Hello to everyone!
I am a greek high school student (11th) and my dream is to study in the us. However, I need a full financial aid package. That’s why I want to get admitted in mit, Harvard, penn, yale, Dartmouth, Princeton, Amherst or Columbia, as they all offer need based aid. I calculate my gpa around 3,9. I have Cambridge proficiency, Sorbonne b2 at French and Goethe b1 at german. I was 3rd in the Pan-hellenic astronomy contest for junior high students and 3rd girl in my class in the Pan-hellenic chess tournament. I was amongst the winners of Pan-hellenic physics contests the last 4 years ( also went to a physics summer school) and last year I was also amongst the winners of maths contest. I passed the test of cty Greece but didn’t attend the summer programme (maybe i’ll go to some weekend programme). I played basketball and chess for 5 years and table-tennis for 1, participated in some tournaments, too. Of course, I will participate this year in a lot of contests and I aim to make it to the astronomy Olympiad. I haven’t given sat yet, but I think that I can get pretty good grades. I don’t know if there is any chance of getting in any of the universities that I mentioned, even if I have perfect sat. So, I wonder if taking the sat test at all is worth it. Do you think I should go for it or it is a waste of time? Please, help!!!
Many of the colleges you mentioned require that you take the SAT (or ACT).
But I plan to write sat. I just worry that i will study for nothing, because i dont know if i got any chances of getting admitted, even with 2400
It is very, very difficult. And getting a 2400 is very rare even for native English speakers. Astronomy Olympiad accomplishments could help if you also get great test scores. Note that junior high accomplishments aren’t reported on US college applications. One approach would be to get the SAT preparation book supplied by the CollegeBoard (company that gives the SAT) and try some practice tests. If your results are very strong, then it could be worth moving forward.
American universities will want to see 2100+ (often, even 2200 for the colleges you’re talking about) on the SAT Reasoning Test, plus a 100+ TOEFL and several Subject Tests (which you should take in June 2016 since it’s the only date you can take both French and German + in May 2016 for Math2 and either Physics or Chemistry). You can take the SAT for the first time this Spring, after preparing very seriously, and once again in October after studying over the summer, in order to increase your scores. Your EC’s are excellent, keep going.
Is there a certainty? None. But you have an excellent record and you want to go. You’d regret it if you didn’t at least try.
If you continue having great EC’s and grades, and manage to get a high score on the SAT, your odds aren’t high, but they’re better than zero. They’re probably about 5% if you apply to Harvard or Yale SCEA/REA. MIT doesn’t allow internationals with financial need to apply in the early round and there’s a cap on how many internationals they admit, with rough limits per region (in your case, Western Europe - you wouldn’t be pitted against Chinese or Indian kids, but against Italian, German, French, Swedish, Spanish, Austrian… kids, and only a handful would get in.)
Applying ED to Amherst may be a better bet considering how high your financial need is - I know this name lacks the “wow” factor back home, but it’s truly superb and better than most universities in Europe.
Anyway you’ll only be able to decide on a college to “ED” if you score 2200, so, let’s cross that bridge when we get to it.
Dartmouth is no longer need-blind for internationals (was wavering about it for the past 2-3 years anyway, so now it’s clear.)
Second, you need to acquire a “Fiske Guide” or " Princeton Review’s Best Colleges". It can be a 2016, 2015? 2014, 2013 edition, depending on what you find online for cheap. In any case, start reading :). Feel free to ask many questions on this forum. 
Third, you must apply to colleges that promise big merit awards, like Temple, UAlabama, MiamiOhio…
You can read Evelynne1996’s story, her first round of applications, and the second one.
You have been very careful, but why have you focused on ED? I dont have chances with RD?
*helpful
Well, Amherst is need blind/meet full need for internationals, and fills a lot of its class with ED applicants. You may well be deferred (most internationals are) but by doing ED you’ll have demonstrated the highest possible form of interest.
Applying ED is only possible at need blind/meet full need colleges for international students who need FA.
The odds for internationals with high financial need, at the schools you mentioned but also elsewhere, are abysmally low. Have you read the threads I recommended?