Pre-Calculus : All-In-One for Dummies / Mary Jane Sterling.

Format:

Book

Author/Creator:

Sterling, Mary Jane, author.

Series:

--For dummies.

For dummies

Language:

English

Subjects (All):

Precalculus.

Physical Description:

1 online resource (627 pages)

Edition:

1st ed.

Place of Publication:

Newark : John Wiley & Sons, Incorporated, 2023.

Summary:

The easy way to understand and retain all the concepts taught in pre-calculus classes Pre-Calculus All-in-One For Dummies is a great resource if you want to do you best in Pre-Calculus. Packed with lessons, examples, and practice problems in the book, plus extra chapter quizzes online, it gives you absolutely everything you need to succeed in pre-calc. Unlike your textbook, this book presents the essential topics clearly and concisely, so you can really understand the stuff you learn in class, score high on your tests (including the AP Pre-Calculus exam!), and get ready to confidently move ahead to upper-level math courses. And if you need a refresher before launching into calculus, look no further--this book has your back. Review what you learned in algebra and geometry, then dig into pre-calculus Master logarithms, exponentials, conic sections, linear equations, and beyond Get easy-to-understand explanations that match the methods your teacher uses Learn clever shortcuts, test-taking tips, and other hacks to make your life easier Pre-Calculus All-in-One For Dummies is the must-have resource for students who need to review for exams or just want a little (or a lot of!) extra help understanding what's happening in class.

Contents:

Intro

Title Page

Copyright Page

Table of Contents

Introduction

About This Book

Foolish Assumptions

Icons Used in This Book

Beyond the Book

Where to Go from Here

Unit 1: Getting Started with Pre-Calculus

Chapter 1: Preparing for Pre-Calculus

Recapping Pre-Calculus: An Overview

Checking in on Number Basics and Processes

Understanding the multitude of number types: Terms to know

Looking at the fundamental operations you can perform on numbers

Knowing the properties of numbers: Truths to remember

Looking at Visual Statements: When Math Follows Form with Function

Using basic terms and concepts

Graphing linear equalities and inequalities

Gathering information from graphs

Getting Yourself a Graphing Calculator

Practice Questions Answers and Explanations

Whaddya Know? Chapter 1 Quiz

Answers to Chapter 1 Quiz

Chapter 2: Operating with Real Numbers

Describing Numbers on the Number Line

Solving Inequalities

Recapping inequality how-tos

Solving equations and inequalities involving absolute value

Expressing solutions for inequalities with interval notation

Working with Radicals and Exponents

Defining and relating radicals and exponents

Rewriting radicals as exponents (or, creating rational exponents)

Getting a radical out of a denominator: Rationalizing

Whaddya Know? Chapter 2 Quiz

Answers to Chapter 2 Quiz

Chapter 3: Cementing the Building Blocks of Pre-Calculus Functions

Identifying Special Function Types and Their Graphs

Even and odd functions

One-to-one functions

Dealing with Parent Functions and Their Graphs

Linear functions

Quadratic functions

Square-root functions

Absolute-value functions

Cubic functions

Cube-root functions

Setting the Stage for Rational Functions.

Searching for vertical asymptotes and holes

Searching for horizontal asymptotes

Seeking out oblique asymptotes

Locating the x- and y-intercepts

Putting the Results to Work: Graphing Rational Functions

Whaddya Know? Chapter 3 Quiz

Answers to Chapter 3 Quiz

Chapter 4: Operating on Functions

Transforming the Parent Graphs

Stretching and flattening

Graphing translations

Seeing reflections

Combining various transformations (a transformation in itself!)

Transforming functions point by point

Sharpen Your Scalpel: Operating on Functions

Adding and subtracting

Multiplying and dividing

Breaking down a composition of functions

Adjusting the domain and range of combined functions (if applicable)

Turning Inside Out with Inverse Functions

Graphing an inverse

Inverting a function to find its inverse

Verifying an inverse

Whaddya Know? Chapter 4 Quiz

Answers to Chapter 4 Quiz

Unit 2: Getting the Grip on Graphing

Chapter 5: Graphing Polynomial Functions

Understanding Degrees and Roots

Factoring a Polynomial Expression

Always the first step: Looking for a GCF

Unwrapping the box containing a trinomial

Recognizing and factoring special polynomials

Grouping to factor four or more terms

Finding the Roots of a Factored Equation

Cracking a Quadratic Equation When It Won't Factor

Using the quadratic formula

Completing the square

Solving Polynomial Equations with a Degree Higher Than Two

Counting a polynomial's total roots

Tallying the real roots: Descartes's rule of signs

Accounting for imaginary roots: The fundamental theorem of algebra

Guessing and checking the real roots

Put It in Reverse: Using Solutions to Find Factors

Graphing Polynomials.

