variety of carefully guided “what-if” scenarios, they will develop a better understanding of the concepts presented in the section. Students will learn by doing and have fun in the process.
- Author Solves It MathXL Videos show Mike Sullivan III working by section through MathXL exercises typically requested by students for more explanation or tutoring. These videos are a result of Sullivan’s experiences in teaching online.
- Showcase Examples are used to present examples in a guided, step-by-step format. Students can immediately see how each of the steps in a problem is employed. The “How To” examples have a two-column format in which the left column describes the step in solving the problem and the right column displays the algebra, complete with annotations.
- Exercise sets have been updated and expanded to integrate new question types that give instructors more flexibility and help students build their conceptual understanding.
- Mixed Practice problems offer comprehensive assessment of the skills learned in the section by asking questions that relate to more than one concept or objective. These problems may also require students to utilize skills learned in previous sections, helping them to see how concepts are tied together.
- Concepts and Vocabulary exercises have been written to serve as reading quizzes and are now assignable in MyMathLab® and MathXL®.
- Model It exercises and examples are now highlighted, making it easy to identify which exercises ask students to build a mathematical model from verbal descriptions or from data.
- Enhanced! Applications and Extensions have been updated and many new problems have been added involving sourced information and data sets to bring relevance and timeliness to these exercises.
- Annotated Instructor’s Edition now provides the answers to all problems right on the page where they appear, with longer answers in the back of the book. Sample homework assignments are pre-selected by the author for each section–these are indicated by a blue underline within the exercise set, and are assignable in MyMathLab.
Table of Contents
R.1 Real Numbers
R.2 Algebra Essentials
R.3 Geometry Essentials
R.5 Factoring Polynomials
R.6 Synthetic Division
R.7 Rational Expressions
R.8 nth Roots; Rational Exponents
1. Equations and Inequalities
1.1 Linear Equations
1.2 Quadratic Equations
1.3 Complex Numbers; Quadratic Equations in the Complex Number System
1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations
1.5 Solving Inequalities
1.6 Equations and Inequalities Involving Absolute Value
1.7 Problem Solving: Interest, Mixture, Uniform Motion, and Constant Rate Job Applications
2.1 The Distance and Midpoint Formulas
2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry
3. Functions and Their Graphs
3.2 The Graph of a Function
3.3 Properties of Functions
3.4 Library of Functions; Piecewise-defined Functions
3.5 Graphing Techniques: Transformations
3.6 Mathematical Models: Building Functions
4. Linear and Quadratic Functions
4.1 Linear Functions and Their Properties
4.2 Building Linear Functions from Data
4.3 Quadratic Functions and Their Properties
4.4 Quadratic Models; Building Quadratic Functions from Data
4.5 Inequalities Involving Quadratic Functions
5. Polynomial and Rational Functions
5.1 Polynomial Functions and Models
5.2 Properties of Rational Functions
5.3 The Graph of a Rational Function
5.4 Polynomial and Rational Inequalities
5.5 The Real Zeros of a Polynomial Function
5.6 Complex Zeros: Fundamental Theorem of Algebra
6. Exponential and Logarithmic Functions
6.1 Composite Functions
6.2 One-to-One Functions; Inverse Functions
6.3 Exponential Functions
6.4 Logarithmic Functions
6.5 Properties of Logarithms
6.6 Logarithmic and Exponential Equations
6.7 Compound Interest
6.8 Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models
6.9 Building Exponential, Logarithmic, and Logistic Functions from Data
7. Analytic Geometry
7.2 The Parabola
7.3 The Ellipse
7.4 The Hyperbola
8. Systems of Equations and Inequalities
8.1 Systems of Linear Equations: Substitution and Elimination
8.2 Systems of Linear Equations: Matrices
8.3 Systems of Linear Equations: Determinants
8.4 Matrix Algebra
8.5 Partial Fraction Decomposition
8.6 Systems of Nonlinear Equations
8.7 Systems of Inequalities
8.8 Linear Programming
9. Sequences; Induction; the Binomial Theorem
9.2 Arithmetic Sequences
9.3 Geometric Sequences; Geometric Series
9.4 Mathematical Induction
9.5 The Binomial Theorem
10. Counting and Probability
10.1 Sets and Counting
10.2 Permutations and Combinations