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The Complete Idiot's Guide To Precalculus

by: Kelley, W. Michael

The Complete Idiot's Guide To Precalculus

by: Kelley, W. Michael

ISBN 13:
9781592573011
ISBN 10:
1592573010
Format: Paperback
Copyright: 06/07/2005
Publisher: Alpha

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Summary

You're no idiot, of course. At least, you never felt that way until precalculus came along. But now the equations are getting harder, there's this thing called trigonometry that you can't quite pin down, and every time someone says "hyperbola," you get a nervous twitch.

Part 1: A Preponderance of Prioritized Precalculus Prerequisites

(84)

Reviewing Numbers and Arithmetic

(12)

Number Classifications

(2)

Algebraic Properties

(2)

Exponential Rules

(2)

Radical Expressions

(5)

Fractional Powers

(1)

Simplifying Radical Expressions

(4)

Equations and Inequalities

(14)

Solving Equations in One Variable

(1)

Writing Equations of Lines

(3)

Graphing Linear Equations

(2)

Solving Linear Inequalities

(3)

Interval Notation

(2)

Simple Inequalities Taste Like Chicken

(1)

Absolute Value Inequalities

(4)

Less Than Inequalities

(2)

Greater Than Inequalities

(2)

Practicing with Polynomials

(14)

Polynomial Classifications

(1)

Adding and Subtracting Polynomials

(2)

Multiplying Polynomials

(2)

Long Division of Polynomials

(2)

Synthetic Division

(2)

Complex Numbers

(4)

Factoring Polynomials

(12)

Greatest Common Factors

(4)

Finding Greatest Common Factors of Integers

(2)

Finding Greatest Common Factors of Polynomials

(2)

Factoring by Grouping

(1)

Common Factor Patterns

(2)

Factoring Quadratic Trinomials

(1)

The Bomb Method of Factoring Trinomials

(3)

Rational Expressions and Weird Inequalities

(14)

Adding and Subtracting Rational Expressions

(4)

The Least Common Denominator

(2)

Combining Rational Expressions

(2)

Multiplying Rational Expressions

(1)

Dividing Rational Expressions

(1)

Solving Rational Equations

(2)

Graphing Weird Inequalities

(5)

Quadratic Inequalities

(2)

Rational Inequalities

(2)

Functions

(16)

Combining Functions

(3)

Operations on Functions

(1)

Composition of Functions

(1)

Graphing Functions

(6)

Four Important Function Graphs

(1)

Function Transformations

(4)

Inverse Functions

(2)

Inverse Function Behavior

(2)

Creating an Inverse Function

(1)

Asymptotes of Rational Functions

(5)

Part 2: Nonlinear Equations and Functions

(42)

High-Powered Functions and Equations

(14)

Solving Quadratic Equations

(3)

Completing the Square

(2)

The Quadratic Formula

(1)

Finding Roots Forensically

(5)

Equations vs. Functions

(1)

The Fundamental Theorem of Algebra

(1)

Leading Coefficient Test

(1)

Descartes' Rule of Signs

(2)

Rational Root Test

(1)

Wrapping Up the Case

(4)

Logarithmic Functions

101

(12)

Evaluating Logarithms

102

(1)

Graphs of Logarithms

103

(4)

Common and Natural Logarithms

107

(1)

Change of Base Formula

108

(2)

Logarithmic Properties

110

(3)

Exponential Functions

113

(14)

Graphing Exponential Functions

114

(3)

The Logarithmic/Exponential Balance of Power

117

(2)

Solving Logarithmic and Exponential Equations

119

(4)

Exponential Growth and Decay

123

(4)

Part 3: Trigonometry

127

(74)

Tangling with Angles

129

(16)

Angles in the Coordinate Plane

130

(2)

Measuring Angles

132

(3)

Degrees and Radians

132

(2)

Converting Between Degrees and Radians

134

(1)

Coterminal Angles

135

(2)

Right Triangle Trigonometry

137

(3)

The Unit Circle

140

(5)

Graphing Trigonometric Functions

145

(14)

Periodic Functions

146

(2)

Graphing Sine and Cosine

148

(5)

Connect the Dots for Fun and Profit

149

(2)

Cosine's Time to Shine

151

(1)

