[Music] welcome YouTubers to another episode in my grammar hero Series in this video there will be 86 math knowledge practice test questions that should fully prepare you for the arm Services vocational aptitude battery that is the ASVAB as well as the pre-screening internet delivered computer adaptive test that is the piecat of course in order to get the most from this video you'll want to pause the video before I read a practice test question attempt to work out the question on your own and then resume playing the video to check your solution as a brief reminder on the actual ASVAB and PCAT you are not permitted to use a calculator or reference sheet so as you work your way through these 86 math knowledge practice test questions try not to use any of those resources as far as evaluating your performance on this practice test goes I want to say this if you can answer 70 to8 80% or more of these questions correctly I would consider that very good and outstanding and chances are you're ready to take this test right now if on the other hand you answer 60 to 69% of these questions correctly I would personally consider that average and in that case I would recommend that you study for a few weeks more before you go take the test finally if you answer 59% or fewer of these questions correctly I would say you need to make some significant improvements and for that reason I would consider study studying for a few months before you go and take this test thankfully enough my channel has videos for every topic that you should encounter in this math knowledge subtest and for that reason I'll include timestamps that are going to be associated with each question in the description of this video so if you struggle with a particular topic look in the description uh find a link to the video on that topic and you should be able to understand it from there finally I want to say this uh so far my free courses study guides and practice tests have helped more than 70,000 people significantly improve their test scores so if you want to support my mission of helping everyone including those who can't afford expensive test prep get ready to take the asab or PCAT for free uh please consider becoming a channel member uh you could do that simply by clicking the join button on my homepage it should be right next to the Subscribe button so with all that finally being said let's go ahead and get started with today's video this Matt knowledge practice test question for the ASAP and pip at says 5.12 * 105 power can be expressed as so I'm going to write 5.12 nice and big down here if this was times 10 to the positive 5ifth power I'd take my decimal and move it to the right five times since it's 10 to theg 5th power however I'm going to move my decimal five times to the left 1 2 3 four five and I'm going to add zeros accordingly so that is is our answer again this is a test of your knowledge of some basic scientific notation uh the answer Choice with four zeros is B on this test you do have to know some Basics about scientific notation so check out my linked video if you need more help with this one this ASVAB PCAT ma knowledge practice test question says simplify the ratio 12 to 18 so we're given the ratio 12 to 18 and we want to simplify it in other words we want to find a number that goes into both both uh 12 and 18 evenly you should recognize right away that both 12 and 18 are divisible by six specifically 12 ID 6 is going to be 2 and 18 ID 6 is going to be three so when we simplify this ratio it becomes two to three that's all there is to that one don't overthink it because it's as simple as that this as faab M knowledge practice test question says this what is the next number in the following series we have 36 6 12 12 and 8 you should see that this series is broken into two patterns the first pattern is pretty easy to recognize to go from three to uh six you multiply by two of course to go from 6 to 12 you multiply by two again and to go from 12 to this missing number in the series you're going to multiply by two again which is going to make this 24 uh so the answer to this one is d24 the second part in this series is as follows to go from 16 to 12 you subtract 4 from 12 to 8 you subtract four and to go from 8 to the number after 24 you would subtract by four if you needed to that is that one this math knowledge practice test question for the ASVAB and podcat says this what fraction of the figure is shaded as you can see we have a figure below and in that figure two parts of it are shaded the easiest approach to solving this one is to draw a line from the left side to the right side of the figure and in doing so you'll see that we create 10 equal parts to this Figure 1 2 3 4 5 6 7 8 9 10 of course it should be pretty obvious that two out of the 10 parts are shaded in other words two10 of this figure is shaded of course that's not one of our answer choices because we could reduce this by a common factor of two two divided two is 1 uh 10 divided by two is five so in other words d 1 of this total figure is shaded what if is the missing number in the following series we have 1 4 27 blank and then 3,125 all right so the pattern is as follows we have 1 to the one one to the first power is 1 we have 2^ 2 2 * 2 is 4 3 to the 3 3 * 3 * 3 is in fact 27 so that must mean our missing number is going to be 4 to the 4th of course that looks like this 4 to the 4 is equal to 4 multiplied by itself four times and if you can't work that out mentally you can work it off to the side as needed should be able to get started by saying 4 * 4 is 16 so then we have 16 * 4 again if you can't do it mentally do it off to the side like this uh 4 * 6 is 24 carry a 2 1 * 4 is 4 + 2 is 64 so this becomes 64 * 4 once we work this out we'll have our answer 4 * 4 is 16 carry a 1 6 * 4 is 24 + 1 is uh 25 so this is C this m practice test question for the ASVAB and Pat says that 40% is equal to the fraction X over 30 what is the value of x so for this one we're going to translate this statement into an equation that we can then solve says if 40% well 40% is going to be expressed in decimal form as 04 or as a fraction as two fits I'm going to use the decimal point4 is equal to so we need an equal sign the fraction X over 30 this is a one-step equation to solve it we have to multiply both sides of the equation by 30 this crosses out here leaving you with X on this side clearly the only thing we have left to do is 30 * point4 move our decimal one place to the right to make this 30 * 4 once we work this out we'll move our decimal place one place to the left uh this is 0 12 move our decimal back into the left X in this case equals 12 which is answer Choice D math knowledge practice test question for the ASAP and pet says if x + 5 cents = 83 cents then x equals so for this one we're solving an equation albe it with decimals I'm going to go ahead and write it down like this and you don't have to include that zero in front of the decimal if you don't want to uh as we would when we solve equations we're just going to get x equal to something by itself so in other words we're going to subtract uh five cents from both sides this crosses out leaving you adjust X on this side and we can see X is equal to 83 cents - 5 Cent if you can't do this mentally do it off to the side like I am 3 minus 5 we can't do so we have to borrow from this eight this becomes a 7 this becomes 13 13 - 5 is going to be eight of course 7 minus uh 0 is just 7 so X in this case is 78 cents which is answer Choice B again the ASVAB is a computer adaptive test so in the beginning of the test you will see questions that are as simple as this one answer this as faab math knowledge practice test question in six seconds it says this if 2 to the X power = 32 what is X so if you don't know this one right away uh you can use some Brute Force to figure this one out uh for instance we could say 2^2 = 2 * 2 and of course 2 * 2 is 4 2 to the 3 is 2 multiplied by itself three times 2 * 2 is 4 * 2 is 8 likewise 2 to the 4th is 2 multiplied by itself