I am trying to understand how I can best learn from examinations that I take as an undergraduate pure mathematics student, now taking a variety of advanced undergraduate and beginning graduate math courses. To preface this post, I must admit that most of the graduate courses I am taking do not have "typical" timed examinations where you have to solve a bunch of questions; instead, there are report-writing and presentation tasks, which I believe I am good at.

Here's what I've noticed about timed examinations (midterms, endterms, etc.) in mathematics:

I am hardly ever able to complete solving the entire question paper during the examination; I generally fall short on time, etc. I understand this may depend on the difficulty of questions asked, but let me tell you, all exams I have seen so far have included fairly non-trivial questions (certainly not rephrasing of definitions, or something very immediate) - in that, a non-trivial train of thought is required to arrive at the solution.

I wish to know, if it is just me, or do others also struggle with completing such examinations in time-constrained settings? Also, to what extent does the ability to complete such examinations correlate with my understanding of the material, especially if I am able to solve all or most problems without the time limit? In any case, the answer to this is important to me so that I can push myself to be a better mathematician, and work on my shortcomings.

I do understand the importance of examinations (to test one's understanding of the material), but I am unable to comprehend whether not being able to solve all problems in a (time-constrained) exam implies that I do not have a good grasp of the subject? Regardless of the answer, I also wonder how to get better at pure math examinations, and how to take away the most from the experience.

Thank you very much for reading, and I request whoever sees this to consider sharing their personal experiences/anecdotes, so we know that we're not alone, and can learn from everyone's experiences!