focus on math

7/28/2019 Focus on Math

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Entry Level Mathematics

Examination (ELM)

2009 Edition

Focus on mathEmatics


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Table of Contents

College Readiness for All at the California State University 1

The Entry Level Mathematics Placement Test at the California State University 2

CSU Admissions Requirement in Mathematics 2

The Entry Level Mathematics Requirement 3

Description of the ELM Placement Test 3

Content of the Test 4

Timing 4

Calculators Not Allowed 4

Table 1: CSU ELM Topics 5

Scores on the ELM Placement Test 6

How the ELM Placement Scores are Used 6

Questions about the ELM 7

Appendix A: CSU Mathematics Placement Test: Sample Problems

Appendix B: Sample Score Report


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CSU Focus on Mathematics 2009 Editio

Page 1

College Readiness for All at the California State University

Increasing student access to and success in the California State University (CSU) system is oneof the primary goals ofAccess to Excellence, the strategic plan adopted by the CSU Board of

Trustees in 2008. College readiness for first-time freshmen is critical if the CSU is to meet the

workforce and economic needs of the state. To ensure student success, the CSU hasimplemented a number of strategies, such as the Early Assessment Program (EAP), the Entry

Level Mathematics Test (ELM), and the English Placement Test (EPT), to properly place

students in the appropriate college courses.

The Early Assessment Program is a nationally recognized collaboration involving the State

Board of Education (SBE), the California Department of Education (CDE), and the California

State University (CSU). The California County Superintendents of Education ServicesAssociation (CCSESA) is also a collaborator in the area of professional development. The EAP

provides an opportunity for students to learn about their readiness for college-level English andmathematics in their junior year of high school, and it facilitates opportunities for them toimprove their skills during their senior year.

Those students who are admitted to the CSU and have not demonstrated proficiency in Englishor math in their senior year of high school take the English Placement Test (EPT) and the Entry

Level Math Test (ELM) as a way of ensuring they are placed in the appropriate classes upon

enrollment in the university. All campuses are committed to implementing effective practices

to guide and support first time freshman in attaining college level proficiency in mathematicsand English. The CSU hosts an English Success and a Math Success website to provide

students, parents, teachers, counselors and testing coordinators further information regarding

these requirements. The websites can be found at:http://www.csuenglishsuccess.org/eshomefor English andhttp://www.csumathsuccess.org/mshomefor math.

This brochure provides information about how students demonstrate proficiency in Mathematicsand more specifically about the Entry Level Mathematics Placement Test (ELM). Another

brochure,Focus on English, available from the CSU Chancellors Office or online athttp://www.calstate.edu/sas/documents/focusonenglish.pdf,

provides information about the

English assessment test, the English Placement Test (EPT).
http://www.csuenglishsuccess.org/eshomehttp://www.csuenglishsuccess.org/eshomehttp://www.csuenglishsuccess.org/eshomehttp://www.csumathsuccess.org/mshomehttp://www.csumathsuccess.org/mshomehttp://www.csumathsuccess.org/mshomehttp://www.calstate.edu/sas/documents/focusonenglish.pdfhttp://www.calstate.edu/sas/documents/focusonenglish.pdfhttp://www.calstate.edu/sas/documents/focusonenglish.pdfhttp://www.csumathsuccess.org/mshomehttp://www.csuenglishsuccess.org/eshome


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Page 2

The Entry Level Mathematics Placement Examination

The California State University (CSU) publishes Focus on Mathematics to ensure that high

school teachers and students are aware of entry level requirements for admission to and successin the CSU.

Students planning to enroll at one of CSUs 23 campuses will be joining more than 450,000

students and 47,000 faculty and staff in an academic enterprise requiring college-level skills inreading, writing, and computation. The CSU is committed to ensuring that those who earn

degrees from the university possess the knowledge and skills necessary to function in an

increasingly complex and technological society. This booklet describes the CSU admission

requirements in mathematics and the CSU Entry Level Mathematics (ELM) placementexamination developed to ensure that students possess entry-level skills before undertaking

baccalaureate coursework in quantitative reasoning.

CSU Admissions Requirement in Mathematics

All students in the CSU are required to take college-level courses in mathematics or quantitative

reasoning in order to graduate. It is important that all students arrive at the university with the

necessary entry-level mathematics skills. If, on entry, a student is found to need additional workin college preparatory subjects and is placed in appropriate remedial coursework, such remedialcoursework will notcount toward credit for graduation.