four times let's work that out 2 * 2 is 4 * 2 is 8 * 2 is 16 so that's not it about 2 to the 5th 2 the 5th is 2 multiplied by itself five times that's 2 * 2 which is 4 * 2 is 8 * 2 is 16 * 2 is 32 so the correct answer to this one is D5 solve this as faab math knowledge practice test question in 60 seconds it says this what are the factors of x^2 + 4x + 3 so right away you should Rec that this is a quadratic trinomial specifically it's quadratic trinomial where the leading coefficient is one therefore you should know that if we can Factor this it's going to look like this now our only task here is to find two numbers that multiply to positive3 and add to positive4 that should be easy enough to do uh + one and + 3 should work and as much as 1 * 3 is 3 1 + 3 is 4 so the answer answer to this one is a x +1 X+ 3 if you need help with factoring check out my channel solve this ASVAB math knowledge practice test question in 60 seconds it says what is the value of five factorial to answer this one you have to know what factorial means factorial means take the number that's given multiply it by every number that's less than the given number until you get to one so for instance 3 factorial is equal to 3 * 2 * 1 let's apply this to 5 5 factorial that's going to be equal to 5 * 4 * 3 * 2 * 1 let's work this out mentally it's not that hard to do 5 * 4 of course is 20 20 * 3 is 60 60 * 2 is 120 120 Time 1 is going to be 120 so the answer to this one is D 120 this ASVAB PCAT ma knowledge practice test question says if the following series continues the same pattern what is the next number in the series all right so for this one uh it looks like to get from 1 to 10 we're going to add nine and to get from 10 to 7 we're going to subtract three again to get from 7 to 16 we're going to add nine which means to get to 16 to the next number in this series we're going to subtract three 16 minus 3 is 13 so the correct answer to this one is B13 if you want more practice as you have an entire video on series and sequences that you may want to check out what is 12 over 50 in simplest form so for this one we're being asked to reduce the fraction 12 over 50 in other words we want to find a number that goes into both 12 and 50 and if you think about it there's only one number and that is two uh so we're going to reduce this by a factor of two 12 / 2 is 6 of course whereas 50 / to is 25 so the furthest we can reduce this is 6 over 25 which is answer Choice C some of you may be asking grammar hero is this really how hard the ASVAB gets well remember the ASVAB and PCAT are computer adaptive test so in the beginning of the test the questions are going to be as simple as this the more easy questions you answer correctly the harder the questions get later on in the test so you want to be able to answer the simple one uh quickly and accurately this practice test question says 192 is what perent of 600 let's write this as an equation and then solve 192 is is equal what percent is unknown call it P of is multiply 600 divide both sides by 600 to get P by itself this crosses out leaving you with p on this side let's go ahead and reduce this fraction you should know that 192 and 600 are both divisible by three this becomes 200 what's 19 divid 3 that's going to be uh six uh and you're going to have a remainder of 1 12 / 3 is going to be four all right so we want to express this as a percent so let's go ahead and write it as a fraction over 100 uh 200 divided 2 is 100 uh 64 divid 2 is 32 so as a percent this is 32% solve this ASV math knowledge practice test question in 60 Seconds it says if C is 30 what is f use C = 5 9 * f - 32 in parentheses let's start by plugging in 30 for C this becomes 30 = 5 9 * f - 32 the next thing we want to do is clear this 59s in front of this set of parentheses so we're going to multiply both sides of the equation by its reciprocal notably by 9 over5 this crosses out here and here leaving you with Fus 32 on this side let's do this math mentally real quick uh five goes into five one time five goes into 30 uh six times so this is just 9 * 6 9 * 6 you should know is 54 let's get F by itself by adding 32 to both sides of this this crosses out here leaving you with just F on this side uh 54 32 that's uh 68 so F in this case is 86 which is D solve this as Fab matat knowledge practice test question in 60 Seconds it says this what is the reciprocal of 0.25 well for this one you're going to have to know what the fraction equivalent of 0.25 is and that's 1/4 likewise you have to know how to find the reciprocal to find the reciprocal of any number n you simply take that number n and place it under one like so all right so let's go ahead and find the reciprocal of 1/4 that's going to be 1 over 1/4 again we're doing division involving a fraction here so we're going to follow the algorithm Keep Change Flip we're going to keep this uh one the same of course we're going to change change from division to multiplication like so then we're going to take the number in the denominator and flip it so instead of writing it as 1 over4 we're going to write it as 4 over 1 let's think about what we're doing here this becomes 1 time what is four divid 1 4id 1 is Just 4 1 * 4 is four so the answer to this one is B4 this Matt knowledge practice test question for the ASVAB and Pat says if six is 25% of a number what is 50% of the same number so let's translate this part into an equation that we can then solve says 6 is is is equal 25% is 0.25 in decimal form our one qu as a fraction I use the fraction one quarter of in math is multiply a number that's unknown so we'll call that n let's solve this for n by multiplying both sides of this equation by the reciprocal of 1/4 which is 4 over one this crosses out leaving us with n 4 over 1 is just four so this is 4 * 6 which is 24 all right so now we we have to go to the second part 50% of the same number so we got to figure out what 50% of 24 is that's 24 / by two which is 12 so this is B12 this practice test question for the asab and Pat says this -2x + 8 is less than 30 what is the value of x so let's copy this one down we have -2x + 8 is less than 30 we're going to solve this inequality the same way we would solve an equation that is to say we're going to get X by itself so we're going to subtract eight from both sides in doing so this leaves us with -2X less than 30 minus 8 is going to be 22 now we're going to divide both sides by -2 to get X by itself and doing so this crosses out leaving us with just X on this side when you multiply or divide across an inequality sign by a negative value you have to change the direction of the inequality sign that is to say you have to flip it so we're going to go ahead and flip it as you can see uh 22 / -2 is going to be1 so the correct answer to this one is c x is greater than1 solve this math knowledge practice test question for the asab and PCAT it says what is the sum of 3x 3r - 2x + 8 2x^2 + 5x and x 3r + 2x^2 - 3x - 3 so in other words we're going to add all of these polinomial together in other words we're going to combine their like terms again like terms have the same letter variables raised to the same power so let's start with X 3r it's X is raised to the 3 power it's corresponding like terms right there 3x3 + x 3r is 4 x 3r Let's cross it out now let's move on to 2x^2 X raised to the second power it's corresponding like terms right there 2x^2 + 2x^2 is 4x^2 cross it out now uh let's do -2X -2x + 5x is + 3x uh 3x - 3x is zero so all these just cross out to nothing and then finally we have 8us 3 which is + 5 so our answer is a this asvat Pat practice test question test your understanding of circles specifically we have two cameras A and B on a racetrack here they have a central angle of 40° and given that we want to figure out how far apart they are which is the same thing as figuring out this Arc Length right here well to find the arc length in a circle you're going to take Theta which is the measure of the central angle over 360 you're going to multiply it by the circumference