I was writing a 3-question examination today (undergrad) with 1200 other students when our professor comes in after ~2/3 of the exam and changes a question to make it solvable. This was a 1.5 hour exam where each question was designed to take 30 minutes so unless you did the other two questions knowing that question was impossible to solve and waited for an announcement on instructions of how to solve, you would not be able to finish. When I walked out of the exam, you could tell that everyone was mad that this changed question could have impacted their overall mark by 15-20%. What should I do to help out myself and my fellow classmates who were screwed over by this change? Has anyone ever had a similar situation?
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1If one notices that a question is not solveable, it might be better to switch to one of the other questions immediately. After having solved them, there might or might not be time to switch back to the other one. Or some things might have happened, e. g. what you describe. – glglgl Oct 24 '18 at 08:58
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30@glglgl Exam questions are often difficult. Switching questions the instant you get stuck is going to lead to a lot of context switching. So, in reality, one has to make a decent attempt at a question before giving up on it; that could still waste quite a bit of time. – David Richerby Oct 24 '18 at 11:46
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5You mention that each question was designed to take 30 minutes. Was that a stated metric, or one you assume based on number of questions/time given? – Winterborne Oct 24 '18 at 14:30
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Where do you study? In Italy this wouldn't be a such a huge issue. During the oral examination the professors know about this and will handle this accordingly. Don't you have something like this? Was this a part of the exam or the whole singleshot-exam for the course? – Bakuriu Oct 24 '18 at 18:13
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2@Bakuriu What is a "slingshot-exam"? – Azor Ahai -him- Oct 24 '18 at 21:00
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Anecdote: This happened to me once ... and worse. It was only the first section that got called out halfway. The other three sections knew about the change at the beginning of the test. People were not happy. Since it was a lab midterm, there was no way to do a make-up test. The solution ended up being some complicated method of scaling everyone's scores based on their cohorts usual performance, as well as their performance on the correct questions, and the attempts they made on the impossible question. I don't envy that professor/TA team ... – Azor Ahai -him- Oct 24 '18 at 21:02
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@AzorAhai singleshot-exam, i.e. you don't have homework, you don't have lab assignments. You go to lecture for 1 year, you have 2 hours of exam. What you get for those 2 hours are your grade. Period. Nothing you did before matters or contributes to your grading only those 2 hours of examination. – Bakuriu Oct 24 '18 at 22:09
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@Bakuriu That sounds terrible. I'm not sure I understand the connection to a slingshot, though? – Azor Ahai -him- Oct 24 '18 at 22:10
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3@AzorAhai I never wrote slingshot, you misread my original message. FYI most exams in Italy are like that with the catch that they (at least most) are not really single-shot. If you fail them you can retry for a certain number of times. But your grade is still just the grade of the single exam session, you cannot earn anything with homework during the year. – Bakuriu Oct 24 '18 at 22:17
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@bak Oh haha that makes seane – Azor Ahai -him- Oct 24 '18 at 22:18
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On a side note: This happened to an Electrical Engineering professor at my university in 2014, and he was fired as a result – Barney Chambers Oct 25 '18 at 13:36
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Side note: I knew a numerical analysis professor that provided an unsolvable problem that caused a student to fail a WPE for the second time, and washed him out of the Ph.D. program. As far as I know, nothing happened to the professor, and the student got nothing. – David Thornley Oct 25 '18 at 20:39
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@glglgl Hard questions often seem unsolvable. Do you really expect students the stressful environment of an exam to recognise a truly unsolvable question? If this particular question was easy to recognise as unsolvable, then the professor must have been truly incompetent. – Brian Drake Mar 12 '21 at 13:55
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@BrianDrake I meant to say (more than 2 years ago) that if the question is not solvable now by the student, move on. – glglgl Mar 12 '21 at 13:57
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@glglgl I would say, if the questions are designed to take 30 minutes each, then none of them are solvable “now” by the student (unless the student is exceptional). – Brian Drake Mar 12 '21 at 14:00
5 Answers
This does happen sometimes, despite a professor's best efforts to check the exam beforehand. Professors are humans and make mistakes.
You can write a polite email to the professor (or whoever is in charge of grading the exam, if different), letting them know that you feel this had a disproportionate negative impact on your score.
That's about all you can do. It is ultimately up to the professor (or grading committee, etc) to decide what to do about this issue, if anything. They might:
Do nothing, reasoning that although the correction was unfortunate, it affected all students equally.
Give credit to students who made an appropriate attempt to solve the impossible version of the problem.
