There are many online applications that allow you to calculate your typing speed. I'm not sure if we can give outside links, so the best way is to google words typed per minute, or something along those lines.

You could just try typing something up, whether it be part of a newspaper article or whatever else into a blank document as fast as possible (set a limit for how much you'll type) then see how many errors you make.

Also, get to bed early so you can wake up earlier and not be too tired for the typing test. Go in with confidence, as that is winning half the battle. If you go in nervous, you're more likely to make more errors and possibly type slower.