welcome YouTubers to another episode in my grammar hero Series in this video there's going to be 45 practice test questions that should closely mirror what you should expect to see in the mathematics knowledge subtest of both the arm Services vocational aptitude battery that is the ASVAB as well as the pockat of course on the actual test you'll have 20 minutes to answer 16 questions so you want to make sure that you can answer these questions quickly as well as accurately as a quick reminder you do not get a calculator or a reference sheet on the actual test so as you take this practice test try not to use any of those resources and let me say this everything on the asab is very basic that said you have to understand the basic formulas to pass this test so if I said to you how do you find the area of a square you should be able to tell me it's side length squared if I ask you to find the volume of a cylinder you should be able to do that uh for that reason I'm going to put a link to my free reference sheet in the description of this video of course in order to get the most from this video you'll want to pause the video after I read a practice test question attempt to solve it on your own and then resume playing the video to check your solution finally I want to say this please don't waste your hard-earned money or time on tutoring or expensive online boot camps truth be told the vast majority of you will pass this very simple test on your first try as long as as you spend a few weeks studying for it in my opinion it should take most of you less than a month to get ready for this test so those tutors who are offering monthly subscriptions are really doing you a disservice so with all that being said let's go ahead and get started with these practice test questions the practice test questions are in no particular order you'll see an easy one followed by hard one followed by easy one so let's get started math knowledge practice test question for the As F and Pat says what is 250.0 25 rounded to the nearest 100th so again we're rounding 250.0 to5 to the nearest 100th again that's going to be to the right of the decimal this zero is in the 10 spot this two is in the 100th spot and this five is in the thousandth spot so we're going to look at this two since it's in our 100th spot and specifically we're going to look to the number to the right of two if the number to the right of two is five or greater we round up if it's below five we keep this to the same since this is five we're going to round this up and this becomes 250.0 3 all right so this one is C it's map knowledge practice test question for the ASVAB and Pat says the absolute value of 13 minus 15 equals so let's do this math 13 - 15 is -2 what is the absolute value of2 two that's just two why is it two because I know I'm going to get that question well the absolute value of a number is its distance away from zero without regard to its sign so here's -2 how far away is -2 from zero it's one two places away from ne0 so again that's absolute value uh and this one is D this math now it's practice test question for the As faab PCAT says 1/2 + 1/3 + 1/4 so we're adding these three fractions together and again you can't use calculator on this test in order to add fractions they all have to have the same or common denominator so what we're going to do is rewrite all three of these fractions with a common denominator so that we can add them of course 2 3 and four all go into 12 so 12's going to be our common denominator to write two as 12 i' multiply it by six I'm also going to do that to its numerator to write three is 12 I have to multiply it by four I also have to do that to its numerator and to write four as 12 I have to multiply it by three I'm also going to have to do that to its numerator again when you add fractions you keep your denominator the same uh 6 + 4 is 10 + 3 is 13 all right so we got the improper fraction 13 over2 the next thing we have to do is convert this improper fraction to mixed number and we could do that via long division we could read this as 13 / 12 how many times does 12 go to 13 without going over that's one time 1 * 12 is 12 13 - 12 is 1 all right we have enough to write our mixed number this one is going to be our whole number this remainder one's going to be our numerator and this 12 is going to be our denominator so this one as you can see is a one and 112 this math knowledge practice test question says how many minutes are there in one week so for this one you have to know that there are seven days in one week and there are 24 hours in one day so if there are seven days in a week and 24 hours in a day there are 24 * 7 hours in a week uh 4 * 7 is 28 bring down an 8 carry it two 7 * 2 is 14 + 2 is 16 so there are 168 hours in a week what else do you need to know to convert this to minutes you have to know that there are 60 Minutes in every hour so if there are 168 hours in a week there are 168 * 6 60 Minutes in a week uh 0 * these three is going to give you three zeros before we start multiplication with this six we have to add a zero placeholder uh 6 * 8 is going to be 48 carry a 4 6 * 6 is 36 + 4 is uh 40 carry of 4 6 * 1 is 6 + uh 4 is 10 add this together this is going to be 10,000 80 minutes in a 7-Day week since there are 24 hours in a day 168 hours in a week and 60 minutes in an hour so this one is a this math knowledge practice test question says what is 6 factorial so factorial means you take the number that you're given so three factorial for