UMich is definitely my dream school. Everything about it fits me. It's number one on my list right now. I will be applying as part of the Class of 2017 (enrolling in Fall 2013). I will apply to the College of Engineering, not sure yet on what I'll major in. Here is what you need to know:
Ethnicity: Pakistani (Asian)
Income Bracket: Low (<30K)
Hooks: Brother attends UMich Engineering right now.
I'm an in state student.
GPA: 3.86 W, 3.79 UW (Huge upward trend. 3.975 UW my sophomore and junior years combined)
ACT: 31 (will retake in September, expecting 32-33)
AP's: Calc AB, European History, and Stats this past year. Expect a 4 or 5 on all of them. Will be taking Calc BC, Chem, and Physics B senior year (next year).
SAT II's: Will take Math I/II and Physics in October.
Islamic Association 9, 10, 11, 12. (Tresurer in 11, President in the upcoming year)
Debate 9, 10
Quiz Bowl 9, 10
Physics Club, 11, 12
NHS 11, 12
150+ Hours of Community service (Hospitals, NHS events etc.)
Also will do some internship work for a telecommunications company in native Pakistan this upcoming summer.
Essays: Gonna be Great
Teacher recs: Great
Counselor rec: Great
Miscellaneous: Father passed away during the start of my freshman year, which is primary reason for such a bad start.
Make sure admissions knows of your circumstance freshman year. Everything else seems good though. Try and raise that UW GPA and get a really high math subscore on your ACT. SAT subject tests don't really do anything with the application but it can hurt you if you do poorly or help you if you do well. One question, why not take AP Physics C? Though you do need a 5 on the AP to get credit, calculus-based physics is required through CoE. Algebra-based (B) gives you the concepts to apply to things but C gives you the math part. Good luck!
UofM will totally forgive you for your freshman year, you don't need to worry about that. Your ACT is a bit low, as dntlmewticntdo pointed out the average for 2011 was a 32, and as the applicant pool for Michigan is growing, so will these averages. The fact that you are instate and that your brother attended will help you a little.
Overall I think you have a pretty good chance. Good luck!
I would be very surprised if you are not admittted. Your ACT score is fine. I wouldn't waste my time and money taking it again unless there is some other objective to be had by taking them.
I'm sorry about your father. I would let U-M know about. It would probably be best if the counselor mentioned it. Your high school record is pretty strong. I'm sure your father would be proud of your accomplishments.
The low income and single parent situation should help immensely (having a sibling there also helps). You already have good stats I would think your chances are very high unless your High School blows.
You will definitely have a good shot. As some previous posters mentioned, Engineering weighs math and science on the ACT the highest, so as long as those scores are solid I wouldn't worry too much. Good luck!