of the circle we have all these things they have a central angle of 40° so we'll place that over 360 uh what is the circumference of our Circle it's the same thing as the perimeter so that's going to be 360 let's go ahead and reduce this cross out these corresponding zeros 4 over 36 reduces to 1 nth * 360 uh this becomes 360 over 9 again 36 divid 9 is four just tack on that zero so these two cameras are b 40 ft apart on this track in this video I quickly want to address something that can be a source of confusion in the math knowledge subtest of the asbab and PCAT specifically let's talk about negative numbers raised to Powers with parentheses as opposed to not with parentheses when you have parentheses that means you can do this -2 * -2 * -2 * -2 Nega * a negative is a positive positive * a negative is a negative negative * a negative is a positive if you don't have parentheses however you break this apart like this -1 * 2 to the 4th and then you follow the order of operations you do exponents before this multiplication so this becomes 1 * 2 * 2 * 2 * 2 we know this is 16 so this is- 1 * 16 positive time a negative is going to be a 16 pay close attention to how things are are notated as you can see a set of parentheses can make a big difference as to what answer you get for this map knowledge practice test question for the As faab and Pat we have to find the area of a circle that has a diameter of 14 in and we're told to use 22 over 7 for pi so we have to know this formula area equals Pi * the radius squar in addition we're only given the diameter of this circle not its radius we're going to need the radius so we have to know that the diameter of a circle is two times as big as its radius that is d = 2 R plug in 14 for diameter solve for R and this is going to be 7 = R plug in 7 accordingly this becomes 22 over 7 * 7^ 2ar uh this is 22 over 7 * 49 again place this over one so we can quickly cross reduce seven goes in a 7 one time 7 goes in 49 7 times 22 over 1 is 22 7 over 1 is 7 so this is 22 * 7 if you can't do that mentally do it off to the side very quickly this is going to be C 154 in squared for this arithmetic reasoning practice test question for the ASVAB and Pat we have to find the area of the Shaded region in this figure as you can see we have a rectangle which is L * width minus two circles which is going to be two for each of the circles time pi r 2 of course let's go ahead and plug those values in this becomes 20 * 10 - 2 * piun the radius is right here it's five so this is 5^ SAR this becomes 200 minus uh 5^ s is 25 * 2 is 50 so this is minus 50 Pi so for pi we're going to use 3.14 this would be 50 time 3.14 I'm going to let you work that out work that out on your own that said I know that that becomes 157 200 - 157 is 43 so the answer to this one is c43 this math knowledge practice test question says this F xal 8 what is the value of y in the following equation we have y = x^2 / 4 - 2 let's go ahead and start by plugging in 8 for X accordingly this becomes y = 8^2 / 4 - 2 again we have to simplify this according to the order of operations that's pemos we do parentheses first exponents next multiplication and division after that and addition and subtraction after that uh here we have an exponent so 8^2 is 8 * 8 this becomes 64 / 4 - 2 64 ID 4 is 16 so this is 16 - 2 16 - 2 is 14 if you couldn't do this math mentally you have to do the long division off the side 64 / 4 4 * 1 is 4 6 - 4 is 2 drop down this 4 4 * 6 is 24 with no remainder that is that one this math knowledge practice test question for the asab and PCAT we need three formulas we need the perimeter of a rectangle which is two width plus two length a perimeter of a square which is 4S and the area of a square which is s s we know the width and length this is uh 12 this is 20 let's do this mentally 2 * 12 is 24 2 * 20 is 40 24 and 40 is 64 again according to the problem these perimeters are the same so this becomes 64 = 4 S divide both sides by four this crosses out leaving with s = 64 over 4 which is 16 now that we know what s is we can go ahead and plug it in here this becomes 16 SAR that's the same thing as 16 * 16 which I'm going to let you work out on your own I happen to know it's 256 CM squ D I have that memorized but you could work it out using this multiplication over here so that is that one this math knowledge practice test question says convert 24% to a fraction to convert percents to fractions you can simply place that number that you're given over 100 so this becomes 24 over 100 of course we can see that this isn't one of our answer choices which means we could probably reduce this fraction a little bit further uh specifically you should see that we can divide our numerator and denominator by a common factor of four 24 divid 4 is 6 100 ID 4 of course is 25 uh 6 and 25 don't have any common factors so that's as far as we can reduce that fraction the answer to this one is a 6 over 25 this math knowledge practice test question for the ASAP and PCAT says this what is the sum of the interior angles of a hexagon so to answer this one you first have to know that a hexagon has six sides and in addition you also have to know that to find the sum or S of the interior angles of a figure it's going to be S = 180 * n minus 2 where n is the number of sides that that figure has so this becomes 180 times again we know a hexagon has six sides so this is 6 minus 2 this becomes 180 * 4 and if you can't do that mentally you could always do it off to the side like this 180 * 4 uh 4 4 * 0 is 0 8 * 4 is 32 bring down a 2 carry a 3 4 * 1 is 4 + 3 is 7 so the sum of the interior angles of this hexagon is C 720° math knowledge practice test question it says which of the following is a prime number again a number is considered Prime if it's only divisible by one in itself in other words if it's divisible by something like two or three then it's not primed thankfully enough two and three have divisibility rules we can apply to these answer choices to figure out what to them is prime the divisibility rule for two says this if the last digit in your number is even then it is divisible by two and can't be prime we look at answer Choice a this ends in six which is even therefore 26 is div divisible by two and can't be prime the divisibility rule for three says this sum the digits that you're given in the number if the sum is divisible by three then the number itself is divisible by 3 so for instance 5 + 1 is 6 6 is divisible by 3 therefore I know 51 1 is divisible by 3 and is in Prime let's check 171 1 + 7 + 1 is 9 9 is divisible by 3 therefore 171's also divisible by three and can't be primed so the correct answer to this one is C this MTH knowledge practice test question for the asab and Pat says this 13 over 4 equals which of the following decimals so this improper fraction tells you what to do uh improper fractions can be read as follows 13 / by 4 now all we have to do is work this out to get our answer four goes into 13 three times without going over 4 * 3 is 12 13 - 12 is 1 to continue doing this long division we're going to add a couple of zero placeholders as well as a decimal bring that decimal into our answer drop down one of our zero placeholders uh 4 * 2 is 8 10 - 8 is going to be two drop down our zero placeholder four * 5 is 20 20 minus 20 is zero can't do anym so we know our answer is 3.25 D solve this math knowledge practice test question for the ASVAB and Pat it says what percentage of the grid is shaded so first and foremost we have to figure out how big this grid is it's 1 2 3 4 5 6 7 8 9 10 by 1 2 3 4 5 6 7 8 9 10 so this is a 10x1 grid which means that there are 100 total squares in it uh of those 100 10 20 1 2 3 4 5 25 of them are shadeed all right let's convert this to a percentage very quickly uh we can divide out a common factor of 25 to reduce this 25 ID 25 is 1 100 divid 25 is 4 you should know that the decimal equivalent of 1/4 is 0.25 which if you multiply it by 100 converts it to a % so this is 25% which is answer Choice C this ASVAB