Learn Hardcore Spanish (Spain): Para conseguir una beca, es posible que tengas que mejorar tus notas este semestre. - To get a scholarship, it is possible that you have to improve your grades this semester.

Estudio mucho para conseguir una beca.
I study a lot (in order) to get a scholarship. → purpose/goal
Conseguí la beca por mis buenas notas.
I got the scholarship because of my good grades. → cause/reason

So here para is the correct choice for a goal you’re aiming at.

Why is it es posible que tengas and not es posible que tienes?

Because es posible que triggers the subjunctive in Spanish. After many expressions of possibility, doubt, emotion, etc., Spanish uses the subjunctive:

Es posible que tengas que mejorar…
It’s possible that you (might) have to improve…

Using tienes (indicative) would sound unnatural or incorrect to native speakers in this structure. Other expressions that also take the subjunctive:

Es probable que vengas. – It’s likely that you’ll come.
Dudo que sea verdad. – I doubt it’s true.

So: es posible que + subjunctive → es posible que tengas.

What exactly does tengas que mean, and how is it different from just tengas?

Tener que + infinitive = to have to / must + verb (obligation or necessity).

tengas que mejorar → you (might) have to improve / you may need to improve

If you just said es posible que tengas mejorar, that would be wrong; mejorar needs something like tener que, necesitar, etc., before it.

Compare:

Es posible que tengas que mejorar tus notas.
You might have to improve your grades.
Es posible que tengas mejores notas.
It’s possible that you have better grades. (different meaning; here tengas is just have, not have to)

Could we say es posible que necesites mejorar tus notas instead? What’s the nuance compared to tengas que mejorar?

Yes, you can say:

Es posible que necesites mejorar tus notas este semestre.

It’s grammatically correct and natural. Nuance:

tengas que mejorar → focuses on obligation / requirement
(you may be required to improve your grades to get the scholarship)
necesites mejorar → focuses more on need / convenience
(it might be necessary or advisable for you to improve them)

In context of a scholarship, tengas que mejorar sounds slightly more like an external condition or rule; necesites mejorar sounds a bit more like general necessity.

What does beca mean in Spain? Is it only for university scholarships?

In Spain, beca is a general term for scholarship / grant / financial aid for studies. It’s not limited to universities.

It can refer to:

School scholarships (primary/secondary)
University scholarships
Grants for studying abroad (e.g. Erasmus)
Sometimes internships that are paid as a “scholarship” (e.g. una beca de prácticas)

So conseguir una beca is broadly to get some kind of financial help or scholarship for your studies or training.

Why is it una beca and not la beca here?

Una beca is indefinite: a scholarship (not a specific one that has already been identified in the conversation).

Para conseguir una beca…
In order to get a scholarship… (any scholarship that fits this situation)

If the speaker and listener already knew exactly which scholarship they were talking about, they might say:

Para conseguir la beca, es posible que tengas que mejorar tus notas.
To get the scholarship, you might have to improve your grades.

In your sentence, the idea is more general: to get some scholarship.

In Spain, is notas the usual word for “grades”? Are there other options?

Yes, in Spain notas is the everyday word for grades / marks at school or university.

Sacar buenas notas – to get good grades
Tus notas – your grades

Other words:

calificaciones – more formal/technical, used in official contexts or documents
puntuaciones – scores (more for points on a test, sports, etc.)

In normal conversation in Spain, people almost always say notas when talking about school grades.

Why does it say tus notas and not las notas?

Tus shows that the grades belong to you (the person being spoken to):

tus notas = your grades

If you said las notas without a possessive, it would mean the grades, in a very general or context-dependent way. For example:

Tienes que mejorar las notas de la clase.
You have to improve the class’s grades.

Here, we clearly mean your own grades, so Spanish uses the possessive pronoun tus.

Is the word order fixed, or can we move para conseguir una beca to the end of the sentence?

You can move it; the meaning stays the same. For example:

Para conseguir una beca, es posible que tengas que mejorar tus notas este semestre.
Es posible que tengas que mejorar tus notas este semestre para conseguir una beca.

Both are correct and natural.

Putting para conseguir una beca at the beginning emphasizes the goal first.
Putting it at the end makes it sound slightly more like an afterthought or explanation of why you might need to improve your grades.

In everyday speech, both orders are used.

Could we use puede que or a lo mejor instead of es posible que? Would the grammar change?

Yes, but the grammar does change depending on the expression:

puede que + subjunctive
- Puede que tengas que mejorar tus notas este semestre.
  This is very similar in meaning to es posible que tengas que…
  Both take the subjunctive (tengas).
a lo mejor + indicative
- A lo mejor tienes que mejorar tus notas este semestre.
  Maybe you have to improve your grades this semester.
With a lo mejor, Spanish normally uses the indicative (tienes), not the subjunctive.

So:

es posible que / puede que → subjunctive (tengas)
a lo mejor → indicative (tienes)

Why is there no article before este semestre in Spanish, when in English we say “this semester”?

In Spanish, demonstratives like este, esta, estos, estas already include the idea of “this/these”, so you don’t use an extra article:

este semestre = this semester (no article)
esta semana = this week
estos días = these days

You only use an article if the demonstrative is a pronoun (standing alone), as in:

Este es el último semestre. – This is the last semester.

In your sentence, este is an adjective modifying semestre, so no extra el is needed: este semestre is the correct form.