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The AMC 10/12 test is a test used in a math competition for high school students.

I have a few students that know LaTeX who are very young and are extremely advanced for their age in high school. As a teacher, I feel it is my job to get into some of the top tier schools for math when they graduate high school.

Background: When I was in college, I became obsessed with graph theory and loved it! I became a high school math teacher to give back to the subject.

As a high school math teacher, I quickly realized that I am awful when it comes to the AMC 10/12 tests. In my opinion, every question is really cute. I feel the test gauges one's ability to memorize tricks in a methodically roundabout way. I want to teach students proofs by induction, more about LaTeX, and how to conjecture and prove beautiful theorems in math. Not to focus on having them think a certain way in order to memorize a set of tricks to tackle a set of questions.

$\textbf{Question:}$ So, what should I do to help students get into these top schools? How much do the AMC 10/12 tests help students to get into top tier schools? If I show them a ton of theoretical math in LaTeX that they keep track of, would that be enough to get them into a school like MIT, etc.? Or should I keep on learning about this test for the sake of their educational future and not knowledge?

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    $\begingroup$ This isn't an answer, but I would recommend "yes, you should show them AMC 10/12 because it is cool and fun, and you should show them cool and fun things," instead of "yes, you should show them AMC 10/12 because it will make higher-ranked admissions algorithms rank them higher." $\endgroup$
    – Chris Cunningham
    Nov 29 '20 at 19:59
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    $\begingroup$ I'm guessing this is in the U.S. (AMC 10/12 certainly is), in which case a very strong showing in just math (unless it's something like a bronze or higher medal in the IMO) will probably not make up for maybe only top 10% or so in other areas, even for mathy schools such as MIT and Caltech. For very strong math students who weren't stellar in other areas (and I've known several), or at least who didn't put forth the effort to be stellar in other areas, a strong graduate program is what you want to aim for, and this is definitely achievable from many non-top U.S. universities. $\endgroup$ Nov 29 '20 at 20:20
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Those tests are not key to admissions to undergrad, even at top schools. That will depend more on overall grades and standardized test scores. What schools used to call the whole man.

I would also be careful about only pushing what appeals to you. I see that way too much from the proofy types. But other aspects may appeal to other people. Realize also, that it's probably too early to predict the kids will even be math majors in undergrad. Just because they are bright and following advanced topics you like to show them doesn't mean they will follow your path. Could go into physics or some other STEM.

And the time to worry about top schools is grad school. At a different stage. The top school undergrad thing is way too emphasized in the us. Many kids in undergrad are better off with a small liberal arts school or an affordable public university than Harvard. At a minimum, the relative benefit of Harvard is marginal. What is more crucial is the ability of the student.

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    $\begingroup$ Or even community college. It is way easier on the wallet, and STEM programs are often excellent. $\endgroup$
    – Sue VanHattum
    Nov 30 '20 at 3:27

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