welcome everyone to our session for AP Calculus AB I'm John from Marco learning I'm joined by Melissa Neil Melissa how are you doing tonight I'm great thanks I'm ready for this exam yes well good thing you've been teaching it for three decades and helping students at AP Calculus AB BC all levels of mathematics everyone in the chat let us know where you're joining from what exam you're taking tomorrow at Marco learning we have a review tonight for AP Calculus AB of course AP Calculus AB is kind of the core of AP calbc so if you're taking BC you're in the right place too but I also want to point you to a video on our channel it's right there on the homepage for AP Calculus BC review so I want to make sure that's muted on YouTube um and that we are all set so by the way we have people joining from New York we've got some AP Cal AB students here any teachers here we want to shout out to them and also since it's Mother's Day shout out to all the moms too so um one question Melissa I'm we're already getting in the chat is are we going to cover every single unit tonight are we gonna learn the entire ad calculus course in the next hour no no no the the objective tonight is um so I'm under the assumption that students have spent 30 to 32 weeks in the classroom learning the content so tonight is not a Content review it's not a cram session so as an AP reader I'm bringing to you the tools that you need to communicate the content that you know so you know your stuff now let's just make you let's just make sure you can say it right you can read the D you know things like that and I'm G to maximize your points especially on the frq we're gonna work on communicating what you know great so that we can get the points we deserve we got a bunch of smart people in this stream and people watching this at three o'clock in the morning how do you all get the points you need so Melissa I'm GNA let you go ahead and share your screen with your slide deck this session by the way where're since we're getting the question will last just about an hour or so we're going to um if you like this video press that like button subscribe to our Channel and I'll be here throughout the chat answering questions so with that I'm going to turn it over to Melissa and wish you all the best of luck as we study for AP Cal all right thanks John well as you said I'm Melissa Neil I am from Southern Indiana I'm really close to uh Louisville Kentucky I've been an AP Calculus AB and BT BC teacher for many years um I've had the privilege of being an AP reader I will I will be an AP reader again this summer um my goodness it's it's kind of a nice summer gig to be a reader you get a little extra income but wow the um the knowledge that teachers take away from that reading session is unbelievable and it's so exciting to bring that back to my students and to bring that back to you um I was also a presenter at the AP National Conference in July of 2023 in Seattle so it was really cool to be um in a room of a bunch bunch of calculus teachers and just sharing some fun things and some and some neat ways to to teach calculus um now I teach in a public high school and I will say that we I have had I have set school records for my my students pass rate in ab and BC from the 2014 school year which is when I started AB uh to 2023 so I'm just I'm not really here to brag on myself I just want to let you know that I believe you are in good hands and it is my goal to maximize your success that's what tonight is all about it's not about me it's about hey I've got some things that can help you and I just want you to trust me okay so I plan on I plan on things going really well tonight and maybe you've got a pencil and paper and you can like jot down some notes really quickly uh my first thing that I want well yes I will I will talk about tonight's objectives the first thing I want to do is introduce you to the test maybe your Calculus teacher has told you exactly what the test is like and maybe he or she hasn't I want to make sure you know what to expect tomorrow morning at 8 am I have some site reading strategies to go over with you because if you are um if you are any in any kind of music class like choir band Orchestra handbells whatever there might be um you've done some site reading strategies and that's kind of what an AP test is you've never seen this test before and they're throwing something at you and you're expected to perform right then so I've got some cool site reading strategies for you I would like to show you some common frq topics um these are things that I can pretty much guarantee you is going to be in the F frq section I have some test taking tips for you and dos and don'ts not on tonight's agenda is a Content review so this is not the time to teach you optimization related rates anything like that I'm really going to focus on the frqs now why am I going to focus on the F frqs and not the multiple choice well the frqs is where you have to write you have to show your work and you get credit for work shown and you also get credit for writing a sentence to prove that you know your Calculus so in in going over the F frqs with you I'm going to help you earn points on oh I need to make sure that I show this I need to make sure that I say it this way um and then you know the content what you've been learning that's going to pull you through most of the multiple choice in the exam format so at 8: am tomorrow morning you're going to start out with multiple choice questions and you can see there are two parts to the multiple choice we have 30 questions 60 Minutes no calculator and then the next portion you have fewer questions 15 questions 45 minutes and you get to use your graphing calculator do know that just because you have a graphing calculator on your desk does not mean it's required for all 15 questions okay and then you'll take a nice break and then we'll start on the F frq's so on the first session of the frq's part A you're going to have two questions 30 minutes and you're going to have your graphing calculator on your desk and you will need your graphing calculator for most Parts on those questions this is interesting once the 30 minutes are up they're going to ask you put your graphing calculator away get it off your desk put it away and you may continue through the remaining four questions and you have 60 minutes now what's interesting is while you're working without a calculator you are allowed to go back to questions one and two you just cannot pick up your calculator again now