in this video we're going to go over a full length 22 question GED math practice test that was a mouthful now the first three are no calculator and this one here if you have division with fractions you could always change it to a multiplication you're just going to keep the first fraction change division to multiplication and flip the last fraction and that's much easier because then you could just multiply straight across there and that'll give us 15 up top 20 in the bottom and finally we just want to simplify this 5 goes into 15 three times five goes into twenty four times so 3 over 4 that is our final for this one here in order to solve an equation for x just find whatever is on that side and do the opposite there because then 12 minus 12 those will end up canceling 0 out and then drop down the 4X and 32 minus 12 that'll give us 20 on that side okay then X is being multiplied by 4 we're going to do the opposite and divide both sides by 4. because these will cancel and then 20 divided by 4 x is five so that's all for this guy here they love asking a question about when something is undefined and in math something's undefined when the bottom equals zero or when you divide by zero now let's highlight the bottom here and let's just plug in a couple of these answers and let's see what happens so when X is 3 we're going to change this to 3 and this to 3. so let's do that but inside the parentheses we get 3 minus 3 we get 0. and then we just get three times zero so that does in fact give us 0 in the bottom and that'll make it undefined okay this time let's try it with X is zero let's plug that in and then we get this guy but this time when you have something in front of parentheses it's going to multiply and make all of that zero so once again that'll also make the whole bottom zero so those are our two answers X is three x is zero they make the bottom equal to zero therefore that make the whole thing undefined here for this problem we want to average 32 hours and we're given all of these hours here what could we plug into the messing one well you could always just plug in the answers they give you let's try 43 see if all of those ones average to become 32 let's do it okay we'll start with 28 plus 33 26 We'll add in 43 and 30. but be careful because you don't want to divide by 5 right here that would just divide 30 by 5. so let's go ahead and delete that you'll always want to get the total first and then we'll go ahead and divide by how many we have five boom and that ends up giving us a perfect average of 32. so that was nice it was the first one got lucky but that made the whole average exactly 32 there in order to find the surface area for a volleyball let's just draw that out real quick any ball is the same thing as a sphere and then you could look this formula up in the formula sheet they give you and then essay for surface area now we're just going to change the radius R to a number but they've given us the diameter that goes all the way across and that's a 0.2 but R the radius is exactly half of that half of 8.2 4.1 and that's what we're going to change that R2 right there so let's type all of this into the calculator here by the way this is the exact same calculator that you'll use for the GED so okay let's do four then we have a pi button on the left side there times our radius 4.1 and notice this one squared to the power 2 you could use that x squared button all of that to 11.2 so that is the surface area here we have an election and we're told that Jones received 6279 votes we also can see that Jones received 23 percent of the votes we want to find out how many votes were cast in the election total now whenever you're given a percent and you're asked a problem you could always draw a triangle and here's how you could label it if you know the percent you're going to go ahead and put it in the bottom right and we do we know that's 23 percent and then you're going to put one other number somewhere now we're given 6279 is that part of the votes or the whole votes well that's just part of them so we'll put it up top and from there we could find the whole or total amount of votes when they're stacked on top of each other it's just going to become a division problem so we'll do that divided by that and that'll give us the total here let's see that okay six thousand two seventy nine divided by 23 to do the percent just hit the second left parentheses boom so there were 27 300 votes in this election here and that's the hole right there now what's nice is we could double check it because if you know the whole and the percent these should multiply to give you that let's do that real fast here so let's clear 27 300 times 23 percent and sure enough that gets us back to the part right there so they all fit perfectly in this triangle for a percent problem for these problems it's usually easiest to find the cost per one hour so for lunar launch let's just do 62 divided by two and that'll give us 31 bucks per hour now for over the moon we could see okay one hour that's just gonna cost 28 bucks so let's add that in but then we're renting for eight hours so we'll multiply each of those by eight and that'll give us these amounts here but then finally we're finding the difference in cost so that always means subtract we'll do that minus that and that'll give us 24 bucks now there's a lot going on with this one here but the main thing is it's a quotient and that means division so notice all of them are fractions okay so far so good now the next part is twice the quantity but that just means 2 times quantity is parentheses but they all have that so far so