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Algebra for Military Exams (Math Knowledge)

Arithmetic Knowledge Online Quiz
Math Knowledge Online Quiz
Mechanical Knowledge Online Quiz

Checkout our DVDs that will teach you Algebra needed for the exam.  Click picture below.

Algebra DVDs

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Basic Enlisted/Officer Enlisted Entrance Exams

Presently, both the ASVAB and CAT-ASVAB are given in about 14,000 schools and numerous METS (Military Entrance Testing Sites). About 900,000 students and many others take them.

Armed Services Vocational Aptitude Battery (ASVAB)
ASVAB began in 1968 as a joint military effort to standardize military entrance testing. The ASVAB is largely a pencil and paper type of exam with several categories or subtests. The ASVAB is still given in high school and at several MEPS nationwide.

Computerized Adaptive Testing
Armed Services Vocational Aptitude Battery (CAT-ASVAB)

CAT-ASVAB began in 1997 and is largely an automated testing system. Several of the MEPS are currently giving the CAT-ASVAB.

1. What is the difference between the ASVAB and the CAT-ASVAB?
The straightforward pencil and paper test is just that?a set list of questions that the candidate answers and then waits for military processing personnel to correct and compute. The CAT-ASVAB not only corrects the answers immediately, it is also adaptive to the candidate’s answers.

2. CAT-ASVAB: How does it work?
Students are seated in front of a computer station and terminal. The test is displayed on the screen. As the students answer the test questions, the program immediately scores and records the answers, including the subtests. When the candidates have completed the CAT-ASVAB, the AFQT (Armed Forces Qualification Test, the math and verbal sections of the ASVAB) and composite scores for all the services are already computed.

Advantage (Alleged):
The CAT-ASVAB bases the next question you answer on the ability level pattern you exhibited from the previous question’s answer. In other words, if you answer the question correctly, you are given a harder question. If you answer the question incorrectly, you are then given an easier question. This process is continued for each subtest until you have completed the entire CAT-ASVAB.


Unlike the ASVAB, the CAT-ASVAB does not allow candidates to go back and change answers.

3. Scoring
The straightforward pencil and paper test ASVAB raw score equals the total number of questions answered correctly.

The CAT-ASVAB raw scores are not equal to the total number of correct answers. The CAT-ASVAB subtest scores are computed using formulas that take into account the difficulty level of the question and the number of correct answers. Because the test is adaptive, a process called "equating" is used to compute the standard scores, AFQT, and the service composites.

Although the CAT-ASVAB is designed so that individuals with no computer experience can take the exam, it is highly recommended that a candidate practice using a computer before taking the CATASVAB. A well prepared candidate will always do better than one who is not.

Tip It is critical that you do well on either of these tests. The better your score, the more military career choices you will have. These exams are used to determine what military occupational specialties or opportunities you qualify for. They can literally limit your future in the military. This author strongly recommends that you study and practice before taking them.

Math Topics

Arithmetic Reasoning

The military exams have several sections that deal with math.  The Arithmetic Reasoning section tests your ability to apply basic math (addition, subtraction, multiplication, division) to solve problems encountered in everyday life.  You need to know how to apply math to solve these problems.

An example question would be:

A car dealership has 32 cars on their lot.  Of the 32 cars 3/8 of them are on sale with employee pricing.  How many cars are on sale?

To solve this problem you need to multiply 3/8 times 32. If you do this you will get 12.  Another way to think of it is to figure out what 1/8 of 32 is and then multiply it 3. One-eight of 32 or 32/8 is 4.  Multiply it by 3 (1/8 * 3 = 3/8) will give you 12.

Math Knowledge

Math knowledge involves the application of mathematical principles and measures the ability to use learned mathematical relationships.  The subjects include:

  • Equation Solving
  • Plane / Solid geometry
  • Exponents
  • Roots
  • Powers
  • Fractions
  • Decimals
  • Percents
  • Least common denominator
  • Greatest common factor
  • Smallest common multiple
  • Prime numbers
  • Factorials
  • Linear equations
  • Transforming verbal problems

An example problem would be:

Find x if 22x-3 = 32.

To solve this you need to know how exponents work.  You can rewrite 32 as 25. You have both side with 2 raised to some power.  Since both sides of the equation are equal to exponents need to be equal.

2x-3 = 5

x = 4

If these concepts look foreign to you, you will need to freshen up on your Algebra skills.  Check out our Intermediate and College Algebra DVDs here.  They will help out a lot.  We also can tutor you in these subjects online from the convenience of your home anywhere in the world, as long as you have internet access, microphone, and speakers.  Checkout our tutoring page and free lessons page.

Math Knowledge Practice Problems

Download the ASTB Gouge

Download the ASTB Mechanical Gouge

Practice Tests from the military

Here is a book that we recommend you buy to help study for your military exam.

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