2014
Examination Guide
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College Algebra

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Introduction
This is the only official guide to the 33 College-Level Examination Program® (CLEP®) exams. CLEP exams are administered on computers at test centers across the country. This Guide has been written mainly for adults who are making plans to enroll in college, but it contains information of interest to others as well. College-bound high school students, current college students, military personnel, professionals seeking certification and persons of all ages who have learned or wish to learn college-level material outside the college classroom will find the Guide helpful as they strive to accomplish their goals. CLEP is based on the premise that some individuals enrolling in college have already learned part of what is taught in college courses through job training, independent reading and study, noncredit adult courses and advanced high school courses. Often, their jobs and life experiences have enhanced and reinforced their learning. CLEP provides these individuals with the opportunity to demonstrate their mastery of college-level material by taking exams that assess the knowledge and skills taught in college courses. The first few sections of this study guide explain how CLEP can help you earn credit for the collegelevel learning you have acquired and provide suggestions for preparing for the exams. The guides to the individual exams include test descriptions, sample questions and tips for preparing to take the exams. CLEP has also made available a demonstration video (CLEP Tutorial) that walks test-takers through the registration process and the Internet-based testing experience. You may also refer to the CLEP Tutorial to access sample questions and a demonstration on how to use the online calculators. Then, use this Guide to become familiar with the description and content of each exam you’re interested in taking. This Guide contains sample questions and an answer key for each exam, as well as in-depth information about how to decide which exams to take, how to prepare to take those exams, and how to interpret your scores.

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Preparing to Take CLEP Examinations
Having made the decision to take one or more CLEP exams, most people then want to know how to prepare for them — how much, how long, when, and how should they go about it? The precise answers to these questions vary greatly from individual to individual. However, most candidates find that some type of test preparation is helpful. Most people who take CLEP exams do so to show that they have already learned the key material taught in a college course. Many of them need only a quick review to assure themselves that they have not forgotten what they once studied, and to fill in some of the gaps in their knowledge of the subject. Others feel that they need a thorough review and spend several weeks studying for an exam. Some people take a CLEP exam as a kind of “final exam” for independent study of a subject. This last group requires significantly more study than do those who only need to review, and they may need some guidance from professors of the subjects they are studying. The key to how you prepare for CLEP exams often lies in locating those skills and areas of prior learning in which you are strongest and deciding where to focus your energies. Some people may know a great deal about a certain subject area but may not test well. These individuals would probably be just as concerned about strengthening their test-taking skills as they would about studying for a specific test. Many mental and physical skills are required in preparing for a test. It is important not only to review or study for the exams but also to make certain that you are alert, relatively free of anxiety, and aware of how to approach standardized tests. Suggestions about developing test-taking skills and preparing psychologically and physically for a test are given in this chapter. The following section suggests ways of assessing your knowledge of the content of an exam and then reviewing and studying the material.

Using the Examination Guides
The individual exam guides, available for purchase on www.collegeboard.org/clep, contain the same information you will find in this Guide. Each exam guide includes an outline of the knowledge and skills covered by the test, sample questions similar to those that appear on the exam, and tips for preparing to take the exam. You may also choose to contact a college in your area that offers a course with content comparable to that on the CLEP exam you want to take, or read the suggested resources for each exam on http://clep.collegeboard.org/exam. If possible, use the textbook and other materials required for that course to help you prepare. To get this information, check the college’s catalog for a list of courses offered. Then call the admissions office, explain what subject you’re interested in, and ask who in that academic department you can contact for specific information on textbooks and other study resources to use. You might also be able to find the course syllabus, which will list course materials and assignments, online at the college’s website. Be sure that the college you’re interested in gives credit for the CLEP exam for which you’re preparing. Begin by carefully reading the test description and outline of knowledge and skills required for the exam in the exam guide. As you read through the topics listed, ask yourself how much you know about each one.

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Also note the terms, names and symbols that are mentioned, and ask yourself whether you are familiar with them. This will give you a quick overview of how much you know about the subject. If you are familiar with nearly all the material, you will probably need a minimum of review; however, if topics and terms are unfamiliar, you will probably require substantial study to do well on the exam. If, after reviewing the test description provided in the exam guide, you find that you need extensive review, put off answering the sample questions until you have done some reading in the subject. If you complete them before reviewing the material, you will probably look for the answers as you study, and this will not be a good assessment of your ability at a later date. Do not refer to the sample questions as you prepare for the exam. The sample questions are representative of the types of questions you will find on a CLEP exam, but none of the questions will actually appear on an exam, so concentrating on them without broader study of the subject won’t help you. If you think you are familiar with most of the test material, try to answer the sample questions, checking your responses against the answer key. Use the test-taking strategies described in the next chapter.

