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

by Barron's Educational Series, Lawrence S. Leff M.S., Christina Pawlowski-Polanish M.S.

Overview

Barron’s Math 360: Pre-Calculus is your complete go-to guide for everything pre-calculus

This comprehensive guide is an essential resource for:

• High school and college courses
• Homeschooling
• Virtual Learning
• Learning pods

Inside you’ll find:

• Comprehensive Content Review: Begin your study with the basic building blocks of pre-calculus and build as you go. Topics include, algebraic methods, functions and graphs, complex numbers, polynomial and rational functions, and much more.
• Effective Organization: Topic organization and simple lesson formats break down the subject matter into manageable learning modules that help guide a successful study plan customized to your needs.
• Clear Examples and Illustrations: Easy-to-follow explanations, hundreds of helpful illustrations, and numerous step-by-step examples make this book ideal for self-study and rapid learning.
• Practice Exercises: Each chapter ends with practice exercises designed to reinforce and extend key skills and concepts. These checkup exercises, along  with the answers and solutions, will help you assess your understanding and monitor your progress.
• Access to Online Practice: Take your learning online for 50 practice questions designed to test your knowledge with automated scoring to show you how far you have come.

Product Details

ISBN-13:	9781506281384
Publisher:	Barrons Educational Services
Publication date:	09/07/2021
Series:	Barron's Test Prep
Pages:	528
Sales rank:	201,879
Product dimensions:	7.00(w) x 10.00(h) x 1.40(d)
Age Range:	14 - 17 Years

About the Author

About the Authors:
Lawrence S. Leff, Former Assistant Principal, Mathematics Supervision, Franklin D. Roosevelt High School, Brooklyn, NY

Christina M. Pawlowski is a math teacher at Commack High School in Commack, New York. She is an NYSMTP Emeritus and was the Association of Mathematics Teachers of New York State (AMTNYS) County Chairperson 2018. She was also a NYS Teach of the Year Finalist and received the Governor’s Teaching Award.

About the Publisher:
In the 1930s, Manuel H. Barron opened a bookstore in Brooklyn, New York. 

People from the community asked Mr. Barron about books that might be available to help their children study for the New York State Regents exams. After realizing there wasn't anything available, Mr. Barron created his own study guides.

80 years later, Barron's has helped millions of people prepare for their next step.

