University of North Dakota
From over 16 years of teaching experience, he has philosophy that it takes humor, patience and understanding when teaching tough subjects.
University of North Dakota
From over 16 years of teaching experience, he has philosophy that it takes humor, patience and understanding when teaching tough subjects.
My name is John Postovit and this is advanced placement calculus AB. In this course we're going to cover a ton of stuff. We're going to do the problems involving the basics of calculus. And we're also going to do problems involving those strange theoretical things that you'll definitely see on AP test. You can use this of course in a couple of different ways. You could use it all year long as a supplement to your regular calculus course. I have a lot of episodes where I do lots of problems involving things like the chain rule, things like finding areas between curves, finding volumes, all sorts of the essentials that you need. Or, maybe using this course at the very end of the year in that last month or two while you were leaving for the AP test. Either way, I first recommend that you go to the bonus materials, down with the follow alongs.
The reason I want you to do that is because, I often do a lot of writing and you have more coordinated, organised notes if you're writing them down and can look at the tips and the hints and the problem itself, without having to madly scribble that down. You can just concentrate on taking good notes for yourself. Of course you can always stop the video to give yourself a second to catch up.
After you watch every episode, I'd also say that you ought to try the extra practise problems. I've written up a bunch of practise problems along the lines of what I show you during this course, so that you can try two or three of them on your own.
These practise problems also involve the solution including every step, it's probably first it'll do that sometimes that the calculus text book will say, "Well okay, here's a problem. Do this problem and there is one example, and by the way we left out a bunch of steps because you're just too smart to need all the steps." Well I'm assuming that you're like me and when you were taking calculus, sometimes I didn't see those steps that were left off. And I had to think how did they get from there to there. In my extra practices, I've tried to show you everything. Well settle in, relax a little bit, and I hope you enjoy the course.
Before you walk into the room on that fateful day where you're going to be a total success on the calculus test, you need to know how it's organised, so that you're prepared and ready to go. Sections, questions and time. Tests are broken up into two large sections. The first large section is multiple choice. The second one is free response. Each of these two sections is weighted the same. So you get an equal amount of credit for multiple choice and free response on the whole.
When they score it, they'll score this part, they'll score this part, add up the results and then compare that to their standards for what's considered a one, two, three, four or five on the test. Depending what college you go to, you'll need a three or a four, or sometimes even a five in order to get credit for moving on to the next level of calculus. The whole test takes 3 hour and 15 minutes and that doesn't include the fiddling around time for passing out the test, reading the rules, collecting the tests and all of that.
Now within each part of multiple choice and free response, there is two subsections. So when you get the test, the first thing they'll tell you is, "Put your calculator away." And they give you part A. They say, "Do this part A and when your done stop. Put our head on down and just sit soundly."
Then on part B they'll allow you to get your calculator out to do just part B. Well, look at the timing on the number of questions. Part A, 28 questions in 55 minutes, that's about two minutes a question. Part B, 17 questions, 50 minutes, that's about three minutes a question. That should tell you something right there. They're allowing you more time because they think you'll need it.
Part B is more likely to have some unusual theoretical problems that might have to pause and think about just to organise your thoughts. And part A will tend to have the more straight forward ones that don't require a lot of calculations, or they're fairly direct derivative, chain rules, that kind of thing.
A little bit of strategy, you might have felt, go through the test first and decide which problems to do. I wouldn't recommend that because of the amount it takes. But I'd recommend something very similar. Look at question number one, and if you immediately think you know, "I think that's more than a two minute question." Circle it and then go on to the next one. Then you can go back later to those harder questions that you circled. The reason I recommend that is because hard and easy, on multiple choice they're all worth the same. So you don't want to spend a time on a hard question when you could be knocking out some of those thirty second questions.
Go back later to finish the harder ones, same thing for part B of the multiple choice.
Free response, you're allowed a total of 90 minutes and that's broken up into two sections. The first part takes a calculator. So after you finish this they'll let you keep your calculator. The second part doesn't and there is only three questions for each part. What that tells you is that, each of those three questions has a lot of subsections. So there may be four or five things you need to find for each of those questions. But still, I would recommend the strategy of looking it over first.