why would you want to do that if you can't pick up your calculator well we all know this is a time test and sometimes you get short on time so in part A when you're working on those two questions and you have your calculator if you see that the time is running out do everything that you need on your calculator save your justifications for later okay use the graphing calculator while you have it for those last two minutes or so while you're looking at the clock because once you put your graphing calculator down you can go back and do your justifications for questions one and two all right so the total time on this I believe I added up it's like three hours and 15 minutes but by the time we get everyone assembled we get everyone started everyone takes a break and things like that it's it's close to a 4-Hour exam the exam composition um again maybe your Calculus teacher has shown you this throughout the course of your year sitting in calculus and maybe he or she hasn't um but this is kind of the breakdown you can see how heavy topics are weighted on the exam all right now how do they calculate your score well there are six frqs so let's look at the second line first there are six F frqs each frq is worth nine points * 6 is 54 so the frq portion is worth 54 now they want the multiple choice section to be worth 54 points as well however there are only 45 questions so if you take 45 question times 1.2 you get 54 so they're going to they're going to bump up your um the weight on the multiple choice just a bit to make it match the weight on the frq so that they're equal 50 50/50 um and then we'll take all of your points that you've earned divide that by 108 and you get a percent now in my school our grade distributions the cut the cutof score is 90 for an a 80 for a b 70 for a c and 60 for a d on the AP exam however this should make you breathe a sigh of relief so um now don't I wouldn't publish this if I were you these are sample cut off scores that I have seen throughout the course of about 10 years so let me explain what this is the highest cut score that I've seen to earn a five is a 69% the lowest cut score that I have seen to earn a five is a 60% oh my gosh most of you right now are crossing your fingers and saying oh my gosh please let the cut score be about 60% because if it's 60% I've got this I want to make a five yeah so I believe that the cut score for a five will be somewhere between 60 and 69% and likewise for a four somewhere between 44 and 54% okay so that's what you can see there is a there is what I would call a huge curve on the AP exam all right that should give you a little vote of confidence as we go into this exam all right and here is some random information this is these are things that I've I saw people ask about exams in the years's past first of all acceptable writing utensils you can use just about anything in the physics exam uh on the physics exam they want you to use a pen not necessarily true on the Calculus exam you can use whatever a pen a number two pencil mechanical pencil whatever um abbreviations are acceptable you can see some that I've got on my screen here intermediate value theorem mean value theorem continuity positive negative um increasing decreasing I would do I Inc and DEC CCU for concave up CCD for concave down the main thing you need to worry about is write legibly you need to write legibly absolutely you can use abbreviations just write legibly I've got a couple of students in my classes this year and just praying oh my gosh please please please write legibly they know their stuff I just want to make sure that their reader can read their handwriting also know and I and I don't want to be a downer here but just know that on the multiple choice questions there is usually a right answer unless it's a none of these so there's usually a right answer however the distractors the wrong answers this is where teachers have worked out the problem incorrectly based on errors that their students have made like common errors like forgetting to chain rule or or um forgetting to do the product rule or things like that so just pay attention um don't rush through it make sure you're doing the right thing okay and then units are only necessary when asked for you don't need units on every single frq but please pay attention and know what the question is asking for and I have a sample of that here um when you see in my in my slideshow here when you see a snippet of an frq in the bottom right corner I'm going to tell you what year that came from so this is U frq number one this means they students could use their graphing calculator and this came from the year 2014 now the student was very confident the student thought they got all parts correct you can see that they've checked off yes I've done this yes I've done this unfortunately the red is what the reader uh thought that they earned for points so I don't have the scoring rubric here but you're just G to have to take my word for it part A was worth one point find the average rate of change good and indicate units of measure so just to get one point you have to have the correct decimal rounded to three places and you have to have units of measure unfortunately the student did not get the one point for part A Part B was worth two points one point this is according to the rubric one point was for the decimal value negative. 614 and the other point was using correct units interpret the meaning of the value and the student did put units but they didn't read the whole question and say oh I've got explain what this means okay um and honestly y'all not every time uh when you see something so simple like here's the function a find a prime of 15 and oh by the way here's a graphing calculator like that is so easy so there you know consider that first point a freebie because you can use math 8 the math 8 function on your graphing calculator and just get Nega 614 you but then they back it up with okay now to get the next point you got to know what it means okay read and reread the question please please please okay and now we're going to go on to site reading tips so um my both of my children uh went through four years of music classes at our high school and my goodness their choir teacher prepared them for site reading she was awesome and I thought you know what I need to be as awesome as she is I need to prepare my students for site reading so here you go you ready we are going to start with a graphing calculator question so here we go number one it's G to be a