like share sub hey y'all welcome back in this video I'm going to review the concepts that you will need to be familiar with to be successful on the tsa2 math test this test used to be called the TSI test but has recently been updated and has been given a new name the tsia A2 first let's talk about what you can expect to see on the recently updated test the TSI math test is a 20 question test and if you get enough of those questions right you're done congratulations you passed the test however if you don't pass the first set of 20 Questions you'll be directed to a 48 question diagnostic math test that will help pinpoint the areas that you're struggling with the most now schools can use this diagnostic section to help put you in the right class but if you get to that diagnostic section do not give up this is really important if you get enough of those questions right in that 48 diagnostic section you can still pass the test this is one of the major differences between the original TSI and the TSI A2 math test so do your best on those first 20 Questions that's your best shot of passing the test however if you do end up getting taken to that diagnostic section don't give up do your best because you could still have an opportunity to pass the test now if you want an idea of what kinds of questions you can expect expect to see on this test the College Board has released a practice test and if you click this link right above here it'll take you to a playlist where I work out every problem on that practice test so without further Ado let's jump into this video so let's go ahead and jump into some of these practice problems I've got 40 here for you and that's a little bit longer than what the actual test will be but I think this these questions I do a good job of covering all the bases here so we'll go through these and hopefully by the end of this video you'll have a better idea of what to expect on the tsa2 test all right so let's begin number one says if 3T minus 7 = 5T then what does 6t equal so here we can approach this two ways we can either try to isolate 6t but I think it's actually easier to just find T and then we'll multiply it by six to figure out what 6t is so the equation here is 3T - 7 = 5T first I will uh subtract 3T from both sides so doing that 5T minus 3 T is going to be 2T and then if I divide both sides by T I get -7 as T -7 hves as a decimal is going to be -3.5 and then if I want to get my final answer here 6t is going to be 3T I'm sorry it's going to be T 6t will be -3.5 * 6 which equals 21 so our answer is number two says if variables X and Y are proportional directly proportional and Y = 2 when x = 3 What is the value of y when x = 9 so to be directly proportional that means there is a constant that we can multiply by X to get y okay there's no Y intercept essentially so to figure out what this constant is set X to be 3 and Y to be 2 and so to figure out this constant we'll divide both sides by three and so k a will be 2/3 so the equation we'll use here is y = 2/3 * X and so if we want to find the value of y when X is 9 we'll multiply 2/3 times 9 and that equals six so our answer answer is B number three says find the equation of a line passing through 6 comma 9 and 0 comma 0 so first we'll find the slope the change in y is going to be minus n to get from 9 to zero we subtract nine and our change of x from 6 to 0 is going to be Min - 6 so the change in y is -9 the change in X is -6 so our slope will be -9 over6 we can clearly reduce this a negative divided by a negative is a positive so we can get rid of those negatives and then if we divide both the numerator and the denominator by three we're going to get three halves so our slope is three halves that pretty much gives us our answer here because there's only one equation that has a slope of three halves but if you wanted to actually up with the equation using point slope form you would do y - y1 and I think I'll use this second Point as my X1 y1 because they're both zero and so it'll make the equation a little bit easier to to write um actually we don't even need that however we can see that z z is a point on the line This is the Y intercept so our Y intercept is just guaranteed to be zero anyway that's number three number four says there are 3x minus 2 trees planted in each row of a rectangular parcel of land if there are a total of 24x - 16 trees planted in the parcel how many rows of trees are there in the parcel so we've got uh a rectangle essentially here and each row has 3x - 2 trees so I'll just say it's going to be our length here we make the rectangle a little smaller it says there are a total of 2 24x minus 16 trees so that's going to be kind of like our area here says how many rows are in the parcel so essentially what we need to do is figure out what do I need to multiply 3x - 2 by to get 24x - 16 and for both terms you can see that we could just multiply in 8 so that's going to be the number of rows and our answer is D number five says a group of 18 people ordered soup and sandwiches for lunch each person in the group had either one soup or one sandwich the sandwiches cost $7.75 each and the soups cost $4.50 each if the total cost of all lunch 18 lunches was $13.50 how many sandwiches were ordered so there are going to be two equations that we can set up here the two variables that we want to use are going to be the number of sandwiches and the number of soups and we know that at least the number of sandwiches has to be a variable because that's what it's asking for so I'll just say since they both start with s I'll just use X and Y so I'll let X be the number of sandwiches and I'll let y be the number of soups so since each person either had one super for one sandwich we know that the total number of sandwiches plus the total number of soups is 18 if the sandwiches cost $7.75 we can multiply that by how many sandwiches were ordered plus $4.50 for the number of soups that were ordered and the total amount was $13.50 so we can solve this as a system of equations but I think it might be easier to just use our answer choices here to solve for uh to figure out which one is our our answer so let's start with seven so it's saying okay if seven was the number of sandwiches that were ordered then we could plug in seven right here right to figure out how many soups there would be so 18 - 7 would be 11 7 + 11 is 18 and basically what I want to check here is to see if seven and 11 work in this second equation if they do then I've got my answer if they don't I'll go back and try the next one so $7.75 * 7 + $4.50 times $7.75 time 7 plus $450 * 11 that equals $13.75 so that's not what we're looking for we want it to be 113 so we know the answer is not a so let's try a couple different numbers here we'll let X be8 for this second guess switch the color here and so if x is 8 then y would need to be 10 in order for them to add up to 18 I'm going to put eight here I'm going to put 10 here I'm going to type