Day Before the Test: Last Advice and 2019 AMC 10 A, Problem 18

all right how's it going i wanted to do a quick video for you guys this is the day before the test this will actually come out about 11 30 p.m pacific on tuesday and then you'll probably see it on wednesday at some point if you see it before this test that's great i wanted to give some last minute advice about what you should be doing the day before and the day of the test as far as your prep work goes and your thought processes go so we will start with what to expect right everybody asks what do you expect on this test is it going to be hard is it going to be easy we don't know but here's one thing i'm definitely certain of every year the maa committee puts things on the test that nobody has seen before and i have a theory about why this is now i'm not privy to any of their private discussions they don't see me in their emails which is carbon copy for those who don't understand that they don't they don't tell me i've never seen a memo and part of that might be because this is actually leading to an international competition and we don't want to let the other countries that we're competing with know what our overall strategy is as a country for the usa imo participants and so this is a theory just my idea of what their goal is to accomplish and here's what i think that goal is why are there problems on the test every year that no one's seen before um i think the reason for that is the following and i will give an example of how to handle these in a moment at the end of this video i think and i don't know this is my opinion i forgot what i've inferred this happens every year and my understanding is this i don't think they want people to make it far in the competition who only know how to repeat processes if all you can do is repeat what you've learned if that's all you can do you can't innovate you can't react on the fly you can't overcome adversity you weren't expecting they don't want that student to make it to probably i would say no farther than usamo right because it means that all you can do is do what's been done before if somebody told you how to do it then you can do it and if nobody told you how to do it you can't do it and guess what if that's you if all you can do is look at all of the past tests and repeat all of the things that you learned from them oh if they give me a circle with a tangent line i know to do this and i apply formula x and if i just apply all the formulas that i learned i'm going to succeed no you're not right they don't want that kind of student to make it far you might make it to amy with that skill level set but you're going to need to develop another gear you're going to need to be able to innovate the student who sees the question that no one's seen before oh i wasn't prepared for this oh i don't know the formula i can't do this weakness give up walk away you're not gonna make it you need to think on the fly you need to innovate they want the students who can innovate to make it to the the uh usamo and beyond mlp all of that the questions are designed to be unique there's unique twists that have never appeared on amc 10 or 12 in the previous years it happens every year if you are the one that comes across that and you immediately give up that's what they want give up you're too weak or you can say i refuse to accept my limitations i will think of a way right now in the spot in the moment i will think of a way to solve it under time pressure that's who they want to advance again i don't know that to be true but it's what you can expect there will probably be at least six seven questions at least that are first time never before seen kind of concepts that you're gonna have to unravel like a ball of thread you're going to have to unravel it in the in the moment at that time another student mentioned to me once that it seems like they're going for with the equivalence of something called ad hoc problem solving which i didn't look up before this video and i should have but i believe it's kind of the equivalent of that you are innovating in the moment without previous direction what can you come up with that's what you're going to face so when it happens there cannot be panic that cannot be oh i don't know what to do no expect it expect it so that when you see those questions those six or seven questions those are the difference between people who will qualify for amy and who will not they are the difference between people who will make it to usamo or who barely qualify for amy right that's what's going to separate the men and the women from the boys and the girls so to speak so if you can't do it this year it's okay you got another year to grow now you know what to attack you're going to have to make an attack plan for how to develop those skills but don't be weak don't be scared don't freak out don't panic there's no time for that you need to react you need to expect and when it happens understand that every single test taker taking that test is having that same exact moment of fear and panic at that point that's the point they want you to feel that and the ones that overcome that that adversity and they march beyond it and they get the necessary score that's what they want they want those students they want those the students who are going to succeed to get usa to the imo medal again don't know that that to be true it's just what i suspect okay so i will give an example of how to do that in a moment i'm going to use the 2019 amc 10a problem 18. um approximate cutoff i get asked this a lot i don't know this is again an inference i think their goal the goal is to make approximately for the amc 10 a cutoff of around 110. you know it can't be 110 it can be 109.5 or 111. i think this is the goal every year like to be around there this is just a guess i don't know it's just what i think so but you cannot rely on this you don't know for sure what it's going to be last year it was 103.5 and 102. right so you don't know okay so the best strategy is not to worry about the cut cutoff necessarily at least in advance during the test i will sometimes think about oh this