Learn Hardcore Norwegian: Hun er nervøs fordi eksamen er viktig for henne. - She is nervous because the exam is important to her.

In this sentence, eksamen is understood as the exam (she is about to take) from context. You could say Hun er nervøs fordi den eksamenen er viktig for henne, but that sounds too heavy and specific, like pointing to one very clearly identified exam.

So the bare eksamen is natural and idiomatic here and covers what English expresses with the exam.

What is the difference between hun and henne, and why do we need both in this sentence?

Norwegian distinguishes between subject and object forms of pronouns, similar to she vs her in English.

hun = she (subject form)
henne = her (object / stressed form)

In the sentence:

Hun er nervøs – Hun is the subject of er (is).
viktig for henne – henne is the object of the preposition for (important for her).

So you need hun in the first part and henne in the second, just like English needs she and her.

Why is it viktig for henne and not viktig til henne?

In Norwegian, the preposition used with important (to someone) is for, not til:

Det er viktig for meg. – It is important to/for me.
Eksamen er viktig for henne. – The exam is important to her.

til is often more literal: to, towards, until:

Gi boka til henne. – Give the book to her.
Jeg går til skolen. – I walk to school.

So with viktig, the fixed and natural pattern is viktig for + person.

I thought Norwegian has the verb in second position. Why is it fordi eksamen er viktig and not fordi er eksamen viktig?

The verb-second (V2) rule applies to main clauses, not to subordinate clauses.

Main clause: Eksamen er viktig.
- Verb (er) is in second position.
Subordinate clause after fordi: fordi eksamen er viktig
- Word order is normally subject – verb – rest (S–V–O/adv).

So:

Hun er nervøs, fordi eksamen er viktig for henne. ✅
Hun er nervøs, fordi er eksamen viktig for henne. ❌ (ungrammatical in standard Norwegian)

Could I move for henne earlier and say Hun er nervøs fordi for henne er eksamen viktig?

You can move for henne for emphasis, but you need to keep correct subordinate-clause word order.

Neutral, most natural:
Hun er nervøs fordi eksamen er viktig for henne.
With a bit of emphasis on for henne:
Hun er nervøs fordi eksamen, for henne, er viktig. (spoken, with pauses)
or
Hun er nervøs fordi, for henne, er eksamen viktig. (quite marked/poetic)

Your exact version fordi for henne er eksamen viktig sounds somewhat marked but can appear in spoken language for strong emphasis:

Hun er nervøs, fordi for henne er eksamen viktig.

In ordinary, neutral speech and writing, stick to:
… fordi eksamen er viktig for henne.

Why is it er nervøs (is nervous) and not blir nervøs (becomes nervous)?

Both are possible, but they describe slightly different situations:

Hun er nervøs – She is in a nervous state now. It describes her current condition.
Hun blir nervøs – She becomes / gets nervous (a change from not nervous to nervous).

Your sentence explains why she is already nervous:

Hun er nervøs fordi eksamen er viktig for henne.
She is (already) nervous, because the exam is important.

If you say:

Hun blir nervøs fordi eksamen er viktig for henne.
then you highlight the process of becoming nervous whenever she thinks about the exam.

Why is the adjective just nervøs, without any ending?

Adjectives in Norwegian behave differently depending on where they appear:

Attributive (in front of a noun)
They agree in gender/number/definiteness:
- en nervøs student – a nervous student
- et nervøst barn – a nervous child
- nervøse studenter – nervous students
Predicative (after er, blir, etc.)
In standard Bokmål, adjectives in this position do not change with gender or number:
- Hun er nervøs. – She is nervous.
- Han er nervøs. – He is nervous.
- De er nervøse. – They are nervous. (here plural -e is common)

For many speakers:

singular: er nervøs (same for male and female)
plural: er nervøse

So Hun er nervøs is the normal singular predicative form.

Does viktig change form like nervøs does?

Yes, viktig follows the regular adjective pattern:

en viktig eksamen – an important exam (masc/fem)
et viktig prøveresultat – an important test result (neuter)
viktige eksamener – important exams (plural)

In eksamen er viktig, the adjective is predicative (after er) in the singular, so it stays viktig:

Eksamen er viktig. – The exam is important.
Eksamener er viktige. – Exams are important. (plural -e)

Could I use another conjunction like siden or fordi at instead of fordi?

Yes, but there are nuances and style preferences:

fordi – the most neutral and common for because.
- Hun er nervøs fordi eksamen er viktig for henne.
siden – often means since (because), slightly more formal or explanatory.
- Hun er nervøs siden eksamen er viktig for henne. (OK, but a bit more formal/written in some contexts.)
fordi at – possible in speech and some dialects, but often considered less elegant or redundant in standard written Bokmål.
- Hun er nervøs fordi at eksamen er viktig for henne. (Many style guides would recommend dropping at.)

For clear, standard Bokmål, fordi alone is the best choice here.

What is the difference between nervøs, spent, and redd?

These three words all relate to feelings around expectations, but they are not the same:

nervøs – nervous, anxious (often with worry or stress)
- Hun er nervøs før eksamen.
spent – excited / anxious in the sense of tense with expectation (can be positive or neutral)
- Hun er spent på hvordan eksamen går. – She is eager/curious to see how the exam goes.
redd – afraid, scared (stronger fear)
- Hun er redd for å stryke på eksamen. – She is afraid of failing the exam.

In your sentence, nervøs is the best match: she feels stressed and tense because the exam matters to her.

Could we leave out for henne and just say Hun er nervøs fordi eksamen er viktig?

Yes, grammatically that is fine:

Hun er nervøs fordi eksamen er viktig.

However, for henne adds a personal perspective:

with for henne: It is important to her, maybe more than to others.
without for henne: It sounds more general, like the exam is important (objectively, for everyone).

So for henne emphasizes that this importance is specifically from her point of view.

How do you pronounce eksamen?

Approximate pronunciation in standard Eastern Norwegian:

eksamen: [ek-SA-men]

Details:

ek-: like ek in “deck” (short e).
-sa-: stressed syllable, sa like English “sah” (open a sound).
-men: like men in English “men”, but often with a slightly more closed e.

Stress is on the second syllable: ek-SA-men.