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ACT Prep Math 2/18/2022

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ACT Math Prep February 18,2022

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we're going to get started can you all hear me do I need to use the microphone so we're going to start off going over like calculator tips I'm so if you have your go ahead and get it out hey so why you guys are doing that first thing you need to check you need to make sure your calculator is allowed if you have a TI-83 or TI-84 your fine you can check the ACT website if you're not sure if you have a TI-89 or if they talk to you later says Cas it is not allowed so that's mostly what you need to double-check but you'll probably most you probably have an 83 and 84 and then if you don't have a calculator since we're online you'll get to you as most anyways if you have a calculator or not so that's kind of nice queso worst comes to worst don't bring a calculator you can just use those most no goodbye right now the Patriot k a couple others every problem on the ACT can be solved without a calculator but calculators can be helpful to make it go little bit faster so you don't have to do everything by hand so make sure you practice using your car later so you're familiar with it if you don't have a calculator or think you might want to use Desmos on the ACT makes you practice with that as well just use it a little bit do you get in that habit hey it's still a couple things to make sure you know where the buttons are square root exponent pie and trig functions on your calculator they should I'm sure you guys know where they are but square root is right here and blue you just press second and then you can type a square root 8 the exponent button is the one that looks like the carrot and that's how you type any up on it that you want what else opai and trig so sorry that was the wrong thing to press queso trig your stuff like your sine cosine tangent they're all right here and then high is usually on your calculators if you have a 83 and 84 it's right above the exponent button so you're going press s and then press your exponent button. okay so that's a useful thing to know probably for your math classes as well as you can type I on your calculator a couple other things that are just like take some time to if you if you press the math button on your calculator there's lots of things right can turn it to a fraction you can turn your fraction to a decimal you can do it has a cube done it a cube root if you need to do like a 5th root or anything I'm here there's blog if you need to log with a base that's not 10 and then you can also scroll over there is absolute value there's a factorial I don't know if that usually shows up on the act or not but yeah I don't think it's usually there fraction so there's lots of stuff that you just have right on your calculator that you do got to look around a little bit for okay and then we all know how to graph right we go to y equals type in sum function K-PAX buttons right next to Al and then just press craft no graph your function hey another thing your calculator can do for you is if you need to find like the intersection points or anything if you press second so the blue button and then Trace which is the button right next to Grass it pulls up this menu and there's a few things you can do you can find your zeros which are your x-intercepts he can find a minimum or maximum you can find an intersection between two lines and you can also find a value click on that one you type in any x-value the of the whole thing and it'll tell you what the Y value for that is okay those are just a couple of tricks you can use on your actual calculator Wednesday other thing I want to go over but I don't think we talked about last time make sure you can go from fraction to decimal 2% and all around okay so fraction you can just type in your divided some can I do put in a battle turn it to a decimal K if you would like to turn that to a fraction again that's just the first option in math it turns into a fraction if you want to go back to Adele you can hit mass and then the second option is decimal K and then how do we go to percent yeah okay so we're going to actually * 100 K and then to get back so if you times by hundred this wasn't a good once this is over 100% of 2/4 so we have worth is that decimal is 8 is a few times by 100 but gets you the percent so that's 80% and then if you want to go back to the decimal you just divide 100 okay so those ones aren't as hard with like .8 but if you have something like maybe you have .15 to 3 and you're just not totally sure times that by 100 and I don't give you the percent at 15.23% okay any questions on how to do anything on your calculator so that's your calculator now I want to look at Desmos for a minute because I'm assuming as anybody not used as most good so it's face play just the same thing right but you can type it with your keyboard type in f of x equals x squared minus 5x you grab a couple things with Dez most and you can just cover over the points I'll tell you what the X intercepts are the y-intercept and I'll also tell you the vertex and noblesse over a little bit hey so you can hover over the vertex and it'll tell you what that is if you click on it it'll but if you just have her over it it goes away when you leave so you can click on it if you need it to stay or anyting you can also if you've said f of x equals zero then you can say I want to know fa5 is and it'll tell you K but you can't have multiple like if you do find to FX is it won't be able to do that so you can only have one f of x you could do another equation that we could say G of x is maybe that's the natural log that day and then you can say well I want to know what G of 6 is and it'll tell you what that is okay that makes sense you can also do let's see I can't remember hold on I can't remember if this works without numbers I just mix the graph nevermind you can also type in just use it as a regular calculator so type in like 4 / 6 day gives you the decimal if you want the fraction just press this little button right here it'll take refraction if you just looking to see what may be the simplest form that could be is you can also go through if you click on these