Accuplacer Math Crash Course Overview

what is up everybody this is Mr Tui Crea of the acup Placer math crash course series and I'm so excited to announce that acup Placer math crash course has been updated to include even more questions from the quantitative reasoning algebra and statistics section of the test in this video I'm going to teach you the easiest and fastest way to solve a variety of questions from the quantitative reasoning algebra and statistics section of the test using my unique and Powerful test taking strategies that simplify the questions these are some of the most recently released questions from the qas section that I found online and I'm happy to share them with you today oh and by the way if you like this video you're definitely going to want to get access to the full version of the course just click the link in the description below to access the full version in the meantime sit back relax and enjoy these questions from the quantitative reasoning algebra and statistics section of the accuplacer all right welcome everybody to accuplacer math crash course this is day five uh this is the day five update we are on the quantitative algebra uh wait quantitative reasoning algebra and statistics section of uh of the test and I've got some some questions that I found online some new qas quantitative reasoning algebra and statistics questions um that are popped up and uh and I kind of want to go over those questions a lot of it's going to be familiar but there's a couple new things that are on here as well and I just want to uh provide you with the latest questions and and the latest Concepts that are being tested on the accuplacer so that's why we're going over this today we've got a student with us today this is mato say hi to everybody please M hello all right thanks Mato appreciate it all right and we got a question up on the screen let's just jump right into questions and we'll solve these together go and read question number one for us please all right which of the foll one is equivalent to -14 - 8 * 0.5 plus 0.75 yeah yeah yeah yeah and there's there's a word in here in this question this word equivalent what does the word equivalent mean uh the same two or equal the same or equal absolutely yes we had to find the answer is that's equivalent or equal to that big mess right there now um this is this is a tough question especially because I I think here on this question they're not going to give you access to the online calculator in fact I just checked before uh recording the session with Mato um you don't have access to a calculator so you got be able to do the arithmetic here on this one but really what they're test you on more than anything else I think on this question is pemos pemos of operations yeah so even though like some stud I look at this question like a come on I got this like you know this is just arithmetic but like P pendos order of operations appears on so many questions you have to be able to simplify expressions the right way so I think this is a really important question to go over and start with right now so let's review pemos quickly before uh we try to solve this one together you've got uh access to my rules for accuplacer math go and open that up and it's toward the end of the document this is like on page seven of the document there we go I'm going to zoom in just a little bit and let's just review pendos this is this is important okay so uh pen order operations when simplifying expressions simplify in the order below go and read that first bullet point for us please on parentheses so yeah so the first one is going to be parentheses it's going to be calculate what is the side the parenthesis first before doing anything else okay great and now if you don't have any parentheses in the question you don't have to worry about that but if you got them you got to start there go and read the next part please so exponents calculate anything raised to a power for example negative 9 raised to the power of two yeah yeah yeah so if you see any of those little Powers right that's going to be sort of the number above another number then uh you have the EXP and sometimes you'll see exponents out side parentheses but still kind of do it in the order of parentheses first and then do the exponents go and read the next uh bullet points please next one is going to be uh multiplication which you know what that is yeah yes sir uh we got Division division okay and then lastly addition and subtraction yeah addition and subtraction you can really kind of lump those together it's funny we're going to talk about when we when we uh address this question some students are like wait I saw you do a subtraction first in a question it's like addition subtraction are roughly the same operation right because if you're if you're subtracting you're really adding a negative number so really for the last two steps it doesn't really matter sort of like which which one you end up doing first as long as addition and subtraction are last but if you just want to do it in the addition first then subtraction that's fine but be aware you know either either one doesn't really matter let's go back to the question here so notice we obviously have some addition going on with that plus. 75 we got some subtraction going on with4 and the ne8 and we got some multiplication here as well what step are we doing first here if we're doing pemos Mato uh multiplication we're doing the multiplication absolutely now this is a little bit trickier because we could ask I mean this a legitimate question say okay well what are we multiplying here what are we multiplying 8 times uh 0.5 that's probably what I would do yeah eight times 05 that's what I would do some students might looking at that be like well don't have to do8 * 005 which by the way you could do as well you could do as well um as long as once you calculated like8 * 05 then you just added that to the -14 does that make sense why you could multiply ne8 * 05 as well yes sir yeah but I think it's much it's just easier to understand if we just multiply these guys here eight times 05 and then we'll subtract whatever that product is from 14 does that make some sense sir that's just easier for me to wrap my head around okay so let's talk about that I mean like we could do the operation I think we might we might do it here just a moment because again we don't have a calculator so you got to be able to calculate it you might logically be able to tell me what 8 time 05 is do you know what that would be logically or no yeah so if 05 is multiplied by two I mean by four is going to be two yeah yeah yeah and here's it's just eight times 05 what's that going to be going to be four it's going to be four yeah point or 0.5 is the same as 1/2 is that clear I mean it's really helpful to understand that just like 0.25 would be 1/4 one quarter you know if you can recognize that you're like oh I'm just finding half of eight and like anybody can figure out what half of eight is just logically right it's just four now if we need to do the op the operation we we could and in fact I do want to go over that because you might see on the test you might see some other other um decimals that are a little more complicated do you know how to multip apply 8 * 05 like how to carry out that operation this is like Elementary School math but sometimes you got to do it on the test could you do that on the white yeah let me see do on the white let's go over it together I just want to verify it looking good yeah so you get 40 and then notice like some students might think that's 40 right if they're count that that multiplication right because 5 time 8 is 40 but you got to pay close attention when you're multiplying by you know something that has numbers to the right of the decimal you got to ask okay how many digits are to the right of the decimal so it's going to be