PCAT math knowledge practice test question says if one side of a regular hexagon is x + 2 then its perimeter is so to answer this question you have to know some properties of hexagons uh specifically you have to know that in regular hexagons all the side lengths are equal so if this side is x + 2 that means all the other sides of this hexagon are X + 2 in addition you have to know how to find the perimeter of polygons including hexagons well to find the perimeter of any polygon you simply add up all of its sides in a hexagon there are six sides so we could do 6 * x + 2 of course we're going to take this six we're going to multiply it here as well as here this becomes 6X + 12 so the perimeter of this regular uh hexagon is c6x + 12 this arithmetic in practice test question for the as VAP and PCAT says a plumber has a car payment of $250 per month $225 of which goes to paying off the principal and the rest goes toward the interest what percent is being paid for interest so if he pays 225 out of 250 for the principal that means he pays 25 again 250 minus $225 is $25 toward the interest uh let's go ahead and place this over his total payment amount that is 250 and by doing 25 / by 250 we can convert this to a decimal and then a percent pretty easily that said you should see that we can also simplify this by a common factor 25 25 divid 25 is 1 250 divided by 25 is 10 this is the same thing as 0.1 you should know that which is the same thing as 10% in other words 10% of his payment is for the interest the answer choice is B solve this as faab mat knowledge practice test question in 60 seconds it says what is the area of the rectangle for the As faab and PCAT you have to know some very basic formulas including how to find the area of a rectangle in case you forgot that's area is equal to the length of the rectangle times the width of the rectangle you should see that the length of this rectangle is six whereas the width of this rectangle is four let's plug those values in accordingly this becomes 6 * 4 four and as a reminder on the ASVAB you cannot use a calculator so you have to know that 6 * 4 is going to be 24 uh so the correct answer to this is the area of this rectangle is D 24 Square fet this ASVAB PCAT math knowledge practice test question we're trying to figure out what the reciprocal of seven is and the reciprocal of 3 and 1/5 let's start with seven the first thing I'm going to do is write that as a fraction by placing it over one again 7id 1 is just 7 to find the reciprocal we're just going to flip-flop these two reciprocal of 7 over 1 is 1 over 7 let's do the same thing for 3 and 1/5 first thing we have to do however is convert this to an improper fraction we do that like this 3 * 5 is 15 + 1 is 16 so this is 16 over 5 as an improper fraction now to find the reciprocal let's just do a flip-flop here uh this becomes 5 over 16 so our two reciprocals are one 7th and 5 over 16 which is answer Choice D this math knowledge practice test question for the ASVAB and Pat says when the temperature is 20° CI what is it on the Fahrenheit scale use the following Formula F equal 9 over5 * Celsius + 32 uh so for this one we're told that Celsius or C is 20 all we have to do in this case is plug it into this formula and solve accordingly so this becomes 9 over 5 * 20 + 32 again according to your order of operations you do multiplication before addition and to make this math a little bit easier I'm going to place 20 over one which is going to enable me to Cross Reduce by saying five goes into a five one time 5 goes into a 24 times 9 over 1 is just 9 * 4 over 1 that's just 4 + 32 9 * 4 is 36 so this is 36 + 32 should be able to do this mentally 30 and 30 is 60 uh 6 and 2 is 8 so the correct answer to this one is D 68° solve this as V Matt knowledge practice test question in 60 seconds it says this what is 3 A2 + a 2 added to a + 6 you should recognize that you're being asked to combine two polinomial notably 3 A2 + a 2 and a plus 6 via addition to do that it looks like this 3 a 2 plus a 2 plus a + 6 now that we've created this expression we have to simplify it by combining like terms again like terms have the same letter variables raised to the same power here you can see we have a raised to the 2 power and a raised to the 2 power here therefore we can combine these two again if it's helpful put that one in front of a s 3 a2+ 1 a^ s is 4 A2 cross these out now a doesn't have corresponding like terms just go ahead and bring it down as is likewise 6 doesn't have corresponding like terms just go ahead and bring it down as is clearly the answer is 4 a^2 Plus a + 6 this math knowledge practice test question for the asab and PCAT says what is the result of adding -3 x^2 - 5x + 1 and 8 x^2 - 2x - 9 so we're just adding this polinomial to this polinomial via simp simple addition like so uh all we have to do is reduce this expression by combining like terms again like terms have the same letter variables raised to the same power so - 3x^2 and postive 8x^2 are like terms uh that simplifies to 5x^2 cross these out uh now we have -5x and -2X 5x plus -2X is going to be -7x cross them out now that we've combined them 1 + -9 is going to be -8 so the correct answer to this one is 5x^2 - 7x 7X - 8 which is answer Choice C of course solve this math knowledge practice test question for the ASVAB and PCAT in 60 seconds it says what is the slope of the line y - 12x = 3 so first and foremost you should recognize that this equation is almost in slope intercept form again slope intercept form for equation of a line is y = mx + b what we have here is y - 12x = 3 clearly to get this in slope intercept form all we have to do is move this 12x to the other side of the equal sign the addition uh in doing so this crosses out here and leaving with Y = 12x + 3 now again this m right here is the slope and now that this is in slope intercept form we can see that the slope is 1/2 so the answer to this is B2 this math knowledge practice test question for the asab and PCAT says if a triangle has a height of 12 in and an area of 42 Square in how long is the base of the triangle so for all triangles we're going to use this formula to find area area equals 12 base time height you have to memorize that one for the test in this case we're not finding area we're going to be solving for B that said we were given H we know that's 12 and we were given area or a we know that's 42 let's plug those in this becomes 42 equals 12 base and the height is 12 all right so this is 42 equal what's 1 12 * 12 1 12 * 12 is going to be six so this is 6 B all we have to do is solve for b or base by dividing both sides by six this crosses out leaving you with B on this side uh 42 divid 6 is 7 so the answer to this one is b s the base is 7 in long this ma knowledge practice test question for the ASAP and Pat says Factor this of course you can use the answer to figure this one out otherwise you have to use the AC method a * C in this case is going to be 2 * -3 is-6 B is one there's coefficient of one there we're looking for two numbers that multiply to6 and add to one that's going to be 3 -2 I using those two numbers we can rewrite this expression to be 2x^2 - 2x y + 3x y - 3 y^ 2 now we can Factor this one via grouping we're going to factor out of 2x here this comes x - Y in parentheses here we're going to factor out a 3 y this becomes x - Y in parentheses combine the these this becomes 2x + 3 y * xus y this is answer Choice uh B of course solve this math knowledge practice test question for the ASVAB and Pat in 60 seconds it says if AAL 6 and b equal 5 what is value of a^ 2 minus b^2 all squar so let's start by plugging in 6 for a and 5 for B respectively of course this becomes 6^ 2 - 5^ 2 all squar we're going to use the order of operations to figure out what to do next order of operations is pemos according to the order of operations we do parentheses first and then we do uh all this after that in parentheses you can see we have three operations 6^ squ that's one operation subtraction that's another operation