When I was in high school I was on the math team, which meant that we
went to a few math contests held at local universities. We also took
some nationwide written tests. I did find that with practice my score
on these tests improved considerably. I found a book at the library,
"The Contest Problem Book", which had sample tests from previous years.
While the problems did not repeat, often the principles were similar
and the problem solving techniques I practiced helped me a great deal
in the contests. So I agree with David that practice in specific areas
like this can make a difference.
> What I'm working on now, with my math, and this can be applied to lots of
> other areas too, is to stop hesitating so much between steps. I have the
> unfortunate habit of interrupting myself when I am working on a problem and
> pausing frequently. I want to train myself to just do the problem straight
> through, in one swift, fluid motion. It is hard for me to break this habit,
> but I am getting better, and I am getting faster at solving problems, as a
> result.
One simple example of this which we all face is when adding a long column
of numbers. I find that I tend to say to myself, "7 and 9 is 16, and 5 is
21, and 6 is 27, and 7 is 34, and 8 is 42." I've read many books on
speedy mental arithmetic and they advise training yourself not to verbalize
so much. Say, "7, 16, 21, 27, 34, 42." Keep just your running total
in your head, don't allow yourself to verbalize the "and 5 is" part, just
think 16, see 5, and think 21. It takes practice and discipline but you
soon find that you can add about twice as fast.
Hal