again so far so good but the next part is important because it's 6 less than the number whenever they say six less than it always means minus six at the end so therefore it could be C or it could be D But A and B those have six in the beginning so those are no good and then we're going to divide all of that by the product of 3 and a number but product just means multiply and 3 times a number a number is X so 3 times x d is the only one that does that mushes them together to multiply so that is the correct expression here this one becomes very easy when you know this trick whenever you have an x squared and an equal sign you could always plug it into the calculator because there's a button on here called table and then it's going to give you a y equals we're just going to type in the left side of this equation so let's do five there's the X right there squared is Right Above It plus another X and then minus 4. okay then you want to go usually it's going to be set to Auto go ahead and switch it over to ask because that'll allow us to plug in our own X values here okay Enter and let's try X is negative one basically we want to see if the whole thing equals zero but if we plug in X is negative one that does make the whole thing zero so this is definitely an answer let's go ahead and try it with five over four so five there's the fraction four enter but that's no good because that doesn't give us zero so that one is not an answer there okay let's go ahead and plug in four over five let's keep going for fraction five awesome that one does give us zero so basically negative one four-fifths made the whole thing zero those have to be our two answers here here we're finding the circumference of this manhole a circumference is the distance all the way around the outside now you could look up in the formula sheet and there's two options for circumference formula because they've given us the diameter here is 48 then we want to plug into this one here just change D to 48. so let's go ahead and do that here okay we got pi times our diameter 48. it just gives you that so hit the button above enter multiply it out 150.8 and there we have it D that is the number of inches all the way around the outside there for this problem we're finding the slope of the line now this one's a little extra but to do that we want to get y all by itself here because we have this minus 5x we want to get rid of it let's plus 5x and we'll do it to both sides because these will cancel and then drop everything down and we're really close to getting y by itself but it's being multiplied by two so let's divide by two do the opposite because these will cancel and then just copy everything down once you get y equals by itself whatever it is in front of X is the slope so in this case the slope is five over two and we're done the reason that works is when you have y equals it's actually m x plus b m is the slope it's always multiplied by X there so that's why that was the slope sometimes the easier problems come later for this one we're finding how many combinations of one bread one cheese and one meter possible from this menu just count how many of each you have and then don't blink you'll miss it just multiply those because then three times four twelve there'd be 12 options of just these two and then 12 times 4 that'll give us 48 options for all of them total so combinations usually involve multiplication and that's it there they've given us a function it may look intimidating but it's not that bad because they mentioned that X is the number of jerseys and then we want to find the cost for 12 jerseys in other words we're just going to change X to 12 here and here and that's going to give us the total cost so let's see what this does here okay 3 times x is 12 and that one squared minus eight times x again 12 and at the end plus fifteen boom 351 that is the total cost and we're down there here we're finding what is the surface area for this shape but the problem is if you look up a pentagonal prism or container it's not going to be in the formula sheet so we're going to use a different approach to find the surface area you could always break this down into all of its shapes and then let's see what we're given here they tell us the bottom has an area of 26 so this guy 26 let's label that but then we have two of those shapes multiply that by two so the total area for the top and the bottom is 52. all of the sides are these rectangles but you could just multiply 11 times 5 length times width that'll give us 55 for the area for those and then we've got five of those guys so multiplying that out we get all the sides have an area of 275. and finally you know what to do just add these together and that'll give a grand total of 327. so that is the surface area when you have an inequality here it's just like what we did to get X all by itself so find what's on that side here we have a positive 5 but we want that to go away so we're going to Minus 5 from both sides here that'll get these to cancel but let's use the calculator here four thirds minus five the calculator is great for fractions so four down three minus five Okay negative 11 thirds there let's write that on the right side and then we want to get X by itself it's being multiplied by negative one-third we want to do the opposite so divide by negative one-third because these will cancel and once again let's just plug this into the calculator here so let's do it from the beginning we've got negative fraction eleven thirds divided by another negative fraction one-third and it's quite nice actually because that just turns into positive 11. so this