Domani ho una prova di matematica.

Putting domani first is very natural in Italian when you want to set the time right away: Tomorrow, I have a math test.

Italian word order is more flexible than English word order. You could also say:

• Ho una prova di matematica domani.

That still means the same thing. Starting with domani just makes the time feel slightly more prominent.

Italian often uses the present tense to talk about the near future, especially when a time word already makes the future clear.

So:

• Domani ho una prova di matematica.

is completely normal.

You could also say:

• Domani avrò una prova di matematica.

That is also correct, but it may sound a bit more formal, deliberate, or emphatic. In everyday speech, the present tense is very common for planned future events.

Italian usually leaves out subject pronouns when they are not needed, because the verb ending already shows who the subject is.

• ho = I have

So io is not necessary here.

You could say:

• Domani io ho una prova di matematica

but that would usually add emphasis, as if you were contrasting yourself with someone else.

In this sentence, prova means test or quiz.

But prova can have other meanings too, depending on context, such as:

• attempt
• trial
• proof
• rehearsal

In a school context, una prova di matematica is naturally understood as a math test.

Prova is a singular feminine noun, so it takes the feminine singular indefinite article una.

• una prova = a test

If the noun were masculine, the article would be different, for example:

• un libro = a book

So this is simply article agreement:

• feminine singular noun -> una

In Italian, when you talk about the subject matter of a class, test, book, or lesson, you often use di + subject without an article.

So:

• una prova di matematica = a math test
• un libro di storia = a history book
• un professore di inglese = an English teacher

Using della matematica would usually sound wrong here. Di matematica is the normal way to say in math / of math in this kind of expression.

Yes. Matematica means mathematics or math.

In everyday translation:

• prova di matematica = math test

Italian uses the full word matematica, while English often shortens mathematics to math.

In Italian, the h in ho is silent.

So ho is pronounced basically like o.

The h is there to distinguish forms of the verb avere from other words:

• ho = I have
• o = or

They sound the same, but they mean different things.

Sometimes, but not always.

• prova is a general word for test, quiz, or assessment
• esame usually means a more important exam

So if you mean an ordinary school test, prova sounds very natural.
If you say esame, it may sound more serious or formal.

Depending on the school context, Italians might also say:

• verifica = a school test/check
• compito in classe = an in-class written test

Yes. Italian allows some flexibility.

All of these are possible:

• Domani ho una prova di matematica.
• Ho una prova di matematica domani.

The first version is probably the most neutral if you want to emphasize when.
The second may sound a little more conversational in some contexts.

No. Domani is not normally capitalized unless it begins the sentence, as it does here.

So:

• Domani ho una prova di matematica.

The capital D is only there because it is the first word of the sentence, not because domani itself is a special kind of word.

It could, depending on context, but test is usually the safest translation for prova here.

If the meaning shown to the learner is Tomorrow I have a math test, that is a very natural match.

If you specifically want exam, Italian would more often use:

• Domani ho un esame di matematica.

So prova is usually less formal and less high-stakes than esame.