one one yeah so you've got if you got one digit to right decimal you got to shift the decimal from uh basically over one space here over one unit over one digit and that would give us 4.0 or just four does that make some sense all right great so we could rewrite this expression and we should now that we've got the multiplication but there's nothing really to calculate in the parenthesis uh there's no exponents here we could go right to the multiplication which we did I would rewrite the expression like this I'd be like ne14 minus 4 plus 0.75 does that make sense Mato sure okay good good now what would we do next if we're we can we can subract the the four from A4 yeah I'd probably do that i' like just go like once you've got all addition subtraction I just like going from left to right if you wanted to follow pemos strictly you might be like well I got to do the addition first which you could do you could do4 plus 75 and then that's going to give you a negative number and then subtract that from from -14 um I'd probably just go left to right here so yeah let's do let's do4 minus 4 what would that be do you have any idea Mato yeah it's going to be10 Ah that's not -10 interestingly Oo we got to talk about this we got to talk about this right now think about this hold on hold on let's step back and think about what this means so we've got4 imagine that you've got ne14 in your bank account Mato Nega you know like you know that's hopefully you have a little bit more than that in your bank bank account like it happens right we've all been there right good evens I've been there all right ne4 in your bank account and then like and then you take away four more dollars H right or you somehow like you know withdraw draw $ four more dollars you depending on your bank's policy that that may may not be possible but you lose $ four more dollars what are you going to have in your bank account you starting with negative4 and you lose four more dollars you take away four more what are you GNA have okay got what are you have your negative 18 absolutely that right and like this is really how I recommend thinking about think about in concrete terms as much as you can or you could talk about like temperatures like imagine it's like -14 degrees you know below zero outside okay that's cold all right I grew up in Michigan by the way like it does get that cold up there but let's say it's 14° you know and then the temperature drops four more degrees you take away four more degrees okay gotta right like it's dropping even it's going to be even more negative does that make sense Mato yes sir yeah now14 + 4 would be -10 but that would be increasing it does that make sense here why it's going to be like even more negative than4 does that make sense yeah yeah cuz Trucking for yeah yeah like negative 100 is really really negative some looking at that and they're like well that's a 100 is a bigger number which true 100 is a bigger number than like you know 14 or 18 but like you know the the the the bigger the negative number incredibly right like the the more negative the smaller it is like negative a million is very very small and here we're getting smaller than4 so it's G to be8 does that make sense sure okay okay good so we've got negative 18 and then we still have that plus 75 or 0.75 same thing what do we do now uh we just add you just add those yeah some students might be able to do that logically you might want to actually like carry out the operation do you think you can do this logically here or or um or do you want to carry out the operation what are your thoughts uh we can do it logically yeah I would do especially when you kind of look at the answer choices here right so we've got we've let me make that real clear that that's a zero I'm going to fix that zero there okay so we've got8 and then we're adding something a little bit less than one do you see that so make we're g to make it a little more positive a little bit you know but like if we're adding one what's ne8 plus one be 17 negative 17 righta 18 plus 1 isga 177 yeah y it's negative still yeah yeah so what do you think the right answer is here if you're just guessing or we're making a I would say it's going to be C it's probably c yeah it's going to be C for sure because it's going to be just a little bit more positive than negative 18 that would be C so your best bet is to solve it logically basically initially right and realize it's going to be negative 17.25 that's that's the best way to do it there and that's kind of like one of the themes all the way throughout my courses right is that like sometimes like trying to approach questions from an operational perspective there's a lot of traps there it's easy to get get it mixed up think about what things mean focus on what things mean and let that guide you does that make some sense Mato yes sir okay great all right let's go to the next question go and read question number two what do you see that on the screen please faan receive a $100 gift card to a clothing uh to a clothing store using only the gift card he was able to purchase and sweaters that cost 32 each and one bill for 20 if there was no tax on the sweater and build which of the following must be true okay what did we I actually I actually saw a similar question okay okay yeah yeah yeah on the on the recent test you took this is dude this is tough because like if you're trying to create sort of the expression like trying to create the inequality even if you set it up correctly like there's no guarantee what you create is going to match the answer choices here this is super tough if you're trying to create the inequality okay I'm I'll be honest like I'm not even certain exactly how to do probably figure it out but like there's an easier way to do this and that's why plug it in values right Val yeah we can create a value for n and what does n represent here in this question what does n mean sweaters it's the number of sweaters right because it says he was able to purchase n sweaters and if we create a value for n right that leaves it's meets the requirements of the question we can just plug that into the answer choices and see which one or which ones are true does that make sense some sense yes sir okay okay now so he's got a $100 gift card because we got to pick the we can't just pick any value for we're limited sort of by the scenario in the question he's got a $100 gift card each sweater cost 32 bucks and he purchased some unknown number of sweaters and he purchased a a belt for 20 bucks okay so I think I think we can figure out how many sweaters he could potentially buy here do you have any idea how many sweaters you could buy here if he's got a $100 gift card sweaters cost 32 bucks he buys some number of those and he buys a belt for 20 bucks how many sweaters can you buy I say I'll say three well let's try let's test it let's test it okay let's say n equals 3 how much would three sweaters cost so it's going to be 32 and you can use your calculator here this this you'd have access to a calculator in this question oh 96 yeah yeah lot so yeah so that's 96 bucks but then he's got to buy the belt also do you see that right and then the belt's going to be 20 bucks would you have enough money to buy three sweaters in one belt no no way no way and this is where I'm you I'm glad we're going over this right because like plug in valleys is my favorite strategy of all time for this test there's no question about it but um but you can't just plug anything in always right like sometimes they give you limits to what works you can't do three or higher here you can't can we try another number Matel give me another number that's a two let's just try two okay and let's test it to make sure it works first so if he buys two sweaters how much is that going to cost you can use your calculator it's just 2 * 32 that's going to be 64 64 bucks