placement test preparation guides

7/29/2019 Placement Test Preparation Guides

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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 this Placement

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.
http://www.tri-c.edu/


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July 15, 2013

When you have completed the Placement Test Preparation Guides, you may test at any of the Tri-CTesting Centers. 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


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Placement Test Preparation

English and math assessment is mandatory at Cuyahoga Community College (Tri-C) and determinesthe initial courses for which you may register. Taking the placement tests seriously and doing well on

them save you time and money because you may have fewer courses to take. Tri-C requires you to

prepare for the placement tests by reviewing general test taking information and basic math and

English concepts.

Students may use other qualifying assessments, such as ACT or SAT scores, instead of taking the

COMPASS

Mathematics Skills and Writing Skills tests. Please contact a Tri-C Testing Center for

information.

The placement tests may be referred to as assessment tests or the COMPASS

tests. The

COMPASS placement tests are computer-delivered and untimedthat is, you may work at yourown pace. After you complete the tests, you will get a score and placement report to help you make

appropriate choices when you register for classes.

To prepare for the placement tests, review the following General Test Taking Strategies and answer

the questions to check for understanding. Then work through the English and/or Mathematics Skills

Preparation Guides and answer the sample test items to prepare for those assessments.

After you complete the COMPASS

tests, you will receive a copy of your scores and course

placement options. Next, you will contact the Counseling Office to schedule your New Student

Orientation or to meet with a counselor.

General Test Taking Strategies

Many students may experience text anxiety. Some test anxiety is normal and may help students focus

during preparation and testing. Too much anxiety, however, can negatively affect performance.

Students should try to think of testing is an opportunity to show what they know. The followingtesting strategies will help you increase your chances of performing better on the placement tests.

Start the Night Before

You will be able to concentrate better on the tests if you get plenty of rest and eat properly. Beforetesting, eat something healthy to give you energy to solve complex problems and help you focus, but

avoid heavy foods that make you groggy.


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Be Prepared

Work through this preparation guide and the English and/or the Mathematics guides to help youdecide when you are as ready as possible to take the placement tests. When you test at Tri-C, bring

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

All ow Enough TimeThe COMPASS

placement tests are not timed, and individual testing times vary. We suggest that

you allow yourself at least one hour to complete each test. Dont rush.

FocusWhen you carry extra emotional baggage - "I've got to ace this exam" or "If I mess up, I'll never get

into 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 and

skills.

Read Careful ly

Be 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.

Answer ing Mul tiple Choice Questions

Read 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.

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

On the COMPASS

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

However, once you choose your final answer and click submit, you cannot go back to change your

answer.


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Placement Test Preparation Questions

Circle the letter of the correct answer to each of these questions. You will turn in these answers

to the Testing Center prior to taking the COMPASS

placement tests.

1. Students may use qualifying ACT scores instead of taking the COMPASS MathematicsSkills and Writing Skills tests.

A. TrueB. False

2. What is the time limit for the COMPASS Mathematics Skills Test?A. 30 minutesB. 60 minutesC. 45 minutesD.No time limitE. 75 minutes

3. Which of the following is not likely to help you to do your best on the placement tests?A. Eat wellB. Complete the preparation guidesC. Come in 30 minutes before closingD. Read directions carefullyE. Get plenty of rest the night before testing

4. Proctors cannot answer specific test questions for you, but they can help with other types ofproblems.

A. TrueB. False

5. On the COMPASS placement tests, there is no penalty for guessing.A. TrueB. False


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PLACEMENT TEST

PREPARATION GUIDEENGLISH


Are you prepared?

Placement testing is mandatory for all new students. Taking time to work through this Placement Test

Preparation Guidewill help you


resulting in

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


7/26

July 15, 2013

COMPASS

Writing 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. You will be tested

on punctuation, basic grammar and usage, sentence structure, strategy, organization, and style.

Depending on your Writing Skills Placement Test score, you also may need to take the Reading SkillsPlacement Test to determine your English course placement.

In this preparation guide, you will edit one sample essay. For additional practice, go to the COMPASS

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

Find More Sample Questions near the bottom of the page. Click on the Writing Skills link.

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 theWriting 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.

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

COMPASS Writing Skills Placement Test, sections are not numbered.

When you take the computerized 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.

After clicking on a passage, you can still leave the passage unchanged; simply choose no answer and go

on or A, which will always leave the section unchanged.

You may also find these online resources helpful.

Academic Writing

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

Grammar and General Writing

http://grammar.ccc.commnet.edu/grammar/
http://www.act.org/compass/sample/index.htmlhttp://www.act.org/compass/sample/index.htmlhttp://www.act.org/compass/sample/index.htmlhttp://owl.english.purdue.edu/owl/section/1/2/http://owl.english.purdue.edu/owl/section/1/2/http://grammar.ccc.commnet.edu/grammar/http://grammar.ccc.commnet.edu/grammar/http://grammar.ccc.commnet.edu/grammar/http://owl.english.purdue.edu/owl/section/1/2/http://www.act.org/compass/sample/index.html


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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 a useful tool.

