ASVAB Math Knowledge Practice Test

[00:00:20]Hey fellow problem solvers, Kfax Math here today. Got a live session. Got a practice ASVAB mathematical knowledge exam. Um here's the first problem. It's a few minutes before 2 o'clock. I couldn't make it on Wednesday at 3, so this is a makeup session. Um, I'll let a few folks join and I got your comments on this computer here. I have my laptop here where the problems are and I'll be marking here displaying right here. If you got a second, if you're here early, make sure you have paper and pencil out, doing the problems before I do them, and then watch how I do them. Um, I might have a tip or trick, a different way to solve the problem. There is no best way to solve the problem. lot of ways to solve these math problems, but they are about a minute per problem. So, it's a timed exam and they are no calculator problem. So, there's always some sort of checking to see how well you know your math knowledge.

[00:01:19]I will give it a minute more. Bring this up here.

[00:01:37]Any questions or comments? Uh, just post them right in there. I could read them pretty well. I think we're looking pretty good. Hopefully sounds good as well.

[00:02:05]If you want more resources, here's a book, uh, Math Test Success. It's on Amazon. I came up with this book after 30 years of teaching math. Um, for every chapter in this book, there's a video.

[00:02:17]So, you don't have to watch or read the book by yourself. I'll be there right alongside of you. Uh, you watch the video, have the book in front of you.

[00:02:24]But right now, what you need to make sure you have is paper and pencil out.

[00:02:28]You can't really learn these problems by watching me. You have to do them. So really, the best thing to do is to do this problem while we're waiting to get started. Paper and pencil out. Remember, no calculator exam. All right. Oh, I see. Yeah, I watched your practice videos and got 68. Great. 13 above my last one, so I'm grateful. Well, that's a fantastic comment.

[00:02:52]Oh, that's great to hear. Yeah, that I mean a lot of people haven't done these standardized math exams in so long. So some practice really helps a lot kind of acquaint you with the exam the style of problem refresh a lot of those ideas in your head. All right, I think are we at two o'clock? Just a minute or two more.

[00:03:12]Gregory, uh I won't answer that yet, but good to see the posted answer up there. Uh let's just go ahead and jump in. It's 159.

[00:03:24]Okay. So, this algebra problem kind of when you start these problems, you're thinking in your head, you're trying to get into the test maker's head. What are they testing you here? Well, they are testing you two things. One is, do you know how to reverse order of operations?

[00:03:41]And then the second is, do you have a basic understanding of algebra? So, the basic understanding of algebra says I have to get that variable x by itself.

[00:03:50]And then the second part, the reverse order of operations, order of operations is PEMDAS. But when you are solving for X, you got to do that backwards. So the first thing I'm going to do here is subtract seven from both sides, giving me 3x = 22 - 7. After I've done my subtraction in reverse order because I'm solving for x, I then do division. I divide both sides by three. These cancel, give me x by itself. 15 / 3 is five. So, answer C right there. I'm not sure if that's right. I could plug it back in. 5 * 3 is 15. 15 + 7 is 22.

[00:04:34]The other way to do this one really quickly is take the solutions and plug them in. 3 * 3 is 9. 9 + 7 is 16. That doesn't equal 22.

[00:04:45]21 + 7 doesn't equal 22.

[00:04:49]5 + 7 does. Correct answer C. All right.

[00:04:54]Good. Good, Joseph. All right. Let's move on to number two here.

[00:05:01]This one is actually very little computation. It is really only asking the single question. Do you know what that PI is? And do you know what the formula for area is?

[00:05:16]Paper and pencil in front of you. First thing I do when I read this question right here is I circle that word area.

[00:05:23]Circumference is a distance around the outside of the circle. Area is that circle colored in. What is the area of a circle with a radius of six? So the radius is equal to six, not the diameter. Leave your answer in terms of pi. Pi is a Greek letter pi. It looks like this in the Greek alphabet spelled pi. And it is a ratio of circumference to diameter. It is approximated by the decimal 3.14 or approximated by the fraction 227.

[00:06:01]But we're not going to use any of that.

