Elementary and Intermediate Algebra

Table of Contents

1. Foundations of Algebra
   • 1.1 Number Sets and the Structure of Algebra
   • 1.2 Fractions
   • 1.3 Adding and Subtracting Real Numbers; Properties of Real Numbers
   • 1.4 Multiplying and Dividing Real Numbers; Properties of Real Numbers
   • 1.5 Exponents, Roots, and Order of Operations
   • 1.6 Translating Word Phrases to Expressions
   • 1.7 Evaluating and Rewriting Expressions
2. Solving Linear Equations and Inequalities
   • 2.1 Equations, Formulas, and the Problem-Solving Process
   • 2.2 The Addition Principle of Equality
   • 2.3 The Multiplication Principle of Equality
   • 2.4 Applying the Principles to Formulas
   • 2.5 Translating Word Sentences to Equations
   • 2.6 Ratios and Proportions
   • 2.7 Percents
   • 2.8 Solving Linear Inequalities
3. Graphing Linear Equations and Inequalities
   • 3.1 The Rectangular Coordinate System
   • 3.2 Graphing Linear Equations
   • 3.3 Graphing Using Intercepts
   • 3.4 Slope–Intercept Form
   • 3.5 Point–Slope Form
   • 3.6 Graphing Linear Inequalities
   • 3.7 Introduction to Functions and Function Notation
4. Systems of Linear Equations and Inequalities
   • 4.1 Solving Systems of Linear Equations Graphically
   • 4.2 Solving Systems of Linear Equations by Substitution; Applications
   • 4.3 Solving Systems of Linear Equations by Elimination; Applications
   • 4.4 Solving Systems of Linear Equations in Three Variables; Applications
   • 4.5 Solving Systems of Linear Equations Using Matrices
   • 4.6 Solving Systems of Linear Inequalities
5. Polynomials
   • 5.1 Exponents and Scientific Notation
   • 5.2 Introduction to Polynomials
   • 5.3 Adding and Subtracting Polynomials
   • 5.4 Exponent Rules and Multiplying Monomials
   • 5.5 Multiplying Polynomials; Special Products
   • 5.6 Exponent Rules and Dividing Polynomials
6. Factoring
   • 6.1 Greatest Common Factor and Factoring by Grouping
   • 6.2 Factoring Trinomials of the Form x² + bx + c
   • 6.3 Factoring Trinomials of the Form ax² + bx + c, where a ≠ 1
   • 6.4 Factoring Special Products
   • 6.5 Strategies for Factoring
   • 6.6 Solving Quadratic Equations by Factoring
   • 6.7 Graphs of Quadratic Equations and Functions
7. Rational Expressions and Equations
   • 7.1 Simplifying Rational Expressions
   • 7.2 Multiplying and Dividing Rational Expressions
   • 7.3 Adding and Subtracting Rational Expressions with the Same Denominator
   • 7.4 Adding and Subtracting Rational Expressions with Different Denominators
   • 7.5 Complex Rational Expressions
   • 7.6 Solving Equations Containing Rational Expressions
   • 7.7 Applications with Rational Expressions, Including Variation
8. More on Inequalities, Absolute Value, and Functions
   • 8.1 Compound Inequalities
   • 8.2 Equations Involving Absolute Value; Absolute Value Functions
   • 8.3 Inequalities Involving Absolute Value
9. Rational Exponents, Radicals, and Complex Numbers
   • 9.1 Radical Expressions and Functions
   • 9.2 Rational Exponents
   • 9.3 Multiplying, Dividing, and Simplifying Radicals
   • 9.4 Adding, Subtracting, and Multiplying Radical Expressions
   • 9.5 Rationalizing Numerators and Denominators of Radical Expressions
   • 9.6 Radical Equations and Problem Solving
   • 9.7 Complex Numbers
10. Quadratic Equations and Functions
    • 10.1 The Square Root Principle and Completing the Square
    • 10.2 Solving Quadratic Equations Using the Quadratic Formula
    • 10.3 Solving Equations That Are Quadratic in Form
    • 10.4 Graphing Quadratic Functions
    • 10.5 Solving Nonlinear Inequalities
    • 10.6 Function Operations
11. Exponential and Logarithmic Functions
    • 11.1 Composite and Inverse Functions
    • 11.2 Exponential Functions
    • 11.3 Logarithmic Functions
    • 11.4 Properties of Logarithms
    • 11.5 Common and Natural Logarithms
    • 11.6 Exponential and Logarithmic Equations with Applications
12. Conic Sections
    • 12.1 Parabolas and Circles
    • 12.2 Ellipses and Hyperbolas
    • 12.3 Nonlinear Systems of Equations
    • 12.4 Nonlinear Inequalities and Systems of Inequalities
13. R. Elementary Algebra Review

Appendices

1. Mean, Median, and Mode
2. Arithmetic Sequences and Series
3. Geometric Sequences and Series
4. The Binomial Theorem
5. Synthetic Division
6. Solving Systems of Linear Equations Using Cramer’s Rule