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, whom I met last night, will not be appearing on center stage.o The man whom 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 grammatically correct, but it may contain too many words that make it

awkward or even too confusing to follow.

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

CorrectThe 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.

CorrectMany 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 myopinion, 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 paper.o 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 They 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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Writing Skills Sample Test Questions

Sample Essay

Read the following passage. After you have read the passage, answer items 1-24. You will turn in

these items to the testing center prior to taking the COMPASS Writing Skills Placement Test.

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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Choose the best version of the items below.

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

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

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

business productive,

B. Credit, which allows people to obtain the resources and equipment they need to maketheir businesses productive,

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

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


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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, manyB. Although, many

C. Nevertheless, manyD. 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 creditD. people whos would benefit from creditE. 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.

Item 11.

A. The Grameen Bank, founded in 1976 by economist Muhammad Yunis, who was a finesoccer player in his youth, providesB. The Grameen Bank, founded in 1976 by economist Muhammad Yunis, who visited theUniversity of Michigan, providesC. The Grameen Bank, founded in 1976 by economist Muhammad Yunis, who studied

economics at a highly regarded university, providesD. The Grameen Bank, founded in 1976 by economist Muhammad Yunis, who is married and

has three children, providesE. 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 alternative

B. the sole unique alternativeC. the lone unique alternativeD. a unique alternative

E. the exclusive unique alternative

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


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Item 13.

A. via loans to prospective business owners, whether they are given only to those who fallbelow 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 inB. and congregation in

C. congregate inD. so congregating inE. congregating between

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 creditC. 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 supportC. 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


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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 billion

dollars,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.

Item 22.Suppose the writer wants to show that lending programs similar to the one administered by the

Grameen Bank have been widely accepted. Which of the following phrases, if added to the lastsentence of the essay, would best achieve that goal?A. to make credit available

B. over the yearsC. around the world

D. to encourage development

E. 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 articlefulfill 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 doesnot 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.


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Item 24.

Which of the following sentences, if added at the end of the first paragraph, would best makethe 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.

For additional placement testing information, please contact the testing center of your choice.







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

Inc.


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July 15, 2013

PLACEMENT TEST

PREPARATION GUIDE

MATHEMATICS


Are you prepared?

Placement testing is mandatory for all new students. Taking time to work through this Placement

TestPreparation Guidewill help you


resulting in

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


18/26

July 15, 2013

COMPASS

Mathematics 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 Windows

calculator, click Start, All Programs, Accessories, and

Calculator.

The calculator has two viewsstandard 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

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

Find More Sample Questions near the bottom of the page.

When you take the COMPASS

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

Algebra 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 to

each correct answer, you will see the content category for that question. Use the content category to

find additional review resources online or at the library.

Additional Online Math Resources:www.hippocampus.org

www.purplemath.com

www.khanacademy.org

www.patrickjmt.com

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

college 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 by

clicking 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 testing

centers. For additional placement testing information, contact the testing center of your choice.







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

Inc.
http://www.act.org/compass/sample/index.htmlhttp://www.act.org/compass/sample/index.htmlhttp://www.act.org/compass/sample/index.htmlhttp://www.hippocampus.org/http://www.hippocampus.org/http://www.purplemath.com/http://www.purplemath.com/http://www.khanacademy.org/http://www.khanacademy.org/http://www.patrickjmt.com/http://www.patrickjmt.com/http://www.patrickjmt.com/http://www.khanacademy.org/http://www.purplemath.com/http://www.hippocampus.org/http://www.act.org/compass/sample/index.html


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July 15, 2013

Cuyahoga Community CollegeMathematics 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. Doctors

recommend 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 the THR of a 43-year-old person whoseRHR is 54 beats per

minute?

A. 197

B. 169

C. 162

D. 134 Content Category: Substituting Values into Algebra ExercisesMath 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 QuestionsA Guide for Students and ParentsMathematics (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 heartbeats

per 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 SituationMath 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 thesubjects age (a) from 220 Subtraction (220a)

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

.75 220h a

The answer is A.



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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. 24B. 12 Content Category: Operations with FractionsMath 0910C. 6D. 4E. 3

Solution:

First, recall the order of operations and work inside each set of parentheses. When adding or subtractingfractions 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, the LCD is 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

TheLCD of 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 acommon factor.

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



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Problem #10 (Numerical Skills/Prealgebra)If the total cost ofx apples is b cents, what is a general formula for the cost, in cents, ofy apples?

A.b

xy

B.x

by

C.xy

b

D.by

x Content Category: Ratios and ProportionsMath 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 byx apples and simplify the result:

apCo sst plex

applesx

cents applesb y

applesx

Cost centsby

x

The answer is D.

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

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


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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 ExpressionsMath 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 anddenominator:

2 12 32 4

4

x x

x

x

8

4

x

x

This fraction can now be simplified to give:

2 12 32

84

x x

xx

The answer is B.



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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 ofx solves 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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Mathematics Sample Test Questions

(4) If

3x , what is the value of

21

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

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