example means you take the number three you multiply it by every number that's less than three until you get to one so that would be 3 * 2 * 1 3 * 2 is 6 6 * 1 is 6 so 3 factorial is 6 let's do the same thing with 6 factorial that's 6 * 5 * 4 * 3 * 2 * 1 6 * 5 is 30 30 * 4 well 3 * 4 would be 1 3 * 4 would be 12 therefore 30 * 4 is 120 120 * 3 well 12 * 3 would be uh 36 therefore 120 * 3 is going to be 360 uh 36 * 2 would be 72 therefore 360 * 2 is going to be 720 720 * 1 is 720 so this one is B 720 asab piket ma knowledge practice test question says what is 7 a minus a B plus 8 B subtract it from 3 a - 9 a B plus b so a lot of people don't set this one up correct this is how you have to set it up down here what if this problem said what is 10 subtract it from 20 most people would say 20 minus 10 well that's the same thing we did down here the only difference is we have to take this negative and distribute it here here and here this becomes 3 a - 9 a B plus b - 7 a negative times a negative is a positive plus a b negative times a positive is a negative a just go ahead and combine like terms 3 A and negative 7 a is -4 a uh 9ab and 1 a is 8 A and B and negative a is -7 B so this one is going to be a this math knowledge practice test question for the ASVAB and PCAT says in a standard deck of playing cards a king of hearts is drawn and not replaced what is the probability of drawing another king from the deck so in a standard deck of playing cards there are four Kings and there are 52 cards in total so according to the problem uh King of Hearts is drawn so when that card is drawn what happens to the deck well we're down to three kings in the deck and 51 cards in the deck um we can see that this isn't an answer choice so uh what do we know about 51 5 + 1 is 6 therefore 51 is divisible by three so we in other words we could reduce this fraction 3 ID 3 is 1 what is 51 / 3 well if you can't do that mentally do the long division here three goes into five one time without going over 1 * 3 is 3 5 - 3 is 2 drop down this 1 3 * 7 is 21 we have no remainder so this is 1 over 17 your odds of drawing another king from the deck which had one removed previously is C1 over 177 this math knowledge practice test question for the ASVAB and pet says simplify 32 over 7 so 32 over 7 is an improper fraction because the numerator is bigger than the denominator so we can convert this to mixed number and to do that we use long division we read this as 32 / 7 how many times does 7 go into 32 without going over that's 4 * 4 * 7 is 28 32 - 2 28 is four so we have enough information to write our mixed number this four is going to be our whole number this remainder of four is going to be our numerator and this seven is going to be our denominator so this one is uh B4 and 47 this math knowledge practice test question for the ASAP and Pat says 3 -1 * 7 -2 / 2 equals so we're evaluating this expression here it's all jumbled up with uh parth es multiplication and division so that's a clue that uh as you work on this one you need to follow the order of operations which I remember using the acronym pemos that is parentheses exponents multiplication division addition and subtraction this tells you the order in which to work this out you do parentheses first exponents next if there if there are any you do multiplication and division as they appear in the expression from left to right that is to say they're treated as equals and then you do addition and subtraction likewise after that as they appear in the expression from left to right that is to say addition and subtraction are treated as equals so let me copy this down and we'll go through it we have 3 - 1 * 7 - 12 / 2 all right so right away we have our highest order that is parentheses so we're going to work that out first 3 - 1 is 2 so this is 2 * 7 - 12 / 2 do we have any exponents in this expression we do not so we move on what do we have left we have multiplication subtraction and division again we do multiplication and division before addition and subtraction but as I said we do multiplication and division as they appear from left to right so we're going to do this multiplication 2 * 7 is 14 14 - 12 / by uh two what do we have left we have subtraction and division again we do division before subtraction so let's do that this is 14 minus 12 / 2 is 6 14 - 6 again we only have one operation left is eight so this one is eight again if your instructor or wherever you're studying with does not tell you that multiplication and division have equal precedents and are worked out from left to right likewise addition and subtraction have equal precedents and they're worked out from left to right they are misleading you they're probably not an expert instructor this math knowledge practice test question for the asab and pet says what is the volume of a cube with Edge lengths of 7 cm so to find the volume of a cube you take its Edge length which I'm going to call a and you're going to cube it well in this case we're told that a is 7 cm so this is 7 3 what is 7 3 equal to that's 7 multiplied by itself three times 7 * 7 is 49 what is 49 time 7 well if you can't do that one mentally there's no shame in doing it off to the side uh 9 * 7 is going to be 6 uh 3 so bring down a three carry a 6 4 * 7 is 28 29 30 31 32 33 34 all right so the volume of a cube with Edge length of 7 cm is 343 cm and since we're talking about volume this is going to be Cub so this one is C you just have to know this formula for this test this matth knowledge practice