Placement Test Preparation Guide

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PLACEMENT TEST

PREPARATION GUIDE

Taking Your Placement Tests

Are you prepared?

Placement testing is mandatory for all new students. Taking time to work through thisPlacement TestPreparation Guidewill help you

be ready to take your Math and English placement tests and be accurately assessed

resulting in

proper placement in courses that match your skill level and possible reduction of unnecessary coursework.


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Preparation Guide

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Placement Test Prearation

English and math assessment tests are mandatory at Cuyahoga Community College (Tri-C) and

determine the initial courses for which you may register. Taking the assessment tests seriously and

doing well on them saves you time and money because you will have fewer courses to take. Tri-Cstrongly encourages you to prepare for the assessment tests by reviewing general test taking

information and basic math and English concepts. Placement testing is mandatory for all new

students.

The COMPASS

placement tests are computer delivered and untimedthat is, you may work at your

own pace. After you complete the tests, you will get a score and placement report to help you makegood choices when you register for classes.

To prepare for the placement tests, review the General Test Taking Tips below and answer theCOMPASS

Sample Test Questions at http://www.act.org/compass/sample/index.html

General Test Taking Tips

Before the Test

Start the Night BeforeYou will be able to concentrate better on the tests if you get plenty of rest and eat properly.

Be PreparedWork through this review guide. When you take the placement tests at Tri-C, bring photo

identification, your Tri-C student number, and your glasses, if you need them.

Allow Enough Time

The COMPASS

placement tests are not timed. Give yourself sufficient time to complete the tests.Dont rush.

FocusWhen you carry extra emotional baggage -- "I've got to ace this exam" or "If I mess up, I'll never getinto my program" your performance may suffer. The most constructive approach is to focus on the

task at hand, put in as much time preparing as you can, and do your best.

RelaxThe COMPASS

placement tests are designed to help you succeed in college. Your scores help you

and Tri-C determine which courses are most appropriate for your current levels of knowledge andskills.

Placement Test Preparation


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During the Test

Read CarefullyBe sure you understand the directions for each test, and be sure to ask questions if you dont.

Read each question, passage, and problem carefully until you understand what the question is asking.

If answering an item requires several steps, be sure you consider all of them.

If you have a problem or question during the test, ask the test proctor for help. Although proctors

cannot answer specific test questions for you, they can help with other types of problems.

Answering Multiple Choice QuestionsRead the question carefully. Think of an answer before looking at the possible answers. This way the

choices given on the test won't mislead you.

Read all the answer choices. Eliminate answers you know are not correct.

On the COMPASS

placement tests, there is no guessing penalty; therefore, answer every question.

Select an answer, but don't keep changing your response. Usually your first choice is the best one,unless you misread the question.

After the Test

After you complete the COMPASStests, you will receive a copy of your scores and course

placements. Next, you will contact the Counseling Office to schedule your New Student Orientationor to meet with a counselor.

Sample Test Questions

Now, go to the COMPASSSample Test Questions at http://www.act.org/compass/sample/index.html


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Preparation Guide

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Find More Sample Questions near the bottom of the page.

Click on the Writing Skills link.

COMPASSWriting Skills Placement Test

The Writing Skills Placement Test helps determine if you are ready for entry-level college writing

courses or other courses with significant writing loads, or if you require additional writing

instruction. Depending on your Writing Skills Placement Test score, you also may need to take

the Reading Skills Placement Test to determine your English course placement.

The test item content categories include punctuation, basic grammar and usage, sentence structure,

strategy, organization, and style.

Open the Writing Skills document. Read the general test information and answer the sample items for

all three writing passages.

Check your answers with the correct answers beginning on page 24. The content categories for the

Writing Skills sample items are also listed next to the correct answers. Use the content category to

find additional review resources online or at the library.

Additional Online English Resources:Academic Writing

http://owl.english.purdue.edu/owl/section/1/2/

Grammar and General Writing

http://grammar.ccc.commnet.edu/grammar/

Please note that in the test sample passages, each section is numbered.In the computerized COMPASS

Writing Skills Placement Test, sections

are not numbered.

On the actual test

Read the section looking for errors. When you find an error, move the cursor to the section of text where the error is located. Click the left mouse button to make the alternative text options appear. Choose the best answer.

(Note that for each set of answer options, option A is always identical to the text as

it appears in the passage. As such, option A represents no change.)


