CliffsTestPrep FCAT Grade 10 Reading and Math: 10 Practice Tests

CliffsTestPrep ® FCAT Grade 10 Reading and Math: 10 Practice Tests by Enrique Ortiz and Thomas R. Davenport CliffsTe...

Author: Enrique Ortiz EdD | Thomas R. Davenport

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CliffsTestPrep

®

FCAT Grade 10 Reading and Math: 10 Practice Tests by Enrique Ortiz and Thomas R. Davenport

CliffsTestPrep

®

FCAT Grade 10 Reading and Math: 10 Practice Tests by Enrique Ortiz and Thomas R. Davenport

About the Authors

Publisher’s Acknowledgments

Enrique Ortiz is an associate professor at the University of Central Florida, Department of Teaching and Learning Principles.

Editorial

Thomas R. Davenport is an English teacher at Immokalee High School and has served on numerous development committees that actually developed the FCAT.

Technical Editor: David Herzog

Project Editor: Kelly D. Henthorne Acquisitions Editor: Greg Tubach Production Proofreader: Debbye Butler Wiley Publishing, Inc. Composition Services

CliffsTestPrep® FCAT Grade 10 Reading and Math: 10 Practice Tests Published by: Wiley Publishing, Inc. 111 River Street Hoboken, NJ 07030-5774 www.wiley.com

Note: If you purchased this book without a cover, you should be aware that this book is stolen property. It was reported as “unsold and destroyed” to the publisher, and neither the author nor the publisher has received any payment for this “stripped book.”

Copyright © 2006 Wiley, Hoboken, NJ Published by Wiley, Hoboken, NJ Published simultaneously in Canada Ortiz, Enrique, 1955CliffsTestPrep FCAT grade 10 reading and math : 10 practice tests / by Enrique Ortiz and Thomas R. Devenport. p. cm. ISBN-13: 978-0-7645-9933-0 (pbk.) ISBN-10: 0-7645-9933-X 1. Florida Comprehensive Assessment Test—Study guides. 2. Reading (Secondary)—Florida—Examinations, questions, etc. 3. Mathematics—Florida— Examinations, questions, etc. I. Title: FCAT grade 10 reading and math. II. Title: Cliffs Test Prep FCAT grade 10 reading and math. III. Davenport, Thomas R., 1949- IV. Title. LB3060.33.F54077 2006 373.126'2—dc22 2005025968 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 1B/RQ/RR/QV/IN No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400, fax 978-646-8600, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Legal Department, Wiley Publishing, Inc., 10475 Crosspoint Blvd., Indianapolis, IN 46256, 317-572-3447, fax 317-572-4355, or online at http://www.wiley.com/go/permissions. THE PUBLISHER AND THE AUTHOR MAKE NO REPRESENTATIONS OR WARRANTIES WITH RESPECT TO THE ACCURACY OR COMPLETENESS OF THE CONTENTS OF THIS WORK AND SPECIFICALLY DISCLAIM ALL WARRANTIES, INCLUDING WITHOUT LIMITATION WARRANTIES OF FITNESS FOR A PARTICULAR PURPOSE. NO WARRANTY MAY BE CREATED OR EXTENDED BY SALES OR PROMOTIONAL MATERIALS. THE ADVICE AND STRATEGIES CONTAINED HEREIN MAY NOT BE SUITABLE FOR EVERY SITUATION. THIS WORK IS SOLD WITH THE UNDERSTANDING THAT THE PUBLISHER IS NOT ENGAGED IN RENDERING LEGAL, ACCOUNTING, OR OTHER PROFESSIONAL SERVICES. IF PROFESSIONAL ASSISTANCE IS REQUIRED, THE SERVICES OF A COMPETENT PROFESSIONAL PERSON SHOULD BE SOUGHT. NEITHER THE PUBLISHER NOR THE AUTHOR SHALL BE LIABLE FOR DAMAGES ARISING HEREFROM. THE FACT THAT AN ORGANIZATION OR WEBSITE IS REFERRED TO IN THIS WORK AS A CITATION AND/OR A POTENTIAL SOURCE OF FURTHER INFORMATION DOES NOT MEAN THAT THE AUTHOR OR THE PUBLISHER ENDORSES THE INFORMATION THE ORGANIZATION OR WEBSITE MAY PROVIDE OR RECOMMENDATIONS IT MAY MAKE. FURTHER, READERS SHOULD BE AWARE THAT INTERNET WEBSITES LISTED IN THIS WORK MAY HAVE CHANGED OR DISAPPEARED BETWEEN WHEN THIS WORK WAS WRITTEN AND WHEN IT IS READ. Trademarks: Wiley, the Wiley Publishing logo, CliffsNotes, the CliffsNotes logo, Cliffs, CliffsAP, CliffsComplete, CliffsQuickReview, CliffsStudySolver, CliffsTestPrep, CliffsNote-a-Day, cliffsnotes.com, and all related trademarks, logos, and trade dress are trademarks or registered trademarks of John Wiley & Sons, Inc. and/or its affiliates. FCAT is a trademark of the Florida Department of Education. All other trademarks are the property of their respective owners. Wiley Publishing, Inc. is not associated with any product or vendor mentioned in this book. For general information on our other products and services or to obtain technical support, please contact our Customer Care Department within the U.S. at 800-762-2974, outside the U.S. at 317-572-3993, or fax 317-572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. For more information about Wiley products, please visit our web site at www.wiley.com

Message to Educators and Parents Florida educators from across the state are intricately involved with every significant aspect of the FCAT. Any educator wishing to serve on any of the committees responsible for any of the FCAT assessments should contact the Florida Department of Education (DOE) to volunteer. By way of a brief overview to those who have not explored the DOE website, the following information is provided to shed some light as to but some of the components of the FCAT Reading assessment development process. A Reading Content Advisory Committee comprised of reading and/or Language Arts professionals from schools, school districts, and universities advise the DOE on such matters as which Sunshine State Standards benchmarks should be assessed, item types for each benchmark, types of reading materials, range of difficulty of passages, and the number of benchmarks, passages, and items per grade level. Following the initial presentation by contracted professional writers, materials are reviewed by a Community Sensitivity Committee to ensure that the primary purpose of assessing achievement is not undermined by inadvertently including in the test any material that may be deemed inappropriate by parents and other citizens. All materials also pass through a Bias Review Committee to ensure that any bias, whether it be gender, racial/ ethnic, linguistic, religious, geographic, or socioeconomic is excluded. The Item Content Review Committee review materials to ensure whether passages/items are appropriate for the targeted grade level proposed, evaluate whether items measure the targeted benchmark, and that items are appropriately structured. A Rangefinder Committee reviews representative experimental performance item responses and establish sample groups at each score level to enable assembling of training materials for hand scoring. A Rangefinder Review Committee review actual student performance responses to ensure appropriate score levels against the rubric for each item to enable any necessary review and revision for training materials for hand scorers. Hand scorers are selected, trained, and must qualify in order to assess actual student performance responses. Each scorer is required to have at least a Bachelor’s Degree in a field related to the subject area being scored. All responses are assessed by at least two trained scorers to yield the resultant raw score. Careful monitoring is conducted throughout the assessment process to ensure accuracy of each hand scorer. The FCAT Reading test employs a wide variety of both informational and literary reading passages to assess students’ reading comprehension as defined in the Sunshine State Standards. Informational passages may include, but are not limited to, magazine and newspaper articles, editorials, and biographies. Literary passages may include, but are not limited to, short stories, poems, folk tales, and selections from novels. Grade 10 FCAT Reading passages will approximate 30 percent literary and 70 percent informational. The FCAT Reading test is comprised of between 45–50 multiple-choice questions and between 5–7 performance tasks. It is designed to take 160 minutes over 2 sessions. The content may be broken into four subject groupings as follows: Percent of Raw Score

Area

15–20

Words and Phrases in Context

20–50

Main Idea, Plot and Purpose

10–25

Comparisons and Cause/Effect

20–40

Reference and Research

While multiple-choice responses are machine scored, the following are some special concerns regarding performance tasks, which are hand scored based on rubrics:

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Respondents should try to answer all questions even if not sure of the answer as partial credit may be awarded for partially correct responses. Respondents should not include non-related information in a response. Information not contained in the source material is construed as not relevant. Remember, this is a comprehension assessment, not an assessment of prior knowledge. The respondent should use direct quotations from the material judiciously. Answers that are simply copied from the source material cannot receive full credit. Responses are digitally captured and routed to assessment centers for scoring. It is very important for the respondent to restrict written answers to the framed area specifically lined for their response. Information written outside the framed area cannot be reviewed by the assessor as it will escape digital capture. It is very unfortunate when points that might have been awarded are not, simply because the response could not be captured. It is not necessary for the respondent to restate the question in the answer on performance tasks. In fact, it is recommended they do not as there are times when the space provided for the response will barely be sufficient to contain an adequate response for full credit. It is important to base the response with details and information from the source materials as directed. If, however, a complete response is given, the respondent should not write more just to fill all lines. The respondent should not get distracted or disturbed if they are presented with a story or article about a topic with which they have limited exposure or are totally unfamiliar. It should be kept in mind that all answers will be in the story or article somewhere and that every effort is made to give all earned credit to each response. Respondents will not be given credit for extraneous information or responses not related to the question. They will not have credits taken away for such errors, so long as it does not materially detract from the correctness of other portions of the response. Be sure respondents address all parts of the questions. It is quite common for these questions to require multiple answers for total credit. This may take different forms. One way is for the question to ask for A and B data and direct the respondent to use details and information from the source to support their response. Another way is the for question to only ask for A data but require the respondent to support their response with details and information from both the source article and graphics used within the source article. Unless the respondent identifies information from both sources in their response, they cannot be awarded full credit.

While some stems may tend to reveal answers to other stems in these practice tests, this is allowed only on occasion to show a variety of stems relative to a given point. It should be noted however that FCAT takes great care is to ensure one stem does not provide an answer to another stem. Additionally, some distracters on these practice tests are specifically designed to give practice to students paying attention to detail. While not a standard used on FCAT, it is an important tool and is thereby included within these practice tests. By way of example, the text may state a direction of North. In these practice tests, a distracter with correct information except ‘South’ may be used in order to sharpen attention to detail. It is strongly recommended that both educators and parents explore the Florida Department of Education website for additional information including practice tests, released items, and a link to FCAT Explorer at www.FLDOE.ORG or http://www.firn.edu/doe/sas/fcat.htm. Additionally, please read the Introduction to both sections of this book for additional information.

Table of Contents Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 FCAT Grade 10 Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Format/Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Cognitive Complexity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Duration and Number of Items . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 FCAT Grade 10 Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Format/Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Cognitive Complexity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Duration and Number of Items . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

PART I: FCAT READING TEST Practice FCAT Reading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Practice FCAT Reading 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Passage 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Passage 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Answer Key for Practice Test 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Answers and Explanations for Practice Test 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Practice FCAT Reading 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Passage 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Passage 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Answer Key for Practice Test 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Answers and Explanations for Practice Test 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

Practice FCAT Reading 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Passage 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Passage 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Answer Key for Practice Test 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Answers and Explanations for Practice Test 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

Practice FCAT Reading 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Passage 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Passage 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Passage 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Passage 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Answer Key for Practice Test 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Answers and Explanations for Practice Test 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

Practice FCAT Reading 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Passage 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Passage 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Passage 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 Answer Key for Practice Test 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Answers and Explanations for Practice Test 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

PART II: FCAT MATH TEST Practice FCAT Math—Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Grade 10 FCAT Math Reference Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

CliffsTestPrep FCAT Grade 10 Reading and Math: 10 Practice Tests

Practice FCAT Math 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 First Part of Practice FCAT Math 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Second Part of Practice FCAT Math 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Answer Key for Practice Test 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Solutions for Practice FCAT Math 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

Practice FCAT Math 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 First Part of Practice FCAT Math 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Second Part of Practice FCAT Math 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 Answer Key for Practice Test 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 Solutions for Practice FCAT Math 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

Practice FCAT Math 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 First Part of Practice FCAT Math 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 Second Part of Practice FCAT Math 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 Answer Key for Practice Test 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 Solutions for Practice FCAT Math 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222

Practice FCAT Math 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 First Part of Practice FCAT Math 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 Second Part of Practice FCAT Math 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 Answer Key for Practice Test 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 Solutions for Practice FCAT Math 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

Practice FCAT Math 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 First Part of Practice FCAT Math 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 Second Part of Practice FCAT Math 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 Answer Key for Practice Test 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 Solutions for Practice FCAT Math 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

Dedication The Reading portion of this book is dedicated to all those with the Florida Department of Education who tirelessly give of themselves to the betterment of the assessment process for all students across this great state. I would like to especially mention Donna Wolak for her sacrificial dedication to the FCAT process. I would be remiss if I failed to thank Dr. Pat Wachholz whose direction and inspiration drive all aspiring writers to live the process. I suppose no one should author anything without giving credit to his or her Mom. So, Mom, for those times when you least knew but most greatly impacted my life, this is for you. And to my daughter, Jennifer, who makes me more proud than she could ever know. I wish to thank Teressa for standing by me through more difficulties than I could have possibly faced without her support. Finally, let me dedicate this to all those students who strive everyday to perform to the best of their abilities. I know you can succeed! — Tom Davenport The Mathematics portion of this book is dedicated to the many people who have molded and helped me along the way. Each of them is very special to me. My family and loved ones are obviously connected to me and have had a tremendous impact on my life: in loving memory of Ramón and Juana Scott, Ana Celia Reccy-Castro, and Enrique Ortiz, Sr.; Rosalina Scott, my mother, for her unconditional love; Enrique Gabriel, Samuel Enrique, and Natalie Marie, my kids, for their inspiration; Diana, my wife, for her patience, perseverance, and kindness; CastroReccy’s family, Castro-Mojica’s family, Rivera-Scott’s family and extended family in Daytona Beach, Florida, for their unselfish support. Beyond that are all those I have met in the classroom, each of whom has exerted some level of influence on me, including teachers and students: past, present, and future. To all of you I say—Thanks!

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— Enrique Ortiz

Introduction The Florida Department of Education (FDOE) indicates that the Florida Comprehensive Assessment Test (FCAT) is a key element of the statewide educational assessment and accountability program. The FCAT program includes assessments in the following areas: ■ ■ ■

Writing for students in grades 4, 8, and 10 Reading and mathematics for students in grades 3 through 10 Science for students in grades 5, 8, and 10

According to the FDOE the purpose of the statewide assessments is to gather information of two kinds: ■ ■

Parents, students, and teachers need FCAT data to provide information about student mastery of skills. The public needs FCAT data to understand the “educational health” of students and to hold schools and districts accountable for progress.

The FCAT measures student knowledge and understanding in the content areas of reading, writing, science, and mathematics as described in the Sunshine State Standards (SSS). A direct connection exists between the SSS and the questions included on the FCAT. The SSS are skills and competencies that Florida students should be able to learn from an early age. The FCAT writing test is usually taken in February, and the FCAT reading, mathematics, and science tests are taken in March. Specific schools’ teachers, principals, or guidance counselors should have more exact testing dates. The FCAT is part of Florida’s effort to improve the teaching and learning of higher educational standards (Florida Test Development Center, 2004). The SSS portion of the FCAT is a criterion-referenced test. A secondary intention of the FCAT is to compare these students’ performance to the performance of students across the nation. This comparison is made possible by using a norm-referenced test (NRT) for reading and mathematics. Unlike the other test prep books for the FCAT already on the market, this prep book is unique in that it offers an introductory section on the format and structure of the exams, rather than sacrificing a great amount of space on review, and combines 10 full-length practice tests (five for the reading test, and five for the math test). The intention of this book is to serve as a tool to practice and learn more about the FCAT math and reading tests. This book is not a substitute for quality learning and teaching in the regular classroom, but it provides practice of test-taking skills needed for the FCAT in these areas. The FDOE uses electronic scoring for most grades and a combination of electronic scoring and handscoring for grades with performance tasks. Students’ multiple-choice and gridded-response answers are scored using computer programs that read the students’ bubbled answers and score them based on an answer key. Qualified and trained scorers read and evaluate students’ answers to the performance tasks (free response, short response, and long response items). They use answer keys and rubrics (criteria) that have been established and validated by Florida educators. The total score that a student may receive in reading and mathematics ranges from 100 to 500. In the FCAT writing test, students receive a score from 1 to 6, a 6 being the highest possible score. The reading and mathematics scores are also reported as developmental scale scores that range from 0–3000. More information and materials are available from the FDOE’s Office of Assessment and School Performance: Florida Department of Education 325 West Gaines Street, Suite 414 Tallahassee, Florida 32399-0400 Phone: (850) 245-0513 or Suncom 205-0513, Fax: (850) 245-0771 http://www.firn.edu/doe/sas.fcat.htm These materials include FCAT Explorer (www.fcatexplorer.com), FCAT Developmental Scores, Test Taking Tips (http://www.firn.edu/doe/family/home0077.htm), assessment rubrics, calculator descriptions and uses, Keys to FCAT,

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CliffsTestPrep FCAT Grade 10 Reading and Math: 10 Practice Tests

Frequently Asked Questions, Sample Test booklets (http://www.firn.edu/doe/sas/fcat.htm), and FCAT Myths and Facts. Many of these materials are available as easy-to-download files. We recommend that you use this test preparation manual in conjunction with the FDOE resources and materials. The following is a general introduction to the FCAT Grade 10 Reading and FCAT Grade 10 Math. It includes information about the tests’ format/structure, cognitive complexity, duration, and number of items.

FCAT Grade 10 Reading Format/Structure The reading test covers four main areas (percent of the test dedicated to each area is given in parentheses): ■ ■ ■ ■

Words and Phrases in Context (15–20 percent) Main Ideas, Plot, and Purpose (20–50 percent) Comparisons and Cause/Effect (10–25 percent) Reference and Research (20–40 percent)

Two types of questions are included on the FCAT Reading: ■ ■

45–50 multiple-choice questions, and 5–8 performance tasks (free response).

Cognitive Complexity Webb’s (2005) classification system, which involves depth of knowledge, is used now to classify FCAT items: ■ ■ ■

Low complexity items rely heavily on recall and recognition. Moderate complexity items require more flexible thinking and may require informal reasoning or problem solving. High complexity items are written to elicit analysis and abstract reasoning.

The items are classified on the cognitive demand inherent in the item, not on assumptions about the student’s approach to the item. This is a change in how items are classified and not a change in the items or in the tests. This system is also used for the National Assessment of Educational Progress (NAEP). The percentage points by cognitive complexity level for each area in 10th grade FCAT Reading are the following (Florida Test Development Center, 2004): ■ ■ ■

Low 10–20 Moderate 45–65 High 25–35

The 10th grade reading FCAT tests include performance tasks, which are typically moderate to high complexity items.

Duration and Number of Items The duration of 10th grade reading FCAT (number of minutes allowed at this time) for each SSS and NRT test are the following: ■ ■

2

SSS Reading: 160 minutes NRT Reading: 60 minutes

Introduction

The approximate range for the number of items on each 10th grade FCAT Reading is the following: ■ ■

SSS Reading: 50–55 NRT Reading: 50–55

The approximate ranges for the number of items by each 10th grade item type (these ranges include both operational and field-test items) for the SSS Reading FCAT: ■ ■ ■

45–50 Multiple Choice 5–7 Short Response Extended Response

FCAT Grade 10 Math Format/Structure The Math test covers five content areas (percent of the test dedicated to each area is given in parentheses): ■

Number Sense and Operations (17 percent) ■ ■ ■

identifies addition, subtraction, multiplication, and division and knows what they do determines estimates knows how numbers are represented and used

■

Measurement (17 percent) ■ recognizes measurements and units of measure ■ compares, contrasts, and converts measurements

■

Geometry and Spatial Sense (25 percent) ■ describes, draws, identifies, and analyzes two- and three-dimensional shapes ■ visualizes and illustrates changes in shape ■ uses coordinate geometry

■

Algebraic Thinking (25 percent) ■ describes, analyzes, and generalizes patterns, relations, and functions ■ writes and uses expressions, equations, inequalities, graphs, and formulas

■

Data Analysis and Probability (17 percent) ■ organizes, interprets, and analyzes data ■ identifies patterns and makes predictions, inferences, and valid conclusions ■ uses probability and statistics

Cognitive Complexity According to the Florida Test Development Center (2004), prior to 2004, Bloom’s Taxonomy was used as the cognitivelevel classification system for FCAT items. This system involved assumptions about students’ instructional backgrounds and approaches to a given problem. Webb’s (2005) classification system, which involves depth of knowledge, is used now to classify FCAT items: ■

Low complexity items rely heavily on recall and recognition.

■

Moderate complexity items require more flexible thinking and may require informal reasoning or problem solving. High complexity items are written to elicit analysis and abstract reasoning.

■

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CliffsTestPrep FCAT Grade 10 Reading and Math: 10 Practice Tests

The items are classified on the cognitive demand inherent in the item, not on assumptions about the student’s approach to the item. This is a change in how items are classified, and not a change in the items or in the tests. This system is also used for the National Assessment of Educational Progress (NAEP). The percentage points by cognitive complexity level for each area in 10th grade Math FCAT are the following (Florida Test Development Center, 2004): ■ ■ ■

Low 10–20 Moderate 50–70 High 20–30

The 10th grade Math FCAT tests include performance tasks, which are typically moderate to high complexity items.

Duration and Number of Items The duration of 10th grade Math FCAT tests (number of minutes allowed at this time) for each SSS and NRT test are the following: ■ ■

SSS Math: 160 minutes NRT Math: 60 minutes

The approximate ranges for the number of items by each 10th grade item type (these ranges include both operational and field-test items) for the SSS Math: ■ ■ ■

30–35 Multiple Choice 15–20 Gridded Response 5–8 Short Response and Extended Response

References FCAT Test Development Center (2004). Florida Comprehensive Assessment Test Summary and Design. Tallahassee, Florida: Florida Department of Education. Webb, N. L. (2004). Norman Lott Webb’s Homepage. Madison, Wisconsin: Wisconsin Center for Education Research, University of Wisconsin-Madison. Retrieved January 22, 2005: http://facstaff.wcer.wisc.edu/normw.

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PART I

F CAT R EAD I N G TE ST

Practice FCAT Reading The FCAT reading test is comprised of a number of articles sufficient to yield 50–55 questions for the purpose of assessing student comprehension levels based on the Sunshine State Standards. Each article is 300–1700 words with a general average length of 900 words. For the practice tests, we have included articles of more substantial length to better prepare students for the actual test. The breakdown of items on the test is 45–50 multiple-choice questions and 5–7 performance tasks. Multiple-choice questions require respondents to select the best answer from four possible choices. These questions are machine scored. Performance task questions require respondents to answer questions in their own words. Two types of performance task questions are on the FCAT reading test: Short-Response (SR) and Extended-Response (ER). Each performance task answer is scored separately by a minimum of two professional evaluators. The final raw score is the result of these multiple evaluations. All performance task questions are scored using rubrics. All performance task evaluators must successfully complete mandated training approved by the Department of Education (DOE) and are carefully monitored throughout the entire process to ensure continued accuracy and compliance with all established assessment criteria. Scoring for each type performance task is as follows: Short-Response (SR) Task Complete and Correct Answer

2 Raw Score Points

Partially Correct Answer

1 Raw Score Point

Extended-Response (ER) Task Complete and Correct Answer

4 Raw Score Points

Partially Correct Answer

3, 2, or 1 Raw Score Point(s)

Respondents are given 8 lines to complete an SR answer and 14 lines to complete an ER answer. It is important to keep all writing within the framed area provided for the response as all responses are digitally scanned and routed to assessment centers. It is impossible for a student to get credit for any portion of a performance task that is written outside the framed response area. Some things to remember when preparing to take the actual FCAT reading test: ■ ■ ■ ■

■

■

■

■

As FCAT is a nonpenalty test, try to answer all questions. No pattern exists for the correct answers. The myth that the longest answer (normally ‘D’) is the correct answer is absolutely not true. The developers and reviewers of the actual FCAT review items to ensure that the answer to any question is not provided in another question. The reading test is geared to 10th grade vocabulary. Vocabulary questions may appear on the test where context clues are considered sufficient to give direction to a correct response. This is a reading comprehension test. Performance task answers should not include opinions of the respondent, and correct answers are always somewhere in the material presented. Be certain to address all parts of a question, particularly performance tasks. Some tasks will ask for more that one answer, and other tasks will ask for one data type but require the respondents to support their answers from more than one source (for example, details and information from both the article and the graphic). It is perfectly acceptable to mark in your test booklet. If underlining or making margin notes helps you as you read, feel free to do so on the actual test. You may want to practice this discipline as you take these practice tests. (Do not use highlighters or other marking implements during the practice tests, as this is not allowed on the actual FCAT.)

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Part I: FCAT Reading Test

You should explore the Florida Department of Education website for additional information including practice tests, released items, and a link to FCAT Explorer at www.FLDOE.ORG or http://www.firn.edu/doe/sas/fcat.htm. Additionally, please read the Message to Educators and Parents in this book.

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Practice FCAT Reading 1 This practice test contains two reading passages and 52 sample questions. Read each passage and answer all the questions that follow each passage.

Passage 1 Read the following passage before answering Questions 1 through 26.

Air Force One Air Force One is the air traffic control call-sign of any U.S. Air Force aircraft carrying the President of the United States. Since 1990, the presidential fleet has consisted of two specifically configured, highly customized Boeing 747-200B series aircraft. It is important to note that the aircraft are only referred to as Air Force One while the President is on board; the planes are given different call-signs in other situations. These planes are maintained by the U.S. Air Force solely for presidential air transport. The plane is capable of flying 7,800 miles—roughly one-third of the distance around the world—without refueling and can accommodate more than 70 passengers. From its inception Air Force One has become a symbol of Presidential power and prestige. The Secret Service refers to Air Force One by the codename Angel.

Operation These aircraft are maintained and operated as military operations by the Presidential Airlift Group, part of Air Mobility Command’s 89th Airlift Wing, based at Andrews Air Force Base in Suitland, Maryland. The President is often flown in a U.S. Marine Corps helicopter, call-sign Marine One, between the Andrews AFB and the White House. Similarly, a U.S. Army aircraft carrying the President has the call-sign Army One; U.S. Navy aircraft are called Navy One. A civilian plane carrying the President has the call-sign “Executive One,” and a plane carrying a member of the first family will be called “Executive One Foxtrot.”

Capability and Features The planes that serve as Air Force One differ from the standard Boeing 747 in size, features, and security precautions. While Air Force One has three floors, like a regular Boeing 747, its interior has been reconfigured for presidential duties. The planes’ 4,000 square feet of interior floor space include multiple modifications. The planes’ lowest level is mostly cargo space, carrying luggage and the planes’ food supply. The food can supply up to 2,000 meals when fully loaded, some of which are stored in freezers. Meals are prepared in two galleys, which together are equipped to feed about 100

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Part I: FCAT Reading Test

people at a time. The main passenger area is on the second floor, and communications equipment and the cockpit are on the third floor. Onboard Air Force One are medical facilities, including a fold-out operating table, emergency medical supplies, and a well-stocked pharmacy. On every flight there is a staff doctor. In addition, there are separate sleeping quarters for guests, senior staff, Secret Service and security personnel, and the news media; the president’s executive suite includes a private dressing room, workout room, lavatory, shower, and private office. These offices, including the president’s suite, are mostly located on the right side of the aircraft (while facing forward), and a long corridor runs along the left side. Whenever Air Force One finishes taxiing on the tarmac, it always comes to a stop with the left side of the aircraft facing gathered onlookers as a security measure to keep the President’s side of the aircraft out of view. In the office areas, Air Force One features access to photocopying, printing, and word processing, as well as telecommunication systems (including 85 telephones and 19 televisions). There are also secure and non-secure voice, fax, and data communications. Most of the furniture onboard was hand-crafted by master carpenters. The planes can also be operated as a military command center in the event of an incident such as a nuclear attack. Operational modifications include aerial refueling capability and anti-aircraft missile countermeasures. The electronics onboard include around 238 miles of wiring, twice the amount in a regular 747. These are covered with heavy shielding to protect wires and electronics from the electromagnetic pulse generated by a nuclear attack. The planes also have electronic countermeasures (ECMs) which jam enemy radar, and flares to avoid heat-seeking missiles. Much of Air Force One’s other capabilities are classified for security reasons.

History

The C-54 Skymaster aircraft, nicknamed the Sacred Cow.

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Practice FCAT Reading 1

Prior to World War II, overseas and cross-country presidential travel was rare. Lack of telecommunications and quick transportation made long-distance travel impractical, as it took up much time and isolated the President from events in Washington. In the 1940s and 1950s, however, air travel became much more convenient. The first president to fly in an airplane while in office was Franklin D. Roosevelt, who traveled on a Boeing 314 “flying boat” aircraft to a 1943 conference in Casablanca on the progress of World War II. The main reason at the time for presidential air travel was the threat of the German Navy’s U-boats in the Atlantic. The continuing threat from the submarines established air travel as a usual means of distance transportation for the President. The first aircraft officially designated for Presidential flight was the C-87A Liberator Express. This plane was called Guess Where Two. However, the plane was no longer used for Roosevelt after another C-87A crashed; the Secret Service reconfigured a C-54 Skymaster as a replacement. This plane was nicknamed the Sacred Cow and included a sleeping area, radio telephone, and retractable elevator for Roosevelt’s wheelchair. It carried the President to several important events, most notably the Yalta Conference.

The Independence. After Roosevelt died in spring 1945, Vice President Harry S. Truman became President. He replaced the C-54 with a modified C-118 Liftmaster, calling it the Independence, possibly in reference to President Truman’s hometown of Independence, Missouri. This was the first aircraft acting as Air Force One that had a distinctive exterior (an eagle head painted on its nose). The call signs were established for security purposes during the administration of Dwight D. Eisenhower, the first American president to have been a pilot in his own right. The change stemmed from a 1953 incident where an Eastern

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Part I: FCAT Reading Test

Airlines commercial flight (8610) had the same call-sign as a flight the President was on (Air Force 8610). The planes accidentally entered the same airspace, and after the incident the unique call sign “Air Force One” was made for the Presidential aircraft.

The Columbine III. Eisenhower also introduced two other propeller aircrafts, the Lockheed C-121 Constellations (VC-121E) to Presidential service. These planes were named Columbine II and Columbine III by Mamie Eisenhower after the official state flower of Colorado, her adopted home state. President Eisenhower also upgraded Air Force One’s technology by adding an air-toground telephone and an air-to-ground teletype machine. Towards the end of Eisenhower’s term, in 1958, the Air Force added two Boeing 707 jets to the fleet. With John F. Kennedy, presidential air travel officially entered the jet age. In 1962, a modified long-range 707 was added to the fleet—SAM 26000. He also commissioned industrial designer Raymond Loewy to create a distinctive exterior for the plane. Loewy came up with a powder blue and white design, the same colors used today; he also had the words “United States of America” put on the fuselage’s side, the U.S. flag painted on the tail, and the Presidential seal added to both sides of the nose. Lyndon B. Johnson became the first and only president to take the oath of office on Air Force One after Judge Sarah T. Hughes swore him in following the assassination of John F. Kennedy. In 1974, when Richard M. Nixon resigned the presidency and departed from Andrews AFB on Air Force One, it was arranged that the plane’s call sign would switch from Air Force One to SAM (Special Air Mission) designation the moment Gerald Ford took the oath of office.

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Practice FCAT Reading 1

1. Air Force One is called by the codename Angel A. B. C. D.

when the First Lady is onboard. when it is referred to by the Secret Service. when the plane is en route to the White House. when it is referred to by the Central Intelligence Agency.

2. What similar action did both President Truman and President Kennedy take in regards to Air Force One? A. B. C. D.

modifications to the plane’s name modifications to the plane’s exterior addition of a retractable elevator for a wheelchair modifications to the interior to include a sleeping area

3. This article would probably be most useful for someone doing research on A. B. C. D.

national security. the Secret Service. the history of Air Force One. the presidency of Franklin D. Roosevelt.

4. Describe some specific developments that made Presidential overseas travel less prohibitive. Use details and information from the text to support your answer.

5. How are communications systems on Air Force One protected from electromagnetic pulses generated by a nuclear attack? A. B. C. D.

heavy shielding reverse polarity stealth capabilities special jamming devices

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Part I: FCAT Reading Test

6. The most significant contributing factor to the first presidential use of an airplane was A. B. C. D.

safety due to attack by sea. radio telephone communications. the speed an airplane could travel. the overall convenience of air travel.

7. What caused the Secret Service to change from the C-87A Liberator Express to a C-54 Skymaster? A. B. C. D.

the ability to use radio communications advances in technology and design of aircraft safer air travel due to similar aircraft crashing increased size of sleeping area available on larger aircraft

8. What incident caused the need for a special naming of the president’s plane? A. B. C. D.

the beginning of World War II duplicate call-signs with Eastern Airlines the commencement of the Yalta Conference the experience President Eisenhower had as a pilot

9. Franklin Roosevelt’s plane was often referred to as a “flying boat” because A. B. C. D.

the President usually compared it to his boat. the Boeing 314 resembled a boat on the inside. the President usually traveled overseas by boat. the Boeing 314 was not as aerodynamic as a boat.

10. Which president was responsible for initially upgrading communications on Air Force One? A. B. C. D.

Nixon Truman Kennedy Eisenhower

11. Which event would cause the call sign of Air Force One to be changed during flight? A. B. C. D.

a nuclear attack a terrorist threat the President no longer being onboard the President retiring to private quarters onboard

12. President Johnson holds what distinction as it relates to Air Force One? A. B. C. D.

14

He was the first president to use jet propulsion. He was the first president to fly around the world. He was the first president to be sworn in onboard. He was the first president to send air-to-ground teletype messages.

Practice FCAT Reading 1

13. Read this sentence from the article. Operational modifications include aerial refueling capability and anti-aircraft missile countermeasures. What does the word “countermeasures” mean? A. B. C. D.

offsetting methods counting messages reverse measurements method to detect missile distance

14. What are some of the differences between a standard Boeing 747 and Air Force One? Why were some of these modifications made? Use details and information from the article to support your answer.

15. What is the main idea of the story? A. B. C. D.

Air Force One is a much needed aircraft. Air Force One has evolved much over the years. Air Force One is the most secure aircraft in the world. Air Force One is the most advanced aircraft in the world.

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Part I: FCAT Reading Test

16. Which statement does the article BEST support? A. B. C. D.

Air Force One replicates presidential living quarters. Air Force One is designed for press conferences in the air. Air Force One fully functions as a mobile command center. Air Force One is designed as a fully functional passenger aircraft.

17. During landing, why does the pilot position Air Force One with the left side of the craft toward onlookers? A. B. C. D.

because the reporters leave from that side because the Presidential seal is on the left because the Presidential suite is on the right because the exit door is located on the left side

18. The term ‘One’ is only used in the call-sign when A. B. C. D.

The President is not onboard. The President is on the plane. The aircraft is used to transport the press. The aircraft is on official presidential business.

19. Air Force One is considered a symbol of both A. B. C. D.

power and prestige. power and command. power and superior air transport. prestige and superior air transport.

20. What is the purpose of Air Force One being able to fly a long distance? A. B. C. D.

The plane can stay aloft during an attack. The need for constant contact is eliminated. The need for constant refueling is eliminated. The plane can communicate for military needs.

21. If a member of the President’s family is flying on a civilian plane, the call-sign would be A. B. C. D.

Sacred Cow. Executive One. Special Air Mission. Executive One Foxtrot.

22. Planes that are used for Air Force One are different from Boeing 747s in all of the following EXCEPT A. B. C. D.

16

size. features. number of levels. safety precautions.

Practice FCAT Reading 1

23. Read this sentence from the article. Much of Air Force One’s other capabilities are classified for security reasons. What does the author mean by this statement? A. B. C. D.

Other capabilities of Air Force One are secret. Other capabilities of Air Force One are unknown. The author was told Air Force One has other capabilities. The author believes that Air Force One has other capabilities.

24. Prior to World War II, why was long-distance travel for presidents unrealistic? A. B. C. D.

The C-87A Liberator Express had not yet been invented. The Boeing 314 “Flying Boat” had not yet been invented. Travel was time consuming and separated the President from his work. Travel became more convenient in the 1940s and even more so in the 1950s.

25. While acting as Air Force One, what aircraft was the first to have its outside appearance modified? A. B. C. D.

Sacred Cow Independence Columbine III Guess Where Two

26. Who is responsible for the current design of Air Force One? A. B. C. D.

Sarah Hughes Raymond Loewy Mamie Eisenhower Dwight Eisenhower

Passage 2 Read the following passage before answering Questions 27 through 52.

Carlsbad Caverns National Park Carlsbad Caverns National Park is a United States National Park located in the southeastern corner of New Mexico. It was established to preserve Carlsbad Cavern and numerous other caves. The park contains 83 separate caves, including the nation’s deepest and third longest limestone cave—1,597 feet. Carlsbad Cavern, with one of the world’s largest underground chambers and countless formations, is highly accessible, with both self-guided and a variety of rangerguided tours offered year-round. Visitors can hike into the interior rooms on their own via the natural entrance, or take an elevator (the exit for everyone) directly down into the center of the public cave area.

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Part I: FCAT Reading Test

Carlsbad was first designated a National Monument on October 25, 1923. It was redesignated a national park on May 14, 1930. Carlsbad Caverns was also designated a World Heritage Site on December 6, 1995. Carlsbad Caverns National Park is open year-round, but the majority of park visitors come during the months of June, July and August and on weekends and holidays. The month with the least visitors is January. The park is open 24 hours a day, seven days a week, except Christmas Day.

Geology The story of the creation of Carlsbad Cavern begins 250 million years ago with the creation of a 400-mile-long reef in an inland sea that covered this region. This horseshoe-shaped reef formed from the remains of sponges, algae and seashells and from calcite that precipitated directly from the water. Cracks developed in the reef as it grew seaward. Eventually the sea evaporated and the reef was buried under deposits of salts and gypsum.

The forces of water decorated the cave in an almost endless array of spectacular limestone formations like this column and array of stalactites. Then, a few million years ago, uplift and erosion of the area began to uncover the buried rock reef. Rainwater, made slightly acidic from the air and soil, seeped down into the cracks in the reef, slowly dissolving the limestone and beginning the process that would form large underground chambers. At the same time, hydrogen sulfide gas was migrating upward from vast oil and gas deposits beneath the ancient reef. This gas dissolved in the percolating ground water to form sulfuric acid. The added power of this corrosive substance explains the size of the passageways. The exposed reef became part of the Guadalupe Mountains and the underground chambers became the wonder of Carlsbad Cavern.

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Practice FCAT Reading 1

The Witch’s Finger in Carlsbad Caverns. The decoration of Carlsbad Cavern with stalactites, stalagmites and an incredible variety of other formations began more than 500,000 years ago after much of the cavern had been carved out. It happened slowly, drop by drop, at a time when a wetter, cooler climate prevailed. The creation of each formation depended on water that dripped or seeped down into the limestone bedrock and into the cave. As a raindrop fell to the ground and percolated downward, it absorbed carbon dioxide gas from the air and soil, and a weak acid was formed. As it continued to move downward the drop dissolved a little limestone, absorbing a bit of the basic ingredient needed to build most cave formations—the mineral calcite. Once the drop finally emerged in the cave, the carbon dioxide escaped into the cave air. No longer able to hold the dissolved calcite, the drop deposited its tiny mineral load as a crystal of calcite. Billions and billions of drops later, thousands of cave formations had taken shape. Where water dripped slowly from the ceiling, soda straws and larger stalactites appeared. Water falling on the floor created stalagmites. Sometimes a stalactite and stalagmite joined, forming a column, such as the Witch’s Finger. Draperies were hung where water ran down a slanted ceiling. Water flowing over the surface of a wall or floor deposited layers of calcite called flowstone. Cave pearls, lily pads and rimstone dams appeared where pools of water or streams occurred in the cave. Like oyster pearls, cave pearls were made as layer upon layer of calcite built up around a grain of sand or other tiny object. Lily pad-shapes formed on the surface of pools, while dams formed where water flowed slowly on the floor. Another type of cave formation that decorated cave walls and even other formations are popcorn-shapes, which may have formed when water evaporated and left behind calcite deposits.

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Some of the more unusual formations to occur in Carlsbad Cavern are helictites, which grow seemingly without regard to gravity, their twisting shapes governed by crystal shapes, impurities and the force of water under pressure. Other rare formations are those composed not of calcite, but of aragonite, a mineral chemically identical to calcite but with a different crystal structure. These formations tend to be small, delicate and needle-like.

Bats

The natural entrance to Carlsbad Cavern lies just beyond the bat amphitheater. Carlsbad Cavern is a sanctuary for about one million Mexican Freetail Bats. During the day the bats crowd together on the ceiling of Bat Cave, a passageway near the natural entrance of Carlsbad Cavern. In their darkened home they are seen only by scientific researchers. At nightfall, however, the bats leave the cave in gigantic swarms. Silhouetted against the night sky like a dark, swift-moving cloud, the bats make their most dramatic display. The Bat Cave serves as a warm weather home, as a daytime refuge, and perhaps most importantly, as a maternity roost, for Mexican Freetail Bats. The bats migrate from Mexico to Carlsbad Cavern each year to give birth and raise their young. Under cover of darkness, away from predators or disturbances, the young are born in June. As many as six other types of bats roost in the Cavern. The spectacular night flight of the Mexican Freetail begins with a few bats fluttering out of the natural entrance of Carlsbad Cavern. Then, in a matter of minutes, a thick whirlwind of bats spirals out of the cave up into the darkening night sky. The exodus can last 20 minutes or as long as 2.5 hours. Once out of the cave the undulating mass of thousands of bats flies, in serpentine fashion, towards the southeast to feed in the Pecos and Black River valleys. Once there, they begin gorging themselves on moths and other night-flying insects. Using echolocation, each bat may catch and eat several stomachfuls of insects in a single night. With the coming of dawn, the bats begin flying back to the cave individually or in small groups. They re-enter the cave in a fashion almost as remarkable as their departure. Each bat positions itself

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Practice FCAT Reading 1

high above the cave entrance. It then folds its wings close to its body, and plummets like a hailstone into the blackness of Carlsbad Cavern, making a strange buzzing sound as it does. One by one, the bats return to the safety of the Bat Cave, where they sleep until reemerging in the dusk of the next day.

History More than 1,000 years ago prehistoric Native Americans ventured into the Cavern seeking shelter. Their cave drawings still remain near the entrance. Much later, in the 19th century, U.S. settlers discovered the cavern, drawn to it by the spectacle of hundreds of thousands of bats rising up out of the natural entrance in the evening. Some stayed to mine the huge deposits of bat guano in the cave and sell it as fertilizer. One such man, a cowboy named Jim White, became fascinated by the cave and spent hour after hour exploring it. White was eager to show the many natural wonders of this extraordinary place to others, but few persons believed his improbable tales of a huge underground wilderness full of unusual cave formations. It took photographs to convince skeptics that Carlsbad Caverns was everything it was said to be and more. In 1923 the U.S. Department of the Interior sent inspector Robert Holley to investigate and see whether Carlsbad Cavern was truly an outstanding natural scenic wonder. Originally a skeptic, Holly wrote in his final report: “...I am wholly conscious of the feebleness of my efforts to convey in the deep conflicting emotions, the feeling of fear and awe, and the desire for an inspired understanding of the Divine Creator’s work which presents to the human eye such a complex aggregate of natural wonders....” Later that year Carlsbad Cavern was proclaimed a national monument. Seven years later Carlsbad Caverns National Park was created to protect the cave. Through illustrated articles published in magazines such as National Geographic and by word of mouth, Carlsbad Cavern became one of the world’s most celebrated caves. Since its establishment, the park has been expanded and today includes 46,766 acres and more than 80 other smaller caves.

27. Carlsbad holds all of the following designations EXCEPT A. B. C. D.

National Park. World Heritage Site. National Monument. National Geographic.

28. Carlsbad Cavern is open to tourists during which of the following times? A. B. C. D.

24 hours per day year around 24 hours per day June, July, and August 24 hours per day weekends and holidays 24 hours per day everyday but Christmas

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Part I: FCAT Reading Test

29. The cavern was created from a reef formed from the remains of what components? A. B. C. D.

algae, salts, gypsum, and sponges algae, seashells, gypsum, and calcite seashells, algae, sponges, and calcite seashells, salts, gypsum, and sponges

30. What is a basic element used to form most cave formations? A. B. C. D.

calcite gypsum aragonite limestone

31. The Witch’s Finger is an example of what type of cave formation? A. B. C. D.

a stalactite a stalagmite a drape type cave formation a column type cave formation

32. Stalagmites are formed when calcite does which of the following? A. B. C. D.

when calcite drips onto the floor when calcite drips from the ceiling when calcite flows over a wall or floor when calcite runs down a slanted ceiling

33. Soda straws are an example of what type of cave formation? A. B. C. D.

stalactites cave pearls stalagmites cave drapes

34. One of the contributing factors in the forming of helictites is which of the following? A. B. C. D.

the force of gravity the concentration of calcite the concentration of aragonite the force of water under pressure

35. Formations composed of aragonite tend to have which of the following characteristics? A. B. C. D.

They are shaped like lily pads. They are shaped like draperies. They are delicate, needle-like, and small. They are needle-like, columnar, and draped.

36. The Bat Cave serves as all of the following to the bats EXCEPT A. B. C. D.

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a daytime roost. a feeding ground. a maternity roost. a warm weather roost.

Practice FCAT Reading 1

37. Read this sentence from the article. The exodus can last 20 minutes or as long as 2.5 hours. What does the word “exodus” mean? A. B. C. D.

flying to food exiting the cave flying in serpentine fashion entering the cave after eating

38. Read this sentence from the article. Once there, they begin gorging themselves on moths and other night-flying insects. What does the author mean by this statement? A. B. C. D.

The bats eat less than necessary. The bats eat more than necessary. The bats drive insects into the cave. The bats drive insects from the cave.

39. Native Americans once used the cave for what purpose? A. B. C. D.

a place to seek shelter a place to make drawings a place to live permanently a place to meet and prepare food

40. What geologic formations are visible to the tourists of Carlsbad Cavern? Use details and information from the article and graphics to support your answer.

41. What spectacle initially drew U. S. settlers to the cave? A. B. C. D.

the formation of stalactites the formation of stalagmites the swarming of the cave bats the discovery of cave drawings

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42. Carlsbad Caverns became a National Park in what year? A. B. C. D.

