If I went to school full time for a semester during may through august do I qualify as a full time student

No.  You need to attend some part of 5 months during the tax year.   Per the IRS, a full-time student is a student who is enrolled for the number of hours or courses that the school considers to be full-time attendance.  To qualify as a student, the person must be, during some part of each of any five calendar months of the year:

1. A full-time student at a school that has a regular teaching staff, course of study, and a regularly enrolled student body at the school, or
2. A student taking a full-time, on-farm training course given by a school described in (1), or by a state, county, or local government agency.

The five calendar months do not have to be consecutive.   

A more complete answer depends on why you are asking that question.

The 5 month rule was not met.  You were not a full time student for purposes of being a "qualifying child" dependent and some other tax purposes.

But you (or your parent, if you are dependent under the other rules) can still claim the tuition credit.