It seems I got a 12, which means that I'll likely be taking the USAMO this year.
I didn't like this AIME very much though. Here is my analysis:
1: This problem was essentially testing the knowledge of well-known formulas, which #1 should definitely not do.
2, 3, 4: I realize that these are near the beginning of the test, but they are seriously too easy for AIME. All three of them are completely trivial.
5, 6: Nice problems.
7: Also completely trivial, assuming sufficient experience with this kind of stuff.
8: I don't have much to say about this one
9: my favorite problem on this AIME; it actually required some playing around more than just bashing things out.
10: The first one I got wrong. Although this seems to be a mindless bash, there is a nice bijective solution. But it's still possible to mindlessly bash.
11: So horrible... again, a mindless bash.
12: Apparently this is well-known, but I'm not sure. I got this one wrong too.
13: This was so easy to make a mistake on. (luckily, I didn't.) It was also way too easy for a #13.
14: What seems to be the most commonly used method on this problem was guessing and checking. And it's problem 14.
15: I don't know. Apparently this can be solved by guessing $AM = 10$ and verifying that it works.
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Hm the common solution to 15 was to set r_1s_1/r_2s_2 = BM/MC => easily factorable cubic after Stewart. Apparently Carl made a nicer solution but it was really long...
ReplyDeleteIt seems that I got an 8, which means it is very likely that I will not be taking the USAMO this year.
ReplyDeleteMaybe it was because I ignored Andrew's advice to perform a Sonnhard prayer.
It seems that I got a 12 by bashing #10 and guessing AM = 10 on #15...I had three equations and three unknowns on that one but it did not look very pretty. It seemed to be turning into a quartic at least. On the whole, the AIME was too easy this year.
ReplyDeleteYes, I agree that #5, 6, and 9 were only good problems in this year's AIME. #9 was especially good, since it was a problem that really killed me. I spent too long on #9 and #12, so I did not have much time for #14 and #15, which were both easily guessable.
ReplyDelete#14 was especially bad; I remember seeing a similar (or even harder, your mileage may vary) problem in 2007, and it was #7 for goodness's sake. I still can't get over the fact that I was checking 110 when time ran out.
#9 was great, since it directly punished people who just knew a well-known identity. I lolled when Mitchell showed me how easy the problem is if I stop thinking that I had to use the identity.
Yeah, my score could have been much better... I am now praying that USAMO cutoff line will be low enough. -_-
#15 wasn't that guessable... it's just that I know two people who got it by guessing "hey, AM might be 10"
ReplyDeleteWait easily factorable cubic? Shit? Maybe I should've continued with that. I did indeed set s1/s2=BM/CM, and Stewarted it.
ReplyDeleteAnd yes Alex, you should've done a Sonnhard prayer.