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Recently I did my retake exam for Advanced Maths in college. Compared to the ordinary exam, it was easier. My grade was 9/10. I worked very hard for it, non-stop for 5 months, dealing with anxiety and depression.

However, instead of feeling happy and relieved I feel bad and guilty. I feel I didn't deserve to pass this subject via an easier exam, and that I should have taken the regular exam to prove that I was deserving to pass the subject. It's obvious that now I will never know.

Has anybody been through this? How to overcome this situation?

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    Perhaps it was easier because you worked hard on the subject for months. Tests are much easier if you really know the material.
    – Jon Custer
    Commented Jan 22, 2023 at 1:43
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    This question might be of help.
    – Tom Carpenter
    Commented Jan 22, 2023 at 12:52
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    The question is, do you understand the math and can you use the math in the tasks it's designed for in your life, career, or future studies? Exams are rough tools, mostly useful for sorting hundreds of people by a number, and have many points where the connection to your actual understanding can be arbitrary (choice of material, design of questions, human judgement in marking, writing time and environment...). Whether you do poorly or excellently on an exam is only roughly matched to your abstract understanding of the content, and almost totally unmatched to your ability to put it in practice.
    – Luke Sawczak
    Commented Jan 22, 2023 at 14:02
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    If an objective observer would agree that the second exam you took was substantially easier than the first, then perhaps the conclusion should be that the first was too hard, not that the second was too easy.
    – John Bollinger
    Commented Jan 22, 2023 at 16:18
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    "I should have taken the regular exam to prove that I was deserving to pass the subject." Prove to whom, and why? Deserving according to what criteria? I guarantee that there is not a single person in the world (besides you, apparently) who is interested in any kind of "proof" that johny36 is "deserving to pass the subject" according to some strange, unspecified criterion which is distinct from actually successfully passing the subject.
    – Adam Přenosil
    Commented Jan 22, 2023 at 23:42

9 Answers 9

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Congrats on your success! You deserve it.

Some people think that they do not deserve academic achievements because things are not as challenging as they expected, but they often forget what they have gone through in order to achieve that success. Sometimes, they also forget how hard it is to learn things.

Even if the exam was unreasonably easy or hard, you should move on. Do not dwell on the past. If you still think that you do not deserve the success, just work hard. Eventually, you will believe that you deserve every good thing that comes to your life.

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    "Eventually, you will believe that you deserve every good thing that comes to your life" - or not. But this is something to work on for sure :)
    – Lodinn
    Commented Jan 22, 2023 at 15:55
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    It is like moving up in the ranking because your opponent did not show up. You may feel "I should have moved up by beating my opponent! I moved up even though I did nothing!". Maybe. But you did move up, and now you have a new match scheduled against a different opponent. However it happened, you passed Math and now have a new challenge coming up. Prepare! You are good at that now.
    – Willk
    Commented Jan 22, 2023 at 19:49
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Just to reinforce Pikachu's excellent answer, here's a couple of things to keep in mind.

  • It is the responsibility of those who design and grade the exam to make sure it accurately tests the knowledge and skills it is intended to test. If you passed this test and somehow don't have that knowledge and skills, then those people screwed up. Since these people are experts in their field and in assessment of students, that is very unlikely. It's also not your problem.
  • There's no such thing as a "hard" test. It's always relative. Any test is "hard" if you approach it underprepared; an algebra test that you could do in your sleep would be an insurmountable challenge to the average twelve-year-old. And any test is "easy" if you approach it overprepared. If you work hard to prepare for a test and you find it easy, that means that your preparation was very successful, and you should feel proud of that.
  • Try and remind yourself that it is a well-known fact that we are generally lousy at assessing our own abilities. Sometimes we think we're much better than we are; more often, especially among academics, we think we're much worse. To get a better picture of your strengths and weaknesses, ask an expert who is in a position to assess you - an instructor you've worked with, for example.
  • The way you feel is important, even though it isn't based on facts. Don't try to shove it down or bottle it up. Talk over your feelings with someone you trust, like a close friend or a therapist. And take time for self-care.
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    I feel this link is also needed en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect
    – N A McMahon
    Commented Jan 23, 2023 at 13:43
  • I would argue against point 2. There are plenty of poorly designed tests that intentional or not may include elements being tested that no reasonable preparation would've accommodated. I understand what you're getting at, but you're not talking about a universally relative situation in which the test is measured up against humanity. You're basically saying there is no such thing as difficult encryption. That its all relative and a any encryption is easy with a powerful enough computer. I mean, its a nice point that feels good, it just isn't true.
    – David S
    Commented Jan 24, 2023 at 0:04
  • @DavidS I think you misunderstand my point. I absolutely am talking about a universally relative situation in which the test is measured up against humanity. My point is that just because OP found this test easy does not mean it would have been unreasonable for someone else (including OP's past self, the first time they took it) to find it very difficult. I make no claims about "reasonable preparation", because I don't think any of us is in a position to decide whether OP's preparation was "reasonable".
    – Reese Johnston
    Commented Jan 24, 2023 at 14:51
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In one of my college math classes, the day after an exam, the professor had this quote already written in a small corner of the board at the beginning of class:

It is not Justice — the servant of men, but accident, hazard, Fortune — the ally of patient Time — that holds an even and scrupulous balance. -Lord Jim

And we stared at it, off and on, during class. Finally, at the end of class he made a few remarks about the exam, and ended by saying that if we were unhappy with our scores, we could be comforted by the words of Lord Jim.

