A tanulmányi feladat nehéz.

Hungarian has two forms of the definite article:

• a before a consonant sound
• az before a vowel sound

Since tanulmányi starts with t, a consonant, the correct form is a tanulmányi feladat.

Examples:

• a feladat
• a könyv
• az iskola
• az ember

In Hungarian, the verb to be is usually left out in the present tense, third person when the predicate is a noun or adjective.

So:

• A tanulmányi feladat nehéz. = The academic task is difficult.

There is no separate word for is here.

But compare:

• A tanulmányi feladat nehéz volt. = The academic task was difficult.
• A tanulmányi feladat nehéz lesz. = The academic task will be difficult.

And with other persons, the verb appears:

• Nehéz vagyok. = I am difficult / I am hard
• Nehéz vagy. = You are difficult

Tanulmányi is an adjective meaning study-related, academic, or connected with studies.

It is formed from tanulmány (study, academic work, study matter) plus the suffix -i, which often creates adjectives meaning related to something.

So:

• tanulmány → study / academic matter
• tanulmányi → academic, study-related

This is a very common pattern in Hungarian.

Examples:

• iskola → iskolai = school-related
• egyetem → egyetemi = university-related
• tanulmány → tanulmányi = study-related

Because in Hungarian, adjectives normally come before the noun they modify, just as in English.

So:

• tanulmányi feladat = academic task

This is the normal order. Putting tanulmányi after feladat would not be the standard way to form this noun phrase.

Not in the way adjectives do in many Indo-European languages.

In Hungarian, an adjective before a noun usually does not change for number or case to match the noun.

So:

• tanulmányi feladat = academic task
• tanulmányi feladatok = academic tasks

Notice that tanulmányi stays the same. Only feladat changes to feladatok in the plural.

That is very normal in Hungarian.

Here, nehéz is a predicate adjective: it tells us what the subject is like.

With a singular subject, it appears in singular form:

• A tanulmányi feladat nehéz.

If the subject is plural, the predicate adjective is usually plural too:

• A tanulmányi feladatok nehezek. = The academic tasks are difficult.

So in your sentence, nehéz is singular because feladat is singular.

Yes, Hungarian word order is flexible, but different orders can change the focus or emphasis.

The given sentence:

• A tanulmányi feladat nehéz.

is a neutral statement: As for the academic task, it is difficult.

You could also say:

• Nehéz a tanulmányi feladat.

This puts more emphasis on nehéz: The academic task is difficult / It’s the academic task that is difficult.

So the original order is natural and neutral, but other orders are possible depending on what you want to highlight.

The noun phrase a tanulmányi feladat is in the nominative form, which is the basic dictionary form and also the usual form for the subject of a sentence.

So:

• feladat = nominative singular
• tanulmányi = adjective modifying it
• nehéz = predicate adjective

There are no visible case endings here because nothing in the sentence requires them.

You would make the noun plural, and the predicate adjective would also normally be plural:

• A tanulmányi feladatok nehezek.

Breakdown:

• feladat → feladatok = tasks
• nehéz → nehezek = difficult, plural predicate form

But tanulmányi stays unchanged:

• tanulmányi feladat
• tanulmányi feladatok

A careful pronunciation is approximately:

• A = aw / short open a
• tanulmányi = TA-nool-maa-nyi
• feladat = FE-la-dot
• nehéz = ne-HAYZ

A more phonetic approximation:

• [ɒ ˈtɒnulmaːɲi ˈfɛlɒdɒt ˈnɛheːz]

A few useful pronunciation notes:

• Stress in Hungarian is almost always on the first syllable of each word.
• ny sounds like the ny in canyon or the Spanish ñ.
• á is long.
• é is also long.

Yes, but it changes the meaning.

• A tanulmányi feladat nehéz. = The academic task is difficult.
• Egy tanulmányi feladat nehéz. = An academic task is difficult / One academic task is difficult.

So a makes the noun phrase definite, while egy makes it indefinite.

In many contexts, the version with a sounds more natural if you are talking about a specific task already known in the conversation.