<p>Be able to derive double angle formulas and the like (those are used a lot), be good with triangles. Just get very solid with the basics, and you’ll be ahead of the game. I didn’t have formal training, and it seemed like most of the competition was just spit out by the system anyway. If you’re astute, you’ll learn what’s necessary in 1/4 of the time yourself.</p>
<p>As for what calculus actually is, I recommend again getting your hands on thinkwell calculus. It will teach you, to about 40%-70% depth, most of the topics covered in both differential and integral calculus.</p>
<p>If you’d like a generalization now:</p>
<p>Differential Calculus (cal 1): Looking at a system and finding how it changes instantaneously. Shrinking everything you’ve learned in math down to an infintecimal level, so you can use it in real life situations (or abstractions), that change frequently.</p>
<p>Integral Calculus (cal 2): Same thing but in reverse. Look at how something is changing, and from that, derive the thing that’s changing. Uses the same process but in reverse. Requires intuition to be good at (or if you’re asian…I’ll get back to you on that). Most easily understood as finding position from velocity, or velocity from acceleration. Many cool applications (being able to find the areas or volumes of funky shapes by adding up small pieces of their volume).</p>
<p>Newton invented calculus so that he could then invent physics (glorious ■■■■■■■, wasn’t he?). It’s where math starts seeming very powerful, and rightfully it should. Everything from the industrial revolution onward has been made possible by calculus.</p>