Homework Helpers: Algebra, Revised Edition

by Denise Szecsei

Overview

Homework Helpers: Algebra is a straightforward and easy-to-read review of arithmetic skills emphasizes the role that arithmetic plays in the development of algebra covering all of the topics in a typical Algebra I class, including:

Solving linear equalities and inequalities

Solving systems of linear equations

Factoring polynomials

Graphing functions

Working with rational functions

Solving quadratic equations

Understanding word problems

Homework Helpers: Algebra will help build a solid mathematical foundation and enable students to gain the confidence they need to study Algebra II. This book also contains a summary of important formulas for easy reference.

Product Details

ISBN-13:	9781601631695
Publisher:	Red Wheel/Weiser
Publication date:	09/15/2011
Series:	Homework Helpers
Edition description:	Second Edition, Revised
Pages:	256
Product dimensions:	6.00(w) x 8.90(h) x 0.80(d)

About the Author

Denise Szecsei earned BS degrees in Physics, Chemistry and Mathematics from the University of Redlands. She served four years as a technical instructor in the U.S. Navy before she went on to receive her doctorate degree in Mathematics from the Florida State University. She has been teaching since 1985 and is currently teaching Mathematics at Stetson University. She is the author of Homework Helpers: Algebra, Calculus, and Trigonometry.

Table of Contents

Preface 11

Capter 1 Numbers 13

Lesson 1-1 Types of Numbers 14

Lesson 1-2 Operations and Symbols 19

Lesson 1-3 Properties of Real Numbers 20

Lesson 1-4 Properties of Zero and One 23

Lesson 1-5 Absolute Value 26

Lesson 1-6 Manipulating Rational Numbers 27

Lesson 1-7 The Order of Operations 34

Lesson 1-8 The Distributive Property 35

Lesson 1-9 Evaluating Expressions 37

Chapter 2 Exponents 41

Lesson 2-1 Positive Integer Powers 41

Lesson 2-2 Rules for Exponents 45

Lesson 2-3 Negative Integer Powers 49

Lesson 2-4 Zero as an Exponent 51

Lesson 2-5 Powers of Quotients and Products 52

Lesson 2-6 Scientific Notation 54

Chapter 3 Equations and Equality 59

Lesson 3-1 Equations 59

Lesson 3-2 Equality 60

Lesson 3-3 Algebraic Properties of Equality 62

Lesson 3-4 Solving Linear Equations in One Step 63

Lesson 3-5 Solving Linear Equations Using Several Steps 68

Lesson 3-6 Equations Involving Absolute Value 74

Chapter 4 Inequalities and Graphs 81

Lesson 4-1 Properties of Inequalities 83

Lesson 4-2 Solving Inequalities in One Step 84

Lesson 4-3 Solving Inequalities Using Several Steps 88

Lesson 4-4 Graphing Inequalities Using the Number Line 90

Lesson 4-5 Graphing Compound Inequalities 95

Lesson 4-6 Inequalities and Absolute Value 97

Chapter 5 Relations, Functions, and Graphs 105

Lesson 5-1 Relations 105

Lesson 5-2 Functions 107

Lesson 5-3 Formulas 108

Lesson 5-4 Tables 109

Lesson 5-5 The Cartesian Coordinate System 110

Lesson 5-6 Graphs of Functions and Relations 114

Chapter 6 Linear Equations 121

Lesson 6-1 Linear Functions and Calculating Slopes 121

Lesson 6-2 Intercepts 127

Lesson 6-3 Point-Slope Form 129

Lesson 6-4 Slope-Intercept Form 130

Lesson 6-5 Standard Form 132

Lesson 6-6 Horizontal and Vertical Lines 135

Lesson 6-7 Graphing Linear Equations 138

Chapter 7 Systems of Linear Equations 147

Lesson 7-1 The Graphical Method 148

Lesson 7-2 The Substitution/Elimination Method 150

Lesson 7-3 The Addition/Subtraction Method 153

Chapter 8 Monomials and Polynomials 161

Lesson 8-1 Terminology 161

Lesson 8-2 Adding and Subtracting Monomials 163

Lesson 8-3 Multiplying and Dividing Monomials 164

Lesson 8-4 Monomials as the Base of an Exponential Expression 167

Lesson 8-5 Adding and Subtracting Polynomials 168

Lesson 8-6 Multiplying Polynomials 170

Lesson 8-7 Special Products 173

Lesson 8-8 Dividing Polynomials by Monomials 176

Lesson 8-9 Factoring Techniques 177

Lesson 8-10 Solving Factored Equations 180

Chapter 9 Quadratic Equations 185

Lesson 9-1 Square Roots 185

Lesson 9-2 The Difference Between Two Squares 188

Lesson 9-3 Factoring Quadratic Expressions of the Form X² + bx + c 193

Lesson 9-4 Factoring Quadratic Expressions in General 197

Lesson 9-5 Solving Quadratic Equations by Factoring 200

Lesson 9-6 Solving Quadratic Equations by Completing the Square 202

Lesson 9-7 Solving Quadratic Equations Using the Quadratic Formula 206

Chapter 10 Rational Expressions 213

Lesson 10-1 Simplifying Rational Expressions 213

Lesson 10-2 Multiplying Rational Expressions 216

Lesson 10-3 Dividing Rational Expressions 217

Lesson 10-4 Adding and Subtracting Rational Expressions 219

Chapter 11 Applications 225

Lesson 11-1 How to Approach Word Problems 225

Lesson 11-2 Rates and Percentages 227

Lesson 11-3 Finding Integers 229

Lesson 11-4 Rate, Time, and Distance Problems 232

Lesson 11-5 Money Problems 234

Lesson 11-6 Mixture Problems 236

Final Exam 241

Index 251

About the Author 255