Adjust the "curve" or other statistical correction of the exam score to take this into account.
Discard the question's score, and reweight the scores on the other questions.
Discard the entire exam and hold a new one.
Discard the entire exam and reweight other exams in the course to compensate.
In principle, if you don't agree with the professor's decision, you may be able to appeal to some higher authority. This would depend on your university's regulations, and my guess is that it would be unlikely to succeed, if the professor did anything halfway reasonable. I'd consider that any of the above options would satisfy that.

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44Not doing anything doesn't affect all students equally because it makes it complete luck if you started with the other questions or not. Legally (at least in Germany) you'd have a very strong standing because it's generally not allowed to mark students differently based on this kind of luck. This is comparable to announcing the solution to one question midway through, you're not grading the students knowledge anymore, but their luck in choosing which question to start with. – DonQuiKong Oct 24 '18 at 09:56
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@DonQuiKong Very true. On the other hand, the decision of what to do will be made with the benefit of knowing what the actual marks were. It may be that, in this case, the correction did seem to affect most of the students about equally. – David Richerby Oct 24 '18 at 12:30
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7@DonQuiKong I would disagree. Ability to wisely choose rights questions, spot difficult ones, focus on questions yielding most points is part of good strategy, not luck. In old days, universities in Poland based their admissions on exam performance. In maths at Warsaw University questions were scored differently depending on difficulty. Spending too much time on difficult question could prove perilous strategy and applicants were aware of that. – Konrad Oct 24 '18 at 13:05
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11@Konrad difficulty is subjective so the students will have a different order of going through the questions -> not everyone is affected equally. Or are you saying everyone should instantly know a question is impossible without wasting a single second thinking about it? Because else that second would be something someone else has more -> still unfair. – DonQuiKong Oct 24 '18 at 13:10
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@DonQuiKong I see your point; where I tend to disagree (slightly, as I reckon it's a subtle issue) is that the one may choose to reward students who scan the whole exam paper first and then prioritize questions accordingly over students who progress one-by-one and get stuck in the middle. It's not an obvious strategy,but there are some tests that offer that. Some IQ test do not have fixed number of questions but time limit, skipping difficult questions may prove a good strategy in terms of gaining more points. Ability to assess difficulty and prioritize accordingly may be seen as skill. – Konrad Oct 24 '18 at 13:16
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7@Konrad but there is no such thing a the "correct" strategy in deciding which question to tackle first. You can go for the hard ones and stop after x mins or go for the easy ones or whatever. It boils down to - this mid-exam change affects students differently based on luck. Imagine two exactly equal students. Both know everything perfectly and will finish the exam in the given time. Both chose at random which question to do first. One of them is interrupted mid question with a change of question, the other one hadn't started that question. Now those exactly equal students get different grades – DonQuiKong Oct 24 '18 at 13:24
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=> the students were tested on something completly unrelated to the course -> their luck. That's unfair and cannot be "legally ok". Whatever the exact legal course of action and possibilites are, there is no retrospectively saying "oh well the students should just have done the questions in a different order or instantly known there was a problem and just corrected it" - that's completly unfair to everyone involved. – DonQuiKong Oct 24 '18 at 13:28
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@DonQuiKong My point was that you shouldn't choose on random but choose strategically. I reckon that mid-exam interruption complicates the situation further. Nevertheless, if you consider wider context of preparing students for real life, it is pragmatic and desired that law or medical students face cases of different difficulty as this makes them more prepared to real life. The wider goal of an University exam is to test ability and knowledge. The one could argue that variable difficulty makes it more real, although at expense of being less fair, which is a sensible point. – Konrad Oct 24 '18 at 13:33
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1@Konrad I agree. But it's important that the situtation be the same for everyone. That wasn't the case here. So I think it's futil to argue about whether it could be done fairly if done on purpose. – DonQuiKong Oct 24 '18 at 15:01
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Another option for the professor is to do nothing now, but when calculating final grades, look at any students who were close to the points needed for a higher (letter) grade, and adjust their points if they were harmed by this issue. This option is commonly used by the lecturers that I TA'd for. Also, you're less likely to come across as a "grade grubber" if you say "I'm not asking you to change my grade, but later if I end up on the borderline for a higher grade, I'd appreciate it if you could take this into consideration". – mhwombat Oct 24 '18 at 16:17
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If you are a university professor and can't write a three question exam without major issues (like a whole question isn't solvable), then perhaps you should seek employment elsewhere... – JeffC Oct 25 '18 at 19:31
