I happen to be a professor at a reputed college. I want to design an online exam for over 1000 students via around 50 computers right after the vacation ends. Now the problem is that I have heard that many students use Google on a different tab to find answers when no invigilator is around. 

I want to know if there is a way to backtrace it after the exams via some kind of history or any other possible way. 

In our university there is a standard system. I am not good with computers but I will try to explain. Each computer uses Mozilla to connect to a server centrally located via an IP. The students open it and enter a unique ID and password to start the exams. Many questions are jumbled and different groups of students give exam in a different time slot. 

Is there any way to trace it since I want to set an example for students so they won't cheat and give exams in an honest way. 

Additional details: Since the number of computers are less than the number of students, more than 10 students are going to use a single computer on a single day over a period of 10 hours. After this, if I check the history (and let's say someone even forgot to delete the history and I see it), will I able to figure out who among the 10 has done it? Moreover, is it even practical and feasible?