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Preparation Guide

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COMPASSMathematics Skills Placement Test

The Mathematics Skills Placement Test helps determine if you have the skills to succeed in entry-level college courses or if you need additional mathematics instruction.

The Microsoft

Windows

calculator is the only one that you will be able to use on the Math Skillsplacement test at Tri-C.

To practice with the Windowscalculator, click Start, All Programs, Accessories, and

Calculator.

The calculator has two views standard and scientific. You can change the view by clicking onView and selecting the alternate version. Below is an example of the standard view.

Notice that the square root key is labeled sqrt and appears only on the standard view.

This is an example of the scientific view.


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Preparation Guide

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Go to the COMPASS



When you take the COMPASS

Mathematics Placement Test at Tri-C, you will begin with theAlgebra Placement Test.

Click on the Numerical Skills/Pre-Algebra and Algebra link. Begin on page 6 with the algebrasample questions. As you work the sample problems, notice the amount of reading.

Answer the sample questions and check your solutions with the correct answers on page 10. Next toeach correct answer, you will see the content category for that question. Use the content category to


Additional Online Math Resources:www.hippocampus.orgwww.purplemath.comwww.khanacademy.orgwww.patrickjmt.com

Depending on your answers to the algebra problems, you also may need to answer pre-algebra orcollege algebra problems.

Practice in pre-algebra begins on page 1. After answering these sample questions, check your

solutions with the correct answers on page 5 and note the content category for each question.

If you have studied college algebra and/or trigonometry, answer those sample test questions byclicking on the College Algebra, Geometry, and Trigonometry link under More Sample

Questions.

When you have completed the Placement Test Preparation, you may test at any of the Tri-C testingcenters. For additional placement testing information, contact the testing center of your choice.

Brunswick University Center BUC 214 216.987.3877

Corporate College West CCW 221 216.987.5888

Eastern Campus ESS 1108 216.987.2256

Metropolitan Campus MSS 103 216.987.4311

Western Campus WTLC GT 115 216.987.5256

Westshore Campus SHCS 130A 216.987.3887 or 216.987.3888

The COMPASSplacement test information in this preparation guide has been reproduced with permission from ACT,Inc.


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Preparation Guide

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PLACEMENT TEST

PREPARATION GUIDEENGLISH

Taking Your Placement TestsAre you prepared?

Placement testing is mandatory for all new students. Taking time to work through thisPlacementTestPreparation Guidewill help you


resulting in

proper placement in courses that match your skill level and possible reduction of unnecessary coursework.


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Preparation Guide

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Writing Skills Placement Review

COMPASSWriting Skills Placement Test

The Writing Skills Placement Test helps determine if you are ready for entry-level college writing

courses or other courses with significant writing loads, or if you require additional writinginstruction. Depending on your Writing Skills Placement Test score, you also may need to take

the Reading Skills Placement Test to determine your English course placement.

The test item content categories include punctuation, basic grammar and usage, sentence structure,strategy, organization, and style.

Open the Writing Skills document. Read the general test information and answer the sample items forall three writing passages.

Check your answers with the correct answers beginning on page 24. The content categories for the

Writing Skills sample items are also listed next to the correct answers. Use the content category tofind additional review resources online or at the library.

Additional Online English Resources:Academic Writing

http://owl.english.purdue.edu/owl/section/1/2/

Grammar and General Writing

http://grammar.ccc.commnet.edu/grammar/

Please note that in the test sample passages, each section is numbered.

In the computerized COMPASSWriting Skills Placement Test, sectionsare not numbered.

On the actual test

Read the section looking for errors. When you find an error, move the cursor to the section of text where the error is located. Click the left mouse button to make the alternative text options appear. Choose the answer that is the best.

(Note that for each set of answer options, option A is always identical

to the text as it appears in the passage. As such, option A represents no change.)


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Preparation Guide

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Writing Skills Sample Test Questions

Read the following passage. After you have read the passage, answer questions 1-24.

Grameen Bank

(1)Bangladeshs economy is based primarily on small-scale (2) enterprises

ran by self-employed men and women. (3)These small-business owners, who make a

living as shopkeepers or providers of services, (4) face a problem common to proprietors

everywhere: lack of access to credit, (5)particularly among the early start-up phase of an

enterprise. (6)Credit, which allows people to obtain the resources and equipment he needs

to make his business productive, (7)is often, frequently unavailable to those who possess

little collateral. (8)Thus, many (9)people which would benefit from credit (10)are denied access to

it.