question was super tricky i bet 80 percent of people fall for the trap answer and this one oh man i really had to have a slick amount of ingenuity to solve that if there's a lot of those expect the cutoff to be lower if there's not so many of those then the cut-off's going to be higher i do remember some kind of memo they put out a while back that they wanted more separation at the top approximately 2014 or 2015 they made some kind of announcement like that and so to do that they were going to be making the test more difficult maybe that was the only the amc8 i don't remember where i saw it maybe i'm faulty memory but i think they had something like that so uh what where do you want to aim for get a feel for it during the test the best strategy don't guess number one we're going to get there in a second don't guess the best strategy is answer as many as you feel confident and answering and maybe maybe one or two where you're 99 sure but not a 100 sure now you had to rely on some kind of an inference that you couldn't prove in the moment but without that inference there's no way you're gonna get it that's a risky decision but sometimes i've done it and it's worked out in my favor and sometimes i've done it and it hasn't you're gonna have to make that risk decision in the moment at that time okay so approximate cut off that's covered um i i would say here's your target for minimum scores answered to get qualified um if you can answer 15 questions and skip 10 uh you will get a 105. and this is getting nothing wrong right okay if you answer 16 and skip nine you will get a 109 109.5 and if you answer 17 and skip the last 8 you will get a 114 by the way we're just adding 4.5 points each time if you didn't notice because you're converting a skip into a correct which is 6 minus 1.5 so uh then where what are these the likelihood if you only answered 15 i would give you maybe a 10 chance to qualify you might you might but probably not you never know though uh if you answer 16 get them all right no mistakes i would give this probably about a 50 chance to qualify um i believe this would have qualified you on each of the last four tests meaning the a and b last year in the a and b before this is going to get you a lot higher i would put it at probably 80 percent chance to qualify with a score of 114. just rough this is a rough guess i have no idea what's on the task this is just a guess about approximate amounts that you should be aiming for so if you get to this range you know understand that every question in this range is a premium value it could be the difference between qualifying and not but i don't recommend that if you can only answer 16 you're trying to get to a higher percent chance of qualifying that you guess on something don't guess okay there's two things no and don't know plus if you guess are you really gonna feel like you made it aren't you gonna feel like you had to get carried up the rest of the way up the mountain or are you gonna feel like you climbed it i know what i'd rather have i'd rather have achieved it and not have guessed my way to an amy qualification um to a certain extent obviously if you get close to an answer you know it's one or two you've done a lot of work put a lot of work in oh that's okay but if if you're if you're you know just outright flat out just randomly guessing no no not worth it okay so um the next thing up is i do know people by the way who have guessed on a problem thinking they needed it to qualify guess how many points they missed qualifying by 1.5 they would have qualified if they hadn't guessed it's up to you it's your strategy you do what you think is right for that situation and it's in the moment you have to decide but i don't recommend it next question i get asked a lot and i see it in the forums uh will people cheat for this one i wanted to share a message that i found on the forums it was shared on aops forums that is um somebody asked us in my comments and i said this is a fair question and i think from a youthful perspective it can be a little more alarming than for someone with the benefit of more life experience similar posts have been found on amy's amc forums and one of the moderators responded with the following quote from the maa director i'm reading what they wrote because i think it's needs to be heard i will also include my comment and their statement in the description of the video um so uh the mission of the ma this is the statement from the director um the mission of the maa competitions is to increase interest in mathematics and to develop problem solving through a fun competition students gain the opportunity to learn and achieve through competition sorry i have a stutter sometimes with students in their school and from around the world teachers and schools benefit from the chance to challenge students with interesting mathematical questions that are aligned with curriculum standards at all levels of difficulty cheating at the amc contest is pointless institute and stupid and those who engage in it or even discuss it have completely missed our purpose the purpose of education and the joy of learning lift your heads up steve dunbar maa director american mathematics competition i completely agree with this statement director dunbar's remarks as i said in my comments are extremely wise and demonstrative of leadership and so my additional thoughts i'll try to summarize them here without reading directly from it because it's not as engaging but i'll leave my comment in the description of the video um basically uh you know you you through life are gonna have things that you can control and things that you cannot are people gonna possibly cheat they might is there anything you can do about it there's not nothing you can do um you can you can you can think about it if you want but it's a waste of time really that's on them they're gonna have to live with themselves the rest of their life right and uh you might think oh i should cheat too then no probably not you're not gonna feel good about it if you have any kind of character or integrity in the years that follow after you are given so much praise from