Now this, since they are only three questions probably is worth reading each question and deciding which one to do first. You want to do the one first that you immediately know how to do. Then say you're going through one of those questions and you get to the second or last part and you think, "I don't know how to do that." Think about it for just a little while, but not too long. And if you can't do the last part, that's okay. It's free response and you get credit for each sub-section that you do of each question. And actually within each sub section there is different things they are looking for. They'll be looking for having the integral written up properly, looking for some of the details, the solution etcetera. So remember you can get partial credit, don't panic and give up. If you can write something down that you think can makes sense, do it. 15 minutes a question so that's a lot of steps.
Now after you've done this 45 minutes they'll say, "Stop," to have you put away your calculator. Then for the next 45 minutes, you'll have part B. Three questions again, tend to be questions that don't allow a calculator. Which means that they tend to be more theoretical questions where you'll have charts to work from or with the calculations are very simple. Whereas part A, with the calculator, will often have integrals that you can't do by hand, and where you'll have to approximate the solutions by using some of the functions on your graphing calculator.
If you finish the three questions on part B and still have some time left, they're going to let you go back to part A, on the free response section only. They won't let you have your calculator back because no one else in the room will have one. But at least you can go in and maybe fill in some more of the theoretical parts and almost finish some of the problems that you're asked to do in the calculator section.
Now that I've shown you how the test is organised, I'm going go to show you some general strategies for preparing for the test and for actually taking the test.
I'm going to begin by covering some basic strategies that can really help you earn high score on AP test. First strategy, go back and review. That's kind of vague isn't it? So I want to give you some specific hints on how you could do that.
First thing I would recommend doing, is going and finding all your old tests. Find the problems that you got wrong the first time, that's what you should concentrate on. Look at the problems you got wrong in the first time, and then stop and think, "Do I know how to do this now?" If you do, then don't spend a lot of time on it. Just enough time to remember how it works. Go back and review.
The reason I'm saying this is because in order to score well on the AP test, you really have to know the calculus. You have to be able to do the basic operations like differentiation and integration, and even things like chain rule, which is fairly basic. You have to be able to them instinctively. So you don't have to concentrate on how you do that when you're trying to figure out what the problem is asking for. There are a lot of problems where it's not entirely clear what they want. There are a lot of problems where it'll say do such and such, find the rate of change of an integral. It won't just always say, "Here is something integrated." Sure you have some of those problems where you just do an operation, but knowing how to do those isn't enough.
Next, do the official AP practise test. Of course before you do that, this course is designed to get you through that stuff. What I've done is, I've gone through the officially released course description which includes, multiple choice questions and free response questions. And I've modelled a lot of what I'm teaching you on what they are asking you there. And sometimes I've taken it a step beyond.
Once you've done that, then you'll want to do the practise problems that I give you, so that you get these down a little bit better. And then go do the official test, which is going to have a lot of similarities. Take that official test, try to figure out which technique you are using. You might even want to go back and say, "Hey! What episode was this on?" And go through it. It's really important to do the AP practise test.
Next thing you need to do, is be really strategic on the free response section. First off, the problems are weird. They are seriously weird problems because, the AP people want to find out if you really know calculus, or whether not you're just parroting a bunch of operations. So they've put in questions where you have to know the theory behind calculus, and you know how to be calm and collected. To read a problem and realise, "Well are they asking me to integrate it, or to eliminate some or do the derivative. Just what are they asking for?" You have to be strategic on it.
Also, while you're doing the free response section, you have to make sure that the scorer can read what you're doing. That's actually humans that grade these. The way it's set up is, the AP people hire calculus teachers to come in during the summer and grade your test. Now, they are given really strict guidelines on how it should be graded, how many points you get for each part. Do you notice I said each part? yeah. Because you get points for everything that you do right. But there is a lot of particularities that they look for.
For example, if you're not using correct notation, you're probably going to loose some points. If you skip a detail at the end of an integral like putting the constant integration, that's right.
One of the points that you can get is actually for just writing plus C at the end of the integral. Make your writing clear. Again these are humans that are grading this. If they can't read what you did, guess how many points you get? Zero. That's right.
Also since you're under time constraints, you want yo page through the entire section, that entire section that you're allowed to do at that point and see which problems you can do first, most quickly. Otherwise there's chance that you might just sit there looking at a problem and then your head gets filled up and starts buzzing and you start thinking, "How do I do this one?" You panic, and that actually makes it harder for you to do the easier problems.
