A vizsgadíj drága.

In Hungarian, the verb van (is) is usually left out in simple present-tense sentences when the subject is third person.

So:

• A vizsgadíj drága. = The exam fee is expensive.

But in other persons, you do use the verb:

• Én fáradt vagyok. = I am tired.
• Te fáradt vagy. = You are tired.

So this omission is completely normal here.

A is the Hungarian definite article, meaning the.

So:

• a vizsgadíj = the exam fee

Hungarian has two forms of the definite article:

• a before most consonant sounds
• az before vowel sounds

For example:

• a könyv = the book
• az autó = the car

Yes, vizsgadíj is one word. Hungarian often forms compound nouns this way.

It is made from:

• vizsga = exam
• díj = fee

So literally it is exam-fee, and naturally in English that becomes exam fee or examination fee.

This kind of compounding is very common in Hungarian.

A rough English-friendly guide would be:

• vizsga sounds approximately like VEEZH-gaw
• díj sounds roughly like deey

So the whole word is approximately:

• VEEZH-gaw-deey

A few helpful notes:

• zs is like the s in measure
• í is a long ee sound
• Hungarian stress is always on the first syllable: VIZSga-díj

Here, drága is not directly modifying the noun inside a noun phrase. It is the predicate of the sentence.

So the structure is:

• A vizsgadíj = the subject
• drága = the predicate adjective

That is why it comes after the noun phrase, just like in English:

• The exam fee is expensive.

If you wanted to say the expensive exam fee, then the adjective would go before the noun in Hungarian:

• a drága vizsgadíj

So compare:

• A vizsgadíj drága. = The exam fee is expensive.
• A drága vizsgadíj... = The expensive exam fee...

Yes, drága can mean more than one thing depending on context.

Common meanings include:

• expensive
• dear or beloved

For example:

• Ez a kabát drága. = This coat is expensive.
• drága barátom = my dear friend

In A vizsgadíj drága, the meaning is clearly expensive.

Not in this kind of sentence.

Hungarian adjectives do not change for gender, because Hungarian has no grammatical gender. They also do not change in predicate position just because the noun is singular or plural.

So:

• A vizsgadíj drága. = The exam fee is expensive.
• A vizsgadíjak drágák. = The exam fees are expensive.

Notice that in the plural, the adjective can take a plural marker when it is used predicatively:

• drága → drágák

But there is still no gender agreement like in many Indo-European languages.

Yes, they matter a lot. In Hungarian, accents are part of the spelling and usually show vowel length or vowel quality.

Here:

• á is different from a
• í is different from i

These are not optional marks. They can change pronunciation and sometimes meaning.

So you should learn the words with the accents included:

• drága
• díj
• vizsga

Usually, A vizsgadíj drága is the normal neutral form if you mean the exam fee or are speaking generally about that fee in context.

Without the article, Vizsgadíj drága sounds incomplete or unnatural in most ordinary contexts.

Hungarian uses articles a lot, and they often correspond to English the. So if English would naturally say the exam fee, Hungarian will usually use a as well.

Yes. Hungarian word order is flexible, but changes in word order often change emphasis.

The neutral sentence is:

• A vizsgadíj drága.

If you say:

• Drága a vizsgadíj.

that can sound more emphatic, like:

• The exam fee is expensive
• or It’s the exam fee that’s expensive

So both are possible, but the first one is the most straightforward basic version for learners.

You would usually make both the noun and the predicate adjective plural:

• A vizsgadíjak drágák. = The exam fees are expensive.

Breakdown:

• vizsgadíj = exam fee
• vizsgadíjak = exam fees
• drága = expensive
• drágák = expensive, plural predicate form

This is a useful pattern to learn for simple statements in Hungarian.