for the two sweaters and then the belt is 20 bucks right is that going to be is he have money to buy two sweaters and one belt yeah I think so CU how much would that be two sweaters and one belt 84 84 bucks yeah so that would work does that make sense why n could be two yeah yes sir I think uh one could work as well here it could oh yeah yeah it could work uh but two or one would be fine you know all right so let's let's just roll with two because we know that meets the requirements of the question so if we plug in a two for n into the expressions in the question the right answer has to give us a true statement so let's plug into answer Choice a can I see you plug in a two into answer Choice a on the Whiteboard can I see you do that yes sir all right okay good um let's let's let's talk about what the statement means here do you know what 80 divided two is yeah it's GNA be 40 it's gonna be 40 right so we could rewrite this expression as 40 is greater than or equal to 32 got to interpret that sign the right way is that clear by the way the sign is greater than or equal to Sir okay great so Mato is 40 greater than or equal to 32 it sure is it sure is let let's keep answer Choice a right now I wouldn't stop here we got to test the other answer choices right because it's very possible that uh that multiple answer choices could give you a true statement if you're plugging in values right you know this you know working your way through the course so let's test answer Choice b as well but we'll keep answer Choice a for right now let's plug into the answer Choice B let me see you do it looking good what's 32 divided by two it's going to be 16 yeah so 16 is greater than or equal to 80 yeah so true statement or no GNA be false statement definitely not true so it's not answer Choice gone absolutely let's try answer Choice C and right now you might even be able to look at that oh yeah is that give us a true statement no no it's gonna give us 40 right 40 is uh less than or equal to 32 so that's not right either is that is that clear yeah that's what about answer Choice uh D actually let's plug in answer Choice D here that's a little bit more complicated so let me see plug into D let's see what happens all right looking good looking good now here I I think in terms of pem do once again right before we do this addition or subtraction what do we have to do here multiply we got multiply absolutely yeah so 32 * yeah go ahead you got it you got it two 64 yeah yeah you've got to calculate on this question so I mean as long as you're you're following pemos and you got your order of operations you should be good so that's going to be 36 yeah great so it's 36 less than or equal to 20 all work so it's got to be answer a which it is does that make some sense Mato yes sir okay now you said you saw a question like this on the test did you plug in values I did it was actually it was actually percentage to oh interesting okay yeah that could be tough that could be tough but did it work out do you think you got it yeah I think did great great yeah but it's still by far the most useful strategy on this test put value very few questions where you have to carry out a specific algebraic operation very few but uh certainly works here any questions before we move on no sir okay great escape roll looks like another plugin and values question here go and read question number three for us please expression is equivalent to or n three power two plus n yeah yeah that's a messy that's a messy looking expression there Mato um so what do we solving for uh which uh which expression is uh equal or the same yeah there's that word equivalent again you got to know that here for this test which expression is equivalent to that big mess all right is it clear that we can just plug in values for n here for this question is that obvious yeah all right so uh so the strategy here right we're going to create a value for n we're going to plug into this expression here we'll find out what that equals for some value of N and then we'll plug that same value into the answer choices and we'll see what matches make sense all right sir okay okay what value do you want to plug in for n we've got some here we can do one let's start with one yeah one works great I love ones ones and zeros are wonderful so let's make n equal one okay now plug that into the expression here in the question let's see what it equals let me see you work that out on the Whiteboard Mato looking good looking good all right so 1 minus three or let's do it first yeah that's right yeah yeah I mean you could um you know it's like you know you think about like some students might wonder like should we to do parenthesis first and it's like yeah well to calculate what's in the parenthesis you have to do the exponents right does that make sense yeah yeah yeah yeah so strangely because we're C we're calculating what's in the parentheses first we have to do the exponents first it's a little bit tricky but you navigated that beautifully yeah so what do that can equal so 9 minus one is going to be eight well hold on just a minute it's not 9 minus one it's not 9us one Sor yeah yeah yeah so we're going to start with the exponent absolutely okay so what's 3 squared let's talk about that it's going to be n that's going to be nine so we could rewrite this expression as 1 - 9 in parentheses do you see that Mato sure yeah and what's one minus 9 eight what did you say it is eight it's not eight one - 9 is not eight right right oh yeah hold think think about it hold on let's go back to what we're were talking about on that first question you got $1 in your bank account and I take away nine bucks how much money do you have in your bank account uh yeah it's going to be a negative eight negative eight does that make sense or if it's one degree outside one degree above zero and then it drops N9 degrees it's going to be8 degrees yes sir you sometimes with negatives I think the best way to do is just think in concrete terms Okay so all right so we've got 4 * 8 + 1 uh let's keep doing pendos here what's next so four times8 it's going to be -32 32 all right let me see continue to work this out here two plus one okay all right and then what's ne32 + 1 -3 exactly does that mean makes sense why we're kind of it's becoming just a little bit more positive yes sir it's not going to be33 that would be -32 minus 1 would be yeah yeah but -32 plus 1 is -31 okay great so we know the right answerers got to give us -31 which answer Choice gives us - 31 well let's plug in I'm going to clear some space here let's plug into answer Choice a and we'll see if that gives us -31 going find a clear spot on the Whiteboard and plug that in is that a one sorry you're you're good you're good good I just want sure okay I got you all right so three * one three that is going to be uh neg3 yeah so is that 31 no that is that a dumb question right yeah that's not his choice hey I'm going to fix this netive 31 I just want to make really clear that that is is a Nega 31 right there hold on there we go okay good um just in case there's any confusion plug into an Choice B I'll clear some space on the Whiteboard all right plug into B three so yeah true no good right yeah not true we're looking for 31 so B is gone c space let's plug into answer Choice uh C you're doing great Matta o five times 30 that is going to be 31 yeah yeah and like let's talk about how this work right because when we're going to that first arithmetic question right I kind of told that trick like you can just take 30 you you can take the bigger number subtract the smaller number and just make it negative right like that's probably the best way to do it right I mean first of all is it clear that 5 minus 36 is going to be negative is that clear yes sir yeah so if you need to car that operation you could just do 36 5 which I think pretty much anybody can