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"Paper" is a strange term. Math "journal article" is probably more accurate. Basically, what you do is give a brief history of the topic you're covering, some necessary definitions and lemmas, exploratory argument, and usually finish with a proof and its corollaries. Math "papers" are strange objects; so are pure science papers, which have the same format.

They are great classes for me. 4 tech classes and one humanities? Heaven. And the courseload is easier than this semester by far. Speaking of which, I have problem sets to work on...

::pat pat:: it's okay. I'm sure you'll do fine. Besides, the main test is the AP test, aye?

On a (half-)related note, I started studying for the math GRE today. A full 50% of the test is based on Calc I, with another 10-20% being on pre-calculus notions. With a couple months of studying basics, I should do well (except I tend to be bad at basics sweatdrop )

It's 'cos the easy stuff was just so long ago. I totally forgot conic sections even existed. I think there's only a scant amount of information on the test that I haven't at least been introduced to - namely point-set topology and number theory, from what I've seen - but a LOOOOT of topics I've forgotten about. Related rates, conic sections, polynomial factoring, slope fields...etc.

So, conic sections you should know. They're the intersections of planes with a double cone: parabola, hyperbola, ellipse, circle, line, and point. Basically, know the equations for all of those. Slope fields may or may not still be part of the calc AP test...you'll get to it eventually, maybe. It's a way to visualize what the implicit derivative of a function looks like, and allows you to integrate them a bit better.

Well, the conic sections are easiest to see with a diagram. But you know of all those geometric figures, right? Parabola, hyperbola, ellipse? I can almost guarantee that you do.
http://mathworld.wolfram.com/ConicSection.html
The implicit derivative is a way of working with non-separable equations, i.e. ones that can't be written in the nice neat form f(x) = y (like x^2+y^2=r^2, since you have to write two separate functions describing the circle, and the derivatives on neither side look pretty). Actually, let's take that example:
x^2+y^2=1 ==> y = (1-x^2)^(1/2)
dy/dx = y' = (d/dx (-x^2))/(2*(1-x^2)^(1/2)) = -x/(1-x^2)^(1/2)=-x/y
and similarly for y= negative blah blah blah. With implicit stuffs, still using dy/dx = y',
x^2+y^2 = 1 take the derivative on both sides:
d/dx(x^2) + d/dx(y^2) = d/dx(1)
2x + 2yy' = 0
y' = -x/y

No mess, no fuss. Slope fields then allow you to do that kind of implicit differentiation and then find approximate integrals of those equations. Or, more accurately, they allow you to draw graphs of initial-value problems - those that give you an equation like xyy' + y^3 - (y')^2 = 4 and y'(2) = 3, y(1) = -8 - without needing to solve for y' or find y. Trust me, if you don't know implicit differentiation and slope fields now, you'll know it by the end of February. If I remember right, it's a huge part of the AP test and an even bigger part of being able to use calculus in sciences.

Whoot! I'm on break!! That means I have 3 weeks to study for all my exams and the GRE and do Christmas shopping and clean up the dorm and write a paper and...grr. Maybe it's not so good that break is here already.

Oh, that's kewl. Are you doing the second semester? I don't know if slope fields are a common topic in college...they really are kinda useless. But implicit differentiation is a simple extension of regular differentiation and so insanely important in being able to actually *use* calc.

How'd the final go?

It depends on what they cover in Cal II. It feels kinda strange, 'cos I took it as an AP class, so it was divided into 3 "semesters": limits and differentiation, integration, and "special topics" (integration techniques and reparametrization). But all three in college, I thought, were done in calc I and II, 'cos when I took calc III, it was multivar. It just feels kinda wierd, y'know?

Pfeh, you'll do fine. Just keep the textbook and look back over it during summer; chances are even the people who take calc I next semester are going to forget a lot over the summer, too.