What are the uses of though?

Though he had studied for the test, he still did not feel prepared to take it..

"He killed someone even though he knew he would go to jail for it"

Use "even if" when it is followed by something contrary to fact (not believed to be true). For example: Even if pigs could fly, they would not go to the trouble of doing it.Pigs can't really fly, so...

Though I do not like cooking very much, I love to eat.

There's nothing wrong with using "even though." I imagine you've had a teacher caution you against starting a sentence with "even though" because you've been writing fragments or incomplete...