This text is designed for students in technical, trade, allied health, and other career programs that require a solid understanding of basic math, elementary algebra, trigonometry, and geometry. Topics are introduced and reinforced using a step-by-step spiral learning approach supported by numerous examples and applications
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Essentials of Technical Mathematics is an introductory technical math text that covers arithmetic, algebra, statistics, geometry, and trigonometry. Topics in these areas are introduced and reinforced using a step-by-step approach and are supported by numerous examples. The approach to presenting the concepts, examples, and applications supports the standards set by AMATYC (American Mathematical Association of Two-Year Colleges), NCTM (National Council of Teachers of Mathematics), MAA (Mathematical Association of America), and the U. S. Department of Labor SCANS Report (Secretary's Commission on Achieving Necessary Skills).
Features of this text offer a holistic approach to learning mathematics through:
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To the Student
The mathematics you learn in this book will be helpful in your career. We have given much thought to the best way to teach mathematics and have done extensive research on how students learn. We suggest that you use the special features we have included in the text and supplementary materials to get the most from this book and your course. The following features are designed to help you learn the mathematics in this text.
Learning Outcomes. The chapter opening pages list the learning outcomes for the chapter. Each section begins with its particular learning outcomes to show you what you will learn in that section. If you read and think about these outcomes before you begin the section, you will know what to look for as you work through the section.
Good Decisions through Teamwork. Each chapter opens with a class project designed to promote teamwork. The projects incorporate a wide variety of team-building strategies. Each project engages your skills in a unique way—your computational skills, interpersonal skills, oral and written communication skills, organizational skills, research skills, critical-thinking and/or decision-making skills—skills that are highly valued by employers. You will prepare and present project reports for a variety of audiences, including instructors, peers, employers, and immediate supervisors.
Your instructor may use some or all of the projects, or he or she may organize teams within the class and have each team select a project from a different chapter. Even if a particular project is not used in your class, reading the projects will broaden your perception of the usefulness of mathematics.
Six-Step Approach to Problem Solving. This approach gives you a system for solving a variety of math problems. You will learn how to organize the information given and how to develop a plan for solving the problem. You are asked to analyze and compare and also to estimate as you solve problems. Estimation helps you decide whether your answer is reasonable. You will learn to interpret the results of your calculations within the context of the problem, a skill you will use on your job.
Use of Color in the Text. As you read the text and work through the examples notice the items shaded with color or with gray. These will help you follow the logic of working through the example. Color also highlights important items and boxed features such as the Tips!, Learning Strategies, and rules, procedures, and formulas.
Tip! Boxes. These boxes give helpful hints and calculator strategies for doing mathematics, and they draw your attention to important generalizations or restrictions that you might otherwise overlook. Many of our students tell us that the tip boxes seem to anticipate and answer many of the questions they have when studying alone.
Learning Strategies. In each chapter you will find a number of learning strategies. These strategies can help you build a framework for successful learning. The strategies show ways to manage your learning of mathematics that you may not have thought of before. Use them to improve your "mathematical sense" and to give you a greater appreciation for the power of mathematics in your workplace and everyday life. You may find them useful in other areas of study also.
Using Your Calculator. Calculators are essential in all types of math, and especially in college math for technology. Some of the tips introduce useful and easy-to-follow calculator strategies. The tips show you how to analyze the procedure and set up a problem for a calculator solution; a sample series of keystrokes is often included. In addition, some tips give you strategies so you can determine how your calculator handles various operations.
Self-Study Exercises. These practice sets are keyed to the learning outcomes and appear at the end of each section. Use these exercises to check your understanding of the section. The answers to every problem are at the end of the text so you can get immediate feedback on your level of understanding of the material.
Career Applications. At the end of most chapters there is a career application. These applications resulted from interviews and research in the workplace, and they demonstrate how widespread math applications are in the workplace and the world around you. They provide opportunities to solve real-world problems, and demonstrate the ways that you regularly use the math concepts you are learning.
