I’ve thought of myself as decently good at math, but I took two old AMC tests and the results weren’t pretty. At all. I’m not a “plug and chug” student, I always look up proofs and theorems and try to understand why, so I was somewhat surprised with how much difficulty I was having.
I’m only a freshman so I still have plenty of time to learn AMC strategies, and I was going to devote more time to it later, maybe next summer. However, there’s a math summer program I want to do, and placement is based on a mock AMC10 test. I don’t think they actually test you officially, it seems to be a self-assessment. I could probably take the course even if I don’t do well, but that might not be a good idea. Going a level lower might not be an option because the level below is designed for middle schoolers. I am a pretty fast learner, so if I don’t pass then I could sign up anyway and get myself started on the material ahead of time and hope to learn how to think like a true mathematician. I’m also planning on working through all the problems and not letting myself see the answers until I’ve completed the problem, and reworking all the ones I missed so I understand everything.
Also, the mock test is based on how many you got right and it’s not multiple choice, so strategies about guessing or answering X number of problems aren’t useful for this particular instance.
In short, I’m willing to work hard but I don’t have enough natural ability.
Rather than books and material to learn, I want to ask people familiar with the AMC and similar tests: what strategies do you use to “see it”? What are general strategies for tackling a problem to figure out what method is applicable?
Ultimately it depends on your learning style. A lot of people I’ve talked with always say, “Oh the test was so easy, question X was just a lot of bashing blah blah” - i.e. they just attack the problem head on - but I understand (and prefer) your “seeing it” approach. The best way is still to do many old tests to understand how problems are worded and presented. After doing these problems for a while, I think you’ll just have these sudden moments in which the strategy becomes clear. Of course, this is assuming that you review the solutions and their reasoning enough. And read the question carefully for keywords and what it specifically wants! (I know, this is such basic information lol)
For more specific strategy…well (at least for me) just probe the question using various perspectives, and eventually you’ll find one that can at least appear to work. This could be working backwards, considering casework, substitutions, extending lines in geometry, and so on among some basic initial steps in solving problems. Honestly all of this comes along with practice.
By no means am I an AMC expert, but I hope this partially answered your question! ^^
This usually works better for AIME/USAMO, but a good strategy in some problems is: Try small cases. Instead of 2015 people in a circle, try 3 or 4 or 5. See if you can generalize.
In general, just try stuff. For example, on #15-25 geo problems, try extending lines, dropping altitudes, constructing cyclic quadrilaterals, coordinate bashing, whatever looks suitable. For counting/combo-type problems, you could try using good casework, or finding some sort of bijection from what you want to count, to something that is easier to count.