There are 8 levels in Arcade mode. Every 2 levels that you beat will earn you up to one bonus mark on the Chapter 7 Test (for a total of up to 4 bonus marks). You can get one more bonus mark for completing all 4 levels in Professor mode. However, you cannot get more than perfect on the test.
In order to prove what level you have reached, you must take a screen shot of your game. If you don't know how to do this, click here. Another option would be to take a photo of the screen with a cell phone camera and email it to me (but please make certain you let me know who you are in the email since I can't recognize someone's cell phone number).