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ACT MATH Prep 2/25/2022

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ACT MATH Prep 2/25/2022

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hey that's time so hopefully that helps you get a little bit of a feel for the act so we're going to spend the rest of the time going over this hey what did you guys get for number four do we get we should have got GK that's okay jeez -3 case we have absolute values what do absolute value mean it snowed means ever interns positive queso 6 - 4 is 2 and the positive version of 2 is just too what's 3 - 8 - 5 going to turn to a positive five with two -5 which is -3 any questions on that one hey that one you also can type in your calculator if you member you have absolute values in your calculator so if you see that test hopefully you can just do that but if you can't do your calculator hey 45 what did we get good Easter this one we have to multiply outs we the first one to everything in the second so 12 c squared plus 4 cd can we do the second one to everything in the second so - 9 C -3 G squared okay and then we can combine these once we have 12 c squared - 5 CD - 3D do see any questions on that one hey hopefully we'll get through these first one's pretty quick and then we can work out the harder one hey number 9 what did we get D Goode Dave do for this one we use similar triangles hey let's be quiet guys similar triangles so this triangle it's similar to this overall triangle hey I'm we're trying to find a sea so we're trying to find this lame day so we're going to do that's tied to this long side sox2 and that long side is 8 + 7 + 6 which is 21 equals then we're going to look at our little triangle we're going to do alongside which it tells us is 16 two shorter side which is 8 K when you do comparisons like this you have to do like the same spot in each one case of like this was the short side so this has to be the short side and then we just solve it so for this one just got a * 21 and when you do that you get 42 and that's something you can just do in your calculator it don't try and do that in your head do it in your calculator K questions on that one hey I feel like there's always a similar triangle test question so make sure you know how to do similar triangles another thing there's always a question for our a bag of marbles for some reason hey what you guys get for 11 it is B okay so there's a couple different ways to do this one so first we want to get it equal to 3/5 right and when we're finding proportions we're doing the number of whatever we're looking for over the total hey so the total number of marbles in or right now or 24 and we have a tread right we want to get that to equal 3/5 so we're going to add in some red marbles so we're going to add in some red so we're going to have X Plus red marbles but then we also have to add that to the total right cuz our total marbles will change that makes sense. Set up hey you can do it a few different ways but. the one that I thought of first any questions I'm just getting that product K let me solve it so we X or denominator so we end up with 5 * x + 8 + 3 * x + 24 a slots 5x + 43x + 72 let me stop for X so - 3x + -40 we end up with two x what's 32 / 2 + x equals 16 any questions on that one and sometimes you have to do remember one of the strategies we talked about on the first date if you don't know how to do it immediately move on to all the ones you know how to do right away or within 30 seconds and then come back to the ones that you don't know how to do K questions on that one hey 13d is correct did everybody get d hey so he gets fit $10 an hour and he works he works 46 hours case over 40 hours he's going to get 15 bucks a so that's the first 40 hours and then we're going to add that to he gets time-and-a-half for overtime so he had 6 hours of overtime day and time and a half to find that we can just do our 15 * 1.5 what time's the time and a half and that'll tell us how much she makes does that make sense if questions hey so 40 * 15600 if we multiply 615 and 1.5 to get 1:35 which is 735 Kate and then the other thing is to pay attention to is they take $117 out for what taxes deductions so you might have to 117 you get 6:18 hey do we have questions on how we did this ready for the next one hey let's go the next one then hey in this right triangle what is the sign of a when we get degood remember sohcahtoa another way to remember this that I just learned this week someone told me is some old hippie caught another wait no some old some old hippie caught another hippie tripping on acid what's another one but if you remember stuff with her that's little bit shorter hey so sohcahtoa sign is opposite over hypotenuse queso opposite of a is 7 and then the hypotenuse 9 remember hypotenuse is always your long side it's straight across from the right angle any questions on that one okay so make sure you remember sohcahtoa 18 but we get Yay good okay this one looks really hard but we can just type it in the calculator if it doesn't have any variables or anything report my calculator Maybe for those of you who got it you just typed it in the calculator right okay good so I'm just going to type it in so we can look at it if you didn't type it in so we've got 27 / 64 I'm