Contents

Preface

1   Numbers of Algebra

Natural Numbers, Whole Numbers, and Integers

Rational, Irrational, and Real Numbers

Properties of the Real Numbers

2   Computation with Real Numbers

Comparing Numbers and Absolute Value

Addition and Subtraction of Signed Numbers

Multiplication and Division of Signed Numbers

3   Roots and Radicals

Squares, Square Roots, and Perfect Squares

Cube Roots and nth Roots

Simplifying Radicals

4   Exponentiation

Exponents

Natural Number Exponents

Zero and Negative Integer Exponents

Unit Fraction and Rational Exponents

5   Order of Operations

Grouping Symbols

PEMDAS

6   Algebraic Expressions

Algebraic Terminology

Evaluating Algebraic Expressions

Dealing with Parentheses

7   Rules for Exponents

Product Rule

Quotient Rule

Rules for Powers

Rules for Exponents Summary

8   Adding and Subtracting Polynomials

Terms and Monomials

Polynomials

Like Terms

Addition and Subtraction of Monomials

Combining Like Terms

Addition and Subtraction of Polynomials

9   Multiplying Polynomials

Multiplying Monomials

Multiplying Polynomials by Monomials

Multiplying Binomials

The FOIL Method

Multiplying Polynomials

Special Products

10   Simplifying Polynomial Expressions

Identifying Polynomial Expressions

Simplifying Polynomial Expressions

11   Dividing Polynomials

Dividing a Polynomial by a Monomial

Dividing a Polynomial by a Polynomial

12   Factoring Polynomials

Factoring and Its Objectives

Greatest Common Factor

GCF with a Negative Coefficient

A Quantity as a Common Factor

Factoring Four Terms

Factoring Quadratic Trinomials

Factoring Perfect Trinomial Squares

Factoring Binomials

Guidelines for Factoring

13   Rational Expressions

Reducing Algebraic Fractions to Lowest Terms

Multiplying Algebraic Fractions

Dividing Algebraic Fractions

Adding (or Subtracting) Algebraic Fractions, Like Denominators

Adding (or Subtracting) Algebraic Fractions, Unlike Denominators

Simplifying Complex Fractions

14   Solving Linear Equations and Inequalities

Solving One-Variable Linear Equations

Solving Two-Variable Linear Equations for a Specific Variable

Solving One-Variable Linear Inequalities

15   Solving Quadratic Equations

Solving Quadratic Equations of the Form ax2 + c = 0

Solving Quadratic Equations by Factoring

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Using the Quadratic Formula

16   The Cartesian Coordinate Plane

Definitions for the Plane

Ordered Pairs in the Plane

Quadrants of the Plane

Finding the Distance Between Two Points in the Plane

Finding the Midpoint Between Two Points in the Plane

Finding the Slope of a Line Through Two Points in the Plane

Slopes of Parallel and Perpendicular Lines

17   Graphing Linear Equations

Properties of a Line

Graphing a Linear Equation That Is in Standard Form

Graphing a Linear Equation That Is in Slope-y-Intercept Form

18   The Equation of a Line

Determining the Equation of a Line Given the Slope and y-Intercept

Determining the Equation of a Line Given the Slope and One Point on the Line

Determining the Equation of a Line Given Two Distinct Points on the Line

19   Basic Function Concepts

Representations of a Function

Terminology of Functions

Some Common Functions

20   Systems of Equations

Solutions to a System of Equations

Solving a System of Equations by Substitution

Solving a System of Equations by Elimination

Solving a System of Equations by Graphing

21   Signal Words and Phrases

Common Signal Words and Phrases for Addition

Common Signal Words and Phrases for Subtraction

Common Signal Words and Phrases for Multiplication

Common Signal Words and Phrases for Division

Common Signal Words and Phrases for Equality

22   Word Problems

Algebraic Problem-Solving Process

Be Careful with Units

Age Relationships

Consecutive Numbers

Ratios

Mixtures

Coins

Rate-Time-Distance

Work

Percentage

Simple Interest

Number Relationships

Geometric Shapes

Appendix: Measurement Units and Conversions

Answer Key

Index