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During a time-limited closed-book final exam, I was asked to write an essay summarizing what I learned in this course. I used a lot of key knowledge points and conceptual explanations from the memorized textbook in the essay (about 20% of the 1000 words), but did not add a citation for the textbook, since I did not have the opportunity to find the accurate citation format in the closed-book exam.
Would this be considered plagiarism by the professor?
Under time-limited exam conditions, it is usual to expect that a candidate may recall a point without recalling its source or having the ability to look it up. If it is a closed-book exam, that is all the more reason to expect that they are unable to look it up. Consequently, unless there is some specification to the contrary, exams of this kind would not expect you to cite your sources. Failure to do so would not be considered plagiarism.
While it is difficult to predict what the professor will do, a reasonable professor should not consider that plagiarism.
Was this exam part of an essay you have to write that needs to be professionally written with all possible citations? If yes, and this was made clear, and the professor is able to find the plagiarized content, you might be in trouble. In such a case, I would not expect more than a small proportion of a reduced grade.
Did you have to sign a declaration of independent work? I am guessing "No", so no legal trouble as well.
Was this exam a 'normal' written exam? I am assuming this is the case. Then no. It might also make running it through a plagiarism checker difficult. In fact, I believe your thorough reading of the literature illustrates the fact that you can write verbatim what you read. You are in very safe territory if you did not claim the verbatim text to be your own (i.e. I believe ...), but covered it up with an external source (i.e. It has been mentioned ...).
There is a difference between plagiarism and cheating. Plagiarism is taking someone else's work or ideas and representing them as your own (no matter whether verbatim or with some modification to hide their origin). Cheating during an exam, on the other hand, is using any help or sources of information you are not supposed to use (like peeking at a hidden cheatsheet or textbook, or having someone read it to you via a small earbud).
In your case, it appears that you are supposed to summarize what you have learned from lectures and the textbook. This implies that your answer can contain information taken from the textbook, so plagiarism is not an issue here (unless you were asked to come up with your own examples demonstrating the application of the knowledge you learned, but you took your examples from the textbook or some source rather than creating your own).
Now, about cheating. Unless you did peek at a textbook or other source of information you were not supposed to use, reproducing parts of it from memory is not cheating. But your professor might suspect cheating if you reproduce large fragments from the textbook verbatim, because it is unusual to have such a good memory (unusual, but not impossible—I knew a person who could recite many pages of text verbatim after reading it once or twice). If you have such a good memory, then it is likely that either your professor has already noticed it or that you can prove your unusual abilities. To avoid suspicion and possible need to explain yourself, I would recommend asking your professor about it beforehand.
Another concern that your professor might have is that, although you can reproduce large portions of learned material from memory verbatim, your essay does not show that you understand the material or can apply it in practice when the need arises. Make sure your essay includes your own thoughts that demonstrate your understanding.
Occasionally, when I've recalled an odd fact to support an argument and remembered more or less where I got it I've thrown in a partial citation like this:
Snails are very slow (from course textbook "Introduction to Zoology")
But I would imagine that a professor is more likely to be concerned that you were looking at the textbook rather than not providing a citation on an exam (which is not a common thing to do).
If you do have a problem (unlikely, I think), I would hope that they allow you to demonstrate that you've memorized the relevant passages from the textbook.
