Drupal - Creating an exam system

Maybe you could use the Closed Question module.
You can find more information about the module here.

Features

• Designed for practicing: students can take as many attempts as they like.
• Many feedback options, feedback can change with attempts.
• Many question types.
• Questions can be added anywhere in a site.
• Only Questions. Ordering questions in a quiz or case is done by a separate module.

I am looking to perform something similar for a project. I have not gotten into more than a cursory consideration yet, but would immediately recommend looking at the Quiz contributed module. Its V7.x version is still a dev. level module, but if it appears to do everything and more that you could want. If not, check out the related modules on the project page.

At the very least, it will provide a reference for how to accomplish many of the tasks you will need to meet your requirements.

As Kolo mentions, Closed question also relates to your concept and it has another list of related projects. Please return to this question and let us know what you find out as you investigate, I am interested in what you learn!