College Algebra CLEP pdf

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Test InformationGuide:College-LevelExaminationProgram®

2011-12

College Algebra

© 2011 The College Board. All rights reserved. College Board, College-Level ExaminationProgram, CLEP, and the acorn logo are registered trademarks of the College Board.

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CLEP TEST INFORMATIONGUIDE FOR COLLEGE ALGEBRA

History of CLEP

Since 1967, the College-Level Examination Program(CLEP®) has provided over six million people withthe opportunity to reach their educational goals.CLEP participants have received college credit forknowledge and expertise they have gained throughprior course work, independent study or work andlife experience.

Over the years, the CLEP examinations have evolvedto keep pace with changing curricula and pedagogy.Typically, the examinations represent material taughtin introductory college-level courses from all areasof the college curriculum. Students may choose from33 different subject areas in which to demonstratetheir mastery of college-level material.

Today, more than 2,900 colleges and universitiesrecognize and grant credit for CLEP.

Philosophy of CLEP

Promoting access to higher education is CLEP’sfoundation. CLEP offers students an opportunity todemonstrate and receive validation of theircollege-level skills and knowledge. Students whoachieve an appropriate score on a CLEP exam canenrich their college experience with higher-levelcourses in their major field of study, expand theirhorizons by taking a wider array of electives andavoid repetition of material that they already know.

CLEP Participants

CLEP’s test-taking population includes people of allages and walks of life. Traditional 18- to 22-year-oldstudents, adults just entering or returning to school,homeschoolers and international students who needto quantify their knowledge have all been assisted byCLEP in earning their college degrees. Currently,58 percent of CLEP’s test-takers are women and52 percent are 23 years of age or older.

For over 30 years, the College Board has worked toprovide government-funded credit-by-examopportunities to the military through CLEP. Militaryservice members are fully funded for their CLEP examfees. Exams are administered at military installations

worldwide through computer-based testing programsand also — in forward-deployed areas — throughpaper-based testing. Approximately one-third of allCLEP candidates are military service members.

2010-11 National CLEP Candidates by Age*

These data are based on 100% of CLEP test-takers who responded to this survey question during their examinations.

*

Under 189%

18-22 years39%

23-29 years22%

30 years and older30%

2010-11 National CLEP Candidates by Gender

41%

58%

Computer-Based CLEP Testing

The computer-based format of CLEP exams allowsfor a number of key features. These include:

• a variety of question formats that ensure effectiveassessment

• real-time score reporting that gives students andcolleges the ability to make immediate credit-granting decisions (except College Composition,which requires faculty scoring of essays twice amonth)

• a uniform recommended credit-granting score of50 for all exams

• “rights-only” scoring, which awards one point percorrect answer

• pretest questions that are not scored but providecurrent candidate population data and allow forrapid expansion of question pools

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CLEP Exam Development

Content development for each of the CLEP examsis directed by a test development committee. Eachcommittee is composed of faculty from a widevariety of institutions who are currently teachingthe relevant college undergraduate courses. Thecommittee members establish the test specificationsbased on feedback from a national curriculumsurvey; recommend credit-granting scores andstandards; develop and select test questions; reviewstatistical data and prepare descriptive material foruse by faculty (Test Information Guides) and studentsplanning to take the tests (CLEP Official Study Guide).

College faculty also participate in CLEP in otherways: they convene periodically as part ofstandard-setting panels to determine therecommended level of student competency for thegranting of college credit; they are called upon towrite exam questions and to review forms and theyhelp to ensure the continuing relevance of the CLEPexaminations through the curriculum surveys.

The Curriculum Survey

The first step in the construction of a CLEP exam isa curriculum survey. Its main purpose is to obtaininformation needed to develop test-contentspecifications that reflect the current collegecurriculum and to recognize anticipated changes inthe field. The surveys of college faculty areconducted in each subject every three to five yearsdepending on the discipline. Specifically, the surveygathers information on:

• the major content and skill areas covered in theequivalent course and the proportion of the coursedevoted to each area

• specific topics taught and the emphasis given toeach topic

• specific skills students are expected to acquire andthe relative emphasis given to them

• recent and anticipated changes in course content,skills and topics

• the primary textbooks and supplementary learningresources used

• titles and lengths of college courses thatcorrespond to the CLEP exam

The Committee

The College Board appoints standing committees ofcollege faculty for each test title in the CLEP battery.Committee members usually serve a term of up tofour years. Each committee works with contentspecialists at Educational Testing Service to establishtest specifications and develop the tests. Listedbelow are the current committee members and theirinstitutional affiliations.