and 5^ S that's another operation we're going to take care of our exponents before our subtraction uh this becomes 36 - 25 2ar again we're still working in parentheses uh 36 - 25 is 11 uh this is 11^ squar which is 121 so the answer to this one is a 121 this asab PCAT math knowledge practice test question says what is the circumference of a circle that has a diameter of 10 cm use 3.14 for pi so for circumference you have to know one of two formulas circumference is either going to be found by using pi * diameter or it's going to be uh 2 pi r or R stands for radius of course uh we were given diameter so we're going to use this first Formula circumference equals Pi the diameter according to the problem is 10 so this becomes 3.14 * 10 again you could do this like this 10 * 3.14 but you should be able to do this one mentally when you multiply something by a power of 10 you move that decimal uh to the right according to how many zeros there are in the power of 10 uh so we're going to shift this one place to the right 3.14 * 10 is 31.4 so the correct answer to this one is going to be C 31.4 CM this asvat PCAT arithmetic reasoning practice test question says this the area of one circle is four times as large as a smaller circle with a radius of 3 in the radius of the larger circle is so we're talking about area of circles that's going to be area equals PK R 2 let's talk about the area of the smaller Circle that's going to be area equals Pi time its radius squar its radius is three so this is going to be 3 squ in other words its area is 9 pi um we know that the larger Circle has four times the area of the smaller Circle so its area is going to be four * 9 pi uh 9 Time 4 is going to be 36 so the larger Circle has an area of 36 Pi uh again we want to know its radius not R 2 this is R 2 how we how are we going to go from R 2 to R we're going to take the square root of 36 the square root of 36 is simply six so the radius of our larger circle is D6 in this math knowledge practice test question for the ASVAB and Pat it says if xal -2 and yal 3 What is the value of 2x - 3 over y - 5 so we're going to evaluate this expression and of course we're going to plug in -2 for x and 3 for y let's go ahead and do that this becomes 2 * -2 - 3 all over 3 -5 let's go ahead and work this out 2 * -2 a positive times a negative is going to be negative so this is4 - 3 over 3 - 5 that's going to be2 um let's go ahead and continue working this out -4 - 3 is going to be -7 over -2 now you have a negative over a negative a negative over a NE negative becomes a positive in other words those two negatives cancel each other out so the correct answer to this one is B 7 over2 solve this math knowledge practice test question for the ASVAB in PCAT it says if x = 2 and y = -3 then x y^2 equals so let's copy this one down as if we're writing on our own scratch paper again we're told to let xal 2 Y is going to be -3 and we're going to be plugging those values into x y^ 2 let's go ahead and substitute them in this becomes 2 * -3 2 well according to the order of operations again that's pemos we do exponents before we do multiplication of course uh that means we're going to do -32 before we multiply by two let's do this off to the side -32 is the same thing as -3 * -3 you should know that a negative * a negative is a positive specifically -3 * -3 is positive 9 so this simply becomes 2 * 9 which is 18 so the answer to this one is B8 this math knowledge practice test question for the ASAP and Pat says if xal -3 what is the value of x^2 - 2x + 4 so we're going to take X equaling -3 and we're going to plug it in here x^2 - 2x + 4 let's go ahead and plug that in for X accordingly this becomes -3 2 - 2 * -3 + 4 -3 2ar is the same thing as -3 * -3 which is going to be a positive 9 uh -2 * -3 is going to be postive 6 again a negative * a negative is a positive + 4 uh 9 + 6 is 15 plus four is going to be 19 so the correct answer to this one is D9 this math knowledge practice test question for the ASAP and PCAT says if x = -2 and Y = 3 What is the value of 2 y - x so we're going to be evaluating the expression 2 y - x when x = -2 and Y = 3 of course let's plug those values in and then simplify this becomes 2 * 3 - 2 uh 2 * 3 is 6 of course now what are we going to do with a minus -2 a minus minus becomes a plus so this becomes 6 + 2 which you should know is eight so the correct answer to this one is B8 be very careful on this test because negatives can mess you up a minus a negative becomes a plus as we just saw this MTH now it's practice test question says if xal Y what is 100 + 3 * x - Y in parentheses so the quickest way to solve this one is to give x a real value I'm going to give it a real value of five since five in general is pretty easy to work with if xals Y and xal 5 that means Y Must also equal 5 let's go ahead and plug this in this becomes 100 + 3 * x - y we now know what X and Y are this becomes three x is five Y is also five this becomes 100 100 + 3 5 - 5 is 0 you should know that 3 * 0 is 0 so this is just 100 which is answer Choice B of course this map knowledge practice test question for the ASAP and Pat we're going to be evaluating the expression 3 * 2x - y all over x + y when x = 2 and y = -3 let's plug those in and evaluate accordingly this becomes 3 * 2 * 2 minus again Y is -3 all over 2 + -3 let's start with the denominator uh 2 +3 is going to be 1 let's work out what's in parentheses very quickly uh 2 * 2 is 4 minus-3 and minus a negative becomes a plus so this is plus three this becomes 3 * uh 7 over1 3 * 7 is 21 over1 positive divid negative is going to be a negative so this is D -21 this math knowledge practice test question for the asab and PCAT says this if xal 4 which of the following Expressions does not equal 9 so wherever we see X in each of these Expressions we're going to plug in four and in doing so we're going to be able to determine which of these does not equal nine so we have 3 * 4 + -3 3 * 4 is 12 + -3 that's the same thing as 12 - 3 which is in fact 9 uh this one is simply 4 + 5 which equals 9 this one becomes 4 -3 which equals 9 so this one does not equal 9 therefore we know C is the expression that does not equal nine we don't even have to check D because we have our answer already solve this math knowledge practice test question it says what is 5X * 3x^2 - 5 so we have 5x * 3x^2 - 5 in other words we're going to take this 5x and multiply here as well as here this becomes 15 x 3r minus 255x which is answer Choice B uh in case you didn't know how this became x to the 3 let's take a look at the product rule real quick says a to the m * a to the N = A to the m + n and let's see how this applies here here we have 5x * 3x^2 again this becomes this 15 then we have x to the 1 * x^2 of course according to the product rule that becomes 15 to the X1 + 2 which is equal to 15x to the 3 okay so that's the product rule you need to know it for the asab this asab Pat math knowledge practice test question says this what is 5 to the X power when x = 3 so we have 5 to the X power power and we're told to let x equal 3 Let's Start by plugging in 3 for X this becomes 5 to the 3 power which is the same thing as 5 * 5 * 5 you should be able to work this one out mentally again 5 Time 5 is 25 25 Time 5 is going to be 125 so the answer is D on test day of course you might be a little bit nervous so it's okay to work things out the long way you could have said 25 * 5 off to the side like this 25 5 Time 5 is 25 bring down a five carry a 2 2 * 5 is 10 + 2 is 12 all right that is that one this math knowledge practice test question for the ASAP and Pat says solve the following equation for D says b equals CD well this is a literal equation and our goal here is to get D equal to something by itself as you can kind of see from our answer choices this says C * D to get rid of C we're going to do the opposite operation of multiplication that is we're going to divide both sides of the equation by C in doing so this crosses out says D equals B over C and then if you want to