this in let's see if that works $7.75 * 8 plus $4.50 * 10 and that one equals $17 so it's not going to be B is it going to be D are we G to have to go through all four of these sometimes that happens sometimes you get lucky and it's the first answer choice so I wouldn't give up on this strategy next I'll make X9 and that would make y also nine I'm going to plug these two numbers in for X and Y 775 * 9 + 450 * 9 is $10.25 so unfortunately C doesn't work either and we'll try d i I'm assuming it's going to work if it doesn't that means we made a mistake somewhere so you know we're still we're still going to test this out if x is 10 that means y has to be eight so 775 * 10 + 450 * 8 does in fact give me the $13.50 So my answer is d number six which of the following equations has both one and -3 as Solutions so what I would do here is work backwards there's two ways I you could approach this you could just plug in Nega one and3 into X and see which one works that's definitely a good strategy if you're not really sure algebraically how to answer this so you just plug in one into X make sure that one works but you also have to check3 but this one is not so hard to solve so I'm going to just solve it directly here if one is a solution then that means xus one must be one of the factors and if xal -3 is a solution then that means x + 3 must be a factor as well and so if I multiply these two factors together I should get my answer x x x is x^2 just using the distributive property here x * X and then I'll do x * 3 which will be 3 X followed by -1 * X which is --1x and then finally -1 * 3 is -3 so combining my two like terms which are these two linear terms right here get x^2 + 2x - 3 and so we can see that our answer is B number seven in the XY plane what is the Y intercept of the graph of this equation so the Y intercept is going to be the value of the function when X is zero just make a little Point here x must be zero so all you have to do here is substitute 0o into this equation Y = 2 * 0 + 3 * 0 - 4 0 + + 3 is 0o is zero is three and 0 - 4 is -4 so we're just going to multiply 2 * 3 which is 6 * -4 is -4 so our answer is a number eight says X 4th minus 1 and this is a of two squares so the difference of two squares factoring technique says that if you've got a s minus b^ 2 we can Factor this as a + b * a minus B all right this is called the difference of two squares and so we have this kind of setup here for number eight where a is X squ so I'll just put X squ here got x s squared and B is still is just one 1 s is one so this is going to factor as x^2 + 1 * x^2 minus one you might notice that none of the answer choices are this exactly but that's because we actually have another instance of the difference of two squares over here with the x^2-1 can factor that a a little bit further and write this as x +1 * x -1 so looking at our answer choices we can see that the correct answer is a now if you forget how to do the difference of two squares factoring one thing that you could do to answer this question is just to pick any value you want for X so like pick seven or something like that and then type seven in for X for the original equation and go through your answer choices plugging in s for x and find out which one equals the same thing you can definitely get this one right uh using that strategy you can use a similar strategy for number nine just pick different values for X and Y plug them in and see what the expression equals and then you can plug those same numbers in for X and Y for the answer choices and see which one is the same thing and you can get the right answer that way but I I'll show you how to work this one out using our properties of exponents so the first thing we need to do is apply that cubic exponent that's on the outside of the parenthesis to every factor that is on the inside of the parentheses including the three which is what most people will forget so 3 cubed is 3 * 3 * 3 which is 27 then when you raise each of these other factors to the third power since they already have an exponent on them you need to multiply the powers raising a power to a power uh or to raise a power to a power you've got to multiply the power so 2 * 3 would be 6 so this would be x 6 and 3 * 3 would be 9 so this would be y 9th we get 27 x 6 y the 9th and our answer is D number 10 says if the square root of 5 - xal 4 then what does x equal the first thing we want to do here is to isolate x square both sides but before we go any further here any problem that's just a solve for x problem like this where you're just trying to figure out what x is you want to take advantage of the fact that this test is multiple choice so if you know on any of these questions where you're solving for x you really could just take the answer choices plug them in and and see which one works um so just know that that is an option for you but I'll go ahead and solve it sort of the proper way here so you can see how to do it after you square both sides you get 5 - x = 16 then you could subtract five from both sides leaving you with x = 11 and then divide both sides by-1 to get xal -1 again you could just plug in these answer choices and plug in1 here you'll see that it works so don't forget about that strategy number 11 says if x - 1/x = 20 then what does x equal again this is another solve for x problem so you really could just plug these answer choices into X and see what works but I'll show you how to solve it otherwise first thing I would do here is multiply X on both sides of the equation so that I get rid of that fraction x - one then would equal 20x then I can subtract X on both sides to get -1 = 19x then if I divide both sides by 19 I'm going to get x = -1 over 19 and our answer is C number 12 says a ball was kicked into the air From A Balcony 20 feet above the ground and the ball's height above the ground in feet T seconds after the ball was kicked is given by the equation Y of T = -16 T ^2 + 32t + 20 what was the maximum height in feet of the ball above the ground after it was kicked so just to give you a little visual of what's Happening Here ball starts at 20 feet goes up and then comes back down what we're looking for is this point right here now this point is called the vertex okay I'm going to call it h comma K and to find the maximum height of the ball really what we need to do is find this K value so we need to find the maximum to find that maximum we need to find the vertex so to find the H of the vertex we can compute B over 2 a using the coefficients of the equation that was given so B over here is 32 and a is -16 we can simplify this as 32 divided by -32 oh no no uh 32 over 32 so this is just going to equal one that means that the maximum occurs at 1 second so at that point you want to plug in one into the function to find out what the maximum height is so the K is going to be -16 * 1^ 2 is just one plus 32 * 1 + 20 this is something that you could probably get away without using a calculator