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BEGINNING AND 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 algebraic concepts, problem solving, and communication skills. Students develop sound mathematical skills by learning how to solve problems generated from realistic applications, instead of learning techniques without conceptual understanding. Authors Mark Clark and Cynthia Anfinson have developed several key ideas to make concepts real and vivid for students. First, the authors place an emphasis on developing strong algebra skills that support the applications, enhancing student comprehension and developing their problem solving abilities. Second, applications are integrated throughout, drawing on realistic and numerically appropriate data to show students how to apply math and to understand why they need to know it. These applications require students to think critically and develop the skills needed to explain and think about the meaning of their answers. Third, important concepts are developed as students progress through the course and overlapping elementary and intermediate content in kept to a minimum. Chapter 8 sets the stage for the intermediate material where students explore the "eyeball best-fit" approach to modeling and understand the importance of graphs and graphing including graphing by hand. Fourth, Mark and Cynthia's approach prepares students for a range of courses including college algebra and statistics. In short, BEGINNING AND INTERMEDIATE ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS develops strong mathematical skills using an engaging, application-driven and problem solving-focused approach to algebra.
- Prealgebra Review. The text begins in Chapter R by reviewing some prealgebra concepts, providing students with a review of those topics most necessary for beginning algebra such as operations with integers, operations with fractions, operations with decimals and percents and the real number system.
- Extensive End-of-Chapter Material includes Chapter Summaries, Review Exercises, Chapter Tests, Chapter Projects, Cumulative Reviews and Equation Solving Toolboxes. 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 on-line research or activities that students must perform to analyze data and make conclusions.
- Cumulative Reviews. Cumulative Reviews group together the major topics across chapters. Answers to all the exercises are available to students in the answer appendix.
- Equation Solving Toolbox. The equation-solving toolbox covers the processes for finding models as the models are introduced.
- 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.
- Appendixes. Several useful appendixes are included—on Matrices and Using the Graphing Calculator, and Answers to Practice Problems and Selected Exercises.
- An Innovative Critical-Thinking Feature: Concept Investigations. These 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 concepts being studied.
- Worked Examples That Reinforce Problem Solving. This text provides a broad range of examples that give students more practical experience with mathematics. All examples are immediately followed by a practice problem that is similar to that example and all examples are labeled to help students connect the example and concept being studied. Examples of hand-drawn graphs in the intermediate section also help students visualize what their own work should look like.
- Integrated "Student" Work. Clearly identifiable examples of "student" work appear throughout the Exercises in the text. These boxes ask students to find and correct common errors in "student" work.
- An Eyeball Best-Fit Approach in the intermediate section of the text. Modeling is introduced in the intermediate part of the book as students now have the beginning algebra skills to handle "messy data" at this point in the course. 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 three kinds of notes written to help the student with specific types of information:
- Reinforcement of Visual Learning through Graphs and Tables. Graphs and tables are used throughout the book to organize data, examine trends, and have students gain knowledge of graphing linear and quadratic equations. The graphical and numeric approach helps support visual learners, incorporating realistic situations into the text and reinforcing the graphs and data that students see in their daily lives.
- 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. Some 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.
- Flexible Use of the Calculator: Calculator Details. The calculator emphasis across the beginning and intermediate portions of the text differ in keeping with the goals of each course. Calculator Details margin boxes will appear as necessary to instruct students on the correct use of a scientific calculator in the beginning portion of the text though most exercises do not require its use. These boxes also appear in the intermediate portion of the text and include tips on graphing calculators. Modeling is introduced in chapter 8 and though students are required to solve problems, graph and do other algebraic skills by hand, calculators are used to create scatterplots of real data and to check the reasonableness of algebraic models for the data. They are used to check solutions both graphically and numerically and to do some numerical calculations.
Operations with Integers. Operations with Fractions. Operations with Decimals and Percents. The Real Number System.