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Assessing Your Readiness for a CLEP Examination
Select Exam Title from Table of Contents (pp. iii-v)

Read Exam Description and Knowledge and Skills Required

Understand Terms

Do Not Understand Terms

Try Sample Questions

Review Study Materials suggested in the Study Resources section of each chapter; See also pp. 16-18

Most Sample Questions Answered Correctly

Difficulty Answering Sample Questions

Take CLEP Examination

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Suggestions for Studying
The following suggestions have been gathered from people who have prepared for CLEP exams or other college-level tests. 1. Review the CLEP Tutorial video. The CLEP Tutorial video walks you through the registration process and the Internet-based testing experience. Through this tutorial you will become familiar with the internet-based format of the CLEP exams, access sample questions through a virtual experience and view a demonstration on how to use the online calculators. Remember, if you want to review content covered by each examination, Chapter VII of this Study Guide contains a complete exam description — including a content outline, a description of the knowledge and skills required to do well, and sample questions — for each subject. An answer key for each subject is also included. However, the Study Guide is not intended to replace a textbook. Additional study may be required. 2. Define your goals and locate study materials. Once you’ve determined how much preparation you’ll need to do, you’ll need to define your study goals. Set aside a block of time to review the exam guides provided in this book, and then decide which exam(s) you will take. Using the guidelines for knowledge and skills required, locate suitable resource materials. If a preparation course is offered by an adult school or college in your area, you might find it helpful to enroll. (You should be aware, however, that such courses are not authorized or sponsored by the College Board. The College Board has no responsibility for the content of these courses, nor are they responsible for books on preparing for CLEP exams that have been published by other organizations.) If you know others who have taken CLEP exams, ask them how they prepared. You may want to get a copy of a syllabus for the college course that is comparable to the CLEP exam(s) you plan to take. You can also ask the appropriate professor at the school you’ll be attending, or check his or her website, for a reading list. Use the syllabus, course materials and/or reading list as a guide for selecting textbooks and study materials. You may purchase these or check them out of your local library. Some websites offer course materials and lectures online; these can be an excellent resource. Examples of these include: ⦁ MIT OpenCourseWare (http://ocw.mit.edu), ⦁ Carnegie Mellon’s Open Learning Initiative (http://www.cmu.edu/oli/), ⦁ and the National Repository of Online Courses (http://www.montereyinstitute.org/nroc).

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Most of this material is offered for free. Educational websites, like those offered by PBS (www.pbs.org) or the National Geographic Society (www.nationalgeographic.com), can be helpful as well. You can also find a list of suggested textbooks and online resources for each CLEP exam at http://clep.collegeboard.org/exam. Check with your librarian about locating study aids relevant to the exams you plan to take. These supplementary materials may include videos or DVDs made by education-oriented companies and organizations, language tapes and computer software. And don’t forget that what you do with your leisure time can be very educational, whether it’s surfing current-events websites, watching a PBS series, reading a financial newsletter, or attending a play. 3. Find a good place to study. To determine what kind of place you need for studying, ask yourself the following questions: Do I need a quiet place? Does the telephone distract me? Do objects I see in this place remind me of things I should do? Is it too warm? Is it well lit? Am I too comfortable here? Do I have space to spread out my materials? You may find the library more conducive to studying than your home. If you decide to study at home or in your dorm, you might prevent interruptions by other household members by putting a sign on the door of your study room to indicate when you will be available. 4. Schedule time to study. To help you determine where studying best fits into your schedule, try this exercise: Make a list of your daily activities (for example, sleeping, working, eating, attending class, sports or exercise) and estimate how many hours a day you spend on each activity. Now, rate all the activities on your list in order of their importance and evaluate your use of time. Often people are astonished at how an average day appears from this perspective. You may discover that your time can be scheduled in alternative ways. For example, you could remove the least important activities from your day and devote that time to studying or to another important activity. 5. Establish a study routine and a set of goals. To study effectively, you should establish specific goals and a schedule for accomplishing them. Some people find it helpful to write out a weekly schedule and cross out each study period when it is completed. Others maintain their concentration better by writing down the time when they expect to complete a study task. Most people find short periods of intense study more productive than long stretches of time. For example, they may follow a regular schedule of several 20- or 30-minute study periods with short breaks between them. Some people like to allow themselves rewards as they complete each study goal. It is not essential that you accomplish every goal exactly within your schedule; the point is to be committed to your task. 6. Learn how to take an active role in studying. If you have not done much studying for some time, you may find it difficult to concentrate at first. Try a method of studying, such as the one outlined below and on the next page, that will help you concentrate on and remember what you read. a. First, read the chapter summary and the introduction so you will know what to look for in your reading.