but hopefully you have at least a four function calculator for this one -16 + 32+ 20 is 36 so our answer is c number 13 says the yard behind Cindy's house is rectangular in shape and has a perimeter of 72t so two two times the length plus 2 * the width is 72 if the length of the yard is 18 ft longer than the width of the yard what is the area of the yard in square feet so the area here is going to be length time width and so we're going to need to find both the length and the width so unfortunately because of the way this problem set up I don't think it's really going to be reasonable to uh find to kind of work backwards from the answer choices here so we're going to solve this using a technique called substitution since the length is 18 more than the width we can replace the L in the second equation or I guess the first since we wrote it first with that 18 + W so I get 2 * 18 + W plus 2 W = 72 solve this I need to distribute the two 2 * 18 is 36 so 36 + 2 W plus another 2 W is 72 2 W + 2 W is 4 w now I can subtract 36 from both sides to get 4 W equal 36 and then dividing both sides by four is going to result in the width being 9 ft now once we figure out what the width is it should be pretty easy to calculate the length because the length is 18t more than the width so 18 + 9 is going to be 27 so so the length is 27 now we can calculate the area which is length time width so the area will be 27 * 9 which is 243 and that would be in square feet so our answer here is C let's move on to number 14 this says the table above shows the high temperature last Thursday for five cities a through e if the median of this Thursday high temperature for these cities was 81° F which of the following could not have been the high temperature last Thursday for City a so what I'll do first is write these values in order so the smallest or the lowest temperature here is 62 then we've got 81 and 87 and finally 93 we've got one more temperature here we don't know what it is though it's t so it says that the median of the high temperature was 81 degre so for that to be the median it needs to be the number that's in the middle of the list and so in order for 81 to be in the middle so you've got two numbers to the right of that we also need two numbers to the left of it so that means that this temperature T de F needs to come like not necessarily before the 62 but definitely before the 81 so that we could have um two uh two values that are less than 81 so really any number less than 81 is going to do do it for us um and this says just to you know add one more little complexity here here it says which of the following could not have been the high temperature so three out of these four are going to be less than 81 okay so you can see 75 is less than 81 so that's not going to be our answer um 65 and 55 are all less than 81 so our correct answer here will be a number 15 says there are 20 children in the cast of a play of a cast of a class play and eight of the children are boys of the boys four have a speaking part in the play and of the girls eight do not have a speaking part of the play if a child from the cast of the play is chosen at random what is the probability that the child has a speaking part so the way that we calculate probability um not sure what's going on with the the text there but the probability is going to be a fraction it's going to be the number of desired outcomes divided by the total number of outcomes just to make this look a little nicer I'm going to throw in a little space here can no here's what I'll do put a little space like this okay so we've got the desired outcomes divided by the total number of outcomes uh so the desired outcomes here are going to be that a child has a speaking part so what we need to do is figure out how many total children there are and how many of them have a speaking part so if we look back at here it says there's 20 children it doesn't really matter if they're boys or girls the total number of children is 20 so it's going to be something over 20 the number of desired outcomes here are the people are the kids that have a speaking part so it says four have a speaking part um that's going to be the boys but then you have to figure out okay well how many girls have a speaking part it says of the girls eight do not have have a speaking part so if there are eight boys then that means there are 12 girls if eight do not have a speaking part in the play that means four of those 12 do so four plus 4 is a total of eight and so our probability is going to be 8 over 20 which will reduce if we divide both of those by four to two fths so the correct answer is a number 16 the variables X and Y are directly proportional so that means that we can write an equation yal MX with no B for a directly proportional equation there's no Y intercept or I guess to be more accurate the Y intercept is zero so we know there's some constant which is the rate of change time x okay and again I'm right starting this equation just from the fact that it said it was directly proportional It also says that y = 4 when xal 9 using that information we can figure out what our slope or our rate of changes when Y is four x is 9 so if I divide both sides by 9 here I get my slope which is 4 9th so then the followup question here is what is the value of y when X is 18 so if I have my equation yal MX and I already figured out what my M was right I figured out that my slope was 4 9ths so when X is 18 we want to know the value of y y is going to be 4 9th * 18 you could put this in your calculator most likely but 18 ID 9 is 2 and 2 * 4 is 8 so we get our answer when X is 18 Y is 8 number 17 says evaluate the expression when X is 2 Y is 3 sorry -3 and Z is1 so we've got this expression and all we need to do really is just plug in 2 -3 And1 into X Y and Z into the ex expression so we've got 2 * 2 plus 3 * uh -3 minus -1 just type it in kind of exactly like that and then put it in your calculator that's what I'm doing now 2 * 2 + 3 * -3 -1 and so I'm getting ne4 here number 18 asks us to factor this difference of two squares the format for doing this is if you've got something like a^2 minus b^2 so just like I said exactly a difference between two squares we can factor that out as a + b * a minus B so if we've got something like number 18 which is 25 x^2 - 36 we can write that as 5X x + 6 * 5x - 6 that's basically our answer oops that's a b not a six um so yeah you just need to know how to actually do this so to come up with these numbers you just find the square root of each of these two terms and so we can see our answer is D if you're worried about D because the factors are in a different order multiplication is commutative which means that the order doesn't matter 2 * 3 is the same as 3 * 2 so it's okay that this one has the minus one first it that doesn't really make a difference number 19 19 we are solving an equation for x so I'm just going to retype it over here so we can have all the work