I have a lot of experience working with PHP and javascipt for your system to proposed registration of the user who will through their accounts will be able to see the tests and make them work as well as their results are remembered for your (supervisor tests) there would be a separate admin panel where you will be able to ask questions and delete, create tests and everything you want, the whole system would be done very efficiently and with the AJAX and that will be very optimized, please contact me for more information, I expect cooperation.
Regards,
Alex