Everyday math demystified

Everyday Math Demystified

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Everyday Math Demystified

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Statistics Demystified

Trigonometry Demystified

Everyday Math Demystified

STAN GIBILISCO

McGRAW-HILL

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CONTENTS

Preface xv

PART 1: EXPRESSING QUANTITIES 1

CHAPTER 1 Numbers and Arithmetic 3

Sets 6

Numbering Systems 8

Integers 10

Rational, Irrational, and Real Numbers 14

Number Operations 19

More Principles Worth Memorizing 23

Still More Principles 26

Quiz 30

CHAPTER 2 How Variables Relate 33

This versus That 33

vii

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Simple Graphs 38

Tweaks, Trends, and Correlation 43

Quiz 49

CHAPTER 3 Extreme Numbers 52

Subscripts and Superscripts 52

Power-of-10 Notation 54

In Action 60

Approximation and Precedence 65

Significant Figures 68

Quiz 71

CHAPTER 4 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

viii CONTENTS

PART 2: FINDING UNKNOWNS 103

CHAPTER 5 Basic Algebra 105

Single-Variable Linear Equations 105

Two-by-Two Linear Equations 110

Quiz 116

CHAPTER 6 More Algebra 119

Quadratic Equations 119

Beyond Reality 129

One-Variable, Higher-Order Equations 133

Quiz 140

CHAPTER 7 A Statistics Sampler 143

Experiments and Variables 143

Populations and Samples 146

Distributions 149

More Definitions 154

Quiz 163

CHAPTER 8 Taking Chances 165

The Probability Fallacy 165

CONTENTS ix

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

CHAPTER 10 Geometry in Space 229

Points, Lines, and Planes 229

Straight-Edged Objects 235

Cones, Cylinders, and Spheres 240

Quiz 247

x CONTENTS

CHAPTER 11 Graphing It 250

The Cartesian Plane 250

Straight Lines in the Cartesian Plane 254

The Polar Coordinate Plane 260

Some Examples 263

Quiz 271

CHAPTER 12 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

CONTENTS xi

Vectors in Cartesian Three-Space 316

Flat Planes in Space 323

Straight Lines in Space 326

Quiz 330

CHAPTER 14 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

CHAPTER 15 How Things Move 362

Mass and Force 362

Displacement 367

Speed and Velocity 368

Acceleration 373

xii CONTENTS

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

CONTENTS xiii