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CliffsTestPrep
CBEST
6th Edition
by
Jerry Bobrow, Ph.D.
Contributing Authors
Peter Z Orton, Ph.D.
William A. Covino, Ph.D.
Debbie Budesa, M.A.
Jean Eggenschwiler, M.A.
Allan Casson, Ph.D.
Bill Burns, M.A.
Howard Horwitz, M.A.
Michael E. Carr, M.A.
BestSelling Books • Digital Downloads • eBooks • Answer Networks • eNewsletters • Branded Web Sites • eLearning
New York, NY ◆ Cleveland, OH ◆ Indianapolis, IN
About the Author
Dr. Jerry Bobrow, Ph.D., is a national authority in the field of
test preparation. As executive director of Bobrow Test
Preparation Services, he has been administering the test
preparation programs at over 25 California institutions for
the past 27 years. Dr. Bobrow has authored over 30 national
bestselling test preparation books, and his books and
programs have assisted over two million testtakers. Each
year, Dr. Bobrow personally lectures to thousands of
students on preparing for graduate, college, and teacher
credentialing exams.
Publisher’s Acknowledgments
Editorial
Project Editor: Kathleen A. Dobie
Copy Editor: Janet M. Withers
Editorial Assistants: Carol Strickland, Laura Jefferson,
Melissa Bluhm
Production
Proofreaders: Paula Lowell, Susan Moritz, Charles Spencer
Hungry Minds Indianapolis Production Services
CliffsTestPrep TM CBEST, 6th Edition
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Note: If you purchased this book without a cover,
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has received any payment for this "stripped book."
Copyright © 2000 Jerry Bobrow, Ph.D. All rights reserved. No part of this book, including interior design, cover design, and icons, may be reproduced or transmitted
in any form, by any means (electronic, photocopying, recording, or otherwise) without the prior written permission of the publisher.
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LIMIT OF LIABILITY/DISCLAIMER OF WARRANTY: THE PUBLISHER AND AUTHOR HAVE USED THEIR BEST EFFORTS IN PREPARING THIS
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Dedication
This book is dedicated to the memory of four close friends who devoted their
lives to helping with the youth of Fontana, California:
Ron Jeffers, Ellis E. Robbins, Joe DeAugustine, John McGowan
Acknowledgments
Jerry Bobrow
I would like to thank Kathleen Dobie, editor for Hungry Minds, for her careful review
of the manuscript. I would also like to thank my office manager, Joy
Mondragon, for her assistance. And finally, I would like to thank my wife, Susan,
daughter, Jennifer (22), and sons, Adam (19) and Jonathan (15), for their moral
support and comic relief during the writing process.
A special thankyou to the following author and publishing companies who have
given me permission to reprint excerpts from their fine works:
“Why and How Bacteria Communicate,” by Richard Losick and Dale Kaiser,
Scientific American, Volume 276, No. 2, February 1997. Page 69.
On the Subjection of Women, by John Stuart Mill, 1869.
iii
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Table of Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Study Guide Checklist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
PART I: INTRODUCTION TO CBEST: CALIFORNIA BASIC
EDUCATIONAL SKILLS TEST
General Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Questions Commonly Asked about the CBEST Examination . . . . . . . . . . . . . . 4
Three Successful Approaches to the MultipleChoice Questions . . . . . . . . . . . 7
The “PlusMinus” System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
The Elimination Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
The “Avoiding Misreads” Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
PART II: ANALYSIS OF EXAM AREAS
The Reading Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Ability Tested . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Basic Skills Necessary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Analysis of Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
General Procedure for Answering Reading Questions. . . . . . . . . . . . . . . . . . . 14
Some General Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Preread the Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Suggested Approaches with Sample Passages . . . . . . . . . . . . . . . . . . . . . . . . . 16
Regular Passages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Understand What Is Given . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Eliminate and Mark Out Choices That Are Incorrect . . . . . . . . . . . . . . . 17
Understand What Is Implied in the Passage . . . . . . . . . . . . . . . . . . . . . . 17
Make Sure That Your Answer Is WellSupported by the Information
in the Passage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Know Where to Look for Information . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Read All the Choices to Look for the Best Answer . . . . . . . . . . . . . . . . . 20
Know Where to Locate a Specific Detail in the Passage. . . . . . . . . . . . . 20
Notice What Is Stated and What Is Implied . . . . . . . . . . . . . . . . . . . . . . . 21
Recognize the Tone and Purpose of the Passage . . . . . . . . . . . . . . . . . . 22
Always Look for the Main Point of the Passage . . . . . . . . . . . . . . . . . . . 23
Be Aware of Information Not Directly Stated in the Passage . . . . . . . . . 23
Watch for Important Conclusions or Information
That Supports a Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Understand the Meaning and Possible Reason
for Using Certain Words or Phrases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Eliminate Those Choices That Are Not Supported by the Passage . . . . 25
Passages with Numbered Sentences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Be Careful to Spot the Words Least, Most, and Except
in a Question . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Know How to Differentiate Opinion from Fact . . . . . . . . . . . . . . . . . . . . 27
Read the Passage Looking for the Main Point . . . . . . . . . . . . . . . . . . . . 27
Use the Context to Figure Out the Meaning of Words . . . . . . . . . . . . . 28
v
CliffsTestPrep CBEST, 6th Edition
Passages with Missing Words or Phrases. . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Read FillIns into the Passage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Note Specific Information in the Passage . . . . . . . . . . . . . . . . . . . . . . . . 29
Understand the Author’s Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Note the Differences in FillIn Choices. . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Read for the Main Point and How the Passage Is Organized. . . . . . . . . 31
Make Sure Any Addition to a Passage Is Consistent with the
Style and Relates to the Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Tables of Contents or Indexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Look carefully to find specific information. . . . . . . . . . . . . . . . . . . . . . . . 33
Know Where to Look and What to Look For . . . . . . . . . . . . . . . . . . . . . 33
Know Where to Find a Specific Kind of Information. . . . . . . . . . . . . . . . 34
Notice How Information Is Organized . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Focus on What Information Is Needed . . . . . . . . . . . . . . . . . . . . . . . . . . 35
The Five Key Questions for Understanding and Interpreting
What You Read . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
What Is the Main Idea of the Passage? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
What Details Support the Main Idea? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
What Is the Purpose of the Passage? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Are the Style and Tone of the Passage Objective or Subjective? . . . . . . . . 36
What Are the Difficult or Unusual Words in the Passage? . . . . . . . . . . . . . 36
The Mathematics Section. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Ability Tested . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Basic Skills Necessary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Basic Algebra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Graphs, Charts, and Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Analysis of Directions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Suggested Approach With Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Mark Key Words . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Pull Out Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Identify the Facts Needed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Recognize When Not Enough Information Is Given . . . . . . . . . . . . . . . . . . 47
Work Forward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Work Backward from the Answers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Plug in Simple Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Use 10 or 100 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Approximate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Simplify the Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Make Comparisons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Mark Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Draw a Diagram If None Is Given . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Try Some Possibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Be Reasonable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Glance at the Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Read the Question First . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Review Information Carefully . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Watch for Missing Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
vi
Table of Contents
Introduction to Graphs and Charts . . . . . . . . . . . . . . . . . . . . . . . . 76
Ability Tested . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Basic Skills Necessary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Suggested Approach with Samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Charts and Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Bar Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Line Graphs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Circle Graphs (Pie Charts). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
The Writing Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Ability Tested . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Basic Skills Necessary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Analysis of Directions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Some General Tips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Scoring the CBEST Essays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
The Descriptive/Narrative Essay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Preparing to Write Using Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Writing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Proofreading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
A Specific Approach: The Story Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
The Finished Descriptive/Narrative Essay . . . . . . . . . . . . . . . . . . . . . . . . 96
A Second Look at the Finished Essay (With Comments) . . . . . . . . . . . . 99
Another Prewriting Method: Outlining . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Two Additional Finished Essays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
A WellWritten Essay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
A Poorly Written Essay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Analysis of Essay 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Another Poor Essay (What NOT to Do). . . . . . . . . . . . . . . . . . . . . . . . . 103
Analysis of Essay 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
One More Descriptive/Narrative Topic . . . . . . . . . . . . . . . . . . . . . . . . . 104
Another WellWritten Essay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
The Analytical/Expository Essay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Preparing to Write . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
A Specific Approach: The Why Essay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
The Finished Analytical/Expository Essay . . . . . . . . . . . . . . . . . . . . . . . . . . 108
A Second Look at the Finished Essay (With Comments) . . . . . . . . . . . 110
Poorly Written Essay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Analysis of Essay 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
One More Analytical/Expository Topic . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Two WellWritten Essays (With Comments) . . . . . . . . . . . . . . . . . . . . . . . . 113
Analysis of Essay 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Analysis of Essay 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Important Terms Used in Essay Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Compare and Contrast. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Practice Essay Topics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Topic 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Essay Topic Checklist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
CBEST Essay Analysis Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
Topic 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Essay Topic Checklist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
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CBEST Essay Analysis Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Topic 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
Essay Topic Checklist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
CBEST Essay Analysis Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
Topic 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Essay Topic Checklist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
CBEST Essay Analysis Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Topic 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
Essay Topic Checklist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
CBEST Essay Analysis Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
Topic 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Essay Topic Checklist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
CBEST Essay Analysis Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Topic 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
Essay Topic Checklist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
CBEST Essay Analysis Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
Topic 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Essay Topic Checklist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
CBEST Essay Analysis Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
PART III: ASSESSMENT MINITEST
Answer Sheet for the MiniTest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Section I: Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Section II: Mathematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
MiniTest. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Section I: Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Section II: Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Section III: Writing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
Topic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
Answer Key and Analysis for the MiniTest . . . . . . . . . . . . . . . . 176
Answer Key for the MiniTest. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
Scoring Your CBEST MiniTest. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
Analyzing Your Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
MiniTest Essay Checklist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
Answers and Complete Explanations for the MiniTest. . . . . . . 179
Section I: Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Section II: Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
PART IV: MATHEMATICS REVIEW
viii
Symbols, Terminolgy, Formulas, and
General Mathematical Information . . . . . . . . . . . . . . . . . . . . . . . 187
Common Math Symbols and Terms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Symbol References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Math Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
Important Equivalents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
Math Words and Phrases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
Mathematical Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
Some Properties (Axioms) of Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
Some Properties (Axioms) of Multiplication. . . . . . . . . . . . . . . . . . . . . . . . 192
A Property of Two Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
Basic Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
Table of Contents
Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
Arithmetic Diagnostic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
Arithmetic Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
Rounding Off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
Place Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
Estimating Sums, Differences, Products, and Quotients . . . . . . . . . . . . . . 197
Estimating Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
Estimating Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
Estimating Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
Estimating Quotients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
Common Fractions and Improper Fractions. . . . . . . . . . . . . . . . . . . . . . . . 199
Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
Reducing Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
Adding Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
Adding Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
Subtracting Fractions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
Subtracting Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
Multiplying Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
Multiplying Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
Dividing Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
Simplifying Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
Decimals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
Adding and Subtracting Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
Multiplying Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
Dividing Decimals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
Changing Decimals to Percents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
Changing Percents to Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
Changing Fractions to Percents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
Changing Percents to Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
Changing Fractions to Decimals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
Changing Decimals to Fractions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
Finding Percent of a Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
Other Applications of Percent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
Finding Percentage Increase or Percentage Decrease. . . . . . . . . . . . . . . . 206
Prime Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Squares. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Signed Numbers (Positive Numbers and Negative Numbers) . . . . . . . . . . . 208
Addition of Signed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
Subtraction of Signed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
Multiplying and Dividing Signed Numbers. . . . . . . . . . . . . . . . . . . . . . . . 209
Parentheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
Order of Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
Arithmetic Mean or Average . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
Median . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
Simple Permutations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
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CliffsTestPrep CBEST, 6th Edition
Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Algebra Diagnostic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Algebra Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
Understood Multiplying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
Proportions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
Evaluating Expressions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
Monomials and Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
Adding and Subtracting Monomials . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Measurement Diagnostic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
Measurement Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
Measurement Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
Converting Units of Measure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
Calculating Measurements of Basic Figures. . . . . . . . . . . . . . . . . . . . . . . . 220
Perimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
Area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
Surface Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
PART V: PRACTICEREVIEWANALYZEPRACTICE
Answer Sheet for Practice Test 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
Practice Test 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
Section I: Reading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
Section II: Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Section III: Writing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
Topic 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
Topic 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
Answer Key and Analysis for Practice Test 1 . . . . . . . . . . . . . . . 259
Answer Key for Practice Test 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
Scoring Your CBEST Practice Test 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
Analyzing Your Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
Essay Checklists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
Diagnosis of Timed Writing Exercise: Topic 1 . . . . . . . . . . . . . . . . . . . . . . 261
Diagnosis of Timed Writing Exercise: Topic 2 . . . . . . . . . . . . . . . . . . . . . . 262
Answers and Complete Explanations for Practice Test 1 . . . . . 263
Section I: Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
Section II: Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
Practice Test 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
Answer Sheet for Practice Test 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
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Practice Test 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
Section I: Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
Section II: Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
Section III: Writing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
Topic 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
Topic 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308
Table of Contents
Answer Key and Analysis for Practice Test 2 . . . . . . . . . . . . . . . 311
Answer Key for Practice Test 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
Scoring Your CBEST Practice Test 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
Analyzing Your Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
Essay Checklists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
Diagnosis of Timed Writing Exercise: Topic 1 . . . . . . . . . . . . . . . . . . . . . . 313
Diagnosis of Timed Writing Exercise: Topic 2 . . . . . . . . . . . . . . . . . . . . . . 314
Answers and Complete Explanations for Practice Test 2. . . . . . 315
Section I: Reading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
Section II: Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
Practice Test 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
Answer Sheet for Practice Test 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
Practice Test 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
Section I: Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
Section II: Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
Section III: Writing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
Topic 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
Topic 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358
Answer Key and Analysis for Practice Test 3 . . . . . . . . . . . . . . . 361
Answer Key for Practice Test 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361
Scoring Your CBEST Practice Test 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
Analyzing Your Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
Essay Checklists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
Diagnosis of Timed Writing Exercise: Topic 1 . . . . . . . . . . . . . . . . . . . . . . 363
Diagnosis of Timed Writing Exercise: Topic 2 . . . . . . . . . . . . . . . . . . . . . . 364
Answers and Complete Explanations for Practice Test 3 . . . . . 365
Section I: Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
Section II: Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
Practice Test 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
Answer Sheet for Practice Test 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
Practice Test 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
Section I: Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
Section II: Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396
Section III: Writing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
Topic 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
Topic 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410
Answer Key and Analysis for Practice Test 4 . . . . . . . . . . . . . . . 413
Answer Key for Practice Test 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413
Scoring Your CBEST Practice Test 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414
Analyzing Your Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414
Essay Checklists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
Diagnosis of Timed Writing Exercise: Topic 1 . . . . . . . . . . . . . . . . . . . . . . 415
Diagnosis of Timed Writing Exercise: Topic 2 . . . . . . . . . . . . . . . . . . . . . . 416
Answers and Complete Explanations for Practice Test 4. . . . . . 417
Section I: Reading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417
Section II: Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421
xi
CliffsTestPrep CBEST, 6th Edition
PART VI: FINAL PREPARATION
FINAL PREPARATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
The Final Touches. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
xii
Preface
We know that getting a good score on the CBEST is important to you.
Because the CBEST requires you to use some basic skills that you may not have
used in many years, thorough preparation is the key to doing your best. This
makes your study time more important than ever.
To help you use your study time most effectively, leading test preparation experts
and instructors have developed this CliffsTestPrep CBEST. It is thorough, direct,
and easy to use. The materials, techniques, and strategies presented here have
been carefully researched, tested, and evaluated. They are presently used at
CBEST preparation programs throughout California in colleges, universities, and
teachers’ associations.
This guide is divided into five parts:
• Part I — Introduction to CBEST: A general description of the exam,
recent format, questions commonly asked, and basic overall strategies.
• Part II — Analysis of Exam Areas: Focuses on ability tested, basic skills
necessary, directions, analysis, suggested approaches with lots of samples,
and additional tips.
• Part III — Assessment MiniTest: A short test you can take to familiarize
yourself with the various test sections and to assess your strengths and
weaknesses.
• Part IV — Mathematics Review: A short, intensive review of the basics
of arithmetic, algebra, and measurement, starting with a diagnostic test in
each area. Important terminology is also included.
• Part V — PracticeReviewAnalyzePractice: Four complete, fulllength
practice tests with answers and indepth explanations.
• Part VI — Final Preparation: A list of lastminute testtaking tips.
The MiniTest and each practice test are followed by analysis charts to assist you
in evaluating your progress. This guide is not meant to substitute for comprehensive
courses, but if you follow the Study Guide Checklist (the next section) and
study regularly, you’ll get the best CBEST preparation possible.
xiii
Study Guide Checklist
Study Guide Checklist
❏
❏
❏
❏
1. Read the CBEST information materials available at the Testing Office,
Counseling Center, or Credentials Office at your undergraduate institution.
2. Become familiar with the test format (see Format of the CBEST on
page 3).
3. Read General Description and Questions Commonly Asked about the
CBEST Examination, starting on page 1.
4. Learn the techniques of Three Successful Approaches to the Multiple
Choice Questions, starting on page 7.
❏ 5. Carefully read Part II, Analysis of Exam Areas, starting on page 11.
❏ 6. Take the MiniTest, starting on page 161.
❏ 7. Check your answers and analyze your results, starting on page 178.
❏
8. Fill out the Tally Sheet for Questions Missed to pinpoint your mistakes,
page 71.
❏ 9. Review Mathematical Terminology, starting on page 187.
❏ 10. Take the Arithmetic Diagnostic Test, starting on page 194, check your
answers, and review the appropriate areas in the Arithmetic Review.
❏ 11. Take the Algebra Diagnostic Test, starting on page 213, check your
answers, and review the appropriate areas in the Algebra Review.
❏ 12. Take the Measurement Diagnostic Test, starting on page 217, check your
answers, and review the appropriate areas in the Measurement Review.
❏ 13. Strictly observing the time allotment, take Practice Test 1, starting on
page 229.
❏ 14. Check your answers and analyze your Practice Test 1 results, starting on
page 259.
❏ 15. Fill out the Tally Sheet for Questions Missed to pinpoint your mistakes,
page 260.
❏ 16. Study all the Answers and Complete Explanations to Practice Test 1, starting
on page 263.
❏ 17. Have a friend or English instructor read and evaluate your essays using the
Essay Checklists, pages 261 and 262.
❏ 18. Review weak areas as necessary.
❏ 19. Strictly observing the time allotment, take Practice Test 2, starting on
page 279.
xiv
Preface
❏ 20. Check your answers and analyze your Practice Test 2 results, starting on
page 311.
Follow the same procedures as for Practice Test 1: Fill out the Tally Sheet
for Questions Missed; study all the Answers and Complete Explanations;
have a friend or English instructor evaluate your essays using the Essay
Checklists; review weak areas as necessary.
❏ 21. Strictly observing the time allotment, take Practice Test 3, starting on
page 329.
Follow the same procedures as for Practice Tests 1 and 2: Fill out the Tally
Sheet for Questions Missed; study all the Answers and Complete
Explanations; have a friend or English instructor evaluate your essays
using the Essay Checklists; review weak areas as necessary.
❏ 22. As time allows, take Practice Test 4, starting on page 381.
Follow the same procedures as for Practice Tests 1, 2 and 3: Fill out the
Tally Sheet for Questions Missed; study all the Answers and Complete
Explanations; have a friend or English instructor evaluate your essays
using the Essay Checklists; review weak areas as necessary.
❏ 23. Carefully read Final Preparation: The Final Touches, page 431.
xv
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PART I
Introduction to CBEST: C
California Basic
Educational Skills TestT
General Description
The CBEST measures proficiencies in three general areas: reading, mathematics,
and writing. The test was developed to meet requirements related to
credentialing and employment, and is based upon the theory that teachers
should be able to use the same skills taught to students — skills essential to
students both in the classroom and outside school.
CBEST examinees have a fourhour test session to complete one, two, or all
three sections of the test. Prior to August 1995, each of the sections — reading,
mathematics, and writing — was timed separately. Although you may divide
your time among the three sections in any way you want, in order to be
sure that you have enough time to finish all sections, we recommend that
you budget your time approximately as follows: Reading, 70 minutes;
Mathematics, 75 minutes; Writing, 65 minutes. Use the final 30 minutes to
check your work.
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INTRODUCTION
Reading
Mathematics
Writing
Total testing time: 4 hours
Format of the CBEST
50 Questions
50 Questions
2 Topics
All questions (except the essays in the Writing section) are multiple choice with
five answer choices for each question. Each of the three sections receives a score
ranging from 20 to 80. The passing score for each section is 41; the total passing
score for the CBEST is 123. If you score below the passing mark on one section
(or even on two sections) but your total score is 123 or higher, you can still pass
the exam but only if your score in each section is 37 or above.
Note: Format and scoring are subject to change.
The following chart can give you some indication of your performance level:
Percent Right
Scoring
Performance Level
90 to 100 Superior
80 to 90 Above Average
70 to 80 Average
60 to 70 Marginal
Below 60
Needs Improvement
You need to get about 70 percent of the questions right to receive a passing score.
3
Part I: Introduction to CBEST: California Basic Educational Skills Test
4
Questions Commonly Asked about
the CBEST Examination
Q: Who administers the CBEST?
A: The CBEST is administered by National Evaluation Systems with guidelines
drawn up by the California Superintendent of Public Instruction with the assistance
of the California Commission on Teacher Credentialing (CCTC) and
an advisory board.
Q: Who needs to pass the CBEST?
A: The CBEST is typically required for initial issuance of a credential. It may
also be required for issuance of a permit, certificate, authorization, administrative
credential, or renewal of emergency credential. You may need to take the
exam if you have not been employed in teaching for more than 39 months. It’s
important that you check with your state’s department of education to see
whether you must take the test.
Q: Do I need the CBEST for student teaching?
A: Some universities require it. Check with the appropriate department or credentials
office.
Q: When and where is the CBEST given?
A: The CBEST is administered statewide six times each year. You can get dates
and test locations by contacting CBEST Program, National Evaluation
Systems, Inc., P.O. Box 340880, Sacramento, CA 958340880, phone
9169284001.
Q: Do I have to pay again if I repeat the test?
A: You must pay the test fee each time you register to take the CBEST. In addition,
if you register after the regular deadline but before the late registration
deadline, an additional fee will be charged. Check with the registration center
to be sure of current fees.
Q: What materials should I take to the test?
A: Be sure you take with you your admission ticket, some form of photo and signature
identification, several Number 2 soft lead pencils with good erasers,
and a watch to help pace yourself during the exam. No calculators or other
aids are permitted in the test center.
Q: What is on the CBEST?
A: The exam consists of three areas: 50 multiplechoice reading comprehension
questions, 50 multiplechoice math questions, and two essays.
Q: What is a passing score?
A: The total passing score, as established by the Superintendent of Public
Instruction, is a total of 123 on all three sections combined and a minimum of
37 on each of the sections.
Introduction
Q: When will I get my score report?
A: Your test score will be mailed to you about four weeks after you take the
CBEST. If you pass, you will also receive a Permanent Verification Card and
two transcript copies of this card to use as may be required. No additional
transcripts will be provided to school districts or universities. You may, however,
receive additional sets of transcript copies for a small fee.
Q: May I take the CBEST more than once?
A: Yes, but remember, your plan is to pass on your first try.
Q: Do I need to take all three parts of the test?
A: You must pass all three parts of the test. However, if you previously have
passed any part of the exam at one administration, you may take only those
sections you have not yet passed. Thus, you do not have to pass all sections
in one examination; you can achieve a total passing score in separate
administrations.
Q: Should I guess on the test?
A: Yes! Since there is no penalty for guessing, guess if you have to. If possible,
first try to eliminate some of the choices to increase your chances of choosing
the right answer. But don’t leave any of the answer spaces blank.
Q: Suppose I do terribly on the test. May I cancel my CBEST score?
A: Yes, you may cancel your CBEST score, but only if you notify the test supervisor
before leaving the test center after you take the test. However, since no
one will know your score except you, there is no reason to cancel — no refunds
are given.
Q: May I write on the test?
A: Yes! Because scratch paper is not provided, you must do all of your work in
the test booklet. Your answer sheet, however, must have no marks on it other
than your personal information (name, registration number, and so on) and
your answers.
Q: How should I prepare?
A: Understanding and practicing testtaking strategies help a great deal. Subject
matter review in arithmetic, simple algebra, and measurement is also invaluable.
Some teachers’ unions and universities offer preparation programs to
assist you in attaining a passing score. Check with them for further
information.
Q: How do I get further information?
A: For questions about registration procedures, the admission ticket, or the score
report, you should contact CBEST Program, National Evaluation Systems,
Inc., P.O. Box 340880, Sacramento, CA 958340880, phone 9169284001.
5
Part I: Introduction to CBEST: California Basic Educational Skills Test
For late and emergency registration services, phone 9169284001.
For Telecommunications Device for the Deaf (TDD), phone 9169280430.
For questions about CBEST policies, contact the California Commission on
Teacher Credentialing, P.O. Box 944270, Sacramento, CA 942442700, phone
9164457254, or Oregon Teacher Standards and Practices Commission, 255
Capitol Street NE, Suite 105, Salem, OR 973101332, phone 5033783586.
6
Introduction
Three Successful Approaches to
the MultipleChoice Questions
The “PlusMinus” System
Many who take the CBEST don’t get their best possible score because they spend
too much time on difficult questions, leaving insufficient time to answer the easy
questions. Don’t let this happen to you. Since every question within each section
is worth the same amount, use the following system:
1. Answer easy questions immediately.
2. When you come to a question that seems “impossible” to answer, mark a
large minus sign (“”) next to it on your test booklet.
Then mark a “guess” answer on your answer sheet and move on to the next
question.
3. When you come to a question that seems solvable but appears too timeconsuming,
mark a large plus sign (“+”) next to that question in your test
booklet and register a guess answer on your answer sheet. Then move on to
the next question.
If you budget your time as suggested, you have just over a minute to a
minute and a half per question. A “timeconsuming” question is a question
that you estimate will take you more than several minutes to answer. But
don’t waste time deciding whether a question is a “+” or a “”. Act quickly
because the intent of this strategy is, in fact, to save you valuable time.
After working all the easy questions, your booklet should look something
like this:
1.
+2.
3.
4.
+5.
and so on
4. After working all the problems you can do immediately (the easy ones) and
writing and reading over the essays, go back and work your “+” problems.
Change your “guess” on your answer sheet, if necessary, for those problems
you are able to work.
7
Part I: Introduction to CBEST: California Basic Educational Skills Test
5. If you finish working your “+” problems and still have time left, you can
either:
(A) Attempt those “” questions — the ones that you considered impossible.
Sometimes another problem will “trigger” your memory and you’ll be
able to go back and answer one of the earlier, “impossible” problems.
or
(B) Don’t bother with those “impossible” questions. Rather, spend your time
reviewing your work to be sure you didn’t make any careless mistakes on
the questions you thought were easy to answer.
Remember: You don’t have to erase the pluses and minuses you make on your
question booklet. And be sure to fill in all your answer spaces — if necessary,
with a guess. Because there is no penalty for wrong answers, it makes no sense to
leave an answer space blank.
The Elimination Strategy
Take advantage of being allowed to mark in your testing booklet. As you eliminate
an answer choice from consideration, make sure to mark it out in your question
booklet as follows:
A
?B
C
D
?E
Notice that some choices are marked with question marks, signifying that they
may be possible answers. This technique helps you avoid reconsidering those
choices you have already eliminated. It also helps you narrow down your possible
answers.
Again, the marks you make on your testing booklet do not need to be erased.
The “Avoiding Misreads” Method
Sometimes a question may have different answers depending upon what is asked.
For example:
If 6y+ 3x= 14, what is the value of y?
8
Introduction
The question may instead have asked “what is the value of x?”
or
If 3x+ x= 20, what is the value of x+ 2?
Notice that this question doesn’t ask for the value of x, but rather the value of x+ 2.
Be aware that the words except and not change a question significantly.
All of the following statements are true except . . .
or
Which of the expressions used in the first paragraph does not help develop
the main idea?
To avoid misreading a question (and therefore answering it incorrectly), simply
circle what you must answer in the question. For example, do you have to find x
or x+ 2? Are you looking for what is true or the exception to what is true? To help
you avoid misreads, mark the questions in your test booklet in this way:
If 6y+ 3x= 14, what is the value of y ?
If 3x+ x= 20+ 4, what is the value of x+ 2 ?
All of the following statements are true except
Which of the expressions used in the first paragraph does not help develop
the main idea ?
And, once again, you don’t have to erase the circles you make in your question
booklet.
9
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PART II
PART II
Analysis of Exam Areas
This part is designed to introduce you to each area of the CBEST by
carefully reviewing
• Ability Tested
• Basic Skills Necessary
• Directions
• Analysis of Directions
• Suggested Approach with Samples
This part emphasizes important testtaking techniques and strategies and
how to apply them to a variety of problem types. Sample essays are also
included in this section as a guideline to assist you in evaluating your
own essays and to point out some of the common errors in essay writing.
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THE READING SECTION
Introduction
The Reading section contains 50 questions. It consists of long passages (200 or
more words), short passages (approximately 100 words), short statements (1 or 2
sentences), tables of contents, outlines, indexes, graphs, charts, and tables.
Each passage, statement, graph, and so on, is followed by questions based on its
content.
Ability Tested
This section tests your ability to understand, interpret, and analyze the passages
and materials given. The common types of questions are those that ask you
■
■
■
■
■
■
■
■
■
■
■
■
■
■
■
about the main point, main idea, or possible title of the passage
about the author’s purpose
about specific details stated or given
about supporting ideas or information
about information that is assumed, implied, suggested
about inferences that can be drawn from the material
about the meaning of a word or phrase
about the organization of a passage
to recognize the style or tone of a passage
to evaluate how the author develops and presents the passage
to recognize applications of the author’s opinions or ideas
to recognize the intended audience
to evaluate strengths and weaknesses of an argument
to find information
to fill in information
No outside knowledge is necessary; all questions can be answered on the basis of
what is stated or implied in the passage or information given.
13
Part II: Analysis of Exam Areas
Basic Skills Necessary
Understanding, interpreting, and analyzing passages and information are important
skills for this section. Being able to comprehend what is specifically stated in
the lines and what is “suggested or implied” between the lines are also necessary
skills.
Directions
A question or number of questions follow each of the statements or passages in
this section. Using only the stated or implied information given in the statement or
passage, answer the question or questions by choosing the best answer from
among the five choices given. Make sure to mark your answers for this section in
the Reading section of the answer sheet.
Analysis of Directions
You should take about 70 minutes to do the 50 questions. If any question takes
you more than about a minute and a half, take a guess and keep going.
If you do not know the answer to a question, try to eliminate one or more of the
choices so that you increase your odds of guessing the correct answer. But even if
you cannot eliminate any of the choices, take a guess because there is no penalty
for wrong answers.
Answer all of the questions for one passage before moving on to the next passage.
Use only information given or implied in a passage. Don’t consider outside information,
even if it seems more accurate than the information in the passage.
Above all, be sure that your answers on the answer sheet correspond to the numbers
in your question booklet. Placing one answer in the incorrect number on the
answer sheet can shift all your answers to the incorrect spots. Be careful!
General Procedure for Answering
Reading Questions
14
1. Preread the questions, circling the word or phrase that stands out in each
question. Don’t read the answer choices.
2. Read and mark the passage, paying special attention to information relevant
to the questions you’ve skimmed.
The Reading Section
3. As you read the passage, also watch for names, definitions, places and numbers,
but don’t try to memorize the passage. Remember, you need to understand
the main point. What is the author trying to say?
4. Answer the questions. Base your answers only on the material given in the
passage. Assume that the information in each passage is accurate. The questions
test your understanding of the passage alone; they do not test the historical
background of the passage, the biography of the author, or previous
familiarity with the work from which the passage is taken.
5. Make sure that the answer you select answers the question. A good or true
answer may not be correct, if it doesn’t answer the question.
6. Don’t get stuck on the passage or any one question. Remember, each question
is of equal value.
Some General Strategies
Two strategies that can improve your reading comprehension are prereading the
questions and marking the passage. Readers who use these strategies tend to score
much higher on reading tests than readers who don’t.
Preread the Questions
Before reading the passage, read each question (but don’t spend time reading all
the multiplechoice answers) and circle the most important word or phrase.
Sample
1. The author’s argument in favor of freedom of speech may be summarized
in which of the following ways?
A. If every speaker is not free, no speaker is.
B. Speech keeps us free from the animal kingdom
C. As we think, so we speak.
D. The Bill of Rights ensures free speech.
E. Lunatic speeches are not free speeches.
The most important part is usually the most concrete and specific one. In this
case, you might circle “freedom of speech.” The question parts that you circle will
be those you’ll tend to remember when you read the passage. In this case, you
would be likely to notice and pay close attention to “freedom of speech” when it
occurs in the passage. Thus, prereading allows you to focus on the parts of the
passage that contain the answers.
15
Part II: Analysis of Exam Areas
After prereading the questions, read and mark the passage. Always mark those
spots that contain information relevant to the questions you’ve read. In addition,
you should mark other important ideas and details. In general, remember not to
overmark; never make more than a few marks per paragraph in order to make
those parts you mark stand out. More specific advice on marking, in reference to
specific subareas of reading skills, follows.
Suggested Approaches with
Sample Passages
Regular Passages
Read the passage below and answer the three questions that follow.
*By the time a child starts school, he or she has mastered the major part of the rules of
grammar. The child has managed to accomplish this remarkable feat in such a short
time by experimenting with and generalizing the rules all alone. Each child, in effect,
rediscovers language in the first few years of life.
*When it comes to vocabulary growth, it’s a different story. Unlike grammar, the chief
means by which people learn vocabulary is memorization.
* And some people have a hard time learning and remembering new words.
*Indicates portions of the passage that refer directly to a question you’ve
skimmed. Also marked are the main points and key terms.
Understand What Is Given
Sample
2. From the information given, which of the following is the approximate age
at which a child has mastered many rules of grammar?
A. 3
B. 5
C. 8
D. 10
E. 18
16
The Reading Section
The first sentence of the passage contains several words from this question, so it is
likely to contain the correct answer. The phrase “By the time a child starts school”
indicates that the answer is 5. Before choosing B, you should look at all the answers
and cross out those that seem incorrect.
Eliminate and Mark Out Choices That Are Incorrect
Sample
3. Although vocabulary growth involves memorization and grammar learning
does not, which of the following can be concluded about both vocabulary
and grammar ?
A. Both make use of memorization.
B. Both make use of study skills.
C. Both make use of words.
D. Neither makes use of words.
E. Neither makes use of writing skills.
You should mark out choices A, D, and E. Choice A contradicts both the passage
and the question itself. Choices D and E are not reasonable. Choice B is a possibility,
but choice C is better because grammar learning in young children does not
necessarily involve study skills but does involve words.
Understand What Is Implied in the Passage
Sample
4. Which of the following is implied by the last sentence in the passage?
A. Some people have no trouble learning and remembering new words.
B. Some people have a hard time remembering new words.
C. Grammar does not involve remembering words.
D. Old words are not often remembered.
E. Learning and remembering are kinds of growth.
Implies tells you that the answer is something suggested but not explicitly stated
in the passage. B is explicitly stated in the passage, so you may eliminate it. But
choice B implies the opposite: If some people have a hard time, then it must be
true that some people don’t. A is therefore the correct choice. C, D, and E are
altogether different from the meaning of the last sentence.
17
Part II: Analysis of Exam Areas
Read the passage below and answer the three questions that follow.
St. Augustine was a contemporary of Jerome. After an early life of pleasure,
he became interested in a philosophical religion called Manichaeism, a derivative
of Persian religion, in which the forces of good constantly struggle
with those of evil. Augustine was eventually converted to Christianity by
St. Ambrose of Milan. His Confessions was an autobiography that served
as an inspiration to countless of thousands who believed that virtue would
ultimately win.
Make Sure That Your Answer Is WellSupported
by the Information in the Passage
Sample
5. St. Augustine’s conversion to Christianity was probably influenced by
which of the following?
A. his confessional leanings
B. his contemporaries
C. the inadequacy of a Persian religion to address Western moral problems
D. his earlier interest in the dilemma of retaining virtue
E. the ravages of a life of pleasure
Having skimmed this question, you may have marked the portion of the passage that
mentions Augustine’s conversion and paid attention to the events (influences) leading
to it. Choice A requires speculating beyond the facts in the paragraph; there is also no
evidence in the passage to support C or E. Choice B is too vague and general to be
the best answer. Choice D points toward Augustine’s earlier interest in Manichaeism,
and the last sentence suggests that Augustine’s interest in retaining virtue continued
through his Christian doctrine. Well supported as it is, D is the best answer.