graphing calculator question you are given a rate at which gravel arrives and here's the function they call it capital G it tells you and now keep in mind G is a rate it tells you how much gravel there was at the beginning of this time period and then how much how what the rate is gravel leaving so here's what I want you to do when you see this something like this on your paper I want you to take your pencil and I want you to say G stands for rate in that's the rate that it's coming in and you know what I know I said that units aren't necessary but this is going to help you I promise write down the units uh that g is in G is measured in tons per hour write that down um and then you can see on the left hand side I went ahead and stored that in my y1 in my graphing calculator you know you're going to need that and just go ahead and type it in automatically and make a note to yourself that that's where I stored it and likewise the rate out is 100 it doesn't have a specific name but I said that's the rate out it's in tons per hour and look I've stored that in Y2 see I don't even know what the question's asking yet I'm just taking the information storing it in my graphing calculator and I'm saying I'm ready bring on the questions so here's what it looks like when they're stored in my calculator make sure you're in radians by the way all right now because they're stored in my calculator I never a and they that g has a name because G has a name and I've stored it in my calculator I never need to write on my paper 90 + 45 cosine t^2 over you don't need to write all that it's stored in your calculator and it has a name whenever you need to use it let's call it g all right and then once we have it stored in our calculator look at all this fancy stuff that your calculator can do um I'm hoping you all know how to grab a function on your graphing calculator it's Alpha Trace Alpha Trace grabs that function really quickly and you can grab the function and put it in function notation so if you need G of six this is the way it looks on your graphing calculator type it in you'll get G of six if you want the derivative of g at six that's a math 8 function and if you want an integral on G from 0 to 8 that's your math 9 function function okay and that's really easy to do once you have your functions stored in your graphing calculator okay so here's another example um this is another question from 2022 this is a rate of vehicles that enter a line a toll plaza again I'm going to immediately write on my paper hey a is a rate in it's in vehicles per hour and I stored it in y1 now also once you do this let me point out the fundamental theorem of calculus the evaluation part says hey if you do an integral on a if you do an integral a definite integral on a let's say from uh number of hours after five so let's say you go from zero to five if you go 0 to five integral on a you know what that gets you V Vehicles when you do an integral on this rate it gets you number of vehicles entering it's the number in vehicles in whenever you integrate a rate that's what you get you get the change in your numerator so keep that in mind oh look that's what it asks for look part a right an inter integral expression that gives the total number of vehicles that arrive we've got that so again don't write don't write the expression here's what you write on your paper a represents that function please call it by name just say that you're going to integrate from one to five a of T DT all right now um just a tiny little smidge about volumes of revolution so I tell my students when we do volumes of Revolution um and I hope this makes sense because I hope you visualize you know volumes of Revolution but as you are revolving around the x-axis or any horizontal line you're revolving around the x-axis we are going to take those circles and we're going to accumulate them from left to right like plates in a dishwasher so when you're doing a volume of revolution around the xaxis this is bunch of circles stacked like plates in a dishwasher your limits are X values your expressions are in terms of X and you have a DX as your variable of integration however when you revolve around the Y AIS now think about revolving around the y- axis you're making a flat circle and we're accumulating the areas of all these circles stacked on top of each other kind of like plates in a cabinet and so we're accumulating areas of circles from a low y to a high Y our expressions are in terms of Y and our variable of integration is dy okay and then of my favorite topics does a donut have a radius this is kind of a trick question most people say yes but I'm gonna say it's no I don't think a doughnut has a radius let me take that back I don't think a doughnut with a hole in the middle has a radius now maybe a cream fill donut has a radius but not a doughnut with a hole in the middle and so this is a good um I think it's a good example of showing you the washer method and so look I've I've put some I've drawn two radi and a random segment on this donut see it so from the center of the donut all the way through to the outer edge I'm going to call that my outer radius do you see that that outer radius spans some white space and some goodness some some doughnut space okay that's my outer radius my inner radius the part that you would subtract that is just the doughnut hole that's what gets punched out that's my inner radius now the difference between those two is a segment length do you see that the segment length goes from the inner edge of the donut to the outer edge of the donut that's not a radius that is some random segment because it's not a radius because it doesn't start at the center okay so why why on Earth I'm telling you this here's why I'm telling you this look on the left if we want to determine the sprinkled area so that we can integrate it and find accumulated volume um if we want to look at sprinkled area we're going to have to go area equation for outer radius minus area equation for inner radius right you have to make two separate area equations have to two separate area equations now if you want to you can pull the pi out but you still have this radius squared minus this radius squared okay over here on the right this is incorrect you cannot subtract your two radius lengths and then square that if you subtract these two you just get some random segment I like to call it the sprinkle width that's just a Sprinkle width that is not a radius you cannot do pi r squared on a Sprinkle width so you need to make