convert F to X for exchange study

I'm heading to China for a summer camp trip that I won to Changsha (finishing in Beijing) from the 20th of August to the 1st of July 2013. I've also organised an exchange to Beijing University of Technology which starts on the 1st of September 2013 to the 30th of June 2014. There is a month in between these dates that I'd rather not waste money on plane tickets for, but I'm wondering whether this is possible in terms of visas.

I'll be doing my summer camp under a business (F) and my exchange on a study (X), then apply for a temporary residence permit for the rest of my exchange. I know you can usually extend F, but is it possible to extend my F until my X comes into effect? Will I need to re-enter or have to jump through any other hoops for this to happen?

Thanks for any help!