Calculus BC: study advice, please?

[todpose]

Last year I took an AP Calc AB course at my school.. I didn't take the AB exam because of scheduling conflict. Now I'm trying to self study Calc BC and take the BC exam on this year's May. But I haven't reviewed stuff from AB for almost a year, and I totally forgot almost everything. I'm using Princeton Review's 2005 edition book, online lessons, and Stewart's textbook, but I rarely read my textbook except for using it as a source of extra problems.

Could you guys give me tips on mastering the BC material?

I heard that some people who got 5 in AP Calc BC exam didn't do well later in university math and science courses simply because how they got 5 on the exam wasn't because they had a true mastery of Calculus but because they were just good test takers. How can I prevent the same thing from happening to me?

If I try, I can also get 5 without really understanding it, because I consider myself a good test taker just like those I mentioned above. But I don't want to get a 5 with the help of my test-taking skill; I want my true mastery of calculus to naturally get me a 5. Learning it properly now will not only get me a 5 on the AP exam but also help me keep exceling in university and graduate level math and science-related courses later.

I would really appreciate your advice on how I can master the BC material. Thanks!

 

[tkhunny]

Study hard?
Focus?

Who is paying for the exam?

Why not pass the AB rather than fail the BC?

 

[todpose]

I'm paying for the exam.
Why I'm taking BC rather than AB is because BC gives me 3 additional credits.
I'm certainly not going to fail the BC. I'm confident that I can get at least a 3, but I want a score no below than 5.

 

[Count Iblis]

From my own experience, I can only advise you to forget about high school level courses (they are too simple and keep students dumb), buy university level books and study math from these books. When I was 12 years old, I studied math from my father's engineering textbooks. At age 15 I had mastered calculus at approximately second year university level.

The key to understanding math is to understand things from first principles. Don't look up integrals, series expansions etc. but take your time to derive them from first principles. By doing problems this way you practice not only the problem itself but all the other important techniques. Make a habit of writing down the problem you want to solve on a blank sheet of paper and then close all books.

Sometimes you'll find that you really need to look up something. That then means that you don't know enough about that thing you needed to solve the problem so you should study that thing.

You should only look up things (e.g. to save time) if you know for sure that you could derive it yourself from first principles.

 

[Count Iblis]

Lack of time can be a problem. But when people are still in school they have more than enough time to study.

 

[todpose]

Count Iblis: Thanks for your advice. But I'm not sure on one thing. You said that I should only look up things if I know I could derive it from first principles. I don't quite understand what you mean. Could you elaborate on that? One more thing-what do you mean by "first principles"?
Thanks so much.

 

[Count Iblis]

Count Iblis: Thanks for your advice. But I'm not sure on one thing. You said that I should only look up things if I know I could derive it from first principles. I don't quite understand what you mean. Could you elaborate on that? One more thing-what do you mean by "first principles"?
Thanks so much.

To give a simple example, suppose you solve a quadratic equation using the "abc" formula. Then it would be wrong to solve many problems using that formula if you don't know how the formula is derived. By deriving something from "First principles " I mean from "basic facts" that you know very well.

When you study maths make sure that you can reproduce everything you learn if you were locked up in a room with nothing else than paper and pencil (given enough time, of course).

Some examples:

Do you remember why the derivative of sin(x) is cos(x)? If not then try to understand why this is the case using the definition of the derivative and the definition of sin(x) and cos(x). You should do this even if you don't need to know it to pass your exams.

Have you ever wondered how general third degree equations are solved? If not then why not look it up on the internet? You'll find that you need to use complex numbers to be able to fully understand the solution. You don't know about complex numbers? Then read about complex numbers! Don't limit yourself to whatever the current courses you follow require from you!