Introductory & Intermediate Algebra

<h2>Table of Contents</h2> <div class="c-non-traditional-number-list_container"> <ul> <li>R. Prealgebra Review</li> <li>R.1 Fractions</li> <li>R.2 Decimals and Percents</li> <li>Study Skills Using Your Math Text</li> </ul> <ol> <li><strong>The Real Number System</strong> <ul> <li>1.1 Exponents, Order of Operations, and Inequality <ul> <li><strong>Study Skills</strong> Taking Lecture Notes</li> </ul></li> <li>1.2 Variables, Expressions, and Equations <ul> <li><strong>Study Skills</strong> Reading Your Math Text</li> </ul></li> <li>1.3 Real Numbers and the Number Line <ul> <li><strong>Study Skills</strong> Using Study Cards</li> </ul></li> <li>1.4 Adding Real Numbers</li> <li>1.5 Subtracting Real Numbers <ul> <li><strong>Study Skills</strong> Completing Your Homework</li> </ul></li> <li>1.6 Multiplying and Dividing Real Numbers <ul> <li><strong>Summary Exercises</strong> Performing Operations with Real Numbers</li> </ul></li> <li>1.7 Properties of Real Numbers</li> <li>1.8 Simplifying Expressions <ul> <li><strong>Study Skills</strong> Reviewing a Chapter</li> </ul></li> </ul></li> <li><strong>Equations, Inequalities, and Applications</strong> <ul> <li>2.1 The Addition Property of Equality <ul> <li><strong>Study Skills</strong> Managing Your Time</li> </ul></li> <li>2.2 The Multiplication Property of Equality</li> <li>2.3 More on Solving Linear Equations <ul> <li><strong>Study Skills</strong> Using Study Cards Revisited</li> <li><strong>Summary Exercises</strong> Applying Methods for Solving Linear Equations</li> </ul></li> <li>2.4 An Introduction to Applications of Linear Equations</li> <li>2.5 Formulas and Additional Applications from Geometry</li> <li>2.6 Ratio, Proportion, and Percent <ul> <li><strong>Summary Exercises</strong> Applying Problem-Solving Techniques</li> </ul></li> <li>2.7 Solving Linear Inequalities <ul> <li><strong>Study Skills</strong> Taking Math Tests</li> </ul></li> </ul></li> <li><strong>Graphs of Linear Equations and Inequalities in Two Variables</strong> <ul> <li>3.1 Linear Equations and Rectangular Coordinates <ul> <li><strong>Study Skills</strong> Analyzing Your Test Results</li> </ul></li> <li>3.2 Graphing Linear Equations in Two Variables</li> <li>3.3 The Slope of a Line</li> <li>3.4 Slope-Intercept Form of a Linear Equation</li> <li>3.5 Point-Slope Form of a Linear Equation and Modeling <ul> <li><strong>Summary Exercises</strong> Applying Graphing and</li> <li>Equation-Writing Techniques for Lines</li> <li><strong>Study Skills</strong> Preparing for Your Math Final Exam</li> </ul></li> <li>3.6 Graphing Linear Inequalities in Two Variables</li> </ul></li> <li><strong>Systems of Linear Equations and Inequalities</strong> <ul> <li>4.1 Solving Systems of Linear Equations by Graphing</li> <li>4.2 Solving Systems of Linear Equations by Substitution</li> <li>4.3 Solving Systems of Linear Equations by Elimination <ul> <li><strong>Summary Exercises</strong> Applying Techniques for Solving Systems of Linear Equations</li> </ul></li> <li>4.4 Applications of Linear Systems</li> <li>4.5 Solving Systems of Linear Inequalities</li> </ul></li> <li><strong>Exponents and Polynomials</strong> <ul> <li>5.1 The Product Rule and Power Rules for Exponents</li> <li>5.2 Integer Exponents and the Quotient Rule <ul> <li><strong>Summary Exercises</strong> Applying the Rules for Exponents</li> </ul></li> <li>5.3 An Application of Exponents: Scientific Notation</li> <li>5.4 Adding and Subtracting Polynomials</li> <li>5.5 Multiplying Polynomials</li> <li>5.6 Special Products</li> <li>5.7 Dividing a Polynomial by a Monomial</li> <li>5.8 Dividing a Polynomial by a Polynomial</li> </ul></li> <li><strong>Factoring and Applications</strong> <ul> <li>6.1 Greatest Common Factors; Factor by Grouping</li> <li>6.2 Factoring Trinomials</li> <li>6.3 Factoring