Graphing Trig Transformations

151

(2)

Meet the Rest of the Family

153

(6)

Tangent

154

(1)

Cotangent

155

(1)

Secant and Cosecant

156

(3)

Trigonometric Identities

159

(12)

Basic Training

160

(4)

Sign Identities

160

(1)

Cofunction Identities

161

(1)

Reciprocal Identities

162

(1)

Pythagorean Identities

163

(1)

Advanced Training: Simplifying Trigonometric Expressions

164

(2)

Proving Identities

166

(2)

Identities with Guts

168

(3)

Sum and Difference Formulas

169

(1)

Double-Angle Identities

169

(2)

Solving Trigonometric Equations

171

(12)

Inverse Trigonometric Functions

172

(3)

Is That Your Final Answer?

175

(1)

Basic Equations

176

(1)

Quadratic Equations

177

(1)

Mismatched and Needy Equations

178

(2)

Needy Equations with Squares

178

(1)

Needy Equations Without Squares

179

(1)

Equations with Multiple Angles

180

(3)

Oblique Triangle Theorems

183

(18)

Checking References for Unfriendly Angles

184

(5)

Behold the Bowtie

184

(4)

Tying in Trig Functions

188

(1)

Obliterating Oblique Triangles

189

(7)

The Law of Cosines

191

(2)

The Law of Sines

193

(3)

Calculating an Oblique Triangle Area

196

(5)

SAS Triangles

197

(1)

SSS Triangles

198

(3)

Part 4: Conic Sections

201

(32)

Parabolas and Circles

203

(16)

Introducing Conic Sections

204

(2)

Polishing Off Parabolas

206

(9)

Quadratics Containing an x2 Term

207

(5)

Quadratics Containing a y2 Term

212

(3)

The Vicious Circle

215

(4)

Ellipses and Hyperbolas

219

(14)

Eclipsing Ellipses

220

(7)

Elliptical Anatomy

221

(1)

Standard Form of an Ellipse

222

(4)

Calculating Eccentricity

226

(1)

Handling Hyperbolas

227

(6)

Freshly Popped Hyperbola Parts

228

(1)

Standard Form of a Hyperbola

229

(4)

Part 5: Matrices and a Mathematical Montage

233

(92)

Matrix Operations and Calculations

235

(14)

Adding and Subtracting Matrices

236

(2)

Multiplying Matrices

238

(1)

Calculating Determinants Using Shortcuts

239

(3)

2 x 2 Matrices

240

(1)

3 x 3 Matrices

241

(1)

Calculating Determinants Using Expansions

242

(4)

Calculating Minors and Cofactors

243

(1)

Expanding Rows and Columns

244

(2)

Cramer's Rule

246

(3)

The Jagged Little Red Pill of Matrix Applications

249

(18)

Miscellaneous Matrix Matters

250

(2)

Augmented Matrices

250

(1)

The Identity Matrix

251

(1)

Matrix Row Operations

252

(2)

Row-Echelon Form

254

(3)

Reduced Row-Echelon Form

257

(2)

Why Row-Echelon Forms Even Exist

259

(2)

Inverse Matrices

261

(2)

Solving Matrix Equations

263

(4)

Final Exam

267

(58)

Chapter 1

268

(1)

Chapter 2

268

(1)

Chapter 3

269

(1)

Chapter 4

269

(1)

Chapter 5

270

(1)

Chapter 6

270

(1)

Chapter 7

270

(1)

Chapter 8

271

(1)

Chapter 9

271

(1)

Chapter 10

272

(1)

Chapter 11

273

(1)

Chapter 12

273

(1)

Chapter 13

274

(1)

Chapter 14

274

(1)

Chapter 15

275

(1)

Chapter 16

275

(1)

Chapter 17

275

(1)

Chapter 18

276

(1)

Solutions

276

(9)

Appendixes

A Solutions to ``You've Got Problems'' Sidebars

285

(30)

B Glossary

315

(10)

Index

325

Amazon no longer offers textbook rentals. We do!

The Complete Idiot's Guide To Precalculus

The Complete Idiot's Guide To Precalculus

9781592573011

1592573010

Summary

Author Biography

Table of Contents

Supplemental Materials

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