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Summary
For Basic College Mathematics, Beginning Algebra, and Intermediate Algebra courses including lecture-based, self-paced, discussion oriented, and modular classes.This clear, accessible treatment of mathematics features a building-block approach toward problem solving and realistic, diverse applications. Students practice problem solving and decision making with interesting applications throughout the text. The Putting Your Skills to Work and new chapter-end feature, Math in the Media, present students with opportunities to utilize critical thinking skills, analyze and interpret data, and problem solve using applied situations encountered in daily life.The problem solving strategy, highlighted by *A Mathematics Blueprint for Problem Solving, helps students determine where to begin the problem-solving process, as well as how to plan subsequent problem-solving steps. Chapter organizers help students focus their study on the concepts and examples. Developing Your Study Skills boxes throughout the text give students tips to help them improve their study skills. These features, together with the applications and emphasis on problem solving, help students to become effective and confident problem solvers.*Please note: Intermediate Algebra includes a similar feature called Problem Solving Procedure.
Table of Contents
0. A Brief Review of Arithmetic Skills.
Simplifying and Finding Equivalent Fractions. Addition and Subtraction of Fractions. Putting Your Skills to Work: The High Jump: Raising the Bar. Multiplication and Division of Fractions. Use of Decimals. Putting Your Skills to work: The Mathematics of Major World Languages. Use of Percent. Estimation. Mathematics Blueprint for Problem Solving.
1. Real Numbers and Variables.
Addition of Real Numbers. Subtraction of Real Numbers. Multiplication and Division of Real Numbers. Exponents. Order of Arithmetic Operations. Using the Distributive Property to Simplify Expressions. Combining Like Terms. Using Substitution to Evaluate Expressions and Formulas. Putting Your Skills to Work: Measuring Your Level of Fitness. Grouping Symbols. Putting Your Skills to Work: Consumer Price Index.
2. Equations and Inequalities.
The Addition Principle. The Multiplication Principle. Using the Addition and Multiplication Principles Together. Equations with Fractions. Formulas. Putting Your Skills to Work: Controlling Emissions Levels. Writing and Graphing Inequalities. Solving Inequalities.
3. Solving Applied Problems.
Translating English Phrases into Algebraic Expressions. Using Equations to Solve Word Problems. Solving Word Problems: Comparisons. Solving Word Problems: The Value of Money and Percents. Putting your Skills to Work: Automobile Loans and Installment Loans. Solving Word Problems Using Geometric Formulas. Putting Your Skills to Work: Examination of Weather Patters. Using Inequalities to Solve Word Problems. Putting Your Skills to Work: Using Mathematics for Search and Rescue.
4. Exponents and Polynomials.
The Rules of Exponents. Negative Exponents and Scientific Notation. Putting Your Skills to Work: The Mathematics of Forests. Fundamental Polynomial Operations. Multiplication of Polynomials. Multiplication: Special Cases. Putting Your Skills to Work: The Mathematics of DNA. Division of Polynomials. Putting Your Skills to Work: The Enrollment Polynomial.
5. Factoring.
Introduction to Factoring. Factor by Grouping. Factoring Trinomials of the Form x^2 + bx + c. Factoring Trinomials of the Form ax^2 + bx + c. Special Cases of Factoring. A Brief Review of Factoring. Solving Quadratic Equations by Factoring. Putting Your Skills to Work: Predicting Total Earnings by a Mathematical Series. Putting Your Skills to Work: The Sum-of-the-Digits Depreciation Method.
6. Rational Expressions and Equations.
Simplifying Rational Expressions. Multiplication and Division of Rational Expressions. Addition and Subtraction of Rational Expressions. Putting Your Skills to Work: Estimating the Surplus or Deficit. Simplifying Complex Rational Expressions. Equations Involving Rational Expressions. Ratio, Proportion, and Other Applied Problems. Putting Your Skills to Work: Mathematical Measurement of Planet Orbit Time.
7. Graphing and Functions.
Rectangular Coordinate Systems. Graphing Linear Equations. Slope of a Line. Putting Your Skills to work: Underwater Pressure. Obtaining the Equation of a Line. Graphing Linear Inequalities. Functions. Putting Your Skills to Work: Graphing the Size of Rain Forests.
8. Systems of Equations.
Solving a System of Equations by Graphing. Solving a System of Equations by the Substitution Method. Solving a System of Equations by the Addition Method. Putting Your Skills to Work: The Mathematics of Sports Cars. Review of Methods for Solving Systems of Equations. Solving Word Problems Using a System of Equations. Putting Your Skills to Work: Using Mathematics to Predict the Number of Pets. Putting Your Skills to Work: The Mathematics of the Break-Even Point.
9. Radicals.
Square Roots. Simplifying Radicals. Addition and Subtraction of Radicals. Multiplication of Radicals. Division of Radicals. The Pythagorean Theorem and Radical Equations. Word Problems Involving Radicals: Direct and Inverse Variation. Putting Your Skills to Work: Determining Free-Fall Times.
10. Quadratic Equations.
Introduction to Quadratic Equations. Finding Solutions Using the Square Root Property and by Completing the Square. Finding Solutions Using the Quadratic Formula. Graphing Quadratic Equations. Putting Your Skills to Work: Helping the Football Coach Plan the Defense. Formulas and Applied Problems. Putting Your Skills to Work: The Mathematics of a Reflecting Pool.
Appendix A: Tables. Appendix B: Metric Measurement and Conversion of Units. Appendix C: Interpreting Data from Tables, Charts, and Graphs. Appendix D: Inductive and Deductive Reasoning. Solutions to Practice Problems. Selected Answers. Index.