CLEP® College Mathematics Book + Online
By Stu Schwartz
()
About this ebook
Everything you need to pass the exam and get the college credit you deserve.
REA's CLEP® test preps are perfect for adults returning to college (or attending for the first time), military service members, high-school graduates looking to earn college credit, or home-schooled students with knowledge that can translate into college credit.
Our test prep for CLEP® College Mathematics and the free online tools that come with it, allow you to create a personalized CLEP® study plan that can be customized to fit you: your schedule, your learning style, and your current level of knowledge.
Diagnostic exam at the REA Study Center focuses your study
Our online diagnostic exam pinpoints your strengths and shows you exactly where you need to focus your study. Armed with this information, you can personalize your prep and review where you need it the most.
The most complete subject review for CLEP® College Mathematics
The CLEP® College Mathematics exam covers material taught in a college course for non-mathematics majors. Written by a math expert, REA's comprehensive review covers all the topics found on the exam: algebra and functions, counting and probability, data analysis and statistics, logic and sets, financial mathematics, numbers, and geometry.
Two full-length practice exams
The online REA Study Center gives you two full-length practice tests and the most powerful scoring analysis and diagnostic tools available today. Instant score reports help you zero in on the CLEP® College Math topics that give you trouble now and show you how to arrive at the correct answer - so you'll be prepared on test day.
REA is the acknowledged leader in CLEP® preparation, with the most extensive library of CLEP® titles available. Our test preps for CLEP® exams help you earn valuable college credit, save on tuition, and get a head start on your college degree.
Start earning college credit with CLEP®!
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CLEP® College Mathematics Book + Online - Stu Schwartz
Mel Friedman, M.S.
and
Stu Schwartz
Research & Education Association
61 Ethel Road West
Piscataway, New Jersey 08854
E-mail: [email protected]
CLEP® College Mathematics with Online Practice Exams
Copyright © 2016 by Research & Education Association, Inc.
Prior editions copyright © 2013, 2008. All rights reserved. No part of this book may be reproduced in any form without permission of the publisher.
Printed in the United States of America
Library of Congress Control Number 2015956926
ISBN-13: 978-0-7386-1205-8
ISBN-10: 0-7386-1205-7
LIMIT OF LIABILITY/DISCLAIMER OF WARRANTY: Publication of this work is for the purpose of test preparation and related use and subjects as set forth herein. While every effort has been made to achieve a work of high quality, neither Research & Education Association, Inc., nor the authors and other contributors of this work guarantee the accuracy or completeness of or assume any liability in connection with the information and opinions contained herein and in REA’s software and/or online materials. REA and the authors and other contributors shall in no event be liable for any personal injury, property or other damages of any nature whatsoever, whether special, indirect, consequential or compensatory, directly or indirectly resulting from the publication, use or reliance upon this work.
CLEP® is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, this product. All other trademarks cited in this publication are the property of their respective owners.
Cover image: © iStockphoto.com/cisale
CLEP® COLLEGE MATHEMATICS
Access Your Online Exams
by following the instructions found at the back of this book.
CONTENTS
About Our Authors
About REA
Acknowledgments
CHAPTER 1
Passing the CLEP College Mathematics Exam
Getting Started
The REA Study Center
An Overview of the Exam
All About the CLEP Program
Options for Military Personnel and Veterans
SSD Accommodations for Candidates with Disabilities
6-Week Study Plan
Test-Taking Tips
The Day of the Exam
Online Diagnostic Test www.rea.com/studycenter
CHAPTER 2
Numbers
Properties of Real Numbers
Components of Real Numbers
Fractions
Odd and Even Numbers
Factors and Divisibility Numbers
Absolute Value
Integers
Inequalities
Scientific Notation
Unit Conversions
Drill Questions
CHAPTER 3
Algebra and Functions
Equations
Linear Equations
Simultaneous Linear Equations
Dependent Equations
Parallel Lines
Perpendicular Lines
Absolute Value Equations
Inequalities
Linear Inequalities
Complex Numbers
Quadratic Equations
Quadratic Formula
Advanced Algebraic Theorems
Relations and Graphs
Functions: Definition and Notation
Linear Equations
Transformation of Graphs
Exponents
Exponential Equations
Logarithms
Linear and Exponential Growth
Drill Questions
CHAPTER 4
Counting and Probability
Sample Spaces and Counting