Some questions assess your overall understanding of the meaning, style, tone, and
point of view of the passage.
Sample
6. From the information in the passage, it can be concluded that Augustine was
which of the following?
18
A. a fairweather optimist
B. a cockeyed optimist
C. a hardworking optimist
D. a failed optimist
E. a glib optimist
The Reading Section
Skimming this question is not very helpful because it doesn’t point specifically to
any information in the passage. Questions of this sort usually assess your overall
understanding of the meaning, style, tone, or point of view of the passage. In this
case, you may recognize that Augustine is a serious person; therefore, more lighthearted
terms like fairweather A, cockeyed B, and glib E are probably inappropriate.
Choice D contradicts Augustine’s success as an “inspiration to countless
thousands.” Choice C corresponds with his ongoing, hopeful struggle to retain
virtue in the world; it’s the best answer.
Know Where to Look for Information
Sample
7. Judging from the reaction of thousands to Augustine’s Confessions, it can
be concluded that much of his world at that time was in a state of
A. opulence.
B. misery.
C. heresy.
D. reformation.
E. sanctification.
Having skimmed this question, you may have marked the last sentence of the passage
as the place to look for the answer. That Augustine’s readers were inspired
implies that they required inspiration, that they were in some sort of uninspiring,
or negative situation. You can therefore eliminate A and E because they are positive
terms. Choice D is not necessarily a negative term, and so is probably not the
best answer. Choice C, although a negative term, does not describe a state of being
which thirsts for inspiration. Choice B does, and B therefore is the best
choice.
Read the passage below and answer the two questions that follow.
The fact that bacteria are capable of chemical communication first emerged
from investigations into marine bacteria able to glow in the dark. In 1970,
Kenneth H. Nealson and John Woodland Hastings of Harvard University observed
that luminous bacteria in culture do not glow at a constant intensity. In
fact, they emit no light until the population reaches a high density.
Nealson and Hastings knew that the light resulted from chemical reactions
catalyzed by the enzyme luciferase. They postulated that this enzyme was ultimately
controlled not by some mechanism inside each bacterial cell but by a
molecular messenger that traveled between cells. Once inside target cells, the
messenger, which the researchers called autoinducer, could induce expression
of the genes coding for luciferase and for the other proteins involved in light
19
Part II: Analysis of Exam Areas
production; that is, autoinducer could stimulate synthesis of the encoded proteins
and, thus, of light. Their theory met with skepticism at first but has since
been confirmed and expanded.
Read All the Choices to Look for the Best Answer
Sample
8. According to the passage, Nealson and Hasting’s research was instrumental
in indicating that
A. bacteria communicate through molecular messengers that travel
between cells.
B. luminous bacteria glow not at a constant density but at various densities.
C. bacteria are genetically coded by the autoinducer.
D. the molecular messenger luciferase causes bacteria to glow at high
densities.
E. the autoinducer, not the enzyme luciferase as was previously believed,
produces the luminosity of certain marine bacteria.
The best choice is A. Although the research focused on marine bacteria that glow,
its broader significance is that it shows the chemical communication between bacteria.
Choice B is the observation that led to the theory, but is not the best answer.
Choice C is inaccurate; an autoinducer does not code genes but induces their expression.
Choice D is also incorrect because the molecular messenger that causes
bacteria to glow is not the enzyme luciferase. Choice E might seem correct at first
reading, but although the autoinducer allows the expression of the lightproducing
enzymes such as luciferase, it doesn’t produce light itself.
Know Where to Locate a Specific Detail in the Passage
Sample
9. Which of the following are characteristic of the autoinducer involved in
light production by marine bacteria?
I. It catalyzes chemical reactions in bacterial cells.
II.
III.
It stimulates synthesis of certain proteins.
It acts as a messenger between enzymes and bacteria.
20
A. I and II only
B. II and III only
C. II only
D. III only
E. I, II, and III
The Reading Section
The best choice is C. Only statement II is correct (sentence 6). Luciferase, not the
autoinducer, catalyzes the reactions that cause light, making statement I incorrect
(sentence 4). Statement III is incorrect because the autoinducer acts as a messenger
between bacteria cells (sentence 5), not between enzymes and bacteria.
Read the passage below and answer the two questions that follow.
History gives a cruel experience of human nature, in showing how exactly the
regard due to the life, possessions, and entire earthly happiness of any class
of persons, was measured by what they had the power of enforcing; how all
who made any resistance to authorities that had arms in their hands, however
dreadful might be the provocation, had not only the law of force but all other
laws, and all the notions of social obligation against them; and in the eyes of
those whom they resisted, were not only guilty of crime, but of the worst of
all crimes, deserving the most cruel chastisement that human beings could inflict.
The first small vestige of a feeling of obligation in a superior to acknowledge
any right in inferiors began when he had been induced, for
convenience, to make some promise to them. Though these promises, even
when sanctioned by the most solemn oaths, were for many ages revoked or
violated on the most trifling provocation or temptation, it is probable that
this, except by persons of still worse than average morality, was seldom done
without some twinges of conscience.
Notice What Is Stated and What Is Implied
Sample
10. The author implies that laws are based on
A. the necessity of protecting the weakest members of a society.
B. the interests of those in a society who possess the most power.
C. the notions of social obligation that are passed from generation to
generation.
D. promises made to those without power by those with the most power.
E. the belief that “earthly happiness” is the right of everyone in society,
including those who resist authority.
The best choice is B. The author makes it clear that the person with the most power
has “not only the law of force but all other laws” behind him or her, implying that
the law itself exists to protect the interests of the powerful. Choices A and E are incorrect;
in fact, the passage suggests the contrary. Choice C is also inaccurate; “all
the notions of social obligation” support the powerful, according to the passage.
Choice D might be tempting, but according to the author, promises are made only
for the convenience of the powerful; laws are made to protect their interests.
21
Part II: Analysis of Exam Areas
Recognize the Tone and Purpose of the Passage
Would the author agree or disagree with something?
Sample
11. The author of this passage would be most likely to agree with which of the
following statements?
A. In order to prevent chaos in a society, authority must be strong and
unquestioned.
B. All men, whether weak or strong, desire justice in their dealings with
others.
C. Social obligation is the most important factor ensuring protection of the
weak by the strong.
D. Rights are granted to those without power when to do so will benefit
those with power.
E. In the past, when rights have been granted to people, only the most
extreme circumstances have led to their being rescinded.
The best choice is D. According to the passage, the rights of the weak were acknowledged
only when the strong were induced to do so for their own convenience
(sentence 2). Choice A is irrelevant; the author doesn’t advocate strong,
unquestioned authority; the passage only defines what the author sees as the realistic
situation. Choice B is incorrect; the author states that the powerful are concerned
with their own interests, not with justice. Choice C is also incorrect;
notions of social obligation are, like laws, based on the needs of the powerful.
Choice E is refuted in the passage; the author states that rights have been “revoked
or violated on the most trifling provocation.”
As you read the following longer passage, focus on what the author is really saying
or what point the author is trying to make. Also pay attention to how the passage
is put together — the structure.
Read the passage below and answer the five questions that follow.
22
Woodrow Wilson won his first office in 1910 when he was elected governor
of New Jersey. Two years later, he was elected president in one of the most
rapid political rises in our history. For a while, Wilson had practiced law but
found it both boring and unprofitable; then he became a political scientist
and finally president of Princeton University. He did an outstanding job at
Princeton, but when he was asked by the Democratic boss of New Jersey, Jim
Smith, to run for governor, Wilson readily accepted because his position at
Princeton was becoming untenable.
Until 1910, Wilson seemed to be a conservative Democrat in the Grover
Cleveland tradition. He had denounced Bryan in 1896 and had voted for the
The Reading Section
National Democratic candidate who supported gold. In fact, when the
Democratic machine first pushed Wilson’s nomination in 1912, the young
New Jersey progressives wanted no part of him. Wilson later assured them
that he would champion the progressive cause, and so they decided to work
for his election. It is easy to accuse Wilson of political expediency, but it is
entirely possible that by 1912 he had changed his views as had countless
other Americans. While governor of New Jersey, he carried out his election
pledges by enacting an impressive list of reforms.
Wilson secured the Democratic nomination on the 46th ballot. In the campaign,
Wilson emerged as the middleoftheroad candidate — between the
conservative William H. Taft and the more radical Theodore Roosevelt.
Wilson called his program the New Freedom, which he said was the restoration
of free competition as it had existed before the growth of the trusts. In
contrast, Theodore Roosevelt was advocating a New Nationalism, which
seemed to call for massive federal intervention in the economic life of the nation.
Wilson felt that the trusts should be destroyed, but he made a distinction
between a trust and legitimately successful big business. Theodore Roosevelt,
on the other hand, accepted the trusts as inevitable but said that government
should regulate them by establishing a new regulatory agency.
Always Look for the Main Point of the Passage
There are many ways to ask about the main point of a passage. What is the main
idea? What is the best title? What is the author’s purpose?
Sample
12. The author’s main purpose in writing this passage is to
A. argue that Wilson is one of the great U.S. presidents.
B. survey the difference between Wilson, Taft, and Roosevelt.
C. explain Wilson’s concept of the New Freedom.
D. discuss some major events of Wilson’s career.
E. suggest reasons that Wilson’s presidency may have started World War I.
The best answer is D. Choices A and E are irrelevant to the information in the passage,
and choices B and C mention secondary purposes rather than the primary one.
Be Aware of Information Not Directly
Stated in the Passage
Read between the lines. Implied information can be valuable in answering some
questions.
23
Part II: Analysis of Exam Areas
Sample
13. The author implies which of the following about New Jersey progressives?
A. They did not support Wilson after he was governor.
B. They were not conservative Democrats.
C. They were more interested in political expediency than in political
causes or reforms.
D. Along with Wilson, they were supporters of Bryan in 1896.
E. They particularly admired Wilson’s experience as president of Princeton
University.
The best choice is B. In the second paragraph, Wilson’s decision to champion the
progressive cause after 1912 is contrasted with his earlier career, when he seemed
to be a conservative Democrat. Thus, one may conclude that the progressives,
whom Wilson finally joined, were not conservative Democrats, as was Wilson earlier
in his career. Choices A and D contradict information in the paragraph, while
choices C and E are not suggested by any information given in the passage.
Watch for Important Conclusions or Information
That Supports a Conclusion
Sample
14. The passage supports which of the following conclusions about the
progress of Wilson’s political career?
A. Few politicians have progressed so rapidly toward the attainment of
higher office.
B. Failures late in his career caused him to be regarded as a president who
regressed instead of progressed.
C. Wilson encountered little opposition after he determined to seek the
presidency.
D. The League of Nations marked the end of Wilson’s reputation as a
strong leader.
E. Wilson’s political allies were Bryan and Taft.
The best choice is A. This choice is explicitly supported by the second sentence in
the first paragraph which states that Wilson was “elected president in one of the
most rapid political rises in our history.”
24
The Reading Section
Understand the Meaning and Possible Reason
for Using Certain Words or Phrases
Sample
15. In the statement “Wilson readily accepted because his position at Princeton
was becoming untenable” in the first paragraph of the passage, the meaning
of untenable is probably which of the following?
A. unlikely to last for years
B. filled with considerable less tension
C. difficult to maintain or continue
D. filled with achievements that would appeal to voters
E. something he did not have a tenacious desire to continue
The best choice is C. On any reading comprehension test, be alert to the positive
and negative connotations of words and phrases in each passage as well as in the
questions themselves. In the case of “untenable,” the prefix un suggests that the
word has a negative connotation. The context in which the word occurs does so as
well. Wilson left his position at Princeton; therefore, we may conclude that the
position was somehow unappealing. Only two of the answer choices, C and E,
provide a negative definition. Although choice E may attract your attention because
tenacious looks similar to tenable, the correct choice is C, which is the
conventional definition of untenable.
Eliminate Those Choices That Are
Not Supported by the Passage
Your answer choice must be supported by information either stated or implied in
the passage.
Sample
16. According to the passage, which of the following was probably true about
the presidential campaign of 1912?
A. Woodrow Wilson won the election by an overwhelming majority.
B. The inexperience of Theodore Roosevelt accounted for his radical position.
C. Wilson was unable to attract twothirds of the votes but won anyway.
D. There were three nominated candidates for the presidency.
E. Wilson’s New Freedom did not represent Democratic interests.
25
Part II: Analysis of Exam Areas
The best choice is D. Choices A, B, and C contain information that is not addressed
in the passage. We may eliminate them as irrelevant. Choice E contradicts the fact
that Wilson was a Democratic candidate. The discussion of Taft and Roosevelt as
the candidates who finally ran against Wilson for the presidency supports choice D.
Passages with Numbered Sentences
Read the passage below and answer the four questions that follow.
[1]The fundraising practices of the political parties in this country are clearly
out of control. [2]A previously undisclosed transcript has revealed that Richard
Nixon’s secret White House slush fund, which was used to silence the
Watergate burglars, came from illegally donated campaign money. [3]After
Nixon resigned, his successor, Gerald Ford, pardoned him. [4]Gerald Ford has
joined former Presidents Carter and Bush in urging campaign funding reforms.
[5]Recent hearings have shown all too clearly that both parties have been guilty
of highly questionable fundraising practices. [6]Unless the laws are changed,
the shoddy practices of the last 30 years will undoubtedly continue.
Be Careful to Spot the Words Least, Most,
and Except in a Question
Sample
17. Which of the following numbered sentences is the least relevant to the
main idea of this paragraph?
A. Sentence 1
B. Sentence 2
C. Sentence 3
D. Sentence 4
E. Sentence 5
The best answer is C. The paragraph is about campaign financing and the need for
reform. All the other references to former presidents are relevant to this issue, but
Ford’s pardon of Nixon is not.
26
The Reading Section
Know How to Differentiate Opinion from Fact
Sample
18. Which of the following numbered sentences of the passage expresses a
matter of opinion rather than a fact?
A. Sentence 1
B. Sentence 2
C. Sentence 3
D. Sentence 4
E. Sentence 5
The best answer is A. The assertion that fundraising practices are “out of control”
is an opinion of the author. Though there is some evidence to support this belief,
it’s not factual in the way that the four other sentences in the paragraph are.
Read the Passage Looking for the Main Point
Sample
19. Which of the following numbered sentences best expresses the central
point of the paragraph?
A. Sentence 1
B. Sentence 2
C. Sentence 4
D. Sentence 5
E. Sentence 6
The best answer is E. Though the first sentence makes an important point, the
central purpose of the paragraph is to encourage reform.
27
Part II: Analysis of Exam Areas
Use the Context to Figure Out the Meaning of Words
Sample
20. Which of the following is the best definition of the word shoddy as it is
used in the last sentence of this passage?
A. illegal
B. avaricious
C. shabby
D. opportunistic
E. adventitious
The best answer is C. The adjective “shoddy” means “made of inferior material.”
Of the choices given here, the best choice is “shabby.”
Passages with Missing Words or Phrases
Read the passage below and answer the three questions that follow.
To transfer a design to be crossstitched onto fabric, use graph paper with
boxes the size of the stitches you plan to embroider. ______ mark the crosses
on the graph paper to correspond to the design. ______ place a piece of carbon
paper face down on the material and adjust the graph paper over it. ______,
being careful to avoid smudging, use a fine pencil to mark each cross.
Working from left to right, bring the needle out at the lower lefthand corner
of the first square. Now insert the needle in the upper righthand corner of the
square and bring it out at the lower lefthand corner of the next cross. Do not
complete the cross, but continue making halfcrosses from bottom left to top
right to the end of the row. Then turn the work and repeat the process, making
the second half of the crosses to complete the row. Repeat this process on the
next row.
Often the context can “frame” the word and give it meaning.
Sample
21. As it is used in the first paragraph, the word material refers to
28
A. money.
B. fabric.
C. graph paper.
D. a flat surface.
E. table.
The Reading Section
The best answer is B. In this context, material is the fabric on which the crosses
are to be drawn.
Read FillIns into the Passage
Sample
22. To make the instructions in the first paragraph clear, which of the following
should replace the three blanks in this order?
A. First; On the other hand; Then
B. You should; You can; You should
C. To begin; Or; As a last step
D. Initially; Then; Carefully
E. First; Then; Finally
The best answer is E. The addition of these three adverbs, which specify the order
of the steps, make the instructions clearer.
Note Specific Information in the Passage
Sample
23. According to the instructions in the second paragraph, the first stitch in the
second row of cross stitches would begin
A. with the needle coming out of the top lefthand corner of the first cross
on the left in the second row.
B. with the needle coming out of the top lefthand corner of the first cross
on the right in the second row.
C. with the needle coming out of the bottom lefthand corner of the first
cross on the left in the second row.
D. with the needle coming out of the bottom lefthand corner of the first
cross on the right in the second row.
E. with the needle coming out of the top righthand corner of the first cross
on the right in the second row.
The best answer is C. The last sentence instructs the embroiderer to turn the
work and begin again to complete the crosses. After the fabric is turned, the first
halfcross begins on the lefthand side and runs from left top to right bottom. To
complete the cross, the stitch would go from the left bottom to the right top, just
as it did when the row was stitched for the first time.
29
Part II: Analysis of Exam Areas
Read the passage below and answer the four questions that follow.
As the 20th century draws to a close, the coyote can be found in 49 of the 50
states. Thirty years ago, most of the coyote population was confined to the
West, but now they prowl from Maine to Florida, and increasingly in urban
areas. Their range has extended north as far as Alaska and south through almost
all of Central America.
This population explosion has alarmed sheep ranchers in the western states,
and they have responded with a new weapon: a collar worn by sheep that
contains the fiercely toxic Compound 1080. Ranchers say the amount of
deadly poison is so small that it presents no threat to the environment.
______ the Environmental Protection Agency has approved the use of the
collars in several sheepraising states. ______ there is still opposition from
many environmental groups. They point to the cruelty of the coyotes’ death,
which can last from three to twelve hours. They claim that Compound 1080
can kill innocent animals and poses a special threat to eagles. Because the
collars may find their way into stream beds, they fear the widespread killing
of fish and fisheating birds and animals.
Understand the Author’s Position
Sample
24. Which of the following best describes the position of the author of this
passage on the use of poisoned collars to protect sheep?
A. The author favors their use since the passage points out that they have
been approved by the Environmental Protection Agency.
B. The author disapproves of their use since the passage describes the
poison as “fiercely toxic.”
C. The author presents the point of view of both sides without clearly
taking sides.
D. The author favors their use if they can be used without posing a threat to
other wild animals.
E. Though the author’s position is never explicit, the author disapproves of
the killing of any wild animals.
The best answer is C. In this passage, the author does not commit to one side or
the other. On the one hand, the author reports what the ranchers and the EPA
have said in favor of the devices, yet he or she also reports the objections of the
environmentalists.
30
The Reading Section
Note the Differences in FillIn Choices
Sample
25. The second paragraph would be clearer if which of the following words
filled the blanks in this order?
A. However; Also
B. Thus; And
C. But; On the other hand
D. Furthermore; But
E. Yet; However
The best answer is D. The use of “Furthermore” makes clear that the sentence
about the EPA is part of the argument on one side. The “But” signals the shift to
the opposition’s point of view.
Read for the Main Point and How
the Passage Is Organized
Sample
26. Which of the following most accurately represents the content of this passage?
A. I. the coyote overpopulation problem
II. the ranchers’ solution to coyote expansion
B. I. the expanding range of the coyote
II. the case for and against poisoning the coyote
C. I. coyotes in America today
II. protecting sheep against coyote predation
D. I. new data on the coyote population
II. the dangers to the environment of Compound 1080
E. I. the population increase of the coyote
II. coyote overkill and the western environment
The best answer is B. None of the summaries of the first paragraph is bad, although
A, unlike the passage, calls the coyote range a “problem.” The best summary
of the second paragraph should refer to the positions of both the ranchers
and the environmentalists.
31
Part II: Analysis of Exam Areas
Make Sure Any Addition to a Passage Is Consistent
with the Style and Relates to the Content
Sample
27. Which of the following is the most appropriate addition as a final sentence
for the second paragraph?
A. So you can see that there is no easy answer to the problem of the coyote
versus the sheep rancher.
B. Americans have been trying to eradicate the coyote for over one hundred
years, but its population and range have relentlessly increased; there is
no reason to be optimistic about the results of this latest battle in the
coyote wars.
C. I think that maybe we should try out the collar under restrictions which
could prevent any accidents and make sure nothing goes wrong to hurt
the environment.
D. If the collar can save the sheep, don’t you think it’s a good idea?
E. The rancher’s battle with the coyote is part of a long war with nature,
and the collar is a new device, like a James Bond gadget, that might
bring victory.
The best answer is B. This sentence is consistent with the style of the rest of the
paragraph and relates the content of the second paragraph to the information about
the coyote’s range that began the first paragraph. Choice A is bland and, unlike
the rest of the passage, directly addresses the reader. Choice C is wishywashy,
and it uses the first person pronoun for the only time. Choice D surprisingly takes
sides, and it uses a direct question for the only time. Choice E overuses figures of
speech and also takes sides.
Tables of Contents or Indexes
32
Use the excerpt from an index below to answer the two questions that follow.
parable, 53, 56, 3445
parody, 102, 14759, 223, 30206, 313
pastoral poetry, 99101, 155167, 243, 341343, 366
Pater, Walter, 238, 255, 277
Petronius, 249, 30912; Satyricon, 22, 3343
picaresque novel, 45, 310
Pindaric ode, 240
Plato, 108, 111, 145, 168, 18990, 28897; Apology, 26778; Republic,
11214; Symposium, 67, 69, 7778;
Platonism, 5966
Poe, Edgar Allan, 118, 119, 12324, 22145; The Bells, 278; The Gold Bug,
26466; Ligeia, 5962; The Poetic Principle, 16667; The Raven, 33849
popular art and literature, 4, 12634
The Reading Section
Look carefully to find specific information
Sample
28. On what pages would one look to find information about Plato’s Republic?
A. 10811
B. 11214
C. 12634
D. 26778
E. 28897
The best answer is B. The entry for Plato includes a listing for Republic on pages
11214.
Know Where to Look and What to Look For
Sample
29. In the discussion of which of the following works of Poe is one most likely
to find comments on Platonic influence?
A. The Bells
B. The Gold Bug
C. Ligeia
D. The Poetic Principle
E. The Raven
The best answer is C. To answer this question, you must compare the pages indexed
for these works of Poe with the pages listed under Plato. The entry on
Platonism refers to pages 5966, while Poe’s Ligeia is discussed on pages 5962.
Because none of the other works by Poe has pages in common with the listings
under Plato, the answer must be Ligeia.
33
Part II: Analysis of Exam Areas
Use the following excerpt from a table of contents to answer the three
questions that follow.
PREALGEBRA
PRELIMINARIES AND BASIC OPERATIONS. . . . . . . . . . . . . . . . . . . 3
Preliminaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Groups of numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Ways to show multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Common math symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Properties of Basic Mathematical Operations . . . . . . . . . . . . . . . . . . . 5
Some properties (axioms) of addition . . . . . . . . . . . . . . . . . . . . . . . 5
Some properties (axioms) of multiplication. . . . . . . . . . . . . . . . . . . 6
A property of two operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Multiplying and Dividing Using Zero . . . . . . . . . . . . . . . . . . . . . . . . . 8
Powers and Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Squares and cubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Operations with powers and exponents . . . . . . . . . . . . . . . . . . . . . 10
Square Roots and Cube Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Square roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Cube roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Approximating square roots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Simplifying square roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Grouping Symbols: Parentheses, Brackets, Braces . . . . . . . . . . . . . . 15
Parentheses ( ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Brackets [ ] and braces { } . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Order of operations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Divisibility Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Know Where to Find a Specific Kind of Information
Sample
30. On which page should one look to find which operation should be performed
first, multiplication or addition?
34
A. 4
B. 8
C. 10
D. 14
E. 16
The Reading Section
The best answer is E. To find which operation comes first, multiplication or
addition, you would have to look at Order of operations on page 16.
Notice How Information Is Organized
Sample
31. Which of the following best describes the organizational pattern used in
dividing the book?
A. by topics, alphabetically
B. by category and subcategory
C. by level of difficulty
D. by length of section
E. by importance of concepts
The best answer is B. A careful review of the table of contents shows that the
organizational pattern is by category and subcategory.
Focus on What Information Is Needed
Sample
32. On what page would you look to find information about the distributive
property involving multiplication and division?
A. 3
B. 4
C. 6
D. 8
E. 10
The best answer is D. The distributive property involving multiplication and
division would be found under a property involving two operations, page 8.
35
Part II: Analysis of Exam Areas
The Five Key Questions for Understanding
and Interpreting What You Read
What Is the Main Idea of the Passage?
After reading any passage, try summarizing it in a brief sentence. To practice this
very important skill, read the editorials in your local paper each day and write a
brief sentence summarizing each one.
What Details Support the Main Idea?
Usually such details are facts, statistics, experiences, and so on, that strengthen
your understanding of and agreement with the main idea.
What Is the Purpose of the Passage?
Ask yourself what the author is trying to accomplish. The four most common general
purposes are (1) to narrate (tell a story), (2) to describe, (3) to inform, and (4)
to persuade.
Are the Style and Tone of the Passage
Objective or Subjective?
In other words, is the author presenting things factually or from a personal point
of view? If an author is subjective, you may want to pin down the nature of the
subjectivity. Ask yourself, is the author optimistic? pessimistic? angry? humorous?
serious?
What Are the Difficult or Unusual
Words in the Passage?
Readers who do not mark words that are difficult or used in an unusual way in a
passage often forget that the words occurred at all and have difficulty locating
them if this becomes necessary. By calling your attention to difficult or unusual
words, you increase your chances of defining them by understanding their meaning
in context.
36
The Reading Section
A PATTERNED PLAN OF ATTACK
Reading Section
Preread. Skim the question first,
marking the important words or phrases.
Read the passage actively, marking main points,
and information relevant to questions.
Always look for the main point of the passage.
Is the passage regular? Does it have missing words? Is it a table of contents or an index?
For Regular Passages
For Passages with Missing Words
For Tables of Contents and Indexes
Understand what is given.
Read fillins
into the passage.
Look carefully to find
specific information.
Understand what is implied
in the passage.
Note the difference in fillin choices.
Know where to look and
what to look for.
Make sure that the answer is
supported by the passage.
Notice how information
is organized.
Watch for style, tone, and
point of view.
Know where to
look for information.
Use context to figure out the
meaning of words.
Know where to locate detail.
Read all the choices.
Eliminate and mark out choices that are incorrect.
37
THE MATHEMATICS SECTION
Introduction
The Mathematics section of the test contains 50 questions. The questions are
selected from different areas of mathematics, with questions on measurement, ratios,
percentages, probability, and reading and interpreting tables, graphs, and charts.
Complex computations are not required, and most of the terms used are general,
commonly encountered mathematical expressions (for example: area, perimeter,
integer, and prime number). Most questions are presented as word problems.
Ability Tested
This part of the exam tests your ability to use your cumulative knowledge of
mathematics and your reasoning ability. Computation is minimal; you are not required
to have many specific formulas or equations memorized. What’s most important
is that you demonstrate a working understanding of general math concepts
that any teacher may need — the skill to average grades, read charts and graphs,
understand diagrams, interpret test results, and so on.
Basic Skills Necessary
A cumulative knowledge of mathematics is necessary for this section of the
CBEST — math from elementary grades through at least one year of high school,
and possibly one year of college. Thus, no single math course can prepare you
specifically for this part of the test.
The math topics covered include those in the following areas.
Arithmetic
You need to be able to:
■
■
■
Use operations involving whole number and fractions, decimals and
percents.
Apply arithmetic operations to practical math, such as invoices, unit cost,
totals.
Understand basic statistics and averages.
The Mathematics Section
■
■
■
■
■
■
Work with ratios and proportions.
Determine percents, including percent increase, decrease, and change.
Compare fractions, decimals, and positive and negative numbers.
Approximate values and roundoff numbers.
Estimate results of addition, subtraction, multiplication, and division prior
to actual computation.
Understand basic principles of probability and predict likely outcomes.
Basic Algebra
You need to be able to
■
■
■
■
■
■
Set up simple equations.
Solve equations with one variable.
Understand problemsolving terminology:
• Logical connectives, such as ifthen, and, and or
• Quantifiers, such as some, all, few, and none
Recognize different methods of solving a problem.
Identify important facts in a problem.
Determine whether enough information is given to solve a problem.
Measurement
You need to be able to
■
■
Understand and use standard units in the U.S. measurement system,
including length, temperature, weight, and capacity.
Measure length, perimeter, area, and volume.
Graphs, Charts, and Tables
You need to be able to
■
■
■
■
Understand data entry and information given.
Find missing information.
Use numerical information to solve math problems.
Work with line, bar, and circle graphs.
39
Part II: Analysis of Exam Areas
Directions
Each of the questions in this section is followed by five choices. Select the one
best answer for each question. Make sure to mark your answers for this section on
the Mathematics section of your answer sheet.
Analysis of Directions
You should spend about 75 minutes to do the 50 problems. This averages to a
minute and a half per problem, so keep that in mind as you attack each problem. If
you know that you can work a problem but that it will take you far, far longer than
a minute and a half, skip it and return to it later if you have time. Remember, you
want to do all the easy, quick problems first, before spending valuable time on the
others.
There is no penalty for guessing, so don’t leave any blanks. If you do not know the
answer to a problem but you can size it up to get a general range for your answer,
you may be able to eliminate one or more of the answer choices, thus increasing
your odds of guessing the correct answer. But even if you cannot eliminate any of
the choices, take a guess because there is no penalty for wrong answers.
Above all, be sure that your answers on your answer sheet correspond to the numbers
on your question sheet. Placing one answer in the incorrect number on the
answer sheet may shift all your answers to the incorrect spots. Be careful!
Also, make sure that you mark your answers to math questions on the
Mathematics section of your answer sheet.
Suggested Approach With Samples
A number of different approaches can be helpful in attacking many types of mathematics
problems. Of course, the strategies in this section don’t work on all the
problems, but if you become familiar with them, you will find them helpful in answering
quite a few questions.
40
Mark Key Words
Circling and/or underlining key words in each question is an effective testtaking
technique. You can easily be misled if you overlook a key word in a problem. By
circling or underlining these key words, you help yourself focus on what you are
being asked to find. Remember, you are allowed to mark and write on your testing
booklet. Take advantage of this opportunity.
The Mathematics Section
Samples
1. In the following number, which digit is in the thousandths place?
6574.12398
A. 2
B. 3
C. 5
D. 6
E. 9
The key word here is “thousandths.” By circling it, you pay closer attention to it.
This is the kind of question which, under the pressures of time and testing, you
may misread. You may easily misread it as thousands place. Hopefully, circling
the important words minimizes misreading. Your completed question may look
like this after you mark the important words or terms:
1. In the following number, digit is in the thousandths place?
A. 2
B. 3
C. 5
D. 7
E. 9
6574.12398
The correct answer is B.
2. Hal goes to the local gift shop to buy 3 yards of ribbon. If the 3 yards of
ribbon cost $2.97, what price is Hal paying per foot?
A. $ .33
B. $ .99
C. $2.94
D. $3.00
E. $8.91
The key word here is “foot.” Dividing $2.97 by 3 tells you only the price per yard,
and, of course, that price is choice B — $.99. Therefore it would be very helpful
to circle the words “price per foot” in the problem. You must still divide by 3 (because
there are 3 feet per yard) to find the cost per foot. $.99 divided by 3 is $.33,
which is choice A.
41
Part II: Analysis of Exam Areas
3. If 3x
+ 1= 16, what is the value of x
4?
A. 19
B. 16
C. 5
D. 1
E. –1
The key here is “find the value of x 4.” Therefore circle “x  4.” Note that
solving the original equation gives you only the value of x.
3x
+ 1=
16
3x
= 15
x=
5
Here again notice that 5 is one of the choices, C. But the question asks for the
value of x 4, not just x. To continue, replace x with 5 and solve:
x 4=
5 4=
1
The correct answer choice is D.
4. Together a bat and ball cost $1.25. The bat costs $.25 more than the ball.
What is the cost of the bat?
A. $ .25
B. $ .50
C. $ .75
D. $ 1.00
E. $ 1.25
The key words here are “cost of the bat,” so circle those words. If you solve this
alegebraically:
x = ball
x + $. 25 = bat (costs $.25 more than the ball)
Together they cost $1.25.
42
The Mathematics Section
^x+ . 25h+ x=
1.
25
2x
+ . 25=
125 .
2x
= 100 .
x=
. 50
But x is the cost of the ball. Notice that $.50 is one of the choices, B. Because
x= . 50, then x+ . 25= . 75. Therefore the bat costs $.75, which is choice C.
Always answer the question being asked. Circling the key word or words can help
you do that.
5. Tia is trying to round off the number 4,547 to the nearest hundred. If she
gets the right answer, she receives extra credit. What answer must Tia get
to receive extra credit?
A. 5,000
B. 4,600
C. 4,550
D. 4,500
E. 4,540
To round off to the nearest hundred, you must check to see whether the tens place
is 5 or more. If it is 5 or more, you round the hundreds place up one number and
put zeros in back — 4,500. The correct answer is D.
Pull Out Information
Pulling information out of the word problem structure often gives you a better
look at what you’re working with; therefore, you gain additional insight into the
problem.
Samples
6. If a mixture is 3 ⁄7 alcohol by volume and 4 ⁄7 water by volume, what is the
ratio of the volume of alcohol to the volume of water in this mixture?
A. 3/7
B. 4/7
C. 3/4
D. 4/3
E. 7/4
43
Part II: Analysis of Exam Areas
The first bit of information to pull out is what you’re looking for: “ratio of the volume
of alcohol to the volume of water.”
(You should have circled or underlined this information in the question.)
Rewrite the question as A (alcohol):W (water) and then put this ratio into working
form:
W A
Next, pull out the volumes of each:
A = 3 ⁄7 and W = 4 ⁄7
Now, you can figure out the answer easily by inspection or substitution using 3/7 ⁄4/7.
Invert the bottom fraction and multiply to get 3 ⁄7 × 7 ⁄4 = 3 ⁄4. The ratio of the volume
of alcohol to the volume of water is 3 to 4. The correct answer is C.
When pulling out information, actually write the numbers and/or letters to the
side of the problems to put them into a helpful form and eliminate some of the
wording.
7. Phil works for a furniture store 3 ⁄4 of the year and for a pool supply store
for 1 ⁄6 of the same year. He takes a vacation for the remainder of the year.
How much more time does he spend working for the furniture store than
for the pool supply store?
A. 1 month
B. 2 months
C. 7 months
D. 9 months
E. 11 months
First circle or underline “How much more time.” Next, pull out the information
regarding Phil’s work for the year:
furniture store 3 ⁄4 of a year is 3 ⁄4 × 12, or 9 months
pool supply store 1 ⁄6 of a year, or 2 ⁄12, which is 2 months
The difference is 9 months minus 2 months, which is 7 months. The correct answer
is C. Notice that taking a quick look at the answer choices is helpful, letting
you know that the answer is in months.
44
The Mathematics Section
8. If the ratio of boys to girls in a drama class is 2 to 1, which of the following
is a possible number of students in the class?
A. 10
B. 16
C. 19
D. 25
E. 30
First underline or circle “possible number of students.” Then, pulling out information
gives you the following.
b:g = 2:1
Because the ratio of boys to girls is 2:1, the possible total number of students in
the class must be a multiple of 2 + 1 (boys plus girls), or 3. The multiples of 3 are
3, 6, 9, 12, 15 and so on. Only choice E, 30, is a multiple of 3.
9. An employee’s annual salary was increased $15,000. If her new annual
salary now equals $90,000, what was the percent increase?
A. 15%
B. 16 2 ⁄3%
C. 20%
D. 22%
E. 24%
Circle or underline what you are looking for. In this case, “percent increase.”
Percent increase = change/starting point
Now pull out information.
If the employee’s salary was increased by $15,000 to $90,000, then the starting
salary was $90,000 − $15,000 = $75,000.
Therefore, 15,000 ⁄75,000 = 1 ⁄5 = 20%.
The correct answer is C.
Identify the Facts Needed
Not all the facts given are always needed to work out the problem. Pull out the
given facts and identify which of those facts help you work the problem.