test question for the As faab and Pat says if AAL 5 over2 then 1/ a equals so again a is 5 over2 according to the problem and we want to know what 1/ a is well what are we going to do we're going to take 5 over2 and plug it in for a this becomes 1 over 5 over2 what is this we're dividing a whole number by a fraction so what are we going to do we're going to follow the algorithm Keep Change Flip we're going to keep this top number the same so this equals one we're going to change from division here to multiplication and then we're going to flip this bottom fraction here so instead of 5 over 2 it's going to be 2 over 5 1 time any number is that number itself so 1 * 2 over 5 is just 2 over 5 so we can see that 1 over a is c 2 over5 by the way this is how you find the reciprocal of a number 1 over a math knowledge practice test question says what percent of 34s is 1/8 so I'm going to translate this statement into an equation and then solve it that said I'm going to rephrase this one and I'm going to rephrase it like this 1/8 is is in math is equal what percent that's unknown so call that P of 34s so we're going to be solving this equation for p first thing we're going to do is multiply both sides of the equation by the reciprocal of 3 over four that is 3 4 over3 and in doing so this clears out leaving you with p on this side all right here we're multiplying two fractions so we're going to multiply straight across 4 * 1 is 4 3 * 8 is 24 so p is equal to 4 over 24 uh we can reduce this to make it a little bit easier by a common factor of 4 4 ID 4 is 1 24 ID 4 is 6 now what percent is 1 16 well we can figure that out by doing log Division I could read this as 1 / 6 6 does not go into one so I have to add a decimal and I'm going to add a couple of zero placeholders bring my decimal into my answer how many times does 6 go into 10 without going over that's one time 6 * 1 is 6 10 - 6 is 4 again drop down one of our zeros how many times does 6 go into 40 without going over that 6 times 6 * 6 is 36 40 - 36 is 4 drop down this zero as you can see this pattern is going to repeat so this is 1.1 1666 which is the same thing as 16.67% this is answer Choice C this math knowledge practice test question for the ASVAB and Pat says how many distinct prime factors are there in 120 again what are prime factors prime factors are only divisible by one in itself one is never Prime so don't include one two's Prime three's Prime five's Prime and Seven's Prime so these are possible prime factors so we're going to take 120 and we're going to break it down using 2 three5 and probably not seven until we have it uh factorized uh so let's start let's do uh 2 and 60 60 is 3 and 20 20 is uh five and four and four is 2 and two so what are our prime factors there're 2 three five 2 and two so let's write that out we have two 2 2 three and five if we multiply all these prime factors together we'll get 120 how many distinct prime factors are there well we have two that's one distinct prime factor three that's another distinct prime factor and five that's another distinct prime factor so we have three distinct prime factors so this one is B this math knowledge practice test question for the ASVAB and Pat says what is the area of a circle that has a diameter of four units use 3.14 to approximate Pi so for the ASAP and PCAT you have to know some basic formulas from geometry including how to calculate the area of a circle area of a circle is pi r SAR where R is the radius of course in this case we were given the diameter of the circle so we also have to know that the diameter of a circle is always equal to twice its radius that is D equal 2 R since our diameter is four we can plug it in for D here this is 4 = 2 R divide both sides by two now to get R by itself uh 4 / 2 is 2 now that we know R is two we can plug it in right here and likewise we were told to use 3.14 to approximate Pi so that's what we'll do there this becomes 3.14 * 2^ 2ar uh 2^ 2ar is the same thing as 2 * 2 which is 4 so this is 3.14 * 4 all right let's do this math off to the side if you can't do it mentally this is 3.14 4 * 4 we have to move this decimal and 3.14 two times to the right to rewrite this as 314 * 4 Al be it with two decimals to move back into to the left when we're done 4 * 4 is 16 carry a 1 1 * 4 is 4 + 1 is 5 3 * 4 is 12 bring our two decimals back in we can see that the area of our circle is 12.56 square units which is answer Choice C of course this math knowledge practice test question says if xal 2 What is the value of 8x - x so again we're going to be evaluating the expression 8x - x when x = 2 so we're going to take two and plug it in for X here and here this becomes 8 * 2 minus 2 uh we're going to follow the order of operation so we're going to do multiplication first and subtraction after that 8 * 2 is 16 16 - 2 is 14 so this one is D14 math knowledge practice test question for the ASVAB and Pat says if one side of a hexagon is X+ 2 what is its perimeter so here's a hexagon as you can see it's a six-sided figure and all the sides are equal if one side's x + 2 then all these other sides are x + 2 that said how do you find the perimeter of a regular polygon including a hexagon you add up all of its sides uh instead of doing x + 2 + x + 2 + x + 2 6 times we're going to do 6 * x + 2 and again we're just going to take this six and multiply it here and here this becomes 6X + 12 so the perimeter of a hexagon with one side being x + 2 is 6 x + 12 answer Choice C in this case this math knowledge