Guided Notebook for Intermediate Algebra

<p><strong>Study Skills</strong></p> <ul> <li>Study Skill 1: Using Your Math Text</li> <li>Study Skill 2: Reading Your Math Text</li> <li>Study Skill 3: Taking Lecture Notes</li> <li>Study Skill 4: Completing Your Homework</li> <li>Study Skill 5: Using Study Cards</li> <li>Study Skill 6: Managing Your Time</li> <li>Study Skill 7: Reviewing a Chapter</li> <li>Study Skill 8: Taking Math Tests</li> <li>Study Skill 9: Analyzing Your Test Results</li> <li>Study Skill 10: Preparing for Your Math Final</li> </ul> <ol> <li><strong>Review of the Real Number System</strong> <ul> <li>R.1 Fractions, Decimals, and Percents</li> <li>R.2 Basic Concepts from Algebra</li> <li>R.3 Operations on Real Numbers</li> <li>R.3 Exponents, Roots, and Order of Operations</li> <li>R.4 Properties of Real Numbers</li> <li>Chapter R Summary</li> <li>Chapter R Test</li> </ul></li> <li><strong>Linear Equations, Inequalities, and Applications</strong> <ul> <li>1.1 Linear Equations in One Variable</li> <li>1.2 Formulas and Percent</li> <li>1.3 Applications of Linear Equations</li> <li>1.4 Further Applications of Linear Equations <ul> <li>Summary Exercises: Applying Problem-Solving Techniques</li> </ul></li> <li>1.5 Linear Inequalities in One Variable</li> <li>1.6 Set Operations and Compound Inequalities</li> <li>1.7 Absolute Value Equations and Inequalities</li> <li>Summary Exercises: Solving Linear and Absolute Value Equations and Inequalities</li> <li>Chapter 1 Summary</li> <li>Chapter 1 Review Exercises</li> <li>Chapter 1 Mixed Review Exercises</li> <li>Chapter 1 Test</li> <li>Chapters R and 1 Cumulative Review Exercises</li> </ul></li> <li><strong>Linear Equations, Graphs, and Functions</strong> <ul> <li>2.1 Linear Equations in Two Variables <ul> <li>Study Skills: Managing Your Time</li> </ul></li> <li>2.2 The Slope of a Line</li> <li>2.3 Writing Equations of Lines <ul> <li>Summary Exercises: Finding Slopes and Equations of Lines</li> </ul></li> <li>2.4 Linear Inequalities in Two Variables</li> <li>2.5 Introduction to Relations and Functions</li> <li>2.6 Function Notation and Linear Functions</li> <li>Chapter 2 Summary</li> <li>Chapter 2 Review Exercises</li> <li>Chapter 2 Mixed Review Exercises</li> <li>Chapter 2 Test</li> <li>Chapters R–2 Cumulative Review Exercises</li> </ul></li> <li><strong>Systems of Linear Equations</strong> <ul> <li>3.1 Systems of Linear Equations in Two Variables</li> <li>3.2 Systems of Linear Equations in Three Variables</li> <li>3.3 Applications of Systems of Linear Equations</li> <li>Chapter 3 Summary</li> <li>Chapter 3 Review Exercises</li> <li>Chapter 3 Mixed Review Exercises</li> <li>Chapter 3 Test</li> <li>Chapters R–3 Cumulative Review Exercises</li> </ul></li> <li><strong>Exponents, Polynomials, and Polynomial Functions</strong> <ul> <li>4.1 Integer Exponents</li> <li>4.2 Scientific Notation</li> <li>4.3 Adding and Subtracting Polynomials</li> <li>4.4 Polynomial Functions, Graphs, and Composition</li> <li>4.5 Multiplying Polynomials</li> <li>4.6 Dividing Polynomials</li> <li>Chapter 4 Summary</li> <li>Chapter 4 Review Exercises</li> <li>Chapter 4 Mixed Review Exercises</li> <li>Chapter 4 Test</li> <li>Chapters R–4 Cumulative Review Exercises</li> </ul></li> <li><strong>Factoring</strong> <ul> <li>5.1 Greatest Common Factors and Factoring by Grouping</li> <li>5.2 Factoring Trinomials</li> <li>5.3 Special Factoring</li> <li>5.4 A General Approach to Factoring</li> <li>5.5 Solving Equations by the Zero-Factor Property</li> <li>Chapter 5 Summary</li> <li>Chapter 5 Review Exercises</li> <li>Chapter 5 Mixed Review Exercises</li> <li>Chapter 5 