sure that you square each radius before you put it into your integral all righty now let's move on to Common frq topics I've already talked a little bit about rate in versus rate out that was on the um site reading slides rate in versus rate out very common and it's common to be in number one or number two so that you can use your graphing calculator another common topic is linear motion position velocity and acceleration we're going to go over that a bit another common topic is the accumulation function where you're given a graph of fime and often you're going to have a different function defined by an integral on F okay and this this is going to take us into fundamental theorem of calculus the um what's it called the derivative part I believe it's what it's called um We're going to look at some tabular data you can guarantee that one of your f frqs is going to have a table of values at the top and differential equations I can also guarantee that one of your f frqs is going to have a different differential equation in it and we're going to hit on that as well all right and I said need to be at the halfway mark and we're just about there so looks like we're doing good on time let's jump into some linear motion ready all right brief Brief Review position is often labeled with an S I have no idea why sometimes an X tells us where an object is located on a horizontal line velocity is typically called V or you if if your position is defined as s you can call it S Prime that's fine it tells us how fast and in which direction acceleration you can note it as S Prime V prime or a now this is going to seem really weird but just hang with me here I like to say that acceleration is kind of like peanut butter because on its own it's not very useful so I like to ask I like to do a poll in my classes and say okay how many of you all can eat peanut butter and aren't allergic to it um and then how many of you all like to eat peanut butter by itself with nothing else like just a spoon does anybody ever eat peanut butter just on a spoon yeah maybe one or two uh I have in the past but does it happen very often absolutely not peanut butter is best paired with chocolate or jelly right that's how people eat peanut butter not many people eat peanut butter on its own that's similar to acceleration you all aren't going to be asked about acceleration all by itself often maybe once there might be one point where it asks hey what's the acceleration but more importantly they're going to be asked about where's the particle speeding up where is it slowing slowing down and that all need to pair it with velocity okay so here we go let me show you this is how you're going to pair it with velocity so I've worked out a sample problem I've given you position I've got my velocity function set it equal to zero don't youall forget make sure you set that equal to zero and then I've solved it and I found that velocity was Zero at time equals 2 seconds and time equals 4 seconds so notice over to the right I I made my handy dandy little sign chart for velocity I know when it was stopped I know when it was moving right left and right fantastic now let's keep going and let's do another derivative and let's find acceleration found it set it equal to zero found the time when the acceleration was Zero did my Nifty little sign chart so you can see that acceleration was negative from 0er to three and positive from three on big deal it is not that important by itself acceleration paired with velocity is powerful so you can see that from like 0 seconds to two from 0er to two the particle was moving to the right okay but now drop your eyes down it had a negative acceleration so the particle was moving to the right but there was a force pulling it to the left so it was moving right and somebody was pulling back on it slowing it down well I hope it was slowing down because look what happened at two it stopped I was hope I hope it's slowing down before it stops and it was because velocity was positive acceleration was negative okay now look at velocity look at the blue just beyond two just beyond two the particles moving to the left drop your eyes to acceleration moving to the left left so now we've got something moving to the left and there's a force on it being pushed to the left it's speeding up so speeding up to Second three and then it's like whoever was pushing it left they're like three seconds hands off now let's pull the other way so it's still moving left but somebody's pulling it in the positive direction slowing it down again I hope it was slowing down because it stopped at four all right acceleration make sure you pair it with velocity to answer your questions another common question about position velocity and acceleration is displacement versus total distance so keep in mind when you integrate velocity just straight up velocity your integral knows that some of your velocity was above the x-axis and some of it was below the x-axis and it takes that into account so without the absolute values that gets you displacement displacement is just a comparison how does where it end compare to where it began versus throw absolute values on velocity now all of a sudden your if you've gotten absolute values on your velocity now all of your velocity function is above the x-axis so we're counting all movement all movement considered in the positive direction it's like a step counter you get credit for all your steps when you do an absolute value of the integral uh absolute when you when you do an integral of the absolute value of velocity position Voss acceleration there we go now let's jump into fundamental theorem of calculus this is where a function is defined by the integral of another function so you'll often see notations somewhat like this and when you do when you do the derivative on the left side of this equation obviously how you write the derivative of G is you write G Prime but when you do a derivative on an integral you get the function called F the function named F only where before it had a t in it as its variable now it has an X in it as its variable right so we've kind of like integrated we've substituted these in and then we went ahead and red derivatized everything and now we just have a function with an X in it same function though just with an X in it all right now here's where this is important you're going to see a graph and it's going to have nice geometric shapes on it you've got segments you've got semicircles or quarter circles you can divide this graph into