Ideas for a math club

Hello CC, I have just submitted my application to start a math club at my high school and currently wondering what I can do to make the club more interesting. So far, we have been hosting unofficial meetings to practice for the AMC (American Mathematics Competition) with 16 members, but it would be boring to just keep doing this for the months and years to come. So, does anyone have any suggestion to expand the future club and make it more fun? Thank you so much for helping me out!

Oh, and btw, does anyone have any effective fundraising ideas for the math club, I have some in mind, but they have nothing to do with math.

How were you practicing for the AMC? Studying specific topics or taking old tests and reviewing solutions? While the latter is a great way to actually prep for the tests, I would think a math club would focus more on a topic by topic basis, examining related concepts, theorems, etc.

My D’s math team is university-based and covers a large area, but I would think a similar approach would work for a HS team. They break up the year into 4 segments - Algebra, Geometry, Number Theory, Counting/Combinatorics, just like the AMC mostly does.

Fortunately, they publish much of their material, going back several years. Much of it is warm-up problems, challenge problems, etc., but some have definitions, theorems, proofs, etc. Much is also quite unstructured, going back many years, with different leaders, approaches. But it’s raw material that can at least show how others have done it and I suspect provide enough materials for a couple years of a HS club, as long as someone is willing to sort through it.

https://sites.google.com/site/westernpaarmlteam/downloads
http://www.math.cmu.edu/~mlavrov/arml/spring-2017.html (with links to previous years)
http://math.cmu.edu/~cargue/arml/archive.html#s17

In addition to teaching math outside the normal school curriculum, sessions on math history and key figures (Euler, Gauss, Ramanujn, Euclid) could be interesting. Have someone pick a person and spend a meeting discussing his/her life.

Maybe a topic on famous mathematical concepts and how they affected the world. I wore this just yesterday - https://www.amazon.com/Math-Seventeen-Equations-Changed-T-Shirt/dp/B082GGXDHS

@RichInPitt thank you for the website, they are very helpful for the juniors in the club who is taking AMC 12, which cover a lot more topics than basic algebra and geometry. Once again, thank you for your help!