In order to ensure that students entering the university are ready to take courses in college levelmathematics or quantitative reasoning, freshmen must complete three years of college

preparatory coursework (Algebra I, Geometry, and Algebra II). Although not required foradmission to the CSU, a fourth year of precalculus mathematics is advisable, especially for

students planning to pursue majors in technical fields. This fourth year course is a prerequisite

to the freshman calculus courses required in most technical curricula.

Students who do not intend to major in technical fields in college may choose a course in

statistics and probability in their senior year of high school. All students are encouraged to takemathematics in theirsenior year of high school since students whose last math course wascompleted in the junior year orearlier often have difficulties with the required college-levelmathematics courses and with the EntryLevel Mathematics (ELM) requirement.


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Page 3

The Entry Level Mathematics Requirement

The Entry Level Mathematics (ELM) Examination is designed to assess and measure the level of

mathematics skills acquired through three years of rigorous college preparatory mathematicscoursework (Algebra I and II, and Geometry) of students entering the California State University

(CSU). The CSU ELM must be completed by all non-exempt entering undergraduates prior toenrollment in any course, including remedial courses. Students who score 50 or above on the

ELM will be placed in college-level mathematics classes.

Exemptions from the ELM are granted only to those who present proof of one of the following:

A score of 550 or above on the mathematics section of the College Board SAT ReasoningTest

A score of 550 or above on a College Board SAT Subject Test in Mathematics (level 1 orlevel 2)

A score of 23 or above on the American College Testing (ACT) Mathematics Test A score of 3 or above on the College Board Advanced Placement Calculus AB or

Calculus BC exam

A score of 3 or above on the College Board Advanced Placement Statistics examination Completion and transfer to CSU of a college course that satisfies the requirement in

Quantitative Reasoning, provided such a course was completed with a grade of C or better

A score of Exempt or Ready for college-level Mathematics courses on the CSUEarly Assessment Program (EAP), taken in grade 11 in conjunction with the CST in

Summative High School Mathematics or Algebra II

A score of Conditionally ready for college-level Mathematics courses or Conditionalon the CSU Early Assessment Program (EAP) taken in grade 11 along with the

California Standards Test in Summative High School Mathematics or Algebra II,

provided successful completion of a CSU-approved 12th

grade math course that require

Algebra II as a prerequisite

Description of the ELM Placement Test

The ELM placement test described in theFocus on Mathematics reflects the desire of the

CSU mathematics and mathematics education community to employ a placement test that

assesses mathematical skills needed in campus General Education (GE) programs in

quantitative reasoning and to serve the needs of entering students planning both quantitativeand non-quantitative courses of study. The placement test was developed by a committee of

CSU mathematics professors, mathematics education professors, and chairs of mathematicsdepartments. The ELM placement test described here has been used by the CSU since March

2002.


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Page 4

Content of the Test

The ELM emphasizes working with numbers and data, the connections between algebra

and geometry, and problem solving rather than on working pure algebra problems. Thetest provides the major geometric formulae for reference because its purpose is to assess

understanding of mathematical concepts and problem-solving skills rather than recall of

facts and equations. The placement test is predicated on the idea that students areresponsible for mastering the content of three years of high school mathematics. Table 1

contains a list of the topics covered by the placement test and shows the proportion of the

test devoted to each of the three major content areas: Numbers and Data, Algebra, andGeometry.

Timing

The ELM contains 50 multiple-choice questions. Students will be allotted 90 minutes to

complete the test.

Calculators Not Allowed

Test takers are not allowed to use calculators for the ELM placement test. The questions

on the ELM do not require involved computation. Rather, the placement test includesproblems that emphasize quantitative reasoning and problem solving.


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Table 1: CSU ELM Topics

NUMBERS AND DATA (approximately 35%)

Carry out basic arithmetic calculationsUnderstand and use percent in contextCompare and order rational numbers expressed as fractions and/or decimalsSolve problems involving fractions and/or decimals in contextInterpret and use ratio and proportion in contextUse estimation appropriatelyEvaluate the reasonableness of a solution to a problemEvaluate and estimate square rootsRepresent and understand data presented graphically (including pie charts, bar and line graphs, histograms,

and other formats for presenting data visually used in print and electronic media)

