Elementary Algebra: Graphs and Models Book

1. Introduction to Algebraic Expressions.

Introduction to Algebra.

The Commutative, Associative, and Distributive Laws.

Fraction Notation.

Positive and Negative Real Numbers.

Addition of Real Numbers.

Subtraction of Real Numbers.

Multiplication and Division of Real Numbers.

Exponential Notation and Order of Operations.

2. Equations, Inequalities, and Problem Solving.

Solving Equations.

Using the Principles Together.

Formulas.

Applications with Percent.

Problem Solving.

Solving Inequalities.

Solving Applications with Inequalities.

3. Graphs and Linear Equations.

Reading Graphs, Plotting Points, and Estimating Values.

Graphing Equations.

Solving Equations by Graphing.

Graphing and Intercepts.

Rates and Models.

Slope.

Slope-Intercept Form.

Point-Slope Form.

4. Systems of Equations and Problem Solving.

Systems of Equations and Graphing.

Systems of Equations and Substitution.

Systems of Equations and Elimination.

More Applications Using Systems.

Linear Inequalities in Two Variables.

Systems of Linear Inequalities.

5. Polynomials.

Exponents and Their Properties.

Polynomials.

Addition and Subtraction of Polynomials.

Multiplication of Polynomials.

Special Products.

Polynomials in Several Variables.

Division of Polynomials.

Negative Exponents and Scientific Notation.

6. Polynomials and Factoring.

Introduction to Factoring.

Factoring Trinomials of the Type x ² + bx + c.

Factoring Trinomials of the Type ax² + bx + c.

Factoring Perfect-Square Trinomials and Differences of Squares.

Factoring: A General Strategy.

Solving Quadratic Equations by Factoring.

Solving Applications.

7. Rational Expressions and Equations.

Rational Expressions.

Multiplication and Division.

Addition, Subtraction, and Least Common Denominators.

Addition and Subtraction with Unlike Denominators.

Complex Rational Expressions.

Solving Rational Equations.

Applications Using Rational Equations and Proportions.

Direct and Inverse Variation.

8. Radical Expressions and Equations.

Introduction to Square Roots and Radical Expressions.

Multiplying and Simplifying Radical Expressions.

Quotients Involving Square Roots.

Radical Expressions with Several Terms.

Radical Equations.

Applications Using Right Triangles.

Higher Roots and Rational Exponents.

9. Quadratic Equations.

Solving Quadratic Equations: The Principle of Square Roots.

Solving Quadratic Equations: Completing the Square.

The Quadratic Formula and Applications.

Formulas and Equations.

Complex Numbers as Solutions of Quadratic Equations.

Graphs of Quadratic Equations.

Functions.

Appendix A: Sets.

Appendix B: Factoring Sums or Differences of Cubes.

Table 1: Fractional and Decimal Equivalents.

Table 2: Squares and Square Roots.

Table 3: Geometric Formulas.