side here is 11. but one other thing we need to keep track of when you divide by a negative with inequalities it's going to flip the direction of this so the final answer X is greater than or equal to positive 11. so D there in order to factor completely you could always take the answers foil them out and see which one gives you back the original thing here so let's do that for a now to foil you're just going to multiply the first thing here times the first thing here 3x times x will be 3x squared that was the first thing here times the first thing here so that's the F in foil then you're going to do the outer ones that's going to be 3x times this is going to be a negative 5 right there 3 times negative 5 negative 15 and keep the X so those were the outers there next you're going to multiply the inner ones 2 times x but that'll just give us 2x those are the inners and then the last two two times negative five so negative 10 those were the last all right so that's foil right there but then you're always going to be able to combine like terms in the middle so if we do negative 15 plus 2 that's going to give us negative 13 in the middle and lucky for us that actually does match the original thing so a was the correct factored form for this expression here for this problem we're finding the greatest distance that the subway gets from the main hub but on the y-axis that is what they've told us this is the distance from the main hub and the largest the Y value gets here is right at this point 20. so that right there is the greatest distance 20 miles there and looking at the graph as a whole we ended up leaving the Hub went 20 miles and then we came back 20 miles so that's why that was the furthest that we went right there okay same data but this time we're finding the Train's average speed that's always going to be distance divided by time and we're going to do that from 20 to 30 minutes here so let's go ahead and highlight that segment now what was the distance that we went well we just went from 15 to 20. so we bumped up and went five miles there and then from 20 to 30 minutes that just took 10 minutes so finally 5 divided by 10 same thing as one half or same thing as 0.5 50 cents there and you could always verify it once again you could just do fraction 5 over 10 enter then this one and boom that's another way to verify it in order to find coordinates you'll always start right in the middle and then you're going to go right or left first up or down second now to get to that green point we're going to go to the right one and then up three put them in that order one comma three that is the point now the blue one we don't go right or left so the first number is zero since we stay in the middle but then we go down to so negative two and that's that the third one we go to the left one two three so negative three then up one positive one those are the three points so A's got all the right coordinates there in order to find the slope of a line through two points you could always sketch a grid out on your scratch paper and then we're going to go ahead and find the point negative one two start right in the middle left one up two so boom right there and then the point five comma four we know we're just going to go to the right five up four so right there and then to find the slope that's always rise over run in other words how do you get from this point to this point how much do we go up one two so the rise is to and from there we go to the right one two three four five six so Boom the run is sex stack them in that order that is the slope but that's going to be the same thing as one-third there they're both even so just take half of that one half of that three and that matches because you really did do that you went up one over one two three hit the graph up one over one two three so it really did have a slope of one-third same thing as 2 6 there in order to find the area for this shape we just need to know what shape it is one of my students used to say it looks like the thing the elephant stands on at the circus I agree now if you're at the circus then there's probably a trapeze artist and therefore think trapezoid to find the area we're going to plug this hot mess on the calculator H just represents the height but that's just going to be straight up and down so 6 right there it'll always be a 90 degree angle okay so we know that's the height and then B1 and B2 those are the bases just think the bottom and the top is also a base because that's also going to be perfectly flat there and let's plug all these in here and let's see what that gets us so it'll be a one-half to start and then times our height 6 then parentheses it actually doesn't matter which one you call which because you're just adding them together but we'll add our two bases 18 and 12. and we get an area of 90. so that is the area for that trapezoid and you made it one last one here what is the perimeter for the shape here now perimeter you just add the lengths around the outside so let's highlight all the ones that have an X if there's nothing in front of an X it's always a one and let's add these we got four plus seven eleven plus one we have 12 X's could be B could be C we'll get rid of the other two there same thing for the Y's highlight those this one doesn't have anything so it's got a one in front and then three plus five eighty minus one y so therefore 7y and that's the correct expression for the perimeter so we're done so I hope this gives you a lot of confidence going into the test let me know what questions you run into good luck you got these we'll see in the next video doodles