Is it appropriate to ask a professor how I may be able to improve my letter of recommendation? Background
I graduated with a BS in math about a year and a half ago from a not well known school and with a less than stellar academic record. I did not go to graduate school (I was not accepted). Since then, I have improved my mathematical ability considerably, but I have not kept in touch with my professors. I can demonstrate this improvement in many ways, the most obvious of which is by referring to my subject GRE score.
Given that I was a mediocre student, I assume that my professors' letters of recommendation did not paint me in as positive of a light as they would have if they knew me now.
I am now interested in applying to graduate school again but this time I would like to secure stronger letters of recommendation.
Question
Is it appropriate to ask a professor the following question:

&quot;Is there any way I can demonstrate my current mathematical ability
and thereby improve your letter of recommendation for me?&quot;

If so, how should I ask this question?
Further Considerations
If the answer to the above question is &quot;Yes&quot;, then for at least two of the professors, I can suggest showing them my typed solutions to every question (save the trivial ones) in the textbook used for their class. These classes were both upper level classes (second level Linear Algebra and second level Real Analysis). With the last professor, I can demonstrate knowledge of Calculus of Variations (a subject that this professor is interested in) as well as Functional Analysis. Should this be my approach?
I think it is okay to ask the question.  However, I do not think you should suggest that professors read your solutions since they are likely very busy.  

You may do better to tell the professors what you have been working on, including your GRE score, and then ask them if there is anything else you can do to prepare yourself for graduate school.  Then follow their suggestions.  Essentially it is the same question, but I think it could show you are a "deep learner" rather than a "strategic learner" who only cares about the letter.