45
Part II: Analysis of Exam Areas
Samples
10. Bill is 10 years older than his sister. If Bill was 25 years of age in 1983, in
what year could he have been born?
A. 1948
B. 1953
C. 1958
D. 1963
E. 1968
The key words here are “in what year could he have been born.” Thus the solution
is simple: 1983  25 = 1958, choice C. Notice that you pull out the information
“25 years of age” and “in 1983.” You don’t need the information about Bill’s age
in comparison to his sister’s, so you don’t need to pull it out.
11. John is 18 years old. He works for his father for 3 ⁄4 of the year, and he
works for his brother for the rest of the year. What is the ratio of the time
per year that John spends working for his brother to the time he spends
working for his father?
A. 1
⁄4
B. 1
⁄3
C. 3
⁄4
D. 4
⁄3
E. 4
⁄1
The key word “rest” points to the answer:
1 – 3 ⁄4 =
4
⁄4 – 3 ⁄4 = 1 ⁄4 (the part of the year John works for his brother)
Also key is the way you write the ratio. The problem becomes that of finding the
ratio of 1 ⁄4 to 3 ⁄4.
1
4 1
4
4 1 4 3 1 4 14 3 3 1
3 = ' = # =
Therefore the answer is choice B. Note that you don’t need John’s age to solve the
problem.
46
The Mathematics Section
Recognize When Not Enough
Information Is Given
Sometimes you may not have sufficient information to solve the problem. Focus
on what information is needed to get the answer.
Sample
12. A woman purchased several skirts at $15 each plus one more for $12. What
was the average price of each skirt?
A. $12
B. $13
C. $14
D. $15
E. not enough information given
To calculate an average, you must have the total amount and then divide by the
number of items. The difficulty here, however, is that “several skirts at $15” does
not specify exactly how many skirts were purchased at $15 each. Does several
mean two? Or does it mean three? Several is not a precise mathematical term.
Therefore there is not enough information to pull out to calculate an average. The
answer is E.
Work Forward
If you immediately recognize the method or proper formula to solve the problem,
then go ahead and do the work. Work forward.
Samples
13. Which of the following numbers is between 1 ⁄3 and 1 ⁄4?
A. .45
B. .35
C. .29
D. .22
E. .20
First underline or circle “between 1 ⁄3 and 1 ⁄4.” If you know that 1 ⁄3 is .333. . . and 1 ⁄4
is .25, you have insight into the problem and should be able to work it forward.
Because .29 is the only number between .333. . . and .25, the correct answer is C.
A quick peek at the answer choices tips you off that you should work in decimals.
47
Part II: Analysis of Exam Areas
14. What is the final cost of a watch that sells for $49.00 if the sales tax is 7%?
A. $49.07
B. $49.70
C. $52.00
D. $52.43
E. $56.00
Because the sales tax is 7% of $49.00,
7% of $ 4900 . = (. 07)($ 4900 . )
= $ 343 .
The total cost of the watch is therefore:
$ 49. 00 + $ 3. 43 = $ 52.
43
So the correct answer is D.
Use the information below to answer the question that follows.
Price List
Top sirloin $2.99 per pound or 2 pounds for $5.00
Filet mignon
$4.00 per pound
London broil $1.79 per pound or 3 pounds for $5.00
15. Randy owns and manages Randy’s Steakhouse. He needs to buy the
following meats in order to have enough for the weekend: 9 pounds of top
sirloin, 8 pounds of filet mignon, and 7 pounds of London broil. What is
the least amount Randy can spend to buy the meat he needs for the
weekend business?
A. $97.00
B. $71.44
C. $66.78
D. $54.99
E. $34.78
The correct answer is C.
48
The Mathematics Section
top sirloin:
filet mignon:
London broil:
8 pounds + 1 pound
= ^4 # $ 5. 00h + $ 2.
99 (note: 2 pounds for $5.00)
= $ 20. 00 + $ 2.
99
= $ 22.
99
8 pounds
= 8#
$ 400 .
= $ 32.
00
6 pounds + 1 pound
= ^2 # $ 5. 00h + $ 1.
79 (note: 3 pounds for $5.00)
= $ 10. 00 + $ 1.
79
= $ 11.
79
Add to find the total: $ 22. 99 + $ 32. 00 + $ 11. 79 = $ 66.
78
Work Backward from the Answers
If you don’t immediately recognize a method or formula, or if using the method or
formula would take a great deal of time, try working backward — from the answers.
Because the answers are usually given in ascending or descending order,
always start by plugging in choice C first. Then you know whether to go up or
down with your next try. (In some cases, you may want to plug in the simplest
answer first.)
Samples
16. If
x 3
2
+
4
= 1
1
4
, what is the value of x?
A. –2
B. –1
C. 0
D. 1
E. 2
49
Part II: Analysis of Exam Areas
You should first underline or circle “value of x.” If you’ve forgotten how to solve
this kind of equation, work backward by plugging in answers. Start with choice C
and plug in 0:
2 0 +
4 3 =Y 1
1
4
Because this answer is too small, try choice D, a larger number. Plugging in 1
gives you:
2 1 +
4 3 ? 1
1
4
2
4
+
4 3 ? 1
1
4
4 5 = 1
1
4
This answer is true, so D is the correct answer.
Working from the answers is a valuable technique.
17. What counting number is less than 15, and when divided by 3 has a
remainder of 1, but when divided by 4 has a remainder of 2?
A. 5
B. 8
C. 10
D. 12
E. 13
By working from the answers, you can eliminate wrong answer choices. For example,
you can eliminate choices B and D immediately because they are divisible
by 4, leaving no remainder. Eliminate choices A and E also because they each leave
a remainder of 1 when divided by 4. Therefore the correct answer is C: 10 leaves a
remainder of 1 when divided by 3 and a remainder of 2 when divided by 4.
18. What is the greatest common factor of the numbers 18, 24, and 30?
A. 2
B. 3
C. 4
D. 6
E. 12
You can work from the answers, but here you should start with the largest answer
choice, because you’re looking for the “greatest” common factor. The largest
number which divides evenly into 18, 24, and 30 is 6, so the correct answer is D.
50
The Mathematics Section
Plug in Simple Numbers
Substituting numbers for variables can often help you understand a problem.
Remember to plug in simple, small numbers, because you have to do the work.
Samples
19. If r represents an even integer, then an odd integer is represented by which
of the following?
A. 3r
B. 2r
+ 1
C. 3r
+ 2
D. 4r
 2
E. 5r
 4
Because the question says that “r represents an even integer,” substitute 2 for r. You
should underline or circle “an odd integer” because that’s what you’re looking for.
So as you plug 2 into each choice, you can stop when you get an odd integer.
A. 3r
= 3^2h=
6
B. 2r
+ 1= ^2h2+ 1=
5
Because 5 is an odd integer, the correct answer is B.
20. If x is a positive integer in the equation 2 x= y, then what must y be?
A. a positive even integer
B. a negative even integer
C. zero
D. a positive odd integer
E. a negative odd integer
At first glance, this problem appears quite complex. But plug in some numbers
and see what happens. First plug in 1 (the simplest positive integer) for x.
2 x=
y
21=y ^h
2=y
51
Part II: Analysis of Exam Areas
Now try 2:
2 x=
y
22=y ^ h
4=y
Try it again. No matter what positive integer you plug in for x, y is always positive
and even. Therefore, the answer is A.
21. If x>
1, which of the following decreases as x decreases?
I. x + x 2
II. 2x 2  x
III.
1
x+
1
A. I only
B. II only
C. III only
D. I and II only
E. II and III only
You can solve this problem most easily by taking each situation and substituting
simple numbers.
However, in the first situation — I. x+ x 2
— you should recognize that this expression
will decrease as x decreases.
Trying x= 2produces 2+ ^2h 2
, which equals 6.
2
Now trying x= 3gives you 3+ ^h 3 = 12.
Notice that choices B, C, and E are already eliminated because they do not contain
I. You should also realize that now you need to try only the values in II —
because III is not paired with I as an answer choice, III cannot be one of the
answers.
2
2
Trying x = 2 in the expression 2^xh
 xgives you 22 ^ h  2, or 2^4h
 2, which
leaves 6.
Now trying x= 3gives you 2^h 3 2  3, or 2^9h
 3= 18 3=
15. This expression
also decreases as x decreases. Therefore, the correct answer is choice D. Notice
that III was not even attempted because it was not one of the possible choices.
Be sure to make logical substitutions. Use the appropriate type of number — a
positive number, a negative number, zero, and so on — to get the full picture.
52
The Mathematics Section
Use 10 or 100
Some problems may deal with percent or percent change. If you don’t see a simple
method for working the problem, try using values of 10 or 100 and see what
you get.
Samples
22. If 40% of the students in a class have blue eyes and 20% of those with blue
eyes have brown hair, then what percent of the original total number have
brown hair and blue eyes?
A. 4%
B. 8%
C. 16%
D. 20%
E. 32%
First underline or circle “percent of the original total number,”“brown hair,” and
“blue eyes.” In this problem, if you don’t spot a simple method, start with 100 students
in the class. Because 40% of them have blue eyes, then 40 students have
blue eyes. Now, the problem says that 20% of those students with blue eyes have
brown hair. So take 20% of 40, which gives you:
. 20 # 40 = 8.
0
Because the question asks what percent of the original total number have blue
eyes and brown hair, and because you started with 100 students, the answer is
choice B, 8 out of 100, or 8%.
23. A corporation triples its annual bonus to 50 of its employees. What percent
of the employees’ new bonus is the increase?
A. 50%
B. 66 2 ⁄3%
C. 100%
D. 200%
E. 300%
53
Part II: Analysis of Exam Areas
Use $100 for the normal bonus. If the annual bonus was normally $100, tripled it
is now $300. Therefore the increase, $200, must be placed over the new bonus of
$300:
$ 200
$ 300 = 2 3
2
⁄3 = 66 2
⁄3%
The correct answer is B.
Approximate
If it appears that you need to do extensive calculations to solve a problem, check
to see how far apart the choices are and then approximate. The reason for checking
the answers first is to give you a guide to see how freely you can approximate.
Samples
24. What is the value of ^. 889 # 55h/ 9.
97 to the nearest tenth?
A. 49.1
B. 17.7
C. 4.9
D. 4.63
E. .5
First underline what you are looking for: “nearest tenth.” Before starting any computations,
take a glance at the answers to see how far apart they are. Notice that
the only close choices are C and D, but D is not a possible choice because it is to
the nearest hundredth, not tenth. Some quick approximations — .889 , 1 and
9.
97 , 10 — leaves the problem in this form:
1#
55
10
= 55 10
= 55 .
The closest answer is C; therefore it is the correct answer. Notice that choices A
and E are not reasonable.
25. If 2,100 people work in a factory, and 21% of them work only the night
shift, approximately how many people work the other shifts?
54
A. 400
B. 800
C. 1,100
D. 1,600
E. 2,000
The Mathematics Section
First underline or circle “approximately how many people” and “other shifts.”
Remember, you’re looking for “other shifts.” Notice that the answers are spread out.
Now, approximate 21% as 20%. Next, approximate 2,100 people as 2,000 people.
So, 20% of 2,000 is .20 × 2,000 = 400.
But be careful; 400 is the number of those who work only the night shift, and you
want the number of people who work the other shifts. So subtract 400 from 2,000,
leaving 1,600. The correct answer is D.
Another method is to approximate, then subtract 20% from 100%, to get 80%,
which is the percent of other workers. Multiply 80% times 2,000 and you get 1,600.
Simplify the Problem
Sometimes combining terms, performing simple operations, or simplifying the
problem in some other way gives you insight and makes the problem easier to
solve.
Samples
26. Which of the following is between 1 ⁄4 and 0.375?
A. 0.0094
B. 0.291
C. 0.38
D. 0.4
E. 0.51
First underline the word “between.” Next, simplify 1 ⁄4 to .25. A quick glance at the
choices is valuable because it tips you off that you are working in decimals.
Simply check which decimal is between .250 and .375. The correct answer is B —
.291 is between .250 and .375. Notice that changing .25 to .250 makes the problem
even easier. (Adding or eliminating zeros to the far right of a decimal doesn’t
change the value of the number.)
27. Which of the following is equal to 1 ⁄5 of 0.02 percent?
A. 0.4
B. 0.04
C. 0.004
D. 0.0004
E. 0.00004
55
Part II: Analysis of Exam Areas
Simplifying this problem first means changing 1 ⁄5 to .2. Next change 0.02 percent
to 0.0002 (that is . 02 # . 01 = 0.
0002).
Now that you have simplified the problem, multiply . 2 # 0.
0002 which gives
0.00004. The correct answer is E.
Simplifying can make a problem much easier to solve.
Make Comparisons
At times, questions require you to compare the sizes of several decimals, or several
fractions. If you’re comparing decimals, make sure that the numbers you compare
have the same number of digits. (Remember: You can insert or eliminate zeros to
the far right of a decimal point without changing the value of the number.)
Samples
28. Which of the following answer choices places the decimal fractions .6, .16,
.66 2 ⁄3, .58, in order from smallest to largest?
A. .6, .16, .66 2 ⁄3, .58
B. .58, .16, .6, .66 2 ⁄3
C. .16, .58, .6, .66 2 ⁄3
D. .66 2 ⁄3, .6, .58, .16
E. .58, .6, .66 2 ⁄3, .16
Rewrite .6 as .60 so that all the decimals have the same number of digits: .60, .16,
.66 2 ⁄3, .58. Treating these as though the decimal point were not there (you can do
this only when all the numbers have the same number of digits to the right of the
decimal), the order is as follows: .16, .58, .60, .66 2 ⁄3. The correct answer is C.
Remember to circle “smallest to largest” in the question.
29. Which of the following answer choices places the fractions 5 ⁄8, 3 ⁄4, 2 ⁄3, in
order from smallest to largest?
A. 2
⁄3, 3 ⁄4, 5 ⁄8
B. 2
⁄3, 5 ⁄8, 3 ⁄4
C. 5
⁄8, 2 ⁄3, 3 ⁄4
D. 3
⁄4, 5 ⁄8, 2 ⁄3
E. 3
⁄4, 2 ⁄3, 5 ⁄8
Find the common denominator: 5 ⁄8 = 15 ⁄24, 3 ⁄4 = 18 ⁄24, 2 ⁄3 = 16 ⁄24.
56
The Mathematics Section
Therefore the order becomes 5 ⁄8, 2 ⁄3, 3 ⁄4.
Using decimal equivalents:
5
⁄8 = .625
3
⁄4 = .75 or .750
2
⁄3 = .66 2 ⁄3 or .666 2 ⁄3
The order again becomes: 5 ⁄8, 2 ⁄3, 3 ⁄4. The answer is C.
Mark Diagrams
When a figure is included with the problem, mark the given facts on the diagram.
This helps you visualize all the facts given.
Samples
Use the figure to answer the question that follows.
30. If each square in the figure has a side of length 1, what is the perimeter?
A. 8
B. 12
C. 14
D. 16
E. 20
57
Part II: Analysis of Exam Areas
Mark the known facts:
1
1
1
1
1
1
1
1
1
1
Now you have a calculation for the perimeter: 10 plus the darkened parts. Now
look carefully at the top two darkened parts. They add up to 1. (Notice that sliding
the top square over illustrates that fact.)
Together these total 1
1
1
1
1
1
1
1
1
1
The same is true for the bottom darkened parts. They add to 1. Thus the total
perimeter is 10 + 2, or 12, choice B.
Use the figure below to answer the question that follows.
1
58
The Mathematics Section
31. In the preceding figure, if each small square is 2 inches in length, what is
the perimeter of the shaded area?
A. 20 inches
B. 24 inches
C. 40 inches
D. 48 inches
E. 60 inches
Mark in the diagram as you start counting from the lower lefthand corner. As you
go around the outside of the shaded region, your markings can help you make sure
that you don’t miss a side. You should have 20 numbered sides in the perimeter.
But remember, each side is 2 inches long, so multiply 20 # 2 = 40 inches. The correct
answer is C.
5
12
4 6
11
7
13
3
8
10
9
14
2
15
1
16
17
2''
20 19
18
2''
Use the figure below to answer the question that follows.
59
Part II: Analysis of Exam Areas
32. In the preceding figure, if each small square is 3 inches in length, what is
the measure of the shaded area?
A. 144 square inches
B. 100 square inches
C. 72 square inches
D. 9 square inches
E. 8 square inches
There are 12 halfshaded squares and 2 fully shaded squares, for a total of 8 fully
shaded squares. Each square is 3# 3, so the area of each is 9 square inches. Now
multiply 8# 9= 72square inches. The correct answer is C.
3"
3"
Draw a Diagram If None Is Given
Drawing diagrams to meet the conditions set by the word problem can often make
the problem easier for you to work. Being able to see the facts is more helpful
than just reading the words.
Samples
33. If all sides of a square are doubled, the area of that square
A. is doubled
B. is tripled
C. is multiplied by 4
D. remains the same
E. cannot be determined from the information given
60
2 S
The Mathematics Section
One way to solve this problem is to draw a square, then double all its sides. Then
compare the two areas:
Your first diagram:
S
S
S
S
Double every side:
S
2 S
S
S
S
Notice that the total area of the new square is now four times the original square.
The correct answer is C.
34. What is the maximum number of pieces of birthday cake of size 4" by 4"
that can be cut from a cake 20" by 20"?
A. 5
B. 10
C. 16
D. 20
E. 25
Sketching the cake and marking it as follows makes this a fairly simple problem.
20"
4 4 4
4 4
4
4 20"
4
4
61
Part II: Analysis of Exam Areas
Notice that five pieces of cake will fit along each side; therefore, 5# 5= 25. The
correct answer is E. Finding the total area of the cake and dividing it by the area
of one of the 4# 4pieces also gives you the correct answer, but beware of this
method because it may not work if the pieces do not fit evenly into the original
area.
35. If the area of one face of a cube is 16 square inches, what is the volume of
the cube in cubic inches?
A. 8
B. 12
C. 24
D. 64
E. 96
First underline or circle the word “volume.” Now draw a cube.
Next, label one face of the cube. This helps you determine that each edge of the
cube is 4 inches, because the face of a cube is square and all edges are equal.
4"
4"
4"
16"
4"
The formula for the volume of a cube is length times width times height, or
V = lwh.
So the volume is 4# 4# 4= 64, which is choice D.
Keep in mind that in a cube all edges are the same length and all six sides have the
same area.
62
The Mathematics Section
36. What is the maximum number of milk cartons, each 2" wide by 3" long by
4" tall, that can fit into a cardboard box with inside dimensions of 16" wide
by 9" long by 8" tall?
A. 12
B. 18
C. 20
D. 24
E. 48
The correct answer is E. Drawing a diagram, like the following one, can be helpful
in envisioning the process of fitting the cartons into the box. In the diagram,
you see that 8 cartons fit across the box, 3 cartons deep, and two levels high,
which gives you 8# 3# 2= 48cartons.
8"
4"
2"
3"
9"
16"
Try Some Possibilities
Some questions involve probability and possible combinations. If you don’t know
a formal method, try some possibilities. Set up what could happen. But set up
only as much as you need to.
Samples
37. What is the probability of throwing two dice in one toss so that they total 11?
A. 1/6
B. 1/11
C. 1/18
D. 1/20
E. 1/36
You can simply list all the possible combinations resulting in 11 — (5+ 6and 6+
5
), and realize that the total possibilities are 36, ^6#
6h. Thus the probability equals:
possibilities totaling 11
total possibilities =
36 2 =
18 1
Answer C is correct.
63
Part II: Analysis of Exam Areas
38. What is the probability of tossing a penny twice so that both times it lands
heads up?
A. 1/8
B. 1/4
C. 1/3
D. 1/2
E. 2/3
The correct answer is B. The probability of throwing a head in one throw is
chances of a head
=
total 2 1
chances ^1
head + 1 tailh
Because you’re trying to throw a head twice, multiply the probability for the first
toss ( 1 ⁄2) times the probability for the second toss (again 1 ⁄2). Thus, 1 ⁄2 × 1 ⁄2 = 1 ⁄4, and
1
⁄4 is the probability of throwing heads twice in two tosses. Another way of approaching
this problem is to look at the total number of possible outcomes:
First Toss
H
H
T
T
Second Toss
H
T
H
T
So, there are four different possible outcomes, and only one way to throw two
heads in two tosses. Thus, the probability of tossing two heads in two tosses is 1
out of 4 total outcomes, or 1/4.
Use the figure below to answer the question that follows.
Red
Blue
Green
Red
Blue
Blue
Green
Red
64
The Mathematics Section
39. In the preceding spinner, all sections are equal. What is the probability of
getting a blue on the first spin?
A. 1/8
B. 1/4
C. 3/8
D. 3/5
E. 5/8
Because there are 8 different places for the spinner to land, and 3 of those places
are blue, the probability is 3/8:
blue
total
possibilities
possibilities
=
The correct answer is C.
8 3
Read the information below and answer the three questions that follow.
Tom is pulling marbles out of a hat. There are 6 red marbles, 4 green marbles,
and 2 yellow marbles. There are no other marbles in the hat.
40. What is the probability that Tom will pull a green marble on his first pull?
A. 1/4
B. 1/3
C. 2/5
D. 1/2
E. 2/3
Because there are 12 total marbles and 4 green marbles, the probability is
greenpossibilities
total possibilities
=
12 4 =
3 1
The correct answer is B.
41. What is the least number of marbles that Tom can pull to ensure that he
gets at least one of each color?
A. 3
B. 4
C. 5
D. 7
E. 11
65
Part II: Analysis of Exam Areas
To ensure getting at least one of each color, Tom must pull 11 marbles. He could
pull 6 reds and then 4 greens, so he would have pulled 10 marbles, and still only
have two different colors. But on his next pull he would have to get a yellow because
only yellow marbles would be left. The correct answer is E.
42. If Tom pulls a green marble first, and doesn’t put it back in the hat, what is
the probability that his next pull will be another green marble?
A. 1/12
B. 1/11
C. 1/4
D. 3/11
E. 1/3
When the first green marble is pulled and not put back, it leaves 3 greens, 6 reds,
and 2 yellows. So the probability of pulling another green marble is
greenpossibilities
total possibilities
=
11 3
The correct answer is D.
Corey charts the hair color of the students in her drama class. The chart gives the
following information:
Hair Color Number of Students
Black hair 12
Brown hair 18
Red hair 4
Blonde hair 6
43. From the information given in the preceding chart, if the teacher randomly
picks a student to read a passage, what is the probability of the teacher
selecting a student with black hair or red hair?
A. 2/5
B. 3/10
C. 1/5
D. 3/20
E. 1/10
66
Because you’re looking for a probability of selecting a student with black hair or
red hair to read a passage, you must first add:
black hair + red hair =
12 + 4 =
The Mathematics Section
Then get the total number of students in the class:
12 + 18 + 4 + 6 = 40
And finally set up the fraction 16/40, which reduces to 2/5. The correct answer is A.
44. How many combinations of outfits are possible if a person has 4 sports
jackets, 5 shirts, and 3 pairs of slacks?
A. 4
B. 5
C. 12
D. 60
E. 120
The correct answer is D. Because each of the 4 sports jackets may be worn with 5
different shirts, there are 20 possible combinations. These 20 combinations may
be worn with each of the 3 pairs of slacks for a total of 60 possible combinations.
Stated simply, 5# 4# 3= 60possible combinations.
Be Reasonable
Make sure that your answer is reasonable. That is, if you read it back into the
problem, does it make sense? Is it a possible answer?
Sample
45. Mo works at a diner and spends Monday and Tuesday washing dishes. On
Monday he washes 22 more dishes than he washes on Tuesday. If Mo
washed a total of 88 dishes on the two days, how many dishes did he wash
on Tuesday?
A. 22
B. 33
C. 66
D. 99
E. 110
First circle or underline “how many dishes did he wash on Tuesday.” Notice that
answer choices D and E are greater than the total for both days. Those choices are
not reasonable and can be eliminated. If you work the problem and come up with
choice C, you again have an unreasonable answer, because if Mo washes 66
dishes on Tuesday, and 22 more than the 66 on Monday, that is 88 dishes on
Monday alone, which equals the total for the two days.
67
Part II: Analysis of Exam Areas
To solve the problem, let x be the number of dishes Mo washes on Tuesday, then
x+ 22is the number of dishes he washes on Monday. So the equation looks like
this:
Tuesday Monday Total
x + (x + 22) = 88
Solving gives you:
2x
+ 22=
88
Subtract 22 from each side:
2x
+ 22=
88
22
22
2x =66
Dividing by 2 leaves:
2x
2
=
66
2
x = 33
So the correct answer is B. Is this reasonable? Well, if Mo washes 33 dishes on
Tuesday, and 22 more than 33 on Monday, he washed 55 dishes on Monday. So
the total of Monday and Tuesday is 33 + 55 = 88. Yes, it is reasonable. It checks.
Glance at the Choices
Glance at the choices on procedure problems. Some problems may not ask you to
solve for a numerical answer or even an answer including variables. Rather, you
may be asked to set up the equation or expression without doing any solving. A
quick glance at the answer choices can help you know what is expected.
Samples
46. 51 # 6 could be quickly mentally calculated by
A. 50 # 6 + 1
B. 51 + 51 + 51 + 51 + 51 + 51
C. ( 50 # 6) + ( 1 # 6)
D. ( 50 # 6)
+ 1 ⁄6
E. adding 51 sixes
68
Answer C is correct. The quickest method of calculating 51 # 6 is to first multiply
50# 6(resulting in 300), then multiplying 1# 6(resulting in 6), and adding the
products together ^300 + 6 = 306h. Answer choices B and E give the correct
answer (306) as well, but neither is the best way to quickly calculate the answer.
The Mathematics Section
Sometimes, however, actually working the problem can be helpful, as the next
sample demonstrates.
47. The fastest method to solve 7 ⁄48 # 6 ⁄7 is to
A. invert the second fraction and then multiply.
B. multiply each column across and then reduce to lowest terms.
C. find the common denominator and then multiply across.
D. divide 7 into the numerator and denominator, divide 6 into the
numerator and denominator, and then multiply across.
E. reduce the first fraction to lowest terms and then multiply across.
In this problem, the way to determine the fastest procedure may be to actually
work the problem as you would if you were working toward an answer. Then see
whether that procedure is listed among the choices. You should then compare it to
the other methods listed. Is one of the other correct methods faster than the one
you used? If so, select the fastest.
These types of problems are not constructed to test your knowledge of obscure
ways to solve mathematical equations. Rather, they test your knowledge of common
procedures used in standard mathematical equations. Thus, the fastest way to
solve this sample problem is to first divide 7 into the numerator and denominator:
1
7 6
48
# =
7
1
Then divide 6 into the numerator and denominator:
1 1
7 6
# =
48 7
8 1
Then multiply across:
1 1
7 6
# =
48 7 8 1
8 1
The correct answer is D.
48. Which equation can be used to find the perimeter, P, of a rectangle that has
a length of 18 feet and a width of 15 feet?
A. P= ^18h^15h
B. P= 18+
15
C. P = 2^15h^18h
D. P = ^2h15 + 18
E. P = 2^15 + 18h
The correct answer is E. The perimeter of a rectangle can be found by adding the
length to the width and doubling this sum. P = 2^15 + 18h.
69
Part II: Analysis of Exam Areas
Read the Question First
If information is given in a box, read the question outside of the box first (usually
below the box), then read the information in the box.
Samples
Use the information below to answer the question that follows.
Celia travels 4 1 ⁄2 miles. She runs most of the way, but walks the last 1 mile.
Lillian travels 2 1 ⁄4 miles, but runs all the way.
49. From the preceding information, which of the following methods could be
used to find out how many total miles Celia and Lillian ran?
A. (4 1 ⁄2 − 1) − 2 1 ⁄4
B. 4 1 ⁄2 − 2 1 ⁄4
C. (4 1 ⁄2 +1) − 2 1 ⁄4
D. (4 1 ⁄2 − 1) + 2 1 ⁄4
E. 4 1 ⁄2 + 2 1 ⁄4
To find the total distance run by Celia and Lillian, you need to first find out how
many miles Celia ran,which is (4 1 ⁄2 −1). Add that to how many miles Lillian ran,
which is 2 1 ⁄4. So the correct answer is D.
Read the information below and answer the question that follows.
Rick is three times as old as Maria, and Maria is four years older than Leah.
50. If Leah is z years old, what is Rick’s age in terms of z?
A. 3z
+ 4
B. 3z
 12
C. 3z
+ 12
D. ( z+
4)/
3
E. ( z
4)/
3
Because:
z=Leah’s age
z+ 4= Maria’s age
3( z + 4)
= Rick’s age or
3z
+ 12= Rick’s age
70
The correct answer is C.
The Mathematics Section
Review Information Carefully
Some problems may ask you to use mathematical or logical reasoning. Review the
information carefully before you work the problem. Write in given values and
mark diagrams to help you see the reasoning involved.
Samples
Use the figure below to answer the question that follows.
A
B
C
51. What conclusion can be drawn from the preceding diagram?
A. Circles A and B have nothing in common.
B. Circles A and C have nothing in common.
C. Circles B and C have nothing in common.
D. Circle C has something in common with circles A and B.
E. Not enough information is given to draw a conclusion.
Because circle C intersects (overlaps) with circles A and B, it must have something
in common with A and B, as the shaded area in the following figure shows.
A
B
C
The correct answer is D.
Use the information below to answer the question that follows.
If Spencer’s class starts at noon, then he will leave the house at 10 a.m.
If Spencer’s class starts at 2 p.m., then he will leave the house between 11
a.m. and noon.
If Spencer’s class starts at 3 p.m., then he will leave the house before 1 p.m.
71
Part II: Analysis of Exam Areas
52. If Spencer leaves the house at 11:30 a.m., which of the following must be true?
A. His class starts at 10 a.m.
B. His class starts at 2 p.m.
C. His class starts at 3 p.m.
D. His class starts after 1 p.m.
E. His class starts before 3 p.m.
Since Spencer leaves the house at 11:30 a.m., he must be going to a 2 p.m. or
3 p.m. class. So, the correct answer is D.
Use the figure below to answer the question that follows.
A
y
w
x
z
B
C
Circle A is composed of multiples of 3, circle B is composed of multiples of 5,
and circle C is composed of multiples of 2.
53. From the preceding information and diagram, which of the following is a
possible value for x?
A. 5
B. 6
C. 10
D. 15
E. 30
72
The Mathematics Section
All the circles intersect at x, so x must be a multiple of 2, 3, and 5, as shown in the
following figure.
3 15 5
30
6 10
2
From the diagram, you can see that the answer is E, 30, which is a multiple of 2,
3, and 5, because 2# 3# 5= 30.
Watch for Missing Information
Some questions require you to fill in missing information in a chart or table. Be
careful to focus on what is given and how you can use it to obtain what is needed.
Samples
Use the information given below to answer the question that follows.
Hillary’s lunch bill was as follows:
Salad $ 2.95
Sandwich $ 4.95
Soft Drink $??.??
Subtotal $ 8.65
Tax $ .61
Tip $ 1.50
TOTAL $10.76
54. From the preceding information, what was the cost of Hillary’s soft drink?
A. $1.75
B. $1.25
C. $1.00
D. $ .95
E. $ .75
73
Part II: Analysis of Exam Areas
To answer this question, simply add the cost of the salad and the sandwich and
then subtract that total from the subtotal to find the cost of the soft drink.
Salad $2.95
Sandwich $4.95
TOTAL $7.90
Now subtract that total from the subtotal of $8.65:
$ 865 .
$ 790 .
$ . 75
The correct answer is E.
74
The Mathematics Section
A PATTERNED PLAN OF ATTACK
Math Ability
Read the question, circling what you are solving for.
Pull out important information.
Identify the facts needed.
Sketch or mark in diagrams.
Do you know a simple method or formula?
YES
NO
Work forward.
Use your method and work the
problem out as simply as possible.
Work backward from
the answers.
Plug in simple numbers.
Use 10 or 100 in percent problems.
Try simplifying the problem.
Approximate.
Try some possibilities.
Eliminate unreasonable choices.
ALWAYS MAKE SURE THAT YOUR ANSWER IS REASONABLE.
DON'T GET STUCK ON ANY ONE PROBLEM!
INTRODUCTION TO GRAPHS
AND CHARTS
75
INTRODUCTION TO GRAPHS
AND CHARTS
Graphs and charts appear on the Reading and Mathematics sections of the CBEST.
Ability Tested
You need to be able to understand and derive information from graphs, charts, and
tables. Many of the problems require brief calculations based on the data, so your
mathematical ability is also tested.
Basic Skills Necessary
When a graph or chart appears in the Reading section, typically you are asked to
read or interpret it. When a graph or chart appears in the Mathematics section, you
are asked not only to read and interpret but also to do some mathematical computations.
Your familiarity with a wide range of chart and graph types will help you
feel comfortable with these problems and read the data accurately.
Directions
The directions for these questions are the same as those for the Reading or
Mathematics sections. However, the graph or chart is typically preceded by a
statement similar to: “Use the graph or chart below to answer the question(s) that
follow.”
Description
You are given data represented in chart or graph form. Following each set of data
is one, two, or three questions based on that data. You are to select the best answer
to each question by referring to the appropriate chart or graph, or the appropriate
part of the chart or graph. To determine your answer, use only the information
given or implied.
Introduction to Graphs and Charts
Suggested Approach with Samples
This section contains some helpful strategies for extracting accurate information
followed by some sample graph questions.
Skim the question and quickly examine the whole graph before starting to work
the problem; this sort of prereading tells you what to look for.
Sometimes the answer to a question is available in the supplementary information
given with a graph (headings, scale factors, legends, and so on); be sure to read
this information.
Look for the obvious — dramatic trends, high points, low points, and so on.
Obvious information often leads directly to an answer.
Charts and Tables
Often, charts and tables are used to give an organized picture of information or
data. Be sure that you understand what is given. Column headings and line items
give the important information — they give the numbers meaning.
Pay special attention to what information is given in the chart. The following chart
shows the number of burger sales for the week of August 8–14. The days of the
week are along the left side of the chart. The number of hamburgers for each day
is given in one column and the number of cheeseburgers in the other column.
Samples
Use the table below to answer the three questions that follow.
Burger Sales for the Week of August 8–14
Day Hamburgers Cheeseburgers
Sunday 120 92
Monday 85 80
Tuesday 77 70
Wednesday 74 71
Thursday 75 72
Friday 91 88
Saturday 111 112
77
Part II: Analysis of Exam Areas
1. On which day were the most burgers sold (hamburgers and cheeseburgers)?
A. Sunday
B. Monday
C. Friday
D. Saturday
E. Tuesday
Answer D is correct. To answer this question, you must understand the chart and
do some simple computation. Working from the answers is probably the easiest
method.
A. Sunday: 120 + 92 = 212
B. Monday: 85 + 80 = 165
C. Friday: 91 + 88 = 179
D. Saturday: 111 + 112 = 223
E. Tuesday: 77 + 70 = 147
Another method is to approximate the answers.
2. On how many days were more hamburgers sold than cheeseburgers?
A. 7
B. 6
C. 5
D. 4
E. 3
The correct answer is B. To answer this question, you must compare the sales for
each day. Hamburgers outsold cheeseburgers every day except Saturday.
3. If the pattern of sales continues,
A. The weekend days will have the fewest number of burger sales next
week.
B. The cheeseburgers will outsell hamburgers next week.
C. Generally, when hamburger sales go up, cheeseburger sales will go up.
D. Hamburgers will be less expensive than cheeseburgers.
E. More customers will buy hamburgers than cheeseburgers next Saturday.
78
Introduction to Graphs and Charts
The correct answer is C. To answer this question, you must notice one of the
trends. Most days that hamburger sales go up, cheeseburger sales also go up (with
the exception of Saturday to Sunday).
Graphs
Graphical information may be displayed in many ways. The three basic types of
graphs you should know are: bar graphs, line graphs, and circle graphs (or pie
charts).
Bar Graphs
Bar graphs convert the information in a chart into separate bars or columns. Some
graphs list numbers along one edge, and places, dates, people, or things (individual
categories) along another edge. Always try to determine the relationship between
the columns in a graph or chart.
Samples
Use the graph below to answer the question that follows.
Number of Delegates Committed to Each Candidate
Candidate 1
Candidate 2
Candidate 3
Candidate 4
0
200 400
Delegates
600 800
4. Candidate 1 has approximately how many more delegates committed than
does Candidate 2?