like red and green dots it'll keep your graph saved but it won't show it I'm so if you have a couple typed in but you'll need to look at 1 yeah I know you can zoom out and in pretty easily I'm try to think there's anything else that easy it also if you have rubber intersection points it'll tell you that point as well but basically it'll do everything your calculator will do it's just a lil bit more user-friendly questions about decimals hey I'm one other thing that you can do that I'll just mention really quick is let's say you wanted your equation to be like you were looking at maybe I'm looking at vertex form of a quadratic hbr member vertex form SK it has little option add a slider if you press on those it adds that it's called a slider and you can change the values for that and see what happens to the graph Hazel like if it's there's sometimes there's questions we'll talk about 1 today where will be like how does this equation compare to equation what's going to happen is this equation going to be greater than this equation so you can kind of look at it like that play Sasha's another thing but it's pretty user-friendly just type in your equation or whatever calculation want to do there's also this keyboard down here if you need like less than or equal to greater than or equal to compress functions and they've got all your trig stuff and some other stuff in here case we'll just look around on that messed around on it play on it yeah it's not too hard to understand so I'm your calculator does order of operations it's going to do the order of operations on whatever you type in so make sure you use parentheses and use them correctly hey a lot of people get things wrong because they don't use parentheses or they maybe have the right equation on the paper but they just type in the couch so we're going to practice typing some stuff in the calculator if x equals 3 I don't get to type this in your calculator and tell me what it is equals okay it's everybody have an answer so I'm going to type it on my calculator what was it 2x squared + 10 so too and then I'm going to put parentheses around whatever I'm typing in whatever I'm plugging in so 3 squared + 10 you should have got 28 everybody got 28 hey we need another one but this time we're going to do one with a negative number so if x equals -1 what's 3 x squared + 4x - 5 okay we all have an answer secret square plus Square x - 5 so 3 make sure you put especially when you're typing and negatives put them in parentheses it's not usually as important with parentheses for positive numbers but if it's negative you have to put parentheses or you will get the wrong answer Houston got - 6 any questions I'm typing that one in case makes your careful with that especially if you're swearing something a lot of people will type in if they're trying to do negative 2 squared they'll type it in like this negative 2 squared that's going to give me -4 but that's not negative 2 squared right - 2 * -2 is positive 4K if you do it with parentheses you'll get the correct answer so just always use friend be on the safe side hey I'm going to another one with a fraction hey so if x equals 5 what is x squared / 4x - 10 okay be ready and waiting on the 2nd expert AB so what do you have to be careful with on this one while you're typing it in parentheses where yeah around the denominator right if you don't put parentheses it's going to think let's see let me type this in without parentheses first so if we put no parentheses 5 squared / 4 * 5 -10 the calculator is going to do order of operations what's going to do 5 squared and then after exponents we do multiplication and division so then it's going to / 4 that's going to be I do like 6 point something and then then it's going to multiply that whole thing by 5 and then it's going to subtract 10 from that whole thing that's not what we want to do right we how to do 5 squared on top / denominator put parentheses around your denominator when we do 4 * 5 - 10 it does that first it does it all together and then it will divide the 25 by whatever you get inside the front seat so you should have got 2.5 ATC how different those are 21.25 or 2.5 with and without parentheses in parentheses are really important so fraction and negative numbers make sure use Prince Beast okay now we're going to do both at the same time we're going to do a negative Ana fraction they so try and type that one in for this one I would put parentheses around your numerator and a denominator they don't just do the top and don't just do the bottom hey does anybody need another second hey let's see how she written this town's going to 8 so number so I'm a put parentheses around my negative number squared 34 + 10 eight and then close your prep because that's your whole numerator / the bottom which was x - 8 we had -6 -8 you should have got -11 anybody not get that do we have any questions okay so can see is around numerator and denominator and around not fraction negative numbers okay so if you got any of those wrong I'd maybe practice doing practice typing stuff in another thing is as you're going through your test practice using your calculator does it again you only have one minute for question right cuz they're 60 questions you have 60 minutes that's one a question so I'm you don't want to spend a whole bunch of time trying to figure out how to use your calculator you want to only use it if it's going to speed up your process okay so if you're familiar with it then it won't slow you down okay any questions about the calculator at all on the ACT okay so my biggest advice there again is just practice with it work on it do stuff with it so if you were here last time we started doing some practice problems we went through some basic problems and some word problems and now we're going to go through some challenging problem okay so since these are a little bit higher I'm going to tie me one minute still tell you when one minute is up but if we need a little bit longer then we can keep going okay so I'm going to start the timer try and figure this out he's got one minutes hey that's time does anybody need a little longer it would you guys get G dead can someone explain to me why they picked you good so is always less than negative ones that means it's always going to be a negative