(11)The Grameen Bank, founded in 1976 by economist Muhammad Yunis, who was a

fine soccer player in his youth, provides (12) the only unique alternative (13)via loans to

prospective business owners, whether they are given only to those who fall below a

certain level of assets. (14)Instead of putting up collateral, Grameen customers are

accountable with one another, (15)congregating in (16)small groups that meet as a week.

(17)If one member will fail to repay a loan, the entire group is unable to obtain credit

(18)in the future thus, group members have a strong incentive to succeed and support

others in the group. (19)In the last twenty years, the Grameen Bank has lent two billion

dollars, (20)and his customers have repaid 97 percent of their loans. (21)Such results have led to the

creation of similar programs.


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Item 1.A. Bangladesh's economy is based primarily on small-scale

B. Bangladesh's economy's is based primarily on small-scale

C. Bangladesh's economies' are based primarily on small-scaleD. Bangladesh's economys' is based primarily on small-scale

E. Bangladesh's economies' is based primarily on small-scale

See TEST PREP QUICK GRAMMAR GUIDE: Types of Sentences, Comma Usage

Item 2.A. enterprises ran by self-employed men and women.

B. enterprises run by self-employed men and women.C. enterprises have run by self-employed men and women.

D. enterprises was run by self-employed men and women.

E. enterprises had been run by self-employed men and women.

See TEST PREP QUICK GRAMMAR GUIDE: Types of Agreement: Tense

Item 3.A. These small-business owners, who make a living as shopkeepers or providers of services,B. These small-business owners, who make a living, as shopkeepers or providers of services

C. These small-business owners, who make a living as shopkeepers, or providers of services

D. These small-business owners who make a living as shopkeepers or providers of services,E. These small-business owners; who make a living as shopkeepers or providers of services,

See TEST PREP QUICK GRAMMAR GUIDE: Types of Sentences, Comma Usage

Item 4.

A. face a problem common to proprietors everywhere: lack of access to credit,B. face a problem common to proprietors everywhere: lack of access credit,

C. face a problem common to proprietors everywhere: lack of access from credit,

D. face a problem common to proprietors everywhere: lack of access in credit,E. face a problem common to proprietors everywhere: lack of access for credit,

Item 5.A. particularly among the early start-up phase of an enterprise.B. particularly between the early start-up phase of an enterprise.

C. particularly below the early start-up phase of an enterprise.

D. particularly during the early start-up phase of an enterprise.

E. particularly now the early start-up phase of an enterprise.


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Item 6.A. Credit, which allows people to obtain the resources and equipment he needs to make hisbusiness productive,

B. Credit, which allows people to obtain the resources and equipment they need to make

their businesses productive,C. Credit, which allows people to obtain the resources and equipment we need to make our

business productive,

D. Credit, which allows people to obtain the resources and equipment one needs to make our

business productive,E. Credit, which allows people to obtain the resources and equipment you need to make

one's business productive,

See TEST PREP QUICK GRAMMAR GUIDE: Types of Agreement: Pronoun/Antecedent

Item 7.A. is often, frequently unavailable to those who possess little collateral.

B. is often unavailable many times to those who possess little collateral.C. is often unavailable to those who possess little collateral.

D. is often unavailable frequently to those who possess little collateral.

E. is often unavailable, all the time, to those who possess little collateral.

See TEST PREP QUICK GRAMMAR GUIDE: Wordiness: Wordy (and redundant)

Item 8.A. Thus, many

B. Although, manyC. Nevertheless, many

D. Since, many

E. Anyway, many

Item 9.A. people which would benefit from creditB. people whom would benefit from credit

C. people whose would benefit from credit

D. people whos would benefit from credit

E. people who would benefit from credit

See TEST PREP QUICK GRAMMAR GUIDE: Types of Agreement: Pronoun/Antecedent

Item 10.

