okay this is M Sher and this is your Keystone exam review so we're going to do four days of review and this is the first day of review so this is review one and this is module one so these are questions that are released by um the Keystone exam administrators um for student use and for Teacher use so let's look at these multiple choice items so first it says which monomial is the greatest common factor of and then you're given X 4th y 8th and x to the 6 y 4th now the problem with greatest common factor is we see this word greatest and I'm actually going to cross it out because that can be very confusing for students so we want the greatest common factor yes but basically when we're dealing with VAR abl the greatest common factor is the smallest power on the variable so it is the smallest power not the largest power which will get you to the wrong answer very quickly in a question that's very easy so let's look at the powers of X so we have two powers of X here in the two expressions x to the 4th power and x to the 6th power and and we want to pick the smaller of the two Powers so this is four factors of X so that's the smaller of the two Powers so we certainly want our answer to have x to the 4th in it let's look at the Y so we have y to the 8th and Y 4th and the smallest power of the Y's is this four factors of Y here so as as a result our answer should be x to the 4th and Y to 4th so when you're finding common factors the greatest common factor and you're dealing with variables it's actually the smallest power of the variable let's look at our second problem so for problem two it says why it incorrectly simplified this expression and his work is shown below so we have a cube root of x 6 y 12th and a square root of x the 10th and Y to 4th so for the top the index of the cube root is three that means that when we apply it to x to the 6 and Y 12th we should be dividing by three so in other words you would would have 6 / 3 and 12 / 3 for the bottom the index is 2 and that means you should be dividing by two so you would have 10 / 2 and four / two for your exponents so let's now look at the work let's look at line one so in line one he should be dividing by three so dividing by three because of this cube root and he's not he's dividing by two so right off the out of the gate here he is doing this incorrectly by dividing by two so we've already found the mistake let's look at our answer choices so for our first answer Choice it says going from the given expression to line one why it divided the exponents in the numerator by two instead of by three and that's exactly what he did so that would be our answer for that problem let's move on to another sample okay so we have a local store and it sells different types of fruit drinks for2 to $4 each John buys D drinks so we don't don't know how many drinks he buys and he pays $36.54 which value could be the number of of fruit drinks that John Buys so let's look at this and let's look at the extremes of the situation so we have $2 drinks and we have $4 drinks so if John bought let's look at the first answer Choice six drinks of the least expensive kind so the $2 drinks it would be 6 * 2 or $12 so he certainly didn't do that and if he bought six drinks of the $400 kind then 6 * 4 would be $24 and he certainly spent more than that so that's not right what about nine well if he bought the cheapest type it would be six time 9 * 2 sorry which would be $18 and he spent more than that and if he bought nine of the most expensive it would be 9 * 4 and that would be $36 which is closer but it's still not it moving on if we look at 12 then 12 * 2 would give us $24 we're getting closer to the amount that he actually spent and 12 * 4 would give us $48 so that gets us at least in between the two so that's a possible answer because $36.54 is in between 24 and 48 so that could happen so that would be our answer and then we're we're going to be able to see that 19 would take us out of that range um so let's just look at that so that you understand why we're eliminating it if we take 19 * 2 we get $38 so we're outside of our range and then if we take 19 * 4 we're outside of our range so it's 40 and 36 which is $76 so we're way out of the range because we have to have our range in here so this is the range that we have so the answer should be C12 let's go on to number four okay so this one's pretty algebraic which is what we do in algebra one so we have a polinomial expression and we look like we're subtracting them so when when you're subtracting polinomial Expressions the easiest way to do is to put them on top of each other if you can if it just makes things visually make more sense for you so let's write our first expression out so 7 x^2 y - 5x + 8 y^2 and we're subtracting which is the harder type because when we're subtracting we're going to have to change the signs of all of the expressions in the second polom so instead of 3x2 Y we're going to have - 3x^2 y instead of positive 2x we're going to have -2X and instead of - 6 y^2 we're going to have positive 6 Y 2 and then it's just a matter of adding these together so 7 x^2 Y and -3 x^2 Y is 7 - 3 and that's 4 x^2 y's so we can already see that we're eliminating these two but there's no need to rush on your Keystone exam because you can take as much time as you like on it -5x and -2X this is like owing me $5 and owing me $2 so I owe $7 Al together so it's -7x so I'm already going toward b as my answer Choice and then Plus 8 + 6 which gives us 14 y s so the answer choice is B so B let's move on to sample number five Kaden wants to have exactly $600 in his bank account by the end of 12 months his bank account currently has $84 in it the bank account does not earn interest he decides to deposit the same amount each month for the next 12 months so he could for example go ahead and deposit $10 every month and then after 12 months he would have 12 * 10 or $120 extra in his account to add to the $84 that he already has in there so if he saved $10 every month he would have $24 so he wants to save more