I checked term paper on OED and it shows that it is AmE. So what is the British one for it?
The UK education system doesn't usually require a long assessed essay at the end of each term. If a particular teacher does decide to set such an essay it would be called an end of term essay. (or end of year, if due in June/July). In general assessment by essay or similar during the course (in contrast to examinations) is called "coursework"
I can't believe that my History teacher set an end of term essay. It has to be 5 pages long!
I've to do my Art coursework this week, so I won't have time to do any other homework.