# Barron’s Math 360: A Complete Study Guide to Pre-Calculus with Online Practice Genres:

## Book Preface

Barron’s Math 360: Pre-Calculus is designed for self-learners and for those looking for a comprehensive guide to everything pre-calculus.

This book includes a number of helpful tools that will reinforce your knowledge of the topics as you learn. You’ll find:

What You Will Learn Each chapter begins with a list of the topics covered. This is a useful tool for categorizing the learning process and for devising a study plan.

Terms and Definitions Important terms are defined where necessary to help guide you through topics successfully.

Examples with Solutions Numerous examples for each topic are included throughout, along with answers to check your progress.

Review Exercises Each chapter closes with review questions that will help determine which topics you have a solid understanding of and which topics you need to revisit.

Online Practice Questions Access to 50 online multiple-choice questions designed to enhance your understanding and to test your knowledge. To access, see the card at the front of the book.

## SET GOALS AND OBJECTIVES

As you use Barron’s Math 360: Pre-Calculus, it is a good idea to set personal goals to chart and direct your learning objectives. A goal is something that you wish to achieve over a period of time. Objectives are short-term targets that help you reach a particular goal. For example, suppose that your goal is to learn how to use all of the functions on a graphing calculator. You can reach this goal by establishing short-term objectives—such as committing to learning one of the functions a day and practicing it using different data—that will enable you to successfully reach your long-term goal of learning how to use all of the functions on a graphing calculator.

Barron’s Math 360: Pre-Calculus does not need to be studied in a linear fashion. If there is a particular topic that you want to study or reinforce, just turn to that page or chapter, and all the information along with the features mentioned above will be available to you. There are also some things you can do to optimize your study time and ensure you are retaining the important information you want to learn.

Review: Review all chapter headings and subheadings and the information in the “What You Will Learn” sections.

Scan: Glance over any illustrations, tables, or graphs in the chapter you’ll be reading.

Locate Terms and Definitions: Read any bold or italicized words, and study their definitions.

Get Ahead of Yourself: Review the Practice Exercises at the end of the chapter, and keep them in mind as you study the chapter.

Predict: Try to predict the answers to the questions in the Practice Exercises. This will help flag important information to keep an eye out for as you read.

Read Aloud: Hearing what is written on the page leads to better comprehension and retention of information.

Visualize: Developing a picture in your mind of the information, concepts, or material presented makes it much easier to remember.

#### Highlighting and Note Taking

Identify Important Facts: Don’t overhighlight. This will have the opposite effect and actually negatively impact your ability to retain the information you need to remember.

Take Notes: Jot down key ideas and concepts you are having a hard time understanding.

Draw It Out: Sketch out pictures, graphs, diagrams, or tables to help visualize what you’re reading. This is particularly helpful with complex topics.

#### After You Read the Chapter

Talk It Out: Summarize what you have learned from the chapter aloud to a friend or a family member. Explain it as if they are learning it for the first time.

Answer the Questions in the Practice Exercises: Did you need to look them up, or were you able to answer them from memory?

Reinforce: If you found yourself having to look up the answers to the questions, go back and read those portions of the chapter again until you feel confident moving on to the next chapter.