a quarter Circle triangles or trapezoids or rectangles or whatever you want but you're going to use area under this graph to answer these questions but here's what I want you to focus on look at how they Define little G this is how they've defined little G I tried to highlight it for you this is how they defined little G as soon as you see this as soon as you see this I want you to know they're going to ask for they're going to ask questions about G you're going to need G Prime and you're going to need g double Prime so immediately once you see this please write this on your paper do a derivative on both sides so G Prime equals F and then go ahead and do another derivative G Prime equal fime because I can I can guarantee they're going to ask you about where G is increasing or decreasing or has relatives mens than relative Maxes and you're going to need G Prime more than likely they're going to ask you about the concavity of G and you're going to need gble Prime for that for the concavity all right so when you need concavity you're going to look at F Prime when you need increasing decreasing Maxes and mins you're going to look for f to help you answer those questions all right um let's see yep we're going to move on real quick to tabular uh tabular data so you can see this was 2014 you're given a nice table you've got some time you've got some [Music] velocities okay those are velocities warning do not make up data so you may only use the times 02 5 8 and 12 you may only use the Y values 0 4020 and negative 150 you may not assume that there is A1 comma 50 on this graph you do not know that you do not know that it was a linear increase from 0 to two this you don't know that it went just strictly from 0 to 100 in a nice linear motion goodness from zero to two this could have gone this velocity could have gone greater than 100 and come back down to 100 at Tal to you just don't know okay so don't make up data you can only use the numbers in the table now we're going to look at this table and I want to make sure you do not get hung up on ivt versus mvt so I'm I'm pretty confident you all rocked ivt when your teacher taught it to you I'm also pretty confident that you rocked mvt when your teacher taught it to you well here now we are at the end of the year can you tell the difference so one thing I want to point out um probably ivt was first introduced to you in like Algebra 2 or preal intermediate value theorem has nothing to do with Calculus it's an Algebra 2 or pre-cal topic IBT just says hey you know what there was a y value down here and there's a y value up here and if your function's continuous and doesn't jump we can guarantee guarantee that it that the function's going to slide up through all these y values to the next one so we're guaranteed to hit all these y values in between at least once do you think maybe it slides up and back down and back up and hits it maybe maybe it hits some of these y values three times between we don't know but IBT says if your function's continuous so if it's not jumping we're guaranteed that it hits all those y values between now mvt on the other hand this requires calculus mvt says the average rate of change I'm gonna call it a rock average rate of change that's just straight up slope between two points that's slope of a secant average over a period of time the average rate of change has to equal the instantaneous rate of change as long as your function is continuous and differentiable all right so we can't have jumps um we can't have jumps we can't have cusps all right it has to be a nice smooth continu differentiable function and we're guaranteed that the instantaneous rate of change AKA derivative will equal the ack slope at least once okay so IBT no calculus mvt calculus ready let's see if you can tell the difference between the two so again we're going to look at some tabular data okay look at our y values see our y values these y values represent the amount of coffee in ounces all right so we're looking at y values that represent C amount of coffee and look at what this says is there a time where the instantaneous rate of change is two that's inbt that's mean value theorem okay now do a real quick check you can do this in your head y'all are like youall are mathy right so on on the interval from two to four do a real quick a rock for me two to four 8.8 to 12.8 do your change in y over your change in X real quick what do you get change in y that's four change in X that's two what' you get you got two a rock your a rock was two is your I rock going to be two well let's make sure our function is continuous and differentiable is it it is look it said c is differentiable which means it had to have been continuous yeah so that's Mt check out this one your given velocity you're given velocity and look at the question do you think that the velocity will be negative 100 I don't see any indication of a derivative here it's just asking will these values could these values ever be 00 between between time five and time 8 well heck yeah it was it started at 40 and dropped to negative 120 we know that 100 is definitely between these two let's just make sure it didn't jump we got to make sure it didn't jump did it jump no it didn't jump because it was differentiable thus continuous this is IBT okay next one look H do you think H Prime will ever be two what do y'all think I BT or mvt you're going to rock this velocity this is velocity look look look do you think V Prime the acceleration will ever be zero what do you think IBT or MBT mean value theorem make sure you say my function has to be or my function is since my function is differentiable and continuous okay and oh look be careful this was kind of tricky just a little bit at a real quick glance if this is all you look at you're like oh derivative well no this is the function so your values are RP Prime it's asking about R Prime this be careful this was ivt intermediate value theem all right awesome let's move on to differential equations one of my favorites so I don't know if you knew this or not but um all first semester when you were doing derivatives every single day you were finding differential equations okay so a differential equation is just an equation involving derivative however for a lot of you this this phrase differential equation was not introduced until maybe like second semester now all of our sudden not now all of a sudden our derivative equation has a y in it along with an X okay so look at look at the notation um leits Li nits