study for (something)
To learn or memorize information in order to prepare for some upcoming quiz, test, examination, etc. I didn't study for my driving test because I figured it would all be intuitive. Needless to say, I don't have my driver's license yet. A: "Do you want to come to the party with us tonight?" B: "Sorry, I'm busy studying for my physics exam."
study for something
to try to learn in preparation for an examination. I have to study for my calculus exam. Have you studied for your exam yet?