practice test question for the As faab and Pat says which number is Prime so here are the prime numbers from 1 to 100 as you can see one is never considered Prime uh and we can see that two is prime well how do we know that two is prime a number is considered Prime if it's only divisible by one in itself so two only has two factors notably two and one that is one in itself but that said how do we quickly know that 57 and 87 are divisible by something other than one in it itself well you have to know your divisibility rules the divisibility rule for two says if the last digit in the number is even then that number is divisible by two and can't be prime both of these end in seven which is odd so we can't use this divisibility rule the divisibility rule for five says if the last digit ends in zero or five then that number is divisible by five and can't be prime these are both seven and the divisibility rule for three says sum the digits if the sum of the digits is divisible by three then the number itself is divisible by three so for example here we have five and seven our digits are five and seven when we add those up we get 12 is 12 divisible by 3 it is 12 / 3 is 4 since the sum of the digits in 57 is divisible by 3 I know 57 is divisible by three what about 87 again sum the digits our digits are 8 and seven 8 and 7 is 15 is 15 divisible by 3 it is 15 divid 3 is 5 since the sum of the digits is divisible by three I know 87 is also divisible by three and therefore cannot be prime all right so that is that one maack knowledge practice test question for the ASVAB and PCAT says if the diameter of a circle is 57.3 cm what is its diameter in meters so we have a circle with a diameter of 57.3 cim and we want to convert that to be in terms of meters well this is a part of the metric system and the good thing about the metric system as you can see is you either divide by 10 100 or a th000 or multiply by a th000 100 or 10 accordingly in this case we're going from centim to meters so you can see we're going to take the number that we're given and we're going to divide it by 100 well why is this math so easy whenever you take a number that has a decimal and you multiply or divide it by a power of 10 such as 10 100 or a th you just take that decimal and you either shift it left or right according to how many zeros there are in that power of 10 in 100 there are two zeros and we're doing division so I'm GNA take this decimal and 57.3 I'm going to move it to the left one two times to make this 573 of course that's meters now that we've converted this so this one is B again you should know these common conversions for the metric unit all you're really doing is taking your decimal place and moving it left or right either once twice or three times accordingly this math knowledge practice test question for the ASVAB and pet says which equation can be used to calculate the hyp hypotenuse of the right triangle so to answer this one you have to know the Pythagorean theorem again you don't get a reference sheet on this test so you do have to commit that one to memory if you don't know it already that is Pythagorean theorem says a^2 + b^2 = c^2 where C is the hypotenuse of the right triangle and a and b are its legs so I'm going to say a is 4 and B is 6 and let's go ahead and plug the those values in accordingly this becomes uh 4^ 2 + 6^ 2 = c^ 2 and if you look at our answer choices they either start with C or c^ 2 so I'm going to move this c^ squ over here this becomes c^2 = 4^2 + 6^ 2 uh does this match one of our answer choices because if it does we can stop right here we don't have to go any further uh c^2 = 4^2 + 6^ 2 so we can use equation B uh to calculate the hypotenuse of this right triangle we do not have to go any further this math knowledge practice test question for the ASVAB and Pat says solve for x we have x^2 - x - 6 = 0 so this is a quadratic trinomial with a leading coefficient of 1 therefore we should be able to factor it and if we can it's going to look like this x * X in parentheses equals 0 now we're looking for two numbers that multiply to -6 but add to -1 it's going to be -3 and pos2 again -3 * pos2 is -6 -3 + 2 is -1 now that we factored this we're going to set each of these equal to zero independently and then we're going to solve for x so I'm going to say x - 3 equal 0 that's going to be one of our Solutions and x + 2 = 0 that's going to be our our other solution to get X by itself over here we just add three to both sides this says xal 3 to get X by itself over here we're going to subtract two from both sides this says x = -2 so our solution is X = 3 or x equals -2 so this one as you can see is going to be B this math knowledge practice test question for the ASAP and PCAT says seven more than three times a number is equal to 70 find the number so we're going to translate these statements into an equation that will then solve seven more means seven plus 3 times a number three times a number let's call that number n so that's 3 * n is is in math is equal to 70 so also we have to do is solve this equation for n subtract seven from both sides to get started this crosses out leaving you a 3 n over here 70 - 7 is 63 divide both sides by three now to get n by itself again don't do the long division here do some Mental Math 6 / 3 is 2 3 / 3 is 1 so n is c21 this math knowledge practice test question for the asab and Pat says this what is the area of this Square we can see that we have a square and it's 5T across that way how do you