right underneath it first thing I'm going to do is Use the distributive property on this seven so I'm going to multiply 7 * X and 7 * 1 to get 7 x + 7 next I'm going to start to combine like terms to simplify the left hand side of my expression my equation 4x + 7 x is going to be 11x and then -5 + 7 is going to be positive2 next I'm going to subtract this 6X on both sides and 11x - 6X is 5X now we've got a nice little two-step equation here so I'm going to subtract two from both sides and then divide both sides by five and I get one so my answer is one number 20 looks like we've got a rational equation so we need to find a common denominator here and to do that we're going to multiply each fraction by the other fa fraction's denominator so I'm just going to rewrite number 20 here we got 3x + 6 all over 3 - 4x over x - 3 = x so I'm going to multiply this first fraction by x - 3 over x - 3 so that I can get this denominator in there so x - 3 on the top and times x - 3 on the bottom for the second fraction I'm going to multiply that by 3 over three so you can see if I multiply this Bottom by three then I'll have the common denominator so I'm going to multiply this by three and I'm going to multiply this by three once you've got your common denominator you can go ahead and subtract those fractions and when you do that the denominator will stay the same and you'll just subtract the numerator multiplying these two together I'll do that kind of in the same step x * 3x is going to be four sorry it's going to be 3x^2 and then x * 6 is 6 x -3 * 3x is going to be -9x and then 6 * -3 is going to be 8 6 - 9 is going to be -3x so this is the numerator of that first fraction and then I'm going to subtract this numerator on the second fraction four * 3 is 12 so just to simplify things I'm going to write write it as 12x and then my denominator here I'm just really not going to mess with it because there's a possibility that we're going to get xus 3 as a factor and then if I multiply it together I won't necessarily catch that I can cancel that factor out so now I'm going to combine like terms in the numerator and try to factor what I have so 3x^2 - 3x - 12x would be - 15x - 18 all that is over 3 * uh x - 3 that equals x this problem's got a little bit of a doozy here okay so we do need to factor that numerator just to make sure that these xus 3s don't get canceled out and I guess we need to decide if this is even factorable to begin with so since the first term is 3x^2 I know my first two terms are going to be 3x and X multip get that I'm going to just kind of take a guess here um usually doesn't take me too many guesses to get there but two numbers that multiply to give me 8 would be 6 and three where one of those is negative so I'm going to put the -6 here and then plus three here and then to see if I did that right 3x * 6 is um 18- 18x + 30X does give me that5 so actually that that's correct the other thing I see here is I do have a GCF that I can divide out of that first one and it is a three so I'm going to take this whole equation here and re just rewrite this as 3 * x + 1 okay now you can see that these threes are going to reduce um I was kind of hoping we could get that xus 3 to reduce but we can't and that's okay so next I'm going to set these two things equal to each other so I'm going to multiply both sides by xus 3 and then I'm going to um actually multiply all this out so I'll foil the left hand side which will give me x^2 minus let's see - 6 + 1 would be - 5x and then - 6 = x^2 - 3x so if I subtract x^2 on both sides these will go away and then um if I add 5x to both sides I'm going to end up with -6 = 2X and then finally dividing both sides by two gives me x = -3 you saw you're seeing here um the algebra is pretty intense for this problem and I think this is probably going to be a little bit beyond what you can expect to see on the test I don't know that for a fact but I have not really seen too many that were this complicated now that all being said we've got all the work here shown to the left the right here but one way that you could work out this number 20 which I would probably recommend over doing all this algebra is just to use your answer choices and plug them in into X so like if I plug in -3 into X everywhere where I see X and I evaluate that out I should getg -3 so TR I should get a true statement I should say where the left hand side equals the right hand side so as you go through your answer choices and plug these into the calculator if you're going to use this technique of just working backwards from the answers uh you'll find that -3 is the solution number 21 is also a solve for x kind of problem and so I think just to kind of showcase that strategy here I'll just do what I was talking about for number 20 and just plug in the answer choices and see which one works so for this one I'm going to start by trying to plug in six so this would be like 6+ 3 we want to know is that equal to 6 - 3 so the sare root of let's see 6 + 3 is 9 6 - 3 is 3 does the sare root of 9 equal 3 well yeah sure it does square of 9 is three so that means that six is a solution which means that it's either going to be a b or d because C doesn't have six as a solution so now we need to test is there could only be like one more answer here and it's either going to be one or 13 or maybe there's nothing maybe there just is one solution we're going to test out both of those numbers so first I'll test 13 I've got 13 + 3 and 13 minus 3 so 13 + 3 is the square < TK of 16 it's making me think this actually is not going to be an answer and 13 - 3 is 10 so the square root of 16 is 4 that does not equal 10 so this equality is not true just scratch out the equal sign on all these and that means that 13 is not a solution so the last thing to check here would be one just to verify or confirm that that either is or is not a solution so we do this last one here 1 + 3 underneath the square root on the left side and on the right side we've got 1 minus 3 so the left hand side uh is the square root of four because 1 plus 3 is four and on the right side we get 1 minus 3 which is -2 and the sare < TK of 4 just equals positive2 it does not equal -2 so that means that one is not a solution to this one either so the correct answer then is a number 22 solve the inequality I think I'll go back and actually work this one out rather than just trying to plug in answers here because it is a good idea to know how to do these so first I will add 3x to both sides well I guess first maybe let's just retype the equation so we got it ready to go but yeah I want to add 3x to both sides to get it rid of it on this right hand side so -2x + 3x is positive 1X and then I want to add one to both sides and 8 + 1 is 9 X is greater than 9 now it doesn't really look like that in the answer choices for some reason they flipped it here not really sure why they did that but the x is still the greater number in this statement so it's still