A. are denied access to it.B. are denying access to it.

C. deny access to it.D. denied access to it.

E. there is access denied to it.


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Item 11.A. The Grameen Bank, founded in 1976 by economist Muhammad Yunis, who was a finesoccer player in his youth, provides

B. The Grameen Bank, founded in 1976 by economist Muhammad Yunis, who visited the

University of Michigan, providesC. The Grameen Bank, founded in 1976 by economist Muhammad Yunis, who studied

economics at a highly regarded university, provides

D. The Grameen Bank, founded in 1976 by economist Muhammad Yunis, who is married andhas three children, provides

E. The Grameen Bank, founded in 1976 by economist Muhammad Yunis, who returned to

Bangladesh in 1972, provides

See TEST PREP QUICK GRAMMAR GUIDE: Wordiness: Avoid Unnecessary Information

Item 12.A. the only unique alternativeB. the sole unique alternative

C. the lone unique alternative

D. a unique alternative

E. the exclusive unique alternativeSee TEST PREP QUICK GRAMMAR GUIDE: Wordiness: Wordy (and redundant)

Item 13.A. via loans to prospective business owners, whether they are given only to those who fall

below a certain level of assets.

B. via loans to prospective business owners, which are given only to those who fall below acertain level of assets.

C. via loans to prospective business owners are given only to those who fall below a certainlevel of assets.

D. via loans to prospective business owners. Which are given only to those who fall below a

certain level of assets.E. via loans to prospective business owners, when given only to those who fall below a

certain level of assets.

Item 14.A. Instead of putting up collateral, Grameen customers are accountable with one another,

B. Instead of putting up collateral, Grameen customers are accountable in one another,

C. Instead of putting up collateral, Grameen customers are accountable one another,D. Instead of putting up collateral, Grameen customers are accountable at one another,

E. Instead of putting up collateral, Grameen customers are accountable to one another,

Item 15.A. congregating in

B. and congregation inC. congregate in

D. so congregating in

E. congregating between


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Item 16.A. small groups that meet as a week.B. small groups that meet every weekly.

C. small weekly groups that meet.

D. small groups that meet weekly.E. small groups weekly each meet.

Item 17.A. If one member will fail to repay a loan, the entire group is unable to obtain credit

B. If one member fails to repay a loan, the entire group is unable to obtain credit

C. If one member do fail to repay a loan, the entire group is unable to obtain credit

D. If one member is fail to repay a loan, the entire group is unable to obtain creditE. If one member failing to repay a loan, the entire group is unable to obtain credit

Item 18.A. in the future thus, group members have a strong incentive to succeed and support

B. in the future and thus, group members have a strong incentive to succeed and support

C. in the future, thus, group members have a strong incentive to succeed and support

D. in the future, and, thus, group members have a strong incentive to succeed and supportE. in the future; thus, group members have a strong incentive to succeed and support

Item 19.A. others in the group. In the last twenty years, the Grameen Bank has lent two billion

dollars,

B. others in the group. In the last twenty years, the Grameen Bank has lended two billiondollars,

C. others in the group. In the last twenty years, the Grameen Bank lend two billion dollars,D. others in the group. In the last twenty years, the Grameen Bank did lent two billion

dollars,

E. others in the group. In the last twenty years, the Grameen Bank lends two billion dollars,

Item 20.A. and his customers have repaid 97 percent of their loans.B. and their customers have repaid 97 percent of their loans.

C. and its customers have repaid 97 percent of their loans.

D. and itselfs customers have repaid 97 percent of their loans.

E. and our customers have repaid 97 percent of their loans.

Item 21.A. Such results have led to the creation of similar programs.

B. Such results: have led to the creation of similar programs.C. Such results have led, to the creation of similar programs.

D. Such results, have led to the creation of similar programs.E. Such results; have led to the creation of similar programs.


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Item 22.Suppose the writer wants to show that lending programs similar to the one administered by theGrameen Bank have been widely accepted. Which of the following phrases, if added to the last

sentence of the essay, would best achieve that goal?

A. to make credit availableB. over the years

C. around the world

D. to encourage developmentE. with some variations

Item 23.Suppose the writer had been asked to write an essay explaining the influence of the creditsystem developed by Muhammad Yunis on the economy of the United States. Does this article

fulfill that assignment?

A. Yes, because the article explains the work of Yunis and his success since 1976.B. Yes, because the article says that there are similar credit programs in the United States.

C. Yes, because the economic influence of the Grameen Bank is felt throughout the world.

D. No, because the article says that similar credit systems have been established but does

not specifically mention the United States.E. No, because the article is concerned with the reputation of Yunis as an economist, rather

than the credit system he developed.

