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

Lawrence S. Leff, Christina Pawlowski-Polanish

• Verlag: Barrons Educational Services
• Jahr: 2021
• ISBN:
  9781506281391
• Thema: Study Aids
• Thema: Study Guides

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.

STUDY UNIT I

ALGEBRA AND GRAPHING METHODS

1 BASIC ALGEBRAIC METHODS

WHAT YOU WILL LEARN

This chapter reviews basic algebraic terms and skills that you may have forgotten or never learned. If you have already mastered the algebraic skills reflected in any of the lessons listed below, you may want to skip that lesson and move ahead to the next one.

LESSONS IN CHAPTER 1

•Lesson 1-1: Real Numbers, Variables, and Exponents

•Lesson 1-2: Solving Linear Equations

•Lesson 1-3: Solving Linear Inequalities

•Lesson 1-4: Operations with Polynomials

•Lesson 1-5: Factoring Polynomials

•Lesson 1-6: Factoring Quadratic Trinomials

•Lesson 1-7: Special Products and Factoring Patterns

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

KEY IDEAS

Algebra is generalized arithmetic that uses both letters and numbers. These letters, called variables, are placeholders for unknown numbers. By using variables rather than specific numbers, the language of algebra allows general statements to be made about numbers. We know, for example, that 2 + 3 = 3 + 2. To generalize that the order in which any two numbers are added together does not matter, we can write a + b = b + a, where the variables a and b stand for any two numbers.

ORDERING REAL NUMBERS ON A NUMBER LINE

Positive 3 and negative 3 are opposites in the same sense that winning three games (+3) and losing three games (−3) are opposite situations. The size relationship between positive and negative numbers can be represented by using a ruler-like diagram called a number line. A number line extends indefinitely in opposite directions on either side of the point labeled 0, which is called the origin. On a horizontal number line, positive numbers are labeled in increasing order to the right of 0, and negative numbers in decreasing order to the left of 0. The opposite of each positive number lies on the left side of the origin and at the same distance from the origin as its positive counterpart, as shown in Figure 1.1.

FIGURE 1.1 A number line

Any number on the number line is greater than any number to its left. For example, −2 is greater than −3, −1 is greater than −2, 0 is greater than −1, and 1 is greater than 0.

CLASSIFYING NUMBERS

The set of all points on the number line cor...