Elementary and Intermediate Algebra

Table of Contents



1. Review of Real Numbers

1.1 Integers, Opposites, and Absolute Values

1.2 Operations with Integers

1.3 Fractions

1.4 Operations with Fractions

1.5 Decimals and Percents

1.6 Representing Data Graphically

1.7 Exponents and Order of Operations

1.8 Introduction to Algebra

2. Linear Equations

2.1 Introduction to Linear Equations

2.2 Solving Linear Equations; A General Strategy

2.3 Problem Solving; Applications of Linear Equations

2.4 Applications Involving Percentages; Ratio and Proportion

2.5 Linear Inequalities

3. Graphing Linear Equations

3.1 The Rectangular Coordinate System; Equations in Two Variables

3.2 Graphing Linear Equations and Their Intercepts

3.3 Slope of a Line

3.4 Linear Functions

3.5 Parallel and Perpendicular Lines

3.6 Equations of Lines

3.7 Linear Inequalities

4. Systems of Equations

4.1 Systems of Linear Equations; Solving Systems Graphically

4.2 The Substitution Method for Solving Systems of Equations

4.3 Solving Systems of Equations by the Addition Method

4.4 Applications of Systems of Equations

4.5 Systems of Linear Inequalities

5. Exponents and Polynomials

5.1 Exponents

5.2 Negative Exponents and Scientific Notation

5.3 Polynomials; Addition and Subtraction of Polynomials

5.4 Multiplying Polynomials

5.5 Division of Polynomials
6. Factoring and Quadratic Equations

6.1 An Introduction to Factoring: The Greatest Common Factor, Factoring by Grouping

6.2 Factoring Trinomials of the Form x2 + bx --+ c

6.3 Factoring Trinomials of the Form ax2 + bx --+ c

6.4 Factoring Special Binomials

6.5 Factoring Polynomials: A General Strategy

6.6 Solving Quadratic Equations by Factoring

6.7 Quadratic Functions

6.8 Applications of Quadratic Equations and Quadratic Functions

7. Rational Expressions and Equations

7.1 Rational Expressions and Functions

7.2 Multiplication and Division of Rational Expressions

7.3 Addition and Subtraction of Rational Expressions
with the Same Denominator

7.4 Addition and Subtraction of Rational Expressions
with Unlike Denominators

7.5 Complex Fractions; Simplifying Rational Expressions

7.6 Rational Equations

7.7 Applications of Rational Equations

8. Transition

8.1 Linear Equations and Absolute Value Equations

8.2 Linear Inequalities and Absolute Value Inequalities

8.3 Graphing Linear Equations and Functions; Graphing Absolute Value Functions

8.4 Review of Factoring, Quadratic Equations and Rational Equations

8.5 Systems of Equations (Two Equations in Two Unknowns, Three Equations in Three Unknowns)

9. Radical Expressions and Equations

9.1 Square Roots, Radical Notation

9.2 Rational Exponents

9.3 Simplifying Radical Expressions; Adding and Subtracting Radical Expressions
9.4 Multiplication and Division of Radical Expressions

9.5 Radical Equations

9.6 Applications of Radical Equations

9.7 The Complex Numbers

10. Quadratic Equations

10.1 Solving Quadratic Equations by Extracting Square Roots;
Completing the Square

10.2 Quadratic Formula

10.3 Applications of Quadratic Equations

10.4 Equations that are Quadratic in Form

10.5 Graphing Quadratic Equations and Quadratic Functions

10.6 Quadratic and Rational Inequalities

11. Functions

11.1 General Introduction to Functions

11.2 Linear Functions

11.3 Quadratic Functions

11.4 Other Functions and Their Graphs

11.5 Algebra of Functions

11.6 Inverse Functions

12. Logarithmic and Exponential Functions

12.1 Exponential Functions

12.2 Logarithmic Functions

12.3 Properties of Logarithms

12.4 Exponential and Logarithmic Equations

12.5 Applications of Exponential and Logarithmic Functions

12.6 Graphing Exponential and Logarithmic Functions

13. Conic Sections

13.1 Parabolas

13.2 Circles

13.3 Ellipses

13.4 Hyperbolas

13.5 Nonlinear Systems of Equations
14. Sequences, Series, and the Binomial Theorem

14.1 Sequences and Series

14.2 Arithmetic Sequences and Series

14.3 Geometric Sequences and Series

14.4 The Binomial Theorem



Appendixes

A1. Synthetic Division

A2. Systems of Equations and Matrices