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INTERMEDIATE ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS shows students how to apply traditional mathematical skills in real-world contexts. The emphasis on skill building and applications engages students as they master concepts, problem solving, and communication skills. It modifies the rule of four, integrating algebraic techniques, graphing, the use of data in tables, and writing sentences to communicate solutions to application problems. The authors have developed several key ideas to make concepts real and vivid for students. First, the authors integrate applications, drawing on real-world data to show students why they need to know and how to apply math. The applications help students develop the skills needed to explain the meaning of answers in the context of the application. Second, they emphasize strong algebra skills. These skills support the applications and enhance student comprehension. Third, the authors use an eyeball best-fit approach to modeling. Doing models by hand helps students focus on the characteristics of each function type. Fourth, the text underscores the importance of graphs and graphing. Students learn graphing by hand, while the graphing calculator is used to display real-life data problems. In short, INTERMEDIATE ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS takes an application-driven approach to algebra, using appropriate calculator
- An Innovative Critical-Thinking Feature: Concept Investigations. The directed-discovery activities called Concept Investigations are ideal as group work during class, incorporated as part of a lecture, or as individual assignments to investigate concepts further. Inserted at key points within the chapter, each Concept Investigation helps students explore patterns and relationships such as the graphical and algebraic representations of the functions being studied.
- Extensive End-of-Chapter Material. Includes Chapter Summaries, Review Exercises, Chapter Tests, Chapter Projects, Equation Solving Toolbox, and Cumulative Reviews. Chapter Summaries revisit the big ideas of the chapter and reinforce them with new worked-out examples. Students can also review and practice what they have learned with the Chapter Review exercises before taking the Chapter Test.
- Chapter Projects. To enhance critical thinking, end-of-chapter projects can be assigned either individually or as group work. Instructors can choose which projects best suit the focus of their class and give their students the chance to show how well they can tie together the concepts they have learned in that chapter. Some of these projects include online research or activities that students must perform to analyze data and make conclusions.
- Equation Solving Toolbox. This feature appears after every two chapters and revisits and summarizes skills students have used to solve equations in preceding chapters and processes for finding models.
- Cumulative Reviews. Cumulative reviews appear after every two chapters, and group together the major topics across chapters. Answers to all the exercises are available to students in the answer appendix.
- Worked Examples with In-Text Practice Problems. This text offers a comprehensive range of examples from basic techniques (solving by hand, exponent rules, graphing) to realistic applications with manageable data sets to intriguing applications that call for critical thinking about phenomena (population growth) and daily activities (interest rates in action, the cost of a truck rental). Worked examples are labeled so students can make the connection between the example and the concept being studied. The accompanying in-text practice problems help students to gain a sense of a concept through an example and then to practice what has been taught in the preceding discussion. In addition, examples of hand-drawn graphs help students visualize what their own work should look like.
- Practical Help for Instructors. Practical tips are provided in the Annotated Instructor's Edition on how to approach and pace chapters as well as integrate features such as Concept Investigations. In addition, for every student example in the student text, there is a different instructor classroom example in the AIE, with accompanying answers that can be used for additional in-class practice and/or homework.
- Integrated "Student" Work. Clearly identifiable examples of "student" work appear throughout the text in Examples and Exercises. These boxes ask students to find and correct common errors in "student" work.
- An Eyeball Best-Fit Approach. Linear, quadratic, and exponential functions are analyzed through modeling data using an eyeball best-fit approach. These models investigate questions in the context of real-life situations. Creating models by hand leads students to analyze more carefully the parts of each function reinforcing solving techniques and making a better connection to the real-life data and how they affect the attributes of the function's graph. Graphing calculators are used to plot data and check the fit of each model.
- Margin Notes. The margin contains four kinds of notes written to help the student with specific types of information: Skill Connections provide a just-in-time review of core mathematical concepts, reinforcing student skill sets; Connecting the Concepts reinforce a concept by showing relationships across sections; Specific vocabulary of mathematics and the applications are helpfully defined and reinforced through margin notes called "What's That Mean?"; and Using Your TI-Graphing Calculator offers just-in-time calculator tips for students. Additional material is available in the Using the Graphing Calculator Appendix.
- Exercise Sets. The exercise sets include a balance of both applications and skill-based problems developed with a clear level of progression in terms of difficulty level. Most exercise sets begin with a few warm-up problems before focusing on applications. Exercise sets typically end with additional skill practice to help students master the concepts when needed. A balance of graphical, numerical, and algebraic skill problems is included throughout the book to help students see mathematics from several different views. End-of-book answers are written in full sentences to underscore the emphasis on student communication skills.
- Enhanced WebAssign, used by over one million students at more than 1,100 institutions, allows you to assign, collect, grade, and record homework assignments via the Web. This proven and reliable homework system includes thousands of algorithmically generated homework problems, links to relevant textbook sections, video examples, problem-specific tutorials, and more. New Assignable Stand Alone Master It questions are unique to INTERMEDIATE ALGEBRA, and reinforce student understanding and develop conceptual knowledge. These modeling type problems contain real-life data, break the question into multiple parts, and reflect the step-by-step process that is taught in the text. These problems support the conceptual and applied approach of the textbook and force students to confirm their understanding as they work through each step of the problem.