going to put A M C stands for raising it to a power make clear this whole thing 27 / 64 that's our fraction and then we're going to raise it to the power so we do the little camera button above division and then I would put parentheses around this too we need - 2/3 - 2 / 3 something that's really important that a lot of people messed up is they don't use the negative sign that use the minus sign okay you have to use - 4 - + - 4 - or you will get the wrong answer hey so when you read it out loud in your head if you stay a negative type the negative bun down by the zero if you say minus or subtract type the subtraction sign hey make sure you don't mix those up and then you press enter you got this decimal and then don't forget you can turn it to a fraction if you're on Desmos you just have to click the little side action button on here you going to click math and then it's just the very first ones you just press enter we had 16 / 9 any questions on that one we're really your calculator is your band right okay number 20 for a given set of data the standard zorzi response the Roswell High wondering what you guys get for 20 is everybody get  okay so let's walk through this so we've got our equation right here okay and then we've got this mule is 78 and this is our standard deviation that sticks and we knows he's too so we have the song for ex so all we're doing is we're going to plug everything in and solve for x those e is too so we get two equals x minus our mean is 78 all over sand deviation of 6 he stopped how we set it up and we just stopped for XO what do we need to do * by 6 so we get 12 equals x minus 78 and then add the 78 so we get 90 equals X does that make sense came for the people who said no does that make sense hey y'all if you're not going to pay attention just leave does that make sense everybody do we have any questions 22 what is the slope of the line parallel to x + 5y equals 9 what do we get all of the answers the answer is G okay so let's let's see do this do to be parallel that has to have the same slope because of the line goes like this you have to have another line that matches it no matter where it's at it has to have the same slope okay so we have to figure out what the slope is the slope remember y equals MX plus b this is your slope your M value if that's your slope so we're going to solve this. It looks like that we're going to get y by itself so we're going to track the X we have negative x + 9 and then / 5 the Y equals negative x / 5 + 9 so this right here is our slow -1 / 5 questions alright that's okay so we've got this triangle we know the angle is 58 degrees and we know that side a b and a c or equal to each other what is the measure of angle c d kaisa one thing to read this is this is an isosceles triangle they've got the sides are equal to each other okay that makes it an isosceles triangle and then we have this is 58 right how many how much do the angles add up to in a triangle 180 we do 180 - 58 that's not divided by -58 22 is that means these two angles that add up to 122 and since the sides are equal that means their angles are equal ASO we just have to split 122 and half and 61 hey so it's kind of nice to know just some random properties about triangles cuz they always randomly show up any questions on that one 27 what do we get answers okay so let's thing but this one really quick cuz this one honestly a lot of people probably over think this one that's one of the biggest mistakes on it I think so we've got our scores but we've got 61 6170 679 8080 84 and 91 and then we're going to add in the 90's that's going to go before the 91 hey when we're finding mean median and mode always put them in order these are our new numbers Hey Now the easiest one to check is the is which the man is probably the hardest yet probably the mode cuz who knows what the motor has the most frequent number so before we have the 90 it was 80 after we have the 90 it's still 80 that means are modes going to be equal so we can automatically cross off anywhere the motograter that leaves us with two answers Kate and both of them the main says greater so we know that means going to be great or we don't have to check that we need to check the median if it's greater than or equal to now the median is your middle number correct so if we do it without the 90 if we find the middle number here we get to Katie Wright if we put in the 90 and we crossed off and get to our middle number we get between 80 and 80 that means it's just 80 so it's the exact same it's equal to us that gives s e e hey that makes sense to have questions on that hey so if you have a list of asking you what's change mode and median are the easiest mean you have to do some actual math course hey let's look at 35 so that was 27 so all these first questions have come from the first half of the test say and remember they get harder as they go so the second half is going to be harder than the first half play so we've got this Jean yq 77k and we've got just a regular test for it and then the Sam 77 test hey so they test a thousand people a thousand people take both tests on the the original test this is how many people say positive the Sami people say negative and on Sam's test this top row is positive and bottom Rose negative right so if it cost $2,500 