# The Prosperous ASVAB Mathematics Knowledge Study Guide in 2023

**The Mathematics Knowledge (MK)** is a subtest of** ASVAB (Armed Services Vocational Aptitude Battery)** which indicates test takers’ abilities as well as assesses their qualification for the military occupations. This subtest is designed to gauge your knowledge of basic high school math concepts and principles.

*The number of questions you are requested to answer will depend on the type of test you take. More specifically, on the CAT (Computer-Adaptive Test) – ASVAB, you will have 16 questions to answer within 20 minutes. Whereas, on the Paper-and-Pencil ASVAB, you’ll give 24 minutes to complete 25 questions. Follow our informative blog to keep yourself updated with the most useful ASVAB Mathematics Knowledge Study Guide. *

**1. Is The ASVAB Mathematics Knowledge Test Hard To Pass?**

It is believed that the ASVAB Mathematics Knowledge section can be difficult for many people because it includes some challenging high-school concepts and principles. However, there is nothing you can’t do if you set your mind to it so let’s equip yourself with right preparation and enough practice to make it easier and more enjoyable.

>>> See Also: **Can You Use A Calculator On The ASVAB ?**

**2. What Is Covered On The ASVAB Mathematics Knowledge Test?**

Here are some mathematics topics and terms you need to be familiar with so as to achieve a high score on this subtest:

**2.1. Algebra**

**Algebra** – a branch of mathematics – represents problems or situations in the form of mathematical expressions. It refers to integer constants, variables like X, Y, Z and many mathematical operations such as addition (+) , subtraction (-), multiplication (x) and division(/). “5Y + 6” is an example of an algebraic expression in which 5 and 6 are fixed numbers and “Y” is a variable. Note that we might use simple variables using alphabets like x, y, z or complex ones like x2, x3, xn, xy, x2y, etc.

By using algebraic expressions, we are able to solve equations more easily. For instance, if you want to buy 4 new pens, with each one costing $2, you could calculate the price by addition: $2 + $2 + $2 + $2 = $8. But you also could represent the price by algebraic expression: TOTAL PRICE = 4*P, in which “P” represents the price per pen.

**2.2. Circles**

**Radius (r)**: The distance from the center of a circle or sphere to any point on its perimeter.

**Formula **

**r = radius **

**C= circumference**

**π = pi **

**Diameter (d)**: The distance straight from one point on the perimeter, across the center, meeting the perimeter on the other side.

**Circumference (C):**The perimeter of a circle.

**Formula: C= 2 x π x r**

**r = radius **

**C= circumference**

**π = pi **

**2.3. Exponents**

Exponents of a number represent how many times to multiply the number. The lower number is called the “base,” and the power to raise it to is called the “exponent.”

*For example: **6^ 2 could be called “6 to the power 2” or “6 to the second power”. Here, 6 is the base, and 2 is the exponent/ index/ power. You just multiply the base by itself exponent times to calculate as follows: 6 x 6 = 36.*

**2.4 Fraction**

Fractions representing a part of the whole are constituted by numerators and denominators. For example, a cake is divided into 5 equal pieces, so each piece of it is represented as 1/5 of the pizza. Here 1 is the numerator and 5 is the denominator.

There are three separate types of fractions:

**Proper Fractions**: Numerator is less than Denominator**Improper Fractions**: Numerator is more than Denominator**Mixed Fractions**: The combination of a natural number and fraction

**Note*

*Mixed fractions might be transformed into a fraction.**An improper fraction can be converted into a mixed fraction.**The value of a mixed fraction is always greater than 1.*

**2.5. Inequalities**

An inequality displays the unequal relationship between 2 values in an algebraic expression. Some Inequality Signs you need to know:

**“=”: “Equals” sign.****“>”: “Greater than” sign.****“<“: “Less than” sign.****“>=”: “Greater than or equal to” sign.****“<=”: “Less than or equal to” sign.**

Keep in mind that when you multiply or divide by a negative number, the inequality direction changes. In contrast, multiplying or dividing by a positive number keeps inequality direction unchanged.

Related topics >> **ASVAB ****Electronics Information Study Guide**

**3. What Basic Steps To Solve The ASVAB Mathematical Problems?**

There are multiple approaches to help you get the right solution to a problem. Here are 5 simplified steps you should go through to solve any math problems successfully, even the toughest ones and build your mathematics skills. Let’s check it out.

**3.1 Step 1: Read carefully, understand and identify the type of problems**

First and foremost, you should take time to read the problem thoroughly to ensure that you understand the problems exactly and identify what types of problems – fractions, quadratic equations and so on.

**3.2 Step 2: Draw and review the problems**

Having understood the problems, you should look for patterns or make use of graphs to solve the mathematical problems and then review your analysis to develop the optimal solving plan in the next steps.

**3.3. Step 3: Develop the plan to solve it**

In this stage, there are 5 proposed tips you need to take in order to develop the plan of solving any problem as follows:

- Figure out the formula needed to solve the problem.
- Write down your step-by-step list of the things which you need to solve the problem and also help you to stay organized
- Work on the easier problems first and solve the difficult ones later.
- Make educated guesses about the answer so that you can try and get the estimate of the answer unless you know how to answer.
- Check your plan carefully to ensure that you haven’t left out any numbers or other factors.

**3.4. Step 4: Solve the problem**

Right after your plan to solve the problem are ready, you will start to solve the problem according to the note below:

- Ensure that all of the solving steps have been followed and completed properly.
- Cross-check each of your answers to make sure that your answers are perfect.
- If you realize in the middle that your plan isn’t working, don’t panic. You should take time to go back to the planning stage to review it and make a new plan if necessary.

**3.5. Step 5: Double check **

After you have solved the problem successfully, you should check your answer again. Don’t skip this step!

Related article >>> **ASVAB Assembling Objects Study Guide**

**4. ASVAB Mathematics Knowledge Study Guide**

We propose some useful tips to help you succeed at the math subtest of the ASVAB exam:

**4.1.Knowing the order of operations**

Note: Some priority rules for operations in algebra need to be known as follows:

- Work on all operations in parentheses first. Besides, the parentheses outward must be performed after doing operations in the innermost parentheses.

- Prioritize dealing with
**Multiplication and Division**before performing**Addition and subtraction.**

**4.2.Memorizing proper formulas**

** **When you take the actual test, you can recall the formulas that you memorized well to save your time.

**4.3. Using pencil and drafting paper**

Once you solve the problems, you should write the steps down on your draft to avoid common mistakes. Don’t try to solve the problems in your head because it can lead to unnecessary mistakes.

**4.4. Trying the answer choices**

For difficult problems that you don’t know how to solve, let’s try to substitute each answer choice back into the equation.

To sum up**, **you will almost equip yourself with the best **ASVAB Mathematics Knowledge Study Guide **and may get your desired result if you follow our study guide. Start to take our **ASVAB Mathematics Knowledge Practice Test** in order to ace the ASVAB.