[00:06:03]We just need to know the equation for area is pir squared. Again, this is also a test on order of operations. You got to do that exponent before multiplication. I take that six, plug it in there for radius.

[00:06:22]6^2 is 36 times pi. So my answer is 36 pi. Correct answer. Answer B right there.

[00:06:35]Talked a lot about circles there.

[00:06:37]Hopefully some of that stuff makes sense. Um, again, I guess there are two questions on this. One is, do you know the area for a circle? Do you know that equation pi r squ? And then the second is, do you know your order operations?

[00:06:52]You have to do that square before the multiplication.

[00:06:56]On the previous one, I had an equation and I'm isolating the x. So I'm going backwards getting everything away from the x. This one I have an expression where I'm just evaluating it. And that's why I do my order of operations exponents before multiplication.

[00:07:13]All right, questions here. Moving on to problem number three here.

[00:07:19]So before I even get started on number three, I I'll give you a minute to do it. I'm just thinking like a test um writer. What What is this? What is the key here? What are they really saying?

[00:07:32]Do you know this skill? And I'll just give you a little bit of a help. The question really is, do you know how to distribute that quantity? So, I'll give you a second to do that.

[00:08:15]All right, let's go ahead and do this one. Make sure you're doing it before me. So, I have to take that four and distribute it through the quantity. So, I got to go four * x is 4x. And then I have to do it four times everything in that quantity. 4 * -3 is -2.

[00:08:34]So I got 4x - 12. Then the second one distributing that -2 through the quantity -2x and then -2 * 5 10.

[00:08:51]I am then going to combine similar terms. I have a 4x and a -2x.

[00:08:56]This going to give me 2x -12 -102.

[00:09:03]Correct answer.

[00:09:05]Answer A right there. Good, Gregory.

[00:09:08]Good. Lucario opened. Open. Got it right. Good. I'll just say a couple more things on this.

[00:09:18]You could see that all of these answers are distractors. Like it would have been easy to get any one of these four with just a simple mistake. If you had done -12 + 10, forgotting to distribute that -2 through the quantity, you would have got that -2. So the answers usually on there that are wrong. Um they do them by doing a simple mistake. Second thing I was just going to say is if I have 4x + 2x + 5, whatever it is, that is an expression. and there is no equal sign.

[00:09:54]All I could do is simplify. The only thing I have to do there is combine similar terms. If however I put a equal sign in there, then now I have an equation and I could do whatever I want as long as I do it to both sides of that equal sign. So then I would have 6x= -5x= -56. So my point there is a difference between an expression no equal sign and an equation with an equal sign. All right, moving on to number four.

[00:10:27]Give you a second to do this one. I'm also going to just glance down at the answers here before I get started. And I notice um what's kind of funny that answers A and C are kind of similar. So there's a little bit of a giveaway right there.

[00:10:44]I'll give you a second to do this one.

[00:10:59]Oh, that's a great comment, Glitch Core Devs. Fantastic. Great to hear you're shipping out this Sunday. Good luck. We appreciate your service.

[00:11:13]All right, I'm on number four right now.

[00:11:16]First thing I'm going to do is get that x by itself by adding nine to both sides. That don't look too good. So I have x^2 = 9.

[00:11:27]Then that is saying what number times itself is equal to 9. To get rid of a square, I square root both sides and x is equal to three. But before you jump on answer a, you got to think about it.

[00:11:40]Look at all those other answers. This is saying what times itself equals 9. 3 * 3 = 9. That one works.

[00:11:51]But -3 times -3 also equals 9. So there are two answers there. Uh and that's how Jake got it right. Answer C is the correct answer because there are two ways two numbers that you could plug in for x to get nine. And a lot of times we don't remember to do that because when we go the square root of nine, it's actually equal to three org -3. But we forget to do that frequently because we use uh square roots a lot in the Pythagorean theorem. And then in the Pythagorean theorem, we're looking for the length of a line. So we just discard the negative. But here, this is a pure algebra problem. And the question is, do you know if it's positive and negative both? All right, moving right along to number five.

[00:12:41]Oh, well, speaking of Pythagorean theorem, here we are right here. I won't do this. I'll give you a second or two more.

