I am not sure if this is the right forum for this question; nonetheless, I persist: I am a rising junior at a high school in Westchester, New York that has a very impoverished math department (we didnt even have precalc at my school last year), and I am interesting in forming a math club. In doing so, I must find some contests for us to partake in. I have already taken the AMC 10/12 individually last year and (with no studying, mind you!) did not fare very well. I would like to expand beyond that, along with my assemblage of 10 people. Ive heard of the New York State Mathematics League but the website is quite hard to navigate on, and I am not sure how to bring it to my school. The Harvard- MIT contest is appealing, but looks to be expensive (my school is quite literally poverty-ridden; at some point, we didnt even have paper in the school.) Any suggestions and/or advice would be most appreciated!!
HMMT is a pretty major contest (one of the largest student-run competitions in the US), and the problems can be pretty difficult, perhaps mid-AIME level with less time.
There is also PUMaC, which might be slightly closer in terms of travel.
Are there several middle schools that feed your high school? Would it perhaps be better to focus on a math club that works with those students to build a pipeline for a strong math team down the road? Perhaps build and support competition among the schools feeding your school, so the students are prepared when they enter high school to compete against other high schools? I would think that type of leadership experience might be more valuable for the current high school students.