The Counting Principle
Factorial
Permutations
Combinations
Probability
Odds
Mutually Exclusive and Complementary Events
Conditional Probability
Independent Events
Expected Value
Drill Questions
CHAPTER 5
Statistics and Data Analysis
Measures of Central Tendency
Comparing the Mean, Median, and Mode in a Variety of Distributions
Measures of Variability
Normal Distributions
Data Analysis
Bivariate Data
Drill Questions
CHAPTER 6
Financial Mathematics
Rates
Percents
Taxes
Markups and Markdowns
Types of Interest
Future Value and Maturity Value
Present Value
Inflation
Drill Questions
CHAPTER 7
Geometry Topics
Triangles
The Pythagorean Theorem
Quadrilaterals
Similar Polygons
Circles
Formulas for Area and Perimeter
Drill Questions
CHAPTER 8
Logic and Sets
Logic
Sentences
Statements
Basic Principles, Laws, and Theorems
Necessary and Sufficient Conditions
Deductive Reasoning
Truth Tables and Basic Logical Operations
Logical Equivalence
Sentences, Literals, and Fundamental Conjunctions
Sets
Subsets
Union and Intersection of Sets
Laws of Set Operations
Cartesian Product
Drill Questions
Practice Test 1 (also available online at www.rea.com/studycenter)
Answer Key
Detailed Explanations of Answers
Practice Test 2 (also available online at www.rea.com/studycenter)
Answer Key
Detailed Explanations of Answers
Answer Sheets
Glossary
Index
ABOUT OUR AUTHORS
Mel Friedman, M.S., has a diverse background in mathematics, having taught both high school and college-level mathematics courses. Mr. Friedman was awarded his B.A. in Mathematics from Rutgers University and received his M.S. in Mathematics (with honors) from Fairleigh Dickinson University. A former adjunct professor at Kutztown University of Pennsylvania, Mr. Friedman also developed test items for Educational Testing Service and ACT, Inc.
Stu Schwartz has been teaching mathematics since 1973. For 35 years he taught in the Wissahickon School District, in Ambler, Pennsylvania, specializing in AP Calculus AB and BC and AP Statistics. Mr. Schwartz received his B.S. degree in Mathematics from Temple University, Philadelphia. Mr. Schwartz was a 2002 recipient of the Presidential Award for Excellence in Mathematics Teaching and also won the 2007 Outstanding Educator of the Year Award for the Wissahickon School District.
Mr. Schwartz’s website, www.mastermathmentor.com, is geared toward helping educators teach AP Calculus, AP Statistics, and other math courses. Mr. Schwartz is always looking for ways to provide teachers with new and innovative teaching materials, believing that it should be the goal of every math teacher not only to teach students mathematics, but also to find joy and beauty in math as well.
ABOUT REA
Founded in 1959, Research & Education Association (REA) is dedicated to publishing the finest and most effective educational materials—including study guides and test preps—for students of all ages. Today, REA’s wide-ranging catalog is a leading resource for students, teachers, and other professionals. Visit www.rea.com to see a complete listing of all our titles.
ACKNOWLEDGMENTS
We would like to thank Pam Weston, Publisher, for setting the quality standards for production integrity and managing the publication to completion; John Paul Cording, Vice President, Technology, for coordinating the design and development of the REA Study Center; Larry B. Kling, Vice President, Editorial, for overall direction; Diane Goldschmidt, Managing Editor, for coordinating development of this edition; Transcend Creative Services for typesetting this edition; and Eve Grinnell, Graphic Designer, for designing our cover.
In addition, we would like to thank Mary Berlinghieri Willi for technically reviewing the manuscript, Linda Robbian for copyediting, and Ellen Gong for proofreading.
CHAPTER 1
Passing the CLEP College Mathematics Exam
CHAPTER 1
PASSING THE CLEP COLLEGE MATHEMATICS EXAM
Congratulations! You’re joining the millions of people who have discovered the value and educational advantage offered by the College Board’s College-Level Examination Program, or CLEP. This test prep focuses on what you need to know to succeed on the CLEP College Mathematics exam, and will help you earn the college credit you deserve while reducing your tuition costs.
GETTING STARTED
There are many different ways to prepare for a CLEP exam. What’s best for you depends on how much time you have to study and how comfortable you are with the subject matter. To score your highest, you need a system that can be customized to fit you: your schedule, your learning style, and your current level of knowledge.
This book, and the online tools that come with it, allow you to create a personalized study plan through three simple steps: assessment of your knowledge, targeted review of exam content, and reinforcement in the areas where you need the most help.
Let’s get started and see how this system works.