Table of Contents

How to Use This Book vii

Study Unit I Algebra and Graphing Methods

1 Basic Algebraic Methods 3

Lesson 1-1 Real Numbers, Variables, and Exponents 3

Lesson 1-2 Solving Linear Equations 6

Lesson 1-3 Solving Linear Inequalities 10

Lesson 1-4 Operations with Polynomials 15

Lesson 1-5 Factoring Polynomials 19

Lesson 1-6 Factoring Quadratic Trinomials 22

Lesson 1-7 Special Products and Factoring Patterns 24

Review Exercises 27

2 Rational and Irrational Expressions 31

Lesson 2-1 Operations with Rational Expressions 31

Lesson 2-2 Simplifying Complex Fractions 37

Lesson 2-3 Radicals and Fractional Exponents 39

Lesson 2-4 Operations with Radicals 41

Review Exercises 46

3 Graphing and Systems of Equations 51

Lesson 3-1 Graphing Points and Linear Equations 52

Lesson 3-2 Midpoint and Distance Formulas 53

Lesson 3-3 The Slope of a Line 56

Lesson 3-4 Graphing a Linear Equation 58

Lesson 3-5 Graphing a Linear Inequality 59

Lesson 3-6 Writing Equations of Lines 61

Lesson 3-7 Solving Linear Systems Graphically 68

Lesson 3-8 Solving Linear Systems Algebraically 72

Review Exercises 76

4 Functions and Quadratic Equations 81

Lesson 4-1 Function Concepts 82

Lesson 4-2 Quadratic Functions and Their Graphs 89

Lesson 4-3 Solving Quadratic Equations 92

Lesson 4-4 Solving a Linear-Quadratic System 97

Lesson 4-5 Applying Quadratic Equations 99

Lesson 4-6 Solving Quadratic Inequalities 102

Review Exercises 105

5 Complex Numbers and the Quadratic Formula 111

Lesson 5-1 Complex Numbers 111

Lesson 5-2 Multiplying and Dividing Complex Numbers 114

Lesson 5-3 Completing the Square 115

Lesson 5-4 The Quadratic Formula 117

Review Exercises 122

Study Unit II Functions and their Graphs

6 Special Functions and Equations 129

Lesson 6-1 Absolute-Value Equations and Inequalities 129

Lesson 6-2 Transformations of Graphs 134

Lesson 6-3 Special Functions and Their Graphs 138

Lesson 6-4 Radical Equations 142

Lesson 6-5 Rational Equations and Inequalities 144

Review Exercises 149

7 Polynomial and Rational Functions 155

Lesson 7-1 Division of Polynomials 156

Lesson 7-2 Zeros of Polynomial Functions 165

Lesson 7-3 Solving Polynomial Equations 176

Lesson 7-4 Graphing Polynomial Functions 181

Lesson 7-5 Graphing Rational Functions 191

Lesson 7-6 Decomposing Rational Expressions 198

Review Exercises 203

8 Exponential and Logarithmic Functions 207

Lesson 8-1 Inverse Functions 207

Lesson 8-2 The Exponential Function 217

Lesson 8-3 The Logarithmic Function 219

Lesson 8-4 Logarithm Laws and Equations 223

Lesson 8-5 Exponential and Logarithmic Models 229

Review Exercises 237

Study Unit III Trigonometric Analysis

9 Trigonometry 247

Lesson 9-1 Degree and Radian Measures 248

Lesson 9-2 Right-Triangle Trigonometry 250

Lesson 9-3 The General Angle 254

Lesson 9-4 Working with Trigonometric Functions 258

Lesson 9-5 Trigonometric Functions of Special Angles 261

Review Exercises 264

10 Graphing Trigonometric Functions 271

Lesson 10-1 Periodic Functions and Their Graphs 271

Lesson 10-2 Graphing Trigonometric Functions 277

Lesson 10-3 Transformations of Trigonometric Functions 283

Lesson 10-4 Inverse Trigonometric Functions 286

Review Exercises 289

11 Trigonometric Identities and Equations 297

Lesson 11-1 Pythagorean Trigonometric Identities 297

Lesson 11-2 Solving Trigonometric Equations 301

Lesson 11-3 Sum and Difference Identities 303

Lesson 11-4 Double-Angle Identities 306

Lesson 11-5 Half-Angle Identities 308

Review Exercises 310

12 Solving Triangles 315

Lesson 12-1 The Area of a Triangle 315

Lesson 12-2 The Law of Sines 317

Lesson 12-3 The Law of Cosines 323

Review Exercises 326

Study Unit IV Polar Coordinates and Conic Sections

13 Polar Coordinates and Parametric Equations 337

Lesson 13-1 Parametric Equations 338

Lesson 13-2 The Polar Coordinate System 341

Lesson 13-3 The Polar Form of a Complex Number 350

Lesson 13-4 Powers and Roots of Complex Numbers 354

Review Exercises 359

14 Conic Sections and their Equations 363

Lesson 14-1 The Parabola 364

Lesson 14-2 The Ellipse 372

Lesson 14-3 The Hyperbola 380

Lesson 14-4 General Equations of Conics 388

Lesson 14-5 Polar Equations of Conics 396

Review Exercises 400

Study Unit V Number Patterns and Calculus PREVIEW

15 Sequences, Series, and Counting 407

Lesson 15-1 Arithmetic Sequences and Series 408

Lesson 15-2 Geometric Sequences and Series 412

Lesson 15-3 Generalized Sequences 414

Lesson 15-4 Mathematical Induction 418

Lesson 15-5 Permutations and Combinations 422

Lesson 15-6 The Binomial Theorem 424

Review Exercises 427

16 Calculus Preview 433

Lesson 16-1 Limits of Functions 433

Lesson 16-2 Slope of a Tangent Line 446

Lesson 16-3 Rules for Finding Derivatives 451

Lesson 16-4 Finding Antiderivatives 454

Lesson 16-5 Integration and Area Under a Curve 457

Review Exercises 461

Appendix: Graphing with a Calculator 465

Answers to Chapter Review Exercises 469

Index 507