A. 150
B. 200
C. 250
D. 400
E. 450
79
Part II: Analysis of Exam Areas
C is the correct answer. To understand this question, you must be able to read the
bar graph and make comparisons. Notice that the graph shows the “Number of
Delegates Committed to Each Candidate,” with the number of delegates given
along the bottom of the graph in increments of 200. The candidates are listed
along the left side. Candidate 1 has a few more than approximately 800 delegates.
The bar graph for Candidate 2 stops about three quarters of the way between 400
and 600. Halfway between 400 and 600 is 500, so Candidate 2 has about 550
delegates.
800 − 550 = 250
Use the graph below to answer the three questions that follow.
3.5
Gross Receipts of Several FastFood Restaurants
19941996
3.0
Gross Receipts Millions
2.5
2.0
1.5
1.0
0.5
0.0
1994 1995
Monster
Burger
1996 1994 1995 1996
Cruncho
Chicken
1994 1995 1996
Pizza in a
Pot
5. The 1994–96 gross receipts of Monster Burger exceeded those of Pizza in a
Pot by approximately how much?
A. 0.2 million
B. 2 million
C. 8.2 million
D. 8.4 million
E. 17 million
In this graph, multiple bars represent each fastfood restaurant; each single bar
represents the receipts from a single year.
80
Introduction to Graphs and Charts
You may be tempted to write the numbers as you do your arithmetic (3.5 million =
3,500,000), but this is unnecessary since it often is on graphs that use large numbers.
Because all the measurements are in millions, adding zeros does not add precision
to the numbers.
The correct answer is B. Referring to the Monster Burger bars, you can see that
gross receipts are as follows: 1994 = 2.5 million, 1995 = 2.5 million, 1996 = 3.4
million (if you have trouble seeing how the bars line up with the numbers, you can
use your answer sheet as a straightedge to determine a number such as this last
one). Totaling the receipts for all three years, you get 8.4.
Referring to the Pizza in a Pot bars, you can see that gross receipts are as follows:
1994 = 1 million, 1995 = 2.1 million, 1996 = 3 million (don’t designate numbers
beyond the nearest tenth, because the graph numbers and the answer choices prescribe
no greater accuracy than this). Totaling the receipts for all three years, you
get 6.1 million.
So Monster Burger exceeds Pizza in a Pot by 2.3 million. The answer that best
approximates this figure is B.
6. From 1995 to 1996, the percent increase in receipts for Pizza in a Pot
exceeded the percent increase for Monster Burger by approximately how
much?
A. 0%
B. 2%
C. 10%
D. 15%
E. 43%
The correct answer is C. Graph questions on the CBEST may ask you to calculate
percent increase or percent decrease. The formula for figuring either of these is
the same:
amount of the change
the startingamount (followsthe word "from")
In this case, you may first calculate the percent increase for Monster Burger:
Gross receipts in 1995 = 2.5 million
Gross receipts in 1996 = 3.4 million
Amount of the change = 0.9 million
81
Part II: Analysis of Exam Areas
The 1995 amount is the “starting” or “from” amount:
Amount of the change 09
starting amount =
25
. . = 036 . = 36%
Percent increase for Pizza in a Pot:
Gross receipts in 1995 = 2.1 million
Gross receipts in 1996 = 3 million
Amount of the change = 0.9 million
Amount of the change 09 . , ,
starting amount =
25 .
0. 428 43%
So, Pizza in a Pot exceeds Monster Burger by 7% (43% − 36%). The answer that
best approximates this figure is C.
7. The 1996 decline in Cruncho Chicken’s receipts may be attributed to
A. an increase in the popularity of burgers
B. an increase in the popularity of pizza
C. a decrease in the demand for chicken
D. a predictable slump attributable to the increase in terrorist activity
E. cannot be determined from the information given
The correct answer is E. Never use information that is not given. In this case, the
multiple factors that could cause a decline in receipts are not represented by the
graph. All choices except E require you to speculate beyond the information given.
Line Graphs
Line graphs convert data into points on a grid. These points are then connected to
show a relationship between the items, dates, times, and so on. Notice the slopes
of lines connecting the points. These lines show increases and decreases. The
sharper the slope upward, the greater the increase. The sharper the slope downward,
the greater the decrease. Line graphs can show trends or changes in data
over a period of time.
82
Introduction to Graphs and Charts
Samples
Use the graph below to answer the two questions that follow.
American Indian Population in the United States from 1910 to 1980
800,000
700,000
600,000
500,000
Population
400,000
300,000
200,000
100,000
0
1910 1920 1930 1940 1950 1960 1970 1980
Years
8. In which of the following years were there about 500,000 American
Indians?
A. 1940
B. 1950
C. 1960
D. 1970
E. 1975
Choice C is the correct answer. To answer this question, you must be able to read
the graph. The information along the left side of the graph shows the number of
Indians in increments of 100,000. The bottom of the graph shows the years from
1910 to 1980. Notice that in 1960 there were about 500,000 American Indians in
the United States. Using the edge of your answer sheet as a straightedge can help
you see that the dot representing 1960 lines up with 500,000.
83
Part II: Analysis of Exam Areas
9. During which of the following time periods was there a decrease in the
American Indian population?
A. 1910 to 1920
B. 1920 to 1930
C. 1930 to 1940
D. 1960 to 1970
E. 1970 to 1980
The correct answer is A. Because the slope of the line goes down from 1910 to
1920, there must have been a decrease. If you read the actual numbers, you notice
a decrease from 300,000 to 250,000 between those years.
Use the graph below to answer the three questions that follow.
100%
Average Score (Statewide)
on Student Aptitude Test
19781983
90%
Scores
80%
70%
60%
50%
1978 1979 1980 1981 1982
Years
1983
10. Between which two years was the greatest rise in average test scores?
A. 1978 and 1979
B. 1979 and 1980
C. 1980 and 1981
D. 1981 and 1982
E. 1982 and 1983
84
Introduction to Graphs and Charts
Choice E is the correct answer. The most efficient way to compute greatest rise is
to locate the steepest upward slope on the chart. Note that the steepest climb is between
1982 and 1983. Therefore, choice E indicates the greatest rise in average
test scores.
11. In which year was the average score approximately 85%?
A. 1978
B. 1979
C. 1980
D. 1981
E. 1982
The correct answer is choice C. According to the graph, the average test score was
approximately 85% in 1980. In such cases, when you must read the graph for a precise
measurement, remember that it may be helpful to use your answer sheet as a
straightedge to more accurately compare points with the grid marks along the side.
12. Approximately what was the highest score achieved statewide on the test?
A. 80%
B. 85%
C. 90%
D. 97%
E. cannot be determined from the information given
The first thing to do when confronted with a graph or chart is to read its title to
understand what the graph is telling you. In this case, the graph is relating information
about average scores. It tells you nothing about the highest score achieved.
Thus, E is the correct answer.
Circle Graphs (Pie Charts)
A circle graph, or pie chart, shows the relationship between the whole circle
(100%) and the various slices that represent portions of that 100%. The larger the
slice, the higher the percentage.
85
Part II: Analysis of Exam Areas
Samples
Use the graph below to answer the three questions that follow.
20%
in the bank
25%
entertainment
20%
car and bike
repair
10%
misc.
items
10%
school
supplies
15%
his hobby
How John Spends His Monthly Paycheck
13. John puts 1 ⁄4 of his monthly paycheck toward
A. his hobby
B. car and bike repair
C. entertainment
D. school supplies
E. the bank
To answer this question, you must be able to read the graph and apply some simple
math. Notice how the information is given in the graph. Each item is given along
with the percent of money spent on that item. Onequarter is the same as 25%, so
entertainment is the answer you are looking for, and C is the correct answer.
14. If John receives $100 in this month’s paycheck, how much will he put
in the bank?
A. $2
B. $20
C. $35
D. $60
E. $80
To answer this question, you must again read the graph carefully and apply some
simple math. John puts 20% of his income in the bank, and 20% of $100 is $20.
So he will put $20 in the bank, which is choice B.
86
Introduction to Graphs and Charts
15. The ratio of the amount of money John spends on his hobby to the amount
he puts in the bank is
A. 1:2
B. 5:8
C. 2:3
D. 3:4
E. 7:8
To answer this question, you must use the information in the graph to make a
ratio.
his hobby %
in the bank
=
15 15
20%
=
20
=
4 3
Notice that the ratio of 15%:20% reduces to 3:4, so the correct answer is D.
Use the graphs below to answer the three questions that follow.
Gross Receipts of All Major
FastFood Restaurants
19941996
CC
46.3%
OTHER
5.3%
CC
40.6%
OTHER
7.3%
PP
12.8%
MB
33.6%
PP
24.6%
MB
29.5%
1994 1995
OTHER
10%
CC
13.3%
PP
40%
MB
44.7%
1996
Gross Receipts for 1994: $7,500,000
Gross Receipts for 1995: $8,550,000
Gross Receipts for 1996: $8,100,000
MB–Monster Burger
CC–Cruncho Chicken
PP–Pizza in a Pot
87
Part II: Analysis of Exam Areas
16. The gross receipts for 1994 are approximately what percentage of the gross
receipts for all three years?
A. 30%
B. 46.3%
C. 46.7%
D. 50%
E. cannot be determined from the information given
You can solve this problem without referring to the graphs; the necessary information
is available in the list of gross receipts below the graphs. Don’t write out all
the zeros when calculating with these large figures; brief figures are easier to work
with.
Gross receipts for 1994 = 7.5 million
Gross receipts for all three years = 7.5 + 8.6 + 8.1 = 24.2 million
75 .
24.
2
= 31%
The answer that best approximates 31% is 30%, choice A. Even without doing the
calculations, you can approximate 30% by realizing that the gross receipts for any
one year are about a third of the total.
17. Over all three years, the average percentage of gross receipts for Cruncho
Chicken exceeds the average percentage of gross receipts for Pizza in a Pot
by approximately how much?
A. 53%
B. 30%
C. 23%
D. 8%
E. 4%
To calculate the average percentage for Cruncho Chicken, add the percentages for
each year and divide by 3.
46.3 + 40.6 + 13.3 = 100.2 ÷ 3 = 33.4%
Do the same for Pizza in a Pot.
12.8 + 24.6 + 40 = 77.4 ÷ 3 = 25.8%
Cruncho Chicken exceeds Pizza in a Pot by 33.4 − 25.8 = 7.6%. Choice D, 8%,
best approximates this figure.
88
Introduction to Graphs and Charts
18. The gross receipts earned by other restaurants in 1996 amount to precisely
how much?
A. $1,810,650
B. $ 810,000
C. $ 547,500
D. $ 453,150
E. $ 405,000
In 1996, other restaurants earned precisely 10%. 10% of $8,100,000 = $810,000,
so choice B is correct.
89
Part II: Analysis of Exam Areas
A PATTERNED PLAN OF ATTACK
Graphs and Charts
Skim the first question.
Examine the entire graph.
Notice headings, scale factors, legends, and dramatic trends.
Focus on what you are looking for in each question.
If a great deal of calculating is necessary,
check the proximity of the answers to each other and approximate.
90
THE WRITING SECTION
Introduction
The Writing section of the CBEST contains two essay questions — usually one
Descriptive/Narrative and one Analytical/Expository. You are asked to draw upon
your personal experience and observations for information, examples, and generalizations
to use in your writing.
Each essay is rated from 1 to 4 by two readers. These readers generate a raw score
for the Writing section that ranges from 4 to 16, which converts to a scaled score
of approximately 20 to 80.
Ability Tested
This section of CBEST tests your ability to read a topic carefully, to organize your
ideas before you write, and to write with clarity and precision.
Basic Skills Necessary
This section requires a basic collegelevel writing background. Papers are scored
on the writer’s ability to demonstrate the following:
■
■
■
■
Development and organization of ideas with supporting evidence or
specific details
Understanding of the essay’s intended audience (for example, a speech
urging members of the Board of Education to vote a certain way)
Comprehension of the assigned task
Skillful use of language; correctness of mechanics, usage, and paragraphing
Directions
In this section, you plan and write two essays, one for each topic given. Read each
topic carefully to make sure that you are properly addressing the issue or situation.
You must write on the specified topic. An essay on another topic will not
be acceptable.
Plan your time wisely. Each essay is equally weighted. Plan to spend the same
amount of time on each.
91
Part II: Analysis of Exam Areas
The two essay questions are designed to give you an opportunity to write clearly
and effectively. Use specific examples whenever appropriate to aid in supporting
your ideas. Keep in mind that the quality of your writing is much more important
than the quantity.
Write your essays in pencil on the special answer sheets provided. No other paper
may be used. Your writing should be neat and legible. Because you have only a
limited amount of space in which to write, please do not skip lines, do not write
excessively large, and do not leave wide margins.
You may use the bottom of the topic page in the test booklet to organize and plan
your essay before you begin writing.
Analysis of Directions
On the written essay portion of the CBEST, you are instructed to write on two
assigned topics. Spend about 30 minutes on each topic since they are equally
weighted.
You will have space for prewriting. You are urged to use this space to organize
your thoughts. Doublecheck how much space you have in which to write your
essay. At present, the test provides two blank sides of lined 8 1 ⁄2x11inch paper
per essay.
Some General Tips
1. Read the topic twice — three times if necessary — before writing. Circle key
words. This helps you focus on the task assigned.
2. You may wish to put the topic or question in your own words. This often
helps you understand what is required.
3. Use a form of prewriting before you begin writing your actual essay.
Prewriting can consist of outlining, brainstorming, clustering, and so on.
4. Spend about five minutes organizing your thoughts before you begin writing.
A poorly written essay is often the result of inadequate planning.
5. Don’t let spelling slow down your writing. That is, keep the flow of your
writing going and correct spelling errors later.
6. Take several minutes to reread and edit or correct your essay. Don’t make
extensive changes when you reread; just correct spelling errors and other
minor flaws.
7. Don’t use excessively large writing, don’t leave wide margins, and don’t skip
any lines.
8. Doublecheck the amount of space you have in which to write each essay.
92
The Writing Section
Scoring the CBEST Essays
Each essay is scored on a scale of 1 to 4 as follows:
4 = pass
3 = marginal pass
2 = marginal fail
1 = fail
Since each essay is scored twice, the total raw score range for the two essays is
from 4 to 16. This score is scaled to 20 to 80. A raw score of approximately 12
should get you a passing score.
Focus on the components of a good essay.
A good essay:
❑ addresses the assignment
■ stays well focused
■ expresses a clear thesis statement on the topic
❑ organizes points logically
■ uses smooth transitions between paragraphs
■ has coherent, unified paragraphs
❑ develops ideas presented
■ gives specific examples to support points
■ anticipates and addresses opposing views
❑ is grammatically sound (with only minor flaws)
■ uses correct sentence structures
■ uses correct punctuation
■ uses standard written English
❑ uses language skillfully
■ uses a variety of sentence types
■ uses a variety of words
❑ is legible
■ shows clear handwriting
■ appears neat
93
Part II: Analysis of Exam Areas
The Descriptive/Narrative Essay
This type of essay topic asks you to draw directly from personal experience, to show
(describe) and tell about (narrate) a significant event in your life. For example:
Students can look back on their years in school and pinpoint one particular
course or one particular teacher most instrumental in shaping their lives.
Reflect on your own school years and focus on one such instructor or course.
Describe the conditions or qualities that made that particular experience or
teacher special.
You should understand that the test is concerned with your writing ability, not
your personal experience. Therefore, you can describe a fictional character or
course. You can make up the conditions or qualities. Try making up information or
a fictional character at least once when you practice writing an essay. This can
help you in the event that you get stuck trying to recall a person or situation on the
actual test.
Preparing to Write Using Clustering
Inventing and organizing information on short notice, given only a few minutes,
can be difficult unless you are ready with an effective technique. One technique
well suited to the timed essay is called clustering.
Use clustering as a way of organizing your thoughts before you write. Clustering
provides a way to put all of your thoughts down on paper before you write so that
you can quickly see the structure of the whole paper.
After you choose a topic, write it down in the prewriting area (given under the actual
topic question) and draw a circle around that topic:
Psychology
Course
For a few moments, think of all the elements of that topic and connect them to the
central topic cluster:
94
The Writing Section
field
experience
2
school
1
Greg
6
see through
labels
3
Psychology
Course
winter
4
hospital
5
up
8
flexible
7
You can then number the parts of the cluster to give an order to your thoughts.
You don’t have to use all the elements of your cluster.
Spend about five minutes prewriting and organizing your ideas.
Writing
A strong opening paragraph is essential. An effective first paragraph tells your
reader what to expect in the body of the essay.
Writing the body of the essay involves presenting specific details and examples
related to the aspects you have introduced. You can take several paragraphs to do
this, but make sure that each paragraph consists of at least three sentences. Very
short paragraphs may make your essay appear scattered.
A conclusion may function to
■
■
■
complete your response to the essay question.
add information not introduced earlier.
point toward the future.
Proofreading
Always allow a few minutes to proofread your essay for errors in grammar, usage,
and spelling. If you detect an error, either erase it cleanly or simply line it out
carefully and insert the correction neatly. Keep in mind, both while you are writing
and while you are correcting, that your handwriting must be legible.
95
Part II: Analysis of Exam Areas
A Specific Approach: The Story Formula
One good way to approach a question that asks you to describe one experience is
through the use of the story formula. The story formula consists of
■
■
■
■
■
Setting: The location of the story
Main characters: The people in the story
Plot: The problem in the story or the crisis to be overcome
Climax: The turning point in the story
Resolution: The ending or how you are now as a result of the experience
So, although the number of paragraphs may vary, generally the sample essay is
structured as follows:
■
■
■
■
Paragraph 1: Introduces the setting and the main characters in the story
Paragraph 2: Introduces the plot
Paragraph 3: Introduces the climax
Final paragraph: Introduces the resolution
The story formula allows you to describe one experience in detail, using clear
transitions, while keeping a unifying theme throughout your essay.
The Finished Descriptive/Narrative Essay
A finished essay using the story formula follows. The writer used clustering to organize
the essay’s elements.
96
The Writing Section
97
Part II: Analysis of Exam Areas
98
The Writing Section
A Second Look at the Finished Essay (With Comments)
Good specific information
setting up the story.
Notice the setting.
Gives a specific example
of "labels."
Actually introduces another
main character and plot here.
Notice the turning point or
climax. Again the "label"
is mentioned.
Essay 1
Ten years ago, I was twentyone and a junior at
California State University at Long Beach. My schooling had
been quite traditional, and because of this I regarded my college
experience as a necessary means to an end and rarely
educational. Shortly after I began my second semester in the
Education Department, however, I took a course in abnormal
psychology that became most instrumental in shaping my
life.
On a cold blustery winter day, as I drove to my parttime
job in the neuropsychiatric hospital, I had a nagging
feeling that the psychology class I enrolled in was slowly
changing my point of view. As I drove onto the damp parking
lot and walked in the doorway to the childrenÕs unit, my
professorÕs words haunted me: "The challenge of the new
psychology is to look beyond the 'labels' given to people and
to see for oneself the human being that is there." I mulled over
in my mind whether this day would bring me any closer to that
goal.
That day a new patient arrived. He was a fouryearold,*
child pinned tightly with the label of "autistic." His name
was Gregory, and in him I saw immediately all that I had
previously only read about. He had all of the usual behavior of a
child who was autistic. He would not respond to touch or
affection, engaged in constant finger flicking and hand gazing,
and seemed to withdraw into his own world.
In the days that passed I spent much time with Gregory,
involving him in whatever I was doing, always maintaining
some physical contact with him. It was not until the fourteenth
day that I dropped my eversoprecious label.
Gregory and I frequently engaged in games, but his favorite
game was entitled "Up." In this game I was to lift Gregory into
the air as he gleefully shouted, "up, up!" After several times my
arms grew weary, and instead of putting him down, I held
Gregory in my arms. There we stood in an embrace of trustÑan
opening to a place beyond his label. Tears flowed freely from
my eyes as he calmly touched each one with his fingers, smiling
as their wetness served to cement our relationship. Somehow, in
that moment, all of what I had read mattered little compared
to what I now know. As my professor had warned us in
class, "The labels only serve to make things easyÑit is up to
you to discover the truth."
Each day I went to the neuropsychiatric institute filled me
with a joy I had never known, yet in one sharp moment it was
all shattered. On December 26, 1972, Gregory was transferred
to the state mental institution. Over the advice of the staff and
the doctors, Gregory was taken to a place where he would wear
his label forever.
The next few weeks at the hospital seemed empty to me. A
challenge by a professor to see through the labels and the
willingness and trust of a fouryearold child enabled me to
learn a lesson that I shall never forget. For the first time a
college course provided me with a real learning experience;
all of the coursework that I had taken never touched me as
deeply as this one course.
Interesting introduction,
giving some background
with the last sentence giving
the direction and focus of
the essay.
Adds information about
the psychology class.
*Note minor comma error.
Remember that the essay is
graded holistically, minor
flaws are okay.
Nice transition into how the
label was dropped.
Paragraph gives good
specific detail reinforcing
the "label" issue and ties
back very cleanly to the
psychology class.
A strong ending, explaining
the result of the experience.
99
Part II: Analysis of Exam Areas
Another Prewriting Method: Outlining
Another way to prewrite is make an outline. A simple outline for a
Descriptive/Narrative essay may go something like this:
Course: Music 101 — Introduction to Mozart
I. Caused me to change my major
A. Hated economics but never knew it
B. Music raised my spirits — new outlook on life
II. Broadened my life
A. Began attending concerts — became more social
B. Got out of the house
C. Appreciation for a new art form — now more open about other things
as well
III. Developed new skills
A. Learned how to listen better
B. Began learning to play French horn
1. Made new friends in Community Orchestra
2. Met my present husband who played firstchair French horn in
Community Orchestra
Organizing an outline like the preceding one (it need not be this formal) can help
you write a wellstructured, wellplanned essay. You can readily see that constructing
a good essay from the preceding outline would be a fairly simple task.
Whatever way you prewrite — cluster, outline, or another method — the important
thing is that you think and plan before you actually begin writing your essay.
Two Additional Finished Essays
Following are two more attempts using the same topic. Both essays are evaluated
in some detail. Analyze each essay’s strengths and weaknesses.
100
The Writing Section
A WellWritten Essay
Essay 2
Orienting the reader to
the writerÕs background
and experience.
Restricting the discussion
appropriately.
Balanced, contrasting sentence
addressing point (1) from first
paragraph. Able to control
syntax, reference to specific
details, orderly phrasing.
Thesis sentence, highlighting the
significance of this paragraph.
Summary sentence, reinforcing
the overall point of the paragraph.
Reference to point (3) of the
opening paragraph.
Specific supporting detail.
By the time I was a junior in college, I had
developed criteria for good teaching and bad
teaching, criteria based on my experiences during
those first two college years. The good teachers
were always (1) models of enthusiasm and
curiosity about their subject, (2) interested in
studentsÕ fulfilling their own potential and not
trying to please the instructor, and (3) friendly as
well as scholarly. Of the few good teachers I
enjoyed, Bob Lincoln (a professor of English) was
the best. Four times a week, sluggish and yawning
from listening to my classics professor drone
endlessly in a muffled monotone about Zeus and
the Olympians, I slumped into Dr. LincolnÕs class
on the Victorian novel. And always he would lift my
spirits with his own spirited approach; his was a
remarkable talent for making connections
between the experiences of Jane Eyre, Becky
Sharp, and Adam Bede, and very modern
problems of repression, alienation, and greed. He
showed that good teachers make their subjects
part of their own life and time and that literature
can help us understand ourselves.
But Dr. Lincoln never imposed his viewpoints on
us. The importance of the literature was ours to
decide. We kept journals in which we wrote about
how instances in the novels were like those in our
own experience, and by sharing those responses in
class we learned how many different viewpoints a
novel can provoke and learned to respect each
otherÕs differences. All this came about because
Dr. Lincoln was more interested in what the
subject meant to us than what it meant to him.
His attention to our learning didnÕt stop at the
end of a class meeting. Always willing to make
himself available for further discussion, Dr. Lincoln
even invited us to his home at times. These
uncommon occasions, sharing the professorÕs
"natural habitat," helped us to learn that teachers are
people, too, and that the best teachers are those who
transform their students into a community, not just a
bunch of anonymous paper pushers.
Designating the points to be
discussed; focusing the essay.
Vivid portrait of bad teacher and
the effects of bad teaching.
Effective transition (but),
reference to point (2).
Clear, brief sentence; interesting
contrast with longer ones.
Specific supporting details,
logical parallel structure.
Additional information, fluency,
and humor; clearly states the
significance of the experience
and its relationship to the
general topic.
Ties the past into the
present gracefully.
Each day of my own training in education and
practice in teaching, I try to remember what Dr.
Lincoln taught me. Good teaching takes energy,
commitment, and good humor; it is a product of
people, not merely of books and papers.
Summary conclusion that does
more than simply restate what
has already been said.
101
Part II: Analysis of Exam Areas
A Poorly Written Essay
Fragment sentence, which states
information irrelevant to the
topic and already known to
the audience.
Seemingly irrelevant point.
Paragraph as a whole lacks focus
and clarity.
Faulty logic.
Runon sentences, full of vague
cliches, missing verb preceding
in, spelling error; in general a
crazy quilt of undeveloped ideas.
Restatement of part of the
question, disguised attempt to
focus the conclusion,
inappropriate verb (doing).
Vague pronoun reference.
Essay 3
As a person who would like to be a fulltime teacher
and who is right now student teaching until I pass
my courses and this test, so that I can apply for
promising positions. I can say that my best teachers
throughout elementary, secondary school and higher
was always on my side and very much a sense of
humor. As long as we had the assignment read, he
would discuss it with us.
Good teaching makes you want to know more,
especially for tests since they are how we learn. I
remember one day I have studied extremely
complete, and then the test was not what I expected.
This is what I mean by good teaching.
And then another time I enjoyed the class so much
that when it came time to "show what you know" I
was ready, willing and able, with so many of the
lectures in an interesting fashion, to show me that if
the teacher likes his job, than there is nothing to
worry about.
How many times have you looked for the teacher
and he doesnÕt answer the phone or even make an
effort to be their. Giving of yourself is when you
take extra time to make sure that students know how
they got the answers.
The conditions or qualities that made the particular
experience special, in conclusion, were what I find
myself doing whenever I think about teaching and
try to do something out of the ordinary. And it
works.
Faulty parallelism, subjectverb
disagreement, missing verb,
vague sentence structure
and diction.
Example of unclear relevance,
ungrammatical verb,
adjectiveadverb confusion.
Vague pronoun reference, vague
sentence in general. Paragraph
lacks a clear thesis.
Faulty logic, missing question
mark, misspelling.
Vague sentence.
Analysis of Essay 3
In general, the response is disunified, lacks relevant and specific details, does not
address only one instructor or experience, lacks planning and organization, and
displays a number of mechanical errors.
102
The Writing Section
Another Poor Essay (What NOT to Do)
See whether you can spot the weaknesses and errors in the following essay. Add
your comments in the blank boxes.
Essay 4
One course I had in college which was instrumental
in shaping my life was a college speech course. I
was not a talkative person. During classroom
discussions, my teacher made me participate and
that was something I had not done in a long time.
This particular subject was a coed class and I had to
discuss the current issues of today. There were only
three females in a class of forty men.
After the semester was over, I was quite a different
person than before the speech class.
I am now employed by the Over the Rainbow
School District as a kindorgotten teacher in an area
where people donÕt speak good. I feel happy to see
the children grow up with the kind of experiences I
can give them.
Analysis of Essay 4
This sample essay contains major faults in the writing. The essay lacks unity, focus,
and a clear description of one experience.
The essay has only a brief description that gives the reader a hint of the setting
and early experiences.
The essay rushes to the conclusion (resolution) without giving the reader an experience
that caused a change. Simply enrolling in a class does not cause one to
change. The writer left out a description of any experience that caused this
change.
The essay lacks a unified, clear focus without a described experience and fails to
go beyond a general discussion. The final sentence doesn’t seem to fit because we
still don’t know why this course was special and how it helped this person in his
or her job as a teacher.
The essay also contains many flaws in grammar and usage.
103
Part II: Analysis of Exam Areas
One More Descriptive/Narrative Topic
Often many different people help us shape our lives and formulate or reach
our goals. You are preparing a speech to be given to a group of educated
adults. Select a person who has had a major influence in shaping your life
and formulating or reaching your goals. Give specific details or examples in
your speech.
Read the topic two or three times and circle or underline key words or phrases.
This helps focus your essay. Use the key words in your essay to reinforce staying
on topic.
Often many different people help us shape our lives and formulate or reach
our goals. You are preparing a speech to be given to a group of educated
adults. Select a person who has had a major influence in shaping your life
and formulating or reaching your goals. Give specific details or examples in
your speech.
Begin by using key words to frame your introductory paragraph and point to the
body of your essay.
■
■
■
Introduction: The person who shaped your life goals
Body: Who the person was and how they did it
Conclusion: Summary of introduction and body
104
The Writing Section
Another WellWritten Essay
Essay 5
The body sets the stage, then
provides flowing narrative of
what took place.
Gives specific examples of
how Mrs. Simpson worked
at "shaping lives."
DoesnÕt get too specific.
Stays in general overview.
Clear examples.
Variety of sentence structures.
Nice, tight reminder to audience
of main focus of speech.
Many people have had an effect on my life. But
the person who had the greatest influence in
helping me formulate and reach my goals was my
senior English teacher, Mrs. Simpson. It was her
sound advice that helped me choose the career
path that has served me well.
As a young rebellious teenager I had dreams of
making great waves on this planet. I thought that
the field of law was the one where I could make
my mark. I decided to enter college as a prelaw
major, and I went to Mrs. Simpson to share my
decision with her and seek her advice.
Mrs. Simpson was one of those teachers with
that special gift. She would always listen, smile,
ask a few questions and suddenly the person who
had come to her would find their own answer.
Mrs. Simpson rarely said Òyou should,Ó rather she
would offer a Òwell, if I were in your shoes I
might...Ó And in this crafty way she would offer a
few options that were soundly based upon her
knowledge and personal experience.
I donÕt remember exactly how our
conversation went on that particular day when I
sought her counsel. I only remember that she agreed
with me. She was well aware of my verbal and
acting skills and thought that I would make an
excellent lawyer. She went on to say that my final
career decision was a long way off, and that I might
find myself later choosing to be a journalist, a
doctor or some other professional. She advised me
that instead of majoring in prelaw it might be
better to major in English. She explained that an
English major would lead to a BA and offer
courses in critical reading, thinking and writing.
These were skills, she said, that could be used in
any field. This way I wouldnÕt be boxed into one
specific area and could choose the specifics later
when I was in graduate school.
I took her advice and entered college as an
English major. My goal was still that of becoming
a lawyer, but I could take my time. Mrs. SimpsonÕs
manner and advice were so sound that years later
I realized it wasnÕt the field of law that really
interested me. During my undergraduate years I
decided to become a teacher. Mrs. Simpson
certainly helped shape my life and formulate my
goals.
Nice intro.
¥ Brief, but to the point.
¥ Sets focus for body of essay.
¥ Points way to body without
going too far: Who is Mrs.
Simpson? What was sound
advice? How did she help me
choose my career?
Good detail of how
Mrs. Simpson helped.
Remember: This is a speech.
Write as though you are speaking
to an educated adult audience.
Nice summary/conclusion.
Shows Mrs. SimpsonÕs influence
on the writer's life.
Repeats the topic's key words:
"formulate" and "reach goals."
105
Part II: Analysis of Exam Areas
The Analytical/Expository Essay
This type of essay topic asks you to explain and analyze an issue, problem, or
quotation. You are asked to agree or disagree and support your opinion with specific
examples.
A recent movement in education has been called “Back to Basics.” Its proponents
argue that the curriculum should concentrate only on reading, writing,
and mathematics skills and completely ignore such courses as sociology, art
appreciation, and drama.
Imagine that you are a school principal faced with the task of making policy for
your school. Present your argument(s) either for or against “Back to Basics.”
Preparing to Write
Using the clustering technique for prewriting, the following diagram shows what
the cluster for this topic might look like:
global
society
5
restrictive
curriculum
2
Back to
Basics
new definition
of back to basics
4
creativity
1
advancement
of system
3
A Specific Approach: The Why Essay
One good way to approach a question that asks you to explain, analyze, or evaluate
is to use a why essay format. A why essay is built around a thesis sentence.
The thesis sentence begins with your opinion followed by the word because and
then a list of the most important reasons why the opinion is valid, reasonable, or
wellfounded.
106
The Writing Section
For example, in the following sample Analytical/Expository essay, the thesis statement
is:
I am against the “Back to Basics” movement because it inhibits creativity,
fails to recognize the importance of the arts, and restricts the curriculum.
The thesis statement comes at the end of the introductory paragraph followed by
paragraphs that explain each supporting point. The paper ends with a summary of
the reasons and a restatement of the thesis sentence. Each paragraph should contain
approximately three to five sentences.
The introduction invites the reader to read on. The following reasons (three are
usually sufficient) should give supporting examples or evidence. Your concluding
paragraph summarizes your reasons and restates the thesis statement.
The why essay format looks like the following table in outline form:
Paragraph Why Essay Format Examples by Paragraph
Number
1 Introduction — Thesis Sentence Paragraph 1
2 Reason 1 Paragraph 2
3 Reason 2 Paragraph 3
4 Reason 3 Paragraph 4
5 Conclusion Paragraph 5
107
Part II: Analysis of Exam Areas
The Finished Analytical/Expository Essay
108
The Writing Section
109
Part II: Analysis of Exam Areas
A Second Look at the Finished Essay (With Comments)
Essay 6
Clear introduction. Nice
leadin to thesis statement.
Three clear reasons.
Starts paragraph with support
of reason 1, "inhibits creativity."
Reason 2, "fails to realize the
importance" is discussed and
supported with specifics.
This paragraph addresses
reason 3, "restricts curriculum,"
and ends with a strong
supporting sentence.
Restates thesis statement using
clear wording and an effective
closing sentence.
As principal of your school, I have seen many
educational movements come up and go. Some are
worthy of the attention given to them, and others should
be ignored because of their devastating effect on the
educational system. One such movement that falls into
the latter category is the ÒBack to BasicsÓ movement. Its
proponents argue that education should concentrate on
reading, writing, and mathematics skills and completely
ignore such courses as drama, art appreciation, and
sociology. I am against the ÒBack to BasicsÓ
movement because it inhibits creativity, fails to
recognize the importance of the arts, and restricts the
curriculum.
The enhancement of creative thinking is primal to
the advancement of any educational system. To create,
to invent, or to discover, one needs not only have
freedom of thought but the exposure and application of
that creativity to all areas of the curriculum.To
concentrate on only reading, writing, and mathematics
would restrict thinking to a narrow focus. The future
needs thinkers who can create in the widest spectrum
so as to be able to meet the challenges of a global society.
The ÒBack to BasicsÓ proponents also fail to see
that a restrictive curriculum of only mathematics,
reading, and writing fails to support the many great
advancements made in our culture by those whose first
exposures to art, drama, or sociology took place in the
schools. The great artists who have changed the way
people see; the great dramatists who have told their
stories worldwide; and the great sociologists who have
helped us to understand social relations, organization,
and changes in our culture have all been products of an
education that included the arts as basic to a wellrounded
education.
Finally, the ÒBack to BasicsÓ supporters fail to see
*their narrow view of education that the basics include
art, drama, and sociology as well as music, dance, and
computer literacy. ÒBasicsÓ by definition, means that
knowledge which is needed by children in our society in
order to compete and simply survive in that society. The
ÒBack to BasicsÓ movement is an attempt to take
education back to a time that has long since passed. The
narrow focus of the movement also overlooks the
integrative value of reading, writing, and
mathematics throughout all curriculum areas and
especially in the arts.
The ÒBack to BasicsÓ issue is a sad attempt to
restrict the information that children need for their
future. It will stifle creativity in those knowledge areas
upon which our society is dependent. So, as your
principal, I hope that you on the school board continue to
support an education for the futureÑan education that
defines the ÒbasicsÓ as those curriculum areas beyond
the courses of reading, writing, and mathematics. We
must meet the future with an education that includes
art, drama, and sociology.
Thesis statement at end of
first paragraph gives
direction and focus.
Additional support and
clarification is given.
Strong last sentence.
*The word in is missing. But
this is only a minor flaw in
the complete picture of this
wellwritten essay.
Reviews reasons using
strong languageÑ
"sad attempt to restrict."
