It's been a little more than 10 years since I finally finished grad school (chemistry), but all the exams there were essay-style questions, save for when they made me take a couple of the standardized ACS exams toward the end. The vast majority was hand-written, since it's real hard to type all those chemical structures and reaction mechanisms ;-)

I write in a mix of cursive and block-printed letters. My capitals are all block letters and I fill in between with mostly cursive and little squiggles. It's a style I pretty well developed on my own in the first semester of college when I realized that I needed to be able to read my notes after the ink had dried.