<p>As someone who got a 114 on the AMC 12 (freshman year) and a 2 on the AIME, would it be reasonable to aim for making USAMO this year? I plan to study ~4 hours a day from now until the test. </p>
<p>[Note: I wasn't able to take the tests sophomore year and didn't do much in the realm of math problem solving that year. I'm a junior now.]</p>
<p>Also, I recently took an AMC 12 and I'm sad to say that my score didn't change much.</p>
<p>Increasing AIME scores from 2 to 9-10 in one year is quite a jump. I took the AIME every year since 7th grade and didn’t make the USAMO until I scored an 11 in 10th grade.</p>
<p>However, I know someone who went from “barely passed AMC’s” in 10th grade to IMO gold medalist in 12th grade (2006), with a ton of practice. So, it’s doable.</p>
<p>How do you recommend I practice? I’ve signed up for the AMC 12 and AIME prep classes, and I devote time to doing sample tests.</p>
<p>Preparing for the AMC’s is tricky…I didn’t really have a “set” method for practicing. I’m assuming you’re already familiar with the regular high school math curriculum. Also, quite a few theorems/techniques to know. To really understand them, I suggest you try deriving them on your own.</p>
<p>Algebra:
*Factoring polynomials(e.g. “Simon’s favorite factoring trick”)
*Vieta’s formulas, Vieta jumping</p>
<p>Geometry:
*Ceva’s and Menelaus’ theorem
*Stewart’s theorem
*Theorems/identities from trig
*Using complex numbers in geometry (this comes up occasionally on harder AMC/AIME problems)</p>
<p>Inequalities:
*“Trivial” inequality (x^2 >= 0 for all real x)
*AM-GM, generalized version
*Cauchy-Schwarz
*Schur’s, Muirhead’s, Jensen’s inequalities (more likely on USAMO though)</p>
<p>Number theory:
*Mod, binomial theorem, etc.
*Chinese remainder theorem
*Use other bases (base 2, base n), when needed
*Fibonacci sequence, Pascal’s triangle</p>
<p>Of course, the other 90% of the test is logic and knowing how to apply these theorems/techniques well, many of the harder questions can involve using them in an unusual way. Obviously this is not a complete list but it really helps to know these theorems.</p>
<p>wow, what is the max score on the AMC AND AIME, is it too late to start perparing if you are a current junior.</p>
<p>Max. AMC score = 150
Max. AIME score = 15</p>
<p>Max. index (AMC + 10*AIME score) = 300, usually USAMO cutoff ranges from 190-210.</p>
<p>If I improved my score on the AMC drastically, wouldn’t it be only necessary to score a 5-8 on the AIME to make USAMO?</p>
<p>If you get a perfect score on the AMC12, you can very likely make USAMO with a 6…a score of 5 or 4 is pushing it. The tests would have to be super hard to qualify with a 190 (as was the case with the 2011 AIME I).</p>
<p>1 more question. . .
Do you think it’s better/harder to qualify for the AIME or the USAPhO semfinals?</p>
<p>I never did the USA Physics Olympiad, so sorry I can’t tell you…but each year several thousand students out of about 100,000 qualify for AIME, and only about 500 qualify for either USAMO or USAJMO.</p>
<p>Of course its possible!
My sophomore year: AMC12: 94.5, AIME: 2
Junior year: AMC12: 111 (sadface…got consisten >130s in practice :/), AIME: 10, USAMO: 14 (Top 100 :D)
Currently a senior</p>