College Mathematics CLEP pdf

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Test InformationGuide:College-LevelExaminationProgram®

2011-12

College Mathematics

© 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 COLLEGEMATHEMATICS

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.

Frank Bauerle,Chair

University of California —Santa Cruz

Tuncay Aktosun University of Texas atArlington

Helen Burn Highline CommunityCollege, Seattle

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 CollegeMathematics course or curriculum, the validity of thecontent for a specific course or curriculum is bestdetermined locally through careful review andcomparison of test content, with instructional contentcovered in a particular 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 Mathematics

Description of the Examination The College Mathematics examination covers material generally taught in a college course for nonmathematics majors and majors in fi elds not requiring knowledge of advanced mathematics.

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.

The examination places little emphasis on arithmetic calculations, and it does not contain any questions that require the use of a calculator. However, an online scientifi c calculator (nongraphing) is available to candidates during the examination as part of the testing software.

It is assumed that candidates are familiar with currently taught mathematics vocabulary, symbols and notation.

Knowledge and Skills RequiredQuestions on the College Mathematics 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 ofthe examination)

The subject matter of the College Mathematics examination is drawn from the following topics. The percentages next to the main topics indicate the approximate percentage of exam questions on that topic.10% Sets

Union and intersectionSubsets, disjoint sets, equivalent setsVenn diagramsCartesian product

10% LogicTruth tablesConjunctions, disjunctions, implications

and negationsConditional statementsNecessary and suffi cient conditionsConverse, inverse and contrapositiveHypotheses, conclusions and

counterexamples20% Real Number System

Prime and composite numbersOdd and even numbersFactors and divisibilityRational and irrational numbersAbsolute value and orderOpen and closed intervals

20% Functions and Their GraphsProperties and graphs of functionsDomain and rangeComposition of functions and inverse

functionsSimple transformations of functions:

translations, refl ections, symmetry 25% Probability and Statistics

Counting problems, including permutations and combinations

Computation of probabilities of simple and compound events

Simple conditional probabilityMean, median, mode and range Concept of standard deviationData interpretation and representation: tables,

bar graphs, line graphs, circle graphs, pie charts, scatterplots, histograms

15% Additional Topics from Algebra and GeometryComplex numbersLogarithms and exponentsApplications from algebra and geometryPerimeter and area of plane fi guresProperties of triangles, circles and rectanglesThe Pythagorean theoremParallel and perpendicular linesAlgebraic equations, systems of linear

equations and inequalitiesFundamental Theorem of Algebra,

Remainder Theorem, Factor Theorem

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C O L L E G E M A T H E M A T I C S

4. m is an odd integer. For each of the following numbers, indicate whether the number is odd or even.

Number Odd Even 2m – 1 2m + 1 m2 – m m2 + m + 1

Click on your choices.

3. Triangle DEF (not shown) is similar to �ABC shown, and the length of side DE is 6 cm. If the area of �ABC is 5 square centimeters, what is the area of �DEF ?

(A) 10 cm2

(B) 12 cm2

(C) 18 cm2

(D) 45 cm2

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 four 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.

Some questions refer to a table in which statements appear in the fi rst column. For each statement, select the correct properties by check-marking the appropriate cell(s) in the table.

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3 4 0x − ≥

10. Which of the following subsets of the real numbers best describes the solution set of the inequality above?

(A) 0 43

,⎡⎣⎢

⎞⎠⎟

(B) 43

, ∞⎡⎣⎢

⎞⎠⎟

(C) −∞ ∞( ),

(D) −∞ −( ]∪ ∞[ ), ,4 3

11.

12.

13.

8. x is the standard deviation of the set of numbers a b c d e{ }, , , , . For each of the following sets,

indicate which sets must have a standard deviation equal to x .

Must Have Standard Deviation Equal to xSet


a b c d e

2 2 2 2 2

⎧⎨⎩

⎫⎬⎭

, , , ,

a b c d e{ + + + + + }2 2 2 2 2, , , ,

a b c d e{ − − − − − }2 2 2 2 2, , , ,

2 2 2 2 2a b c d e, , , ,{ }

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14. On an exam for a class with 32 students, the mean score was 67.2 points. The instructor rescored the exam by adding 8 points to the exam score for every student. What is the mean of the scores on the rescored exam?

15. In the truth table below, T and F are used to indicate that statements are true and false, respectively. In the fourth column, click on each box for which the statement is true. (Note: p means not p)

p q p p q

T T FT F FF T TF F T


16.

17. The faces of a fair cube are numbered 1 through 6; the probability of rolling any number from 1 through 6 is equally likely. If the cube is rolled twice, what is the probability that an even number will appear on the top face in the fi rst roll or that the number 1 will appear on the top face in the second roll?

