Mi hermana aprobó en la primera convocatoria y salió muy contenta del aula.

Aprobó is the preterite form, which is used for a completed action in the past. In this sentence, the idea is that your sister passed at a specific moment or in a specific exam session.

• Mi hermana aprobó... = My sister passed...
• Mi hermana aprobaba... would usually suggest a repeated, ongoing, or background action, which does not fit as well here.

So aprobó is the natural choice because the sentence refers to a finished result.

Not in this context. In Spanish, aprobar often means to pass an exam, subject, or course.

So:

• aprobar un examen = to pass an exam
• aprobar una asignatura = to pass a subject

It can also mean to approve in other contexts:

• El comité aprobó la propuesta. = The committee approved the proposal.

Here, because of convocatoria and the academic context, aprobar clearly means to pass.

In Spain, convocatoria often refers to an official exam sitting, exam session, or opportunity to take an exam.

So en la primera convocatoria means something like:

• in the first exam session
• at the first attempt
• in the first sitting

This is very common in Spanish academic language. Many courses or exams may give students more than one convocatoria, so passing en la primera convocatoria means she passed at the first official chance.

Because en la primera convocatoria expresses the context or occasion in which she passed.

It is not saying that she passed the exam session itself as a direct object. Instead, it means she passed during or on that first call/session.

So:

• aprobó en la primera convocatoria = she passed in the first exam sitting / at the first attempt

This use of en is idiomatic in Spanish academic contexts.

Salió is the preterite of salir, meaning to leave, to go out, or to come out.

Here:

• salió del aula = she left the classroom / she came out of the classroom

It is also in the preterite because it is another completed past action, coordinated with aprobó:

• she passed
• and then she left the classroom very happy

Because contenta agrees with mi hermana, who is female.

In Spanish, adjectives usually agree in gender and number with the noun they describe.

• mi hermano salió muy contento
• mi hermana salió muy contenta

So contenta is feminine singular, matching hermana.

It describes how she came out of the classroom. It works as a subject complement after the verb salir.

So:

• salió muy contenta = she came out very happy

The adjective refers back to the subject, mi hermana, not to aula.

This is common in Spanish with verbs like:

• salir
• llegar
• volver
• quedarse

Examples:

• Llegó cansado. = He arrived tired.
• Volvió contenta. = She came back happy.

Yes, you could say salió muy feliz del aula, and it would sound natural.

However, there is a small nuance:

• contenta often suggests pleased / satisfied
• feliz can sound a bit stronger, more like happy

In this context, muy contenta fits very well because she has just passed an exam and feels pleased and relieved.

Because aula is a feminine noun that takes the masculine singular article el when it comes directly before it.

So:

• el aula
• del aula = de + el aula

This happens because aula begins with a stressed a sound. Spanish avoids la aula because it sounds awkward.

But the noun is still feminine, which you can see in other words around it:

• el aula grande
• esta aula
• las aulas

So:

• singular: el aula
• plural: las aulas

It is feminine, even though it uses el in the singular.

This is a very common point of confusion. The article changes for pronunciation reasons, not because the noun becomes masculine.

So you get:

• el aula
• un aula
• esta aula
• la misma aula
• las aulas

Notice that adjectives and other determiners still behave as if aula were feminine.

Yes. Spanish often leaves it out if it is already understood from context.

So all of these are possible:

• Mi hermana aprobó en la primera convocatoria...
• Mi hermana aprobó el examen en la primera convocatoria...
• Mi hermana aprobó la asignatura en la primera convocatoria...

If the listener already knows what exam or subject is being discussed, omitting it sounds perfectly natural.

Yes, that is also correct.

Both of these are natural:

• salió muy contenta del aula
• salió del aula muy contenta

The difference is mostly one of rhythm or emphasis.

• salió muy contenta del aula puts the emotional state a little earlier
• salió del aula muy contenta first gives the movement, then adds how she felt

Both mean essentially the same thing.

Because Spanish often omits subject pronouns when the verb form already makes the subject clear.

• aprobó already tells you it is he/she/you formal in the past
• salió does the same

And since mi hermana is already stated, adding ella would usually be unnecessary.

Spanish does this much more than English:

• Mi hermana aprobó...
  not usually
• Mi hermana ella aprobó...

So the sentence sounds natural and complete without a separate word for she.