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January 3rd, 2010, 05:14 PM   #1
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Extending Horizon in Highschool

Hello, I'm currently a sophomore in high school, and one of my favorite topics is Math (Which brought me here).
I took Algebra2/Trig during freshman year, and the class went really slow for me, I just didn't feel like I was working to my full potential. So, after seeking out a path more suitable for my interests, I took a Precalculus course over the summer, went over the A level textbook in the transition period between summer school and sophomore year (the course was I level, so I had to do some enrichment work on some of the material), and am finishing up first semester of AP Calculus BC, doing extremely well.

I really enjoy studying math, and I would consider it my largest hobby. What I've come here for is tips. I'm currently participating in our schools math team, and at practice we do some practice problems and just go home basically - it doesn't take much time, and its usually over quickly. I feel like there's something more I should be doing. Any recommendations to help increase my chances of winning basic high school math competitions? They don't really cover any advanced material outside of Calculus, so I won't really have to worry about self studying statistics or differential equations. They do have those weird word problems, tricky questions in number theory, along with other oddities that a normal student wouldn't explore in a basic class such as Algebra, Geometry, or Precalculus/Calculus.

As of right now, I've just been looking at some of these problems and solutions, and picking up new methods I can use to solve these questions. I was wondering if any of you knew any good resources to use that really helps teach how to overcome bizarre questions like these that don't show up in an everyday middle/high school classroom. It's not that I don't have the talent or skills needed to understand problems like these, its just that I have yet to find a vast collection of how to solve and do the sort of problems that show up in math tournaments. Wandering from website to website picking up tiny bits of information and learning to solve a problem here and there do help, but not at the pace I'm looking for.

So, any tips for how to study for math competitions/tournaments at the high school level?
Any help is appreciated!
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January 3rd, 2010, 10:23 PM   #2
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Re: Extending Horizon in Highschool

I've almost certainly recommended it before on this site, but "How to Solve It" by Pólya is a well deserved classic. It covers systematic techniques for solving problems you haven't seen before. Going through the book diligently will improve your problem solving skills.

Practicing on past AP exams (both AB and BC) will help as well. Although the long-form questions are primarily calculus, some of them can be solve much more easily by other methods, such as geometry. Recognizing this type of problem will keep you flexible in using the tools at your disposal. Once you've mastered the material, the most efficient way to increase your competition scores is to practice for the competition. Past questions from the same competition are your best source for this, if they are available.
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January 5th, 2010, 05:28 PM   #3
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Re: Extending Horizon in Highschool

Thanks a lot, I'll be sure to give that book a look at
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