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The Basic College Mathematics form serves as a valuable resource for students preparing for academic success in mathematics. This form outlines effective strategies to use the accompanying textbook. At the start of each section, students will find suggested topics to review, aimed at providing a solid foundation. Clear objectives identify the skills that learners should master, while getting started sections preview relevant applications to engage them. Throughout the text, examples illustrate concepts, and green math examples showcase environmental applications. Additional paired margin problems reinforce these skills by offering practice opportunities, with answers conveniently located at the bottom of each page.

To ensure comprehension, the form includes tools for checking mastery. A concept checker highlights key terms leading up to a mastery test that assesses understanding of each section. Students are encouraged to engage with exercises that connect learned material to practice problems, comprehensive self-tests, and instructional videos. Exercises are thoughtfully grouped by objectives and feature interesting, real-world applications, including green applications that apply mathematics to environmental issues.

The summary and review sections provide an easy-to-read grid summarizing studied topics, enhancing retention. Coded review exercises allow for targeted practice, ensuring that the material is not only understood but also applied effectively. For those looking to consolidate their knowledge, cumulative reviews cover broader material spanning multiple chapters. Additionally, a solutions manual offers worked-out solutions for odd-numbered problems, reinforcing learning opportunities. Students can also access online videos featuring authors demonstrating problem-solving steps from the practice tests, further enhancing their understanding. Through these structured elements, the Basic College Mathematics form aims to provide a comprehensive approach to mastering mathematics in a collegiate setting.

Basic College Mathematics Example

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Bello Basic College Mathematics

How to Use this Book: A Manual for Success

This brief guide shows you how to use the book effectively: Use It and Succeed! It is as easy as 1, 2, 3.

BEGINNING OF THE SECTION

1.To succeed: Review the suggested topics at the beginning of each section

2.Objectives: Identify the tasks you should be able to perform (organized by section)

3.Getting Started: Preview the topics being discussed with a familiar application

EXAMPLES AND PAIRED MARGIN PROBLEMS

1.Examples: Explain, expand and help you attain the stated Objectives

2.Green Math Examples: Usually the last Example in each section deals with the environment

3.Paired Margin Problems: Reinforce skills in the Examples. (Answers at the bottom of page)

CHECK FOR MASTERY

1.Concept Checker: To reinforce key terms and get ready for the Mastery Test that follows

2.Mastery Test: Get a quick checkup to make sure you understand the material in the section

3.Skill Checker: Check in advance your understanding of the material in the next section

CONNECT WITH THE EXERCISES

1.Connect: Boost your grade with Connect Practice Problems, Self Tests, and Videos.

2.Exercises (Grouped by Objectives): Practice by doing! Interesting Applications included

3.Green Applications: Marked with a Green bar in the margin; math applied to the Environment

SUMMARY, REVIEW AND PRACTICE TEST

1.Summary: Easy-to-read grid details the items studied and their meaning and gives an Example

2.Review: Coded by Section number; do them and get extra reinforcement and practice!

3.Practice Test: Answers give Section, Example and Pages for easy reference to each question

EXTRA, EXTRA

1.Cumulative Review: Covers topics from present and prior chapters. Review all the material!

2.Solutions Manual: Worked out odd numbered solutions, all Reviews and Cumulative Reviews

3.Videos on the Web: Authors working problems from the Practice Test step by step

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IGNACIO BELLO

BASIC COLLEGE

mathematics

A REAL-WORLD APPROACH

FOURTH EDITION

Ignacio Bello

Hillsborough Community College/University of South Florida

TM

TM

BASIC COLLEGE MATHEMATICS: A REAL-WORLD APPROACH, FOURTH EDITION

Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020. Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. Previous editions © 2009 and 2006. No part of this publication may be reproduced or distributed in any form or by

any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning.

Some ancillaries, including electronic and print components, may not be available to customers outside the United States.

This book is printed on recycled, acid-free paper containing 10% postconsumer waste.

1 2 3 4 5 6 7 8 9 0 QDQ/QDQ 1 0 9 8 7 6 5 4 3 2 1

ISBN 978–0–07–338438–2

MHID 0–07–338438–0

ISBN 978–0–07–734330–9 (Annotated Instructor’s Edition)

MHID 0–07–734330–1

Vice President, Editor-in-Chief: Marty Lange

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All credits appearing on page or at the end of the book are considered to be an extension of the copyright page.

Library of Congress Cataloging-in-Publication Data

Bello, Ignacio.