family members or friends or school you get some kind of an award if you had actually cheated on the test it's gonna gnaw at your conscience and you're not gonna feel good about it in the aftermath trust me okay i've heard it from people before who have done such things if you want a tainted victory look at the steroids era of baseball a lot of them did really great none of them are in the hall of fame up to you think about what you think is important to you i wouldn't think about this anymore after you've hear what the director said and read the comments on it it's not really anything to think about think about what you're doing and what your plan is and what you're going to accomplish and some people might say oh you know they succeeded and you because they qualified for amy by cheating and you failed because you didn't by not cheating i would say it's exactly the opposite they might have a tainted success and i shouldn't have the question they should have a tainted success where they've succeeded in qualifying for amy by cheating but really the truth is you succeeded by having integrity and character think about that okay so uh what to study the day of and the day before i get asked this a lot it's my opinion okay there are other people that have different opinions they have they're very qualified to hold those opinions this is just mine and it's what i think and so understand that it's my advice i don't think it's worth it to do whole tests the day before i think but you've studied for a year or six months or eight months as hard or as difficult as you've put in the work you're not going to change your scores significantly by doing mocks the day before instead this should be a time to review all of those concepts that you've learned the theorems the ideas the pictures right all the things that you've written in the small notebook um any formulas that you learned this year any underlying concepts you want to review those okay uh maybe do five problems from the mid-range like anywhere from six to fifteen just to keep sharp you know on problems but i wouldn't do a whole mock test mostly it should be review review review over and over and over again throughout the day that's my advice on that if you look on the forums currently sohil rothy uh who has the omega learn website has got a post in the blue forum the contest and programs forum and he made a pdf of all kinds of formulas and concepts that he breaks down it's like i think 36 pages or 86 pages i don't know it's long and he put in a lot of really great effort for it you might want to check that out on the forums and just glean some concepts off of there that you might not have thought of recently it's not just about knowing concepts it's about having them at the tip of your mind ready to implement them right because if you've recently thought of the concept like in the last 24 hours the chance have you seen the opportunity to use it in a problem increases exponentially so um what's next uh eight hours oh the day of same thing more study of the notebooks and the concepts um eight hours of sleep i just don't you can go a little bit lower if you're one of those people who survives on five hours generally and you might think you can i've never seen anybody do well on seven hours less than seven hours of sleep typically kids uh need about nine hours of sleep to actually get what they need so if you're going to go lower you know 7 is the absolute minimum you go below that and your thinking capacity and ability to think quickly diminishes each less you know half hour of sleep that you get i think it's too much of a risk and it's absolutely not worth it you're not going to change anything by staying up late to study more right get the sleep that you need so that you can be well rested and ready to perform okay food before the test uh i would eat before you have the test i would not eat anything that has ever upset your stomach uh right before you take the test because the last thing you need is in the middle of the test you're having to run to upset stomach kind of thing right you don't want that nobody wants that really so make sure you do get something to eat you don't want to be hungry you don't want to be thinking about oh man i wish i had a sandwich right now or i should have eaten you know maybe have a granola bar next to you just in case for an emergency but eat a little bit maybe a few hours before the test so that you're a couple hours you know so that you're good you're not thinking about food at all you're trying to eliminate any distractions in advance and you're planning this out okay um coffee sugar and chocolate everybody asks about this if you don't normally drink coffee and you probably shouldn't cause if you're taking the test for merit you're still in school and most kids in school don't really need coffee you have a you convert uh you know calories into energy much better than adults do and so you typically don't need these things sugar sugar highs wear off right so if you have sugar before the test it's not going to last the whole time maybe the last half hour you have a your sugar high drops off if you've ever drinking like four mountain dews which you should never do but i did as a kid because hey we didn't know any better uh and then a little bit later all of a sudden the sugar crash right you crash because you don't have the sugar high anymore i don't think it's worth it i wouldn't mess with that stuff i wouldn't think about this but if you've used chocolate before or something every people talk about that you do you you whatever works for you i don't know for sure different people react differently to different things okay but i don't really recommend these kinds of things um i'll get to this one in a moment i want to talk about these ones the noise environment talk to your family in advance siblings right let's not have them having a rock concert in the next room let's not have people laughing and joking with the dog or you know tv up really loud or anything like that you need to talk to them in advance and ask them you know to respect this is a big moment the super bowl's this sunday