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Some background: I'm 14, in 9th grade, and go to a good public school. About 5 months ago, for whatever reason, I really got into physics and math, but mostly physics. I read Brian Greene's

*Fabric of the Cosmos.*Meh. No math or rigor. Then I got Feynman's

*Six Not So Easy Pieces*, and it is not so easy (although I new most of the things in

*Six Easy Pieces*). I'm kind of trying to barrel though it, and take my time and do month a chapter (work on it during free periods), although I'm taking a break for a little while. It prompted me to learn some basic trig, so that's good. Another book I've been using since the beginning of this year was the Thompson book

*Calculus Made Easy.*This book is quite good at explaining things, and I'm having a good time going through a few pages a week. In between, I've challenged myself with problems I've given myself, such as deriving an equation for the distance that a projectile will travel if you know the launch velocity and angle. (I felt very proud when I checked online and got it right.)

However, I'm getting an A- in math class, and got a B+ last quarter... not so great, especially since I want to be doing this stuff for a while. I have a hard time thinking on my feet, and can frequently make stupid arithmetic errors. I took the amc10, and got two easy problems wrong at the last step. I want to be able to take the aime next year, so I have to get my act together.

Sorry, that's a lot to read, and here's my question: with all this math I'm trying to teach myself, should I be taking a slower approach where I carefully go over stuff in the curriculum, SAT, etc, OR is it good to be doing stuff above your level and drag yourself up to that level, even if you don't COMPLETELY understand what you're doing?

Thanks