whatever he he I like his notation you all probably don't you'd probably rather write y Prime but look I like his notation because he says this is the derivative of and he calls the function by name the name of the function was y so somewhere at some point there was a y equals blah blah blah equation and you know what this is the derivative of it and also in his notation he says with respect to X so he says Hey X is your variable Y is the name of the function X is your variable you know why that's important because this y that you see on the E this Y at the exponent that represents some y equals blah blah blah messy function you've got to take that into consideration if you ever need to do an additional derivative on it okay so anyway differential equation often has a y in it as well as an X see often has a y in it as well as an X okay now um make sure you know what it asks what they what they mean when they ask for a solution so if this is your differential equation these are the same ones I had on my previous Slide the solution is the original y equals function now this General solution was super easy to find because I just unpower ruled it so so easy and it's a general solution because we don't know what c is there are so many possibilities it's a general solution not a particular solution okay now to do this solution I had to use separation of variables as well as the third solution I had to use separation of variables but I want to point out this these are both called the general solution because look they both contain an unknown C okay General solution to a differential equation basically just means anti-derivative how often is differential equations tested on the exam every single year pretty much guaranteed you can see in my data that I left off 2020 oh my gosh 2020 was a wash it was ridiculous but all the other years look how often differential equations were on a test and you can see that the sum years goes on twice or three times holy moly three of the question in three of the questions involve the differential equation now I got to warn you I gotta warn you two things first of all let's talk about the ones that are not highlighted ready the ones that are not highlighted did ask you to solve so in order to solve a differential equation um if it's got a y in it more than likely you're going to have to use separation of variables if it asks you to solve a differential equation with a Y in it you're going to have to use separation of variables warning in 2012 13 14 16 17 18 in all those years they ask you to solve out of nine points you solving the differential equation was worth five it was over half it like the points just to find that anti-derivative was over 50% of the points for that particular question five out of nine okay and here's what the rubrics say I I wish I would have thrown in a picture of this but I didn't the rubric let's say for number um 2023 number three the rubric said if the student did not use separation of variables to solve they get zero out of five stop grading here just gone all right um also on the rubric if let's say that you're you're like oh my gosh I know how to do this I'm going to separate my variables separate them do your anti-derivative put your C on right away like the moment that you do an anti-derivative plus C you don't have to do it on both sides you can just do it on one side but it has has to be on there the very moment that you do your anti-derivatives because also in the rubric it says if no constant of integration two points is the max the student gets out of five and I've even seen I don't I think I have it on here I've seen a student put it on too late they didn't get the points it has to be on the moment you do your anti-derivative okay don't forget that plus c you want to maximize those points out of five okay now let's let's look at the highlighted questions really quickly the ones that are highlighted be careful you were given a differential equation but it was not solvable like you couldn't separate your variables legally using proper algebra so sometimes you're given a differential equation and you're not asked to solve but you might ask you might be asked about hey is the function increasing or decreasing on this interval is there a Max here use use the differential equation right where am I here you go if you've got a differential equation dydx you've got the slope you can answer all kinds of questions about increasing or decreasing also you could be ask about concavity which is just going to require you to do one derivative on your differential equation so just be careful the the ones that are highlighted did give you a differential equation they did not want you to solve it they just asked about the function now I'm going to show you some examples so this is 2015 look at this differential equation I tell you what my students even this year tried to add y to both sides and they thought they had separated it correctly and they didn't they didn't they they were they used illegal algebra they got it wrong and you know what it never asked them to do that in the first place look at the wording for part C it says okay let F ofx be the particular solution but it doesn't ever say find it it just wants wants to call it something so that it can ask questions about it okay just be careful read it it might not want you to solve it it might just want you to use this this is your slope use this to answer questions uh let's see I think this one I didn't highlight it so it must have write equation the tangent find the no this one also this one never asked you to solve use it to write an equation of a tangent line use it to find where your tangent Line's horizontal and then or sorry vertical I said the wrong thing and then do your second derivative on it and see what that gets you okay now this one let's see if I can find it really quickly yes look at part C part C says do it do it find the particular solution so you're going to have to separate you're going to have to integrate and you're going to have to use your initial condition right separate integrate don't forget your plus C right away and then you can integrate or and then you can uh solve for y sorry all right um just a reminder calculus is about change everything is changing amounts are changing rates are changing everything's changing so when on a question it asks you to approximate this and tell me what it means okay so not only do you have to say it represents the total distance traveled you have to say over what time