do is it clear that's going to be 31 yeah so it's going to you make it negative just make it negative that's the best way to handle that because you're trying to set up that op like you know doing the operation of that is just not obvious so they do it logically or just think about that little trick subtract the smaller number from the bigger number make it negative but that's looking good okay let's test answer Choice D we'll keep C I'll clear some space I mean you just look at that is that going to work is that going to give us NE 30 no be super going be like negative hund something or 30 something yeah yeah no not happening so it's got to be C which it is W any questions about that sir I think a zero would work great here as well it would let's just talk about that real quick yeah like if n is zero you might even be able to do this mentally if n is zero what is this expression here in the question equal so uh well it would be 0 minus 9 right so it would be four time what's 0 - 9 by the way 9 it's going to be uh just nine 0 minus 9 is not nine oh negative n negative 9 0 + 9 is 9 but 0 minus 9 does that make sense yes sir negative 9 yeah and then Plus but that's that's just going to be 4 * 9 does that make some sense sure so what's 4 * 9 that be uh 36 36 so the right answer is got to give USG 36 when n is zero does that make some sense sir yeah does answer C give us 36 when n is zero yeah yeah yeah 5 * 0 is 0 then - 36 is 36 what any of the other answer choices give us 36 oh no way no way okay M like your op your operations are very very good you've got a good handle on these questions you approach them the right way I think the only thing you need to be really conscious of and really careful of right as you're taking this test you're taking it this afternoon uh is those negatives is those NE you see that now and you see how you have to think about it now and if there's any confusion as best you can like think about it in concrete terms think about it like in terms of money in a bank account or temperatures and kind of let that logical understanding guide you does that make sense yes sir you'll be all right like that's the only thing I'm seeing so far um you know that's tripping up so pay close attention to those negatives all right Mato go ahead and read question number four for us please so AO bought some pens for $2 each and some pencils for $1 each she bought three more pens that pen and pencils and spent a total of 12 how how many pencils did uh he will buy okay mat what are we solving for here with this question how many pencils did she buy yeah how many pencils she bought yeah and they give us four possible answer choices right four possible numbers of pencils that that she bought are two or three or four or five okay does this question make some sense at least what we're solving for here yes sir okay okay now um this is a system of equations question and I think a lot of students you certainly those that haven't watched my videos or taking my course are going to try to set up a system of equations here which you can do it's just kind of complicated are you familiar with systems of equations do you know how to set those up or not so much that's much yeah yeah don't don't worry about I mean like you know some students watching this might be familiar with it there's like two unknown here's some unknown number of pencils and some unknown number of pens and there's two equations you can create and then you can do a specific algebraic operation to solve for those missing variables and that's fine but again like as we've seen many times right the more steps you're doing the likelier it is you're going to make a silly mistake so we want to simplify this much we can and we can we can test these answer choices okay we can test these answer choices without doing any algebra okay so like for example look at answer Choice a answer Choice a says uh two right so the question is how many pencils did she buy anoid say saying okay maybe she bought two pencils okay two pencils so all the anoid really represent some possible number of pencils I'm going to make a note of that these are the pencils and if answer Choice a is correct if she bought two pencils you know exactly how many pens she bought how many pens did she buy if she bought two pencils how many pens so she bought three more so it's gonna be five it's gonna be five does that make sense yeah does that make sense mat yes sir yeah because it says she bought three more pens and pencils just logically be like oh she bought two pencils and she bought five pens now we can calculate really easily how much two pencils and five pens would cost really easily uh because it says the pens were $2 each and the pencils were a dollar each so let's let's start with the pencils how much would the pencils cost so two is going to be $2 $2 for the two pencils does that make sense sure and then how much for the pens so five time two is going to be 10 5 * 2 is 10 and What's the total uh $12 $12 so what do you think about an Choice a yeah I'll keep it let's keep it that could work absolutely I mean in fact it should work right I mean like I I doubt they're going to give us multiple answer choices here that would that would work here we're not really plugging Val we're just testing the answer choices here I would still be careful and let let's make sure we're on the right track and test the others but a is looking really really good but let's let's let's practice the process again of testing these answer choices so look at answer chice B so that's suggesting she bought three pencils if she bought three pencils how many pens did she buy so six that' be six pens yeah because you're about three more pens pencils how much would three pencils cost uh $3 $3 just testing this and then how much would six P cost uh 12 uh yeah hold on uh yeah 12 so what would the total be it's going to be 15 GNA be 15 so what do you think my answer is is B no no way yeah the question said she spent a total 12 bucks does that make sense yes sir yeah I mean we could test C and D if we wanted to do you think we need to or no oh because the higher the number the higher the more yeah we're good man we're good I I would still probably double check make sure we're on the right track cuz sometimes like if you make an arithmetic error somewhere you know like and then you test B and you're like oh wait that works too or somehow that gave you 12 you'd be like okay maybe I approached it the wrong way somewhere I did a uh you know addition or subtraction error something like that some arithmetic so it's not a bad idea but I feel pretty confident here about stopping and pick this Choice a and it is a any questions about that Mato no sir if you look at it so again like finding the right answer like calculating the number of pencils here is tricky it is even if you're familiar with systems of equations it's just tricky and there's a lot of steps if you see a question like this you're like man I don't know how to calculate that ask yourself this question can I just test these answers and 95% of the time maybe more than maybe 100% of the time that's an easier path than trying to calculate it look for ways to test answer choices for