18.

19. A scientist estimated the number of bacteria in a sample every hour and recorded the estimates in the table above. Then the scientist used the data to create the scatterplot above. Based on the information, which of the following equations best models the number of bacteria, f t( ), at time t, in hours?

(A) f t t( ) = ( )100 2(B) f t t( ) = +100 2(C) f t t t( ) = + +2 220 100(D) f t t( ) = +( )120 1log

20. Which of the following integers is a prime number?

(A) 104(B) 105(C) 109(D) 111

21.

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22. In country I when a house is sold to a fi rst-time buyer, a purchase tax is paid based on the tax rate table above. Last week Liam, a fi rst-time buyer, purchased a house for $275,000. How much purchase tax did he pay?

(A) $8,250

(B) $11,000

(C) $12,375

(D) $13,750

23. m 4 and n 2

For each of the following expressions, indicate whether the value will be a rational or irrational number.

Expression Rational Irrational

m n3

m3

mn

3

m n2


24.

25. The graph above shows the closing price of one share of stock of Company Y for each of the fi ve business days last week. Which of the following is closest to the percent change in the closing price of one share of stock from Tuesday to Wednesday?

(A) 40%

(B) 55%

(C) 67%

(D) 150%

26. Let A be a nonempty set and let B and C be any two subsets of A. Which of the following statements must be true?

(A) B C A∪ =(B) B C∩ ={ }, the empty set

(C) B C A⊆ ⊆(D) B C A∪ ⊆

27. The area of a rectangular fi eld is the product of its length and width. If each dimension of a certain fi eld is multiplied by 3, then the area of the new fi eld is how many times the area of the original fi eld?

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30.

31.

32. The results of a survey of 200 college students showed that some students who were business majors were women and all students who were business majors took calculus. Which of the following is a valid conclusion from the survey?

(A) All students who were women took calculus.

(B) Some students who were women took calculus.

(C) Some students who were women did not take calculus.

(D) Some students who were women were not business majors.

33.

34.

35.

28.

29.

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36.

37.

38.

39.

40.

41.

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42.

,where a, b, and c are distinct numbers.

43.

44. Each number in data set A is increased by 3 to form data set B. Which of the following is the same for sets A and B ?

(A) Mean

(B) Median

(C) Mode

(D) Range

45.

46. In a group of 33 students, 15 students are enrolled in a mathematics course, 10 are enrolled in a physics course, and 5 are enrolled in both a mathematics course and a physics course. How many students in the group are not enrolled in either a mathematics course or a physics course?

(A) 3

(B) 8

(C) 13

(D) 20

50. If x – 3 is a factor of x4 – 3x3 + kx + 3, what is the value of k ?

(A) –1

(B) 0

(C) 13

(D) 1

51. Which of the following is NOT a subset of the set 2 4 6 8, , , ?{ }

(A) The empty set

(B) 2{ }(C) 2 8,{ }(D) 2 4 6, ,{ }{ }

47.

48.

49.

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52. If f xx

( ) = 12

, where x 2, and g x x( ) = 2 for

all values of x, then f g 0( )( ) is(A) 1

(B) 12

(C) 0

(D) undefi ned

53. The six students, P, Q, R, S, T, and U in a class took four exams, and the scores for the four exams were recorded in the following graphs. In which graph do the scores shown have the least standard deviation?

(A) Exam 1

70

80

90

100

P Q R S T UStudents

Scor

e

(B) Exam 2

70

80

90

100

P Q R S T UStudents

Scor

e

(C) Exam 3

70

80

90

100

P Q R S T UStudents

Scor

e

(D) Exam 4

70

80

90

100

P Q R S T UStudents

Scor

e

54. For all nonzero numbers, if f x xx

( ) =+

2

2

11

and g xx

( ) = 12 , then g f x( )( ) =

(A)x

x

2 2

2 2

1

1

+( )( )

(B)x

x

2 2

2 2

1

1

( )+( )

(C)xx

4

4

11

+

(D)xx

4

4

11+

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56. A rectangular fl at-screen computer monitor has a diagonal that measures 20 inches. The ratio of the length of the screen to the width of the screen is 4 to 3. What is the perimeter of the screen, in inches?

(A) 48

(B) 56

(C) 64

(D) 192

57. Which of the following is an equation of the line in the xy-plane that passes through the point 2 1,−( ) and that is parallel to the line with

equation 2 3 5x y− = ?

(A) y x= − −2 32

(B) y x= − +32

2

(C) y x= −23

73

(D) y x= −23

1

55. Which of the following best represents the graph

of the function f xx x

x( ) = <2 1

1 for

2 for

in the xy-plane?