1900 1923 1930 1995

43. Stalagmites and stalactites are similar because they both A. B. C. D.

formed from calcite. formed from aragonite. build from the cave floor. hang from the cave ceilings.

44. All of the following are examples of cave formations EXCEPT A. B. C. D.

drapes. columns. lily straws. cave pearls.

45. Carlsbad Cavern can be described as all of the following EXCEPT A. B. C. D.

a World Heritage Site a National Historic Site a chamber under the Guadalupe Mountains a cave where Native Americans drew on walls

46. What two things caused the uncovering of the 400-mile-long buried rock reef? A. B. C. D.

uplift and erosion rainwater and hydrogen sulfide gas and oil deposits sulfuric acid and percolation

47. Why do bats migrate from Mexico to Carlsbad Cavern? A. B. C. D.

to get away from predators to give birth and raise their young to swarm like a dark swift-moving cloud to gorge themselves on moths and other night-flying insects

48. What unique method do bats use to re-enter the cave? A. B. C. D.

They spiral in mass exodus. They fly in serpentine fashion. They fold their wings and plummet like hailstones. They form an undulating mass and swarm into the cave.

49. Visitors inside Carlsbad Cavern have what experience in common? A. B. C. D.

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They all take a guided tour. They all see bats swarming. They all exit by an elevator. They all enter via the natural entrance.

Practice FCAT Reading 1

50. All of the following statements are true about Carlsbad Caverns National Park EXCEPT A. B. C. D.

It contains over 80 separate caves. It contains the nation’s deepest limestone cave. It was established to preserve Carlsbad Cavern. It was established to give New Mexico a National Park.

51. How was the geologic formation known as a flowstone formed? A. B. C. D.

when water ran down a slanted ceiling when water flowed over a wall or floor when dams formed and water flowed to the floor when pools of water or streams formed and stood

52. According to the article, what has been mined from Carlsbad Cavern? A. B. C. D.

guano pearls stalactites stalagmites

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Part I: FCAT Reading Test

Answer Key for Practice Test 1 Passage 1: Air Force One 1. B 2. B 3. C 4. Sample 2-Point Response: The inability for the President to maintain communications with Washington while away from office was overcome with advancements in telecommunications. Enhanced speed of travel and refueling in air capabilities also helped make Presidential overseas travel less prohibitive. 5. A 6. A 7. C 8. B 9. C 10. D 11. C 12. C 13. A 14. Sample 4-Point Response: One of the first differences between Air Force One and other Boeing 747s is the call sign itself, which is necessary for security and safety measures to set it apart from regular air traffic. Other differences include such things as Air Force One containing twice the normal wiring with heavy shielding to protect wires and electronics from harmful electromagnetic pulses; complete medical facilities and a staff doctor for medical emergencies; aerial refueling capabilities so Air Force One can be used as a military command center without landing; electronic counter measures to jam enemy radar; flares to avoid heat-seeking missiles; private offices, sleeping quarters, and a work-out room so the President can conduct business, maintain privacy, and keep physically fit. 15. B 16. C 17. C 18. B 19. A 20. C 21. D 22. C 23. A 24. C 25. B 26. B

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Practice FCAT Reading 1

Passage 2: Carlsbad Caverns National Park 27. D 28. D 29. C 30. A 31. D 32. A 33. A 34. D 35. C 36. B 37. B 38. B 39. A 40. Sample 2 Point Response: According to the graphics, a tourist could see some column limestone formations and an array of stalactites as well as the Witch’s Finger. The article states a tourist might see such formations as stalagmites, cave pearls, drapes, flowstone, lily pads, soda straws, popcorn-shaped formations, and even the more unusual helictites. 41. C 42. C 43. A 44. C 45. B 46. A 47. B 48. C 49. C 50. D 51. B 52. A

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Part I: FCAT Reading Test

Answers and Explanations for Practice Test 1 Passage 1: Air Force One Note: Although all answer choices are text based, only one will correctly answer the question. 1. B. The article states, “The Secret Service refers to Air Force One by the codename Angel.” 2. B. The article states that Truman, “. . .had a distinctive exterior (an eagle head painted on its nose),” and that Kennedy, “. . .commissioned industrial designer Raymond Loewy to create a distinctive exterior for the plane.” 3. C. As the main idea of the article is to discuss the history of Air Force One, answer C is correct. 4. The sample response addresses the prohibitions to overseas travel mentioned in the article, “Lack of telecommunications and quick transportation made long-distance travel impractical, as it took up much time and isolated the President from events in Washington.” The sample response also is text-based in that it addresses the advances made in communications, speed of travel, and refueling capabilities. 5. A. The article states that the wiring in the plane is “. . .covered with heavy shielding to protect wires and electronics from the electromagnetic pulse generated by a nuclear attack.” 6. A. The article states that, “The main reason at the time for presidential air travel was the threat of the German Navy’s U-boats in the Atlantic.” 7. C. Speaking of the C-87A, the article states, “. . .the plane was no longer used for Roosevelt after another C-87A crashed. . ..” 8. B. The article states, “The change stemmed from a 1953 incident where an Eastern Airlines commercial flight (8610) had the same call-sign as a flight the President was on (Air Force 8610).” 9. C. The article discusses the usual mode of overseas transport as being a boat prior to the advances in aviation, and when Roosevelt used a plane to cross the Atlantic, it was referred to as the “flying boat.” 10. D. The article states that, “President Eisenhower also upgraded Air Force One’s technology by adding an air-toground telephone and an air-to-ground teletype machine.” 11. C. Although departing as Air Force One when Richard M. Nixon departed Andrews Air Force Base, the article states that, “. . .the plane’s call sign would switch from Air Force One to SAM (Special Air Mission) designation the moment Gerald Ford took the oath of office.” 12. C. The article states, “Lyndon B. Johnson became the first and only president to take the oath of office on Air Force One. . .” 13. A. The article speaks of some offsetting methods to divert missile attacks such as flares and jamming enemy radar. 14. This is a multiple part question. It asks that both differences between a standard Boeing 747 and Air Force One be identified, and a rationale as to why those modifications were made. Although not all differences stated in the article would be required to receive a 4-point score, it is necessary to cite multiple examples and identify the reasons for those modifications stated in the article. 15. B. As the article relates the development of Air Force One since its inception, the choice of how it has evolved over the years is appropriate. 16. C. The article states, “The planes can also be operated as a military command center. . ..” 17. C. The article states, “. . .it always comes to a stop with the left side of the aircraft facing gathered onlookers as a security measure to keep the President’s side of the aircraft out of view.” 18. B. The article states, “It is important to note that the aircraft are only referred to as Air Force One while the President is on board. . ..” 19. A. The article states, “From its inception Air Force One has become a symbol of Presidential power and prestige.”

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Practice FCAT Reading 1

20. C. The article indicates the ability to fly long distances alleviates the need for frequent stops for refueling and has even devised modifications to, “. . .include aerial refueling capability. . .” 21. D. The article states, “. . .a plane carrying a member of the first family will be called ‘Executive One Foxtrot.’” 22. C. The article states, “While Air Force One has three floors, like a regular Boeing 747. . ..” 23. A. The article refers to the security surrounding Air Force One and the need to keep certain modifications secret. 24. C. The article states prior to World War II, overseas travel was rare. Further, the article states, “Lack of telecommunications and quick transportation made long-distance travel impractical, as it took up much time and isolated the President from events in Washington.” 25. B. The article states that the Independence, “. . .was the first aircraft acting as Air Force One that had a distinctive exterior (an eagle head painted on its nose).” 26. B. The article states that President Kennedy, “. . .commissioned industrial designer Raymond Loewy to create a distinctive exterior for the plane.”

Passage 2: Carlsbad Caverns National Park 27. D. The correct answer refers to the magazine cited in the article, not a designation of the park. 28. D. The article states, “The park is open 24 hours a day, seven days a week, except Christmas Day.” 29. C. The article states, “This horseshoe shaped reef formed from the remains of sponges, algae, and seashells and from calcite that precipitated directly from the water.” 30. A. When referring to the seeping drops of water, the article states, “As it continued to move downward the drop dissolved a little limestone, absorbing a bit of the basic ingredient needed to build most cave formations—the mineral calcite.” 31. D. The article states, “Sometimes a stalactite and stalagmite joined, forming a column, such as the Witch’s Finger.” 32. A. The article states, “Water falling on the floor created stalagmites.” 33. A. The article states, “Where water dripped slowly from the ceiling, soda straws and larger stalactites appeared.” 34. D. When referring to helictites, the article states that, “. . .their twisting shapes governed by crystal shapes, impurities and the force of water under pressure.” 35. C. When referring to formations composed of aragonite, the article states, “These formations tend to be small, delicate and needle-like.” 36. B. The article refers to all choices except a feeding ground. Bats leave the cave to feed. 37. B. The article discusses the bats exiting the cave in a spectacular fashion to go to their feeding. 38. B. The article states, “. . .each bat may catch and eat several stomachfuls of insects in a single night.” 39. A. The article states, “. . .Native Americans ventured into the Cavern seeking shelter.” 40. This is a multiple-part question. Although it only asks what geologic formations are visible to a tourist, it specifically asks for detail and support from both the article and the graphics. The response clearly distinguished where the information provided is located and is labeled such that the person scoring the response can appropriately give points for the multiple-part answer. 41. C. When referring to the cave, the article states that settlers were, “. . .drawn to it by the spectacle of hundreds of thousands of bats rising up out of the natural entrance in the evening.” 42. C. The article states, “It was re-designated a national park on May 14, 1930.” 43. A. The article states, “. . .the basic ingredient needed to build most cave formations—the mineral calcite.” 44. C. All answers can be found in the text as examples of formations except for “lily straws.”

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45. B. The only selection not found in the text is “a National Historic Site.” 46. A. The article states, “. . .uplift and erosion of the area began to uncover the buried rock reef.” 47. B. The article states, “The bats migrate from Mexico to Carlsbad Cavern each year to give birth and raise their young.” 48. C. When referring to the bats re-entering the cave after feeding, the article states, “It then folds its wings close to its body, and plummets like a hailstone into the blackness of Carlsbad Cavern. . ..” 49. C. The article states, “. . .or take an elevator (the exit for everyone). . ..” 50. D. The article makes no reference to establishing a National Park for New Mexico. 51. B. The article states, “Water flowing over the surface of a wall or floor deposited layers of calcite called flowstone.” 52. A. The article states, “Some stayed to mine the huge deposits of bat guano in the cave and sell it as fertilizer.”

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Practice FCAT Reading 2 This practice test contains two reading passages and 50 sample questions. Read each passage and answer all the questions that follow each passage.

Passage 1 Read the following passage before answering Questions 1 through 32.

Crash Test Dummy

Hybrid III crash test dummy. Crash test dummies are full-scale replicas of human beings, weighted and articulated to simulate the behavior of a human body in a vehicle mishap, and instrumented to record as much data as possible on variables such as speed of impact, crushing force, bending, folding, or torque of the body, and deceleration rates during a collision. In modern times, they remain indispensable in the development of new makes and models of all types of vehicles, from family sedans to fighter aircraft.

The Need for Testing The need for a means of analyzing and mitigating the effects of motor vehicle accidents on human bodies was felt very soon after the commercial production of automobiles began in the late 1890s, and by the 1930s, with the automobile a common part of daily life, the number of motor vehicle injuries was becoming a serious issue.

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Part I: FCAT Reading Test

In 1930, the interior of a car was not a safe place even in a low-speed collision. Dashboards were made of rigid metal, steering columns were non-collapsible, and protruding knobs, buttons, and levers were ubiquitous. Seat belts were unheardof, and in a frontal collision, passengers hurled through the windshield stood very little chance of avoiding serious injury. The vehicle body itself was rigid, and impact forces were transmitted directly to the vehicle occupants. As late as the 1950s, car manufacturers were on public record as saying the forces in a crash were too great and the human body too frail.

Volunteer Testing Some researchers took it upon themselves to serve as crash test subjects. Colonel John Paul Stapp USAF (United States Air Force) propelled himself over 630 mph on a rocket sled and stopped in less than a second. Lawrence Patrick, a now-retired Wayne State University professor, endured some 400 rides on a rocket sled in order to test the effects of rapid deceleration on the human body. He and his students allowed themselves to be smashed in the chest with heavy metal pendulums, impacted in the face by pneumatically driven rotary hammers, and sprayed with shattered glass to simulate window implosion. While admitting that it made him “a little sore,” Patrick has said that the research he and his students conducted was seminal in developing numerical models against which further research could be compared. But while data from live testing was valuable, human subjects could not withstand tests which went past a certain degree of physical discomfort. To gather information about the causes and prevention of serious injuries would require a different kind of subject.

Dummy Evolution

Sierra Sam tested ejection seats.

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Practice FCAT Reading 2

As early as 1949, “Sierra Sam” was created by Samuel W. Alderson at his Alderson Research Labs (ARL) and Sierra Engineering Co. to test aircraft ejection seats and pilot restraint harnesses. This testing involved the use of high acceleration to 600 mph rocket sleds, beyond the capability of human volunteers to tolerate. In the early 1950s, Alderson and Grumman produced a dummy which was used to conduct crash tests in both motor vehicles and aircraft. Alderson went on to produce what it called the VIP-50 series, which was adopted by the National Bureau of Standards. In 1971 Hybrid I was born. Hybrid I was what is known as a “50th percentile male” dummy. That is to say, it modeled an average male in height, mass, and proportion. The original “Sierra Sam” was a 95th percentile male dummy (heavier and taller than 95 percent of human males). Since then, considerable work has gone into creating more and more sophisticated dummies. Hybrid II was introduced in 1972, with improved shoulder, spine, and knee responses, and more rigorous documentation. Hybrid II became the first dummy to comply with the American Federal Motor Vehicle Safety Standard (FMVSS) for testing of automotive lap and shoulder belts. In 1973, a 50th percentile male dummy was released. Though a great improvement over previous models for standardized testing purposes, Hybrid I and Hybrid II were still very crude, and their use was limited to developing and testing seat belt designs. A dummy was needed which would allow researchers to explore injury-reduction strategies. It was this need that pushed researchers to develop the current Hybrid line, the Hybrid III family of crash test dummies.

The Hybrid III Family

The original 50th percentile male Hybrid III. Hybrid III, the 50th percentile male dummy which made its first appearance in 1976, is the familiar crash test dummy, and he is now a family man. If he could stand upright, he would be 5’6” tall and would have a mass of 170 lb. He occupies the driver’s seat in all the Insurance Institute for Highway Safety 40 mph offset frontal crash tests. He is joined by a

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Part I: FCAT Reading Test

“big brother,” the 95th percentile Hybrid III, at 6’2” and 223 lb. Ms. Hybrid III is a 5th percentile female dummy, at a diminutive 5 ft. tall and 110 lb. The two Hybrid III child dummies represent a 47 lb. six-year-old and a 33 lb. three-year-old. The child models are very recent additions to the crash test dummy family; because so little hard data are available on the effects of accidents on children, and such data are very difficult to obtain, these models are based in large part on estimates and approximations.

The Test Process Every Hybrid III undergoes calibration prior to a crash test. Its head is removed and a 40 centimeter bounce test is performed. Then the head and neck are reattached, set in motion, and stopped abruptly to check for proper neck flexure. Hybrids wear chamois skin; the knees are struck with a metal probe to check for proper puncture. Finally, the head and neck are attached to the body, which is attached to a test platform and struck violently in the chest by a heavy pendulum to ensure that the ribs bend and flex as they should. When the dummy has been determined to be ready for testing, it is dressed entirely in yellow, marking paint is applied to the head and knees, and calibration marks are fastened to the side of the head to aid researchers when slow-motion films are reviewed later. The dummy is then placed inside the test vehicle. Forty-four data channels located in all parts of the Hybrid III, from the head to the ankle, record between 30,000 and 35,000 data items in a typical 100–150 millisecond crash. Recorded in a temporary data repository in the dummy’s chest, these data are downloaded to computers once the test is complete. Because the Hybrid is a standardized data collection device, any part of a particular Hybrid type is interchangeable with any other. Not only can one dummy be tested several times, but if a part should fail, it also can be replaced with a new part. A fully instrumented dummy is worth about US$150,000.

Hybrid’s Successors Hybrid IIIs are designed to research the effects of frontal impacts, and have no ability to assess the effects of other sorts of impacts, such as side impacts, rear impacts, or rollovers. After head-on collisions, the most common severe injury accident is the side impact. The SID (Side Impact Dummy) family of test dummies has been designed to measure rib, spine, and internal organ effects in side collisions. It also assesses spine and rib deceleration and compression of the chest cavity.

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Practice FCAT Reading 2

BioRID is a dummy designed to assess the effects of a rear impact. Its primary purpose is to research whiplash, and to aid designers in developing effective head and neck restraints. BioRID is more sophisticated in its spinal construction than Hybrid; 24 vertebra simulators allow BioRID to assume a much more natural seating posture, and to demonstrate the neck movement and configuration seen in rear-end collisions.

CRABIs test child restraints. CRABI is a child dummy used to evaluate the effectiveness of child restraint devices including seat belts and air bags. There are three models of the CRABI, representing 18-month, 12-month, and 6-month old children. THOR is an advanced 50th percentile male dummy. The successor of Hybrid III, THOR has a more humanlike spine and pelvis, and its face contains a number of sensors which allow analysis of facial impacts to an accuracy currently unobtainable with other dummies. THOR’s range of sensors is also greater in quantity and sensitivity than those of Hybrid III.

The Future of the Dummy Crash test dummies have provided invaluable data on how human bodies react in crashes and have contributed greatly to improved vehicle design. The future of crash testing has begun at the same place it all started: Wayne State University. King H. Yang is one of Wayne State’s researchers involved in creating detailed computer models of human systems. Currently, computers are neither fast enough nor programmers skilled enough to create full-body simulations, but injury analysis of individual body systems is producing reliable and encouraging results. The advantage of the computer is that it is unbound by physical law. A virtual vehicle crashed once can be uncrashed and then crashed again in a slightly different manner. A virtual back broken can be unbroken, the seatbelt configuration changed, and the back re-broken. When every variable is controllable and every event is repeatable, the need for physical experimentation is greatly reduced.

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Part I: FCAT Reading Test

At the beginning of the 21st century, legal certification of new car models is still required to be done using physical dummies in physical vehicles. However, the future is almost certainly one where neither skin and bone, nor plastic and steel will determine the shape of vehicles to come. The next generation of crash test dummies will perform their tasks entirely on a computer screen.

1. Crash test dummies are designed to record all of the following EXCEPT A. B. C. D.

crushing force. speed of impact. deceleration rates. torque of collision.

2. What is one of the primary reasons for using crash test dummies in modern times? A. B. C. D.

They are greatly improved over previous models. They are used to perform injury reduction strategies. They are used to measure the effects of side impacts. They are used in development of new makes and models of vehicles.

3. Describe some of the conditions found in automobiles that made them unsafe during accidents. Use details and information from the text to support your answer.

4. Read the following sentence from the article. Seat belts were unheard-of, and in a frontal collision, passengers hurled through the windshield stood very little chance of avoiding serious injury. What does the author mean by “unheard-of”? A. B. C. D.

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Seat belts could save many lives. Seat belts had not yet been tested. Seat belts had not yet been installed. Seat belts could cause serious injuries.

Practice FCAT Reading 2

5. Which researcher endured 400 rides on a rocket sled to test the effects of rapid deceleration? A. B. C. D.

King H. Yang Lawrence Patrick Samuel W. Alderson Colonel John Paul Stapp

6. During testing, Professor Patrick and his students endured all of the following EXCEPT A. B. C. D.

being smashed with pendulums. being sprayed with shattered glass. being broad-sided with heavy objects. being impacted in the face with hammers.

7. According to the article, why was testing on humans of limited value? A. B. C. D.

because humans were too expensive because humans could only stand so much pain because humans were slow to recover from testing because humans would sometimes die from testing

8. “Sierra Sam” was designed to test which of the following safety related incidents? A. B. C. D.

aircraft ejection seats motor vehicle crashes capabilities of humans high speed deceleration

9. Who was credited with designing the first crash test dummy for use with motor vehicles? A. B. C. D.

Stapp and Patrick Alderson and Gruman Wayne State University Sierra Engineering Company

10. As it relates to crash test dummies, what is the meaning of the term “50 percentile male”? A. B. C. D.

one that replicates 50 percent of men one that replicates 50 percent of women one that is 50 percent lighter than most men one that is 50 percent heavier than most men

11. What distinction does the crash test dummy known as the series VIP-50 hold? A. B. C. D.

It was the first used to test frontal impact. It was the first used to test rapid deceleration. It was adopted by the National Bureau of Standards. It was adopted as the American Federal Motor Vehicle Safety Standard.

12. Which crash test dummy was the first to comply with standards for testing of automotive lap and shoulder belts? A. B. C. D.

Hybrid I Hybrid II Hybrid III Sierra Sam

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Part I: FCAT Reading Test

13. According to the article, what were Hybrid I and Hybrid II limited to testing? A. B. C. D.

the effects of frontal impacts the effects of seat belt designs the effects of rapid acceleration the effects of rapid deceleration

14. The Hybrid III family consists of all of the following EXCEPT A. B. C. D.

a male dummy. a child dummy. a sister dummy. a female dummy.

15. Describe the typical procedure the Hybrid III goes through prior to each test crash. Use details and information from the article to support your answer.

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Practice FCAT Reading 2

16. Read the following sentence from the article. “Because the Hybrid is a standardized collections device, any part of a particular Hybrid type is interchangeable with any other.” What does the word “standardized” mean as used in this sentence? A. B. C. D.

is the same as parts in like Hybrid designs meets all measurement criteria for Hybrids is the same as parts in other Hybrid designs meets all required design criteria for Hybrids

17. Why are crash test dummies dressed in yellow with marking paint and calibration marks added? A. B. C. D.

to aid researchers in reviewing parts for damage to aid researchers in reviewing parts for durability to aid researchers reviewing high-speed replays of the crash to aid researchers reviewing slow-speed replays of the crash

18. Where in the Hybrid design is data temporarily stored in a standard crash test? A. B. C. D.

back repository head repository chest repository ankle repository

19. The Hybrid III series were specifically designed to measure what type of impact? A. B. C. D.

the effects of a rear impact the effects of a frontal impact the effects of a driver-side impact the effects of a passenger-side impact

20. The SID dummies were designed to measure all of the following EXCEPT A. B. C. D.

the effects of a crash on the ribs. the effects of a crash on the spine. the effects of a crash on the ankles. the effects of a crash on the organs.

21. The BioRID is specifically designed to measure the effects of what type of impact? A. B. C. D.

the effects of a rear impact the effects of a head impact the effects of a frontal impact the effects of a whiplash impact

22. What specific design feature of the BioRID allows it to demonstrate neck movement? A. B. C. D.

neck restraints head restraints spinal placement vertebra simulators

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Part I: FCAT Reading Test

23. Which of the crash test dummies reviewed in the article has the best capability to analyze facial impacts? A. B. C. D.

THOR CRABI BioRID Hybrid III

24. What are some of the advantages to computer testing over physical testing? Use details and information from the article to support your answer.

25. Read the following sentence from the article. The advantage of the computer is that it is unbound by physical law. What does the author mean by the word “unbound”? A. B. C. D.

not freed loosened restrained not constrained

26. According to the article, where will crash test dummies exclusively perform their testing in the future? A. B. C. D.

in the physical world on the computer screen behind the wheel of a car in a computer in the chest

27. When did the need to analyze the effects of motor vehicle accidents begin? A. B. C. D.

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after the 1890s after the 1930s after the first automobile was made after the first automobile accident happened

Practice FCAT Reading 2

28. What has been the common design goal observed throughout the evolution of crash test dummies? A. B. C. D.

to make cheaper replacement parts to make a cheaper, more efficient dummy to more efficiently measure auto durability to more accurately replicate the human body

29. What is the main idea of the article? A. B. C. D.

Crash test dummies are a much needed commodity. Crash test dummies have evolved much over the years. Crash test dummies have saved many lives over the years. Crash test dummies are better than humans for crash testing.

30. What is the main purpose of the story? A. B. C. D.

to educate the reader about auto accidents to educate the reader about computerized testing to inform the reader about crash test dummy research to inform the reader about frailty of humans in accidents

31. Based on the article, what conclusion can you draw about the future of crash test dummies? A. B. C. D.

They will be made cheaper over time. They will serve a useful purpose in the future. They will be replaced with virtual units over time. They will continue to be upgraded and improved over time.

32. If you were to be a crash test dummy designer in the future, which of the following skills would you likely need most? A. B. C. D.

knowledge in wiring design knowledge in sensors development knowledge in computer programming knowledge in molded plastics manufacturing

Passage 2 Read the following passage before answering Questions 33 through 50.

Growth: An Evidence of Education There is a type of mind which, when trained to a certain point, crystallizes, as it were, and refuses to move forward thereafter. This type of mind fails to give one of the essential evidences of an education. It has perhaps acquired much and promised much; but somehow or other the promise is not fulfilled. It is not dead, but in a trance. Only such functions are performed as serve to keep it where it is; there is no movement, no development, no new power or accomplishment. The impulse to continuous study, and to that self-education which are the conditions of permanent intellectual growth, is wanting. Education has so far failed of one of its chief purposes.

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Part I: FCAT Reading Test

A human mind continuing to grow and to develop throughout a long life is a splendid and impressive sight. It was that characteristic in Mr. Gladstone which made his personality so attractive to young and ambitious men. They were fired by his zeal and inspired by his limitless intellectual energy. To have passed from being “the rising hope of the stern and unbending Tories” in 1838 to the unchallenged leadership of the anti-Tory party in Great Britain a generation later, and to have continued to grow throughout an exceptionally long life, is no mean distinction; and it is an example of what, in less conspicuous ways, is the lot of every mind whose training is effective. Broadened views, widened sympathies, deepened insights, are the accompaniments of growth. For this growth a many-sided interest is necessary, and this is why growth and intellectual and moral narrowness are eternally at war. There is much in our modern education which is un-educational because it makes growth difficult, if not impossible. Early specialization, with its attendant limited range both of information and of interest, is an enemy of growth. Turning from the distasteful before it is understood is an enemy of growth. Failure to see the relation of the subject of one’s special interest to other subjects is an enemy of growth. The pretense of investigation and discovery before mastering existent knowledge is an enemy of growth. The habit of cynical indifference toward men and things and of aloofness from them, sometimes supposed to be peculiarly academic, is an enemy of growth. These, then, are all to be shunned while formal education is going on, if it is to carry with it the priceless gift of an impulse to continuous growth. “Life,” says Bishop Spalding in an eloquent passage, “is the unfolding of a mysterious power, which in man rises to selfconsciousness, and through self-consciousness to the knowledge of a world of truth and order and love, where action may no longer be left wholly to the sway of matter or to the impulse of instinct, but may and should be controlled by reason and conscience. To further this process by deliberate and intelligent effort is to educate”—and to educate so as to sow the seed of continuous growth, intellectual and moral.

33. Read the following sentence from the story. This type of mind fails to give one of the essential evidences of education. What does the author mean by the term “This type of mind”? A. B. C. D.

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a mind that has acquired much a mind that has promised much a mind that stops moving forward a mind that stops concentrating continuously

Practice FCAT Reading 2

34. According to the story, what is one of the chief purposes of education? A. B. C. D.

to create a desire for continuous study to show the range of the power of the mind to create an opportunity to evidence knowledge to show the accomplishments possible in the mind

35. What characteristic in Mr. Gladstone made his personality attractive to young and ambitious men? A. B. C. D.

He was a leader of the Tory party. He had a mind that continued to grow. He had a mind that had been educated. He was a splendid and impressive sight.

36. All of the following accompany growth, or education, EXCEPT A. B. C. D.

broadened views. deepened insights. furthered thoughts. widened sympathies.

37. Identify several enemies of growth and discuss why they are enemies according to the author. Use details and information from the story to support your answer.

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Part I: FCAT Reading Test

38. According to the story, what is at eternal war with growth? A. B. C. D.

intellectual and moral breadth intellectual and moral narrowness deepened insights but moral narrowness broadened views but narrowed sympathies

39. According the story, what is the priceless gift of a formal education? A. B. C. D.

a sowing of the seed of growth an impulse to continuous growth the unfolding of mysterious power to control by reason and conscience

40. According to the story, what types of continuous growth should education sow? A. B. C. D.

impulses of instinct intellectual and moral reason and conscience deliberate and intellectual

41. Which of the following would be the best alternative title for the story? A. B. C. D.

To Grow Is to Educate Stagnation Causes Apathy Education: A Necessary Evil Specialization: An Educational Requirement

42. Read the following sentence from the story. There is a type of mind which, when trained to a certain point, crystallizes, as it were, and refuses to move forward thereafter. What is the author trying to convey by using the word “crystallizes”? A. B. C. D.

that a mind must be pliable in order to learn that a mind set in its ways is indeed teachable that a mind should harden around learned facts that a mind stops accepting knowledge at some time

43. Which statement BEST describes the theme of the story? A. B. C. D.

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A person who specializes does not grow. A person who continues to study gets wiser. A person who does not grow is not educated. A person who continues his or her education continues to grow.

Practice FCAT Reading 2

44. Read the following sentence from the story. It is not dead, but in a trance. To what is the author referring? A. B. C. D.

current growth a person’s mind a person’s being modern education

45. According to the story, what are the conditions of permanent intellectual growth? A. B. C. D.

notable movement or development appreciable new power or accomplishment the impulse to continuous study and self-education a recognized lack of intellectual and moral self-narrowing

46. The author shows a relationship in which of the following stated attributes? A. B. C. D.

training, education, and growth growth, education, and intellect leadership, intellect, and training education, growth, and leadership

47. When discussing Mr. Gladstone, what does the author suggest is a direct result of his growth? A. B. C. D.

He became a political leader. He reversed his political views. He became politically active in the Tory party. He became a political activist in Great Britain.

48. Which of these statements BEST expresses the author’s point of view? A. B. C. D.

An open mind can be persuaded with facts. An educated person can be a political leader. Continuing an education is good if specializing. Continuing an education is necessary for growth.

49. The author suggests that intellectual growth is dependant upon which of the following criteria? A. B. C. D.

having developed a specialty having a many-sided interest having some prior knowledge having possession of self-consciousness

50. The author quotes Bishop Spalding in the story. Which of the following BEST expresses the meaning of that quote? A. B. C. D.

Life can be directed with knowledge, and continuing education increases that knowledge. Life is a series of mysterious events, and through living and experiencing these events, man becomes educated. Through self-consciousness and understanding the many events in life, a full continuing education is created. Through self-consciousness, actions left wholly to the sway of matter create growth, which becomes whole education.

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Part I: FCAT Reading Test

Answer Key for Practice Test 2 Passage 1: Crash Test Dummies 1. D 2. D 3. Sample 2-Point Response: The article states that, “Dashboards were made of rigid metal, steering columns were non-collapsible, and protruding knobs, buttons, and levers were ubiquitous.” Seat belts had not been installed in cars and passengers could be hurled through the windshield during a frontal collision. Because the vehicle frame was rigid, impact forces were directly transmitted to the occupants. 4. C 5. B 6. C 7. B 8. A 9. B 10. A 11. C 12. B 13. B 14. C 15. Sample 4-Point Response: Prior to each test crash, the article states the Hybrid III is totally re-calibrated. A bounce test is performed on the head and after being reattached, is checked for proper neck flexure. Knees are struck with a metal probe to check for proper puncture, and finally, after attaching the head and neck to the body, the body is struck with a heavy pendulum to check for proper flex in ribs. The dummy is fully dressed in yellow, and marking paint with calibration indicators are added just prior to loading the dummy into the crash vehicle. 16. A 17. D 18. C 19. B 20. C 21. A 22. D 23. A 24. Sample 2-Point Response: Physical testing can be performed only once and then physical replacement of all damaged parts is required. Computer testing can occur over and over by slightly modifying the program to measure differing results, and there is no need to replace any expensive equipment. In other words, “The advantage of the computer is that it is unbound by physical law.” 25. D 26. B 27. A

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Practice FCAT Reading 2

28. D 29. B 30. C 31. C 32. C

Passage 2: Growth: An Evidence of Education 33. C 34. A 35. B 36. C 37. Sample 4-Point Response: The author states that early specialized studies is an enemy to growth because specialization limits the range of both information and interests in other subjects. Turning from the distasteful, or that which is not interesting or easily understood, is an enemy of growth. This would make the more difficult things to understand not studied and, therefore, limit growth. Failure to see the interrelation of one subject of special interest to other subjects limits growth because it restricts focus to the one special area. Finally, adopting a habit of being cynical and indifferent stifle growth. 38. B 39. B 40. B 41. A 42. A 43. D 44. B 45. C 46. A 47. B 48. D 49. B 50. A

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Answers and Explanations for Practice Test 2 Passage 1: Crash Test Dummies Note: Although all answer choices are text based, only one will correctly answer the question. 1. D. The article states that, “Crash test dummies are. . .instrumented to record. . .speed of impact, crushing force, bending, folding, or torque of the body, and deceleration rates during a collision.” 2. D. The article states, “In modern times, they remain indispensable in the development of new makes and models of all types of vehicles. . ..” 3. The response lifts information directly from the text and either quotes or restates the conditions that made automobiles unsafe during accidents. This information can be found under the sub-heading, The Need for Testing. 4. C. Until motor vehicle accidents and injuries to humans became an issue, no one had installed seat belts in cars. 5. B. The article states, “Lawrence Patrick,. . .endured some 400 rides on a rocket sled in order to test the effects of rapid deceleration on the human body.” 6. C. Answer “C” is the only answer selection not mentioned in the article. 7. B. The article states, “. . .human subjects could not withstand tests which went past a certain degree of physical discomfort.” 8. A. The article states, “. . .‘Sierra Sam’ was created. . .to test aircraft ejection seats. . ..” 9. B. The article states, “. . .Alderson and Grumman produced a dummy which was used to conduct crash tests in both motor vehicles and aircraft.” 10. A. The article states, “Hybrid I was what is known as a ‘50th percentile male’ dummy. That is to say, it modeled an average male in height, mass, and proportion.” 11. C. The article states, “. . .the VIP-50 series, which was adopted by the National Bureau of Standards.” 12. B. The article states, “Hybrid II became the first dummy to comply with the American Federal Motor Vehicle Safety Standard (FMVSS) for testing of automotive lap and shoulder belts.” 13. B. The article states, “Hybrid I and Hybrid II were still very crude, and their use was limited to developing and testing seat belt designs.” 14. C. The article mentions all selections except a sister dummy in the Hybrid family of crash test dummies. 15. Under the sub-heading The Test Process, the article describes in detail the process each Hybrid III test dummy undergoes prior to actual crash testing. The sample response delineates the process as put forth in the article. 16. A. The context clues of any part of a particular Hybrid type being interchangeable with any other indicates the correct answer reflects the meaning of standardized as used in the quoted sentence to mean that it is the same as parts in like Hybrid designs. While distracter “C” appears to be the same, it indicates the parts of all Hybrid types are interchangeable and the quote states that they must be of a particular type. 17. D. The article states that dummies are so dressed and marked in order to, “. . .aid researchers when slow-motion films are reviewed later.” 18. C. The article states, “Recorded in a temporary data repository in the dummy’s chest. . .” 19. B. The article states, “Hybrid IIIs are designed to research the effects of frontal impacts. . .” 20. C. The article cites all of the distracters except selection “C.” 21. A. The article states, “BioRID is a dummy designed to assess the effects of a rear impact.” 22. D. The article states, “. . .24 vertebra simulators allow BioRID to assume a much more natural seating posture, and to demonstrate the neck movement and configuration seen in rear-end collisions.”

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Practice FCAT Reading 2

23. A. The article states, “. . .THOR. . .and its face contains a number of sensors which allow analysis of facial impacts to an accuracy currently unobtainable with other dummies.” 24. The discussion of the advantages of the computer is found in the sub-heading The future of the dummy. The response restates the information from the article to support the specific details therein. 25. D. The prefix ‘un’ is a definite context clue to the correct answer. Since ‘not’ appears in two of the answer selections, it is likely one of them will be the correct answer. Since ‘bound’ is an antonym to ‘freed’, Choice D is correct. 26. B. The article states, “The next generation of crash test dummies will perform their tasks entirely on a computer screen.” 27. A. The article states, “The need for a means of analyzing and mitigating the effects of motor vehicle accidents on human bodies was felt very soon after the commercial production of automobiles began in the late 1890s. . ..” 28. D. The article relates a historical progression and the need to improve the measuring capabilities of crash test dummies for the purposes of limiting bodily harm to occupants of automobiles involved in crashes. Toward this end, the article clearly demonstrates the progression to more accurately replicate the human body. 29. B. The article takes the reader through a chronological development of crash test dummies and shows how they have evolved over time. 30. C. The main purpose of the story is to inform the reader about the research and development of the crash test dummy and how that research has aided mankind. 31. C. This response can be found in the subheading The Future of the Dummy. The article clearly predicts that virtual test dummies will replace the physical dummies in the future. 32. C. Since the future of crash test dummies will be relegated to computer screens, a knowledge of computer programming will be essential for dummy designers.

Passage 2: Growth: An Evidence of Education 33. C. The sentence preceding the one quoted reads, “There is a type of mind which, when trained to a certain point, crystallizes, as it were, and refuses to move forward thereafter.” “This type of mind. . .” refers back to the one that stops moving forward. 34. A. The sentence, “Education has so far failed of one of its chief purposes,” is preceded by, “The impulse to continuous study, and to that self-education which are the conditions of permanent intellectual growth, is wanting.” 35. B. The article states, “A human mind continuing to grow and to develop throughout life is a splendid and impressive sight. It was that characteristic in Mr. Gladstone which made his personality so attractive to young and ambitious men.” 36. C. The article states, “Broadened views, widened sympathies, deepened insights, are the accompaniments of growth.” 37. This is a multiple-part question. It asks the respondent to identify several enemies of growth and to discuss why they are enemies according to the author. The response not only states the enemies of growth cited by the author, but also goes on to tell why they, in fact, are enemies. 38. B. The article states, “. . .this is why growth and intellectual and moral narrowness are eternally at war.” 39. B. The article states, “. . .while formal education is going on, if it is to carry with it the priceless gift of an impulse to continuous growth.” 40. B. The article states, “. . .and to educate so as to sow the seed of continuous growth, intellectual and moral.” 41. A. The overall theme is that in order to grow, a continued education is necessary, making A the appropriate choice. 42. A. The word crystallizes suggests a hardening that would seal the object from further penetration. The author suggests that the mind must be kept soft or pliable in order to be accepting of ideas, growth, and education.

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43. D. The entire article discusses the necessity for education for continued growth. The author suggests that only education can produce continued growth. Answer choice D reflects this theme. 44. B. The quote refers back two sentences in the article that reads, “This type of mind. . .”, so answer choice B is correct. 45. C. The article states, “The impulse to continuous study, and to that self-education which are the conditions of permanent intellectual growth, is wanting.” 46. A. The author relates growth and education throughout the article and in the title. He also relates the continued growth of Mr. Gladstone as, “. . .an example of what, in less conspicuous ways, is the lot of every mind whose training is effective.” 47. B. The article, when discussing the continued growth of Mr. Gladstone, “To have passed from being ‘the rising hope of the stern and unbending Tories’ in 1838 to the unchallenged leadership of the anti-Tory party in Great Britain a generation later,. . .is no mean distinction. . ..” 48. D. Throughout the story, the author relates the benefits and goodness of continuing to grow and relates that this is only made possible by continuing education as a life-long pursuit. 49. B. The article states, “for this growth a many-sided interest is necessary. . ..” 50. A. The quote from Spalding relates that life can be directed rather than left to the demise of happenstance, but only if done through continued growth furthered by the continued deliberate and intelligent effort to educate.

50

Practice FCAT Reading 3 This practice test contains two reading passages and 50 sample questions. Read each passage and answer all the questions that follow each passage.

Passage 1 Read the following passage before answering Questions 1 through 29.

Mail

A British pillar box.

Japanese Post.

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Part I: FCAT Reading Test

The postal system is a system by which written documents typically enclosed in envelopes, and also small packages containing other matter, are delivered to destinations around the world. Anything sent through the postal system is called mail or post. In principle, a postal service can be private or official. Restrictions are generally placed on private systems by governments. Since the 19th century, national postal systems have generally been established as government monopolies with a fee on the article prepaid, often in the form of adhesive stamps. Government monopolies generally do not extend to delivery of parcels or courier services providing express mail. Postal systems often have functions other than sending letters. In some countries, the postal system also has some authority over telephone and telegraph systems. In others, postal systems allow for savings accounts and handling applications for passports.

Early Postal Systems Communication via written documents, which an intermediary carries from one person or place to another, almost certainly dates back nearly to the invention of writing. The development of a formal postal system occurred much later, however. The first documented use of an organized courier service for the diffusion of written documents is in Egypt, where Pharaohs used couriers for the diffusion of their decrees in the territory of the State (2400 BC).

Modern Mail Modern mail is usually organized by national services (that in recent times are increasingly being replaced by privately owned companies), reciprocally interconnected by international regulations, organizations and agreements.

Organization

In the United States, private companies such as FedEx and UPS compete with the United States Postal Service, particularly in package delivery. Different mailboxes are also provided for local and express service.

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Practice FCAT Reading 3

The world-wide postal system comprising the individual national postal systems of the world’s self-governing states is coordinated by the Universal Postal Union, which among other things sets international postage rates, defines standards for postage stamps and operates the system of International Reply Coupons. In many countries a system of codes has been created (they are called ZIP Codes in the United States and postal codes in most other countries), in order to facilitate the automation of operations. This also includes placing additional marks on the address portion of the letter or mailed object, called “bar coding.” Bar coding of mail for delivery is usually expressed either by a series of vertical bars, usually called POSTNET coding, or a block of dots as a two-dimensional barcode. The “block of dots” method allows for the encoding of proof of payment of postage, exact routing for delivery, and other features. The ordinary mail service was improved in the 20th century with the use of planes for a quicker delivery (air mail). The first scheduled airmail service took place between the London suburbs of Hendon and Windsor on September 9, 1911. Some methods of airmail proved ineffective, however, including the United States Postal Service’s experiment with guided missiles for international mail transport. Receipts services were made available in order to grant the sender a confirmation of effective delivery. Mail going to naval vessels is known as the Fleet Post Office.

Payment Worldwide the most common method of prepaying postage is by buying an adhesive postage stamp to be stuck to the envelope before mailing; a much less common method is to use a postage-prepaid envelope. Franking is a method of creating postage-prepaid envelopes under license using a special machine. They are used by companies with large mail programs such as banks and direct-mail companies. When the pre-paid envelope or package is accepted into the mail by an agent of the postal service, the agent usually indicates by means of a cancellation that it is no longer valid for pre-payment of postage. The exceptions are when the agent forgets or neglects to cancel the mail piece, or for stamps that are pre-cancelled and thus do not require cancellation.

Rules and Etiquette Mail is quite generally protected by the secret of correspondence, meaning that no letter or other document can be read by other than the receiver (under U.S. law, this only applies to First Class Mail). This right is usually guaranteed by most national constitutions. Usually, special procedures are required in case correspondence has to be, openly or

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discreetly, controlled by police. The operation of control of private citizens’ mail is called censorship and concerns social, political and legal aspects of civil rights. While in most cases this censorship is exceptional, military censorship of mail, particularly of soldiers at the front, is routine and almost universally applied. The use of mail is subject to common rules and a particular etiquette. After the discovery of new communicating systems and vehicles, mail lost most of its special charm in favor of more quickly connecting systems such as the telephone, and remained as a vehicle for commercial or formal documents. It is, however, still widely in use in more cultivated classes for personal communication; in particular, wedding invitations are customarily sent by mail.

Collecting Postage stamps are also the objects of a particular form of collecting, and in some cases, when demand greatly exceeds supply, their commercial value on this specific market may become enormously greater than face value, even after use. For some postal services the sale of stamps to collectors who will never use them is a significant source of revenue. Stamp collecting is commonly known as philately, although strictly the latter term refers to the study of stamps. Another form of collecting regards postcards, a document written on a single robust sheet of paper, usually decorated with photographic pictures or artistic drawings on one of the sides, and short messages on a small part of the other side, that also contained the space for the address. In strict philatelic usage, the postcard is to be distinguished from the postal card, which has a pre-printed postage on the card. The fact that this communication is visible by other than the receiver often causes the messages to be written in jargon. Postcards are often printed today to promote tourism, with pictures of resorts, tourist attractions or humorous messages on the front and allowing for a short message from the sender to be written on the back. The postage required for postcards is generally less than postage required for standard letters, although the United States Postal Service has imposed a surcharge for the purchase of postal cards, over and above the required postage. Postcards are also used by magazines for new subscriptions. Inside many magazines are postage-paid subscription cards that a reader can fill out and mail back to the publishing company to be billed for a subscription to the magazine. In this fashion, magazines also use postcards for other purposes, including reader surveys, contests or information requests.

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Practice FCAT Reading 3

Types of Mail

Woman putting letter in a mailbox, United States, 1909.

Letters Letter-sized mail comprises the bulk of the contents sent through most postal services. These are usually documents printed on letter-sized 8.5 × 11 inches, or smaller paper and placed in envelopes. While many things are sent through the mail, interpersonal letters are often thought of first in reference to postal systems. Handwritten correspondence, while once a major means of communications between distant people, is now used less frequently due to the advent of more immediate means of communication, such as the telephone or e-mail. Traditional letters, however, are often considered to harken back to a “simpler time” and are still used when someone wishes to be deliberate and thoughtful about their communication. Bills and invoices are often sent through the mail, like regular billing correspondence from utility companies and other service providers. These letters often contain a self-addressed envelope that allows the receiver to remit payment back to the company easily. While still very common, many people now opt to use online bill payment services, which eliminate the need to receive bills through the mail. Bulk mail, often called junk mail, are commercial solicitations sent by advertisers. The senders of these messages sometimes purchase lists of addresses (which are sometimes targeted towards certain demographics), and then send letters advertising their product or service to all recipients. Other times, commercial solicitations are sent by local companies advertising local products, like a restaurant delivery service advertising to their delivery area or a retail store sending their weekly advertising circular to a general area. Bulk mail is also often sent to companies’ existing subscriber bases, advertising new products or services.

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Part I: FCAT Reading Test

1. Who generally places restrictions on private postal systems? A. B. C. D.

monopolies governments private carriers courier services

2. According to the author, what is a typical method of paying the postal fee for an article? A. B. C. D.

metering the article prepaying a courier charging postal cards buying adhesive stamps

3. Government monopolies generally do not extend to any of the following EXCEPT A. B. C. D.

express mail. courier services. delivery of parcels. delivery of documents.

