MATH 10021 Core Mathematics I

MATH 10021

Core Mathematics I



Department of Mathematical Sciences Kent State University July 23, 2010

2

Contents

1 Real Numbers and Their Operations

5

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2 Integers, Absolute Values and Opposites . . . . . . . . . . . . 19

1.3 Integer Addition and Subtraction . . . . . . . . . . . . . . . . 36

1.4 Integer Multiplication and Division . . . . . . . . . . . . . . . 55

1.5 Order of Operations . . . . . . . . . . . . . . . . . . . . . . . 62

1.6 Primes, GCF, & LCM . . . . . . . . . . . . . . . . . . . . . . 77

1.7 Fractions and Mixed Numbers . . . . . . . . . . . . . . . . . . 91

1.8 Fraction Addition and Subtraction . . . . . . . . . . . . . . . 125

1.9 Fraction Multiplication and Division . . . . . . . . . . . . . . 146

1.10 Decimals and Percents . . . . . . . . . . . . . . . . . . . . . . 162

1.11 Decimal Operations . . . . . . . . . . . . . . . . . . . . . . . 189

1.12 Introduction to Radicals . . . . . . . . . . . . . . . . . . . . . 207

1.13 Properties of Real Numbers . . . . . . . . . . . . . . . . . . . 216

2 Algebra

229

2.1 Variables and Algebraic Expressions . . . . . . . . . . . . . . 229

2.2 Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . 241

2.3 Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . 260

2.4 Proportions and Conversion Factors . . . . . . . . . . . . . . 270

2.5 Linear Inequalities . . . . . . . . . . . . . . . . . . . . . . . . 285

3 Graphing and Lines

299

3.1 Cartesian Coordinate System . . . . . . . . . . . . . . . . . . 299

3.2 Graphing Linear Equations . . . . . . . . . . . . . . . . . . . 312

3.3 Function Notation . . . . . . . . . . . . . . . . . . . . . . . . 323

3.4 Slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334

3.5 Equations of Lines . . . . . . . . . . . . . . . . . . . . . . . . 348

3

4

A Real Number Operations B Multiplying or Dividing Mixed Numbers C Answers to Exercises

CONTENTS

361 365 369

Chapter 1

Real Numbers and Their Operations

1.1 Introduction

Welcome to Core Mathematics I (Math 10021) or Core Mathematics I and II (Math 10006)! Beginnings are always difficult, as you and your fellow students may have a wide range of backgrounds in previous math courses, and may differ greatly in how long it has been since you last did math. So, to start, we want to suggest some ground rules, refresh your memory on some basics, and demonstrate what you are expected to know already. Let's start with the ground rules.

First, this course will be easier if you keep up with the material. Math often builds upon itself, so if you don't understand one section, the next section may be impossible. To avoid this, practice, practice, practice, and get help from a tutor or the instructor immediately if you are having trouble. This book has many problems after each section with answers to all in the back, so feel free to do more than what is assigned to be collected! The student who shows up an hour prior to the exam and tells the instructor that they need to go over everything is going to be sorely disappointed.

Second, please do NOT ask your instructor "When am I ever going to use this?", as this may lead him or her to develop nervous tics or to begin muttering under his or her breath. This is college, and the student's role at college is to acquire knowledge. Some of the material in this book may have obvious applications in your future job, some may have surprising applications, and some you may never use again. ALL OF IT is required to pass this course!

5

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download