Reviewing for Calculus

[Helanna]

I have a bit of a problem.

I am enrolled in AP Calculus, which means that in May, I'll be taking a test. If I score a 4 or 5 (out of 5), I'll get full college credit for the course. If not, I'll retake calculus in college.

The problem is that my entire class is absolutely screwed. I don't think there's anyone in the class that'll pass. And to be honest, I think a lot of the problem is the teacher. I like the teacher, and he's not bad at teaching, he's just not very . . . efficient. For example, we're taking a practice test right now. None of us can do literally half the questions because we're more than halfway through the course and none of us even know what an integral IS.

So it's basically up to me to teach myself/review enough calculus in time for the test. I'm trying to go through my notes from class but I really just don't understand a lot of them.

So does anyone know of any good websites that review/teach calculus? Any help would be greatly appreciated, because . . . I don't want to retake calculus . . .

[Starscream]

In college I had the worst calculus teacher ever. She never did examples, only proofs. She made glaringly obvious mistakes, and never noticed them unless they were pointed out. She took any opportunity to drop what she was talking about and babble about her children and pets for the whole class period.

In short, she sucked. One of the other Calc teachers actually sent us an email on the sly saying basically "we all know that your professor is...difficult (read: incompetent) so if you want to attend my lecture (which is at the same time) and only show up to hers for tests, I will conveniently not notice that my class has doubled in size."

So that's what I and about a hundred other people did. But it didn't help that we were about 3 weeks behind in a ten week course at the time, so I needed to teach myself some stuff as well. I bought a book of examples from a store, visited a tutoring room a few times, and did a lot of looking things up online.

You can find examples for any sort of calculus concept in abundance online. I'd just look through your textbook and google the topics you need. It's faster than a classroom anyway.

[averagejoe]

:smallcool: Did somebody say reviewing for calculus?

I don't know of any good web resources (at least, not that are good for anyone just learning calc) but my personal services are always available. I have an IM, but I always tend to forget to go on, so it would probably just be easiest to PM me to set up a date/time. Or just communicate through PM's. Whatever works. Point is, I'm always up for answering these sorts of questions.

[Tirian]

Oh gosh. You should be talking to the department head or the principal or the school board about this, because this guy just essentially cost you all $3000 from having to retake the class. Grrrr. I don't know if the administrators didn't see this coming or if it happens every year and they don't care.

Problem is that you're not reviewing the second half of Calc AB but learning it. And I don't mean to sound pessimistic, but integration is the hard half. Differentiation is "plug and chug", but solving integration problems is more of an art. Then again, I don't think a 4 on the AP is an impossible challenge even if you don't understand every question. That's exactly what happened to me when I took the CompSci AP. If you can get even halfway through integration and be able to solve those questions dependably, then I think you're a lock to pass.

If you don't have a calculus textbook, you should get one. This should be remarkably cheap, because you don't care about the latest version. The tenth edition of what us old-timers would call "Thomas and Finney" (although Finney seems to be delisted now) costs $150, but the previous edition (http://www.amazon.com/Calculus-Analytic-Geometry-George-Thomas/dp/0201531747) is $9. As you can imagine, the mathematics of freshman calculus hasn't changed in two hundred years. Or you can find a sibling of an older friend or a parent who didn't throw out their college textbooks.

Another good resource (and this is awesome for everyone) is MIT OpenCourseWare (http://ocw.mit.edu/OcwWeb/Mathematics/18-01Fall-2005/CourseHome/index.htm). These are lecture notes, homework assignments, and tests for MIT's Calc I course. There also seems to be video (http://www.youtube.com/watch?v=jbIQW0gkgxo) of the lectures.

And, of course, you've got a forum full of teaching assistants here if there's stuff that you don't quite get even after reading it three times. And that's not unusual even in the best of teaching environments.

[averagejoe]

And, of course, you've got a forum full of teaching assistants here if there's stuff that you don't quite get even after reading it three times. And that's not unusual even in the best of teaching environments.

Hell, I absolutely struggled through high school calculus like I'd never struggled before, got a 3 or 4 on the exam, then breezed through all the other calculus I ever had to do ever. Math is one of those things where you struggle for a long time until you can't remember why you ever thought it was hard.