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b. Next, convert the section or paragraph headlines into questions. For example, if you are reading a section entitled “The Causes of the American Revolution,” ask yourself, “What were the causes of the American Revolution?” Compose the answer as you read the paragraph. Reading and answering questions aloud will help you understand and remember the material. c. Take notes on key ideas or concepts as you read. Writing will also help you fix concepts more firmly in your mind. Underlining key ideas or writing notes in your book can be helpful and will be useful for review. Underline only important points. If you underline more than a third of each paragraph, you are probably underlining too much. d. If there are questions or problems at the end of a chapter, answer or solve them on paper as if you were asked to do them for homework. Mathematics textbooks (and some other books) sometimes include answers to some or all of the exercises. If you have such a book, write your answers before looking at the ones given. When problem solving is involved, work enough problems to master the required methods and concepts. If you have difficulty with problems, review any sample problems or explanations in the chapter. e. To retain knowledge, most people have to review the material periodically. If you are preparing for an exam over an extended period of time, review key concepts and notes each week or so. Do not wait for weeks to review the material or you will need to relearn much of it.

Test Preparation Tips
1. Familiarize yourself as much as possible with the test and the test situation before the day of the exam. It will be helpful for you to know ahead of time: a. how much time will be allowed for the test and whether there are timed subsections. (This information is included in the examination guides and in the CLEP Tutorial video.) b. what types of questions and directions appear on the exam. (See the examination guides.) c. how your test score will be computed. d. in which building and room the exam will be administered. e. the time of the test administration. f. direction, transit and parking information to the test center. 2. Register and pay your exam fee through My Account at https://clepportal.collegeboard.org/myaccount and print your registration ticket. Contact your preferred test center to schedule your appointment to test. Your test center may require an additional administration fee. Check with your test center and confirm the amount required and acceptable method of payment.

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3. On the day of the exam, remember to do the following. a. Arrive early enough so that you can find a parking place, locate the test center, and get settled comfortably before testing begins. b. Take the following with you:
⦁ ⦁

completed registration ticket any registration forms or printouts required by the test center. Make sure you have filled out all necessary paperwork in advance of your testing date. your driver’s license, passport or other government-issued identification that includes your photograph and signature, as well as a secondary form of ID that includes a photo and/or your signature, such as a student ID. You will be asked to show this identification to be admitted to the testing area. Military test-takers, bring your military ID and Social Security card. two number 2 pencils with good erasers. Mechanical pencils are prohibited in the testing room.

⦁

⦁ ⦁

c. Leave all books, papers and notes outside the test center. You will not be permitted to use your own scratch paper; it will be provided by the test center. d. Do not take a calculator to the exam. If a calculator is required, it will be built into the testing software and available to you on the computer. The CLEP Tutorial video will have a demonstration on how to use online calculators. e. Do not bring a cell phone or other electronic devices into the testing room. 4. When you enter the test room: a. You will be assigned to a computer testing station. If you have special needs, be sure to communicate them to the test center administrator before the day you test. b. Be relaxed while you are taking the exam. Read directions carefully and listen to all instructions given by the test administrator. If you don’t understand the directions, ask for help before the test begins. If you must ask a question that is not related to the exam after testing has begun, raise your hand and a proctor will assist you. The proctor cannot answer questions related to the exam. c. Know your rights as a test-taker. You can expect to be given the full working time allowed for taking the exam and a reasonably quiet and comfortable place in which to work. If a poor testing situation is preventing you from doing your best, ask whether the situation can be remedied. If it can’t, ask the test administrator to report the problem on a Center Problem Report that will be submitted with your test results. You may also wish to immediately write a letter to CLEP, P.O. Box 6656, Princeton, NJ 085416656. Describe the exact circumstances as completely as you can. Be sure to include the name of the test center, the test date and the name(s) of the exam(s) you took.

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Arrangements for Students with Disabilities
CLEP is committed to working with test-takers with disabilities. If you have a learning or physical disability that would prevent you from taking a CLEP exam under standard conditions, you may request special accommodations and arrangements to take it on a regularly scheduled test date or at a special administration. Contact a CLEP test center prior to registration about testing accommodations and to ensure the accommodation you are requesting is available. Each test center sets its own guidelines in terms of deadlines for submission of documentation and approval of accommodations. Only students with documented hearing, learning, physical or visual disabilities are eligible to receive testing accommodations. Also, it is important to ensure that you are taking the exam(s) with accommodations that are approved by your score recipient institution. Testing accommodations that may be provided with appropriate disability documentation include: ⦁ ZoomText (screen magnification) ⦁ Modifiable screen colors ⦁ Scripts for the listening sections of the language exams ⦁ Use of a reader or amanuensis or sign language interpreter ⦁ Extended time ⦁ Untimed rest breaks

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Taking the Examinations
Test-taking skills enable a person to use all available information to earn a score that truly reflects his or her ability. There are different strategies for approaching different kinds of exam questions. For example, free-response and multiple-choice questions require very different approaches. Other factors, such as how the exam will be graded, may also influence your approach to the exam and your use of test time. Thus, your preparation for an exam should include finding out all you can about the exam so you can use the most effective test-taking strategies.