what is up everybody this is Mr Tui Crea of the acup Placer math crash course series and I&#39;m so excited to announce that acup Placer math crash course has been updated to include even more questions from the quantitative reasoning algebra and statistics section of the test in this video I&#39;m going to teach you the easiest and fastest way to solve a variety of questions from the quantitative reasoning algebra and statistics section of the test using my unique and Powerful test taking strategies that simplify the questions these are some of the most recently released questions from the qas section that I found online and I&#39;m happy to share them with you today oh and by the way if you like this video you&#39;re definitely going to want to get access to the full version of the course just click the link in the description below to access the full version in the meantime sit back relax and enjoy these questions from the quantitative reasoning algebra and statistics section of the accuplacer all right welcome everybody to accuplacer math crash course this is day five uh this is the day five update we are on the quantitative algebra uh wait quantitative reasoning algebra and statistics section of uh of the test and I&#39;ve got some some questions that I found online some new qas quantitative reasoning algebra and statistics questions um that are popped up and uh and I kind of want to go over those questions a lot of it&#39;s going to be familiar but there&#39;s a couple new things that are on here as well and I just want to uh provide you with the latest questions and and the latest Concepts that are being tested on the accuplacer so that&#39;s why we&#39;re going over this today we&#39;ve got a student with us today this is mato say hi to everybody please M hello all right thanks Mato appreciate it all right and we got a question up on the screen let&#39;s just jump right into questions and we&#39;ll solve these together go and read question number one for us please all right which of the foll one is equivalent to -14 - 8 * 0.5 plus 0.75 yeah yeah yeah yeah and there&#39;s there&#39;s a word in here in this question this word equivalent what does the word equivalent mean uh the same two or equal the same or equal absolutely yes we had to find the answer is that&#39;s equivalent or equal to that big mess right there now um this is this is a tough question especially because I I think here on this question they&#39;re not going to give you access to the online calculator in fact I just checked before uh recording the session with Mato um you don&#39;t have access to a calculator so you got be able to do the arithmetic here on this one but really what they&#39;re test you on more than anything else I think on this question is pemos pemos of operations yeah so even though like some stud I look at this question like a come on I got this like you know this is just arithmetic but like P pendos order of operations appears on so many questions you have to be able to simplify expressions the right way so I think this is a really important question to go over and start with right now so let&#39;s review pemos quickly before uh we try to solve this one together you&#39;ve got uh access to my rules for accuplacer math go and open that up and it&#39;s toward the end of the document this is like on page seven of the document there we go I&#39;m going to zoom in just a little bit and let&#39;s just review pendos this is this is important okay so uh pen order operations when simplifying expressions simplify in the order below go and read that first bullet point for us please on parentheses so yeah so the first one is going to be parentheses it&#39;s going to be calculate what is the side the parenthesis first before doing anything else okay great and now if you don&#39;t have any parentheses in the question you don&#39;t have to worry about that but if you got them you got to start there go and read the next part please so exponents calculate anything raised to a power for example negative 9 raised to the power of two yeah yeah yeah so if you see any of those little Powers right that&#39;s going to be sort of the number above another number then uh you have the EXP and sometimes you&#39;ll see exponents out side parentheses but still kind of do it in the order of parentheses first and then do the exponents go and read the next uh bullet points please next one is going to be uh multiplication which you know what that is yeah yes sir uh we got Division division okay and then lastly addition and subtraction yeah addition and subtraction you can really kind of lump those together it&#39;s funny we&#39;re going to talk about when we when we uh address this question some students are like wait I saw you do a subtraction first in a question it&#39;s like addition subtraction are roughly the same operation right because if you&#39;re if you&#39;re subtracting you&#39;re really adding a negative number so really for the last two steps it doesn&#39;t really matter sort of like which which one you end up doing first as long as addition and subtraction are last but if you just want to do it in the addition first then subtraction that&#39;s fine but be aware you know either either one doesn&#39;t really matter let&#39;s go back to the question here so notice we obviously have some addition going on with that plus. 75 we got some subtraction going on with4 and the ne8 and we got some multiplication here as well what step are we doing first here if we&#39;re doing pemos Mato uh multiplication we&#39;re doing the multiplication absolutely now this is a little bit trickier because we could ask I mean this a legitimate question say okay well what are we multiplying here what are we multiplying 8 times uh 0.5 that&#39;s probably what I would do yeah eight times 05 that&#39;s what I would do some students might looking at that be like well don&#39;t have to do8 * 005 which by the way you could do as well you could do as well um as long as once you calculated like8 * 05 then you just added that to the -14 does that make sense why you could multiply ne8 * 05 as well yes sir yeah but I think it&#39;s much it&#39;s just easier to understand if we just multiply these guys here eight times 05 and then we&#39;ll subtract whatever that product is from 14 does that make some sense sir that&#39;s just easier for me to wrap my head around okay so let&#39;s talk about that I mean like we could do the operation I think we might we might do it here just a moment because again we don&#39;t have a calculator so you got to be able to calculate it you might logically be able to tell me what 8 time 05 is do you know what that would be logically or no yeah so if 05 is multiplied by two I mean by four is going to be two yeah yeah yeah and here&#39;s it&#39;s just eight times 05 what&#39;s that going to be going to be four it&#39;s going to be four yeah point or 0.5 is the same as 1/2 is that clear I mean it&#39;s really helpful to understand that just like 0.25 would be 1/4 one quarter you know if you can recognize that you&#39;re like oh I&#39;m just finding half of eight and like anybody can figure out what half of eight is just logically right it&#39;s just four now if we need to do the op the operation we we could and in fact I do want to go over that because you might see on the test you might see some other other um decimals that are a little more complicated do you know how to multip apply 8 * 05 like how to carry out that operation this is like Elementary School math but sometimes you got to do it on the test could you do that on the white yeah let me see do on the white let&#39;s go over it together I just want to verify it looking good yeah so you get 40 and then notice like some students might think that&#39;s 40 right if they&#39;re count that that multiplication right because 5 time 8 is 40 but you got to pay close attention when you&#39;re multiplying by you know something that has numbers to the right of the decimal you got to ask okay how many digits are to the right of the decimal so it&#39;s going to be one one yeah so you&#39;ve got if you got one digit to right decimal you got to shift the decimal from uh basically over one space here over one unit over one digit and that would give us 4.0 or just four does that make some sense all right great so we could rewrite this expression and we should now that we&#39;ve got the multiplication but there&#39;s nothing really to calculate in the parenthesis uh there&#39;s no exponents here we could go right to