1. BUILDING BLOCKS OF ALGEBRA.
Exponents, Order of Operations, and Properties of Real Numbers Exponents. Algebra and Working with Variables. Simplifying Expressions. Graphs and the Rectangular Coordinate System.
2. LINEAR EQUATIONS AND INEQUALITIES WITH ONE VARIABLE.
Addition and Subtraction Properties of Equality. Multiplication and Division Properties of Equality. Solving Equations with Variables on Both Sides. Solving and Graphing Linear Inequalities on a Number Line.
3. LINEAR EQUATIONS WITH TWO VARIABLES.
Graphing Equations with Two Variables. Finding and Interpreting Slope. Slope-Intercept Form of Lines. Linear Equations and Their Graphs. Finding Equations of Lines.
4. SYSTEMS OF LINEAR EQUATIONS.
Identifying Systems of Linear Equations. Solving Systems Using the Substitution Method. Solving Systems Using the Elimination Method. Solving Linear Inequalities in Two Variables Graphically.
5. EXPONENTS and POLYNOMIALS.
Rules for Exponents. Negative Exponents and Scientific Notation. Adding and Subtracting Polynomials. Multiplying Polynomials. Dividing Polynomials.
6. FACTORING AND QUADRATIC EQUATIONS.
What It Means to Factor. Factoring Trinomials. Factoring Special Forms. Solving Quadratic Equations by Factoring.
7. RATIONAL EXPRESSIONS AND EQUATIONS.
The Basics of Rational Expressions and Equations. Multiplication and Division of Rational Expressions. Addition and Subtraction of Rational Expressions. Solving Rational Equations. Proportions, Similar Triangles, and Variation.
8. MODELING DATA AND FUNCTIONS.
Solving Linear Applications. Using Data to Create Scatterplots. Finding Linear Models. Functions and Function Notation.
9. INEQUALITIES AND ABSOLUTE VALUES.
Absolute Value Equations. Absolute Value Inequalities. Non-Linear Inequalities of One Variable. Solving Systems of Linear Inequalities.
10. RADICAL FUNCTIONS.
From Squaring a Number to Roots and Radicals. Basic Operations with Radical Expressions. Multiplying and Dividing Radical Expressions. Radical Functions. Solving Radical Equations. Complex Numbers.
11. QUADRATIC FUNCTIONS.
Quadratic Functions and Parabolas. Graphing Quadratics in Vertex Form. Finding Quadratic Models. Solving Quadratic Equations by Square Root Property. Solving Equations by Completing the Square. Solving Quadratic Equations by Using the Quadratic Formula. Graphing Quadratics from Standard Form.
12. EXPONENTIAL FUNCTIONS.
Exponential Functions: Patterns of Growth and Decay. Solving Equations Using Exponent Rules. Graphing Exponential Functions. Finding Exponential Models. Exponential Growth and Decay Rates and Compounding Interest.
13. LOGARITHMIC FUNCTIONS.
Functions and Their Inverses. Logarithmic Functions. Graphing Logarithmic Functions. Properties of Logarithms. Solving Exponential Equations. Solving Logarithmic Equations.
14. CONIC SECTIONS, SEQUENCES AND SERIES.
Parabolas and Circles. Ellipses and Hyperbolas. Arithmetic Sequences. Geometric Sequences. Series
Appendix A: Matrices.
Appendix B: Using the Graphing Calculator.
Appendix C: Practice Problems Answers.
Appendix D: Answers to Selected Exercises.
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.
PowerLecture with ExamView®
This CD-ROM 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. Microsoft Powerpoint lecture slides, figures, calculator practice, and additional new examples from the annotated instructor's edition are also included on this CD-ROM.
Complete Solutions Manual
The Complete Solutions Manual provides worked-out solutions to all of the problems in the text.
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
Student Solutions Manual
Prepare for exams and succeed in your mathematics course with this comprehensive solutions manual! Featuring worked out-solutions to the problems in BEGINNING AND INTERMEDIATE ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS, 1st Edition, this manual shows you how to approach and solve problems using the same step-by-step explanations found in your textbook examples.