Learn Hardcore Russian: Мой старший брат часто забывает проездной дома и покупает разовый билет. - My older brother often forgets his pass at home and buys a single ticket.

старший брат = older brother (relative age within a family).
старый брат would sound like an old (aged) brother, focusing on age in years, not birth order.
большой брат literally means big brother in size or metaphorically (like Big Brother from Orwell), but not “older brother” in the family sense.

For siblings, Russian almost always uses старший (older) and младший (younger):
старший брат, младшая сестра, etc.

Why is the word order мой старший брат, not старший мой брат?

The normal order of modifiers before a noun in Russian is:

possessive pronoun → qualitative adjective → noun

So:

мой старший брат = my older brother
(мой = my, старший = older, брат = brother)

Orders like старший мой брат are possible but sound poetic, emphatic, or old-fashioned. In everyday speech you virtually always say мой старший брат.

What grammatical form is проездной here, and why doesn’t it change?

Проездной in this sentence is:

masculine
singular
inanimate
accusative case

The verb забывать takes a direct object in the accusative:

забывать что? → проездной

For masculine inanimate nouns (and adjectives used as nouns), the accusative = nominative, so:

Nominative: проездной
Accusative: проездной (same form)

That’s why it doesn’t look any different, even though it’s the object of забывает.

Why is it just проездной and not проездной билет?

In everyday Russian, проездной is a shortened form of проездной билет (travel pass). The noun билет is simply omitted because it’s obvious from context.

This is common with some fixed expressions:

проездной (билет) – travel pass
проездной на месяц – monthly pass
обеденный (перерыв) – lunch break (literally lunch
- break)

So забывает проездной дома really means “forgets his travel pass at home”. You could say проездной билет, but people usually drop билет.

What exactly is дома here? Is it a case form of дом?

Дома in this sentence means “at home” and functions as an adverb of place, not as a regular case form.

Compare:

дом – house, home (noun, nominative)
дома – at home (adverb)
домой – (to) home (direction)

Examples:

Я дома. – I am at home.
Я иду домой. – I am going home.
Он забыл проездной дома. – He forgot his pass at home.

So дома here explains where he forgets it (i.e. leaves it behind), not whose house or anything like that.

Why is часто placed before забывает? Could I say забывает часто?

The neutral, most common position for adverbs of frequency (like часто = often) is before the verb:

Он часто забывает проездной дома.

You can say Он забывает проездной дома часто, but:

часто забывает sounds natural, neutral, and unmarked.
забывает часто places a bit more emphasis on how often he forgets; it can sound slightly more expressive or colloquial, depending on intonation.

For a learner, часто забывает is the default, safest choice.

Why is забывает (imperfective present) used and not забудет?

Забывает (imperfective) describes:

a repeated, habitual action: something he does regularly.

Забудет (perfective future) would be used for:

a single, one-time future event: He will forget (once).

So:

Он часто забывает проездной дома.
He often forgets his pass at home. (habit)
Он обязательно забудет проездной дома.
He will definitely forget his pass at home. (this time, in the future)

In your sentence we’re talking about a habit, so забывает is correct.

Why is покупает used, and how is it different from купит?

Same aspect difference as with забывает / забудет:

покупает – imperfective, present, here = repeated/habitual action:
- Он покупает разовый билет. → He (usually) buys a single-use ticket.
купит – perfective, future, one completed action:
- Он купит разовый билет. → He will buy a single-use ticket (on that occasion).

Since the sentence describes what he often does in such situations, both забывает and покупает are imperfective.

What does разовый билет literally mean, and why not just один билет?

Разовый билет literally means “one-time ticket” or “single-use ticket”:

разовый comes from раз (time, occasion) → for one time / per ride.
In transport context, разовый билет contrasts with:
- проездной (билет) – pass (for multiple rides, usually time-based).

Один билет just means “one ticket” (quantity = 1), with no implication about type. You could buy один проездной билет (one pass) or один разовый билет (one single-use ticket).

So разовый билет is the standard term for a single ride ticket, not simply “one ticket”.

How do the adjectives agree with the nouns in старший брат and разовый билет?

Both брат and билет are:

masculine
singular
nominative case

So their adjectives are also:

masculine
singular
nominative

Agreement:

старший брат
- старший (masc. sg. nom.) + брат (masc. sg. nom.)
разовый билет
- разовый (masc. sg. acc. = nom. here) + билет (masc. sg. acc. = nom.)

In Russian, adjectives must match the noun they modify in gender, number, and case.

Could I say забывает о проездном, and what would be the difference from забывает проездной?

Yes, but the meaning changes:

забывать что?
- accusative → literally to forget (leave behind, not take with you):
- Он забывает проездной дома.
  He leaves his pass at home; he fails to take it.
забывать о чём?
- prepositional → to forget about something (as in not remember it):
- Он забывает о проездном.
  He forgets about the pass (it slips his mind; he stops thinking about it).

In your sentence we’re talking about him physically leaving his pass at home, so the direct object проездной (accusative) is correct.

Can we omit мой and just say Старший брат часто забывает…?

Yes, you can, and it will often sound natural:

Мой старший брат часто забывает… – explicit my.
Старший брат часто забывает… – understood from context that it’s my older brother (especially if you’re talking about your family).

Russian frequently omits possessive pronouns for close relatives and body parts when it’s obvious whose they are:

Мама позвонила. – (My) mom called.
У меня болит голова. – My head hurts. (no моя)

Including мой is also fine; it just makes it more explicit.

Could I use свой instead of мой: Свой старший брат…?

Here, свой старший брат is not natural and usually incorrect in standard usage.

Свой normally refers back to the subject and is used for possessions of the subject:
- Он забыл свой проездной дома. – He forgot his (own) pass at home.
- Я люблю свою семью. – I love my (own) family.

In Мой старший брат…, the subject of the whole sentence is мой старший брат, so using свой inside that noun phrase doesn’t really work. You use свой later in the sentence, referring back to the subject, not inside the subject itself.