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Over the holidays (very long ones), I intend on going through the two Calculus volumes of Apostol. However, I feel my pre-calc knowledge of math is very shaky. There's lots of little tricks I just can't see. I'm not saying I can't do harder problems, just that they're not very obvious to me.

Take this problem for instance: http://www.khanacademy.org/video/iit-jee-hairy-trig-and-algebra--part-1?playlist=IIT+JEE+Questions [Broken]

At first look, I have no clue what's going. After poking around for a few minutes, I could have gotten a little further but I would have taken a longer route to square that polynomial. With a little push, I would have gotten somewhere. That's just *one* example of an exercise that I have trouble with.

Like a recent poster in the "who wants to be a mathematician?" thread, I feel like I am very, very late and I want to sort this out asap. I don't know where to begin though. I also don't have *that* much time, so my learning will have to be somewhat structured. Initially, I thought a fun way to go about this would be going through every Math Olympiad problem I come across, then moving on to the JEE questions but that seems a tad haphazard and I'm not certain if that is the most appropriate way to proceed.

Any suggestions?

Take this problem for instance: http://www.khanacademy.org/video/iit-jee-hairy-trig-and-algebra--part-1?playlist=IIT+JEE+Questions [Broken]

At first look, I have no clue what's going. After poking around for a few minutes, I could have gotten a little further but I would have taken a longer route to square that polynomial. With a little push, I would have gotten somewhere. That's just *one* example of an exercise that I have trouble with.

Like a recent poster in the "who wants to be a mathematician?" thread, I feel like I am very, very late and I want to sort this out asap. I don't know where to begin though. I also don't have *that* much time, so my learning will have to be somewhat structured. Initially, I thought a fun way to go about this would be going through every Math Olympiad problem I come across, then moving on to the JEE questions but that seems a tad haphazard and I'm not certain if that is the most appropriate way to proceed.

Any suggestions?

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