Introductory and Intermediate Algebra Book

R. Prealgebra Review

R.1 Fractions

R.2 Decimals and Percents

Study Skills: Using Your Math Textbook

Study Skills: Reading Your Math Textbook

1. The Real Number System

1.1 Exponents, Order of Operations, and Inequality

Study Skills: Taking Lecture Notes

1.2 Variables, Expressions, and Equations

Study Skills: Tackling Your Homework

1.3 Real Numbers and the Number Line

Study Skills: Using Study Cards

1.4 Adding Real Numbers

1.5 Subtracting Real Numbers

1.6 Multiplying and Dividing Real Numbers

Summary Exercises Performing Operations with Real Numbers

1.7 Properties of Real Numbers

Study Skills: Reviewing a Chapter

1.8 Simplifying Expressions

Study Skills: Taking Math Tests

2. Equations, Inequalities, and Applications

2.1 The Addition Property of Equality

Study Skills: Managing Your Time

2.2 The Multiplication Property of Equality

Study Skills: Analyzing Your Test Results

2.3 More on Solving Linear Equations

Study Skills: Using Study Cards Revisited

Summary Exercises Applying Methods for Solving Linear Equations

2.4 An Introduction to Applications of Linear Equations

2.5 Formulas and Additional Applications from Geometry

2.6 Ratio, Proportion, and Percent

Summary Exercises Applying Problem-Solving Techniques

2.7 Solving Linear Inequalities

3. Graphs of Linear Equations and Inequalities in Two Variables; Functions

3.1 Linear Equations in Two Variables; The Rectangular Coordinate System

Study Skills: Preparing for Your Math Final

3.2 Graphing Linear Equations in Two Variables

3.3 The Slope of a Line

3.4 Writing and Graphing Equations of Lines

Summary Exercises Applying Graphing and Equation-Writing Techniques for Lines

3.5 Graphing Linear Inequalities in Two Variables

3.6 Introduction to Relations and Functions

3.7 Function Notation and Linear Functions

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 Applying Techniques for Solving Systems of Linear Equations

4.4 Applications of Linear Systems

4.5 Solving Systems of Linear Inequalities

5. Exponents and Polynomials

5.1 Adding and Subtracting Polynomials

5.2 The Product Rule and Power Rules for Exponents

5.3 Multiplying Polynomials

5.4 Special Products

5.5 Integer Exponents and the Quotient Rule

Summary Exercises Applying the Rules for Exponents

5.6 Dividing a Polynomial by a Monomial

5.7 Dividing a Polynomial by a Polynomial

5.8 An Application of Exponents: Scientific Notation

6. Factoring and Applications

6.1 Factors; The Greatest Common Factor

6.2 Factoring Trinomials

6.3 Factoring Trinomials by Grouping

6.4 Factoring Trinomials by Using the FOIL Method

6.5 Special Factoring Techniques

6.6 A General Approach to Factoring

6.7 Solving Quadratic Equations by Factoring

6.8 Applications of Quadratic Equations

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 Simplifying Rational Expressions vs Solving Rational Equations

7.5 Applications of Rational Expressions

7.6 Variation

8. Equations, Inequalities, and Systems Revisited

8.1 Review of Solving Linear Equations and Inequalities

8.2 Set Operations and Compound Inequalities

8.3 Absolute Value Equations and Inequalities

Summary Exercises Solving Linear and Absolute Value Equations and Inequalities

8.4 Review of Systems of Linear Equations in Two Variables

8.5 Systems of Linear Equations in Three Variables; Applications

9. Roots, Radicals, and Root Functions

9.1 Radical Expressions and Graphs

9.2 Rational Exponents

9.3 Simplifying Radical Expressions

9.4 Adding and Subtracting Radical Expressions

9.5 Multiplying and Dividing Radical Expressions

Summary Exercises Performing Operations with Radicals and Rational Exponents

9.6 Solving Equations with Radicals

9.7 Complex Numbers

10. Quadratic Equations, Inequalities, and Functions

10.1 Solving Quadratic Equations by the Square Root Property

10.2 Solving Quadratic Equations by Completing the Square

10.3 Solving Quadratic Equations by the Quadratic Formula

10.4 Equations Quadratic in Form

Summary Exercises Applying Methods for Solving Quadratic Equations

10.5 Formulas and Applications

10.6 Graphs of Quadratic Functions

10.7 More about Parabolas and Their Applications

10.8 Polynomial and Rational Inequalities

11. Inverse, Exponential, and Logarithmic Functions

11.1 Operations on Functions and Composition

11.2 Inverse Functions

11.3 Exponential Functions

11.4 Logarithmic Functions

11.5 Properties of Logarithms

11.6 Common and Natural Logarithms

11.7 Exponential and Logarithmic Equations and Their Applications

12. Nonlinear Functions, Conic Sections, and Nonlinear Systems

12.1 Additional Graphs of Functions; Operations and Composition

12.2 The Circle and the Ellipse

12.3 The Hyperbola and Other Functions Defined by Radicals

12.4 Nonlinear Systems of Equations

12.5 Second-Degree Inequalities and Systems of Inequalities

Appendix A: Review of Exponents, Polynomials, and Factoring (Transition from Introductory to Intermediate Algebra)
Appendix B: Solving Systems of Linear Equations by Matrix Methods Appendix C: Synthetic Division Answers to Selected Exercises Solutions to Selected Exercises Index