Algebra and Trigonometry 10th Edition

Book Preface

As a professor of mathematics at an urban public  university for 35 years, I understand the varied  needs of algebra and trigonometry students. Students  range from being underprepared, with little mathematical  background and a fear of mathematics, to being highly  prepared and motivated. For some, this is their final course  in mathematics. For others, it is preparation for future  mathematics courses. I have written this text with both  groups in mind.

A tremendous benefit of authoring a successful series is  the broad-based feedback I receive from teachers and students  who have used previous editions. I am sincerely grateful for  their support. Virtually every change to this edition is the  result of their thoughtful comments and suggestions. I hope  that I have been able to take their ideas and, building upon a  successful foundation of the ninth edition, make this series an  even better learning and teaching tool for students and teachers.

Features in the Tenth Edition
A descriptive list of the many special features of  Algebra & Trigonometry can be found on the endpapers in  the front of this text.

This list places the features in their proper context, as  building blocks of an overall learning system that has been  carefully crafted over the years to help students get the most  out of the time they put into studying. Please take the time to  review this and to discuss it with your students at the beginning  of your course. My experience has been that when students  utilize these features, they are more successful in the course.

New to the Tenth Edition

• Retain Your Knowledge This new category of problems  in the exercise set are based on the article “To Retain
New Learning, Do the Math” published in the Edurati  Review. In this article, Kevin Washburn suggests that “the more students are required to recall new content or skills,  the better their memory will be.” It is frustrating when  students cannot recall skills learned earlier in the course.

To alleviate this recall problem, we have created “Retain  Your Knowledge” problems. These are problems considered  to be “final exam material” that students can use to maintain  their skills. All the answers to these problems appear in the  back of the text, and all are programmed in MyMathLab.

• Guided Lecture Notes Ideal for online, emporium/ redesign courses, inverted classrooms, or traditional  lecture classrooms. These lecture notes help students  take thorough, organized, and understandable notes  as they watch the Author in Action videos. They ask  students to complete definitions, procedures, and  examples based on the content of the videos and text.

In addition, experience suggests that students learn by  doing and understanding the why/how of the concept or  property. Therefore, many sections will have an exploration  activity to motivate student learning. These explorations  introduce the topic and/or connect it to either a real-world  application or a previous section. For example, when the  vertical-line test is discussed in Section 3.2, after the  theorem statement, the notes ask the students to explain  why the vertical-line test works by using the definition  of a function. This challenge helps students process the  information at a higher level of understanding.
• Illustrations Many of the figures now have captions to  help connect the illustrations to the explanations in the  body of the text.
• TI Screen Shots In this edition we have replaced all  the screen shots from the ninth edition with screen shots  using TI-84Plus C. These updated screen shots help  students visualize concepts clearly and help make stronger  connections between equations, data, and graphs in full  color.
• Chapter Projects, which apply the concepts of each  chapter to a real-world situation, have been enhanced  to give students an up-to-the-minute experience. Many  projects are new and Internet-based, requiring the student  to research information online in order to solve problems.
• Exercise Sets All the exercises in the text have been  reviewed and analyzed for this edition, some have been  removed, and new ones have been added. All time-sensitive  problems have been updated to the most recent information  available. The problem sets remain classified according to purpose.

The ‘Are You Prepared?’ problems have been  improved to better serve their purpose as a just-in-time  review of concepts that the student will need to apply in  the upcoming section.
The Concepts and Vocabulary problems have been  expanded and now include multiple-choice exercises.
Together with the fill-in-the-blank and True/False  problems, these exercises have been written to serve as  reading quizzes.

Skill Building problems develop the student’s  computational skills with a large selection of exercises  that are directly related to the objectives of the section.  Mixed Practice problems offer a comprehensive assessment  of skills that relate to more than one objective. Often  these require skills learned earlier in the course.

Applications and Extensions problems have been  updated. Further, many new application-type exercises  have been added, especially ones involving information  and data drawn from sources the student will recognize,  to improve relevance and timeliness.

The Explaining Concepts: Discussion and Writing exercises have been improved and expanded to provide  more opportunity for classroom discussion and group  projects New to this edition, Retain Your Knowledge exercises  consist of a collection of four problems in each exercise set  that are based on material learned earlier in the course.
They serve to keep information that has already been  learned “fresh” in the mind of the student. Answers to all  these problems appear in the Student Edition.

The Review Exercises in the Chapter Review have  been streamlined, but they remain tied to the clearly  expressed objectives of the chapter. Answers to all these  problems appear in the Student Edition.
• Annotated Instructor’s Edition As a guide, the author’s  suggestions for homework assignments are indicated by  a blue underscore below the problem number. These  problems are assignable in the MyMathLab as part of a  “Ready-to-Go” course. Content Changes in the Tenth Edition
• Section 3.1 The objective Find the Difference Quotient  of a Function has been added.
• Section 5.1 The subsection Behavior of the Graph of a  Polynomial Function Near a Zero has been removed.
• Section 5.3 A subsection has been added that discusses  the role of multiplicity of the zeros of the denominator  of a rational function as it relates to the graph near a  vertical asymptote.
• Section 5.5 The objective Use Descartes’ Rule of Signs  has been included.
• Section 5.5 The theorem Bounds on the Zeros of a  Polynomial Function is now based on the traditional  method of using synthetic division