[00:12:49]But with that hint, this is Pythagorean theorem. And also another hint before you do this. The Pythagorean theorem isn't one number squared plus another number squared. It is one leg squared plus the other leg squared always equals the hypotenuse squared. All right, I'll give you a second to do this, then we'll do it together.

[00:13:26]All right. A right triangle has a base of five cm and a hypotenuse of 13 cm. I know that hypotenuse is always opposite that right angle. I am checking units that everything's the same. What is the length of the missing side? So this is what I don't have right here. So it's not 5^2 + 13^2 = x^2. It is one leg squared. 5^2 plus the other leg squared = 13 squared.

[00:13:59]Again, this is um one minute per problem, no calculator test. So it's got to be pretty quick.

[00:14:05]It's not going to be too hard to do.

[00:14:08]I could pay pick these values and plug them in. I know this is 5^2 is 25 plus what equals 13^2 is 169.

[00:14:20]So I could go 64 and 25 that's not 169.

[00:14:26]144 and 25 that is 169. So the correct answer is B by plugging it in. The other way to do it solve it algebraically. I have my x squar here. I'm gonna subtract 25 from both sides to get x^2 = 169us 25.

[00:14:47]144 square<unk> of 144 is 12 or -12. But the length of that side can't be that negative. So I discard that negative.

[00:14:57]And there's only one answer. 12 square<unk> of 144 is 12. Correct answer is B. Oh, I'm blocking my view. right in there.

[00:15:11]This is also what they call a Pythagorean triple. There's a couple that you'll see that'll always kind of work out uh to be integers and integers a whole number. So there's no calc, you know, no calculation required. And that's why they're so common on the math knowledge portion. The f first one that you see the most frequently is called a three four five triangle.

[00:15:36]When one of the legs is three, the other leg is four. The hypotenuse is five. So if you're given any two of those numbers, you can find the third. That's called the Pythagorean triple because it works out to be integers because 3^2 is 9, 4^2ar is 16, and 5^2 is 25. 9 + 16 equals 25.

[00:16:02]This actually works two ways. One is if you are told it is a right triangle, then the Pythagorean theorem works. But the converse is true. If the Pythagorean theorem works, then you know it has to be a right triangle. So you do this in construction a lot. If you want to make sure something's square, you measure three feet down, four feet along, and then pull a string at exactly five feet.

[00:16:28]And then it has to be right. So our first Pythagorean triple is at 3, four, five, and then the other one is 5 12 13.

[00:16:38]And most of these Pythagorean theorem problems will be one of those two. So you don't have a decimal approximation.

[00:16:45]All right, moving on to number six.

[00:16:48]Before you even start doing this, the question is, do you know what you're doing here? Right? Like, what are they really asking you to do? This is not an x. This is a multiplication sign. So, I'll give you a second to do that.

[00:17:14]Oh, if you're already done, make sure you hit that subscribe button notifications.

[00:17:19]Uh, that helps the channel more than anything are the subscribers. If you know anybody studying for a test, please share the links to the channel with them.

[00:17:28]So, I'd love it if you subscribed if you haven't yet.

[00:17:32]Okay, I look at this problem and because I've been teaching math for 30 years, I see multiplication, exponents, addition, subtraction, I know immediately in this problem, the number one thing they're testing is order of operations, especially in a math knowledge as so to the 4th is two times itself four times.

[00:17:53]So 2 to the 4th is actually let me do this first. Sorry. I'm going to write down PEMDAS, multiplication, division, addition, subtraction. That's order of operation saying you always do parentheses first, then you do exponents, then you do multiplication, division equally from left to right, then you do addition, subtraction equally from left to right. So there are no parentheses in this, but there are exponents. I'm going to do my exponents first. 2 4th is saying 2 * 2 4 * 2 8 * 2 16. So 2 4th is 16 - 3 * 2 + 5. After I've done my exponents, I now need to do my multiplication, division.

[00:18:47]That's this right here. So now I have 16 - 3 * 2 is -6 + 5. Then addition and subtraction are equal weighted from left to right. So now I have 16 - 6 10 + 5 15. Correct answer. Answer A right there. Greggy Lucario killing it there.