going to be true number 13 it asks us to solve this using the square root property but you could just approach it like we did earlier and just test the answer choices into X but I'll go ahead and just show you how you get the answer the proper way first I'm just going to retype the equation and then we'll start solving it so to solve this I'm going to add 36 to both sides move that 36 over and then I'm going to take the square root of both sides now the thing you got to remember is anytime you take the square root of both sides of an equation you do have to put a little plus or minus over here on the other side of the equation so that' be plus or minus 6 and then finally I'm going to subtract N9 from both sides so I get x = 9 plus or minus 6 we do get two answers here one with the plus one with the minus if I use the plus and I get 9 + 6 that's going to be -3 and if I use the minus -5 - 6 would be -15 so our answer is B number 24 wants us to solve using the zero Factor probably uh Pro probably prop property and so we will go ahead and Factor this but 2425 these problems can also be solved by just plugging in the answer choices into X so don't forget about that strategy but yeah so here we want to factor so we've got 10 x^2 + 23x x + 12 = 0 so we want to try to factor this into a pair of binomials here so I'll just kind of set up my binomials and here I'm going to do a little guess and check here I need that first term to be 10 x^2 just going to throw down 5x and 2x as my first two terms 5 * 2 is 10 x * X is x^2 I might have to change these but I don't know it's just my gut feeling that those are going to be the first terms for the last term we've got 12 so we you have to find two numbers that multiply to give me 12 I'll just you know to kick this off start with three and four as a guess but really how you're going to figure out what that correct combination is is you're going to multiply the first and the last term the inside terms so the outside terms the inside terms the inside terms 3 * 2x is 6X for the outside terms we got 20x and what we actually want here is for these to add up to 23 which obviously that's not happening with this problem so we've got the wrong combination so we're going to have to try something else how about instead of three and four we try six and two and see if that leads us anywhere 6 * 2 is going to be 12 so this is 12x these together 5 * 2 is 10 we get 10 x we're so close we're trying to get these add to add up to 23 but just not there yet okay how about four and three feel like maybe the four and three might work let's see we try four and three uh we get 4 * 2 is 8x 5 * 3 is 15 actually does this work 15 and 8 yeah that's 23 okay so here we go so here's our two factors then once you factorize this out we can use the zero product property which says that if you have a product that equals zero then at least one of the factors must be zero so the way that applies here is since we've got a product of binomials that equals zero at least one of those binomials does need to be zero so we're either going to have 5x + 4al 0 or 2x + 3al 0 then if I solve this L equation but left equation by subtracting four and then dividing by five I get X = -45 and if I do the same thing for this other linear equation I get x = -3 those are my two solutions so I'm going to look for those in my answer choices and looks like I got them right here Choice D number 25 says use the uh solve the equation using the quadratic formula so the quadratic formula in case you've forgotten is xal B plus or minus the Square t of b^ 2 - 4 a c all ID 2 a and the B sorry the a the B and the C are all going to be coming from these coefficients so the a is four the B is eight and the C's just going to copy this over so I don't have to retype it and fill in my a b and c so my B is eight my eight is four and then my C is one now this is something that we can basically put in the calculator it looks like we're going to have to do a little simplifying to get our Solutions here uh but let's go ahead and start that simplification process so 2 * 4 is 8 do that and then in this numerator we've got 8^ squar which is 64 8^ 2 minus 4 * 4 * 1 and so what that gives me is 48 then you can see we're very close to being done here but we do need to simplify this a little bit so 48 see here that would be be a perfect square factor of that 16 is it is it divisible by 16 I think it might be yeah 16 * 3 okay so this is going to be 4 < tk3 when we go to rewrite it so right here 48 root 48 reduces to 4 < tk3 and then I can divide all this stuff by two to reduce my fraction so this will be four this will be two and this will be four oh and actually you know what I could go one F step further I don't need to divide these by two let's divide by four so 8id 4 is 2 4id 4 is 1 8id 4 is 2 we have -2 plus orus root3 over two our answer is c number 26 says the height of a box is s in so we've got this box so it says the height of the box is 7 in the length is six more than the width so if we'll say this is the width then the length and it doesn't really matter which ones which here but the length is going to be six more than the width so 6 plus W then it says find the length of the find the length which is this 6+ W find the length if the volume is 280 so we'll set up our little volume equation here which is length times with time height fill in the values so L here is 6 plus W W is just GNA leave that as W and then the height is seven so here I've got 7 W Times this so I'm going to just mult I'm going to distribute that inly 7 * 6 is 42 so we get 42 W plus 7 w okay so if the volume is 280 cubic inches I'm going to set the volume equal to 280 and now we're going to solve for w 42 + 7 is going to be 49 so I've got 280 equals 49 W and then if we divide both sides by 49 wait a minute something's not right here oh I see when I distributed this 7 W in I forgot to multiply the W here so this should actually be 7 w^2 um so unfortunately we're going to have to solve it a little bit differently um what I would do here at this point is probably do a little guess and check to make sure you know I think versus doing like the quadratic formula uh now we did the quadratic formul in the last problem so if you know how to do that that's fine um but yeah I think at this point let's just plug some numbers in and see what works so first we'll try four and so I've got got 280 = 42 * 4 + 7 * 4^ squared and the question is really does this actually equal 280 so I'm not going to put that yet so 42 * 4 + 7 * 4^ 2 is actually it works out 280 look at that so yeah uh our answer here is going to be 4 in Number 27 says a ladder is resting against a wall so here's your building here's a little ladder that is not a ladder you can see um here's a ladder okay so it says the top of the ladder touches the wall at a height at 9 ft so right here here's 9 ft find the height of the ladder if the length is three more than the distance from the wall so the