Po pierwszym teście moja średnia ocena była niska, ale później się poprawiła.

The preposition po in the sense of “after (something)” normally requires the locative case in Polish.

• pierwszy test – nominative (dictionary form)
• po pierwszym teście – locative (after the first test)

So:

• pierwszym = locative singular masculine of pierwszy
• teście = locative singular of test

A structure like *po pierwszy test is ungrammatical here, because po cannot be followed by nominative in this meaning.

Both words are in the locative singular:

• pierwszym – locative singular masculine of the adjective pierwszy
• teście – locative singular masculine of the noun test

Clue: after po in the meaning “after (an event)”, you almost always need the locative:

• po obiedzie – after lunch
• po lekcji – after the lesson
• po egzaminie – after the exam
• po pierwszym teście – after the first test

Many masculine nouns in Polish change their final consonant when you add the locative ending.

• test → teście

Spelling change:

• st becomes ść before the ending -ie

This is a regular pattern for some masculine nouns:

• most → moście (on the bridge)
• gość → gościu / gości (in older or dialect forms; similar softening idea)

So teście is just the normal locative form of test.

Both are possible, but they mean slightly different things:

• moja średnia ocena – my average grade (explicitly says it belongs to you)
• średnia ocena – the average grade (could be yours, but context has to make that clear)

Polish doesn’t have articles (a / the), so possessives like mój / moja / moje often do the job of specifying whose something is.
You could say:

• Po pierwszym teście średnia ocena była niska… – If it’s already obvious that you are talking about your own grade, this is fine.

The neutral, default order in Polish is:

[possessive] + [descriptive adjective] + [noun]
moja średnia ocena

Putting the adjective after the noun (moja ocena średnia) is possible but sounds marked or poetic and usually adds emphasis or contrast, e.g.:

• To była ocena średnia, nie wysoka. – It was an average grade, not a high one.

In everyday speech, stick to moja średnia ocena.

Średnia ocena can mean both, depending on context:

1. Mathematical average (mean of all your grades):

   • Moja średnia ocena w semestrze to 4,2. – My average grade this semester is 4.2.

2. Mediocre / not very good (less formal, more colloquial feeling sometimes):

   • To tylko średnia ocena. – That’s just an average/so-so grade.

If you want to clearly say “mediocre / not very good”, you can also use:

• przeciętna ocena – a mediocre / average-at-best grade
• słaba ocena – a poor / weak grade

The form of the verb and adjective must agree with the gender and number of the subject.

The subject is moja średnia ocena:

• ocena is feminine singular

So you need:

• była – past tense feminine singular of być (to be)
• niska – feminine singular form of niski (low)

If the subject were masculine singular, e.g. mój średni wynik (my average result), you would say:

• Mój średni wynik był niski.

This is a false-friend issue:

• niski = low (height, level, value)

  • niska ocena – low grade
  • niska temperatura – low temperature
  • niska pensja – low salary

• mały = small (size, quantity, physical dimensions)

  • mały dom – small house
  • małe dziecko – small child

For grades, salaries, scores, etc., Polish uses “niski”, not “mały”.
So niska ocena is correct; *mała ocena sounds wrong in this sense.

Both później and potem often mean “later / afterwards”, and in this sentence they are interchangeable:

• …ale później się poprawiła.
• …ale potem się poprawiła.

Nuance (very subtle):

• potem – a bit more like “after that / then” in a sequence
• później – a bit more like “at a later time”

In most everyday contexts, you can treat them as synonyms and use either.

Yes, both word orders are correct:

• ale później się poprawiła
• ale później poprawiła się

Rules:

• się is a clitic (unstressed particle), and it usually:
  • comes right after the first stressed element of the clause, or
  • stands immediately after the verb

So you can usually have:

• Ona się poprawiła.
• Ona poprawiła się.

In your sentence, ale później się poprawiła is slightly more common in speech, but ale później poprawiła się is also fully correct.

Poprawiła (się) is the past tense, feminine singular of the perfective verb poprawić (się).

• poprawić coś – to improve something
  • Nauczyciel poprawił błąd. – The teacher corrected the mistake.
• poprawić się – to improve (itself / oneself)
  • Moja średnia ocena się poprawiła. – My average grade improved.

So in …ale później się poprawiła, the verb means “(it) improved”, and się makes it reflexive, expressing that the subject’s own state got better, not that someone improved something else.

Polish verbs in the past tense agree with the grammatical gender of the subject, even if the subject is just implied.

The understood subject is moja średnia ocena (mentioned earlier), and:

• ocena is feminine singular

Therefore:

• (moja średnia ocena) się poprawiła – my average grade improved

If the subject were masculine singular, you’d use:

• (mój wynik) się poprawił – my result improved

So the verb’s form tells you the gender/number of the implied subject.