Beginning 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: 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 Operations 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 and Inequalities 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

Summary Exercises on Linear Equations and Graphs

3.5 Graphing Linear Inequalities in Two Variables

3.6 Introduction to Functions



Chapter 4: Systems of Linear Equations and Inequalities

4.1 Solving Systems of Linear Equations by Graphing

4.2 Solving Systems of Linear Equations by Substitution

4.3 Solving Systems of Linear Equations by Elimination

Summary Exercises on Solving Systems of Linear Equations

4.4 Applications of Linear Systems

4.5 Solving Systems of Linear Inequalities



Chapter 5: Exponents and Polynomials

5.1 The Product Rule and Power Rules for Exponents

5.2 Integer Exponents and the Quotient Rule

Summary Exercises on the Rules for Exponents

5.3 An Application of Exponents: Scientific Notation

5.4 Adding and Subtracting Polynomials; Graphing Simple Polynomials

5.5 Multiplying Polynomials

5.6 Special Products

5.7 Dividing Polynomials



Chapter 6: Factoring and Applications

6.1 The Greatest Common Factor; Factoring by Grouping

6.2 Factoring Trinomials

6.3 More on Factoring Trinomials

6.4 Special Factoring Techniques

Summary Exercises on Factoring

6.5 Solving Quadratic Equations by Factoring

6.6 Applications of Quadratic Equations



Chapter 7: Rational Expressions and Applications

7.1 The Fundamental Property of Rational Expressions

7.2 Multiplying and Dividing Rational Expressions

7.3 Least Common Denominators

7.4 Adding and Subtracting Rational Expressions

7.5 Complex Fractions

7.6 Solving Equations with Rational Expressions

Summary Exercises on Rational Expressions and Equations

7.7 Applications of Rational Expressions

7.8 Variation



Chapter 8: Roots and Radicals

8.1 Evaluating Roots

8.2 Multiplying, Dividing, and Simplifying Radicals

8.3 Adding and Subtracting Radicals

8.4 Rationalizing the Denominator

8.5 More Simplifying and Operations with Radicals

Summary Exercises on Operations with Radicals

8.6 Solving Equations with Radicals

8.7 Using Rational Numbers as Exponents



Chapter 9: Quadratic Equations

9.1 Solving Quadratic Equations by the Square Root Property

9.2 Solving Quadratic Equations by Completing the Square

9.3 Solving Quadratic Equations by the Quadratic Formula

Summary Exercises on Quadratic Equations

9.4 Complex Numbers

9.5 More on Graphing Quadratic Equations; Quadratic Functions



Appendixes

A. An Introduction to Calculators

B. Review of Decimals and Percents

C. Sets

D. Mean, Median, and Mode

E. Solving Quadratic Inequalities