(A)

(B)

(C)

(D)

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58. In triangle ABC shown above, what is the length of line segment AB ?

(A) 17 3(B) 16

(C) 14

(D) 2 34

59. A circular pizza with a 16-inch diameter is cut into 12 equal slices. What is the area, in square inches, of each slice?

(A) 163π

(B) 83π

(C) 43π

(D) 23π

60. A square tablecloth lies fl at on top of a circular table with area π square feet. If the four corners of the tablecloth just touch the edge of the circular table, what is the area of the tablecloth, in square feet?

square feet

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Answer Key

Study ResourcesMost textbooks used in college-level mathematics 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 Mathematics exam, it is advisable to study one or more introductory college-level mathematics textbooks, which can be found in most college bookstores. Elementary algebra textbooks also cover many of the topics on the College Mathematics exam. 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 math resources. You can also fi nd suggestions for exam preparation in Chapter IV of the Offi cial Study Guide. In addition, many college faculty post their course materials on their schools’ websites.

1. B 2. A 3. D 4. to the right 5. C 6. B 7. A 8. to the right 9. C 10. B 11. C 12. B 13. C 14. 75.2 15. to the right 16. C 17. B 18. B 19. A 20. C 21. C 22. B 23. to the right 24. C 25. C 26. D 27. 9 28. D 29. D 30. A

31. C 32. B 33. –5 34. C 35. A 36. D 37. D 38. 4 39. B 40. D 41. C 42. C 43. B 44. D 45. C 46. C 47. C 48. A 49. D 50. A 51. D 52. A 53. A 54. A 55. D 56. B 57. C 58. C 59. A 60. 2

Number Odd Even2m – 12m + 1m2 – mm2 + m + 1

Must Have Standard Deviation Equal to xSet

a b c d e{ + + + + + }2 2 2 2 2, , , ,

a b c d e{ − − − − − }2 2 2 2 2, , , ,

2 2 2 2 2a b c d e, , , ,{ }a b c d e

2 2 2 2 2

⎧⎨⎩

⎫⎬⎭

, , , ,

8.

15. p q ~ p ∼ p ∧ q T T F T F F F T T F F T

23. Expression Rational Irrational

m n3 √

m3 √

mn

3 √

m n2 √

4.

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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 2006. The recommendedcredit-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 determine

the 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 this study were:

Jeffrey Baumgartner Hesston CollegeEd Harri Whatcom Community CollegeRonda Sanders University of South Carolina —

ColumbiaAdriana Aceves University of New MexicoKate Acks Maui Community CollegeTuncay Aktosun University of Texas at ArlingtonMichael Hall Arkansas State UniversityDavid Hamrick Boston UniversityJonathan Kalk Kauai Community CollegeKathleen Kane Community College of

Allegheny CountyJames Lapp Truckee Meadows Community

CollegeKeith Leatham Brigham Young UniversityKaren Longhart Flathead Valley Community

CollegeIoana Mihaila California State Polytech

University — PomonaStephanie Ogden University of Tennessee —

KnoxvilleErick Hofacker University of Wisconsin

River FallsBenjamin Kennedy Rutgers UniversityNasser Dastrange Buena Vista UniversityDennis Reissig Suffolk County Community

CollegeThomas Smotzer Youngstown State UniversityLola Swint North Central Missouri CollegeRobert Talbert Franklin 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 MathematicsInterpretive Score Data

American Council on Education (ACE) Recommended Number of Semester Hours of Credit: 6

Course Grade Scaled Score Number Correct80 5079 4978 -77 4876 4775 4674 4673 4572 4471 4370 4369 4268 4167 4066 39-4065 3964 3863 37

B 62 3661 35-3660 3559 3458 3357 3256 31-3255 3154 3053 2952 2851 27-28

C 50* 26-2749 2648 2547 2446 23-2445 22-2344 2243 2142 2041 19-2040 18-1939 1838 1737 1636 15-1635 1534 1433 1332 12-1331 1230 1129 1028 1027 926 825 724 723 622 521 520 0-4

*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 CollegeMathematics selected the content of the test toreflect the content of the general CollegeMathematics curriculum and courses at mostcolleges, as determined by a curriculum survey.Since colleges differ somewhat in the content of thecourses they offer, faculty members should, and areurged to, review the content outline and the samplequestions to ensure that the test covers core contentappropriate to the courses 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. If thereliability 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 examinationin College Mathematics are estimated to have areliability of 0.90. The standard error ofmeasurement is 3.69 scaled-score points.1

True score is a hypothetical concept indicating what an individual’s score on atest would be if there were no errors introduced by the measuring process. It isthought of as the hypothetical average of an infinite number of obtained scoresfor a test-taker with the effect of practice removed.

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