Todays Lesson

use an apostrophe to indicate possession- ie today's

Today's lesson was as tedious as the other ones.

My math teacher handed me out a piece of paper, which was revealed as an exam.

I was truly furious, because I hadn´tdidn't like the concept of taking a non-well accuratedsurprise exam, where I wasn´t prepared at all.

I tried to figure out the quwestions Ithat were given to me out but Iit challenged me a lot, thus I attempted it as well. as I could

I was not given to you, the QUESTIONS were given to you. Also you don't challenge yourself; the EXAM challenged you.

Otherwise; I´m not secure, if I had solved anything correctly, but at least I tried my best and prosper toto get a good mark.

secure is more in a physical sense. ie I felt secure about where I was. Otherwise, you use "sure" when you are referring to a feeling. You also don't need "had" here because we already know it's the past tense because of "solved". Prosper is a bit too formal. A good mark is something that you are striving for, therefore you use the word get.

Todays lesson was as tedious as the other ones.

My math teacher handed me out a piece of paper, which was revealed asto be an exam.

you could say "handed out to me a piece of paper" but thats pretty choppy and unnatural but technically works

I was truly furious, cause I hadn´t the concept of taking a non-well accurated exam, where. I had no idea we were taking a test, so I wasn´t prepared at all.

not exactly sure what you were trying to say with accurated but i think this works for what you were trying to say

I tried to figure out the quwestions I were given to me out but I challenged me a lot, thus, but they were really challenging, so I attempted it as well as I could.

"they challenged me a lot" instead of "but they were really challenging" is technically correct if you wanted to remain similar to your original sentence but again not the most natural way to say it.
thus is also a bit formal, so works better here

Otherwise; I´m not secure, if I had solved anything correctly, but at least I tried my best and proshoper to get a good mark.