# Intermediate Algebra 4e

### Reference: Review of Basic Algebraic Concepts

#### R.1 Study Skills

#### R.2 Sets of Numbers and Interval Notation

#### R.3 Operations of Real Numbers

#### R.4 Simplifying Algebraic Expressions

### Chapter 1: Linear Equations and Inequalities in One Variable

#### 1.1 Linear Equations in One Variable

Problem Recognition Exercises-Equations versus Expressions

#### 1.2 Applications of Linear Equations in One Variable

#### 1.3 Applications of Geometry and Literal Equations

#### 1.4 Linear Inequalities in One Variable

#### 1.5 Compound Inequalities

#### 1.6 Absolute Value Equations

#### 1.7 Absolute Value Inequalities

Problem Recognition Exercises-Identifying Equations and Inequalities

### Chapter 2: Linear Equations in Two Variables and Functions

#### 2.1 Linear Equations in Two Variables

#### 2.2 Slope of a Line and Rate of Change

#### 2.3 Equations of a Line

Problem Recognition Exercises-Characteristics of Linear Equations

#### 2.4 Applications of Linear Equations and Modeling

#### 2.5 Introduction to Relations

#### 2.6 Introduction to Functions

#### 2.7 Graphs of Functions

Problem Recognition Exercises-Characteristics of Relations

### Chapter 3: Systems of Linear Equations and Inequalities

#### 3.1 Solving Systems of Linear Equations by the Graphing Method

#### 3.2 Solving Systems of Linear Equations by the Substitution Method

#### 3.3 Solving Systems of Linear Equations by the Addition Method

Problem Recognition Exercises-Solving Systems of Linear Equations

#### 3.4 Applications of Systems of Linear Equations in Two Variables

#### 3.5 Linear Inequalities and Systems of Linear Inequalities in Two Variables

#### 3.6 Systems of Linear Equations in Three Variables and Applications

#### 3.7 Solving Systems of Linear Equations by Using Matrices

### Chapter 4: Polynomials

#### 4.1 Properties of Integer Exponents and Scientific Notation

#### 4.2 Addition and Subtraction of Polynomials and Polynomials Functions

#### 4.3 Multiplication of Polynomials

#### 4.4 Division of Polynomials

Problem Recognition Exercises-Operations on Polynomials

#### 4.5 Greatest Common Factor and Factoring by Grouping

#### 4.6 Factoring Trinomials

#### 4.7 Factoring Binomials

Problem Recognition Exercises-Factoring Summary

#### 4.8 Solving Equations by Using the Zero Product Rule

### Chapter 5: Rational Expressions and Rational Equations

#### 5.1 Rational Expressions and Rational Functions

#### 5.2 Multiplication and Division of Rational Expressions

#### 5.3 Addition and Subtraction of Rational Expressions

#### 5.4 Complex Fractions

Problem Recognition Exercises-Operations on Rational Expressions

#### 5.5 Solving Rational Equations

Problem Recognition Exercises-Rational Equations versus Expressions

#### 5.6 Applications of Rational Equations and Proportions

#### Variation

### Chapter 6: Radicals and Complex Numbers

#### 6.1 Definition of an nth Root

#### 6.2 Rational Exponents

#### 6.3 Simplifying Radical Expressions

#### 6.4 Addition and Subtraction of Radicals

#### 6.5 Multiplication of Radicals

Problem Recognition Exercises-Simplifying Radical Expressions

#### 6.6 Division of Radicals and Rationalization

#### 6.7 Solving Radical Equations

#### 6.8 Complex Numbers

### Chapter 7: Quadratic Equations, Functions and Inequalities

#### 7.1 Square Root Property and Completing the Square

#### 7.2 Quadratic Formula

#### 7.3 Equations in Quadratic Form

Problem Recognition Exercises-Quadratic and Quadratic Type Equations

#### 7.4 Graphs of Quadratic Functions

#### 7.5 Vertex of a Parabola: Applications and Modeling

#### 7.6 Polynomial and Rational Inequalities

Problem Recognition Exercises-Recognizing Equations and Inequalities

### Chapter 8: Exponential and Logarithmic Functions and Applications

#### 8.1 Algebra of Functions and Composition

#### 8.2 Inverse Functions

#### 8.3 Exponential Functions

#### 8.4 Logarithmic Functions

Problem Recognition Exercises-Identifying Graphs of Functions

#### 8.5 Properties of Logarithms

#### 8.6 The Irrational Number e and Change of Base

Problem Recognition Exercises-Logarithmic and Exponential Forms

#### 8.7 Logarithmic and Exponential Equations and Applications

### Chapter 9: Conic Sections

#### 9.1 Distance Formula, Midpoint Formula, and Circles

#### 9.2 More on the Parabola

#### 9.3 The Ellipse and Hyperbola

Problem Recognition Exercises-Formulas and Conic Sections

#### 9.4 Nonlinear systems of Equations in Two Variables

#### 9.5 Nonlinear Inequalities and Systems of Inequalities

### Chapter 10: Binomial Expansions, Sequences, and Series

#### 10.1 Binomial Expansions

#### 10.2 Sequences and Series

#### 10.3 Arithmetic Sequences and Series

#### 10.4 Geometric Sequences and Series

Problem Recognition Exercises-Identifying Arithmetic and Geometric Series