Eksamenen er overstået.

Because Danish usually marks the by adding an ending to the noun.

• en eksamen = an exam
• eksamenen = the exam

Eksamen is an en-word (common gender), so its definite singular form ends in -en.

This is one of the biggest differences from English: instead of a separate word like the, Danish often attaches the definite article to the noun itself.

Overstået is the past participle of the verb at overstå.

In this sentence, it functions like a predicate adjective after er, so you can think of it as meaning something like:

• finished
• over
• done with

So Eksamenen er overstået works like The exam is finished.

Here, -et is part of the participle form itself. It is not the same kind of ending as the definite -en in eksamenen.

A useful way to think about it is:

• eksamenen: noun + definite ending
• overstået: participle form of overstå

So the sentence is not built from a plain adjective overstå. The correct form is overstået.

Because this sentence is describing a state: the exam is over.

So er is a linking verb, like in:

• Døren er lukket = The door is closed
• Mødet er færdigt = The meeting is finished

If you used har, the structure would be different and would usually mean that someone has gotten through or completed something:

• Jeg har overstået eksamenen = I have gotten through the exam

So er overstået is not the same as English has passed. It is more like is over / is finished.

Not in the most useful learner sense.

Even though overstået comes from a verb, Eksamenen er overstået is best understood as a sentence describing the exam’s resulting state.

So it is closer to:

• The exam is over
• The exam is finished

than to a true action-passive like:

• The exam was prepared by the teacher

For a learner, it is safest to treat er overstået here as a state description.

Yes. Overstået often suggests that something has been gotten through, sometimes with a feeling of relief.

Compare:

• Eksamenen er slut = the exam is finished
• Eksamenen er forbi = the exam is over
• Eksamenen er overstået = the exam is over and done with, often implying thank goodness

So overstået is especially natural for things that may feel stressful, difficult, or unpleasant.

Usually not in this exact situation.

If you are talking about a specific exam, Danish normally wants the definite form:

• Eksamenen er overstået

Without the definite ending, it sounds less natural here.

However, bare eksamen does appear in other expressions, especially when talking about the activity of taking an exam in a general way:

• Jeg skal til eksamen i morgen = I have an exam tomorrow
• Hun er til eksamen nu = She is in an exam right now

So the bare noun is possible in Danish, but not usually in this particular sentence about a specific exam already being referred to.

You invert the verb and the subject:

• Er eksamenen overstået? = Is the exam over?

That is standard Danish word order for a yes/no question.

Yes. It is very common with events, tasks, or difficult situations that someone has had to get through.

For example:

• Mødet er overstået = The meeting is over
• Operationen er overstået = The operation is over
• Arbejdet er overstået = The work is finished
• Flytningen er overstået = The move is over

It is especially common when the speaker feels that something demanding is now behind them.