4. According to the article, postal systems may have authority over all of the following EXCEPT A. B. C. D.

courier services. savings accounts. telephone and telegraph. applications for passports.

5. Read this sentence from the article. Communication via written documents which an intermediary carries from one person or place to another almost certainly dates back to the invention of writing. What does the word “intermediary” mean? A. B. C. D.

the sender of the article the recipient of the article someone other than the sender or recipient someone assigned to read for the sender or recipient

6. Which of the following countries is the one in which the first documented use of a formal postal system occurred? A. B. C. D.

Japan Egypt Great Britain United States

7. According to the article, national services and privately owned companies are interconnected by all of the following EXCEPT A. B. C. D.

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regulations. agreements. monopolies. organizations.

Practice FCAT Reading 3

8. Which organization coordinates the individual national postal systems? A. B. C. D.

Fleet Post Office Bulk Mail Systems United Parcel Service Universal Postal Union

9. Which of the following systems has facilitated automating postal operations? A. B. C. D.

system of codes system of airmail system of franking system of mailboxes

10. According to the article, the particular method of coding called “block of dots” allows for all of the following EXCEPT A. B. C. D.

exact routing. proof of payment. automated handling. international reply coupons.

11. Improvements to the postal system during the twentieth century include all of the following EXCEPT A. B. C. D.

delivery by air. delivery by missile. navel vessel delivery. sender receipt services.

12. According to the article, what is the most common way to prepay postage worldwide? A. B. C. D.

use of franking use of postcards buying postal cards buying adhesive stamps

13. Franking is a method of performing which of the following tasks? A. B. C. D.

mailing bulk letters world-wide creating postage-prepaid envelopes delivering mail to fleet post offices guaranteeing delivery with receipts services

14. According to the article, franking is used by all of the following EXCEPT A. B. C. D.

banks that mail. direct-mail companies. companies with large mail programs. companies with overseas branch offices.

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15. How does a postal agent generally indicate that a prepaid envelope or package is no longer valid for pre-payment of postage? A. B. C. D.

by using a block of dots by means of a censorship by means of a cancellation by using a bar code system

16. According to the article, exceptions to canceling prepaid postage articles to indicate that it is no longer valid for prepayment include all of the following EXCEPT A. B. C. D.

use of precancelled stamps. use of premetered envelopes. agent accidentally forgets to cancel. agent accidentally neglects to cancel.

17. What is the term commonly used for the secret correspondence usually guaranteed by most national constitutions? A. B. C. D.

etiquette censorship open communication discreet correspondence

18. The operation of control of private citizens’ mail concerns all of the following EXCEPT A. B. C. D.

legal aspects of civil rights. social aspects of civil rights. military aspects of civil rights. political aspects of civil rights.

19. According to the article, when is censorship usually NOT employed? A. B. C. D.

for military mail for first class mail for wedding invitations for international reply coupons

20. According to the article, following the development of systems that allowed a quicker way of communicating such as the telephone, the use of mail remained as a primary vehicle for all of the following EXCEPT A. B. C. D.

legal documents. commercial documents. general communications. personal communications.

21. Why is using the term philately in reference to stamp collecting technically erroneous? A. B. C. D.

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because it actually refers to the use of stamps because it actually refers to the study of stamps because it actually concerns the collection of stamps that have already been cancelled because it actually concerns the collections of stamps that have not yet been cancelled

Practice FCAT Reading 3

22. Postcards are often printed with all of the following on the front EXCEPT A. B. C. D.

resort pictures. sender messages. tourist attractions. humorous messages.

23. Read this sentence from the article. The fact that this communication is visible by other than the receiver often causes the messages to be written in jargon. What does the term “jargon” mean? A. B. C. D.

code colors humor pictures

24. Which of the following differentiates the postal card from a postcard? A. B. C. D.

preprinted postage on the card preprinted pictures on the card preprinted space for sender message preprinted space for receiver address

25. According to the article, magazines use postcards for all of the following EXCEPT A. B. C. D.

reader surveys. new subscriptions. information requests. subscription renewals.

26. According to the article, even though telephone and e-mail provide a more immediate means of communication, traditional letters are still used in which of the following circumstances? A. B. C. D.

when one wishes to be deliberate when one wishes to be immediate when serving or visiting a military fleet when living or visiting in another country

27. All of the following are employed to speed communication EXCEPT A. B. C. D.

e-mail services. receipt services. airmail services. telephone services.

28. Which of the following specifically qualify as junk mail? A. B. C. D.

official notifications commercial solicitations utility companies’ billings service providers’ correspondence

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29. Bulk mail includes all of the following EXCEPT A. B. C. D.

advertising new services. advertising new products. advertising local products. advertising remote services.

Passage 2 Read the following passage before answering Questions 30 through 50.

Imponderables Move the World This twentieth century world abounds in problems that will tax the highest capacity of men to solve. Some of these are human problems, some are industrial problems, some are economic problems, some are financial problems, some are political problems, and some are religious problems. The point upon which to insist is that they can never be solved by hate, by conflict or by force. These problems may be suppressed in one of those ways but they cannot so be solved. If they are to be solved they must be solved in a spirit of kindly cooperation, of friendly association and of consultation with the fixed purpose of doing justice and establishing liberty among men. These are the true and lasting foundations of peace. Peace, it must never be forgotten, is itself not an ideal at all; it is a state attendant upon the achievement of an ideal. The ideal itself is human liberty, justice, and the honorable conduct of an orderly and humane society. Given this, a durable peace follows naturally as a matter of course. Without this, there is no peace, but only a rule of force until liberty and justice revolt against it in search of peace. These are the fundamental facts never to be forgotten. It is liberty and justice of which we are instantly and directly in search, and this means that we must be ready with open minds to consider any question which is raised anywhere in the world involving these great principles and ends, and try to settle it fairly and justly that human content may follow and the foundation of peace be thereby rendered more secure. Among the older nations the process of nation-building is completed. There are problems of national ambition and of minorities submerged under and surrounded by majorities of different race and different language. There are problems of religious controversy and there are problems of historic racial jealousies and antagonisms which must be resolved through the years with patience, with frankness, with open-mindedness and in a spirit of justice. Nothing is ever really settled until it is settled right. What is now before our world is to make sure that we do not attempt to settle things right by force, by violence, by war, but that we attempt to settle them right by study, by conference, by consultation. All these are among the intangibles that rule the world.

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The peace of the world cannot rest with permanence upon any theory of domination by force whether that domination be military or economic or racial or religious, for such domination is always a temptation to its disturbance and overthrow. Peace can only rest secure upon a liberal, enlightened and convinced public opinion. That public opinion, having itself brought about the renunciation of war as an instrument of national policy, will now proceed to build for its own expression and for its own satisfaction institutions that will regulate and guide the contacts and relations of men organized in nations as a substitute for those suspicions and fears and displays of power which have been so common in years gone by. These institutions, it would seem safe to predict, will be of three kinds, each kind having a moral foundation and a moral purpose. There will first be the intangible institution of intellectual international penetration, contact and association. Already large progress has been made toward this end. Science is international and literature, although it always speaks with a nation’s tongue. Nowhere is Shakespeare more widely read, better understood, or more effectively presented on the stage than in Germany. The speech of Goethe was German but his thought is familiar the world around. Music has a Russian, a Polish, a Scandinavian, a German, a French, an Italian, a Spanish or an English cast, but its charm and its power are not stopped by the boundaries of any nation. The richness and the fertility of intellectual and aesthetic diversity are multiplied many times by the power of what these have in common. All that belongs to the intangible. The third type of institution which must come into existence to meet present-day necessities is economic. Man lives by labor, nations thrive by labor, and international relations may be made either more easy or more difficult according to the methods by which the fruits of labor are exchanged between one nation and another. When life was very simple and wants were few, a relatively restricted territory and a substantially uniform climate might perhaps provide what was necessary to satisfy the simple wants of an undeveloped people. Times have changed. What were once the almost unattainable luxuries of life have become not only its comforts but its necessities. For the food supply of any considerable population, an extent of territory that is literally enormous must be drawn upon day by day and almost hour by hour. No industry can be maintained, much less flourish, without metal and rubber and lumber and oil and a dozen other natural resources that usually come from far beyond the boundaries of that nation whose industry it is. In other words, the economic life of any nation, however immense and however rich, has already ceased to be national and independent and has long since become international and dependent. The meaning of this is that the international commerce of the world must be set increasingly free from narrow, petty, prejudiced restrictions and administrative hindrances in order that the population of any nation may most easily and most favorably exchange their own products for those which they wish to import.

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There are two different ways in which any great question which involves national pride and national interest may be approached. One is in a spirit of confidence and good feeling and hope. The other is in a spirit of suspicion and jealousy and fear. Both are intangibles and the contest for the government of the world and for the heart of mankind is between these. In any case, it will be an intangible that will rule the world and it is for public opinion to determine whether the choice shall be of an intangible which is lofty and fine and noble and helpful to all mankind, or whether it shall be an intangible that is low and mean and jealous and selfish and grasping. Today the world stands at the crossroads and must quickly choose the road which it will travel toward one or the other of these two intangibles. Which way shall people turn? May not one who has drunk deep and long at the well of their scholarship, their learning, their literature, and their science, answer that the people, mindful of the great signposts which guide and represent them, will answer in the spirit of the eloquent voice and in that of the calm and constructive philosophy of Immanuel Kant, German Heart, do not dismay, But thy Conscience’ voice obey.

30. According to the story, problems attendant upon the twentieth century include all of the following EXCEPT A. B. C. D.

human and industrial problems. political and religious problems. economic and financial problems. natural and institutional problems.

31. According to the author, problems of the nature discussed cannot be solved by any of the following EXCEPT A. B. C. D.

hate. strife. force. conflict.

32. What must be the purpose in all attempts in solving the problems presented by the author? A. B. C. D.

establishing peace and doing justice doing justice and establishing peace doing justice and establishing liberty establishing peace and liberty among men

33. The author describes peace as what? A. B. C. D.

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a state a force a cooperation a consultation

Practice FCAT Reading 3

34. Discuss the ideal upon which peace is dependant. Use details and information from the story to support your answer.

35. The author states, “Nothing is ever really settled until it is settled right.” What does the author mean by this statement? Use details and information from the story to support your answer.

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36. Which of the following is NOT considered to be a theory of domination? A. B. C. D.

racial religious economical enlightenment

37. According to the story, once public opinion renounces war as a policy, it will build which of the following to guide behavior? A. B. C. D.

institutions associations governments organizations

38. According to the story, institutions employed to regulate and guide contacts and relations with other nations possess all of the following attributes EXCEPT A. B. C. D.

moral purpose. desire for peace. display of power. moral foundation.

39. According to the story, Shakespeare is best understood in what country? A. B. C. D.

Italy France England Germany

40. The author states that one of the institutions necessary for a lasting peace will be an intangible one of intellect that will do all of the following EXCEPT A. B. C. D.

contact. associate. penetrate. renounce.

41. According to the article, which of the following will NOT stop the charm and power of music? A. B. C. D.

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national politics national religion national boundaries national governments

Practice FCAT Reading 3

42. Read the following sentence from the story. Man lives by labor, nations thrive by labor, and international relations may be made either more easy or more difficult according to the methods by which the fruits of labor are enhanced between one nation and another. What does the term “fruits of labor” mean? A. B. C. D.

fruit picked by labor things made by work things exported to other countries fruit exchanged with other countries

43. According to the author, in order for industry to be maintained, it must have all of the following EXCEPT A. B. C. D.

oil. fruits. rubber. lumber.

44. According to the story, world commerce must be set free from all of the following types of restrictions EXCEPT A. B. C. D.

petty restrictions. import restrictions. narrow restrictions. prejudiced restrictions.

45. Read the following sentence from the story. The meaning of this is that the international commerce of the world must be set increasingly free from narrow, petty, prejudiced restrictions and administrative hindrances in order that the population of any nation may most easily and most favorably exchange their own products for those which they wish to import. What does the word “import” mean? A. B. C. D.

swap important move in to take out from

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46. What different ways are there to approach questions including national pride and interest? Use details and information from the story to support your answer.

47. What does the author repeatedly state will rule the world? A. B. C. D.

an ideal an economy an intangible an imponderable

48. According to Kant, whose voice should be obeyed? A. B. C. D.

that of their heart that of their conscience that of the German Heart that of the German people

49. What would be the BEST alternative title for this story? A. B. C. D.

Peace is for Intellectuals Intangibles Rule the World The Heart of Immanuel Kant Shakespeare, Goethe, and Music

50. Which statement BEST expresses the theme of the story? A. B. C. D.

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Following the teaching of Kant can lead to lasting peace. Studying literature, music, and drama is the best route to peace. Lasting peace is best attained through intellectual and economic exchange. Drinking long and deep from the well of scholarship will lead to lasting peace.

Practice FCAT Reading 3

Answer Key for Practice Test 3 Passage 1: Mail 1. B 2. D 3. D 4. A 5. C 6. B 7. C 8. D 9. A 10. D 11. B 12. D 13. B 14. D 15. C 16. B 17. B 18. C 19. A 20. C 21. B 22. B 23. A 24. A 25. D 26. A 27. B 28. B 29. D

Passage 2: Imponderables Move the World 30. D 31. B 32. C

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33. A 34. Sample 2-Point Response: The author states that peace is not an ideal itself but rather a state attendant upon the ideals of human liberty, justice, and the honorable conduct of an orderly humane society. The author further states that the achievement of this ideal is the only way to ensure a durable peace. 35. Sample 4-Point Response: The author is referring to the problems identified that pose a barrier to peace. He identifies such problems as those that are human, industrial, economic, financial, political, and religious. The author states that if these problems, “. . .are to be solved they must be solved in a spirit of kindly cooperation, of friendly association and of consultation with the fixed purpose of doing justice and establishing liberty among men.” He goes on to say that what is not right is to attempt to settle things by force, violence, or war but rather to settle them right by study, conference, and consultation. Further, he states that a lasting right way to settle the problems must be resolved through the years with patience, frankness, and open-mindedness in a spirit of justice. Finally, he states the right way to settle any great question that involves national pride is one in a spirit of confidence and good feeling of hope. 36. D 37. A 38. C 39. D 40. D 41. C 42. B 43. B 44. B 45. C 45. Sample 2-Point Response: According to the story, one way to approach such questions is in a spirit of confidence and good feeling of hope. The alternative way to approach such questions, according to the author, is in a spirit of suspicion and jealousy, and fear. 47. C 48. B 49. B 50. C

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Practice FCAT Reading 3

Answers and Explanations for Practice Test 3 Passage 1: Mail Note: Although all answer choices are text based, only one will correctly answer the question. 1. B. The article states, “Restrictions are generally placed on private systems by governments.” 2. D. The article states, “. . .with a fee on the article prepaid, often in the form of adhesive stamps.” 3. D. The article states, “Government monopolies generally do not extend to delivery of parcels or courier services providing express mail.” 4. A. The article states, “In some countries, the postal system also has some authority over telephone and telegraph systems. In others, postal systems allow for savings accounts and handling applications for passports.” 5. C. Postal systems use someone other than the sender or recipient, an intermediary, to carry the article. 6. B. The article states, “The first documented use of an organized courier service for the diffusion of written documents is in Egypt. . .” 7. C. The article states, “Modern mail is usually organized by national services. . .reciprocally interconnected by international regulations, organizations and agreements.” 8. D. The article states, “The world-wide postal system. . .is coordinated by the Universal Postal Union. . ..” 9. A. The article states, “In many countries a system of codes has been created. . .in order to facilitate the automation of operations.” 10. D. The article states, “The ‘block of dots’ method allows for the encoding of proof of payment of postage, exact routing for delivery, and other features.” Remember, the article previously stated that coding systems facilitated the automation of operations. 11. B. The article identifies all of the responses but the article states, “Some methods of airmail proved ineffective, however, including the United States Postal Service’s experiment with guided missiles for international mail transport.” 12. D. The article states, “Worldwide the most common method of prepaying postage is by buying an adhesive postage stamp to be stuck to the envelope before mailing. . ..” 13. B. The article states, “Franking is a method of creating postage-prepaid envelopes under license. . .” 14. D. In relation to franking, the article states, “They are used by companies with large mail programs such as banks and direct mail companies.” 15. C. The article states, “. . .the agent usually indicates by means of a cancellation that it is no longer valid for prepayment of postage.” 16. B. The article lists all of the choices except “use of pre-metered envelopes” in the following excerpt, “The exceptions are when the agent forgets or neglects to cancel the mail piece, or for stamps that are pre-cancelled and thus do not require cancellation.” 17. B. The article states, “The operation of control of private citizens’ mail is called censorship. . ..” 18. C. The article states, “. . .is called censorship and concerns social, political and legal aspects of civil rights.” 19. A. The article states, “While in most cases this censorship is exceptional, military censorship of mail. . .is routine and almost universally applied.” 20. C. When discussing quicker systems of communicating becoming more popular, the article states, “. . .mail. . . remained as a vehicle for commercial or formal documents. It is, however, still widely in use in more cultivated classes for personal communication; in particular, wedding invitations are customarily sent by mail.”

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21. B. The article states, “In strict philatelic usage, the postcard is to be distinguished from the postal card, which has a pre-printed postage on the card.” 22. B. The article states, “Postcards are often printed today to promote tourism, with pictures of resorts, tourist attractions or humorous messages on the front and allowing for a short message from the sender to be written on the back.” 23. A. Content clues as to the meaning of “jargon” as “code” can be found within the sentence it is used, in that it indicates the need or desire for some privacy not normally afforded those who use postcards. 24. A. The article states, “. . .the postcard is to be distinguished from the postal card, which has a pre-printed postage on the card.” 25. D. The article states, “Postcards are also used by magazines for new subscriptions.” The article also states, “...magazines also use postcards for other purposes, including reader surveys, contests or information requests.” 26. A. The article states, “Traditional letters, however. . .are still used when someone wishes to be deliberate. . ..” 27. B. All of the choices speed the routing and delivery except the “receipt service,” which is designed to provide a proof of delivery of the article. 28. B. The article states, “Bulk mail, often called junk mail, are commercial solicitations sent by advertisers.” 29. D. The article states, “. . .commercial solicitations are sent by local companies advertising local products. . ..” The article also states, “Bulk mail is also often sent to companies’ existing subscriber bases, advertising new products or services.”

Passage 2: Imponderables Move the World 30. D. The article states, “Some of these are human problems, some are industrial problems, some are economic problems, some are financial problems, some are political problems, and some are religious problems.” 31. B. The article states, “The point upon which to insist is that they can never be solved by hate, by conflict or by force.” 32. C. The article states, “If they are to be solved they must be solved. . .with the fixed purpose of doing justice and establishing liberty among men.” 33. A. The article states, “Peace, it must never be forgotten, is itself not an ideal at all; it is a state. . .” 34. While not a direct quote, the response is extracted from the text. It identifies the ideal and reflects the author’s point when he states, “Given this, a durable peace follows naturally as a matter of course.” 35. This question allows the respondent to identify a full range of responses from various points in the story. The sample response identifies the problems to which the question refers, then goes on to indicate the statements made by the author throughout the story indicating the only “right” way to solve those problems in order to create an atmosphere capable of sustaining a lasting peace. 36. D. The article states, “the peace of the world cannot rest with permanence upon any theory of domination by force whether that domination be military or economic or racial or religious. . .” 37. A. The article states, “The public opinion, having itself brought about the renunciation of war as an instrument of national policy, will now proceed to build for its own expression and for its own satisfaction institutions. . ..” 38. C. The article states the institutions will each have, “. . .a moral foundation and a moral purpose.” Further, the article previously established that a public opinion wishing to establish peace would build the institutions necessary for that peace. 39. D. The article states, “Nowhere is Shakespeare more widely read, better understood or more effectively presented on the stage than in Germany.” 40. D. The article states, “There will be the intangible institution of intellectual international penetration, contact and association.”

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41. C. The article states, when speaking of music, “. . .but its charm and its power are not stopped by the boundaries of any nation.” 42. B. Context clues are given in the sentence as the author suggests that these “fruits” may be exchanged between one nation and another. Those items of exchange are those items produced by any given country through its labor or work force. 43. B. The article states, “No industry can be maintained, much less flourish, without metal and rubber and lumber and oil and a dozen other natural resources. . ..” 44. B. The article states, “. . .international commerce of the world must be set increasingly free from narrow, petty, prejudiced restrictions and administrative hindrances. . .” 45. C. Context clues are given in the sentence as the leading information speaks of a country exchanging its own products for others it does not possess. 46. The article states, “There are two different ways in which any great question which involves national pride and national interest may be approached.” The article then goes on to discuss those two alternatives and the response extracts both methods from the article. 47. C. In one statement, the article reads, “All these are among the intangibles that rule the world.” In another, it reads, “In any case, it will be an intangible that will rule the world. . .” 48. B. Kant is speaking to the German people and directing them to obey the voice of their conscience. 49. B. As the author repeatedly states that an intangible will rule the world, Choice B is correct. 50. C. The article refers to two types of institutions that necessarily be created in order for a lasting peace to take place. One of the institutions is the “. . .intangible institution of intellectual international penetration. . .” and one is the “. . .institution which must come into existence to meet present-day necessities is economic.”

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Practice FCAT Reading 4 This practice test contains four reading passages and 50 sample questions. Read each passage and answer all the questions that follow each passage.

Passage 1 Read the following passage before answering Questions 1 through 28.

Plate Tectonics

The tectonic plates of the world were mapped in the second half of the twentieth century. Plate tectonics (from the Greek word for “one who constructs”) is a theory of geology developed to explain the phenomenon of continental drift, and is currently the theory accepted by the vast majority of scientists working in this area. In the theory of plate tectonics the outermost part of the Earth’s interior is made up of two layers, the outer lithosphere and the inner asthenosphere. The lithosphere essentially “floats” on the asthenosphere and is broken up into seven major plates: African, Antarctic, Australian, Eurasian, North American, South American, and the Pacific. These plates (and the more numerous minor plates) move in relation to one another at one of three types of plate boundaries: convergent (two plates push against one

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another), divergent (two plates move away from each other), and transform (two plates slide past one another). Earthquakes, volcanic activity, mountain-building, and oceanic trench formation occur along plate boundaries. Plate tectonic theory arose out of two separate geological observations: seafloor spreading and continental drift. The theory itself was developed during the late 1960s and has since almost universally been accepted by scientists and has revolutionized the Earth sciences.

Key Principles The division of the Earth’s interior into lithospheric and asthenospheric components is based on their mechanical differences. The lithosphere is cooler and more rigid, whilst the asthenosphere is hotter and mechanically weaker. This division should not be confused with the chemical subdivision of the Earth into (from innermost to outermost) core, mantle, and crust. The key principle of plate tectonics is that the lithosphere exists as separate and distinct tectonic plates, which “float” on the fluid-like asthenosphere. The relative fluidity of the asthenosphere allows the tectonic plates to undergo motion in different directions. One plate meets another along a plate boundary, and plate boundaries are commonly associated with geological events such as earthquakes and the creation of topographic features like mountains, volcanoes and oceanic trenches. The majority of the world’s active volcanoes occur along plate boundaries, with the Pacific Plate’s Ring of Fire being most active and famous.

Types of Plate Boundaries Plate

Plate

Asthenosphere Convergent plate boundary

Island arc

h nc Tre Stratovolcano

Transform plate boundary

Shield volcano

Divergent plate boundary

Convergent plate boundary

Oceanic spreading ridge Lithospere Asthenosphere

Tre n

Continental rift zone (young plate boundary)

ch

Continental cru

st

Oceanic crust Subducting plate

Hot spot

Three types of plate boundaries.

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Practice FCAT Reading 4

There are three types of plate boundaries, characterized by the way the plates move relative to each other. They are associated with different types of surface phenomena. The different types of plate boundaries are 1. Transform boundaries occur where plates slide, or perhaps more accurately grind, past each other along transform faults. 2. Divergent boundaries occur where two plates slide apart from each other. 3. Convergent boundaries (or active margins) occur where two plates slide toward each other commonly forming either a subduction zone (if one plate moves underneath the other) or an orogenic belt (if the two simply collide and compress).

Transform Boundaries The left- or right-lateral motion of one plate against another along transform faults can cause highly visible surface effects. Because of friction, the plates cannot simply glide past each other. Rather, stress builds up in both plates and when it reaches a level that exceeds the slipping-point of rocks on either side of the transform-faults the accumulated potential energy is released as strain, or motion along the fault. The massive amounts of energy that are released are the cause of earthquakes, a common phenomenon along transform boundaries. A good example of this type of plate boundary is the San Andreas Fault complex, which is found in the western coast of North America and is one part of a highly complex system of faults in this area.

Divergent Boundaries At divergent boundaries, two plates move apart from each other and the space that this creates is filled with new crustal material sourced from molten magma that forms below. The genesis of divergent boundaries is sometimes thought to be associated with the phenomenon known as hotspots. Here, exceedingly large convective cells bring very large quantities of hot asthenospheric material near the surface and the kinetic energy is thought to be sufficient to break apart the lithosphere. The hotspot believed to have created the Mid-Atlantic Ridge system currently underlies Iceland which is widening at a rate of a few centimeters per century. Such hotspots can be very productive of geothermal power and Iceland is actively developing this resource and is expected to be the world’s first hydrogen economy within twenty years. Divergent boundaries are typified in the oceanic lithosphere by the rifts of the oceanic ridge system, including the Mid-Atlantic Ridge, and in the continental lithosphere by rift valleys such as the famous East African Great Rift Valley. Divergent boundaries can create massive fault zones in the oceanic ridge system. Spreading is generally not uniform, so where spreading rates of adjacent ridge blocks are different massive transform faults occur. These are the fracture zones, a major source of submarine earthquakes.

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It is at mid-ocean ridges that one of the key pieces of evidence forcing acceptance of the sea-floor spreading hypothesis was found. Airborne geomagnetic surveys showed a strange pattern of symmetrical magnetic reversals on opposite sides of ridge centers. The pattern was far too regular to be coincidental as the widths of the opposing bands were too closely matched. Scientists had been studying polar reversals and the link was made. The magnetic banding directly corresponds with the Earth’s polar reversals. This was confirmed by measuring the ages of the rocks within each band. In reality the banding furnishes a map in time and space of both spreading rate and polar reversals.

Convergent Boundaries The nature of a convergent boundary depends on the type of lithosphere in the plates that are colliding. Where a dense oceanic plate collides with a less-dense continental plate, the oceanic plate is typically thrust underneath, forming a subduction zone. At the surface, the topographic expression is commonly an oceanic trench on the ocean side and a mountain range on the continental side. An example of a continental-oceanic subduction zone is the area along the western coast of South America where the oceanic Nazca Plate is being subducted beneath the continental South American Plate. As organic material from the ocean bottom is transformed and heated by friction, a liquid magma with a great amount of dissolved gasses will be created. This can erupt to the surface, forming long chains of volcanoes inland from the continental shelf and parallel to it. The continental spine of South America is dense with this type of volcano. In North America the Cascade mountain range, extending north from California’s Sierra Nevada, is also of this type. Such volcanoes are characterized by alternating periods of quiet and episodic eruptions that start with explosive gas expulsion with fine particles of glassy volcanic ash and spongy cinders, followed by a rebuilding phase with hot magma. The entire Pacific Ocean boundary is surrounded by long stretches of volcanoes and is known collectively as The Ring of Fire. Where two continental plates collide the plates either crumple and compress or one plate burrows under or (potentially) overrides the other. Either action will create extensive mountain ranges. A most dramatic effect is seen where the northern margins of the Indian subcontinental plate is being thrust under a portion of the Eurasian plate, lifting it and creating the Himalaya. When two oceanic plates converge they form an island arc as one oceanic plate is subducted below the other. A good example of this type of plate convergence would be Japan.

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Tre nc h

Volcanic arc

Practice FCAT Reading 4

Oceanic crust Continental crust Lithosphere

Lithospere

Asthenosphere

Oceanic-continental convergence

au

Oceanic/Continental

nt a

High

i

ou

plate

ge

an nr

M

Continental crust

Continental crust

Lithosphere

Lithospere

Ancient oceanic crust

Asthenosphere

Continental-continental convergence

arc d an Isl

Tre n

ch

Continental/Continental

Oceanic crust Continental crust Lithospere Lithosphere Asthenosphere

Oceanic-oceanic convergence Oceanic/Oceanic

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The movement of plates has caused the formation and breakup of continents over time, including occasional formation of a supercontinent that contains most or all of the continents. The super-continent Rodinia is thought to have formed about 1,000 million years ago and to have embodied most or all of Earth’s continents, and broken up into eight continents around 600 million years ago. The eight continents later re-assembled into another supercontinent called Pangaea; Pangaea eventually broke up into Laurasia (which became North America and Eurasia) and Gondwana (which became the rest).

1. According to the article, all of the following are types of plate boundaries EXCEPT A. B. C. D.

transform. divergent. continental. convergent.

2. The theory of plate tectonics was developed during which period? A. B. C. D.

1960–1965 1965–1970 Pangea Laurasia

3. The chemical subdivision of the earth consists of all of the following EXCEPT A. B. C. D.

corke. crust. plate. mantle.

4. Upon which of the following differences are the lithosphere and asthenosphere components based? A. B. C. D.

motion chemical boundary mechanical

5. All of the following geological activities occur along plate boundaries EXCEPT A. B. C. D.

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volcanic. earthquakes. river-trenching. mountain-building.

Practice FCAT Reading 4

6. According to the article, which is the outer most layer in the plate tectonic theory? A. B. C. D.

core mantle lithosphere asthenosphere

7. Which of the following is one of the geological observations out of which the plate tectonic theory arose? A. B. C. D.

volcanic activity seafloor spreading continental boundaries mechanical differences

8. According to the article, all of the following components are used to differentiate between the lithosphere and asthenosphere EXCEPT A. B. C. D.

rigidity. temperature. relative size. mechanical strength.

9. Which of the following is the key principle upon which the theory of plate tectonics is based? A. B. C. D.

Plate boundaries are fixed boundaries. Tectonic plates move in one direction. Lithosphere plates float on the asthenosphere. The asthenosphere overrides the lithosphere plates.

10. Describe what geological events and kinds of topography are commonly associated with plate boundaries. Use details and information from the article to support your answer.

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11. Discuss the various boundary types and the motions associated with each. Use details and information from the article to support your answer.

12. What prevents transform faults from being able to simply slide past each other? A. B. C. D.

strain friction left-lateral motion right-lateral motion

13. According to the article, what is a common phenomenon when massive energy is released along a transform fault? A. B. C. D.

volcanoes earthquakes ridge blocks ocean trenches

14. Which of the following fills the space created by divergent plate boundaries? A. B. C. D.

ridge material crustal material lithospheric material asthenospheric material

15. Which statement BEST describes the phenomenon known as “hotspots”? A. B. C. D.

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Geothermal energy, creating hydrogen, breaks through the lithosphere. Large convective cells and kinetic energy break through the lithosphere. Large quantities of hot asthenospheric materials break apart the lithosphere. Crustal material formed from molten magma that forms below breaks through the lithosphere.

Practice FCAT Reading 4

16. According to the article, what is a major source of submarine earthquakes? A. B. C. D.

ridge rifts ridge blocks fracture zones colliding plates

17. Read the following sentence. These are the fracture zones, a major source of submarine earthquakes. As used in this sentence, what does the term “submarine” mean? A. B. C. D.

oceanic underwater underwater vessel oceanic disturbance

18. What specific scientific study linked with geomagnetic surveys forced the acceptance of the sea-floor spreading hypothesis? A. B. C. D.

polar reversals magnetic banding airborne geomagnetic surveys symmetrical magnetic surveys

19. Upon which of the following does the nature of a convergent boundary depend? A. B. C. D.

type of lithosphere type of asthenosphere force of plate movement speed of plate movement

20. Read the following sentence. An example of a continental-oceanic subduction zone is the area along the western coast of South America where the oceanic Nazca Plate is being subducted beneath the continental South American Plate. What does the term “subducted” mean? A. B. C. D.

thrust underneath wrapped underneath underwater collision underwater convergence

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21. When a dense oceanic plate collides with a less-dense continental plate, all of the following typically occur EXCEPT A. B. C. D.

an oceanic trench is formed. a subduction zone is formed. a mountain range is formed. an earthquake fault is formed.

22. Where two continental plates collide, all of the following events may occur EXCEPT A. B. C. D.

plates merge. plates crumble. one plate overrides the other. one plate burrows under the other.

23. According to the article, what is a certain outcome when two continental plates collide? A. B. C. D.

A volcanic range is created. An explosive gas is created. A mountain range is created. An earthquake fault is created.

24. According to the article, what country represents the result of two oceanic plates converging? A. B. C. D.

Japan Iceland North America South America

25. What is the name of the oldest supercontinent discussed in the article? A. B. C. D.

Rodinia Pangaea Laurasia Gondwana

26. The San Andreas Fault complex found in the western coast of North America is a good example of what type plate boundary? A. B. C. D.

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divergent transform continent to oceanic continent to continent

Practice FCAT Reading 4

27. Describe the activity typically found in convergent plat boundaries. Use details and information from the article and graphics to support your answer.

28. Which of the following is typically formed with the convergence of two oceanic plates? A. B. C. D.

an island arc a mountain range a subduction zone an earthquake fault

Passage 2 Read the following passage before answering Questions 29 through 41.

The Mississippi River The world and the books are so accustomed to use, and overuse, the word “new” in connection with our country, that we early get and permanently retain the impression that there is nothing old about it. We do of course know that there are several comparatively old dates in American history, but the mere figures convey to our minds no just idea, no distinct realization, of the stretch of time which they represent. To say that De Soto, the first white man who ever saw the

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Mississippi River, saw it in 1542, is a remark which states a fact without interpreting it: It is something like giving the dimensions of a sunset by astronomical measurements, and cataloguing the colors by their scientific names—as a result, you get the bald fact of the sunset, but you don’t see the sunset. It would have been better to paint a picture of it. The date 1542, standing by itself, means little or nothing to us; but when one groups a few neighboring historical dates and facts around it, he adds perspective and color, and then realizes that this is one of the American dates which is quite respectable for age. For instance, when the Mississippi was first seen by a white man, Michelangelo’s paint was not yet dry on the Last Judgment in the Sistine Chapel; Mary Queen of Scots was not yet born, but would be before the year closed. Catherine de Medici was a child; Elizabeth of England was not yet in her teens; Calvin, Benvenuto Cellini, and the Emperor Charles V were at the top of their fame, and each was manufacturing history after his own peculiar fashion. Unquestionably the discovery of the Mississippi is a datable fact which considerably mellows and modifies the shiny newness of our country, and gives her a most respectable outside-aspect of rustiness and antiquity. De Soto merely glimpsed the river, then died and was buried in it by his priests and soldiers. One would expect the priests and the soldiers to multiply the river’s dimensions by ten—the Spanish custom of the day—and thus move other adventurers to go at once and explore it. On the contrary, their narratives when they reached home, did not excite that amount of curiosity. The Mississippi was left unvisited by whites during a term of years which seems incredible in our energetic days. One may “sense” the interval to his mind, after a fashion, by dividing it up in this way: After De Soto glimpsed the river, a fraction short of a quarter of a century elapsed, and then Shakespeare was born; lived a trifle more than half a century, then died; and when he had been in his grave considerably more than half a century, the SECOND white man saw the Mississippi. In our day we don’t allow a hundred and thirty years to elapse between glimpses of a marvel. If somebody should discover a creek in the county next to the one that the North Pole is in, Europe and America would start fifteen costly expeditions thither: one to explore the creek, and the other fourteen to hunt for each other. For more than a hundred and fifty years there had been white settlements on our Atlantic coasts. These people were in intimate communication with the Indians: in the south the Spaniards were robbing, slaughtering, enslaving and converting them; higher up, the English were trading beads and blankets to them for a consideration, and throwing in civilization and whiskey, “for lagniappe”; and in Canada the French were schooling them in a rudimentary way, missionarying among them, and drawing whole populations of them at a time to Quebec, and later to Montreal, to buy furs of them.

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Practice FCAT Reading 4

Necessarily, then, these various clusters of whites must have heard of the great river of the far west; and indeed, they did hear of it vaguely, so vaguely and indefinitely, that its course, proportions, and locality were hardly even guessable. The mere mysteriousness of the matter ought to have fired curiosity and compelled exploration; but this did not occur. Apparently nobody happened to want such a river, nobody needed it, nobody was curious about it; so, for a century and a half the Mississippi remained out of the market and undisturbed. When De Soto found it, he was not hunting for a river, and had no present occasion for one; consequently he did not value it or even take any particular notice of it.

29. To what does the author compare the noninterpreted date of 1542? A. B. C. D.

painting a picture of a sunset watching the view of a sunset scientifically describing a sunset describing the varied colors in a sunset

30. What must the reader know in order for the events used by the author to show the significance of the year 1542 to become meaningful? A. B. C. D.

their historical importance each individual nationality where the events took place the exact dates of each event

31. According to the author, what is the discovery of the Mississippi? A. B. C. D.

a datable fact a curious event a rudimentary fact a mysterious event

32. The author states all of the following about De Soto EXCEPT A. B. C. D.

He studied the Mississippi River. He was buried in the Mississippi River. He merely glimpsed the Mississippi River. He was the first white man to see the Mississippi River.

33. According to the author, what was the usual Spanish method of reporting an exploration? A. B. C. D.

overstate their findings understate their findings often omit their findings exactingly detail their findings

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34. Read the following sentence. Unquestionably the discovery of the Mississippi is a datable fact which considerably mellows and modifies the shiny newness of our country, and gives her a most respectable outside-aspect of rustiness and antiquity. To what does the word “her” refer? A. B. C. D.

fact country newness Mississippi

35. Which of the following events does the author use to illustrate the amount of time that passes between the first and second sighting of the Mississippi River by a white man? A. B. C. D.

Shakespeare was born, lived, and died. Mary Queen of Scots was born, lived, and died. Elizabeth of England was born and crowned Queen. Michelangelo paints the Last Judgment in the Sistine Chapel.

36. Read this sentence from the story. If somebody should discover a creek in the county next to the one that the North Pole is in, Europe and America would start fifteen costly expeditions thither: one to explore the creek, and the other fourteen to hunt for each other. The phrase, “one to explore the creek and the other fourteen to hunt for each other” is an example of which literary device? A. B. C. D.

irony sarcasm symbolism foreshadowing

37. According to the author, all of the following clusters of whites must have heard of the Mississippi River EXCEPT A. B. C. D.

the coastal English. the Canadian French. the southern Spanish. the plains Americans.

38. According to the story, which of the following groups were trading beads and blankets to Indians? A. B. C. D.

French English Spanish Canadians

39. According to the author, what should have caused people to explore the Mississippi River? A. B. C. D.

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the course of the river the mysteriousness of the matter the specific locality of the matter the mapping of the proportions of the river

Practice FCAT Reading 4

40. What BEST describes the overall tone of the story? A. B. C. D.

subtle disbelief matter-of-fact tongue-in-cheek

41. What bias does the author reveal in this story? A. B. C. D.

that America really does have an important history that early settlers were slow to understand the value of American history that the Mississippi River discovery deserves a more prominent place in history that early explorers did not give much significance to the discovery of the Mississippi River

Passage 3 Read the following passage before answering Questions 42 through 46.

Robert Frost Acquainted with the Night I have been one acquainted with the night. I have walked out in rain—and back in rain. I have outwalked the furthest city light. I have looked down the saddest city lane. I have passed by the watchman on his beat And dropped my eyes, unwilling to explain. I have stood still and stopped the sound of feet When far away an interrupted cry Came over houses from another street, But not to call me back or say good-bye; And further still at an unearthly height, O luminary clock against the sky Proclaimed the time was neither wrong nor right. I have been one acquainted with the night.

42. Read this line from the poem I have looked down the saddest city lane What literary device does the author use in this line? A. B. C. D.

hyperbole alliteration onomatopoeia personification

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43. What activity is MOST responsible for acquainting the speaker with the night? A. B. C. D.

looking down city lanes walking at night only in the rain walking at all hours of the night speaking with the night watchman

44. Which line BEST informs the reader that the speaker has walked a great distance? A. B. C. D.

When far away an interrupted cry I have outwalked the furthest city light I have walked out in rain—and back in rain I have stood still and stopped the sound of feet

45. What tells the reader that the speaker prefers to walk alone? Use details and information from the poem to support your answer.

46. Read this line from the poem. O luminary clock against the sky To what is the poet referring? A. B. C. D.

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a lighted watchtower the lighted moon far from earth a lighted clock in a tall building the lighted street lamps in the city

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Passage 4 Read the following passage before answering Questions 47 through 50.

PuddinHead Wilson He happened to be up very early—at dawn, in fact; and he crossed the hall, which divided his cottage through the center, and entered a room to get something there. The window of the room had no curtains, for that side of the house had long been unoccupied, and through this window he caught sight of something which surprised and interested him. It was a young woman—a young woman where properly no young woman belonged; for she was in Judge Driscoll’s house, and in the bedroom over the judge’s private study or sitting room. This was young Tom Driscoll’s bedroom. He and the judge, the judge’s widowed sister Mrs. Pratt, and three Negro servants were the only people who belonged in the house. Who, then, might this young lady be? The two houses were separated by an ordinary yard, with a low fence running back through its middle from the street in front to the lane in the rear. The distance was not great, and Wilson was able to see the girl very well, the window shades of the room she was in being up, and the window also. The girl had on a neat and trim summer dress, patterned in broad stripes of pink and white, and her bonnet was equipped with a pink veil. She was practicing steps, gaits and attitudes, apparently; she was doing the thing gracefully, and was very much absorbed in her work. Who could she be, and how came she to be in young Tom Driscoll’s room? Wilson had quickly chosen a position from which he could watch the girl without running much risk of being seen by her, and he remained there hoping she would raise her veil and betray her face. But she disappointed him. After a matter of twenty minutes she disappeared and although he stayed at his post half an hour longer, she came no more. Toward noon he dropped in at the judge’s and talked with Mrs. Pratt about the great event of the day, the levee of the distinguished foreigners at Aunt Patsy Cooper’s. He asked after her nephew Tom, and she said he was on his way home and that she was expecting him to arrive a little before night, and added that she and the judge were gratified to gather from his letters that he was conducting himself very nicely and creditably—at which Wilson winked to himself privately. Wilson did not ask if there was a newcomer in the house, but he asked questions that would have brought light-throwing answers as to that matter if Mrs. Pratt had had any light to throw; so he went away satisfied that he knew of things that were going on in her house of which she herself was not aware.

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47. Although not specifically stated, who does the author suggest might be familiar with the mysterious young lady? A. B. C. D.

Wilson Mrs. Pratt Tom Driscoll Judge Driscoll

48. Read this sentence from the story? Wilson had quickly chosen a position from which he could watch the girl without running much risk of being seen by her, and he remained there hoping she would raise her veil and betray her face. What does the author mean by the word “betray”? A. B. C. D.

turn hide defy show

49. According to the story, all of the following people could have properly been in the room EXCEPT A. B. C. D.

Wilson. Mrs. Pratt. Tom Driscoll. Judge Driscoll.

50. Which word BEST describes the character of Wilson? A. B. C. D.

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jovial private serious secretive

Practice FCAT Reading 4

Answer Key for Practice Test 4 Passage 1: Plate Tectonics 1. C 2. B 3. C 4. D 5. C 6. C 7. B 8. C 9. C 10. Sample 2-Point Response: The article states that when one plate meets another along a plate boundary, geological events such as earthquakes occur. The types of topography generally found along plate boundaries include features like, “. . .mountains, volcanoes and oceanic trenches.” 11. Sample 2-Point Response: The first boundary types discussed are transform boundaries where plates slide or grind past each other along transform faults. The second are divergent boundaries where two plates slide apart from each other and the last are convergent boundaries, or active margins. These occur where plates slide toward each other and form either a subduction zone or orogenic belt. 12. B 13. B 14. B 15. C 16. C 17. B 18. A 19. A 20. A 21. D 22. A 23. C 24. A 25. A 26. B 27. Sample 4-Point Response: The article states that convergent boundaries occur where two plates slide toward each other commonly forming either a subduction zone or an orogenic belt. The nature of convergent boundaries and resultant topographical changes are dependent upon the type of lithosphere in the colliding plates. The graphic shows a dense oceanic plate colliding with a less-dense continental plate wherein the oceanic plate is thrust underneath the continental plate forming a subduction zone. The article states an oceanic trench and a mountain

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range are typical with this collision. According to the article, two convergent continental plates typically produce extensive mountain ranges and two convergent oceanic plates typically form an island arc, such as the one seen on the far left side of the graphic. 28. A

Passage 2: The Mississippi River 29. C 30. A 31. A 32. A 33. A 34. B 35. A 36. B 37. D 38. B 39. B 40. B 41. C

Passage 3: Acquainted with the Night 42. D 43. C 44. B 45. Sample 2-Point Response: The speaker tells us he has walked in rain which is when most people prefer to stay indoors. He tells us he walks great distances and prefers not to speak to the watchman. He says that if he stops walking, then there is no sound of feet, indicating he is walking alone. Finally, he says that the moon indicated it was alright to walk at any hour even though most people would be sleeping. 46. B

Passage 4: PuddinHead Wilson 47. C 48. D 49. A 50. D

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Answers and Explanations for Practice Test 4 Note: Although answer choices are text based, only one will correctly answer the question.