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1@JeffC: No offense, but that's easy to say for someone who's not a university professor (per your profile). Everybody makes mistakes, and an unsolvable question can be the result of something as minor as a typo. Professors have lots of other duties besides writing an exam and don't have the luxury of spending a lot of time checking and re-checking everything. – Nate Eldredge Oct 25 '18 at 19:38
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1@NateEldredge Yes, yes, everyone is busy... not just university professors. If you expect students to write complete answers with no mistakes, surely you can be held to the same standard? Minor typos are more understandable but if your typo (or whatever) causes an entire question of a three question exam to be unsolvable, that's not just a ... "that's easy for you to say"... I wonder if this prof's supervisor knows about this and what they think of it. I bet they don't just shrug it off. – JeffC Oct 25 '18 at 20:10
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@NateEldredge If some math student came to you after an exam and said I typo'd a 3 here when it should have been a 6 and because of that my answer was completely wrong... I want credit for the question because I didn't "have the luxury of spending a lot of time checking and re-checking everything."... I'm sure you would give them full credit, right? – JeffC Oct 25 '18 at 20:11
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@JeffC: No, I wouldn't give them full credit, but I also wouldn't advise them to drop out of college, which is what your suggestion equates to. Likewise, I would advise this professor to try to be more careful in future, but I wouldn't suggest that they ought to quit being a professor altogether. Anyway, I don't care to debate this any further (that whole busy thing) - feel free to have the last word. – Nate Eldredge Oct 25 '18 at 21:14
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@JeffC +1 “If you expect students to write complete answers with no mistakes, surely you can be held to the same standard?” Not only that, but you expect students to write complete answers with no mistakes in limited time, in an artificial environment that deliberately limits students’ ability to work optimally. (I cannot complain about this enough!) – Brian Drake Mar 12 '21 at 14:03
Yes, these things happen. No one is perfect, not even a professor. But what you need is a fair resolution. One would be to just cancel the exam and adjust grading rubric accordingly. Another, not quite as good, would be to reschedule another exam.
But you need to find a, hopefully polite, way to let the professor know that some people spent a lot of time on an impossible question and others did not. Even giving everyone full marks on that question isn't fair due to the frustration that some experienced.
If the professor is focused on teaching and not just on grading, then it should be possible to work out a solution.
With 1200 people it is hard to form a delegation to meet with the professor, but that would be a logical step.
But if this just happened, it may be that the professor will announce a suitable accommodation at the next meeting. If not, you might bring it up with the TAs for the course. I wouldn't escalate it to any formal complaint, however, until you have more evidence about how the professor intends to deal with it.
My advice to the professor, however, is that if you give a diagnostic that you know is invalid, you need to drop it entirely. It can't be finessed.

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2'One would be to just cancel the exam and adjust grading rubric accordingly' Depending on the OPs location, that one exam could be the only source of grading. – Joren Vaes Oct 24 '18 at 07:55
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2it is far more unfair to adjust the grading system partway through the course than to change an exam problem at the same time for all students. At the least you should get consent from all the students for a major change to the syllabus. – A Simple Algorithm Oct 24 '18 at 13:52
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@ASimpleAlgorithm. Hmmm. The grading system has been changed when this happens. Pretty much by definition. – Buffy Oct 24 '18 at 13:55
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@buffy I'm not even sure what you mean. I doubt the syllabus explicitly promises such details during an exam won't happen. However it likely does promise a certain calculation for grades. Change this, and I would support the complaint of any student who's grade is hurt as a result, as would the administration where I am. – A Simple Algorithm Oct 24 '18 at 14:02
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@ASimpleAlgorithm, I don't see how the grade could be hurt by dropping an invalid measure. I clearly see how grades of students who spent time on an impossible question (assuming there wasn't warning prior) could well be hurt by any finessing of it. You are prioritizing grading over teaching. I call that malfeasance. Find a better way. – Buffy Oct 24 '18 at 14:07
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@buffy What do exam scores have to do with teaching? You say "prioritizing grading over teaching" these seem to have little to do with each other. Grading is only useful for teaching in as much as it's a feedback tool. The other (primary?) goal of grading is providing a rating for future employers, teachers, grant/stipend committees to help them decide whether the student is qualified for something. From my experience in math (given 1200 students the most likely subject in the US) this kind of issue will harm essentially no one. – DRF Oct 24 '18 at 14:44