find the area of a square it's one of the formulas that you do have to know for this test area of a square is its side length squared what is the side length of this Square well in squares all the sides are equal and we could represent its side length with the letter S and you should be able to see that this 5T corresponds to the side length of this Square so we know s is five in this case let's plug that in here this is 5^ squ 5^ squ is 5 * 5 which is 25 so this one is C the area of this square is 25 Square fet this math knowledge practice test question for the ASVAB and PCAT says what is the area of the rectangle you can see that we have a rectangle that's 2 and2 units wide and 8 units long how do you find the area of a rectangle it's area equals length time width I think they teach this formula in middle school if not elementary school but for the ASVAB and pet you have to have it memorized since you don't get a formula sheet on the test uh so let's go ahead and plug these values in and solve accordingly we know our length is eight units and our width is 2 and 1/2 units so this is 8 * 2 and 1/2 now many you could solve this mentally because you can break two and a half apart 8 * 2 is 16 1 12 * 8 is 4 16 + 4 is 20 so the area of this rectangle is 20 square units that said let's say you haven't done this math with fractions in a long time let me show you how to do it we got 8 time 2 and a half we're going to write 2 and A2 to be an improper fraction and I'm going to write eight to be a fraction by placing it over one so this is 8 over 1 to write 2 and2 as an improper fraction we do 2 * 2 which is 4 + one so that's 5 over two again now we're multiplying two fractions when you multiply two fractions you just multiply straight across uh 8 * 5 is 40 1 * 2 is 2 40 ID 2 is 20 so if you forgot how to do this mentally you could always do it the oldfashioned way as well so so that is that one this practice test question for the math knowledge subtest of the ASVAB and Pat says which pairs of angles are equal in measurement so the first thing I want to point out is that angles 1 2 3 and four share of vertex angles that are on opposite sides of a share vertex are equal so angles one and four are equal three and two are equal down here 5 six seven and eight share a Vertex so seven and six are equal five and eight are equal Additionally you have to know the alternate interior angles theorem which says if two parallel lines are cut by a transversal then the alternate interior angles are also congruent that is equal to each other so let's go through our answer choices one by one uh one and two one and two form a straight line therefore they are supplementary angles four and five well as you can see those those are alternate interior angles therefore they are going to be equal so this one is B this MTH knowledge practice test question for the ASVAB and Pat says which expression represents the volume of a cylinder whose height is equivalent to the length of the radius so what's the cylinder look like it has a circular top and bottom that are connected via a tube how do you find its volume well you really don't have to memorize anything as long as you know how to find the area of a circle again this is a circular face its area is p pi r 2 and then all we do is multiply that by the height of the cylinder which is H all right so uh that's how you derive the formula in this case we're told that its height is equal to its radius so in place of H here we can actually plug in R this becomes pi r 2 time R Now using the uh laws of exponents notably the product law we can actually do R 2 * R again the product law says a to the m * a to the N is equal to a to the m + n that is you add their exponents so R 2 * R again there is no power here so we assume it's one it's equal going to it's going to be equal to R 2 + 1 which is is R the 3 so this is pi * R the 3 which as you can see is answer Choice B again uh you would never Square Pi for any reason so those are obviously wrong all right so this one is B this math knowledge practice test question for the ASAP and pet says if x + 7 is greater than three then X could equal so we have x + 7 being greater than three we're going to solve this one step inequality by subtracting in seven from both sides this crosses out this says X is greater than uh 3 - 7 is -4 uh what does this look like on a number line so we're going to go to-4 on the number line we're going to put an open circle here because we do not include -4 and X is greater than all the values that are greater than4 so -3 -21 so we put an Arrow going this way to indicate that X is all the values that are greater than -4 and the only value of our answer choices that is greater than4 is D3 so this one is D this B knowledge practice test question for the ASVAB and Pat says what is the area of a triangle that has a base of 12 units and a height of 10 units so you really don't have to sketch anything for this one instead you just have to know the formula to find the area of a triangle that's area equals 12 base time height of course we're told that the base is 12 units so B is 12 and the height is 10 units so we'll just go ahead and plug those values in respectively this becomes 1/2 times again the base was 12 and the height was 10 and we could do this math very quickly what is 1 12 of 12 1 12 * 12 is 6 so this is 6 * 10 6 * 10 is 60 so its area is B 60 square units now if you couldn't do 1 12 * 12 I'll do it off to the side very quickly for you you have 12 * 12 you