Passage 1: Plate Tectonics 1. C. The article states, “. . .one of three types of plate boundaries: convergent. . .divergent. . .and transform. . .” 2. B. The article states, “The theory itself was developed during the late 1960s. . .” 3. C. The article states, “This division should not be confused with the chemical subdivision of the Earth into (from innermost to outermost) core, mantle, and crust.” 4. D. The article states, “The division of the Earth’s interior into lithospheric and asthenospheric components is based on their mechanical differences.” 5. C. The article states, “Earthquakes, volcanic activity, mountain-building, and oceanic trench formation occur along plate boundaries.” 6. C. The article states, “In the theory of plate tectonics the outermost part of the Earth’s interior is made up of two layers, the outer lithosphere and the inner asthenosphere.” 7. B. The article states, “Plate tectonic theory arose out of two separate geological observations: seafloor spreading and continental drift.” 8. C. The article states, “The lithosphere is cooler and more rigid, whilst the asthenosphere is hotter and mechanically weaker.” 9. C. The article states, “The key principle of plate tectonics is that the lithosphere exists as separate and distinct tectonic plates, which “float” on the fluid-like asthenosphere.” 10. This is actually a two-part question. It is asking for information regarding both the geological events themselves and the resultant topographical changes. The response addresses both of these questions and is based on information taken directly from the article. 11. This is another two-part question. It is asking the respondent to discuss the various boundary types and discuss the motions associated with each of those boundary types. The response addresses both of these questions and is based on information taken directly from the article. 12. B. The article states, “Because of friction, the plates cannot simply glide past each other.” 13. B. The article states, “The massive amounts of energy that are released are the cause of earthquakes, a common phenomenon along transform boundaries. 14. B. The article states, “At divergent boundaries, two plates move apart from each other and the space that this creates is filled with new crustal material sourced from molten magma that forms below.” 15. C. The article states, “The genesis of divergent boundaries is sometimes thought to be associated with the phenomenon known as hotspots. Here, exceedingly large convective cells bring very large quantities of hot asthenospheric material near the surface and the kinetic energy is thought to be sufficient to break apart the lithosphere.” 16. C. The article states, “These are the fracture zones, a major source of submarine earthquakes.” 17. B. The prefix “sub” coupled with the surrounding context regarding ocean or marine activity should help the respondent answer this question. 18. A. The article states, “Scientists had been studying polar reversals and the link was made.” The “link” refers back to the airborne geomagnetic surveys. 19. A. The article states, “The nature of a convergent boundary depends on the type of lithosphere in the plates that are colliding.”

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20. A. Context clues from the article states, “Where a dense oceanic plate collides with a less-dense continental plate, the oceanic plate is typically thrust underneath, forming a subduction zone.” These clues are not found in the same sentence but in a preceding sentence. It is important that respondents know that context clues may be found in other parts of the article. 21. D. The article states, “Where a dense oceanic plate collides with a less-dense continental plate, the oceanic plate is typically thrust underneath, forming a subduction zone. At the surface, the topographic expression is commonly an oceanic trench on the ocean side and a mountain range on the continental side.” 22. A. The article states, “Where two continental plates collide the plates either crumple and compress or one plate burrows under or (potentially) overrides the other.” 23. C. The article states, “Where two continental plates collide the plates either crumple and compress or one plate burrows under or (potentially) overrides the other. Either will create extensive mountain ranges.” 24. A. The article states, “When two oceanic plates converge they form an island arc as one oceanic plate is subducted below the other. A good example of this type of plate convergence would be Japan.” 25. A. The article states, “The supercontinent Rodinia is thought to have formed about 1,000 million years ago...” This is the oldest supercontinent mentioned in the article. 26. B. In the section discussing transform boundaries, the article states, “A good example of this type of plate boundary is the San Andreas Fault complex...” 27. This is a multiple-part question. While it only asks the respondent to describe the activity typically found in convergent plate boundaries, it specifically directs the respondent to use information from both the article and the graphics to support the answer. It is important to note that information is taken from different areas of the article and especially to note that the sample response is careful to state where the source of the information being presented is found, either in the article or the graphic. Both sources are required in order to receive full credit for this type question. 28. A. The article states, “When two oceanic plates converge they form an island arc as one oceanic plate is subducted below the other.”

Passage 2: The Mississippi River 29. C. The article states, “To say that De Soto, the first white man who ever saw the Mississippi River, saw it in 1542, is a remark which states a fact without interpreting it: It is something like giving the dimensions of a sunset by astronomical measurements, and cataloguing the colors by their scientific names. . .” 30. A. The comparative events used by the author are of themselves little more than statement of fact and therefore must be “interpreted” to give relevance to the comparison. Unless the reader knows of the historical importance of the events presented, they will give little illustrative meaning for the significance of the date of 1542. 31. A. The article states, “Unquestionably the discovery of the Mississippi is a datable fact which considerably mellows. . .” 32. A. The article states, “To say that De Soto, the first white man who ever saw the Mississippi river. . .” Further, the article states, “De Soto merely glimpsed the river, then died and was buried in it by his priests and soldiers.” 33. A. The article states, “One would expect the priests and the soldiers to multiply the river’s dimensions by ten— the Spanish custom of the day. . .” 34. B. Response B is correct in that “her” refers to “country” as the datable fact gives our country “a most respectable outside-aspect of rustiness and antiquity.” 35. A. The article states, “After De Soto glimpsed the river, a fraction short of a quarter of a century elapsed, and then Shakespeare was born; lived a trifle more than half a century, then died; and when he had been in his grave considerably more than half a century, the SECOND white man saw the Mississippi.” 36. B. The author is clearly using sarcasm to describe the need for all expedition parties to have to look for the first one, as this would certainly not be the case in reality. This also helps set the tone of the story.

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37. D. The article refers to, “. . .in the south the Spaniards. . .” and, “. . .the English. . .” and, “. . .in Canada the French. . .” before stating, “Necessarily, then, these various clusters of whites must have heard of the great river of the far west. . .” 38. B. While referring to the Indians, the article states, “. . .higher up, the English were trading beads and blankets to them for a consideration. . .” 39. B. Referring to the Mississippi River, the article states, “The mere mysteriousness of the matter ought to have fired curiosity and compelled exploration: but this did not occur.” 40. B. The author expresses his disbelief that the discovery of the Mississippi River was not of a more notable event in history. His use of sarcasm and word choice coupled with his expression of opinion as opposed to only relating facts, negate the possibility of any other choice. 41. C. The author clearly believes that the discovery of the Mississippi River should be considered a major historical event and his tone and choice of words used throughout the story reveal this bias.

Passage 3: Acquainted with the Night 42. D. The author has given the lane a human-like quality which is personification. 43. C. The sheer quantity of walking at night through all hours is what gives the author this closeness of acquaintance with the night. This is supported by the various climates and times illustrated in the poem. 44. B. To have outwalked the distance the light can shine expresses the great distance the speaker has walked. 45. The sample response lifts information directly from the poem to cite incidents that inform the reader the speaker prefers to walk alone. All of the information is text-based and none is superfluous. 46. B. The speaker tells the reader that the luminary clock is at an unearthly height. This information alone alleviates all choices except for B.

Passage 4: PuddinHead Wilson 47. C. The author indicates that Tom Driscoll might be familiar with the mysterious young lady in two ways. Firstly, the young lady is in his bedroom and is there with seeming familiarity. Secondly, when Wilson is speaking to Mrs. Pratt, the author says, “He asked after her nephew Tom and she said he was on his way home and that she was expecting him to arrive a little before night, and added that she and the judge were gratified to gather from his letters that he was conducting himself very nicely and creditable—at which Wilson winked to himself privately.” The private wink indicates that Wilson believes Tom Driscoll may not be telling all he knows of the mysterious lady and that Tom may have a surprise in store for the family upon his return. 48. D. As the young lady was wearing a hat with a veil, Wilson could not see her face. He hoped she would lift the veil and reveal her identity by showing her face. Choice D is, therefore, the correct choice. 49. A. The author states, “This was young Tom Driscoll’s bedroom. He and the judge, the judge’s widowed sister Mrs. Pratt, and three Negro servants were the only people who belonged in the house.” 50. D. Wilson was secretly watching the mysterious girl in Judge Driscoll’s house. He also kept it a secret from Mrs. Pratt that he had seen the girl in Tom Driscoll’s bedroom earlier that day. Therefore, Choice D is correct.

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Practice FCAT Reading 5 This practice test contains three reading passages and 50 sample questions. Read each passage and answer all the questions that follow each passage.

Passage 1 Read the following passage before answering Questions 1 through 16.

Platypus The platypus is a small, semi-aquatic mammal endemic to the eastern part of Australia, and one of the four extant monotremes, the only mammals that lay eggs instead of giving birth to live young. It is the sole representative of its family (Ornithorhynchidae) and genus (Ornithorhynchus), though a number of fossilized relatives have been found, some of them also in the Ornithorhynchus genus. The scientific name Ornithorhynchus is derived from “ornithorhynkhos,” which literally means “bird nose” in Greek, and anatinus means “duck.” The common name is derived from the Greek words platus (flat) and pous (foot), meaning “flat foot.” The correct plural of platypus is “platypuses” and not “platypi,” as is sometimes heard. Australian Aborigines call the platypus by many names including mallangong, boondaburra, and tambreet. Early British settlers called it by many names as well, such as watermole, duckbill, and duckmole. The name platypus is often prefixed with the adjective “duck-billed” to form duck-billed platypus, despite there being only one species of platypus.

Physiology and Anatomy The physiology of the platypus is unique. The metabolic rate of the animal is remarkably low compared to other mammals, with a body temperature averaging 90°F rather than the 100.4°F typical of placental mammals. The body and the broad, flat tail of the platypus are covered with brown fur. It has webbed feet and a large, rubbery snout that are more reminiscent of a duck than any known mammal.

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Size varies considerably between less than two pounds and just under four and one-half pounds; with body length ranging from nearly 1’ to 1’3”, and tail length from 4” to 6” for males and 3” to 5” for females. Males are around onethird larger than females. There is substantial variation in average size from one region to another, though oddly this pattern does not seem to follow any particular climatic rule. Modern platypus young have tribosphenic* (three-cusped) molars, which are one of the hallmarks of mammals; adults are toothless. The platypus jaw is constructed somewhat differently from that of other mammals, and the jaw opening muscle is different. As in all true mammals, the tiny bones that conduct sound to the inner ear are fully incorporated into the skull, rather than lying in the jaw. However, the external opening of the ear still lies at the base of the jaw. The platypus has extra bones in the shoulder girdle, including an interclavicle, which is not found in other mammals. It also has a reptile-like gait, with legs that are on the sides of rather than underneath the body. The male platypus has venomous ankle spurs, used in vicious territorial battles and fights over mates. The poison is not lethal to humans but produces excruciating pain and swelling that may last for several months. The venom can be lethal to dogs and smaller domestic animals.

Platypus Venom Venom is produced in the crural glands of the male during the breeding season and is aggressively inflicted through a calcaneous spur on each hind limb. Because the venom appears to have a different function from venoms produced by nonmammalian species, it may contain peptides or molecules whose principal effects are non-life threatening but nevertheless may seriously impair the victim. That this could be the case is evident from the symptoms of platypus envenomation. In the human the most remarkable symptom is an immediate and excruciating pain. Edema rapidly develops around the wound and gradually spreads throughout the affected limb. Information obtained from case histories and anecdotal evidence indicates that the pain develops into a long-lasting hyperalgesia that persists for days or even months.

Ecology and Behavior The platypus is an excellent swimmer and spends much of its time in the water. When swimming they are distinguished from other Australian mammals by the absence of visible ears. It keeps its eyes tightly shut when swimming, relying completely on its other senses. All four feet of the platypus are webbed. When it swims, it propels itself by paddling with the front two feet. The tail and hind feet assist in steering but not propulsion.

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The platypus is a carnivore. It feeds on worms and insect larvae, freshwater shrimps, and freshwater crayfish that it digs out of the riverbed with its snout or catches while swimming. Its bill is very sensitive, allowing it to hunt its food without using sight. It is one of the few mammals known to have a sense of electroception: it locates its prey in part by detecting their body electricity. Its electroception is the most sensitive of any mammal. When not in the water, the platypus retires to a short, straight burrow of oval cross-section, nearly always in the riverbank not far above water level, and often hidden under a protective tangle of roots. For breeding, the female digs much larger and more elaborate burrows, up to 60 feet long and blocked with plugs at intervals. She fills the nest at the end of the tunnel with reeds for bedding material. As a monotreme, the platypus does not give birth to live young but instead lays eggs in its nest. The eggs are retained in the body for some time before they are laid and cared for actively by the parent. When the eggs hatch after an incubation period of roughly ten days, the small hairless babies cling to the mother. Like other mammals, the mother produces milk for the young. The platypus does not have nipples, but excretes the milk through pores in her skin. The young suckle milk off the mother’s belly while she lies on her back.

Electrolocation in the Platypus In the platypus, electroreceptors are located in rostro-caudal rows in skin of the bill, while mechanoreceptors are uniformly distributed across the bill. The electrosensory area suggests a close association between the tactile and electric senses. The platypus can determine the direction of an electric source, perhaps by comparing differences in signal strength across the sheet of electroreceptors as the animal characteristically moves its head from side to side while hunting. The cortical convergence of electrosensory and tactile inputs suggests a mechanism for determining the distance of prey items which, when they move, emit both electrical signals and mechanical pressure pulses. Distance could be computed from the difference in time of arrival of the two signals. Much of the platypus’s feeding is done by digging in the bottom of streams with the bill. Perhaps the electroreceptors could also be used to distinguish animate and inanimate objects in this situation where the mechanoreceptors would be continuously stimulated. Much of this is speculation, and there is still much to be learned about electroreception in the platypus.

Scientific History When the platypus was first discovered by Europeans in the late 1700s, a pelt was sent back to Britain for examination by the scientific community. The British scientists were at first convinced that the seemingly odd collection of physical

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attributes must be a hoax, produced by some Asian taxidermist. It was thought that somebody had sewn a duck’s beak onto the body of a beaver-like animal. Scientists were also divided over whether the female platypus laid eggs, until this was later confirmed in Australia. Much of the world was introduced to the platypus in 1939 when National Geographic magazine published an article on the platypus and the efforts to study and raise it in captivity. This is a very difficult task, and only a few young have been successfully raised since. Seeing a platypus in the wild is more a matter of luck and of patience than of difficulty. They tend to dislike populated areas, spend almost all their time underground or under water, and are primarily nocturnal. However, they are not especially uncommon, and in suitable areas most keen anglers or birdwatchers see a platypus feeding quietly along a riverbank every year or two. The platypus was hunted for its fur, but now does not appear to be in immediate danger of extinction. It is variously classified as secure but faces future threat or common but vulnerable, mainly because the species is sensitive to water pollution.

1. Australian Aborigines call the platypus by all of the following EXCEPT A. B. C. D.

tambreet. duckmole. mallangong. boondaburra.

2. According to the article, why is the adjective “duck-billed” NOT necessary when referring to the platypus? A. B. C. D.

Because there is only one species of the platypus. Because it belongs in the Ornithorhynchus genus. Because the two nostrils are on top of the upper bill. Because the scientific name in Greek means “birdnose” and “duck.”

3. The platypus differs from other mammals in all of the following features EXCEPT which of the following? A. B. C. D.

The platypus has webbed feet. The platypus has a higher metabolic rate. The platypus has a large rubbery snout like a duck. The platypus’ external opening of the ear lies at the base of the jaw.

4. Differences between the male and female platypuses include all of the following EXCEPT A. B. C. D.

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size. weight. ankle spurs. extra bones.

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5. All of the following statements regarding platypus envenomation are true EXCEPT A. B. C. D.

it causes immediate and excruciating pain. it is delivered through spurs on the hind limb. it is produced by females during breeding season. it can cause hyperalgesia in humans lasting for months.

6. All of the following characteristics about platypuses while swimming are true EXCEPT A. B. C. D.

it feeds on plants, fish, and worms. its tail and hind feet assist in steering. it keeps its eyes shut while swimming. it uses electroception to help find food.

7. According to the article, of which of the following should an enemy of the platypus be most wary? A. B. C. D.

tail teeth spurs claws

8. When not breeding or not in the water, where does the platypus retire? A. B. C. D.

nest burrow tree roots hollow log

9. Describe the physical variations to the platypus’s living quarters when not in the water. Use details and information from the article to support your answer.

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10. According to the article, after hatching, how is the young platypus nourished? A. B. C. D.

It eats from the mother’s mouth. It eats the fluids left inside the egg. It sucks milk from the mother’s belly. It sucks milk from the mother’s nipples.

11. According to the article, electroreceptors assist the platypus in performing all of the following EXCEPT A. B. C. D.

establishing distance to prey. knowing the size of potential prey. measuring electrical impulse differences. determining direction of electrical impulses.

12. Upon first examining a platypus pelt, what did British scientists think it represented? A. B. C. D.

a duck a hoax a beaver a breakthrough

13. According to the article, why was the platypus hunted? A. B. C. D.

for its fur for scientific research for a breeding program for raising it in captivity

14. According to the article, what causes the greatest threat to the future of the platypus? A. B. C. D.

being overhunted for its fur being hunted by its predators extinction due to pollution to its habitat extinction due to them not producing enough young

15. Read the following sentence. It is variously classified as secure but faces threat or common but vulnerable, mainly because the species is sensitive to water pollution. Why are the phrases “secure but faces future threat” and “common but vulnerable” most likely written in italics? A. B. C. D.

because they represent an opinion to make sure the reader notices them because they are scientific speculation to set them apart from the author’s words

16. What attributes would be MOST useful for someone wanting to view a platypus in the wild? A. B. C. D.

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patience hard work perseverance physical fitness

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Passage 2 Read the following passage before answering questions 17 through 40.

Mount St. Helens

Eruption of Mount St. Helens on May 18, 1980. The 1980 eruption of Mount St. Helens is the most significant volcanic eruption to occur in the lower 48 U.S. states in recorded history. The eruption was preceded by a two-month-long series of earthquakes and steam venting episodes, caused by an injection of magma at shallow depth below the mountain which created a huge bulge and a fracture system on Mount St. Helens’ north slope. An earthquake on May 18, 1980, caused the entire weakened north face to slide away, suddenly exposing the partly molten, gas- and steam-rich rock in the volcano to lower pressure. The rock responded by exploding into a super-heated mix of pulverized lava and older rock that sped toward Spirit Lake so fast that it quickly passed the avalanching north face.

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A volcanic ash column rose high into the atmosphere and deposited ash in eleven U.S. states. At the same time, snow, ice, and several entire glaciers on the mountain melted, forming a series of large lahars* (volcanic mudslides) that reached as far as the Columbia River. Less severe outbursts continued into the next day only to be followed by other large but not as destructive eruptions later in 1980. By the time the ash settled, hundreds of square miles had been reduced to wasteland, over a billion U.S. dollars in damage had occurred, and the once graceful face of Mount St. Helens was scarred with a huge crater open to the north. The area was later preserved, as it was, in the Mount St. Helens National Volcanic Monument.

Mount St. Helens from Spirit Lake before the eruption.

Mount St. Helens from Spirit Lake after the eruption.

Buildup to Disaster Several small earthquakes beginning as early as March 16, 1980, indicated that magma may have been moving below the volcano. Then on March 20, at 3:47 PM Pacific Standard Time, a shallow Richter magnitude 4.2 earthquake, centered below the mountain’s north flank, definitely signaled the volcano’s violent return from 123 years of hibernation. A gradually building earthquake swarm saturated area seismographs and started to climax at about noon on March 25, reaching

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peak levels in the next two days (a total of 174 shocks of 2.6 or greater were recorded during those two days). Shocks of 3.2 or greater occurred at a slightly increasing rate through April and May with five earthquakes of magnitude 4 or above per day in early April, and 8 per day the week before May 18. Initially there was no direct sign of eruption but small earthquake-induced avalanches of snow and ice were reported from aerial observations. Then at 12:36 PM on March 27 at least one but possibly two nearly simultaneous phreatic eruptions* (exploding groundwater-derived steam) ejected pulverized rock from within the old summit crater, excavating a new crater 250 feet wide and sending an ash column about 6,000 feet into the air. Also by this date, a 16,000-foot-long east-trending fracture system had developed across the summit area. This was followed by more earthquake storms and a series of steam explosions that sent ash 10,000 to 11,000 feet above their vent. Most of this ash fell within 3 to 12 miles from its vent but some was carried as far as 150 miles south to Bend, Oregon, and 285 miles east to Spokane, Washington.

Photo showing the bulge on April 27. A second new crater and a blue flame were observed on March 29. The flame danced to and from the two craters and was probably created by burning gases. Static electricity generated from ash clouds rolling down the mountain sent out lightning bolts that were up to two miles long. By April 8 the two craters merged. A US Geological Survey (USGS) team determined in the last week of April that a 1.5-mile diameter section of St. Helens’ north face was displaced out at least 270 feet. For the rest of April and early May this bulge grew 5 to 6 feet per day and by mid-May it extended more than

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400 feet north. As the bulge moved northward, the summit area behind it progressively sank, forming a complex downdropped block called a graben. Geologists announced on April 30 that sliding of the bulge area was the greatest immediate danger and that such a landslide may spark an eruption. These changes in the volcano’s shape were related to the overall deformation that increased the volume of the mountain by 0.03 cubic mile by mid-May. This volume increase presumably corresponded to the volume of magma that pushed into the volcano and deformed its surface. Because the intruded magma remained below ground and was not directly visible, it was called a cryptodome, in contrast to a true volcanic dome exposed at the surface. The rising magma forced the volcano’s north flank outward nearly 500 feet and heated the volcano’s ground water system, causing many steam-driven explosions.

North Face Slides Away On May 18 without warning at 8:32 AM a magnitude 5.1 earthquake (seismograph) centered directly below the north slope triggered that part of the mountain to slide an estimated 10 seconds after the shock. One of the largest landslides in recorded history, the slide traveled at 110 to 155 miles per hour and moved across Spirit Lake’s west arm; part of it hit a 1,150-foot-high ridge about 6 miles north. Some of the slide spilled over the ridge but most of it moved 13 miles down the North Fork Toutle River, filling its valley up to 600 feet deep with avalanche debris.

Lateral Blast Result The near-supersonic lateral blast, loaded with volcanic debris, caused widespread devastation as far as 19 miles from the volcano. The area affected by the blast can be subdivided into three roughly concentric zones: 1. Direct blast zone, the innermost zone, averaged about 8 miles in radius, an area in which virtually everything, natural or artificial, was obliterated or carried away. For this reason, this zone also has been called the “tree-removal zone.” The flow of the material carried by the blast was not deflected by topographic features in this zone. 2. Channelized blast zone, an intermediate zone, extended out to distances as far as 19 miles from the volcano, an area in which the flow flattened everything in its path and was channeled to some extent by topography. In this zone, the force and direction of the blast are strikingly demonstrated by the parallel alignment of toppled large trees, broken off at the base of the trunk as if they were blades of grass mown by a scythe* (an implement with a long curving blade fastened to a long bent handle). This zone was also known as the “tree-down zone.” 3. Seared zone, also called the “standing dead” zone, the outermost fringe of the impacted area, a zone in which trees remained standing but were singed brown by the hot gases of the blast. Later studies indicated that one-third of the 0.045 cubic miles of material in the flow was new lava and the rest was fragmented older rock.

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Ash Column Grows As the avalanche and initial pyroclastic flow were still advancing, a huge ash column grew to a height of 12 miles above the expanding crater in less than 10 minutes and spewed tephra into the stratosphere for 10 straight hours. Near the volcano, the swirling ash particles in the atmosphere generated lightning, which in turn started many forest fires. During this time, parts of the now mushroom-shaped ash cloud column collapsed, sending additional pyroclastic flows speeding down St. Helens’ flanks. Later slower flows came directly from the new north-facing crater and consisted of glowing pumice bombs and very hot pumiceous ash. Some of these hot flows covered ice or water which flashed to steam, creating craters up to 65 feet in diameter and sending ash as much as 6,500 feet into the air.

Spokane Ritzville Yakima Mount St. Helens

Mount St. Helens' May 18, 1980 Ash Fallout Distribution within the U.S.

2 to 5 inches 1/2 to 2 inches Trace to 1/2 inch

Map of ash distribution. Strong high-altitude wind carried much of this material east-northeasterly from the volcano at an average speed of about 60 mph. By 9:45 AM it had reached Yakima, Washington, 90 miles away and by 11:45 AM it was over Spokane, Washington. A total of 4 to 5 inches of ash fell on Yakima and areas as far east as Spokane were plunged into darkness by noon where visibility was reduced to 10 feet and half an inch of ash fell. Continuing east, St. Helens’ ash fell in the western part of Yellowstone National Park by 10:15 PM and was seen on the ground in Denver, Colorado, the next day. In time ash-fall from this eruption was reported as far away as Minnesota and Oklahoma and some of the ash drifted around the globe within about 2 weeks.

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Aftermath North Mount St. Hellens May 18, 1980 Devastation Riv

n

Gree

Toutle

Spirit Lake

Rive

Toutle R iv

t Cre ek Sw if

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Outline of crater Pyroclastics flow deposits Mudflow deposits Lateral blast deposits Debris avalanche deposits

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ee Cr

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South Fo rk

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ater Coldw Creek

Elk Rock Fork

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Map showing 1980 eruption deposits. The May 18, 1980, event was the most economically destructive volcanic eruption in the history of the United States. U.S. President Jimmy Carter surveyed the damage and stated it looked more desolate than a moonscape. In all, St. Helens released an amount of energy equivalent to 27,000 Hiroshima-sized atomic bombs and ejected more than 1 cubic mile of material. One fourth of that volume was fresh lava in the form of ash, pumice, and volcanic bombs while the rest was fragmented older rock. The removal of the north side of the mountain reduced St. Helens’ height by about 1,313 feet and left a crater 1 to 2 miles wide and 2,100 feet deep with its north end open in a huge breach.

17. The huge bulge eventually erupting on Mount St. Helens was on which slope? A. B. C. D.

east west north south

18. Which of the following was the earliest incident of the May 28, 1980 eruption of Mount St. Helens? A. B. C. D.

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19. Which event indicated that magma might have been moving below the volcano? A. B. C. D.

fractures steam vents earthquakes ash columns

20. On what date did a 4.2 magnitude earthquake signal that the volcano was once again active? A. B. C. D.

March 16, 1980 March 20, 1980 March 25, 1980 March 27, 1980

21. During the week prior to the eruption on May 18, 1980, how many earthquakes above 4.0 were recorded daily? A. B. C. D.

3 4 5 8

22. According to the article what was the probable cause of the flame observed burning between the two craters in late March of 1980? A. B. C. D.

magma lightening burning gases static electricity

23. Static electricity generated from ash clouds caused which of the following events? A. B. C. D.

flash fires burning gases lightening bolts seismic activity

24. According to the article, which of the following events did scientists predict might spark an eruption? A. B. C. D.

magma flow bulge landslide steam explosion major explosion

25. Read the following sentence. This volume increase presumably corresponded to the volume of magma that pushed into the volcano and deformed its surface. To what specific deformity is this sentence referring? A. B. C. D.

a graben the bulge new craters fracture zones

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26. Why was this volcanic feature where magma was building called a cryptodome rather than a volcanic dome? A. B. C. D.

because of the shape of the ash column because of the number of steam channels because the magma remained below ground because of the heat in the ground water systems

27. What magnitude earthquake did the seismograph record that generated the north slope landslide? A. B. C. D.

2.6 3.2 4.0 5.1

28. Discuss the characteristics of the north face landslide of May 18, 1980. Use details and information from the article to support your answer.

29. Widespread devastation from the Mount St. Helens eruption extended how far out from the volcano? A. B. C. D.

2 miles 12 miles 19 miles 285 miles

30. The subdivision of zones named after the eruption include all of the following EXCEPT A. B. C. D.

Ash Zone. Seared Zone. Direct Blast Zone. Channelized Blast Zone.

31. Alternative names for the zones named after the eruption include all of the following EXCEPT A. B. C. D.

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Tree-down Zone. Ash Column Zone. Tree-removal Zone. Standing Dead Zone.

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32. Zones included in the area of widespread devastation from the lateral blast include all of the following EXCEPT A. B. C. D.

Tree-down Zone. Direct Blast Zone. Ash Column Zone. Tree-removal Zone.

33. According to the article, what feature is credited with somewhat channeling the volcanic flow from the blast? A. B. C. D.

altitude topography seismic activity weather patterns

34. According to the article, which of the following did studies show comprised one-third of the material in the volcanic flow? A. B. C. D.

new lava older rock pumice bombs pumiceous ash

35. To what height did the ash column grow within minutes of the eruption? A. B. C. D.

12 miles 19 miles 6,500 feet 11,000 feet

36. The time element it took the ash column to reach the stratosphere took less than how long? A. B. C. D.

10 days 10 hours 10 weeks 10 minutes

37. All of the following events occurred within hours of the initial eruption EXCEPT A. B. C. D.

Ash generated from forest fires climbed to 6,500 feet into the air. Forest fires were started by lightening generated from swirling ash particles in the atmosphere. The new north-facing crater emitted slower flows consisting of pumice bombs and pumiceous ash. Parts of the mushroom-shaped ash cloud collapsed sending additional pyroclastic flows down Mount St. Helens.

38. According to the map, mudflow deposits reached all of the following rivers EXCEPT A. B. C. D.

Green River. Smith Creek River. North Fork Toutle River. South Fork Toutle River.

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39. Discuss the phenomenon of avalanche debris as related in the article. Use details and information from the article and the map to support your answer.

40. All of the following are physical changes to Mount St. Helens as a result of the 1980 eruption EXCEPT A. B. C. D.

the eruption left a 2,100 foot deep crater. the eruption left a crater 1 to 2 miles wide. the eruption removed the south face of the mountain. the height of Mount St. Helens was reduced by about 1,313 feet.

Passage 3 Read the following passage before answering questions 41 through 50.

On Woman’s Right to Suffrage—1873 Friends and fellow-citizens: I stand before you tonight, under indictment for the alleged crime of having voted at the last presidential election, without having a lawful right to vote. It shall be my work this evening to prove to you that in thus voting, I not only committed no crime, but, instead, simply exercised my citizen’s rights, guaranteed to me and all United States citizens by the national Constitution, beyond the power of any Senate to deny.

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The preamble of the Federal Constitution says: “We, the people of the United States, in order to form a more perfect union, establish justice, insure domestic tranquility, provide for the common defense, promote the general welfare, and secure the blessings of liberty to ourselves and our posterity, do ordain and establish this Constitution for the United States of America.” It was we, the people; not we, the white male citizens; nor yet we, the male citizens; but we, the whole people, who formed the Union. And we formed it, not to give the blessings of liberty, but to secure them; not to the half of ourselves and the half of our posterity, but to the whole people—women as well as men. And it is a downright mockery to talk to women of their enjoyment of the blessings of liberty while they are denied the use of the only means of securing them provided by this democratic-republican government—the ballot. The early journals of Congress show that when the committee reported to that body the original articles of confederation, the very first article which became the subject of discussion was that respecting equality of suffrage. Article IV said: “The better to secure and perpetuate mutual friendship and intercourse between the people of the different States of the Union, the free inhabitants of each of the States (paupers, vagabonds and fugitives from justice excepted), shall be entitled to all the privileges and immunities of the free citizens of the several States.” Thus, at the very beginning, did the fathers see the necessity of the universal application of the great principle of equal rights to all. “The law of the land” is the United States Constitution, and there is no provision in that document that can be fairly construed into a permission to the States to deprive any class of their citizens of their right to vote. Hence, New York can get no power from that source to disfranchise one entire half of her members. Nor has “the judgment of their peers” been pronounced against women exercising their right to vote; no disfranchised person is allowed to be judge or juror, and none but disfranchised persons can be women’s peers; nor has the Legislature passed laws excluding them on account of idiocy or lunacy; nor yet the courts convicted them of bribery, larceny or any infamous crime. Clearly, then, there is no constitutional ground for the exclusion of women from the ballot-box in the State of New York. No barriers whatever stand today between women and the exercise of their right to vote save those of precedent and prejudice. For any State to make sex a qualification that must ever result in the disfranchisement of one entire half of the people is to pass a bill of attainder, or an ex post facto law, and is therefore a violation of the supreme law of the land. By it the blessings of liberty are forever withheld from women and their female posterity. To them this government has no just powers derived from the consent of the governed. To them this government is not a democracy. It is not a republic. It is

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an odious aristocracy; a hateful oligarchy of sex; the most hateful aristocracy ever established on the face of the globe; an oligarchy of wealth, where the rich govern the poor. An oligarchy of learning, where the educated govern the ignorant, or even an oligarchy of race, where the Saxon rules the African, might be endured; but this oligarchy of sex, which makes father, brothers, husband, sons the oligarchs over the mother and sisters, the wife and daughters of every household; which ordains all men sovereigns, all women subjects; carries dissension, discord and rebellion into every home of the nation. Webster, Worcester and Bouvier all define a citizen to be a person in the United States, entitled to vote and hold office. The only question left to be settled now is: Are women persons? And I hardly believe any of our opponents will have the hardihood to say they are not. Being persons, then women are citizens, and no State has a right to make any law, or to enforce any old law, that shall abridge their privileges or immunities. Hence, every discrimination against women in the constitutions and laws of the several States is today null and void, precisely as is every one against Negroes.

41. According to the speech, which document or organization does the speaker accuse of violating her citizen’s rights? A. B. C. D.

Constitution U.S. Congress New York Senate National Constitution

42. Upon which group of words of the preamble to the Federal Constitution does the speaker most heavily rely? A. B. C. D.

establish justice we, the people of the United States in order to form a more perfect union secure the blessing of liberty to ourselves and our posterity

43. The speaker believes she has the right to vote because she is A. B. C. D.

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a person a woman not a pauper not a vagabond

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44. Through what means does the speaker believe is the only way to secure the blessings of liberty? A. B. C. D.

through voting through wealth through education through citizenship

45. According to the speech, with respect to equality of suffrage, Article IV addresses all of the following EXCEPT A. B. C. D.

the free citizens of each of the States. the free inhabitants of the several States. the men and women of the different States. the people of the different States of the Union.

46. Read this sentence from the speech. Hence, New York can get no power from that source to disfranchise one entire half of her members. To what does “that source” refer? A. B. C. D.

New York Congress The United States Constitution Preamble of the Federal Constitution Article IV of the United States Constitution

47. According to the speaker, an oligarchy of sex carries into the home of every nation all of the following EXCEPT A. B. C. D.

rivalry. discord. rebellion. dissension.

48. According to the speech, the speaker believes all women should have the right to vote unless A. B. C. D.

they are single. they are married. they are paupers. they are aristocrats.

49. This speech is BEST classified as what type writing? A. B. C. D.

expository persuasive informative comparative

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50. What positions are taken by the speaker to make her point that she has violated no law by casting a vote in a presidential election? Use details and information from the speech to support your answer.

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Answer Key for Practice Test 5 Passage 1: Platypus 1. B 2. A 3. B 4. D 5. C 6. A 7. C 8. B 9. Sample 2-Point Response: When not breeding, the platypus stays in a short, straight burrow of oval cross-section. This is normally protected by roots and is located just above water level. During breeding season, however, the burrow is elaborate and up to 60 feet long with plugs at intervals and a nest at the end with reeds for bedding. 10. C 11. B 12. B 13. A 14. C 15. D 16. A

Passage 2: Mount St. Helens 17. C 18. D 19. C 20. B 21. D 22. C 23. C 24. B 25. B 26. C 27. D 28. Sample 2-Point Response: The article states the landslide was one of the largest recorded in history. The speed of slide reached 155 miles per hour. Although part of the slide spilled over an 1,150-foot high ridge at Spirit Lake’s west arm, most of it moved down the North Fork Toutle River, filling it with debris to a depth of up to 600 feet.

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29. C 30. A 31. B 32. C 33. B 34. A 35. A 36. D 37. A 38. A 39. Sample 4-Point Response: The article states that the avalanche of the north slope of Mount St. Helens was one of the largest recorded in history. The slide moved at up to 155 miles per hour and moved across the west arm of Spirit Lake. Although some of the sledge spilled over an 1,150-foot high ridge, most of the debris moved down the North Fork Toutle River filling its valley with up to 600 feet of debris. The map indicates the coverage of avalanche debris and shows that it extends northward from the crater blast area to Spirit Lake and Coldwater Creek. The map also shows the debris following the valleys of the North Fork Toutle River in a northwest direction extending to the western edges of the lateral blast deposits. 40. C

Passage 3: On Woman’s Right to Suffrage 41. C 42. B 43. A 44. A 45. C 46. B 47. A 48. C 49. B 50. Sample 4-Point Response: The speaker takes the position that she and all women are people. She also takes the position that the Constitution of the United States guarantees the people of the United States suffrage, allowing for the stated exclusions. Further, she takes the position that no individual state has the individual power to write laws contrary to the Constitution. Finally, she takes the position that as she does not belong to any of the exclusion groups to citizenry, she and all such women, are members “of the people” referred to in the United States Constitution, and as no individual state can override said Constitution, she had every right to vote in the presidential election and has, therefore, not violated any law.

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Answers and Explanations for Practice Test 5 Note: Although all answer choices are text based, only one will correctly answer the question.

Passage 1: Platypus 1. B. The article states, “Australian Aborigines call the platypus by many names including mallangong, boondaburra, and tambreet.” 2. A. The article states, “The name platypus is often prefixed with the adjective ‘duck-billed’ to form duck-billed platypus, despite there being only one species of platypus.” 3. B. In describing the platypus, the article states, “It has webbed feet and a large, rubbery snout that are more reminiscent of a duck than any known mammal.” The article also states, “However, the external opening of the ear still lies at the base of the jaw.” 4. D. The article states, “Size varies considerably. . .with body length ranging from nearly 1' to 1'3", and tail length from 4" to 6" for males and 3" to 5" for females. Males are around one-third larger than females.” The article also states, “The male platypus has venomous ankle spurs. . ..” 5. C. The article states, “The poison is not lethal to humans but produces excruciating pain and swelling that may last for several months.” The article also states, “Information obtained from case histories and anecdotal evidence indicates that the pain develops into a long-lasting hyperalgesia that persists for days or even months.” Finally, the article states, “Venom is produced in the crural glands of the male during the breeding season and is aggressively inflicted through a calcaneous spur on each hind limb.” 6. A. The article states, “It keeps its eyes tightly shut when swimming, relying completely on its other senses.” The article also states, “The tail and hind feet assist in steering but not propulsion.” Finally, the article states, “It is one of the few mammals known to have a sense of electroception: it locates its prey in part by detecting their body electricity.” 7. C. The article states, “Venom is produced in the crural glands of the male during the breeding season and is aggressively inflicted through a calcaneous spur on each hind limb.” 8. B. The article states, “When not in the water, the platypus retires to a short, straight burrow of oval crosssection. . ..” 9. The response is text based and gives information on both types of living quarters discussed; that during normal conditions, and that during breeding times. 10. C. The article states, “The young suckle milk off the mother’s belly while she lies on her back.” 11. B. The article states, “The platypus can determine the direction of an electric source, perhaps by comparing differences in signal strength across the sheet of electroreceptors. . ..” The article also states, “The cortical convergence of electrosensory and tactile inputs suggests a mechanism for determining the distance of prey items. . ..” 12. B. The article states, “The British scientists were at first convinced that the seemingly odd collection of physical attributes must be a hoax. . ..” 13. A. The article states, “The platypus was hunted for its fur. . ..” 14. C. The article states, “It is variously classified as secure but faces future threat or common but vulnerable, mainly because the species is sensitive to water pollution.” 15. D. As the phrases were the words of those ascribing the classifications, italics show that these are not words used by the author of the article. 16. A. The article states, “Seeing a platypus in the wild is more a matter of luck and of patience than of difficulty.”

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Passage 2: Mount St. Helens 17. C. The article states, “The eruption was preceded by a two-month long series of earthquakes and steam-venting episodes, caused by an injection of magma at shallow depth below the mountain which created a huge bulge and a fracture system on Mount St. Helens’ north slope.” 18. D. The article states, “An earthquake on May 18, 1980, caused the entire weakened north face to slide away, suddenly exposing the partly molten, gas-and steam-rich rock in the volcano to lower pressure.” 19. C. The article states, “Several small earthquakes beginning as early as March 16, 1980, indicated that magma may have been moving below the volcano.” 20. B. The article states, “Then on March 20, at 3:47 PM Pacific Standard Time, a shallow Richter magnitude 4.2 earthquake, centered below the mountain’s north flank, definitely signaled the volcano’s violent return from 123 years of hibernation.” 21. D. The article states, “Shocks of 3.2 or greater occurred at a slightly increasing rate through April and May with five earthquakes of magnitude 4 or above per day in early April, and 8 per day the week before May 18.” 22. C. The article states, “A second new crater and a blue flame were observed on March 29. The flame danced to and from the two craters and was probably created by burning gases.” 23. C. The article states, “Static electricity generated from ash clouds rolling down the mountain sent out lightning bolts that were up to two miles long.” 24. B. The article states, “Geologists announced on April 30 that sliding of the bulge area was the greatest immediate danger and that such a landslide may spark an eruption.” 25. B. Prior to using the term “deformed,” the article stated, “As the bulge moved northward, the summit area behind it progressively sank, forming a complex down-dropped block called a graben.” The deformity in the sentence referred to the bulge. 26. C. The article states, “Because the intruded magma remained below ground and was not directly visible, it was called a cryptodome, in contrast to a true volcanic dome exposed at the surface.” 27. D. The article states, “On May 18 without warning at 8:32 AM a magnitude 5.1 earthquake (seismograph) centered directly below the north slope triggered that part of the mountain to slide an estimated 10 seconds after the shock.” 28. The response lifts information directly from the text to describe the events of the north slope landslide. In this instance, the respondent was only directed to support the answer with detail and information from the article. 29. C. The article states, “The near-supersonic lateral blast, loaded with volcanic debris, caused widespread devastation as far as 19 miles from the volcano.” 30. A. The article states, “The area affected by the blast can be subdivided into three roughly concentric zones. . .” The article then goes on to discuss the, “Direct blast zone,” the “Channelized blast zone,” and the “Seared zone.” 31. B. The article states the alternative names of the zones to be, “tree-removal zone,” “tree-down zone,” and “standing dead zone,” respectively. 32. C. Including the innermost Direct blast zone (also known as the “tree-removal zone”), when discussing the Channelized blast zone (also know as the “tree-down zone”), the article states, “...extended out to distances as far as 19 miles from the volcano, an area in which the flow flattened everything in its path...” 33. B. In the section discussing the Channelized blast zone, the article states, “. . .flattened everything in its path and was channeled to some extent by topography.” 34. A. The article states, “Later studies indicated that one-third of the 0.045 cubic miles of material in the flow was new lava and the rest was fragmented older rock.” 35. A. The article states, “As the avalanche and initial pyroclastic flow were still advancing, a huge ash column grew to a height of 12 miles above the expanding crater. . ..”

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36. D. The article states, “. . .a huge ash column grew to a height of 12 miles above the expanding crater in less than 10 minutes and spewed tephra into the stratosphere for 10 straight hours.” 37. A. The article states, “Near the volcano, the swirling ash particles in the atmosphere generated lightning, which in turn started many forest fires. During this time, parts of the now mushroom-shaped ash cloud column collapsed, sending additional pyroclastic flows speeding down St. Helens’ flanks. Later slower flows came directly from the new north-facing crater and consisted of glowing pumice bombs and very hot pumiceous ash.” 38. A. The map key indicates that only the Green River escaped mudflow deposits even though lateral blast deposits did extend to a large part of the river. 39. This is a two-part question. It asks the respondent to discuss the phenomenon of avalanche debris but to support the answer with details and information from both the article and the map. The response clearly presents information from both sources and identifies the relevant source for that portion of the response being presented. 40. C. The article states, “The removal of the north side of the mountain reduced St. Helens’ height by about 1,313 feet and left a crater 1 to 2 miles wide and 2,100 feet deep with its north end open in a huge breach.”

Passage 3: On Woman’s Right to Suffrage 41. C. The speech states, “. . .guaranteed to me and all United States citizens by the national Constitution, beyond the power of any Senate to deny.” The speech also states, “Hence, New York can get no power from that source to disfranchise one entire half of her members.” 42. B. Since one of the speaker’s basic premises is that women are people, it necessarily follows that the portion of the preamble most heavily relied upon reads, “We, the people of the United States. . ..” 43. A. The speaker states, “It was we, the people; not we, the white male citizens; nor yet we, the male citizens; but we, the whole people, who formed the Union.” 44. A. The speech states, “And it is a downright mockery to talk to women of their enjoyment of the blessings of liberty while they are denied the use of the only means of securing them provided by this democratic-republican government—the ballot.” 45. C. The speech states, “Article IV said: ‘The better to secure and perpetuate mutual friendship and intercourse between the people of the different States of the Union, the free inhabitants of each of the States (paupers, vagabonds and fugitives from justice excepted), shall be entitled to all the privileges and immunities of the free citizens of the several States.’” 46. B. The reference of “that source” is to the United States Constitution referred to in the previous sentence. 47. A. The speech states, “. . .but this oligarchy of sex. . .carries dissension, discord and rebellion into every home of the nation.” 48. C. The speaker brings no challenge to Article IV which excludes “paupers” from enjoying the privileges and immunities of the free citizens. 49. B. The speaker is trying to persuade the listener that there has been no crime committed in her action of voting in a presidential election. 50. The response is entirely text-based and depicts positions taken by the speaker in her attempt to persuade the listener that rather than it being a crime to have voted in a presidential election, that it is a violation of her rights as a citizen to prevent her from casting a ballot in such an election. It is important to note that the response does not present any opinion of the respondent on the subject.

