Vor der Sprachprüfung brauchst du nur ruhig zu atmen und langsam zu sprechen.

Because vor here is a preposition used in a time expression: before the language exam.

With temporal vor, German uses the dative case, so:

• die Sprachprüfung = the language exam
• vor der Sprachprüfung = before the language exam

Since Sprachprüfung is a feminine noun, its dative singular article is der.

So:

• nominative: die Sprachprüfung
• dative: der Sprachprüfung

Yes. German very often combines nouns into a compound noun.

Here:

• Sprache = language
• Prüfung = exam/test

Together, they form Sprachprüfung = language exam.

A few things to notice:

• The final -e in Sprache disappears in the compound.
• The last part usually determines the grammatical gender.
• Since Prüfung is feminine (die Prüfung), die Sprachprüfung is also feminine.

This is very normal in German.

Because German main clauses follow the verb-second rule.

That means the finite verb must come in the second position. Position 1 can be taken by different elements, not just the subject.

Here, Vor der Sprachprüfung is placed first for emphasis or context, so the verb comes next:

• Vor der Sprachprüfung | brauchst | du ...

If you start with the subject instead, that is also possible:

• Du brauchst vor der Sprachprüfung nur ruhig zu atmen und langsam zu sprechen.

Both are grammatical. The original sentence just puts the time phrase first.

It means you only need to.

So brauchst du nur expresses that the required action is simple or limited:

• du brauchst nur ... = you only need to ...

It is less forceful than du musst ... (you must ...).

Compare:

• Du musst ruhig atmen. = You must breathe calmly.
  
  • stronger, more demanding
• Du brauchst nur ruhig zu atmen. = You only need to breathe calmly.
  
  • gentler, reassuring

In this sentence, it sounds encouraging.

Because brauchen here is followed by an infinitive with zu.

The pattern is:

• brauchen + zu + infinitive

So:

• ruhig zu atmen
• langsam zu sprechen

This is standard German in a sentence like this.

You can think of it as similar to English to breathe / to speak, although German uses zu only in certain constructions.

Because nur applies to the whole infinitive phrase:

• ruhig zu atmen und langsam zu sprechen

So the idea is:

You only need to do these things:

1. breathe calmly
2. speak slowly

German does not need to repeat nur before each verb.

If you did repeat it, it would sound more deliberate or stylistically heavier, but here one nur is enough and most natural.

Yes, they are functioning like adverbs here.

A very important point for English speakers is that German usually does not add a special ending like English -ly.

So:

• ruhig can mean calm or calmly
• langsam can mean slow or slowly

In this sentence:

• ruhig zu atmen = to breathe calmly
• langsam zu sprechen = to speak slowly

The form stays the same. German adjectives used adverbially are usually unchanged.

Here it most naturally means calmly.

Ruhig can have several related meanings, including:

• calm
• calmly
• quiet
• quietly
• steady / relaxed

In the context of a language exam, ruhig zu atmen means something like:

• breathe calmly
• breathe steadily
• don’t panic

It is not mainly about making no sound. Context tells you which shade of meaning is intended.

In standard German, in this kind of sentence, zu is expected:

• Du brauchst nur ruhig zu atmen.

You may sometimes hear forms without zu, especially in colloquial speech or in certain regions, often in negative or question contexts, such as:

• Du brauchst nicht kommen.
• Brauchst du das machen?

But for learners, the safest rule is:

• use brauchen + zu + infinitive in standard written German

So the sentence as given is the best model.

Because ruhig zu atmen and langsam zu sprechen are two coordinated infinitive phrases joined by und, and they belong together under brauchst du nur.

German normally does not use a comma before und in a simple coordination like this.

So:

• ... nur ruhig zu atmen und langsam zu sprechen.

is correct.

A comma would only appear in more specific structures, not in this straightforward pairing.

You could say Du musst nur ruhig atmen und langsam sprechen, but it changes both the grammar and the tone a little.

Two points:

1. With müssen, you do not use zu:

   • Du musst atmen
   • not Du musst zu atmen

2. müssen is stronger than brauchen:

   • du brauchst nur ... = you only need to ...
   • du musst ... = you must ...

So the original sentence sounds more reassuring and supportive.
Using müssen sounds a bit more forceful.

This is another result of the verb-second rule.

Since Vor der Sprachprüfung is in first position, the conjugated verb must be second:

• Vor der Sprachprüfung | brauchst | du

So the subject du comes after the verb.

This does not make it a question. It is still a normal statement, because the first position is occupied by the time phrase.

Compare:

• Du brauchst nur ruhig zu atmen.
• Vor der Sprachprüfung brauchst du nur ruhig zu atmen.

Both are statements; they just start differently.