Fluther grammarians, I need your help. Which sentence is better?

I’m trying to make some changes in a document and decide which wording is correct. In the scenario, someone has taken an online course, failed the test and needs to take the course and test again.

My wording: “Review the course and re-take the exam.”

The wording of someone-who-shall-remain-nameless: “Review the course again and re-take the exam.”

Since the person needs to review the course, isn’t the word “again” redundant?

Also, is “re-take” correct or should it be “retake”?