length all that L that's what we're trying to find is three or here I'll type it out so it looks a little nicer the length is 3 more than we'll call this x the distance from the one find the length of the ladder so this is what we're trying to find okay so basically what we're got to do here is set up a little Pythagorean theorem a^2 + b^2 = c squared so before I start substit stituting things in for a b and c I think what might make this problem a little easier is If instead of throwing in an extra variable here x we don't really need that variable instead of trying to write the length in terms of the distance from the building you know here I've got three more than the the length of the building let's put this distance from the building let's make write that in terms of L and so what I mean by that is like if we just make this side l then this distance down here would be three less than l so instead of X I'm going to write this as L minus 3 so now I can go in and substitute all these expressions in for a b and c just make sure that the hypotenuse here the L that's going to be our C here so the setup here will be lus 3^ 2 + 9^ 2 = l^2 where L is the length of the ladder and so first I'll square out this binomial which just means you multiply it by itself and you'll get x2 or l^2 minus 6 L + 9 and then 9 s is 81 so+ 81 = l^2 If I subtract l s from both sides I can get rid of both of those quadratic terms and this will just be zero on this side then I can combine my like terms here 81 + 9 is 90 now I've got a nice little two-step equation here that shouldn't be too bad to solve first I'll subtract 90 from both sides and then I'll divide both sides by -6 so you should get L equals let's see here 90 / 6 is 15 so our answer is D number 28 says if an object is propelled upward from a height of 144t at an initial velocity of 128 ft per second then its height after T seconds is given by this equation after how many seconds does the object hit the ground so the object will hit the ground when the height is zero so that's kind of our key piece of information here okay so we want to know when is the height zero the height is zero when it's on the ground so what we need to do is we need to figure out what value can we plug in for T that will make it zero so really we're trying to solve this equation -16 T ^2 Plus 128t plus 144 equal 0 now we I think we want to take advantage of the fact that this is a multiple choice question and we could just plug in the values here for the number of seconds into T and see which one actually gives us a zero we can also solve this using the quadratic formula but I just think it's a lot easier to solve this by plugging in the answer choices so that's what I'm going to do here so first we'll try 9 seconds and so I'll just replace t with nine so -16 * 9^ 2ar + 128 * 9 plus 144 I want to know what that equals hopefully it equals zero we could be done but if it doesn't we'll try the next the next option so I'm going to go to my calculator start typing this in -16 * 9^ 2 plus plus 128 time 9 plus 144 and I get oh wow I get zero so yeah there you go our answer is a always love it when it's that first answer Choice number 29 says a rocket is propelled upward from a the top of a building 210 ft tall at an initial velocity of 112 ft per second the function that describes the height of the rocket in terms of T is given here I'll go ahead and uh let's highlight this function so this is giving the height and we want to know when does it reach the maximum height so what we need to do here is figure out you know which of these T values is going to maximize the height so I think what we ought to do is just plug those numbers in and see which one gives us the biggest height there is a roundabout way of finding that basically what you want to do is find the vertex but again this is a multiple choice test so let's take advantage of that so I'll just test each one of these and see which one gives me the the biggest height so negative 16 * 2.8 squared + 112 * 2.8 plus 210 see what that thing equals -16 * 2.8 squared + 112 * 2.8 + 210 and that gives me forgot something on there much better 3 98.16 so that is our number to beat that is our height that we want to get that you know we want to know if this is the maximum height or not so we'll do that again uh but for 3.5 so let's see what we get there just going to replace these 2.8 with 3.5 type that into your calculator which is what I'm doing behind the scenes here and on this one I get 406 so now we got a new height to beat okay 7 Seconds now one thing I'll say if this is the answer well I I'll wait till we get past that okay so let's let's test seven and see that gives me here I'll just replace all these 3.5s with seven -16 * 7^ SAR go okay I got it all typed in that gives me 210 so that is definitely not going to be right kind of thinking it's going to be 3.5 I just got a feeling about that one here's 5.6 so we get -16 times 5.6 squared got a lot of extra stuff here let's fix that up uh plus 112 * 5.6 plus that last 210 and let's see what we get here just typing this in with replacing the seven with a 5.6 and I'm getting 335.40 so we can see that the time at which our height is maximum is going to be 3.5 seconds because this number is the biggest number 30 says if an object is propelled upward from a height of 48t at an initial velocity of 98 ft per second then its height after T seconds is given so we got kind of a similar setup here to the last couple problems after how many seconds will the object reach a height of 192 ft once again we're just going to test these out and see which one equals 19 192 we'll start with 1.5 and uh yeah we got6 * 1.52 + 96 * 1.5 plus 48 and I'm going to type all that in we're looking for the one that equals 192 here so we won't necessarily have to test all of them we just need to test them until we get the answer now if you want to be 100% confident that you got it right doesn't hurt to test the other ones I'm getting 156 here so I'm guessing it's going to be a little bit above 1.5 three seems like H maybe that'll work I don't know let's see so we'll just throw in a three here instead of a 1.5 going to type that into my calculator I would assume on a problem like this that you would definitely get a calculator and I get 192 which is going to be our answer I had a feeling about that three so yeah so this is it this is our answer and so our our answer here is going to be B he's oh I guess not number 31 find the length of a rectangular lot with a perimeter of 82 and a length of uh a length that's 5 m more than the width so if we got this rectangle the perimeter is all the sides added together so that would be like two lengths and two widths add up all those we should get 82 it says the length so I'll make this the length is five more than the width so 5 plus W or I'll just write as W + 5 and here's the width so what we want to do is find the length so I'm going to replace actually if I'm