Intermediate Algebra

Overview

Table of contents

Intermediate AlgebraChapter 1: The Real Numbers1.1 Numbers and Their Properties1.2 Operations and Properties of Real Numbers1.3 Properties of Exponents1.4 Algebraic Expressions and the Order of OperationsChapter 2: Linear Equations and Inequalities2.1 Linear Equations in One Variable2.2 Formulas, Geometry, and Problem Solving2.3 Problem Solving: Integers and Geometry2.4 Problem Solving: Percent, Investment, Motion, and Mixture Problems2.5 Linear and Compound Inequalities2.6 Absolute-Value Equations and InequalitiesChapter 3: Graphs and Functions3.1 Graphs 3.2 Using Slopes to Graph Lines3.3 Equations of Lines3.4 Linear Inequalities in Two Variables3.5 Introduction to Functions3.6 Linear FunctionsChapter 4: Solving Systems of Linear Equations and Inequalities4.1 Systems with Two Variables4.2 Systems with Three Variables4.3 Coin, Distance-Rate-Time, Investment, and Geometry Problems4.4 Systems of Linear InequalitiesChapter 5: Polynomials5.1 Polynomials: Addition and Subtraction5.2 Multiplication of Polynomials5.3 The Greatest Common Factor and Factoring by Grouping5.4 Factoring Trinomials5.5 Special Factoring 5.6 General Methods of Factoring5.7 Solving Equations by Factoring: ApplicationsChapter 6: Rational Expressions6.1 Rational Expressions6.2 Multiplication and Division of Rational Expressions6.3 Addition and Subtraction of Rational Expressions6.4 Complex Fractions6.5 Division of Polynomials and Synthetic Division6.6 Equations Involving Rational Expressions6.7 Applications: Problem Solving6.8 VariationChapter 7: Rational Exponents and Radicals7.1 Rational Exponents and Radicals7.2 Simplifying Radicals7.3 Operations with Radicals7.4 Solving Equations Containing Radicals7.5 Complex NumbersChapter 8: Quadratic Equations and Inequalities8.1 Solving Quadratics by Completing the Square8.2 The Quadratic Formula: Applications8.3 The Discriminant and Its Applications8.4 Solving Equations in Quadratic Form8.5 Nonlinear InequalitiesChapter 9: Quadratic Functions and the Conic Sections9.1 Quadratic Functions and Their Graphs9.2 Circles and Ellipses9.3 Hyperbolas and Identification of Conics9.4 Nonlinear Systems of Equations9.5 Nonlinear Systems of InequalitiesChapter 10: Functions-Inverse, Exponential, and Logarithmic10.1 The Algebra of Functions10.2 Inverse Functions10.3 Exponential Functions10.4 Logarithmic Functions and Their Properties10.5 Common and Natural Logarithms10.6 Exponential and Logarithmic Equations and ApplicationsAppendix A: Sequences and SeriesA1: MatricesA2: Determinants and Cramer’s RuleA3: Sequences and SeriesA4: Arithmetic Sequences and SeriesA5: Geometric Sequences and SeriesA6: The Binomial Expansion