Trinomials by Grouping</li> <li>6.4 Factoring Trinomials Using the FOIL Method</li> <li>6.5 Special Factoring Techniques</li> <li>6.6 A General Approach to Factoring</li> <li>6.7 Solving Quadratic Equations Using the Zero-Factor Property</li> <li>6.8 Applications of Quadratic Equations</li> </ul></li> <li><strong>Rational Expressions and Applications</strong> <ul> <li>7.1 The Fundamental Property of Rational Expressions</li> <li>7.2 Multiplying and Dividing Rational Expressions</li> <li>7.3 Least Common Denominators</li> <li>7.4 Adding and Subtracting Rational Expressions</li> <li>7.5 Complex Fractions</li> <li>7.6 Solving Equations with Rational Expressions <ul> <li><strong>Summary Exercises</strong> Simplifying Rational Expressions vs. Solving Rational Equations</li> </ul></li> <li>7.7 Applications of Rational Expressions</li> <li>7.8 Variation</li> </ul></li> <li><strong>Equations, Inequalities, Graphs, and Systems Revisited</strong> <ul> <li>8.1 Review of Solving Linear Equations and Inequalities in one Variable</li> <li>8.2 Set Operations and Compound Inequalities</li> <li>8.3 Absolute Value Equations and Inequalities <ul> <li><strong>Summary Exercises</strong> Solving Linear and Absolute Value Equations and Inequalities</li> </ul></li> <li>8.4 Review of Graphing Linear Equations in Two Variables; Slope</li> <li>8.6 Systems of Linear Equations in Three Variables; Applications</li> </ul></li> <li><strong>Relations and Functions</strong> <ul> <li>9.1 Introduction to Relations and Functions</li> <li>9.2 Function Notation and Linear Functions</li> <li>9.3 Polynomial Functions, Operations, and Graphs</li> <li>9.4 Variation</li> </ul></li> <li><strong>Roots, Radicals, and Root Functions</strong> <ul> <li>10.1 Radical Expressions and Graphs</li> <li>10.2 Rational Exponents</li> <li>10.3 Simplifying Radical Expressions</li> <li>10.4 Adding and Subtracting Radical Expressions</li> <li>10.5 Multiplying and Dividing Radical Expressions <ul> <li><strong>Summary Exercises</strong> Performing Operations with Radicals and Rational Exponents</li> </ul></li> <li>10.6 Solving Equations with Radicals</li> <li>10.7 Complex Numbers</li> </ul></li> <li><strong>Quadratic Equations, Inequalities, and Functions</strong> <ul> <li>11.1 Solving Quadratic Equations by the Square Root Property</li> <li>11.2 Solving Quadratic Equations by Completing the Square</li> <li>11.3 Solving Quadratic Equations by the Quadratic Formula</li> <li>11.4 Equations Quadratic in Form <ul> <li><strong>Summary Exercises</strong> Applying Methods for Solving Quadratic Equations</li> </ul></li> <li>11.5 Formulas and Further Applications</li> <li>11.6 Graphs of Quadratic Functions</li> <li>11.7 More about Parabolas and Their Applications</li> <li>11.8 Polynomial and Rational Inequalities</li> </ul></li> <li><strong>Inverse, Exponential, and Logarithmic Functions</strong> <ul> <li>12.1 Composition of Functions</li> <li>12.2 Inverse Functions</li> <li>12.3 Exponential Functions</li> <li>12.4 Logarithmic Functions</li> <li>12.5 Properties of Logarithms</li> <li>12.6 Common and Natural Logarithms</li> <li>12.7 Exponential and Logarithmic Equations and Their Applications</li> </ul></li> <li><strong>Nonlinear Functions, Conic Sections, and Nonlinear Systems</strong> <ul> <li>13.1 Additional Graphs of Functions</li> <li>13.2 Circles and Ellipses</li> <li>13.3 Hyperbolas and Functions Defined by Radicals</li> <li>13.4 Nonlinear Systems of Equations</li> <li>13.5 Second-Degree Inequalities and Systems of Inequalities</li> </ul></li> </ol> <h3>Appendix A: Review of Exponents, Polynomials, and Factoring (Transition from Introductory to Intermediate Algebra)</h3> <h3>Appendix B: Synthetic Division</h3> <h3>Appendix C: Solving Systems of Linear Equations by Matrix Methods</h3> <h3>Answers to Selected Exercises</h3> <h4 class="h5">Index</h4> </div>