Used to be pretty deep into the TI calculator hacking scene, I know that there were definitely programs/firmware images out there that allowed you to fake clearing the calculator's RAM and archive, as ridiculous as it sounds. But in my high school by the point teachers were manually clearing calculators most students were resorting to cheating other ways rather than advancing the graphing calc cheating arms race.
Decisions on par with blacking out the internet. (But clearly not as severe.)
If your test depends on preventing students from precomputing the answers, your not testing what you think you're testing. (Or what you should be testing as a teacher)
The big issue is it's hard to test the actual problem solving process in math with a multiple choice exam so you're either stuck doing it in higher level classes with less people so you're not drowning in grading or clearing/removing calculators entirely. The option of just not having calculators and formulating the problems so they could be solved without them was the most common solution to that when I was in college. Usually it's relatively easy to select a set of parameters for the problem to make the solution easy to compute numerically.
I'm in the UK and there was nearly no multiple choice exams, both external and internal. Most external exams used scanning software with questions split out to make it faster to mark them. Somehow our teachers managed.
The only multiple choice exams were optional additions the school could purchase, ie: Maths Challenge, benchmarking, career advice...
In the US basically every large exam especially the end of year and college admissions tests (except the essay portion recently added to the SAT when I took it) were all bubble forms. In college it was most common in the large classes that were part of the options for the general education requirements that would use them instead of open ended questions so they could be automatically graded for the 50-100 students who'd be taking each exam. It was also way more common in classes where answers would be numerical rather than say my proofs and logic class where we needed to write out a proof. IMO it was deployed logically where multiple choice made sense it was used and classes where the path to the solution was important they'd not use it.
There was a program you could run on the TI calculators before clearing that did some voodoo magic so that you could memorize some short “binary” program that restored it all. My memory is vague but between clearing and executing this very short executable, it at least appeared to be completely wiped.
IIRC it was an applet that hooked the key shortcuts and menu entries for a wipe, and the really advanced ones would drop you into an imitation shell that appeared as a freshly wiped calculator would, but there was a magic keystroke to drop back to the (untouched) main system.
I have recently learned that the introductory calculus classes at one of our local community colleges bans the use of calculators - any calculators - entirely during exams, and the syllabus and problem sets are accordingly structured in a way that makes using calculators largely redundant.
They tried this when I was in HS, but we resisted on the grounds that our science teachers let us create programs for their classes, and if we erased the memory we'd lose those programs.
