Mandatory courses should be somewhat abstract and applicable to multiple disciplines. Mathematics and English are bread and butter subjects absolutely fundamental to basic education and there is no doubt these are useful. There should also be more initiative to exposure to different ways of thinking and doing things, giving the student the opportunity to make their own decisions.
Logic courses should be taught throughout high school gradually increasing from informal logic to maybe predicate logic or at the least syllogisms and basic formal logic by the time students are seniors. Our society is permeated with sloppy thinking, and now, more than ever, critical, logical thinking is crucial to continuing and improving civilization. Debates are thrown around, in politics, advertisements, and personal conversations fraught with fallacies and frankly most of the time they get a free pass. The decisions being made about the future of our civilization, the people getting elected into office and the other issues of our time are too quickly glossed over. They are not being given due consideration, and sloppy thinking is the culprit. The rush to oversimplify is literally everywhere and it can be stopped.
Foreign languages are mandatory in most places and this is definitely something that should continue, if not all four years, at least two. Our aptitude to easily learn foreign languages and truly absorb them diminishes quickly as we age. Not to say that we cannot learn later, just that the mental flexibility is greater when we are of middle school and high school age. It broadens the way of thinking and exposes you to something, well, foreign. It presents a challenge in a way that we are not normally accustomed to.
Civics and government are also mandatory but not given enough emphasis. These should be taught to juniors and seniors when the students are more mature and better able to appreciate the importance of the subject. This would work well in conjunction with logic and foreign language or cultural courses to analyze the philosophy behind our government and others and effectively discern the differences. Many are woefully ignorant of our own government because they were taught civics for one semester when they were fourteen years old and had little to no interest in it.