# ASVAB AFQT For Dummies

**Published: **10-30-2017

**Score higher on the ASVAB AFQT**

Having a stable and well-paying career in the military can change your life for the better—and this book makes it easier than ever to pass the ASVAB AFQT so you can serve your country and set your future up for success.

Inside, you’ll find all the guidance and instruction you need to practice your way through the Math Knowledge, Paragraph Comprehension, Word Knowledge, and Arithmetic Reasoning sections of the exam so nothing comes as a surprise on test day. Plus, you get a one-year subscription to the online companion, where you can take additional full-length practice tests and focus your study where you need it the most.

- Updated guidelines and tools to analyze test scores and understand how to master these critical sections of the exam
- Advice and tips for becoming more confident with vocabulary, word knowledge, and reading comprehension skills
- A review of math basics, including algebra and geometry instruction
- Four full-length practice exams with complete explanations and answers to track your progress

Your future in the military awaits! Get there faster and more confidently with *ASVAB AFQT For Dummies!*

## Articles From ASVAB AFQT For Dummies

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Cheat Sheet / Updated 02-11-2022

If you're thinking about joining the U.S. military, your Armed Forces Qualification Test (AFQT) score may well be the most important score you achieve on any military test. You need a qualifying score on the AFQT, or your plans for enlistment come to a dead end — and each branch of the military has its own minimum AFQT score requirements. Part of getting a high score on the AFQT involves brushing up on your math skills. You need to memorize key formulas and use proven test-taking strategies to maximize your chances for a high math score. The other part is making sure you have a firm grasp on English; in order to ace the language parts of the AFQT, you need a solid vocabulary and good reading comprehension skills.

View Cheat SheetArticle / Updated 01-13-2018

Anything that saves you time and brain power on the ASVAB AFQT Mathematics Knowledge subtest is useful for two reasons: first, because you're working on a limited time budget, and second, because you can't use a calculator. That's where math properties, like the commutative and associative properties, can help. The commutative and associative properties let you break the rules about adding or multiplying from left to right: The commutative property of addition says you can rearrange the numbers you're adding without changing the result. Similarly, the associative property of addition lets you decide how to group the numbers you're adding. Together, these properties let you add a string of numbers in whatever order you like. For example, you can make calculations easier by pairing up numbers whose ones digits add up to 10 before adding other numbers in the list. Because subtracting is essentially the same thing as adding a negative number, you can extend these addition properties to subtraction problems, too — just be careful to keep track of the negative signs. The following example shows how smart groupings can let you add and subtract figures faster. Notice which calculations are easier to do in your head. Similarly, the commutative and associative properties of multiplication let you multiply numbers in any order you like. Check out how switching the numbers around can make mental math easier: You can even use these multiplication properties with division, as long as you remember that division is the same thing as multiplying by a fraction:

View ArticleArticle / Updated 01-13-2018

Some problems on the ASVAB AFQT will require you to apply formulas to solve real-world problems. It's important to not only be familiar with these formulas, but also to know when and how to apply them. Practice exercise In the following practice exercise, you need to match the word problem to the appropriate formula. (You don't actually need to solve the problems—this exercise is just to test your ability to choose the right formula.) When you're finished, check the "Answers and explanations" that follow. Answers and explanations The correct answer is Choice E. The problem asks you to find the circumference of a circle, and the formula for that is where C represents circumference and r represents the circle's radius. Remember, the radius of a circle is half its diameter. The correct answer is Choice C. The formula to solve a work problem that asks you how long it will take two people together to accomplish a task is The correct answer is Choice A. Investment and loan problems can typically be solved with the interest formula, which is I = prt. I stands for interest, p represents the principal, r represents the interest rate, and t represents the amount of time you're evaluating. The correct answer is Choice B. When a problem asks you, "How many square feet … ," it's looking for an area. The formula for the area of a rectangle is A = lw, where A represents area, l represents length, and w represents width. The correct answer is Choice D. In this problem, you need to use the formula for the volume of a cube, which is V = s3, where V represents volume and s represents the length of a side.

View ArticleArticle / Updated 01-13-2018

Some problems on the ASVAB AFQT involve working with percentages, such as discount savings, pay raises, and so on. You often see these problems on the Arithmetic Reasoning subtest, and they're relatively simple to solve. Here's an example: Jamie makes $8.95 per hour. He's such a good worker that his boss gives him a 25 percent raise. How much per hour does Jamie make now? To find the dollar amount of the raise, multiply Jamie's previous salary by the decimal equivalent of 25 percent: Round this number up to $2.24, just to make Jamie smile. Now add the raise to Jamie's original salary: $8.95 + $2.24 = $11.19. Let's try another one: Katie is very excited. For only $45, she bought a set of towels that usually sells for $60. What was the percentage of her discount? Divide the new price by the original price: The new price is 75 percent of the original price, which means Katie's discount was 25 percent.