Calculate and understand the arithmetic meanCalculate and understand the medianMake estimates and predictions based on dataDistinguish between reasonable and unreasonable claims based on dataALGEBRA (approximately 35%)Evaluate and interpret algebraic expressionsSimplify algebraic expressionsExpress relationships among quantities using variablesUse properties of exponentsPerform polynomial arithmetic (add, subtract, multiply, divide, and factor)Perform arithmetic operations involving rational expressionsSolve linear equations (with both numerical and literal coefficients)Solve systems of linear equations in two unknownsSolve linear inequalitiesSolve problems in context that are modeled by linear equationsSolve quadratic and rational equations (with both numerical and literal coefficients; real solutions only)Solve problems in context that are modeled by quadratic equationsSolve equations involving absolute value (in one variable)Solve inequalities involving absolute value (in one variable)Find and use slopes and intercepts of linesUse constant and average rates to solve problems in context (using appropriate units)GEOMETRY (approximately 30%)

Find the perimeter, area, or volume of geometric figures (including triangles, quadrilaterals, rectangularparallelepipeds, circles, cylinders, and combinations of these figures)

Calculate the ratio of corresponding geometric measurements of similar figures (e.g., if the perimeters are ina 3:2 ratio, the areas are in a 9:4 ratio)

Use the Pythagorean TheoremUse properties of congruent or similar geometric objectsSolve geometric problems using the properties of basic geometric figures (including triangles, quadrilaterals,polygons, and circles)Determine angles in the plane (using properties of intersecting lines, parallel lines, and perpendicular lines)Identify and plot points on the number lineIdentify and plot points in the coordinate planePlot points on the graph of a function determined by an algebraic expressionGraph linear functions in one variableGraph quadratic functions in one variableRelate basic information about a function to features of its graph (e.g., linearity, positivity or negativity,

increasing or decreasing)

Find the length or midpoint of a line segment in the coordinate plane


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Page 6

Scores on the ELM Placement Test

The ELM placement test consists of 50 multiple-choice questions. The reported score willbe based on 45 of these questions. The remaining five questions are being field tested for

possible use on future tests. The ELM is scored on a scale of 0-80.All scores are reportedas even numbers on this scale. The passing scaled score is 50. The ELM is reviewedregularly, and new editions are developed several times each year. Therefore, the

questions on one edition of the test are not identical to those on another. However, steps

are taken to ensure that each edition represents the same level of difficulty. The inevitableslight differences in difficulty between one edition of the test and another are

accommodated through the statistical practice of equating the scores to the ELM scale. A

scaled score earned by taking any given ELM test administered on or after March 23,

2002, indicates the same level of proficiency as the same scaled score earned by takingany other given ELM test administered on or after that date. A scaled score earned on the

ELM placement test before the March 23, 2002, administration cannot be compared to a

scaled score earned by taking the ELM placement test on or after that date and cannot beused for placement. The score that determines proficiency on the new scale was

recommended by a panel of expert judges chosen from faculty in mathematics and related

departments throughout the CSU.

How the ELM Placement Test is Used

The ELM placement test must be taken by all nonexempt students before they can enrollin the CSU. Students receiving a total scaled score of 50 or above may enroll directly in a

baccalaureate quantitative reasoning course. Students receiving a total scaled score below

50 are typically required to take remedial coursework. Campuses have the option of

permitting students who score below 50 to take the ELM placement test again after self-study or tutorial.


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Questions About the ELM Placement Test

Q. Is this an admission test?

A.No. The ELM is a placement test designed to determine a students proficiency in

mathematics. The results of the placement test will not affect a students admission to anyCSU campus.

Q. When is the ELM placement test given?A. The ELM placement test is given periodically throughout the year. There are three

systemwide administration dates, when the placement test is given on all campuses. Inaddition to the three systemwide administrations (late March, early May, and late June),

each campus establishes several additional dates to accommodate local needs. Systemwide

and campus dates are published each year and are included in materials sent to applicants.Information about test dates and test registration can be obtained from testing offices on

CSU campuses. A full listing of campus test dates is available online at

http://www.ets.org/portal/site/ets/menuitem.1488512ecfd5b8849a77b13bc3921509/?vgnextoid=e1b72d3631df4010VgnVCM10000022f95190RCRD&vgnextchannel=353ef71898eb9110VgnVCM10000022f95190RCRD.

Q. Suppose a student has scored 550 on the math part of the SAT. Does the student

still need to take the ELM placement examination?

