how to make a calculus 1 reference sheet

Organichu

i'm taking calc 1. so far we've covered: a basic review of algebra 2, expanding polynomials, rationalizing radicals, analytical geometry , etc.. then we covered basic functions, exponential functions, some trig stuff, composite functions, and inverse functions. we're currently covering an intro to limits (generally and from either direction), the squeeze theorem, vertical asymptotes, etc.

we're permitted a single cheat page on the test. i figure 'write small, write organized' are givens, but i'm looking for suggested content. right now i'm thinking:

-form of logarithms, base, powers
-trig identities
-a few small, common graphs (x^2, 1/x, sinx, etc)
-theorems regarding how to combine the limits of multiple functions, and how to evaluate limits w/ constants
-basic properties of commutativity, additivity, distributivity, etc, contextualized for rationals (since algebra's a weak point of mine)

what else would you guys consider 'must have' for an exam covering this material? fwiw i'm not permitted a calculator.

Jimmy King

Here's what my calc1 teacher has said we'd better know and has used some of on our first test which sounds like it was over about the same material... and I don't get a cheat sheet, all memory. blargh.

On top of what you've already listed:
-pythagorean identities
-cofunction identities for sin and cos
-sum and difference formulas - sin(a +- b) and cos(a +- b)
-double angle formulas
-Power reducing formulas for sin^2 and cos^2
-the unit circle (my calc 1 teacher loves to thrown in cos(pi/2) and tan(3pi) and whatnot)
-I don't have a better name for these: "special limits", which would be sin(x)/x = 1 and (1-cos(x))/x = 0, both ONLY when x -> 0
-Possibly how to recognize and test for even/odd functions

Other than that, just do lots of algebra to practice. That's really been the hardest part of my class so far.

Organichu

dang it sounds like your material is much more trig-focused than mine. it's rare that we're given problems with trig functions in them.

Jimmy King

Must be nice. My teacher has the attitude of "You took a math class covering the material before you took this one, so it's fair game for me to include." I guess it's good, I'm learning a lot and re-learning a lot that I memorized once and then forgot. The challenge being that not every teacher actually taught all of these things in the previous classes.

Sentry

for the love of god, don't skimp on trig. If your teacher doesn't include it then do problems from your book with them in it, especially if you're planning on going to calc 2. Trig substitution will destroy you if you don't.

That being said, a lot of it is really easy if you just use it over and over again. learn the unit circle, it will be a big help. learn the basic trig functions, but also learn the inverse functions, arctan, arcsec, etc... and know what the graphs look like.

Also, the last bit of advice I'm going to give for cacl 1 comes to min-max and rate-of-change problems... never forget what you're looking for. I know that sounds simple, but you'd be surprised how easy it is to get lost in the forest when it comes to those rate-of-change problems.

oh, yeah, you'd also better know your log rules. e^x and ln x are soon going to be everywhere... including your dreams.