View ArticleArticle / Updated 01-13-2018

Many of the algebra and geometry questions on the ASVAB AFQT require you to plumb the depths of your memory for a specific mathematical formula. If you can't remember it, you're going to have a tough time coming up with the right answer. In the following practice exercise, you need to match each type of problem with the appropriate formula to solve it. Make sure you've connected the right pairs by checking your answers under "Answers and explanations." Practice exercise Answers and explanations The correct answer is Choice C. The quadratic equation is The correct answer is Choice D. The formula to find the area of a triangle is where A represents area, b represents the length of the base, and h represents the triangle's height. The correct answer is Choice E. The formula for slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. In this formula, x and y represent coordinate points. The correct answer is Choice A. The formula to find the area of a circle is where A represents area and r represents the circle's radius (the distance, in a straight line, from the circle's center to its outer edge). The correct answer is Choice B. The formula to find the volume of a rectangular prism is V = lwh, where V represents volume, l represents length, w represents width, and h represents height.

View ArticleArticle / Updated 01-13-2018

When you take the ASVAB AFQT, you'll encounter plenty of equations and inequalities. Fortunately, the test proctor will provide an unlimited supply of scratch paper to help you work through them. Simple errors in an equation or inequality can throw off your entire game; the following practice exercise will show you whether you need more practice in this area before the big day. Practice exercise When you're finished solving each problem in the table, check your work under "Answers and explanations." Answers and explanations The correct answer is x = 6. The correct answer is x < 3. The correct answer is y = –2.

View ArticleArticle / Updated 01-13-2018

In mathematics, just like in the military, order of operations is very important. On the ASVAB AFQT, every time you tackle a math equation, you'll need to follow the correct order of operations or you may not get the right answer. If you have trouble remembering the correct order, think of the acronym 'PEMDAS': Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Of course, PEMDAS itself may not be too easy to remember at first, so think of the phrase, "Please Excuse My Dear Aunt Sally!" Practice exercise The following table contains a series of problems. For each one, you need to determine which operations you'll do first, then which you'll do second. (You don't need to actually perform the calculations—this exercise is just about order of operations.) When you're done writing down your solutions, compare them with the ones under "Answers." Answers

View ArticleArticle / Updated 01-13-2018

Quadratic equations on the ASVAB AFQT can often be solved with the square-root method (when they're simple) or the factoring method (as long as a = 1 in the form, ax2 + bx + c = 0). But what if they're more complicated? And what if you try to use the factoring method, but you find that a doesn't equal 1, or that you can't easily find two numbers that multiply to c and add up to b? In these cases, you can rely on the quadratic formula to solve any quadratic equation. So why not just use the quadratic formula and forget about the square-root and factoring methods? Because the quadratic formula is kind of complex: The quadratic formula uses the a, b, and c from ax2 + bx + c = 0, just like the factoring method. Armed with this knowledge, you can apply your skills to a complex quadratic equation: Solve: 2x2 – 4x – 3 = 0 In this equation, a = 2, b = –4, and c = –3. Plug the known values into the quadratic formula and simplify:

View ArticleArticle / Updated 01-13-2018

If you encounter a quadratic equation on an ASVAB AFQT math subtest, don't panic: you may be able to solve it by simply putting the equation into the quadratic form and then factoring. The quadratic form is ax2 + bx + c = 0, where a, b, and c are just numbers. All quadratic equations can be expressed in this form, as in the following examples. 2x2 – 4x = 32: This equation can be expressed in the quadratic form as 2x2 + (–4x) + (–32) = 0. In this case, a = 2, b = –4, and c = –32. x2 = 36: You can express this equation as 1x2 + 0x + (–36) = 0. So a = 1, b = 0, and c = –36. 3x2 + 6x + 4 = –33: Expressed in quadratic form, this equation reads 3x2 + 6x + 37 = 0. So a = 3, b = 6, and c = 37. Ready to factor? How about trying the following equation? Solve: x2 + 5x + 6 = 0. The equation is already expressed in quadratic form here (the expression on the left is equal to zero), saving you a little time. You can use the factoring method for most quadratic equations where a = 1 and c is a positive number. The first step in factoring a quadratic equation is to draw two sets of parentheses on your scratch paper, and then place an x at the front of each, leaving some extra space after it. As with the original quadratic, the equation should equal zero: (x )(x ) = 0. The next step is to find two numbers that equal c when multiplied together and equal b when added together. In the example equation, b = 5 and c = 6, so you need to hunt for two numbers that multiply to 6 and add up to 5. For example, and 2 + 3 = 5. In this case, the two numbers you're seeking are positive 2 and positive 3. Finally, put these two numbers into your set of parentheses: (x + 2)(x + 3) = 0 Any number multiplied by zero equals zero, which means that x + 2 = 0 and/or x + 3 = 0. The solution to this quadratic equation is x = –2 and/or x = –3.

View ArticleArticle / Updated 01-13-2018

Some math questions on the ASVAB AFQT may involve simple quadratic equations. These are quadratics that consist of just one squared term and a number, and they can be solved by using the square-root rule: Remember that the exponent in a quadratic is never higher than 2 (because it would then no longer be the square of an unknown but a cube or something else). An equation that includes the variable x3 or x4 is not a quadratic. Also remember to include the plus/minus sign, which indicates that the answer is a positive or negative number. Take the following simple quadratic equation: Solve 3x2 + 4 = 31. First, isolate the variable by subtracting 4 from each side. The result is 3x2 = 27. Next, get rid of the 3 by dividing both sides of the equation by 3. The result is x2 = 9. You can now solve by using the square root rule.

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