Donna Flint South Dakota StateUniversity

William Haver Virginia CommonwealthUniversity

Jing Ling Wang Lansing CommunityCollege

The primary objective of the committee is to producetests with good content validity. CLEP tests must berigorous and relevant to the discipline and theappropriate courses. While the consensus of thecommittee members is that this test has high contentvalidity for a typical introductory College Algebracourse or curriculum, the validity of the content for aspecific course or curriculum is best determinedlocally through careful review and comparison oftest content, with instructional content covered in aparticular course or curriculum.

The Committee Meeting

The exam is developed from a pool of questionswritten by committee members and outside questionwriters. All questions that will be scored on a CLEPexam have been pretested; those that pass a rigorousstatistical analysis for content relevance, difficulty,fairness and correlation with assessment criteria areadded to the pool. These questions are compiled bytest development specialists according to the testspecifications, and are presented to all the committeemembers for a final review. Before convening at atwo- or three-day committee meeting, the membershave a chance to review the test specifications andthe pool of questions available for possible inclusionin the exam.

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At the meeting, the committee determines whetherthe questions are appropriate for the test and, if not,whether they need to be reworked and pretestedagain to ensure that they are accurate andunambiguous. Finally, draft forms of the exam arereviewed to ensure comparable levels of difficulty andcontent specifications on the various test forms. Thecommittee is also responsible for writing anddeveloping pretest questions. These questions areadministered to candidates who take the examinationand provide valuable statistical feedback on studentperformance under operational conditions.

Once the questions are developed and pretested,tests are assembled in one of two ways. In somecases, test forms are assembled in their entirety.These forms are of comparable difficulty and aretherefore interchangeable. More commonly,questions are assembled into smaller,content-specific units called testlets, which can thenbe combined in different ways to create multiple testforms. This method allows many different forms tobe assembled from a pool of questions.

Test Specifications

Test content specifications are determined primarilythrough the curriculum survey, the expertise of thecommittee and test development specialists, therecommendations of appropriate councils andconferences, textbook reviews and other appropriatesources of information. Content specifications takeinto account:

• the purpose of the test

• the intended test-taker population

• the titles and descriptions of courses the test isdesigned to reflect

• the specific subject matter and abilities to be tested

• the length of the test, types of questions andinstructions to be used

Recommendation of the AmericanCouncil on Education (ACE)

The American Council on Education’s CollegeCredit Recommendation Service (ACE CREDIT)has evaluated CLEP processes and procedures for

developing, administering and scoring the exams.Effective July 2001, ACE recommended a uniformcredit-granting score of 50 across all subjects, withthe exception of four-semester language exams,which represents the performance of students whoearn a grade of C in the corresponding collegecourse.

The American Council on Education, the majorcoordinating body for all the nation’s higher educationinstitutions, seeks to provide leadership and a unifyingvoice on key higher education issues and to influencepublic policy through advocacy, research and programinitiatives. For more information, visit the ACECREDIT website at www.acenet.edu/acecredit.

CLEP Credit Granting

CLEP uses a common recommended credit-grantingscore of 50 for all CLEP exams.

This common credit-granting score does not mean,however, that the standards for all CLEP exams arethe same. When a new or revised version of a test isintroduced, the program conducts a standard settingto determine the recommended credit-granting score(“cut score”).

A standard-setting panel, consisting of 15–20 facultymembers from colleges and universities across thecountry who are currently teaching the course, isappointed to give its expert judgment on the level ofstudent performance that would be necessary toreceive college credit in the course. The panelreviews the test and test specifications and definesthe capabilities of the typical A student, as well asthose of the typical B, C and D students.* Expectedindividual student performance is rated by eachpanelist on each question. The combined average ofthe ratings is used to determine a recommendednumber of examination questions that must beanswered correctly to mirror classroom performanceof typical B and C students in the related course. Thepanel’s findings are given to members of the testdevelopment committee who, with the help ofEducational Testing Service and College Boardpsychometric specialists, make a final determinationon which raw scores are equivalent to B and C levelsof performance.

*Student performance for the language exams (French, German and Spanish)is defined only at the B and C levels.

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College Algebra

Description of the ExaminationThe 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 scientifi c 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.

Knowledge and Skills RequiredQuestions 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.

25% Algebraic OperationsFactoring and expanding polynomialsOperations with algebraic expressionsOperations with exponentsProperties of logarithms

25% Equations and InequalitiesLinear equations and inequalitiesQuadratic equations and inequalitiesAbsolute value equations and inequalitiesSystems of equations and inequalitiesExponential and logarithmic equations

30% Functions and Their Properties*Defi nition and interpretation Representation/modeling (graphical,

numerical, symbolic and verbal representations of functions)

Domain and rangeAlgebra of functionsGraphs and their properties (including

intercepts, symmetry and transformations)Inverse functions

20% Number Systems and OperationsReal numbersComplex numbersSequences and seriesFactorials and Binomial TheoremDeterminants of 2-by-2 matrices

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

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C O L L E G E 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 diffi culty 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 scientifi c calculator will be available for the questions in this test.

