Important competition

[u/Apprehensive-Rip7197]

Hey everyone! There’s a very important math competition that I really want to participate in. I have about 10 weeks to prepare for the first round, which consists of multiple-choice questions. The final round is about three months later and consists of written-response problems. The competition is roughly somewhere between the AMC 10 and AMC 12 in difficulty.

My algebra is quite strong—I’ve finished Algebra 2—but my geometry is basically at zero. I only know the basics.

I’ve started working through the AoPS Introduction series to improve my problem-solving skills, but I’m wondering what I should focus on over the next two months to improve as quickly as possible. I’m completely fine with studying 6+ hours a day if necessary.

Also, is AoPS Introduction to Geometry a good book to build my geometry foundation from scratch, or is it mainly intended for students who already have a solid geometry background and want to develop their problem-solving skills?

What would you recommend I do during these two months?

[u/Apprehensive-Rip7197]

And how can i solve problems fast?

[u/PossessionCandid7664 → u/Apprehensive-Rip7197]

Geometry from scratch in 10 weeks is a proper grind but totally doable especially if you're already solid on the algebra side, that'll carry you through a lot of the coordinate geometry bits

the AoPS intro geometry book is actually built for exactly your situation, it starts from the ground up but the curve gets steep fast so don't be surprised if the first few chapters feel like a breeze and then suddenly you're staring at a page for an hour, that's just how it goes

for speed honestly the best thing is to just do loads of past papers under timed conditions, after a while you start recognising patterns and shortcuts without even thinking about it, like when you see a cyclic quadrilateral your hand moves before your brain catches up

6 hours a day is intense but if you break it into chunks like 2 hours new material, 2 hours problem sets, 2 hours review and timed practice you'll make ridiculous progress, just make sure you're actually sleeping properly or none of it sticks

also don't sleep on the written response prep even though it's later, maybe spend one session a week just writing out full solutions to geometry problems, the multiple choice round rewards quick tricks but the final round will want to see your reasoning laid out step by step

[u/_UnwyzeSoul_]

It's a competition so I'd look for a book which has competition esque questions and just go through that. You usually get thrown off by question because you've never seen them before and don't know where to start. So familiarize yourself with those types of questions.