Dual Major, Crappy Cum. GPA, can I apply to top schools

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MPKU
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Stats after the fall semester (the time I will be applying for graduate school for Physics)

Best case scenario

I will have a 3.4 cumulative GPA, 3.85 Physics GPA, and a 3.0 Math GPA

Dual Mathematics and Physics major, took 5 years to complete.

1st - 3rd year grade were par or less than. (I didn't care about school, or anything for that matter... regret deeply)

4th year, 3.93 fall, 4.0 spring <---- bulk of Physics classes taken here.

5th year, hoping for repeat.

Research:

Have done research on oscillatory granular systems for a semester.

Will be taking two research classes (independent study) in fall, one with a solar cell, one dealing with spectroscopy.

Nothing published, may attend fall conferences.

Have not taken GREs or PGREs, obviously planning to kick a** on them.

Extra:

Tutored math for one year

Supplementary instructor for college algebra for one year

Any advice is appreciated. Thanks.
 
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Of course you can apply. Guessing what the committees' responses will be would be difficult enough if we had your admission packet in front of us, and we don't.

As for the GRE (and please, keep the language family friendly), everyone on PF thinks they will do remarkably well. The key is to put the effort into actually do so.