Item 24.Which of the following sentences, if added at the end of the first paragraph, would best make

the point that there was a need for the Grameen Bank?A. This led to a stagnant economy in Bangladesh.

B. Other people, however, are able to overcome a lack of credit.C. Collateral, therefore, is essential for a healthy economy.

D. Of course, there are some start-up businesses that do not need loans at all.

E. The banks, however, are able to lend their money in other countries.

On page nine of this handout, you will find the Test Prep Quick Grammar Guide.This guide covers

some of the major concepts in the Writing Skills Placement Test. This is not a complete list of all the

concepts, but it is useful review tool. In addition to the Test Prep Quick Grammar Guide,you canstudy the web sites listed earlier in this document.

The COMPASSplacement test information in this preparation guide has been reproduced with permission from ACT,

Inc.


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Preparation Guide

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Test Prep Quick Grammar Guide

Types of Sentences Simple Sentence (one Independent Clause)

o Brittany wrote a paper.o Cierra and Brittany wrote a paper.o Cierra and Brittany wrote a paper and then took a walk.

Complex sentence (one or more Dependent Clauses and one Independent Clause)o Although Brittany wrote a paper, Cierra did not.o Cierra wrote a paper although Brittany did not.o Jackie, who is my student, works very hard.o All of the students who take English 0980 work very hard.

Compound Sentences (two or more Independent Clauses)*o Brittany wrote a paper, and Cierra checked it over.o Brittany wrote a paper; Cierra checked it over.o Brittany wrote a paper; next, Cierra checked it over.

*Run-on Sentences occur only in compound sentences when you do not punctuate them

correctly, as above.

Comma Usage

Use a comma to separate introductory words, phrases, and clauses from the rest of the sentence.o Darn, I will not be there.o Working hard on the project, Mark will be tired most of the week.o

After he opens his account, he will send you a check.

Use a comma to set off non-essential adjective clauses. Essential adjective clauses are not set offwith commas.

o Greg Smith, who I met last night, will not be appearing on center stage.o The man who I met last night will not be appearing on center stage.

Use commas to separate items in a series.o Roger, Billy, Matt, and Susan are in place.o Dont worry, fret, or be anxious.o Bill and Sam and Ray are gone


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Wordiness: A sentence may be grammatical, but it may contain too many words that make it

awkward or even too confusing to follow.

Wordy As far as I am concerned, the major weakness of the hair salon in question is that the owneris rude, in a matter of speaking.

Correct The major weakness of the hair salon is the rude owner.

Wordy (and redundant) Many unskilled workers who have no training in a particular job areunemployed and do not have any work.Correct Many unskilled workers are not employed.

Watch out for the following phrases which contribute to wordiness and redundancy: at this time

period, at the present time, because of the fact that, circle around, there is, there are, as far as I am

concerned, in my opinion, last but not least, more or less.

Avoid unnecessary information. Leave out phrases in a sentence which detract from the main

thought.

Incorrect: My boss, who wears a hearing aid, is a very fair person.

Correct: My boss is a fair person.

Types of Agreement

Subject /VerbIn present tense singular subjects agree with verbs plus s.Plural verbs agree with the verb

without s.

o John writes a paper.o Sally and Blake write a papero The presidents of each community work long hours.

Pronoun/AntecedentPronouns need to agree in gender and number with the nouns they are replacing.

o I need to give each person his or her book.o Please tell the members of the team that they must return their books.o Everyone left his or her book behind.o The man who lives next door is creepy.

ParallelismItems in a series must be of the same grammatical form.

o Place all the containers, dishes, and placemats in the bin.o The worked hard to remove the pollutants, rebuild the fisheries, and restock the ponds.o We will place them in mailboxes, on porches, and on cars.

TenseTenses should remain consistent unless the actions happen at different times.

o Last year I gave her my favorite dress. I was very generous.o As we go along, we see many colorful plants.o I picked her up at her house. Nowadays, I pick her up at the bus stop.


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PLACEMENT TEST

PREPARATION GUIDE

MATHEMATICS

Taking Your Placement Tests

Are you prepared?

