Felt tips are great because they dry pretty quickly and aren't a problem if you're right handed, and you don't have to press hard, and are therefore able to write for longer and at greater speed without getting muscle ache.
I personally like a fountain pen (Lamy studio is my choice for school stuff) with a Fine nib because the extra fine is a bit scratchy, but the medium or bold nib chews through the ink pretty quickly. A fine nib and full ink easily lasts a full 3 hour exam with constant writing. I've never had a problem with ink going through the page, but in exams you only write on one side of the page anyway. If you get a soft nib, it can adapt to your writing style, making it even smoother and easier to write. I probably wouldn't recommend for left handed people though because it can smudge in the first second or two after writing.