Basic college mathematics : a real-world approach / Ignacio Bello. — 4th ed.

p.cm.

Includes index.

ISBN 978–0–07–338438–2 — ISBN 0–07–338438–0 (hard copy : alk. paper) 1. Mathematics. I. Title. QA39.3.B44 2012

510—dc22

2010020137

www.mhhe.com

V About the Author

Bello

Ignacio Bello

attended the University of South Florida (USF), where he earned a B.A. and M.A. in Mathematics. He began teaching at USF in 1967, and in 1971 became a member of the Faculty at Hillsborough Community College (HCC) and Coordinator of the Math and Sciences Department. Professor Bello instituted the USF/HCC

remedial program, a program that started with 17 students taking Intermediate Algebra and grew to more than 800 students with courses covering Developmental English, Reading, and Mathematics. Aside from the present series of books (Basic College Mathematics, Introductory Algebra, and Intermediate Algebra), Professor Bello is the author of more than 40 textbooks including Topics in Contemporary Mathematics (ninth edition), College Algebra, Algebra and Trigonometry, and Business Mathematics. Many of these textbooks have been translated into Spanish. With Professor Fran Hopf, Bello started the Algebra Hotline, the only live, college-level television help program in Florida. Professor Bello is featured in three television programs on the award-winning Education Channel. He has helped create and develop the USF Mathematics Department Website (http://mathcenter.usf.edu), which serves as support for the Finite Math, College Algebra, Intermediate Algebra, and Introductory Algebra, and CLAST classes at USF. You can see Professor Bello’s presentations and streaming videos at this website, as well as at http://www.ibello.com. Professor Bello is a member of the MAA and AMATYC and has given many presentations regarding the teaching of mathematics at the local, state, and national levels.

McGraw-Hill Connect

Less Managing.

More Teaching.

Greater Learning.

McGraw-Hill conducted in-depth research to create a new learning experience that meets the needs of students and instructors today. The result is a reinvented learning experience rich in information, visually engaging, and easily accessible to both instructors and students.

McGraw-Hill’s Connect is a web-based assignment and assessment platform that helps students connect to their coursework and prepares them to succeed in and beyond the course.

Connect enables math and statistics instructors to create and share courses and assignments with colleagues and adjuncts with only a few clicks of the mouse. All exercises, learning objectives, and activities are directly tied to text- specific material.

McGraw-Hill has partnered with BlackboardInc.toofferthedeepest integration of digital content and tools with Blackboard’s teaching and learning platform.

How was McGraw-Hill’s Connect better developed than other sites in the market?

McGraw-Hill’s Connect was developed with the instructor’s needs in mind. Instructors with subject matter expertise in their respective course area worked with our vendors to build content that is accurate, maintains the intent of the original problem from the text, and is consistent with our authors’ teaching methods.

Simple User Interface

Connect offers a variety of problem types with easy to use interface for students to input answers and receive various levels of feedback and help.

Simple Assignment

Management

Connect allows instructors to quickly and easily build and organize assignments utilizing various sorting features for questions.

Grade Reporting

View scored work immediately and track individual or group

performance with various assignment and grade reports

Media-rich eBooks

Connect reinvents the textbook learning experience for the modern student. Each subject area is seamlessly integrated with ConnectPlus eBooks, which are designed to keep students focused on the concepts key to their success.

VPreface

VFrom the Author

The Inspiration for My Teaching

I was born in Havana, Cuba, and I encountered some of the same challenges in mathematics that many of my current students face, all while attempting to overcome a language barrier. In high school, I failed my freshman math course, which at the time was a complex language for me. However, with hard work and perseverance, I scored 100% on the final exam the second time around. While juggling various jobs in high school (roofer, sheetrock installer, and dock worker), I graduated and received a college academic scholarship. I first enrolled in calculus and made a “C.” Never one to be discouraged, I became a math major and worked hard to excel in the courses that had previously frustrated me.

While a graduate student at the University of South Florida (USF), I taught at a technical school, Tampa Technical Institute, a decision that contributed to my resolve to teach math and make it come alive for my students the way brilliant instructors such as Jack Britton, Donald Rose, and Frank Cleaver had done for me. My math instructors instilled in me the motivation to work toward success. Through my teaching, I have learned a great deal about the way in which students learn and how the proper guidance through the developmental mathematics curriculum leads to student success. I believe I have developed a strong level of guidance in my textbook series by carefully explaining the language of mathematics and providing my students with the key fundamentals to help them reach success.

