PLACEMENT TEST PREPARATION GUIDE MATHEMATICS

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 this Placement Test Preparation Guide will 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

COMPASS® Mathematics Skills Placement Test The Mathematics Skills Placement Test helps determine if you have the skills to succeed in entrylevel 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 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.

Mathematics Preparation Guide 7/15/2013 2

Go to the COMPASS® Sample Test Questions at http://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 algebra sample 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. 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 COMPASS® placement test information in this preparation guide has been reproduced with permission from ACT, Inc. Mathematics Preparation Guide 7/15/2013 3

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 person’s 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

THR = RHR + .65 ( MHR − RHR ) Which of the following is closest to the THR of a 43-year-old person whose RHR is 54 beats per minute? A. B. C. D. E.

197 169 162 134 80

Content Category: Substituting Values into Algebra Exercises – Math 0910

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

=RHR

+ .65 (

−

MHR

RHR

)

( Training Heart Rate ) = ( Resting Heart Rate ) + .65 ( Maximum Heart Rate ) − ( Resting Heart Rate ) Notice that the question gives the resting heart rate (RHR) and a method to calculate the maximum heart rate (MHR): RHR = 54 MHR = 220 − Age =

220 − 43 =

177

Now use this information and the above formula to find the training heart rate (THR). THR =RHR + .65 ( MHR − RHR ) THR =54 + .65 (177 − 54 ) = THR

54 + .65 (123)

= 54 + 79.95 THR THR = 133.95 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.



Problem #3 (Algebra) When getting into shape by exercising, the subject’s maximum recommended number of heartbeats per minute (h) can be determined by subtracting the subject’s age (a) from 220 and then taking 75% of that value. This relation is expressed by which of the following formulas? A.

= h .75 ( 220 − a ) Content Category: Setting Up Equations for Given Situation – Math 0950

h B. =

.75 ( 220 ) − a

C. D.

= h .75 = h

220 − .75a 220 − 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…” “…subtracting the subject’s age (a) from 220…” “…then taking 75% of that value.”

  

Equals (=) Subtraction (220 – a) Multiplication (.75 × that value)

So “the subject’s maximum recommend number of heartbeats per minute (h) can be determined by subtracting the subject’s age (a) from 220 and then taking 75% of that value” is given by:

= h .75 ( 220 − a ) The answer is A.

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


Cuyahoga Community College Mathematics Placement Review Problem #3 (Numerical Skills/Prealgebra)

 3 2 1 1 −  +  +  is calculated and the answer is reduced to simplest terms, what is the denominator of  4 3  2 3

If 

the resulting fraction? A. B. C. D. E.

24 12 6 4 3

Content Category: Operations with Fractions – Math 0910

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 common denominator along.

3 2 − 4 3

=

3× 3 2× 4 − 4× 3 3× 4

=

9 8 − 12 12

9−8 12

=

=

1 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× 3 1× 2 + = = + 2 3 2× 3 3× 2

3 2 3+ 2 = + = 6 6 6

5 6

After doing these operations the question becomes:

 3 2 1 1  − + +  =  4 3  2 3

1 5 + 12 6

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

 3 2 1 1  − + +  =  4 3  2 3

1 5 + = 12 6

1 5× 2 + = 12 6 × 2

1 10 + = 12 12

1 + 10 = 12

11 12

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. 12 is the correct answer. Problems taken from COMPASS/ESL: Sample Test Questions – A Guide for Students and Parents Mathematics (Numerical Skills/ Pre-Algebra & Algebra), ©2004 by ACT, Inc.

Cuyahoga Community College Mathematics Preparation Guide 7/15/2013 6

Mathematics Placement Review

Problem #10 (Numerical Skills/Prealgebra) If the total cost of x apples is b cents, what is a general formula for the cost, in cents, of y apples? A. B. C. D. E.

b xy x by xy b by x bx y

Content Category: Ratios and Proportions – Math 0950

Solution: Set up a proportion to solve this question: Cost1 # of apples1

=

Cost 2 # of apples 2

b cents x apples

=

Cost y apples

Using the given information:

Now cross multiply:

( Cost )( x apples )

=

( b cents )( y apples )

Divide both sides by x apples and simplify the result:

( Cost ) ( x apples ) ( x apples )

=

Cost =

( b cents ) ( y

apples

( x apples )

)

by cents x

The answer is D. Problems taken from COMPASS/ESL: Sample Test Questions – A Guide for Students and Parents Mathematics (Numerical Skills/ Pre-Algebra & Algebra), ©2004 by ACT, Inc.



Problem #13 (Algebra) For all x ≠ − 4 , which of the following is equivalent to the expression below? x 2 + 12 x + 32 x+4 A. B. C. D. E.

x+3 x + 8 Content Category: Rational Expressions – Math 0960 x + 11 x + 16 x + 28

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: x 2 + 12 x + 32 x+4

=

( x + 4 )( x + 8) ( x + 4)

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

x 2 + 12 x + 32 x+4

=

( x + 4 ) ( x + 8) ( x + 4)

This fraction can now be simplified to give: x 2 + 12 x + 32 = x+4

x+8

The answer is B.

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


Mathematics Sample Test Questions Work out these sample questions and return this packet to an Assessment Center before taking the placement tests. (1)

(2)

(3)

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

What value of x solves the following proportion? A.

5

1 3

B.

6

3 4

C.

10

D.

11

E.

12



9 x = 6 8

1 2

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. 16 C. 21 D. 30 E. 48 Mathematics Preparation Guide 7/15/2013 9

Mathematics Sample Test Questions (4)

(5)

(6)

If x = − 3 , what is the value of

A.

−4

B.

−2

C.

2

D.

3

E.

5

x2 − 1 ? x +1

2 3

Which of the following is equivalent to A.

16ab

B.

−3a + b

C.

−3a + 7b

D.

9a + b

E.

9a + 7b

If

3a + 4b − ( −6a − 3b ) ?

2 ( x − 5) = − 11 , then x = ?

A.

−21 2

B.

−8

C.

−11 2

D.

−3

E.

−1 2 Mathematics Preparation Guide 7/15/2013 10