[00:19:15]Open.

[00:19:18]Nice, nice, Jake. Good to see. All right, moving on to number seven.

[00:19:27]Again, this is um this is going to be a cartisian coordinate. I'm kind of thinking like a test writer. What are they checking me on? Uh and I'll give you a minute to work on this, but this is on the coordinate system. X always comes before Y in the alphabet just like X comes before Y in that coordinate.

[00:19:50]But I'll give you a minute to do this.

[00:20:10]All right. Before I do this one, I'll break down I'll go back. I'm going to spend a lot of time on this one because there's a lot of this um in math knowledge.

[00:20:21]Um this guy named Descard came up watching laying in his bed looking up at his ceiling saw a spider walking around and try to figure out where he was and where he's going. And that kind of led to this coordinate system, also known as the XY system. X is always horizontal. Y is always vertical. If I have a coordinate 24, this is always X first and then Y. So that is saying you go over two up four. And that's a dot in space.

[00:20:52]No, my drawing is not that good. Then my second point 513 is same thing. You go over five up 13. Just another coordinate in space.

[00:21:05]And then it's saying connect those two dots and draw a line and figure out the slope of that line. Slope is represented with the variable m. A lot of times m is always rise over run. How far you go up over how far you go over. So this isn't too hard because I drew that picture out. So from four to 13, you can't read there. I go up nine and I go over three.

[00:21:41]Not a very good drawing. So my rise is nine. My run is three. That's it.

[00:21:49]However, that is not a reduced fraction.

[00:21:52]So three goes into three one time. Three goes into nine three times. And my answer is three over one, which is the equivalent of just three.

[00:22:04]Good.

[00:22:06]Oh, all right. Um, what else I was going to say? Like on this cartisian coordinate system? Well, you always start right here. I mean, if you go back to the beginning of your math, you start on this number line, you count steps, right? 0, one, two, three. You learn how to do addition, subtraction on here. You go to the to the left to subtract, to the right to add, and this is actually your x axis. And then later in school, that's when you're in your y axis. And then rather than add and subtract, you're now able to find area because you have two dimensions. So you could create points, you create lines, or you could create shapes. And that's how a lot of that CNC programming is done is all on the coordinate system. All right, a lot of talking in there. Let's move on.

[00:22:58]Number eight.

[00:23:01]Um, before you get started on this one, I'll just throw out a couple key things. Head of, you know, mindset of what are they testing you on? Soon as I read this, I know they're testing me on vocab. It's really a vocab question. Do you know what supplementary means? All right, I'll tell you how I remember that in a second, but I'll give you uh a second to work on it.

[00:23:36]All right. So there are two really important I guess there are a lot of important angles but two of the biggest angles in math are right angle that is a 90° angle that little box is telling you it's right so the Pythagorean theorem would work right perpendicular plum all those things mean the same thing two angles that add up to 90 are called complimementary the other one is called a straight eight angle. Two angles that add up to a half circle or 180° are called supplementary sal.

[00:24:19]And the way I remember the difference between those two words, C comes before S in the alphabet. 90 comes before 180 when you're counting. So complimentary angles are angles that add to 90.

[00:24:32]Supplementary angles are angles that add up to 180. So I read this problem. And what are the supplement angle to 72? I just have to do 180 minus 72 or what + 72 is going to give me a full straight angle 180 and that's going to be 108°.

[00:24:51]Uh, answer B. Here we go. There we go.

[00:24:58]All right, moving on to number nine. Oh, let me go over a little more vocab while we're here. Couple other angle measurements. If you have an angle less than 90, it is called acute. If it is exactly 90, it is right.

[00:25:16]Or if it is greater than 90, it is obtuse.

[00:25:21]You can see that in word knowledge as well. Acute is somebody who's kind of sharp. Obtuse is somebody who's a little slow or dull or wide. So those are other angle measures you might see. All right, moving on. Number nine, inequalities.