A Lively Approach to Build Students’ Confidence

Teaching math at the University of South Florida was a great new career for me, but I found that students, professors, including myself, and administrators were disappointed by the rather imposing, mathematically correct but boring book we had to use. So, I took the challenge to write a book on my own, a book that was not only mathematically correct, but student-oriented with interesting applications— many suggested by the students themselves—and even, dare we say, entertaining! That book’s approach and philosophy proved an instant success and was a precursor to my current series.

Students fondly called my class “The Bello Comedy Hour,” but they worked hard, and they performed well. When my students ranked among the highest on the common final exam at USF, I knew I had found a way to motivate them through common-sense language and humorous, realistic math applications. I also wanted to show students they could overcome the same obstacles I had in math and become successful, too. If math has been a subject that some of your students have never felt comfortable with, then they’re not alone!This book was written with the mathanxious students in mind, so they’ll find it contains a jovial tone and explanations that are patient instead of making math seem mysterious, it makes it down-to-earth and easily digestible. For example, after explaining the different methods for simplifying fractions, readers are asked: “Which way should you simplify fractions? The way you understand!” Once students realize that math is within their grasp and not a foreign language, they’ll be surprised at how much more confident they feel.

A Real-World Approach: Applications, Student Motivation, and Problem Solving

What is a “real-world approach”? I found that most textbooks put forth “real-world” applications that meant nothing to the real world of my students. How many of my students would really need to calculate the speed of a bullet (unless they are in its

viii

Form Characteristics

Fact Name Description
Title This form is titled "Bello Basic College Mathematics".
Purpose This guide aims to help students succeed in basic college mathematics.
Structure The book includes sections with suggested topics, objectives, and previews.
Examples Provided Multiple examples help clarify concepts and reinforce skills.
Environment Focus Green Math Examples relate mathematical concepts to environmental issues.
Mastery Checks Concept Checkers and Mastery Tests help assess understanding of the material.
Additional Resources The book includes access to solutions manuals and videos for further assistance.

Guidelines on Utilizing Basic College Mathematics

Completing the Basic College Mathematics form involves several steps to ensure that all relevant information is accurately provided. Following the instructions carefully will facilitate a smooth experience in utilizing the accompanying materials effectively.

  1. Start with the header section. Fill in your name, date, and any other identifying information required.
  2. Review suggested topics at the beginning of each section. This aids in understanding the materials better.
  3. Identify objectives outlined in each section. Make note of what tasks you should be able to perform.
  4. Preview topics with familiar applications to get a good grasp of the content being discussed.
  5. Work through examples provided in the form. These examples are designed to explain and expand on the objectives.
  6. Utilize the Green Math Examples, typically found at the end of each section, to bring environmental context to your learning.
  7. Complete the Paired Margin Problems to reinforce the skills learned in the examples.
  8. Engage in the Concept Checker to prepare for the Mastery Test. This section reinforces key terms.
  9. Take the Mastery Test to assess your understanding of the material in that section.
  10. Use the Skill Checker to evaluate your preparedness for the next section's material.
  11. Access Connect Practice Problems, Self Tests, and Videos. These additional resources can enhance your learning experience.
  12. Practice by completing Exercises grouped by objectives. These exercises offer interesting applications of the material.
  13. Pay attention to the Green Applications, marked with a green bar, which apply math concepts to environmental issues.
  14. Refer to the Summary section for a concise grid outlining the items studied along with examples.
  15. Review the coded exercises by section number for extra reinforcement and practice.
  16. Complete the Practice Test. Answers should be easy to reference by their respective Section, Example, and Page numbers.
  17. Engage with the Cumulative Review covering current and previous chapters to reinforce your understanding.
  18. Consult the Solutions Manual for worked-out odd-numbered solutions, Reviews, and Cumulative Reviews.
  19. Explore Videos on the Web where authors demonstrate problem-solving techniques step by step.

What You Should Know About This Form

What is the purpose of the Basic College Mathematics form?

The Basic College Mathematics form serves as a guide to help students succeed in their studies. It outlines essential components and strategies to effectively navigate the textbook material, ensuring that learners can grasp the concepts and perform tasks as they progress through each section.

How can I effectively use the material in this book?

To make the most of this book, start by reviewing the suggested topics at the beginning of each section. This will provide context for the material you will encounter. Next, identify the objectives, which are organized by section to help you understand what you need to accomplish. Lastly, preview the topics using familiar applications to gain insights before diving into the details.