Some questions will require you to select from among fi ve choices. For these questions, select the BEST of the choices given.

Some question will require you to type a numerical answer in the box provided.

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

(A) x = and x =

(B) x = and x = –

(C) x = – and x =

(D) x = – and x = –

(E) x = 0 and x = 1

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19. Which of the following is the equation of the line that passes through the points with coordinates (–2, 1) and (1, 2) ?

(A) 2x + y = –3

(B) x + 3y = 7

(C) x + 2y = 0

(D) x – 3y = –5

(E) – x + 2y = 0

23. What is the determinant of the matrix ?

(A) – 5 (B) – 3 (C) – 1 (D) 1 (E) 5

25. Which of the following is the solution set of the

inequality 4 – 7� – 3� ≥ – 3 ?

(A) (– �, 4]

(B) [8, �)

(C) [4, 8]

(D) (– �, 4] ∪ [8, �)

(E) (– �, – 4]

x2

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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?

(A) 2 (B) 3 (C) 4 (D) 5 (E) 6

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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) x2 4+

(B) x x2 2 4− −

(C) x x2 2 4− +

(D) x x2 2 4+ +

(E) x x2 4 4+ +

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52. If y x x= + −8 4 12 is expressed in the form

y a x h k= − +( ) ,2 where a, h, and k are constants, what is the value of k ?

(A) −3(B) −2

(C) −32

(D) −1716

(E) − 12

53. If b and c are integers such that the equation 3 02x bx c+ + = has only one real root, which of the following statements must be true?

I. b is even.

II. c is odd.

III. b2 is a multiple of 3.

(A) I only

(B) III only

(C) I and II only

(D) I and III only

(E) I, II, and III

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 − + +16 56 42t t . For how many seconds will the height of the rock be at least 28 feet above the ground?

(A) 0.5

(B) 1.5

(C) 2.5

(D) 3.0

(E) 3.5

55. log log5 2

125 2� �

56. In the fi gure 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 x( ) = − +12

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(B) g x x( ) = − − +12

2 32( )

(C) g x x( ) = − − −12

2 32( )

(D) g x x( ) = − + +12

2 32( )

(E) g x x( ) = − + −12

2 32( )

57. The polynomial p x x x( ) = + −3 2 11 has a real zero between which two consecutive integers?

(A) 0 and 1

(B) 1 and 2

(C) 2 and 3

(D) 3 and 4

(E) 4 and 5

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58. Which of the following could be the graph of

y ax bx c= + +2 , where b ac2 4 0− = ?

(A) (B)

(C) (D)

(E)

59. Consider each function below. Is the domain of the function the set of all real numbers?

Function Yes No

f x xx

( ) =+– 1

22

g x xx

( ) =+2

1

h x xx

( ) =+2 3

60. The sum of the fi rst n terms of an arithmetic sequence a a a an1 2 3, , , ,… is 1

2 1n a an+( ) , where a1 and an are the fi rst and the nth terms of the sequence, respectively. What is the sum of the odd integers from 1 to 99, inclusive?

(A) 2,400

(B) 2,450

(C) 2,475

(D) 2,500

(E) 2,550

61. The function f is defi ned for all real numbers x by f x ax bx c( ) ,= + +2 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 0t II. f t f( ) ( )< −2 III. f t f( ) ( )> 1

(A) I only

(B) II only

(C) I and III only

(D) II and III only

(E) I, II, and III

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x h x( )

−3 5

−2 −4

2 c

62. The table above shows some values of the function h , which is defi ned 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 ann=∑ =1

10

50, what is the value of 4 31

10

ann

+( )=∑ ?

(A) 53

(B) 80

(C) 203

(D) 223

(E) 230

64. If z i= − +1 and z denotes the complex conjugate of z , which of the following points in the complex plane above represents z z+ ?

(A) A

(B) B

(C) C

(D) D

(E) E

65. What is the remainder when the polynomial 9 7 2 123 12 5x x x− − + is divided by x +1 ?

(A) −19(B) −13(C) −7(D) 1

(E) 11

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66. f x x

g x x

( )

( )

= +

= −

1

2

Functions f and g are defi ned as shown above. What is the domain of the function f g+ ?

