Pismeni dio ispita bit će u petak.

Because pismeni is an adjective agreeing with dio.

• dio is masculine singular nominative
• so the adjective must also be masculine singular nominative: pismeni

The key point is that pismeni describes dio (part), not ispita.

So the structure is:

• pismeni dio = written part
• ispita = of the exam

Because dio normally takes the genitive: part of something.

So:

• dio = part
• ispita = of the exam

The base noun is ispit. Its genitive singular is ispita.

This is a very common Croatian pattern:

• dio knjige = part of the book
• kraj filma = end of the film
• početak sata = beginning of the class

So dio ispita is a normal noun + genitive structure.

In standard Croatian, biti će is not the normal written form here.

The correct standard form is bit će.

What is happening:

• infinitive: biti
• future auxiliary: će
• when the infinitive comes before the auxiliary, biti is shortened to bit
• so you get bit će

Compare:

• će biti = auxiliary first
• bit će = infinitive first, shortened

So this sentence uses the standard form bit će.

Yes, but the word order would have to be arranged differently.

Croatian clitic words like će usually want to appear very early in the sentence, often in the second position. Because of that, speakers often prefer bit će when they do not want to break up the noun phrase pismeni dio ispita.

So these are possible patterns:

• Pismeni dio ispita bit će u petak.
• Pismeni će dio ispita biti u petak.

The version Pismeni dio ispita će biti u petak is often avoided in careful standard usage, because će is sitting later than expected.

So bit će is a very natural choice here.

Here petak is in the accusative singular, and the phrase u petak means on Friday.

This is a common time expression in Croatian:

• u ponedjeljak = on Monday
• u utorak = on Tuesday
• u srijedu = on Wednesday
• u petak = on Friday

Even though u often means in, with days of the week it is commonly used for time expressions like on Friday.

So this is not about physical location. It is a set time phrase.

Because u does not always take the same case.

With location, u often takes the locative:

• u školi = in school
• u gradu = in the city

But with movement toward something, it often takes the accusative:

• u školu = into school

And with many time expressions, especially days of the week, Croatian also uses u + accusative:

• u petak = on Friday

So here the case is accusative because this is a time expression, not a location.

Because Croatian does not have articles like English a/an and the.

Croatian usually leaves definiteness to be understood from context.

So ispita can correspond to:

• the exam
• an exam

depending on the situation.

In a sentence like this, the listener usually understands which exam is meant from context.

Because those do not mean exactly the same thing.

• pismeni dio ispita = the written part of the exam
• pismeni ispit = a written exam / written test

The sentence with dio suggests that the exam has more than one part, for example:

• a written part
• an oral part

So dio is important here because it tells you this is just one section of the whole exam.

Yes, very often.

For scheduled events, Croatian can use the present tense much like English can:

• Pismeni dio ispita je u petak.

That sounds natural in everyday speech and means the same kind of thing as a scheduled future.

The version with bit će is also correct, but it may sound a bit more explicitly future-oriented.

Yes. Croatian word order is fairly flexible, although not completely free.

For example, you could also say:

• U petak će biti pismeni dio ispita.

That puts more focus on when it will happen.

The original order:

• Pismeni dio ispita bit će u petak.

starts with the topic the written part of the exam and then says when it will be.

So word order can shift depending on what you want to emphasize.

By itself, u petak usually just means on Friday.

Whether that is:

• this coming Friday
• next Friday
• a specific Friday already known in context

depends on the situation.

If Croatian speakers want to be more precise, they can add words such as:

• ovaj petak = this Friday
• sljedeći petak = next Friday

But in many real conversations, u petak is enough because the context makes it clear.