<p>I thought I was a halfway decent math student until I saw how tough AIME was. How does one get better with this type of thinking? Are there any formulas/theorems needed that aren't taught to the mainstream public? Also, does anyone have copies of the AIME and AMC 12 from this past year? If you could e-mail me those questions it would be greatly appreciated.</p>
<p>Like everything else: Practice with adequate resources. Try the Art of Problem Solving books.</p>
<p>You can find a lot of the old contest problems(AMC, AIME, USAMO etc.) from here - <a href="http://www.artofproblemsolving.com/Forum/resources.php?c=182%5B/url%5D">http://www.artofproblemsolving.com/Forum/resources.php?c=182</a></p>
<p>And there usually aren't a lot of formulas or theoroms that most people who do well on these contests, that otheres don't. The more important thing is to figure out how to derive formulas and theoroms, and understand why they work, and not just how to use them.</p>
<p>But if you want a really great resource, get the last two books listed here - <a href="http://www.artofproblemsolving.com/Books/AoPS_B_Texts.php%5B/url%5D">http://www.artofproblemsolving.com/Books/AoPS_B_Texts.php</a>. And even though they say the first one is for grades 7-10, you should still get both, since the first one is still a great resource, and will probably teach you new things about stuff you already know (at least, it did for me).</p>
<p>"contest math" is basically all the cool stuff that normal school curricula don't leave out. it's really sad that the curriculum in america is like this :(</p>
<p>you'll definitely want "The Art of Problem Solving" vol. 1 and vol. 2 by Lehoczky and Rusczyk. A lot of the problems are hard, so it's not a bad idea to get the solution books either.</p>
<p>A different book is "The Art of Problem Solving" by Paul Zeitz. It's also really good. Although it assumes some background in vector calculus and linear algebra, you can still get a lot out of it even if you don't know that. BUT THIS IS A COMPLETELY DIFFERENT BOOK from "art of problem solving volumes 1 and 2." Don't confuse them!</p>
<p>Actually, I think the Zeitz book is called "The Art and Craft of Problem Solving." It's not just an art, it's a craft.</p>
<p>zogoto is correct!</p>
<p>my bad</p>
<p>Lol, yeah, also <a href="http://www.artofproblemsolving.com%5B/url%5D">www.artofproblemsolving.com</a> is a website as well, and it has alot of helpful resources, and alot of people really good at math hang around there. There are alot of different forums, one of which is specifically designated towards helping with AMC/AIME/USAMO. In fact, right now, there is are Mock AIME tests, AIME level tests written by the students themselves. Those are always helpful as well.</p>
<p>The best way to get to the USAMO is to take old AMCs and AIMEs.</p>