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PART II

F CAT MATH TE ST

Practice FCAT Math—Introduction This section of the book contains five practice exams. These exams should be used as a way to get ready for the real Grade 10 FCAT Math test. They are not intended as a substitute for the studying you have done throughout the years. The intention is to give you the opportunity to fine-tune your test-taking skills and practice this particular format. After you take each practice test, you should take a close look at what you did well and what you did not do so well and use this information to target the appropriate study areas. Each practice FCAT math test has 50 items, similar to the Grade 10 FCAT Math test, which has 55–58 items. Of those items, 40 items are multiple choice, 5 are response-grid, 4 are short-answer, and 1 requires a long-answer. Multiplechoice and response-grid items are worth one point each. You do not need to show your work for the response-grid items. The response grid looks like the following figure:

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The icon used to identify items requiring the use of a response grid shows a pencil filling in an oval on a response grid. Four items on each practice test require you to fill in short answers. This type of question is worth up to two points and may take you up to five minutes to answer each one. In order to receive partial credit for your response for one of these items, your response needs to show an understanding of the question. The icon that identifies short-answer items features the instructions, “Think, Solve, and Explain,” on a simple black background.. One item on this practice test requires you to fill in a long answer. This question is worth up to four points. As with the short-answer items, it may take you five minutes to answer, and, in order to receive partial credit for your response, your response needs to show an understanding of the question. The icon that identifies long response items is very similar to the short-answer icon, but it includes a series of blank lines indicating that a longer response is necessary. Use a number 2 pencil (prepare several sharpened pencils) and take the practice FCAT math tests as if you were taking the real Grade 10 FCAT Math test (remember to bring several sharpened pencils the day of the FCAT, too). In other words, set aside time (two and a half hours) and a quiet place (no phone, cell phone, television, radio, stereo, or other forms of electronic entertainment) to do the complete practice test during the same day. You should probably use a desk for this and avoid any disruption. The Grade 10 FCAT Math test is taken in a two and a half hour session, which is divided in two sections with a short break in between. You should take the practice FCAT math test in that amount of time or less (with or without a short break in the middle). If you do take a short break (no more than 10 minutes), you should

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divide the time into around 70 minutes sections (you should have completed about 25 of the practice items by that time). This will give you an idea on how to time yourself. Remember that every person is different in terms of timing. You need to know yourself, and during the actual test, not pay attention to what others do. You should take the practice FCAT math test with a calculator, because calculators are allowed on the real Grade 10 FCAT math test. A small nonscientific calculator will be provided for this FCAT. You can also use a formula reference sheet like the one provided during the real Grade 10 FCAT Math test. A copy of this sheet is provided in the next page of this guide. You may copy this sheet and use it during the practice test. A solution manual is provided at the end of each practice FCAT math test. Use this manual to help you understand possible solutions and improve your test-taking ability. You should not take more than one practice exam per day. You need some wait time before taking and reviewing the other practice exams. You might have used a different path for your solution. This is okay; if you get to the same answer, and the procedures you used are mathematically accurate, you don’t need to have the same solution process. It is good to also learn other ways to solve the problem. Get R-E-A-D-Y before the test! The following are some ideas to keep in mind before you take the test: Rest and sleep well before the test (at least several days before the test). You will not do as well if you are not rested and feel tired or tense. Eat well. A nutritious and balanced breakfast and lunch (if the test is taken in the afternoon) can go a long way. Accessories you need for the test: several number 2 sharpened pencils. You will be supplied with a calculator and reference sheet. No scrap paper is allowed. All computation needed should be done directly on the test book. Dress comfortably and in layers so you can adapt to the testing room conditions. You need to relax and get R-E-A-D-Y for what you need during the test. Get double R-E-A-D-Y during the test! The following are some ideas to keep in mind during the test: Read and review the directions carefully (at least twice). Make sure that you understand and follow the instructions for the test and for each item of the test. This fist step is crucial. When answering multiple-choice questions, make sure that you read all of the answer choices before choosing an answer. Remember that you are selecting the best possible answer out of your choices. Estimate and use common sense before calculating problems; this should give you a rough idea of what the answer should be before starting to work on the problem. You can also use your estimate to check your final answer and calculation errors. Sometimes with multiple-choice items, you can eliminate one or two of the choices that contain errors or don’t make sense and then chose the best answer out of the remaining choices. You should mark an answer to the multiple-choice items, even if you are not sure of the correct answer. Your score will not be reduced because of wrong answers. However, you should attempt to figure out the best answer before guessing. Always refer to the original directions and context of the problem, especially when an answer doesn’t make sense. You might have missed something about the problem setting. Double-check your answer, choice, and work. Don’t skip steps. Work carefully and avoid accidental computational or reasoning errors. However, don’t over do your checking. Remember to time yourself. You can do it! You are R-E-A-D-Y!

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Practice FCAT Math

Grade 10 FCAT Math Reference Sheet The following formulas are provided as part of a similar reference sheet for the Grade 10 FCAT. Use it for the practice FCAT math tests. Area Triangle

Rectangle

Circumference

Key

A = 1⁄2b ⋅ h

b = base

d = diameter

h = height

r = radius

l = length

A = area

w = width

C = circumference

A=l⋅w

= slant height Trapezoid

A = 1⁄2h(b1 + b2)

V = volume

S.A. = Surface Area Use 3.14 or 22/7 for π

Parallelogram

A = bh

Circle

A =1⁄2πr 2 C = πd = 2π ⋅ r

Volume

Total Surface Area Right Circular Cone:

V = 1⁄3πr 2h or 1⁄3Bh S.A. = 1⁄2(2πr) ⋅ l + πr 2 = πr , + πr 2

Square Pyramid:

V = 1⁄3lwh = 1⁄3Bh S.A. = 4(1⁄2l , ) + l 2 = 2l , r 2

Sphere:

V = 4⁄3πr 3 S.A. = 4πr 2

Right Circular Cylinder:

V = πr 2h or Bh S.A. = 2πrh + 2πr 2

Rectangular Solid:

V = lwh = Bh S.A. = 2(lw) + 2(hw) + 2(l ⋅ h)

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Grade 10 FCAT Math Reference Sheet Continued . . . In the following formulas, n represents the number of sides: In a polygon, the sum of the measures of the interior angles is equal to 180(n – 2). 180 ^ n - 2 h In a regular polygon, the measure of an interior angle is equal to . n

Pythagorean Theorem: c2 = a2 + b2

Distance between two points: P1( x1, y1) and P2 ( x 2 , y2):

c

a

_ x 2 - x 1i + _ y 2 - y 1i 2

2

Midpoint between two points: P1( x1, y1) and P2( x 2 , y2): d

x 1 + x 2 y1 + y 2 , 2 2 n

b y = mx + b Slope-intercept form of an equation of a line, where m = slope and b = the y-intercept.

I = pr t Simple interest formula, where p = principal, r = rate, t = time

d = rt Distance, rate, time formula, where d = distance, r = rate, t = time

Conversions 1 yard = 3 feet = 36 inches

1 cup = 8 fluid ounces

1 mile = 1,760 yards = 5,280 feet

1 pint = 2 cups

1 acre = 43,560 square feet

1 quart = 2 pints

1 hour = 60 minutes

1 gallon = 4 quarts

1 minute = 60 seconds

1 liter = 1000 milliliters = 1000 cubic centimeters 1 meter = 100 centimeters = 1000 millimeters 1 kilometer = 1000 meters 1 gram = 1000 milligrams 1 kilogram = 1000 grams

1 pound = 16 ounces 1 ton = 2,000 pounds

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Practice FCAT Math 1 Remember to read and follow the instructions carefully. You have two and a half hours to complete the test. You may want to take a short break in the middle of the test.

First Part of Practice FCAT Math 1 1. Peter, Mary, and Sarah were comparing the distances from their houses to school 2.4 miles, 2 1 miles, 2 3 miles, 3 8 and 2 3 miles. Which one should Peter and Mary select as the least of these numbers? 5 A. 2 3 miles. 5 1 B. 2 miles. 3 C. 2 3 miles. 8 D. 2.4 miles. 2. What is the value of x in the equation 2–4 ⋅ –1 = x? A. B. C. D.

16 1 16 – 16 -1 16

3. Mary has 235 books at her home library; 141 of these books are softcover books, and the rest of the books are hardcover books. What percent of Mary’s books are hardcover books?

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4. When Alfredo makes a long-distance call, he pays 75 cents for the first minute and 40 cents for each additional minute. He was charged $11.15 for his last long-distance call. How long was this long-distance call? A. B. C. D.

26 minutes 28 minutes 27 minutes 29 minutes

5. Anne was reading a novel and decided to keep track of the number of pages she read per day on the graph that follows. She read 20 pages the first day. Reading of Novel 70 60 50 40 30 20 10 0 0

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What is the slope of the line made by connecting the dots in the preceding graph? What is represented by the slope of this graph?

6. Paula works for a supermarket. She earns $25.00 per day and receives $1.25 per extra hour. She worked five days last week and received a check for $150.00. What is the average number of extra hours she worked during these five days? A. B. C. D.

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4 hours 20 hours 6 hours 5 hours

Practice FCAT Math 1

7. The box-and-whisker plot that follows displays the list of Peter’s test scores this semester in a math class. What percent of Peter’s test scores is between the end points of the box?

n = 10

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8. Samuel has to graph a transformation of the triangle ABC on the following grid. The triangle must include the points plotted on the following grid using the y-axis as the reflection line. A. B.

Explain in your own words how to find the coordinates for the reflection of the triangle using the y-axis as the reflection line and coordinates for points A, B, and C as a guide. Using the following grid, plot, label, and connect the coordinates of the reflection of the triangle ABC over the y-axis. y 6

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9. The slopes of six lines are AB = , BC = -1 , CD = , DE = 9 , EF = 8 , and FG = AB. 2 12 -4 Which of these lines is the line perpendicular to AB?

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D.

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x

Practice FCAT Math 1

10. Which of the following is the same as 10–3? A. B. C. D.

-1 1000 1000 1 1000 – 1000

11. At a circus show, a clown was shot out of a cannon at ground level. Her height above ground at any time was represented by the following formula: h = –16t2 + 64t. Which of the following equations is the same as h = –16t2 + 64t? A. B. C. D.

h + 64t = 16t2 h + 64t = –16t2 h – 16t2 = 64t h – 64t = –16t2

12. Natalie ate 3 slices of a pie for dessert. Each slice was about 10 percent of the pie (as illustrated). A

B C

What is the measure of the central angle (mACB) that represents the area of the pie that Natalie ate? A. B. C. D.

10 degrees 108 degrees 30 degrees 180 degrees

13. Find the slope of the line represented by the equation 3x – 2 = 3 – 4y. A. B. C. D.

-3 4 3 4 0 – 5

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14. The following figure shows five concentric circles. The shaded regions were labeled A, B, C, and E. Region D is not shaded. Assuming the width of each ring is the same, how do the areas of the two shaded regions compare (area of the combination of shaded regions A, B, and C compared to the area of shaded region E)? E D C B A

A. B. C. D.

Area of the combination of shaded regions A, B, and C is greater than the area of shaded region E. Area of the combination of shaded regions A, B, and C is less than the area of shaded region E. Area of the combination of shaded regions A, B, and C is equal to the area of shaded region E. Not enough information was provided to calculate areas of the regions.

15. A survey of 1,188 students at a high school was taken to find how they get to school each day. The results are shown in the following table.

How Students Get to School Each Day by Grade Level Take a Bus

Walk

Adult Drives

Other

Total

10th Grade

139

123

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85

423

11th Grade

47

140

113

89

389

12th Grade

158

143

41

34

376

Total

344

406

230

208

1188

Which statement can be verified using the information in the table? A. B. C. D.

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At this high school, fewer 11th graders use different forms of transportation than 12th graders, because fewer students attend 11th grade. At this high school, the number of 11th graders who take the bus is greater than the number of 10th graders who walk to school. At this high school, more students in all grade levels take the bus to get to school than any of the other types of transportation. At this high school, the number of 12th graders who take the bus is greater than the number of 11th graders who walk to school.

Practice FCAT Math 1

16. There are two boxes of books in Peter’s room. One box contains 2 biography books, 3 children’s books, 2 selfhelp books, and 1 romance book. The other box contains 4 biography books, 1 children’s book, 2 self-help books, and 3 romance books. If Peter randomly selects one book from each box, what is the probability that both books are biography books? A. B. C. D.

2/81 9/20 1/10 1/3

17. A math tutor charges a $10.50 initial fee and $15.50 for each hour of tutoring. Which of the following equations could be used to find the cost, c, of a tutoring session lasting h hours? A. B. C. D.

c = 15.50 + 10.50h c = 10.50 + 15.50h c = 15.50 – 10.50h c = 15.50(10.50 – h)

18. A scale drawing of a desk is 1/4 inch to 1 foot. The actual desk is 50 feet wide. What is the width in inches of the model? A. B. C. D.

12.5 200 25 100

19. A train takes 3 hours to travel 225 miles. Assuming there are no stops, how many miles will this train travel in 12 hours? A. B. C. D.

825 miles 56.25 miles 900 miles 1125 miles

20. A bowl contains 5 blue marbles, 11 red marbles, 15 green marbles, and 7 yellow marbles. The red marbles and yellow marbles are the only ones that have a plastic cover for each marble. What is the probability that you will randomly select a marble that has a plastic cover for it from the bowl? A. B. C. D.

7/38 11/38 1/2 9/19

21. Parker bought a new square table that is approximately 4 2 feet wide. In order to get a box for this table, how wide must the box at least approximately be? A. B. C. D.

6 feet 5.5 feet 5 feet 4.5 feet

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22. Which of the following rates has the highest unit price? A. B. C. D.

16 ounces : $4.64 10 ounces : $3.30 18 ounces : $5.40 12 ounces : $3.75

23. Find the approximate volume of the circular cone illustrated here in cubic centimeters.

12 cm

6 cm

A. B. C. D.

113 cubic centimeters 452 cubic centimeters 339 cubic centimeters 103 cubic centimeters

24. A car dealer was selling a used car for a 9 percent discount of the original price. If you paid $9,920.12 for this car, what was the original price of the car? This problem does not include taxes and other fees. Round to the nearest hundredth. A. B. C. D.

$10,812.93 $9,027.31 $10,901.23 $110,223.55

25. Simplify the following expression: 300 – 40 ÷ 5 ⋅ (23 – 2) ⋅ 3 + 8. A. B. C. D.

944 148 308.44 164

You may take a short break (optional 5 or 10 minutes) but must complete the test on the same day.

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Practice FCAT Math 1

Second Part of Practice FCAT Math 1 Continue the test. Remember to read and follow the instructions carefully. You have 70 minutes to complete the test.

y

B

x

C

A

26. Which of these are the coordinates for point C on the coordinate plane shown here? A. B. C. D.

( –3, 3) (4, –4) (3, –3) ( –4, 4)

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27. If ABC is an isosceles triangle what is the measure of ∠ABC? B

115 C

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28. A recipe for an apple pie requires 12 large apples to make 8 apple pies. If 20 apple pies were needed for a meeting, about how many large apples would you need? A. B. C. D.

about 13 large apples about 30 large apples about 14 large apples about 240 large apples

29. A regular and fair six-sided number cube was thrown once. What is the probability that you will roll something other than 4? Show or explain your answer using words and numbers.

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30. Peter has 46 bicycles and tricycles in his shop. When he adds together all the wheels for all of his bicycles and tricycles, he has a total of 126 wheels. How many bicycles and how many tricycles does Peter have? (Note: The bicycles have two wheels each, and the tricycles have three wheels each.) Write a system of equations representing the possible combination of bicycles, tricycles, and wheels. Show all the steps for solving this system of equations. 31. At a supermarket, Samuel needs to arrange cans of food (all the same size) in seven shelves. He estimated that he could fit about 45 cans of food in half a shelf. The cans of food come in boxes of 30 cans each. Approximately how many boxes of cans of food will Samuel need to fill up the seven shelves? A. B. C. D.

21 boxes 10.5 boxes 3 boxes 630 cans

32. The two triangles in the figures here are similar. What is the length of side n?

18 m 15 m

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33. On a coordinate grid, the point (–5, 4) is reflected over the x-axis. Find the coordinates of this new point. A. B. C. D.

(–5, 4) (5, –4) (5, 4) (–5, –4)

34. Enrique earned $82,000.00 last year. He earned $69,290.00 this year. What was the approximate percent of decrease in salary he had from last year to this year? A. B. C. D.

18.3% 15.5% 84.5% 81.66%

35. A travel agency pays $175 for each airplane ticket from Tampa to Orlando. The travel agency makes a 15% markup to the ticket, and after that charges 11% for service charges and taxes for each ticket. How much would it cost in dollars to buy one airplane ticket from Tampa to Orlando at this travel agency? A. B. C. D.

$223 for one airplane ticket $178 for one airplane ticket $221 for one airplane ticket $220 for one airplane ticket

36. The perimeter of a rectangle is 28 centimeters. One of the sides of this rectangle is equal to 5.3 centimeters. Using the given information, what is the area of this rectangle? A. B. C. D.

5.28 square centimeters 27.98 square centimeters 46.11 square centimeters 120.31 square centimeters

37. Robert painted 3/4 of a wall yesterday, and 25 percent of the same wall today. What percent of the wall did Robert paint in these two days? A. B. C. D.

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Practice FCAT Math 1

height = 12 in

38. The following figure is a rectangular solid. It has a planar cross section shaded (diagonally). What is the area of this shaded planar cross section in square inches?

th wid

=7

in

length = 9 in

A. B. C. D.

84 square inches 105 square inches 108 square inches 180 square inches

39. Carlos earned $1,450.00 last month for his regular monthly salary, plus $10.55 for each overtime hour. Including regular salary and overtime, his total earnings last month were $2,505.00. This month he received the same regular salary and worked the same amount of overtime hours as last month, but the payment for overtime hours this month was increased to $11.55 per overtime hour. How much more money did he earn this month than last month? A. B. C. D.

$3,037.44 $100.00 $2,605.00 $532.44

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40. What is the slope of the line in the following graph? y

(2,2) (-1,1)

x

0

A. B. C. D.

1/3 – 1/3 3 – 3

41. Mike made the following table based on the number of hours he worked per day last month. Find the median number of hours he worked last month. Number of Hours

Tally

Frequency

7

//// //// //

12

8

///

3

9

//

2

10

//// //

7

A. B. C. D.

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Practice FCAT Math 1

42. Find the volume in cubic centimeters of the pyramid with a square base illustrated in the following figure.

13 cm

Height 12.27 cm

5 cm

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43. Miranda runs twice around a triangular lot (see the following figure) three times every month. How many miles does she run per month? Approximate your answer to the nearest tenth.

b = 1 mile

c

a = 2 miles

A. B. C. D.

10.48 miles 10.00 miles 30.00 miles 31.44 miles

44. The following figure represents a regular hexagon. Find the measure in degrees of angle BFE. A

B

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E

A. B. C. D.

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D

Practice FCAT Math 1

45. A company has 300 workers. The following Venn diagram illustrates the numbers of workers at this company in different categories. Some of them share duties. How many workers are secretaries and administrators?

Secretaries 40

Trainers 55

75 15 12

83

Administrators 20

A. B. C. D.

87 workers 60 workers 27 workers 72 workers

46. Airplane A arrives early in the morning to the Miami International Airport and departs later in the afternoon. This will happen again every 17 days. Airplane B does the same thing, but it makes the trip every 13 days instead. Today in the morning, both Airplanes A and B arrived at the airport, and as usual departed later in the afternoon. How many days would it take before both airplanes arrive at the Miami International Airport the same day? A. B. C. D.

120 days 221 days 68 days 30 days

47. Find the mean for the data set given in the following table. Round your answer to the closest hundredth. Number of Hours

Frequency

1

23

2

13

3

2

4

7

A. B. C. D.

20.75 hours 2.5 hours 11.25 hours 1.84 hours

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48. Anna spent $29.00 for 5 oranges and 16 apples. Each apple cost her 1.5 times as much as each orange. How much did each orange cost Anna? Write a system of equations to figure out how much each orange and each apple cost Anna. Use this system of equations to find out how much each orange cost Anna. 49. Toothpicks were used to make the following figures. The first figure takes three toothpicks; the second takes 9; and the third takes 15. Extend the pattern and find the number of toothpicks needed for the sixth figure.

first figure

A. B. C. D.

second figure

third figure

33 toothpicks 27 toothpicks 21 toothpicks 39 toothpicks

50. What is the approximate percent for a $9.50 payment out of $350? A. B. C. D.

0.3% 30% 3% 0.03%

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Practice FCAT Math 1

Answer Key for Practice Test 1 1. B 2. D 3. 40 percent 4. C 5. 10/1 or 10 6. A 7. 50 8. The new points A', B', and C' for the reflection of the triangle are (4, 5), (5, –3), and (2, –1). 9. C 10. C 11. D 12. B 13. A 14. B 15. D 16. C 17. B 18. A 19. C 20. D 21. A 22. B 23. A 24. C 25. D 26. C 27. 50° 28. B 29. 5/6 30. There are 12 bicycles and 34 tricycles. 31. A 32. 12 meters 33. D 34. B 35. A

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36. C 37. D 38. B 39. B 40. A 41. C 42. 106.2 or 106.3 43. D 44. A 45. C 46. B 47. C 48. $1.00 49. A 50. C

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Practice FCAT Math 1

Solutions for Practice FCAT Math 1 Use these answers and explanations to help you understand possible solutions and improve your test-taking ability. You should not take more that one practice exam per day. You need some wait time before taking and reviewing the other practice exams (at least one day). You might have used a different path for your solution. This is okay; if you get to the same answer and the procedures you used are mathematically accurate, you don’t need to have the same solution process. It is good to also learn other ways to solve the problem. 1. The best choice for this item is B. Change all the possible answers to decimal form and compare to each other (including 2.4), or order them from least to greatest (or greatest to least): 2 1 = 2.3333333 . . ., 2 3 = 2.375, 2.4, 2 3 = 2.6. 3 8 5 The calculator could be used to change the fractions to decimal form. You can also change 2.4 to fraction form and compare to the other fractions: 2.4 = 2 4 = 2 2 . 10 5 Ordering the fractions from least to greatest yields the following: 2 1 , 2 3 , 2 2 , 2 3 . 3 8 5 5 2. The best choice for this item is D. You need to solve the negative exponent first and then multiply for negative one. 2–4 is equal to 1/24 = 1/16, and 1/16 ⋅ –1 = –1/16. 3. You could start by find out how many hardcover books Mary had in her library: 235 total books – 141 softcover books = 94 hardcover books. Then you can use this information to find the percent of hardcover books that she has: 94 ÷ 235 = 0.4 or 40 percent. 40 percent of the books in Mary’s library are hardcover books. Now you need to enter this information in the response grid:

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You can also enter your grid response in the following manner:

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Another way to interpret this problem is to find out what percent of hardcover books by subtracting the number of softcover books from the total number of books (235 – 141 = 94) and then asking, what percent of 235 is equal to 94? x 235 = 94 100 $ 235 = 94 x 47x = 94 (simplify) 20 1 47x ⋅ 1 = 94 ⋅ 20 (cross multiply) 47x = 94 ⋅ 20 47x ÷ 47 = 1880 ÷ 47 x = 1880 ÷ 47 = 40 Still another way could be the following: Find the percent for softcover books by solving: 141 ÷ 235 = 0.6 or 60 percent. Then 100 – 60 = 40, which is the percent of hardcover books. 4. The best choice for this item is C. Alfredo was charged $11.15 for his last long-distance call, which includes the first minute and all the additional minutes. First, you need to subtract the first minute of the call: $11.15 – $0.75 (this is the same as the 75 cents) = $10.40 (this is the cost of the additional minutes). You need to remember to add this minute at the end. Second, you need to divide $10.40 by $0.40 (this is the same as 40 cents) = 26 minutes. Finally, you need to add the first minute of the phone call (remember?). The answer is 26 additional minutes + 1 first minute = 27 minutes. 5. This short-answer item is worth two points. The answer is worth one point, and the explanation/solution is worth one point. The slope of the line made by connecting the dots in this graph is 10/1 or 10. The slope of a line is an indication of its steepness or inclination. It is the change in y-values (the vertical axis), over the change in the x-values (the horizontal axis). In this case, the vertical axis goes up in increments of 10 (each box represents ten pages read), and the horizontal axis goes up in increments of one (each box represents one day). Remember that the slope of a line can be positive (slant upward from left to right), negative (slant downward from left to right), zero (flat or horizontal lines), or undefined (vertical lines).

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6. The best choice for this item is A. Paula made a total of $150.00 for her five days of work. This is including her extra hours. We know that she earned $25.00 per day, multiplying this by 5 gives what she earned per day without including what she earned for the extra hours, which is $125.00. Subtracting $125.00 from $150.00, gives us $25.00, which is what she earned for the extra hours alone. Dividing $25.00 by $1.25 per hour gives us 20 hours, which is the total number of extra hours she worked during those five days. Since we only need the total number of hours to find the average, we can divide these 20 hours by 5 days, and get the average number of extra hours she worked during these five days, which is 4 hours per day. 7. In a box-and-whisker plot, half (or 50 percent) of the data fall inside the box.

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Part II: FCAT Math Test

The following are the parts of a box-and-whisker plot:

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The lowest number is the left whisker. The highest number is the right whisker. The median is in the middle of the box. In this case, the median is 81, lowest score is 67, highest score is 98, lower quartile is 73, and upper quartile 88. The lower quartile is the middle of the lower half of the numbers. The upper quartile is the middle of the upper half of the numbers. Joining the lower quartile, upper quartile, and median forms the box. Joining the box to the high number on the right and the low number on the left forms the whiskers. 8. This short-answer item is worth two points. You need to have an acceptable explanation to earn two points. For this part of the item, you need to explain how to reflect the point of the original triangle ABC over the y-axis. To do this, you need to use the same y-coordinate and multiply the x-coordinate by –1. The original points A, B, and C of the triangle are, respectively, (–4, 5), (–5, –3), and (–2, –1). The new points A’, B’, and C’ for the reflection of the triangle are, respectively, (4, 5), (5, –3), and (2, –1). The wording of this explanation may vary. The following grid illustrates the plotting, labeling, and connecting of the points (A’, B’, and C’) for triangle A’B’C’.

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9. The best choice for this item is C. Lines are perpendicular when the slopes are opposite reciprocals of each other like in –2 and 1/2. 10. The best choice for this item is C. The following will help you visualize what happens with the different exponents (positive or negative). Observe the pattern shown here: 103

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h + 64t = –16t2 48 + 64(1) = 16(1)2 112 ≠ 16

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h + 64t = 16t2 48 + 64(1) = 16(1)2 112 ≠ –16

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C.

h – 16t2 = 64t 48 – 16(1)2 = 64(1) 48 – 16 = 64 32 ≠ 64

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h – 64t = –16t2 48 – 64(1) = –16(1)2 48 – 64 = –16 –16 = –16

Notice that only D results in an equality. 12. The best answer for this item is B. Natalie ate three slices of the pie at 10 percent each for a 30 percent total. You know that a pie (or circle) is 360 degrees. The measure of the central angle (m∠ACB) is 30% of 360 degrees, which is equal to 108 degrees. Another way to solve this problem is by noticing that the measure of central angle ACB is between 90 to 180 degrees. This leaves B as the only possible answer. 13. The best answer for this item is A. One way to solve this problem is by using the formula for slope: y = mx + b, where m is the slope of the equation. You need to get the equation 3x – 2 = 3 – 4y to look like this formula: 3x – 2 = 3 – 4y 3x – 3x – 2 = –3x + 3 – 4y 0 – 2 + 2 = –3x + 3 + 2 – 4y 0 + 4y = –3x + 5 – 4y + 4y 4y = –3x + 5 + 0 4y - 3x + 5 = 4 4 3 y= x+ 5 4 4 In this case, m = –3/4. Another way to solve this problem is by using the equation in standard form: ax + by + c = 0. You need to get the equation 3x – 2 = 3 – 4y to look like the standard form: 3x – 2 = 3 – 4y 3x – 2 – 3 = 3 – 3 – 4y 3x – 5 = 0 – 4y 3x – 5 + 4y = – 4y + 4y 3x + 4y – 5 = 0 When an equation is written in this form, the slope is represented by –a/b, where a is the coefficient of x and b is the coefficient of y. For this equation, we have yields of a = 3, b = 4, and the slope (m) is –a/b or –3/4. 14. The best choice for this item is B. The formula for finding the area of a circle is πr2. You need to calculate the area of four different regions to solve this problem. You can use the diameter of the circle A as the measuring unit (other approaches can be used too). Area of the combined shaded regions A, B and C is equal to π(2.5 units)2 = 6.25π square units. No need to multiply by π at this time.

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To find the area of shaded region E, you need to find the area of regions A, B, C, D, and E combined and A, B, C, and D combined. You will then subtract area of regions A, B, C, and D combined from area of A, B, C, D, and E combined. Area of combined regions A, B, C, D, and E is equal to π(4.5 units)2 = 20.25π square units, and the area of combined regions A, B, C, and D is equal to π(3.5 units)2 = 12.25π square units. Area of shaded region E is equal to 20.25π square units – 12.25π square units = 8π square units. Area of shaded regions A, B, and C (6.25π square units) combined is less that the area of shaded region E (8π square units). 15. The best choice for this item is D. The best way to find the best choice for this item is by analyzing each alternative. Choice A indicates that there are more 12th graders than 11th graders attending this high school, but this is not true. There are more 11th graders (389) than 12th graders (376). Choice B indicates that more 11th graders take the bus that 10th graders who walk to school, but this is not true. The number of 11th graders who take the bus is 47, and the number of 10th graders who walk to school is 123, which indicates that there are more 10th graders walking than 11th graders taking the bus. Choice C indicates that more students take the bus than students who use any of the other types of transportation. This is not true because fewer students (344) take the bus than students who walk to school (406). More students walk to school that any of the other types of transportation. Choice D for this item indicates that more 12th graders (158) take the bus than 11th graders who walk to school (140). This is true, and is the only alternative that can be verified by the information provided in the table. 16. The best choice for this item is C. You need to calculate the probability for selecting a book from each box separately. There are 8 books in the first box (2 biography books + 3 children’s books + 2 self-help books + 1 romance book = 8 books). Of these 8 books in this first box, 2 are biography books. Then, the probability of randomly selecting one biography book from this first box is 2/8 or 1/4. There are 10 books in the second box (4 biography books + 1 children’s book + 2 self-help books + 3 romance books = 10 books). Of these 10 books in this first box, 4 are biography books. Then, the probability of randomly selecting one biography book from this second box is 4/10 or 2/5. You need to multiply these two probabilities to obtain: 1/4 ⋅ 2/5, which is equal to 2/20 or 1/10. The probability of randomly selecting a biography book from each of the two boxes is 1/10. 17. The best choice for this item is B. Remember that you are trying to translate the word problem into a mathematical sentence that represents the relationship of the quantities in the problem. You know that 10.50 will stay the same since it is the initial fee, and the 15.50 needs to be multiplied by the number of hours for the tutoring session. 18. The best choice for this item is A. You need to set up a proportion. There are several ways to establish the proportion to solve this problem. One possible proportion is the following: 1/4 inch to 1 foot = x to 50, where x represents the width of the model in inches. Then by cross multiplying (1/4 ⋅ 50 = 1 ⋅ x), and solving for x, you get that x = 12.5, or that the width of the model is 12.5 inches. 19. The best choice for this item is C. You might notice that 12 hours is four times as long as a three-hour trip. Then you have that 225 ⋅ 4 = 900, or the train will travel 900 miles in 10 hours. One way to solve this problem is by establishing a proportion: 225 hours to 3 hours = x to 12 hours. By cross multiplying and solving for x, you have 225 ⋅ 12 = 3x; 2700 ⋅ 3 = x; and 900 = x. You can also notice the ratio for miles per hours in 75 miles/1 hour. For 12 hours, you have 75 ⋅ 12 = 900. The following table illustrates different increments in terms of miles and hours. Miles

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20. The best choice for this item is D. You have a total of 38 marbles (5 blue marbles + 11 red marbles + 15 green marbles + 7 yellow marbles = 38 marbles). The marbles with plastics bags are 11 red marbles + 7 yellow marbles or 18 marbles altogether. The probability for randomly selecting a marble with a plastic bag from the bowl is 18/38 or 9/19.

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21. The best choice for this item is A. The table is approximately 4 2 feet wide or 4 ⋅ 1.4, which is equal to 5.6. The choice is that the box needs to be approximately 6 feet wide. The other choices (5.5, 5, or 4.5 feet) are too small. 22. The best choice for this item is B. One way to solve this problem is by changing each alternative to unit price: A. 16 ounces : $4.64

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This one is the lowest.

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This one is the highest.

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23. The best choice for this item is A. The formula for finding the volume of a circular cone is the following: V = 1/3 π r2 h, which is included in the reference sheet provided. You can use 3.14 for the approximate value for π (other values could be used as an approximation of π). For the value of the radius of the circular base of the cone, you need to divide the given diameter (6 cm) by 2 to find the radius, which yields 3 cm for the radius. The height is equal to 12 cm. Using these values for the formula: 1/3(3.14)(32)(12) ≈ 113 cubic centimeters. 24. The best choice for this item is C. There are several correct ways to solve this problem. One way to solve this problem is by noticing that if you paid a 9 percent discount of the original price, then the new price is 91 percent of the original price (100% – 9% = 91%). This implies that 91 percent ⋅ original price = new discount price, or 91 percent ⋅ original price = $9,920.12. You can find the original price by dividing $9,920.12 by 91 percent or 0.91. This will give you the original price: $10,901.23. 25. The best choice for this item is D. You need to use the correct order of operations for this expression: 300 – 40 ÷ 5 ⋅ (23 – 2) ⋅ 3 + 8 300 – 40 ÷ 5 ⋅ (8 – 2) ⋅ 3 + 8:

First, calculate exponentials: 23 = 8.

300 – 40 ÷ 5 ⋅ (6) ⋅ 3 + 8:

Second, solve parentheses: (8 – 2) = (6).

300 – 144 + 8:

Third, calculate multiplication and division, as they appear, from left to right:

40 ÷ 5 ⋅ (6) ⋅ 3 = 144 300 – 144 = 156 + 8 = 164:

Fourth, calculate addition and subtraction, as they appear, from left to right.

26. The best choice for this item is C. You need to count the number of spaces on the x-axis (positive value) first going to the right, and y-axis (negative value) second going down for point C. 27. ∠BCA is equal to 65 degrees (interior angle + exterior angle = 180 degrees: 65° + 115° = 180°). ∠BAC = ∠BCA because this is an isosceles triangle. To find the measure of ∠ABC, we can then subtract 65° two times from 180°: 180 – 65 – 65 = 50 (or you can 180 – 2(65) = 50). This means that ∠ABC = 50°.

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28. The best choice for this item is B. You need to set up a proportion using the rates provided in the problem: 12 = x 8 20 12 ⋅ 20 = 8x

Where x is the number large apples you would need.

204 ÷ 8 = (8x) ÷ x

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x = 30

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Part II: FCAT Math Test

Remember that there are other ways to establish the rates and proportion. You just need to be consistent. For example, you can also have the following proportions: 8 = 20 x 12 12 = x 20 8 29. This short-answer item is worth two points. You need to have an acceptable explanation to earn two points. The probability for rolling something other than a 4 is 5 . 6 The probability for each outcome in a regular and fair six-sided number cube thrown once is 1 . 6 You can have up to five outcomes that are not a 4: 1, 2, 3, 5, or 6. This implies that the probability to obtain something other than a four is 5/6. 30. This is a long-response item, which are worth four points each. You will receive four points if you answer all parts of the item fully and correctly. You must show an understanding of the mathematical ideas presented in this problem. You will receive three points if you make minor errors but show an understanding as you solve and explain the solution of the problem. You will receive two points if you make several errors, the explanations are incomplete and not clear, and do not show proper understanding of the problem. When solving this problem, you need to consider two different relationships. One is between the number of bicycles and tricycles, and the other is in terms of the number of wheels. Then you need to solve the system of equations. You can start by naming the variables for the equation: b = the number of bikes, t = the number of tricycles. From this, you can form the equation needed to represent the relationship between the variables based on the problem: b + t = 46 (total number of vehicles). Each bicycle has two wheels or 2 times the number of bicycles: 2b. Each tricycle has three wheels or 3 times the number of tricycles: 3t. Remember that 2b is the same as 2 ⋅ b, and that 3t is the same as 3 ⋅ t. This gives you a second equation for the total number of bicycles’ and tricycles’ wheels: 2b + 3t = 126 wheels. The system of equations is the following: b + t = 46, and 2b + 3t = 126. Solving the first equation for t, you have t = 46 – b (notice that you could have used other forms of the equation like 46 – b = t, or solving for b: b = 46 – t). Then you need to substitute t = 46 – b for b in the second equation (2b + 3t = 126): 2b + 3(46 – b) = 126 2b + 138 – 3b = 126 (Using the distributive property of multiplication over subtraction.) 138 – b = 126 138 – 138 – b = 126 – 138 –b = –12 –b ⋅ –1 = –12 ⋅ –1 b = 12 Since b = 12, then you have the following: b + t = 46 12 + t = 46 12 – 12 + t = 46 – 12 t = 34 There are 12 bicycles, and 34 tricycles. (Remember that you need to go back to the initial problem and answer the question.)

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Check your answer by substituting these values in the second formula: 2b + 3 t = 126 2(12) + 3(34) = 126 24 + 102 = 126 Alternative solution for this problem can involve solving the first equation for b instead of solving for t, and substituting for b in the second equation: b = 46 – t 2b + 3t = 126 2(46 – t) + 3t = 126 (Substituting for b in the second equation.) 92 – 2t + 3t = 126 92 + t = 126 92 – 92 + t = 126 – 92 t = 34 Since t = 34, then you have the following: b + t = 46 b + 34 = 46 b + 34 – 34 = 46 – 34 b = 12 You end up with the same answer: There are 12 bicycles and 34 tricycles. Check your answer as before. 31. The best choice for this item is A. Samuel could fit 45 cans of food in half a shelf, which means that he can fit about 90 cans in a full shelf (45 cans of food ⋅ 2). He has seven shelves, which means he could fit up to 630 cans of food altogether (7 shelves ⋅ 90 cans of food per shelf). Each box of cans of food has 30 cans. You need to divide total number of cans that can fit in the seven shelves by 30 cans of food for each box: 630 ÷ 30 = 21 boxes. This means that he can fit 21 boxes in the seven shelves. 32. Since the two triangles are similar, the ratios of their corresponding angles are equal. You can write and solve a proportion to find n. You need to make sure to compare similar sides to each other and include the side that contains the side and its corresponding side in the other triangle. This is one of the several ways to set up and solve the proportion: 6 =4 18 n 6n = 4 ÷ 18

Cross multiply.

6n = 72

Simplify.

6 ÷ 6n = 72 ÷ 6

Set up the proportion.

Divide each side by six to solve for n.

n = 12 The length of the side n is 12 meters.

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33. The best choice for this item is D. In order to reflect this point, you need to use the same x coordinate and multiply the y-coordinate by negative one: (–5, 4) becomes (–5, –4). The following figure illustrates this situation.

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34. The best choice for this item is B. The amount of change in this problem is equal to x percent times the original salary (the number you are starting with in this problem): $82,000 – $69,290 = x% ⋅ $82,000, $12,710 = (x/100) ⋅ $82,000 $12,710 ÷ 82,000 = (x/100) ⋅ $82,000 ÷ 82,000 0.155 ⋅ 100 = (x/100) ⋅ 100

or $82,000 – $69,290 = (x/100) ⋅ $82,000. Subtract $82,000 – $69,290.00 = $12,710. Simplify by dividing both sides by $82,000. Multiplying both sides by 100.

15.5% = x 35. The best choice for this item is A. The travel agency will add 15 percent markup to the initial price of the airplane ticket ($175): 15% ⋅ $175 = 0.15 ⋅ $175 = $26.25 markup. This gives a new price of $175 + $26.25 markup, or $201.25. The travel agency will then apply the 11 percent service charge and taxes to this new price: 11% ⋅ $201.25 = 0.11 ⋅ $201.25 = $22.1375. The final price would be $201.25 + $22.1375 = $223.3875 or 223 (the closest dollar) for each airplane ticket from Tampa to Orlando at this travel agency. Another way to solve this problem is by multiplying the initial price ($175) by 115% or 1.15 ($175 + ($175 ⋅ 15%) = 115% ⋅ $175, or 1.15 ⋅ $175) to get the new price with added markup and then multiply this quantity by 111% or 1.11 to get the final price of the airplane ticket: 175 ⋅ 1.15 ⋅ 1.11 = 223.3875 or 223 (the closest dollar).

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Part II: FCAT Math Test

36. The best choice for this item is C. First, you need to find the value for the other side of the rectangle. The formula for the perimeter of a rectangle (sum of the lengths of its sides) is the following: P = 2(a) + 2(b) 28 = 2(5.3 cm) + 2(b)

Let a = 5.3, and P = 28.

28 = 10.6 cm + 2(b)

Multiply 2 ⋅ 5.3 = 10.6.

28 – 10.6 = 10.6 – 10.6 + 2(b)

Subtract 10.6 from both sides of the equality.

17.4 = 0 + 2(b) 17.4 ÷ 2 = 2(b) ÷ 2

Divide by 2 on both sides to solve for b (2 ÷ 2 = 1).

8.7 = b Now you need to use this information to find the area of the rectangle: A = a⋅b = 5.3 ⋅ 8.7 = 46.11 cm2

This is the area of the rectangle.

37. The best choice for this item is D. You need to convert 3/4 to a percent (3 ÷ 4 = 0.75), which is 75%. Then add this to 25%: 75% + 25% = 100%. 38. The best choice for this item is B. You need to solve this problem by using the Pythagorean Theorem: a2 + b2 = c2. Notice that some of the information is provided. You have the value for one of the sides of the shaded planar section inside the rectangular solid (width = 7 inches), but you still need to find one of the sides, which is the hypotenuse (value for c) of the right triangle formed by this side (diagonal line segment). One of the legs of this triangle is the length of the rectangular solid, which is 9 inches long (value for a). The other leg of this triangle is the height of the rectangular solid, which is 12 inches (value for b). Using the Pythagorean Theorem, this yields 92 + 122 = c2; 81 + 144 = c2; 225 = c2; 225 = c; or 15 = c. You can now calculate the area of the shaded planar section: 15 feet ⋅ 7 feet = 105 square feet. 39. The best answer for this item is B. Carlos earned $2,505.00 total salary for last month. Since this salary includes the regular salary and overtime hours last month, you need to subtract the regular salary from the total salary; the remaining quantity is the amount earned in overtime hours: $2,505.00 – $1,450.00 = $1,055.00 for overtime hours. This amount needs to be divided by $10.55 earned per overtime hour to get the number of overtime hours worked last month: $1,055 ÷ $10.55 per overtime hour = 100 overtime hours for last month. This month Carlos earned the same regular salary ($1,450.00), plus the same amount of overtime hours times $11.55 per overtime hour (overtime hourly rate was increased). He worked the same amount of overtime hours as last month, which was 100: 100 ⋅ $11.55 = $1,155.00 for the overtime hours this month. Since he earned the same salary last month, we can subtract what Carlos earned in overtime this month from what he earned in overtime hours last month: $1,155 – $1,055 = $100. Carlos earned $100.00 more this month than last month. 40. The best choice for this item is A. The change in y (vertical axis) with respect to the change in x (horizontal axis) is called the slope of a line. The slope of a graph is the number that tells how steep the line is. In this case, the vertical axis goes up in increments of one each, and the horizontal axis goes up by increments of three each: (2 – 1)/(2 – 1) = 2/(2 + 1) = 1/3. 41. The best choice for this item is C. The median is a measure of central tendency of data. The median of a set of data is the middle number of the ordered data, or the mean of the middle two numbers: 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 10, 10, 10, 10, 10, 10, 10 The median divides the data in half. In this case, the middle of the data is between the 11th and 12th number because we have 24 numbers: (7 + 8)/2 = 7.5. The median number of hours that Mike worked last month is 7.5 hours.

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Practice FCAT Math 1

42. The volume formula of a pyramid is V = 1/3(lwh) = 1/3(5 ⋅ 5 ⋅ 12.75) = 106.25 cubic centimeters ≈ 106.2 or 106.3

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43. The best choice for this item is D. First, you need to approximate how much is the 5 (using the Pythagorean Theorem: c2 = a2 + b2 = c2 = 22 + 12 = 4 + 1 = 5; then c = 5 ≈ 2.24). Then, you need to find the perimeter of this triangular lot: a + b + c = 2 + 1 + 2.24 ≈ 5.24 miles around. She takes two laps around this distance: 2 ⋅ 5.24 = 10.48 miles. She does this three times a month: 3 ⋅ 10.48 = 31.44. She runs around 31.44 miles every month. 44. The best answer for this item is A. Fist, you need to find the measure of each angle of the hexagon. Draw all diagonals from one vertex, as shown in the following figure, and count the number of triangles formed (four). Second, you need to find the sum of the angles’ measures in the hexagon: number of triangles formed times 180 degrees = sum of angle measures in the hexagon, 4 ⋅ 180° = 720°. Third, you need to find the measure for each angle of the hexagon: 720° ÷ 6 = 120°. The measure of each angle in the hexagon is 120°.

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Part II: FCAT Math Test

B

A 1 2 F

C 3 4 E

D

Since this is a regular hexagon, all of the sides are equal, triangle ABF is an isosceles triangle (a triangle with two equal sides), and angles AFB and ABF are equal. You know that angle BAF is equal to 120° and the sum of the angles in a triangle equals 180º, then these angles must be equal to (180° – 120°) ÷ 2 = 60° ÷ 2 = 30°. The measure of angle BFE is equal to 120° (the measure of angle AFE) minus 30° (the measure of angle AFB), which is equal to 90°. This problem can also be solved by using the measure of angle AFE (120º) and dividing it by four (the number of equal angles after drawing all diagonals from one vertex as shown in the preceding figure: 120° ÷ 4 = 30° for each angle formed. Then multiply 30° by 3 (the number of these angles forming angle BFE), which gives us 90°. 45. The best choice for this item is C. There are 27 workers (12 + 15) that are both secretaries and administrators. You should notice that 15 of these workers are also trainers. 46. The best choice for this item is B. You need to find the least common multiple (LCM) of 13 and 17 (including nonzero multiples only). Since 13 and 17 are relatively primes, their LCM is equal to 13 times 17 = 221. Another way to find the LCM is by finding the common nonzero multiples of 13 and 17 and finding the least common multiples of these two numbers: Multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169, 182, 195, 208, 221, . . . Multiples of 17: 17, 34, 51, 60, 85, 102, 119, 136, 153, 170, 187, 204, 221, . . . The two airplanes will be back at the Miami International Airport together in 221 days. 47. The best choice for this item is C. To find the mean, multiply each number of hour by its frequency, add the products, and divide the sum by the total frequency (45): (23 ⋅ 1 + 13 ⋅ 2 + 2 ⋅ 3 + 7 ⋅ 4) ÷ 45 = 83 ÷ 45 ≈ 1.84 (to the closest hundredth). The mean is 1.84 hours. 48. This short-answer item is worth two points. You need to have an acceptable explanation to earn two points. You need to write an equation to find out how much the oranges (x) and apples (y) cost: 5x + 16y = $29.00, where x = number of oranges and y = number of apples. This equation could be written in other ways (like 16y + 5x = $29.00). You also have that the price for each orange is 1.5 times as much as each apple: x = 1.5y. You need to solve for x using a system of equations: 5x + 16y = $29.00 5x + 16(1.5x) = $29.00

Substitute for y (y = 1.5x).

5x + $24.00 = $29.00 5x + $24.00 – $24.00 = $29.00 – $24.00

Subtract $24.00 from each side of the equality.

5x = $5.00 5x ÷ 5 = $5.00 ÷ 5 x = $1.00

164

Divide both sides by 5. Each orange costs $1.00.

