Learn Swedish: Han oroar sig för provet. - He is worried about the exam.

In Swedish, the verb for "to worry" is reflexive: att oroa sig, which literally means "to worry oneself". If you leave out the reflexive pronoun and just say oroar, it means you are making someone else worry. For example, han oroar mig would mean "he worries me".

Could I use honom instead of sig?

No, because han is the subject of the sentence, so you must use the reflexive pronoun sig to show that he is worrying himself. If you said han oroar honom, it would mean "he worries him" (meaning he is causing a completely different person to worry).

Why does the sentence use för instead of om for "about"?

Prepositions rarely translate perfectly between English and Swedish! The fixed expression for "to worry about" is att oroa sig för. It is best to memorize the verb and the preposition together as a single phrase.

How do we know provet means "the exam" and not just "exam"?

In Swedish, "the" isn't a separate word like in English, but an ending added to the noun. Because the base word for exam is an ett-word (ett prov), adding the definite ending -et gives us provet (the exam).