What types of exercises are included in the book?

The book contains a variety of exercises aimed at reinforcing the skills introduced in the examples. These include paired margin problems that correspond to the examples, as well as practice problems connected to real-world applications. There is also a section for self-tests and videos that further enhance learning.

What is the Concept Checker?

The Concept Checker is a tool designed to help you reinforce key terms and concepts from each section. By completing this check, you prepare yourself for the Mastery Test that follows, ensuring you have a solid grasp on the material before moving forward.

What is included in the Mastery Test?

The Mastery Test consists of questions that allow you to assess your understanding of the material covered in the section. This quick evaluation helps you identify areas where you may need additional review before proceeding to more advanced topics.

How should I approach the Practice Tests?

Practice Tests are an opportunity to review what you have learned. Each question is referenced with the corresponding section, example, and page number for easy access. Approach these tests as a way to gauge your comprehension and readiness to move on to new material.

What are Green Applications?

Green Applications are exercises marked with a Green bar in the margin, focusing on how mathematics applies to environmental topics. These examples aim to connect mathematical concepts to real-world issues, providing a broader perspective on the importance of math in everyday life.

What resources are available for cumulative review?

For cumulative review, the book includes material that reflects topics from both current and prior chapters. This comprehensive review ensures that you are well-prepared for tests and assessments. Additionally, the Solutions Manual provides worked-out solutions for odd-numbered problems, all reviews, and cumulative reviews to aid your understanding.

How can videos on the web enhance my learning experience?

The videos available online feature the authors working through problems from the Practice Test step-by-step. These visual aids can clarify concepts and techniques, making it easier for you to follow along and understand the problem-solving process.

What should I do if I am struggling with the material?

If you find yourself struggling, it is important to utilize all available resources. Review the examples and practice problems directly related to the areas you find challenging. Consider reaching out to instructors or peers for assistance, and make use of supplemental materials, such as the Solutions Manual and online videos, to strengthen your understanding.

Common mistakes

Completing the Basic College Mathematics form can be straightforward, but many make common mistakes. One frequent error is skipping over essential sections, especially the objectives listed at the beginning. These objectives provide clarity on what students are expected to learn. Ignoring them can lead to confusion about the material covered.

Another mistake involves overlooking the examples provided in the book. The examples are designed to clarify concepts and demonstrate how to achieve the stated objectives. When students bypass these, they miss out on critical guidance that can enhance their understanding.

Many students also forget to engage with the paired margin problems. These problems are intended to reinforce skills learned through the examples. Not practicing them diminishes the chances of mastering the material, which is vital for long-term retention.

Checking for mastery is another crucial step often neglected. Students tend to skip the concept and skill checkers at the end of sections. These tools offer a way to assess understanding and prepare for upcoming tests. Missing them means potentially being unprepared when assessments arise.

Another common oversight is not utilizing the connect practice problems and exercises grouped by objectives. This can limit opportunities to apply what has been learned. Students should remember that practicing through varied exercises enhances learning.

In addition, some individuals rush through the summary and review sections. Although it might seem repetitive, reviewing these components helps solidify knowledge. Taking time to understand the summaries can lead to better outcomes.

Lastly, failing to use the solutions manual is a significant mistake. This resource can clarify where students might have gone wrong in their answers. Understanding mistakes is key to improving and achieving a deeper grasp of the material.

By being aware of these frequent mistakes, students can navigate the Basic College Mathematics form more effectively. Attention to detail and utilizing all resources available will greatly aid in their success.

Documents used along the form

In academic settings, several forms and documents are commonly associated with the **Basic College Mathematics** form. Each document serves a specific purpose, providing additional support and resources for students striving to understand mathematical concepts. The following list outlines some of the most frequently used documents that complement the Basic College Mathematics form.

  • Syllabus: This document provides an overview of the course, including objectives, required materials, grading policies, and key dates. It serves as a roadmap for students, outlining what they can expect throughout the term.
  • Homework Assignments: Regularly assigned work helps reinforce the material covered in class. Each assignment typically corresponds to a specific chapter or section of the mathematics form, promoting practice and comprehension.
  • Class Notes: Often compiled by students or instructors, class notes capture key points, examples, and explanations discussed during lectures. These notes are invaluable for review, especially before exams.
  • Study Guide: This comprehensive document offers a summary of critical concepts and problem-solving strategies. It usually includes practice problems and solutions, guiding students in preparing for tests effectively.
  • Mastery Test Results: Following the Mastery Test in the Basic College Mathematics form, students receive feedback on their performance. This document highlights strengths and areas needing improvement, helping them focus their study efforts.
  • Tutoring Requests: Many institutions provide tutoring services to support students who may require additional help. A tutoring request form allows students to seek out personalized assistance from qualified peers or instructors.

