Il mio amico è sempre disponibile ad aiutarmi con i compiti di matematica.

In Italian, possessive adjectives like mio, tuo, suo usually go together with the definite article:

• il mio amico = my friend
• la mia casa = my house
• i miei libri = my books

This is different from English, which normally uses no article before my.

A very common exception is with many singular family members:

• mio padre = my father
• mia sorella = my sister

But amico is not a family word, so il mio amico is the normal form.

Amico is the masculine singular form meaning friend when the friend is male.

• amico = male friend
• amica = female friend

So Il mio amico tells you the friend is male. If the friend were female, it would be:

• La mia amica è sempre disponibile...

The accent is important because è means is.

• è = is
• e = and

So:

• Il mio amico è sempre disponibile = My friend is always available/helpful
• Il mio amico e sempre disponibile would be incorrect

The accent helps distinguish the verb from the conjunction.

That is the normal word order in Italian.

• è sempre disponibile = is always available

Italian often puts adverbs like sempre, spesso, mai after the verb:

• È sempre gentile = He is always kind
• Sono spesso stanco = I am often tired

You may sometimes see other word orders for emphasis, but è sempre disponibile is the standard, natural choice here.

Here disponibile means something like willing, ready, or available to do something.

A common pattern is:

• disponibile a/ad + infinitive

So:

• disponibile ad aiutarmi = willing/ready to help me

The d in ad appears because the next word begins with a:

• a aiutarmi sounds awkward
• ad aiutarmi is smoother and more common

This extra d is often used before another a.

You may occasionally see a by itself in modern usage, but before a word starting with a, Italian very commonly uses ad for smoother pronunciation.

So in this sentence, ad aiutarmi is the most natural and expected form.

Aiutarmi is made up of:

• aiutare = to help
• mi = me

When attached to the infinitive, mi becomes part of the word:

• aiutare + mi = aiutarmi

So ad aiutarmi means to help me.

This happens a lot in Italian:

• vedermi = to see me
• dirti = to tell you
• lavarsi = to wash oneself

Yes, but it sounds different.

• ad aiutarmi = to help me
• ad aiutare me = to help me specifically

The version with the separate pronoun me is more emphatic, as if contrasting with someone else.

So in a normal sentence, aiutarmi is the natural choice.

Con means with, and i compiti means the homework assignments or the exercises.

• compito = assignment, task
• compiti = assignments, homework

Italian often uses the plural compiti when talking about homework in general, especially schoolwork made up of multiple tasks.

So:

• aiutarmi con i compiti = help me with my homework

Italian often uses the definite article where English does not.

English says:

• with homework

Italian usually says:

• con i compiti

This does not necessarily mean a specific set in the way English the homework might. It is simply the normal Italian structure here.

After a noun like compiti, Italian commonly uses di + subject to mean in/of a subject area:

• compiti di matematica = math homework
• libro di storia = history book
• professore di inglese = English teacher

Using della matematica would sound different and less natural here. Di matematica is the standard way to name the school subject.

Not always. Disponibile can mean several related things depending on context:

• available
• willing
• ready
• helpful/open to helping

In this sentence, because it is followed by ad aiutarmi, it has the sense of willing/ready to help me, not just physically available.

Because of sempre and the present tense è, it suggests a general habit or repeated quality:

• He is always willing to help me

It describes what the friend is generally like, not just what he is doing right now.

Yes. Depending on context, i compiti di matematica can refer to:

• math homework in general
• math assignments
• math exercises/tasks

If the larger meaning has already been given to the learner, this phrase is still useful to recognize as a normal school-related expression.

It breaks down like this:

• Il mio amico = subject
• è = verb
• sempre disponibile = description of the subject
• ad aiutarmi = what he is willing to do
• con i compiti di matematica = what kind of help

So the structure is roughly:

My friend + is + always willing + to help me + with math homework

This is a very natural Italian sentence pattern.