When you find the answer to this question let me know. I have had the same issue my whole life. I don't know how old you are, so I'm sorry if guessing high school would be an underestimation. The reason I assumed that age range is because I had these exact problems with motivation for my whole high school career, but now I'm in college and they've almost entirely gone away (and were sent directly to other areas of my life, but that's a different story). I've found that college work is more meaningful - no "busy work", and for some classes no homework at all. Not only that but also once you are working towards a degree in something, you don't have to spend much time learning about things that don't interest you. I realize this isn't very helpful information for you now, regardless of whether you're in high school or college. But when I had classes I couldn't stand, I don't remember ever having a strategy for dealing with them. I hated every minute of it and was selectively lazy about the work, but in the end the grade was mine for the taking. If you know you're capable of doing it, you might as well just power on through. A good grade for its own sake can be pretty satisfying.
Completely dependent on the professor. I'd imagine most schools will have a LOT of classes to offer, mine does at least. So even though there are gen ed requirements that I have to take, it's easy to find classes I'll enjoy despite them having nothing to do with my major.
The curriculum for classes in college is a lot more liberal so it's the teacher's responsibility to make his/her class interesting. I'm studying music, but I took meteorology and that was really cool. My Israeli-Palestinian conflict class has been my favorite so far. But then I also took a public speaking class which made me feel like I was in high school again. Since I'm going to an art school, the standards for gen ed teachers are understandably lower, but on the whole I've been impressed.
Good luck with the remainder of your high school work! I'd say if you can figure out what you want to do now, you'll spend a lot less time doing "busy work" for the rest of your life. Although I'm only a couple years older than you, so someone with more experience might disagree with me about that.