I asked if you were making the claim that you could, in general, measure how well someone could guess the teacher's password (on a test for any subject) and get results which measured their literacy (implied: or calculus) skills. You indicated yes.

If that is the case, it is impossible for people in general to have different literacy and calculus skills, because the same test would generally measure both skills.

Did you instead want to make the claim that people who are poor at guessing passwords are in general worse at a skill than their performance on a hypothetical test which measured only that skill would indicate, and vice versa for people who are good at guessing passwords?

My default case for considering a typical 'official' test is that it measures mostly the ability to guess the password, and only somewhat the mastery of the subject. Based on my experience with IQ tests, there is a significant factor of password guessing in them as well.