When you find yourself maintaining two very similar tables (in this case Past and Present Students) it is usually a sign that you should have the records in just one table, and add a field called 'Status' which defines the difference that would previously have allocated them to one table or the other.
In this case I would keep all students in one table, and have a Status Field that is a Radio Button with values 'Graduate' and 'Current'. It will not be hard for even tech-unsavvy people to tick the additional 'Current' button when defining their searches. Additionally, if they really do find that a problem, you could think about scripting to automatically show only only current students, say.
I think they will be able to master searching in one file every time, rather than having to remember which file to look in. And you will find it a lot easier to maintain one table than two, and be exporting complete records, assignments, etc as students graduate.
Thank you for your reply. What you said makes sense and I think I am going to go with your suggestion. I was starting to lean that way, so it was nice to get my concerns validated!