Test-Taking Strategies for Multiple-Choice Questions
1. Listen carefully to any instructions given by the test administrator and read the on-screen instructions before you begin to answer the questions. 2. Keep an eye on the clock and the timing that is built into the testing software. You have the option of turning the clock on or off at any time. As you proceed, make sure that you are not working too slowly. You should have answered at least half the questions in a section when half the time for that section has passed. 3. Before answering a question, read the entire question, including all the answer choices. Instructions usually tell you to select the “best’’ answer. Sometimes one answer choice is partially correct but another option is better, so it’s a good idea to read all the answers even if the first or second choice looks correct to you. 4. Read and consider every question. Questions that look complicated at first glance may not actually be so difficult once you have read them carefully. 5. Do not spend too much time on any one question. If you don’t know the answer after you’ve considered it briefly, go on to the next question. Mark that question using the mark tool at the bottom of the screen, and go back to review the question later, if you have time.

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6. Watch for the following key words in test questions: all always but except every generally however may must necessary never none not often only perhaps rarely seldom sometimes usually

When a question or answer option contains words such as ‘‘always,’’ ‘‘every,’’ ‘‘only,’’ ‘‘never’’ and “none,” there can be no exceptions to the answer you choose. Use of words such as ‘‘often,’’ “rarely,” ‘‘sometimes’’ and ‘‘generally’’ indicates that there may be some exceptions to the answer. 7. Make educated guesses. There is no penalty for incorrect answers. Therefore, you should guess even if you do not know an answer. If you have some knowledge of the question and are able to eliminate one or more of the answer choices as wrong, your chance of getting the right answer is improved. Do not waste your time looking for clues to right answers based on flaws in question wording or patterns in correct answers. CLEP puts a great deal of effort into developing valid, reliable and fair exams. CLEP test development committees are composed of college faculty who are experts in the subjects covered by the exams and are appointed by the College Board to write test questions and to scrutinize each question that is included on a CLEP exam. They make every effort to ensure that the questions are not ambiguous, that they have only one correct answer, and that they cover college-level topics. These committees do not intentionally include ‘‘trick’’ questions. If you think a question is flawed, ask the test administrator to report it, or write immediately to CLEP Test Development, P.O. Box 6600, Princeton, NJ 08541-6600. Include the name of the exam and test center, the exam date, and the number of the exam question. All such inquiries are investigated by test development professionals.

8.

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Answering Essay Questions
The College Composition exam is the only CLEP exam that includes two mandatory essays. Both the multiple-choice section and the essay section of the exam are administered on the computer. You are required to type your essays using a format similar to word processing. The essays for the College Composition exam will be graded by English professors from a variety of colleges and universities who are trained by CLEP. A process called holistic scoring is used to rate your writing abilities. This process is explained in the examination guide for College Composition, which also includes graded sample essays and essay questions. Four other CLEP exams have optional essays. Some colleges or universities may require you to take one of these optional essays as part of the American Literature, Analyzing and Interpreting Literature, English Literature or College Composition Modular exam. There is an additional fee of $10 for each of the optional essays, payable to the institution that administers the exam. These essays are graded by the faculty of the institution that grants the credit. Therefore, you may find it helpful to talk with someone at your college to find out what criteria will be used to determine whether you will get credit. Ask how much emphasis will be placed on your writing ability and your ability to organize your thoughts, as opposed to your knowledge of the subject matter. Find out how much weight will be given to your multiple-choice test score in comparison with your free-response grade in determining whether you will get credit. This will give you an idea of where you should expend the greatest effort in preparing for and taking the exam.

Test-Taking Strategies for Essay Writing
1. Before you begin to respond, read all the questions carefully and take a few minutes to jot down some ideas or create an outline. Scratch paper will be provided at the test center. 2. If you are given a choice of questions to answer, choose the questions that you think you can answer most clearly and knowledgeably. 3. Determine the order in which you will answer the questions. First, answer those you find the easiest so you can spend any extra time on the questions you find more difficult. 4. When you know which questions you will answer and in what order, determine how much testing time remains and estimate how many minutes you will devote to each question. Unless suggested times are given for the questions, try to allot an equal amount of time for each question.

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5. Before answering each question, read it again carefully to make sure you are interpreting it correctly. Pay attention to key words, such as those listed below, that often appear in free-response questions. Be sure you know the exact meaning of these words before taking the exam. analyze apply assess compare contrast define demonstrate derive describe determine discuss distinguish enumerate explain generalize illustrate interpret justify list outline prove rank show summarize

If a question asks you to ‘‘outline,’’ ‘‘define’’ or ‘‘summarize,’’ do not write a detailed explanation; if a question asks you to ‘‘analyze,” ‘‘explain,’’ “illustrate,’’ ‘‘interpret’’ or ‘‘show,’’ you must do more than briefly describe the topic.