write it like an answer choice you just do this D equal B over C which we can see is answer Choice C in this case this math knowledge practice test question for the asab and Pat says which of the following is the smallest prime number greater than 200 so first we have to understand that a number is considered Prime if it's only divisible by one in itself seven is prime because it only has two factors notably one and seven and one is never a prime number so we're going to use divisibility rules for two three and five to figure this one out divisibility rule for two says if the last digit number is even then that number is divisible by two and is in Prime 214 ends in a four which is even 214 is divisible by two uh the divisibility rule for five says if the last digit the number is a zero or a five that number is divisible by five and therefore is in Prime divisibility rule for three says if the sum of the digits is divisible by three uh then that number is going to be divisible by divisible by three and can't be Prime 2 + 0 + 1 is 3 3 is divisible by three therefore 2011 is divisible by three and can't be prime so the correct answer to this one is c211 this asvat PCAT ma knowledge practice test question says this what is z to x + 2 power when x = 2 and zal 2 so let's start by plugging in those values accordingly again we're going to plug in two for Z here and two for X there that comes this uh 2 to the 2 + 2 power in other words we have 2 to the 4th power 2 to the 4th power is the same thing as two multiplied by itself four times you should be able to work that out mentally 2 * 2 is 4 4 * 2 is 8 8 * 2 of course is 16 so the answer to this one is c16 solve this as Fab math knowledge practice test question it says what is the product of the reciprocals of 0.5 1/4 and three so we have to know the fraction equivalent of 0.5 is 1/2 to find its reciprocal we just flip it so that's going to be 2 over one reciprocal of 1/4 we just flip it that's going to be 4 over one reciprocal of three three can be written as a fraction as 3 over one find its reciprocal by flipping it that's 1/3 so we're multip Ling together 2 over 1 * 4 over 1 * 1 over 3 again when you multiply fractions you just multiply straight across so this becomes 2 * 4 which is 8 * 1 which is 8 this is 1 * 1 which is 1 * 3 is 3 so now we have to convert 8/3 to a mixed number we're going to do that via division this becomes 8 / 3 three goes in8 two times without going over 2 * 3 is 6 8 - 6 is 2 so this is 2 and 23 so our answer is C2 and 2/3 solve this as faab math knowledge practice test question in 60 seconds says find the slope of the line that passes through the points5 -2 and 39 so for this one you have to know the slope formula which is M referring to slope = Y2 - y1 all over X2 - X1 let's identify those this is X1 this is y1 this is X2 this is Y2 let's plug those in and solve so this equals Y2 which is -9 - y1 which is -2 all over X2 which is 3 - X1 which is-5 these double negatives become positive so 9 minus -2 is the same thing as9 + 2 3 minus5 is the same thing as 3 + 5 let's do the bottom first 3 + 5 is 8 uh9 + 2 is -7 so the correct answer to this one is going to be B -7 eight question for the ASAP and PCAT says which of the following fractions is the largest right away you should say that uh 7 out of 10 is 7 which may be the largest uh two out of five you should know is 04 that said you should also be able to say that 2.5 out of five would be exactly 0.5 this of course is smaller than 7 uh similarly you should be able to say that four out of eight would be 0.5 this is smaller than that so it's smaller than 7 this last one's a little bit harder so I'm going to revert to doing long division I could read this as 13 / 16 add a decimal and a zero placeholder bring that decimal up so if this is bigger than 7 we know D is the biggest fraction let's do 16 time 8 off to the side to see if it is going to be bigger uh 8 time 6 is 48 carry a four 8 * 1 is 8 99 10 11 12 so this is going to be 08 something8 something is bigger than 7 solve this ma knowledge practice test question for the ASVAB and piecat it says simplify 25ths X Plus X so I know many of you could solve this one mentally that said sometimes on test a people get a little nervous and a simple problem like this uh can stump them uh that said let's work through it together this says two fits X Plus X well as it happens these are like terms so we can simply add them together if it's helpful you can put that imagin one in front of the X so 2s x + 1 x is 1 and 2s X that said we look through our answer choices and we don't see it there so we think we may have made a mistake uh you haven't all you have to do is convert this which is very easy to do again our denominator is not going to change 1 Time 5 is 5 + 2 is 7 so this is b 75s x this ASV Matt knowledge practice test question says this if a circle has a diameter of 75 units how many units is its radius you have to know that in all circles the diameter is always going to be twice as long as the radius that is diameter equals 2 R this problem tells you that D equal 75 and you're going to be solving for R uh now that we know D equal 75 let's plug it in right here equals 2 R again we're solving for R so we're going to divide both sides by two in doing so we get to cross this out this equals R 75 divid it by two if you can't do that in your head you could always do it off to the side like this 75 / it by two two goes into seven three times without going over two times uh three is six 7 - 6 is 1 bring down this five two goes into 15 seven times without going over 2 * 7 is 14 15 - 14 is 1 add a decimal there add a decimal there add a zero placeholder Drop it Down 2 * 5 is 10 so the radius is 37.5 for this ASVAB PCAT Mac knowledge practice test question we're trying to figure out what 9 to the 1/2 power is whenever you see a number raised to a fraction such as 1/2 1/3 and 1/4 you automatically want to think about writing it as a radical um in this case we're going to take our nine it's called the radican we put it inside the radical symbol this one is our exponent and this two is our index typically when we have an index of two we don't express it and we have when we have a exponent of one we don't express it again 9 to the first power is just nine uh you have a two outside uh the radical symbol it just means square root so in other words 9 to the 1/2 power is the same thing as taking the square root of nine which is three so the answer to this one is A3 if you need more help check out my link video on this topic the ASAP and Pat says Jose is twice as old as Karen if Karen is n years old now how old was Jose seven years ago so again Karen is n years old now and Jose is is twice as old as Karen so that means Jose is 2 N years old now uh the question is how how old was he seven years ago so we're going to take 2 N which is his current age and we're going to subtract seven from that and that's all we have to do for this one this one is c 2nus 7 for this math knowledge practice test question we're trying to factor 9x 3r + 18 x^2 - x - 2 to do so we're going to to use a technique called factoring by grouping which means I'm going to look at 9x 3r and 18 x^2 factor that then I'm going to factor ITX minus 2 so from 9x 3r + 18 x^2 I can of course factor out 9 x^2 and in doing so that leaves me with x + 2 in parentheses now from x -2 I want to factor out a number such that I get X plus 2 in parentheses so I'm going to factor out a NE 1 this becomes x + 2 in parentheses now I have my answer it's going to be 9 x^2 -1 * x + 2 which is answer Choice a for this math knowledge practice test question we're subtracting one polom from the other so let's go ahead and set it up like this 3 a - 9 a B plus b from that we're subtracting this other polinomial and I'm going to rewrite it to match this first polinomial this is 7 a minus a b + 8 B uh let's go ahead and take this distributed here here and here this becomes 3 a - 9 a B+ b - 7 a again negative * positive is negative negative * a negative