Everyday math demystified by stan gibilisco (461 pages, 2004)

Everyday Math Demystified


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Everyday Math Demystified

STAN GIBILISCO

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DOI: 10.1036/0071431195


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CONTENTS

Preface

xv

PART 1:

EXPRESSING QUANTITIES

1

CHAPTER 1

Numbers and Arithmetic

3

Sets

6

Numbering Systems

8

CHAPTER 2

Integers

10

Rational, Irrational, and Real Numbers

14

Number Operations

19

More Principles Worth Memorizing

23

Still More Principles

26

Quiz

30

How Variables Relate

33

This versus That

33
vii

CONTENTS

viii

CHAPTER 3

CHAPTER 4

Simple Graphs

38

Tweaks, Trends, and Correlation

43

Quiz

49

Extreme Numbers

52

Subscripts and Superscripts

52

Power-of-10 Notation

54

In Action

60

Approximation and Precedence

65

Significant Figures

68

Quiz

71

How Things Are Measured

74

Systems of Units

75

Base Units in SI

76

Other Units in SI

83

Conversions

87

Quiz

91

Test: Part 1

93


CONTENTS

ix

PART 2:

FINDING UNKNOWNS

103

CHAPTER 5

Basic Algebra

105

Single-Variable Linear Equations

105

Two-by-Two Linear Equations

110

Quiz

116

More Algebra

119

Quadratic Equations

119

Beyond Reality

129

One-Variable, Higher-Order Equations

133

Quiz

140

A Statistics Sampler

143

Experiments and Variables

143

Populations and Samples

146

Distributions

149

More Definitions

154

Quiz

163

Taking Chances

165

The Probability Fallacy

165

CHAPTER 6

CHAPTER 7

CHAPTER 8


CONTENTS

x

Definitions

167

Properties of Outcomes

172

Permutations and Combinations

181

Quiz

184

Test: Part 2

187

PART 3:

SHAPES AND PLACES

197

CHAPTER 9

Geometry on the Flats

199

Fundamental Rules

199

Triangles

208

Quadrilaterals

214

Circles and Ellipses

223

Quiz

226

Geometry in Space

229

Points, Lines, and Planes

229

Straight-Edged Objects

235

Cones, Cylinders, and Spheres

240

Quiz

247

CHAPTER 10


CONTENTS
CHAPTER 11

xi

Graphing It

250

The Cartesian Plane

250

Straight Lines in the Cartesian Plane

254

The Polar Coordinate Plane

260

Some Examples

263

Quiz

271

A Taste of Trigonometry

274

More about Circles

274

Primary Circular Functions

277

Secondary Circular Functions

283

The Right Triangle Model

287

Pythagorean Extras

290

Quiz

292

Test: Part 3

295

PART 4:

MATH IN SCIENCE

307

CHAPTER 13

Vectors and 3D

309

Vectors in the Cartesian Plane

309

Rectangular 3D Coordinates

313

CHAPTER 12


CONTENTS

xii

CHAPTER 14

CHAPTER 15

Vectors in Cartesian Three-Space

316

Flat Planes in Space

323

Straight Lines in Space

326

Quiz

330

Growth and Decay

332

Growth by Addition

332

Growth by Multiplication

338

Exponential Functions

345

Rules for Exponentials

347

Logarithms

350

Rules for Logarithms

352

Graphs Based on Logarithms

355

Quiz

359

How Things Move

362

Mass and Force

362

Displacement

367

Speed and Velocity

368

Acceleration

373


CONTENTS

xiii

Momentum

378

Quiz

381

Test: Part 4

384

Final Exam

396

Answers to Quiz, Test, and
Exam Questions

424

Suggested Additional References

428

Index

431


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PREFACE

This book is for people who want to refine their math skills at the high-school
level. It can serve as a supplemental text in a classroom, tutored, or homeschooling environment. It should also be useful for career changers

who want to refresh or augment their knowledge. I recommend that you
start at the beginning and complete a chapter a week. An hour or two
daily ought to be enough time for this. When you’re done, you can use
this book as a permanent reference.
This course has an abundance of practice quiz, test, and exam questions.
They are all multiple-choice, and are similar to the sorts of questions used
in standardized tests. There is a short quiz at the end of every chapter.
The quizzes are ‘‘open-book.’’ You may (and should) refer to the chapter
texts when taking them. When you think you’re ready, take the quiz,
write down your answers, and then give your answers to a friend. Have the
friend tell you your score, but not which questions you got wrong.
The answers are listed in the back of the book. Stick with a chapter until
you get most of the answers correct.
This book is divided into multi-chapter sections. At the end of each
section, there is a multiple-choice test. Take these tests when you’re done
with the respective sections and have taken all the chapter quizzes. The
section tests are ‘‘closed-book,’’ but the questions are easier than those in
the quizzes. A satisfactory score is 75% or more correct. Again, answers are
in the back of the book.
There is a final exam at the end of this course. It contains questions drawn
uniformly from all the chapters. A satisfactory score is at least 75% correct
answers. With the section tests and the final exam, as with the quizzes, have
a friend tell you your score without letting you know which questions
you missed. That way, you will not subconsciously memorize the answers.
You can check to see where your knowledge is strong and where it is not.

