My experience is from SUNY Stony Brook (a university run by the state of New York). What goes into the grade, is pretty much entirely up to the professor. I have had very few classes where the whole of the grade was an exam; but there were a few. More often, the homework is some portion of the grade, but it could be minimal (e.g., 10%). For computer science classes and some humanities classes, it was more likely there would be larger projects or term papers. For things like math, the homework was usually a smaller part of the grade. The real advantage of doing the assignments was that you could practice for what would potentially be on the test, and there would be a TA to grade it and give you feedback.