Flash Review Series: Algebra Book

UNIT 1. INTRODUCTION TO ALGEBRA.

1. Variables, Algebraic Expressions, and Equations.

Exponential Notation and Order of Operations: Inequality.

Variables, Algebraic Expressions, and Equations.

Real Numbers; Ordering of Real Numbers.

2. Operations on Real Numbers.

Addition and Subtraction of Real Numbers.

Multiplication and Division of Real Numbers.

The Commutative, Associative, and Distributive Properties.

Simplifying Expressions.

UNIT 2. LINEAR EQUATIONS AND INEQUALITIES IN ONE VARIABLE.

3. Introduction to Equations.

Linear Equations: Properties of Equality.

Using the Properties of Equality Together.

4. Applications of Linear Equations.

Solving an Application Problem.

Applications from Geometry: Solving for a Specified Variable.

Ratios and Proportions.

Applications of Ratios and Proportions.

5. Introduction to Linear Inequalities in One Variable.

Graphing Intervals on a Number Line.

Properties of Inequality.

Using the Properties of Inequality Together.

Solving Compound Inequalities.

6. Applications of Linear Inequalities.

Solving Applied Problems Using Linear Inequalities.

UNIT 3. LINES.

7. Linear Equations in Two Variables.

Linear Equations in Two Variables: Writing Solutions as an Ordered Pair.

Creating a Table of Values.

8. The Rectangular Coordinate System.

The Cartesian Plane.

Graphing Linear Equations.

Graphing Horizontal and Vertical Lines.

9. The Slope of a Line.

Finding the Slope of a Line Given Two Points.

Finding the Slope of a Line Given its Equation.

Slopes of Parallel and Perpendicular Lines.

UNIT 4. EXPONENTS AND POLYNOMIALS.

10. Introduction to Polynomials.

Classification of Polynomials: Evaluating Polynomials.

Addition and Subtraction of Polynomials.

11. Exponents.

The Product Rule and the Power Rule.

The Zero Power Rule: The Quotient Rule: Negative Exponents.

12. Multiplication and Division of Polynomials.

Multiplication of Polynomials.

Division of Polynomials.

13. Scientific Notation.

Expressing Numbers in Scientific Notation.

Multiplying and Dividing Using Scientific Notation.

UNIT 5. FACTORING AND RATIONAL EXPRESSIONS.

14. Factoring and Applications.

Greatest Common Factor and Factoring by Grouping.

Factoring Trinomials of the form x² + bx + c and ax² + bx + c.

Special Factoring Rules.

15. Solving Polynomial Equations.

Using the Zero Product Rule.

Problem Solving Using the Zero Product Rule.

16. Rational Expressions.

The Domain.

Simplifying Rational Expressions: Multiplication and Division of Rational Expressions.

Least Common Denominator: Addition and Subtraction of Rational Expressions.

Complex Fractions.

17. Rational Equations.

Solving Rational Equations.

Solving Applications Using Rational Equations.