precalc clep pdf

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Test InformationGuide:College-LevelExaminationProgram®

2011-12

Precalculus

© 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 PRECALCULUS

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.

Karen Bolinger,Chair

Clarion University

Donald Campbell Middle TennesseeState University

Lisa Townsley University of Georgia

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 Precalculus courseor 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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Precalculus

Description of the ExaminationThe Precalculus examination assesses student mastery of skills and concepts required for success in a fi rst-semester calculus course. A large portion of the exam is devoted to testing a student’s understanding of functions and their properties. Many of the questions test a student’s knowledge of specifi c properties of the following types of functions: linear, quadratic, absolute value, square root, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric and piecewise-defi ned. Questions on the exam will present these types of functions symbolically, graphically, verbally or in tabular form. A solid understanding of these types of functions is at the core of all precalculus courses, and it is a prerequisite for enrolling in calculus and other college-level mathematics courses.

The examination contains approximately 48 questions, in two sections, to be answered in 90 minutes. Any time candidates spend on tutorials and providing personal information is in addition to the actual testing time.

• Section 1: 25 questions, 50 minutes.The use of an online graphing calculator (non-CAS) is allowed for this section. Only some of the questions will require the use of the calculator.

• Section 2: 23 questions, 40 minutes.No calculator is allowed for this section.

Although most of the questions on the exam are multiple-choice, there are some questions that require students to enter a numerical answer.

Graphing CalculatorA graphing calculator, which is integrated into the exam software, is available to students only during Section 1 of the exam. Students are expected to know how and when to make use of it. The graphing calculator, together with a brief tutorial, is available to students as a free download for a 30-day trial period. Students are expected to become familiar with its functionality prior to taking the exam.

For more information about downloading the practice version of the graphing calculator, please visit the Precalculus exam description on the CLEP website, www.collegeboard.org/clep.

In order to answer some of the questions in Section 1 of the exam, students may be required to use the online graphing calculator in the following ways:

• Perform calculations (e.g., exponents, roots, trigonometric values, logarithms).

• Graph functions and analyze the graphs.

• Find zeros of functions.

• Find points of intersection of graphs of functions.

• Find minima/maxima of functions.

• Find numerical solutions to equations.

• Generate a table of values for a function.

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P R E C A L C U L U S

Knowledge and Skills RequiredQuestions on the examination require candidates to demonstrate the following abilities.

• Recalling factual knowledge and/or performing routine mathematical manipulation.

• Solving problems that demonstrate comprehension of mathematical ideas and/or concepts.

• Solving nonroutine problems or problems that require insight, ingenuity or higher mental processes.

The subject matter of the Precalculus examination is drawn from the following topics. The percentages next to the topics indicate the approximate percentage of exam questions on that topic.

20% Algebraic Expressions, Equations and Inequalities

Ability to perform operations on algebraic expressions

Ability to solve equations and inequalities, including linear, quadratic, absolute value, polynomial, rational, radical, exponential, logarithmic and trigonometric

Ability to solve systems of equations, including linear and nonlinear

15% Functions: Concept, Properties and Operations

Ability to demonstrate an understanding of the concept of a function, the general properties of functions (e.g., domain, range), function notation, and to perform symbolic operations with functions (e.g., evaluation, inverse functions)

30% Representations of Functions: Symbolic, Graphical and Tabular

Ability to recognize and perform operations and transformations on functions presented symbolically, graphically or in tabular form

Ability to demonstrate an understanding of basic properties of functions and to recognize elementary functions (linear, quadratic, absolute value, square root, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric and piecewise-defi ned functions) that are presented symbolically, graphically or in tabular form

10% Analytic Geometry Ability to demonstrate an understanding of

the analytic geometry of lines, circles, parabolas, ellipses and hyperbolas

15% Trigonometry and its Applications* Ability to demonstrate an understanding of

the basic trigonometric functions and their inverses and to apply the basic trigonometric ratios and identities (in right triangles and on the unit circle)

Ability to apply trigonometry in various problem-solving contexts

10% Functions as Models Ability to interpret and construct functions

as models and to translate ideas among symbolic, graphical, tabular and verbal representations of functions

* Note that trigonometry permeates most of the major topics and accounts for more than 15 percent of the exam. The actual proportion of exam questions that requires knowledge of either right triangle trigonometry or the properties of the trigonometric functions is approximately 30–40 percent.

