Intermediate Algebra

Note: Each chapter begins with a Prep Test and concludes with a Chapter Summary, Review Exercises, and a Chapter Test. Chapters 2-12 include Cumulative Review Exercises. AIM for Success 1. Review of Real Numbers 1.1 Introduction to Real Numbers 1.2 Operations on Rational Numbers 1.3 Variable Expressions 1.4 Verbal Expressions and Variable Expressions Focus on Problem Solving: Polya's Four-Step Process Projects and Group Activities: Water Displacement 2. First-Degree Equations and Inequalities 2.1 Solving First-Degree Equations 2.2 Applications: Puzzle Problems 2.3 Applications: Mixture and Uniform Motion Problems 2.4 First-Degree Inequalities 2.5 Absolute Value Equations and Inequalities Focus on Problem Solving: Understand the Problem Projects and Group Activities: Electricity 3. Linear Functions and Inequalities in Two Variables 3.1 The Rectangular Coordinate System 3.2 Introduction to Functions 3.3 Linear Functions 3.4 Slope of a Straight Line 3.5 Finding Equations of Lines 3.6 Parallel and Perpendicular Lines 3.7 Inequalities in Two Variables Focus on Problem Solving: Find a Pattern Projects and Group Activities: Evaluating a Function with a Graphing Calculator; Introduction to Graphing Calculators; Wind-Chill Index 4. Systems of Equations and Inequalities 4.1 Solving Systems of Linear Equations by Graphing and by the Substitution Method 4.2 Solving Systems of Linear Equations by the Addition Method 4.3 Solving Systems of Equations by Using Determinants 4.4 Application Problems 4.5 Solving Systems of Linear Inequalities Focus on Problem Solving: Solve an Easier Problem Projects and Group Activities: Using a Graphing Calculator to Solve a System of Equations 5. Polynomials 5.1 Exponential Expressions 5.2 Introduction to Polynomial Functions 5.3 Multiplication of Polynomials 5.4 Division of Polynomials 5.5 Factoring Polynomials 5.6 Special Factoring 5.7 Solving Equations by Factoring Focus on Problem Solving: Find a Counterexample Projects and Group Activities: Astronomical Distances and Scientific Notation 6. Rational Expressions 6.1 Multiplication and Division of Rational Expressions 6.2 Addition and Subtraction of Rational Expressions 6.3 Complex Fractions 6.4 Ratio and Proportion 6.5 Rational Equations 6.6 Variation Focus on Problem Solving: Implication Projects and Group Activities: Graphing Variation Equations; Transformers 7. Exponents and Radicals 7.1 Rational Exponents and Radical Expressions 7.2 Operations on Radical Expressions 7.3 Solving Equations Containing Radical Expressions 7.4 Complex Numbers Focus on Problem Solving: Another Look at Polya's Four-Step Process Projects and Group Activities: Solving Radical Equations with a Graphing Calculator; The Golden Rectangle 8. Quadratic Equations 8.1 Solving Quadratic Equations by Factoring or by Taking Square Roots 8.2 Solving Quadratic Equations by Completing the Square 8.3 Solving Quadratic Equations by using the Quadratic Formula 8.4 Solving Equations That Are Reducible to Quadratic Equations 8.5 Quadratic Inequalities and Rational Inequalities 8.6 Applications of Quadratic Equations Focus on Problem Solving: Inductive and Deductive Reasoning Projects and Group Activities: Using a Graphing Calculator to Solve a Quadratic Equation 9. Functions and Relations 9.1 Properties of Quadratic Functions 9.2 Graphs of Functions 9.3 Algebra of Functions 9.4 One-to-One and Inverse Functions Focus on Problem Solving: Proof in Mathematics Projects and Group Activities: Finding the Maximum or Minimum of a Function Using a Graphing Calculator; Business Applications of Maximum and Minimum Values of Quadratic Functions 10. Exponential and Logarithmic Functions 10.1 Exponential Functions 10.2 Introduction to Logarithms 10.3 Graphs of Logarithmic Functions 10.4 Solving Exponential and Logarithmic Equations 10.5 Applications of Exponential and Logarithmic Functions Focus on Problem Solving: Proof by Contradiction Projects and Group Activities: Solving Exponential and Logarithmic Equations Using a Graphing Calculator; Credit Reports and FICO Scores 11. Conic Sections 11.1 The Parabola 11.2 The Circle 11.3 The Ellipse and the Hyperbola 11.4 Solving Non-linear Systems of Equations 11.5 Quadratic Inequalities and Systems of Inequalities Focus on Problem Solving: Using a Variety of Problem-Solving Techniques Projects and Group Activities: The Eccentricity and Foci of an Ellipse; Graphing Conic Sections Using a Graphing Calculator 12. Sequences and Series 12.1 Introduction to Sequences and Series 12.2 Arithmetic Sequences and Series 12.3 Geometric Sequences and Series 12.4 Binomial Expansions Focus on Problem Solving: Forming Negations Projects and Group Activities: ISBN and UPC Numbers Final Exam Appendix A Keystroke Guide for the TI-83/83 Plus Calculators Appendix B Proofs of Logarithmic Properties Proof of the Formula for the Sum of n Terms of an Geometric Series Proof of the Formula for the Sum of n Terms of an Arithmetic Series Table of Symbols Table of Properties Table of Algebraic and Geometric Formulas Solutions to You Try Its Answers to Selected Exercises Glossary Index Index of Applications