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Interpreting Your Scores
CLEP score requirements for awarding credit vary from institution to institution. The College Board, however, recommends that colleges refer to the standards set by the American Council on Education (ACE). All ACE recommendations are the result of careful and periodic review by evaluation teams made up of faculty who are subject-matter experts and technical experts in testing and measurement. To determine whether you are eligible for credit for your CLEP scores, you should refer to the policy of the college you will be attending. The policy will state the score that is required to earn credit at that institution. Many colleges award credit at the score levels recommended by ACE. However, some require scores that are higher or lower than these. Your exam score will be printed for you at the test center immediately upon completion of the examination, unless you took College Composition. For this exam, you will receive your score four to six weeks after the exam date. Your CLEP exam scores are reported only to you, unless you ask to have them sent elsewhere. If you want your scores sent to a college, employer or certifying agency, you must select this option through My Account. This service is free only if you select your score recipient at the time you register to take your exam. A fee will be charged for each score recipient you select at a later date. Your scores are kept on file for 20 years. For a fee, you can request a transcript at a later date. The pamphlet What Your CLEP Score Means, which you will receive with your exam score, gives detailed information about interpreting your scores. A copy of the pamphlet is in the appendix of this Guide. A brief explanation appears below.

How CLEP Scores Are Computed
In order to reach a total score on your exam, two calculations are performed. First, your “raw score” is calculated. This is the number of questions you answer correctly. Your raw score is increased by one point for each question you answer correctly, and no points are gained or lost when you do not answer a question or answer it incorrectly. Second, your raw score is converted into a “scaled score” by a statistical process called equating. Equating maintains the consistency of standards for test scores over time by adjusting for slight differences in difficulty between test forms. This ensures that your score does not depend on the specific test form you took or how well others did on the same form. Your raw score is converted to a scaled score that ranges from 20, the lowest, to 80, the highest. The final scaled score is the score that appears on your score report.

How Essays Are Graded
The College Board arranges for college English professors to grade the essays written for the College Composition exam. These carefully selected college faculty members teach at two- and four-year institutions nationwide. The faculty members receive extensive training and thoroughly review the College Board scoring policies and procedures before grading the essays. Each essay is read and graded

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by two professors, the sum of the two grades for each essay is combined with the multiple-choice score, and the result is reported as a scaled score between 20 and 80. Although the format of the two sections is very different, both measure skills required for expository writing. Knowledge of formal grammar, sentence structure and organizational skills are necessary for the multiple-choice section, but the emphasis in the free-response section is on writing skills rather than grammar. Optional essays for CLEP Composition Modular and the literature examinations are evaluated and graded by the colleges that require them, rather than by the College Board. If you take an optional essay, it will be sent with a copy of your score report (which includes only the results of your multiple-choice test) to the institution you designate when you take the test. You may opt not to have your score sent to a college until after you have seen it. In this case, your essay can still be sent to the college of your choice as long as you request a transcript within 18 months after you take the exam. Copies of essays are not held beyond 18 months or after they have been sent to an institution.

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College Algebra
Description of the Examination
The College Algebra examination covers material that is usually taught in a one-semester college course in algebra. Nearly half of the test is made up of routine problems requiring basic algebraic skills; the remainder involves solving nonroutine problems in which candidates must demonstrate their understanding of concepts. The test includes questions on basic algebraic operations; linear and quadratic equations, inequalities and graphs; algebraic, exponential and logarithmic functions; and miscellaneous other topics. It is assumed that candidates are familiar with currently taught algebraic vocabulary, symbols and notation. The test places little emphasis on arithmetic calculations. However, an online scientific calculator (nongraphing) will be available during the examination. The examination contains approximately 60 questions to be answered in 90 minutes. Some of these are pretest questions that will not be scored. Any time candidates spend on tutorials and providing personal information is in addition to the actual testing time. 25% Algebraic operations Factoring and expanding polynomials Operations with algebraic expressions Operations with exponents Properties of logarithms Equations and inequalities Linear equations and inequalities Quadratic equations and inequalities Absolute value equations and inequalities Systems of equations and inequalities Exponential and logarithmic equations Functions and their properties* Definition and interpretation Representation/modeling (graphical, numerical, symbolic and verbal representations of functions) Domain and range Algebra of functions Graphs and their properties (including intercepts, symmetry and transformations) Inverse functions Number Systems and operations Real numbers Complex numbers Sequences and series Factorials and Binomial Theorem

25%

30%

Knowledge and Skills Required
Questions on the College Algebra examination require candidates to demonstrate the following abilities in the approximate proportions indicated. • Solving routine, straightforward problems (about 50 percent of the examination) • Solving nonroutine problems requiring an understanding of concepts and the application of skills and concepts (about 50 percent of the examination) The subject matter of the College Algebra examination is drawn from the following topics. The percentages next to the main topics indicate the approximate percentage of exam questions on that topic. 20%

*Each test may contain a variety of functions, including linear, polynomial (degree ≤ 5), rational, absolute value, power, exponential, logarithmic and piecewise-defined.