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Notes and Reference InformationThe following information will be available for reference during the exam.

(1) Figures that accompany questions are intended to provide information useful in answering the questions. All fi gures lie in a plane unless otherwise indicated. The fi gures are drawn as accurately as possible EXCEPT when it is stated in a specifi c question that the fi gure is not drawn to scale. Straight lines and smooth curves may appear slightly jagged on the screen.

(2) Unless otherwise specifi ed, all angles are measured in radians, and all numbers used are real numbers. For some questions in this test, you may have to decide whether the calculator should be in radian mode or degree mode.

(3) Unless otherwise specifi ed, the domain of any function f is assumed to be the set of all real numbers for which is a real number. The range of f is assumed to be the set of all real numbers where is in the domain of f.

(4) In this test, denotes the common logarithm of (that is, the logarithm to the base 10) and

denotes the natural logarithm of (that is, the logarithm to the base e).

(5) The inverse of a trigonometric function f may be indicated using the inverse function notation 1 or with the prefi x “arc” (e.g., 1 ).

(6) The range of 1 is p2 2

p

The range of 1 is 0 p

The range of 1 is p p2 2

(7) Law of Sines:

Law of Cosines: 2 2 2 2

(8) Sum and Difference Formulas:

a b a b a b

a b a b a b

a b a b a b

a b a b a b

Sample Test QuestionsThe 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.

Section 1Directions: A graphing calculator will be available for the questions in this section. Some questions will require you to select from among fi ve choices. For these questions, select the BEST of the choices given. If the exact numerical value of your answeris not one of the choices, select the choice that best approximates this value. Some questions will require you to enter a numerical answer in the box provided.

1. The fi gure above shows the complete graphs of the functions f and g. Based on the graphs, the equation 0 has how many roots?

(A) One

(B) Two

(C) Four

(D) Five

(E) Seven

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x g x( ) –2 – 4 –1 0 0 2 1 2 2 4

2. The graph of the function f and a table of values for the function g are shown above. What is the value of 0

(A) – 4

(B) – 2

(C) 0

(D) 2

(E) 4

3. The domain of the function f is 1 5 If 2

what is the domain of the function g ?

(A) 10 2

(B) 5 1

(C) 2 10

(D) 1 5

(E) 1 5

4. 2

(A) 1

(B) 1 2

(C) 1 2

(D) 2 2

(E) 2 22

1

5. The functions f and g are defi ned above. What are all values of for which

(A) 0 1(B) 0 2(C) 0 1(D) 0 2(E) 1 2

6. If π θ π2≤ ≤ and cos � cos 1, what is the value of ? Round your answer to the nearest hundredth.

2

7. The function h is defi ned above. Which of the following are true about the graph of

I. The graph has a vertical asymptote at 0 II. The graph has a horizontal asymptote at

0

III. The graph has a minimum point.

(A) None

(B) I and II only

(C) I and III only

(D) II and III only

(E) I, II, and III

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8. An antenna that is 90 feet high is on top of a hill. From a point at the base of the hill, the angles of elevation to the top and bottom of the antenna are 28.5° and 25°, respectively. To the nearest whole number of feet, how high is the hill?

(A) 189 ft

(B) 213 ft

(C) 548 ft

(D) 623 ft

(E) 697 ft

9. Let g be the function defi ned by 10 20 30 The maximum

value of g is attained at which of the following values of x ?

(A) p2

(B) p10

(C) p20

(D) p30

(E) p40

10. In the xy-plane, the equation of line is y x6 3. What is the measure, in degrees, of the acute angle formed between and the x-axis?

(A) 26.6°

(B) 60.0°

(C) 63.4°

(D) 71.6°

(E) 80.5°

11. The fi gure above shows the graph of 0 5 2 5 0 5 10 54 3 2

where k is a constant. Which of the following could be the value of k ?