xv
Copyright © 2004 by The McGraw-Hill Companies, Inc. Click here for terms of use.

PREFACE

xvi

When you’re finished with this supplemental course, you’ll have an
advantage over your peers. You’ll have the edge when it comes to figuring
out solutions to problems in a variety of situations people encounter in
today’s technological world. You’ll understand the ‘‘why,’’ as well as the
‘‘what’’ and the ‘‘how.’’
Suggestions for future editions are welcome.
Stan Gibilisco

Acknowledgments
Illustrations in this book were generated with CorelDRAW. Some of the clip
art is courtesy of Corel Corporation.
I extend thanks to Emma Previato of Boston University, who helped with
the technical editing of the manuscript.

Copyright © 2004 by The McGraw-Hill Companies, Inc. Click here for terms of use.


Everyday Math Demystified


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PART ONE

Expressing

Quantities

1
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CHAPTER

1

Numbers and
Arithmetic

Mathematics is expressed in language alien to people unfamiliar with it.
Someone talking about mathematics can sound like a rocket scientist.
Written mathematical documents are often laden with symbology. Before
you proceed further, look over Table 1-1. It will help you remember symbols
used in basic mathematics, and might introduce you to a few symbols you’ve
never seen before!
If at first some of this stuff seems theoretical and far-removed from ‘‘the
everyday world,’’ think of it as basic training, a sort of math boot camp. Or
better yet, think of it as the classroom part of drivers’ education. It was good
to have that training so you’d know how to read the instrument panel, find
the turn signal lever, adjust the mirrors, control the headlights, and read the
road signs. So get ready for a drill. Get ready to think logically. Get your
mind into math mode.

3
Copyright © 2004 by The McGraw-Hill Companies, Inc. Click here for terms of use.


PART 1 Expressing Quantities

4
Table 1-1

Symbols used in basic mathematics.

Symbol

Description

{}

Braces; objects between them are elements of a set

)

Logical implication; read ‘‘implies’’

()

Logical equivalence; read ‘‘if and only if ’’

8

Universal quantifier; read ‘‘for all’’ or ‘‘for every’’

9

Existential quantifier; read ‘‘for some’’

|

Logical expression; read ‘‘such that’’

&

Logical conjunction; read ‘‘and’’

N

The set of natural numbers

Z

The set of integers

Q

The set of rational numbers

R

The set of real numbers

1

The set with no elements; read ‘‘the empty set’’ or ‘‘the null set’’

\

Set intersection; read ‘‘intersect’’

[

Set union; read ‘‘union’’

&

Proper subset; read ‘‘is a proper subset of ’’



Subset; read ‘‘is a subset of ’’

2

Element; read ‘‘is an element of ’’ or ‘‘is a member of ’’

2
=

Non-element; read ‘‘is not an element of ’’ or ‘‘is not a member of ’’

¼

Equality; read ‘‘equals’’ or ‘‘is equal to’’

6¼

Not-equality; read ‘‘does not equal’’ or ‘‘is not equal to’’
(Continued )


CHAPTER 1 Numbers and Arithmetic
Table 1-1

Continued.

Symbol

Description

%

Approximate equality; read ‘‘is approximately equal to’’

<

Inequality; read ‘‘is less than’’
Weak inequality; read ‘‘is less than or equal to’’

>

Inequality; read ‘‘is greater than’’

!

Weak inequality; read ‘‘is greater than or equal to’’

þ

Addition; read ‘‘plus’’

À

Subtraction, read ‘‘minus’’

Â
Á

Multiplication; read ‘‘times’’ or ‘‘multiplied by’’

*
Ä
Quotient; read ‘‘over’’ or ‘‘divided by’’
/
Ratio or proportion; read ‘‘is to’’
:
Logical expression; read ‘‘such that’’
!

Product of all natural numbers from 1 up to a certain value; read ‘‘factorial’’

()

Quantification; read ‘‘the quantity’’

[]

Quantification; used outside ( )

{}

Quantification; used outside [ ]

5