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A L G E B R A

The following sample questions do not appear on an actual CLEP examination. They are intended to give potential test-takers an indication of the format and difficulty level of the examination and to provide content for practice and review. Knowing the correct answers to all of the sample questions is not a guarantee of satisfactory performance on the exam. Directions: An online scientific calculator will be available for the questions in this test. Some questions will require you to select from among five choices. For these questions, select the BEST of the choices given. Some questions will require you to type a numerical answer in the box provided.

4. The radius of the Sun is approximately 109 meters, and the radius of an oxygen atom is approximately 10-12 meter. The radius of the Sun is approximately how many times the radius of an oxygen atom? (A) (B) (C) (D) (E)
10-21 10-3 103 109 1021

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6. Which of the following are the solutions of the equation 2x(1 – 3x) – 1 + 3x = 0 ?

A L G E B R A

1 1 and x = 2 3 1 1 (B) x = and x = – 2 3 1 1 (C) x = – and x = 2 3 1 1 (D) x = – and x = – 2 3 (E) x = 0 and x = 1
(A) x =

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19. Which of the following is an equation of the line that passes through the points ( -2, 1) and (1, 2) in the xy-plane? (A) (B) (C) (D) (E) x x x x x + 3y + 3y + 3y - 3y - 3y = = = = = 1 5 -5 -5 -1

23. The illuminance of a surface varies inversely with the square of its distance from the light source. If the illuminance of a surface is 120 lumens per square meter when its distance from a certain light source is 6 meters, by how many meters should the distance of the surface from the source be increased to reduce its illuminance to 30 lumens per square meter? (A) (B) (C) (D) (E) 3 6 12 15 18

25. Which of the following is the solution set of the x –3 ≥ –3 ? inequality 4 – 7 2





(A) (B) (C) (D) (E)

(– , 4] [8, ) [4, 8] (– , 4] ∪ [8, ) (– , – 4]

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31. A clothing company has budgeted $58,000 for the purchase of 7 sewing machines. The 7 sewing machines are to be chosen from two models, model X and model Y. If a model X sewing machine costs $8,000 and a model Y sewing machine costs $9,000, how many model X sewing machines should the company purchase to use exactly the budgeted money? 28. Which of the following is the expansion of ( 2 x + 3)3 ? (A) (B) (C) (D) (E)
2 x 3 + 3( 2 x 2 ) + 3( 2 x ) + 1 2 x 3 + 3( 2 x 2 ) + 32 ( 2 x ) + 3 2 x 3 + 3( 2 x 2 ) + 32 ( 2 x ) + 33 ( 2 x )3 + 3( 2 x )2 + 32 ( 2 x ) + 33 ( 2 x )3 + 32 ( 2 x )2 + 33 ( 2 x ) + 33

(A) 2

(B) 3

(C) 4

(D) 5

(E) 6

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48. A company’s daily cost c, in hundreds of dollars, to manufacture n items of a certain product can be modeled by the function c( n ). According to the model, which of the following is the best interpretation of c -1 (5) = 80, where c -1 is the inverse function of c ? (A) The company’s daily cost to manufacture 5 items of the product is $80. (B) The company’s daily cost to manufacture 5 items of the product is $8,000. (C) The company’s daily cost to manufacture 500 items of the product is $80. (D) The company’s daily cost to manufacture 80 items of the product is $5. (E) The company’s daily cost to manufacture 80 items of the product is $500.

51. A rectangular box has volume x3 − 8 cubic inches. If the height of the box is x − 2 inches, what is the area of the base of the box, in square inches? (The volume of a box equals the area of the base times the height.) (A) x 2 + 4 (B) (C) (E)

x2 − 2 x − 4 x2 − 2 x + 4 x2 + 4 x + 4

(D) x 2 + 2 x + 4

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52. If y = 8 x 2 + 4 x − 1 is expressed in the form

A L G E B R A
55. log 125 log 2

y = a ( x − h) 2 + k , where a, h, and k are constants, what is the value of k ?
(A) −3 (B) −2 3 (C) − 2 17 (D) − 16 1 (E) − 2

