COMPASS Preparation
Pre-Algebra
Welcome to the online COMPASS preparation module!
My name is Molly Craker and I am an Academic Services Instructor. I have been with CVTC since 2004 and have worked extensively with students, just like you, to help them prepare for the COMPASS exam. Everything that you need to review for the Pre-Algebra portion of the COMPASS exam is available on this site. Work your way through the site and visit as often as necessary. If you feel that you would benefit from more help in preparing for the COMPASS, please visit your local CVTC Academic Services. To find the Academic Services closest to you or for additional information please call 715-833-6400.
*The COMPASS test is an entrance exam used by Chippewa Valley Technical College (CVTC) to help place you in general education courses.
*All students who enter CVTC must take the test.
*The COMPASS test is a computerized test that you schedule to take at your convenience.
*COMPASS is an adaptive placement test which means that the test administers questions based on your answers. COMPASS operates at your comfort level rather than your frustration level, by tailoring the items to your skill level, the test will challenge but not discourage.This means that the number of questions and the time to take the test varies for every student.
*You must finish at least 8 questions so we can determine the classes that you need.
*You are allowed a calculator on both portions of the math test.
*All mathematics items are multiple choice.
*Once you answer a problem you cannot go back to it.
Basic operations with integers, fractions, and decimals
Ratios and proportions
Conversions between fractions and decimals
Absolute values of numbers
Exponents, square roots, and scientific notation
Percentages
Multiples and factors of integers
Averages
Step 1: Get a common denominator. (This means the bottom numbers of both fractions needs to be the same.) To get a common denominator you can use the Least Common Denominator method or simply multiply each fraction by the denominator of the other. Feel free to watch the video for a more in depth explanation.
Step 3: Add/Subtract top numbers—bottom stays the same
Step 4: Reduce. This means to divide the top and bottom by the same number so that the fraction is in its lowest form.
This video explains how to obtain a common denominator.
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Step 1: Make sure numbers are in fractional form and not mixed numbers. Convert if necessary. A mixed number is a whole number and a fraction together like 1½. To convert a mixed number to a fraction multiply the whole number times the bottom number and then add the top value. The bottom of the fraction will remain the same. 1½ = 3/2
Step 3: Multiply tops and multiply bottoms.
Step 4: Simplify by reducing the numbers and converting your answer back to a mixed number.
This video explains how to multiply fractions.
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Step 1: Make sure numbers are in fractional form and not mixed numbers. Convert if necessary.
Step 2: Change the sign to multiply and flip the second fraction over.
Step 3: Multiply tops and multiply bottoms.
Step 4: Simplify.
This video demonstrates the division of fraction.
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Step 1: Write vertically and line decimals up in a straight line.
Step 2: Fill in any empty places with zeros.
Step 3: Either Add or Subtract
2.05
+ 7.90
9.95
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Step 1: Multiply like normal. Feel free to write vertically if it is more comfortable for you.
Step 2: Count the number of places (from right to left) to where the decimal is located in both the numbers you multiplied.
Step 3: Move the decimal the same number of places in your answer.
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Division ( 2 types of problems)
Identify if the decimal is in the first, second or both numbers.
*If the decimal is in the first number only follow the instructions below.
Step 1: Write the division problem in customary form.
Step 2: Move the decimal straight up above the division bar.
Step 3: Ignore the decimal and divide like normal.
*If the decimal is located in the second number only or if it is in both numbers follow the instructions below.
Step 1: Write the division problem in customary form.
Step 2: Move the decimal on the outside to the right until it is a whole number.
Step 3: Move the decimal on the inside the same number of places.
Step 4: Move the decimal straight up above the division bar.
Step 5: Ignore the decimal and divide like normal.
This video shows how to divide with decimals.
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To change a fraction to a decimal, divide the numerator (top of fraction) by the denominator (bottom of fraction).
Feel free to use a calculator to assist you with the division.
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A ratio is a comparison between two similiar things. It can be written several ways such as ⅜ , 3:8, or 3 to 8. Express each ratio as a fraction with the same units in the numerator and the denominator. Then reduce the ratio to its lowest terms.
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A proportion is a comparison between 2 ratios. Solve each equation by cross multiplying.
If 3 oranges cost $5, what would 7 oranges cost?
3 / $5 = 7 / ?
7 x 5 = 35 / 3 = $11.67
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To solve a percentage problem, set up a proportion as described above.
Is (Part) = %
Of (Whole) 100
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Very large and very small numbers may be abbreviated by writing them in scientific notation.
Step 1 : Move the decimal to a position immediately following the first digit in the number.
Step 2: Count the number of places you have moved the decimal and write that number as the exponent of 10.
Step 3: If the decimal was moved to the left, the exponent is positive. If the decimal was moved to the right, the exponent is negative.
280 = 2.8 x 102
0.0012 = 1.2 x 10-3
If it is written in scientific notation convert it to decimal notation, if it is written in decimal notation convert it to scientific notation.
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Step 1: Add all numbers together.
Step 2: Divide your answer by the number of values in the data set.
12 + 19 + 22 = 53 / 3 = 17.67
Note: Average is the same as mean.
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Absolute Value means that they want the value of the number but do not care what direction from zero the number is located. It is Indicated by 2 vertical lines l l.
I-2I = 2
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The base is the larger number and the smaller, raised number is the exponent or power.
You need to multiply the base times itself for as many times as the exponent indicates.
3 2 means 3 x 3
45 means 4 x 4 x 4 x 4 x 4
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The √ symbol asks for a value when "squared" or multiplied by itself equals the value beside the symbol.
√9 is 3 because 32= 3 x 3 =9
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Integers are positive and negative whole numbers.
1. If the signs are the same, add and your answer will have the same sign.
2. If signs are different, subtract and your answer will have the sign of the larger value.
- 9 + - 5 = - 14
-12 + 8 = - 4
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Leave the first numer alone, change subtract to add, and then take the opposite of the second number.
- 9 - 5 = - 9 + - 5 = -14
6 - (- 5) = 6 + 5 = 11
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1. If the signs are the same, your answer is positive.
2. If signs are different, your answer is negative.
-10 x - 8 = 80
-12 / 4 = - 3
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Below are websites where you will find more explanations and additional practice problems. I hope that you have found this module helpful and remember that if you want more help please visit your local CVTC Academic Services.
www.math.com
www.purplemath.com
www.act.org/compass/sample/math.html