Practice FCAT Math 1

49. The best choice for this item is A. First, you should make a table, like the following one, using each figure and the number of toothpicks for each one; continue the pattern (adding six more toothpicks to the previous quantity). This is enough for this problem; however, in other situations, it could be better to find a rule or expression to represent the relationship between quantities and to use it to find the number of toothpicks for a given figure. Possible rules for this situation are the following: 3(n – 1) + 3n or 6n – 3, where n represents the number of the figure. Figure number

Number of Toothpicks

Pattern

1st

3

3

2nd

9

3+6

3rd

15

9+6

4th

21

15 + 6

5th

27

21 + 6

6th

33

27 + 6

50. The best choice for this item is C. 9.50 = x 350 100 9.50 ⋅ 100 = 350 ⋅ x

Establish a proportion using the information you have. Cross multiply.

950 = 350x 950 ÷ 350 = 350 ÷ 350x 2.7% = x

Divide by 350 on both sides of the equality to isolate x, and get the percent. Approximate the answer: 3%.

165

Practice FCAT Math 2 Remember to read and follow the instructions carefully. You have two and a half hours to complete the test. You may want to take a short break in the middle of the test.

First Part of Practice FCAT Math 2 1. Which of the following expressions is equivalent to 3(4x – 8) + 5? A. B. C. D.

12x + 29 12x + 19 12x – 19 12x – 29

2. Simplify the following expression for x = –5. 9x - 15 6x A. B. C. D.

2 – 2 1 – 1

3. Elena is 15 years older than Marie, who is three times Peter’s age. If Marie is 9 years old, how old is Elena? A. B. C. D.

72 years old 52 years old 3 years old 24 years old

4. Mario utilizes 23 percent of his salary in traveling expenses every month. If his salary is $3,595.00 a month, how much does he have left for other expenses? A. B. C. D.

$ 2,768.15 $ 826.85 $ 8,268.50 $27,681.50

5. Albert took a 48-mile trip from Orlando to Daytona. This trip took him one hour, 28 minutes, and 45 seconds. What is the estimated average of miles per hour he traveled for this trip? Explain your answer.

167

Part II: FCAT Math Test

6. What is the approximate surface area of a cylinder that has a diameter of 15 cm and a height of 35 cm (see following figure)?

h = 35 cm

d = 15 cm

A. B. C. D.

1825 cm2 2002 cm2 4710 cm2 4003 cm2

7. In this figure, the measure of ∠ZYH is equal to 45°. What is the measure of ∠ZYX?

Z 45° X

Y

P

A. B. C. D.

168

225° 50° 215° 135°

H

Practice FCAT Math 2

8. Illustrated here is the route Albert travels in meters from point M to point N along the curve inside the circle. The diameter of this circle is 20 meters. Find the distance from point M to point N along the inside curve that Albert travels.

M

N

20 m

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9. A cake was baked using a hexagonal pan and divided in six equal parts. What is the measure in degrees of each interior angle of the hexagon? A. B. C. D.

40° 360° 120° 180°

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Part II: FCAT Math Test

10. Oranges cost $0.58 for a pound. Laura buys 13 pounds every day from Monday to Friday for her restaurant. How much will she have spent after four weeks? A. B. C. D.

$150.80 $ 7.54 $ 37.70 $ 30.16

11. Oscar bought 15 gallons of water at $1.98 per gallon. He wants to divide this water in bottles of 1/8 gallon each. How many bottles can he fill?

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12. The driver’s hourly wage was increased 3.5% to $7.21 per hour. What was the driver’s approximate hourly wage before the increase per hour? A. B. C. D.

$0.25 $7.46 $206 $6.97

13. What is the value of 4.1 ⋅ 10–2? A. B. C. D.

0.41 0.041 410 41

14. Sue found the following measures for a project she was doing. Which of the following sets of fractions is arranged in ascending order (from smallest to largest)? A. B. C. D.

170

5/8, 3/8, 1/4, 3/16 3/16, 1/4, 3/8, 5/8 3/16, 3/8, 5/8, 1/4 1/4, 5/8, 3/8, 3/16

Practice FCAT Math 2

15. The circumference of a circular pizza is approximately 37.68". What is the approximate size of the radius of this circular pizza in inches? A. B. C. D.

6" 12" 18.84" 6.28"

16. The perimeter of a square is 80 cm. What is the area of this square? A. B. C. D.

40 cm2 36 cm2 4,000 cm2 400 cm2

17. Albert can read 5 pages every 10 minutes. At this reading rate, how many pages could he read in 2 hours? A. B. C. D.

1 page 4 pages 60 pages 240 pages

18. Which of the following is an acute isosceles triangle? A.

C.

D.

B.

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Part II: FCAT Math Test

19. What is the sum of the measures of ∠MNQ and ∠PNR in the following figure? M

N

P

Q

A. B. C. D.

R

270° 90° 180° 360°

20. What is the measure of ∠ABC in the parallelogram here? C

D 36°

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A. B. C. D.

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E

144° 54° 324° 90°

21. This figure illustrates the measures of a parking lot in meters. 21 m A

B

? 10 m

C

D 15 m

What is the length in centimeters of line segment BD? Explain how you found the answer.

172

Practice FCAT Math 2

22. In the following figure, MN is parallel to YZ, and ∠XYZ = 90°. What is the length of XN? X

? 12 in M

N 5 in

Y

A. B. C. D.

9 in

Z

15 in. 3 in. 7 in. 10 in.

23. A scale drawing of a desktop is 4 cm long (l) and 1.5 cm wide (w). The actual desktop is 1.2 m wide. How long is the actual desktop? A. B. C. D.

4m 3.2 m 0.45 m 5m

24. In the following figure, the shaded rectangular plane is parallel to the base of the cylinder. The height of the cylinder is 35 cm, and its volume is 4,643.275 cm3. The width of the rectangular plane is 15 cm, and the length is 25 cm.

15 cm 35 cm

25 cm

Which of the following represents the area of the shaded part of the rectangular plane? A. B. C. D.

242.335 cm2 132.665 cm2 392.335 cm2 484.18 cm2

173

Part II: FCAT Math Test

25. Find the length of the line segment AC in the diagram . y 6 5 4

A (-4,3)

B (4,3)

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10 units 100 units 2 units 2 units

You may take a short break (optional 5 or 10 minutes) but must complete the test on the same day.

174

STOP

Practice FCAT Math 2

Second Part of Practice FCAT Math 2 Continue the test. Remember to read and follow the instructions carefully. You have 70 minutes to complete the test. 26. The area of the shaded rectangle inside the cube below is equal to 408 cm2. What is the volume of the cube?

x

24

A. B. C. D.

cm

6,936 cm3 9,792 cm3 4,913 cm3 13,824 cm3

27. What is the midpoint of XY when X is located at (–8, 2) and Y is at (10, –6)? A. B. C. D.

(–4, 1) (1,–4) (5, 0.5) (9, 5.5)

28. Anna spends $5.50 for each batch of cookies she bakes for a bake sale. Each batch of cookies is sold for $7.75. How many batches does she need to bake in order to make a $22.50 profit?

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Part II: FCAT Math Test

29. Select the pair of equations that represents perpendicular lines. A. B. C. D.

y = 3x + 9, and y = 3x – 9 y = –3x + 6, and y = 3x – 9 y = (2/7)x + 3, and y = –3.5x – 5 y = 5x – 3, and y = (1/5)x + 6

30. Which one of the following pairs of point coordinates falls on the same vertical line? A. B. C. D.

Points L (6, 5) and M (5, 6) Points P (5, –8) and S (4, –8) Points X (6, 9) and Y (–6, –9) Points T (5, 7) and R (5, –8)

31. Find the 20th number in the following sequence: 13, 17, 21, 25, . . . A. B. C. D.

85 89 93 41

32. How many trapezoids will be needed to make the 20th ornament in the sequence illustrated in the following figure? The first ornament takes 6 trapezoids.

The second ornament takes 10 trapezoids.

The third ornament takes 14 trapezoids.

The fourth ornament takes 18 trapezoids.

A. B. C. D.

176

82 trapezoids 80 trapezoids 78 trapezoids 86 trapezoids

Practice FCAT Math 2

33. Mary wants to buy books that sell for the same x number of dollars. She has $150.00 to purchase as many of these books as possible. Select the expression that best represents the number of books that she can purchase. A. B. C. D.

150x x/150 150 – x 150/x

34. Peter works at a department store. He makes 6.5 percent on commission for all of his sales at this department store. He received $345.00 on commissions last month. To the nearest dollar, what was the amount of his sales last month?

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35. A box of 12 donuts costs $5.25 each. How much should a box of 24 donuts cost? A. B. C. D.

$7.87 $54.86 $10.50 $10.00

36. Which of the following is the solution of the equation 25 = –5y – 4? A. B. C. D.

–

5.8 25 5.8 – 5.25

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Part II: FCAT Math Test

37. Beatrice is packing some documents in a 12 cm high, 15 cm wide, and 8 cm long box. She discovers that she needs a new box that is twice as high, wide, and long as the box that she has now. How will the volume of these two boxes compare to each other?

12 cm

15 cm

8 cm

In the space provided, draw a sketch of the new box that Beatrice needs, including its dimensions.

Explain how the volumes of the two boxes compare to each other. 38. The sale price of a car last year was $45,960.00. A year later, the sale price of the same car was 10 percent less than last year. What was the sale price of the car a year later? A. B. C. D.

$50,556.00 $4,596.00 $45,503.40 $41,364.00

39. Last year, Elena received a base salary (before hours of extra time) of $45,690.00, plus $10.50 for x hours of extra time. How many hours of extra time did she work last year if she had a total salary of $49,365.00? A. B. C. D.

178

35 hours 350 hours 3,500 hours 3.5 hours

Practice FCAT Math 2

NOTE: Use the following data set for items 40, 41, 42, and 43. The students in a class received the following scores in a test worth 25 points: 12, 13, 10, 14, 23, 12, 13, 22, 12, 12, 10, 11, 15, 20, 10, 12, 10, 15, 22, 23 40. What is the mean of the data set? A. B. C. D.

14.55 291 12 12.5

41. What is the median of the data set? A. B. C. D.

14 12 12.5 13

42. What is the mode of the data set? A. B. C. D.

2 10 and 12 10 12

43. What is the range of the data set? A. B. C. D.

13 4 12 14

44. At a local school, Carlos decided to develop and administer a survey for a school project. He wanted to know whether the students in the school county were in favor of a new rule mandated by the school board. At the end of the school day, he stood outside the school exit and asked a few students to complete the survey as they went out. Some students participated, and others did not. He gathered and analyzed the data and concluded that the students in the school county were not in favor of the new rule mandated by the school board. Did Carlos interpret the results of the survey correctly? Explain your answer.

179

Part II: FCAT Math Test

45. Abraham works part time at a bus station and is paid an hourly wage of $7.50 for 30 hours per week. Hector works full time at this station and is paid an hourly wage of $9.50 for 40 hours per week. How much more does Hector earn than Abraham per week?

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1/2 1/6 1/18 1/36

47. Oswald drilled six holes in a 15 cm by 10 cm rectangular piece of metal (see figure).

10 cm

15 cm

Find the percent of the remaining metal (shaded area in the figure above). Use 3.14 for π. Explain how you found you answer.

180

Practice FCAT Math 2

NOTE: Use the following table for items 48, 49, and 50. The table lists the 26 countries with the top medal total in the 2004 Olympic Games, Athens, Greece.

26 Countries with the Top Medal Total 2004 Olympic Games, Athens, Greece Country

Gold

Silver

Bronze

Total

United States

35

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29

103

Russia

27

27

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92

China

32

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63

Australia

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49

Germany

14

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48

Japan

16

9

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37

France

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33

Italy

10

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32

Korea

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12

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30

Great Britain

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Cuba

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27

Ukraine

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Netherlands

4

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22

Romania

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19

Spain

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Hungary

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Greece

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Belarus

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Canada

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Bulgaria

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Brazil

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Turkey

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Poland

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Thailand

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Czech Republic

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181

Part II: FCAT Math Test

48. Of the 26 countries included in the table winning the most medals, what approximate percent of the total bronze medals was won by Australia? A. B. C. D.

6% 33% 2% 17%

49. Using the table, what approximate percent of China’s medals were gold? A. B. C. D.

100% 13% 4% 51%

50. Using the table, which one of the following statements is true? A. B. C. D.

United States won more gold medals than silver medals. Japan won three times as many gold medals as the amount of gold medals won by the Netherlands. Three-fourths of Bulgaria’s medals were bronze medals. Australia won 25 percent of the total medals.

STOP 182

Practice FCAT Math 2

Answer Key for Practice Test 2 1. C 2. A 3. D 4. A 5. 32 miles per hour 6. B 7. D 8. 31.4 9. C 10. A 11. 120 12. D 13. 0.042 14. B 15. A 16. D 17. C 18. A 19. B 20. A 21. 800 centimeters 22. D 23. B 24. C 25. A 26. C 27. B 28. 10 29. C 30. D 31. B 32. A 33. D 34. 5308 35. C

183

Part II: FCAT Math Test

36. A 37. The volume of the new box will be eight times larger than the volume of the first box. 38. D 39. B 40. A 41. C 42. D 43. A 44. It is not clear whether the procedures used by Carlos to develop the survey were systematic and valid, and the interpretation of the survey’s results is not correct. 45. $155 46. C 47. The percent of metal material remaining is 21.5%. 48. A 49. D 50. C

184

Practice FCAT Math 2

Solutions for Practice FCAT Math 2 Use these answers and explanations to help you understand possible solutions and improve your test-taking ability. You should not take more that one practice exam per day. You need some wait time before taking and reviewing the other practice exams (at least one day). You might have used a different path for your solution. This is okay; if you get to the same answer and the procedures you used are mathematically accurate, you don’t need to have the same solution process. It is good to also learn other ways to solve the problem. 1. The best choice for this item is C. 3(4x – 8) + 5 (3 ⋅ 4x – 3 ⋅ 8) + 5

You need to multiply the first part of the expression then add 5 to it.

12x – 24 + 5

Then you have that 3 ⋅ 4x is equal to 12x and – 3 ⋅ 8 = –24.

12x – 19

Finally, you have that – 24 + 5 = –19.

2. The best choice for this item is A. The expression is solved by using the following steps: 9x - 15 6x 9 ^ - 5h - 15 6 ^ - 5h - 45 - 15 - 30 - 60 - 30

You need to substitute –5 for x. You need to multiply: 9(–5) = –45, and 6(–5) = –30. Then, you need to subtract: (–45) – 15= –60.

Divide –60 by –30 = 2. 3. The best choice for this item is D. Let e = Elena’s age, m = Marie’s age, and p = Peter’s age. Then, you have that e = m + 15 and m = 3p (or m ÷ 3 = p. Since you are given that m = 9, p = m ÷ 3 or p = 9 ÷ 3 = 3; e = m + 15 = 9 + 15 = 24, which is Elena’s age. 4. The best choice for this item is A. You need to find 23 percent of the initial salary: $3,595.00 ⋅ 0.23 = $826.85 (quantity used for traveling expenses). Then, subtract this amount from the initial salary: $3,595.00 – $823.85 = $2,768.15. Another way to solve this problem is by subtracting 100% – 23% = 77%, which is the percent of the salary not used for traveling. You need to find then 77% of the initial salary: 77% ⋅ $3,595.00, or 0.77 ⋅ $3,595 = $2,768.15. This is the same answer using different procedures. 5. This short-answer item is worth two points—one point for the answer and one for an acceptable explanation. Peter traveled an estimated 32 miles per hour in this trip. You need to explain how you solved the problem. Velocity (V) is equal to miles (m) per hour (h) or V = m/h. For this case, you have 48 miles/1.5 hours (approximate number of hours), or 32 miles/1 hour. 6. The best choice for this item is B. You need to use the Surface Area formula given in the reference sheet: 2πrh + 2πr2. Since the diameter of this cylinder is 15 cm, the radius (r) is equal to 1/2 of that (7.5 cm). This is because d = 2r or 1/2d = r (divide by 2 for each side of the equality). Let π ≈ 3.14. 2πrh + 2πr2 2(3.14)(7.5)(35) + 2(3.14)(7.5)2 1648.5 + 353.25 = 2001.75 ≈ 2002 cm2

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7. The best choice for this item is D. You need to use the idea of supplementary angles for this item: The sum of the measures of two supplementary angles is equal to 180°. In this case, angles ZYX and ZYH are supplementary angles: m(∠ZYX) + m(∠ZYH) = 180°. Then, m(∠ZYX) = 180° – m(∠ZYH). Since m(∠ZYH) = 45°, you have that m(∠ZYX) = 180° – 45° = 135°. 8. You need to use the formula for the circumference of a circle given in the reference sheet earlier: C = 2πr, and use 3.14 ≈ π. As illustrated in the following figure, the curve inside the circle is part of the two concentric circles, and the radius of these circles is 5 meters long (20 meters from the diameter of the original circle ÷ 4). Notice that the distance of the curve is equal to one of the circles inside the original circle, which implies that you only need to find the circumference of one of these small circles. The circumference of this circle is 2πr ≈ 2 ⋅ 3.14 ⋅ 5 ≈ 31.4 m or 31.40 m.

r=5m M

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9. The best choice for this item is C. The sum of the interior angles of the hexagon is 180 ⋅ 4, which is equal to 720°. You need to divide this by 6 (the number of interior angles): 720° ÷ 6 = 120°. 10. The best choice for this item is A. You need to translate the word problem into a mathematical sentence. You have 13 pounds of oranges for $0.58 times fives days for four weeks: 4(5(13 ⋅ $0.58)) = 4(5(7.54)) = 4(37.70) = $150.80.

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11. The cost per gallon is not needed to solve this problem. You need to find out how many one-eighths are contained in 15 gallons, which is a form of division: 15 ÷ 1/8 = 15 ⋅ 8/1 (reciprocal of 1/8) = 15 ⋅ 8 = 120 bottles. You can enter your grid response in one of the following two manners:

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12. The best answer for this item is D. One way you can solve this problem is working backward: x + (3.5% ⋅ x) = $7.21 x(1 + 0.035) = $7.21 x(1.035) = $7.21 x(1.035 ÷ 1.035) = $7.21 ÷ 1.035 x = $6.97

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Where x is the initial hourly wage (any number). Use the distributive property of multiplication over addition for decimals. 1 + 0.035 = 1.035. Divide by 1.035 on each side of the equality.

Practice FCAT Math 2

13. You have that 4.1 ⋅ 10–2 = 4.2 ⋅ 1/100 = 0.042 (move the decimal point twice to the left). 14. The best choice for this item is B. One way to solve this problem is by changing all the fractions to common denominators and arranging them from there. The denominators involved in this case are 4, 8, and 16. The least common multiple (LCM) or least common denominator (LCD) is 16. You can find this by finding the nonzero multiples of these denominators and selecting the least common multiple: 4:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, . . .

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8, 16, 24, 32, 40, 48, ...

16: 16, 32, 48, ... Notice that there are other common multiples, but you want to select the least common multiple (or denominator). Another way to find the least common multiple is by using prime factorization: 4 = 22, 8 = 23, and 16 = 24. You select the common and noncommon multiples out of the prime factorizations. In this case 24 = 16 is the least common multiple (denominator). You still need to use this denominator to change each fraction to its equivalent fraction (whenever needed) and then arrange them in order from least to greatest: 5/8 = 10/16, 3/8 = 6/16, 1/4 = 4/16, and 3/16. The order is the following: 3/16, 4/16, 6/16, 10/16 or 3/16, 1/4, 3/8, 5/8. You can also change all the fractions to their equivalent decimal forms and arrange them from least to greatest using this information: 5/8 = 0.625, 3/8 = 0.375, 1/4 = 0.25, and 0.1875. Order these decimal numbers from least to greatest and then convert back to the reduced fractions. The order of the fractions is still the same. A number line could also be a useful and proper representation for these fractions. The following figure presents this alternative. 1 2

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15. The best choice for this item is A. You need to use the formula for circumference given in the reference sheet: C = 2πr, and use 3.14 ≈ π. You know that the C ≈ 37.68". Given this information, you have that 37.68" ≈ 2(3.14)(r). Solving for r, you have now that r ≈ (37.68") ÷ (2 ⋅ 3.14) = 6", which is the size of the radius of this circle in inches. 16. The best choice for this item is D. You know that a square has four equal sides. Since the perimeter is 80 cm, the size of each side is 80 cm ÷ 4 = 20 cm, which means that each side of the square is 20 cm long. The area formula for a square is A = s2. In this case, you have A = 202 = 400 cm2. The area of this square is 400 cm2. 17. The best choice for this item is C. First, you need to convert the hours to minutes: 2 hours = 2 ⋅ 60 minutes = 120 minutes. Then, you need to establish and solve a proportion: 5 pages x = 10 min . 120 min . 5 pages ⋅ 120 min. = 10 min. ⋅ x (600 pages ⋅ min.) ÷ 10 min. = 10 min. ⋅ x ÷ 10 min. 60 pages = x

Cross multiply the proportion. Divide by 10 on both sides of the equality. He can read 60 pages in two hours.

18. The best choice for this item is A. An acute isosceles triangle contains angles that measure less than 90 degrees, and two sides are the same length. The only triangle that meets these criteria is A. B is an isosceles right triangle, C is a scalene triangle, and D is an obtuse isosceles triangle.

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Part II: FCAT Math Test

19. The best choice for this item is B. You have that ∠MNQ + ∠QNP + ∠RNP = 180° because they form a line. ∠MNQ + ∠QNR + ∠PNR = 180°

It is given that ∠QNR is a right angle (90°).

∠MNQ + 90° + ∠PNR = 180°

Substitute ∠QNR for 90°.

∠MNQ + 90° – 90° + ∠PNR = 180° – 90°

Subtract 90° from both sides of the equality.

∠MNQ + ∠PNR = 90° 20. The best choice for this item is A. Since you are dealing with a parallelogram, you have that line segments CD and BE are parallel to each other. Similarly, line segments BC and ED are also parallel to each other. This implies that ∠EDC is opposite to ∠CBE, and by definition, measures of opposite angles are equal: m(∠EDC) = m(∠CBE) = 36°. Also given this parallelogram, the sum of the measures of an interior angle and exterior angles is equal to 180°: m(∠CBA) + m(∠CBE) = 180° m(∠CBA) + 36° = 180°

Substitute m(∠CBE) for 36°.

m(∠CBA) + 36° – 36° = 180° – 36° m(∠CBA) + 0 = 144°

Subtract 36° from both sides of the equality. Solve each subtraction: 36° – 36° = 0, and 180° – 36° = 144°

m(∠CBA) = 144° 21. This short-answer item is worth two points—one point for the answer and one for an acceptable explanation. The length of line segment BD is 800 centimeters. You can add point (X) on AB, and form XC that is perpendicular to AB (see figure). This forms right triangle AXC. The length of BD is the same as the length of the height of this right triangle (XC). The length of AX is equal to length of AB – length of XB, which is the same as the length of CD: 21 m – 15 m = 6 m. You can find the height of the triangle AXC by using the Pythagorean theorem: c2 = a2 + b2 102 = 62 + b2 100 = 36 + b 100 - 36 = b 8=b

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22. The best choice for this item is D. Use the Pythagorean Theorem to find the measure of line segment XZ: c2 = a2 + b2 c2 = 92 + 122

Substitute using the information from the figure: a = 9 and b = 12.

c2 = 81 + 144

Solve: 92 = 81, and 122 = 144.

c = 81 + 144

Solve for c: 81 + 144 = 225, and the square root of 225 is 15.

c = 15

The length of line segment XN is equal to 15 inches.

Now you have to find the length of line segment XN: m(XZ) = m(XN) + m(NZ) 15 = m(XN) + 5

Substitute for the values of the respective line segments.

15 – 5 = m(XN) + 5 – 5

Subtract 5 from each side of the equality.

10 = m(XN) + 0

Solve: 15 – 5 = 10, and 5 – 5 = 0.

10 = m(XN)

The length of line segment XN is equal to 10 inches.

23. The best choice for this item is B. You can set up a proportion with the given information: 1.5

1.2 1.5 = 1x.2 4 1.5 ⋅ x = 1.2 ⋅ 4

Let x = actual desktop’s length in meters.

1.5 ⋅ x = 4.8

You have that 1.2 ⋅ 4 = 4.8.

Cross multiply.

1.5 ÷ 1.5 ⋅ x = 4.8 ÷ 1.5

Divide by 1.5 on both sides of the equality.

1 ⋅ x = 3.2

You have that 1.5 ÷ 1.5 = 1, and 4.8 ÷ 1.5 = 3.2.

x = 3.2

The actual size of the desktop’s length is 3.2 meters.

The proportion can be established in other ways, but the final answer should be the same if the relationship is set correctly. 24. The best choice for this item is C. You need to find the area of the whole rectangular plane and then subtract the area of the unshaded circular portion in the middle. The difference represents the remaining shaded portion of the rectangular plane. The area of the whole rectangular plane is equal to A = lw = 15 cm ⋅ 25 cm = 375 cm2. In order to find the area of the circular portion (which is the same as the base of the cylinder, see figure), you need to find its radius. To find this radius, you need to work backward from the volume formula using the given height and volume of the cylinder: V = πr2h 4,643.275 cm3 = 3.14 ⋅ r2 ⋅ 35 cm

Let π = 3.14, h = 35 cm, and V = 4,643.275 cm3.

4,643.275 cm3 = r2 ⋅ 109.9 cm

Solve 3.14 ⋅ 35 = 109.9.

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Divide both sides of the equality by 109.9. Solve 4,643.275 cm3 ÷ 109.9 cm = 42.25 cm. Find the square root of 42.25, which is 6.5 cm. The radius of the circle is 6.5 cm.

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6.5 cm

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The area of the circular portion is found by using the area of a circle formula, and the radius you just found (see figure): A = πr2 = 3.14 ⋅ 6.52 = 3.14 ⋅ 42.25 = 132.665 cm2. The area of the shaded part of the rectangular plane is equal to the area of the whole rectangular plane minus the area of the circular portion in the middle: 375 cm2 – 132.665 cm2 = 242.335 cm2. 25. The best choice for this item is A. You need to use a variation of the Pythagorean Theorem to find distances on a coordinate plane: _ x 1 - x 2i + _ y1 - y 2i

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Substitute for the values on the coordinates provided.

_ - 8i + ^ 6 h

Subtract following the rules of integer operations.

64 + 36

Add 64 to 36, which is equal to 100.

100 = 10 units

Find the square root of 100.

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26. The best choice for this item is C. You need to use the formula for area of a rectangle to find the size of one of the sides of the cube (since it is a cube all sides are equal). This side of the rectangle is also the width of the shaded rectangle: A=l⋅w 408 cm2 = l ⋅ w

The area of the rectangle is equal to 408 cm2.

408 cm2 = 24 cm ⋅ w

The length of the rectangle is equal to 24 cm.

408 cm2 ÷ 24 cm = 24 cm ÷ 24 cm ⋅ w 17 cm = w

Divide by 24 cm both sides of the equality. The width of the rectangle and sides of the cube is 17 cm.

The volume of the cube is then equal to a3 = (17 cm) 3 = 4,913 cm3. 27. The best choice for this item is B. The midpoint for (–8, 2) and (10, –6) is ((–8 + 10) ÷ 2, and (2 + 6) ÷ 2)) or (1, –4). First, you need to add the two x-coordinates together and divide by 2 and then add the two y-coordinates together and divide by 2.

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28. You need to subtract $5.50 from $7.75 to calculate the profit she makes per batch of cookies: $7.75 – 5.50 = $2.25. Then, you need to divide $22.50 by $2.25 to calculate the amount of batches of cookies she needs to bake for a $22.50 profit: $22.50 ÷ $2.25 = 10. She needs to bake 10 batches of cookies to make a $22.50 profit. You can enter your answer in the response grid in the following manner:

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29. The best choice for this item is C. Two equations form perpendicular lines if their slopes are opposite reciprocals of each other. Since the equations in this item are given in slope-intercept form, their slopes are represented by the coefficient of their respective x. The slope of y = (2/7)x + 3 is 2/7, and the opposite reciprocal of this slope is –7/2 or –3.5, which happens to be the coefficient for x in the other equation (y = –3.5x – 5). Then these equations are perpendicular to each other.

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30. The best choice for this item is D. Two points are on the same vertical line if they have the same x-coordinate. This is the case of points T (5, 7) and R (5, –8). 31. The best choice for this item is B. The 20th number in the sequence (13, 17, 21, 25, . . .) may be found by continuing the sequence up to the 20th number in the sequence. The pattern involves adding four more to the previous number in the sequence: 13 (1st), 17 (2nd), 21 (3rd), 25 (4th), 29 (5th), 33 (6th), 37 (7th), 41 (8th), 45 (9th), 49 (10th), 53 (11th), 57 (12th), 61 (13th), 65 (14th), 69 (15th), 73 (16th), 77 (17th), 81 (18th), 85 (19th), 89 (20th), . . . You might have used an expression or formula to find the 20th number in the sequence. Possible expressions are 4(n + 2) + 1 or 4n + 9, where n is the position of the number in the sequence. For example, the 20th number is 4(20 + 2) + 1 = 4(22) + 1 = 88 + 1 = 89, or with the other expression, 4(20) + 9 = 80 + 9 = 89. You may use other variations of these expressions. Finding the expressions or formulas requires some exploration with the quantities, but you get better as you practice with different patterns. 32. The best choice for this item is A. The number of trapezoids needed to make the 20th ornament in the sequence may be found by continuing the sequence up to the 20th member of the sequence. You may also find an expressions or formula that will work for this relationship between quantities. For example, you might notice that you always have two trapezoids in the middle of the ornament, which is a constant (or + 2). Then, you might notice that you are adding four more for every new ornament (or multiplying by four), and this is incremented by one as you continue the pattern (see table). Using this information, the expression might look like this 4n + 2, where n is the position of the ornament in the sequence (1st, 2nd, 3rd, and so on). Position of the Ornament

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33. The best choice for this item is D. You need to find out how many times “an x amount of dollars” is contained in $150.00. This is a type of division and is represented by the expression 150/x.

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34. This problem is represented by the following equation: 6.5% ⋅ s = $345.00, where s represents the amount of Peter’s sales last month, and $345.00 is the commission he received last month. You need to divide $345.00 by 0.065 to get the amount of the sales: 345 ÷ 0.065 = 5307.69 ≈ 5308 to the nearest dollar. You can enter your grid response in the following manner:

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Part II: FCAT Math Test

35. The best choice for this item is C. In this case, you are going from 12 donuts to 24 donuts, which is double the quantity. This might imply that you want to also double the price. The best answer in this case is 2 ÷ $5.25 = $10.50. You can also solve this problem by using a proportion like the following: 12 = 24 5.25 n 12n = 24 ⋅ 5.25

Cross multiply the proportion.

12n = 126

Multiply 24 ⋅ 5.25 = 126

12 ÷ 12n = 126 ÷ 12 n = 10.50

Where n represents the new value of the donuts.

Divide by 12 on both sides of the equality. The price for 24 donuts should be $10.50.

36. The best choice for this item is A. The solution of the equation is the following: 25 = –5y – 4 25 + 4 = –5y – 4 + 4 –

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37. This short-answer item is worth two points—one point for the answer and one for an acceptable explanation. The following is a possible sketch of the new box with new dimensions (double height, width, and length): 24 cm high, 30 cm wide, and 16 cm long box.

24 cm

30 cm

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The volume of the new box will be eight times larger than the volume of the first box. The volume of the first box is equal to 12 cm ⋅ 15 cm ⋅ 8 cm = 1,440 cm3. The volume for the second box is 24 cm ⋅ 30 cm ⋅ 16 cm = 11,520 cm3. Divide the volume of the second box by the volume of the first box: 11,520 ÷ 1,440 = 8. The volume of the second box is eight times the volume of the first box after doubling the height, width, and length dimensions of the first box. The following figure illustrates this relationship. 6

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Practice FCAT Math 2

38. The best choice for this item is D. You need to find 10% of $45,960.00 and subtract that amount from $45,960.00: $45,960.00 – (10% ⋅ $45,960.00) = $45,960.00 – (0.10 ⋅ $45,960.00) = $45,960.00 – $4,596.00 = $41,364.00. This is the new sale price of the car a year later. You can also multiply $45,960.00 by 90% (because 100% – 10% = 90%): $45,596.00 ⋅ 90% = $45,596.00 ⋅ 0.90 = $41,364.00. 39. The best answer for this item is B. First, you need to find how much more money was earned after the base salary: $49,365.00 – $45,690.00 = $3,675.00 earned after the base salary. Divide this quantity by the hourly wage ($10.50): $3,675.00 ÷ 10.50 = 350 hours of extra time. 40. The best choice for this item is A. To find the mean of this data set, you need to add the scores and divide by 20 (number of scores): 291 ÷ 20 = 14.55. 41. The best choice for this item is C. To find the median, you need to order the data set and find the middle score. 10, 10, 10, 10, 11, 12, 12, 12, 12, 12, 13, 13, 14, 15, 15, 20, 22, 22, 23, 23 Scores 12 and 13 are in the middle. You need to average these two scores to find the median: (12 + 13) ÷ 2 = 25 ÷ 2 = 12.5. 42. The best choice for this item is D. The mode is the most frequent score. A frequency table should be used to organize the data. Scores

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43. The best choice for this item is A. The range of the date set is the highest score minus the lowest score: 23 – 10 = 13. 44. This short-answer item is worth two points. You need to have an acceptable explanation to earn two points. In your explanation, you need to mention that it is not clear whether the procedures used by Carlos to develop the survey were systematic and valid, and the interpretation of the survey’s results is not correct. Asking students in one school is not enough of a sample to make generalizations about a whole school county. This is not representative of the whole intended population.

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45. Abraham’s part-time salary per week is 30 hours ⋅ $7.50 per hour = $225. Hector’s full-time salary per week is 40 hours ⋅ $9.50 per hour = $380. The difference is $380 – $225 = $155.

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46. The best choice for this item is C. You need to find the possible combinations for the two dice: 6 ⋅ 6 = 36 combinations (see table). Of these possible combinations, two involve 5 and 6 as possible outcomes: (5, 6) and (6, 5) (because order is not relevant). This is two out of 36 possible number combinations: 2/36 or 1/18 for the probability.

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Practice FCAT Math 2

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47. This is a long-response item, which are four points each. You will receive four points if you answer all parts of the item fully and correctly. You must show understanding of the mathematical ideas presented in this problem. You will receive three points if you make minor errors and show understanding as you solve and explain the solution of the problem. You will receive two points if you make several errors, the explanations are incomplete and not clear, and do not show proper understanding of the problem. When solving this problem, you need to consider two different relationships. The percent of metal material remaining is 21.5%. First, you need to find the area of the whole rectangle: A = l ⋅ w = 15 cm ⋅ 10 cm = 150 cm2. Second, you need to find the area of one circle and multiply that by six (the number of circular holes on the rectangular metal). The diameter of the circles is equal to 15 ÷ 3 or 10 ÷ 2 = 5 cm. The radius is half of the diameter: 5/2 = 2.5 cm. This yields 6(A of circle) = 6(πr2) = 6(3.14)(2.5)2 = 6(3.14)(6.25) = 6(19.625) = 117.75 cm2 is the total area of all six circles that were cut from the metal. You need to subtract this amount from the total area of the rectangular area (calculated before): 150 – 117.75 = 32.25 cm2 left over, which is 21.5% of the rectangular piece of metal: 32.25 ÷ 150 = 0.215. 48. The best choice for this item is A. Using the table provided, you need to calculate the total number of bronze medals awarded in the 2004 Olympic Games (not the total overall number of medals), which was 267 total bronze medals. Australia won 16 bronze medals out this 267 total bronze medals, which is 6% of them (16/267 ≈ 0.0599≈ 6%). 49. The best choice for this item is D. China won 32 gold medals out of the 63 medals (not the total overall number of medals): 32/63 ≈ 0.5079 ≈ 51%. 50. The best choice for this item is C. You need to check the trustfulness of each statement against the data provided in the table: A. United States won more gold medals than silver medals. This statement is false because United States won more silver medals than bronze medals. B. Japan won three times as many gold medals as the amount of gold medals won by the Netherlands. This statement is false because Japan won four times as many gold medals as the Netherlands. Japan won 16 gold medals and the Netherlands won 4 gold medals (16 is four times 4). C. Three-fourths of Bulgaria’s medals were bronze medals. This statement is true because Bulgaria won 9 bronze medals out of 12 medals: 9/12 = 3/4. D. Australia won 25 percent of the total medals. This statement is not true because Australia won 49 out of 761 total medals, which is approximately 6.4 percent of the total number of medals awarded (not even close to 25 percent).

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Practice FCAT Math 3 Remember to read and follow the instructions carefully. You have two and a half hours to complete the test. You may want to take a short break in the middle of the test.

First Part of Practice FCAT Math 3 1. Select the number that will result in a smaller product after it is squared. A. B. C. D.

3 1.3 – 0.03 0.3

2. Find the volume of the following figure.

24 ft

3 yr

A. B. C. D.

216 ft3 839.16 ft3 1944 ft3 1088.64 ft3

3. What is the value of 27(–3)–2 – (–3)0? A. B. C. D.

2 0 3 243

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4. What is the length of the hypotenuse of the triangle in the following figure? 9 cm 45°

A. B. C. D.

9 cm 2 cm 9 2 cm 6 cm

5. You need to use the following figure to solve this problem: F

D

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A

Given that C is the center of the circle in the figure and B is a point on the circumference of this circle such that rectangle BGCD is a 5 inch by 3 inch rectangle, what is the area in square inches of the shaded region of the circle? Explain your answer.

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6. Which of the following best describes the relationship between ∠ABC and ∠DBE?

A C 30°

B 30° D E

A. B. C. D.

supplementary complementary both supplementary and complementary neither supplementary nor complementary

7. Which of the following shows a translation of the letter Z? A.

C.

B.

D.

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NOTE: Use the following figure for items 8 and 9. 6 cm 3 cm

9 cm 3 cm 3 cm 15 cm

8. To the nearest hundredth of a centimeter, what is the perimeter of the preceding figure?

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10. Find the volume of the solid figure, rounding to the nearest cubic centimeter. 3 cm

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504 cm3 596 cm3 576 cm3 545 cm3

11. Two similar cylinders have a ratio of 2 : 3 for their radii and heights. What is the ratio for their volumes?

A. B. C. D.

4:6 2:3 8 : 27 6:6

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12. Rosie built a model of her neighborhood. In her model, one centimeter is equivalent to three kilometers in the real neighborhood. The following figure shows the arrangement of her model. A

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NOTE: Use the following data set for items 13, 14, and 15: 80, 23, 55, 58, 45, 32, 40, 55, 50 13. Find the mean of the data set (round to the nearest one). A. B. C. D.

50 55 49 57

14. Find the median of the data set. A. B. C. D.

57 49 55 50

15. Find the range of the data set (round to the nearest one): A. B. C. D.

57 49 50 55

16. Ernest’s salary last year was $45,000. If he spent 5/8 of his salary in expenses and saved the rest, which of the following quantities should he use to multiply his salary and find the portion of the salary that he saved? A. B. C. D.

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3.75 0.375 0.625 6.25

Practice FCAT Math 3

17. Maria is traveling to her job in Tampa. She has been traveling for two hours at an average speed of r miles per hour. Select the equation that represents the distance (d) she has traveled after these two hours. A. B. C. D.

2 = rd 2 = d/r d = r/2 d = 2r

18. Natalie has two bags with marbles. One bag has 5 marbles: 2 red, 2 blue, and 1 yellow. The other bag has 7 marbles: 3 orange, 2 green, and 2 purple. If she draws randomly once from each bag, what is the probability that she will get one red marble from the first bag and an orange marble from the second bag? A. B. C. D.

2/3 1/35 6/35 1/9

19. A basketball team played 50 games in last season. They lost 20 of these games last season. What percent of the games played did they lose? A. B. C. D.

4% 0.4% 2.5% 40%

20. Wages were found to have risen by108 percent over the last year at a company in the United States. If the current wage is $9.99 this year, what was the average wage last year? A. B. C. D.

$9.95 $4.80 $9.19 $9.25

21. Samuel is making a vacation trip that is taking him 325 miles per day. He has been traveling and vacationing for nine days. He decides to head back home after this nine days. After four days of traveling on his way back home, he realizes that he has only driven 250 miles per day in the last four days. He has slowed down some. If he drives at an average of 65 miles per hour, about how many hours per day would he have to drive to make his remaining return trip back home in three days? Explain how you found the answer. 22. At a department store, jackets are 20 percent off the original price. To the nearest cent, what is the total cost of one of these jackets if the original price is $74.99, and the sale tax is 8 1 %? 2 A. $110.98 B. $59.99 C. $65.09 D. $16.07

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23. The line graph that follows shows the percent of buyers at a shopping center from 1980 to 2005. Using this graph, predict the percent of buyers for the year 2010 at this shopping center. Buyers at a Shopping Center

Percent (%)

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NOTE: Use the following situation and figure for items 24 and 25. Mr. Ortiz has 25 students in his class. After receiving the scores for these students’ final exams in math, science, and history, he identified the students who scored 90 percent or above on each of the tests for these areas and drew the Venn diagram that follows based on this information. Math

History

Peter Mary

Elba

Samuel Natalie Sarah Raul Beth

Mathew

Carlos Peter

Science

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24. Using the Venn diagram, Raul and Beth are in which of the following areas? A. B. C. D.

science but not history math but not science math but not history math and science but not history

25. Using the Venn diagram, about what percent of the students in Mr. Ortiz’s class had a score of 90 percent or above on exactly 2 tests? A. B. C. D.

12% 27% 22.5% 88%

You may take a short break (optional 5 or 10 minutes) but must complete the test on the same day.

STOP 209

Part II: FCAT Math Test

Second Part of Practice FCAT Math 3 Continue the test. Remember to read and follow the instructions carefully. You have 70 minutes to complete the test. 26. Which of the following represents the simplification of the expression – (–32) + (–2)2? A. B. C. D.

–

13 5 5 13 –

27. A ball has a diameter of 35 cm. If this ball is cut in half, what is the area (to the nearest square centimeter) of the cross section?

d = 35 cm

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962 cm2 3846 cm2 306 cm2 1225 cm2

28. Of 3,695 workers at a private company, 2,690 of them have cellular phones. To the nearest tenth, what percent of the total number of workers at this company have cellular phones?

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Practice FCAT Math 3

29. The distance between two points is approximately 2 40 . Select the one that is closest to 2 40 . A. B. C. D.

6 1⁄3 20 40 12 2⁄3

30. Which of the following is the largest? A. B. C. D.

3 1 4 3 3 7 31 3 3 2 5

31. What is the distance between points M and N on the following graph? y M

N x

A. B. C. D.

2 29 4 29 58 29

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32. If line segment AB is the diameter of the circle in the following figure, what is the area of this circle? Approximate your answer to the nearest hundredth of a unit. Use π = 3.14. y

A

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Practice FCAT Math 3

33. Find the slope of the line that passes through the pair of points given in the following figure. y

A (-1,2)

B (-2,-1)

A. B. C. D.

O (0,0)

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1/3 3 – 1/3 – 3

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34. Aurora had the measures of three angles of a quadrilateral like the one in the following figure. What is the size of the missing measure?

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35. Using the following figure, where AG is perpendicular to EF, and the measure of ∠ACB is equal to 30°, what is the measure of ∠BCF? A B F

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60° 30° 90° 150°

36. Albert bought 16 gallons of gasoline for his lawnmower business. How many quarts of gasoline did he buy? A. B. C. D.

18 quarts 4 quarts 64 quarts 16 quarts

37. At the end of the year, Olga’s income was five-eighths of Peter’s income, and her personal expenses were one-half Peter’s personal expenses. After these expenses, she had 40 percent of her income left for other types of expenses and savings. What percent of his income did Peter have left for other expenses and savings? Explain your answer. 38. According to a recipe to bake a cake, you need 3/4 cup of sugar. How much sugar would you need to make 2 1 2 cakes using this recipe? A. B. C. D.

3 cups of sugar 1 7 cups of sugar 8 1 2 cups of sugar 3 1 3 cups of sugar 4

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39. A cake mix comes in boxes of 10 cups each. It takes 1 1 cups of the cake mix to make one specific recipe. If you 4 have two boxes of the cake mix, how many times can you make this specific cake recipe? A. B. C. D.

12 1 times 2 25 times 16 times 8 times

40. Suppose that you want to build a 400 cm wide walk around a circular garden. The circular garden has a diameter of 132 cm. You also want to build a fence around the outside edge of the walk with an opening of about 50 cm to get in and out of the garden. Express your answer to the nearest meter. Make a drawing describing this problem. About how many meters of fence will you need for this project? If you put the fence around the inside edge of the garden, you save $375. Given this scenario, about how much does one meter of fencing cost? Explain you answer. 41. In a group of workers at a factory, there are 16 males out of 120 people. What is the ratio of male to female as a fraction in simplest form? A. B. C. D.

2/13 2/15 13/2 15/2

42. Assuming all of the following give you the same quality, which one is the best unit price? A. B. C. D.

216

Supermarket A gives you 5 pounds of oranges for $2.99. Supermarket B gives you 3 pounds of oranges for $1.29. Supermarket C gives you 6 pounds of oranges for $2.88. Supermarket D gives you 9 pounds of oranges for $4.50.

Practice FCAT Math 3

43. As described by the illustration, Alexandra is adding 5 meters to the length, and 5 meters to the width of her 40-meter by 30-meter rectangular room. Which of the following expressions best represents the area of room that will be added to the garden? 5m

30 m

5m

A. B. C. D.

40 m

(30 + 5)(40 + 5) (30 – 5)(40 – 5) (30 + 5)(40 + 5) – (30)(40) (30 – 5)(40 – 5) – (30)(40)

44. Oscar is planning a 6,000 mile round trip in an automobile. He has available five tires for his automobile to be used during this round trip. Also, he knows that he can only use four tires at any time, so he is planning to interchange them so that each tire is used the same number of miles in his round trip. What is the number of miles each tire will be used in this round trip? Explain how you found you answer. 45. You roll a fair six-sided die once. What is the probability that you will roll 4, 5, or 6? Express your answer as a fraction.

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46. A group of students were asked about their favorite sport. Their answers are represented in the following circle graph. Which section of the circle graph has an angle of 63°?

Baseball 9 Football 19 Basketball 7

Softball 5

A. B. C. D.

softball football baseball basketball

47. The diameter of a bicycle wheel is 35 inches long. About how far does this bicycle wheel travel in 120 revolutions of the wheel? Use 3.14 for π.