5

2

53. If b and c are integers such that the equation 3 x 2 + bx + c = 0 has only one real root, which of the following statements must be true? I. b is even. II. c is odd. III. b 2 is a multiple of 3. (A) (B) (C) (D) (E) I only III only I and II only I and III only I, II, and III 56. In the figure shown above, the graph of the function g is a transformation of the graph of the function f . Which of the following is the equation of g ? (A) g ( x ) = − 1 x 2 + 3 2 (B) g ( x ) = − 1 ( x − 2) 2 2 (C) g ( x ) = − 1 ( x − 2) 2 2 2 (D) g ( x ) = − 1 ( x + 2) 2 (E) g ( x ) = − 1 ( x + 2) 2 2

54. A rock is thrown straight up into the air from a height of 4 feet. The height of the rock above the ground, in feet, t seconds after it is thrown is given by −16t 2 + 56t + 4. For how many seconds will the height of the rock be at least 28 feet above the ground? (A) (B) (C) (D) (E) 0.5 1.5 2.5 3.0 3.5

+3 −3 +3 −3

57. The polynomial p ( x) = x3 + 2 x − 11 has a real zero between which two consecutive integers? (A) (B) (C) (D) (E) 0 and 1 1 and 2 2 and 3 3 and 4 4 and 5

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58. Which of the following could be the graph of

A L G E B R A
60. The sum of the first n terms of an arithmetic sequence a1 , a2 , a3 , … , an is 1 n a1 + an , 2 where a1 and an are the first and the nth terms of the sequence, respectively. What is the sum of the odd integers from 1 to 99, inclusive?

y = ax 2 + bx + c, where b 2 − 4ac = 0 ?
(A) (B)

(

)

(C)

(D)

(A) (B) (C) (D) (E)

2,400 2,450 2,475 2,500 2,550

(E)

61. The function f is defined for all real numbers x by f ( x) = ax 2 + bx + c, where a , b , and c are constants and a is negative. In the xy-plane, the x-coordinate of the vertex of the parabola y = f ( x) is −1. If t is a number for which f (t ) > f (0), which of the following must be true? I. −2 < t < 0 II. f (t ) < f (−2) III. f (t ) > f (1) (A) (B) (C) (D) (E) I only II only I and III only II and III only I, II, and III

59. Consider each function below. Is the domain of the function the set of all real numbers? Function Yes No

f ( x) = x – 1 x2 + 2
2 g( x ) = x x +1

h( x ) =

x x +3
2

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2

A L G E B R A
65. What is the remainder when the polynomial 9 x 23 − 7 x12 − 2 x 5 + 1 is divided by x +1 ? (A) −19 (B) −13 (C) −7 (D) 1 (E) 11

h( x )
5

−4 c 62. The table above shows some values of the function h , which is defined for all real numbers x . If h is an odd function, what is the value of c ? (A) −5 (B) −4 (C) −2 (D) 2 (E) 4 63. If ∑ an = 50, what is the value of ∑ ( 4an + 3) ? n=1 n =1 10 10

66.

f ( x) = x + 1 g ( x) = 2 − x
Functions f and g are defined as shown above. What is the domain of the function f + g ? (A) (B) (C) (D) (E)

(A) 53 (B) 80 (C) 203 (D) 223 (E) 230

x≥0 x ≥1 x≥2 −1 ≤ x ≤ 2 −2 ≤ x ≤ 1

67. In the xy-plane, the line given by which of the following is perpendicular to the line 5x − 2 y = 7 ? (A) (B) (C) (D) (E)

2x + 5 y = 7 2x − 5 y = 7 5x + 2 y = 7 5 x − 2 y = 10 5 x − 5 y = 10

64. If z = −1 + i and z denotes the complex conjugate of z , which of the following points in the complex plane above represents z + z ? (A) (B) (C) (D) (E) A B C D E

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68. Which of the following statements about the polynomial p ( x) = ( x − 4) 2 ( x 2 + 4) are true? I. The polynomial has two imaginary roots. II. The polynomial has no real roots. III. The polynomial has four complex roots, counting multiplicities. (A) (B) (C) (D) (E) I only II only III only I and III only I, II, and III

A L G E B R A
71. If (A) (B) (C) (D) (E) 72. What is the solution of the equation (A) (B) (C) 2 (D) 3 (E) 8 73. The function f is defined by Which of the following is equal to (A) (B) (C) (D) (E) 74. The population of a certain city was 10,200 on January 1, 2013. If the population increases by 8 percent per year for the next 3 years, which of the following best approximates the population of the city on January 1, 2016 ? (A) (B) (C) (D) (E) what is the value of x ?

69.