(A) x ≥ 0(B) x ≥1(C) x ≥ 2(D) − ≤ ≤1 2x(E) − ≤ ≤2 1x

67. In the xy-plane, the line given by which of the following is perpendicular to the line 5 2 7x y− = ?

(A) 2 5 7x y+ =(B) 2 5 7x y− =(C) 5 2 7x y+ =(D) 5 2 10x y− =(E) 5 5 10x y− =

68. Which of the following statements about the polynomial p x x x( ) ( ) ( )= − +4 42 2 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) I only

(B) II only

(C) III only

(D) I and III only

(E) I, II, and III

69. C x xR x x x( )( )

= += −1200 10001200 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 profi t function P is equal to R C− . Which of the following defi nes the function P ?

(A) P x x x( ) = − +2 200 1200(B) P x x x( ) = + −2 200 1200(C) P x x x( ) = − + −2 200 1200(D) P x x x( ) = − + −2 2200 1200(E) P x x x( ) = − + +2 2200 1200

70. Which of the following is equivalent to 366

4

?

(A) 6 64

(B) 64

(C) 6(D) 6

(E) 1

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Answer Key

Study ResourcesMost 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 fi nd suggestions for exam preparation in Chapter IV of the Offi cial Study Guide. In addition, many collegefaculty post their course materials on their schools’ websites.

36. D 37. C 38. B 39. C 40. E 41. A 42. D 43. B 44. D 45. 3 46. E 47. C 48. E 49. A 50. D 51. D 52. C 53. D 54. C 55. 1 56. D 57. B 58. B 59. See below 60. D 61. C 62. E 63. E 64. B 65. B 66. D 67. A 68. D 69. C70. E

59.

Function Yes No

f x xx

( ) =+– 1

22 √√

g x xx

( ) =+2

1 √

h x xx

( ) =+2 3

√

1. E 2. D 3. D 4. D 5. B 6. A 7. A 8. B 9. E 10. A 11. D 12. C 13. D 14. D 15. B 16. E 17. C 18. E 19. D 20. D 21. 2 22. B 23. A 24. E 25. C 26. C 27. 624 28. E 29. 4 30. C 31. D 32. A 33. – 6 34. E 35. 1

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Test Measurement Overview

Format

There are multiple forms of the computer-based test,each containing a predetermined set of scoredquestions. The examinations are not adaptive. Theremay be some overlap between different forms of atest: any of the forms may have a few questions,many questions, or no questions in common. Someoverlap may be necessary for statistical reasons.

In the computer-based test, not all questionscontribute to the candidate’s score. Some of thequestions presented to the candidate are beingpretested for use in future editions of the test andwill not count toward his or her score.

Scoring Information

CLEP examinations are scored without a penalty forincorrect guessing. The candidate’s raw score issimply the number of questions answered correctly.However, this raw score is not reported; the rawscores are translated into a scaled score by a processthat adjusts for differences in the difficulty of thequestions on the various forms of the test.

Scaled Scores

The scaled scores are reported on a scale of 20–80.Because the different forms of the tests are notalways exactly equal in difficulty, raw-to-scaleconversions may in some cases differ from form toform. The easier a form is, the higher the raw scorerequired to attain a given scaled score. Table 1indicates the relationship between number correct(raw) score and scaled score across all forms.

The Recommended Credit-GrantingScore

Table 1 also indicates a recommendedcredit-granting score, which represents theperformance of students earning a grade of C in thecorresponding course. The recommended B-levelscore represents B-level performance in equivalentcourse work. These scores were established as theresult of a Standard-Setting study, the most recenthaving been conducted in 2005. The recommended

credit-granting scores are based upon the judgmentsof a panel of experts currently teaching equivalentcourses at various colleges and universities. Theseexperts evaluate each question in order to determinethe raw scores that would correspond to B and Clevels of performance. Their judgments are thenreviewed by a test development committee, which, inconsultation with test content and psychometricspecialists, makes a final determination. Thestandard-setting study is described more fully in theearlier section entitled “CLEP Credit Granting” onpage 4.

Panel members participating in the most recent studywere:

Gisela Ahlbrandt Eastern Michigan UniversityTodd Ashby Charleston Southern UniversityJurg Bolli University of New MexicoJames Brawner Armstrong Atlantic State

UniversityMichael Brook University of DelawareHarmon Brown Harding UniversityConnie Buller Metropolitan Community

College — ElkhornCJ Frederick Oklahoma State University —

Oklahoma CityJoe Gallegos Salt Lake Community CollegeBrinn Harberts Big Bend Community CollegeLonnie Hass North Dakota State UniversityLynne Kowski Raritan Valley Community

CollegeCatherine Louchart Northern Arizona UniversityMary Martin Middle Tennessee State

UniversityJohn Thurber Eastern Oregon UniversityDan VanPeursem University of South DakotaJane Zegestowsky Manor College

To establish the exact correspondences between rawand scaled scores, a scaled score of 50 is assigned tothe raw score that corresponds to the recommendedcredit-granting score for C-level performance. Thena high (but in some cases, possibly less than perfect)raw score will be selected and assigned a scaledscore of 80. These two points — 50 and 80 —determine a linear raw-to-scale conversion forthe test.

