Преподавательница настойчиво просила нас не писать ответ наугад.

Преподавательница means female teacher / female instructor / female lecturer. It is the feminine form of преподаватель.

A learner might compare it with учительница, but they are not always the same:

• учительница = usually a schoolteacher
• преподавательница = usually someone who teaches a subject, often in a college, university, or more formal educational setting

So this word gives both the job and the fact that the teacher is female.

Both are possible.

• преподавательница explicitly marks the teacher as female.
• преподаватель can also be used for a woman, especially in more formal or institutional language.

So преподавательница is understandable and natural, but in some contexts Russians may prefer преподаватель regardless of gender. A learner should recognize both.

Просила is:

• past tense
• singular
• feminine
• imperfective aspect

It agrees with преподавательница, which is feminine singular.

Compare:

• преподаватель просил = the male teacher asked
• преподавательница просила = the female teacher asked

So the -а ending shows feminine past tense.

Because it modifies the verb просила.

• настойчивый = persistent, insistent
• настойчиво = persistently, insistently

So настойчиво просила means she asked in an insistent or persistent way.

This is a very common pattern in Russian:

• adjective: внимательный
• adverb: внимательно

Here, the sentence needs an adverb because it describes how she asked.

The verb просить often works like this:

просить + кого + infinitive

That means:

• кого = the person being asked
• infinitive = the action being requested

So:

• просила нас = asked us
• не писать = not to write

Нас is the accusative form of мы. In English, this is like us after asked:

• she asked us
• она просила нас

This is a very common aspect question.

• писать = imperfective
• написать = perfective

After просить in a negative request, Russian often uses the imperfective infinitive:

• просила не писать = asked not to write

Why imperfective here? Because the focus is on avoiding the action in general, not on a single completed result. It sounds like:

• don’t write it
• don’t go and write an answer by guessing

If you used не написать, it would sound more result-focused and is less natural here.

So не писать is the normal choice in this sentence.

Because ответ is the direct object of писать.

The pattern is:

• писать что? — ответ

So ответ is in the accusative case.

But for masculine inanimate nouns, the accusative often looks exactly like the nominative:

• nominative: ответ
• accusative: ответ

That is why there is no visible change.

Наугад is an adverb meaning:

• at random
• by guesswork
• without knowing for sure

In this sentence, it means the teacher asked them not to write an answer just by guessing.

It is a fixed adverb, and learners should treat it as a whole word in meaning, even though historically it comes from на + угад.

Russian uses the infinitive directly, without a separate word like English to.

So:

• не писать = not to write

This is normal in Russian. The infinitive itself carries the idea of to write.

That is why:

• просила нас не писать literally looks more like
• asked us not write

but it naturally means

• asked us not to write

Yes, Russian word order is flexible.

This version is quite neutral:

• Преподавательница = topic / subject
• настойчиво просила = what she did
• нас = who was asked
• не писать ответ наугад = what she asked us not to do

Other orders are possible for emphasis, for example:

• Настойчиво преподавательница просила нас не писать ответ наугад — unusual, more marked
• Нас преподавательница настойчиво просила не писать ответ наугад — emphasizes us
• Преподавательница просила нас ответ наугад не писать — possible, but less neutral

So the original order is a natural, standard choice.

Yes, but the nuance changes.

• просила = imperfective; can suggest repeated asking, a process, or emphasis on the manner
• попросила = perfective; a single completed act of asking

So:

• Преподавательница настойчиво просила нас...
  suggests she was urging us, perhaps more than once or over some period of time.
• Преподавательница настойчиво попросила нас...
  means she made the request, seen as one complete event.

With настойчиво, the imperfective просила works especially well because it matches the idea of persistence.

Yes. In Russian, negative requests and prohibitions very often use the imperfective infinitive or imperfective imperative.

So after просить, it is very natural to say:

• просила не писать
• просил не говорить
• просили не входить

This usually means:

• please don’t do that
• avoid doing that action

So the sentence reflects a very common Russian pattern for negative instructions.