# CONTENTS

HOW TO USE THIS BOOK

STUDY UNIT I: ALGEBRA AND GRAPHING METHODS

1BASIC ALGEBRAIC METHODS

Lesson 1−1Real Numbers, Variables, and Exponents

Lesson 1−2Solving Linear Equations

Lesson 1−3Solving Linear Inequalities

Lesson 1−4Operations with Polynomials

Lesson 1−5Factoring Polynomials

Lesson 1−7Special Products and Factoring Patterns

Review Exercises

2RATIONAL AND IRRATIONAL EXPRESSIONS

Lesson 2−1Operations with Rational Expressions

Lesson 2−2Simplifying Complex Fractions

Review Exercises

3GRAPHING AND SYSTEMS OF EQUATIONS

Lesson 3−1Graphing Points and Linear Equations

Lesson 3−2Midpoint and Distance Formulas

Lesson 3−3The Slope of a Line

Lesson 3−4Graphing a Linear Equation

Lesson 3−5Graphing a Linear Inequality

Lesson 3−6Writing Equations of Lines

Lesson 3−7Solving Linear Systems Graphically

Lesson 3−8Solving Linear Systems Algebraically

Review Exercises

Lesson 4−1Function Concepts

Lesson 4−2Quadratic Functions and Their Graphs

Review Exercises

5COMPLEX NUMBERS AND THE QUADRATIC FORMULA

Lesson 5−1Complex Numbers

Lesson 5−2Multiplying and Dividing Complex Numbers

Lesson 5−3Completing the Square

Review Exercises

STUDY UNIT II: FUNCTIONS AND THEIR GRAPHS

6SPECIAL FUNCTIONS AND EQUATIONS

Lesson 6−1Absolute-Value Equations and Inequalities

Lesson 6−2Transformations of Graphs

Lesson 6−3Special Functions and Their Graphs

Lesson 6−5Rational Equations and Inequalities

Review Exercises

7POLYNOMIAL AND RATIONAL FUNCTIONS

Lesson 7−1Division of Polynomials

Lesson 7−2Zeros of Polynomial Functions

Lesson 7−3Solving Polynomial Equations

Lesson 7−4Graphing Polynomial Functions

Lesson 7−5Graphing Rational Functions

Lesson 7−6Decomposing Rational Expressions

Review Exercises

8EXPONENTIAL AND LOGARITHMIC FUNCTIONS

Lesson 8−1Inverse Functions

Lesson 8−2The Exponential Function

Lesson 8−3The Logarithmic Function

Lesson 8−4Logarithm Laws and Equations

Lesson 8−5Exponential and Logarithmic Models

Review Exercises

STUDY UNIT III: TRIGONOMETRIC ANALYSIS

9TRIGONOMETRY

Lesson 9−2Right-Triangle Trigonometry

Lesson 9−3The General Angle

Lesson 9−4Working with Trigonometric Functions

Lesson 9−5Trigonometric Functions of Special Angles

Review Exercises

10GRAPHING TRIGONOMETRIC FUNCTIONS

Lesson 10−1Periodic Functions and Their Graphs

Lesson 10−2Graphing Trigonometric Functions

Lesson 10−3Transformations of Trigonometric Functions

Lesson 10−4Inverse Trigonometric Functions

Review Exercises

11TRIGONOMETRIC IDENTITIES AND EQUATIONS

Lesson 11−1Pythagorean Trigonometric Identities

Lesson 11−2Solving Trigonometric Equations

Lesson 11−3Sum and Difference Identities

Lesson 11−4Double-Angle Identities

Lesson 11−5Half-Angle Identities

Review Exercises

12SOLVING TRIANGLES

Lesson 12−1The Area of a Triangle

Lesson 12−2The Law of Sines

Lesson 12−3The Law of Cosines

Review Exercises

STUDY UNIT IV: POLAR COORDINATES AND CONIC SECTIONS

13POLAR COORDINATES AND PARAMETRIC EQUATIONS

Lesson 13−1Parametric Equations

Lesson 13−2The Polar Coordinate System

Lesson 13−3The Polar Form of a Complex Number

Lesson 13−4Powers and Roots of Complex Numbers

Review Exercises

14CONIC SECTIONS AND THEIR EQUATIONS

Lesson 14−1The Parabola

Lesson 14−2The Ellipse

Lesson 14−3The Hyperbola

Lesson 14−4General Equations of Conics

Lesson 14−5Polar Equations of Conics

Review Exercises

STUDY UNIT V: NUMBER PATTERNS AND CALCULUS PREVIEW

15SEQUENCES, SERIES, AND COUNTING

Lesson 15−1Arithmetic Sequences and Series

Lesson 15−2Geometric Sequences and Series

Lesson 15−3Generalized Sequences

Lesson 15−4Mathematical Induction

Lesson 15−5Permutations and Combinations

Lesson 15−6The Binomial Theorem

Review Exercises

16CALCULUS PREVIEW

Lesson 16−1Limits of Functions

Lesson 16−2Slope of a Tangent Line

Lesson 16−3Rules for Finding Derivatives

Lesson 16−4Finding Antiderivatives

Lesson 16−5Integration and Area Under a Curve

Review Exercises

APPENDIX: GRAPHING WITH A CALCULATOR  EpubMay 7, 2022