Each of these documents plays a pivotal role in enhancing a student's learning experience and ensuring a firm grasp of the material. By utilizing these resources in conjunction with the Basic College Mathematics form, students are better equipped to succeed in their mathematical studies.

Similar forms

  • Textbook Study Guide: Similar to the Basic College Mathematics form, a study guide offers condensed information and strategies tailored for effective learning. It often includes summaries, objective lists, and practice questions that prepare students for assessments.
  • Homework Workbook: A homework workbook provides exercises aligned with the main textbook content. It typically contains examples, paired problems, and review sections that reinforce students' understanding of the material.
  • Practice Test Booklet: A practice test booklet resembles the structure of the Basic College Mathematics form by including mastery tests and skill checkers. This booklet allows students to evaluate their comprehension and readiness for exams in a straightforward format.
  • Online Learning Platform: Similar to the resource guide in the mathematics form, online platforms often feature interactive exercises and videos. These resources foster engagement and supplement learning through immediate feedback and additional practice options.
  • Concept Review Sheets: Concept review sheets provide brief summaries and key concepts, akin to the summaries and reviews in the Basic College Mathematics document. They assist students in quick recall and understanding of essential topics crucial for later assessments.

Dos and Don'ts

When filling out the Basic College Mathematics form, it's essential to follow certain guidelines to ensure your submission is successful. Here are five dos and don’ts to keep in mind:

  • Do: Carefully review the suggested topics listed at the beginning of each section. This helps you understand what you need to study.
  • Do: Identify the objectives stated in each section. Knowing what tasks you should be able to perform is critical for success.
  • Do: Preview the topics discussed using familiar applications. This will help ground your understanding in real-world contexts.
  • Don't: Skip the Examples and Paired Margin Problems. These resources are designed to reinforce your learning and ensure mastery of the material.
  • Don't: Forget to utilize the Summary, Review, and Practice Test sections. They are vital for solidifying your knowledge and improving your performance.

Misconceptions

Here are some common misconceptions about the Basic College Mathematics form:

  • It's just a textbook with no guidance. Many people think the form does not offer any instructions. In reality, it provides detailed guidance on how to use the book effectively, promoting a structured approach to learning.
  • All examples are the same. Some assume every example in the book will be boring or repetitive. However, the examples include a variety of applications, such as those focusing on environmental topics, making learning more relevant and engaging.
  • The mastery tests are optional. Some believe they can skip the mastery tests without any consequence. In fact, these tests provide valuable feedback on understanding and retention of the material.
  • Exercises are all straightforward. It's a common belief that exercises will be easy. While many are manageable, they also encourage deeper understanding by incorporating interesting applications to challenges encountered in real life.
  • Review sections are unnecessary. Some people think the review sections are not important. These sections reinforce learning and offer extra practice, which can be essential for long-term retention.
  • The solutions manual solves everything. A misconception exists that the solutions manual eliminates the need for learning. While it provides worked-out solutions, it is meant to aid understanding, not replace the effort required to master the concepts.

Key takeaways

This guide provides crucial information on how to effectively fill out and use the Basic College Mathematics form. Here are nine key takeaways to keep in mind:

  1. Start by reviewing the suggested topics at the beginning of each section to set a strong foundation for your learning.
  2. Identify the objectives outlined, which clarify the tasks you should ultimately be able to accomplish.
  3. Preview the upcoming topics using familiar applications to facilitate understanding and retention.
  4. Utilize examples, particularly the Green Math Examples, which often relate mathematics to environmental issues.
  5. Practice with paired margin problems to reinforce the skills learned from each example; answers will be provided at the bottom of the page.
  6. Check your understanding with the concept checker before taking the mastery test that follows each section.
  7. Enhance your learning experience by engaging with Connect Practice Problems, self-tests, and educational videos.
  8. Review summaries and practice tests, which provide an easy reference for the content covered and help gauge your mastery.
  9. Access additional resources such as the solutions manual and online videos, which can offer step-by-step guidance for problem-solving.

By following these steps, you can maximize your learning and become proficient in basic college mathematics.