Chances of getting into Princeton Engineering? Reach, easy to get in schools?

<p>I currently attend Stuyvesant High School as a junior and hope to major in biomedical engineering.
By junior year, I will most like have a GPA of around 96.0 - 96.5. I took the SAT I for the first time and got a 2310. I have taken the Physics SAT, got a 760, the Math I SAT, got an 800. I will take the Math II SAT this June and I am certain of an 800. I also might take biology which will most likely be a 750+. I have taken 2 AP tests (world 4, physics B 5) and am currently taking two AP classes (APCS, APUSH). Senior Year I will be taking 5 AP's (AP Physics C, AP Chem, AP Gov, AP Calc BC, AP English). I have been on Stuyvesant's math team for 3 years, might be going to ARML and NYSML this year. I won the CML freshman year and I have made the AIME during my sophomore (130.5 AMC 10, 4 AIME) and junior year (102 AMC 12, 3 AIME). I am also part of the Physics Olympiad Club at Stuyvesant. I have been on the PSAL cricket team since sophomore year and I plan to be either captain or vice captain next year. I am the President of the Ping Pong Club and I am the Treasurer of the Historical Movie Watchers Club. I am also the homeroom leader for my homeroom and am considered to be part of the Stuyvesant Student Union. This summer I plan to take classes at Harvard which are tissue engineering and calc I. I usually go rock climbing on my own time as my own extracurricular activity. I have 280 volunteer/community service hours from working at my church, which I regularly attend since the summer of 2011. I have also volunteered for the community near Mark Twain, my middle school after Hurricane Sandy hit.</p>

<p>High match!</p>