A.No. Anyone who scores College Ready on the EAP test; 550 or above on the

mathematics section of the College Board SAT I: Reasoning Test; 550 or above on theMathematics Level IC or IIC of the College Board SAT II: Mathematics Test; 23 or above

on the ACT Math test given October 1989 or later; or 3 or above on an AP mathematics

test (Calculus AB, Calculus BC, or Statistics) demonstrates proficiency in mathematicsand is exempt from the ELM placement test. Students also may be exempt through

transferred coursework. See pages 4 and 5 of this publication for more details.

Q. What about the CSU/UC Mathematics Diagnostic Testing Project (MDTP) tests?

Does a student who does well on these tests have to take the ELM placement test?A. Yes. The MDTP tests are diagnostic tests while the ELM examination is a placement

examination. However, the MDTP tests are rigorous, and a student who scores well on theMDTP Intermediate Algebra examination should do well on the ELM placement test.

Q. What should students do who are uncertain whether they are required to take the

ELM placement test?

A. Admissions Office or Test Office staff at the campus the student plans to attend will be

able to answer questions about testing requirements and procedures.

Q. May students use calculators during the ELM placement test?A.No. Calculators are not allowed for the ELM placement test. The questions on the ELM

do not require involved computation. Rather, the placement test includes problems thatemphasize quantitative reasoning and problem solving.
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Page 8

Q. Why is math being tested?

A. With science and technology playing an increasingly important role in our society, all

college-bound students must have an adequate grasp of mathematics. More and more

undergraduate majors require some proficiency in math, and many require either statisticsor calculus or both. These majors include agricultural science and management, business

administration, economics, engineering, environmental sciences, medical physics, nursing,

physical sciences, psychology, and pre-medical/pre-dental programs. Those students inless quantitative majors will also find themselves called upon in their professions and their

personal lives to use effective quantitative reasoning and should, as college graduates,

demonstrate a capacity to do so.

Q. How does this placement test relate to the graduation requirements of a campus?

A. Basic mathematics provides the necessary background for the CSU general educationquantitative reasoning requirement which consists of a course at the level of college

algebra or higher. Such a course is required for graduation from the California State

University. Successful completion of the ELM requirement is prerequisite to that course.

Q. How should a student prepare for the placement test?A. Studies have shown that students who do not continue to use the math they have learned

may have difficulty recalling simple principles. Students with fewer than three years ofcollege preparatory mathematics (who are not regularly admissible to the CSU) or those who

have not used their math knowledge in some time will probably need additional work and

review. An algebra review text or learning assistance center may be helpful in preparing forthe placement test. The CSU makes available a variety of ELM preparation materials at the

CSU Math Success website found athttp://www.csumathsuccess.org/exam_prep. Included

there are in-depth tutorials for which a student can register and receive personalized support

for a very minimal fee.

Q. Should a student who has completed at least three years of math in high school be

ready for college-level math?

A. Yes. But students who have not had recent practice using their math skills will still

benefit from a review. All students are encouraged to take mathematics in their senior year

of high school.

Q. What happens if a student does not demonstrate proficiency on the ELM?

A. The CSU requires students who do not demonstrate proficiency on the ELM placementtest to be placed in appropriate remedial or developmental programs/activities during the

first term of enrollment and each subsequent term until they demonstrate competence. The

placement test is designed to help CSU campuses offer students the help they may need. Alow score on the ELM means that a student probably needs extra help in order to do wellin general education courses that require entry-level mathematics skills. Students who do

not achieve a score of 50 or higher on the ELM may contact the Testing Office on the

Campus of their choice to find out if retaking the examination is a possibility.
http://www.csumathsuccess.org/exam_prephttp://www.csumathsuccess.org/exam_prephttp://www.csumathsuccess.org/exam_prephttp://www.csumathsuccess.org/exam_prep


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Page 9

Q. Do students who receive a low score have to pay for extra help?

A. In most cases, the cost of a remedial mathematics course is included in the mandatoryfees the student pays for enrollment at the university. In other cases, programs offered

through continuing education may have a separate cost. Each campus offers different

services for students who need help in basic mathematics. For example, some campusesoffer pre-baccalaureate courses in the mathematics department while others have

established remedial education courses in the continuing education program. Some

campuses offer tutorial programs using graduate students and peer tutors. Some campuseshave modularized programs, structured to parallel topics covered by the ELM placement

test; others use programmed instruction, especially using interactive computers. Some

campuses use modules that review specific topics that may be taken as directed study toprepare for courses in quantitative reasoning. A few campuses offer review courses for

ELM preparation in continuing education courses. Finally, many campuses have well-

developed learning assistance centers that are able to assist students.