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@buffy (still assuming math) If the exam was an hour and thirty minutes each of the problems should have taken a well prepared student at most 15 minutes to work out. If you struggle you move on. A really well prepared student should have likely been able to guess or even prove whether the problem was solvable. I've never had this kind of problem on a class wide exam (lot's of revision on that and we were lucky I guess) but I did have it on quizzes. It altered the expected score of any given student by essentially nothing each time. I did redo or drop the quizzes but it had zero effect. – DRF Oct 24 '18 at 14:49
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@DRF. It is a mistake to make such assumptions about masses of people. Every student is different. Each approaches exams in a different way. What students "should" do and what they might "reasonably" do are not perfectly aligned. Deal with it. – Buffy Oct 24 '18 at 16:48
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3@Buffy Dropping an invalid grade (without giving additional make up exam/work) increases the weighing of any prior work. Retroactively increasing the weight of work that's already been done punishes anyone who calibrated the effort they applied to that work to the weighting the grade got. An extreme example of this would be, after homework is turned in, announcing that your course grade will be based entirely on that one piece of homework. Obviously, many people would have spent more time on that homework if they knew that. The rubric should be reliable, it's meant to be relied on. – David Schwartz Oct 24 '18 at 18:15
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@DavidSchwartz, but what you are describing is an unsupportable course design. If grades are determined by so few measures, whether homework or exams, you have a very poor system. It is very hard to get appropriate feedback from such a system and everything becomes high risk. If you use a sensible design, none of these bad things should happen. And note, please, that my original answer suggested that scheduling a new exam is an option. If the course design is so fragile that everyone needs to be perfect it is a terrible design. Fix it. Otherwise you just punish the innocent. – Buffy Oct 24 '18 at 18:37
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@buffy I luckily don't have to deal with THAT anymore. I have a job in industry so what I usually have to "deal" with is the outcome of molly coddling students who are utterly unprepared for any real life job and have very unreasonable expectations of both how the world works outside academia and what they actually know. When you sign a contract for developing a piece of hardware and you only figure out that what the customer wanted turns out to be impossible after you've spent 2/3rds of the budget they don't generally go. "Oh sure my bad here's another 2 mil." – DRF Oct 24 '18 at 19:14
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@DRF "Grading is only useful for teaching in as much as it's a feedback tool." No, no, no. For the sake of your students, please disabuse yourself of this poisonous misunderstanding as soon as possible. Assessments may well be the single most powerful teaching tool at the disposal of an instructor. The amount of learning that takes place before, after, and even during an examination absolutely dwarfs what goes on during lecture. Among many other learning processes, asessments bring strong emotion to bear, and also instigate cognitive consolidation. Time to reassess assessment! – Ben I. Oct 25 '18 at 02:52
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@DRF If you really want to learn about this, I cannot recommend strongly enough the incredible book, "How People Learn" from the National Academy of Sciences. It goes through all of the basics of what we really know about learning. It is also a simply beautiful book, well written and well sourced by some of the top academics in educational psychology. Assessments designed to simply rank students are simply lost opportunities. – Ben I. Oct 25 '18 at 03:04
Consider not doing anything.
The issue isn't time sensitive. Its not like the grades can't be changed after the fact. It's very reasonable to believe the professor is going to analyze the grades that came out of the exam and find a solution.
The professor will have information you don't have. While you know your exam was affected, and you can estimate how it affected 1199 other people, the professor will be making decisions with all 1200 graded exams in front of them.
Now if the professor hands you back the graded papers and doesn't do anything to resolve the issues, that's a good time to start making noise.

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One of my professors had a blanket rule that was applied to handle situations like these - You must solve the question to the best of your ability. If the missing piece of information can be simply substituted by a variable, say 'x', your answer must be in terms of 'x'. If you think that a question is not solvable, you should prove so in your answer. If you are successfully able to do it, you get full points for that question. Based on the difficulty of said proof, they also awarded bonus points, thus turning a potentially problematic situation on its head.
This worked wonders. The students were thrilled when they were able to successfully do this, and the professor had achieved a higher goal than what a simple exam would do. In fact there were unconfirmed rumours of the professor 'making a mistake' on purpose every once in a while. You can suggest that your professor adopt a similar policy in the future.
As for what you can do now, your options are limited. People make mistakes. You can contact the professor via a polite email and make your concerns known. You can also ask what strategy they would apply, to make it fairer. Whatever they do, it's probably not going to be 100% fair anyway. If they do nothing, or their strategy is blatantly unfair, that would be the time for you to take your complaint further if need be. But any half decent strategy is probably going to get the support of any grading committee(s) and/or department heads.