Placement testing is mandatory for all new students. Taking time to work through thisPlacementTestPreparation Guidewill help you


resulting in

proper placement in courses that match your skill level and possible reduction of unnecessary coursework


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Preparation Guide

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COMPASSMathematics Skills Placement Test

The Mathematics Skills Placement Test helps determine if you have the skills to succeed in entry-

level college courses or if you need additional mathematics instruction.

The Microsoft

Windows

calculator is the only one that you will be able to use on the Math Skills

placement test at Tri-C.

To practice with the Windowscalculator, click Start, All Programs, Accessories, and

Calculator.

The calculator has two views standard and scientific. You can change the view by clicking on

View and selecting the alternate version. Below is an example of the standard view.

Notice that the square root key is labeled sqrt and appears only on the standard view.

This is an example of the scientific view.


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Go to the COMPASS



When you take the COMPASS

Mathematics Placement Test at Tri-C, you will begin with theAlgebra Placement Test.

Click on the Numerical Skills/Pre-Algebra and Algebra link. Begin on page 6 with the algebrasample questions. As you work the sample problems, notice the amount of reading.

Answer the sample questions and check your solutions with the correct answers on page 10. Next toeach correct answer, you will see the content category for that question. Use the content category to


Additional Online Math Resources:www.hippocampus.orgwww.purplemath.comwww.khanacademy.orgwww.patrickjmt.com

Depending on your answers to the algebra problems, you also may need to answer pre-algebra orcollege algebra problems.

Practice in pre-algebra begins on page 1. After answering these sample questions, check your

solutions with the correct answers on page 5 and note the content category for each question.

If you have studied college algebra and/or trigonometry, answer those sample test questions byclicking on the College Algebra, Geometry, and Trigonometry link under More Sample

Questions.

When you have completed the Placement Test Preparation, you may test at any of the Tri-C testingcenters. For additional placement testing information, contact the testing center of your choice.

Brunswick University Center BUC 214 216.987.3877

Corporate College West CCW 221 216.987.5888

Eastern Campus ESS 1108 216.987.2256

Metropolitan Campus MSS 103 216.987.4311

Western Campus WTLC GT 115 216.987.5256

Westshore Campus SHCS 130A 216.987.3887 or 216.987.3888

The COMPASSplacement test information in this preparation guide has been reproduced with permission from ACT,Inc.


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Preparation Guide

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Cuyahoga Community College

Mathematics Placement Review

Problem #2 (Algebra)Doctors use the term maximum heart rate (MHR)when referring to the quantity found by starting

with 220 beats per minute and subtracting 1 beat per minute for each year of a persons age. Doctorsrecommend exercise 3 or 4 times each week for at least 20 minutes with your heart rate increased

from its resting heart rate (RHR)to its training heart rate (THR), where

.65THR RHR MHR RHR

Which of the following is closest to theTHRof a 43-year-old person whoseRHRis 54 beats perminute?

A. 197

B. 169

C. 162

D. 134 Content Category: Substituting Values into Algebra Exercises Math 0910

E. 80

Solution:First make sure that you understand the formula given:

Training Heart Rate Resting Heart Rate Maximum Heart Rat

.6

e Resting He

5

.65 art Rate

THR RHR MHR RHR

Notice that the question gives the resting heart rate (RHR)and a method to calculate the maximum

heart rate (MHR):

54

220 220 43 177

RHR

MHR Age

Now use this information and the above formula to find the training heart rate (THR).

.65

54 .65 177 54

54 .65 123

54 79.95

133.95

THR RHR MHR RHR

THR

THR

THR

THR

Of the answers given, D. 134,is the closest to the calculated value of 133.95 beats per minute.

Problems taken from COMPASS/ESL: Sample Test Questions A Guide for Students and Parents

Mathematics (Numerical Skills/ Pre-Algebra & Algebra), 2004 by ACT, Inc.


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Problem #3 (Algebra)When getting into shape by exercising, the subjects maximum recommended number of heartbeatsper minute (h) can be determined by subtracting the subjects age (a) from 220 and then taking 75%

of that value. This relation is expressed by which of the following formulas?

A. .75 220h a Content Category: Setting Up Equations for Given Situation Math 0950

B. .75 220h a

C. 220 .75h a

D. .75 220h a

E. 220 .75 h a

Solution:Notice in the question that h is used for heartbeats per minute and a is used for age.Also notice the key words and phrases that mean something mathematical a symbol or an

operation:

can be determined by Equals (=)

subtracting the subjects age (a) from 220 Subtraction (220 a)

then taking 75% of that value. Multiplication (.75 that value)

So the subjects maximum recommend number of heartbeats per minute (h)can be determined by

subtracting the subjects age (a)from 220 and then taking 75% of that value is given by:

.75 220h a

The answer isA.

