Earlier quoted context omitted.
You can easily store notes on a TI calculator. I had a TI-85 in college, and was occasionally guilty of writing TI-BASIC programs to make tests easier (for example, I had one which computed Euler's method).
Most test proctors make you clear your memory before a test in high school. In college they don't care as much because they are used to making "open book tests".
I think it is standardized tests where the "clear your memory" would come up, but again, it was never done. I also don't think they asked any questions where the programs would have been an advantage, either. (The thing that's stuck most in my mind is the quadratic formula. The SAT could ask you "find the roots of this equation", but you don't need to know the quadratic formula to do that... the test is multiple choice so you can just multiply their answers and pick the one that matches the question. For that reason, I don't think they ask that kind of question, but I could be wrong. It has been a while.)