to administer each why cutest and $50 to administer the Sam 77 test what is the total cost to administer both tests to all the volunteers e good is it this one you don't really even need to use the table right so all we're doing is we're doing there was 1,000 test for the first one at Cost 2500 and then they did a thousand test again on the Samsung 7 7 and that would only cost $50 and just type on your calculator you should get two million five hundred fifty thousand are we all clear on that one okay let's look at 36 what percent of the volunteers actually carry y q77 Jay is correct okay so we know from what we read up here it says that the yq test determines with 100% accuracy so this test up here is never wrong it's always correct so it tested 1,000 people + 590 + 25 + 615 that many people tested positive let's 615 out of 1000 people and if you find that percent well actually if you type that in your calculator you get the decimal right you get Point 615k remember to find the percent you either move the decimal over two times or times that by 100 you should get 61.5% best questions on that one hey when you get to questions like this like if they have a big thing that you're going to use for all the questions depends on the person some people like to read the situation then read the question but sometimes it's a good idea to read the questions and see what you're even looking for it before you even read the big situation is that something you can see what works best for you but that's another thing that some people do Kioti 30 ask four questions do you have any questions on this one hey number one it is a hey how many of you used to calculate this how many of you did not age calculator you can not use your calculator and you can do the - 215 over right so it equals 0 you can try and factor that I don't know if it does or not I didn't try not Isley so where you could do quadratic formula if I personally grafted on the calculator cuz we're looking for where it equals 0 right that's an X intercept right wherever it equals 0 that's your x intercept so if you go to your calculator and you click y equals Let Me Clear these out you can type in your equation so we had 24 square if you guys don't know how to type in exits in a button right next to the alpha that's two of them a x squared and then we have + 2x -15 if we go look at our graph we can see where it crosses and it says we want the greater of the two solution so we only have to check the one that's bigger so is the one that's negative or positive going to be bigger positive and so to check 40 this is something that you know might show up on the test might not but it's nice to know how to do cuz if it does show up super easy question okay so you pressed and then you're going to press straight it's the button right next to graph and it pulls up this calculate menu or going to pick 00's another name for X intercepts hey and then we're going to find a cursor and we pick a left band so something to the left of our x intercept and press enter then we're going to pick a ripe bound so we're going to go to the right of our x-intercept and press enter and then we're just going to is it where it is a center and we get point 75 which is 3/4 does anybody want to go through the steps again are we know how to do that okay and again actually on face if he'll have does most so if you just go type in the graph you can just hover over the x-intercept I'll tell you where it is yeah yeah any other questions on this you can't solve algebraically or the other thing you can do is plug your answers in that's probably why did you guys do that know what whatever there's lots of ways to solve it okay so anytime you're looking for a solution to an equation usually grab it but sometimes it's easier not to okay any questions on that one hey let's look at 43 so we had what is the area in square units of a circle that has a circumference of 12 Pi units long yes it is what is the equator for circumference yeah either to pay our or the diameter times pi either one most of the time you'll be dealing with the radius rather than the diameter and if so I would remember eyes that one and then the area is what someone over here said is pi r squared so the way so I personally have the two paillard memorized I don't care which one you do but the way I remember it is there conference is a way longer where than area and 2 pi r is longer than pi r squared I know that's kind of the weird thing that I remember it was but I would know cuz they will probably pop up randomly on the ACT hey so we know that the circumference is 12 pi the 12 Pi is equal to hey 12 pies equal to Earth's circumference 2 pi r hey now we need to solve for our so that we can plug it in and find our area hey so we can / 2 pi rights we want to get our by itself so it's going to cancel out on the right side and we just have our what's 12 Pi / 2 pi 6 Pi / Pi cancel out to be 112 over 26 that means our radius to 6 so when we plug that in for area i r squared + 6 squared + 6 squared is 36 that makes sense if questions hey so those are a couple formulas that I would remember or at the very least remember I'm so the beginning of your test and write down the top okay okay 45 when we get kids anybody else anything or did we all guess the answer is e okay