I am also the CL on the ADHD forum here - http://www.medhelp.org/forums/ADD---ADHD/show/175
I have seen posts like this too many times. She has all the symptoms of a child with either ADHD or ADD. Probably ADD. Because she is not hyperactive. Because she is intellingent - the teachers have missed the obvious clues.
Time on homework is a huge symptom. Being aggressive is a side effect of having "no filters". Not caring is a learned response due to the fact that she can't produce what is asked, and is giving up. I could go on and on. This site has a lot of good info - http://www.helpguide.org/articles/add-adhd/attention-deficit-disorder-adhd-in-children.htm
I would find a psychologist or psychiatrist who specializes in ADHD and have her examined. I really don't trust pediatricians to do this. Typically, these days, they are too busy to do a through job.
If you have any questions or need more info - please post here or on the ADHD site I mentioned above.