[The Extinguisher]

Honestly, I don't even remember doing integration until the last month or two in my high school calculus class. The focus was on differentiation and limits. Which is also generally what most beginner calculus courses in university are as well.

So you should be okay. Maybe.

[Quincunx]

First, get together with your classmates--and if this teacher is as far behind schedule as you say, they ALL have a vested interest in this, friend or foe--and teach yourselves the bare bones of integration, pronto. There's no way you'll even get a 4 on the AB without that. I will hope that your teacher is plodding because he's ensuring everyone knows everything about derivatives, so don't waste your time on rehashing your notes unless there's something specific to pry out of them. Go forward instead and devour everything that class isn't presenting.

If integrals come easier to you than derivatives did (and they might, I can't guess at your mathematical style), lunge as far forward in integrals material as you can in the time remaining, and when the time comes to sign up for AP Exams pick the BC; that'll guarantee you more questions about integration and a sub-score as though it were an AB exam, two chances to impress instead of one. This is an unlikely and risky strategy, but it did work for me as far as accumulating AP credit goes. (I confess it didn't work quite so well being vaulted into Calculus III in the first semester of college, but you implied you'd like to not take calculus again ever.)

[TheLogman]

I'm taking a CHS Calc class right now with a local University.

The class can be difficult, but not terribly. You just need to remember the following stuff:

0. Algebra. Though you didn't learn much Algebra if any in this course, it's arguably one of the most important parts of Calculus. Often, my Calc teacher will do a problem that takes up the whole board, then point to a little point in the middle and say: "There, that's the calculus. That's where we took the derivative. All the rest was algebra. So, make sure you know and are comfortable with Trig, volume formulas, logs, and the special laws of each. If you can make algebraic equations dance, then it's much easier to do Calc.

1. Limits. These are easy. Just know the laws of limits. They form the basis of Calc.

2. Derivatives. You'll probably have to know how to find them the "long" and "short" way. The "long" way is using the definition of derivatives, which IIRC is f(x-h) - f(x) all over h, with the limit h->0, is time consuming, but good to know. The short way is your typical "Reduce constants to 0, reduce exponents by one, multiply the coefficients by the previous exponent". Then you just have to remember the laws of derivatives. Trig identities and inverse trig identities, the laws of exponents, and the logarithmic identities. If you can familiarize yourself with what the derivative of all that is, get a good handle on the chain rule, and then finally know how to use the derivatives to do things (Optimizing area or volume, finding concavity and the like of lines, that kind of thing), then you have a great handle on the first half of the year.

3. Integration. This is not THAT hard. Though it seems complex at first. It took me a few days just to GET why the dummy variable becomes important when you start doing differential equations. Just remember the Inverse Chain Rule, familiarize yourself with what things look like after you've taken the derivative of them. Learn the applications. Some tests may require you to be able to use Homer's Rule, the Trapezoidal Rule, or LRAM, RRAM, and MRAM (The precursors of Integration, they find the same things, just way slower and less accurately).

But as a previous post said, Integration is really an art. You just have to develop a knack for knowing how to make the formula dance until it becomes workable. And that's something that's developed from just a familiarity with the laws of algebra and a good sense of what derivatives look like.

If you have a textbook, get it out and do practice problems. Do a TON of practice problems. If you miss something or get it wrong, check with a friend. See how and where you missed something. Redo the problem, doing it correctly this time. If you don't have a textbook, get one. Do problems from it.

Calculus is not an art that as far as I can tell, rewards much memorization. You really just have to be comfortable with it. I hate to say anything bad about a teacher, especially one I don't have, but learning proofs will not get you through Calc. Practice will.

[hap_hazard]

What does the AP Calculus syllabus cover? If its close enough to mine I could try to find my notes.

[ForzaFiori]

I'm in the same class right now, with an amazing teacher. If you have any questions, feel free to PM me, and if we haven't learned it, I can either check for it in my book, or ask my teacher.

[snoopy13a]

What does the AP Calculus syllabus cover? If its close enough to mine I could try to find my notes.

I believe it is Calc I and II in College. Essentially derivatives and integrals.

I took it a long time ago, in a school far far away so don't take my word for it :smalltongue:

[Deathslayer7]

I'm with averagejoe on this one, except my time is a bit more limited. The essential thing are the following.

