This year I am going to participate at the Astronomy Olympiad, in the beta group (seniors) - 15 years old or above. I have already participated at this Olympiad in the alpha group (juniors)... now, a year later, I am going against 12th graders that know superior mathematics, such as derivatives and integrals. From a quick scan on some problems, I've seen that these mathematical concepts do appear... Since I do not have all the adjacent theory (limits etc.), I supposed I should learn some basic properties and see how can I apply them. My goal is to know how to read a integral, or how can I put it in an easier understanding form. So... What should I know about these derivatives and integrals? Which properties do apply in astronomy? I really appreciate all the help that I can get. And sorry if my question was a little dizzy... I hope it's alright, though.
Thank you for taking the time to read this!
Edit: For narrowing, I would love some websites that have only a few properties useful in mechanics.