How students learn for tests

When our students take the big exams are the only questions they get right the ones the teacher "taught" them? I don't think so. I would like to know how effective is teacher "teaching" as compared to indirect learning.

I think they are answering some questions on the test correctly for items that they were not "taught". If so, then how did they learn them? I believe Comprehensible Input is playing a bigger role than we realize.

Krashen tells the story of how his French teacher wanted to only speak French to them and was explaining a grammar point, in French. Finally frustrated, she told them in English. However, her effort to explain it in French, all that French speaking to explain something, actually constituted Comprehensible Input for the students and helped their French.

Every time the teacher talks to the students in the L2 is Comprehensible Input. Teachers are naturals for adjusting their English speaking so students can understand them.

So between the teacher's speaking and the student's own study they are getting a lot of CI.

Perhaps the student is reading a business text and it is talking about international finance and the teacher wants the student to learn some language about stocks, bonds, interest rates, prime lending rate, etc. Perhaps the student has some degree of success in learning some of those terms but there are many things in the text that the student was not studying but was learning such as "carry on" when it says "banks cannot carry on making risky loans" or something like that.