- Appropriate Use of the Calculator. Graphing calculators are used in this text to help students understand mathematical concepts and to work with real-world data. Graphing calculators are used to create scatterplots of real data and to check the reasonableness of algebraic models for the data. Linear, quadratic, and exponential models are created by hand, using an eyeball best-fit approach and algebraic techniques. The calculator is also used to check solutions both graphically and numerically and to do some numerical calculations. However, students are also required to solve problems, graph, and do other algebraic skills by hand.
1. LINEAR FUNCTIONS.
Solving Linear Equations. Using Data to Create Scatterplots. Using Data to Create Scatterplots. Graphical Models. Intercepts, Domain, and Range. Fundamentals of Graphing and Slope. Introduction to Graphing Functions. Slope-Intercept Form of a Line. The Meaning of Slope in an Application. Graphing Lines Using Slope and Intercept. Intercepts and Graphing. The General Form of Lines. Finding Intercepts and Their Meaning. Graphing Lines Using Intercepts. Horizontal and Vertical Lines. Finding Equations of Lines. Finding Equations of Lines. Parallel and Perpendicular Lines. Interpreting the Characteristics of a Line, a Review. Finding Linear Models. Using a Calculator to Create Scatterplots. Finding Linear Models. Functions and Function Notation. Relations and Functions. Function Notation. Writing Models in Function Notation. Domain and Range of Functions.
2. SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES.
Systems of Linear Equations. Definition of Systems. Graphical and Numerical Solutions. Types of Systems. Solving Systems of Equations Using the Substitution Method. Substitution Method. Dependent and Inconsistent Systems. Solving Systems of Equations Using the Elimination Method. Elimination Method. Solving Linear Inequalities. Introduction to Inequalities. Solving Inequalities. Systems as Inequalities. Solving Inequalities Numerically and Graphically. Absolute Value Equations and Inequalities. Absolute Value Equations. Absolute Value Inequalities Involving Less Than, or Less Than or Equal To. Absolute Value Inequalities Involving Greater Than, or Greater Than or Equal To. Solving Systems of Linear Inequalities. Graphing Linear Inequalities in Two Variables. Solving Systems of Linear Inequalities.
3. EXPONENTS, POLYNOMIAL AND FUNCTIONS.
Rules for Exponents. Rules for Exponents. Negative Exponents and Zero as an Exponent. Rational Exponents. Combining Functions. Defining Polynomials. Adding and Subtracting Functions. Multiplying and Dividing Functions. Composing Functions. Composing Functions. Factoring Polynomials. Factoring Using the AC Method. Factoring Using Trial and Error. Prime Polynomials. Special Factoring Techniques. Perfect Square Trinomials. Difference of Squares. Difference and Sum of Cubes. Multi-Step Factorizations.
4. QUADRATIC FUNCTIONS.
Quadratic Functions and Parabolas. Introduction to Quadratics and Identifying the Vertex. Identifying a Quadratic Function. Recognizing Graphs of Quadratic Functions and Indentifying the Vertex. Solving Quadratics Using the Graph. Graphing Quadratics in Vertex Form. Vertex Form. Graphing Quadratics in Vertex Form. Finding Quadratic Models. Finding Quadratic Models. Domain and Range. Solving Quadratic Equations by Square Root Property and Completing the Square. Solving from Vertex Form. Completing the Square. Converting to Vertex Form. Graphing from Vertex From with x-Intercepts. Solving Quadratic Equations by Factoring. Solving by Factoring. Finding an Equation from the Graph. Solving Quadratic Equations Using the Quadratic Formula. Determining Which Algebraic Method to Use. Solving Systems of Equations with Quadratics. Graphing Quadratics from Standard Form. Graphing from Standard Form. Graphing Quadratic Inequalities in Two Variables.
5. EXPONENTIAL FUNCTIONS.
Exponential Functions: Patterns of Growth and Decay. Exploring Exponential Growth and Decay. Recognizing Exponential Patterns. Solving Equations Using Exponent Rules. Recap of the Rules for Exponents. Solving Simple Exponential Equations. Solve Power Equations. Graphing Exponential Functions. Exploring Graphs of Exponentials. Domain and Range of Exponential Functions. Finding Exponential Models. Finding Exponential Models. Domain and Range for Exponential Models. Exponential Growth and Decay Rates and Compounding Interest. Exponential Growth and Decay Rates. Compounding Interest.