but this is kind of your super bowl if you will and so you're going to have two shots at it you need to control the noise you need to eliminate i mean zero noise no tv no ipad it's only a 75 minute test plus the time you're filling out the forms i'm sure they can be quiet for an hour and a half that's all you're asking so aim for that uh explain the situation i'm sure that your family will be understanding and supportive of that decision um the aftermath after you've finished the test it's time to think about what did you learn right it's like your game film and you're gonna go and look at the game film and think about what was i weak on was i not able to answer these kinds of questions did i not have enough time um was i too slow did i not know certain topics all of those things are idiosyncratic if that's even a word it's uh it's unique to you okay they're your idiosyncrasies you're going to have to take them and make a plan going forward about what you're going to attack in the next year but really you only have a week before the b test less than a week you shouldn't think about that too much now just understand take note of things you can work on and after the b test is over if you did not qualify for amy it's back to the drawing board maybe after a short break i think a short break is good after the test but don't take so long of a break that you just decide you don't want to do it anymore you want to get back to learning and especially in the off-season focus on theory and things like that these are aops books these are various other books and sources that you can use this channel other channels whatever you can find for resources to teach you the concepts that you are going to need on the test um the last thing is i would watch the emu mindset video it's on my channel it's in the competition amc 10 competition preparation playlist in the playlist section where it says playlist and uh you're going to want to watch that i like i think the best time to watch this is right before the test it's just kind of a reminder not right before the day of but like you know earlier maybe even the day of if you're taking it in the afternoon for me i'd rather take it in the afternoon in the morning my brain is like oh i need some like coffee but i'm an adult so um yeah so uh watch this video either wednesday which would be the day the day before the test or the thursday the day of the test i just think it's really helpful to think about the thought processes that you have and the mental preparation you want to have going into the test a lot of people agree that this is this kind of idea is just as important as your problem solving skills okay so give that a watch i will link it in the description as well and probably at the end of this video it will appear at the one of the end screen caps okay so i think that's about it aftermath got it we're gonna go to this i wanna talk about what to do when you've never seen something before it's a brand new concept or at least a new wrinkle on an old concept that is never before appeared how do you handle that we'll be right back to demonstrate exactly how you can handle such a situation be right back all right so as promised i wanted to give a demonstration of what you do in a problem when you've never seen before the underlying concept at least on the amc a lot of people when they encountered this question had never quite seen something exactly like it they've done similar things you know base work and stuff like that number theory but maybe not with the repeated decimal and so they might not have been prepared for it many people were in that situation in fact i wasn't really strong the first time i did this problem with number theory i had only done the intro to number theory book a couple of times more than once as good in my opinion and so i had to kind of come up with a plan for how i was going to attack this and i'm going to share with you what that plan was and how you lead to it one more reminder i will have these solutions that i know how to do for the 2021 test the february ones happening thursday approximately friday morning i should have as many up as i was able to film the day before um yeah so let's get to it uh 2019 amc 10a problem 18 it was also the 12a problem 11. again you'll notice it was number 18. this is in the qualifying range right if you're being able to get this question correct you're probably either making amy or you're making usamo it's distinguishing you right it's it's one of those ones and there's a lot like this isn't the only one but this is one of them for some positive integer k the repeating base k representation of the base 10 fraction so this is in base 10 7 over 51 is this and it's 0.23 repeating but in base k which as they note over here it's this means repeating 2 3 2 3 2 3 forever but in base k and it wants to know what k is so uh for a lot of you who are really strong in number theory the problem is probably trivial for you but for a lot of people that like you know even me at the time i wasn't really prepared for exactly what to do i couldn't remember how repeating that did uh repeating digit numbers work in base a different base besides base 10 right and so what i said was wait a minute how am i going to attack this let's think about this and this is what you have to do you have to come up with the plan based on the things that you do know and you have to ask questions and you are teaching yourself about the concept in that moment under time pressure this is what that looks like here was exactly how i solved the problem there are some faster ways especially if you were stronger at number theory but this is the process that i went through i thought okay what happens if i have something like 0.41 repeating in base 10 what is that i actually know and you should know the shortcut to this it's just 41 over 99. and i asked myself well i see where the 41 came from where does the 99 come from this is a question i'm asking myself and i said wait a minute let's go back to one of the ways that you can get this value for it let's see how it would work if i set x equal to 0.41 repeating okay