interval so this person's explanation told me what the absolute value of V of gets you but it didn't say when okay so you can see that she did her right remon sum correctly um correct answer was obtained but lost the point of explain what it means okay and this is this is so unfortunate this this is why this is why you and I are here tonight because you all know your Calculus can you do a right re and sum absolutely just make sure you read the directions and include your time frames some of your some of your answers involve a specific moment of time some of some of them like this one involves a range of time okay make sure you include those times in your explanation justification whatever okay calculus it's about change everything's changing all the time oh same concept oh such a bummer um this person knows their calculus they really do they knew how to estimate W Prime of 12 look they did ACK on data in the table to estimate iro right and dang it they rounded to two places and lost a point you've got round to three or more you've got a round to three or truncate after three just chop the decimals off but they will not accept two decimal places if it continues beyond that so dang it this person knew their calculus and didn't round to three places there's minus one and then the explanation was good I mean like it makes sense for every one minute the water is heated the temperature increases by and didn't say when you've got to include that time frame in your explanations and or justifications all right let's get those maximum points possible all right more exam tips I'm going to put restrictions on you tomorrow ready no pronouns it is not allowed you can't use the word it do not use the word it also don't say the function or the graph or the slope or the derivative please please please call your functions by name if you're talking about F then call it by name and write F don't say the function if you're talking about F Prime then call it fpre okay don't say don't just say the slope because in most of these problems you've got a lot of functions you could have a you could have a g a g prime a g double Prime an fime and an F okay call your functions by name no pronouns no ambiguity okay be specific also when you write an equation of a tangent line just leave it in point slope form you don't need to distribute you don't need to add the Y value over just leave it in point slope form Soaker your answer and move on when you're doing um absolute Max and absolute men on an interval you all are going to find your derivative you're going to set it equal to zero you're going to find out where it's undefined good because you know your Calculus just don't forget if you're doing a closed interval check the Y values at those end points okay and it might not it might not be blatant that they're giving you a closed interval it might say find the maximum from time Z to time8 yeah do your Calculus and then check the Y value at zero and check the y- value at8 okay um as soon as you get off this webinar go plug your calculator in please make sure it's charged or replace the batteries whatever also as you're doing that turn it on and make sure you're in radiant mode because if you are also in physics class then you could be in degrees and you're going to throw off your entire exam okay make sure you're in radian mode because calculus doesn't work in degrees don't forget your plus three don't get to round a three all right now for those of you in AP comp this is AP C we don't need a novel we don't need a paragraph We just need a one or two sentence explanation okay so say what you mean mean what you say then stop talking you here's the thing you all have a lot of calculus words floating around your brain say what you mean mean what you say and stop talking because what what tends to happen is I know I know you want to get those words out and you want to sound smart and you are but the more you talk like the more you try to include more calculus words the greater chance you're going to contradict yourself from what you originally said that was correct okay so if you say things that are contradictory you won't get the point you're reader is not going to say well they were right here but then they Contra well we'll just give them the point like readers don't do that there is no we'll just give them the point bless their heart you know they don't do that say what you mean mean what you say then stop talking um when I say the function the slope it is not allowed I don't want you to really focus on what this question is but look over on the right the this response I don't have a year on here for for you um but I know what this was this was um 2012 this question was worth two points you had to find where the points of inflection were so this person said -2 0 and one Ching this person got the point for knowing those X values but look at their explanation because the function changes from increasing to decreasing no way no way the reader didn't know which function she was referring to okay again we've got G we've got G Prime we've got G Prime we've got F we've got F Prime and F and F Prime so we've got five functions going on in this problem okay please call them by name please please please call your functions by name um I've got what versus where I'm about to run out of time and I'm really sorry if you have other obligations but I just want to point out really quickly um hey here's a here's a problem I've done the derivative I've set it equal to zero I have found my critical values I've made a sign chart and Just for kicks look I found my y values Now read the question ready identify the location of each relative extrema and justify your answer the location would be xal 0 relative Max because FP Prime switches from positive to negative okay don't say it's because F Prime is zero no no no no it's because F Prime switched from positive to negative the other location is xal 3 and this is a relative Min because fime changes from negative to positive okay these are the locations these are the X values now look at the next question what if it's worded like this find the extrema find them do you see how this number two is asking how high does the function get versus how low does the function get it's not asking where it's happening it says what were they what were they so the relative extrema Let's see we said max was at zero so -4 is a relative maximum -3 is the relative minimum it's the Max and the Min not where they're located okay what versus where and then oh sorry