Chances? Low GPA High ACT

<p>Hey guys, so I'm thinking of applying to UPenn next year. I did really poorly in my sophomore year and managed a 3.5/3.3 both semester UNWEIGHTED. I took 3 honors and it was tough to adapt to the difficulty and the class; also I had family problems so my GC will write about that. right now i'm a junior and got a 3.83 1st semester and working hard for a 4.00. So far it's looking great!
ACT Score: 34 single sitting
Should I bother applying to UPenn? I have decent extracurriculars(leadership,music, stanford medical internship,etc.) and my essays are always at the top in English. I know I will get strong recommendations because I take my time to talk to teachers outside of class when I need help or whatsoever. UPenn is my dream school but I want to be as realistic as well.
Honors/APs I've taken:
Honors English
Honors PreCal
Honors Chem
AP Comp Sci
AP World History
AP Calc AB
AP Biology (one of the most rigorous schedules) and my class rank is top 10%</p>

<p>Thanks!</p>

<p>You should apply. Being in the top 10% of the class means more than just having a good GPA since GPA varies a lot by school.</p>