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For example, are

> 先週の金曜日に試験があります。
>
> 5月5日に難しい試験があります.
>
> 来週の木曜日に友達と約束があります。

correct sentences? In the early chapters of the textbook I use, the pattern
'Noun は (Time phrase) です' is used. But now this seems odd to me. Surely, this
would be saying 'The exam is Friday' as in the exam is not on Friday but
literally IS Friday. As if they are one in the same. Thank you for any help!
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usage
Can time phrases be used in sentences using あります to show possession?
Your example sentences are understandable but not completely correct. You
could say 先週の金曜日に **は** 試験があります

Answer to [this
question](https://japanese.stackexchange.com/questions/43887/what-is-the-
difference-between-ni-and-ni-wa-when-talking-about-a-person) has an example
sentence "彼女にはたくさんの経験があります", and contains more in-depth analysis so I wouldnt
repeat here
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Yes, these are correct and perfectly natural. However, this is not to
**possessive** sense of あります, but the **existential** sense. Refer to [aru
Kanji confusion](https://japanese.stackexchange.com/q/72093/78) for additional
explanation.

> 先週の金曜日に試験がありました。 → Last (week on) Friday there was/existed a test.

And contrary to @Zeyuan's answer, you do not _need_ to use ～には. You can use
either of ～に or ～には. The former is simply neutral while the latter puts
emphasis on the time.

As far as the ～は～です pattern, remember that the particles and copula are as
flexible as they are in English. 試験は金曜日です is fine to say "The exam is Friday",
and just as in English, it doesn't mean "The test equals Friday" or that it
literally is Friday as you say.

>   * [幸子]{さち・こ}： [雅人]{まさ・と}君どこ出身ですか？ → Masato, where is your hometown?
>   * 雅人： 名古屋です。幸子さんは？ → I'm from Nagoya. What about you, Sachiko?
>   * 幸子： 私は大阪です。 → ~~I am Osaka~~ (As for me) It's Osaka
>

You wouldn't equate Sachiko to literally being the same thing as Osaka.
Remember that は is "simply" the topic marker.
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