Assignment Exercises. An extensive set of exercises appears at the end of each chapter so you can review all the learning outcomes presented in the chapter. You may be assigned these exercises, organized by section, as homework, or you may want to work them on your own for extra practice. Challenge problems are at the end of this set of exercises. The answers to the odd-numbered exercises are given at the end of the book, and worked-out solutions appear in a separate Student Solutions Manual. Your instructor has the solutions to the even-numbered exercises in the Instructor's Resource Manual.
Chapter Trial Test. The trial test at the end of each chapter lets you check your understanding of the chapter concepts. You should be able to work each problem without referring to any examples in your text or your notes. Take this test before you take the class test to evaluate your understanding of the chapter material.
Answers to the odd-numbered problems appear at the end of the book, and their solutions appear in a separate Student Solutions Manual available in your bookstore. Your instructor has the solutions to the even-numbered problems in the Instructor's Resource Manual.
Glossary/Index. An extensive glossary/index makes this book a valuable reference. Use the index to .cross-reference topics and to locate other topics that relate to the topic you are studying.
Table of Contents. The table of contents is your "roadmap" to this course. Study it carefully to determine how the topics are arranged. This will aid you in relating topics to each other.
Student Solutions Manual. This manual can be purchased at your bookstore. The manual contains worked-out solutions to the odd-numbered exercises in the Assignment Exercises and the Chapter Trial Test for each chapter of the text. Answers to these exercises appear in the back of your text, but using the manual to study the fully worked-out solutions can enhance your problem-solving skills and your understanding of the concepts covered.
How to Study Technical Mathematics. Your instructor can get free copies of this booklet, which describes various learning techniques you can use in class and to prepare for class that can make your learning of mathematics much more efficient and effective.
StudyWizard Software. This software, which is packaged with the text, provides additional practice with the math concepts presented in the text. Each question contains a reference to the section and learning outcome number in the text where the concept first appears, making it easier to find the sections you want to review. Immediate feedback is provided to all questions, allowing you to strengthen your skills and test your knowledge of the concepts before a class test. The glossary included on the software allows you to review the terms and concepts presented in the text.
Companion Web Site. This free web site, available at www.prenhall.com/cleaves, provides even more practice with the math concepts presented in the form of short quizzes for each section of the text. These quizzes are immediately graded, and you have the opportunity to send the results to your instructor via e-mail.
We wish you much success in your study of mathematics. Many of the features in this book were suggested by students such as yourself. If you have suggestions for improving the presentation, please give them to your instructor or e-mail the authors at firstname.lastname@example.org or email@example.com.
Reading Your Math Textbook
In developing an effective study plan it is important to use all your available resources to their maximum advantage. The most accessible of these resources is your textbook. Incorporate an effective strategy for reading your textbook into your study plan.
Beginning a Chapter
1. Examine the chapter opening page or pages. Read the chapter title, section titles, and learning outcomes to determine what will be covered in the chapter.
2. Use the learning outcomes as a checklist to rate your initial knowledge of the topics presented in the chapter. This rating can be a numerical one. For example, 0 means you know nothing about this topic, 1 means you know a little but not much about this topic, 2 means you know quite a bit but there may be a few gaps, and 3 means you know this topic very well.
Another possible rating strategy can be a minus, check, plus system. Minus means you need to work on this topic, check means you know the topic moderately well, and plus means you know the topic very well.
Beginning a Section
1. Read the section title and the learning outcomes for the section.
2. Read the introductory paragraph.
3. Locate the Self-Study Exercises at the end of the section. Read the directions for each "clump" of exercises. This will give you an idea of the type of problems you will be working and what to look for as you read the section.
4. Begin reading the section. Make notes on concepts that you do not understand or examples for which you are not able to follow the explanation. This will be the basis for questions to ask in class.
Continuing through the Chapter
1. Work on one learning outcome at a time. After reading and studying one learning outcome, try some of the exercises for that outcome. Always check...
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