write 12 as a fraction by placing it over one when you multiply two fractions you multiply straight across 1 * 12 is 12 2 * 1 is 2 12 / 2 is 6 all right so that is that one this math knowledge practice test question for the asab and pet says solve -22 + 33 all right so at first glance this may look challenging Until you realize that we can simply rewrite this to be 33 minus 22 again if you can't do that mentally for some reason go ahead and do it the oldfashioned way here 33 - 22 3 - 2 is 1 3 - 2 is 1 so this one is d11 if you need more help with adding and subtracting integers find that video on my channel and go through it but that is that one this math knowledge practice test question for the asabin PCAT says this simplify 2 * a minus B in parentheses plus 4 * a + 3B in parentheses so on the actual asab and pet you will have scratch paper so let's start by copying this one down we have 2 * a minus b + 4 * a + 3B of course the next step here is to distribute this two here and here and to take this four and distribute it here and here 2 * a is 2 a 2 * B is -2b uh 4 * a is+ a 4 * 3B 4 * 3 is 12 therefore 4 * 3B is 12b now that we've distributed that we're going to go ahead and combine like terms in this expression again like terms have the same letter variable as raised to the same power so we have a to the first Power it's corresponding like terms here 4 a to the first Power 2 a + 4 a is simply 6 a now that we've combined them I like to cross them out and we have -2b its corresponding like term is 12b uh 12 B minus 2B is plus 10 B so this one is going to be a 6 a + 10 B this math now it's practice test question for the asab and Pat says simplify 3x * x^2 - x -1 so to get started I'm going to copy this one down we have 3x * x^2 - x -1 and we're going to take 3x and distribute it here here and here 3x * x^2 a positive time a negative is going to be a negative 3 x the 3 uh 3x * X is going to be 3x^2 and -3x * -1 is -3x so this one is -3x 3r - 3x^2 - 3x which is answer Choice D this has F pet macn knowledge practice test question says if the diameter of a circle is 15 units what is its radius so for this one you have to know that the diameter of a circle is always equal to twice its radius in this case we're told that our diameter is 15 units so D is 15 so we'll plug that in accordingly and we want to know what its radius is so we're going to be solving this equation for R to do that we're going to divide both sides by two this crosses out leaving you with r over here we can see that R is 15 over two most of you could do that mentally and say it's 7.5 that said on test day you might be a little bit nervous so we'll do the long division off to the side again we could read this as 15 / 2 2 goes into 15 7 times without going over 2 * 7 is 14 15 - 14 is 1 again there's technically a decimal here in 15 and a zero after it bring that decimal into our answer drop down that zero 2 * 5 is exactly 10 and we have no remainder so we can stop so that's how we got 7.5 again this one is c7.5 units as Fab pet ma knowledge practice test question says if 100 over 5 * 5 over 100 = 5 C then C equals so I'm going to solve this one two different ways again right here we're multiplying two fractions when you multiply fractions you multiply straight across 100 Time 5 is 500 5 * 100 is 500 = 5 C 500 ID 500 is 1 = 5 C again to get C by itself we're going to divide both sides by five you can see that c is equal to 1 5 all right let's go ahead and solve this one by cross reducing 100 goes into 100 one time 100 goes into 100 one time five goes in a five one time five goes in a five one time one over one is just one one over one is just one 1 Time 1 is just one so this is 1 equal 5 C divide both sides by five now to get C by itself and you can see C is 1/5 this math knowledge practice test question says if xal 2 What is the value of 8x - x so again we're going to be evaluating the expression 8x - x when x = 2 so we're going to take two and plug it in for X here and here this becomes 8 * 2 minus 2 uh we're going to follow the order of operation so we're going to do multiplication first and subtraction after that 8 * 2 is 16 16 - 2 is 14 so this one is D14 this math knowledge practice test question for the asab and P says the angles of a triangle are in the ratio 3 to 4 to 5 what is the measure of the smallest angle so for this one you have to know that triangles always have three angles and those three angles always add up to 180° since our angles have a ratio of 3 to 4 to 5 I can rewrite angle one as 3x angle 2 as 4X and angle 3 as 5x and of course these equal 180 so I can solve for x and then by multiplying X by 3x I'll know that measure of angle one here 3x + 4x + 5x is going to be 12x equals 180 uh divide both sides by 12 now this crosses out leaving you with X on this side you should notice that 18 and 12 or 180 and 12 have a common factor of six so if you can't do this one mentally reduce it 18 ID 6 is 3 uh therefore 180 ID 6 is going to be 30 12 ID 6 is 2 30 ID 2 is 15 so we know angle one is the smallest angle and X is 15° so uh angle 1 is 3x 3 * 15 is 45 the smallest angle in this triangle is C 45° this math knowledge practice test question for the math knowledge subtest of the ASVAB and pet says this using 22 over7 to approximate Pi find the area of a circle that has a diameter of half an inch all right so since we're going to have to calculate the area of a circle the first thing I'm going to do is write down that formula that's area equals Pi R2 you do have