Am I required to offer expiation for an oath after I swore I would not go to school if my father bought my brother a moped, and he did so?

Yes, you are required to offer an expiation for breaking an oath because you did not fulfill your father's vow. You owe one expiation for repeating oaths concerning a single sworn matter. The amount of the expiation is mentioned in Fatwa No. 30252. A Muslim should not excessively swear oaths, as Allah (the Exalted) condemned the one who frequently swears oaths in His saying: "And obey not every [worthless] habitual swearer" and His saying: "And do not make [the name of] Allah an excuse in your oaths" and His saying: "And guard your oaths."