I think the quote means that in human dealings, "fairness" is a concept both hard to define and hard to achieve. There are just too many variables. But it evens out over time. Don't sweat the small stuff. Luck may have given you an easy exam today. Next semester, you may work just as hard on a subject and get an especially hard exam. That exam is just one part of your course grade, your course grade is just one part of your overall college rank for the semester and at graduation. And the importance of your college rank fades more and more as you get a job and get older.

You worked hard, you did the best you could, and you didn't cheat. Take the grade and move on.

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I will add two perspectives to the already great answers above.

First of all, in my experience it is surprisingly tricky for instructors to create two equally challenging exams (in the sense that they are challenging for the same reasons and test the same skills to the same extent), assuming that the subject material is broad enough. It's pretty easy to create two very similar exams that test your multiplication skills, but not very easy for advanced math. It could be that the exam just touched on your strengths, and another student would've struggled with it.

Sometimes an exam may appear easy for student A because they remember a specific method for solving a specific problem, but the same question might seem impossible for student B who is not as comfortable with the method. For example, I had an exam question that was trivial to solve assuming that the students remembered a technique I covered in the course. Students who didn't remember this technique and tried to "brute force" a solution had the dubious pleasure of solving a 4-variable Lagrange optimization problem during the exam (instead of a trivial quadratic equation using the technique).

The second point I want to make is to remember why we go to college. There are two goals: one is to obtain a certificate that will make you more employable. The second is to learn stuff. If your feeling stems from the fact that you are not comfortable with the course material, that's fixable. Go over the material again, take another advanced math class that will deepen your understanding, or any other method you feel comfortable with.

In either case, you should absolutely not feel bad about passing an exam - this is a win, enjoy it!

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Don't worry: you deserve your success! What you experience is classical Imposter Syndrome: "belief that you don’t deserve the achievements you have accomplished, is a common feeling among students". Also read this one on how to deal with it.

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It is worth keeping in mind that in 10 years you will have forgotten about this incident. In case of anxious people - mostly because other incidents have filled the limited "anxiety box".

When passing my driving license, I was shown by the examinator (who was standing outside) to move faster away from one of the spots where I was supposed to back-park. The thing is that I did not even attempt to park, and he thought I was done.

I passed the exam and I was a fraud. A very, very happy fraud because I could have failed.

I had a math exam once when I said "... and then X happens". The prof misheard and said "OK, so now that Y happened, ...". My mind was spinning in a panic because I did not know if I was right with X, or if the answer was supposed to be Y and I got just lucky.

Turned out that I was lucky. A lucky and happy fraud, with his math exam in hand, ready to move ahead.

Has anybody been through this? How to overcome this situation?

Everyone goes through such cases. Some have impostor syndrome (mentioned in other answers), and some do not but it does not matter long term. You have another exam to get ready to pass.

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I agree fully with the other answers that essentially just say "congratulations". They're correct.

However, what you're dealing with is likely a case of imposter syndrome. Fortunately for you, since you actually know where it stems from, there are some concrete steps you can take to address it.

If you're really concerned about whether or not you "deserved" to pass the exam, sit down with the "harder" paper (assuming you can get a copy) and see if you would have passed that too.

Assuming you do, your concerns can melt away. If you don't, well... I'd still argue you deserved to pass the exam because you passed the exam you sat, but you'll be in the same position you're in now.

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I believe that deserving or not doesn't really express your thought exactly.

Let's look at this from the other point of view.

Expectations:

You have spend hard time preparing for your exam.

  • You were looking forward to a thorough exam, a difficult adventure, each step of which would remind you of how good you're prepared.
  • You were looking for something that made an objective assessment of your knowledge.
  • You were going for a "checkpoint" in your education which would be a proof to yourself that the time you've spent on learning is justified and you have indeed make a good progress in maths.

Reality

What did you get instead? An easy test, which doesn't require detailed answers and doesn't really say anything about your knowledge that you could be proud of. It's as learning how to drive a race car in tough conditions on a twisted road, and once it's time for an exam, be presented with just a straight to "check" your knowledge. Needless to say, that wouldn't check anything and wouldn't prove you're a good racer.

What conclusions can be drawn?

  1. The fact that your college didn't bother with making a more objective test may say a lot: they probably don't care about students as much as you expected them to do, or this college is not a such a high-tier educational institution as you would thought it is and graduating high-quality masters is not something they are fighting for. This may sound too harsh, but be ready to get an unconcerned response once you ask your teacher for a more representative exam.

  2. You should have a better understanding of why you're actually studying any particular field. A good mark is not a good goal; if everything you did want was a good mark, you should also ask yourself a question: is it worth it? A rating-based system (gamification) is a nice thing in education and it often works really well, stimulating students to "beat" each other in this game, but you should also look outside this game, you should have an expressible goal of your studying and realize why exactly you're spending time in this topic.

You've passed an exam, and did it with a good score. However, you're not really happy about it. You just suddenly realized that a good score is not a solid goal: you're not the only one who should be willing to get knowledge, but the teachers should also be concerned about teaching you. There's different ways of judging your knowledge in educational institutions. Ones just check that you know at least something and you're good to go, other do really care of the quality of educations. And both of them have their verdict expressed via a mark from 0 to 10, but only one of these marks is actually valuable - the one that was hard-earned in the college that actually wanted you to become great at this topic.

That said, I would suggest you to try working on any project that will utilize "the mighty powers" you've acquired while studying, it should greatly improve your overall satisfaction, reduce stress and the number of times you ask yourself "why am I even studying it at all"

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What is the purpose of having a good grade? To demonstrate to someone that you are competent in a particular area. All anyone after this year is going to care about is whether or not ypu can actually do maths. You studied hard and are therefore pretty competent. You have a grade that suggests to people that you are pretty competent. Sounds like you're all good to me!

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