trying to find the length what I want to do is actually rewrite the width in terms of length so if the length is five more than the width then the width is five less than the length so the length minus 5 doing this will make it so that when I substitute these back into the perimeter equation um I I don't have to like convert anything so yeah basically what we're going to do here is we're going to replace the W with L minus 5 have 2 L plus 2 * the width which is five less than the length equal 82 and now I just need to solve this equation so Distributing that 2 to the lus 5 gives me 2 l - 10 = 82 combining these two like terms is going to give me 4 L so I get 4 L minus 10al 82 have to continue this work over here right out of space adding 10 to both sides is going to give me 4 L = 92 and then if I divide 9 9 2 by 4 I get 23 L is 23 and let's go look at our answer choices here we see that the answer is C 32 Chuck and Dana agreed to meet in Chicago for the weekend Chuck travels 175 I'm sorry 174 miles in the same the same time Dana travels 159 miles if Chuck's rate of travel is 5 mph more than Dana and they travel at the same length of time at what speed does Chuck travel so let's break this down I'm not 100% sure where this is going to go but one thing you might want to be aware of is that distance is equal to rate times time and so we might we might uh or at least the way I'm going to approach this is going to use this little formula here so I'm going to basically try to keep Chuck uh track of both Chuck and Dana we'll see if we can't like put together an equation here so Chuck is traveling 174 miles so that's the distance Dana so I'll just say equals rate Time Time come back to that Dana on the other hand traveled 159 miles so this would be 159 is her rate times time if Chuck's tra rate of travel so that's the rate is five more than Dana so if what are we trying to we're trying to find Chuck's rate so I'm going to leave that as a variable and if he's traveling 5 miles hour more than Dana and that means Dana's rate of travel is five less than Chucks but now this R is the same also says they travel at the same length of time so the t's are the same we want to know what speed does Chuck travel so if we're solving for the rate for Chuck we would divide both sides by the time so we' have 174 equals or 174 divid by tals the rate so if we can figure out what this time is we can solve for this rate um looking them back over at Dana what we want to do is try to rearrange this equation for time so I'm going to divide both sides by Rus 5 so I have 159 divided by r - 5 and that equals the time so now I can replace this time with this expression this 159 over r - 5 that's what I'm going to do over here 174 divided by this other fraction 159 over Rus 5 equals his rate okay so dividing by a fraction is the same as multiplying by its reciprocal so I can rewrite this as 174 * r - 5 over 159 then I'm going to try to clean up this equation just a bit so I'm going to distribute the 174 and divide everything by 159 I'm not actually going to do any of the arithmetic I'm going to leave it as a fraction but so that's going to leave me with 174 R over 159 minus here we've got to multiply 174 * 5 so that's 87 so minus 870 over 159 equals R now we've got a bunch of fractions here and we can clear those fractions by simply multiplying both sides of the equation by 159 so that's going to be my next step here is to multiply both sides of the equation by 159 in effort to get rid of those fractions so that'll leave me with 174 Rus 870 equal 159 R from there I'm going to subtract 174 R from both sides which will give me -5 r on the right hand side lastly I'm going to divide that 870 by 15 to get our answer here for the rate which is there we go the rate which is 58 miles hour yeah 32 is a 33 a triangular shaped Lake Front has a perimeter of 1800 ft going to draw a little triangle here don't know what the angles are or anything but we know the perimeter we'll just call this side A B and C don't know what they are but this those three side lengths uh should add up to 1,800 one side is 100 feet longer than the shortest side I don't know which one's which here so I'm just going to say that um this side is the first side they're talking about one side so I'll call this one is 100 feet longer than the shortest side so I'm going to call the shortest side s so this is the shortest okay the shortest side um and so some other side is going to be 100 feet longer than that so this is going to be 100 plus plus s and the third side is going to be 200t longer than the shortest side so 200 plus s so now we want to find the lengths of all three sides um so what we can do is just set up this little equation I don't know what the A B and C are it doesn't really matter we're just adding up the sides so we've got s which is the shortest side plus the middle side 100 plus S Plus the longest side 200 plus s and this is an equation we can use to solve for S and from s we can get all the other sides I'll combine my like terms S Plus S Plus s is going to be 3 S 100 + 200 is 300 then if I subtract 300 from both sides going to get 1500 and then if I divide 1500 by three I get 500 so the shortest side is 500 looking at our answer choices uh you know it's pretty obvious what our answer is going to be because this the uh D is the only one that has the shortest side is 500 but you can see that this would be right anyway because the two other sides are going to be when you add 100 and 200 to 500 will give you the 600 and 700 so yeah we we've got confirmation here that D is the right answer another thing you could do is just kind of go through the answer choices and find out which one which one adds up to 1,800 and also meets these conditions so you don't necessarily have to solve this one algebraically number 34 said that sum of the squares of two consecutive integers is 41 find the integers so if the first integer is n then the second integer is n + one so it says the sum of the squares so n^ 2ar plus the next number which would be n + 1 squar is 41 and I would just like kind of go through and see you know which which which ones work here so if let's do four and five work let's start with that so does 4^ 2ar + 5^ 2 does that equal 41 four squar is 16 and 5^ squar is 25 and those do in fact add up to 41 so four and five definitely are going to be at least one of our Solutions it looks like there it's possible there's another two but since these second two options uh don't have the four and five option we can cross those out safely so the next thing to do is check -45 and as you're typing this into your calculator make sure that you are putting these negative numbers in parentheses because otherwise you'll get the wrong answer but yes in fact if we do type this in we'd get the same thing we get 41 so our answer is a you could also try to solve this equation over here but this turns into a quadratic and I think solving it that way is