THE REA STUDY CENTER
The best way to personalize your study plan is to get feedback on what you know and what you don’t know. At the online REA Study Center, you can access two types of assessment: a diagnostic exam and full-length practice exams. Each of these tools provides true-to-format questions and delivers a detailed score report that follows the topics set by the College Board.
Diagnostic Exam
Before you begin your review with the book, take the online diagnostic exam. Use your score report to help evaluate your overall understanding of the subject, so you can focus your study on the topics where you need the most review.
Full-Length Practice Exams
Our full-length practice tests give you the most complete picture of your strengths and weaknesses. After you’ve finished reviewing with the book, test what you’ve learned by taking the first of the two online practice exams. Review your score report, then go back and study any topics you missed. Take the second practice test to ensure you have mastered the material and are ready for test day.
If you’re studying and don’t have Internet access, you can take the printed tests in the book. These are the same practice tests offered at the REA Study Center, but without the added benefits of timed testing conditions and diagnostic score reports. Because the actual exam is Internet-based, we recommend you take at least one practice test online to simulate test-day conditions.
AN OVERVIEW OF THE EXAM
The CLEP College Mathematics exam consists of approximately 60 questions to be answered in 90 minutes.
The exam covers the material one would find in an introductory college-level class for nonmathematics majors in fields not requiring knowledge of advanced mathematics.
The approximate breakdown of topics is as follows:
Scientific Calculator
A scientific (nongraphing) calculator is integrated into the exam software, and is available to students during the entire testing time. Students are expected to know how and when to make appropriate use of the calculator. The scientific calculator, together with a brief video tutorial, is available to students as a free download for a 30-day trial period. Visit www.collegeboard.org/clep for more information.
ALL ABOUT THE CLEP PROGRAM
What is the CLEP?
CLEP is the most widely accepted credit-by-examination program in North America. The CLEP program’s 33 exams span five subject areas. The exams assess the material commonly required in an introductory-level college course. Examinees can earn from three to twelve credits at more than 2,900 colleges and universities in the U.S. and Canada. For a complete list of the CLEP subject examinations offered, visit the College Board website: www.collegeboard.org/clep.
Who takes CLEP exams?
CLEP exams are typically taken by people who have acquired knowledge outside the classroom and who wish to bypass certain college courses and earn college credit. The CLEP program is designed to reward examinees for learning—no matter where or how that knowledge was acquired.
Although most CLEP examinees are adults returning to college, many graduating high school seniors, enrolled college students, military personnel, veterans, and international students take CLEP exams to earn college credit or to demonstrate their ability to perform at the college level. There are no prerequisites, such as age or educational status, for taking CLEP examinations. However, because policies on granting credits vary among colleges, you should contact the particular institution from which you wish to receive CLEP credit.
How is my CLEP score determined?
Your CLEP score is based on two calculations. First, your CLEP raw score is figured; this is just the total number of test items you answer correctly. After the test is administered, your raw score is converted to a scaled score through a process called equating. Equating adjusts for minor variations in difficulty across test forms and among test items, and ensures that your score accurately represents your performance on the exam regardless of when or where you take it, or on how well others perform on the same test form.
Your scaled score is the number your college will use to determine if you’ve performed well enough to earn college credit. Scaled scores for the CLEP exams are delivered on a 20-80 scale. Institutions can set their own scores for granting college credit, but a good passing estimate (based on recommendations from the American Council on Education) is generally a scaled score of 50, which usually requires getting roughly 66% of the questions correct.
For more information on scoring, contact the institution where you wish to be awarded the credit.
Who administers the exam?
CLEP exams are developed by the College Board, administered by Educational Testing Service (ETS), and involve the assistance of educators from throughout the United States. The test development process is designed and implemented to ensure that the content and difficulty level of the test are appropriate.
When and where is the exam given?
CLEP exams are administered year-round at more than 1,200 test centers in the United States and can be arranged for candidates abroad on request. To find the test center nearest you and to register for the exam, contact the CLEP Program:
CLEP Services
P.O. Box 6600
Princeton, NJ 08541-6600
Phone: (800) 257-9558 (8 A.M. to 6 P.M. ET)
Fax: (610) 628-3726
Website: www.collegeboard.org/clep
The CLEP iBT Platform
To improve the testing experience for both institutions and test-takers, the College Board’s CLEP Program has transitioned its 33 exams from the eCBT platform to an Internet-based testing (iBT) platform. All CLEP test-takers may now register for exams and manage their personal account information through the My Account
feature on the CLEP website. This new feature simplifies the registration process and automatically downloads all pertinent information about the test session, making for a more streamlined check-in.
