It depends on the exam- some don't want an address, especially if there is a word limit. However, they will deduct some marks for not putting a salutation and closing because it is supposed to be a letter. Again, without knowing the exam, it is not possible to know how many marks would be deducted, and many exam boards don't reveal such detailed information, but it is the body of the letter that is the most important part, so the deduction should be fairly small. It might be a fixed deduction of marks, or it might be something like not being able to get a grade A, of it is graded by letter. In itself, it wouldn't be enough to fail.
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