Limits
Derivatives
Integrals

now within each of these are multiple subsets which you also need to know such as the fundamental theroem of calculus.

If you any other math teachers ask them for any calculus based tests.

and if you are really committed do this:

email this teacher: [email protected] and explain your situation to her. If you can convince her that you wish to study, ask her if she can send you practice tests of any kind. She was my calc BC teach (very very very excellent!) and got me a 5 on the BC and AB calc AP test. Tell here that your currently in AB and have a incompetent teacher and ask her if she can do anything for you. Tell her that you want to apss the AP test. Be specific. She can't help if you generalize. Ask her what's on the test, how to study, etc.

and tell her David Fyda sends his best wishes and we'll try to stop by when he can. :smallsmile:

Calc I = Calc AB in high school
Calc I and II = Calc BC in high school

note: this teacher is sentimental to me. don't be an a butthead to put it nicely. :smallannoyed:

[skywalker]

I believe it is Calc I and II in College. Essentially derivatives and integrals.

I took it a long time ago, in a school far far away so don't take my word for it :smalltongue:

At my University (which is fairly standard), a 3 on Calculus AB will get you credit for "business calculus," or "take this if you're not a science or finance major." A 4 will get you credit for calculus 1. A 3 on BC will also get you credit for calc 1. A 4 on BC will get you credit for calc 1 and 2. A 5 on either gets you honors credit for what a 4 would've gotten you.

[u-gotNOgame]

If you feel that your that far behind just don't take the test in May. They can't force you to pay the 86 dollars... The other thing is that somethings in calculus just "click" the first few times you see an example it isn't always obvious what your supposed to do with it, this is doubley true if the teachers style is either not how you learn or they simply cannot teach. I know that it sucks that you will probably have to pay to take it again but you'll be ages ahead when you see it for a second time, even if you didn't really learn it the first time.

-UGNG

[Schlega]

I don't know about websites, but a book I found helpful when I was learning Calculus was 'Calculus for the Practical Man' (http://www.worldcat.org/oclc/295009277). It doesn't have anything resembling mathematical rigor, but I don't remember any proofs coming up on the AP test.

[hap_hazard]

I believe it is Calc I and II in College. Essentially derivatives and integrals.

I took it a long time ago, in a school far far away so don't take my word for it :smalltongue:

I'm in another country, dude. What's in Calc I and II?

And these two (http://www.calculus-help.com/) sites (http://www.calculus.org/) may help.

[Fortuna]

So one thing that might be helpful is to know what you actually know, so that filling the gaps without going over what you actually don't need filled is easier.

Also, that must suck. Funnily enough, my high school (accelerate) calculus teacher is like that, but still gets something like 1.25-1.5 times the GPAs of the other maths accelerate teacher. Last year she had a year eleven (Third-to-last year) taking NCEA 3 (last year of high school) and getting a stream of Excellence (top 10% of those sitting) and one Merit (top 25% of those sitting). And she still finds time to talk to us about anything and everything apart from maths.

[Helanna]

Huh. I started replying to this, and then I just randomly forgot about it.

Well thanks for all your help, everyone! I think a few of the websites listed will really help, especially MIT's website. I had no idea that they had free notes and stuff, so that's pretty awesome. I'll probably end up checking out a bunch of their classes, actually.

And anyone who offered private help, I may or may not have to take you up on that, I'm not sure yet . . . I guess I'll see how it goes.

One thing I wanted to point out is that my teacher is not necessarily incompetent, but just kind of inefficient. Also my Pre-Calc teacher may be partially to blame - the first week of calculus, everyone got very frustrated as my teacher was angry nobody seemed to be picking up on the concept of limits, and my classmates were angry that he was barely even teaching them. It took us a while to figure out that he was assuming we had already gone over limits in Pre-Calc, which we really didn't . . . now that was an incompetent teacher.

But I think this will all really help. I often forget/never actually grasp the basic concepts anyway, so if I can just go over some clearly-written notes and whatnot, I think I can get through this.

[Warka]

I'm in precal right now and in the same boat as you as far as the teacher goes - this website is really helping me out:

http://mathworld.wolfram.com/

For most part the only help I can offer is to do all the problems available to you, and look up every single word you don't immediately recognize and write it down.

Good luck!