Intermediate Algebra Book

R. Review of the Real Number System

R.1 Basic Concepts

R.2 Operations on Real Numbers

R.3 Exponents, Roots, and Order of Operations

R.4 Properties of Real Numbers

1. Linear Equations and Applications

1.1 Linear Equations in One Variable

1.2 Formulas and Percent

1.3 Applications of Linear Equations

1.4 Further Applications of Linear Equations

2. Linear Inequalities and Absolute Value

2.1 Linear Inequalities in One Variable

2.2 Set Operations and Compound Inequalities

2.3 Absolute Value Equations and Inequalities

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

3.4 Linear Inequalities in Two Variables

3.5 Introduction to Relations and Functions

3.6 Function Notation and Linear Functions

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 Linear Systems of Equations

4.4 Solving Linear Systems of Equations by Matrix Methods

5. Exponents, Polynomials, and Polynomial Functions

5.1 Integer Exponents and Scientific Notation

5.2 Adding and Subtracting Polynomials

5.3 Polynomial Functions

5.4 Multiplying Polynomials

5.5 Dividing Polynomials

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

7. Rational Expressions

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

7.5 Applications of Rational Expressions

7.6 Variation

8. Roots, Radicals, and Root Functions

8.1 Rational 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

8.6 Solving Equations with Radicals

8.7 Complex Numbers

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

9.4 Formulas and Applications

9.5 Graphs of Quadratic Functions

9.6 More About Parabolas and Their Applications

9.7 Polynomial and Rational Inequalities

10. Inverse, Exponential, and Logarithmic Functions

10.1 Composition of Functions

10.2 Inverse Functions

10.3 Exponential Functions

10.4 Logarithmic Functions

10.5 Properties of Logarithms

10.6 Common and Natural Logarithms

10.7 Exponential and Logarithmic Equations and Their Applications

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 Other Functions Defined by Radicals

11.4 Nonlinear Systems of Equations

11.5 Second-Degree Inequalities and Systems of Inequalities

Appendix A: Review of Fractions Appendix B: Solving Systems of Linear Equations by Matrix Methods Appendix C: Synthetic Division Answers to Selected Exercises Solutions to Selected Exercises Index