Problems taken from COMPASS/ESL: Sample Test Questions A Guide for Students and ParentsMathematics (Numerical Skills/ Pre-Algebra & Algebra), 2004 by ACT, Inc.


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Problem #3 (Numerical Skills/Prealgebra)

If3 2 1 1

4 3 2 3

is calculated and the answer is reduced to simplest terms, what is the denominator of

the resulting fraction?

A. 24

B. 12 Content Category: Operations with Fractions Math 0910

C. 6

D. 4

E. 3

Solution:First, recall the order of operations and work inside each set of parentheses. When adding or subtracting

fractions you must have a common denominator.

The lowest common denominator (LCD) in the first parentheses is 12 and each fraction can be written as an

equivalent fraction with 12 in the denominator. Now subtract the numerators and bring the commondenominator along.

4

4

3 2 3 2 9 8 9 8 1

4

3

3 4 3 12 12 13 2 12

Likewise, in the second parentheses, theLCDis 6 and each fraction can be written with 6 in the denominator.

Now add the numerators and bring the common denominator along.

1 1 1 1 3 2 3 2 5

2 3 2 3

3

6

2

3 62 6 6

After doing these operations the question becomes:

3 2 1 1 1 5

4 3 2 3 12 6

TheLCDof these resulting fractions is 12 and each fraction can be written with 12 in the denominator.

3 2 1 1 1 5 1 5 1 10 1 10 11

4 3 2 3 12 6 12 6 12 12 12 12

2

2

This result is already reduced to simplest form because the numerator and denominator do not contain a

common factor.

Note the question does not ask for the solution, but for the denominator. In this case B. 12is the correct

answer.




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Problem #10 (Numerical Skills/Prealgebra)If the total cost ofxapples is bcents, what is a general formula for the cost, in cents, of yapples?

A.b

xy

B.x

by

C.xy

b

D.by

x Content Category: Ratios and Proportions Math 0950

E.bx

y

Solution:Set up a proportion to solve this question:

1 2

1 2

Cost Cost

# of apples # of apples

Using the given information:

cents Cost

apples apples

b

x y

Now cross multiply:

Cost apples cents applesx b y

Divide both sides byxapples and simplify the result:

apCo sst plex

applesx

cents applesb y

applesx

Cost centsby

x

The answer isD.



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Problem #13 (Algebra)

For all 4x , which of the following is equivalent to the expression below?

2 12 32

4

x x

x

A. 3x

B. 8x Content Category: Rational Expressions Math 0960

C. 11x

D. 16x

E. 28x

Solution:

Since x cannot equal -4 the denominator will not equal zero. Therefore, the fraction is defined for all

values in its domain.

See if the numerator and/or denominator are factorable. The numerator is factorable as shown:

2 4 812 32

4 4

x xx x

x x

The fraction can now be simplified by reducing the common factor in the numerator and

denominator:

2 12 32 4

4

x x

x

x

8

4

x

x

This fraction can now be simplified to give:

2 12 328

4

x xx

x

The answer isB.



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Mathematics Sample Test Questions

Work out these sample questions and return this packet to an Assessment Center before taking the placement tests.

(1)1 2 3 4 5

?2 3 4 5 6

A.1

16

B.17

27

C.13

18

D.7

9

E.5

6

(2) What value ofxsolves the following proportion?

9

6 8

x

A. 153

B. 364

C. 1102

D. 11E. 12

(3) On a math test, 12 students earned an A. This number is exactly 25% of the total number of students in the class.How many students are in the class?

A.

15

B. 16C. 21D. 30E. 48


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MathematicsSampleTestQuestions(4) If

3x , what is the value of

2 1

1

x

x

?

A. 4

B. 2

C. 2

D.2

33

E. 5

(5) Which of the following is equivalent to 3 4 6 3a b a b ?

A. 16ab

B. 3a b

C. 3 7a b

D. 9a b

E. 9 7a b

(6) If 2 5 11x , then ?x

A.21

2

B. 8

C.11

2

D. 3

E.1

2

Placement Test Preparation Guide

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