@gibby, the Common Application does allow students to upload documents underneath each school’s individual Questions section or their writing supplement section. Also, although I’m sure this application was sent a long while ago, I’m not sure what it accomplishes to vehemently tell someone that it is a bad idea to submit a resume. Perhaps this resume truly does shed more light on the student’s narrative of his or herself. Maybe there wasn’t enough room on the Common Application to describe the activities, or maybe not all of the activities/awards would fit. I think a much better route to take would be to be as encouraging as possible in these situations, since all colleges really and truly just want to get to know you as a person – are you the kind of person Princeton wants on their campus? @tuty143, best of luck with your application, and I hope you made whatever decision you deemed best in the end! 
Happy New Year.