Learn Hardcore German: Im Schwerpunktbereich Prüfungstraining wiederholen wir Grammatik und sprechen viel. - In the focus area of exam training we review grammar and speak a lot.

In can take the dative when it expresses a location or a more abstract “within” something (rather than movement into).
Schwerpunktbereich is masculine (der Schwerpunktbereich), so in the dative it would be dem Schwerpunktbereich.
Colloquially and in standard written German, in dem is almost always contracted to im.

So im Schwerpunktbereich = in dem Schwerpunktbereich (“in the focus area / module …”) in the dative case.

What case is Schwerpunktbereich Prüfungstraining, and how do we know?

It’s in the dative case, governed by im (= in dem).

Preposition in can take dative (location / “within”) or accusative (movement into).
Here we are “in” a course area (no movement), so in + dative is used.
Because Schwerpunktbereich is masculine, the dative with the article would be in dem Schwerpunktbereich → im Schwerpunktbereich.

Prüfungstraining just belongs to the name and shares the same dative; its form doesn’t change because it’s neuter and here looks the same in all cases.

What is the relationship between Schwerpunktbereich and Prüfungstraining? Is Prüfungstraining genitive?

No, Prüfungstraining is not genitive here. It is part of the name/title of that focus area, like a course label. Think of it as:

im Schwerpunktbereich „Prüfungstraining“ (“in the focus area ‘Exam Training’”)

In educational contexts you often see structures like:

Kurs Grammatik
Seminar Landeskunde
Schwerpunktbereich Zivilrecht

The second noun just specifies or names the first one; there is no article or genitive ending required. So Schwerpunktbereich Prüfungstraining is essentially a two-part label.

Why is Prüfungstraining written as one word and capitalized?

Prüfungstraining is a compound noun:

die Prüfung (exam) + das Training → das Prüfungstraining (exam training).

In German, such combinations are written as one word and capitalized because they are nouns. This is different from English, which often writes them as two words (“exam training”).

Why is Grammatik used without an article?

In German, many abstract or school-subject nouns can be used without an article when talking about them in general as a field of study or content area.

So:

Wir wiederholen Grammatik. = We review grammar (as a subject, in general).

If you said wir wiederholen die Grammatik, it would sound more like a specific grammar portion already known from context (e.g. “the grammar from last week’s unit”), not the subject overall.

What case is Grammatik in, and why doesn’t it change its form?

Grammatik is in the accusative case as the direct object of wiederholen.

Verb wiederholen is transitive: you repeat/review something.
That something (here Grammatik) is in the accusative.

You don’t see a change in the ending because:

die Grammatik (nominative singular) → die Grammatik (accusative singular)
Feminine nouns with the definite article die look the same in nominative and accusative.

Why is the word order Im Schwerpunktbereich … wiederholen wir … and not Wir wiederholen … im Schwerpunktbereich …?

German main clauses must have the finite verb in second position (V2 rule), but position 1 can be almost any single element, not just the subject.

Two possibilities:

Wir wiederholen Grammatik im Schwerpunktbereich Prüfungstraining.
- Subject wir in first position.
Im Schwerpunktbereich Prüfungstraining wiederholen wir Grammatik …
- The prepositional phrase goes in first position to emphasize the setting (“In that module…”).

Both are grammatically correct; the given sentence simply fronts the place/course information for emphasis or textual flow.

Why is there no comma before und in wiederholen wir Grammatik und sprechen viel?

Because und here is joining two verbs with the same subject in a single clause, not two separate main clauses.

Structure:

Subject: wir
Verb 1: wiederholen
Object: Grammatik
Conjunction: und
Verb 2: sprechen
Adverb: viel

In German, you don’t put a comma before und when it simply links two parts of the predicate with the same subject:

Wir essen und trinken. (no comma)

A comma would be used if there were two independent clauses:

Wir wiederholen Grammatik, und wir sprechen viel. (possible, but different rhythm/emphasis)

Why is it sprechen viel and not viel sprechen?

With simple verb + degree adverb like viel, the normal word order is:

wir sprechen viel = we speak a lot.

Viel is an adverb describing how much you speak; it generally comes after the verb in such simple sentences.

Wir viel sprechen is incorrect word order in standard German.
You can, however, see viel sprechen as an infinitive phrase in other contexts, e.g. Wir wollen viel sprechen (“We want to speak a lot”), where viel directly modifies the infinitive sprechen as a chunk.

What exactly does wiederholen mean here – “repeat” or “review”?

In school/university contexts, wiederholen very often means “to go over again / revise / review”, not just to mindlessly repeat.

So in this sentence:

wiederholen wir Grammatik = we revise/review grammar (to practice and consolidate it).

English learners often translate wiederholen only as “repeat”, but in teaching contexts “review” or “revise” is usually the most natural translation.