is a positive negative time a positive is a negative combined like terms 3 a and -7 a is -4 a just like that we know our answer choice is a cross these out9 a and ab are like terms that's going to be -8 a cross this out uh b and8 b are like terms that's going to be -7 B for this math knowledge practice test question for the ASVAB and pet we're trying to find the average of 1/2 1/4 and one 16 to find the average we're going to add them all up and divide by three since there are three of them to add these fractions we have to have a common denominator which you should see is 12 to write two is 12 we have to multiply by six of course to write four is 12 we multiply by three that's right 6 is 12 we multiply by two again this is all divided by 3 uh 6 + 3 is 9 10 11 so this is 11 over 12 / 3 again we can write three as a fraction by placing it over one to do division of two fractions follow the algorithm Keep Change Flip keep this as 11 over 12 change from division to multiplication flip this to be 1 over three again multiplying fractions you just multiply straight across 11 * 1 is 11 12 * 3 is 36 so this is a it says if x^2 - 44 = 100 then x equals so there are two ways to solve this one you could recognize that you have the difference of two perfect squares here or you could Solve IT algebraically difference of two perfect squares says this a^ 2 - b^ 2 is going to be equal to a minus B * A + B and let's take a look at what we have here we have x^2 - 44 = 100 if we move 100 over here via subtraction this crosses out leaving you a zero on this side this becomes x^2 - 144 = 0 and I could rewrite this like this x^2 - 122 = 0 so we do have our two perfect squares so we can write it like this x - 12 x + 12 = 0 let's set these each equal to 0 x - 12 = 0 x + 12 = 0 this is x = 12 or x = -12 which is answer Choice C this math knowledge practice test question for the ASVAB and PCAT says if 4x^2 = 16 then x equals let me say this there are three ways you can solve this one you could recognize that you have the difference of two perfect squares here and solve this one via factoring you could also take your answer choices plug them in and find which pair works and finally you can solve this one algebraically of course let's go ahead and do that we have 4x^2 = 16 again and we're solving for x so we want to get X by itself so let's divide both sides by four this crosses out leaving you with x^2 on this side 16 ID 4 is 4 to get rid of this Square we're going to take the square root of both sides this crosses out leaving you with X on this side the sare OT of 4 is going to be plus or minus 2 as it happens this actually has two solutions notably -2 or positive2 if you plug both those in for X you'll see that they both work this V math practice test question says this if 1/8 / 1/4 equals c then what is C so in this case we're dividing two fractions notably 1/8 by 1/4 when you divide fractions you have to follow the algorithm Keep Change Flip keep refers to this fraction in the numerator you keep it the same so we'll keep 1/8 as 1/8 change refers the operation of division you change it from division to multiplication and flip refers to the fraction the denominator you flip it so instead of being one 4 it's going to be 4 over 1 now that we've done that we're just multiplying two fractions together which means we're going to multiply straight across notably this is going to become 1 * 4 over 8 * 1 1 * 4 is 4 8 * 1 is 8 uh you can reduce this by dividing out a common factor of four four divid 4 is 1 8 divided 4 is two so the answer to this one is clearly B2 solve this as van M knowledge practice test question in 60 seconds it says this which of the following is not an equation of a line so remember equations of lines can be represented in four different forms you have slope intercept form which looks like this y = mx + b uh you have the point slope form which is y - y1 = M * x - X1 you have a vertical line where x equals some constant a and you have a horizontal line where y equals some constant B the easiest way to figure out which of these is not an equation of a line is to find the one where one of the letter variables is raised to some power other than one as you can see in answer Choice D we have X raised to the second power which is going to make this a parabola not a line and all these other answer choices match one of these four forms this math knowledge practice test question for the ASVAB podcast says this if x + a * X plus b = x^2 + 7 x + 12 what is the value of a plus b so the easiest way to solve this one is to go ahead and Factor X2 + 7x + 12 that should be fairly easy to do it's going to look like this um we're looking for two numbers that multiply to 12 and add to seven that's going to be + three + 4 again 4 * 3 is 12 4 + 3 is 7 so we know this is our a this is going to be our B this becomes 3 + 4 which is 7 so the correct answer to this one is A7 this ASVAB PCAT ma knowledge practice test question says a circle has a circumference of 12 Pi CM what is the radius of the circle so when we talk about circumference of circles you have to know one of two formulas notably circumference is equal to 2 pi r or circumference equals piun * diameter in this case we're talking about circumference and radius so we're going to use this top formula notably circumference equals 2 pi r according to the problem we know our Circle has a circumference of 12 Pi so let's plug that in accordingly equals 2 pi r according to this problem we're trying to figure out what r or the radius is so we're going to divide both sides by 2 pi to get R by itself this crosses out here leaving you with r on this side these pies cross out 12 / 2 is 6 so the radius of this circle is C6 CM that's all there is to that one you do have to know both those formulas for this test solve this math knowledge practice test question for the ASVAB and Pat it says what is the area of a parallelogram its length is xus 3 and its height is X+ 5 so to find the area of a parallelogram it's area equals base time height that's one of the formulas you do have to memorize for this test of course we're given both those things in this case we're told H or height is x + 5 and the length or the base or B is x - 3 just plug those in x - 3 * x + 5 of course we're going to have to multiply this out to match one of our answer choices here again you just do x * x x * 5 -3 * x -3 * 5 this becomes x * X which is x^2 uh x * 5 is + 5 x -3 * X is -3x -3 * POS 5 is -15 let's simplify this x^2 + 2x - 15 of course that is answer Choice d as F Pat ma knowledge practice test question says what is the product of the reciprocals of 2/3 1/8 and 5 so we have 2/3 1/8 and 5 the first thing we need to do is find the reciprocal which means we're just going to flip-flop the numbers so this is going to be 3 over two 8 over one five can be written as a fraction by placing it over one so this is going to be 1 over 5 let's find the product of those so multiply them 3 over 2 * 8 over 1 * 1 over 5 when you multiply fractions you just multiply your numerators and then multiply your denominators uh 3 * 8 is 24 * 1 is 24 uh 2 * 1 is 2 * 5 is 10 uh this is 2.4 which is not an answer choice that said we can convert this to mixed number pretty easily uh 10 * 2 would be 20 that gives us a remainder of four out of 10 uh we can simplify that pretty easily uh this becomes 4 ID 2 which is 2 10id 2 is 5 so this is D this ASVAB PCAT math knowledge practice test question we're trying to find the slope of two 4 and -24 so we're going to need the slope equation notably M which means slope is Y 2 - y1 over X2 - X1 of course that we get those values from our points this is X1 this is y1 this is X2 this is Y2 just plug them in and do this arithmetic Y2 is right here it's -4 minus y1 it's 4 over X2 it's right there -2 minus X1 is right there it's two uh 4 - 4 is going to be 8 -2 - 2 is -4 a negative divided by a negative becomes a positive 8 divided four is going to be two so the correct answer to this one is A2 for this bth knowledge practice test question