Must Know High School Pre-Calculus

by Christopher Monahan

Overview

The new Must Know series is like a lightning bolt to the brain

Every school subject has must know ideas, or essential concepts, that lie behind it. This book will use that fact to help you learn in a unique way. Most study guides start a chapter with a set of goals, often leaving the starting point unclear. In Must Know High School Pre-calculus, however, each chapter will immediately introduce you to the must know idea, or ideas, that lie behind the new pre-calculus topic. As you learn these must know ideas, the book will show you how to apply that knowledge to solving pre-calculus problems.

Focused on the essential concepts of pre-calculus subjects, this accessible guide will help you develop a solid understanding of the subject quickly and painlessly. Clear explanations are accompanied by numerous examples and followed with more challenging aspects of pre-calculus. Practical exercises close each chapter and will instill you with confidence in your growing pre-calculus skills.

Must Know High School Pre-calculus features:

• Each chapter begins with the must know ideas behind the new topic
• Extensive examples illustrate these must know ideas
• Students learn how to apply this new knowledge to problem solving
• 250 practical review questions instill confidence
• IRL (In Real Life) sidebars present real-life examples of the subject at work in culture, science, and history
• Special BTW (By the Way) sidebars provide study tips, exceptions to the rule, and issues students should pay extra attention to
• Bonus app includes 100 flashcards to reinforce what students have learned

Product Details

ISBN-13:	9781260458152
Publisher:	McGraw Hill LLC
Publication date:	01/10/2020
Pages:	464
Sales rank:	279,292
Product dimensions:	7.30(w) x 9.00(h) x 1.10(d)
Age Range:	13 - 17 Years

About the Author

Chris Monahan taught mathematics to high school and college students for more than thirty years. He is a national trainer for Texas Instruments' Teachers Teaching with Technology program.

Table of Contents

Introduction ix

The Flashcard App xi

1 Functions 1

Relations and Functions 2

Composition of Functions 6

Inverse Functions 8

2 Quadratic Functions 13

Solving Quadratic Equations 14

Complex Numbers 16

Graphing Quadratic Functions - Parabolas 22

Applications of Quadratic Functions 24

3 Polynomial Functions 31

Factoring Polynomials 32

Remainder and Factor Theorems 33

Synthetic Division 34

Graphing Polynomial Functions 37

Using Graphs to Factor Polynomials 41

Fundamental Theorem of Algebra 46

Polynomial Inequalities 49

Rational Root Theorem and Descartes Rule of Signs 51

Maximum and Minimum Values of Polynomial Functions 55

4 Rational Functions 63

Intercepts for the Graphs of Rational Functions 64

Discontinuities of Rational Functions 65

End Behavior for Rational Functions 70

Graphing Rational Functions 73

Maxima and Minima of Rational Functions 77

5 Conic Sections 83

Analyze and Graph Circles 85

Analyze and Graph Parabolas 86

Analyzing and Graphing Ellipses 91

Analyze and Graph Hyperbolas 100

Eccentricity 108

Solutions of Systems of Quadratic Equations 109

6 Exponential and Logarithmic Functions 118

Exponential Functions 119

Logarithmic Functions 125

Applications of Exponential and Logarithmic Functions 136

7 Sequences and Series 148

Sequences 149

Summation Notation 155

Arithmetic Series 157

Geometric Series 160

Mathematical Induction 167

8 Systems of Equations and Matrices 175

Matrices 175

An Introduction to Matrices 176

Solve Two Variable Linear Systems Using Cramer's Rule and Inverse Matrices 179

Solving Three or More Variable Linear Systems 188

Solving Systems of Linear Inequalities 191

9 Triangle Trigonometry 203

Right Triangle Trigonometry 204

Figuring Out the Area of a Triangle Using Trigonometry 210

Law of Sines 212

The Ambiguous Case 216

Law of Cosines 220

10 Trigonometric Functions 230

Unit Circle 231

The First Quadrant 231

Beyond the First Quadrant 234

Radian Measure 238

Trigonometric Identities 243

Proving Trigonometric Identities 246

11 Graphs and Applications of Trigonometric Functions 255

Graphs of Trigonometric Functions 256

Inverse Trigonometric Functions 270

Applying Trigonometric Functions 273

Solving Trigonometric Equations 276

12 Polar and Parametric Equations 289

Plotting Points on a Polar Coordinate Plane 290

Conversion Between Polar and Rectangular Coordinates 292

Graphs of Polar Equations 294

The Rose 296

The Cardioid 304

The Limaçon 305

The Lemniscate 310

Conic Sections in Polar Coordinates 311

Nonstandard Polar Curves 314

Conversion Between Polar and Rectangular Forms for a Function 319

Conversion Between Parametric and Function Forms 322

13 Complex Numbers 335

Polar Form of Complex Numbers 336

Multiplication and Division of Complex Numbers 338

Powers and Roots of Complex Numbers 340

Exponential Format 344

14 Introduction to Calculus 348

The Concept of a Limit 349

Evaluating Limits 351

Property of Limits 357

Continuity 360

Instantaneous Rates of Change 361

Differentiation Rules 364

Answer Key 375