My first exams.

I am a freshman. I study at in a university in my native town. It is Ukhta State Technical University. On Tuesday I will waiting for my first exam. I am afraid of it. Wish me luck!

This is very good.  Although, you should try to incorporate(add in) your third sentence into your second sentence to make it flow better.  For example, "I study at Ukhta State Technical University, a school in my native town."

Your English definitely seems better than my Russian though haha

Sorry, I made a mistake in my correction.  The first sentence should be "I study in a university in my native town."  Only put "at" or "in", never both.

My first exam.

I am a freshman. I study at university in native town. It is Ukhta State Technical University. On Tuesday I will waiting for my first exam. I am afraid of it. Wish me luck!