Q. What happens if a student is out of the country on the first test date available?A. Such a student should take the placement test at the next opportunity. It is to a students

advantage to take the placement test as soon as possible. All students must take theplacement test before enrollment will be permitted.

Q. Does a student have to take the test at the campus the student plans to attend?

A.No. A student may take the test at any CSU campus. The resulting score will be sent to

the appropriate campus.

Q. How do students receive their placement test scores?

A. Test scores are mailed to the address provided by the student on the day of the test.

Students are also asked on the day of the test to establish a PIN which will allow them toretrieve their scores on line.

Q. How long are ELM testing materials and scores retained by ETS?

A. ETS retains answer sheets and test books for 18 months. Although answer sheets (nottest books) are available for review at the ETS office in Oakland, they may not be returned

to students. ELM scores are retained by ETS for the life of the program and are available

from 1983 to the present.


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Page 10

Appendix A

CSU Mathematics Placement Test

Sample Problems


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CALIFORNIA STATE UNIVERSITY

ENTRY LEVEL MATHEMATICS TEST

Geometry Reference Formulas

Rectangle

Area = w

Perimeter = 2 + 2

w

Triangle

Area =1

2bh

Circle

2

Area=

Circumference=2

r

r

Rectangular Solid

Volume = wh

Right Circular Cylinder

2Volume= r h

Pythagorean Theorem

c a b2 2 2

= +


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Sample ELM ProblemsFollowing are samples ofthe types ofproblems appearing on the ELM examination. Thiscollection does not include every kind ofquestion that might be asked, but the problems aretypical in the way they examine the relevant skills and competencies that are listed in Table I onpage 3. The answen appear on page 26.Directions: Solve each ofthe following problems. You may use the blank space for scratchwork.Notes: (l) Unless otherwise specified, the denominators ofalgebraic expressions appearing in

these problems are assumed to be nonzero.(2) Figures that accompany problems are drawn as accurately as possible EXCEPT whenit is stated that a figure is not drawn to scale.(3) The Geometry Reference Formulas appearing on the previous page will be printedinside the front cover oflhe ELM test book.

d (miles)

2U)150r0050

I (hours)121456l. In the gaph above, d represents the distance, in miles, that a motorist has traveled aftert hours on the road. How many hours did it take the motorist to travel 200 miles?

(A) 4.0 (B) 4.5 (c) 5.0 (D) s.5 (E) 6.0Topic Represent and understand data

z. (3x3y)(-2x2y3) =(A) 6x5ya (B) 6x6y3 (c) "r-' (D) 16y3 1E16rty'Topic Simplify algebraic expressions-


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3. A theater has 25 rows, each with 12 seats. At a certain performance there were, on average,3 empty seats p row. What was the attendance at that performance?(A)225 (B)264 (C)297 (D)300 (E)375Topic Carry od basic arithmetb calculMions-

Irl2

4. In the figure above, It is parallel to 12and y = 127. what is the value oft ?(A) 37 (B) 45 (c) s3 (D) 60 (E) 63Topic Determine angles in the plane-

I5. lfb = 6 and h = lO. then i bh =(A) 8 (B) ls (c) 16 (D) 30 (E) 60Topic Evaluale algebraic expressions-


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MONTHLYEXPENSESOFCOMPANYX

Which ofthe categories shown in the graph above accounts for approximately one-third ofCompany X's expenses?A) Insurance @) Payroll (C) Rent (D) Travel (E) TaxesTopic Represefi od understand data-

7. lf 4x - 5 = l8 - 7r, thenx =(A)-? cs)1+ (o2 @)ff @)+Topic Solve linear equttiow-

8. (2x + 1)(r +:) =(A)3x + 4 (B) 2x2 +3 (C) 2x2 +7x+3 P) 6x2 +5x+1 @) 9.r3Topic Paform polynomial mithrnaic-


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9. A certain medicine is prescribed in an amount proportional to a patient's body weight. If apatient weighing 70 kilograms requires 210 milligams ofthis medicine, then the amount ofmedicine required for a patient weighing 80 kilograms is(A) 220 mg (B) 230 mg (c) 240 mg (D) 250 mg (E) 290 mgTopic Interpret and we ratio and proportion-

J il rI III IV10. Which ofthe figures above are congruent?

