Learn Hardcore Russian: Учитель объявил о контрольной работе на следующей неделе. - The teacher announced a test for next week.

о introduces the topic of the announcement.
The noun phrase контрольная работа must switch to the prepositional case: контрольной работе (adjective ends in -ой, noun in -е).

Why is the time expression на следующей неделе also in the prepositional case?

When you specify “when” something happens using на + a fixed point in time, Russian uses the prepositional case.

следующая неделя (nominative) → на следующей неделе (prepositional) to mean “during next week.”

What’s the difference between на следующей неделе and на следующую неделю?

They look similar but have distinct uses:

на следующей неделе (prepositional) = “at some point during next week”
на следующую неделю (accusative) = “for next week” in the sense of booking or planning (“Let’s schedule it for next week”).

Could I omit о and say Учитель объявил контрольную работу на следующей неделе?

No—объявить meaning “to announce” is not used with a direct object. Dropping о would sound ungrammatical or force you to switch verbs (e.g. назначил контрольную работу).

Why is объявил used here and not a more everyday verb like сказал or сообщил?

объявил implies a formal or official announcement (e.g. in class, over a loudspeaker).
сообщил (“informed”) is more neutral, describing giving information.
сказал simply means “said,” without the nuance of a public announcement.

Why aren’t there any articles before Учитель or контрольной работе (like “the teacher” or “the test”)?

Russian has no articles (no a/an or the). Definiteness and indefiniteness are inferred from context, word order, intonation, or additional words.

Why do контрольная and работа change to контрольной работе?

Both words must agree in gender, number, and case:

работа is feminine singular. Prepositional ending: работе.
контрольная (feminine singular adjective) takes prepositional ending -ой → контрольной.

Can you shorten контрольная работа to just контрольную here?

Yes, in casual school contexts you often hear контрольную alone (spoken shorthand for контрольная работа). You still need the preposition о + prepositional: объявил о контрольной.

Where’s the stress in объявил?

Stress falls on the last syllable: объявИл (o-bya-VIL).