to know that formula for this test of course now if we look back at the question it says our Circle has a diameter of half an inch to use this formula we need radius so you also have to know that the diameter of a circle is always equal to twice its radius in this case we know our diameter is half an inch so that's going to be equal to 2 R and we're going to solve this little equation for R to find out how long our radius is to clear this two in front of the r we're going to multiply both sides by2 this two and this 1/2 cross out again 2 * 1/2 is just one so that's just R over here 1/2 * 1/2 when you multiply fractions you just multiply straight across in other words we do 1 * 1 which is 1 2 * 2 is 4 so now we know our radius is 1/4 we can go ahead and plug it in likewise we know that we're going to be using 22 over7 to approximate Pi so we'll plug that in as well so this becomes 22 over7 time uh 14^ squared so we're going to follow the order of operations here that is we're going to do this exponent first and then we'll do the multiplication after that what is 1/4 squar and I'm going to do this off to the side so you can see it when you square a fraction this Square goes both to the one as well as the four 1 squar is just one so this becomes 22 over 7 * 1 over what is 4 S that's 4 * 4 or 16 all right again we're multiplying two fractions so we're going to multiply straight across before we multiply straight across we want to try to reduce this via cross reduction to make this math a lot easier I know that uh two go goes into 16 uh eight times likewise two goes into 22 11 times so this is going to be 11 * 1 which is 11 over 7 * 8 which is 56 so our area is 1156 Square in uh which we can see is answer Choice d uh this is a pretty hard problem because again you had to know that the diameter of a circle is always twice its radius and you also had to know how to square and multiply fraction so again this is kind of a tough problem this math knowledge practice test question for the ASAP and pad says if x is a positive integer solve x^2 + 6x = 16 so I'm going to copy this one down as is we're trying to solve for x uh we have x^2 + 6 xal 16 again we're told X has to be a positive integer so uh you should recognize that if I subtract 16 from both sides this becomes x^2 + 6x - 16 and 16 - 16 is zero we have a quadratic trinomial with the leading coefficient of one which means if we could Factor it it's going to look like this now we can solve for x we're looking for two numbers that multiply to -16 uh but add to positive 6 that's going to be -2 and postive 8 again -2 * POS 8 is -16 8 - 2 is 6 all right so now we're going to set each of these equal to 0 individually we have x - 2 = 0 and x + 8 = 0 I add two to both sides to solve for x here this crosses out this says x = 2 uh subtract 8 from both sides here this say x = 8 what was the stipulation in this question X has to be a positive integer this is a negative integer so our only solution is x = 2 so this one is a this math knowledge practice test question for the as Fab and Pat says which of the following Expressions is equivalent to 5x - 4 - 8x + 10 right so we have 5x - 4 - 8 x + 10 so all we have to do is go through this expression and combine like terms to find its equivalent expression so 5x and -8x are like terms 5x - 8X is -3x now that we've combined them cross them out uh -4 and 10 are like terms 10 - 4 is 6 so the equivalent expression is -3x + 6 which you can see is answer Choice C of course this map knowledge practice test question for the ASAP and PCAT says if the square root of x + 6 = 16 then x equals so I'm going to start by copying this one down the square < TK of x + 6 = 16 again we're solving this equation for x so we want to get x equal to something by itself so let's subtract six from both sides this crosses out leaving you with the square root of x over here equals 16 - 6 is 10 to get rid of this square root we're going to square both sides of our equation uh the square of a square square root just cancel those out leaving you with X over here 10^ s is the same thing as 10 * 10 which is 100 so X is 100 as you can see that said it's always a good idea to quickly check your work and to do that we're going to take 100 and we're going to plug it in for X this says the squ < TK of 100 + 6 = 16 if this makes a true statement we know we did our work correctly < TK of 100 is 10 + 6 = 16 10 + 6 is 16 does 16 equals 16 it does therefore we know D is the correct answer this math knowledge practice test question for the ASVAB and PCAT says if a square has an area of 64 square units what is its perimeter so we're talking about the area as well as the perimeter of a square you have to know both of these formulas for this test the area of a square is its side length squar that is s squ the perimeter of a square is 4 * one of its side lengths s well in this case we were told the area of our square a is 64 square units so we could go ahead and plug in 64 for a and we can actually solve this for S which we can then plug in down here for S and get our answer again to get rid of this Square on S we're going to do the opposite operation we're going to take these square root of both sides this crosses out leaving us with s over here Square < TK of 64 is 8 now that we know s is 8 we could plug it into the perimeter formula 4 * 8 is 32 so its perimeter is B 32 units this ASV piket ma knowledge practice test question says what is the slope of a line that runs through the points -25 and 17 so