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Table 1: College AlgebraInterpretive Score Data

American Council on Education (ACE) Recommended Number of Semester Hours of Credit: 3

Course Grade Scaled Score Number Correct80 5079 4978 4877 4876 4775 4674 4573 4472 4371 42-4370 4269 4168 4067 3966 3865 3764 36-37

B 63 3662 3561 3460 3359 3258 31-3257 3156 3055 2954 2853 2752 2651 26

C 50* 2549 2448 2347 2246 2145 2144 2043 1942 1841 1740 1739 1638 1537 1436 13-1435 1334 1233 1132 10-1131 1030 929 828 7-827 726 625 524 4-523 422 321 220 0-2

*Credit-granting score recommended by ACE.Note: The number-correct scores for each scaled score on different forms may vary depending on form diffi culty.

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Validity

Validity is a characteristic of a particular use of thetest scores of a group of examinees. If the scores areused to make inferences about the examinees’knowledge of a particular subject, the validity of thescores for that purpose is the extent to which thoseinferences can be trusted to be accurate.

One type of evidence for the validity of test scores iscalled content-related evidence of validity. It isusually based upon the judgments of a set of expertswho evaluate the extent to which the content of thetest is appropriate for the inferences to be madeabout the examinees’ knowledge. The committeethat developed the CLEP examination in CollegeAlgebra selected the content of the test to reflect thecontent of the general College Algebra curriculumand courses at most colleges, as determined by acurriculum survey. Since colleges differ somewhat inthe content of the courses they offer, facultymembers should, and are urged to, review thecontent outline and the sample questions to ensurethat the test covers core content appropriate to thecourses at their college.

Another type of evidence for test-score validity iscalled criterion-related evidence of validity. Itconsists of statistical evidence that examinees whoscore high on the test also do well on other measuresof the knowledge or skills the test is being used tomeasure. Criterion-related evidence for the validityof CLEP scores can be obtained by studiescomparing students’ CLEP scores to the grades theyreceived in corresponding classes, or other measuresof achievement or ability. At a college’s request,CLEP and the College Board conduct these studies,called Admitted Class Evaluation Service, or ACES,for individual colleges that meet certain criteria.Please contact CLEP for more information.

Reliability

The reliability of the test scores of a group ofexaminees is commonly described by two statistics:the reliability coefficient and the standard error ofmeasurement (SEM). The reliability coefficient isthe correlation between the scores those examineesget (or would get) on two independent replicationsof the measurement process. The reliabilitycoefficient is intended to indicate thestability/consistency of the candidates’ test scores,and is often expressed as a number ranging from.00 to 1.00. A value of .00 indicates total lack ofstability, while a value of 1.00 indicates perfectstability. The reliability coefficient can be interpretedas the correlation between the scores examineeswould earn on two forms of the test that had noquestions in common.

Statisticians use an internal-consistency measure tocalculate the reliability coefficients for the CLEPexam. This involves looking at the statisticalrelationships among responses to individualmultiple-choice questions to estimate the reliabilityof the total test score. The formula used is known asKuder-Richardson 20, or KR-20, which is equivalentto a more general formula called coefficient alpha.The SEM is an index of the extent to which students’obtained scores tend to vary from their true scores.1

It is expressed in score units of the test. Intervalsextending one standard error above and below thetrue score for a test-taker will include 68 percent ofthe test-taker’s obtained scores. Similarly, intervalsextending two standard errors above and below thetrue score will include 95 percent of the test-taker’sobtained scores. The standard error of measurementis inversely related to the reliability coefficient. Ifthe reliability of the test were 1.00 (if it perfectlymeasured the candidate’s knowledge), the standarderror of measurement would be zero.

Scores on the computer-based CLEP examination inCollege Algebra are estimated to have a reliability of0.90. The standard error of measurement is 3.74scaled-score points.1 True score is a hypothetical concept indicating what an individual’s score on a test

would be if there were no errors introduced by the measuring process. It is thoughtof as the hypothetical average of an infinite number of obtained scores for atest-taker with the effect of practice removed.

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College Algebra CLEP pdf