the multiplication which we did I would rewrite the expression like this I&#39;d be like ne14 minus 4 plus 0.75 does that make sense Mato sure okay good good now what would we do next if we&#39;re we can we can subract the the four from A4 yeah I&#39;d probably do that i&#39; like just go like once you&#39;ve got all addition subtraction I just like going from left to right if you wanted to follow pemos strictly you might be like well I got to do the addition first which you could do you could do4 plus 75 and then that&#39;s going to give you a negative number and then subtract that from from -14 um I&#39;d probably just go left to right here so yeah let&#39;s do let&#39;s do4 minus 4 what would that be do you have any idea Mato yeah it&#39;s going to be10 Ah that&#39;s not -10 interestingly Oo we got to talk about this we got to talk about this right now think about this hold on hold on let&#39;s step back and think about what this means so we&#39;ve got4 imagine that you&#39;ve got ne14 in your bank account Mato Nega you know like you know that&#39;s hopefully you have a little bit more than that in your bank bank account like it happens right we&#39;ve all been there right good evens I&#39;ve been there all right ne4 in your bank account and then like and then you take away four more dollars H right or you somehow like you know withdraw draw $ four more dollars you depending on your bank&#39;s policy that that may may not be possible but you lose $ four more dollars what are you going to have in your bank account you starting with negative4 and you lose four more dollars you take away four more what are you GNA have okay got what are you have your negative 18 absolutely that right and like this is really how I recommend thinking about think about in concrete terms as much as you can or you could talk about like temperatures like imagine it&#39;s like -14 degrees you know below zero outside okay that&#39;s cold all right I grew up in Michigan by the way like it does get that cold up there but let&#39;s say it&#39;s 14° you know and then the temperature drops four more degrees you take away four more degrees okay gotta right like it&#39;s dropping even it&#39;s going to be even more negative does that make sense Mato yes sir yeah now14 + 4 would be -10 but that would be increasing it does that make sense here why it&#39;s going to be like even more negative than4 does that make sense yeah yeah cuz Trucking for yeah yeah like negative 100 is really really negative some looking at that and they&#39;re like well that&#39;s a 100 is a bigger number which true 100 is a bigger number than like you know 14 or 18 but like you know the the the the bigger the negative number incredibly right like the the more negative the smaller it is like negative a million is very very small and here we&#39;re getting smaller than4 so it&#39;s G to be8 does that make sense sure okay okay good so we&#39;ve got negative 18 and then we still have that plus 75 or 0.75 same thing what do we do now uh we just add you just add those yeah some students might be able to do that logically you might want to actually like carry out the operation do you think you can do this logically here or or um or do you want to carry out the operation what are your thoughts uh we can do it logically yeah I would do especially when you kind of look at the answer choices here right so we&#39;ve got we&#39;ve let me make that real clear that that&#39;s a zero I&#39;m going to fix that zero there okay so we&#39;ve got8 and then we&#39;re adding something a little bit less than one do you see that so make we&#39;re g to make it a little more positive a little bit you know but like if we&#39;re adding one what&#39;s ne8 plus one be 17 negative 17 righta 18 plus 1 isga 177 yeah y it&#39;s negative still yeah yeah so what do you think the right answer is here if you&#39;re just guessing or we&#39;re making a I would say it&#39;s going to be C it&#39;s probably c yeah it&#39;s going to be C for sure because it&#39;s going to be just a little bit more positive than negative 18 that would be C so your best bet is to solve it logically basically initially right and realize it&#39;s going to be negative 17.25 that&#39;s that&#39;s the best way to do it there and that&#39;s kind of like one of the themes all the way throughout my courses right is that like sometimes like trying to approach questions from an operational perspective there&#39;s a lot of traps there it&#39;s easy to get get it mixed up think about what things mean focus on what things mean and let that guide you does that make some sense Mato yes sir okay great all right let&#39;s go to the next question go and read question number two what do you see that on the screen please faan receive a $100 gift card to a clothing uh to a clothing store using only the gift card he was able to purchase and sweaters that cost 32 each and one bill for 20 if there was no tax on the sweater and build which of the following must be true okay what did we I actually I actually saw a similar question okay okay yeah yeah yeah on the on the recent test you took this is dude this is tough because like if you&#39;re trying to create sort of the expression like trying to create the inequality even if you set it up correctly like there&#39;s no guarantee what you create is going to match the answer choices here this is super tough if you&#39;re trying to create the inequality okay I&#39;m I&#39;ll be honest like I&#39;m not even certain exactly how to do probably figure it out but like there&#39;s an easier way to do this and that&#39;s why plug it in values right Val yeah we can create a value for n and what does n represent here in this question what does n mean sweaters it&#39;s the number of sweaters right because it says he was able to purchase n sweaters and if we create a value for n right that leaves it&#39;s meets the requirements of the question we can just plug that into the answer choices and see which one or which ones are true does that make sense some sense yes sir okay okay now so he&#39;s got a $100 gift card because we got to pick the we can&#39;t just pick any value for we&#39;re limited sort of by the scenario in the question he&#39;s got a $100 gift card each sweater cost 32 bucks and he purchased some unknown number of sweaters and he purchased a a belt for 20 bucks okay so I think I think we can figure out how many sweaters he could potentially buy here do you have any idea how many sweaters you could buy here if he&#39;s got a $100 gift card sweaters cost 32 bucks he buys some number of those and he buys a belt for 20 bucks how many sweaters can you buy I say I&#39;ll say three well let&#39;s try let&#39;s test it let&#39;s test it okay let&#39;s say n equals 3 how much would three sweaters cost so it&#39;s going to be 32 and you can use your calculator here this this you&#39;d have access to a calculator in this question oh 96 yeah yeah lot so yeah so that&#39;s 96 bucks but then he&#39;s got to buy the belt also do you see that right and then the belt&#39;s going to be 20 bucks would you have enough money to buy three sweaters in one belt no no way no way and this is where I&#39;m you I&#39;m glad we&#39;re going over this right because like plug in valleys is my favorite strategy of all time for this test there&#39;s no question about it but um but you can&#39;t just plug anything in always right like sometimes they give you limits to what works you can&#39;t do three or higher here you can&#39;t can we try another number Matel give me another number that&#39;s a two let&#39;s just try two okay and let&#39;s test it to make sure it works first so if he buys two sweaters how much is that going to cost you can use your calculator it&#39;s just 2 * 32 that&#39;s going to be 64 64 bucks for the two sweaters and then the belt is 20 bucks right is that going to be is