C ( x) = 1200 + 1000 x R( x) = 1200 x − x 2
For a certain company, the functions shown above model the cost C of producing x units of a product and the revenue R from selling x units of the same product. The profit function P is equal to R − C. Which of the following defines the function P ? (A) (B) (C) (D) (E)

P( x) = x 2 − 200 x + 1200 P( x) = x 2 + 200 x − 1200 P( x) = − x 2 + 200 x − 1200 P ( x) = − x 2 + 2200 x − 1200 P ( x) = − x 2 + 2200 x + 1200
4

70. Which of the following is equivalent to (A) 6 4 6 (B) 4 6 (C) 6 (D) 6 (E) 1

36 ? 6

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75. What is the value of for the function

A L G E B R A
78. When the quadratic functions below are graphed in the xy-plane, is the vertex for each function above the x-axis, below the x-axis, or on the x-axis? Function Above Below On

76. If which of the following expresses x as a base ten logarithm? (A) (B) (C) (D) (E) 77. The owner of a small restaurant earned a profit of $300 during the first month of operation. According to the business model for the next 12 months, it is projected that the profit for each month after the first will be $50 more than the profit for the preceding month. If represents the profit for each month m and represents the first month, which of the following functions describes the business model? (A) (B) (C) (D) (E) 79. A circular cylindrical water tank is filled with water to 75 percent of its total volume of V cubic inches. The radius of the tank is 6 inches, and the height of the tank is h inches. Which of the following represents the height, in inches, of the water in the tank? (Note: The volume of a cylinder with radius r and height h is given by ) (A) (B) (C) (D) (E)

80. Select two of the following choices and place them in the blanks below so that the resulting statement is true.

increasing The function

decreasing

constant

is on its domain.

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Study Resources
Most textbooks used in college-level algebra courses cover the topics in the outline given earlier, but the approaches to certain topics and the emphases given to them may differ. To prepare for the College Algebra exam, it is advisable to study one or more college textbooks, which can be found in most college bookstores. When selecting a textbook, check the table of contents against the knowledge and skills required for this test. Visit www.collegeboard.org/clepprep for additional college algebra resources. You can also find suggestions for exam preparation in Chapter IV of the Official Study Guide. In addition, many college faculty post their course materials on their schools’ websites. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42.

Answer Key
E D D E B A A B E A D C D D B E C E D D 2 B B E C C 624 E 4 C D A –6 E 1 D C B C E A D 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. B D 3 E C E A D D C D C 1 D B B See the following page D C E E B B D A D C E A B E C 4 E C See the following page E See the following page

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59. Function f ( x) = x – 1 x2 + 2
2 g( x ) = x x +1

A L G E B R A

Yes

No

√ √ √

h( x ) =

x x +3
2

78. Function Above
√ √ √ √

Below

On

80. The function is increasing on its domain.

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2013-14 CLEP® Credit-Granting Recommendations
Computer-Based Testing (CBT) and Paper-and-Pencil Testing Semester Hours1 ACE Recommended Score1

Business Financial Accounting 50 3 Information Systems and Computer Applications 50 3 Introductory Business Law 50 3 Principles of Management 50 3 Principles of Marketing 50 3 Composition and Literature American Literature 50 6 Analyzing and Interpreting Literature 50 6 College Composition 50 6 College Composition Modular 50 3/62 English Literature 50 6 Humanities 50 6 World Languages French Language, Level 1 50 6 French Language, Level 2 59 12 German Language, Level 1 50 6 German Language, Level 2 60 12 Spanish Language, Level 1 50 6 Spanish Language, Level 2 63 12 Level 1 — equivalent to the first two semesters (or six semester hours) of college-level world language course work Level 2 — equivalent to the first four semesters (or 12 semester hours) of college-level world language course work History and Social Sciences American Government 50 3 50 3 History of the United States I: Early Colonization to 1877 History of the United States II: 1865 to Present 50 3 Human Growth and Development 50 3 Introduction to Educational Psychology 50 3 50 3 Introductory Psychology Introductory Sociology 50 3 Principles of Macroeconomics 50 3 Principles of Microeconomics 50 3 50 6 Social Sciences and History Western Civilization I: Ancient Near East to 1648 50 3 Western Civilization II: 1648 to Present 50 3 Science and Mathematics Biology 50 6 Calculus 50 4 Chemistry 50 6 College Algebra 50 3 College Mathematics 50 6 Natural Sciences 50 6 Precalculus 50 3
1. The American Council on Education’s College Credit Recommendation Service (ACE CREDIT) has evaluated CLEP processes and procedures for developing, administering and scoring the exams. The scores listed above are equivalent to a grade of C in the corresponding course. The American Council on Education, the major coordinating body for all the nation’s higher education institutions, seeks to provide leadership and a unifying voice on key higher education issues and to influence public policy through advocacy, research and program initiatives. For more information, visit the ACE CREDIT website at www.acenet.edu/acecredit. 2. If the college does not require a supplemental essay for the Modular version of the examination, the ACE credit-granting recommendation is three credits. If the college does require a supplemental essay, the credit-granting recommendation is six credits.

www.collegeboard.org/clep
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