than $10 a month but that's not the question it says which equation can be used to find the total amount of money that's this money X in dollarss he must deposit each month sorry that's this money to reach his goal well we know that he already has $84 in his account so that would be part of the equation his goal is the 600 so we're going to go ahead and eliminate this answer choice and this answer choice because these two end up with him having 60 $684 in his account so we're doing it for 12 months and we're going to multiply and then we're going to add the $84 which we did over here so answer Choice a is the best answer choice so every month we're multiplying by the amount he deposits that's X that's the same amount that he deposits every month for for 12 months and then he's going to add in the $84 that he already has so answer Choice a is your best answer number six we have Franklin and he is solving an equation and his first step is shown below so when we look at the first equation and then we look at the second equation you can see that the -3x has moved over here next to the 4X and this seven has moved over here with the 10 so things have moved around so when we look at our different properties when we're moving things around like you move from your home to your job or your home from school they sometimes call that a commute so when we move things around an equation on the same side of the equation that's called the commutative property so here's the commutative property and then just when we're looking at the other properties so that you know the additive property is when you add the same thing to both sides of an equation the associative property is when you have different groupings or parentheses and then the identity property is uh when something equals it uh times 1 equals itself so let's look at example number seven so in example number seven we have Fernando and he works at a clothing store each week he earns $120 and that's for doing nothing that's just for showing up plus 25% Comm Commission on any clothing he sells the equation below can be used to determine the total amount Y in dollars Fernando earns in a week during which he sells X worth of closing so X is the dollar amount of clothing he sells and Y is his total pay so the $120 is is like the base pay so I'm sorry $120 this is base pay so that's this 120 here and then he gets 25% so 25% as a decimal is 0.25 so this is 25% times the amount that he sells so now that we've sort of understand the equation they ask what does this ordered pair mean in the context of the situation so ordered pairs are in the form X Y so why it says is giving you in dollars how much he earns in a week total so it says here the total amount so this is telling us that he in total he earned $176 125 so 120 of it was the base pay and the rest was commission and then 225 is it says the dollar amount of the clothing that he sold so he sold $225 worth of clothing okay now we just have to sort of go through the answer choice and see which one's correct so it says first in a week during which Fernando sells $176 that's not right because we have that he sold $225 he earns this and that's basically the opposite in a week during which he sells this worth of clothing he earns this much in commission so this is interesting because this is the total and this is the commission the commission for this would be $176 125 minus the base pay so this has nothing to do with the commission so anything with the word Commission in it I'm throwing away so now I'm down to a and C and C is looking better but let's read it it says in a week during which Fernando sells $225 worth of clothing so that's what we figured out he earns a total of $176 125 sense so that makes the most sense so it is answer C and let's do one more example so Nikki and Emily are buying tickets to a school play for their families Nikki buys three adult tickets so she's buying three adult tickets and one student ticket and she's going to pay a total of $115 and then we have Emily who is buying two adult tickets and two student tickets and she's going to end up paying $14 and it's says the coordinate plane below displays a graph that models this situation but the labels for the two axes are missing so they ask what does the point of intersection on the coordinate plane represent so if we look at the intersection Point here that's the point 43 and we know how many tickets they bought we just don't know how much they paid for those tickets but we do know how much they cost total dependent upon um the amount that they bought so let's see if we make this the adult tickets and this the student tickets price so $4 and $3 let's see if that makes both of these situations true so let's look at the first situation which is Nikki's situation so Nikki and she buys three adult tickets so three adult tickets for $4 each and one student ticket for $3 each and we're asking does that give us $15 well 3 + 4 is 12 and 12 + 3 is 15 so it works for that situation but but in order for it to be an intersection point it has to work for both situations so let's look at Emily's situation so for Emily she bought two adult tickets and she bought two student tickets and we're asking is that equal to $14 well 2 * 4 is8 and 2 * 3 is 6 so 8 + 6 does equal 14 so basically basically that intersection point is the cost of an adult ticket and the cost of a student ticket now let's figure out which one is the answer choice so Nikki pays $3 for each ticket that's not right Nikki pays $4 for each ticket that's not right we want the prices of the adult and the student tickets that doesn't even make sense so the price of each adult ticket is $3 well that's not right it's $4 we just said the price of the adult adult tickets is $4 so that's gone so let's see if D which seems to be our answer choice is correct it says the price of each adult ticket is $4 yep and the price of each student ticket is $3 that's correct so this is our answer Choice okay that's the end of today's review and we are going to do more review tomorrow