Intermediate Algebra

Note: each chapter concludes with a Group Activity, Chapter Summary, Chapter Review Exercises, Chapter Test, and after Chapter 1, a set of Cumulative Review Exercises.

 

Chapter 1: Review of the Real Number System

1.1 Basic Concepts

1.2 Operations on Real Numbers

1.3 Exponents, Roots, and Order of Operations

1.4 Properties of Real Numbers

               

Chapter 2: Linear Equations, Inequalities, and Applications

2.1 Linear Equations in One Variable

2.2 Formulas

2.3 Applications of Linear Equations

2.4 Further Applications of Linear Equations

Summary Exercises on Solving Applied

Problems

2.5 Linear Inequalities in One Variable

2.6 Set Operations and Compound Inequalities

2.7 Absolute Value Equations and Inequalities

Summary Exercises on Solving Linear and Absolute Value Equations and Inequalities

 

Chapter 3: Graphs, Linear Equations, and Functions

3.1 The Rectangular Coordinate System

3.2 The Slope of a Line

3.3 Linear Equations in Two Variables

Summary Exercises on Slopes and Equations of Lines

3.4 Linear Inequalities in Two Variables

3.5 Introduction to Functions

 

Chapter 4: Systems of Linear Equations

4.1 Systems of Linear Equations in Two Variables

4.2 Systems of Linear Equations in Three Variables

4.3 Applications of Systems of Linear Equations

4.4 Solving Systems of Linear Equations by Matrix Methods

 

Chapter 5: Exponents, Polynomials, and Polynomial Functions

5.1 Integer Exponents and Scientific Notation

5.2 Adding and Subtracting Polynomials

5.3 Polynomial Functions, Graphs, and Composition

5.4 Multiplying Polynomials

5.5 Dividing Polynomials

 

Chapter 6: Factoring

6.1 Greatest Common Factors; Factoring by Grouping

6.2 Factoring Trinomials

6.3 Special Factoring

6.4 A General Approach to Factoring

6.5 Solving Equations by Factoring

 

Chapter 7: Rational Expressions and Functions

7.1 Rational Expressions and Functions; Multiplying and Dividing

7.2 Adding and Subtracting Rational Expressions

7.3 Complex Fractions

7.4 Equations with Rational Expressions and Graphs

Summary Exercises on Rational Expressions and Equations

7.5 Applications of Rational Expressions

7.6 Variation

 

Chapter 8: Roots, Radicals, and Root Functions

8.1 Radical Expressions and Graphs

8.2 Rational Exponents

8.3 Simplifying Radical Expressions

8.4 Adding and Subtracting Radical Expressions

8.5 Multiplying and Dividing Radical Expressions

Summary Exercises on Operations with Radicals and Rational Exponents

8.6 Solving Equations with Radicals

8.7 Complex Numbers

 

Chapter 9 Quadratic Equations, Inequalities, and Functions

9.1 The Square Root Property and Completing the Square

9.2 The Quadratic Formula

9.3 Equations Quadratic in Form

Summary Exercises on Solving Quadratic Equations

9.4 Formulas and Further Applications

9.5 Graphs of Quadratic Functions

9.6 More about Parabolas and Their Applications

9.7 Quadratic and Rational Inequalities

 

Chapter 10: Inverse, Exponential, and Logarithmic Functions

10.1 Inverse Functions

10.2 Exponential Functions

10.3 Logarithmic Functions

10.4 Properties of Logarithms

10.5 Common and Natural Logarithms

10.6 Exponential and Logarithmic Equations; Further Applications

 

Chapter 11: Nonlinear Functions, Conic Sections, and Nonlinear Systems

11.1 Additional Graphs of Functions

11.2 The Circle and the Ellipse

11.3 The Hyperbola and Functions Defined by Radicals

11.4 Nonlinear Systems of Equations

11.5 Second-Degree Inequalities and Systems of Inequalities

 

Chapter 12: Sequences and Series

12.1 Sequences and Series

12.2 Arithmetic Sequences

12.3 Geometric Sequences

12.4 The Binomial Theorem

 

Appendixes

A: An Introduction to Calculators

B: Determinants and Cramer's Rule

C: Synthetic Division