This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
What you should do is to track the state of the exam and the timer in the session (most likely employing Ajax to send the state to the server periodically). That way, when the user refreshes, you can detect that they were in the middle of an exam, and restore the state at the time of the refresh.