Hey greenneub. I'm sort of in the same position as you, and doing more or less the same thing. (The main difference being that I never learned pre-calculus in the first place, so I can't really skip it).
I'm doing 2-3 hours each day, and I've found that more than that is meaningless. If I cover too much ground too quickly, I don't learn it as well as I want to. I guess the mind needs some time to process things on its own for it to stick. I believe doing more than 3 hours on a single day is ok if you have enough material and problems for a single topic, but that is rarely the case.
I do every single problem in the main book as well as a companion book with problems. I make a note on the areas where I feel like it's not "flowing" the way it is supposed to, and when I'm done with the book I go back and do those chapters again, taking my time and trying to really understand how each step works and why.
A tip that I have "discovered" is this: When you start on a new topic, read the definitions, skip the examples and try the problems. When you get stuck, look at them for atleast a couple of minutes. If you still can't see the answer, THEN read the examples. I can only speak for myself, but atleast I get more "Aha!"'s that way, rather than the "Oh"'s of reading examples first. You only really appreciate the solution if you have tried the problem yourself.
Another thing that I learned, is that I have to be very aware of when I am doing "shortcuts". IE:
4 * 3^x = 9 * 2^x
lg( 4 * 3^x ) = ( lg 9 * 2^x )
lg 4 + x * lg 3 = lg 9 + x * lg 2
x * lg 3 - x * lg 2 = lg 9 - lg 4
x(lg 3 - lg 2) = lg 9 - lg 4
x = ( lg 9 -lg 4 ) / ( lg 3 - lg 2 )
It's a lot to write out, and I frequently find myself thinking "well, I know where this is going" and jumping from the second to the last line without writing the other steps. Then I feel clever. The thing is, that when I get used to this, after a while I tend to forget what the middle part actually did and looked like, and when the problems get more complex, I get stumped.
So, I try to be very aware of when I am doing a shortcut, and at least go through the steps in my mind. (Of course, there are some shortcuts in the example above as well, but those are tried and tested over a long period of time, not new material).
On those days when a lot of the end results are wrong, because I did an early mistake which followed through on the entire problem (wrote down the problem wrong, messed up a sign, multiplied powers instead of adding or whichever), I try to tell myself that it is ok, look at the book: It is written by a professor, proof read by multiple people, and still some of the answers are wrong. Getting to the wrong place now and again is a part of math, and it is ok. What is NOT ok, is using a erroneous approach or failing to understand the problem.
Another really helpful thing are these forums. Looking at what other people has problems with works on many levels. Sometimes you can help (and this reinforce what you know), sometimes you can learn something new or read an explanation which makes something click, and sometimes you get help on problems of your own. There is a lot of highly overqualified people here that take time out of their day to help people like you and me. God bless them.
k