going to take a lot longer and probably lead to more errors than if you were to just check the answer choices and I'm hoping by now by question 34 you're starting to see a pattern here which is that a huge chunk of these questions you don't actually have to know how to solve algebraically just have to know that you can plug in the answer choices and see which one works number 35 says the length of a rectangle is 10 in more than its width so here's my rectangle we'll uh call this the length uh it's 10 more than the width and uh well actually usually I guess the length down here and here's the width doesn't really matter but yeah um this looks like the longer side so I'll make that 10 plus the width it says if five inches are taken from the length and added to the width the figure will become a square okay with an area of 106 Square in so what are the dimensions of the original figure so if we had a square that's 196 the dimensions of that square would be the square root of 196 so the square root of 196 is 14 meaning that the side lengths here would have to be 14 and 14 now this would be if you took 10 five in from the length so subtract 10 I'm sorry subtract five from the length and add five to the width so if that's the case then if we added five to the width then the original width would have been nine and then the original length which is 10 more than the width would be 19 so the dimensions of the original figure that just disappeared on me for some reason I'll just redraw it uh will be 9 and 19 our answer is C number 36 says a bag contains nine red marbles two blue marbles and five green marbles what is the probability of choosing a Blue Marble so to calculate probability we're going to divide the number of desired outcomes by the total number of outcomes this is just how you calculate probability in general so in this case we want to know the probability of choosing a blue marble and we can see that there are two blue marbles so it'll be two over the total number of marbles which is nine there's nothing really to calculate here oh wait a minute bag contains nine red Mar oh I'm sorry I didn't uh uh read that closely enough nine red marbles two blue and five green so the total number of marbles here is not nine sorry there's just nine Reds uh would be 16 so once you that's your probability 2 out of 16 and the only thing left to do here is reduce that which would be 1 over 8 our answer is B number 37 is a very similar problem so we'll use this whole I'll actually leave this up here so you can see it um this is asking for what what is the probability of choosing a marble that's not blue so the number of marbles that are not blue would be the red and the green there's seven red and one green so that's a total of eight not blue marbles and the total number of marbles would be seven and 4 is 11 + 1 is 12 so it' be 8 out of 12 which reduces to two out of uh three I divide both of those by four so our answer is B number 38 says a six-sided die is rolled what's the probability of rolling a number less than six so there are total of five sides on the die one through six and if you want to know the probability of getting less than six there's only five options there one two three four and five out of a total of six options so there's nothing you don't even have to reduce this the answer is D number 39 says a card is randomly drawn uh from a standard 52 card deck you win $10 if this card is a spade or an ace what is the probability that you will win the game so there are um 13 different cards um there's the numbers two through 10 okay there's also a jack here let me instead of trying to handr write this with a mouse let me type it out okay so here's there the possible um uh uh uh what do I want to say suits or not suits but numbers I guess I don't really know what you call these um but anyway so every card is either is any number between two and 10 but it could also be a jack a queen or King so these are 13 um uh 13 they're not suits what are they called um numbers 13 different numbers and then each number appears uh four times because you have one for each suit there's a total of four suits you've got spades clubs diamonds and what's the other one Hearts so there's four different suits okay so this says you win $10 if the card is a spade or an ace what is the probability that you will win the game so you got to be careful here because um we're still going to use this formula right the number of desired outcomes out of the total number of outcomes so what we need to do is figure out out of the 52 cards how many are either Spade or Aces so there are going to be a total of 133 Spades right there's 13 like values oh wait I missed one the ace we recognized that before I did um but yeah so there's 13 Spades so first will 13 but then it's not just if it's a spade it could be an ace or a spade so since there are four aces in a deck you would you might think we want to add four here but one of them is going to be a spade and we've already accounted for that so there's only three more Aces left so this will be 16 over 52 and if we reduce 16 over 52 we get four out of 13 number 40 in our last problem says a coin is tossed three times what is the probability that lands on Tails exactly one time time so to have a combined probability we want to multiply the different events so the probability of oh wait what's going on that it lands on Tails exactly one time so here here are the options here like we could have um a situation where we throw the the coin three times its heads all three times right then we could have um you know one where we get heads twice and then a Tails or we might get one that has a heads and then a tail Tails followed by another head or we might get a head and then two more tails and um I is that all as far as yeah I think that's all as far as getting the head first but let's say we did not get the head first let's say that we got a tail first so that the the possibilities here be um know getting all Tails or getting a tail followed by another tail and then a head followed by a tail um let's see here we could get tail heads Tails or we could get Tails heads Heads I think I got them all there and I think that's all the different possibilities here look at that one more time before I make that conclusion but yeah this is it so there's a total of eight different events and um the ones that have tails exactly one time going to be this case this case and this case down here so there's three out of these eight possibilities and that's going to be our probability if you put 3 divid 8 into the calculator you'll see that it's 0 0.375 and so our answer is B that concludes this review um just remember that the actual test is only going to be 20 questions so this is going to be way longer so yeah I guess that about wraps it up for today uh this is this video is getting a little long so I'm going to cut myself off here yall have a great day thanks for watching and I'll see you next time