Beginning and Intermediate Algebra Book

Note: every chapter concludes with a group activity, chapter summary, review exercises, and chapter test. Every chapter (beginning with chapter 2) also has cumulative review exercises.

Chapter 1: The Real Number System

1.1 Fractions

1.2 Exponents, Order of Operations, and Inequality

1.3 Variables, Expressions, and Equations

1.4 Real Numbers and the Number Line

1.5 Adding and Subtracting Real Numbers

1.6 Multiplying and Dividing Real Numbers

Summary Exercises on Operation with Real Numbers

1.7 Properties of Real Numbers

1.8 Simplifying Expressions

Chapter 2: Linear Equations and Inequalities in One Variable

2.1 The Addition Property of Equality

2.2 The Multiplication Property of Equality

2.3 More on Solving Linear Equations

Summary Exercises on Solving Linear Equations

2.4 An Introduction to Applications of Linear Equations

2.5 Formulas and Applications from Geometry

2.6 Ratios and Proportions

2.7 Further Applications of Linear Equations

2.8 Solving Linear Inequalities

Chapter 3: Linear Equations in Two Variables; Functions

3.1 Reading Graphs; Linear Equations in Two Variables

3.2 Graphing Linear Equations in Two Variables

3.3 The Slope of a Line

3.4 Equations of a Line

Chapter 4: Exponents and Polynomials

4.1 The Product Rule and Power Rules for Exponents

4.2 Integer Exponents and the Quotient Rule

Summary Exercises on the Rules for Exponents

4.3 An Application of Exponents: Scientific Notation

4.4 Adding and Subtracting Polynomials; Graphing Simple Polynomials

4.5 Multiplying Polynomials

4.6 Special Products

4.7 Dividing Polynomials

Chapter 5: Factoring and Applications

5.1 The Greatest Common Factor; Factoring by Grouping

5.2 Factoring Trinomials

5.3 More on Factoring Trinomials

5.4 Special Factoring Techniques

Summary Exercises on Factoring

5.5 Solving Quadratic Equations by Factoring

5.6 Applications of Quadratic Equations

Chapter 6: Rational Expressions and Applications

6.1 The Fundamental Property of Rational Expressions

6.2 Multiplying and Dividing Rational Expressions

6.3 Least Common Denominators

6.4 Adding and Subtracting Rational Expressions

6.5 Complex Fractions

6.6 Solving Equations With Rational Expressions

Summary Exercises on Rational Expressions and Equations

6.7 Applications of Rational Expressions

Chapter 7: Equations of Lines; Functions

7.1 Review of Graphs and Slopes of Lines

7.2 Review of Equations of Lines; Linear Models

Summary Exercises on Slope and Equations of Lines

7.3 Functions

7.4 Operations on Functions and Composition

7.5 Variation

Chapter 8: Systems of Linear Equations

8.1 Solving Systems of Linear Equations by Graphing

8.2 Solving Systems of Linear Equations by Substitution

8.3 Solving Systems of Linear Equations by Elimination

Summary Exercises on Solving Systems of Linear Equations

8.4 Systems of Linear Equations in Three Variables

8.5 Applications of Systems of Linear Equations

8.6 Solving Systems of Linear Equations by Matrix Methods

Chapter 9: Inequalities and Absolute Value

9.1 Set Operations and Compound Inequalities

9.2 Absolute Value Equations and Inequalities

Summary Exercises on Solving Linear and Absolute Value Equations and Inequalities

9.3 Linear Inequalities in Two Variables

Chapter 10: Roots, Radicals, and Root Functions

10.1 Radical Expressions and Graphs

10.2 Rational Exponents

10.3 Simplifying Radical Expressions

10.4 Adding and Subtracting Radical Expressions

10.5 Multiplying and Dividing Radical Expressions

Summary Exercises on Operations with Radicals and Rational Exponents

10.6 Solving Equations with Radicals

10.7 Complex Numbers

Chapter 11: Quadratic Equations, Inequalities, and Functions

11.1 Solving Quadratic Equations by the Square Root Property

11.2 Solving Quadratic Equations by Completing the Square

11.3 Solving Quadratic Equations by the Quadratic Formula

11.4 Equations Quadratic in Form

Summary Exercises on Solving Quadratic Equations

11.5 Formulas and Further Applications

11.6 Graphs of Quadratic Functions

11.7 More about Parabolas and Their Applications

11.8 Quadratic and Rational Inequalities

Chapter 12: Inverse, Exponential, and Logarithmic Functions

12.1 Inverse Functions

12.2 Exponential Functions

12.3 Logarithmic Functions

12.4 Properties of Logarithms

12.5 Common and Natural Logarithms

12.6 Exponential and Logarithmic Equations; Further Applications

Chapter 13: Nonlinear Functions, Conic Sections, and Nonlinear Systems

13.1 Additional Graphs of Functions

13.2 The Circle and the Ellipse

13.3 The Hyperbola and Functions Defined by Radicals

13.4 Nonlinear Systems of Equations

13.5 Second-Degree Inequalities and Systems of Inequalities

Chapter 14: Sequences and Series

14.1 Sequences and Series

14.2 Arithmetic Sequences

14.3 Geometric Sequences

14.4 The Binomial Theorem

Appendixes

A. An Introduction to Calculators

B. Review of Decimals and Percents

C. Sets

D. Mean, Median, and Mode

E. The Metric System and Conversions

F. Review of Exponents, Polynomials, and Factoring

G. Synthetic Division

H. Determinants and Cramer's Rule