# Intermediate Algebra, 3rd Edition

## R Review of Basic Algebraic Concepts

R.1 Study Skills

Group Activity: Becoming a Successful Student

R.2 Sets of Numbers and Interval Notation

R.3 Operations on Real Numbers

R.4 Simplifying Expressions

## 1 Linear Equations and Inequalities in One Variable

1.1 Linear Equations in One Variable

PRE: Equations versus Expressions

1.2 Application of Linear Equations in One Variable

1.3 Applications to 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

PRE: Identifying Equations and Inequalities
Group Activity: Understanding the Symbolism of Mathematics

## 2 Linear Equations in Two Variables

2.1 Linear Equations in Two Variables

2.2 Slope of a Line and Rate of Change

2.3 Equations of a Line

PRE: Characteristics of Linear Equations

2.4 Application of Linear Equations and Modeling

Group Activity: Using Linear Equations to Construct Images

## 3 Relations and Functions

3.1 Relations and Applications

3.2 Introduction to Functions

3.3 Graphs of Basic Functions

PRE: Characteristics of Relations

3.4 Algebra of Functions, Composition, and Applications
Group Activity: Deciphering a Coded Message

## 4 Systems of Linear Equations

4.1 Solving Systems of Linear Equations by the Graphing Method

4.2 Solving Systems of Linear Equations by Using the Substitution Method

4.3 Solving Systems of Linear Equations by Using the Addition Method

PRE: Solving Systems of Linear Equations

4.4 Applications of Systems of Linear Equations in Two Variables

4.5 Linear Inequalities and Systems of Linear Inequalities in Two Variables

4.6 Systems of Linear Equations in Three Variables and Applications

4.7 Solving Systems of Linear Equations by Using Matrices

Group Activity: Creating a Quadratic Model of the Form y = at^2 +bt + c

## 5 Polynomials

5.1 Properties of Integer Exponents and Scientific Notation

5.2 Addition and Subtraction of Polynomials and Polynomial Functions

5.3 Multiplication of Polynomials

5.4 Division of Polynomaisl

PRE: Operations on Polynomials

5.5 Greatest Common Factor and Factoring by Grouping

5.6 Factoring Trinomials and Perfect Square Trinomials

5.7 Factoring Binomials Including Sum and Difference of Cubes

PRE: Factoring Summary

5.8 Solving Equations and Applications by Factoring
Group Activity: Investigating Pascal's Triangle

## 6 Rational Expressions and Rational Equations

6.1 Rational Expressions and Rational Functions

6.2 Multiplication and Division of Rational Expressions

6.3 Addition and Subtraction of Rational Expressions

6.4 Complex Fractions

PRE: Operations on Rational Expressions

6.5 Solving Rational Equations

PRE: Rational Equations versus Expressions

6.6 Applications of Rational Equations and Proportions

6.7 Variation

Group Activity: Computing the Future Value of an Investment

## 7 Radicals and Complex Numbers

7.1 Definition of an nth-Root

7.2 Rational Exponents

7.3 Simplifying Radical Expressions

7.4 Addition and Subtraction of Radicals

7.5 Multiplication of Radicals

PRE: Simplifying Radical Expressions

7.6 Division of Radicals and Rationalisation

7.7 Radical Equations and Applications

7.8 Complex Numbers

Group Activity: Margin of Error of Survey Results

## 8 Quadratic Equations, Functions, and Inequalities

8.1 Square Root Property and Completing the Square

8.2 Quadratic Formula and Applications

8.3 Equations in Quadratic Form

PRE: Equations in Quadratic Form

8.4 Graphs of Quadratic Functions

8.5 Vertex of a Parabola: Applications and Modeling

8.6 Polynomials and Rational Inequalities

PRE: Recognizing Equations and Inequalities

Group Activity: Creating a Quadratic Model of the Form y = a(x - h)^2 + k

## 9 Exponential and Logarithmic Functions

9.1 Inverse Functions

9.2 Exponential Functions

9.3 Logarithmic Functions

PRE: Identifying Graphs of Functions

9.4 Properties of Logarithms

9.5 The Irrational Number e

PRE: Logarithmic and Exponential Forms

9.6 Exponential Equations and Applications

9.7 Logarithmic Equations and Applications

Group Activity: Creating a Population Model

## 10 Conic Sections

10.1 Distance Formula, Midpoint, and Circles

10.2 More of the Parabola

10.3 The Ellipse and Hyperbola

PRE: Formulas for Conic Sections

10.4 Nonlinear Systems of Equations in Two Variables

10.5 Nonlinear Inequalities and Systems of Inequalities

Group Activity: Investigating the Graphs of Conic Sections on a Calculator

## Additional Topics Appendix

A.1 Binomial Expansions

A.2 Determinants and Cramer's Rule

A.3 Sequences and Series

A.4 Arithmetic and Geometric Sequences and Series