he have money to buy two sweaters and one belt yeah I think so CU how much would that be two sweaters and one belt 84 84 bucks yeah so that would work does that make sense why n could be two yeah yes sir I think uh one could work as well here it could oh yeah yeah it could work uh but two or one would be fine you know all right so let&#39;s let&#39;s just roll with two because we know that meets the requirements of the question so if we plug in a two for n into the expressions in the question the right answer has to give us a true statement so let&#39;s plug into answer Choice a can I see you plug in a two into answer Choice a on the Whiteboard can I see you do that yes sir all right okay good um let&#39;s let&#39;s let&#39;s talk about what the statement means here do you know what 80 divided two is yeah it&#39;s GNA be 40 it&#39;s gonna be 40 right so we could rewrite this expression as 40 is greater than or equal to 32 got to interpret that sign the right way is that clear by the way the sign is greater than or equal to Sir okay great so Mato is 40 greater than or equal to 32 it sure is it sure is let let&#39;s keep answer Choice a right now I wouldn&#39;t stop here we got to test the other answer choices right because it&#39;s very possible that uh that multiple answer choices could give you a true statement if you&#39;re plugging in values right you know this you know working your way through the course so let&#39;s test answer Choice b as well but we&#39;ll keep answer Choice a for right now let&#39;s plug into the answer Choice B let me see you do it looking good what&#39;s 32 divided by two it&#39;s going to be 16 yeah so 16 is greater than or equal to 80 yeah so true statement or no GNA be false statement definitely not true so it&#39;s not answer Choice gone absolutely let&#39;s try answer Choice C and right now you might even be able to look at that oh yeah is that give us a true statement no no it&#39;s gonna give us 40 right 40 is uh less than or equal to 32 so that&#39;s not right either is that is that clear yeah that&#39;s what about answer Choice uh D actually let&#39;s plug in answer Choice D here that&#39;s a little bit more complicated so let me see plug into D let&#39;s see what happens all right looking good looking good now here I I think in terms of pem do once again right before we do this addition or subtraction what do we have to do here multiply we got multiply absolutely yeah so 32 * yeah go ahead you got it you got it two 64 yeah yeah you&#39;ve got to calculate on this question so I mean as long as you&#39;re you&#39;re following pemos and you got your order of operations you should be good so that&#39;s going to be 36 yeah great so it&#39;s 36 less than or equal to 20 all work so it&#39;s got to be answer a which it is does that make some sense Mato yes sir okay now you said you saw a question like this on the test did you plug in values I did it was actually it was actually percentage to oh interesting okay yeah that could be tough that could be tough but did it work out do you think you got it yeah I think did great great yeah but it&#39;s still by far the most useful strategy on this test put value very few questions where you have to carry out a specific algebraic operation very few but uh certainly works here any questions before we move on no sir okay great escape roll looks like another plugin and values question here go and read question number three for us please expression is equivalent to or n three power two plus n yeah yeah that&#39;s a messy that&#39;s a messy looking expression there Mato um so what do we solving for uh which uh which expression is uh equal or the same yeah there&#39;s that word equivalent again you got to know that here for this test which expression is equivalent to that big mess all right is it clear that we can just plug in values for n here for this question is that obvious yeah all right so uh so the strategy here right we&#39;re going to create a value for n we&#39;re going to plug into this expression here we&#39;ll find out what that equals for some value of N and then we&#39;ll plug that same value into the answer choices and we&#39;ll see what matches make sense all right sir okay okay what value do you want to plug in for n we&#39;ve got some here we can do one let&#39;s start with one yeah one works great I love ones ones and zeros are wonderful so let&#39;s make n equal one okay now plug that into the expression here in the question let&#39;s see what it equals let me see you work that out on the Whiteboard Mato looking good looking good all right so 1 minus three or let&#39;s do it first yeah that&#39;s right yeah yeah I mean you could um you know it&#39;s like you know you think about like some students might wonder like should we to do parenthesis first and it&#39;s like yeah well to calculate what&#39;s in the parenthesis you have to do the exponents right does that make sense yeah yeah yeah yeah so strangely because we&#39;re C we&#39;re calculating what&#39;s in the parentheses first we have to do the exponents first it&#39;s a little bit tricky but you navigated that beautifully yeah so what do that can equal so 9 minus one is going to be eight well hold on just a minute it&#39;s not 9 minus one it&#39;s not 9us one Sor yeah yeah yeah so we&#39;re going to start with the exponent absolutely okay so what&#39;s 3 squared let&#39;s talk about that it&#39;s going to be n that&#39;s going to be nine so we could rewrite this expression as 1 - 9 in parentheses do you see that Mato sure yeah and what&#39;s one minus 9 eight what did you say it is eight it&#39;s not eight one - 9 is not eight right right oh yeah hold think think about it hold on let&#39;s go back to what we&#39;re were talking about on that first question you got $1 in your bank account and I take away nine bucks how much money do you have in your bank account uh yeah it&#39;s going to be a negative eight negative eight does that make sense or if it&#39;s one degree outside one degree above zero and then it drops N9 degrees it&#39;s going to be8 degrees yes sir you sometimes with negatives I think the best way to do is just think in concrete terms Okay so all right so we&#39;ve got 4 * 8 + 1 uh let&#39;s keep doing pendos here what&#39;s next so four times8 it&#39;s going to be -32 32 all right let me see continue to work this out here two plus one okay all right and then what&#39;s ne32 + 1 -3 exactly does that mean makes sense why we&#39;re kind of it&#39;s becoming just a little bit more positive yes sir it&#39;s not going to be33 that would be -32 minus 1 would be yeah yeah but -32 plus 1 is -31 okay great so we know the right answerers got to give us -31 which answer Choice gives us - 31 well let&#39;s plug in I&#39;m going to clear some space here let&#39;s plug into answer Choice a and we&#39;ll see if that gives us -31 going find a clear spot on the Whiteboard and plug that in is that a one sorry you&#39;re you&#39;re good you&#39;re good good I just want sure okay I got you all right so three * one three that is going to be uh neg3 yeah so is that 31 no that is that a dumb question right yeah that&#39;s not his choice hey I&#39;m going to fix this netive 31 I just want to make really clear that that is is a Nega 31 right there hold on there we go okay good um just in case there&#39;s any confusion plug into an Choice B I&#39;ll clear some space on the Whiteboard all right plug into B three so yeah true no good right yeah not true we&#39;re looking for 31 so B is gone c space let&#39;s plug into answer Choice uh C you&#39;re doing great Matta o five times 30 that is going to be 31 yeah yeah and like let&#39;s talk about how this work right because when we&#39;re going to that first arithmetic question right I kind of told that trick like you can just take 30 you you can take the bigger number subtract the smaller