number K when we do a negative number raised to an odd power it keeps the negative if you do the negative number to an even power that's going to go away Rex if you do negative times negative that's a positive so every time you do it twice that'll make a positive hey so we already know a squared is always going to be bigger than a cube cuz it's going to positive were a cube is going to be making a hay and then we know they're not always going to be equal to each other or ever really we know that they won't be equal to each other even if we add a negative on the 8th cuz they just has to be less than negative one so it could be -5 the cube is going to be bigger than the squared hey I'm fraction that's going to make it even smaller okay any questions on that one case of a lot of times there's problems that are similar to this where you just kind of have to like reason and figure out and think about your rules that you know and try and figure that out okay timer hey here's the next one if 4/5 to the 8th power equals the square root of 5/4 cubed + n equals what a nap time who needs a little bit longer to finish you another minute just finished shopping but just keep in mind the reticle you want to spend only one minute on each problem all right what letter did you guys get a good case and I want to talk about this one cuz there's a couple different ways to solve this so okay let's see so we have your baby so we had 4/5 to the m power equals the square root 5/4 Q hey so who can tell me how they stopped it okay so that's a good use of the you later okay so she typed it into her calculator and then found out where they intersect and that's where they're equal to a so if you have totally no idea how to solve this but you can graph on your calculator do it okay they're going to be equal to wherever they cross over each other hey what's another way we could solve this you could yes so one way to do this do this for us this is really to the three half right cuz that's where route at the end okay so one way to get things out of the exponent is to take the log or the natural log doesn't matter which one and then you can pull the exponent down front so you've got an actual log of 4/5 equals pull this one down front 3/2 natural log of 54 / natural log of 4/5 that's going to be equal to end and you can type that into your calculator and I'll give you - 3/2 K anybody saw it a different way there is a much quicker way that last people don't think up yeah Chris there's another one plug in your answers K member that was one of our strategies if you have a bunch of answers plug them in see if they're equal to each other day that works as well K anybody else okay I'm going to show you the last way really quick so we've got for fifth wheel T I'm going to rewrite this for physics the n and 5/4 to the 3 half day what do you know 4/5 + 5/4 therein versus right so remember what do negative exponents do it flips it so if we said this 5/4 of 3/2 is the exact same as 4/5 to the - 3/2 then we thought for fifth race Leanne equals 4/5 raised to the -3 house that means and how 2 equal -3/2 okay so that's another thing to keep in your pocket negative exponent K but you see how many different ways we have to solve that kid graphene plug in your answers now. or do the reciprocal with a negative exponent he's so there's not just one way to solve all these problems there's lots of waste hey any questions on this one all right let's go to the next one let's see hey a bag of pennies could be divided among 6 children or seven children or eight children with each getting the same number with only one penny left over what is the smallest number of pennies that could be in the back is that means you can divide up the and they can divide into six seven or eight and all of them only have one left over hey that's time if you haven't gotten it or you have totally no idea how to do it I hope you took a guess right cuz if you don't know how to do take a guess move on and come back to it okay to get the answer yeah they is correct I think it's actually in doubt I have your attention I just got off the phone with the boss so I can see what you all happened Friday he is hiding concerned about a storm moving in school he would encourage each of you to quickly get your way your vehicle hey so to do this one you're just going to plug numbers in hey if you're leaving these tax paper over here at practice test there's four of them with answer keys in the back so grab one on your way out so you're just going to plug numbers in case you're leaving let's try and be quiet so we can still here queso we want a number that can be divided into six seven and eight equally right cuz we have to be able to divide it up so we know we're going to have one extra cake I split stop talking so we can all hear it we know we're going to have one extra so we're going to be checking instead of 22 we're going to check 21 cuz we want one extra queso 21 when does 21 go into the six going to tell can you divide 6 evenly in 21 know that means that One automatically knows not going to work she can't divide it between 6 people getting out within the next number we stopped 43 so am I the one down to 42 can you divide 6 into 42 yes can you divide 7 into 42 yes can divide 8 into 42 no so it's not that one we're going to go to H1 down is 56 can you divide 6 into B6 know so we go the next one 168 can you divide 6 into 168 yes 87 yes you divide 8 yes I'm so that's one we wanted to plug things in okay here is the next problem starting at her doorstep Ramona walk down the sidewalk at 1.5 ft per second for 4 seconds I seen that she had forgotten something but she turned she returned to her doorstep along the same route at 1.5 ft per second still I am at the graph of Ramona's distance from her doorstep as a function of time would be would most resemble which the following accuracy those are kind of hard to see hey what letter is it is not gjk still think about it if you're walking you walked for 4 seconds if she walk for 4 seconds and then immediately was like turned around which I guess some people probably do but most people would want for 4 seconds and then you turn around okay so that's kind of a tricky one but she stops for a quick second and then turns around hey we okay on that one k next