Elementary and Intermediate Algebra

1 Real Numbers and Their Properties

1.1 The Real Numbers

1.2 Fractions

1.3 Addition and Subtraction of Real Numbers

1.4 Multiplication and Division of Real Numbers

1.5 Exponential Expressions and the Order of Operations

1.6 Algebraic Expressions

1.7 Properties of the Real Numbers

1.8 Using the Properties to Simplify Expressions

2 Linear Equations and Inequalities in One Variable

2.1 The Addition and Multiplication Properties of Equality

2.2 Solving General Linear Equations

2.3 More Equations

2.4 Formulas

2.5 Translating Verbal Expressions into Algebraic Expressions

2.6 Number, Geometric, and Uniform Motion Applications

2.7 Discount, Investment, and Mixture Applications

2.8 Inequalities

2.9 Solving Inequalities and Applications

3 Linear Equations and Inequalities in Two Variables

3.1 Graphing Lines in the Coordinate Plane

3.2 Slope

3.3 Equations of Lines in Slope-Intercept Form

3.4 The Point-Slope Form

3.5 Variation

3.6 Graphing Linear Inequalities in Two Variables

4 Polynomials and Exponents

4.1 Addition and Subtraction of Polynomials

4.2 Multiplication of Polynomials

4.3 Multiplication of Binomials

4.4 Special Products

4.5 Division of Polynomials

4.6 Nonnegative Integral Exponents

4.7 Negative Exponents and Scientific Notation

5 Factoring

5.1 Factoring Out Common Factors

5.2 Factoring the Special Products and Factoring by Grouping

5.3 Factoring ax2 + bx + c with a = 1

5.4 Factoring ax2 + bx + c with a 1

5.5 Factoring a Difference or Sum of Two Cubes

5.6 Solving Quadratic Equations by Factoring

6 Rational Expressions

6.1 Reducing Rational Expressions

6.2 Multiplication and Division

6.3 Finding the Least Common Denominator

6.4 Addition and Subtraction

6.5 Complex Fractions

6.6 Solving Equations with Rational Expressions

6.7 Applications of Ratios and Proportions

6.8 Applications of Rational Expressions

7 Systems of Linear Equations

7.1 Solving Systems by Graphing and Substitution

7.2 The Addition Method

7.3 Systems of Linear Equations in Three Variables

7.4 Solving Linear Systems Using Matrices

7.5 Determinants and Cramers Rule

8 More on Inequalities

8.1 Compound Inequalities in One Variable

8.2 Absolute Value Equations and Inequalities

8.3 Compound Inequalities in Two Variables

8.4 Linear Programming

9 Radicals and Rational Exponents

9.1 Radicals

9.2 Rational Exponents

9.3 Operations with Radicals

9.4 Quotients, Powers, and Rationalizing Denominators

9.5 Solving Equations with Radicals and Exponents

9.6 Complex Numbers

10 Quadratic Equations and Inequalities

10.1 Factoring and Completing the Square

10.2 The Quadratic Formula

10.3 Graphing Parabolas

10.4 More on Quadratic Equations

10.5 Quadratic and Rational Inequalities

11 Functions

11.1 Functions and Relations

11.2 Graphs of Functions and Relations

11.3 Transformations of Graphs

11.4 Graphs of Polynomial Functions

11.5 Graphs of Rational Functions

11.6 Combining Functions

11.7 Inverse Functions

12 Exponential and Logarithmic Functions

12.1 Exponential Functions and Their Applications

12.2 Logarithmic Functions and Their Applications

12.3 Properties of Logarithms

12.4 Solving Equations and Applications

13 Nonlinear Systems and the Conic Sections

13.1 Nonlinear Systems of Equations

13.2 The Parabola

13.3 The Circle

13.4 The Ellipse and Hyperbola

13.5 Second-Degree Inequalities

14 Sequences and Series

14.1 Sequences

14.2 Series

14.3 Arithmetic Sequences and Series

14.4 Geometric Sequences and Series

14.5 Binomial Expansions

A Diagnostic Test

B Chapters 1-6 Review

C Sets

D Geometry Review Exercises