110
The Writing Section
Poorly Written Essay
Can you spot the weaknesses and errors? Add your comments in the emply boxes.
Essay 7
Back to Basics is wrong for the schools. I donÕt like it.
For one thing what are we going to do with all of the
extra teachers when they fire all of the others. I will
probably lose my job cause I have only been teaching for
four years.
People get bored with the same thing day after day and
the children will come to hate school and that is not
good. I love to teach art and drama in my classroom. I
have not taught sociology yet though. I know the
children in my class could not stand to have only
reading, writing and mathematics. All the time without
ever a break. Behavior problems would increase because
the children would be so board that I would have to be
very strict to have any control. Those people in the back
to basics movement probably have never taught and are
just mad at schools because they have to pay taxes to the
schools and they are mad. Being a teacher I donÕt like the
back to basics movement and donÕt want to see it.
Analysis of Essay 7
This essay has major flaws in organization, development, and grammar. It does
not have a clear beginning, middle, and end. Nowhere in the paper is there a clear
thesis statement; reasons are merely scattered throughout the paper.
In this essay the author fails to choose the two or three most important reasons
and develop them fully, giving examples or evidence. The sentence beginning
“Behavior problems . . .” hints at a possible example; yet this thought is not well
developed with examples or evidence.
The paper contains many basic grammar and usage errors.
111
Part II: Analysis of Exam Areas
One More Analytical/Expository Topic
Some parents encourage their high school students to get an afterschool
or weekend job. Other parents cite the importance of getting good grades,
discouraging their high school students from getting afterschool or weekend
jobs.
What is your opinion or viewpoint on this subject? Use specific supporting
details from your own observations, experience, or reading as you write your
response.
A few reminders:
■
■
■
■
■
Read the topic two or three times.
Underline key words or phrases.
Restate the topic information in your own words. (In this case, parttime
jobs in school versus good grades and no jobs.)
This is a position paper — you need to pick one side and write in support
of that one side only!
It doesn’t matter which side you choose. Usually, it’s best to select the side
you can most comfortably write about — even if you personally disagree
with the position. Select the easiest position to write on and support it with
observations and experiences. Keep in mind that these observations and
experiences can be fictional since this section of the exam is testing your
writing ability.
112
The Writing Section
Two WellWritten Essays (With Comments)
Essay 8
Introduction is focused and
states position clearly
and immediately.
The second paragraph supports
the main position of the
introductionÑagain supports
the position that jobs can lead
to good grades.
The fourth paragraph shows
that not working in parttime
jobs doesnÕt mean that good
grades will necessarily follow.
Notice the supporting example
from the experience and
observation of the writer.
Some parents want their high school aged children to
work parttime, while other parents prefer their children
not work and instead concentrate on studies. I agree
with the parents who want their children to get good
grades, although I believe that after school work,
sports or other activities are helpful in establishing
good study habits and creating a wellrounded,
successful student.
Life is not all study any more than it is all play.
Students need to learn how to manage their time. They
need to learn the organizational skills necessary to do a
lot of different tasks in a timely manner. Work, sports,
and other activities are necessary to provide a break from
continual studying. They also provide experiences that
are essential to education and can lead to
understanding and, hence, better grades.
Since I was responsible for paying for my own
college education, it was necessary for me to work
parttime throughout my college years. I had to
organize my work hours around my class and study
hours, therefore I found a job in a grocery store as this
afforded me the greatest flexibility. I organized my time
and was able to work and keep up my grades.
Many of my college classmates came from wealthier
backgrounds than I did. They didnÕt have to work and
were able to concentrate fulltime on their studies and
their grades. A lot of these kids took study breaks for
coffee or beers or just chatting, and didnÕt organize their
time well. Some did quite poorly in school even
though their parents did all they could to help them
focus on grades.
From my own observations and experience Idonot
feel that afterschool or weekend jobs hinder a
student from getting good grades. I feel that these
activities can be more helpful than harmful by providing
the student with the opportunity to organize their life
activities. Whether in high school or in college a student
should be encouraged to engage in a multiplicity of
activities and to organize their time so they can
succeed in all they do. Interviews with todayÕs
successful people show that the busier and more
involved people are the ones who rise to the top of
their field.
Notice how it uses words
from the counterargument,
"good grades," to support the
position that parttime jobs
are good because they lead to
good grades.
The third paragraph gives
supporting details from
experience as asked for Ñ
personal experience supports
the position.
The conclusion:
¥ again restates the
essay topic;
¥ uses support from
observations to again support
original restated position;
¥ uses observation of
successful business people to
support main thesis.
Analysis of Essay 8
Note: Since the question is “what is your opinion,” it is quite permissible to write
in the first person (I) and give your opinion without saying “in my opinion” or “I
believe” or “my viewpoint is.” Be personal and invent supporting examples!
113
Part II: Analysis of Exam Areas
This is a good first paragraph.
It clearly states the writerÕs
position, and by suggesting that
work can develop nonacademic
skills, it prepares for the
arguments of the next three
paragraphs.
Note how the repetition of the
word "skills" links the second
paragraph with the first.
Paragraph three moves on to
another advantage
(development of a work ethic).
The second sentence explains
fully what the writer
understands a "work ethic"
to be.
The last paragraph is the
weakest paragraph of this essay.
The writer has argued forcefully
in favor of afterschool work.
There is no reason to weaken
the argument with the trite
suggestion that it will depend
on the individual. What doesnÕt?
In an argument essay like this,
it is not necessary (and is
usually a waste of time) to pay
lip service to the opposing point
of view.
Essay 9
There is a great deal of controversy among parents as
to whether or not their children should hold a paying job
while in high school. Some parents believe that working
while in school is a valuable experience; others believe
that the importance of good grades superceeds any value
that a job might offer. I think that working while in
school can be very beneficial to students and provide
them with skills that might enhance their ÒformalÓ
education.
One of the skills is time management. Learning how
to balance your activities and obligations is essential as
an adult. It is invaluable to know what you can handle
and when you are taking on too much. When I got a job
in high school, I began to realize the importance of
using my time wisely since I had less of it to throw
around. I think that I gained a lot from having to make
those decisions as well as earning my own money.
Another benefit is that students can develop a work
ethic which can be applied to their academic schooling
or any task that they choose to take on. Understanding
the importance of working hard, doing a good job
and being responsible are skills that are assets to any
endeavor. Students often develop confidence from being
counted on to get something done and then rising to that
challenge. Additionally, learning to take pride in your
work is really important. When you care about
something your performance often reflects that.
Academic success largely depends upon this same kind
of pride and confidence.
Ultimately, I believe that whether a child should
work while in school depends on the child. Some
children feel that they canÕt handle the responsibility
while others are willing to try. I think that students
stand to gain a lot from working, but should be able to
make that choice for themselves in the end.
A wellchosen word, but
misspelled. It should
be "supersede."
The writer supports her
argument (that parttime work
develops the ability to
manage time efficiently) by
referring to personal
experience.
The move to a second point
in this paragraph (increased
confidence) would be clearer
with the addition of a
transitional word or phrase
(such as "Further" or "Also")
to begin the sentence. But,
the writer rightly does
include a transitional word
("Additionally") at the
beginning of the next sentence.
Analysis of Essay 9
Aside from the last paragraph, this is a very good essay, wellorganized, wellsupported,
and specific. Its word choice, syntax, and mechanics are all competent.
114
The Writing Section
Important Terms Used in Essay Questions
Pay close attention to how the essay question is phrased. Are you being asked to
compare and contrast? Or simply to describe? It is very important to focus on the
exact assigned task; if you don’t answer the question asked, you will receive little
credit for your work. Some terms to look for:
■
■
■
■
■
■
Describe: Requires the use of adjectives, adverbs, and descriptive type
phrases. You are trying to “paint a mental picture” for your reader.
Compare: Requires analyzing similarities and differences between two or
more items.
Explain: Requires reasons substantiating an opinion or strengthening an
argument. Answers the question “why?”
Contrast: Requires setting up a comparison between items, usually focusing
on their differences.
Discuss: Usually allows a more openended approach, enabling the writer
a broader range of possibilities of approach.
Argue (or Present a Point of View): Requires the writer to take only one
point of view (either pro or con) and substantiate the position. Don’t be
concerned about taking the “right” or “wrong” position. That doesn’t matter.
What matters is, whichever position you take, that it be soundly and
clearly supported.
In most essay questions, regardless of type (compare, or describe, or explain), you
need to use examples to support your thoughts. Thinking in terms of examples is
also helpful in planning your writing.
115
Part II: Analysis of Exam Areas
Compare and Contrast
Compare a time in your life when a teacher helped you and a time when a
teacher hindered you. Explain which teacher you learned the most from as a
result of these experiences.
When writing an essay on a question that asks you to compare or contrast two
things, you can use this framework as a basic outline for your paper:
Paragraph 1: Introduction
1. Introduce reader to topic.
2. Restate question and tell opinion and reasons (thesis).
Paragraph 2
1. Describe one teacher and his or her attributes.
2. Tell how the teacher helped you.
3. Include your feelings about the experience.
Paragraph 3
1. Describe second teacher and his or her attributes.
2. Tell how this teacher hindered you.
3. Include your feelings about the experience.
Paragraph 4: Conclusion
1. Tell how and why one teacher was the better one for you.
2. Restate thesis.
116
The Writing Section
A PATTERNED PLAN OF ATTACK
Writing
Read the topic carefully—
at least twice.
Note the important words or main
focus of the assigned task or tasks.
Putting the topic in your
own words can be helpful.
Plan your essay: Prewrite
by clustering or outlining.
Write your essay: Use the appropriate form:
"why," "story," or "comparecontrast" essay.
Make sure to complete each task given.
Reread your essay, making minor
corrections in spelling, grammar, and so on.
117
Part II: Analysis of Exam Areas
Practice Essay Topics
Following are topics to use for practice. Allow about 30 minutes to plan and write
each essay. Use the space provided following each topic to organize your notes or
do your prewriting. Write the essays on the sheets provided. Then, upon completion
of each essay, evaluate, or have a friend evaluate, your writing using either
the simple checklist or the more indepth analysis sheets following each essay.
You may want to use both forms of evaluation because the analysis sheet can
help you take a closer look and assist you in understanding the scoring range.
Remember, you should try writing one Descriptive/Narrative essay using a fictional
character or situation.
Topic 1
Should there be any restriction on how many years a teacher may teach the same
subject or grade level? Explain your answer. Support your opinion with specific
examples.
118
The Writing Section
119
Part II: Analysis of Exam Areas
120
The Writing Section
Essay Topic Checklist
A good essay:
❑ addresses the assignment
■
■
stays well focused
expresses a clear thesis statement on the topic
❑ organizes points logically
■
■
uses smooth transitions between paragraphs
has coherent, unified paragraphs
❑ develops ideas presented
■
■
gives specific examples to support points
anticipates and addresses opposing views
❑ is grammatically sound (with only minor flaws)
■
■
■
uses correct sentence structures
uses correct punctuation
uses standard written English
❑ uses language skillfully
■
■
uses a variety of sentence types
uses a variety of words
❑ is legible
■
■
shows clear handwriting
appears neat
121
Part II: Analysis of Exam Areas
CBEST Essay Analysis Sheet
How well does the writer present the central idea or point of view?
(4) (3) (2) (1)
clearly adequately poorly fails to
presents presents presents present
Is the focus of the topic maintained?
(4) (3) (2) (1)
yes, generally sometimes no,
well focused clear focus loses focus unfocused
How is the reasoning in the response?
(4) (3) (2) (1)
well adequately simplistically lacks
reasoned reasoned reasoned reason
How are the ideas or points organized?
(4) (3) (2) (1)
logically generally some order disorganized
arranged clear evident
How well is the response supported?
(4) (3) (2) (1)
well supported adequately partially unsupported,
with specific supported with supported, no details
examples some examples lacking detail
How good is the choice of words in the essay?
(4) (3) (2) (1)
precise, careful, adequate generally poor choice
accurate choice choice of words imprecise of words
of words
choice of words
How well is the topic addressed?
(4) (3) (2) (1)
completely adequately, incompletely not addressed
addressed but not fully addressed
addressed
Does the essay use language and style appropriate to the given audience?
(4) (3) (2) (1)
yes, appropriate fairly inadequately inappropriate
language and style appropriate appropriate language and
language and style language and style style
To what extent is the writing free from grammatical and mechanical errors?
(4) (3) (2) (1)
only a few some errors, distracting errors numerous
minor flaws but not serious errors
How is the writing sample formed?
(4) (3) (2) (1)
well formed adequately formed partially formed inadequately formed
How well is the message communicated?
(4) (3) (2) (1)
effectively adequately effort made to not
communicated communicated communicate communicated
122
The Writing Section
Topic 2
Describe a particular time in your life when you had difficulty making an important
decision. Identify the situation and explain whether you were able to resolve
the problem. If it was resolved, how? If not, why not — what happened?
123
Part II: Analysis of Exam Areas
124
The Writing Section
125
Part II: Analysis of Exam Areas
Essay Topic Checklist
A good essay:
❑ addresses the assignment
■
■
stays well focused
expresses a clear thesis statement on the topic
❑ organizes points logically
■
■
uses smooth transitions between paragraphs
has coherent, unified paragraphs
❑ develops ideas presented
■
■
gives specific examples to support points
anticipates and addresses opposing views
❑ is grammatically sound (with only minor flaws)
■
■
■
uses correct sentence structures
uses correct punctuation
uses standard written English
❑ uses language skillfully
■
■
uses a variety of sentence types
uses a variety of words
❑ is legible
■
■
shows clear handwriting
appears neat
126
The Writing Section
CBEST Essay Analysis Sheet
How well does the writer present the central idea or point of view?
(4) (3) (2) (1)
clearly adequately poorly fails to
presents presents presents present
Is the focus of the topic maintained?
(4) (3) (2) (1)
yes, generally sometimes no,
well focused clear focus loses focus unfocused
How is the reasoning in the response?
(4) (3) (2) (1)
well adequately simplistically lacks
reasoned reasoned reasoned reason
How are the ideas or points organized?
(4) (3) (2) (1)
logically generally some order disorganized
arranged clear evident
How well is the response supported?
(4) (3) (2) (1)
well supported adequately partially unsupported,
with specific supported with supported, no details
examples some examples lacking detail
How good is the choice of words in the essay?
(4) (3) (2) (1)
precise, careful, adequate generally poor choice
accurate choice choice of words imprecise of words
of words
choice of words
How well is the topic addressed?
(4) (3) (2) (1)
completely adequately, incompletely not addressed
addressed but not fully addressed
addressed
Does the essay use language and style appropriate to the given audience?
(4) (3) (2) (1)
yes, appropriate fairly inadequately inappropriate
language and style appropriate appropriate language and
language and style language and style style
To what extent is the writing free from grammatical and mechanical errors?
(4) (3) (2) (1)
only a few some errors, distracting errors numerous
minor flaws but not serious errors
How is the writing sample formed?
(4) (3) (2) (1)
well formed adequately formed partially formed inadequately formed
How well is the message communicated?
(4) (3) (2) (1)
effectively adequately effort made to not
communicated communicated communicate communicated
127
Part II: Analysis of Exam Areas
Topic 3
Every year more and more computers are used for instruction. Is this good or bad? Discuss and
explain your opinions on the growing use of computerassisted instruction in the classroom.
Support your opinions with specific examples from your personal experience, readings, or general
knowledge.
128
The Writing Section
129
Part II: Analysis of Exam Areas
130
The Writing Section
Essay Topic Checklist
A good essay:
❑ addresses the assignment
■
■
stays well focused
expresses a clear thesis statement on the topic
❑ organizes points logically
■
■
uses smooth transitions between paragraphs
has coherent, unified paragraphs
❑ develops ideas presented
■
■
gives specific examples to support points
anticipates and addresses opposing views
❑ is grammatically sound (with only minor flaws)
■
■
■
uses correct sentence structures
uses correct punctuation
uses standard written English
❑ uses language skillfully
■
■
uses a variety of sentence types
uses a variety of words
❑ is legible
■
■
shows clear handwriting
appears neat
131
Part II: Analysis of Exam Areas
CBEST Essay Analysis Sheet
How well does the writer present the central idea or point of view?
(4) (3) (2) (1)
clearly adequately poorly fails to
presents presents presents present
Is the focus of the topic maintained?
(4) (3) (2) (1)
yes, generally sometimes no,
well focused clear focus loses focus unfocused
How is the reasoning in the response?
(4) (3) (2) (1)
well adequately simplistically lacks
reasoned reasoned reasoned reason
How are the ideas or points organized?
(4) (3) (2) (1)
logically generally some order disorganized
arranged clear evident
How well is the response supported?
(4) (3) (2) (1)
well supported adequately partially unsupported,
with specific supported with supported, no details
examples some examples lacking detail
How good is the choice of words in the essay?
(4) (3) (2) (1)
precise, careful, adequate generally poor choice
accurate choice choice of words imprecise of words
of words
choice of words
How well is the topic addressed?
(4) (3) (2) (1)
completely adequately, incompletely not addressed
addressed but not fully addressed
addressed
Does the essay use language and style appropriate to the given audience?
(4) (3) (2) (1)
yes, appropriate fairly inadequately inappropriate
language and style appropriate appropriate language and
language and style language and style style
To what extent is the writing free from grammatical and mechanical errors?
(4) (3) (2) (1)
only a few some errors, distracting errors numerous
minor flaws but not serious errors
How is the writing sample formed?
(4) (3) (2) (1)
well formed adequately formed partially formed inadequately formed
How well is the message communicated?
(4) (3) (2) (1)
effectively adequately effort made to not
communicated communicated communicate communicated
132
The Writing Section
Topic 4
Some have argued that imagination is not as important as perspiration. To what
extent do you agree or disagree with this argument? Support your opinion with
specific examples.
133
Part II: Analysis of Exam Areas
134
The Writing Section
135
Part II: Analysis of Exam Areas
Essay Topic Checklist
A good essay:
❑ addresses the assignment
■
■
stays well focused
expresses a clear thesis statement on the topic
❑ organizes points logically
■
■
uses smooth transitions between paragraphs
has coherent, unified paragraphs
❑ develops ideas presented
■
■
gives specific examples to support points
anticipates and addresses opposing views
❑ is grammatically sound (with only minor flaws)
■
■
■
uses correct sentence structures
uses correct punctuation
uses standard written English
❑ uses language skillfully
■
■
uses a variety of sentence types
uses a variety of words
❑ is legible
■
■
shows clear handwriting
appears neat
136
The Writing Section
CBEST Essay Analysis Sheet
How well does the writer present the central idea or point of view?
(4) (3) (2) (1)
clearly adequately poorly fails to
presents presents presents present
Is the focus of the topic maintained?
(4) (3) (2) (1)
yes, generally sometimes no,
well focused clear focus loses focus unfocused
How is the reasoning in the response?
(4) (3) (2) (1)
well adequately simplistically lacks
reasoned reasoned reasoned reason
How are the ideas or points organized?
(4) (3) (2) (1)
logically generally some order disorganized
arranged clear evident
How well is the response supported?
(4) (3) (2) (1)
well supported adequately partially unsupported,
with specific supported with supported, no details
examples some examples lacking detail
How good is the choice of words in the essay?
(4) (3) (2) (1)
precise, careful, adequate generally poor choice
accurate choice choice of words imprecise of words
of words
choice of words
How well is the topic addressed?
(4) (3) (2) (1)
completely adequately, incompletely not addressed
addressed but not fully addressed
addressed
Does the essay use language and style appropriate to the given audience?
(4) (3) (2) (1)
yes, appropriate fairly inadequately inappropriate
language and style appropriate appropriate language and
language and style language and style style
To what extent is the writing free from grammatical and mechanical errors?
(4) (3) (2) (1)
only a few some errors, distracting errors numerous
minor flaws but not serious errors
How is the writing sample formed?
(4) (3) (2) (1)
well formed adequately formed partially formed inadequately formed
How well is the message communicated?
(4) (3) (2) (1)
effectively adequately effort made to not
communicated communicated communicate communicated
137
Part II: Analysis of Exam Areas
Topic 5
We meet many people in the course of our lifetimes. Choose one particular
person you would call the most unforgettable and describe why he or she is so
unforgettable.
138
The Writing Section
139
Part II: Analysis of Exam Areas
140
The Writing Section
Essay Topic Checklist
❑ addresses the assignment
■
■
stays well focused
expresses a clear thesis statement on the topic
❑ organizes points logically
■
■
uses smooth transitions between paragraphs
has coherent, unified paragraphs
❑ develops ideas presented
■
■
gives specific examples to support points
anticipates and addresses opposing views
❑ is grammatically sound (with only minor flaws)
■
■
■
uses correct sentence structures
uses correct punctuation
uses standard written English
❑ uses language skillfully
■
■
uses a variety of sentence types
uses a variety of words
❑ is legible
■
■
shows clear handwriting
appears neat
141
Part II: Analysis of Exam Areas
CBEST Essay Analysis Sheet
How well does the writer present the central idea or point of view?
(4) (3) (2) (1)
clearly adequately poorly fails to
presents presents presents present
Is the focus of the topic maintained?
(4) (3) (2) (1)
yes, generally sometimes no,
well focused clear focus loses focus unfocused
How is the reasoning in the response?
(4) (3) (2) (1)
well adequately simplistically lacks
reasoned reasoned reasoned reason
How are the ideas or points organized?
(4) (3) (2) (1)
logically generally some order disorganized
arranged clear evident
How well is the response supported?
(4) (3) (2) (1)
well supported adequately partially unsupported,
with specific supported with supported, no details
examples some examples lacking detail
How good is the choice of words in the essay?
(4) (3) (2) (1)
precise, careful, adequate generally poor choice
accurate choice choice of words imprecise of words
of words
choice of words
How well is the topic addressed?
(4) (3) (2) (1)
completely adequately, incompletely not addressed
addressed but not fully addressed
addressed
Does the essay use language and style appropriate to the given audience?
(4) (3) (2) (1)
yes, appropriate fairly inadequately inappropriate
language and style appropriate appropriate language and
language and style language and style style
To what extent is the writing free from grammatical and mechanical errors?
(4) (3) (2) (1)
only a few some errors, distracting errors numerous
minor flaws but not serious errors
How is the writing sample formed?
(4) (3) (2) (1)
well formed adequately formed partially formed inadequately formed
How well is the message communicated?
(4) (3) (2) (1)
effectively adequately effort made to not
communicated communicated communicate communicated
142
The Writing Section
Topic 6
Many recent high school graduates discover that, despite possessing a high school
diploma, they have no specific skills to enable them to obtain employment. Explain
your feelings about introducing a “vocational skills program” as an alternative
choice to the academic high school curriculum.
143
Part II: Analysis of Exam Areas
144
The Writing Section
145
Part II: Analysis of Exam Areas
Essay Topic Checklist
A good essay:
❑ addresses the assignment
■
■
stays well focused
expresses a clear thesis statement on the topic
❑ organizes points logically
■
■
uses smooth transitions between paragraphs
has coherent, unified paragraphs
❑ develops ideas presented
■
■
gives specific examples to support points
anticipates and addresses opposing views
❑ is grammatically sound (with only minor flaws)
■
■
■
uses correct sentence structures
uses correct punctuation
uses standard written English
❑ uses language skillfully
■
■
uses a variety of sentence types
uses a variety of words
❑ is legible
■
■
shows clear handwriting
appears neat
146
The Writing Section
CBEST Essay Analysis Sheet
How well does the writer present the central idea or point of view?
(4) (3) (2) (1)
clearly adequately poorly fails to
presents presents presents present
Is the focus of the topic maintained?
(4) (3) (2) (1)
yes, generally sometimes no,
well focused clear focus loses focus unfocused
How is the reasoning in the response?
(4) (3) (2) (1)
well adequately simplistically lacks
reasoned reasoned reasoned reason
How are the ideas or points organized?
(4) (3) (2) (1)
logically generally some order disorganized
arranged clear evident
How well is the response supported?
(4) (3) (2) (1)
well supported adequately partially unsupported,
with specific supported with supported, no details
examples some examples lacking detail
How good is the choice of words in the essay?
(4) (3) (2) (1)
precise, careful, adequate generally poor choice
accurate choice choice of words imprecise of words
of words
choice of words
How well is the topic addressed?
(4) (3) (2) (1)
completely adequately, incompletely not addressed
addressed but not fully addressed
addressed
Does the essay use language and style appropriate to the given audience?
(4) (3) (2) (1)
yes, appropriate fairly inadequately inappropriate
language and style appropriate appropriate language and
language and style language and style style
To what extent is the writing free from grammatical and mechanical errors?
(4) (3) (2) (1)
only a few some errors, distracting errors numerous
minor flaws but not serious errors
How is the writing sample formed?
(4) (3) (2) (1)
well formed adequately formed partially formed inadequately formed
How well is the message communicated?
(4) (3) (2) (1)
effectively adequately effort made to not
communicated communicated communicate communicated
147
Part II: Analysis of Exam Areas
Topic 7
Recent educational experiments have included ungraded classrooms which consist
of students grouped by level of achievement rather than by age. Imagine that such
an “ungraded classroom” system is suggested for your school. As a parent, write a
strong argument (either pro or con) to be read at the next meeting of the Board of
Education.
148
The Writing Section
149
Part II: Analysis of Exam Areas
150
The Writing Section
Essay Topic Checklist
A good essay:
❑ addresses the assignment
■
■
stays well focused
expresses a clear thesis statement on the topic
❑ organizes points logically
■
■
uses smooth transitions between paragraphs
has coherent, unified paragraphs
❑ develops ideas presented
■
■
gives specific examples to support points
anticipates and addresses opposing views
❑ is grammatically sound (with only minor flaws)
■
■
■
uses correct sentence structures
uses correct punctuation
uses standard written English
❑ uses language skillfully
■
■
uses a variety of sentence types
uses a variety of words
❑ is legible
■
■
shows clear handwriting
appears neat
151
Part II: Analysis of Exam Areas
CBEST Essay Analysis Sheet
How well does the writer present the central idea or point of view?
(4) (3) (2) (1)
clearly adequately poorly fails to
presents presents presents present
Is the focus of the topic maintained?
(4) (3) (2) (1)
yes, generally sometimes no,
well focused clear focus loses focus unfocused
How is the reasoning in the response?
(4) (3) (2) (1)
well adequately simplistically lacks
reasoned reasoned reasoned reason
How are the ideas or points organized?
(4) (3) (2) (1)
logically generally some order disorganized
arranged clear evident
How well is the response supported?
(4) (3) (2) (1)
well supported adequately partially unsupported,
with specific supported with supported, no details
examples some examples lacking detail
How good is the choice of words in the essay?
(4) (3) (2) (1)
precise, careful, adequate generally poor choice
accurate choice choice of words imprecise of words
of words
choice of words
How well is the topic addressed?
(4) (3) (2) (1)
completely adequately, incompletely not addressed
addressed but not fully addressed
addressed
Does the essay use language and style appropriate to the given audience?
(4) (3) (2) (1)
yes, appropriate fairly inadequately inappropriate
language and style appropriate appropriate language and
language and style language and style style
To what extent is the writing free from grammatical and mechanical errors?
(4) (3) (2) (1)
only a few some errors, distracting errors numerous
minor flaws but not serious errors
How is the writing sample formed?
(4) (3) (2) (1)
well formed adequately formed partially formed inadequately formed
How well is the message communicated?
(4) (3) (2) (1)
effectively adequately effort made to not
communicated communicated communicate communicated
152
The Writing Section
Topic 8
Our lives have high points and low points. Choose one particular high point or
low point and describe why it had such an impact on you. Explain what you
gained from the situation.
153
Part II: Analysis of Exam Areas
154
The Writing Section
155
Part II: Analysis of Exam Areas
Essay Topic Checklist
A good essay:
❑ addresses the assignment
■
■
stays well focused
expresses a clear thesis statement on the topic
❑ organizes points logically
■
■
uses smooth transitions between paragraphs
has coherent, unified paragraphs
❑ develops ideas presented
■
■
gives specific examples to support points
anticipates and addresses opposing views
❑ is grammatically sound (with only minor flaws)
■
■
■
uses correct sentence structures
uses correct punctuation
uses standard written English
❑ uses language skillfully
■
■
uses a variety of sentence types
uses a variety of words
❑ is legible
■
■
shows clear handwriting
appears neat
156
The Writing Section
CBEST Essay Analysis Sheet
How well does the writer present the central idea or point of view?
(4) (3) (2) (1)
clearly adequately poorly fails to
presents presents presents present
Is the focus of the topic maintained?
(4) (3) (2) (1)
yes, generally sometimes no,
well focused clear focus loses focus unfocused
How is the reasoning in the response?
(4) (3) (2) (1)
well adequately simplistically lacks
reasoned reasoned reasoned reason
How are the ideas or points organized?
(4) (3) (2) (1)
logically generally some order disorganized
arranged clear evident
How well is the response supported?
(4) (3) (2) (1)
well supported adequately partially unsupported,
with specific supported with supported, no details
examples some examples lacking detail
How good is the choice of words in the essay?
(4) (3) (2) (1)
precise, careful, adequate generally poor choice
accurate choice choice of words imprecise of words
of words
choice of words
How well is the topic addressed?
(4) (3) (2) (1)
completely adequately, incompletely not addressed
addressed but not fully addressed
addressed
Does the essay use language and style appropriate to the given audience?
(4) (3) (2) (1)
yes, appropriate fairly inadequately inappropriate
language and style appropriate appropriate language and
language and style language and style style
To what extent is the writing free from grammatical and mechanical errors?
(4) (3) (2) (1)
only a few some errors, distracting errors numerous
minor flaws but not serious errors
How is the writing sample formed?
(4) (3) (2) (1)
well formed adequately formed partially formed inadequately formed
How well is the message communicated?
(4) (3) (2) (1)
effectively adequately effort made to not
communicated communicated communicate communicated
157
This Page Intentionally Left Blank
PART III
PART III
Assessment MiniTest
The MiniTest that follows is designed to familiarize you with some of
the basic CBEST question types. It should also assist you in briefly assessing
some of your strengths and weaknesses. This short assessment
includes complete answers and explanations. Take no more than 75 minutes
to complete this MiniTest.
Section I: Reading — 14 Questions
Section II: Mathematics — 14 Questions
Section III: Writing — 1 Essay
The format, levels of difficulty, and question structures are similar to
those on the actual CBEST. The CBEST itself is copyrighted and may
not be duplicated, and these questions are not taken directly from the actual
tests.
ANSWER SHEET FOR THE MINI
TEST
This Page Intentionally Left Blank
                                                                          CUT HERE                                                           
Answer Sheet for MiniTest
(Remove This Sheet and Use It to Mark Your Answers)
Section I: Reading
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
Section II: Mathematics
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
161
                                                                          CUT HERE                                                           
MINITEST
Time: 75 Minutes for Entire MiniTest
Section I: Reading
14 Questions
Directions: A question or number of questions follow each of the statements or passages in
this section. Using only the stated or implied information given in the statement or passage, answer
the question or questions by choosing the best answer from among the five choices given.
Make sure to mark your answers for this section in the Reading section of your answer sheet.
Read the passage below and answer the
two questions that follow.
The new vehicle inspection program is
needed to protect the quality of the state’s air,
for us and for our children. Auto exhausts are
a leading contributor to coughing, wheezing,
choking, and pollution. The state’s longterm
interests in the health of its citizens and in
this area as a place to live, work, and conduct
business depend on clean air.
1. Which of the following is an unstated
assumption made by the author?
A. Working and conducting business
may be different activities.
B. The state has been interested in the
health of its citizens even before
this inspection program was
proposed.
C. Exhaust emissions contribute to
pollution.
D. The new inspection program will
be effective.
E. Our ancestors did not suffer from
air pollution.
2. Which of the following, if true, would
most seriously weaken the preceding
argument?
A. Since smog devices were made
mandatory automotive equipment
by the existing inspection program
three years ago, pollution has
decreased dramatically and
continues to decrease.
B. Pollution problems are increasing
in other states as well as in this one.
C. Sometimes coughing, wheezing,
and choking are caused by
phenomena other than pollution.
D. Vehicle inspectors are not always
careful.
E. The state should not impose its
interests upon the citizenry but
should instead allow public health
to be regulated by private
enterprise.
163
Part III: Assessment MiniTest
Use the excerpt below from a table of
contents to answer the two questions that
follow.
GRAMMAR AND USAGE REVIEW . . . . . . 251
1. Parts of Speech, Adjectives and Adverbs,
Linking Verbs, Comparatives and
Superlatives . . . . . . . . . . . . . . . 251255
2. Case . . . . . . . . . . . . . . . . . . . . . 256261
3. Agreement . . . . . . . . . . . . . . . . 262270
4. Verbs . . . . . . . . . . . . . . . . . . . . 271279
5. Misplaced Parts, Dangling
Modifiers . . . . . . . . . . . . . . . . . 280285
6. Parallelism . . . . . . . . . . . . . . . . 286294
7. Ambiguous Pronouns . . . . . . . 295296
8. Other Errors of Grammar . . . . 296303
9. Errors of Diction, Idiom,
and Style . . . . . . . . . . . . . . . . . 304312
10. Punctuation . . . . . . . . . . . . . . . 313321
3. On which pages should one look to
check whether a colon or semicolon is
necessary in the sentence?
A. 256261
B. 271279
C. 296303
D. 304312
E. 313321
4. Which of the following is the best
description of the organizational pattern
of this section of the table of contents?
A. by alphabetical order
B. by errors of grammar, diction,
idiom, style, then punctuation
C. by levels of difficulty
D. by pronouns, nouns, then verbs and
style
E. by construction, parts of speech,
then grammar
Read the passage below and answer the
question that follows.
Recent federal government studies indicate
that more violent crimes are committed during
hot weather than during cold weather.
Thus, if we could control weather,
________________________________.
5. Which one of the following phrases, if
inserted into the blank at the end of the
passage, would best follow the writer’s
reasoning?
A. the crime rate would grow.
B. nonviolent crimes would increase.
C. we could lower the rate of violent
crimes.
D. we could also control the types of
crimes committed.
E. violent crimes would disappear.
164
Section I Reading
MiniTest
Read the passage below and answer the
three questions that follow.
Today the study of language in our schools
is somewhat confused. It is the most traditional
of scholastic subjects being taught in a
time when many of our traditions no longer
fit our needs. You to whom these pages are
addressed speak English and are therefore in
a worse case than any other literate people.
People pondering the origin of language for
the first time usually arrive at the conclusion
that it developed gradually as a system of
conventionalized grunts, hisses, and cries
and must have been a very simple affair in
the beginning. But when we observe the language
behavior of what we regard as primitive
cultures, we find it strikingly elaborate
and complicated. Stefansson, the explorer,
said that “In order to get along reasonably
well an Eskimo must have at the tip of his
tongue a vocabulary of more than 10,000
words, much larger than the active vocabulary
of an average businessman who speaks
English. Moreover these Eskimo words are
far more highly inflected than those of any
of the wellknown European languages, for a
single noun can be spoken or written in several
hundred different forms, each having a
precise meaning different from that of any
other. The forms of the verbs are even more
numerous. The Eskimo language is, therefore,
one of the most difficult in the world to
learn, with the result that almost no traders
or explorers have even tried to learn it.
Consequently there has grown up, in intercourse
between Eskimos and whites, a jargon
similar to the pidgin English used in
China, with a vocabulary of from 300 to 600
uninflected words, most of them derived
from Eskimo but some derived from English,
Danish, Spanish, Hawaiian, and other languages.
It is this jargon which is usually referred
to by travellers as ‘the Eskimo
language.” 1
1
The Encyclopaedia Britannica, 14th ed.,
Vol. 8, p. 709.
6. The size of the Eskimo language
spoken by most whites is
A. spoken in England, Denmark,
Spain, and Hawaii.
B. less than the size of the language
spoken by Eskimos.
C. highly inflected.
D. inestimable.
E. irrelevant.
7. Some of the evidence about language
in the passage is taken from the
observations of
A. linguists.
B. Eskimos.
C. businessmen.
D. an explorer.
E. primitive cultures.
8. The passage implies that a “traditional”
course in today’s schools would be
A. Advances in Biology: The Creation
of Artificial Life
B. Social Revolution in America
C. The History of the English
Language
D. Television and Its Impact
E. Disco Dancing as Psychotherapy
165
Part III: Assessment MiniTest
Read the passage below and answer the
three questions that follow.