(A) I and II(B) I and III(C) I and IV(D) II and III(E) II and IVTopic properties ofcongruent geomelric objects-Use

-2r r I----!!I -JT(A) -zst (B)t -6 (C)r + 6 (D) stz -6 (E) st2 +6Topic Simplify algebraic expressions-


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12. Which ofthe following is an equarion of line / in the figure above?(A)x+y=-3 (B)r = -3 (C)x = -3y (D) y =-3 (E) y = -3xTopic Graph linet ftttctions-

13. x-2 = r_1(A) + (B) Jt (c) -x' (D) ,2 (E) , 2xTopi c ---\impl fy alge broic acpress ions

14. If3x-d=c,thetx=(A)c+d-3 (B)d +! \"|- \!,P';d -c @\+ @)+ 3Topic * Solve lineff equdions

15. Onefactorof 12 + 2.r - 8 is(A)x-l (B)x-z (C)x-a @)"-6 @)r-8Topic Perform polynomial arithmetic-


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16. In the figure above, CD is parallel to lB. What is the measwe of ZACB ?(A) 25" (B) 35" (C) 60" (D) 120" (E) 125"Topic Determine angles in the plane-

17. Ifthe point (2, 4) is on the line y = 6x + D, then 6 =(A) -22 (B) -8 (C) 12 (D) 16 (E) 26Topic Pbt Wints on the graph of a fimction-

18. An apple falling from a tree is ll feet above the ground / seconds after it begins to fall, whereh = 64 - 16t2. After how many seconds will the apple hit the ground (l, = 0) ?(A) l (B) 2 (c) 4 (D) 8 (E) 48Topic Solve problems modeled by quadratic equations-

19. If Jx - T = 4, then.r =(A) 3 (B) e (c) 15 (D) t7 (E)25Topic Solve rational equations-


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* 3' = 6,r. r, [" ,h"r, ,, =[x=-2y+5,(A) -4 (B) -2 (c) -t (D) 2 (E) 4Topic Solve systems of linear equatiorc-

2l. The area ofsquare IACD in th figure above is 64. What is the area ofthe shadedtriaryle AED 2(A)16 (B) 24 (c) 28 (D) 30 (E) 32Topic Fird a'ea-

22. The operding budget ofthe Westem Robotics Compeny was $300 nillion last year. Iftheoperating budget this year is 12 percent less than last year, what is this year's operatingbudgeg in milliors ofdollars?(A) S36 (B) $264 (c) $274 @) $288 (E) $336Topic Use Wrcent-


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23. In the coordinate plane, which ofthe following is the midpoint of the line segnrent withendpoints (2, 5) and (6, l) ?(A)(s,6) (B)(4,3) (c)(4.4) @r(+.+) @rG,i)Topic Find mifooittt of a line segment-

WeightPlayer (in oounds)R 270s 230T 240U ?24. Ifthe average weight ofthe four players listed in the table above is 250 pounds, what is theweighl in pounds, of Player t/?

(A)220 (B)230 (c)240 (D)250 (E)260Topic Calculate the arithmetic mean-

AB01234567 8925. Which point on the number line above could represent J0 ?

(A)r (B),B (c)c (D) D @)-4Topic sqmre roots-Estimde


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^4"26, Triarrgles ABC and DEF in the figure above are similar. What is the length of EF ?(A) 4 (B) 6 (c) 8 (D) t2 @) 16Topic Use properties of similar geometric objeas-

27. The ratio ofthe number ofboys to the number of gids in an algebra class is 4 to 5. Ifthere are45 students in the class, how many are girls?(A) r 1 (B) 20 (c) 25 (D) 36 (E) 4lTopic Inlerpret and use ratio and proportion-

ENROLLMENT AT CENTRAL COLLEGE

Freshmen 1,816Sophomores 1,473Jmiors |,431Seniors28. According to the table above, which ofthe following best approximates the total enrollment

at Central College?(A) 1,800+ 1y'00+ 1,400 + 1,200(B) 1,800 + 1y'00 + 1,400 + lJ00(c) 1,800 + 1,500 + 1,400 + 1,300(D) 1,900 + 1,500 + 1,400 + 1,300(E) 1,900 + 1,500 + 1,500 + 1,300Topic -Use estimation qpropriately


