It's simpler: in the major scale, every fifth down removes a # or adds a b, every quint up removes b or adds a #, and it's the 7th degree. Other church modes can be derived from a major scale. But that doesn't help you while playing. You have to know the key and scale you're in, and read the accidentals (and what op didn't mention: naturals and double #/b).

There are definitely other ways to derive all this but with a quick glance you don't really need to do any computation involving intervals. The key is either the second to last flat, a half step up from the last sharp, C, or F. To me this is much simpler than seeing 3 sharps and going, C->G->D->A. It's definitely good to know the latter but definitely not necessary for ascertaining the key.