Okay, so I'm currently in grade 11 and taking grade 12 Advanced Functions. I've always been really strong in Math and most of my friends are constantly wondering how I solve incredibly difficult problems.

The problem is, even though I do tend to be able to solve difficult questions, I seem to fail at the most basic things (for example, factoring, addition, subtraction, etc.).

Does anyone know of any good online sites that generate good problems for my grade level to practice on? Also, does anyone know of any good strategies to make fewer mistakes (aside from 'practice more')?

^ I'm a bit confused. Why would you need exercises for your grade when you say your problems are much simpler?
Could you please explain, more precisely, what your difficulties are and in which context?

Advanced functions? Most don't take math at grade 12 over here, and I took AP Statistics... I'm not sure what your class does, but chances are I've done it. What does your class do, exactly? Maybe then I can help you.

^ I'm a bit confused. Why would you need exercises for your grade when you say your problems are much simpler?
Could you please explain, more precisely, what your difficulties are and in which context?

Well, the issue is that when I'm faced with a simple problem, I can't seem to make sense of it. For example, a few weeks ago I was supposed to factor 2+2x and I didn't realize that I could factor out '2'. Just two days ago I tried factoring (x-2)³-(x-2)² and couldn't come to a conclusion; I had to ask one of my friends to help and she saw it right away. Other examples are just plain carelessness; 2+2=0, 3³=9, 135+35=150, etc.

On the other hand, series, sequences, functions, complex numbers, difficult equations, etc. seem to be obvious to me. I'm not sure that solving a hundred two-digit addition questions will help, and solving even more complex problems probably isn't feasible to help me with basics. The most common advice I've been given is 'practice more', so I'm trying to follow that as well as ask for other pieces of advice people might have. I'm actually not sure why I have these difficulties; I just do.

Advanced functions? Most don't take math at grade 12 over here, and I took AP Statistics... I'm not sure what your class does, but chances are I've done it. What does your class do, exactly? Maybe then I can help you.

Currently we're doing polynomial functions. I had a quiz today where all the function stuff I understood (ie. given a function, graph it, or given a graph, find x-intercepts, leading coefficient, degree, etc.) but the last question provided a table of values for a function and I was supposed to use finite differences to find out the degree of the function. I checked all my calculations twice and couldn't find a mistake, but I exhausted all the differences and couldn't come up with an answer.

After checking with my friends, it was apparent that I was given the values for a quartic function, yet I went all the way to 6th differences (which was as far as I could go with the given values) and didn't come up with an answer. It's really simple subtraction, but I seem to have a problem with it.

I'm quite sure that my teachers have gone "WTF?" more than once upon seeing my answers; it's not that I don't understand the material, but I just make a LOT of mistakes doing simple math. I've recently taken to checking over my work, but I never seem to catch the most obvious mistakes; there was a "give a final answer only" question and I wrote 5-2 as the answer.

Some of my previous teachers have given me some advice on how to catch my mistakes (ie. put the test down for 10 minutes, think about something else, then look at it again) but even after using such tactics I still miss the most obvious mistakes.

tl;dr version: I suppose I'm looking for tactics that will help me see what I've done wrong/where I've made mistakes.

I think that in addition to trying to "catch your mistakes" (which you must also systematically do of course), you should simply practice on some mental calculus. Start off with that. I can't guarantee you it's gonna be very helpful, but just have someone give you, or if you can manage do so some yourself, some easy mental calculus stuff. Perhaps it'll help get things in?

Also, try to do things more slowly. Since you don't seem to have many problems with the complex aspect of things, you may have some time to think your calculus through carefully. I am very far away from your grade level in Math, most likely, but I know that I always spend a lot of time reading my calculus over and over sometimes to check if i haven't made a retarded mistake, especially in long ass boring calculus, that seems so easy you just do it carelessly.

For example, calculating a length using coordinates. AB = root [ (Xa - Xb)² + (Ya - Yb)² ]
I ALWAYS make mistakes using that formula because it's so god damn annoying, having to put in the coordinates each time and calculating with very simple numbers.

For factoring, go back to the basic stuff you learned many years ago. Take your time and just do a lot of factorization exercises until it becomes a habit.

So that's my suggestion :
- A lot of mental calculus
- A lot of basic exercises especially for factoring
- Take your time to do things

You should check out:

Art of Problem Solving (http://www.artofproblemsolving.com)

It has got some good info. Under resources, it has some links to some websites with some pretty good questions. If you practice problem solving enough, you'll get better at it (as opposed to "knowing a solution" which does not improve your math ability). XD

Practice Problems: http://www.artofproblemsolving.com/Resources/AoPS_R_Problems.php

And try to do as much as you can in your head. It will do wonders for your math skills.