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29. What is the perimeter ofthe figure above ifall intersecting line segments meet at rightangles?(A) 6r (B) 8r (c) l0r @) rrx @) r2xTopic Find perimaer

-

30. The figure above shows the graph of y = f(x). What are all values of.r for whichf(x) > o?(A)x l (C)x>2 (D)0


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32. Marshall is making com bread. His recipe calls for 3 t cups of commeal, but he wants tomake only halfthe amount given in the recipe. How many cups ofcommeal should he use?(A)1i tr)11 ,",tI ols Oll. y-x>OIII. .lry > 0

(A) I only @) II only (C) Itr only @) II and III only @) I, n, and nITopic Evahute the reasonableness ofa sohtion-

34. Which of the following numbers is between 3.74 and 3 f ?(A) 3 # (B) 3.72 (c) 3.82 (D) 3 + (E) 3 ?Topic Compare and order ratiotal nwnbers-

35. The sale price ofKathy's new coat was redwed 30% from the original price of$80. Whatwas the sale price ofthe briefcase?(A)$30 (B)$40 (c)$50 (D)$s6 (E)$104Topic percent-Use


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36. The figure above shows a right circular cylindrical vessel that is exactly oneAuarter firll. If7 liters ofliquid are added the vessel will be exactly three-fifths full. What is the totalcapacity ofthe vessel in liters?(A) 14 (B) 20 (c)zt @ + (E) 2tr'20Topic Solve problems irwolvingfrrctions-

"77"37. In right triangle ABC above, tC =

(A) s - J6 (B) JIE (c) J3T (D) 5 + J6 (E) 4Topic * Use the Pythagorean Theorem

ts.!*L=@r @h eIf (D)a2 + 6z 1ll1a2!b2Topic Perform arithmetic operations irooling rational expressions-


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39. What is the slope of the line thmugh the points (2,1) nd (4,2) 2(A)-t (B)-f tcrI corI rerzTopic Find and use slopes and futercepts of lines-

40. This yeax Jos6 eamed 3 times as much money as he eamed last year. If Jose eamed f dollarsthis year and he eamed I dollars last year, which ofthe following equations represents therelatiorship between Zand I ?(A)3r=? (B)+=r (c)rxL=3 @+=+ @)+=+Topic Express relatiottships anong qwntities-

41. Ifthe area ofthe square shown above is 36, what is the area ofthe inscribed circle?(A) 6 (B) 36 (c) 6E (D) git (E) 36/Topic Find mea-


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HISTORY TEST SCORESTest I 82Test 2 7lTest 3 93Test 4 88Test 5 86

42. Dan's scores on 5 history tts arc given in the table above. What is the median of Dan'sscorEs?(A) 82 (B) 84 (c) 86 @) 88 (E) e3Topic Calculate the medim-

43. JZ is a number between(A)0and I @) 1and2 (c)2and3 @)3anda @)4and5Topic E$imae squarc rooE-

214. A line I with slope 2 passes through the origin. Which ofthe following is a point on line I ?(A)(2,4) @)(2,2) (c)(2, 1) (D)(2,-0 (E)(2,-4)Topic Find and use slopes and tercepts oflines-


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45. In the picture above, the perimeter ofthe starfish is 30 centimeters. This original picture is tobe enlarged in both dimensiors to an irnage that is similar to the original picture. Ifthe area ofthe enlarged image is 9 times the area ofthe original picture, what is the perimeter incentimeters ofthe starfish in the enlarged image?(A) 30 (B) e0 (c) 180 (D)27o (E)2,430Topic Calculate the ralio of correspnding geometric mea\ttements of similt figu'es-

46. A stack of three cubes of the same size has a volume of 24 cubic inches. What is the lengtllin inches, of an edge ofone oftlre cubes?(A) 2 (")9 (c) 3 (D) 8 (E) 2JZTopic Find vohmte-

47. An investrnent company advertised ttnt last year its clients, on average, made agofrt of g/o.Which of the following claims can legitimaGly be made, based on that information?(A) All oftheir clients made a profit of at least 9/o last year.(B) At least one oftheir clients made a profit of at least 97o last year.(C) Sorne oftheir clients will make a profit ofat least 9olo this year.(D) All oftheir clients will make a profit ofat least 9/o this year.(E) Ifa person becomes one oftheir clients, that person will make a profit of adleasJry/o erchyear.Topic Distinguish between reasonable otd unreasotnble claims-


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WEATI{ER BALLOON TEMPERATURESHeight Temperatur1,000ft. 23o2,000ft. Z0o3,000 ft. t7o

48. A weather balloon is released ard as it rises in the air it records the temperature, in degreesCelsius, as shown in the table above. Ifthe temperatur continues to decrease at a constantrate, the tmperature at 5,500 feet will beo(A) l2.s o (B) 1lo (c) 9.5o (D) 80 (E) 6.5

Topic Use corrstart rdes-49. How many dollan will r pens cost if 5 such pens mst y dollars?