we're trying to figure out which of these is the smallest fraction so let's go ahead and multiply this by two to get started this is 410 which is4 let's convert these to decimals via some quick long division add a decimal and a zero placeholder 9 * 4 is 36 we're not going to keep working these out because this is 04 something this is exactly 04 let's hope one of these is smaller add a decimal zero placeholder bring that decimal up 7 * 4 is 28 we're not going to keep keep working out this is4 something 3 / 8 add a decimal zero placeholder 8 * 4 would be 32 which is too big 8 * 3 is 24 uh so you should see that. 3 is smaller than 04 something exactly 04 and4 something so the correct answer to this one is D this ASVAB PCAT math knowledge practice test question we're trying to figure out which of the following fractions is less than 25% which is the same thing as 1/4 or 0.25 in decimal form let's just go from top to bottom two fits let's multiply this by two and this by two this becomes 4 over 10 which is 40% that's bigger than 25% of course uh 1/3 you should know is uh 33% which is bigger than 25% 516 let's start this long division here 5 / by 16 add a zero and a decimal uh 16 goes into 50 three times without going over 16 * 3 is 48 this is going to be three something so I know this is bigger than 25% what about 1/8 well what is 28 28 is the same thing as 1/4 uh 28 is bigger than 1/8 so the correct answer here is D solve this math knowledge practice test question for the ASVAB and piecat it says if 4 over 3 * 3 over 4 = 5 Z then Z equals let's start by copying this one down again on the ASVAB and PCAT you will have your own scratch paper and you'll want to use it so we're going to be solving for Z of course uh let's take care of this multiplication real quick to make this one a little bit easier to see uh as you can see we're multiplying two fractions which means you're just going to multiply straight across in other words this is going to become four * 3 over 3 * 4 = 5 Z this becomes 12 over 12 = 5 Z 12 / 12 is 1 = 5 z uh divide both sides by 5 to get Z by itself uh this crosses out leaving you with just Z on this side as you can see Z equals 1/5 which is answer Choice C nothing too difficult there that said you had to be able to work with fractions solve this math knowledge practice test question for the ASVAB and PCAT it says if x^2 - 44 = 100 then x equals let's start by copying this one down again on test a you will have your own scratch paper uh we're solving for x so ultimately we want to get x equal to something by itself let's go ahead and add 44 to both sides of this equation this crosses out here leaving us with x^2 over here 100 + 44 is 144 let's get X by itself by taking the square root of both sides in doing so this crosses out leaving us with x uh when you take the square root of a positive number the answer is always going to be plus or minus square root of 144 you should know is 12 uh that said that plus or minus isn't one of our answer choices so you have to know we could write this like this x = 12 or x = -12 since we only have positive2 as an answer choice we're going to go with C pos2 solve this math knowledge practice test question for the ASVAB and PCAT it says if x over 5 + 6 = -14 then x equals let's start by copying this one down again on the ASVAB and Pat you will have your own scratch paper so I encourage you to use it again we're solving for x so ultimately we want to get x equal to something by itself let's subtract six from both sides in doing so we get to cross this out this leaves us with X over five on this side -14 - 6 is -20 and then finally let's get X by itself by removing this five from the denominator to do that we're going to multiply both sides of the equation by five in doing so that crosses out there leaving you with just x -20 * 5 is going to be -100 so the answer to this one is C 00 again for the asab you have to be able to work with positives and negatives negative times a positive is a negative solve this math knowledge practice test question for the ASVAB and PCAT it says if 4x^2 equal 16 then x equals so this is 4x2 = 16 let's start by dividing both sides by four to get x^2 by itself in doing so this crosses out leaving you with x^2 = 16 / 4 is 4 to get rid of the this Square we're going to do the opposite operation notably we're going to take the uh square root of both sides this crosses out leaving you with this x equals when you take the square root of a positive number uh the answer is always plus or minus and the square root of 4 is 2 uh so your answer could look like this X = plus or minus 2 x = 2 or x = -2 if you plug in positive2 or -2 here it will work so we're going to go with answer Choice B xal plus or minus 2 solve this math knowledge practice test question for the asfb and PCAT it says if 4 * x + 6 in parentheses = 44 then x equals let me start by saying this I know many of you like me can solve this one mentally that's great that said on test a things happen you might be a little nervous and your mental math may not be as good as it is when you're sitting in your own house so for that reason let's work this one out off to the side says 4 x + 6 = 44 let's get rid of this four via division of both sides this crosses out leaving you with x + 6 over here 44 ID 4 is 11 subtract 6 from both sides now this crosses out x = 11 - 6 which is 5 answer of course is five let's check it real quick uh 5 + 6 is 11 11 * 4 is 44 so we know we did it correctly for this Matt knowledge practice test question for the ASAP and Pat we're trying to solve the equation 3 3 p - 5 + 2 p = 25 - 5 P for p so let's start by combining 3 p and 2 p to make that 5 P - 5 = 25 minus 5 p uh now we're going to get all the P's to one side of the equal sign and everything else to the other side I'm going to add 5 P to both sides right here in doing so this crosses out and this becomes 10 p and at the same time I'm going to add this five over here via addition this crosses out leaving me with the equal sign over here 25 + 5 is 30 divide both sides by 10 now to get P by itself this becomes P equal 30 ID 10 which you should know is three so the correct answer to this one is B P equal 3 this math knowledge practice test question for the ASAP and Pat we're going to be solving for x the first thing we have to do is distribute this three distribute this -2 and distribute this five accordingly this becomes 3x x + 3 - 6 x + 2 again a negative * a negative is a positive equals 5x - 10 + 7 all right let's combine like terms and solve uh 3x and -6x is going to be -3x 3 and 2 is going to be five uh 5x doesn't have a like term 10 and -7 becomes -3 let's move this over here via addition this crosses out this becomes 8X let's move this one over here via addition this crosses out this becomes 8 divide both sides by eight to get X by itself this becomes one 8 divid by 8 is one so the correct answer is C1 this asab PCAT math knowledge practice test question says this if 3 * x + 6 in parentheses = 39 then x equals so in other words we're going to be solving this equation here we have 3 X x + 6al 39 of course uh let's get rid of this three by dividing both sides of the equation by three this crosses out leaving you with X+ 6 over here um this mental math is actually very easy to do 3 divid 3 is 1 uh 9 / 3 is 3 so to get X by itself all we have to do is subtract six from both sides now this becomes x = 13 - 6 is 7 correct answer is A7 let's go ahead and check it very quickly by plugging in 7 for X right here this becomes 3 * 13 which is in fact 39 so we know we did it correctly this ASVAB math knowledge practice test question says what is the result of subtracting 4x^2 - 3x + 1 from 2x^2 + 5x - 2 so we have to set this one up correctly we have 2x^2 + 5x - 2 from that we're subtracting 4x^2 - 3x + 1 this is 2x^2 + 5x - 2 distribute this negative there there and there this becomes - 4x^2 + 3x - 1 combine like terms 2x^2 4x^2 is -2X ^2 cross them out 5x and 3X is 8x uh -2 +1 is -3 so the correct answer to this one is C [Music] n