so that both Quick Car Rental and Speedy Car Rental the cost in dollars of renting a full size car depends on a fixed daily rental rate fixed charge per mile. The car is driven however the daily rental fee and the charge per mile are the same for the two companies in the graph line Q represents the total cost for Quick Car Rental and asked represents the total cost for Speedy Car rent if you rent a full size car from Kwik car rental for one day how much more would the total rental cost be if you drove the car 78 miles then if you drove it out sorry I skipped the problem get the exact same situation but Robert plans to rent a full size car for one day and drive only 50 miles is his only consideration is to incur the least cost which company should he choose hey what letter is it yes the ACT usually I don't know why but they did a b c d e f g h fgteev Maybe yeah maybe that's why yes cuz I wasn't saying online I think it's only a b c d e f you don't have to worry about the weird but okay so it's ask Kay so we go over he drives 50 miles but everyone knows Q Quick Car Rental hey does anyone have questions on the Hun. Too bad some of these aren't really bad it's more just there a little bit long that kind of took up some of our minute right especially getting to the end of the test you're tired and you have to read the question five times cuz you know when you read it and you don't even you don't really read it okay so that's going to take your time but the question isn't actually that bad okay look at this next one so it's the exact same situation except my pictures covering the answer where to go if you rent a full size car from Kwik car rental for one day how much more would the total rental cost be if you drove the car 78 miles then if you drove at 77 miles K-pop time is anybody getting cancer Trevor it is D that you said the right how'd you get the -15 / 0 so that means so okay so I'm just going to write that out for some of us who maybe didn't do that all in her head right okay so we're trying to find the slope cuz if we're going from 77 to 78 that's only going up one step so if we know the slope we know how much we Adorn one step right cuz the slope is how far you go for every one x value peso to find the slope we need two points you guys remember the equation for slope yeah why cuz rise over run do you subtract the wise then subtract the ex's can divide them that's your slope rise over run case we're going to pick any two points so use points on this one is too big the beginning point which is 0 15 right and then the endpoint which is going to be 155 ghettos are probably the easiest points to see right I'm assuming some of them are like that yep yeah that's I just got your best guess I got these questions from another teacher but I think she got them from old ACT test okay so we have zero 15 and 155 so not always if it ever cross is over a line like that's an easy point right but if you can't figure it out it's probably best just take your guess on the in it's all we've got 0 15 + 100 55 so we do our y values it doesn't matter which one you do first as long as you do the same one first both times some new 55 - 15 / 100 - 0 40 / 100 which is point for that means every mile is $0.40 any questions on that one hey I would say that's probably one of the trick Year One just because it's kind of hard to tell where the graph is and stuff like that Berkeley have a great day hey what would be the total cost of renting a full size car from Speedy Car Rental for one day and driving 150 miles you guys really didn't grab practice test on your way out there's four of them over here okay I forgot to set the timer to this everyone done when you guys get a good kso4 want to get a with 150 Mi but we only go up to 100 right but we've got the slow so a couple things we already found the slope so really you could write the equation of the line but you don't really need you cuz we're all we're going up to a hundred 50 Cent we see how far we got from 0 to 50 that was right at 50 we're up at 35 sorry I'm sorry I was looking at the wrong one we are looking at Speedy so that's the S line so correct cake recipe getting restarted at 2:30 that means to drive 50 miles and cost $15 sorry $10 k52 cost $10 so 100 miles was $50 so 10 more dollars would be 60 that makes sense. Okay with that k okay so those are some examples of challenge problems so there's one other thing when other resource I want to show you guys if you go and you just Google act math questions I don't know if you guys what did this before but if you go to the ACT website they've got practice questions it's not loading but there's a full set there's one full practice test on he still likes that one is I think it's 12 questions and then there's five sets so there's a total of 60 Questions so here's just another practice test I know I keep giving you guys practice test but really just need to keep practicing and get your time done okay I probably took so many practice tests and that's just the best way to do it okay so here's another one if you maybe want to practice doing one online this will be good for that to the only thing is it. have the calculator but you can just plug does or use your calculator hey so that's another thing you also I mean there's a whole bunch of websites that come up I would stick to the Act One first but you can always go look at other ones and see if you can find practice test if you want more just Google them okay and then that's all I have planned for today if anybody would like to practice keyboard problems with can and but if you want to head out I've got a stack of practice test over here at stop for tests on it queso and it has the answer keys in the very back so when you're doing that again time yourself 60 min I'm trying to see how far you can get I don't know he they just they just said that so that they're at that was their excuse for letting teachers leave early there's no store they do that on Friday sometimes they'll come on be like oh we're going to fumigate the building you all better leave they just say that sometimes so that teachers can leave early yes wet saree Trevor Trevor into existence

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ACT Prep Math 2/18/2022

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