so let's go over how to do this one this one's adding fractions right you can only add fractions if what if the denominators are the same we have to get a common denominator hey so to do that what we're going to have to do is my rewrite this we're going to have to multiply this one over here by x minus y and this one over here by x + y that way they're the same right but we can't just X Aranda X - 1 x + y we can x 1 however so we do x + y / x + y + x minus y over x minus y kids that set up why we're doing that okay so then we just multiply everything together so on the left we have x squared minus x y over what's x x minus y + x + y so we get x squared plus x y men - x y - I swear right I'm just multiplying X to both of them and negative white both of them cancel that their left side is there anything that cancels out and the denominator x y + - x y those are going to go away so really we just have x squared minus y squared plus now we're going to multiply the Y out with y x x x o x o plus y squared and on the bottom it's the same thing we just did love x squared minus y squared what kind of a lot of questions so far the whole thing so what we're doing is we have to get a common denominator so to do that we have to multiply this denominator by the last one and vice versa okay so we do x + y * x - why we can't just x a random x- why we have x one cuz one won't change it so we do x minus y over x minus y I'm on the other side but this time it's x + y / x + y cave then we x that out so on top or doing x x x which is x squared + -5 * X which is - x y Hazel that's right there on the bottom we're doing x x x which is x squared x X Y which is X Y 8 - y * X -6pi I'm a Niger W X Y is minus y squared and the ex-wife cancel out and then we do the same thing on the other side we know the denominator is going to be the same cuz that's the same two things mode fine and then the top we just distribute the why we get x y + y squared that help hey so last thing we're going to do is actually combined them okay so they have a common denominator that's going to be x squared minus y squared a n remember it just turns into one denominator kind of like when you have a 3/2 - 1/2 you have two hacks right you don't change the denominator even if it's a big one like this and we're just going to combine the whole tops we've got x squared minus x y + x + y squared play anything that cancels out RX wise again right we had minus and plus the really would stop x squared plus y squared I'm a squared plus b squared all over X minus y squared a question okay that's one that takes a minute right so if you got someone like that on the test you're getting to the end of it and you think it's going to take a minute if you don't know how do it right away and you're going to have to think about it skip it and you can come back to it okay any questions hey what city we're almost done some kind of ghost the next 451 should have got d R51 hey so all over this one so we have 60 people 160 people in the jury pool right we know that out of the total that got called 1/3 are going to be dismissed so if we want 60 that means we need 90 people a 1/3 to go away at least 60 case but if we want a total of 90 people we know only 40% are going to show up so that means 40% of whatever number three pick are going to show up so 90 has to be equal 2.4 that's 40% * X and then you can just use your calculator to divide by 4 and you get to 25 does that make sense let's see 52 what do we get K good it is kk4 this one there is a few different ways you could do it the way I did it in the way I think is the easiest we've got four numbers repeating right so we're going to take we're looking for 275th going to take 275 and I'm going to / 4 and I get 68.75 list .75 that's 3/4 right that means my remainder is 3/4 Diamond account in three one two three and that's nine does that make sense it goes through it a total of 68 * all the way through and then on the last run it only gets 75 and only get 3/4 of the way through hey I'm last to 57 would we get answer Kate's do we know AC is 1 b + C / D is undefined that means D has two equal zero right cuz you can't divide by zero so A B C equals that means A B C equals 0 we know a x d is one so 8 * C that's going to be one so we have be equal zero Islamic Center hey and last one we should have got f little weird okay so it's $15 for the first copy Emma is 12 for each copy after that not including the first case of that means it's $12 for every single book except for one so we want to take away one from the title or one from the total take is the first one class 15 but then all the rest after that or 12 but if you multiply this out 15 + 12 y - 12 + 15 - 12 is 3 Remington hey so that one's tricky at that was the last problem on one of the two then I think it's just tricky because you have to read that make sure you noticed that after the first one they're $12 that is all we're doing today if you have weren't here last time bears practice test over here you can grab a packet of there's four tests in there so just for people who weren't here last time you can grab one of those yeah that's what this one I mean I just have mine

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ACT MATH Prep 2/25/2022

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