siken ga owaru made, mainiti ganbarimasu.

In 試験が終わるまで, 試験 is the thing that ends, so it is the subject of 終わる.

• 終わる = to end
• 試験が終わる = the exam ends / the exams end

So が marks what is ending.

Why not を? Because 終わる is an intransitive verb, so it does not take a direct object.

Why not は? You could say 試験は終わるまで in some special contrastive context, but it sounds unnatural here. が is the normal choice for the subject inside this kind of clause.

This is very normal Japanese grammar. In clauses like this, Japanese often uses the plain non-past form to talk about future events.

So:

• 試験が終わるまで = until the exam ends
• literally, it looks like until the exam ends
• naturally, it refers to a future endpoint

English often changes tense more obviously, but Japanese commonly uses the dictionary/non-past form in subordinate clauses when talking about future actions or events.

まで means until or up to.

In this sentence, 試験が終わるまで gives the time limit for the action 頑張ります.

So the structure is:

• A まで、B
• until A, B

Here:

• 試験が終わるまで = until the exam ends
• 毎日頑張ります = I’ll do my best every day

So the whole idea is: I’ll keep doing my best every day until the exam is over.

Both are possible, but they mean slightly different things.

• 試験まで = until the exam / up to the exam
  This focuses on the point the exam itself.
• 試験が終わるまで = until the exam ends / until the exam is over
  This focuses on the point when the exam has finished.

So if you want to say you will keep trying hard through the exam period and stop after it is over, 試験が終わるまで is more precise.

This is a very common question.

• まで = until
• までに = by, no later than

So:

• 試験が終わるまで頑張ります
  = I’ll keep trying hard until the exam ends.

• 試験が終わるまでに〜
  = I’ll do something by the time the exam ends.

For example:

• 試験が終わるまでにレポートを出します。
  = I’ll submit the report by the time the exam ends.

In your sentence, まで is correct because it describes an action continuing up to a point.

頑張ります is often translated as I’ll do my best, I’ll work hard, or I’ll keep at it.

It is a very common Japanese expression, but it is broader than any one English phrase. Depending on context, it can mean:

• study hard
• work hard
• hang in there
• keep trying
• put in effort

In this sentence, the natural meaning is something like:

• I’ll work hard every day until the exam is over
• or, if the context is studying, I’ll study hard every day until the exam is over

Japanese leaves the exact type of effort unstated unless it needs to be specific.

Japanese often omits the subject when it is obvious from context.

Because 頑張ります is a polite form often used about the speaker’s own action in this kind of sentence, the natural interpretation is:

• I will do my best

So 私は is understood even though it is not said.

If you added it, the sentence would still be grammatical:

• 私は試験が終わるまで、毎日頑張ります。

But Japanese often sounds more natural without repeating subjects unnecessarily.

毎日 means every day, and it functions as a time expression.

Time expressions in Japanese are quite flexible, so you can often move them around without changing the core meaning much. For example:

• 試験が終わるまで、毎日頑張ります。
• 毎日、試験が終わるまで頑張ります。

Both are understandable, though the first one sounds very natural.

Placing 毎日 near 頑張ります makes it clear that doing one’s best happens every day.

Japanese nouns usually do not show singular vs. plural clearly unless the context makes it necessary.

So 試験 could mean:

• the exam
• exams
• the testing period

In many real situations, the listener understands from context whether this is one exam or a set of exams.

That is why English translations may vary a little:

• until the exam is over
• until the exams are over

Both can fit 試験が終わるまで depending on the situation.

頑張ります is the polite form, while 頑張る is the plain form.

So the sentence is phrased politely:

• 頑張ります = polite
• 頑張る = plain/casual

A casual version would be:

• 試験が終わるまで、毎日頑張る。

Using -ます is common in neutral, polite conversation, in class examples, and when speaking to someone you are not very casual with.

The choice does not change the basic meaning; it changes the level of politeness.