[00:25:37]I'll give you a second to do this. Um, again, here's, you know, the question on this is, do you know the important thing to remember on inequalities? And that is when you multiply or divide by a negative, you reverse the sign. Just a big hint. I'll give you a second to do that one.

[00:26:09]All right, let's go ahead and do this inequality. I solve just like an equation. Uh, following my order of operations with that one really important rule. Multiply or divide by a negative, you flip the sign. So the first thing I'm going to do because I'm solving for y, getting the variable y by itself, I'm going to reverse my order of operations. So I'm going to subtract six from both sides, giving me -2 y is now less than 14 - 68.

[00:26:40]Get ready for it. Boom. I am dividing by -2. Soon as I divide by -2, that means that thing right there has to be reversed. It goes from a less than to a greater than whenever you multiply or divide by a negative. So now I have y by itself over here. 8 / -2 is -4. y is greater than -4. Correct answer. Answer D.

[00:27:09]All right. Baldo Flores.

[00:27:14]Any questions on that? Post them in the comments. That's kind of a that's a funny one, a tricky one. this idea of flipping the sign, but it's just one of those rules that you got to have locked in your head because they're going to test you on those rules. All right, bringing you up to number 10, our last problem right here.

[00:27:34]That didn't type out too well. This is saying, what is the product of 2x + 3 times x - 4 I could give you one hit on this. The pneumonic device we use to remember this is foil. It's an acronym I think is I don't know. Foil means you multiply the first terms, the outer terms, the inner terms, the last terms. I'll give you a second to do that before I do it.

[00:28:12]I'll throw something out right now. It is not D just to get a hint.

[00:28:26]Get out of the way.

[00:28:29]Okay, so this is a algebra problem.

[00:28:32]Classic algebra problem. This right here is saying I multiply the first terms together. So I take the first term of this thing and the first term of this and multiply them together. 2x * x is 2x^2 can't eliminate any answers outer I take the outer terms the 2x and the -4 2x * -4 is -8x then I take the inner 3 * x is 3x and go to My last is 3 * -4 -12.

[00:29:19]So I have foiled that out to find the product of one quantity times another quantity. I have to combine similar um terms. This and this are similar. So I got to combine them. That's going to give me 2x^2.8x + 3x is -5x.

[00:29:39]And then there's I could probably just go right there.

[00:29:42]in circle A and then I have that -12.

[00:29:49]And if I had a guess, if I had no idea what this was even about, A and B are so close. A, B, and C all have three terms.

[00:29:58]So, I know that this answer has to have three terms. So, I had no idea how to do this. The least thing I would do is cross out D. There's no penalty for guessing. If you just take a completely random guess on four answers, you got a one in4 chance to get it right. Meaning that for every four you just randomly guess on, you're going to get one right.

[00:30:19]If you can eliminate one answer like that, now your chances of getting it right, if you guess is one and three, so for every three you guess on, you get one right on average over time. It's kind of how probability works. But if I have no idea what they're talking about, I can't remember how to do this. I'm just scanning those answers. I'm going to cross out D because it's really very different than the others. And then I notice A and B are so similar. Is probably one or the others. So I would cross out answer C. Now I got a one in two chance of guessing and getting it right. All right. So that was a 10 problem mathematical knowledge test with a fair bit of talking on my part, explaining some other parts of mathematics and how to do well on a standardized math exam. goal of this channel is really for you to be as successful as possible on any standardized math exam. And I just really enjoy being part of that, helping you get there. Um, so thanks for your support. Any thoughts or comments, any questions.

[00:31:20]Uh, we'll just wrap it up right there.

[00:31:27]Usually what I'm trying to do is, well, one thing I always do is I have a new video come out every Tuesday at 4 PM.

[00:31:34]um almost always ASVAB. Not always, but almost always ASVAB. Math sometimes word knowledge because that word knowledge you have to review that word knowledge is such a big part of your score. Um and then on Wednesday I usually have class at 3 PM. This week I couldn't do it. Uh run around a little bit this summer. But uh thanks for being here picking it back up on Friday. So any thoughts or questions? We'll just wrap it up.

[00:32:02]Make sure you hit subscribe. Thank you for watching.