(A) – 18

(B) – 16

(C) – 9

(D) 9

(E) 16

12. Let f be the function defi ned by The graph of the function g in the xy-plane is obtained by fi rst translating the graph of f horizontally 3 units to the left and then vertically translating this result 2 units up. What is the value of 2

(A) – 7

(B) – 3

(C) 0

(D) 1

(E) 3

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13. In the fi gure above, line passes through the origin and intersects the graph of 2 at the point 0 4 What is the slope of line

(A) 0.200

(B) 0.303

(C) 0.528

(D) 1.322

(E) 3.305

14. In the xy-plane, the graph of 2 is symmetric about the line 3 and passes through the point 5 2 What is the value of c ?

0 001 where k is a constant.

15. When a certain radioactive element decays, the amount, in milligrams, that remains after t years can be approximated by the function A above. Approximately how many years would it take for an initial amount of 800 milligrams of this element to decay to 400 milligrams?

(A) 173

(B) 347

(C) 693

(D) 1,386

(E) 2,772

3 0

0

16. What is the range of the function f defi ned above?

(A) All real numbers greater than or equalto – 3

(B) All real numbers greater than or equalto 0

(C) All real numbers greater than or equal to – 3 and less than or equal to 0

(D) All real numbers greater than or equal to – 3 and less than or equal to 3

(E) All real numbers

64 465

0 10p

17. The function h above gives the height above the ground, in feet, of a passenger on a Ferris wheel t minutes after the ride begins. During one revolution of the Ferris wheel, for how many minutes is the passenger at least 100 feet above the ground? Round your answer to the nearest hundredth of a minute.

18. How many different values of x satisfy the equation sin sin ?x x x+ ( ) =2 2

(A) One

(B) Two

(C) Three

(D) Five

(E) Infi nitely many

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19. A ball is dropped from an initial height of d feet above the fl oor and repeatedly bounces off the fl oor. Each time the ball hits the fl oor,

it rebounds to a maximum height that is 34

of

the height from which it previously fell.The function h models the maximum height, in feet, to which the ball rebounds on the nth bounce. Which of the following is an expression for h n( ) ?

(A) h n dn

( ) = ( )34

(B) h n dn

( ) = ( )34

(C) h n d n( ) = 34

(D) h n dn

( ) =34

(E) h n nd

( ) =34

20. In the xy-plane, the vertex of the parabola x y y= + +2 4 1 is the point h k, .( ) What is the value of k ?

(A) −13(B) −5(C) −2(D) 2

(E) 5

21. The measure of a certain angle is 25°. What is the corresponding radian measure of the angle?

(A) 536π

(B) 518π

(C) 59π

(D) 185π

(E) 365π

22. A rectangular box with a square base is open at the top and has a volume of 12 cubic feet. Each side of the base has a length of x feet. Which of the following expresses the surface area, S, in square feet, of the outside of the box in terms of x ?

(A) S x= 5 2

(B) Sx

= 122

(C) S x x= +2 24

(D) S x x= +2 48

(E) S xx

= +22

48

23. Let the functions f and g be defi ned by

f x x x( ) = − 1 and g x x( ) = . Which of the

following is not in the domain of the composite function g f x�( )( ) ?

(A) −1

(B) − 12

(C) 12

(D) 1

(E) 2

x 0 1 2 3p(x) 11 10 11 14

24. The table above shows selected values for the function p. If p is a quadratic polynomial, what is the value of p 10( ) ?

12


25. If log25

b x T= and b > 12 , then x =

(A) 2 5bT

( )

(B) 2 5bT

(C) 2 5b T

(D) 2 5b T( )

(E) 2

5b T( )

Section 2Directions: A calculator will not be available for the questions in this section. Some questions will require you to select from among fi ve choices. For these questions, select the BEST of the choices given. Some questions will require you to enter a numerical answer in the box provided.

26. If 5 5 5 what is the value of x ?

(A) 5 5

(B) 5 5

(C) 5(D) 10

(E) 30

27. If f x x2 1 and g x x3 1, then f g x

(A) 5x

(B) x 2

(C) 6 1x

(D) 6 2x

(E) 6 12x x

28. The graph in the xy-plane of which of the following equations is a parabola?

(A) 2 1

(B) 2 2 3 1

(C) 2 24 1

(D) 2 2 6 1

(E) 2 2 2

29. An experiment designed to measure the growth of bacteria began at 2:00 p.m. and ended at 8:00 p.m. on the same day. The number of bacteria is given by the function N, where 1000 32 3� and t represents the number of hours that have elapsed since the experiment began. How many more bacteria were there at the end of the experiment than at the beginning of the experiment?

