Reaching the. Texas CCRS. in Developmental Math at Texas State University

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1 Reaching the Texas CCRS in Developmental Math at Texas State University

2 Reaching the Texas CCRS in Developmental Math at Texas State University Preliminary Edition Charles P. McKeague Editorial Director: Patrick McKeague Sales Manager: Amy Jacobs Production Manager: Matthew Hoy Project Manager: Staci Truelson Developmental Editor: Katherine Heistand Shields Sales Representative: Richard Jones Text Designer: Devin Christ Cover Image: WisdomFromIntrospect Printed in the United States of America 2014 McKeague Textbooks, LLC ALL RIGHTS RESERVED. No part of this work covered by the copyright herein may be reproduced, transmitted, stored or used in any form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher. AIE Edition: ISBN-13: / ISBN-10: Student Edition: ISBN-13: / ISBN-10: For product information and technology assistance, contact us at XYZ Textbooks, XYZ Textbooks 1339 Marsh St. San Luis Obispo, CA USA For permission to use material from this text or product, ed: For your course and learning solutions, visit

3 Brief Contents 1 Statistics Probability 65 Geometry 119 Measurement 233 Conic Sections 325 iii

4 Contents 1 Statistics Statistics: Mean, Median, Mode, Variance and Standard Deviation Displaying Information Pie Charts The Binomial Expansion The Binomial Distribution The Normal Distribution 49 Chapter 1 Summary 59 Chapter 1 Review 63 Chapter 1 Test Probability The Fundamental Counting Principle Venn Diagrams, Permutations, and Combinations Introduction to Probability Probabilities and Compound Events Mutually Exclusive Events and Their Probabilities Conditional Probabilities: Independent and Dependent Events 108 Chapter 2 Summary 114 Chapter 2 Review 116 Chapter 2 Test 117 Geometry Angles Parallel Lines Classification of Triangles Congruent Triangles Polygons Proportions Similar Figures Geometric Transformations The Pythagorean Theorem Right Triangle Trigonometry 215 Chapter 3 Summary 225 Chapter 3 Review 229 Chapter 3 Test 231 iv

5 Contents v 4 5 Measurement Unit Analysis I: Length Unit Analysis II: Area and Volume Unit Analysis III: Weight Converting Between the Two Systems, and Temperature Operations with Time, and Mixed Units Perimeter and Circumference Area Surface Area Volume 306 Chapter 4 Summary 316 Chapter 4 Review 321 Chapter 4 Test 323 Conic Sections Circles Parabolas Ellipses Hyperbolas 359 Chapter 5 Summary 368 Chapter 5 Review 369 Chapter 5 Test 370

6 Preface XYZ Textbooks is on a mission to improve the quality and affordability of course materials for mathematics. Our 2013 Concepts with Applications Series brings a new level of technology innovation, which is certain to improve student proficiency. As you can see, these books are presented in a format in which each section is organized by easy to follow learning objectives. Most objectives include helpful example problems, as well as additional practice problems in the margins, and are referenced in each exercise set. To help students relate what they are studying to the real world, most chapters and sections begin with a real-life application of key concepts. You and your students will encounter extensions of these opening applications in the exercise sets. We have put features in place that help your students stay on the trail to success. With that perspective in mind, we have incorporated this navigational theme into the following new and exciting features. QR Codes Unique technology embedded in exercise sets allows students with a smart phone or other internet-connected mobile device to view our video tutorials without being tied to a computer. Vocabulary Review A list of fill-in-the-blank sentences appears at the beginning of each exercise set to help students better comprehend and verbalize concepts. Getting Ready For Class Simple writing exercises for students to answer after reading each section increases their understanding of key concepts. vi

7 Preface vii Key words A list of important vocabulary appears at the beginning of each section to help students prepare for new concepts. These words can also be found in blue italics within the sections. Find the Mistake Complete sentences that include common mistakes appear in most exercise sets to help students identify errors and aid their comprehension of the concepts presented in that section. End of Chapter Reviews and Tests Problems at the end of each chapter provide students with a comprehensive review of each chapter s concepts. XYZ Textbooks is committed to helping students achieve their goals of success. This new series of highly-developed, innovative books will help students prepare for the course ahead and navigate their way to a successful course completion.