We doubt that the latest government report
will scare Americans away from ham, bacon,
sausage, hot dogs, bologna, and salami or
that it will empty out the bars or cause a run
on natural food supplies. _______ a diet
were (was) mandated from Washington,
Americans probably would order the exact
opposite course. ________, the diet that does
make sense is to eat a balanced and varied
diet composed of foods from all food groups
and containing a reasonable caloric intake.
9. Which words or phrases, if inserted in
order into the blanks in the passage,
would assist the reader in understanding
the main point and conclusion of the
passage?
A. While; However
B. Since; Thus
C. If; Therefore
D. Even though; Except
E. Although; In contrast
10. Which of the following is specifically
implied by the passage?
A. Vitamins are necessary to combat
disease.
B. A recent report warned of the risks
of meat and alcoholic beverages.
C. Unorthodox suggestions for a more
nutritional diet were recently made
by the government.
D. Minerals are necessary to combat
fatigue.
E. More Americans eat ham than
bacon.
11. Which of the following is the best
meaning of the word mandated as it is
used in the passage?
A. recommended
B. legally decreed
C. sent
D. obtained
E. selected
Use the graph below to answer the question
that follows.
decibels
130
120
110
100
90
80
70
60
50
40
30
20
10
0
Decibel Levels of Common Noise Sources
shout
noisy office
factory
orchestra
The preceding graph shows the average
decibel levels associated with various
common sources of noise. Listening to
high levels of noise for a long time can
damage the eardrum and cause loss of
hearing.
nightclub
passing train
nearby thunder
gunfire
166
Section I Reading
MiniTest
12. According to the preceding graph,
which of the following sources of noise
would be most likely to damage the
eardrum?
A. an orchestra
B. a passing train
C. nearby thunder
D. gunfire
E. factory
Read the passage below and answer the
two questions that follow.
Beginning this fall, Latino and Asian students
will not be allowed to transfer out of
bilingual classes (that is, a program in which
courses are given in a student’s native language)
until they pass strict competency tests
in math, reading, and writing — as well as in
spoken English. The board and its supporters
say that this will protect children from being
pushed out of bilingual programs before they
are ready. They have hailed this as a victory
for bilingual education.
13. Which of the following, if true, is the
strongest criticism of the position of the
board?
D. Many students prefer to transfer
out of bilingual classes before they
have achieved competency in
English.
E. Holding back students will double
the number of students in bilingual
classes, resulting in twice as many
Latino and Asian children isolated
from the Englishspeaking
mainstream.
14. The argument in the passage would be
most strengthened if the author were to
explain:
A. how efficient the bilingual
program is
B. how well staffed the bilingual
program is
C. whether the community supports
the bilingual program
D. whether any board members do not
support the bilingual program
E. how the students feel about the
bilingual program
A. A foreign student may be quite
competent in math without being
competent in English.
B. Some native students already in
Englishspeaking classes are
unable to pass the competency
tests.
C. Most foreign students require many
months of practice and instruction
before mastering English skills.
167
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Section II Mathematics
MiniTest
Section II: Mathematics
14 Questions
Directions: Each question in this section is followed by five choices. Select the one best answer
for each question. Make sure to mark your answers for this section on the Mathematics
section of your answer sheet.
1. The mixed number 1 7 ⁄9 could be
properly placed between which of the
following fractions?
A.
17
⁄9 and 19 ⁄9
B.
11
⁄9 and 15 ⁄9
C. 7
⁄9 and 11 ⁄9
D. 5
⁄3 and 7 ⁄3
E. 5
⁄6 and 7 ⁄6
Use the information below to answer the
question that follows.
Alice researched five different bakeries
to check the price of chocolate sprinkle
donuts. Her results were as follows:
Bakery #1: 4 for $5
Bakery #2: 5 for $6
Bakery #3: 6 for $7
Bakery #4: 8 for $9
Bakery #5: $1 each
2. From the information given, which of
the following bakeries charges the most
for one chocolate sprinkle donut?
A. Bakery #1
B. Bakery #2
C. Bakery #3
D. Bakery #4
E. Bakery #5
3. Zelma is trying to quickly approximate
the answer to the problem 8.232 × 2.96.
Which of the following is the best
method to make this approximation?
A. multiply, then round off the answer
B. round 8.232 to 8, then multiply
C. round 2.96 to 3, then multiply
D. round 8.232 to 8, and 2.96 to 3,
then multiply
E. count decimal places
169
Part III: Assessment MiniTest
The graph below shows how Ali spent his
budget in a given year.
Student Budget Of $200
tuition
and books
34%
rent
and food
30%
6. In the equation x+ y= 8, which of the
following must be true?
A. x= 4an dy=
4
B. x and y are both positive
C. neither x nor y is zero
D. if x is positive, y is negative
E. if x is negative, y is positive
24%
miscellaneous
12%
Use the diagram below to answer the
question that follows.
transportation
A B C
4. Using the information given in the
preceding graph, how much money was
left in Ali’s budget after rent, food,
tuition, and book expenses?
A. $30
B. $34
C. $36
D. $64
E. $72
5. Kim purchased a portable stereo system
at Al’s Audio Barn. The list price of the
portable stereo system was $132.95.
The tax rate was 7%, so how much in
sales tax did Kim have to add on to the
list price to get the total purchase price?
7. What conclusion can be drawn from the
preceding diagram?
A. A and C have something in
common.
B. A and B have nothing in common.
C. A, B, and C have something in
common.
D. A and B have something in
common, but nothing in common
with C.
E. A and C have something in
common, but nothing in common
in B.
A. $ .93
B. $ 9.00
C. $ 9.31
D. $ 93.07
E. $133.26
170
Section II Mathematics
MiniTest
8. The probability of randomly picking a
yellow block from a set is 2⁄10. What is
the probability of not picking a yellow
block?
A. 4/5
B. 10/38
C. 10/2
D. 6/1
E. 10/1
Use the chart below to answer the
question that follows.
Time
Amount of Snowfall
Reading
in inches
1:00 .88
1:10 .93
1:20 .98
1:30 1.03
1:40 1.12
1:50 1.13
2:00 1.18
9. A student compiled the chart during a
steady snow. If it was later determined
that one of the readings was not correct,
which reading is probably the
inaccurate one?
A. .93
B. .98
C. 1.03
D. 1.12
E. 1.13
10. A large block of ice shaped in a cube is
being cut into smaller cubes. If the large
block has an edge of 48 inches and the
smaller cubes must each have an edge
of 24 inches, how many small blocks
can be produced?
A. 2
B. 4
C. 8
D. 10
E. 16
Read the information below and then
answer the question that follows.
• If the height of the wall is 15 feet
or greater, then Solley will use an
extension ladder to reach the top.
• If the height of the wall is greater
than 5 feet, but less than 15 feet,
then Solley will use a regular ladder
to reach the top.
• If the height of the wall is 5 feet
or less, then Solley will not need a
ladder to reach the top.
11. If Solley used a regular ladder to reach
the top, then which of the following
statements could be true?
A. The wall is 17 feet high.
B. The wall is less than 4 feet high.
C. The wall is 12 feet high.
D. The wall is greater than 15 feet
high.
E. The wall is 5 feet high.
171
Part III: Assessment MiniTest
Using the information given below, answer
the question that follows.
VitaValue Vending Machine
Price List
Soup $ .75
Salad $ 1.00
Sandwich $ 1.20
Hot Entrée $ 1.45
Beverage $ .50
Dessert $ .80
14. Twentyfour people sign up for an art
class. If twice as many women as men
are enrolled for the class, how many
women are enrolled?
A. 8
B. 16
C. 20
D. 21
E. cannot be determined
12. Slim has decided to buy lunch from the
VitaValue Vending Machine. He has
exactly $3.05 in change. If he buys a
salad and a beverage, which of the
following combinations can he also
afford to buy?
A. sandwich and dessert
B. soup and dessert
C. soup and hot entrée
D. soup and sandwich
E. hot entrée and dessert
13. Sam is 5 years older than twice Julie’s
age. Which of the following best represents
Sam’s age if Julie is 17 years old?
A. 217 ^ h+ 5
B. 2+ 5^17h
C. 34^5h
D. 2+ 17+
5
E. 217 ^ h+
25 ^ h
172
Section III Writing
MiniTest
Section III: Writing
1 Essay
Directions: In this section, you will plan and write an essay for the topic given. You may use
the bottom of this page to organize and plan your essay before you begin writing. You should
plan your time wisely. Read the topic carefully to make sure that you are properly addressing
the issue or situation. You must write on the specified topic. An essay on another topic will
not be acceptable.
The essay question included in this section is designed to give you an opportunity to write
clearly and effectively. Use specific examples whenever appropriate to support your ideas.
Keep in mind that the quality of your writing is much more important than the quantity.
Use the bottom of this page for any organizational notes you may wish to make. Write your
essays on the ruled answer sheets provided. No other paper may be used. Your writing should
be neat and legible. Because you have only a limited amount of space in which to write, please
do not skip lines, do not write excessively large, and do not leave wide margins.
Topic
Some people view sports as an integral part of the learning experience. Others, however, feel
that sports are not essential to the learning experience and, in fact, should be eliminated, since
they waste valuable educational funding. Present one side of this argument and substantiate
your views with supporting evidence or reasons.
173
Part III: Assessment MiniTest
174
Section III Writing
MiniTest
175
ANSWER KEY AND ANALYSIS
FOR THE MINITEST
Answer Key for the MiniTest
Section I: Reading
Section II: Mathematics
1. D 1. D
2. A 2. A
3. E 3. D
4. B 4. E
5. C 5. C
6. B 6. E
7. D 7. D
8. C 8. A
9. C 9. D
10. B 10. C
11. A 11. C
12. D 12. B
13. E 13. A
14. A 14. B
176
Answer Key and Analysis for the MiniTest
Scoring Your CBEST MiniTest
To score your CBEST MiniTest, total the number of correct responses for each section of the
test separately. Do not subtract any points for questions attempted but missed, as there is no
penalty for guessing.
Scores on the CBEST are scaled from 20 to 80, and you need to get about 70% of the questions
right to receive a passing score. If you score below the passing mark on one section but your
overall score is above the passing mark, you can pass the exam but only if your scores in each
section meet a minimum threshold.
Analyzing Your Test Results
Use the charts on the following page to carefully analyze your results and spot your strengths
and weaknesses. Analyze each subject area and each individual question of this MiniTest and
of each Practice Test completely. Reexamine the results for trends in types of error (repeated
errors) or poor results in specific subject areas. This reexamination and analysis is of
tremendous importance for effective test preparation.
Reading 14
Mathematics 14
TOTAL 28
MiniTest: Subject Area Analysis Sheet
Possible Completed Right Wrong
One of the most important parts of test preparation is analyzing why you missed a question so
that you can reduce the number of mistakes. Now that you have taken the MiniTest and corrected
your answers, carefully tally your mistakes by marking them in the proper column.
Reading
Mathematics
TOTAL
Tally Sheet for Questions Missed
Reason for Mistake
Total Simple Misread Lack of
Missed Mistake Problem Knowledge
Reviewing the preceding data can help you determine why you are missing certain questions.
When you pinpoint the type of error you’re most likely to make, you can focus on avoiding
those errors when you take Practice Test 1.
177
Part III: Assessment MiniTest
MiniTest Essay Checklist
Use this checklist to evaluate your essay.
A good essay:
❑ addresses the assignment
• stays wellfocused
• expresses a clear thesis statement on the topic
❑ organizes points logically
• uses smooth transitions between paragraphs
• has coherent, unified paragraphs
❑ develops ideas presented
• gives specific examples to support points
• anticipates and addresses opposing views
❑ is grammatically sound (with only minor flaws)
• uses correct sentence structures
• uses correct punctuation
• uses standard written English
❑ uses language skillfully
• uses a variety of sentence types
• uses a variety of words
❑ is legible
• shows clear handwriting
• appears neat
178
ANSWERS AND COMPLETE
EXPLANATIONS FOR
THE MINITEST
Section I: Reading
1. D. In order to argue for a new inspection program, the author must assume that that particular
program, if enacted, will be effective. Choice C, the only other choice related to the
points of the argument, expresses stated information rather than an unstated assumption.
2. A. The argument for further supervision of vehicle use is most weakened by the statement
that present safeguards are already doing the job. Choices C and D slightly weaken the argument
but do not address the overall position of the author.
3. E. Since the placing of a colon or semicolon refers to punctuation, you would look under
the punctuation section (pages 313321).
4. B. A careful look at the section and some reasoning gives you the right answer. Since “8.”
is “Other Errors of Grammar,” then the earlier sections must have also been errors of
grammar. This is followed by “9. Errors of Diction, Idiom, and Style,” and then “10.
Punctuation.”
5. C. It follows logically that if “more violent crimes are committed during hot weather” and
“if we could control the weather,” then we could lower the rate of violent crimes. Choice A
does not follow the reasoning (why would the rate grow?) and refers to “crime rate,” instead
of violent crime. Choice B refers to nonviolent crimes, which we cannot affect (and
why would they increase?). Choice D is not possible and choice E is too absolute.
6. B. Only answers B, D, and E could refer to size. Choice B summarizes the information of
paragraph 2, which tells us that an Eskimo’s vocabulary is over 10,000 words, whereas the
conversation between Eskimos and whites is made up of 300 to 600 words — less than 1 ⁄10
of the total Eskimo vocabulary.
7. D. “Stefansson, the explorer,” makes an observation about the Eskimo language in the
second paragraph.
8. C. The passage says that language “is the most traditional of scholastic subjects.”
The only choice directly involving language is C. And all the other choices are very
untraditional.
9. C. “If a diet were to be mandated . . . Therefore, the diet that does make sense . . .”
assists in understanding the main point and points out the conclusion.
179
Part III: Assessment MiniTest
10. B. The author doubts that Americans will stop eating meats or visiting bars, so you must
conclude that the author is referring to the latest government report warning of the risks of
meat and alcoholic beverages. Choice A concerning vitamins may be true, but is not
specifically implied other than in a very general sense (nutrition). Choice C is not true;
there is nothing to suggest that the government report made “unorthodox” suggestions.
Choices D and E are irrelevant to the passage.
11. A. Although the word “mandated” usually means “ordered, commanded, or decreed,” in
this context it means “recommended.” If it meant choice B, “legally decreed,” then
Americans would have to break the law to order the exact opposite course.
12. D. To answer this question, you must be able to read the graph and understand the information
included. Notice that the decibels of noise are listed along the lefthand side in increases
of 10. The common sources of noises are listed along the bottom of the graph.
Because gunfire has the highest decibel rating, it is the loudest of the choices. This would
cause it to be the most likely to damage the eardrum.
13. E. Choices A and B are irrelevant to the argument, and D is an illogical criticism. Choice
E is a logical conclusion that poses a significant problem.
14. A. All the other choices are much less relevant than the issue of how efficiently and effectively
the program helps students to achieve competency.
180
Answers and Complete Explanations for the MiniTest
Section II: Mathematics
1. D. 1 7 ⁄9 can be expressed as 16 ⁄9 (an improper fraction). Note that expressing the term as
ninths eliminates choices A, B, and C as possible answers. Changing choice D to fractions
expressed in ninths gives 5 ⁄3 = 15 ⁄9. 7 ⁄3 = 21 ⁄9, thus, 16 ⁄9 falls between the fractions listed in
choice D.
2. A. The cost per unit breaks down as follows:
A. $5/4 = $1.25
B. $6/5 = $1.20
C. $7/6 = approximately $1.17
D. $9/8 = approximately $1.13
E. $1.00
Thus, answer A is the most expensive.
3. D. To best approximate the answer to the problem, round off each number to a whole
number. This makes multiplication very simple: 8# 3= 24. Though answer choice A also
yields a roundedoff answer of 24, it is not the best way to approximate.
4. E. Because rent and food (30%) plus tuition and books (34%) totals 64%, Ali must have
36% left:
30% + 34% = 64%
100%  64% = 36%
Now multiply $200 by 36%:
$200
#.36
$ 72.
00
So Ali has $72 left in his budget.
181
Part III: Assessment MiniTest
5. C. To find 7% tax on $132.95, simply round off the price and multiply (the rule for rounding
off is “5 or above rounds up”): 7% times $133.
. 07 # $ 133 = $ 9.
31
6. E. Choices A, B, C, and D are all possibly true but don’t necessarily have to be true. Note
the important word “must” in the question. Only choice E must be true: If x is a negative
number, y must be a positive number so that their sum equals (positive) 8.
7. D. Since A and B overlap, they have something in common. Since neither of them overlaps
with C, they have nothing in common with C.
A B C
2 yellow blocks
8. A. Because the probability given means
10 total blocks
you can subtract as follows:
whole yellow not yellow
10
⁄10 – 2
⁄10 = 8
⁄10
Now simply reduce 8 ⁄10 to 4 ⁄5.
9. D. The chart indicates that, except for the reading at 1:40, the snow accumulated steadily
at a rate of approximately .05 inches every 10 minutes. Thus, if the reading at 1:40 was incorrect
— if the reading was actually 1.08 inches instead of 1.12 as recorded — then the
steady rise of .05 inches each 10 minutes could be maintained.
.88
.93
.98
1.03
1.12
1.13
1.18
+ .05
+ .05
+ .05
+ .09
+ .01
+ .05
182
Answers and Complete Explanations for the MiniTest
10. C. First change 48 inches to 4 feet and 24 inches to 2 feet. You now have a large cube
measuring 4 × 4 × 4, or 64 cubic feet. The small blocks have a volume of 2 × 2 × 2, or 8
cubic feet.
4′
2′
Now dividing 64 by 8 leaves 8 smaller blocks.
11. C. Because Solley uses a regular ladder, the wall must be between 6 and 14 feet high.
12. B. Slim buys:
salad + beverage = $1.00 + $.50 = $1.50
Because he started out with $3.05, this leaves him with $1.55:
$3.05 – $1.50 = $1.55
The only combination that Slim can buy is the one in choice B:
soup + dessert = $.75 + $.80 = $1.55
Each of the other answer choices costs more than the $1.55 Slim has
remaining.
13. A. If Julie is 17 years old, and Sam is 5 years older than twice Julie’s age, then:
twice Julie’s age
5 years older
2(17) + 5 = Sam’s age.
183
Part III: Assessment MiniTest
14. B. Let x = the number of men enrolled.
Let 2x = the number of women enrolled. Then:
x + 2x = 24
3x = 24
x = 24 ⁄3
x = 8
So the number of men enrolled is 8. Twice as many women are enrolled, so 2^8h = 16.
Thus, 16 women are enrolled.
184
PART IV
Mathematics Review
The following pages are designed to give you an intensive review of the
basic skills you need to use on the CBEST Mathematics section.
Arithmetic, basic algebra, measurement, properties of numbers, terms,
and simple statistics and probability are covered. Before you begin the
diagnostic review tests, it would be wise to become familiar with basic
mathematical terminology, simple formulas, and general mathematical
information — a review that begins on the following page. Next, proceed
to the arithmetic diagnostic test, which you should take to spot your
weak areas. Then use the arithmetic review that follows to strengthen
those areas.
After reviewing the arithmetic, take the algebra diagnostic test and once
again use the review that follows to strengthen your weak areas. Next,
take the measurement diagnostic test and carefully read and complete
the measurement review.
Even if you are strong in arithmetic, algebra, and measurement, you may
want to skim the topic headings in each area to refresh your memory. If
you are weak in math, read through the complete review. This is a good
basis for starting your practice testing. Recent CBESTs have emphasized
arithmetic, procedure, and wordtype problems. The practice tests
give good examples of each problem type.
This Page Intentionally Left Blank
SYMBOLS, TERMINOLOGY,
FORMULAS, AND GENERAL
MATHEMATICAL INFORMATION
Common Math Symbols and Terms
Symbol References
= is equal to ! is not equal to
> is greater than < is less than
$ is greater than or equal to # is less than or equal to
 is parallel to = is perpendicular to
Natural numbers — the counting numbers: 1, 2, 3, . . .
Whole numbers — the counting numbers beginning with zero: 0, 1, 2, 3, . . .
Integers — positive and negative whole numbers and zero:
. . . –3, –2, –1, 0, 1, 2, 3 . . .
Odd numbers — numbers not divisible by 2: 1, 3, 5, 7, . . .
Even numbers — numbers divisible by 2: 0, 2, 4, 6, . . .
Prime number — number divisible only by 1 and itself: 2, 3, 5, 7, 11, 13, . . .
Composite number — number divisible by more than just 1 and itself: 4, 6, 8, 9,
10, 12, 14, 15, . . .
Squares — the result when numbers are multiplied by themselves,
^2 : 2= 4h, ^33 : = 9h : 149162536
, , , , , ,. . .
Cubes — the result when numbers are multiplied by themselves twice,
^2 : 2 : 2= 8h, ^3: 3:
3=
27h : 1, 8, 27,
. . .
187
Part IV: Mathematics Review
Math Formulas
Triangle Perimeter = s1+ s2+
s3
Area = 1 ⁄2 bh
Square Perimeter =4s
Area = s · s or s 2
Rectangle
Parallelogram
Perimeter
Perimeter = 2(b + h) or 2b + 2h or
= 2(l + w) or 2l + 2w
Area = bh or lw
Perimeter = 2(l + w) or 2l + 2w
Area = bh
Add length of all sides
Cube Volume = s : s : s=
s 3
Surface area = s · s · 6
Rectangular Solid
Volume = l · w · h
Surface area = 2(lw) + 2(lh) + 2(wh)
188
Symbols, Terminology, Formulas, and General Mathematical Information
Important Equivalents
1
⁄100 = .01 = 1%
1
⁄10 = .1 = 10%
1
⁄5 = 2 ⁄10 = .2 = .20 = 20%
3
⁄10 = .3 = .30 = 30%
2
⁄5 = 4 ⁄10 = .4 = .40 = 40%
1
⁄2 = 5 ⁄10 = .5 = .50 = 50%
3
⁄5 = 6 ⁄10 = .6 = .60 = 60%
7
⁄10 = .7 = .70 = 70%
4
⁄5 = 8 ⁄10 = .8 = .80 = 80%
9
⁄10 = .9 = .90 = 90%
1
⁄4 = 25 ⁄100 = .25 = 25%
3
⁄4 = 75 ⁄100 = .75 = 75%
1
⁄3 = .33 1 ⁄3 = 33 1 ⁄3%
2
⁄3 = .66 2 ⁄3 = 66 2 ⁄3%
1
⁄8 = .125 = .12 1 ⁄2 = 12 1 ⁄2%
3
⁄8 = .375 = .37 1 ⁄2 = 37 1 ⁄2%
5
⁄8 = .625 = .62 1 ⁄2 = 62 1 ⁄2%
7
⁄8 = .875 = .87 1 ⁄2 = 87 1 ⁄2%
1
⁄6 = .16 2 ⁄3 = 16 2 ⁄3%
5
⁄6 = .83 1 ⁄3 = 83 1 ⁄3%
1 = 1.00 = 100%
2 = 2.00 = 200%
3 1 ⁄2 = 3.5 = 3.50 = 350%
189
Part IV: Mathematics Review
Math Words and Phrases
The following key words help you understand the relationships between the
pieces of information given and give you clues as to how the problem should be
solved.
Words that signal an operation:
■
■
■
Add
Addition: as in The team needed the addition of three new players . . .
Sum: as in The sum of 5, 6, and 8 . . .
Total: as in The total of the last two games . . .
Plus: as in Three chairs plus five chairs . . .
Increase: as in Her pay was increased by $30 . . .
More than: as in Four more than a number . . .
Greater than: as in Her income was $100 greater than . . .
Subtract
Difference: as in What is the difference between 8 and 5 . . .
Fewer: as in There were ten fewer girls than boys . . .
Remainder: as in What is the remainder when . . . or How many are left
when . . .
Less: as in A number is six less than another number . . .
Reduced: as in His allowance was reduced by $5 . . .
Decreased: as in His score decreased by 4 points . . .
Minus: as in Seven minus some number is . . .
Have left: as in How many are left when . . .
Multiply
Product: as in The product of 3 and 6 is . . .
Of: as in Onehalf of the people in the room . . .
Times: as in Six times as many men as women . . .
At: as in The cost of five yards of material at $9 a yard is . . .
Total: as in If you spend $20 per week on gas, what is the total for a twoweek
period . . .
Twice: as in Twice the value of some number . . . (multiply by 2)
190
Symbols, Terminology, Formulas, and General Mathematical Information
■
Divide
Quotient: as in The final quotient is . . .
Divided by: as in Some number divided by 5 is . . .
Divided into: as in The coins were divided into groups of . . .
Ratio: as in What is the ratio of . . .
Half: as in Half of the cards were . . . (divide by 2)
As you practice working word problems, you will discover more key words and
phrases that give you insight into the solving process.
Mathematical Properties
Some Properties (Axioms) of Addition
■
Commutative means that the order does not make any difference.
2+ 3= 3+
2
a+ b= b+
a
Note: Commutative does not hold for subtraction.
■
31!
13
ab!
ba
Associative means that the grouping does not make any difference.
^2+ 3h+ 4= 2+ ^3+
4h
^a+ bh+ c= a+ ^b+
ch
The grouping has changed (the parentheses moved), but the sides are still
equal.
Note: Associative does not hold for subtraction.
■
■
4^32h!
^43h2
a^bch!
^abhc
The identity element for addition is 0. Adding any number to 0 gives the
original number.
3+ 0=
3
a+ 0 = a
The additive inverse is the opposite (negative) of the number. Any number
plus its additive inverse equals 0 (the identity element).
3+ ^ 3h = 0; therefore 3 and –3 are inverses
 2+ 2= 0; therefore –2 and 2 are inverses
a+ ^ ah = 0; therefore a and –a are inverses
191
Part IV: Mathematics Review
Some Properties (Axioms) of Multiplication
■
Commutative means that the order does not make any difference.
2# 3=
3#
2
a# b=
b#
a
Note: Commutative does not hold for division.
■
2'
4!
4'
2
Associative means that the grouping does not make any difference.
^2# 3h# 4=
2# ^3#
4h
^a# bh# c=
a# ^b#
ch
The grouping has changed (the parentheses moved), but the sides are still
equal.
Note: Associative does not hold for division.
^8' 4h' 2!
8' ^4'
2h
■ The identity element for multiplication is 1. Multiplying any number by 1
gives the original number.
■
3# 1=
3
a# 1 = a
The multiplicative inverse is the reciprocal of the number. Any number
multiplied by its reciprocal equals 1.
2 × 1 ⁄2 = 1; therefore 2 and 1 ⁄2 are inverses
a × 1 ⁄a = 1; therefore a and 1 ⁄a are inverses
A Property of Two Operations
■
The distributive property is the process of distributing the number on the
outside of the parentheses to each number on the inside.
23 ^ + 4h= 23 ^ h+
24 ^ h
a^b+ ch= a^bh+
a^ch
Note: You cannot use the distributive property with only one operation.
3 (4 × 5 × 6) ≠ 3(4) × 3(5) × 3(6)
a^bcdh!
a^bh# a^ch#
a^dh or a^bcd h!
^abh^ach^adh
192
Symbols, Terminology, Formulas, and General Mathematical Information
Basic Statistics
■
■
■
■
To find the arithmetic mean, or average, simply total the numbers and
divide by the number of numbers.
Find the arithmetic mean of 3, 5, 6, 7, and 9. The total is
3+ 5+ 6+ 7+ 9= 30. Then divide 30 by 5, giving a mean, or average,
of 6.
To find the mode, look for the most frequently occurring score or measure.
Find the mode of these scores: 3, 5, 5, 5, 6, 7. The mode is 5 because it
appears most. If there are two modes, the distribution of scores is called
bimodal.
To find the median, arrange the scores or numbers in order by size. Then
find the middle score or number.
Find the median of these scores: 2, 5, 7, 3, 6. First arrange them in order
by size: 7, 6, 5, 3, 2. The middle score is 5; therefore the median is 5.
If the number of scores is even, take the average of the two middle scores.
Find the median of these scores: 2, 5, 7, 4, 3, 6. First arrange them in order
by size: 7, 6, 5, 4, 3, 2. The two middle numbers are 4 and 5; therefore
the median is 4 1 ⁄2.
To calculate the range of a group of scores or numbers, subtract the smallest
from the largest.
Find the range of the scores 3, 2, 7, 9, 12. The range is 12  2 = 10.
193
ARITHMETIC
Arithmetic Diagnostic Test
Questions
1. 6 = ? ⁄4
2. Change 5 3 ⁄4 to an improper fraction.
3. Change 32 ⁄6 to a whole number or mixed number in lowest terms.
4. 2 ⁄5 + 3 ⁄5 =
5. 1 ⁄3 + 1 ⁄4 + 1 ⁄2 =
6. 1 3 ⁄8 + 2 5 ⁄6 =
7. 7 ⁄9 – 5 ⁄9 =
8. 11 – 2 ⁄3 =
9. 6 1 ⁄4 – 3 3 ⁄4 =
10. 1 ⁄6 × 1 ⁄6 =
11. 2 3 ⁄8 × 1 5 ⁄6 =
12. 1 ⁄4 ÷ 3 ⁄2 =
13. 2 3 ⁄7 ÷ 1 1 ⁄4 =
14. . 07 + 1. 2 + . 471 =
15. . 45  . 003 =
16. $ 78. 24  $ 31.
68 =
17. . 5# . 5=
18. 8. 001 # 2.
3 =
g
19. . 7 . 147
g
20. .002 12
21. 1 ⁄3 of $7.20 =
22. Circle the larger number: 7.9 or 4.35
23. 39 out of 100 means:
24. Change 4% to a decimal.
25. 46% of 58 =
194
Arithmetic
26. Change .009 to a percent.
27. Change 12.5% to a fraction.
28. Change 3 ⁄8 to a percent.
29. Is 93 prime?
30. What is the percent increase of a rise in temperature from 80° to 100°?
31. Average 0, 8, and 10.
32. 8 2 =
Answers
1. 24
2. 23 ⁄4
3. 5 2 ⁄6 or 5 1 ⁄3
4. 5 ⁄5 or 1
13
5. ⁄12 or 1 1 ⁄12
6. 4 5 ⁄24
7. 2 ⁄9
8. 10 1 ⁄3
9. 2 2 ⁄4 or 2 1 ⁄2
10. 1 ⁄36
11. 209 ⁄48 or 4 17 ⁄48
12. 1 ⁄6
68
13. ⁄35 or 1 33 ⁄35
14. 1.741
15. .447
16. $46.56
17. .25
18. 18.4023
19. .21
20. 6,000
21. $2.40
22. 7.9
23. 39% or 39 ⁄100
24. .04
25. 26.68
26. .9% or 9 ⁄10%
27. 125 ⁄1000 or 1 ⁄8
28. 37.5% or 37 1 ⁄2%
29. No
30. 25%
31. 6
32. 64
195
Part IV: Mathematics Review
Arithmetic Review
Rounding Off
To round off any number:
1. Underline the place value to which you’re rounding off.
2. Look to the immediate right (one place) of your underlined place value.
3. Identify the number to the right. If it is 5 or higher, round your underlined
place value up 1. If the number to the right is 4 or less, leave your underlined
place value as it is and change all the other numbers to its right to zeros.
For example:
Round to the nearest thousand:
345,678 becomes 346,000
928,499 becomes 928,000
This works with decimals as well. Round to the nearest hundredth:
3.4678 becomes 3.47
298,435.083 becomes 298,435.08
Place Value
Each position in any number has place value. For instance, in the number 485, 4
is in the hundreds place, 8 is in the tens place, and 5 is in the ones place. Thus,
place value is as follows:
3 , 0
9 2 , 3 4 5 , 8 7 6 . 4 3 6 2 9 7 0 2
billions
hundred millions
ten millions
millions
hundred thousands
ten thousands
thousands
hundreds
tens
ones
tenths
hundredths
thousandths
tenthousandths
hundredthousandths
millionths
tenmillionths
hundredmillionths
and so on
196
Arithmetic
Estimating Sums, Differences,
Products, and Quotients
Estimating Sums
Use rounded numbers to estimate sums. For example:
Give an estimate for the sum 3, 741 + 5,
021 rounded to the nearest thousand.
3, 741 + 5,
021
↓ ↓
4, 000 + 5, 000 = 9,
000
So 3, 741 + 5, 021 . 9,
000
(The symbol ≈ means is approximately equal to.)
Estimating Differences
Use rounded numbers to estimate differences. For example:
Give an estimate for the difference 317, 753  115,
522 rounded to the nearest
hundred thousand.
317, 753  115,
522
↓ ↓
300, 000  100, 000 = 200,
000
So, 317, 753  115, 522 . 200,
000
Estimating Products
Use rounded numbers to estimate products. For example:
Estimate the product of 722 # 489 by rounding to the nearest hundred.
722 # 489
↓ ↓
700 # 500 = 350,
000
So 722 # 489 . 350,
000
197
Part IV: Mathematics Review
If both multipliers end in 50, or are halfway numbers, then rounding one number
up and one number down gives you a better estimate of the product. For example:
Estimate the product of 650 # 350 by rounding to the nearest hundred. Round one
number up and one down.
650 # 350
↓ ↓
700 # 300 = 210,
000
So 650 # 350 . 210,
000
You can also round the first number down and the second number up to get this
estimate.
650 # 350
↓ ↓
600 # 400 = 240,
000
So 650 # 350 . 240,
000
Rounding one number up and one number down gives you a closer approximation
than rounding both numbers up, which is the standard rule.
Estimating Quotients
Use rounded numbers to estimate quotients. For example:
Estimate the quotient of 891 ' 288 by rounding to the nearest hundred.
891 ' 288
↓ ↓
900 ' 300 = 3
So 891 ' 288 . 3
Fractions
Fractions consist of two numbers: a numerator (which is above the line) and a denominator
(which is below the line).
1 numerator
2 denominator or numerator 1 ⁄2 denominator
198
Arithmetic
The denominator indicates the number of equal parts into which something is divided.
The numerator indicates how many of these equal parts are contained in the
fraction. Thus, if the fraction is 3 ⁄5 of a pie, then the denominator 5 indicates that
the pie is divided into 5 equal parts, of which 3 (numerator) are in the fraction.
Sometimes it helps to think of the dividing line (in the middle of a fraction) as
meaning “out of.” In other words, 3 ⁄5 also means 3 “out of” 5 equal pieces from the
whole pie.
Common Fractions and Improper Fractions
A fraction like 3 ⁄5, where the numerator is smaller than the denominator, is less
than one. This kind of fraction is called a common fraction.
But sometimes a fraction may be more than one. This is when the numerator is
larger than the denominator. Thus, 12 ⁄7 is more than one. This is called an improper
fraction.
Mixed Numbers
When a term contains both a whole number (such as 3, 5, 8, 25, and so on) and a
fraction (such as 1 ⁄2, 1 ⁄4, 3 ⁄4, and so on), it is called a mixed number. For instance, 5 1 ⁄4
and 290 3 ⁄4 are both mixed numbers.
To change an improper fraction to a mixed number, divide the denominator into
the numerator. For example:
518 3
18
5 = 33 ⁄ 5
g
15
3
To change a mixed number to an improper fraction, multiply the denominator
times the whole number, add in the numerator, and put the total over the original
denominator. For example:
4 1 ⁄2 = 9 ⁄2 2# 4+ 1=
9
Reducing Fractions
A fraction must be reduced to lowest terms. Do this by dividing the numerator and
denominator by the largest number that divides evenly into both. For example:
Reduce 14 ⁄16 by dividing both terms by 2 to get 7 ⁄8. Likewise, reduce 20 ⁄25 to 4 ⁄5
by dividing both numerator and denominator by 5.
199
Part IV: Mathematics Review
Adding Fractions
To add fractions, you must first change all denominators to their lowest common
denominator (LCD) — the lowest number that can be divided evenly by all the
denominators in the problem. When you make all the denominators the same, you
can add fractions by simply adding the numerators (the denominator remains the
same). For example:
3 =
8
3
8
1 4 + = 2 8
change onehalf
to foureights
1 3 =
4 12
1 4 + = 3 12
change both
fractions to
LCD of 12
7
8
7
12
In the first example, change the 1 ⁄2 to 4 ⁄8, because 8 is the lowest common
denominator, and then add the numerators 3 and 4 to get 7 ⁄8 .
