La uzota plumo kuŝas apud la malfermita kajero.

Uzota is a participial adjective built from:

• uz- = the root of uzi (to use)
• -ot- = future passive participle
• -a = adjective ending

So uzota means to be used, going to be used, or intended to be used.

In this sentence, la uzota plumo is the pen to be used / the pen that will be used.

Because the pen is not the one doing the action of using. It is the thing that will be used.

• uzota = to be used → passive
• uzonta = about to use / going to use → active

So:

• uzota plumo = a pen that will be used
• uzonta homo = a person who is going to use something

If you said uzonta plumo, that would suggest the pen itself is going to use something, which is not the intended meaning.

Because it is functioning as an adjective and describing plumo.

In Esperanto, participles can act like adjectives, and adjective forms end in -a.

Here:

• plumo = pen
• uzota = to-be-used

So uzota must have the adjective ending because it modifies the noun.

If the noun were plural, the adjective would also change:

• la uzotaj plumoj = the pens to be used

This is normal adjective agreement in Esperanto.

Malfermita is also a participial adjective. It is built from:

• mal- = opposite
• ferm- = close, shut
• -it- = past passive participle
• -a = adjective

So:

• fermi = to close
• malfermi = to open
• malfermita = opened / open

In the sentence, la malfermita kajero means the opened notebook or more naturally the open notebook.

This is about the difference between two passive participles:

• -ata = action in progress
• -ita = action completed

So:

• malfermata = being opened
• malfermita = opened, already in the state resulting from opening

In this sentence, the notebook is already open. It is not in the middle of being opened. That is why malfermita is the natural choice.

Because there are two separate noun phrases:

• la uzota plumo
• la malfermita kajero

Each one can have its own definite article.

English also usually does this:

• the pen
• the notebook

You would not normally say the pen lies beside open notebook. Likewise in Esperanto, each definite noun phrase gets its own la.

Because there is no direct object here.

• La uzota plumo is the subject.
• kuŝas is the verb.
• apud la malfermita kajero is a prepositional phrase.

Normally, nouns after prepositions do not take -n, because the preposition already shows the relationship.

So:

• apud la malfermita kajero = beside the open notebook

No accusative is needed.

A learner might expect kajeron, but that would be wrong here.

Kuŝas means lies or is lying. It gives a more specific picture than estas.

Esperanto often uses position verbs where English might simply say is:

• kuŝi = to lie
• stari = to stand
• sidi = to sit

So La uzota plumo kuŝas apud la malfermita kajero paints a physical scene: the pen is lying beside the notebook.

If you said estas apud, that would still be understandable, but kuŝas is more vivid and natural for an object resting on a surface.

Apud means beside, next to, or by.

It is a preposition, and the noun after it normally stays in its basic form:

• apud la kajero would be wrong because kajero needs la here if it is definite, but it still does not take -n
• apud la kajero / apud la malfermita kajero = beside the notebook / beside the open notebook

So apud itself shows the relationship, and that is why no extra case ending is needed on kajero.

Not completely. Esperanto word order is fairly flexible, because endings make the grammar clear.

For example, you could also say:

• Apud la malfermita kajero kuŝas la uzota plumo.

That still means the same thing, though the emphasis changes a little.

Also, adjectives can sometimes come after the noun in Esperanto, so la plumo uzota is possible, but la uzota plumo is the more straightforward and common order for learners.

So the given sentence is a very normal, standard way to say it.