Intermediate Algebra

Note: Each chapter begins with a Prep Test and concludes with a Chapter Summary, Review Exercises, and Test. Chapters 2-6 are followed by Cumulative Review Exercises. 1. Review of Real Numbers Section 1.1 Introduction to Real Numbers Section 1.2 Operations on Rational Numbers Section 1.3 Variable Expressions Section 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 Section 2.1 Solving First-Degree Equations Section 2.2 Applications: Puzzle Problems Section 2.3 Applications: Mixture and Uniform Motion Problems Section 2.4 First-Degree Inequalities Section 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 Section 3.1 The Rectangular Coordinate System Section 3.2 Introduction to Functions Section 3.3 Linear Functions Section 3.4 Slope of a Straight Line Section 3.5 Finding Equations of Lines Section 3.6 Parallel and Perpendicular Lines Section 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 Section 4.1 Solving Systems of Linear Equations by Graphing and by the Substitution Method Section 4.2 Solving Systems of Linear Equations by the Addition Method Section 4.3 Solving Systems of Equations by Using Determinants Section 4.4 Application Problems Section 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 Section 5.1 Exponential Expressions Section 5.2 Introduction to Polynomial Functions Section 5.3 Multiplication of Polynomials Section 5.4 Division of Polynomials Section 5.5 Factoring Polynomials Section 5.6 Special Factoring Section 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 Section 6.1 Multiplication and Division of Rational Expressions Section 6.2 Addition and Subtraction of Rational Expressions Section 6.3 Complex Fractions Section 6.4 Ratio and Proportion Section 6.5 Rational Equations Section 6.6 Variation Focus on Problem Solving: Implication Projects and Group Activities: Graphing Variation Equations, Transformers 7. Exponents and Radicals Section 7.1 Rational Exponents and Radical Expressions Section 7.2 Operations on Radical Expressions Section 7.3 Solving Equations Containing Radical Expressions Section 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 Section 8.1 Solving Quadratic Equations by Factoring or by Taking Square Roots Section 8.2 Solving Quadratic Equations by Completing the Square Section 8.3 Solving Quadratic Equations by Using the Quadratic Formula Section 8.4 Solving Equations that are Reducible to Quadratic Equations Section 8.5 Quadratic Inequalities and Rational Inequalities Section 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 Section 9.1 Properties of Quadratic Functions Section 9.2 Graphs of Functions Section 9.3 Algebra of Functions Section 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 Section 10.1 Exponential Functions Section 10.2 Introduction to Logarithms Section 10.3 Graphs of Logarithmic Functions Section 10.4 Solving Exponential and Logarithmic Equations Section 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(R) Scores 11. Conic Sections Section 11.1 The Parabola Section 11.2 The Circle Section 11.3 The Ellipse and the Hyperbola Section 11.4 Solving Nonlinear Systems of Equations Section 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 Section 12.1 Introduction to Sequences and Series Section 12.2 Arithmetic Sequences and Series Section 12.3 Geometric Sequences and Series Section 12.4 Binomial Expansions Focus on Problem Solving: Forming Negations Projects and Group Activities: ISBN and UPC Numbers