Last thing, if you're doing the test and you suddenly realised, "You know what I made a big mistake." Don't spend time erasing. Cross it off, it's faster to cross it off, and the AP scores are told if something is crossed off, they just ignore it. So be sure as you're going through the course, to follow along with how I model the ways to write out problems.
Guess, guessing is evil. I think so but also, one of your goals of course is to pass the AP test, and there's no way you're going to get every question right. There is no way. Some of the multiple choice questions will have often 70-80-90% of the students who take the test will get those right. There are other questions where only 20-30% of the students taking the test that year, get that one right. And that doesn't mean that they qualified the question, not at all. It's still included.
So be prepared, there is going to be some that you just can't do, and that's okay.
Because they don't really compare you against you know, "Did you get 90% on the test? Did you get 90% right and you can't pass unless you get 70% right." That's not how it's done at all. It's a normed test. What they do is research on students actually taking the test, and they look to see how an overall very large group of students does on the test. And then they figure out what the passing score is and 70% probably isn't a passing score, it's probably lower than that. That being said, guessing in the multiple choice, you don't want just to randomly guess. Sorry they see it coming on that one.
If they didn't correct for guessing, you would score a little bit higher than you should. Because there is five possible choices and if you guessed on every one, you would probably get a 20% on the test and they don't want that to happen. So what they do is they give you one point for every question you get right on multiple choice. They give you nothing for something you leave blank, notice I said leave blank. It's okay to leave questions blank. If you put an answer down and it's wrong, they take away a quarter of a point.
On the average by doing that, the statistics show that if you take a quarter point off for everything that is wrong, it balances out the results of guessing. But still it doesn't mean that you can't guess sometimes. If you can narrow down a little bit and you know that say, two of the possible choices are obviously bogus, and you know it's one of three. Make an educated guess on those one or three, because the odds are a little bit in you're favour at that point.
If you're an old school guy like me, you've got to be told this one, use a calculator when possible. I grew up in the dark ages of slide rules. So I don't instinctively think of calculators.
Or maybe you're a mathematical tough guy, you can do algebra all day long and you're right every time and yo just hate using that calculator. I'd still recommend you do it, when you're allowed to do it. The AP test has basically four sections. There is multiple choice with the calculator, multiple choice without. There is free response with the calculator, free response without.
Especially on the free response part, that involves the calculator, if you don't have a calculator you can't do it because you will be given crazy integrals that you can't integrate by hand. And you don't even want to do that many steps on it by hand, you want to do as little as possible by hand.
For example, later on the course you'll see some problems where I set up an integral and then I don't even try to integrate the thing. What I do is I type it in undistributed, I type it into the calculator and let the calculator find the area underneath that curve. Notice I said undistributed. I know it's instinct because you've done it for years, you always simplify. But you don't want to on this, because the calculator doesn't care if you simplified, as long as you use the correct number of parentheses to make the calculator understand the order of operations. Simplifying just increases the chances that you make some kind of an error.
Finally, when you are using the calculator on the free response section, you have to be careful on how you write down your answer. Part of the required answer is going to be set up for the problem. In other words a correctly written derivative or a correctly written integral or a graph, something like that. You have to write that down, even though you get final answer with your calculator, you have to. If you just write down, "I pressed this button on the calculator and then I pressed graph then I pressed second calculate integrate and got this answer."
Sorry, they're not going to give you any credit for that. They don't care what brand of calculator you use. There is lots of good brands are out there. What they care about is that, you know how to write it out in technical form, write out the calculus with all the correct symbols and then get the answer using whatever calculator you have, and they don't care about those steps.
The functions you should really know on your calculator are finding zeros, usually by using a graph. Finding approximations for intersections between lines, that's a very important one, especially for finding limits of integrals. And finding the area underneath curves. Usually as you use that one, you have to find an integral but find the area underneath a curve for some formula that you can't integrate.
So what you've seen as some strategies for both reviewing for the exam and actually taking the AP exam.
Our introductory episode began with giving you some strategies that you can use to get ready for the test, to really solidify your knowledge for the calculus. Along with some hints that you can use during the test to increase your score, to format your answers in a way that you're going to get maximum credit on it.