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Can every even integer greater than 2 be written as the sum of two primes? You're free to introduce X if you wish or prove unsolvability. – Dmitry Grigoryev Oct 26 '18 at 13:22
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@DimitryGrigoryev You're simply trying to break the rule without context. OP's issue is one of missing or incorrect information in the question (which is a genuine mistake), not of unsolved problems. But, I'll humor you. In the highly unlikely scenario that a question for an undergrad class test, that seems reasonable at face value, turns out unsolved, I would still like to see the students try. That's where "best of your ability" and "bonus points" come in. Having the students make their best attempt allows the professor to come up with a fairer grading strategy. – TheJack Oct 26 '18 at 21:51
Other answers respond to the questions raised in the main body of your message, I'd like to comment on the broader question (asked in the title), What should I do if my professor changes the question mid-exam?, with particular reference to
unless you did the other two questions knowing [the other] question was impossible to solve and waited for an announcement on instructions of how to solve, you would not be able to finish.
Exam strategy can help here: I recommend considering the entire examination script before writing. If you're able to identify an issue with any question, then immediately raise it with invigilators. (They should promptly raise such issues with the professor.) This maximises the window during which a professor can respond to the issue. Divide the remaining time between questions, with the goal of maximising your score. If you were able to identify an issue with a question, then that question should be delayed, because you might receive additional information during the exam. Returning to the question:
What should I do if my professor changes the question mid-exam?
Be prepared: Anticipate this possibility and adopt an exam strategy that optimises your advantage.
Response to comments
You're not answering the question. You're giving advice about [what] one can do before a change [of an exam script] to reduce the impact, not what to do in response to a change.
and
The question of How to preparation for when a professor changes the question mid-exam would be well answered by this. What to do after the fact is the OP's question. Unless you have a time-machine allowing the OP to follow your advice "preemptively", this does not answer the question.
After an event such as the OP's, one must reflect and consider how to improve themselves. My answer explains how the OP should improve themselves for a similar such event in the future. I consider this to be a crucial part of the OP's response.

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4You're not answering the question. You're giving advice about one can do before a change to reduce the impact, not what to do in response to a change. – Acccumulation Oct 24 '18 at 15:29
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@Acccumulation I've answered the question What should I do if my professor changes the question mid-exam? in a pre-emptive fashion, that is, for those who haven't yet experienced a professor changing an exam but might well do so in the future. – user2768 Oct 25 '18 at 06:34
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1The question of How to preparation for when a professor changes the question mid-exam would be well answered by this. What to do after the fact is the OP's question. Unless you have a time-machine allowing the OP to follow your advice "preemptively", this does not answer the question. – Oct 25 '18 at 08:08
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@GypsySpellweaver After a bad event, do you not reflect and consider how to improve yourself in the future? My answer explains exactly what the OP should be doing after the fact, namely, improving themselves for a similar such event. – user2768 Oct 25 '18 at 08:19
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1Planning for the future exams, and learning from the experience are good, as is your advice. It still, however, does not address the OP's concerns. – Oct 25 '18 at 08:24
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As I explain in my opening, other answers have largely addressed the explicit concerns raised by the OP. I'm addressing a broader aspect which is surely useful to the OP (and explicit in the title) and the wider community. – user2768 Oct 25 '18 at 08:27
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I assume that you never have a problem assessing whether a question is answerable or not (or how difficult it is) at a glance. Otherwise, your advice is not particularly useful. – David Thornley Oct 25 '18 at 20:29
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@DavidThornley This isn't about me, this about the body of students. Also, I cannot take credit for the advice, it is a pretty standard exam strategy that is widely taught. – user2768 Oct 26 '18 at 07:02
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As you admit, this answer does not address the explicit concerns raised by the OP. In view of that admission, I conclude that this post is not an answer to the question. Contrary to your claim, this post also does not address the question explicit in the title, which mentions nothing about any potential future exams. – Oct 27 '18 at 01:31
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@GypsySpellweaver I disagree: I consider my answer an answer to this question. – user2768 Oct 29 '18 at 07:12
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@GypsySpellweaver Why don't you ask the OP whether I answered their question? Then you'll have the answer you're searching for. – user2768 Oct 29 '18 at 07:59
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Once the OP selects an answer as the "accepted" one, they'll have their answer. As a user new to the system they may not do that, or even know they should. Often questions with good answers aren't accepted for that reason, and others as well. We may never have a decision since the OP, while returning to the site, has not posted any replies to comments. – Oct 29 '18 at 08:36
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@GypsySpellweaver I just meant you could comment on the OP's question, if you wanted their answer – user2768 Oct 29 '18 at 08:44