@)+


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Answer Key to Sample Problems

1.D2.A3.A4.C5.D

6.D7.D8.C9.C

10.E

11.B12.B13.A14.E15.B

16.C17.B18.B19.D20.E

21.E22.B23.B24.E25.B

26.D27.C28.C29.E30.E

31.D32.C33.B34.E35.D

36.B37.B38.E39.D40.A

41.D42.C43.E44.A45.E

46.A47.B48.C49.A50.B


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The CSU/UC Mathematics Diagnostic Testing Project

Since 1978 the California State University and the University of California have funded jointly

the development of a series of mathematics diagnostic tests. The group writing the tests includeshigh school, university, and community college faculty. Tests are available free of charge to test

skills in pre-algebra, elementary and intermediate algebra, and pre-calculus. Scoring andinterpretation services are provided by regional MDTP service sites. Scores are reported only toteachers in order to ensure that the tests are used solely for diagnosis and improvement of

classroom teaching.

More information about this program can be obtained by contacting:

Donna M. Ames

University of California, San Diego9500 Gilman Dr.-0112

La Jolla, CA 92093-0112Phone: (858) 534-4519

Fax: (858) 534-9058 (Attn: Donna Ames)Email: [email protected]

The web site ishttp://mdtp.ucsd.edu

FOR FURTHER INFORMATION

Additional questions concerning CSU admissions requirements in mathematics should be

directed to Mr. Allison Jones, Student Academic Support, 401 Golden Shore, 6 th Floor,

Long Beach, CA 90802-4210. Telephone: (562) 951-4744.
http://mdtp.ucsd.edu/http://mdtp.ucsd.edu/http://mdtp.ucsd.edu/http://mdtp.ucsd.edu/


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Appendix B: Sample Score ReportThe California State UniversityOFFICE OF THE CHANCELLOR

TEST DATE:Student Name123 North StAnywhere, CA 99999

SOC SEC NUMBER

Scores Reported to: CSU FRESNO

Enqlish Placement TestForm: XX

Total Score: 999Subscores

Essay (raw score): 9Reading Skills: 999

Composing Skills: 999

Entrv Level Mathematics TestForm: XX

Total Score: 99

SEE OTHER SIDE FOR SCORE EXPLANATIONS


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Appendix B: Sample Score ReportEnqlish Placement Test

What do my English PlacementTest (EPT) scores mean?The EPT Total Score is reported on a scale of 120-180. The CSU has determined that a Total Scoreof 151 or higher indicates that you are ready to undertake coursewok that requires college-levelwriting. However, there may be some slight variation in the way campuses use scores to establishpreparedness for college.level course work. You can find out what the campus of your choice doesby consulting the campus catalog or course schedule.Your EPT subscores may help your campus's writing faculty focus instruction where it is mostneeded. Essay subscores range from 1, the lowest score, to 6, the highest. A score of 0 means theessay did not address the assigned topic. Subscores in Reading Skills and Composing Skills arereported on the same scale (120-180) as the EPT Total Score.lf you took the EPT before January 13, 2008, essay subscores ranges were from 2, the lowest score,to 12, the highest.

Entrv Level Mathematics TestWhat do my Entry Level Mathematics (ELM) scores mean?The ELM Total Score is reported on a scale of 0-80. The CSU has determined that a Total Score of50 or higher indicates that you are ready to undertake college-level coursework in mathematics.However, there may be some slight variation in the way campuses use scores to establishpreparedness for college-level coursework. You can find out what the campus of your choice doesby consulting the campus catalog or course schedule.

For more information about EPT and ELM scores and what they mean, you can consult theEPT/ELM Inform ation B ul leti n at www.ets. org/csu.

Copyright @ 2006 by Educational Testing Service


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401 Golden Shore, 6th Floor, Long Beach, CA 90802-4210

focus on math

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