Exams are remarkably location specific. How we express the idea of preparing, taking, grading, and reacting to exams here in the U.S. is very different than what you would hear from our British cousins. Therefore, my advice may not be appropriate. If your application letter is written for a person or company schooled in British English, then you need to seek British advice or bear the risk of sounding inauthentic.
In the U.S., the simple one-line statement could be expressed as:
I prepared and graded exams.
Prepared identifies you as a person who designs exams (which exams are not mentioned, that would be important, but I assume that's discussed elsewhere in the letter). Designing exams would include choosing the vocabulary and sentence structure to express questions about the topics considered by the exam with the goal of evaluating how well the student understands those topics.
Graded identifies you as competent to judge the quality, validity, and veracity of student responses, leading to an evaluation ("grade") that will affect their overall grade for the course.
Please note that I have had to express grading in an intentionally ambiguous way. In the U.S.:
Grade school students may simply get a letter-grade that is averaged (often subjectively) at the end of the grading period (semester, etc.).
High school students often receive a number reflecting a percentage or a strict analysis of quantity (8 out of 11 questions correct) which is often contributed to a flat scale for a final grade (If your total of exams and homework exceeds 75 points you will receive a "B").
My father recounts his verbal exams for his law degree where the evaluating professor either passed him or failed him (all or nothing, eek!).
Thus, there are a lot of ways "grading" occurs, and how that is specifically interpreted has a great deal to do with the context of the exams, which you haven't provided. Note that whomever reads your letter will assume the nature of grading based on the context you provide.