In the second example, you have to change both fractions to get the lowest common
denominator of 12, and then add the numerators to get 7 ⁄12. Of course, if the
denominators are already the same, just add the numerators. For example:
6
⁄11 + 3 ⁄11 = 9 ⁄11
Adding Mixed Numbers
To add mixed numbers, the same rule (find the LCD) applies, but make sure that
you always add the whole numbers to get your final answer. For example:
2 1 ⁄2 = 2 2 ⁄4
+ 3 1 ⁄4 = 3 1 ⁄4
5 3 ⁄4
change onehalf
to twofourths
remember to add
the whole numbers
Subtracting Fractions
To subtract fractions, the same rule (find the LCD) applies, except that you subtract
the numerators. For example:
7
⁄8 = 7 ⁄8
3
⁄4 = 9 ⁄12
− 1 ⁄4 = 2 ⁄8 − 1 ⁄3 = 4 ⁄12
5
⁄8
5
⁄12
200
Arithmetic
Subtracting Mixed Numbers
When you subtract mixed numbers, sometimes you may have to “borrow” from
the whole number, just like you sometimes borrow from the next column when
subtracting ordinary numbers. For example:
4 11
651
129
522
−
−
you borrow 1 from
the 10s column
6 = 5 5 ⁄ 5
− 3 1 ⁄ 5 = 3 1 ⁄ 5
2 4 ⁄ 5
4 1 ⁄ 6
2 5 ⁄ 6
1 2 ⁄ 6 = 1 1 ⁄ 3
you borrow one, in
the form 6 /6, from
the 1s column
To subtract a mixed number from a whole number, you have to “borrow” from the
whole number. For example:
borrow 1 in the form of
5 ⁄ 5 from the 6
remember to subtract the
remaining whole numbers
3 7 ⁄ 6
201
Multiplying Fractions
Simply multiply the numerators, then multiply the denominators. Reduce to lowest
terms if necessary. For example:
2
⁄3 × 5 ⁄12 = 10 ⁄36 reduce 10 ⁄36 to 5 ⁄18
This answer had to be reduced as it wasn’t in lowest terms.
Canceling when multiplying fractions: You can first “cancel” the fractions. That
eliminates the need to reduce your answer. To cancel, find a number that divides
evenly into one numerator and one denominator. In this case, 2 divides evenly into
2 in the numerator (it goes in one time) and into 12 in the denominator (it goes in
6 times). Thus:
1
2
3
#
12 5 =
6
After you cancel, you can multiply out as you did before.
1
2
3
#
12 5 =
18 5
6
Remember, you may cancel only when multiplying fractions.
Part IV: Mathematics Review
Multiplying Mixed Numbers
To multiply mixed numbers, first change any mixed number to an improper fraction.
Then multiply as shown in the preceding section. To change mixed numbers
to improper fractions:
1. Multiply the whole number by the denominator of the fraction.
2. Add this to the numerator of the fraction.
3. This is now your numerator.
4. The denominator remains the same.
3 1 ⁄3 × 2 1 ⁄4 = 10 ⁄3 × 9 ⁄4 = 90 ⁄12 = 7 6 ⁄12 = 7 1 ⁄2
Then change the answer, if in improper fraction form, back to a mixed number
and reduce if necessary.
Dividing Fractions
To divide fractions, invert (turn upside down) the second fraction and multiply.
Then reduce if necessary. For example:
1
⁄6 ÷ 1 ⁄5 = 1 ⁄6 × 5 ⁄1 = 5 ⁄6
1
⁄6 ÷ 1 ⁄3 = 1 ⁄6 × 3 ⁄1 = 3 ⁄6 = 1 ⁄2
Simplifying Fractions
If either numerator or denominator consists of several numbers, combine them
into one number. Then reduce if necessary. For example:
28 + 14
26 + 17
or
=
42
43
4 1 +
3 1 2 1 4 1
12 4 4 1 +
2
= 4 12 3 = 12 743 = 4 3 #
12 7 =
36 9
+ +
28
=
7
=1 2 ⁄7
Decimals
You can write fractions in decimal form by using a symbol called a decimal point.
All numbers to the left of the decimal point are whole numbers. All numbers to
the right of the decimal point are fractions with denominators of only 10, 100,
1,000, 10,000, and so on, as follows:
202
Arithmetic
.6 = 6 ⁄10 = 3 ⁄5
.7 = 7 ⁄10
.07 = 7 ⁄100
.007 = 7 ⁄1,000
.0007 = 7 ⁄10,000
.00007 = 7 ⁄100,000
.25 = 25 ⁄100 = 1 ⁄4
Adding and Subtracting Decimals
To add or subtract decimals, just line up the decimal points and then add or subtract
in the same manner you would add or subtract regular numbers. For example:
23.6 + 1.75 + 300.02 = 23.6
1.75
300.002
325.352
Adding in zeros can make the problem easier to work:
23.600
1.750
300.002
325.352
and 54. 26  1. 1 = 54.
26
110 .
53.16
and 78. 9  37. 43 = 78.
90
37.
43
41.47
You can add decimal places to the right of whole numbers. For example:
6 9 1
17  8. 43 = 1 7.
0 0
8
.4 3
8.5 7
Multiplying Decimals
To multiply decimals, just multiply as usual. Then count the total number of digits
above the line and to the right of all decimal points. Place the decimal point in
your answer so that there are the same number of digits to the right of it as there
are above the line. For example:
203
Part IV: Mathematics Review
40.012
x 3.1
40012
120036
124.0372
3 digits
1 digit
4 digits
total of 4 digits above the line
to the right of the decimal point
decimal point placed so there are
the same number of digits to the
right of the decimal point
Dividing Decimals
Dividing decimals is the same as dividing other numbers, except that if the divisor
(the number you’re dividing by) has a decimal, you move it to the right as many
places as necessary until it is a whole number. Then move the decimal point in the
dividend (the number being divided into) the same number of places. Sometimes
you may have to add zeros to the dividend (the number inside the division sign).
1. 25 5. = 125 500 4
. .
g
or
13000
. 002 26 = 2 26000. .
g
g
g
Changing Decimals to Percents
To change decimals to percents:
1. Move the decimal point two places to the right.
2. Insert a percent sign.
. 75 = 75%
. 05 = 5%
Changing Percents to Decimals
To change percents to decimals:
1. Eliminate the percent sign.
2. Move the decimal point two places to the left (sometimes adding zeros is
necessary).
75% = . 75 5% = . 05
23% = . 23 .% 2 = . 002
204
Arithmetic
Changing Fractions to Percents
To change a fraction to a percent:
1. Multiply by 100.
2. Divide by denominator.
3. Insert a percent sign.
1
⁄2 = 1 ⁄2 × 100 = 100 ⁄2 = 50%
2
⁄5 = 2 ⁄5 × 100 = 200 ⁄5 = 40%
Changing Percents to Fractions
To change percents to fractions:
1. Eliminate the percent sign.
2. Divide the percent by 100.
3. Reduce if necessary.
60% = 60 ⁄100 = 3 ⁄5 13% = 13 ⁄100
Changing Fractions to Decimals
To change a fraction to a decimal, simply do what the operation says. In other
words, 13 ⁄20 means 13 divided by 20, so do just that (insert decimal points and zeros
accordingly):
20g13. . 00
65 = . 65 5
⁄8 = . . 625
8g5 000 = . 625
Changing Decimals to Fractions
To change a decimal to a fraction:
1. Move the decimal point two places to the right.
2. Put that number over 100.
3. Reduce if necessary.
.65 = 65 ⁄100 = 13 ⁄20
.05 = 5 ⁄100 = 1 ⁄20
.75 = 75 ⁄100 = 3 ⁄4
Read it: .8
Write it: 8 ⁄10
Reduce it: 4 ⁄5
205
Part IV: Mathematics Review
Finding Percent of a Number
To determine percent of a number, change the percent to a fraction or decimal
(whichever is easier for you) and multiply. Remember, the word “of ” means
multiply. For example:
What is 20% of 80?
20
⁄100 × 80 = 1600 ⁄100 = 16 or .20 × 80 = 16.00 = 16
What is 12% of 50?
12
⁄100 × 50 = 600 ⁄100 = 6 or .12 × 50 = 6.00 = 6
What is 1 ⁄2 % of 18?
1/2
⁄100 × 18 = 1 ⁄200 × 18 or 18 ⁄200 = 9 ⁄100 or .005 × 18 = .09
Other Applications of Percent
Turn the question wordforword into an equation. For “what” substitute x; for
“is” substitute an equal sign; for “of ” substitute a multiplication sign. Change
percents to decimals or fractions, whichever you find easier. Then solve the equation.
For example:
18 is what percent of 90?
18 = x(90)
18
⁄90 = x
1
⁄5 = x
20% = x
10 is 50% of what number?
10 = .50(x)
10
⁄.50 = x
20 = x
What is 15% of 60?
x = 15 ⁄100 × 60 = 90 ⁄10 = 9 or .15(60) = 9
Finding Percentage Increase or
Percentage Decrease
To find the percentage change (increase or decrease), use this formula:
change
starting point
# 100 = percentage change
206
Arithmetic
For example:
What is the percentage decrease of a $500 item on sale for $400?
Change:500  400 = 100
change
100
100
500
100
1
starting point
# = # =
5
# 100 = 20%
decrease
What is the percentage increase of Jon’s salary if it went from $150 a month to
$200 a month?
Change:
200— 150 = 50
change 50
starting point
# 100 =
150
# 100 =
3 1 # 100 =33 1 ⁄3% increase
Prime Numbers
A prime number is a number that can be evenly divided by only itself and one. For
example, 19 is a prime number because it can be evenly divided only by 19 and 1,
but 21 is not a prime number because 21 can be evenly divided by other numbers
(3 and 7).
The only even prime number is 2; thereafter any even number can be divided
evenly by 2. Zero and 1 are not prime numbers. The first ten prime numbers are 2,
3, 5, 7, 11, 13, 17, 19, 23, and 29.
Squares
To square a number, just multiply it by itself. For example, 6 squared (written 6 2 )
is 6# 6or 36. 36 is called a perfect square (the square of a whole number). Any
exponent means multiply by itself that many times. For example:
3
5 = 5 # 5 # 5 = 125
2
8 = 8#
8=
64
Remember, x
1 = xand x 0 = 1when x is any number (other than 0).
Following is a list of perfect squares:
1 = 1
5 = 25
9 = 81
2 = 4
6 = 36
10 = 100
3 = 9
7 = 49
11 = 121
4 = 16
8 = 64
12 = 144
207
Part IV: Mathematics Review
Signed Numbers (Positive Numbers
and Negative Numbers)
On a number line, numbers to the right of 0 are positive. Numbers to the left of 0
are negative, as follows:
and so on
and so on
−3 −2 −1 0 +1 +2 +3
Given any two numbers on a number line, the one on the right is always larger, regardless
of its sign (positive or negative).
Addition of Signed Numbers
When adding two numbers with the same sign (either both positive or both negative),
add the numbers and keep the same sign. For example:
+5
+ + 7
+12
8
+ 3
11
When adding two numbers with different signs (one positive and one negative),
subtract the numbers and keep the sign from the larger one. For example:
+ 5
+7
2
59
++72
+ 13
Subtraction of Signed Numbers
To subtract positive and/or negative numbers, just change the sign of the number
being subtracted and then add. For example:
+ 12 + 12
19 19
 + 4 + 4
 + 6 + 6
+ 8
 25
14 14
+ 20 + 20
 4 + + 4
 3 + + 3
 10
+ 23
208
Arithmetic
Multiplying and Dividing Signed Numbers
To multiply or divide signed numbers, treat them just like regular numbers, but remember
this rule: An odd number of negative signs produces a negative answer.
An even number of negative signs produces a positive answer. For example:
^ 3h^+ 8h^5h^1h^ 2h=+
240
^ 3h^+ 8h^1h^ 2h=48
64
⁄2 = + 32
64
⁄+2 = − 32
Parentheses
Parentheses are used to group numbers. Everything inside parentheses must be
done before any other operations. For example:
50^2 + 6h= 50^8h=
400
When a parenthesis is preceded by a minus sign, change the minus to a plus by
changing all the signs in front of each term inside the parentheses. Then remove
the parentheses. For example:
6^ 3+ a 2b+ ch=
6+ ^+ 3 a+ 2b ch=
6+ 3 a+ 2b c= 9 a+ 2bc
Order of Operations
If multiplication, division, powers, addition, parentheses, and so on, are all contained
in one problem, the order of operations is as follows:
1. Parentheses
2. Powers and square roots
3. Multiplication or division (whichever comes first, left to right)
4. Addition or subtraction (whichever comes first, left to right)
209
Part IV: Mathematics Review
For example:
2
10  3 # 6 + 10 + ^6 + 1h#
4 =
2
10  3 # 6 + 10 + ^7h
# 4 = (parentheses first)
10  3 # 6 + 100 + ^7h
# 4 = (powers next)
10  18 + 100 + 28 = (multiplication, or division)
 8 + 100 + 28 = (addition/subtraction, left to right)
92 + 28 = 120
An easy way to remember the order of operations after parentheses is: Please My
Dear Aunt Sarah (Powers, Multiplication, Division, Addition, Subtraction).
Arithmetic Mean or Average
To find the average of a group of numbers:
1. Add them up.
2. Divide by the number of items you added.
For example:
What is the average of 10, 20, 35, 40, and 45?
10 + 20 + 35 + 40 + 45 = 150
150 ' 5 = 30
The average is 30.
What is the average of 0, 12, 18, 20, 31, and 45?
0 + 12 + 18 + 20 + 31 + 45 = 126
126 ' 6 = 21
The average is 21.
What is the average of 25, 27, 27, and 27?
25 + 27 + 27 + 27 = 106
126 ' 4 = 26 1
⁄2
The average is 26 1 ⁄2.
210
3
Arithmetic
Median
A median is simply the middle number of a list of numbers after it has been written
in order. (If the list contains an even number of items, average the two middle
numbers to get the median.) For example, in the following list — 3, 4, 6, 9, 21,
24, 56 — the number 9 is the median.
Mode
The mode is simply the number most frequently listed in a group of numbers. For
example, in the following list — 5, 9, 7, 3, 9, 4, 6, 9, 7, 9, 2 — the mode is 9 because
it appears more often than any other number.
Probability
Probability is the numerical measure of the chance of an outcome or event occurring.
When all outcomes are equally likely to occur, find the probability of the
occurrence of a given outcome by using the following formula:
probability =
number of favorable outcomes
number of possible outcomes
For example: Using the spinner shown below, what is the probability of spinning a
6 in one spin?
9
10
1
2
8
7
4
6
5
Because there is only one 6 on the spinner out of ten numbers and all the numbers
are equally spaced, the probability is 1 ⁄10.
What is the probability of tossing heads three consecutive times with a twosided
fair coin?
Since each toss is independent and the odds are 1/2 for each toss, the probability is
1
⁄2 × 1 ⁄2 × 1 ⁄2 = 1 ⁄8
211
Part IV: Mathematics Review
For example: Three green marbles, two blue marbles, and five yellow marbles are
placed in a jar. What is the probability of selecting at random a green marble on
the first draw?
Since there are ten marbles (total possible outcomes) and three green marbles (favorable
outcomes), the probability is 3 ⁄10.
Combinations
If there are a number of successive choices to make and the choices are independent
of each other (order makes no difference), the total number of possible
choices (combinations) is the product of each of the choices at each stage.
For example: How many possible combinations of shirts and ties are there if there
are five different color shirts and three different color ties?
To find the total number of possible combinations, simply multiply the number of
shirts times the number of ties.
5# 3=
15
Simple Permutations
If there are a number of successive choices to make and the choices are affected by
the previous choice or choices (dependent upon order), then permutations are
involved.
For example: How many ways can you arrange the letters S, T, O, P in a row?
Number of choices Number of choices Number of choices Number of choices
for first letter for second letter for third letter for fourth letter
4 × 3 × 2 × 1
4!
= 4# 3# 2#
1=
24
The product 4# 3# 2# 1can be written 4! (read 4 factorial or factorial 4). Thus,
there are 24 different ways to arrange four different letters.
212
ALGEBRA
Algebra Diagnostic Test
Questions
1. Solve for x: x+ 5=
17
2. Solve for x: 4x
+ 9=
21
3. Solve for x: 5x+ 7= 3x9
4. Solve for y: 3 ⁄7 = y ⁄8
5. Evaluate: 3x 2 + 5y+ 7if x= 2and y=
3
6. Simplify: ^5x+ 2zh+ ^3x4zh
7. Simplify: ^4x7zh^3x4zh
8. Solve for x: 2x
+ 3#
11
9. Solve for x: 3x+ 4$
5x8
Answers
1. x=
12
2. x=
3
3. x=8
4. y= 24 ⁄7 = 3 3 ⁄7
5. 34
6. 8x
2z
7. x 3z
8. x#
4
9. x#
6
213
Part IV: Mathematics Review
Algebra Review
Equations
An equation is a relationship between numbers and/or symbols. It helps to remember
that an equation is like a balance scale, with the equal sign (=) serving as
the fulcrum, or center. Thus, if you do the same thing on both sides of the equal
sign (say, add 5 to each side), the equation stays balanced. To solve the equation
x 5= 23, you must get x by itself on one side; therefore, add 5 to both sides:
x 5=
23
+ 5 + 5
x = 28
In the same manner, you may subtract, multiply, or divide both sides of an equation
by the same (nonzero) number, and the equation will not change. Sometimes
you may have to use more than one step to solve for an unknown. For example:
3x
+ 4=
19
Subtract 4 from both sides to get 3x by itself on one side:
3x
+ 4=
19
4  4
3x
= 15
Then divide both sides by 3 to get x:
3x
⁄3 = 15 ⁄3
Remember: Solving an equation is using opposite operations, until the letter
you’re solving for is on one side by itself. (This applies to addition, subtraction;
multiplication, division, and so on.)
Understood Multiplying
When two or more letters, or a number and letters, are written next to each other,
they are understood to be multiplied. Thus, 8x means 8 times x. Or ab means a
times b. Or 18ab means 18 times a times b.
Parentheses also represent multiplication. Thus (a)b means a times b. A raised dot
also means multiplication. Thus, 6 ⋅ 5 means 6 times 5.
214
Algebra
Proportions
Proportions are written as two fractions equal to each other. For example:
Solve this proportion for x: q
p
=
x
y
You read this as “p is to q as x is to y.” Cross multiply and solve:
py = xq
py xq
q = q
py
q = x or x =
py
q
Evaluating Expressions
To evaluate an expression, just insert the value for the unknowns and do the
arithmetic. For example:
Evaluate: 2x
2 + 3y
+ 6 if x = 2 and y=
9
2
2_
2 i + 3^9h
+ 6=
2^4h+ 27 + 6 =
8+ 27+ 6=
41
Monomials and Polynomials
A monomial is an algebraic expression that consists of only one term. For instance,
9x, 4a 2 , and 3mpxz 2 are all monomials.
2 2
A polynomial consists of two or more terms; x+ y, y  x , and 15x 2 x + 3x+
5y
are all polynomials.
2 2
Adding and Subtracting Monomials
To add or subtract monomials, follow the same rules as with regular signed numbers,
provided that the terms are alike:
2
15x yz
2
18x yz
3x+ 2x=
5x
2
 3x yz
215
Part IV: Mathematics Review
Inequalities
An inequality is a statement in which the relationships are not equal. Instead of
using an equal sign (=) as in an equation, an inequality uses > (greater than) and <
(less than), or ≥ (greater than or equal to) and ≤ (less than or equal to).
When working with inequalities, treat them exactly like equations, except: If you
multiply or divide both sides by a negative number, you must reverse the direction
of the sign. For example:
Solve for x: 2x
+ 4>
6
2x
+ 4>
6
44
2x > 2
2x
⁄2 > 2 ⁄2
x>
1
Solve for x:  7x
> 14(divide by 7
and reverse the sign)
7x
⁄7 < 14 ⁄7
x < 2
3x+ 2$
5x10becomes 2x
$ 12by opposite operations. Divide both sides
by 2
and reverse the sign.
2x
⁄2 ≤ 12 ⁄2
x ≤ 6
216
MEASUREMENT
Measurement Diagnostic Test
Questions
1. How many inches are in 1 yard?
2. How many feet are in 1 mile?
3. How many square feet are in 1 square yard?
4. How many ounces are in 1 pound?
5. How many pounds are in 1 ton?
6. How many pints are in 1 quart?
7. How many quarts are in 1 gallon?
8. How many weeks are in 1 year?
9. How many years are in 1 decade?
10. What is the name of a polygon with four equal sides and four equal angles?
11. What is the name of a polygon with three sides?
12. What is the name of a quadrilateral with two sets of parallel sides?
13. What is the name of a quadrilateral with two sets of parallel sides and all
right angles?
14. What is the perimeter of the figure?
16″
15″ 12″ 13″
30″
217
Part IV: Mathematics Review
15. What are the perimeter and area of the parallelogram?
A. area =
B. perimeter =
A
4″ 3″
B
D
6″
C
16. What are the surface area and volume of the cube?
A. surface area =
B. volume =
4″
4″
4″
Answers
1. 36 inches = 1 yard
2. 5,280 feet = 1 mile
3. 9 square feet = 1 square yard
4. 16 ounces = 1 pound
5. 2,000 pounds = 1 ton
6. 2 pints = 1 quart
7. 4 quarts = 1 gallon
8. 52 weeks = 1 year
9. 10 years = 1 decade
10. a square
11. a triangle
12. a parallelogram
13. a rectangle
14. perimeter = 16 + 13 + 30 + 15 = 74 inches
15. A. area = bh
= 63 ^h
= 18 square inches
B. perimeter = 6 + 4 + 6 + 4 = 20 inches
16. A. All six faces have an area of 4# 4or 16 square inches because each
surface is a square. Therefore, 16^6h=
96 square inches in the surface area.
B. Volume = side # side # side or 4# 4# 4= 64cubic inches.
218
Measurement
Measurement Review
Measurement Systems
The English system of measurement is used throughout the United States, although
the metric system is being phased in as well. You should be familiar with
some basic measurements of the English system. It would be valuable to memorize
most of these.
■
■
■
■
■
Length
12 inches (in) = 1 foot (ft)
3 feet = 1 yard (yd)
36 inches = 1 yard
1,760 yards = 1 mile (mi)
5,280 feet = 1 mile
Area
144 square inches (sq in) = 1 square foot (sq ft)
9 square feet = 1 square yard (sq yd)
Weight
16 ounces (oz) = 1 pound (lb)
2,000 pounds = 1 ton (T)
Capacity
2 cups = 1 pint (pt)
2 pints = 1 quart (qt)
4 quarts = 1 gallon (gal)
4 pecks = 1 bushel
Time
365 days = 1 year
52 weeks = 1 year
10 years = 1 decade
100 years = 1 century
219
Part IV: Mathematics Review
Converting Units of Measure
For example: If 36 inches equal 1 yard, then 3 yards equal how many inches?
Intuitively, 3 # 36 = 108 in
By proportion, using yards over inches:
3
x =
36 1
Remember to place the same units across from each other — inches across from
inches, and so on. Then solve:
3
x
=
36 1
Cross multiply:
108 = x
x = 108 in
For example: Change 3 decades into weeks.
Since 1 decade equals 10 years, and 1 year equals 52 weeks, then 3 decades equal
30 years.
30 years # 52 weeks = 1, 560 weeks in 30 years, or 3 decades
Notice that this was converted step by step. It can be done in one step:
3# 10# 52= 1,560 weeks
If 1,760 yards equal 1 mile, how many yards are in 5 miles?
1,
760 # 5=
8,800
yards in 5 miles
Calculating Measurements of Basic Figures
Measurements for some basic figures, such as squares, rectangles, parallelograms,
and triangles, are not difficult to calculate if the necessary information is given
and the proper formula is used. You should first be familiar with each of the following
formulas.
220
Perimeter
Perimeter (P) means the total distance all the way around the outside of any polygon.
The perimeter of any polygon can be determined by adding up the lengths of
all the sides. The total distance around will be the sum of all sides of the polygon.
Measurement
No special formulas are really necessary, although two are commonly seen.
Area
perimeter( P)
of a square = 4s
(s = length of side)
perimeter( P)
of a parallelogram (rectangle and rhombus) = 2l+ 2wor
2 ( l+ w)( l= length, w=
width)
Area (A) means the amount of space inside the polygon. The formulas for each
area are as follows:
■
Triangle: A = 1 ⁄2 bh (b = base, h = height)
h
or
h
b
b
A triangle is a threesided polygon. In a triangle, the base is the side the
triangle is resting on, and the height is the distance from the base to the
opposite point, or vertex. For example:
A = 1 ⁄2 bh
A = 1 ⁄2 (24) (18) = 216 sq in
18″
■ Square or rectangle: A= lw
24″
w
l
l
l
or
w
w
w
l
A square is a foursided polygon with all sides equal and all right angles
(90 degrees). A rectangle is a foursided polygon with opposite sides equal
and all right angles. In a square or rectangle, the bottom, or resting side, is
the base, and either adjacent side is the height. For example:
A= lw ( ) = 4( 4)
= 16sq in
4″
4″
221
Part IV: Mathematics Review
A= lw ( ) = 12( 5)
= 60sq in
12″
5″
■
Parallelogram: A = bh
h
b
A parallelogram is a foursided polygon with opposite sides equal. In a
parallelogram, the resting side is usually considered the base, and a perpendicular
line going from the base to the other side is the height. For
example:
10″
A= b^hh
A= 10^5h=
50sq in
6″ 5″
6″
Volume
In three dimensions, different facts can be determined about shapes. Volume (V) is
the capacity to hold. The formula for volume of each shape is different. Volume is
labeled in cubic units.
■ Rectangular solid: V= ^lwh^hh=
lwh
l
w
h
For example: Volume = 3 # 2 # 5 = 30 cubic inches
5″
2″
3″
222
Measurement
■ Cube: Volume = s # s # s = s 3
(Remember that all the edges of a cube are
equal and all six sides are equal — a threedimensional square.)
For example: Volume = 3 # 3 # 3 or 3 3 = 27cubic inches
3″
Surface Area
The surface area of a threedimensional solid is the area of all the surfaces that
form the solid. Find the area of each surface, and then add up those areas. The surface
area of a rectangular solid can be found by adding up the areas of all six surfaces.
For example:
The surface area of this rectangular solid is:
top 18 # 6 = 108
bottom 18 # 6 = 108
left side 6# 4=
24
right side 6# 4=
24
front 18 # 4 = 72
back 18 # 4 =
72
408
sq in
18″
6″
4″
223
Part IV: Mathematics Review
The surface area of a cube is: s# s# 6or 6s
2 . Because all sides are the same,
simply find the area of one side and multiply that area by 6.
For example: the surface area of the following cube is:
Surface area = 4# 4# 6= 16#
6= 64square inches.
4″
224
PART V
PART V
PracticeReview
AnalyzePractice
Four FullLength Practice TestsT
This section contains four fulllength simulation CBESTs. The practice
tests are followed by complete answers, explanations, and analysis techniques.
The format, levels of difficulty, question structures, and number
of questions are similar to those on the actual CBEST. The actual
CBEST is copyrighted and may not be duplicated, and these questions
are not taken directly from the actual tests.
When taking these exams, try to simulate the test conditions. Remember,
the total testing time for each practice test is 4 hours. Although you may
divide your time among the three sections in any way you wish, in order
to be sure that you have enough time to finish all sections, budget your
time approximately as follows:
■
■
■
■
Reading, 70 minutes
Mathematics, 75 minutes
Writing, 65 minutes
Checking your work, 30 minutes
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Answer Sheet for Practice Test 1
(Remove This Sheet and Use It to Mark Your Answers)
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A B
A B
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A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
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C D E
Section I: Reading
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Section II: Mathematics
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
C D E
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A B C D E
A B C D E
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A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B C D E
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
A B
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A B
A B
A B
A B
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A B
C D E
C D E
C D E
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PRACTICE TEST 1
The total testing time is 4 hours. You may work on any section of the exam during this time
period.
Section I: Reading — 50 Questions
Section II: Mathematics — 50 Questions
Section III: Writing — 2 Essays
Section I: Reading
50 Questions
Directions: A question or number of questions follows each of the statements or passages in
this section. Using only the stated or implied information given in the statement or passage, answer
the question or questions by choosing the best answer from among the five choices given.
Make sure to mark you answers for this section on the Reading section of the answer sheet.
Use this excerpt from an index to answer
the two questions that follow.
Comparative degree of adjectives and
adverbs, 255256; double, 301
Comparison of adjectives, 255256,
301302; of adverbs, 256; illogical,
347348; pronoun case in, 294
Comparison theme based on, 5457
Complement, 186198; intransitive verb,
187188; objective, 194195;
subjective, with linking verb, 188190;
pronoun as, 290291; of verbal, 245
Complex sentence, 216220
Compoundcomplex sentence, 217
Compound sentence, 214216; ineffective
clause in, 355
Compound subject of sentence,
184186; subjectverb agreement with,
275277
Conclusion of theme, 9298
1. On which pages should one look for
information about subjective
complements?
A. 184186
B. 186198
C. 187188
D. 188190
E. 214216
2. On which pages should one look to find
information about organizing an essay
about the similarities and differences of
Mars and the Earth?
A. 5457
B. 9298
C. 186198
D. 255256
E. 347348
229
Part V: PracticeReviewAnalyzePractice
Read the passage below and answer the
three questions that follow.
Despite his enormous ability, Jackie
Robinson did not begin to play major league
baseball until he was twentyeight. In 1947,
he joined the Brooklyn Dodgers as the first
black player. He promptly won the Rookie of
the Year award, and within three years became
the batting champion and the Most
Valuable Player in the National League. He
was, observers agree, the most versatile
player of his era.
When his baseball career was over, Robinson
entered the business world and rose to the
vice presidency of a large coffee company. In
addition, he wrote a sports column for a New
York newspaper, appeared on a weekly radio
program, and was active in the N.A.A.C.P.
________ He was, however, a leader of two
of the earliest civil rights marches and an
ally of Martin Luther King. Robinson’s baseball
achievements were never forgotten. In
1962, he was elected to the Baseball Hall of
Fame.
3. Which of the following is the best
definition of the word versatile as it is
used in the first paragraph of this
passage?
A. famous
B. fiercely competitive
C. accomplished in many areas
D. opportunistic and insightful
E. victimized and courageous
4. Which sentence, if inserted into the
blank space in the second paragraph,
would be most consistent with the
writer’s purpose and intended audience?
A. When I was growing up, I was a
Dodger fan, but when Robinson
retired, I began to lose interest in
baseball.
B. Many expected he would one day
enter politics, but he never really
became an important political
figure.
C. If you lived in New York at this
time, you probably read his column
in the newspaper, or heard his radio
broadcasts.
D. This was in the days when the
N.A.A.C.P. was about to become a
big deal in the campaign for civil
rights.
E. Informed opinion hypothesized that
Robinson would become a political
potentate, but this sanguine
expectation proved to be erroneous.
5. Which of the following best describes
the principles of organization used in
this passage?
A. The first paragraph is contrasted
with the second, using the
opposition of youthful success
versus the decline of old age.
B. The passage is organized
chronologically, with the first
paragraph on his baseball career
and the second on Robinson’s years
after leaving baseball.
C. In the first paragraph, the passage
uses specific details of Robinson’s
baseball career, while the second
paragraph uses generalizations
derived from these details.
230
Section I Reading
Practice Test 1
D. The passage opposes factual
reporting and speculation,
presenting the facts in paragraph
one and the speculations in
paragraph two.
E. The first paragraph gives a
subjective account of Robinson’s
life as a baseball player, and the
second gives an objective report of
his later life.
Read the passage below and answer the
four questions that follow.
The ancient Greeks named the constellations
of the Northern Hemisphere after the gods,
goddesses, beasts, and heroes of their myths.
________, many of the stars of the Southern
Hemisphere, which were not named until
much later, reflect more modern notions
such as instruments or geometric figures.
________, the rocks on Mars that have acquired
names in the 1990s are called after
late twentiethcentury phenomena like the
cartoon characters Calvin and Hobbes.
[1]As we draw near to the year 2000, many
people expect a significant planetary event,
as if the idea of the millennium had some
important meaning throughout the universe.
[2]They fail to see that any point we name in
time is arbitrary, and has no special significance
in the universe or the natural world.
[3]The whole idea of time is manmade.
[4]All any date can tell us is the position of
the earth in relation to the sun. [5]Like the
names of the stars, numbers are useful fictions
that men have created to make relationships
easier to grasp or to remember.
6. Which words or phrases, if inserted in
order into the blanks in the first
paragraph, would help the reader to
understand the writer’s ideas?
A. Thus; On the other hand
B. Perhaps; Therefore
C. Meanwhile; Consequently
D. Although; Yet
E. However; Similarly
7. Which of the following is the best
definition of the word arbitrary as it is
used in the second paragraph?
A. based on whim; capricious
B. lacking in judgment; foolish
C. conveying a truth; informative
D. of no practical value; useless
E. having two meanings; ambiguous
8. Which of the following phrases from
the second paragraph makes most clear
the connection of the ideas of the first
paragraph to those of the second?
A. Sentence 1: “Many people expect a
significant planetary event.”
B. Sentence 2: “Any point we name in
time is arbitrary.”
C. Sentence 3: “The whole idea of
time is manmade.”
D. Sentence 4: “All any date can tell
us is the position of the earth in
relation to the sun.”
E. Sentence 5: “Like the names of the
stars, numbers are useful fictions
that men have created.”
9. Which of the following inferences
about the beliefs of the author may be
drawn from the information that this
passage presents?
A. The author believes in astrology,
since he or she has an interest in
the names of the stars.
B. The author is skeptical about the
claims of astrologers.
231
Part V: PracticeReviewAnalyzePractice
C. The author expects the year 2000 to
be marked by unusually powerful
earthquakes and volcanic eruptions.
D. The author disapproves of reading
comics and cartoons.
E. The author believes that man has
no influence on the events of the
natural world.
Use the chart below to answer the question
that follows.
This chart presents the percentages of students
majoring in the subjects offered in the
three divisions of the college: Natural
Sciences, Humanities, and Social Sciences.
Chemistry
10%
Economics
12%
Political
Science
16%
Biology
20%
Sociology
4%
Physics
8%
Spanish
8%
French
5%
English
17%
Social
Sciences
Humanities
Natural
Sciences
10. In which subject in each of the three
divisions were the enrollments lowest?
A. Physics, French, and Economics
B. Chemistry, English, and Sociology
C. Biology, Spanish, and Political
Science
D. Physics, French, and Sociology
E. Spanish, Economics, and Physics
Read the passage below and answer the
question that follows.
The major function of social psychology as a
behavioral science, and therefore as a discipline
which can contribute to the solution of
many social problems, is its investigation of
the psychology of the individual in society.
Thus, the scientist’s main objective is to attempt
to determine the influences of the social
environment upon the personal behavior
of individuals.
11. Which of the following best
summarizes the passage?
A. Social psychology is a science in
which the behavior of the scientist
in the social environment is a major
function.
B. The social environment influences
the behavior of individuals.
C. Social psychology studies the ways
in which people in society are
affected by their surroundings.
D. Understanding human behavior,
through the help of social
psychology, leads to the eventual
betterment of society.
E. A minor objective of social society
is the solution of social problems.
Read the passage below and answer the
question that follows.
The quiet child is one of our concerns today.
Our philosophy about children and speaking
in the classroom has flipflopped. Today we
are interested in what Ruth Strickland implies
when she refers to the idea of “freeing
the child to talk.”
232
Section I Reading
Practice Test 1
12. Which of the following is implied by
this passage?
A. Teachers in the past have preferred
quiet and reticent students.
B. The behavior of children in the
classroom is a trivial concern that
can change abruptly.
C. Whether or not a child is quiet
determines the quality of his or her
education.
D. Ruth Strickland never explicitly
stated her opinions about children
and speaking in the classroom.
E. There are fewer quiet children
today than in the past.
Read the passage below and answer the
question that follows.
For some, the term creative writing seems to
imply precious writing, useless writing,
flowery writing, writing that is a luxury
rather than a necessity, something that is produced
under the influence of drugs or
leisure, a hobby.
13. By precious the author of this passage
means
A. beloved
B. costly
C. desirable
D. valuable
E. affected
Read the passage below and answer the
question that follows.
No matter how significant the speaker’s message,
and no matter how strongly he or she
feels about it, it will be lost unless the listeners
attend to it. Attention and perception are
key concepts in communication.
14. The primary purpose of the statement
is to
A. imply that some speakers without
strong feelings find an attentive
audience.
B. note that some very important
messages fall on deaf ears.
C. stress the critical role of listening
in oral communication.
D. urge readers to listen more
carefully to spoken language.
E. argue that attention and perception
are unimportant concepts in
communication.