for the ASVAB and pyat you have to know a lot of basic formulas from middle school in high school including how to calculate slope uh slope is found using the formula m m refers to slope equals y 2 - y1 all over X2 - X1 and you might be saying to yourself well where do I get X1 y1 X2 Y2 from again all ordered pairs come in the form XY so I can say -2 is going to be X1 5 is going to be y1 this one is going to be X2 two and this seven is going to be Y2 now that we know those values we can go ahead and plug them in Y2 is right here it's 7 minus y1 is 5 over X2 X2 is right here it's 1 minus X1 which is -2 7 - 5 is pretty easy to do that's 2 1 - -2 minus and negative becomes a plus 1 + 2 is 3 so the slope is D2 2/3 now if you want additional practice with calculating slope check out the playlist on my channel I'll put a link to it in the description of the video but I have playlists for every topic that shows up on the asab ASVAB so for example I have a playlist on slope the first video gives you a review of how to calculate slope followed by about 15 practice test questions so check that out again uh it shouldn't cost you more than $30 to prepare for this test if that and uh it should take you less than a month to get ready for it too so again stick with free resources and you'll be fine on this test math knowledge practice test question for the ASVAB and pcad says 12 is 15% of what number so we're going to translate this statement into an equation that will then solve 12 is in math is equal 12 equals 15% as a decimal is 0.15 of of is multiply what number that number is unknown so call it X so we're going to be solving this one step equation for x by dividing both sides by 0.15 this crosses out leaving you with X over here what is 12 /15 well you can't do long division with the decimal outside the division bar so you have to move this decimal two times to make that 15 and you're going to move this decimal after 12 a corresponding number of times that is 1 2 so this becomes 1,00 / 15 and you know that has to be a pretty big number right uh can't be 1.8 15 * 1.8 is going to be less than 30 this is going to be a very small number so we know that this is either 18 or 80 and if you can't figure that out you can quickly do it off to the side you could do 15 * 18 uh 5 time 8 is 40 so bring down a zero carry a 4 8 * 1 is 8 9 10 11 12 12 add a zero placeholder 1 * 5 is 5 1 * 1 is 1 you can see that this is only going to be 270 which is too small so 15 * 80 is exactly 1,200 and you don't have to work that out with no remainder so this one is going to be d80 this math knowledge practice test question says the greatest common factor of 24 and 36 is so for this one you have to understand the difference between your least common multiple and your greatest common factor so the way I know the difference is like this the greatest common factor of two numbers is always going to be smaller than the given two numbers so I know that our greatest common factor of 24 and 36 is going to be smaller than 24 and 36 so 72 is not an a possibility what are the factors of 24 and 36 well six goes into both of them and 12 goes into both of them the greatest are the biggest common factor is 12 least common multiple the least common multiple as I just said is always going to be bigger than the two numbers and here's why this is how you find the least common multiple line up those two numbers 24 and 36 and then you list out their multiples we have 24 48 72 here we have 36 72 uh what common multiple do they have it's 72 so 72 was their least common multiple 12 was their greatest common factor this math knowledge practice test question for the ASVAB and Pat says if the area of a square is 400 square units what is the length of its side so for this one all you have to know is how to find the area of a square that formula is area of a square is equal to side length squared in this case we know its area is 400 square units so we'll plug that in this becomes 400 equal S2 so we're going to be solving for S because s equals the side length of the square to get S by itself we're going to take the square root of both sides this crosses out here leaving you with s over here the square root of 400 is 20 so this one is the side length of the square is 20 this one is a this has Fab pet math knowledge practice test question says solve for x we have 3 + 4 * x - 2 = 15 in other words we're going to be be solving this equation for x that is we want to get x equal to something by itself let's get started by subtracting three from both sides in doing so this crosses out over here leaving you with 4 * x - 2 on this side 15 - 3 is 12 do we have to take this four and multiply it out to the X and -2 we don't have to do that we can go ahead and divide both sides by four in this case in doing so that leaves you with x - 2 over here here 12 / 4 is 3 again to get X by itself we're now going to add two to both sides this crosses out leaving you with X over here 3 + 2 is 5 so x = 5 that said you always want to check your work we're going to go ahead and plug in five in the original equation and see if it makes a true mathematical statement this becomes 3 + 4 * 5 - 2 = 15 this says 3 + uh again we're going to work out what's in parentheses first 5 - 2 is 3 = 15 uh this is 3 + 4 * 3 is 12 = 15 3 + 12 is 15 does 15 equal 15 it does that's a true statement therefore we know five is the correct solution uh for the asfb and pet you will have to solve at least four or five equations so make sure you can do this