30. The equation of the line shown in the graph above is Which of the following is always true for this line?

(A) 0(B) 0(C) 0(D)

(E)

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31. What is the x-intercept of the graph of 18

83 2

(A) 16

(B) 8

(C) 1

16(D) 16

(E) 512

32. The function h is given by h x xlog .22 2

For what positive value of x does h x 3 ?

(A) 1

(B) 2

(C) 8

(D) 6

(E) 7

33. Which of the following relations defi ne y as a function of x ?

I. 2 23 4 II.

x 0 1 2 3 4y 10 20 30 20 10

III.

(A) II only(B) III only(C) I and II(D) I and III(E) II and III

34. In the xy-plane, the lines with equations 2 2 1 and 4 4 intersect at the point with coordinates What is the value of b ?

35. Which of the following is the graph in the xy-plane of 3 2 p

36. The function f is given by f x x x 10 . Which of the following defi nes f x for all x 10 ?

(A) f x 10

(B) f x 10

(C) f x x10 2

(D) f x x10 2

(E) f x x10 2

14


5 a10 3215 b

37. The table above shows some values for the function f. If f is a linear function, what is the value of

(A) 32

(B) 42

(C) 48

(D) 64

(E) It cannot be determined from the information given.

38. The fi gure above shows the graph of a polynomial function g. Which of the following could defi ne

(A) 3 4

(B) 3 4

(C) 3 4

(D) 4 24

(E) 4 24

39. If a and b are numbers such that 2 1

and 1 4 what is the value of 2

40. If 02

q p and 10 q what is q

in terms of

(A) 100 2

(B) 10

1002

(C) 100

10

2

(D) 2 10010

(E) 100 2

15


41. Based on past sales, a convenience store has observed a linear relationship between the number of units of Product X that will be sold to customers each week and the price per unit. The fi gure above models this linear relationship. Based on the model, how many dollars would the convenience store expect to earn from its sales of Product X in a week when the price per unit is $5 ?

(A) $125

(B) $250

(C) $350

(D) $600

(E) $720

42. The fi gure above shows the graph of the function f defi ned by 2 4 If 1 is the inverse function of f, what is the value of 1 2

(A) 8

(B) 2

(C) 0

(D) 18

(E) 8

16


43. The Statue of Liberty is 46 meters tall and stands on a pedestal that is 47 meters above the ground. An observer is located d meters from the pedestal and is standing level with the base, as shown in the fi gure above. Which of the following best expresses the angle q in terms of d ?

(A) q47 46

(B) q93 47

(C) q47 46

(D) q93 47

(E) q93 47

44. The value of log ,1 732( ) is between what two integers?

(A) 2 and 3

(B) 3 and 4

(C) 4 and 5

(D) 17 and 18

(E) 173 and 174

45. In the xy-plane, which of the following is an equation of a vertical asymptote to the graph of y x= −( )sec ?6 π

(A) x = π6

(B) x = π4

(C) x = π3

(D) x = π2

(E) x = π

f x x xx( ) = − +

−2 5 6

2

46. The function f is defi ned above. Which of the following statements are true?

I. The graph of f in the xy-plane has two x-intercepts.

II. The graph of f in the xy-plane is the same as the graph of y x= − 3.

III. The range of f is the set of all real numbers.

(A) None

(B) II only

(C) I and III only

(D) II and III only

(E) I, II, and III

x yx y

− =

+ =

152 2

47. The point x y,( ) lies in the third quadrant of the xy-plane and satisfi es the equations above. What is the value of y ?

17


48. For all x ≠ 0, the function f is defi ned by

f x xx( ) = . What is the range of f ?

(A) −1 and 1 only

(B) All real numbers between −1 and 1, inclusive

(C) All real numbers greater than or equal to 0.

(D) All real numbers except 0

(E) All real numbers

49. Let the function f be given by f x x( ) = ( )sin . What are all values of x such that f x f x−( ) = ( ) ?

(A) 0

(B) All integer multiples of π(C) All integer multiples of

π2

(D) All real numbers

(E) There are no such values of x.