number and just make it negative right like that&#39;s probably the best way to do it right I mean first of all is it clear that 5 minus 36 is going to be negative is that clear yes sir yeah so if you need to car that operation you could just do 36 5 which I think pretty much anybody can do is it clear that&#39;s going to be 31 yeah so it&#39;s going to you make it negative just make it negative that&#39;s the best way to handle that because you&#39;re trying to set up that op like you know doing the operation of that is just not obvious so they do it logically or just think about that little trick subtract the smaller number from the bigger number make it negative but that&#39;s looking good okay let&#39;s test answer Choice D we&#39;ll keep C I&#39;ll clear some space I mean you just look at that is that going to work is that going to give us NE 30 no be super going be like negative hund something or 30 something yeah yeah no not happening so it&#39;s got to be C which it is W any questions about that sir I think a zero would work great here as well it would let&#39;s just talk about that real quick yeah like if n is zero you might even be able to do this mentally if n is zero what is this expression here in the question equal so uh well it would be 0 minus 9 right so it would be four time what&#39;s 0 - 9 by the way 9 it&#39;s going to be uh just nine 0 minus 9 is not nine oh negative n negative 9 0 + 9 is 9 but 0 minus 9 does that make sense yes sir negative 9 yeah and then Plus but that&#39;s that&#39;s just going to be 4 * 9 does that make some sense sure so what&#39;s 4 * 9 that be uh 36 36 so the right answer is got to give USG 36 when n is zero does that make some sense sir yeah does answer C give us 36 when n is zero yeah yeah yeah 5 * 0 is 0 then - 36 is 36 what any of the other answer choices give us 36 oh no way no way okay M like your op your operations are very very good you&#39;ve got a good handle on these questions you approach them the right way I think the only thing you need to be really conscious of and really careful of right as you&#39;re taking this test you&#39;re taking it this afternoon uh is those negatives is those NE you see that now and you see how you have to think about it now and if there&#39;s any confusion as best you can like think about it in concrete terms think about it like in terms of money in a bank account or temperatures and kind of let that logical understanding guide you does that make sense yes sir you&#39;ll be all right like that&#39;s the only thing I&#39;m seeing so far um you know that&#39;s tripping up so pay close attention to those negatives all right Mato go ahead and read question number four for us please so AO bought some pens for $2 each and some pencils for $1 each she bought three more pens that pen and pencils and spent a total of 12 how how many pencils did uh he will buy okay mat what are we solving for here with this question how many pencils did she buy yeah how many pencils she bought yeah and they give us four possible answer choices right four possible numbers of pencils that that she bought are two or three or four or five okay does this question make some sense at least what we&#39;re solving for here yes sir okay okay now um this is a system of equations question and I think a lot of students you certainly those that haven&#39;t watched my videos or taking my course are going to try to set up a system of equations here which you can do it&#39;s just kind of complicated are you familiar with systems of equations do you know how to set those up or not so much that&#39;s much yeah yeah don&#39;t don&#39;t worry about I mean like you know some students watching this might be familiar with it there&#39;s like two unknown here&#39;s some unknown number of pencils and some unknown number of pens and there&#39;s two equations you can create and then you can do a specific algebraic operation to solve for those missing variables and that&#39;s fine but again like as we&#39;ve seen many times right the more steps you&#39;re doing the likelier it is you&#39;re going to make a silly mistake so we want to simplify this much we can and we can we can test these answer choices okay we can test these answer choices without doing any algebra okay so like for example look at answer Choice a answer Choice a says uh two right so the question is how many pencils did she buy anoid say saying okay maybe she bought two pencils okay two pencils so all the anoid really represent some possible number of pencils I&#39;m going to make a note of that these are the pencils and if answer Choice a is correct if she bought two pencils you know exactly how many pens she bought how many pens did she buy if she bought two pencils how many pens so she bought three more so it&#39;s gonna be five it&#39;s gonna be five does that make sense yeah does that make sense mat yes sir yeah because it says she bought three more pens and pencils just logically be like oh she bought two pencils and she bought five pens now we can calculate really easily how much two pencils and five pens would cost really easily uh because it says the pens were $2 each and the pencils were a dollar each so let&#39;s let&#39;s start with the pencils how much would the pencils cost so two is going to be $2 $2 for the two pencils does that make sense sure and then how much for the pens so five time two is going to be 10 5 * 2 is 10 and What&#39;s the total uh $12 $12 so what do you think about an Choice a yeah I&#39;ll keep it let&#39;s keep it that could work absolutely I mean in fact it should work right I mean like I I doubt they&#39;re going to give us multiple answer choices here that would that would work here we&#39;re not really plugging Val we&#39;re just testing the answer choices here I would still be careful and let let&#39;s make sure we&#39;re on the right track and test the others but a is looking really really good but let&#39;s let&#39;s let&#39;s practice the process again of testing these answer choices so look at answer chice B so that&#39;s suggesting she bought three pencils if she bought three pencils how many pens did she buy so six that&#39; be six pens yeah because you&#39;re about three more pens pencils how much would three pencils cost uh $3 $3 just testing this and then how much would six P cost uh 12 uh yeah hold on uh yeah 12 so what would the total be it&#39;s going to be 15 GNA be 15 so what do you think my answer is is B no no way yeah the question said she spent a total 12 bucks does that make sense yes sir yeah I mean we could test C and D if we wanted to do you think we need to or no oh because the higher the number the higher the more yeah we&#39;re good man we&#39;re good I I would still probably double check make sure we&#39;re on the right track cuz sometimes like if you make an arithmetic error somewhere you know like and then you test B and you&#39;re like oh wait that works too or somehow that gave you 12 you&#39;d be like okay maybe I approached it the wrong way somewhere I did a uh you know addition or subtraction error something like that some arithmetic so it&#39;s not a bad idea but I feel pretty confident here about stopping and pick this Choice a and it is a any questions about that Mato no sir if you look at it so again like finding the right answer like calculating the number of pencils here is tricky it is even if you&#39;re familiar with systems of equations it&#39;s just tricky and there&#39;s a lot of steps if you see a question like this you&#39;re like man I don&#39;t know how to calculate that ask yourself this question can I just test these answers and 95% of the time maybe more than maybe 100% of the time that&#39;s an easier path than trying to calculate it look for ways to test answer choices for

Transcript for:Accuplacer Math Crash Course Overview

Transcript for:
Accuplacer Math Crash Course Overview