Barron’s Math 360: A Complete Study Guide to Pre-Calculus with Online Practice
Genres: Mathematics
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.
BARRON’S 360 STUDY TIPS
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.
CUSTOMIZE YOUR STUDY
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.
Before You Read
•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.
While You Read
•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 1−6Factoring Quadratic Trinomials
Lesson 1−7Special Products and Factoring Patterns
Review Exercises
2RATIONAL AND IRRATIONAL EXPRESSIONS
Lesson 2−1Operations with Rational Expressions
Lesson 2−2Simplifying Complex Fractions
Lesson 2−3Radicals and Fractional Exponents
Lesson 2−4Operations with Radicals
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
4FUNCTIONS AND QUADRATIC EQUATIONS
Lesson 4−1Function Concepts
Lesson 4−2Quadratic Functions and Their Graphs
Lesson 4−3Solving Quadratic Equations
Lesson 4−4Solving a Linear-Quadratic System
Lesson 4−5Applying Quadratic Equations
Lesson 4−6Solving Quadratic Inequalities
Review Exercises
5COMPLEX NUMBERS AND THE QUADRATIC FORMULA
Lesson 5−1Complex Numbers
Lesson 5−2Multiplying and Dividing Complex Numbers
Lesson 5−3Completing the Square
Lesson 5−4The Quadratic Formula
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 6−4Radical Equations
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 9−1Degree and Radian Measures
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
ANSWERS TO CHAPTER REVIEW EXERCISES
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Read Now | Epub | May 7, 2022 |
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