35 in

A. B. C. D.

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Practice FCAT Math 3

48. Philip wants to resize an 8-inch wide by 12-inch long photograph. The resized photo needs to be 3 inches wide. What is the length of the resized photograph in inches?

x

12 in

3 in

8 in

A. B. C. D.

2 inches 4.5 inches 32 inches 5 inches

49. Which of the following is a true statement? A. B. C. D.

All trapezoids are similar. All rhombi are similar. All squares are similar. All triangles are similar.

50. What is the perimeter of a nonagon with sides equal to 25.7 inches? A. B. C. D.

231.3 inches 257 inches 205.6 inches 179.9 inches

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Part II: FCAT Math Test

Answer Key for Practice Test 3 1. D 2. B 3. A 4. C 5. 95.057 6. D 7. A 8. 45.71 cm 9. 90 cm2 10. D 11. C 12. B 13. C 14. D 15. A 16. B 17. D 18. C 19. D 20. B 21. 10 hours per day 22. C 23. A 24. D 25. A 26. B 27. A 28. 72.8 percent 29. D 30. B 31. A 32. C 33. B 34. 153 35. A

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Practice FCAT Math 3

36. C 37. 25% 38. B 39. C 40. 29 meters of fencing; $15 per meter 41. A 42. B 43. C 44. 4,800 miles 45. 1/2 46. D 47. A 48. B 49. C 50. A

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Part II: FCAT Math Test

Solutions for Practice FCAT Math 3 Use these answers and explanations to help you understand possible solutions and improve your test-taking ability. You should not take more that one practice exam per day. You need some wait time before taking and reviewing the other practice exams (at least one day). You might have used a different path for your solution. This is okay; if you get to the same answer and the procedures you used are mathematically accurate, you don’t need to have the same solution process. It is good to also learn other ways to solve the problem. 1. The best choice for this item is D. You need to examine each of the alternatives: A. 32 = 9 > 3 B. (1.3) 2 = 1.69 > 1.3 C.

–

0.032 = 0.0009 > –0.03 (A negative number times a negative results in a positive number.)

D. 0.32 = .09 < 0.3 2. The best choice for this item is B. First, you need to notice that the length of the side of the triangle needs to be converted from yards to feet: 3 yards = 9 feet. Second, you need to find the height of the right triangle by using half the base of this triangle ( 1 (9 ft) = 4.5 ft) and by using the Pythagorean Theorem: c2 = a2 + b2; 32 = (4.5)2 + b2; 81 = 2 20.25 + b2; 81 – 20.55 = b2; then b is equal to the square root of 60.45, which is approximately equal to 7.77 ft. The volume of the figure is 1 bh ⋅ 24 = 1 (7.77 ⋅ 9) ⋅ 24 ≈ 839.16 cubic feet. 2 2 3. The best choice for this item is A. You need to solve the expression: 27(–3)–2 – (–3)0 27(–3) –2 – 1 27(–3)–2 – 1 27 c 1 m – 1 9 3–1=2

First, solve (–3)0 = 1. Any number to the zero power is equal to 1. Second, solve (–3)–2 = 1/(–3)2 = 1 . 9 This is the same as 27 ÷ 9 = 3.

4. The best choice for this item is C. The sum of the angles of the triangle is equal to 180°. You have two of the angles: 45° + 90° = 135°. Then, you can subtract this sum from 180° to get the measure of the other angle: 180° – 135° = 45°. This implies that this triangle is an isosceles right triangle (the two legs of the triangle are congruent, and one angle is 90°). Notice that the orientation of this right triangle does not affect its characteristics. Using the Pythagorean Theorem, you have that c2 = a2 + b2; c2 = 92 + 92 = 2(92); c = 2 _ 9 2 i = 9 2 cm. 5. This short-answer item is worth two points—one for the answer and one for an acceptable explanation. The area of the shaded area is equal to 110.06 –15 = 95.057 square inches. You need to find the area of the rectangle BGCD: 5 ⋅ 3 = 15 square inches. Also, you need to find the radius of the circle by using the Pythagorean Theorem: c2 = a2 + b2. Notice that the radius of this circle is the same as the diagonal of rectangle BGCD: c2 = a2 + b2; c2 = 52 + 32 = 25 + 9 = 34. This is the same as r2. The area of the whole circle is πr2 = π34 106.76 square inches. 6. The best choice for this item is D. The sum of the measures of the supplementary angle is equal to 180°, the sum of the measures of the complementary angle is equal to 90°, and the angles are adjacent if they have a common vertex and a common side. These two angles do not meet any of these requirements. 7. The best choice for this item is A. A translation or slide involves moving the figure without changing its orientation or size. In other words, no flips and turns are involved in a translation. In this case, Choice A is the only one that involves a slide (translation) without flips and/or turns.

222

Practice FCAT Math 3

8. You need to add the length of all the sides of this figure, including the diagonal with a missing value. You need to use the Pythagorean Theorem to calculate the length of this line segment. The base is equal to 6 cm (15 – 3 – 6 from the other sides), and the height is 3 cm (9 – 3 – 3 from the other sides): c2 = a2 + b2; c2 = 62 + 32 = 36 + 9 = 45; then c is equal to the square root of 45, which is approximately equal to 6.71. This added to the other side lengths is equal to 45.71 cm. Now you need to enter this information in the response grid:

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3 x 15 = 45 cm2

3 cm 3 cm

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Another way to calculate the area of the figure is by dividing it in a different manner as in the following figure. One of them, as before, will include the triangle in the middle with base equal to 6 cm, height equal to 3 cm, and area equal to 1 bh = 1 (6 ⋅ 3) = 1 (18) = 9 cm2. This added to the area of the other two portions (9 × 6 = 54 cm2, 2 2 2 and 3 × 9 = 27 cm2) makes the total area (9 + 54 + 27 = 90 cm2).

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Part II: FCAT Math Test

6 cm 3 cm

9x6= 54 cm2 9 cm

1 2

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(6 x 3) = 9 cm2

3 cm

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You can enter your grid response in one of the following two manners:

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3 cm

Practice FCAT Math 3

10. The best choice for this item is D. You need to find the volume of the complete solid without the indentation (rectangular prism) and then subtract the area of the indentation (triangular prism) from this number. V=l⋅w⋅h

Volume of complete solid figure.

V = 9 ⋅ 8 ⋅ 8 = 576 cm

Substitute values given from the figure.

You now need to find the volume of the triangular prism. You have the values for b = 3 cm and w = 8 cm, but not for the height (one of the legs) of the right triangle. c2 = a2 + b2

You need to calculate the height using the Pythagorean Theorem (b = h). Substitute for c = 3, and a = 3 ÷ 2 = 1.5.

32 = 1.52 + b2 9 = 2.25 + b

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Solve.

9 – 2.25 = 2.25 – 2.25 + b2 2

Subtract 2.25 from both sides of the equation.

6.25 = b

9 – 2.25 = 6.25

6.25 = b

Then b = 2.5 (square root of 6.25 = 2.5).

The volume of the triangular prism is the following: V = 1 (bh) ⋅ w 2 V = 1 (3 ⋅ 2.5) ⋅ 8 2 V ≈ 30 cm3

Substitute for the values you have now. Volume for the triangular prism.

Subtract this number from the total volume of the solid figure: 576 cm3 – 30 cm3 = 546 cm3. 11. The best choice for this item is C. Since the ratio for the cylinders’ radii is 2 : 3, the ratio for their volumes is 23 : 33 or 8 : 27. 12. The best answer for this item is B. You need to use proportions in this problem: 1 cm = 9 cm 3 km x km 1⋅x=9⋅3 x = 27 km

Using the information from the problem, the proportion can be established. Cross multiply the proportion. Road 4 is 27 kilometers in the real neighborhood.

13. The best answer for this item is C. Find the sum of the score and divide by the number of elements in the data set: (80 + 23 + 55 + 58 + 45 + 32 + 40 + 55 + 50) ÷ 9 = 438 ÷ 9 = 48.666... ≈ 49 (rounding to the nearest one). 14. The best choice for this item is D. Order the data set from least to greatest and then find the middle of the data: 23, 32, 40, 45, 50, 55, 55, 58, 80. The middle of the data is 50. 15. The best choice for this item is A. The range of this data set is the difference between the highest score and the lowest score: 80 – 23 = 57. 16. The best choice for this item is B. First, you need to subtract 5/8 from 1 to get the portion of the salary that he saved, which is equal to 3/8 or 0.375 (divide 3 by 8). You could also convert 5/8 to a decimal first (0.625), and then subtract this decimal number from 1: 1 – 0.625 = 0.375. This is the number you need to use to multiply the salary and get the amount saved. 17. The best choice for this item is D. The distance formula is d = rt, where d = distance, r = rate or speed, and t = time. The equation or formula “d = 2r” is the one that represents this relationship. 18. The best choice for this item is C. The probability that Natalie will randomly draw a red marble from the first bag is 2 out of 5 marbles or 2/5. The probability that she will randomly draw an orange marble from the second bag is 3 out of 7 marbles or 3/7. The probability of drawing a red marble and an orange marble on the same draw is 2/5 ⋅ 3/7 = 6 out of 35 = 6/35.

225

Part II: FCAT Math Test

19. The best choice for this item is D. To find the percent, you need to divide 20 by 50, which gives you 0.4 or 40 percent. 20. The best choice for this item is B. You need to work backwards for this one (let x represent the wages last year): x + (x ⋅ 108%) = $9.99 x + (x ⋅ 1.08) = $9.99 x (1 + 1.08) = $9.99 x (2.08) = $9.99 x (2.08) ÷ 2.08 = $9.99 ÷ 2.08 x = $4.80

108% = 1.08 After factoring out x from the equation. 1 + 1.08 = 2.08 Divide by 2.08 on both sides of the equation. 2.08 ÷ 2.08 = 1. The wages last year were about $4.80.

21. This short-answer item is worth two points—one point for the answer and one for an acceptable explanation. He needs to drive about 10 hours per day to make his remaining trip back home in three days. The total number of miles he has driven after nine days is 2,925 miles (9 days × 325 miles per day). He has made part of his trip back home: 4 days × 250 miles per day = 1,000 miles. He has 1,925 miles left of his trip back home: 2,925 miles – 1,000 miles = 1,925 miles left. He wants to make this amount of miles in three days: 1,925 miles ÷ 3 days ≈ 642 miles per day. At 65 miles per hour, he will have to drive for about 10 hours per day in order to make the remaining trip in three days: 642 ÷ 65 ≈ 9.88 or 10 hours per day. 22. The best choice for this item is C. First find the price that you will pay after the price reduction: 20% ⋅ $74.99 = 0.2 ⋅ $74.99 = $14.998 reduction; $74.99 – $14.998 = $59.992 or $59.99 reduced price. Another way to calculate this part of the problem is the following: 100% – 20% = 80% is the portion of the price that you will pay. 80% ⋅ $74.99 = 0.8 ⋅ $79.99 = $59.992 or $59.99 reduced price. Finally, you need to add the sales tax to the reduced price. 8 1 % ⋅ $59.99 = 0.085 ⋅ $59.99 = $5.09932 or $5.10 for sales taxes. 2 $59.99 + $5.10 = $65.09 is the final price paid. Another way to calculate this part of the process is the following: 108 1 % ⋅ $59.99 = 1.085 ⋅ $59.99 = 65.09132 = 65.09, which is the same answer as before. 2 23. The best choice for this item is A. There seems to be a pattern of increasing the amount of buyers every five years. There is also a bigger increase every 10 years. The year 2010 seems to be in one of those cycles. That is why 46 percent seems to be the best prediction.

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Practice FCAT Math 3

24. The best choice for this item is D. Raul and Beth are in the section that represents 90 percent or higher in math and science but not history. All of the combinations are illustrated in the following figure. Math

Math but not history or science

History

History but not math or science Math and history but not science Peter Mary

Elba History and math and science Samuel Math Natalie and science but not history Sarah

History and science but not math

Raul Beth

Mathew Science but not math or history Carlos Peter Science

25. The best choice for this item is A. Three students had 90 percent or above on exactly two exams: Raul (math and science), Beth (math and science), and Mathew (history and science). This is 3 out of 25 students for 12% (3 ÷ 25 = 0.12 = 12%). The rest of the 25 students had 90 percent or above on exactly one exam (math, science, or history), all three exams (math, science, and history), or none of the exams. 26. The best choice for this item is B. You need to solve this expression step by step: –(–32) + (–2)2 – 2

2

First work inside the parentheses: 3 = –3 ⋅ –3 = 9 (a negative times a negative = positive).

–( 3 ) + (–2)

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–(9) + (–2)2

(–2)2 = (–2) ⋅ (–2 )= 4 (a negative times a negative = positive).

–9 + 4 = –5 27. The best choice for this item is A. The cross section of the ball is equal to a circle. The area of the circle is equal to πr2. Since the diameter is equal to 35 cm, the radius is equal to 17.5 cm, and π ≈ 3.14. Substituting in the area formula, you have 3.14 ⋅ (17.5)2 = 961.625 ≈ 962 cm2 (rounded to the nearest square centimeter).

227

Part II: FCAT Math Test

28. You need to divide 2,690 by 3,695, which is equal to 72.8 percent. You need to enter your response (72.8) in the grid.

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29. The best choice for this item is D. Two times the square root of 40 is closest to 12 2 because the square root of 3 40 is between 6 and 7; and two times the square root of 40 is between 12 and 14. The value 12 2 is the closest to 3 this number. You can also find the square root of 40 by using the calculator; this gives you approximately 6.33 or 6 1 . Times two, this is approximately 12.67, or 12 2 . 3 3 30. The best choice for this item is B. Change all the quantities to decimal form (when needed) and compare (or order) them from least to greatest: 3 1 = 3.25, 3 1 = 3.33..., 3 2 = 3.4, and 3 37 ≈ 3.43. The largest is 3.43 or 3 37 . 4 3 5

228

Practice FCAT Math 3

31. The best choice for this item is A. You can solve this problem by using the Pythagorean Theorem: c2 = a2 + b2. You will need to form a right triangle and find the distance for each of the legs of this triangle as in the following figure. This yields the values for a and b: a = 10 units, and b = 4 units. y

b = 4 units

M c=

?

N a = 10 units

x

c2 = 102 + 42 = 100 + 16 = 116; c2 = 2 ⋅ 2 ⋅ 29; c = 2 $ 2 $ 29 = 2 29. (In this case you just simplify; do not solve the square root part.) Another way to solve this problem is by using the distance formula (derived from the Pythagorean Theorem): d2 = (x2 – x1)2 + (y2 – y1)2 d2 = (–5 – 5)2 + (5 – 1)2

Substitute for x- and y-coordinates: (–5, 5), and (5, 1).

d2 = (–10)2 + (4)2

Solve inside the parentheses first.

d2 = 100 + 16 = 116 = 2 ⋅ 2 ⋅ 29 d = 2 $ 2 $ 29 = 2 29

Same answer as with the other method.

32. The best choice for this item is C. The distance formula (derived from the Pythagorean Theorem) can be used to find the measure of the diameter of the circle: d2 = (x2 – x1)2 + (y2 – y1)2 d2 = (–4 – 2)2 + (4 – –2)2

Substitute for x- and y-coordinates: (–4, 4), and (2, –2).

d2 = (–6)2 + (6)2

Solve inside the parentheses first.

d2 = 36 + 36 = 72 d=

72 ≈ 8.49

This is the distance for the diameter. Radius is half this or 4.25.*

The area of the circles is πr2 = 3.14(4.25)2 = 3.14(18.06) = 56.71 square units. You can also leave the diameter in radical form as 6 2 , which make the radius 3 2 (6 2 , ÷ 2). Then, πr2 = 3.14(3 2 ) 2 = 3.14(18) = 56.52 square units.

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Part II: FCAT Math Test

33. The best choice for this item is B. The slope of a line is equal to (change in y) ÷ (change in x). For the given points in this line (–1, 2), and (–2, –1), you have (–1 – 2) ÷ (–2 – –1) = –3 ÷ –1 = 3. 34. The sum of all four angles is 360°. To find the measure of the missing angle, you need to add the measures of the given angles and subtract the sum from 360°: 360 – (87 + 87 + 33) = 360 – 207 = 153. You can enter your grid response in the following manner.

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Practice FCAT Math 3

35. The best choice for this item is A. ∠ACB and ∠BCF are complimentary angles. This means that the sum of their angle measures is equal to 90°. The measure of ∠ACB is equal to 30°. Then the measure of ∠BCF = 90° – 30° = 60°. 36. The best choice for this item is C. There are 4 quarts for every gallon. Since Albert bought 16 gallons of gasoline, then 4 ⋅ 16 = 64 quarts of gasoline. 37. This short-answer item is worth two points—one for the answer and one for an acceptable explanation. Peter had 25% of his income for other expenses and savings. You need to write two equations in terms of the income and expenses of Olga and Peter: Olga’s income (Oi) is 5/8 of Peter’s income (Pi): Oi = 5/8 ⋅ Pi Olga’s expenses (Oe) are 1/2 of Peter’s expenses (Pe): Oe = 1/2 ⋅ Pe The remaining income = income – personal expenses. Olga had 40% of her income after her personal expenses. This means that 40% of Olga’s income is left for other expenses and savings: 40% ⋅ Oi = Oi – Oe. You can write this equation by substituting the values for Olga’s income and Peter’s expenses: 40%(5/8 ⋅ Pi) = 5/8 ⋅ Pi – 1/2 ⋅ Pe 0.4(5/8 ⋅ Pi) = 5/8 ⋅ Pi – 1/2 ⋅ Pe

Substitute for the given values. Substitute 40% for 0.4.

0.25 ⋅ Pi = 5/8 ⋅ Pi – 1/2 ⋅ Pe

Solve: 0.4 ⋅ 5/8 (or 0.625) = 0.25.

0.25 ⋅ Pi = 0.625 ⋅ Pi – 1/2 ⋅ Pe

Substitute 5/8 for 0.625 (5 ÷ 8 = 0.625)

0.25 ⋅ Pi – 0.625 ⋅ Pi = 0.625 ⋅ Pi – 0.625 ⋅ Pi – 1/2 ⋅ Pe 0.375 = 1/2 ⋅ Pe

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Subtract on both sides 0.625 ⋅ Pi. Simplify. Multiply by –1/2 on both sides. Peter’s personal expenses were 0.75 or 75%.

Peter’s leftover income after personal expenses is equal to income – personal expenses, or 100% – 75% = 25%. 38. The best choice for this item is B. In this case, you need to translate the word problem into a mathematical sentence: 3 $ 2 1 = 3 $ 5 = 15 = 1 7 cups of sugar to make the recipe 2 1 times. 4 2 4 2 8 8 2 39. The best answer for this item is C. You have two boxes of cake mix for the recipe: 2(10) = 20 cups available for the recipe. You need to find out how many times 1 1 cups are contained in 20 cups or 20 ÷ 1 1 = 20 ⋅ 5 = 16 4 4 4 times. 40. This is a long-response item, which are four points each. You will receive four points if you answer all parts of the item fully and correctly. You must show understanding of the mathematical ideas presented in this problem. You will receive three points if you make minor errors and show understanding as you solve and explain the solution of the problem. You will receive two points if you make several errors, the explanations are incomplete and not clear, and you do not show proper understanding of the problem. Following is a possible diagram for the problem.

231

Part II: FCAT Math Test

Outside edge d = 132 cm Inside edge

400 cm

For finding the amount of fencing for the outside edge, notice that the radius of the inside circle is 132 cm ÷ 2 = 66 cm, and the radius of the outside circle is 400 cm + 66 cm = 466. Using this information, you can calculate the circumference of the outside circle: 2πr = 2(3.14)(466) = 2926.48 cm. Then you need to subtract 50 cm for the opening: 2926.48 – 50 = 2876.48 cm or about 29 m. For finding the amount of fencing for the inside edge, the circumference of the inside circle is equal to 2πr = 2(3.14)(66) = 414.48 cm. Assuming you will also have an opening of 50 cm, you need to subtract 50 cm from 414.48 – 50 = 364.48 cm or about 4 m. The outside fencing – the inside fencing is equal to 29 m – 4 m = 25 extra meters. The number dollars per meter is equal to $375 ÷ 25 m = $15 per meter. 41. The best choice for this item is A. First, you need to subtract 16 (number of males) from 120 workers: 120 – 16 = 104 female. The ratio of male to female is 16/104 = 2/13 (divide by 8/8 to simplify the fraction). 42. The best choice for this item is B. You need to analyze each of the situations and compare them. A. 5 pounds of oranges for $2.99

$0.598 = $0.60 unit price

B. 3 pounds of oranges for $1.29

$0.43 unit price

C. 6 pounds of oranges for $2.88

$0.48 unit price

D. 9 pounds of oranges for $4.50

$0.50 unit price

Choice B gives you the best unit price for the oranges. You save from 5 cents to 17 cents per pound. 43. The best choice for this item is C. You need to find the area of the room with the new dimensions added: (30 + 5)(40 + 5). Then subtract the area of the room before expansions: (30 + 5)(40 + 5) – (30)(40). 44. This short-answer item is worth two points—one for the answer and one for an acceptable explanation to earn two points. Each tire will be used 4,800 miles. To find the total number of miles traveled, you need to think about the number of miles traveled by the four tires. Each tire travels a number of miles independently. Then at a given time, the automobile has traveled a given amount of miles, and you need to multiply that by 4. For example, if Oscar has traveled 1,000 miles, the four wheels have traveled together 4 × 1,000 miles = 4,000 miles. In other words, for this 6,000 miles roundtrip, the tires would have traveled 4 × 6,000 miles = 24,000 miles; then each tire should travel 1/5 of this amount: 1/5 of 24,000 miles = 4,800 miles for each tire. Also, one of the tires should be interchanged every 1,200 miles (or intervals of 1,200 miles). You can also think that each tire will be used for 4/5 of the trip: 4/5 ⋅ 6000 = 4,800 miles. See the table as a way to organize the miles traveled by the tires:

232

Practice FCAT Math 3

Miles Traveled by the Automobile

Miles Traveled by Tire #1

Miles Traveled by Tire #2

Miles Traveled by Tire #3

Miles Traveled by Tire #4

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1,200 miles

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Not in use

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45. The probability of rolling a 4 after one roll is 1/6. The same is true for rolling a 5 or 6 on the same roll. The probability that you will roll 4, 5, or 6 after one roll is 1/6 + 1/6 + 1/6 = 3/6 = 1/2. You can also think of 6 possible outcomes with 3 desirable ones, 3 out of 6 = 3/6 = 1/2.

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233

Part II: FCAT Math Test

46. The best choice for this item is D. You should find the percentage for each value and multiply this percent by 360° (total number of degrees for the complete circle). Since you have a total of 40 students participating in the survey (from the graph, we have 19 + 9 + 7 + 5 = 40 total): A. Softball

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The sum of these degrees should be equal to 360: 45° + 171° + 81° + 63° = 360°. 47. The best choice for this item is A. First, you need to find the circumference of the wheel: C = 2πr or C = πd. If you use the C = 2πr, you need to use r = 35/2 = 17.5. Using π = 3.14, you have that the distance the wheel travels is equal to 120 revolutions ⋅ C = 120 ⋅ 2π(17.5) = 120 ⋅ 2(3.14)(17.5) = 13,188 inches. You need to convert this distance to feet by dividing by 12 (number of inches in one foot): 13,188 ÷ 12 = 1,099 feet. 48. The best choice for this item is B. You need to set a proportion. One of the four ways to set the proportion is the following: 12 = x 8 3 12 ⋅ 3 = 8x 36 = 8x 36 ÷ 8 = 8 ÷ 8x 4.5 = x

Cross multiply. 12 ⋅ 3 = 36 Divide by 8 on both sides of the equation. The length will be equal to 4.5 inches.

49. The best choice for this item is C. You should check each statement: A. All trapezoids are similar.

Not a true statement, only some trapezoids are similar.

B. All rhombi are similar.

Not a true statement, only some rhombi are similar.

C. All squares are similar.

A true statement, all squares are similar.

D. All triangles are similar.

Not true, only some triangles are similar.

50. The best choice for this item is A. A nonagon has nine sides. The perimeter is 9 times 25.7 = 231.3 inches.

234

Practice FCAT Math 4 Remember to read and follow the instructions carefully. You have two and a half hours to complete the test. You may want to take a short break in the middle of the test.

First Part of Practice FCAT Math 4 1. Robert has 6 boxes of 25 apples each and 4 boxes with 30 oranges each. Which expression does not represent the total number of fruits Robert has? A. B. C. D.

4 ⋅ 30 + 6 ⋅ 25 10(25 + 30) 30 + 30 + 30 + 30 + 25 + 25 + 25 + 25 + 25 + 25 30(4 + 5)

2. Select the expression that could be used to find the cost of buying b baseballs each at $30, s baseball shoes each at $55, and u baseball uniforms each at $125. A. B. C. D.

b+s+u 30 + 55 + 125 (b + s + u)(30 + 55 + 125) 30b + 55s + 125u

3. At a school, a principal can accommodate about 365 students per large classroom. The school has 9 large classrooms, and she has scheduled 5 classes a day at each large classroom. How many people could have been accommodated in these large classrooms after 25 days? A. B. C. D.

127,750 people 16,425 people 410,625 people 3,285 people

235

Part II: FCAT Math Test

NOTE: Use the following graph to answer items 4 and 5.

Time in Minutes and Seconds

Length of Songs in a CD Given in Minutes and Seconds 7 6 min 0 s

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4. What is the approximate average number of minutes for the songs included in the preceding graph? (Approximate your answer to the nearest hundredth.) A. B. C. D.

4.7 minutes 33.5 minutes 3.5 minutes 26.5 minutes

5. If you want to burn a 26-minute CD using the songs given in the graph, which of the following group of songs should be selected? A. B. C. D.

A, B, C, D, E, and F A, B, C, D, E, F, and G B, C, D, E, and F A, B, C, D, F, and G

6. Alicia opened a new bank account in June this year. She started with a deposit of $300, and deposited $250 each month after that. How much money would she have deposited by December of the same year? Explain your answer. 7. Robert read 20 pages of a 420-page novel on Saturday. He plans to read twice as many pages on Sunday as he read on Saturday. Then he plans to read twice as many pages on Monday as he read on Sunday. He wants to continue this routine of reading twice as many pages as he read on the previous days until he reads the whole book. On what day will he finish the novel? A. B. C. D.

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Monday Tuesday Wednesday Thursday

Practice FCAT Math 4

NOTE: Use the line plot for items 8, 9, and 10. The graph represents the students’ scores on an exam with 35 items.

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10. What is the median of the data set? A. B. C. D.

30 29.5 26.5 29

237

Part II: FCAT Math Test

11. Which of the following represents 63.5 million in scientific notation? A. B. C. D.

6.35 × 106 0.635 × 106 6.35 × 107 6.53 × 101

12. The value of a stock went down $5 each week for a period of 10 weeks. Which of the following represents this change in value of the stock at the end of 10 weeks? A. B. C. D.

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13. Isabel can make 3 free throws out of every 5 attempts. What number of free throws will she make after 30 attempts?

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14. What is the slope of the line on the following graph that passes through (–2, 3) and (–1, 2)? A. B. C. D.

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15. Which of the following has a slope of 2? A. y 6 5 4 3 2 1 -6

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C. y 6 5 4 3 2 1 -6

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16. As illustrated, you have two concentric circles. The one inside represents the circumference of the earth, which is approximately 25,000 miles. The other circle around the circumference of the earth is 10 feet larger . What is the approximate distance (n) between these two concentric circles? Use π = 3.14 and round your answer to the nearest hundredth.

n = distance between circles r Earth

A. B. C. D.

3.98 miles 3.98 feet 1.59 feet 1.59 miles

17. Find the prime factorization of 126. A. B. C. D.

22 ⋅ 3 ⋅ 7 2 ⋅ 32 ⋅ 7 2 ⋅ 3 ⋅ 72 22 ⋅ 32 ⋅ 72

18. Robert is painting a wall in his house. The wall is 7 feet long by 10 feet wide. He has already painted 49 square feet of the wall. What percent of the wall remains unpainted? A. B. C. D.

30% 70% 43% 51%

19. Maria has a bucket that is 7/9 full of sand for a project, but she fell down and lost some of the sand in the bucket. After this accident, she only had 1/6 of a bucket of sand left. How much sand did Maria lose? A. B. C. D.

8/15 17/18 11/18 1/9

20. A bus can carry up to 7,000 pounds of passengers (without counting other weight for bags and other belongings). Which of the following is the best estimate for the number of adults who can travel in one trip? A. B. C. D.

40 adult passengers 80 adults passengers 35 adults passengers 10 adults passengers

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21. Armando is having a party at his house, and he is serving hamburger patties. Hamburger patties come in packages of 10, and hamburger buns come in packages of 8. If Armando wants to have the same amount of hamburger patties as hamburger buns, what is the least amount of each that he will have to buy? Explain how you found the answer. 22. Rose wants to use a can of concentrated grape juice that makes 48 fluid ounces. How many pints would she be able to make? A. B. C. D.

4 pints 3 pints 6 pints 12 pints

23. Roger’s rectangular lot has a perimeter of 41.5 feet (see figure). What is the width of his lot?

4.75 feet

Length

A. B. C. D.

64 feet 36.75 feet 32 feet 16 feet

24. It takes 3/4 cup of butter to make one batch of cookies. How much butter would it take to make 2 1 batches of 2 cookies? A. B. C. D.

1 1 2 3 1 4 7 1 8 2

25. Find the unit price per orange if it costs $2 for six oranges. Round to the nearest hundredth if necessary. A. B. C. D.

$3.30 per orange $0.33 per orange $3.00 per orange $1.00 per orange

You may take a short break (optional 5 or 10 minutes) but must complete the test on the same day.

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Second Part of Practice FCAT Math 4 Continue the test. Remember to read and follow the instructions carefully. You have 70 minutes to complete the test. 26. Two-thirds of a $4 million deal will go to the realty company. What percent of the money will go to the realty company? A. B. C. D.

23 2 % 3 33 2 % 3 2 66 % 3 2 2 % 3

27. A house has increased in value by 124 percent over 5 years. Which of the following is this percent written as a decimal? A. B. C. D.

1.24 12.4 0.124 0.00124

28. A type of rope costs $16 per yard, and a second type of rope costs $6 per yard. If I bought 12 yards of the second type of rope and 9 yards of the first type of rope, what is the total cost of the ropes together?

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29. A mountain bike costs $299 plus a 9.5 percent service charge and a 4.5 percent delivery charge. What is the cost of the bike including service and delivery charges? A. B. C. D.

$340.86 $4,186.00 $418.60 $717.60

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30. On a map, the distance between two cities is 10.5 cm. If the scale is 1 cm = 250 kilometers, what is the actual distance between these two cities? A. B. C. D.

26.25 kilometers 23 kilometers 2,625 kilometers 230 kilometers

31. Carla opened a new saving account that pays 6.5 percent simple interest. How much money will be in Carla’s account after 3 years if she deposited $250 at the beginning and did not make any other deposits? A. B. C. D.

$248.75 $48.75 $300.00 $298.75

32. Diana needs to make a visit from her home to three other places and come back home at the end. She needs to visit the Eola’s Park, the Orlando Mall, and the area high school, not necessarily in that order. The following figure shows the setup for and distance between these places. Which of the following routes should she select if she wants the shortest one? Diana's Home

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High School

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33. Peter made a set of 20 cards with the numbers 1 through 20, respectively (see following figure). After shuffling them, he asked David to pick a card at random without looking at the cards. What is the probability that the card David selects has a number that is not a factor of 10? 12

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34. A gallon of milk had 56 fluid ounces left. Carl drank 24 fluid ounces of this milk. What fraction of the 56 ounces of milk did he drink? Enter your answer as a fraction in simplest form.

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35. If Carmen wants to have a three-course lunch (only one of each), how many combinations are possible if she has two choices of appetizer (soup or salad), three choices of main entrée (steak, chicken, or fish), and two choices of dessert (ice cream or cake)? A. B. C. D.

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36. Doris placed four marbles in a bag: two blue, one red, and one yellow. If she randomly selects one marble from the bag, what is the probability that she gets a blue marble? A. B. C. D.

3/4 1/2 2/3 1/4

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37. A packing company is designing a box to package 36 cans. They need to decide what dimensions they want to use for the box. For example, they can use a box that is 1 can high, 6 cans wide, and 6 cans long, or 1 ⋅ 6 ⋅ 6 for 36 cans (see figure).

How many different ways can the packing company arrange the 36 cans and make the boxes? Explain your answer. 38. You have two bags of marbles. The first bag has two red, one yellow, and two green. The second bag has two blue, two black, and one purple. What is the probability that you will draw a yellow marble from the first bag and a purple marble from the second bag? A. B. C. D.

1/25 1/50 1/5 2/25

39. What is the measure of an obtuse angle? A. B. C. D.

37° 120° 89° 68°

40. Juanita opened a new savings account at a bank one month. She started with an $80 deposit and deposited $20 each month after the first month. After a few months, she had $200 in her account by August. What month did she start her savings account? Explain you answer in detail.

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41. The table that follows provides data related to ticket sales for a concert in the months of January, February, March, and April. If you have to construct a circle graph using the data given in this table, which section would have an angle measure of about 50°? Tickets Sold Per Month

Quantity

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6,438

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10,262

March

8,700

April

34,600

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April January February March

42. Classify the pair of angles illustrated in the figure as supplementary, complementary, adjacent, or not complementary, supplementary, or adjacent.

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43. As illustrated in the figure, the measure of the external angle at B is equal to 125°, and the measure of angle ACB is equal to 60°. What is the measure of angle BAC? A

125° B

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60° C

55° 65° 165° 60°

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44. Using a discount coupon, Dora bought a $35 meal at a restaurant for $27.30. What was the percent of decrease from the original price to the discount price she was able to get? Explain how you found your answer. 45. The following table provides information about students at a school’s favorite sport. What is the probability that a student’s favorite sport is basketball? Enter your answer as a fraction in lowest terms. Favorite Sport

Number of Students

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Football

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Softball

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46. Find the m∠A in parallelogram ABCD if m∠D = 87°. A. B. C. D.

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47. Which one of the following shapes has line symmetry? A.

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48. Aurora has a square garden in front of her house. Her garden has an area of 1,156 m. Find the perimeter of her garden. A. B. C. D.

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50. Mrs. Harper completely wrapped a cylinder for a poster. The cylinder is 36 inches in height with a diameter of 3 inches. About how much wrapping paper did Mrs. Harper need? A. B. C. D.

734.76 cm2 14.13 cm2 339.12 cm2 353.25 cm2

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Answer Key for Practice Test 4 1. B 2. D 3. C 4. A 5. C 6. $1,800 7. B 8. 27.63 or 27.62 9. A 10. D 11. C 12. A 13. 18 14. C 15. D 16. C 17. B 18. A 19. C 20. A 21. Four packages of hamburger patties and five packages of hamburger buns 22. B 23. D 24. C 25. B 26. C 27. A 28. $216 29. A 30. C 31. D 32. B 33. A 34. 3/7 35. D

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36. B 37. A. The packing company can make 9 different types of boxes. B. They can 10 combinations of cans. 38. A 39. B 40. She started in the month of February. 41. D 42. A 43. B 44. 22% 45. 15/51 46. C 47. D 48. A 49. B 50. D

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Solutions for Practice FCAT Math 4 Use these answers and explanations to help you understand possible solutions and improve your test-taking ability. You should not take more that one practice exam per day. You need some wait time before taking and reviewing the other practice exams (at least one day). You might have used a different path for your solution. This is okay; if you get to the same answer and the procedures you used are mathematically accurate, you don’t need to have the same solution process. It is good to also learn other ways to solve the problem. 1. The best choice for this item is B. You need to take a look at each one of the possible answers: A. 4 ⋅ 30 + 6 ⋅ 25 = 6 ⋅ 25 + 4 ⋅ 30 = 270

This is the same as 6 times 25 and 4 times 30.

B. 10(25 + 30) = 550 ≠ 270

This is the only incorrect answer.

C. 30 + 30 + 30 + 30 + 25 + 25 + 25 + 25 + 25 + 25

This is the same as 4 times 30 plus 6 times 25.

D. 30(4 + 5) = 30 ⋅ 9 = 270

This one has all the factors out and is correct.

2. The best choice for this item is D. 3. The best choice for this item is C. You need to multiply the number of students times the number of classrooms times the number of classes times the number of days: 25(5(9 ⋅ 365) = 410,625 people. 4. The best choice for this item is A. The sum of the minutes and seconds is 33 minutes and 30 seconds, which is approximately 33.5 (30 seconds is about 0.5 of a minute). The average number of minutes is this number divided by 7: 33.5 ÷ 7 = 4.7 minutes. 5. The best choice for this item is C. Remember to be careful with the addition of the seconds (60 seconds equals a minute). You need to check the sum for each one to see which is nearest or equal to 26 minutes: A. A, B, C, D, E, and F: Sum equal to 25 minutes 30 seconds. B. A, B, C, D, E, F, and G: Sum equal to 33 minutes 30 seconds. C. B, C, D, E, and F: Sum equal to 26 minutes. D. A, B, C, D, F, and G: Sum equal to 28 minutes 15 seconds. 6. This short-answer item is worth two points—one point for the answer and one point for an acceptable explanation This is the possible solution for this short-response item: She will have $1,800. She saved $300 in June to begin the account plus the money saved in July, August, September, October, November, and December at $250 each. This is $300 + 6($250) = $300 + $1,500 = $1,800. 7. The best choice for this item is B. You need to find the progression of pages for each day and how they add up: Saturday: 20 pages Sunday: 2 ⋅ 20 = 40 pages: 20 + 40 = 60 total pages read so far. Monday: 2 ⋅ 40 = 80 pages: 20 + 40 + 80 = 140 total pages read so far. Tuesday: 2 ⋅ 140 = 280 pages: 20 + 40 + 80 + 280 = 420 total pages for the whole 420-page novel. 8. The mean of this data set is 27.625, which is approximately 27.63 or 27.62. This is the sum of all the measures divided by the total number of measures: 442 ÷ 6. You can enter your grid response in the following manner.

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9. The best choice for this item is A. The mode of this data set is 30, which is the most frequent measure with three scores. 10. The best choice for this item is D. The median is the middle of the data set. Since we have 16 measures, the middle is the 8th measure. You need to count 8 from left to right and 8 from right to left. The middle measure is 29. 11. The best answer for this item is C. You need to move the decimal point to the ones place in the number. This requires moving the decimal point 7 times to the left because 63.5 million is equal to 63,500,000. 12. The best answer for this item is A. The change in value is 10 times –5 = –50, where v represents the initial value of the stock, and the negative sign represents a drop in value.

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13. She will probably make 18 free throws out of 30 attempts. This can be solved by using proportions: 3= x 5 30 3 ⋅ 30 = 5x

x represents the number of shots she made. Cross multiplication.

90 = 5x

3 ⋅ 30 = 90

90 ÷ 5 = 5x ÷ 5

Solve for x.

18 = x You can also find and continue the pattern by using a table like the following or find a rule (3n/5). Attempts

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14. The best choice for this item is C. The slope is change in y over change in x. The slope of the line that passes through (–2, 3) and (–1, 2) is equal to –1: (2 – 3) ÷ (–1 – –2) = –1/1 = –1. 15. The best choice for this item is D. Just by looking at graphs in items A and B, you can notice that they have negative slopes. Also, you can notice that since all graphs pass through the origin, you can use one of the points and (0, 0) as the other to calculate the slope (change in y over change in x). For the graph in item C, (0, 0) and (4, 2), which yields (2 – 0) ÷ (4 – 0) = 2 ÷ 4 = 1/2 = 0.5. This is not equal to a slope of 2. For the graph in item D, (0, 0) and (2, 4), which gives us (4 – 0) ÷ (2 – 0) = 4 ÷ 2 = 4/2 = 2. This is equal to a slope of 2. 16. The best choice for this item is C. You know that the C = 2πr. You could solve this problem by subtracting 25,000 miles from 25,000 + 10 feet, which is equal to 10 feet. Then you can divide 10 feet by 2π to get the distance (n) between the two concentric circles = 10 feet ÷ 2π = 10 feet ÷ 2(3.14), which is approximately 1.59 feet. You can also convert the feet to miles, add that to 25,000 miles, subtract 25,000 miles, and then divide by 2π, which gives the same answer. 17. The best choice for this item is B. You can multiply each alternative and 2 ⋅ 32 ⋅ 7 = 2 ⋅ 9 ⋅ 7 = 126, which is the correct value for this item. 18. The best choice for this item is A. He has painted 0.7 or 70% of the wall (49 ÷ 70). He still needs to paint 30% of it (100% – 70%). He can also start by subtracting 49 feet from 70 feet, which leaves the amount of unpainted wall: 70 – 49 = 21. This number divided by 70 gives you the percent of unpainted wall: 21 ÷ 70 = 0.3 or 30%. 19. The best choice for this item is C. You need to subtract to solve this problem: 7/9 – 1/6 = 14/18 – 3/18 = 11/18. 20. The best choice for this item is A. If you assume that the adult passengers can weigh 100 pounds each, you will be underestimating because the average weight for adults is higher. Forty is a better estimate if you assume an average weight of about 160 to 170 pounds.

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21. This short-answer item is worth two points—one point for the answer and one point for an acceptable explanation. Four packages of hamburger patties and five packages of hamburger buns is the least amount he needs to buy in order to have the same amount for each. You can solve this by finding the least common multiple (LCM) of 8 and 10. You can do this by finding the nonzero multiples of 8 and 10 and selecting the least common multiple for them: Multiples of 8:

8, 16, 24, 32, 40, 48, . . .

Multiples of 10:

10, 20, 30, 40, 50, 60, . . .

This means that after 5 packages of hamburger buns and 4 packages of hamburger patties, he will have the same amount for both. You can also find the LCM of 8 and 10 by using prime factorization: 8 = 2 ⋅ 2 ⋅ 2 = 23 10 = 2 ⋅ 5 = 21 ⋅ 51 LCM = 23 ⋅ 5 = 8 ⋅ 5 = 40 22. The best choice for this item is B. You need to start by knowing that 1 pint is equal to 16 ounces: 48 ounces ÷ 16 ounces = 3 pints. 23. The best choice for this item is D. Perimeter is equal to the sum of the measures of the sides. For a rectangle, we have that P = 2a + 2b because each pair of sides is equal. In this case, you have the following: 41.5 = 2(4.75) + 2(w)

In this situation, w is the length of the width.

41.5 = 9.5 + 2(w)

2 ⋅ 4.75 = 9.5

41.5 – 9.5 = 9.5 – 9.5 + 2(w) 32 = 0 + 2(w) 32 ÷ 2 = 2(w) ÷ 2

Subtract 9.5 from both sides of the equality. 41.5 – 9.5 = 32, and 9.5 – 9.5 = 0 Divide both sides of the equality by two.

16 = w 24. The best choice for this item is C. She needs to multiply 2 1 times 3/4: 5/2 ⋅ 3/4 = 15/8 = 1 7/8. 2 25. The best choice for this item is B. You have $2.00 for six oranges. $2.00 6 oranges

Write the rate as a fraction.

$2.00 ' 6 6 oranges ' 6

Divide the numerator and denominator by 6.

$0.33 1 orange

Simply, it will cost about $0.33 per orange.

26. The best choice for this item is C. We know that 2/3 = 0.666 ... = 66 1 % 3 27. The best choice for this item is A. You need to move the decimal point two places to the left.

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28. You need to add the cost for each type of rope: 16 ⋅ 9 + 12 ⋅ 6 = 144 + 72 = $216. You can enter your grid response in the following manner.

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29. The best choice for this item is A. You can solve this problem in several ways. One of them is the following set of procedures: $299 + 9.5%($299) + 4.5%($299) = $299 + 0.095%($299) + 0.045%($299) = $299 + $28.405 + $13.455 = $340.86. Another way to solve this problem is the following: $299 + (0.095 + 0.045)$299 = $299 + (0.14)$299 = $299 + $41.86 = $340.86.

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Practice FCAT Math 4

30. The best choice for this item is C. You need to set up a proportion and solve for n: 1 cm = 10.5 cm n km 250 km

n represents the number of kilometers.

1cm ⋅ n = 250 ⋅ 10.5

Find the cross products.

n = 2,625

Simplify.

The actual distance is 2,625 kilometers. 31. The best choice for this item is D. Simple interest is the amount of money earned or paid for the use of money: Interest (I) is equal to principal (p = the amount of money deposited or invested), multiplied by rate (r = annual interest rate written as a decimal), multiplied by time (t = amount of time that money is invested or borrowed in years), or I = prt. In this problem we have that p = $250, r = 0.065, and t = 3 years, the I = 250 ⋅ 0.065 ⋅ 3 = 48.75. Then Carla will have $250 + 48.75 = $298.75 after three years, assuming she did not make any other deposits. 32. The best choice for this item is B. One easy way to answer this question is to remember the fact that the shortest distance between two vertices on a right triangle is the hypotenuse. 33. The best choice for this item is A. Ten has 4 factors: 1, 2, 5, and 10. The other 16 numbers are not factors of 10: 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20. Then the probability of David selecting a number that is not a factor of 10 is 16/20 or 4/5. Another way to solve this problem is by saying that the probability of David selecting a number that is a factor of 10 is 4/20 or 1/5. Then the probability of selecting a number that is not a factor of 10 is 1 – 1/5 or 4/5. Either way, you get the same answer. 34. One gallon is equal to 128 fluid ounces (this is given in the FCAT Mathematics Reference Sheet). Carl drank 24 fluid ounces of the remaining 56 fluid ounces of milk. Then he drank 24/56 = 3/7, in simplest form. You can enter your grid response in the following manner.

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You can also enter the answer in the following manner:

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35. The best choice for this item is D. One way to solve this problem is by finding the possible lunch combinations available to Carmen. This list should be made in a systematic manner. A tree diagram could be used for this purpose. A tree diagram is used to show all the possible combinations. The following figure illustrates a tree diagram for this item. steak soup

chicken

ice cream cake ice cream cake

fish

ice cream cake

steak salad

chicken

ice cream cake ice cream cake

fish

ice cream cake

You can count 12 different combinations for Carmen’s lunch, or 2 ⋅ 3 ⋅ 2 = 12 combinations. 36. The best choice for this item is B. The probability that Doris selects a blue marble is 2 out of 4 = 2/4 = 1/2.