and then this slide just says in words what I what I just said there okay um oh so important oftentimes and this especially occurs on graphing calculator questions you know that your your your functions are stored in your calculator and you're like oh oh I know how to do this I'm gonna go find out where my functions intersect well good find out where your functions intersect but write that on your paper before writing the solution so check this out we needed to find for this one particular problem it doesn't matter what the big picture is but look we needed this function minus this function to equal zero that can totally be done on a graphing calculator and this was the answer to that 6.20 whatever look you get one of three points for stating the equation on your paper like write it on your paper before you head to your calculator write e of T minus L of T equals 0 then go to your calculator and look where your y1 and your Y2 intersect or something like that okay you've got to write that setup on your paper um you can see it like I'm not making this up this is in the rubric here's another one you it wanted you forget about what they represent I don't care what they represent look it wanted you to set them equal to each other and solve you get a point for setting them equal to each other and it could look two ways it could look this way if you called it by name or it could look this way if you you use the Expression okay you get a point for writing that on your paper make sure you write the equation that you're solving and Just for kicks here's another one I kind of want to drill it into your head because it's so important write that equation on your paper before you write the solution to that equation on your paper all right if you're still with me uh I've got a I've got a funny video I hope it pulls up why not say what you mean mean what you say and stop talking oh I think it is g to pull up so I don't know if you all watched The Powerpuff Girls when you were young uh my kids watched The Powerpuff Girls when my when my kids were young and this is just it's a one minute 15c clip about Mojo Jojo and talk about say what you mean mean what you say and stop okay I kind of hope you got a kick out of that but he says I did not I do not talk like that do not reinstate reiterate repeat and that's what I mean just say what you mean mean what you say and stop talking don't be a Mojo Jojo so tomorrow morning um at 7:59 when I poke my head into my students room I'm gonna say make sure your calculators and radians um you've got this and say what you mean me what you say and stop talking and the the last these are the last slides I have just be careful on your um when you're doing an integral um a lot of people use the one overx the the deriv the anti-derivative of one overx is natural log of absolute value of one of of X and that's not true when we've got like a e to the function here okay this this is the correct process for that okay gone a little bit over I'm sorry that I went a little bit over but I think that um with your content knowledge and the communication strategies that I've shared here tonight I believe that you are going to rock this exam um please get a good night's sleep be healthy be awake um calculators make sure they're charg make sure they're in radiant mode I hope you do the very best and be the best you tomorrow amazing Melissa go ahead you can um stop the screen share on your slides um I love this was amazing because um it all descended into um yeah if you let me see I can also stop screen sharing for you I can do it I'm just having a hard time here we go there we go and if you turn your camera back on real quick hey everyone I'm John from um and this was the most like everyone was so professional and focused in the chat like what a great group we've got about 400 students here with us right now um it's been and everyone's really like asking questions about differentiation and then it's spiraled into AP Powerpuff Girls in the final 60 seconds and it was incredible so thank you for for doing that we have a visitor who wants to say hello his name is Marco he's the founder of Marco learning come over here hey Marco he wants to give every AP student a friendly reminder take a seat sit sit sit down give me your PW there we go and his reminder is you are not cooked because all gen Z in the chat is doing their skibby risler jenzy talk and they're saying that they are cooked but they're not cooked they're gonna be fine sit and in fact we're going to give Marco a little treat and you know what's good news is because my other samoy had heard this we get a free Nina sit sit we get a free show with my other dog Mina so both these dogs I want to see some sheeps in the in the emo or Emoji sheeps in the chat for sit down she a sitting she got a one on that exam there we go there we go um but these two doggies they love you they love treats and they know that you're going to do incredibly well in your exam tomorrow so they wanted to say hi give me a PO and they wanted to say you're G to do great tomorrow guys so with that everyone if you like this video press that like button subscribe to our Channel I want to show everyone real quick Melissa just a cple couple of other things that are going on um for AP season this year I pin this to the top of the chat this is the free live online events page which links directly to the physics C reviews we're going to be doing as well as you can see dogs here they're looking they're waiting uh physics C reviews AP English Language world history Spanish language biology physics 2 and physics one for those of you looking for Cal BC we have a review it's right there on our channel for those of you who follow us on Instagram check out all our memes about being cooked and updates about the exams and we hope that you'll join us for these Live reviews thank you Melissa you've been incredible tonight everyone let's give a nice like button and heart for Melissa as we wrap up and Melissa I think your advice is really wise you know so oh hang on there we go this is what they're they're not here for you they're not here for me sit down sit down sit there we go that's a good treat and that's a good treat um it's time to trust yourselves to trust your instincts on this test and do well and I know Melissa that you are an AP uh teacher and reader and you have to live stream with two dogs um and me thank you for everything tonight and best of luck for you all on your AP Cal AB exam thanks everyone good luck you guys