I'm in a semi-tight quandry here about the MathCOUNTS team. I'm willing to assist my MathCOUNTS team once or twice during the school year, e.g. coming in and teaching for an hour and a half after school. But I really...don't know what to teach.

First, vital information. I've noticed that many schools have a math club where they pick the MathCOUNTS team from. Students enthusiastic about math gather together near the beginning of the school year, have several meetings, and then choose the team. We don't do that. Instead, our higher-tests coordinator (if that's even a word) administers a MathCOUNTS School sprint round to almost everybody in the school and chooses the top 8 or 10 from there.

The problem, though, is in the practices themselves. The practices mainly consist of practice MathCOUNTS rounds. This is fine, as it gets the team acclimated to the style of testing that will be found, but the problem arises with the actual concepts. Unless you're studying at home, you won't get the ideas unless you learn that they exist. Our team does relatively well (a.k.a. regularly makes States), but I want the team members to flourish beyond MathCOUNTS. Additionally, our form of testing takes all grades, six through eight. Furthermore, the test isn't normally taken until December, so I don't have much time.

So my question is, what should I teach? I don't have Intro Algebra or Intro Geo, but I do have C&P and Number Theory, as well as Volume 1. What individual concepts should I teach? Additionally, should I just stick with the Intro books, or go on to Vieta'a formulas and other similar concepts from the Intermediate Algebra book if I have time? I've never done anything like this before, so any and all suggestions are welcome.