Spero di prendere un buon voto nell’esame di matematica.

In Italian, when sperare is followed by another verb with the same subject, you normally use di + infinitive.

So:

• Spero di prendere... = I hope to get...
• not Spero prendere...

This is very similar to English I hope to get...

If the subject changes, Italian usually switches to che + subjunctive, for example:

• Spero di prendere un buon voto. = I hope to get a good grade.
• Spero che tu prenda un buon voto. = I hope that you get a good grade.

Yes, prendere often literally means to take, but in Italian it is also commonly used in the sense of to get / to receive, especially with grades, transport, illnesses, and similar things.

So:

• prendere un voto = to get a grade
• prendere un autobus = to take a bus
• prendere un raffreddore = to catch a cold

In this sentence, prendere un buon voto is the natural way to say to get a good grade.

This is because buono often becomes buon before a masculine singular noun.

So:

• un buon voto
• un buon libro
• un buon risultato

This shortening is very common and natural.

Also, voto is a masculine noun, so you need:

• un for the article
• buon in the masculine singular form

You would use buona with a feminine noun, for example:

• una buona idea

In this sentence, voto means grade or mark in a school context.

So un buon voto means:

• a good grade
• a good mark
• a high score

Be careful: voto can also mean vote in political contexts. Italian uses the same word for both ideas, so the meaning depends on context.

Nell’esame is a contraction of:

• in + l’esame → nell’esame

Here is the breakdown:

• in = in / on / during
• l’ = the
• esame = exam

So nell’esame means in the exam or on the exam, depending on how English would express it.

You cannot normally say in esame here, because that would be missing the article. Italian usually needs the article in this kind of phrase.

The apostrophe appears because esame begins with a vowel.

The full form would be based on lo:

• in + lo esame → nello esame

But Italian avoids that awkward vowel sequence and elides it:

• nello esame → nell’esame

This is the normal written form.

The same thing happens in phrases like:

• all’esame
• dell’esame
• l’esame

In Italian, school subjects are usually introduced with just di + subject, without the article.

So:

• esame di matematica = math exam
• professoressa di italiano = Italian teacher
• libro di storia = history book

Using della matematica would sound different and usually less natural here. It would suggest something more like of mathematics in a broader or more abstract sense, not simply math exam.

So for naming the subject of the exam, di matematica is the standard choice.

Yes, and in many situations all’esame di matematica may sound even more natural.

Both are understandable, but they can feel slightly different:

• nell’esame di matematica = in the math exam / on the math exam
• all’esame di matematica = in the math exam / on the math exam / at the math exam

In everyday Italian, many speakers would probably say:

• Spero di prendere un buon voto all’esame di matematica.

That is often the most idiomatic way to refer to getting a grade in a particular exam.

So the original sentence is fine, but all’esame is also very common.

Not if you mean I hope I get a good grade.

If the subject stays the same, Italian normally prefers:

• Spero di prendere un buon voto.

If you say:

• Spero che prenda un buon voto

that usually means:

• I hope that he/she gets a good grade

because prenda is a subjunctive form referring to another subject.

So the difference is:

• spero di prendere = I hope to get
• spero che lui/lei prenda = I hope he/she gets

Yes, it is natural and correct. Still, there are a few other common ways to express the same idea.

For example:

• Spero di prendere un bel voto all’esame di matematica.
• Spero di andare bene all’esame di matematica.
• Spero che l’esame di matematica vada bene.

The original sentence is perfectly good, especially if you want to focus specifically on the grade.
If you want a slightly more conversational tone, andare bene all’esame is also very common.

Yes. Italian word order is fairly flexible, although some versions sound more natural than others.

For example, these are all possible:

• Spero di prendere un buon voto nell’esame di matematica.
• Spero di prendere un buon voto all’esame di matematica.
• All’esame di matematica, spero di prendere un buon voto.

The first version is straightforward and neutral.
The last version puts more emphasis on the math exam.

So the original word order is normal, but Italian can move parts of the sentence around for focus or style.

Esame is masculine:

• l’esame
• un esame
• l’esame di matematica

This matters because it affects articles and adjectives, for example:

• un esame difficile
• il prossimo esame

It may be less obvious in nell’esame, because the contracted form hides the article a little, but the noun itself is definitely masculine.