6. LOGARITHMIC FUNCTIONS.
Functions and Their Inverses. Introduction to Inverse Functions. One-to-One Functions. Logarithmic Functions. Definition of Logarithms. Basic Rules for Logarithms. Change of Base Formula. Inverses. Solving Simple Logarithmic Equations. Graphing Logarithmic Functions. Graphing Logarithmic Functions. Domain and Range of Logarithmic Functions. Properties of Logarithms. Properties of Logarithms. Solving Exponential Equations. Solving Exponential Equations. Compounding Interest. Solving Logarithmic Equations. Applications of Logarithms. Solving Other Logarithmic Equations.
7. RATIONAL FUNCTIONS.
Rational Functions and Variation. Rational Functions. Direct and Inverse Variation. Domain. Simplifying Rational Expressions. Simplifying Rational Expressions. Long Division of Polynomials. Synthetic Division. Multiplying and Dividing Rational Expressions. Multiplying Rational Expressions. Dividing Rational Expressions. Adding and Subtracting Rational Expressions. Least Common Denominator. Adding Rational Expressions. Subtracting Rational Expressions. Simplifying Complex Fractions. Solving Rational Equations.
8. RADICAL FUNCTIONS.
Radical Functions. Modeling Data with Radical Functions. Domain and Range of Radical Functions. Simplifying, Adding, and Subtracting Radicals. Square Roots and Higher Roots. Simplifying Radicals. Adding and Subtracting Radicals. Multiplying and Dividing Radicals. Multiplying Radicals. Dividing Radicals and Rationalizing the Denominator. Conjugates. Solving Radical Equations. Solving Equations with Square Roots. Solving Equations with More than One Square Root. Solving Equations with Higher Order Radicals. Complex Numbers. Definition of Imaginary and Complex Numbers. Operations with Complex Numbers. Solving Equations with Complex Solutions.
9. CONICS, SEQUENCES AND SERIES.
Parabolas and Circles. Introduction to Conic Sections. Equations and Graphs of Circles. Ellipses and Hyperbolas. Equations and Graphs of the Ellipse. Equations and Graphs of the Hyperbola. Arithmetic Sequences. Introduction to Sequences. Arithmetic Sequences. Geometric Sequences. Geometric Sequences. Series. Introduction to Series. Arithmetic Series. Geometric Series.
Basic Algebra Review. Review of Number Systems. Operations with Integers. Operations with Rationals. Review of Solving Linear Equations. Scientific Notation. Interval Notation.
Matrices. Solving Systems of Three Equations. Introduction to Matrices. Matrix Row Reduction. Solving Systems with Matrices. Using Systems of Three Equations to Model Quadratics.
Using the Graphing Calculator. Steps for Using the Graphing Calculator. Troubleshooting Error Messages.
Answers to Odd-Numbered Exercises.
Answers to the Example Practice Problems.
Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.
College Prep Algebra: Instructor’s Resource Binder for Algebra Activities 2011
Each section of the main text is discussed in uniquely designed Teaching Guides containing instruction tips, examples, activities, worksheets, overheads, assessments, and solutions to all worksheets and activities. The community site for this FREE Instructor’s supplement provides more detail for instructors. In addition, the puzzles and activities are included in a Student Workbook that are saleable. http://www.cengage.com/community/mariaandersen
This online instructor database offers complete worked solutions to all exercises in the text, allowing you to create customized, secure solutions printouts (in PDF format) matched exactly to the problems you assign in class. Visit http://www.cengage.com/solutionbuilder.
Complete Solutions Manual
The Complete Solutions Manual provides worked-out solutions to all of the problems in the text.
Honored with two Tellys, a Communicator Award, and an international Aurora Award, these ten- to twenty-minute problem-solving lessons cover almost every learning objective from each chapter. Rena Petrello--recipient of the "Mark Dever Award for Excellence in Teaching"--presents each lesson using her experience teaching online mathematics courses. It was through this online teaching experience that Petrello discovered the lack of suitable content for online instructors, prompting her to develop her own video lessons and ultimately create this video project. Students will love the additional guidance and support when they miss a class or when they are preparing for an upcoming quiz or exam.
PowerLecture with ExamView®
This CD-ROM (or DVD) provides the instructor with dynamic media tools for teaching. Create, deliver, and customize tests (both print and online) in minutes with ExamView® Computerized Testing Featuring Algorithmic Equations. Easily build solution sets for homework or exams using Solution Builder's online solutions manual. Microsoft® PowerPoint® lecture slides and figures from the book are also included on this CD-ROM(or DVD).
Providing the perfect head start, the Student Workbook contains all of the assessments, activities, and worksheets from the Instructor's Resource Binder for classroom discussions, in-class activities, and group work.
Student Solutions Manual
: Contains fully worked-out solutions to all of the odd-numbered end-of section exercises as well as the complete worked-out solutions to all of the exercises included at the end of each chapter in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.
Annotated Instructor's Edition
Offering practical help for instructors, the Annotated Instructor's Edition provides the complete student text with answers next to each respective exercise as well as tips on how to approach and pace chapters and integrate features such as Concept Investigations. In addition, for every student example in the student text, there is a different instructor classroom example in the AIE, with accompanying answers that can be used for additional in-class practice and/or homework.
Student Solutions Manual