OPTIONS FOR MILITARY PERSONNEL AND VETERANS
CLEP exams are available free of charge to eligible military personnel and eligible civilian employees. All the CLEP exams are available at test centers on college campuses and military bases. Contact your Educational Services Officer or Navy College Education Specialist for more information. Visit the DANTES or College Board websites for details about CLEP opportunities for military personnel.
Eligible U.S. veterans can claim reimbursement for CLEP exams and administration fees pursuant to provisions of the Veterans Benefits Improvement Act of 2004. For details on eligibility and submitting a claim for reimbursement, visit the U.S. Department of Veterans Affairs website at www.gibill.va.gov.
CLEP can be used in conjunction with the Post-9/11 GI Bill, which applies to veterans returning from the Iraq and Afghanistan theaters of operation. Because the GI Bill provides tuition for up to 36 months, earning college credits with CLEP exams expedites academic progress and degree completion within the funded timeframe.
SSD ACCOMMODATIONS FOR CANDIDATES WITH DISABILITIES
Many test candidates qualify for extra time to take the CLEP exams, but you must make these arrangements in advance. For information, contact:
College Board Services for Students with Disabilities
P.O. Box 8060
Mt. Vernon, Illinois 62864-0060
Phone: (609) 771-7137 (Monday through Friday, 8 A.M. to 6 P.M. ET)
TTY: (609) 882-4118
Fax: (866) 360-0114
Website: http://student.collegeboard.org/services-for-students-with-disabilities
E-mail: [email protected]
6-WEEK STUDY PLAN
Although our study plan is designed to be used in the six weeks before your exam, it can be condensed to three weeks by combining each two-week period into one.
Be sure to set aside enough time—at least two hours each day—to study. The more time you spend studying, the more prepared and relaxed you will feel on the day of the exam.
TEST-TAKING TIPS
Know the format of the test. Familiarize yourself with the CLEP computer screen beforehand by logging on to the College Board website. Waiting until test day to see what it looks like in the pretest tutorial risks injecting needless anxiety into your testing experience. Also, familiarizing yourself with the directions and format of the exam will save you valuable time on the day of the actual test.
Read all the questions—completely. Make sure you understand each question before looking for the right answer. Reread the question if it doesn’t make sense.
Read all of the answers to a question. Just because you think you found the correct response right away, do not assume that it’s the best answer. The last answer choice might be the correct answer.
Work quickly and steadily. You will have 90 minutes to answer 60 questions, so work quickly and steadily. Taking the timed practice tests online will help you learn how to budget your time.
Use the process of elimination. Stumped by a question? Don’t make a random guess. Eliminate as many of the answer choices as possible. By eliminating just one answer choice, you give yourself a better chance of getting the item correct, since there will only be three choices left from which to make your guess. Remember, your score is based only on the number of questions you answer correctly.
Don’t waste time! Don’t spend too much time on any one question. Your time is limited so pacing yourself is very important. Work on the easier questions first. Skip the difficult questions and go back to them if you have the time.
Look for clues to answers in other questions. If you skip a question you don’t know the answer to, you might find a clue to the answer elsewhere on the test.
Be sure that your answer registers before you go to the next item. Look at the screen to see that your mouse-click causes the pointer to darken the proper oval. If your answer doesn’t register, you won’t get credit for that question.
THE DAY OF THE EXAM
On test day, you should wake up early (after a good night’s rest, of course) and have breakfast. Dress comfortably so you are not distracted by being too hot or too cold while taking the test. (Note that hoodies
are not allowed.) Arrive at the test center early. This will allow you to collect your thoughts and relax before the test, and it will also spare you the anxiety that comes with being late.
Before you leave for the test center, make sure you have your admission form and another form of identification, which must contain a recent photograph, your name, and signature (i.e., driver’s license, student identification card, or current alien registration card). You may not wear a digital watch (wrist or pocket), alarm watch, or wristwatch camera. In addition, no cell phones, dictionaries, textbooks, notebooks, briefcases, or packages will be permitted, and drinking, smoking, and eating are prohibited.
Good luck on the CLEP College Mathematics exam!
CHAPTER 2
Numbers
CHAPTER 2
NUMBERS
Real numbers provide the basis for most precalculus mathematics topics.
Real numbers are all of the numbers on the number line (see Figure 2-1).
In fact, a nice way to visualize real numbers is that they can be put in a one-to-one correspondence with the set of all