Read the passage below and answer the
two questions that follow.
In future decades, what is actually required is
the development of a new type of citizen —
an individual who possesses confidence in his
or her own potential, a person who is not intimidated
by the prospect of not actively pursuing
a career after the age of 45, and an
individual who comprehends that technology
can produce an easier world but only
mankind can produce a better one.
15. Which of the following is an unstated
assumption made by the author of this
passage?
A. Technology is the unrecognized
key to a better future.
B. Present citizens are intimidated by
the prospect of ending their careers
in middle age.
C. Present citizens do not have
limitless potentials.
233
Part V: PracticeReviewAnalyzePractice
D. Many people in the future will
pursue at least two careers in the
course of a lifetime.
E. An easier world is not necessarily a
safer one.
16. The author of the passage would
disagree with which of the following
statements?
A. The new type of citizen described
in the passage does not presently
exist.
B. Future decades may bring about a
change in the existing types of
citizens.
C. A new type of citizen will become
necessary in future decades.
D. Technology should be regarded as a
source of a better life.
E. Human potential is not limited, and
we should be especially careful not
to think of our potential as limited.
Read the passage below and answer the
three questions that follow.
If we must have evaluation, at least do it
without grades. Grades are not good indicators
of intellectual ability; we must abolish
them. Then we will have students who are
motivated by factors such as interest, factors
more important than a letter on a transcript.
And the abolition of grades will encourage
us to concentrate less on evaluation and more
on instruction.
17. In order to agree with this author’s
argument, one must presume that
A. wherever grades exist, instruction
is poor.
B. there are indicators of intellectual
ability that are better than grades.
C. graded students are not good
students.
D. intellectual ability can be measured
only in a school situation.
E. grades are the remaining hindrance
to effective education.
18. A reader of this passage might conclude
that the author feels that graded students
are not motivated by
A. the prospect of a high gradepoint
average.
B. interest in the subject matter of
their course.
C. the evaluation criteria established
by their instructors.
D. a thoroughly prepared instructor.
E. the practicality of academic
disciplines.
19. This passage is most probably directed
at which of the following audiences?
A. politicians
B. parents
C. students
D. teachers
E. civic leaders
Read the passage below and answer the
three questions that follow.
We should spend more time enjoying life
than preparing for its challenges, but sometimes
we don’t. For example, toward the end
of every semester, all students at the university
are tired and grumpy because they have
spent long nights preparing for final exams.
Consequently, they rarely look back on
college as a time spent enjoying good fellowship
and fine entertainment.
234
Section I Reading
Practice Test 1
20. To agree with this author, you must
accept which of the following
implications of his or her argument?
A. It is only worthwhile to prepare for
enjoyment.
B. School examinations do not require
preparation.
C. Preparation is inappropriate only
toward the end of the semester.
D. The result of preparation for exams
is fatigue.
E. College students study too much.
21. According to this writer, the most
memorable characteristic of college life
should be
A. social interaction.
B. academic fastidiousness.
C. the value of sleep.
D. more efficient exam preparation.
E. a pleasant attitude.
22. The author might have strengthened the
argument without abandoning it by
A. changing all to some.
B. advancing arguments in favor of
studying all night.
C. acknowledging that grumpiness is
not necessarily related to fatigue.
D. choosing a different example to
illustrate the initial point.
E. focusing the argument more
explicitly on a particular audience.
Read the passage below and answer the
question that follows.
When asked by his students to comment on
the value of steroids for increasing muscle
size, the physical education teacher said,
“Steroids can be very dangerous. Many
bodybuilders use them for a short period before
a contest. However, the longterm use of
steroids might possibly cause severe damage
to the reproductive system while it helps to
build a beautiful body.”
23. In this statement, the teacher is
A. categorically against the use of
steroids.
B. an advocate of steroids but not of
reproduction.
C. recommending the shortterm use
of steroids.
D. trying not to condemn steroids.
E. preferring muscle definition to
muscle size.
Read the passage below and answer the
five questions that follow.
Creative writing may serve many purposes
for the writer. Above all, it is a means of
selfexpression. It is the individual’s way of
saying, “These are my thoughts and they are
uniquely experienced by me.” But creative
writing can also serve as a safety valve for
dormant tensions. This implies that a period
of time has evolved in which the child gave
an idea some deep thought and that the message
on paper is revealing of this deep, inner
thought. Finally, a worthwhile byproduct of
creative writing is the stimulus it gives students
to do further reading and experimentation
in their areas of interest. A child may be
an ardent reader of good literature in order to
satisfy an appetite whetted by a creative
writing endeavor.
235
Part V: PracticeReviewAnalyzePractice
24. The primary purpose of the author of
this passage is
A. to call attention to a widespread
lack of selfexpression.
B. to address the increasing anxiety
that plagues many individuals.
C. to stress the value of good
literature, both amateur and
professional.
D. to encourage the reader to try some
creative writing.
E. to discuss some positive purposes
and effects of creative writing.
25. The content of the passage indicates
that the passage would be least likely to
appear in which of the following?
A. Journal of English Teaching
Techniques
B. Psychology Today
C. Journal of Technical Writing
D. Teaching English Today
E. The Creative Writer
26. According to the passage, creative
writing can help release dormant
tensions because
A. the writer will usually write
something autobiographical.
B. understanding literature means
understanding the tensions of the
characters.
C. creative writing can express what
the writer has long held within.
D. tensions are a byproduct of
writer’s block.
E. selfexpression is never tense.
27. All of the following are probably
important to the ability to write
creatively except:
A. deep thought
B. time to think and ponder
C. spelling
D. reading
E. good literature
28. According to the passage, creative
writing is most of all a
A. stimulus for further reading.
B. release valve for dormant tensions.
C. way of expressing one’s feelings
and thoughts.
D. chance to let off steam.
E. byproduct of reading.
Read the passage below and answer the
six questions that follow.
Throughout the history of mankind, predictions
of future events have found receptive
audiences: during the thirteenth century, the
English scientist Roger Bacon discussed the
development of such things as optical instruments
and motor boats; in the fifteenth century,
Leonardo da Vinci wrote about tanks
and helicopters; in the nineteenth century,
Jules Verne described trips to the moon. Man
has always been interested in where he is going.
Since humanity’s continued existence is
dependent upon making intelligent decisions
about the future, such fascination has taken
on a very practical dimension. Along with
the changes in social mores and attitudes,
greater numbers of people are demanding a
role in planning the future. The social studies
curriculum must provide students with an
understanding of how significant future challenges
will be with regard to our national
236
Section I Reading
Practice Test 1
survival, social problems, religion, marriage
and family life, and in our political
processes.
It is vital that social studies teachers immerse
themselves in the new field of futuristics —
the study of future prospects and possibilities
affecting the human condition. Futuristics, as
an academic area, is already being taught at
many major universities for the purpose of
encouraging students to achieve an awareness
that they can contribute to the development of
a much better national and global society
than they ever dreamed of. The perspective of
futurism is very important for today’s students,
since they know they can do nothing
about the past.
29. Which of the following is the intended
audience for the passage?
A. students planning which courses to
take in high school
B. teachers considering changing or
enriching the curriculum
C. historians interested in the ways
that the past reflects the future
D. politicians drafting future
legislation that addresses present
social problems
E. parents concerned about what their
children should be learning
30. In order to show that “man has always
been interested in where he is going,”
the author provides which of the
following types of facts?
31. Which of the following is an
assumption of the passage but is not
explicitly stated?
A. Futuristic studies should take
precedence over all other school
studies.
B. Today’s students know little about
the past and less about the future.
C. Many social studies curriculums do
not adequately acknowledge the
importance of futurism.
D. Some figures in the past have been
the equivalent of modern
fortunetellers.
E. Social studies gives little thought to
the future.
32. In the passage, the intended meaning of
global society is which of the
following?
A. a society well aware of the
contributions of Bacon, da Vinci,
and Verne
B. a society whose students have had
courses in international relations
C. a society able to communicate with
other societies around the globe
D. a society including the globes of
other solar systems
E. a society including all the nations
of the earth
A. unfounded
B. extraterrestrial
C. political
D. historical
E. scientific
237
Part V: PracticeReviewAnalyzePractice
33. Which of the following statements, if
true, would most weaken the author’s
argument?
A. Figures other than Bacon, da Vinci,
and Verne might have been
mentioned as well.
B. Apart from Bacon, da Vinci, and
Verne, many others who have tried
to “see into” the future have voiced
prospects and possibilities that did
not come true.
C. Those major universities not
offering courses in futuristics are
considering them.
D. Futuristics has been the
nonacademic interest of great
numbers of people for many
centuries.
E. Futuristic predictions are the stockintrade
of many sincere politicians
trying to urge the passage of
significant legislation.
34. The author of this passage would most
likely be
A. a historian.
B. a traditionalist.
C. a high school teacher.
D. an educator.
E. a pacifist.
Read the passage below and answer the
five questions that follow.
Possibly everyone at some point has been in a
classroom where he or she didn’t dare express
an idea for fear that it would be
chopped off. And if it was expressed, it was
chopped off and no further ideas came forth.
Perhaps everyone at some time has been in a
student group where a participant started to
express an insight but was nipped in the bud
by a teacher who corrected the student’s usage.
Perhaps some have been in a classroom
where a child was groping for just the right
way to express a thought only to have the
teacher or another child supply the words.
And some have wondered why a certain child
was so talkative at age 5 and so reticent at 16.
35. The author implies which of the
following in the passage?
A. Wondering about human
inhibitions will do little to solve the
problem.
B. Only certain children are either
uninhibited at age 5 or inhibited at
age 16.
C. Sixteenyearolds should spend
more time in the classroom with 5
yearolds.
D. Attending school may cause
children to become inhibited.
E. Inhibitions go along with maturity.
36. Which of the following terms is an
appropriate substitute for chopped off?
A. put out
B. removed
C. severely criticized
D. misunderstood
E. cut back
37. Which of the following techniques is
the author using to make the point that
classroom situations can be very
undesirable?
A. an appeal to the personal
experiences of the readers
B. disguised references to recent
educational theory
238
Section I Reading
Practice Test 1
C. unsubstantiated and illogical
anecdotes
D. a story
E. references to his or her own
experiences as a teacher
38. The author’s attitude may be
described as being
A. supportive.
B. critical.
C. skeptical.
D. favorable.
E. affected.
39. The author would probably most
strongly agree with which of the
following statements?
A. Students should think carefully
before expressing ideas in class.
B. Teachers should be critical of
students’ expressions.
C. Talkative students should be
tactfully silenced.
D. Teachers should be careful not to
inhibit students’ expressions.
E. Teachers should assist students in
completing their expressions.
Read the passage below and answer the
six questions that follow.
Learning disabilities are among the most frequently
occurring of all childhood disorders.
It is estimated that 8 million children in the
United States can be classified as learning
disabled. And many more function ineffectually
throughout their entire lives due to
learning disabilities. The Department of
Health, Education, and Welfare’s National
Advisory Committee on Dyslexia and
Related Reading Disorders estimates that fifteen
percent of children in public schools experience
difficulty in learning to read. The
majority of children identified as being
learning disabled are so diagnosed because
of difficulties in mastering the process of
reading.
It is apparent that reading requires a number
of intact auditory processing skills. All levels
of auditory processing also require an intact
sensorimotor system. In language acquisition,
the child must be able to receive
acoustical messages that make up the individual
language system being acquired. In
addition to requiring an adequate auditory
mechanism, auditory processing involves a
complex series of behaviors including but
not limited to: the ability to focus attention
on the content and the source of the message;
the ability to detect and identify the selected
message; the ability to transmit and
conduct the message to the brain for analysis;
the ability to store and retain the message
by sorting out the appropriate
perceptual or cognitive level; and the ability
to retrieve and restore the message.
40. According to the preceding passage, the
number of people who function
ineffectually throughout their entire
lives due to learning disabilities
A. can never be estimated.
B. has never been estimated.
C. has been estimated at less than 8
million.
D. has been estimated at just over 8
million.
E. has been estimated at much greater
than 8 million.
239
Part V: PracticeReviewAnalyzePractice
41. The content indicates that the passage
would be most likely to appear in which
of the following?
A. an article about successful
classroom techniques for teaching
reading
B. a book on the history of linguistic
research in the United States
C. a budget report by the Department
of Education
D. a book on auditory processing and
learning disabilities
E. a technical manual for practicing
audiologists
42. The author of the passage would agree
with which of the following statements?
A. Auditory processing may be either
simple or complex.
B. Those children who have difficulty
reading probably have an
adequately functioning
sensorimotor system.
C. For fewer than eight million
individuals, learning disabilities are
a lifelong impairment.
D. Poor reading may be a learning
disability related to auditory
processing skills.
E. Eight million individuals in the
United States experience difficulty
in learning to read.
43. The primary purpose of the passage is to
A. explain the process of language
control.
B. assure readers that a great number
of individuals are not learning
disabled.
C. discuss relationships between
learning disability, reading
difficulty, and the sensorimotor
system.
D. relate the history of auditory
processing.
E. explain the criteria used to decide
whether a child can spell or not.
44. If the final statement of the passage is
true, which of the following must also
be true?
A. Reading difficulty may not have a
simple cause.
B. Five and only five separate abilities
comprise auditory processing.
C. There are five components in an
intact sensorimotor system.
D. Children may acquire different
auditory processing skills at
different ages.
E. More research into auditory
processing remains to be done.
45. Which of the following conclusions is
implied by the first sentence in the
passage?
A. Childhood disorders are the most
serious type of human psychological
or physiological disorder.
B. Childhood disorders other than
learning disabilities also exist.
C. Learning disabilities are the only
childhood disorders that occur with
any frequency.
D. The only handicapping childhood
disorders are those which occur
with some frequency.
E. Learning disabilities are almost
always reading disabilities.
240
Section I Reading
Practice Test 1
Read the passage below and answer the
question that follows.
Over the last decade, teachers in elementary
schools have received modest pay raises regularly,
but considering inflation, their
salaries have decreased 23 percent.
46. Which of the following best expresses
the point of the preceding statement?
A. Being a teacher means living at or
below the poverty line.
B. Many teachers must hold second
jobs.
C. The effects of inflation can negate
the benefits of a pay raise.
D. Teachers’ salaries are not adequate.
E. Those who teach in elementary
schools can live on less than those
who teach in high schools.
Read the passage below and answer the
question that follows.
For preschool children, television cartoons
could serve to stimulate them to create their
own drawings if their parents provided them
with the graphic materials and the indispensable
encouragement.
47. The author of the statement would
probably agree with which of the
following?
A. A decision to ban television
cartoons as useless is not wise.
B. Television cartoons are the
preschooler’s primary source of
creative inspiration.
C. For older children, cartoons have
no educational value.
D. Cartoons are a viable substitute for
parents when they are not available.
E. Cartoons accelerate a young child’s
learning of new words.
Read the passage below and answer the
question that follows.
It is clear that the first four or five years of a
child’s life are the period of most rapid
change in physical and mental characteristics
and greatest susceptibility to environmental
influences. Attitudes are formed, values are
learned, habits are developed, and innate
abilities are fostered or retarded by conditions
the child encounters during these early
years.
48. Which of the following, if true, would
most weaken the author’s argument?
A. Many young children possess
attitudes and habits similar to those
of their peers.
B. There are significant, basic differences
between a 5yearold from
Samoa and one from New York.
C. “Midlife crisis” provokes many
adults to change their entire
personality structures within only a
few months.
D. The environment continues to
influence personal characteristics
in adolescents.
E. Environmental influences can have
either positive or negative effects
on human development.
241
Part V: PracticeReviewAnalyzePractice
Read the passage below and answer the
two questions that follow.
Integrating sports into the elementary curriculum
can have a far more beneficial effect
than merely allowing students to “blow off
steam” or providing an opportunity for physical
exercise. The inclusion of a physical
rather than a mental skill will allow those
students less adept in the classroom to
____49____ their physical proficiencies to
their peers and to their teachers, thus allowing
egoenhancing experiences which they
might not otherwise get sitting at their desks.
The teachers’ overall knowledge of their students
will also be enhanced, and thus they
will have more to draw upon when relating
to their students and the students’ 50 .
49. The word which best completes 49__
is
A. boast
B. display
C. give
D. relate
E. explain
50. The word which best completes
50 is
A. grades
B. sports
C. work
D. exercise
E. games
242
Section II Mathematics
Practice Test 1
Section II: Mathematics
50 Questions
Directions: In the following questions or incomplete statements, select the one best answer or
completion of the five choices given. Make sure that you mark your answers for this section on
the Mathematics section of the answer sheet.
1. What is the value of 342,499 rounded to
the nearest thousand?
A. 342,000
B. 342,400
C. 342,500
D. 343,000
E. 343,400
2. Of the following, which is the largest in
value?
A. .09
B. 1
⁄11
C. 8 1 ⁄2%
D. .084
E. 1
⁄13
Use the table given below to answer the
question that follows.
Ball Park Snacks Menu
Hot dogs $1.00
Sodas $ .60
Chips $ .35
3. The ball team purchased the following:
3 dozen hot dogs, 23 bags of chips, and
27 sodas. Which answer represents this
purchase?
A. 36^$ 1. 00h+ 23^$. 35h+
27^$.
60h
B. 3^$ 1. 00h+ 23^$. 35h+
27^$.
60h
C. ^36 + 23 + 27h
+
^$ 100 . + $. 35+
$. 60h
D. 36^$ 1. 00h+ 27^$. 35h+
23^$.
60h
E. ^3 # 12h+ $. 1 00 + 23^$.
60h+
27^$.
35h
4. The track team walked the following
distances in April: 4 3 ⁄4 miles, 5 1 ⁄2 miles,
6 miles, and 5 3 ⁄4 miles. What was the
average distance they walked in miles?
A. 5 1 ⁄2
B. 6
C. 6 1 ⁄2
D. 11
E. 22
5. A square 4 inches on a side is cut up
into smaller squares 1 inch on a side.
What is the maximum number of
squares that can be formed?
A. 4
B. 8
C. 16
D. 36
E. 64
243
Part V: PracticeReviewAnalyzePractice
6. Given a number, x, add 4 to it, then
multiply it by 4, then subtract 4 and
divide this by 4. The result is
Use the figure below to answer the question
that follows.
A. x+
3
B. x+
2
C. x
D. x
2
E. x+
1
7. The length of a rectangle is 6l and the
width is 4w. Which of the following is
an expression that represents the
perimeter of the rectangle?
A. 24lw
B. 10lw
C. 6l+
4w
D. 20lw
E. 12l+
8w
Use the information below to answer the
question that follows.
Tommy was given the expression
9x
2 + 3y5to evaluate. Although he
was given the values of –3 for x and –2
for y, he was unsure of his method for
evaluating.
8. If Tommy evaluated the expression
correctly, what value should he have
gotten?
A. 92
B. 65
C. 70
D. 80
E. 82
9. Which answer best represents the
shaded part of the preceding box?
A. 1
⁄8
B. 1
⁄4
C. 1
⁄3
D. 2
⁄5
E. 2
⁄3
10. If x is between 0 and 1, which of the
following statements is (are) true?
2
I. x > 1
2
II. x > 0
2
III. x > x
A. I only
B. II only
C. III only
D. I and II only
E. II and III only
244
Section II Mathematics
Practice Test 1
11. Armand is making a salad from the
following ingredients: three different
kinds of lettuce, three different kinds of
tomatoes, and four different kinds of
beans. If he wants to use only one kind
of lettuce, one kind of tomato, and one
kind of beans, how many different
combinations of salads can he possibly
make?
A. 3
B. 6
C. 10
D. 15
E. 36
C. 6 1 ⁄6
D. 8 1 ⁄6
E. 12 1 ⁄6
14. An art class has 30 students. Each
student needs a piece of ribbon 2 feet 6
inches in length. What is the total
length of ribbon needed?
A. 780 feet 6 inches
B. 240 feet
C. 78 feet 6 inches
D. 78 feet
E. 75 feet
Read the information below and then
answer the question that follows.
Sandra’s weekly wage is $30 less than
three times Harold’s weekly wage.
If Sandra’s weekly wage is $90, what
is Harold’s weekly wage?
12. If t represents Harold’s weekly wage,
which of the following equations can be
used to solve the preceding problem?
A. $ 90 = 3t
$
30
B. $ 90  $ 30 = 3t
C. 3tt $ 30=
$ 90
D. t $ 30= 3^$
90h
E. 3t+ t=
$ 90
15. A color television set is marked down
20% to $320. Which of the following
equations could be used to determine its
original price, P?
A. $ 320 . 20 = P
B. . 20P
= $ 320
C. P = $ 320 + 20
D. . 80P+ . 20P=
$ 320
E. . 80P
= $ 320
Use the diagram below to answer the
question that follows.
100
90
80
13. If 3 divided by a number y is 18, then
what is the value of the number y
plus 2?
Feet
70
60
50
40
A. 2 1 ⁄6
B. 4 1 ⁄6
30
20
10
0
10 20 30 40 50 60 70 80 90 100
Feet
245
Part V: PracticeReviewAnalyzePractice
16. The shading in the preceding diagram
indicates the area needed for the
bandstand being built for prom night.
What is the approximate area needed
for the bandstand?
A. 260 square feet
B. 2,300 square feet
C. 2,500 square feet
D. 2,600 square feet
E. 26,000 square feet
17. Which of the following questions can
be answered on the basis of the
following facts?
Kim can mow 8 lawns in one day. This
year, the average number of days Kim
mowed each month was 20.
A. How many lawns did Kim mow in
the first two weeks?
B. What is the average number of
lawns Kim mowed last year?
C. How many lawns can Kim mow in
3 hours?
D. What is the maximum number of
lawns Kim could have mowed this
year?
E. What is the minimum number of
days Kim mowed each month?
18. What percent of 60 is 15?
A. 4%
B. 15%
C. 25%
D. 40%
E. 60%
19. Sherman rides the bus from home to
work each day. If his bus stops four
times every mile to pick up passengers,
how many stops does it make in 8
miles?
A. 2
B. 4
C. 8
D. 16
E. 32
Use the diagram below to answer the
question that follows.
A
20. What conclusion can be drawn from the
preceding diagram?
A. A, B, and C have something in
common.
B. A, B, and C have nothing in
common.
C. A and B have nothing in common.
D. A and C have nothing in common.
E. B and C have nothing in common.
21. Temperature increases 2 degrees for
every 1,000 feet gained above sea level.
How many degrees warmer is it at 6,000
feet above sea level than at 2,500 feet
above sea level?
C
A. 3,500 (2 − 1,000)
B. (6,000 − 2,500) 2
B
246
Section II Mathematics
Practice Test 1
C.
D.
E.
3,
500
1,
000 # 2
6,
000  2,500
1,000
^2h
( 2,
500 # 6, 000)
( 1,
000 # 6, 000)

2
22. 90% of 80% of 70% is approximately
equal to
A. 25%
B. 40%
C. 50%
D. 65%
E. 80%
23. How many buses are needed to carry 98
children to the park if each bus holds 42
children?
A. 2
B. 2.14
C. 2 1 ⁄3
D. 3
E. 3 1 ⁄2
24. If 5x is the average of two numbers, and
one of the numbers is 3, what is the
other number?
A. 5x
B. 10x
C. 10x
 7
D. 10x
 3
E. 10x
+ 7
25. A school is going to build a new
playground. State regulations require no
more than 50% asphalt and no less than
20% grass for any school playground. If
the school plans to build a playground
of exactly 200 square feet, which of the
following is acceptable?
A. 50 square feet of grass, 110 square
feet asphalt, and the rest sand
B. 30 square feet grass, 90 square feet
asphalt, and the rest sand
C. 20 square feet grass, 95 square feet
asphalt, and the rest sand
D. 50 square feet grass, 95 square feet
asphalt, and the rest sand
E. 45 square feet grass, 115 square
feet asphalt, and the rest sand
26. If a store purchases several items for
$1.80 per dozen and sells them at 3 for
$.85, what is the store’s profit on 6
dozen of these items?
A. $4.20
B. $5.70
C. $9.60
D. $10.60
E. $20.40
247
Part V: PracticeReviewAnalyzePractice
Read the information below and then answer
the question that follows.
Arnold takes 8 weekly tests in his history
class, and his scores range from a
low of 72% to a high of 94%.
27. From the preceding information, which
of the following must be true regarding
Arnold’s average for all 8 tests?
A. His average for all 8 tests is 83%.
B. His average for all 8 tests is above
83%.
C. His average for all 8 tests is lower
than 83%.
D. His average for all 8 tests is any
score between 1% and 100%.
E. His average for all 8 tests is
between 72% and 94%.
28. Assume that inflation will increase the
prices of everything at a rate of 10% a
year over the next 10 years. In 3 years,
what will be the price of a stereo that
now costs $100?
A. $121.00
B. $126.00
C. $130.00
D. $133.10
E. $146.41
29. Using the formula F° = 9 ⁄5 C° + 32°,
where F = Fahrenheit temperature and
C = centigrade temperature, what is the
temperature in Fahrenheit degrees when
the temperature is 25° centigrade?
C. 45°
D. 25°
E. −7°
30. If 1 ml (milliliter) of water occupies
1 cc (cubic centimeter) of space, how
many liters of water are needed to fill
a tank with dimensions
25 cm # 10 cm # 8 cm (cm = centimeter)?
^1 liter = 1, 000 milliliters; V = l# w#
hh
A. 2,000
B. 200
C. 20
D. 2.0
E. .020
Read the information below and then answer
the question that follows.
The PTA is making tablecloths that measure
3 1 ⁄2 square yards. They purchase
49 3 ⁄5 yards of purple fabric and 7 1 ⁄2 yards
of yellow fabric.
31. What is the total amount of fabric
purchased?
A. 60 3 ⁄5 yards
B. 57 1 ⁄10 yards
C. 56 10 ⁄11 yards
D. 56 1 ⁄10 yards
E. 42 2 ⁄3 yards
A. 77°
B. 57°
248
Section II Mathematics
Practice Test 1
Use the information below to answer the
question that follows.
Phil is taking a math quiz. One of the
problems on his quiz requires him to
add the fractions 2 ⁄3, 1 ⁄5, and 1 ⁄6.
32. Which of the following methods should
Phil use to answer this question most
efficiently?
A. use a common denominator of 90
B. use a common denominator of 15
C. use a common denominator of 30
D. use the “invert and multiply”
technique
E. multiply the denominators
33. What is the probability of rolling two
dice that total 7?
A. 1
⁄6
B. 1
⁄4
C.
11
⁄36
D. 1
⁄3
E. 1
⁄2
Use the graph below to answer the two
questions that follow.
Number of Wild Bear Sightings Before and After
Conservation Measures in Five Different Counties
500
450
B = before
A = after
34. According to the graph, which county
had the most bear sightings before the
conservation measures?
A. 1
B. 2
C. 3
D. 4
E. 5
35. To determine in which county the
sightings increased by approximately
25%, one would
A. find the county that had 250 more
sightings after the conservation
measures
B. find the county that had 25 more
sightings after the conservation
measures
C. find the county in that the “B” bar
is 1 ⁄4 taller than the “A” bar
D. find the county in which the
number of sightings indicated by
the “A” bar is 250 more than those
indicated by the “B” bar
E. find the county in which the
number of sightings indicated by
the “A” bar is 1 ⁄4 more than those
indicated by the “B” bar
36. How long will it take a school bus
averaging 40 miles per hour to reach its
destination 10 miles away?
Number of Sightings
400
350
300
250
A. 15 minutes
B. 20 minutes
C. 30 minutes
D. 1 hour
E. 4 hours
200
B A B A B A B A B A
1 2 3 4 5
Counties
249
Part V: PracticeReviewAnalyzePractice
37. The value 68% falls between which one
of the following pairs of fractions?
A. 3
⁄8 and 2 ⁄5
B. 3
⁄5 and 5 ⁄6
C. 1
⁄2 and 2 ⁄3
D. 7
⁄10 and 3 ⁄4
E. 4
⁄5 and 9 ⁄10
38. A commission of $6.80 is paid for each
$50 of sales. How much did sales total
if the commissions equaled $156.40?
A. $1,100
B. $1,150
C. $1,200
D. $1,250
E. $1,300
39. There are 36 students in a certain
geometry class. If 2 ⁄3 of the students are
boys and 3 ⁄4 of the boys are under 6 feet
tall, how many boys in the class are
under 6 feet tall?
A. 6
B. 12
C. 18
D. 24
E. 27
40. An astronaut weighing 207 pounds on
Earth would weigh 182 pounds on
Venus. The weight of the astronaut on
Venus would be approximately what
percent of his weight on Earth?
A. 50%
B. 60%
C. 70%
D. 80%
E. 90%
Read the information below and then
answer the question that follows.
Sylvia is given a worksheet by her tutor
to practice dividing by fractions. The
first question asks her to explain the
operation of dividing some number by 2 ⁄4.
41. Which of the following explanations
should Sylvia give to properly explain
the operation of division by fractions?
A. Dividing some number by 2 ⁄4 is the
same as multiplying that number
by 1 ⁄2.
B. Dividing some number by 2 ⁄4 is the
same as dividing that number by 2.
C. Dividing some number by 2 ⁄4 is the
same as multiplying that number
by 2.
D. Dividing some number by 2 ⁄4 is the
same as multiplying that number
by 2 and then dividing by 4.
E. Some numbers cannot be divided
by fractions.
250
Section II Mathematics
Practice Test 1
42. At Becker High, 1 out of 4 seniors takes
Physics. If there are 1,260 seniors, how
many do not take Physics?
A. 945
B. 630
C. 420
D. 315
E. 126
Use the chart and information given below
to answer the question that follows.
Grade
Sequoia High Enrollment
Total
9 th 267
10 th 176
12 th 139
Use the information below to answer the
question that follows.
Robert’s four paychecks total $840, and
the largest paycheck is $100 more than
the average for the four paychecks and
$200 more than the smallest paycheck.
44. Which of the following cannot be
determined from the preceding
information?
A. the average of the four paychecks
B. the largest paycheck
C. the smallest paycheck
D. the sum of the largest and the
smallest paycheck
E. the sum of the two largest
paychecks
The secretary typing an enrollment list
notices that 11 th grade has not been included.
She also knows that the total
enrollment for grades 9 through 12 is
688. What is an accurate number of the
enrolled 11 th graders?
43. Based upon the chart above and the
given information, the best answer
choice is:
A. 794
B. 688
C. 582
D. 119
E. 106
45. To find the total surface area in square
meters of a rectangular solid whose
length is 7 meters, width is 6 meters,
and depth is 3 meters, one would use
the following calculation:
A. 7m# 6m#
3m
B. 27 ( m# 6m) + 26 ( m#
3m)
+
27 ( m#
3m)
C. 7m# 6m+ 6m# 3m+
3m#
7m
D. 7m# 6m# 3m#
2
E. 7m# 3m#
2
251
Part V: PracticeReviewAnalyzePractice
46. Judith has a purse full of coins totaling
$9.15. She has at least one of every U.S.
coin (dollar, halfdollar, quarter, dime,
nickel, and penny). What is the largest
number of quarters she can have in her
purse?
A. 25
B. 27
C. 28
D. 29
E. 30
47. Alice wants to send 400 wedding
invitations. She can do about 16 per
day. If she begins on January 1, when
would she be expected to be finished?
A. January 25
B. February 18
C. March 30
D. April 15
E. May 1
48. Which of the following number phrases
is not equivalent to 8 # 100?
A. 4 # 200
B. 16 # 50
C. ^2 + 6h#
^25 + 75h
D. ^4 # 50h+
^4 # 150h
E. ^2# 4h+
^5#
20h
Use the graph below to answer the two
questions that follow.
Temperature
100
98
96
94
92
90
88
86
84
82
Maximum Temperature Readings
Los Angeles: July 1016, 1979
10 11 12 13 14 15 16
Date
49. Of the seven days shown, about what
percent of the days did the maximum
temperature exceed the average
temperature?
A. 3%
B. 4%
C. 43%
D. 57%
E. 93%
50. Between which two dates shown was
the greatest increase in maximum
temperature?
A. July 11–12
B. July 12–13
C. July 13–14
D. July 14–15
E. July 15–16
50 year
average
19251975
252
Section III Writing
Practice Test 1
Section III: Writing
2 Essays
Directions: In this section, you plan and write two essays, one for each topic given. Read each
topic carefully to make sure that you are properly addressing the issue or situation. You must
write on the specified topic. An essay on another topic will not be acceptable.
Plan your time wisely. Each essay is weighted equally. Plan to spend the same amount of time
on each.
The two essay questions are designed to give you an opportunity to write clearly and effectively.
Use specific examples whenever appropriate to aid in supporting your ideas. Keep in
mind that the quality of your writing is much more important than the quantity.
Write your essays on the special answer sheets provided. No other paper may be used. Your
writing should be neat and legible. Because you have only a limited amount of space in
which to write, please do not skip lines, do not write excessively large, and do not leave wide
margins.
You may use the bottom of the topic page in the text booklet to organize and plan your essay
before you begin writing.
Topic 1
What particular experience had the greatest impact on your decision to enter the education
field? Explain why that particular experience was so important.
253
Part V: PracticeReviewAnalyzePractice
254
Section III Writing
Practice Test 1
255
Part V: PracticeReviewAnalyzePractice
Topic 2
Some educators believe that the most important trait a teacher can have is selfacceptance. It allows
the teacher to better relate to his or her students, to better deal with student problems, and
to better provide a positive and constructive role model.
Present your arguments in agreement with this statement, or, if you disagree, present your
viewpoints as to what you believe is the most important quality for a teacher to have.
256
Section III Writing
Practice Test 1
257
Part V: PracticeReviewAnalyzePractice
258
ANSWER KEY AND ANALYSIS
FOR PRACTICE TEST 1
Answer Key for Practice Test 1
Section I: Reading
Section II: Mathematics
1. D 18. B 35. D 1. A 18. C 35. E
2. A 19. D 36. C 2. B 19. E 36. A
3. C 20. E 37. A 3. A 20. A 37. B
4. B 21. A 38. B 4. A 21. D 38. B
5. B 22. D 39. D 5. C 22. C 39. C
6. E 23. D 40. E 6. A 23. D 40. E
7. A 24. E 41. D 7. E 24. D 41. C
8. E 25. C 42. D 8. C 25. D 42. A
9. C 26. C 43. C 9. B 26. C 43. E
10. D 27. C 44. A 10. B 27. E 44. E
11. C 28. C 45. B 11. E 28. D 45. B
12. A 29. B 46. C 12. A 29. A 46. D
13. E 30. D 47. A 13. A 30. D 47. A
14. C 31. C 48. C 14. E 31. B 48. E
15. B 32. E 49. B 15. E 32. C 49. D
16. D 33. B 50. C 16. D 33. A 50. C
17. B 34. D 17. D 34. D
259
Part V: PracticeReviewAnalyzePractice
Scoring Your CBEST Practice Test 1
To score your CBEST Practice Test 1, total the number of correct responses for each section of
the test separately. Do not subtract any points for questions attempted but missed, because there
is no penalty for guessing. The score for each section is then scaled from 20 to 80. (About 70%
right is a passing score.)
Analyzing Your Test Results
Use the charts on the following page to carefully analyze your results and spot your strengths
and weaknesses. Complete the process of analyzing each subject area and each individual question
for this Practice Test. Reexamine these results for trends in types of error (repeated errors)
or poor results in specific subject areas. This reexamination and analysis is of tremendous
importance for effective test preparation.
Reading 50
Mathematics 50
TOTAL 100
Subject Area Analysis Sheet
Possible Completed Right Wrong
One of the most important parts of test preparation is analyzing why you missed a question so
that you can reduce your number of mistakes. Now that you have taken Practice Test 1 and corrected
your answers, carefully tally your mistakes by marking them in the proper column.
Reading
Mathematics
TOTAL
Tally Sheet for Questions Missed
Reason for Mistake
Total Simple Misread Lack of
Missed Mistake Problem Knowledge
Reviewing the preceding data can help you determine why you are missing certain questions.
Now that you have pinpointed the type of error you are most likely to make, when you take
Practice Test 2, focus on avoiding those errors.
260
Answer Key and Analysis for Practice Test 1
Essay Checklists
Use these checklists to evaluate your essays.
Diagnosis of Timed Writing Exercise: Topic 1
A good essay:
❏ addresses the assignment
■
■
stays wellfocused
expresses a clear thesis statement on the topic
❏ organizes points logically
■
■
uses smooth transitions between paragraphs
has coherent, unified paragraphs
❏ develops ideas presented
■