Learn Hardcore Indonesian: Jam pelajaran matematika dimulai pukul delapan. - The math lesson period starts at eight o'clock.

Jam literally means hour / o’clock / clock, but in a school context jam pelajaran is a set phrase meaning a lesson period or class period.

jam = hour / period
pelajaran = lesson, something that is taught

So jam pelajaran together means a scheduled lesson slot in the timetable, not a physical clock.
In this sentence, jam pelajaran matematika = the math lesson period / math class period.

Why does the sentence use both jam and pukul? Aren’t they both about time?

They have different functions here:

The first jam in jam pelajaran is part of the phrase jam pelajaran = class period.
pukul is the word normally used before a clock time.

So structurally:

jam pelajaran → lesson period
pukul delapan → at eight o’clock

You could say jam delapan in everyday speech, but pukul delapan is more neutral/formal and very common in written Indonesian, announcements, schedules, etc.

Why is there no word like at before pukul delapan? Should it be pada pukul delapan?

Pukul itself already functions like at (time) in English:

pukul delapan ≈ at eight o’clock

You can say pada pukul delapan, and it’s grammatically correct, but in normal sentences pada is usually dropped:

dimulai pukul delapan (most common)
dimulai pada pukul delapan (more formal/explicit; often in official writing)

What does dimulai mean grammatically, and what is the base verb?

The base verb is mulai = to start, to begin.

From this root you get:

mulai – start, begin (can be used intransitively)
memulai – to start something (active, with an object)
dimulai – is started / is begun / begins (passive-like form)

dimulai is di- (passive prefix) + mulai.
Literally, jam pelajaran matematika dimulai = the math lesson period is started (by someone implied, like the school/teacher).

Why use dimulai instead of just mulai or memulai here?

Style and focus:

Jam pelajaran matematika dimulai pukul delapan.
Focuses on the event; it’s a neutral or slightly formal way to describe a schedule. The agent (who starts it) is not important.
Jam pelajaran matematika mulai pukul delapan.
Also acceptable and common, especially in speech. Slightly more informal/neutral.
Guru memulai pelajaran matematika pukul delapan.
Uses memulai and explicitly mentions the agent (guru).

Indonesian often prefers dimulai when describing timetables, events, programs, etc., because we care more about when it starts than who starts it.

How is pelajaran matematika structured? Why not matematika pelajaran?

Indonesian noun phrases usually follow this order:

Head noun + modifier

Here:

pelajaran = lesson (head)
matematika = math (modifier)

So pelajaran matematika literally = lesson (of) math → math lesson.

Putting it the other way (matematika pelajaran) is ungrammatical in standard Indonesian.
The thing being described (pelajaran) comes first; what kind of lesson (matematika) comes after.

Is jam pelajaran matematika one long noun phrase? How should I group the words?

Yes, you can group the sentence like this:

[Jam pelajaran matematika] [dimulai] [pukul delapan].

Inside the first group:

jam – period
pelajaran – lesson
matematika – math

So from left to right: jam pelajaran matematika = the math lesson period → this whole chunk is the subject of the sentence.

Then:

dimulai – (is) started / begins
pukul delapan – at eight o’clock

There is no the or a here. How do we know if it means “the math class”, “a math class”, or “math class in general”?

Indonesian does not use articles like the or a. The meaning depends on context.

This sentence could be understood as:

The math lesson (on the schedule) starts at eight.
Math class starts at eight. (in a general routine sense)

If you need to be clearly specific, you can add demonstratives or other words:

Jam pelajaran matematika ini dimulai pukul delapan.
This math lesson period starts at eight.
Jam pelajaran matematika itu dimulai pukul delapan.
That math lesson period starts at eight.

If I want to specify “at 8 in the morning / evening”, how do I say that?

Add a time-of-day word after the number:

pukul delapan pagi – at 8 a.m. (in the morning)
pukul delapan siang – around 12–3 p.m. (midday/early afternoon)
pukul delapan sore – around 3–6 p.m. (late afternoon/early evening)
pukul delapan malam – at 8 p.m. (at night)

So:

Jam pelajaran matematika dimulai pukul delapan pagi.
The math class starts at eight in the morning.

Can I replace jam pelajaran with kelas? What’s the difference?

You can, but there is a nuance difference:

jam pelajaran – emphasizes the time slot / period in the timetable.
kelas – can mean class as a group of students, a classroom, or a course.

Examples:

Jam pelajaran matematika dimulai pukul delapan.
Focus: the scheduled lesson period.
Kelas matematika dimulai pukul delapan.
Also natural: The math class starts at eight.
Here you’re focusing more on the class (the session/event) than on the formal period in a timetable.

Is matematika capitalized in Indonesian like Mathematics in English?

No. Names of school subjects are written with a lowercase letter in Indonesian, unless they begin a sentence or are part of a proper title.

So:

Saya suka pelajaran matematika.
Matematika (capitalized) only if it’s the first word in the sentence or in a title.

How would you turn this into a question: “What time does the math class start?”

You can ask in several natural ways:

Jam berapa pelajaran matematika dimulai?
Pelajaran matematika dimulai jam berapa? (more conversational)
Jam berapa jam pelajaran matematika dimulai? (explicit but a bit heavier)

All mean: What time does the math lesson start?

How would you say “The math class has already started” using the same verb?

Add sudah (already) before dimulai:

Jam pelajaran matematika sudah dimulai.
= The math lesson has already started.

Is there any difference between jam delapan and pukul delapan?

Both can mean eight o’clock, but:

jam delapan – very common in everyday speech; informal/neutral.
pukul delapan – common in announcements, written schedules, and slightly more formal contexts.

In your original sentence, pukul delapan fits very well because it sounds like a timetable or official information.