260

Practice FCAT Math 4

37. This short-answer item is worth two points. You need to have an acceptable explanation to earn two points. Each part is worth one point. This is the possible solution for this short-response item. A. The packing company can make 9 different types of boxes. B. They can make the following combination of cans: 1 ⋅ 1 ⋅ 36

1⋅4⋅9

2⋅3⋅6

1 ⋅ 2 ⋅ 18

1 ⋅ 6 ⋅ 6 (given)

3⋅3⋅4

1 ⋅ 3 ⋅ 12

2⋅2⋅9

3⋅2⋅6

3 ⋅ 1 ⋅ 12

38. The best choice for this item is A. These are two independent events. The probability of drawing a yellow marble from the first bag is 1/5. The probability of drawing a purple marble from the second bag is also 1/5. Then the probability of drawing a yellow from the first bag and a purple from the second bag is 1/5 ⋅ 1/5 = 1/25. 39. The best answer for this item is B. An obtuse angle is any angle that measures more than 90°. 40. This is a long-response item, which are four points each. You will receive four points if you answer all parts of the item fully and correctly. You must show understanding of the mathematical ideas presented in this problem. You will receive three points if you make minor errors and show understanding as you solve and explain the solution of the problem. You will receive two points if you make several errors, the explanations are incomplete and not clear, and do not show proper understanding of the problem. She started in the month of February. The following is a possible explanation for the problem. You need to start with the money she has now in her account: $200. Then you need to subtract $80 from this amount, which is the amount she started with and will give the total amount saved month by month after the first deposit: $200 – $80 = $120. You need to divide this amount by $20, which the amount saved each month: $120 saved ÷ $20 per month = 6 months. Counting the months backward, you have August, July, June, May, April, and March. You have that March is six months ago. However, you need to count one more month back since she started a month before that, or February. 41. The best choice for this item is D. You need to find the total number of tickets sold for the four months listed (60,000 tickets), find the percent of tickets sold for each month, and, finally, find the number of degrees for each one of the months (see table). The month that requires about 50° in the circle graph is March. Tickets Sold Per Month

Quantity 60,000

Percent (100%)

Degrees (360°)

January

6,438

11%

40°

February

10,262

17%

61°

March

8,700

14%

50°

April

34,600

58%

209°

42. The best choice for this item is A. These angles are not complementary, supplementary, or adjacent. Two angles are complementary if the sum of their measures is 90°, supplementary if the sum of their measures is 180°, and adjacent if they have a common vertex and a common side. 43. The best choice for this item is B. The measure of angle ABC is 55° because it is supplementary to an angle that measures 125° (180° – 125° = 55°). Now you have the measure for two of the angles inside triangle ABC. The sum of the measure of angles of a triangle is 180°. Then, using the measures of the angles we have so far we have 180° – (60° + 55°) = 180° – 115° = 65°.

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Part II: FCAT Math Test

44. This short-answer item is worth two points—one point for the answer and one point for an acceptable explanation. The percent of discount from the original price to the discount price was 21% or 22%. You have that $35 – $27.50 = $7.50. The percent of discount is then 7.50 ÷ 35 = 0.21428571, or about 21%. Alternately, you paid 78 percent of the original price: 27.30 = 100 ⋅ 27.30 = 35 (Percent of regular price)

35 $ _ Percent of regular pricei . 100 Cross multiply.

2730 _ Percent of regular pricei = 35

Divide.

Percent of regular price = 78% 100% – 78% = 22%

Find percent decrease by subtraction.

45. You need to find the total number of students at this school: 510. The probability for a student’s favorite game is basketball is 150/510 = 15/51. You can enter your grid response in the following manner.

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46. The best choice for this item is C since ABCD is a parallelogram, m∠D = m∠ B, and m∠A = m∠C (see illustration). In this case, 87° is close to 90° but is not the same as a right angle or it does make a rectangle. Also, the length and width of the parallelogram are not relevant to this case. It does not matter how long or short they are; the measure of the angles will stay the same. However, you know that the measure of segment AB is equal to the measure of segment DC, as well as AD and BC are equal; and line segment AB is parallel to line segment DC, as well as AD and BC are parallel. The sum of the measures of the angle in a parallelogram = 360°. Then you have the following relationship between the angles:

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Practice FCAT Math 4

m∠D + m∠B + m∠A + m∠C = 360° 87° + 87° + m∠A + m∠C = 360° 174° + m∠A + m∠C = 360° 174° – 174° + m∠A + m∠C = 360° – 174°

Substitute the measures of angles D and B. Sum of 87° + 87° = 174º Subtract 174° from both sides of the equality.

m∠A + m∠C = 186°

174° – 174° = 0° and 360° – 174° = 186°

m∠A + m∠A = 186°

m∠A = m∠C, then you can substitute m∠A for m∠C.

2(m∠A) = 186° 2(m∠A) ÷ 2 = 186º ÷ 2 m∠A) = 93°

m∠A + m∠A = 2(m∠A) Divide by 2 both sides of the equality. Simplify.

A

B ?

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47. The best choice for this item is D. Figures that match exactly when folded in half have line symmetry. In some cases, a figure might have more than one symmetry line. Each of this type of lines is called a line of symmetry. The only figure in this item that has line symmetry is the one in Choice D, which is a regular pentagon that has 5 lines of symmetry (see figure). 1 2

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48. The best choice for this item is A. Since Aurora’s garden forms a square shape, all sides are equal. In this case, area of the square is equal to a2, where a is equal to the length of the sides. Since A = 1,156 m2, then a2 = 1,156 m2. You need to find the square root of 1,156 m2 to get the length of a, which is equal to 34 m. Then you need to multiply that quantity by 4 to get the perimeter of the square: 4 ⋅ 34 m = 136 m.

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Part II: FCAT Math Test

49. The best choice for this item is B. You can divide the solid in two sections and find the measures for the missing line segments (see figure). One could be the cube on the left side, and the other the rectangular solid on the right side. Find the volume of each and add them together. Volume of the cube is 8 ⋅ 8 ⋅ 8 = 512 cm3. Volume of the rectangular solid is the following: (26.5 – 8) ⋅ 12.5 ⋅ 8

The base is equal to 26.5 – 8, height = 12.5, and width = 8.

18 ⋅ 12.5 ⋅ 8

Solve: 26.5 – 8 = 18.

1,800 cm3

The product and volume of the rectangular solid = 1,800 cm3.

The volume for the whole solid is 512 cm3 + 1,800 cm3 = 2,312 cm3. m

12.5 cm

8 cm

8c

12.5 − 8 = 4.5 cm

8 cm

26 − 8 = 18 cm

26 cm

Another way to solve this problem is to find the volume of the entire rectangular solid including the missing piece (rectangular solid missing on the left side); then subtract the volume of the missing solid from this quantity in order to get the volume of the given solid (see the illustration below): This is the volume for the whole rectangular solid: 26 ⋅ 12.5 ⋅ 8 = 2,600 cm3 Volume for missing rectangular solid is the following: 4.5 ⋅ 8 ⋅ 8 = 288 cm3 Volume of the given solid: 2,600 cm3 – 288 cm = 2,312 cm3. Same answer as before, but found in a different manner. V = 4.5 × 8 × 8 = 288 cm3

8c

12.5 cm

8 cm

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8 cm

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26 cm

There are other ways to solve this problem. You might have used one of them. 50. The best choice for this item is D. You need to find the surface area of the cylinder. This formula is available in the FCAT Mathematics Reference Sheet: 2πrh + 2πr2. Since the diameter of the given cylinder is 3 inches, the radius is half of this measure, or 3 ÷ 2 = 1.5 inches, and the given height is 36 inches. By substituting the values in the formula, you have the following (use π = 3.14): 2(3.14)(1.5)(36) + 2(3.14)(1.5)2 = 339.12 + 14.13 = 353.25 cm2.

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Practice FCAT Math 5 Remember to read and follow the instructions carefully. You have two and a half hours to complete the test. You may want to take a short break in the middle of the test.

First Part of Practice FCAT Math 5 1. The slopes of five lines are LM = –1/8, LN = 8, MP = –8, RL = 1/8, and CX = 1. Which of these lines is the line perpendicular to LM? A.

LN

B.

MP

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2. What is the value of n in the equation 2–6 ⋅ –8 = n? A. B. C. D.

8 1/8 – 1/8 – 8

3. When Sarah bought some roses for her shop, she paid $1.95 for the first 5 roses and $0.35 cents for each additional rose. She was charged $52.45 for all the roses. About how many roses did she buy? A. B. C. D.

127 roses 122 roses 7 roses 150 roses

4. Paul, Samuel, and Greta were comparing the distances from their houses to school: 2 2 miles, 2 1 miles, 3 5 2 3 miles, and 2 3 miles. What is the order of these distances from least to greatest? 8 5 A.

23, 21, 23, 22 8 3 5 5

B.

23, 21, 22 , 23 8 3 5 5

C.

23, 22 , 23, 21 5 5 8 3

D.

21, 23, 22 , 23 3 8 5 5

5. Alice has x books at her home library; 169 of these books are softcover books; and the other 345 books are hardcover books. What percent of Mary’s books are hardcover books? Explain your answer.

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Part II: FCAT Math Test

6. Anne was reading a novel and decided to keep track of the number of pages she read per day on the following graph, from the beginning until she completed reading the whole book. She read 30 pages the first day. What is the average number of pages she read per day? Reading of Novel 70 60 50 40 30 20 10 0 0

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Practice FCAT Math 5

7. Alicia works for a supermarket. She earns $56.00 per day, and receives $5.35 per extra hour. She worked 6 days last week and received a check for $645.00. What is the approximate average number of extra hours she worked during these 6 days? A. B. C. D.

9 hours 10 hours 58 hours 120 hours

8. Samuel has to graph a transformation of the triangle XYZ on the following grid. The triangle must include the points plotted on the grid using the y-axis as the reflection line. Explain in your own words how to find the coordinates for the reflection of the triangle using the y-axis as the reflection line and coordinates for points X, Y, and Z as a guide. Using the grid, you need to plot, label, and connect the coordinates of the reflection of the triangle XYZ over the y-axis. y X (-1,5)

6 5 4 3 2

Y (-5,1)

1 -6

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-1 -2 -3 Z (-3,-4)

-4 -5 -6

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Part II: FCAT Math Test

9. The box-and-whisker plot displays the list of Peter’s test scores this semester in a math class. What is the median of Peter’s test scores?

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10. At a circus show, a clown was shot out of a cannon at ground level. Her height in inches above ground at any time (in seconds) was represented by the following formula: h = –16t2 + 64t. If the time was 1.5 seconds, what was the height above ground? A. B. C. D.

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Practice FCAT Math 5

11. Natalie ate 3 slices of a pie for dessert. Each slice was about 10 percent of the pie (as illustrated). A

B C

What is the measure of the angle BCA that represents the area of the pie that is left? A. B. C. D.

252 degrees 108 degrees 30 degrees 72 degrees

12. Find the slope of the line represented by the equation –3x + –2 = –5 – 6y. A. B. C. D.

–

1/2 1/2 2 – 2

13. The following figure shows five concentric circles. The shaded regions were labeled A, B, C, and E. Region D is not shaded. Assuming the width between each ring is the same, and the circumference of circle C is equal to 34.75 cm, what is the diameter of circle E? Use π = 3.14 and round to the nearest hundredth. E D C B A

A. B. C. D.

11.07 cm 10.46 cm 19.89 cm 5.23 cm

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Part II: FCAT Math Test

14. Which of the following is the same as 6–5? A. B. C. D.

–

7776 7776 –1/7776 1/7776

15. The height from the floor to the ceiling in a scale drawing is 1/10 centimeter to 1 meter. The actual height is 9.75 meters. What is the height in centimeters of the model? You need to round to the nearest cm. A. B. C. D.

97 centimeters 1 centimeter 10 centimeters 100 centimeters

16. There are two boxes with books in Peter’s room. The first box contains 2 biography books, 3 children’s books, 2 self-help books, and 1 romance book. The second box contains 4 biography books, 1 children’s book, 2 selfhelp books, and 3 romance books. If Peter randomly selects one book from each box, what is the probability that one book from the first box is a children’s book, and one book from the second box is a biography book? A. B. C. D.

3/8 2/5 3/20 7/18

17. A survey was taken at a high school to find how students get to school each day. The results are shown in the table below.

How Students Get to School Each Day by Grade Level Take a Bus

Walk

Adult Drives

Other

Total

10th Grade

139

123

76

85

423

11th Grade

47

140

113

89

389

12th Grade

158

143

41

34

376

Total

344

406

230

208

1,188

About what percent of the students take the bus to school? A. B. C. D.

29% 46% 40% 13%

18. A math tutor charges a $20.75 initial fee and $25.90 for each hour of tutoring. Which of the following equations could be used to find the cost t of a tutoring session lasting h hours? A. B. C. D.

270

t = 25.90 + 20.75h t = 25.90 – 20.75h t = 20.75 + 25.90h t = 25.90(20.75 – h)

Practice FCAT Math 5

19. A bowl contains 5 blue marbles, 11 red marbles, 15 green marbles, and 7 yellow marbles. The red marbles and yellow marbles are the only ones that have a plastic cover for each marble. What is the probability that you will randomly select a marble that does not have a plastic cover for it from the bowl? A. B. C. D.

21/38 27/38 1/2 10/19

20. A train takes 3 hours to travel 54 miles. Assuming there are no stops, how many miles will this train travel in 12 hours? A. B. C. D.

216 miles 45.25 miles 162 miles 648 miles

21. Which of the following rates has the lowest unit price? A. B. C. D.

26 ounces: $14.64 28 ounces: $15.40 20 ounces: $13.30 22 ounces: $19.75

22. Find the approximate surface area of the circular cone illustrated in square centimeters.

12 cm

6 cm

A. B. C. D.

113.04 square centimeters 339.12 square centimeters 141.3 square centimeters 122.46 square centimeters

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Part II: FCAT Math Test

23. Samuel bought a used car for a 17 1 % discount of the original price. If he paid $23,654.00 for this car, what was 4 the original price of the car? This problem does not include taxes and other fees. Round to the nearest hundredth. A. B. C. D.

$19,573.68 $137,124.64 $27,734.31 $28,584.89

24. Simplify the following expression: 302 – 60 ÷ 12 ⋅ (4 - 2 – 1/4) ⋅ 15 + 78. A. B. C. D.

978.0375 139.875 – 132 16,875.25

25. Mr. Washington bought a new square table that is approximately 4 2 feet diagonally. In order to get a square box for this table, how wide must the box approximately be without any extra space? A. B. C. D.

2 feet 4 feet 16 feet 2 feet

You may take a short break (optional 5 or 10 minutes) but must complete the test on the same day.

272

STOP

Practice FCAT Math 5

Second Part of Practice FCAT Math 5 Continue the test. Remember to read and follow the instructions carefully. You have 70 minutes to complete the test. 26. A recipe for key lime pies requires 20 key limes to make 8 key lime pies. If 60 key lime pies were needed for a party, about how many key limes would you need? A. B. C. D.

about 3 key limes about 1,200 key limes about 150 key limes about 24 key limes

27. Two regular and fair six-sided number cubes were thrown once. What is the probability that you will roll a 5 and a 6? Show or explain your answer using words and numbers. 28. What is the LCM of 27 and 30?

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Part II: FCAT Math Test

29. Which of these are the coordinates for point A on the coordinate plane shown previously? y

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(–3, 3) (3, –3) (4, –4) (–4, 4)

30. Peter has 60 birds and dogs in his pet shop. When he adds together all the legs for all of his birds and dogs, he has a total of 140 legs. How many birds and how many dogs does Peter have? Write a system of equations representing the possible combination of birds, dogs, and legs. Show all the steps for solving this system of equations. 31. At a store, Olga needs to arrange cans of food (all the same size) in 10 shelves. She estimated that she could fit about 15 cans of food on 1/4 of a shelf. The cans of food come in boxes of 40 cans each. Approximately how many boxes of cans of food will Olga need to fill up the 10 shelves? A. B. C. D.

274

60 boxes 15 boxes 40 boxes 600 boxes

Practice FCAT Math 5

32. Gabriela earned $67,000.00 last year. She earned $85,400.00 this year. What was the approximate percent of increase in salary she had from last year to this year? A. B. C. D.

127.46% 76.11% 21.55% 27.46%

33. On a coordinate grid, the point (3, –4) is reflected over x-axis. Find the coordinates of this new point. A. B. C. D.

(-3, 4) (3, -4) (3, 4) (-3, –4)

34. The two triangles in the following figures below are similar. What is the length of side c? Round your answer to the nearest tenth.

c

6 in

3 5 in

3 in

15 in

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Part II: FCAT Math Test

35. A lawyer paid $1,575.63 for a round-trip airplane ticket from Orlando to London. This includes the original ticket price and 23 percent markup to the ticket for taxes and other charges. How much did the lawyer pay in dollars to buy this airplane ticket without the markup in price? A. B. C. D.

$295 $1,281 $362 $1,938

36. The area of a rectangle is 144 square centimeters. One of the sides of this rectangle is equal to 9 centimeters. Using the given information, what is the perimeter of this rectangle? A. B. C. D.

50 centimeters 16 centimeters 36 centimeters 25 centimeters

e=

us

ten

po

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height = b = 4 in

37. The following figure is a rectangular solid. The height of the rectangular solid is equal to 4 inches, and the width is 9 inches. The area of the shaded planar cross section is equal to 45 square inches. What is the volume of the rectangular solid?

th wid length = ?

A. B. C. D.

276

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=9

in

Practice FCAT Math 5

38. What is the slope of the line in the following graph? y

(-4,1)

x

0

(5,-4)

A. B. C. D.

–

9/5 5/9 9/5 – 5/9

39. A company has 300 workers. The following Venn diagram illustrates the numbers of workers at this company in different categories. Some of them share duties. How many workers are secretaries and administrators?

Secretaries 40

Trainers 55

75 15 12

83

Administrators 20

A. B. C. D.

55 workers 245 workers 27 workers 185 workers

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Part II: FCAT Math Test

40. Grace earned $3,535.00 last month for her regular monthly salary, plus $20.00 for each overtime hour. Including regular salary and overtime, her total earnings last month were $4,535.00. This month she received the same regular salary and worked the same amount of overtime hours as last month, but the payment for overtime hours this month was increased to $22.00 per overtime hour. How much more money did she earn this month than last month? A. B. C. D.

$1,000.00 $1,100.00 $100.00 $20.00

41. Sergio painted 1/7 of a wall yesterday, and 25 percent of the same wall today. What percent of the wall did Sergio paint in these two days? A. B. C. D.

39% 14% 25% 18% of the wall

42. Maria made the following table based on the numbers of hours she worked per day last month. Find the mean number of hours per day that she worked last month. Number of Hours

Tally

Frequency

7

//// //// //

12

8

///

3

9

//

2

10

//// //

7

A. B. C. D.

about 6 hours per day about 48.5 hours per day about 7.5 hours per day about 8 hours per day

43. Find the area in square meters of the shaded region in the circle. Round to the nearest tenth.

3.5 m

M

N 3.5 m

12.5 m

278

Practice FCAT Math 5

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1/3 1/4 1/2 1

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Quadrant I Quadrant II Quadrant III Quadrant IV

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47. Mrs. Alvarez wants to organize groups of boys and girls of the same size for team activities. If there are 12 boys and 18 girls, and each group is all boys and all girls, what is the largest size group she can organize? A. B. C. D.

3 4 36 6

48. Squares were used to form the geometric pattern shown. The first cross takes 5 squares; the second takes 9; the third takes 13; and so on. How many wooden squares would be needed for the 30th cross?

First Cross 5 squares

A. B. C. D.

Second Cross 9 squares

Third Cross 13 squares

124 squares 120 squares 121 squares 116 squares

49. What is the approximate percent for a $29.50 payment out of a $1,593 debt? A. B. C. D.

18.5% 1.85% 185% 0.185%

50. Beatrice spent $45.00 for 12 mangos and 9 oranges. Each mango cost her 3.25 times as much as each orange. How much did each mango cost Beatrice? Write a system of equations to figure out how much each mango and each orange cost Beatrice. Use this system of equations to find out how much each mango and each orange cost Beatrice.

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Answer Key for Practice Test 6 1. A 2. C 3. A 4. D 5. 67% 6. 14 pages per day 7. B 8. The new points X' Y', and Z' for the reflection of the triangle are, respectively, (1, 5), (5, 1), and (3, –4). 9. 81 10. C 11. A 12. B 13. C 14. D 15. B 16. C 17. A 18. C 19. D 20. A 21. B 22. C 23. D 24. A 25. B 26. C 27. The only two possible outcomes involving 5 and 6 are (5, 6), and (6, 5). 28. The LCM of 27 and 30 is 270. 29. C 30. There are 50 birds and 10 dogs. 31. B 32. D 33. C 34. The length of the side c is approximately 33.6 inches. 35. B

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36. A 37. C 38. D 39. C 40. C 41. A 42. D 43. 103.4 square meters (rounded to the nearest tenth) 44. B 45. A 46. C 47. D 48. C 49. A 50. Each mango costs about $3.05. Oranges cost $0.94 each.

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Solutions for Practice FCAT Math 5 Use these answers and explanations to help you understand possible solutions and improve your test-taking ability. You should not take more that one practice exam per day. You need some wait time before taking and reviewing the other practice exams (at least one day). You might have used a different path for your solution. This is okay; if you get to the same answer and the procedures you used are mathematically accurate, you don’t need to have the same solution process. It is good to also learn other ways to solve the problem. 1. The best choice for this item is A. Lines are perpendicular when the slopes are opposite reciprocals of each other like in –1/8, and 8. 2. The best choice for this item is C. You need to solve the negative exponent first and then multiply for negative one. 2–6 is equal to 16 = 1/64, and 1/64 ⋅ –8 = –1/8. 2 3. The best choice for this item is A. The total number of roses was 127. Sarah was charged $52.35 for her order of roses, which includes the first 5 roses and all the additional roses. First, you need to subtract the cost of the first 5 roses from the total: $52.45 – $9.75 = $42.70 (this is the cost of the additional roses). You need to remember to add these roses at the end. Second, you need to divide $42.70 by $0.35 = 122 roses. Finally, you need to add the first 5 roses of the order (remember?). The answer is 122 roses + 5 roses = 127 total roses. 4. The best choice for this item is D. Change all the possible answers to decimal form and compare to each other (including 2.4) or order them from least to greatest: 2 1 = 2.3333 ... , 2 3 = 2.375, 2 2 , 2 3 = 2.6. 3 8 5 5 The calculator could be used to change the fractions to decimal form. You can also change 2.4 to fraction form and compare to the other fractions: 2.4 = 2 4 = 2 2 . 10 5 1 3 2 3 Ordering the fractions from least to greatest we have the following: 2 , 2 , 2 , 2 . 3 8 5 5 5. This short-answer item is worth two points—one point for the answer and one for an acceptable explanation. About 67% of the books in Mary’s library are hardcover books. You could start by finding out how many total books Mary has in her library: 169 softcover books + 345 hardcover books = 514 total books. Then, you can use this information to find the percent of hardcover books that she has: 345 ÷ 514 = 0.67120623. . . or about 67%. 6. She read 30 pages the first day and 10 pages every day for four days: 30 + 10 + 10 + 10 + 10 = 30 + 4(10) = 30 + 40 = 70. The average is 70 pages ÷ 5 days = 14 pages per day. Now you need to enter this information in the response grid:

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7. The best choice for this item is B. Paula made a total of $645.00 for her five days of work. This is including her extra hours. You know that she earned $56.00 per day; multiplying this by 6 gives what she earned per day without including what she earned for the extra hours, which is $336.00. Subtracting $336.00 from $645.00 yields $309.00, which is what she earned for the extra hours alone. Dividing $309.00 by $5.35 per hour yields about 58 hours, which is the total number of hours she worked during those 6 days. Since you need only the total number of hours to find the average, you can divide these 58 hours by 6 days and get the average number hours she worked during these 6 days, which is about 10 hours. 8. This short-answer item is worth two points—one point for the answer and one for an acceptable explanation. For this part of the item you need to explain how to reflect the points of the original triangle XYZ over the y-axis. To do this, you need to use the same y-coordinant and multiply the x-coordinant by –1. The original points X, Y, and Z of the triangle are, respectively, (–1, 5), (–5, 1), and (–3, –4). The new points X', Y', and Z' for the reflection of the triangle are, respectively, (1, 5), (5, 1), and (3, –4). The wording of this explanation may vary.

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The following grid illustrates the plotting, labeling, and connecting of the points (X', Y', and Z') for triangle X'Y'Z'. y 6

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10. The best choice for this item is C. This item involves the manipulation of values included in the equation. You need to be careful with the positive and negative signs. Notice that by substituting for t for 1.5 seconds in h = –16t2 + 64t, h is equal to 60 inches, but you need the answer in feet. Since 12 inches is equal to 1 foot, 60 inches = 5 feet. h = –16t2 + 64t h = –16(1.5)2 + 64(1.5)

Substitute for t = 1.5

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1.52 = 2.25

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–36, and 64(1.5) = 96

h = 60 inches

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= 5 feet

11. The best answer for this item is A. Natalie ate three slices of the pie at 10% each for 30% total. We know that a pie (or circle) is 360 degrees. The measure of the central angle (m∠BCA) is 30% of 360°, which is equal to 108 degrees. This means that she has 360° – 108° = 252° remaining. Another way to solve this problem is subtracting 30% from 100%, which is equal to 70%: 70% ⋅ 360° = 0.7 ⋅ 360° = 252°. 12. The best answer for this item is B. One way to solve this problem is by using the formula for slope: y = mx + b, where m is the slope of the equation. You need to get the equation –3x + –2 = –5 – 6y to look like this formula: –

3x + –2 = –5 – 6y

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3x + –2 + 5 = –5 + 5 – 6y –

3x + 3 = 0 – 6y

(–3x + 3) ÷ –6 = –6y ÷ –6 1/2x + –1/2 = y In this case m = 1/2.

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Another way to solve this problem is by using the equation in standard form: ax + by + c = 0. You need to get the equation –3x + –2 = –5 – 6y to look like the standard form: –

3x + –2 = –5 – 6y

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3x + 6y + 3 = 0

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This yields a = 3, b = –6, and the slope (m) is –a/b or –(–3/6) = 1/2. 13. The best choice for this item is C. The formula for finding the circumference of a circle is 2πr. You need to calculate the radius of circle C: 34.75 = 2(3.14)πr 5.53 cm = r Then calculate the radius of circle A, which is 2.5 the radius of circle C: 5.23 ÷ 2.5 = 2.21 cm. The diameter of E is 9 times this length: 9 ⋅ 2.21 = 19.89 cm. 14. This best choice for this item is D. 6–5 = 1/6–5 = 1/(6 ⋅ 6 ⋅ 6 ⋅ 6 ⋅ 6) = 1/7776 15. The best choice for this item is B. You need to set up a proportion. There are several ways to establish the proportion to solve this problem. One possible proportion is the following: 1/10 cm to 1 meter = x to 9.75, where x represents the height of the model in cm. Then by cross multiplying (1/10 ⋅ 9.75 = 1 ⋅ x), and solving for x, you get that x = 0.975, or that the height of the model is about 1 cm. 16. The best choice for this item is C. You need to calculate the probability for selecting a book from each box separately. There are 8 books in the first box (2 biography books + 3 children’s books + 2 self-help books + 1 romance book = 8 books). Of these 8 books in this first box, 3 are children’s books. Then, the probability of randomly selecting one children’s book from this first box is 3/8. There are 10 books in the second box (4 biography books + 1 children’s book + 2 self-help books + 3 romance books = 10 books). Of these 10 books in this first box, 4 are biography books. Then the probability of randomly selecting one biography book from this second box is 4/10 or 2/5. You need to multiply these two probabilities to obtain the final probability because they are independent events: 3/8 ⋅ 2/5, which is equal to 3/20. 17. The best choice for this item is A. To find the percent, you need to divide the total number of students who take the bus to school and divide it by the total number of students answering the survey: 344/1188 = 0.28956 ≈ 29%. 18. The best choice for this item is C. Remember that you are trying to translate the word problem into a mathematical sentence that represents the relationship of the quantities in the problem. You know that 20.75 will stay the same since it is the initial fee, and the 25.90 needs to be multiplied by the number of hours for the tutoring session: t = 20.75 + 25.90h. 19. The best choice for this item is D. You have a total of 38 marbles (5 blue marbles + 11 red marbles + 15 green marbles + 7 yellow marbles = 38 marbles). The marbles with plastics covers are 11 red marbles + 7 yellow marbles or 18 marbles altogether. The probability for randomly selecting a marble with a plastic cover from the bowl is 18/38, or 9/19. 20. The best choice for this item is A. You might notice that 12 hours is four times as long as a three-hour trip. Then you have that 54 ⋅ 4 = 216, or the train will travel 216 miles in 12 hours. One way to solve this problem is by establishing a proportion: 54 hours to 3 hours = x to 12 hours. By crossmultiplying and solving for x, you have 54 ⋅ 12 = 3x; 2648 ÷ 3 = x; and 216 = x.

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You can also notice that the ratio for miles per hours in 54 miles/3 hour; then for 12 hours, you have 216. The following table illustrates different increments in terms of miles and hours. Miles

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21. The best choice for this item is B. One way to solve this problem is by changing each alternative to unit price: A. 26 ounces : $14.64

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1 ounce : $0.563

B. 28 ounces : $15.40

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1 ounce : $0.55

C. 20 ounces : $13.30

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1 ounce : $0.665

D. 22 ounces : $19.75

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1 ounce : $0.897

This one is the lowest.

This one is the highest.

22. The best choice for this item is C. The formula for finding the total surface area of a circular cone is the following: S.A. = 1 ⋅(2πr) ⋅ l + πr2 = π r ⋅ l + π r2, which is included in the reference sheet provided. You can 2 use 3.14 for the approximate value for π (other values could be used as an approximation of π). For the value of the radius of the circular base of the cone, you need to divide the given diameter (6 cm) by 2 to find the radius, which gives 3 cm for the radius. The length (or height) is equal to 12 cm. Using these values for the formula: 1/2(2)(3.14)(3)(12) + (3.14)(32)(12) ≈ (3.14)(3)(12) + (3.14)32 = 113.04 + 28.26 = 141.3 square centimeters. 23. The best choice for this item is D. There are several correct ways to solve this problem. One way to solve this problem is by noticing that if you paid a 17 1 % discount of the original price, then the new price is 91% of the 4 original price (100% – 17 1 % = 100% – 17.25% = 82.75%). This implies that 82.75% ⋅ original price = new 4 discount price, or 82.75% • original price = $23,654. You can find the original price by dividing $23,654 by 82.75% or 0.8275. This will give you the original price: $28,584.89. 24. The best choice for this item is A. You need to use the correct order of operations for this expression: 302 – 60 ÷ 12 ⋅ (4 - 2 – 1/4) ⋅ 15 + 78 900 – 60 ÷ 12 ⋅ (1/16 – 1/4) ⋅ 15 + 78

Calculate exponentials: 302 = 900; 4-2 = 1/42 = 1/16.

900 – 60 ÷ 12 ⋅ (–3/16) ⋅ 15 + 78

Solve parentheses: (1/16 – 1/4) = (–3/16).

900 – –0.9375 + 78

Calculate multiplication and division, as they appear, from left to right: 60 ÷ 12 ⋅ (–3/16) = –0.9375.

978.9375

Calculate addition and subtraction, as they appear, from left to right.

25. The best choice for this item is B. The table is approximately 4 2 feet diagonally. You can use the Pythagorean Theorem to find how wide the sides of the square are (all sides are equal in a square): c2 = a2 + b2 c2 = a2 + a2 2

2

Since all sides of the square are equal, a and b are equal.

c = 2a

Solve: a2 + a2 = 2a2.

c = 2a 2

Solve for c by finding the square root of c2 and 2a2.

c=a 2

Solve: 2a 2 Needs italics = a 2 .

You know that c = 4 2 , and then 4 2 = a 2 . Solving for a by dividing 2 on both sides of the equality: 4 2 ÷ 2 = a 2 ÷ 2 : 4 = a. The sides of the square are equal to 4 feet wide.

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26. The best choice for this item is C. You need to set up a proportion using the rates provided in the problem: 20 = k 8 60

Where k is the number of key limes you would need.

20 ⋅ 60 = 8k

Cross multiply.

1200 ÷ 8 = (8k) ÷ k

Divide each side by 8.

k = 150 Remember that there are other ways to establish the rates and proportion. You just need to be consistent. For example, you can also have the following proportions: 8 = 60 20 k 60 = k 8 20 27. This short-answer item is worth two points—one point for the answer and one for an acceptable explanation. The probability for rolling a 5 and 6 if two dice are rolled is 1/36. The probability for each outcome in a regular and fair six-sided number cube thrown once is 1/6. The events for each die are 1, 2, 3, 4, 5, and 6. The possible combinations for throwing the two dice once are the following: Die 2 ↓

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The only two possible outcomes involving 5 and 6 are (5, 6), and (6, 5). 28. The LCM of 27 and 30 is 270. You can solve this problem by finding the common multiples of 27 and 30 and selecting the smallest (nonzero) common multiple of 27 and 30, which is 270: Multiples of 27: 27, 54, 81, 108, 135, 162, 189, 216, 243, 270, 297, . . . Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, . . . You can also find the prime factorization of 27 and 30 and use this factorization to find the least common multiple of these two numbers. 27 = 3 ⋅ 9 = 3 ⋅ 3 ⋅ 3 = 33 30 = 2 ⋅ 15 = 2 ⋅ 3 ⋅ 5 LCM = 2 ⋅ 33 ⋅ 5 = 2 ⋅ 27 ⋅ 5 = 270

Select common and not common prime factors with the larger exponent.

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29. The best choice for this item is C. You need to count the number of spaces on the x-axis (positive value) first going to the right, and y-axis (negative value) second going down for point A. 30. This is a long-response item, which are four points each. You will receive four points if you answer all parts of the item fully and correctly. You must show understanding of the mathematical ideas presented in this problem. You will receive three points if you make minor errors and show understanding as you solve and explain the solution of the problem. You will receive two points if you make several errors, the explanations are incomplete and not clear, and do not show proper understanding of the problem. When solving this problem, you need consider two different relationships. One is between the number of birds and dogs, and the other is in terms of the number of legs. Then you need to solve the system of equations.

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You can start by naming the variables for the equation: b = the number of birds, d = the number of dogs. From this, you can form the equation needed to represent the relationship between the variables based on the problem: b + d = 60 (total number of legs). Each bird has two legs or 2 times the number of birds: 2b. Each dog has four legs or 4 times the number of dogs: 4d. Remember that 2b is the same as 2 ⋅ b, and that 4d is the same as 4 ⋅ d. This gives a second equation for the total number of bird and dog legs: 2b + 4d = 140 legs. The system of equations is the following: b + d = 60, and 2b + 4d = 140. Solving the first equation for d, you have that d = 60 – b (notice that you could have used other forms of the equation like 60 – b = d, or solving for b: b = 60 – d). Then you need to substitute d = 60 – b for b in the second equation (2b + 4d = 140): 2b + 4(60 – b) = 140 2b + 240 – 4b = 140 (Using the distributive property of multiplication over subtraction.) 240 – 2b = 140 240 – 240 – 2b = 140 – 240 –

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b = 50 Since b = 50, then you have the following: b + d = 60 50 + d = 60 50 – 50 + d = 60 – 50 d = 10 There are 50 birds and 10 dogs. (Remember that you need to go back to the initial problem and answer the question.) Check your answer by substituting these values in the second formula: 2b + 4d = 60 2(50) + 4(10) = 140 100 + 40 = 140 140 = 140 An alternative solution for this problem can involve solving the first equation for b instead of solving for d and substituting for b in the second equation: b = 60 – d 2b + 4d = 140 2(60 – d) + 4d = 140 (Substituting for b in the second equation) 120 – 2d + 4d = 140 120 + 2d = 140 120 – 120 + 2d = 140 – 120 2d ÷ 2 = 20 ÷ 2 d = 10

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Since d = 10, then you have the following: b + d = 60 b + 10 = 60 b + 10 – 10 = 60 – 10 b = 50 You end up with the same answer: There are 50 birds and 10 dogs. Check your answer as before. 31. The best choice for this item is B. Olga could fit 15 cans of food in one-fourth of a shelf, which means that she can fit about 60 cans in a full shelf (15 cans of food ⋅ 4). She has 10 shelves, which means she could fit up to 600 cans of food altogether (10 shelves ⋅ 60 cans of food per shelf). Each box of cans of food has 40 cans. You need to divide the total number of cans that can fit in the 10 shelves by 40 cans of food for each box: 600 ÷ 40 = 15 boxes. This means that she can fit 15 boxes in the 10 shelves. 32. The best choice for this item is D. The amount of change in this problem is equal to x% times the original salary (the number you are starting with in this problem): $85,400 – $67,000 = x% ⋅ $82,000,

or $85,400 –67,000 = (x/100) • $67,000.

$18,400 = (x/100) • $67,000

Subtract $85,400 – 67,000 = $18,400.

$18400 ÷ 67,000 = (x/100) • $67,000 ÷ 672,000

Simplify by dividing both sides by $67,000.

0.2746 • 100 = (x/100) • 100

Multiply both sides by 100.

27.46% = x 33. The best choice for this item is C. In order to reflect this point, you need to use the same x coordinate and multiply the y-coordinate by negative one: (3, –4) becomes (3, 4). The following figure illustrates this situation. y 6 5 (3,4) 4 3 2 1 -6

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34. Since the two triangles are similar, the ratios of their corresponding angles are equal. You can write and solve a proportion to find c. You need to make sure that you compare similar sides to each other and include the side that contains the side and its corresponding side in the other triangle. This is one of the different ways to set up and solve the proportion: 3 5 c = 3 15 3 5 ⋅ 15 = 3 ⋅ c 45 5 = 3c 45 5 ÷ 3 = 3c ÷ 3 15(2.23606) = c

Set up the proportion. Cross multiply. Simplify. Divide each side by six to solve for c. 45 ÷ 3 = 15; 5 ≈ 2.23606.

33.5 in ≈ c The length of the side c rounded to the nearest tenth is approximately equal to 33.5 inches. You could have also noticed that each of the larger triangle sides is 5 times the length of the corresponding sides in the other triangle. Based on this information, you can say that length of c is 5 times 3 5 = 5 ⋅ 3 5 = 15 ⋅ 5 = 15(2.24) = 33.6 in. You can enter your grid response in the following manner:

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35. The best choice for this item is B. The travel agency will add 23% markup to the initial price of the airplane ticket: x + (23% ⋅ x) = $1,575.63

x = original price of the airplane ticket.

x + (0.23 ⋅ x) = $1,575.63

23% = 0.23.

x(1 + 0.23) = $1,575.63

Factor out the x from the expression.

x(1.23) = $1,575.63 x(1.23) ÷ 1.23 = $1,575.63 ÷ 1.23 x = 1,281 The original price was $1,281 for the airplane ticket. Another way to solve this problem is by multiplying the initial price x by 123% or 1.23 and dividing $1,575.63 by 1.23. Check your answer: 1,281 + 23%(1,281) = 1,281 + 0.23 • (1,281)= 1,281 + 294.63 = 1,575.63; or 1,281 ⋅ 123% = 1281 ÷ 1.23 = 1,575.63 36. The best choice for this item is A. First, you need to find the value for the other side of the rectangle. The formula for the perimeter of a rectangle (sum of the lengths of its sides) is the following: A = bh 144 cm = 9 cm ⋅ h 2

144 cm2 ÷ 9 cm = (9 cm ⋅ h) ÷ 9 cm 16 cm = h

Formula of the area of a rectangle. Substitute for A = 144 cm2 and b = 9 cm. Divide by 9 on both sides of the equality. The other side of the rectangle = 16 cm.

You can use this information to find the length of the perimeter of this rectangle. P = 2(b) + 2(h) 2(9 cm) + 2(16 cm) 18 cm + 32 cm = 50 cm

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Formula for the perimeter of a rectangle. Substitute for b = 9 cm, and h = 16 cm. Solve: Perimeter = 50 cm.

Practice FCAT Math 5

37. The best choice for this item is C. You have the value for one of the sides of the shaded planar section inside the rectangular solid (width = 9 inches), but you still need to find one of the sides, which is the hypotenuse (value for c) of the right triangle formed by this side (diagonal line segment). The area of the planar cross section is equal to 45 square inches. Using this information, we can find the length of the hypotenuse of the triangle: A = bh 45 = 9h 45 ÷ 9 = 9h ÷ 9

Formula for area of the rectangle. A = 45 square units and b = 9 inches. Divide by 9 on both sides of the equality.

5=h Now, you need to use the Pythagorean Theorem: a2 + b2 = c2, using the information you have so far. 42 + b2 = 52 16 + b2 = 25 2

16 – 16 + b = 25 – 16

You know that h = c = 5 inches, and a = height = 4. Solve. Subtract 16 from each side of the equality.

b2 = 9, then b = 3 V = lwh = 3 ⋅ 9 ⋅ 4 = 108 cubic inches. 38. The best choice for this item is D. The change in y (vertical axis) with respect to the change in x (horizontal axis) is called the slope of a line. The slope of a graph in the number tells how steep the line is. In this case, the line is descending 5, and moving 9 to the right: (–4 – 1)/(5 – –4) = –5/9. 39. The best choice for this item is C. There are 27 workers who are secretaries and administrators (12 + 15). 40. The best answer for this item is C. Grace earned $3,535.00 total salary for last month. Since this salary includes the regular salary and overtime hours last month, you need to subtract the regular salary from the total salary, and the remaining quantity is the amount earned in overtime hours: $4,535.00 – $3,535.00 = $1,000.00 for overtime hours. This amount needs to be divided by $20.00 earned per overtime hour to get the number of overtime hours worked last month: $1,000 ÷ $20.00 per overtime hour = 50 overtime hours for last month. This month Grace earned the same regular salary ($3,535.00), plus the same amount of overtime hours times $22.00 per overtime hour (overtime hourly rate was increased). She worked the same amount of overtime hours as last month, which was 50: 50 ⋅ $22.00 = $1,100.00 for the overtime hours this month. This gives a total salary of $3,535.00 + $1,100.00 = $4,635.00. Finally, to find how much more money Grace earned this month than last month, you need to subtract $4,535.00 from $4,635.00, which gives $100.00. Grace earned $100.00 more this month than last month. You can also multiply the $2.00 overtime increase by the 50 hours to get $100.00. 41. The best choice for this item is A. You need to add 1/7 and 1/4 (since 25% = 0.25 = 1/4): 1/7 + 1/4 = 4/28 + 7/28 = 11/28 ≈ 0.392, which is 39%. He has painted approximately 39% of the wall. 42. The best choice for this item is D. The mean is a measure of central tendency of data. The mean of a set of data is the sum of the measures divided by the total frequency: 196/24 = 8.17. 43. The area formula of a circle is A = πr2, where r = d/2 = 12.5 ÷ 2 = 6.25. The area of the whole circle is equal to A = 3.14(6.25)2 ≈ 122.65625 square meters. You need to subtract the area of the small circles: A = πr2, where r = d/2 = 3.5 ÷ 2 = 1.75. = 3.14(1.75)2 ≈ 9.61625 square meters, but you have two of them: 2(9.6125) = 19.2325 square meters. Subtract this amount from 122.65625: 122.65625 – 19.2325 = 103.42375 ≈ 103.4 square meters (rounded to the nearest tenth). You can enter your grid response in the following manner:

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Part II: FCAT Math Test

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44. The best choice for this item is B. Since these are two independent events, you need to multiply the probability of rolling a prime number by the probability of tossing a head. The probability of rolling a prime number is the same as P(2, 3 or 5) = 1/6 + 1/6 + 1/6 = 3/6 = 1/2. The probability of tossing a head is 1/2. Then, P(prime and head) = 1/2 ⋅ 1/2 = 1/4. 45. The best choice for this item is A. The median is a measure of central tendency. You need to have the data in order from least to greatest or from greatest to least. The median is the number that falls in the middle of the data set. In this case, you have 45 numbers, and the middle of the data set is the 23rd number. The median is 2 hours. 46. The best answer for this item is C. There are 4 quadrants in a coordinate grid (or coordinate plane). The ordered pair with a negative x- and y-coordinant will be located in Quadrant III. y

Quadrant II (negative, positive)

Quadrant I (positive, positive)

x

Quadrant III (negative, negative)

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Quadrant IV (positive, negative)

Practice FCAT Math 5

47. The best choice for this item is D. You need to find the greatest common factor (GCF) of 12 and 18. GCF is the largest common factor that divides both numbers evenly. Find the factors of each number. Factors of 12: 1, 2, 3, 4, 6, and 12 Factors of 18: 1, 2, 3, 6, 9, and 18 The GCF (12, 18) = 6. She will be able to make groups of 6 students (boys or girls). Another way to solve this problem is to find the GCF by finding the prime factorization of each number: Prime factorization of 12 = 2 ⋅ 2 ⋅ 3. Prime factorization of 18 = 2 ⋅ 3 ⋅ 3. GCF = 2 ⋅ 3 = 6 48. The best choice for this item is C. First, you should make a table, like the following one, using each figure and the number of squares for each one; continue the pattern (adding four more squares to the previous quantity). It would be a good idea to find a rule or expression to represent the relationship between quantities and to use it to find the number of squares for a given figure. Possible rule for this situation is the following: 4n + 1, where n represents the number of the figure. One is the middle square of the geometric pattern, and 4 is the number of squares added for each iteration of the pattern. Number of Square

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49. The best choice for this item is A. 29.50 = x 1593 100 29.50 ⋅ 100 = 1593 ⋅ x

Establish a proportion with the information you have. Cross multiply.

2950 = 1593x 2950 ÷ 1593 = 1593 ÷ 1593x

Divide by 1593 on both sides.

1.85% = x

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Part II: FCAT Math Test

50. This short-answer item is worth two points—one point for the answer and one for an acceptable explanation. You need to write an equation to find out how much the mangos (m) and oranges (o) cost: 12m + 9o = $45.00, where m = number of mangos, and o = number of oranges. This equation could be written in other ways (like 9o + 12m = $45.00). You also have that the price for each mangos is 3.25 times as much as each orange: m = 3.25o or m/(3.25) = o. You need to solve for m using a system of equations: 12m + 9o = $45.00 12m + 9(m/3.25) = $45.00 12m + 2.77m = $45.00 14.77m = $45.00 14.77m ÷ 14.77 = $45.00 ÷ 14.77 m ≈ $3.05

Substitute for o (o = m/3.25). 9/3.25 ≈ 2.77 12m + 2.77m = 14.77m. Divide both sides by 14.77. Each mango costs about $3.05.

Oranges cost o = m/3.25 = 3.05 ÷ 3.25 = $0.94 each.

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