После неудачной пересдачи ему пришлось ещё неделю готовиться к зачёту.

It is in the genitive case because it follows после.

• после = after
• после always takes the genitive
• so:
  • пересдача → nominative
  • после пересдачи → genitive

So После неудачной пересдачи means After the unsuccessful retake.

Because adjectives must agree with the noun they describe in gender, number, and case.

Here the noun is:

• пересдача — feminine singular
• after после, it becomes genitive singular: пересдачи

So the adjective must match:

• неудачная пересдача — nominative
• после неудачной пересдачи — genitive

That is why you get неудачной.

Пересдача means a retake, usually of an exam, test, or other academic assessment.

It comes from the verb пересдавать / пересдать, meaning to retake.

So:

• сдача экзамена = taking/passing an exam
• пересдача экзамена = retaking an exam

In this sentence, it refers to a failed attempt at a retake.

Ему пришлось is a very common Russian way to say he had to.

The verb прийтись / приходиться is used in an impersonal construction:

• мне пришлось = I had to
• ему пришлось = he had to
• нам пришлось = we had to

The person experiencing the necessity goes in the dative case, so:

• он → nominative
• ему → dative

This construction is slightly different from он должен был:

• ему пришлось = he ended up having to / he was forced by circumstances to
• он должен был = he was supposed to / was obliged to

So ему пришлось often sounds more like a practical necessity caused by the situation.

Пришлось is the past tense form of прийтись.

In this sentence it means something like:

• it turned out necessary
• he had to

Because the sentence describes a completed situation in the past, Russian uses the past tense:

• ему приходится = he has to / he is having to
• ему пришлось = he had to

The infinitive that follows tells you what he had to do:

• ему пришлось готовиться = he had to prepare

Here ещё means another or an additional.

So:

• ещё неделю = for another week

This does not mean still here, even though ещё can sometimes mean that in other contexts.

Compare:

• ещё неделю = another week
• он ещё дома = he is still at home

Context tells you which meaning is intended.

Неделю is in the accusative case, and here it expresses duration of time.

Russian often uses the accusative without a preposition to show how long something lasted:

• ждать час = to wait for an hour
• работать весь день = to work all day
• готовиться неделю = to prepare for a week

So:

• ещё неделю готовиться = to keep preparing for another week

This is a very common pattern.

Because готовиться means to prepare oneself / to prepare for something, especially in the sense of studying or getting ready.

Compare:

• готовить = to prepare something, often food; also to prepare someone/something
• готовиться = to get ready, to prepare oneself

Examples:

• готовить ужин = to cook dinner
• готовиться к экзамену = to prepare for an exam

In your sentence, the person is doing the preparation himself, so готовиться is the natural choice.

The preposition к requires the dative case.

The standard expression is:

• готовиться к чему? = to prepare for what?

So:

• зачёт → nominative
• к зачёту → dative

This is just the normal pattern for this verb:

• готовиться к экзамену
• готовиться к уроку
• готовиться к зачёту

Not exactly.

A зачёт is a kind of academic assessment in Russian-speaking educational systems, often closer to a pass/fail credit than a full graded exam.

Very roughly:

• экзамен = an exam, often graded
• зачёт = a pass/fail assessment, course credit check, or qualifying test

In practice, learners often translate зачёт simply as test or course credit assessment, depending on context.

So готовиться к зачёту means preparing for that kind of academic requirement.

Yes. Russian word order is flexible, and the sentence starts with the time/background frame:

• После неудачной пересдачи = after the unsuccessful retake

Then it gives the main result:

• ему пришлось ещё неделю готовиться к зачёту

This order is natural because it sets up the situation first and then tells you what happened because of it.

You could also say:

• Ему пришлось ещё неделю готовиться к зачёту после неудачной пересдачи.

That is also grammatical, but it may sound a little less smooth depending on context. The original version is very natural.

It means the retake was unsuccessful.

So the sequence is:

1. there was a retake
2. that retake went badly / was failed
3. because of that, he had to prepare for another week

If Russian wanted to say the retake of a previously failed exam, it would usually be phrased differently and more explicitly.

Here, неудачной directly describes пересдачи, so the most natural reading is an unsuccessful retake.

Not in the same way.

• ещё неделю готовиться = to prepare for another week / for one more week
  
  • this expresses duration
• ещё на неделю often suggests for an additional week ahead, frequently with a different structure or emphasis

For pure duration after a verb like готовиться, bare accusative is the normal and simplest choice:

• готовиться ещё неделю

So the sentence as written is the most natural standard form.