I'm 68 going on 69, but I never learned FOIL in school way back when. Then again, math was a subject I was good in, so I may not have needed it. I first heard of it when I did an algebra review on Khan Academy in preparation for science and more advanced math courses here.

Well, first of all no matter your age you should learn things. In this case you have chosen math and I think there are not many other choices which are better than this one. Having said that, in my humble opinion, acronyms or other nmothecnic rules are extremely stupid. You should understand the mathematics behind, no matter if you have a simple reasoning. I know that there's not many rigorous and understandable justifications behind elementary maths, but that's what I try to accomplish everyday. It's better to understand how the cosine is a relation between the adjacent and hypotenuse of a right triangle, and more extended to a whole unit circle than knowing that nmotechnically is called CAH. So that's my recommendation, specially because you will no longer have to memorize but deduct and moreover because further in your mathematical education that type of stupid things won't help anymore. Good luck. 

I think that students should understand the "why" behind the math that they are being taught; however, I see why teachers use mnemonic to help students learn all kinds of things in school so why not math.