Hello!

I have qualified for USJMO twice, and USAMO once. Currently I am in 12th grade. I would say that AoPS certainly helps, but I never really used Alcumus, as the questions there are quite easy. Currently, there is around 1 more month left 'till the amc10a, and if you want to make AIME, you should start spamming tests as of now. I would say 5 amc10 tests MINIMUM a day should prepare you fine. However, you should make sure you understand the concepts to solving the problems. Furthermore, I would say you should get some AoPS books, the introduction to alegebra being the most important. If you want to make USJMO and above, I would say you'd need the precalculus book, which has much information in it.

Now, often times there is time pressure, along with the difficulty of the problems. I would suggest "ftw" on AoPS to help increase your speed in solving and skimming the problems. Note that amc10 questions 1-10 should take each maximum of 2 mins per question. Questions 10-20 take some time, and usually for me, require around 4-5 min to figure out 17-20. I suggest taking some of the newest tests, to get an idea of the difficulty of the current tests. If you can score a 120 and above consistently on amc10 tests, i would say you are fine to make AIME.

Some important concepts for the AMC tests include but are not limited to:

AM-GM

Cauchy-Schwartz Inequality

Triangluar Inequality

Pythagorean Theorem

Shoelace formula

Menelaus Theorem

Stewarts Theorem

Angle-Bisector Theorem

Basic trig (Sum of sins, cosines, law of sines, etc)

Veita's formula (extended)

Geometric and Arithemetic series

Difference and Sum of squares

Binomial Theorem

Telescoping

Minimum/Maximum value

Basic Log

Abs Value

Floor and Ceiling

Recursion

Advanced Factorial Concepts

Combination & Purmutation

Hockey Stick Identity

Mass point geometry

Stars and Bars

Descartes Circle theorem

Roots of Unity

That is all of I can think of now. These concepts are extremely useful in doing well in the AMC tests. Good luck! :_)