there are other ways you can use geometric series and a couple other ways to get this value but i'm just going to show you one of the early ways that you usually learn it in algebra 1 even so x equals 0.41 repeating and the goal was to get rid of these two decimal places so we had to multiply by a hundred to do that to move them outside of the decimal point so it would become 100x equals 41.41 again repeating okay and there are more complicated versions of this concept but this is a basic one and so i wanted to demonstrate how it works the next thing you would do is you want to subtract the repeated portion from this side the goal in general in all problems is to reduce the complexity and the thing that makes this complicated is the repeated part so if we got rid of it then it's not complicated anymore that's kind of the goal right so you're going to subtract 0.41 repeating but on the other side if i was to subtract that is it going to help me what's 100x minus 0.41 repeating who knows so rather than subtract that we're going to subtract what it's equal to we subtracted x we got 99 x equals and the repeated parts cancel leaving you just the 41 and the x was 41 over 99 ah so i thought about this process and i said where did that 99 come from it came from a hundred minus one why why a hundred minus one why did we multiply by a hundred here you have to ask yourself why you do those things for many people we've repeated a process so long we forgot why we do it that's what you have to be able to recall and analyze and you're going to use this to make this easy let's see how so if i did a hundred the reason that you multiplied by a hundred well it shouldn't think about it for a second pause the video and think it's because it's 10 squared and what's significant about 10 squared well for 1 or in base 10 you don't think about base 10 when you're working in base 10 because you're always working in base 10 but for this problem you should because you're multiplying by the base squared and then when you subtract 1 you got the 99 this is the idea the 99 came from the base squared minus 1. let's go to this one if i want to do 0.23 repeating then it's going to equal 23 base k because you're still in base k with the 23 the 41 you don't have to write base 10. i mean you can but it's kind of redundant you're just you're obviously in base 10 if you don't talk about a different base but here you're going to be in base k and a lot of people might have forgot this and got stuck if they just put the number 23 so you have to consider that it's in base k you then divide by k squared minus 1. okay this is not times k it's base k well how do you convert something from base k back to base 10 because i i would like to set it equal to this because it says the repeating base k representation of this but this is in base 10 so i need this to be equal to continue on my path and so i need to convert this and it's not that hard if you take the number 419 in base 10 you can expand it to say it's 4 times 100 plus 1 times 10 plus 9 times 10 to the 0 which is just 1 right and so you have 4 1 9 and these are the powers of 10 because you're in base 10. that's what you do with this it's simply 2 times k to the first just like these would be 10 to the first right and then plus 3. and you could put k to the 0 but why so 2k plus 3 over k squared minus 1 equals 7 over 51. this looks like something you did in algebra 1 possibly algebra 2 from here it's smooth sailing but to think back about how we got here we don't know what we're doing we think about something similar we ask ourselves how did i do this why is it 99 because you've forgotten probably and then you reinforce that it came from 100 minus 1. why 100 minus 1 what would it be in base k well 100 is 10 squared it's k squared minus 1. and that's how we find ourselves here we simply cross multiply you're going to get 102k plus 1 53 equals 7k squared minus 7. okay then i want to move things to where k squared is positive so we're going to have 7k squared minus 102 k and the 153 is gonna be negative 160 equals zero the only way you can factor this first term is seven and one so it's gonna have to be seven k and k and i don't know the first thing that pops in my mind for this is 16 and 10 because it ends in zero it just seems like it's logical it could be 20 and 8 i suppose but if i do 16 and 10 how would that work so i do this i put 16 and 10 i put 7 and 1. this is just my way of factoring 7 times 10 is 70 plus 16 is not 102. how about 7 times 16 that's going to be 70 plus 42 it's 112 and then i would have 10 left over those numbers the 112 and the 10 have a difference of 102 and we want to difference because that's a negative sign so i need the 7 and 16 to multiply which means the 16 is going to go here the 10 is going to go here then i think okay i want a negative 102 so the 112 needs to be negative and that positive seven times this must be the negative this must be the positive this is what it is this equals zero that's going to give me a negative we don't care this gives 16 that's the value of k that's how you think on the fly draw upon whatever resources you have at your disposal your personal resources are the experiences that you've had and what you have learned if you say oh i've never worked with 23 base k i i don't base k with repeated i can't do that that's your fear and that's why you're not going to qualify overcome the fear find a way find a way to think about how to figure it out on the test that's what will distinguish you from the other test takers that's what's going to make you go far okay don't give up on a problem i hope this helps guys good luck on the test look for the solutions to be out sometime morning pacific time on friday i don't know when i'll probably do it when the aops forums open or shortly after because they get locked during the test you guys have a good one see you around

Channel: TheBeautyofMath

Views: 9,039

Keywords: AMC10, AMC12, AIME, Competition Math, AOPS, MathCounts, Math, Mathematics, AMC 10, AMC 12, AMC 8, Math Kangaroo

Id: FFpBMkKnOk8

Length: 31min 17sec (1877 seconds)

Published: Wed Feb 03 2021