Word for being asked many difficult questions

"Grill" would be appropriate here.

Grill (verb): to subject to severe and persistent cross-examination or questioning.
[Dictionary.com]

I also thought of "give me the 3rd degree," but that generally implies that the questions are hostile or uncomfortable. "Grill" can be used for that as well, but is also appropriate for questions that are academically difficult.

You could say:

I'm getting ready for the oral exam. I'm sure the teacher will bombard me with a lot of difficult questions

Bombard someone with something: to direct so many things at someone, especially to ask them so many questions, that they find it difficult to deal with them.

Example: The children bombarded her with questions.

[Cambridge English dictionary]

Or the teacher will shoot questions at me.

To shoot questions at somebody: to ask someone a lot of questions very quickly, one after the other.

Example: He shot questions at me so quickly that I didn't even have time to answer.

[Cambridge English dictionary]

The perfect word would be drill.

To drill someone with questions: to intensely or vigorously interrogate someone
[The Free Dictionary]

The question reminds me of a story detailed in Edward Frenkels Love and Math when as a young Jewish teenager in the former Soviet Union he sits an oral exam.

At that time there were quotas for Jewish students attending technical universities whilst the more prestigious ones were completely banned - not officially - but unofficially. (Actually, I was surprised to learn from Feynmans popular memoirs that there were such quotas at US universities when he attended university - it made me think).

This means that the examiners had to make him fail whatever his merits were. So of course they asked him questions off the syllabus, as well as 'twisting' questions in mid-questions, so throwing him off his stride, and other tricks - he was too young I suppose to tell them where to go - but then, where was he to go? This was the former Soviet Union after all).

He called it 'sadistic' and indicative of the brutal 'totalitarian' regime they had in the former Soviet Union. (Of course no such system could ever be used in the free and liberal West - perish the thought. Otherwise - what would we call the West?)

So I'd go for

sadistically interrogate

Or

sadistically bombard

It depending upon the intentions of the teacher and the educational situation of whatever country or state you're setting this sentence in.

Context counts.

Come to think of it, there are probably a lot of British kids who think maths tests are just sadistic anyway. And the examiners and governing boards are sadists for setting them...especially now.