Ethics of writing another paper to be graded for use as a work sample A particular program I would like to apply to requires a recent (past year) graded work sample in either science, history, or the social sciences.

Of course, I would like to present myself in the best light, however, the assignments I have been given fail to capture the rigor I would like to show. My course assignments have been rather standard and have not allowed me to express any special creativity or interest. I understand that the purpose of such a requirement is to assess how well I write and the topic should be immaterial, but I feel much more confident submitting a piece not in my coursework. 

In an academic situation, is it considered unethical to write my own research paper on my own topic and submit it to my teacher for grading, with the intent of using it as a work sample? I would want the paper to be graded  as honestly as possible of course. I care less about the numerical grade and more about the content and style of writing.

I would appreciate your input. Of course, this would only work if my professor agreed.

Edit: Just to clarify, I do not wish to be deceitful in anyway, however, I could not find evidence of any convention governing this sort of situation. This would be a sample of my work and I am not sure how it would be any different from submitting an open ended assignment. The paper I am referring to would be related to the subject, and in the subject I am thinking of, it is a logical extension of my interests beyond the course. Again, since the requirement is a graded work sample, I wasn't sure if it had to be technical coursework.
I guess you sound like you are trying to game the system and that your "graded assignment" isn't really the sort of thing that is expected. If you are trying to deceive, then, of course it is unethical. 

However, you might ask to submit a second writing sample along with the require one, stating that you think it represents your abilities better than your coursework. 

It would probably also be a mistake to ask your professor to participate in a deceit. But, his comments on a second sample would be fine as long as you are clear about the situation. 

Guard your honor.