Florida Geometry End-of-Course Assessment Book + Online

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To learn…

To succeed…

REA’s preparation for the Florida Geometry EOC

is fully aligned with the Next Generation

Sunshine State Standards and

Common Core State Standards.

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FLORIDA

End-of-Course Assessment

 Geometry

Rebecca Dayton

Mathematics Curriculum Specialist

With a foreword by

Michael Coon

Anclote High School

Holiday, Florida

  Research & Education Association

The benchmarks presented in this book were created and implemented

by the Florida Department of Education (FLDOE).

For further information, visit the FLDOE website at http://fcat.fldoe.org.

Research & Education Association

61 Ethel Road West

Piscataway, New Jersey 08854

E-mail: [email protected]

Ready, Set, Go!®

Florida Geometry End-of-Course Assessment

Copyright © 2013 by Research & Education Association, Inc.

All rights reserved. No part of this book may be reproduced in any

form without permission of the publisher.

Printed in the United States of America

Library of Congress Control Number 2012955614

ISBN-13: 978-0-7386-1112-9

ISBN-10: 0-7386-1112-3

LIMIT OF LIABILITY/DISCLAIMER OF WARRANTY: Publication of this work is for the purpose of test preparation and related use and subjects as set forth herein. While every effort has been made to achieve a work of high quality, neither Research & Education Association, Inc., nor the authors and other contributors of this work guarantee the accuracy or completeness of or assume any liability in connection with the information and opinions contained herein. REA and the authors and other contributors shall in no event be liable for any personal injury, property or other damages of any nature whatsoever, whether special, indirect, consequential or compensatory, directly or indirectly resulting from the publication, use or reliance upon this work.

All trademarks cited in this publication are the property of their respective owners.

REA® and Ready, Set, Go!® are registered trademarks of

Research & Education Association, Inc.

FLORIDA END-OF-COURSE

ASSESSMENT

GEOMETRY

Access your Online Tools

by following the instructions

found at the back of this book.

Contents

Foreword

About Our Author

About Research & Education Association

Acknowledgments

Passing the Florida Geometry EOC Test

About This Book

About the Test

Preparing for Computerized Testing

Next Generation Sunshine State Standards

Benchmarks

Chapter 1: Points, Lines, Planes, and Angles

Your Goals for Chapter 1

Standards

Distance Formula

Midpoint Formula

Angles Formed by a Transversal

End-of-Chapter Quiz: Points, Lines, Angles, and Planes

Answers to the Chapter Quiz

Chapter 2: Polygons

Your Goals for Chapter 2

Standards

Convex vs. Concave

Regular vs. Irregular Polygons

Interior Angles of Polygons

Exterior Angles of Polygons

Exercise 1

Congruent Polygons

Similar Polygons

Transformations

Exercise 2

Perimeter and Area

Perimeter and Area of Similar Polygons

Exercise 3

End-of-Chapter Quiz

Answers to the Exercises

Answers to the Chapter Quiz

Chapter 3: Quadrilaterals

Your Goals for Chapter 3

Standards

Special Quadrilaterals

Properties of Quadrilaterals

End-of-Chapter Quiz: Quadrilaterals

Answers to the Chapter Quiz

Chapter 4: Triangles

Your Goals for Chapter 4

Standards

Classification

Definitions Related to Triangles

Points of Concurrency

Exercise 1

Congruent Triangles

Similar Triangles

Measurements in Similar Triangles

Exercise 2

Proportional Segments

Inequality Theorems

Exercise 3

End-of-Chapter Quiz

Answers to the Exercises

Answers to the Chapter Quiz

Chapter 5: Right Triangles

Your Goals for Chapter 5

Standards

Pythagorean Theorem

Altitude to the Hypotenuse

Special Right Triangles

Trigonometric Ratios

End-of-Chapter Quiz

Answers to the Chapter Quiz

Chapter 6: Polyhedrons and Other Solids

Your Goals for Chapter 6

Standards

Solid Figures

Spheres

Exercise 1

Surface Area and Volume

Exercise 2

Congruent and Similar Solids

Effect of a Dilation on Surface Area and Volume

Exercise 3

End-of-Chapter Quiz

Answers to the Exercises

Answers to the Chapter Quiz

Chapter 7: Mathematical Reasoning and Problem Solving

Your Goals for Chapter 7

Standards

The Axiomatic Structure of Euclidean Geometry

Problem Solving Strategies

Reasoning and Proof

End-of-Chapter Quiz

Answers to the Chapter Quiz

Chapter 8: Logic

Your Goals for Chapter 8

Standards

Conditional Statements

Truth Tables

Direct and Indirect Proof

End-of-Chapter Quiz

Answers to the Chapter Quiz

Chapter 9: Circles

Your Goals for Chapter 9

Standards

Lines and Segments

Arcs

Exercise 1

Angle Types

Angles Formed by Secants and Tangents

Exercise 2

Circumference and Area

Arc Length

Area of a Sector

Exercise 3

Equation of a Circle

Exercise 4

End-of-Chapter Quiz

Answers to the Exercises

Answers to the Chapter Quiz

Practice Test A

Answers: Practice Test A

Practice Test B

Answers: Practice Test B

Practice Tests A & B are also available online at www.rea.com/studycenter

Foreword

With the arrival of high-stakes end-of-course assessments (EOCs) in Florida’s high schools, students and teachers need support to prepare for success. Although teachers are given standards, we are left with questions about how those standards will be assessed on the EOCs. Some standards will point to a broad understanding, while other standards will concern a specific calculation. In facing these standards-driven complexities, students and teachers can often be left with more questions than answers about the EOC.

