Learn Italian: Quanto tempo c'è voluto per preparare l'esame teorico? - How much time did it take to prepare for the theoretical exam?

The verb volerci (to take time or effort) always uses essere as its auxiliary verb in the passato prossimo. Because it uses essere, its past participle must agree with the subject of the sentence.

What is the subject that voluto is agreeing with in this sentence?

The subject is Quanto tempo (how much time). With volerci, the thing that is needed or taken is the grammatical subject. Since tempo is masculine and singular, the participle ends in -o (voluto). If the subject were plural, like two hours (due ore), it would be ci sono volute.

How would this question look if I used metterci instead of volerci?

You would say Quanto tempo ci hai messo per preparare l'esame teorico? (How much time did you take...). The verb metterci focuses on the person taking the time, uses the auxiliary avere, and its past participle (messo) does not change its ending to match the time.

Why isn't there a translation for the word for between preparare and l'esame?

In English, we prepare for an exam, but in Italian, preparare is a direct transitive verb. You literally prepare the exam (preparare l'esame), so no extra preposition is needed.