Graphing when all the roots are real numbers

Graphing when roots are imaginary numbers: Combining all techniques

Whaddya Know? Chapter 5 Quiz

Answers to Chapter 5 Quiz

Chapter 6: Exponential and Logarithmic Functions

Exploring Exponential Functions

Searching the ins and outs of exponential functions

Graphing and transforming exponential functions

Logarithms: The Inverse of Exponential Functions

Getting a better handle on logarithms

Managing the properties and identities of logs

Changing a log's base

Calculating a number when you know its log: Inverse logs

Graphing logs

Base Jumping to Simplify and Solve Equations

Stepping through the process of solving exponential equations

Solving logarithmic equations

Growing Exponentially: Word Problems in the Kitchen

Whaddya Know? Chapter 6 Quiz

Answers to Chapter 6 Quiz

Chapter 7: Piece-Wise and Greatest-Integer Functions

Looking at Functions with More Than One Rule: Piece-Wise Functions

Graphing piece-wise functions

Using piece-wise functions in real-world applications

Grappling with the Greatest-Integer Function

Observing the greatest-integer function

Making use of the greatest-integer function

Whaddya Know? Chapter 7 Quiz

Answers to Chapter 7 Quiz

Unit 3: The Essentials of Trigonometry

Chapter 8: Circling In on Angles

Introducing Radians and Relating to Degrees

Trig Ratios: Taking Right Triangles a Step Further

Following the sine

Looking for a cosine

Going out on a tangent

Discovering the flip side: Reciprocal trig functions

Working in reverse: Inverse trig functions

Defining ranges of inverse trig functions.

Understanding How Trig Ratios Work on the Coordinate Plane

Digesting Special Triangle Ratios

The 45er: Isosceles right triangle

The 30-60-90 right triangle

Triangles and the Unit Circle: Working Together for the Common Good

Placing the major angles correctly

Retrieving trig-function values on the unit circle

Whaddya Know? Chapter 8 Quiz

Answers to Chapter 8 Quiz

Chapter 9: Homing In on the Friendliest Angles

Building on the Unit Circle

Familiarizing yourself with the most common angles

Finding the reference angle to solve for functions of angles

Relating reference angles to their parents

Drawing uncommon angles

Solving Equations Using Inverse Functions

Measuring Arcs: When the Circle Is Put in Motion

Whaddya Know? Chapter 9 Quiz

Answers to Chapter 9 Quiz

Chapter 10: Picturing Basic Trig Functions and Reciprocal Functions

Drafting the Sine and Cosine Parent Graphs

Sketching sine

Looking at cosine

Graphing Tangent and Cotangent Parent Graphs

Tackling tangent

Clarifying cotangent

Putting Secant and Cosecant in Parent Graphs Pictures

Graphing secant

Checking out cosecant

Whaddya Know? Chapter 10 Quiz

Answers to Chapter 10 Quiz

Chapter 11: Graphing and Transforming Trig Functions

Transforming Trig Graphs

Messing with sine and cosine graphs

Tweaking tangent and cotangent graphs

Transforming the graphs of secant and cosecant

Whaddya Know? Chapter 11 Quiz

Answers to Chapter 11 Quiz

Unit 4: Identities and Special Triangles

Chapter 12: Identifying with Trig Identities: The Basics

Keeping the End in Mind: A Quick Primer on Identities.

Lining Up the Means to the End: Basic Trig Identities

Reciprocal and ratio identities

Pythagorean identities

Even/odd identities

Co-function identities

Periodicity identities

Tackling Difficult Trig Proofs: Some Techniques to Know

Dealing with demanding denominators

Going solo on each side

Whaddya Know? Chapter 12 Quiz

Answers to Chapter 12 Quiz

Chapter 13: Advancing with Advanced Identities

Finding Trig Functions of Sums and Differences

Searching out the sine of a b

Calculating the cosine of a b

Taming the tangent of a b

Doubling an Angle and Finding Its Trig Value

Finding the sine of a doubled angle

Calculating cosines for two

Squaring your cares away

Having twice the fun with tangents

Taking Trig Functions of Common Angles Divided in Two

A Glimpse of Calculus: Traveling from Products to Sums and Back

Expressing products as sums (or differences)

Transporting from sums (or differences) to products

Eliminating Exponents with Power-Reducing Formulas

Whaddya Know? Chapter 13 Quiz

Answers to Chapter 13 Quiz

Chapter 14: Getting the Slant on Oblique Triangles

Solving a Triangle with the Law of Sines

When you know two angle measures

When you know two consecutive side lengths

Conquering a Triangle with the Law of Cosines

SSS: Finding angles using only sides

SAS: Tagging the angle in the middle (and the two sides)

Filling in the Triangle by Calculating Area

Finding area with two sides and an included angle (for SAS scenarios)

Using Heron's Formula (for SSS scenarios)

Making Triangles Work for You

Whaddya Know? Chapter 14 Quiz

Answers to Chapter 14 Quiz

Unit 5: Analytic Geometry.

Chapter 15: Coordinating with Complex Numbers.

Notes:

Book + Chapter Quizzes Online.

Includes index.

Description based on publisher supplied metadata and other sources.

ISBN:

1-394-20125-7

OCLC:

1402176521