Learn Hardcore Finnish: Poika sai hyvän arvosanan matematiikan kokeesta. - The boy got a good grade on the math exam.

poika = boy (nominative singular, subject)
sai = got / received (3rd person singular past of saada)
hyvän = good (singular accusative/genitive of hyvä, agreeing with arvosanan)
arvosanan = grade / mark (singular accusative/genitive of arvosana, the object)
matematiikan = of mathematics / math (genitive singular of matematiikka, modifying kokeesta)
kokeesta = from (the) test (elative singular of koe = test, exam)

So structurally: Boy got good grade from (the) mathematics test.
English naturally renders it as: The boy got a good grade in the math test.

Why is it poika and not pojan or something else at the beginning?

Poika is in the nominative case, which is the basic dictionary form and is used for the subject of the sentence.

poika (nominative) = the/a boy as the one doing the action
pojan (genitive) would mean of the boy or boy’s, not suitable for a plain subject here.

So poika is correct because the boy is the subject who performs the action sai (got).

What exactly is sai? How does it relate to the verb saada?

Sai is the 3rd person singular past tense of the verb saada (to get, to receive).

infinitive: saada = to get
present: hän saa = he/she gets
past: hän sai = he/she got

So poika sai literally means the boy got or the boy received.

Why is it hyvän arvosanan and not hyvä arvosana?

Because hyvä arvosana (a good grade) is the basic noun phrase (nominative), but in this sentence it functions as the object of the verb saada.

In Finnish, a total object of a completed action in the past is usually in the accusative, which in singular looks like the genitive:

nominative (dictionary form): hyvä arvosana → a good grade
accusative/genitive (object form here): hyvän arvosanan → a good grade as the thing that was got

Both words in the phrase agree:

hyvä → hyvän
arvosana → arvosanan

So Poika sai hyvän arvosanan = The boy got a good grade (completed event, whole grade).

Is hyvän here genitive or accusative?

Formally, hyvän is the genitive singular form of hyvä.

However, in this sentence it functions as part of a total object, where the accusative singular of most nouns and adjectives has the same form as the genitive.

So:

Morphological form: genitive (hyvän)
Syntactic role: accusative (agreeing with the object arvosanan)

You’ll usually see this described simply as “object in genitive/accusative form.”

Why is arvosanan not just arvosana?

Because arvosanan is the object form in this context.

arvosana (nominative) = a grade (used for subjects, dictionary form)
arvosanan (genitive/accusative) = here used as a total object of sai (got)

The action is seen as complete and it affects the whole grade (he got that one grade), so Finnish uses the total object form: arvosanan.

If it were something like “He was getting good grades” (ongoing, incomplete, plural/indefinite), you’d often see the partitive, e.g.:

Poika sai hyviä arvosanoja. = The boy was getting good grades.

What does matematiikan do in the phrase matematiikan kokeesta?

Matematiikan is the genitive form of matematiikka (mathematics, math). It modifies koe (test, exam):

matematiikka → matematiikan koe = math test / mathematics exam

So matematiikan kokeesta literally means from the math test.
Matematiikan answers the question “what kind of test / test of what?” and acts like “of mathematics” in English.

What case is kokeesta, and what does it express?

Kokeesta is in the elative case (ending -sta / -stä), which basically means “from (inside)” something.

koe = test
kokeesta = from the test

In this context, Finnish idiomatically says that you get a grade from a test:

sai hyvän arvosanan kokeesta = got a good grade from the test

English normally phrases this as “on/in the test,” but Finnish conceptualizes it as coming from the test.

Could you say matematiikan kokeessa instead of matematiikan kokeesta? What would change?

Yes, matematiikan kokeessa is grammatically correct, but the meaning changes:

kokeesta (elative) = from the test → used for things you get as a result of the test (like grades).
kokeessa (inessive) = in the test / during the test → focuses on what happens inside the test situation.

Examples:

Poika sai hyvän arvosanan matematiikan kokeesta.
→ The boy got a good grade from the math test (normal way to talk about grades).
Poika kirjoitti hyvin matematiikan kokeessa.
→ The boy wrote/performed well in the math test.

For grades, kokeesta is the natural choice.

Why does English say “in/on the test” but Finnish says kokeesta (“from the test”)?

This is just a difference in idiomatic expression between the languages.

In English: you typically get a grade on or in a test.
In Finnish: you get a grade from a test (kokeesta).

Finnish often uses the elative (-sta/-stä, “from”) for results coming from some process or event, like:

Sain idean kirjasta. = I got the idea from the book.
Sain hyvän arvosanan kokeesta. = I got a good grade from the test.

So “from the test” is simply the natural Finnish way to phrase it.

Where are the words “the” and “a” in this Finnish sentence?

Finnish does not have articles like a/an or the.

poika can mean a boy or the boy, depending on context.
hyvä arvosana can mean a good grade or the good grade, again from context.

So in Poika sai hyvän arvosanan matematiikan kokeesta, we decide in English to translate it as:

The boy got a good grade in the math test

because that’s the most natural interpretation, but Finnish itself doesn’t mark that difference with any special words.

Can the word order be changed, or must it always be Poika sai hyvän arvosanan matematiikan kokeesta?

The basic neutral order is:

Poika sai hyvän arvosanan matematiikan kokeesta.

But Finnish allows quite flexible word order for emphasis. For example:

Hyvän arvosanan poika sai matematiikan kokeesta.
→ Emphasis on hyvän arvosanan (a good grade is what he got).
Matematiikan kokeesta poika sai hyvän arvosanan.
→ Emphasis on from the math test (maybe in contrast to some other test).

The grammatical roles are mostly shown by case endings, not by position, so changing the order typically changes focus/emphasis, not the basic meaning.

Is there a more colloquial way to say this sentence?

Yes. In everyday speech you might hear:

Poika sai hyvän numeron matikan kokeesta.

Changes:

arvosanan → numeron (number, colloquially for a grade)
matematiikan → matikan (spoken/short form of mathematics)

Meaning stays essentially the same: The boy got a good grade in the math test.

How would you say just “a good grade in the math test” as a noun phrase, without the verb?

You’d use the basic nominative forms:

hyvä arvosana matematiikan kokeesta

Examples in a sentence:

Hän sai hyvä arvosana matematiikan kokeesta. ❌ (wrong – object form missing)
Hän sai hyvän arvosanan matematiikan kokeesta. ✅ (correct)

But if you’re only naming the thing, not using it as an object, nominative is fine:

Hyvä arvosana matematiikan kokeesta on tavoitteenani.
= A good grade in the math test is my goal.