8 STUDENT RESOURCES Instructor Name: Phone: Office Hours: Teacher Assistant Name: Phone: Office Hours: On-Campus Tutoring Location: Hours: Study Group Name: Phone: Name: Phone: Name: Phone: Supplements For the Instructor Online Homework XYZ Homework provides powerful online instructional tools for faculty and students. Randomized questions provide unlimited practice and instant feedback with all the benefits of automatic grading. Tools for instructors can be found at and include the following: Quick setup of your online class More than 3,000 randomized questions, similar to those in the textbook, for use in a variety of assessments, including online homework, quizzes, and tests Text and videos designed to supplement your instruction Automated grading of online assignments Flexible gradebook Message boards and other communication tools, enhanced with calculator-style input for proper mathematics notation MathTV.com With more than 8,000 videos, MathTV.com provides the instructor with a useful resource to help students learn the material. MathTV.com features videos of most examples in the book, explained by the author and a variety of peer instructors. If a problem can be completed more than one way, the peer instructors often solve it by different methods. Instructors can also use the site s Build a Playlist feature to create a custom list of videos for posting on their class blog or website. For the Student Online Homework XYZ Homework provides powerful online instruction and homework practice for students. Benefits for the student can be found at and include the following: Unlimited practice with problems similar to those in the text Online quizzes and tests for instant feedback on performance Online video examples Convenient tracking of class programs MathTV.com Students have access to math instruction 24 hours a day, seven days a week, on MathTV.com. Assistance with any problem or subject is never more than a few clicks away. Online Book This text is available online for both instructors and students. Tightly integrated with MathTV.com, students can read the book and watch videos of the author and peer instructors explaining most examples. Access to the online book is available free with the purchase of a new book. viii Preface

9 Additional Chapter Features Learning Objectives We have provided a list of the section s important concepts at the beginning of each section near the section title, noted with an orange capital letter, which is reiterated beside each learning objective header in the section. Example and Practice Problems Example problems, with work, explanations, and solutions are provided for every learning objective. Beside example problems, we have also provided a corresponding practice problem and its answer in the margin. Margin Notes In many sections, you will find yellow notes in the margin that correspond to the section s current discussion. These notes contain important reminders, fun facts, and helpful advice for working through problems. Colored Boxes Throughout each section, we have highlighted important definitions, properties, rules, how to s, and strategies in colored boxes for easy reference. Blueprint for Problem Solving We provide students with a step-by-step guide for solving application problems in a clear and efficient manner. Facts from Geometry Throughout the book, we highlight specific geometric topics and show students how they apply to the concepts they are learning in the course. Using Technology Throughout the book, we provide students with step-by-step instructions for how to work some problems on a scientific or graphing calculator. Descriptive Statistics In some sections, we call out to the use of descriptive statistics as they are applied to the concepts students are learning, and thus, applied to real life. EXERCISE SETS Vocabulary Review At the beginning of every exercise set, these fill-inthe-blank sentences help students comprehend and verbalize concepts from the corresponding section. Problems Each section contains problems ranging in difficulty that allow students to practice each learning objective presented in the section. The majority of the sections will also include problems in one or more of the following categories: Applying the Concepts Extending the Concepts or One Step Further Improving your Quantitative Literacy Getting Ready for the Next Section Extending the Concepts Chapter Summary At the end of each chapter, we provide a comprehensive summary of the important concepts from the chapter. Beside each concept, we also provide additional example problems for review. Answers to Odd-Numbered Questions At the end of the book, we have supplied answers for all odd-numbered problems that appear in the following features: Landmark Reviews Vocabulary Reviews Exercise Sets Find the Mistake Exercises Navigation Skills at a Glance Compile a resource list for assistance. Set short- and long-term goals for the course. Complete homework completely and efficiently. Pay attention to instructions, and work ahead. Be an active listener while in class. Engage your senses when studying and memorizing concepts. Study with a partner or group. Maintain a positive academic self-image, and avoid burnout. Prepare early for the final exam, and reward yourself for a job well done! Preface ix

10

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