Test</li> <li>Chapters R–5 Cumulative Review Exercises</li> </ul></li> <li><strong>Rational Expressions and Functions</strong> <ul> <li>6.1 Rational Expressions and Functions; Multiplying and Dividing</li> <li>6.2 Adding and Subtracting Rational Expressions</li> <li>6.3 Complex Fractions</li> <li>6.4 Equations with Rational Expressions and Graphs <ul> <li>Summary Exercises: Simplifying Rational Expressions vs. Solving Rational Equations</li> </ul></li> <li>6.5 Applications of Rational Expressions</li> <li>6.6 Variation</li> <li>Chapter 6 Summary</li> <li>Chapter 6 Review Exercises</li> <li>Chapter 6 Mixed Review Exercises</li> <li>Chapter 6 Test</li> <li>Chapters R–6 Cumulative Review Exercises</li> </ul></li> <li><strong>Roots, Radicals, and Root Functions</strong> <ul> <li>7.1 Radical Expressions and Graphs</li> <li>7.2 Rational Exponents</li> <li>7.3 Simplifying Radicals, the Distance Formula, and Circles</li> <li>7.4 Adding and Subtracting Radical Expressions</li> <li>7.5 Multiplying and Dividing Radical Expressions <ul> <li>Summary Exercises: Performing Operations with Radicals and Rational Exponents</li> </ul></li> <li>7.6 Solving Equations with Radicals</li> <li>7.7 Complex Numbers</li> <li>Chapter 7 Summary</li> <li>Chapter 7 Review Exercises</li> <li>Chapter 7 Mixed Review Exercises</li> <li>Chapter 7 Test</li> <li>Chapters R–7 Cumulative Review Exercises</li> </ul></li> <li><strong>Quadratic Equations, Inequalities, and Functions</strong> <ul> <li>8.1 The Square Root Property and Completing the Square</li> <li>8.2 The Quadratic Formula</li> <li>8.3 Equations That Lead to Quadratic Methods <ul> <li>Summary Exercises: Applying Methods for Solving Quadratic Equations</li> </ul></li> <li>8.4 Formulas and Further Applications</li> <li>8.5 Graphs of Quadratic Functions</li> <li>8.6 More about Parabolas and Their Applications</li> <li>8.7 Polynomial and Rational Inequalities</li> <li>Chapter 8 Summary</li> <li>Chapter 8 Review Exercises</li> <li>Chapter 8 Mixed Review Exercises</li> <li>Chapter 8 Test</li> <li>Chapters R–8 Cumulative Review Exercises</li> </ul></li> <li><strong>Inverse, Exponential, and Logarithmic Functions</strong> <ul> <li>9.1 Inverse Functions</li> <li>9.2 Exponential Functions</li> <li>9.3 Logarithmic Functions</li> <li>9.4 Properties of Logarithms</li> <li>9.5 Common and Natural Logarithms</li> <li>9.6 Exponential and Logarithmic Equations; Further Applications</li> <li>Chapter 9 Summary</li> <li>Chapter 9 Review Exercises</li> <li>Chapter 9 Mixed Review Exercises</li> <li>Chapter 9 Test</li> <li>Chapters R–9 Cumulative Review Exercises</li> </ul></li> <li><strong>Nonlinear Functions, Conic Sections, and Nonlinear Systems</strong> <ul> <li>10.1 Additional Graphs of Functions</li> <li>10.2 Circles Revisited and Ellipses</li> <li>10.3 Hyperbolas and Functions Defined by Radicals</li> <li>10.4 Nonlinear Systems of Equations</li> <li>10.5 Second-Degree Inequalities and Systems of Inequalities</li> <li>Chapter 10 Summary</li> <li>Chapter 10 Review Exercises</li> <li>Chapter 10 Mixed Review Exercises</li> <li>Chapter 10 Test</li> <li>Chapters R-10 Cumulative Review Exercises</li> </ul></li> <li><strong>Further Topics in Algebra</strong> <ul> <li>11.1 Sequences and Series</li> <li>11.2 Arithmetic Sequences</li> <li>11.3 Geometric Sequences</li> <li>11.4 The Binomial Theorem</li> <li>Chapter 11 Summary</li> <li>Chapter 11 Review Exercises</li> <li>Chapter 11 Mixed Review Exercises</li> <li>Chapter 11 Test</li> <li>Chapters R-11 Cumulative Review Exercises</li> </ul></li> </ol> <p>Appendix A: Synthetic Division</p> <p>Answers to Selected Exercises</p> <p>Credits</p> <p>Index</p>