Learn Hardcore Japanese: siken ha kuzi ni owarimasu.

In Japanese, は is the topic marker, used to introduce what the sentence is “about.” Here it tells us “as for the exam…” If you used が, you’d be marking 試験 strictly as the grammatical subject. Since we’re talking about the exam in general and then giving information about it, は is more natural:
“As for the exam, it ends at nine.”

Why isn’t there a を particle after 試験? Doesn’t “end” take an object?

The verb 終わります (終わる) is intransitive—meaning the action happens by itself (“to come to an end”). Intransitive verbs never take を. If you wanted a transitive version (“to finish something”), you’d use 終える, and then you could say something like 本を終えた (“finished the book”).

Why do we need に after 九時?

に marks a specific point in time. When you say 九時に, you’re pinpointing “at nine o’clock.” Without に, 九時 could be misinterpreted as a more general time frame or feel incomplete in a scheduled context.

Could I say the time first, as in 九時に試験は終わります?

Yes. Japanese allows fairly flexible word order. Starting with 九時に simply emphasizes “at nine.” Both 試験は九時に終わります and 九時に試験は終わります are perfectly natural.

Why is the verb in the -ます form (終わります) instead of the dictionary form (終わる)?

The -ます form is the polite register, often used in formal announcements, classrooms, or with people you don’t know well. The plain/dictionary form is 終わる; you’d hear it among friends or in casual writing: 試験は九時に終わる.

How would I ask “What time does the exam end?”

Replace 九時に with 何時に and add the question particle か at the end:
試験は何時に終わりますか。
Literally: “As for the exam, at what time does it end?”

How do I say “The exam ended at nine”?

Change the verb to the past polite form 終わりました:
試験は九時に終わりました。

What if I want to say “The exam will end around nine”?

Attach ごろ to indicate approximation:
試験は九時ごろ終わります。
Here, ごろ softens 九時 to “around nine.”