Recommendation letter for my Student (for applying undergraduate admission)

Please, need you guys to comment on the grammatical errors and the suggestions for improvement. Thanks.

It gives me great pleasure to write a reference letter for Ms. xxx. I have known her for the past one year and have had the pleasure of having her in my Calculus 1 class in January 2013 semester.

In my class, she proved to be a diligent and hardworking student. If in doubt, she would seek clarification from me immediately after the lecture. She did most of the exercises in the lecture notes, and constantly consulted me the questions that she couldn't solve. She is friendly and helpful. Throughout the semester, I have observed that she and her peers always at the library together reviewing the lecture notes and going through the examination materials. She performed good in the continuous assessments as well as the final examination and got an A- in Calculus 1.

I believe Ms. xxx would be a capable student in any prominent university. I wish her good luck in all her future endeavors.

Hello,

Here's my take :
At first sight its difficult to say who the recommendation is from. You could mention "I have known her for the past one year in my capacity as a Lecturer/Professor/Teacher "

You seem to have covered on academics. That's good. Any general observations about the student could add some weight to the content and the LOR as a whole.

Hope that helps.
Good luck!

It gives me a great pleasure to write athis reference letter forin favor of Ms. xxx. I have known her for the past one year and have had the pleasure of havingin the capacity of her professor in mythe subject of Calculus 1 class in January 2013 semester.


I have identified her as a diligent and hardworking student.


She would not hesitate to seek clarification from me whenever she has even a slightest doubt in the subject.