Rebecca Dayton’s Florida Geometry End-of-Course Assessment provides the clarity and clarification that geometry students and teachers need for successful completion of the EOC. The chapters are broken down by topic, and each topic contains clear examples while indicating the standards that will be assessed in the topic. Every standard in this book is assessed either directly or indirectly on the EOC and fully aligned with the Common Core State Standards.

Ms. Dayton has unpacked and rated each standard as having low, medium, or high difficulty, so any reader will know the complexity of the concept being explained immediately. The examples in the chapters are conceptually aligned and contain some of the clearest explanations I’ve seen. At the end of the chapters, the reader will be able to take a quiz that assesses understanding of the concepts in the chapter. These assessments will help track the success rate of the concepts and will ultimately improve a student’s score on the EOC. The book concludes with two practice tests aligned with the official geometry EOC. The two full-length practice tests will reveal the student’s mastery of concepts while indicating which concepts still need to be reviewed.

Whether you are a geometry student or teacher, this book will give you a leg up on the EOC. I’m convinced that successful reading and completion of the activities in this book will raise students’ scores.

Michael Coon

Anclote High School

Holiday, Florida

January 2013

Michael Coon teaches mathematics for college readiness at Anclote High School. He is also actively involved in Common Core curriculum planning.

About Our Author

Rebecca Dayton is currently a Mathematics Curriculum Specialist for the Piscataway (N.J.) Township Schools, a position she has held for the past five years. Ms. Dayton earned her B.A. in mathematics from Rutgers University. She taught high school mathematics for seven years.

About Our Technical Editor

Mary Berlinghieri-Willi is a longtime geometry teacher, math editor, and tutor to middle school, high school, and college math students.

About Research & Education Association

Founded in 1959, Research & Education Association (REA) is dedicated to publishing the finest and most effective educational materials—including study guides and test preps—for students in elementary school, middle school, high school, college, graduate school, and beyond.

Today, REA’s wide-ranging catalog is a leading resource for teachers, students, and professionals. Visit www.rea.com for a complete listing of all our titles.

Acknowledgments

In addition to our author and technical editor, we would like to thank Larry B. Kling, Vice President, Editorial, for his overall guidance, which brought this publication to completion; Pam Weston, Publisher, for setting the quality standards for production integrity and managing the publication to completion; Alice Leonard, Senior Editor, for project management; Mel Friedman, Lead Math Editor, for project management and for quality control of the math content; and Kathy Caratozzolo of Caragraphics for typesetting the manuscript.

Introduction

Passing the Florida

Geometry EOC Test

About This Book

This book, along with REA’s true-to-format practice tests, provides you with the most up-to-date preparation for the Florida Geometry End-of-Course Assessment. Known simply as the Geometry EOC, this computer-based test measures your mastery of geometry.

This test prep gives you all the review and practice you need to succeed on exam day. By studying the review and taking our practice tests (either in the book or online), you can pinpoint what you already know and focus on the areas where you need to spend more time studying.

Each of our nine review chapters covers one of the major Geometry EOC subject areas and shows you how each area will be tested. Easy-to-follow examples and a step-by-step approach help you build your knowledge and confidence as you study.

Our two full-length practice tests give you the most complete picture of your strengths and weaknesses. After you’ve finished reviewing with the book, take our practice exams online at the REA Study Center (www.rea.com/studycenter). Because the Geometry EOC is computer-based, we recommend that you take the practice tests online to simulate test-day conditions. Each online test gives you instant score reports, diagnostic feedback, and onscreen detailed answer explanations.

If you’re studying and don’t have Internet access, you can take the printed tests in the book. These are the same tests offered at the REA Study Center, but without the added benefits of timed testing conditions and diagnostic score reports.

About the Test

The Florida EOC Assessments are part of Florida’s Next Generation Strategic Plan, which is designed to increase student achievement and improve college and career readiness. EOC assessments are computer-based, criterion-referenced assessments that measure specific standards that have been developed for several courses, including Algebra 1, Biology 1, Geometry, and U.S. History.

How is this test given?

For the majority of students, the EOC assessments are computer-based. Exceptions are made for students with disabilities who need to take EOC assessments on paper.

What is the format of the test?

The Geometry EOC assessment is delivered in multiple forms with a maximum of 65 questions that include 35–40 multiple-choice items (MC) and 20–25 fill-in response items (FR). Some questions will be field-test items and are not included in student scores. You will also have a