50. In the xy-plane, the graph of

y x x x x= −( ) + +( )2 22 1 intersects the

x-axis in how many different points?

(A) One

(B) Two

(C) Three

(D) Four

(E) Five

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Section 1 Section 2

Answer Key

Section 1 1. B 2. B 3. B 4. C 5. D 6. 5.28 7. D 8. C 9. E 10. E 11. C 12. D 13. B 14. 7 15. C 16. A 17. 2.14 18. D 19. A 20. C 21. A 22. D 23. C 24. 91 25. A

Study ResourcesMost textbooks used in college-level precalculus 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 Precalculus 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 precalculus 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.

26. D 27. C 28. B 29. 80000 30. A 31. D 32. D 33. E 34. –0.4 35. C 36. A 37. D 38. C 39. 2.8 40. A 41. C 42. C 43. E 44. B 45. B 46. A 47. –2 48. A 49. B 50. C

19


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 tests 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 judged to be, the higherthe raw score required to attain a given scaled score.Table 1 indicates the relationship between numbercorrect (raw score) and scaled score across all forms.

The Recommended Credit-GrantingScore

Table 1 also indicates the 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 recommendedcredit-granting scores are based upon the judgmentsof a panel of experts currently teaching equivalentcourses at various colleges and universities. These

experts 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:

Edward Anderson Northern VirginiaCommunity College

John Annulis University of Arkansasat Monticello

Rajappa Asthagiri Miami UniversityEisso Atzema University of MaineJeffrey Baumgartner Hesston CollegeMark Bollman Albion CollegeJudy Broadwin Baruch College of CUNYDonald Campbell Middle Tennessee

State UniversityBlayne Carroll Berry CollegeKeith Chavey University of Wisconsin —

River FallsRoger Contreras University of Texas —

BrownsvillePam Crawford Jacksonville UniversityRoger Day Illinois State UniversityJoseph Fiedler California State University —

BakersfieldAngela Hare Messiah CollegeEd Harri Whatcom Community CollegeAllen Hibbard Central CollegeCarl Libis University of Rhode IslandConnie Meade College of Southern IdahoDaniel Russow Arizona Western CollegeRonda Sanders University of South Carolina —

Columbia

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 function that generates a raw-to-scaleconversion for the test.

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Table 1: PrecalculusInterpretive Score Data

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

Course Grade Scaled Score Number Correct80 4479 4378 4277 4176 4175 4074 3973 3872 3771 3670 35-3669 3568 3467 3366 3265 3164 3163 3062 29

B 61 2860 2759 2758 2657 2556 2455 2354 2353 2252 2151 20

C 50* 1949 18-1948 1847 1746 1645 15-1644 1543 1442 1341 1240 11-1239 1138 1037 936 835 834 733 632 531 -30 429 328 227 -26 125 024 -23 -22 -21 -20 -

*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 Precalculus examinationselected the content of the test to reflect the contentof precalculus courses at most colleges, asdetermined by a curriculum survey. Since collegesdiffer somewhat in the content of the courses theyoffer, faculty members should, and are urged to,review the content outline and the sample questionsto ensure that the test covers core content appropriateto 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 studies comparingstudents’ CLEP scores with the grades they receivedin corresponding classes, or other measures ofachievement or ability. CLEP and the College Boardconduct these studies, called Admitted ClassEvaluation Service or ACES, for individual collegesthat meet certain criteria at the college’s request.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 errorof measurement (SEM). The reliability coefficientis the correlation between the scores thoseexaminees get (or would get) on two independentreplications of the measurement process. Thereliability coefficient 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 (see below) for a test-taker will include68 percent of that test-taker’s obtained scores.Similarly, intervals extending two standard errorsabove and below the true score will include95 percent of the test-taker’s obtained scores.The standard error of measurement is inverselyrelated to the reliability coefficient. If the reliabilityof the test were 1.00 (if it perfectly measured thecandidate’s knowledge), the standard error ofmeasurement would be zero.

Scores on the CLEP examination in Precalculus areestimated to have a reliability coefficient of 0.88. Thestandard error of measurement is 3.69 scaled-scorepoints.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 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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