Sem a calculadora, não consigo terminar a ficha de matemática.

In Portuguese, the subject pronoun is often omitted when the verb already makes the subject clear.

Here, consigo means I manage / I can, so eu is understood:

• (Eu) não consigo terminar... = I can't manage to finish...

Adding eu is possible, but it usually adds emphasis:

• Eu não consigo terminar a ficha de matemática. = I can't finish the maths worksheet.
  This can sound more emphatic, like I can't do it.

Here, consigo is the 1st person singular of conseguir.

Conseguir often means:

• to manage to
• to succeed in
• sometimes to be able to, especially in everyday speech

So:

• não consigo terminar = I can't manage to finish / I can't finish

It is not the same as poder in every context, but in many everyday sentences the meaning overlaps.

In standard Portuguese, não usually comes before the verb it negates.

So:

• não consigo = I can't
• não quero = I don't want
• não tenho = I don't have

Putting não after the verb is not how standard Portuguese normally forms negation.

Sem means without.

• Sem a calculadora = Without the calculator

It is placed at the beginning here to set the condition first:

• Without the calculator, I can't finish the maths worksheet.

This is very natural in Portuguese, just as it is in English. You could also say:

• Não consigo terminar a ficha de matemática sem a calculadora.

That means the same thing.

Both are possible, but they are not exactly the same.

• sem a calculadora = without the calculator
  This usually refers to a specific calculator, or the calculator relevant in the situation.
• sem calculadora = without a calculator / without using a calculator
  This is more general.

So in your sentence, sem a calculadora sounds like there is a particular calculator in mind.

In European Portuguese, ficha can mean several things depending on context, but in school contexts it often means:

• worksheet
• exercise sheet
• sometimes assignment sheet

So a ficha de matemática is most naturally:

• the maths worksheet
• the mathematics exercise sheet

This is a very common word in Portuguese schools.

A means the, while uma means a/an.

• a ficha de matemática = the maths worksheet
• uma ficha de matemática = a maths worksheet

Using a suggests the speaker has a specific worksheet in mind, probably one already known in the conversation or situation.

Portuguese often uses de + subject/topic where English might use a noun before another noun.

So:

• ficha de matemática = maths worksheet
• livro de história = history book
• professor de inglês = English teacher

This structure is extremely common in Portuguese. English often uses noun-noun combinations, but Portuguese usually prefers de.

In Portuguese, school subjects are usually singular:

• matemática = mathematics / maths
• história = history
• geografia = geography

Even though English has mathematics, Portuguese uses the singular form matemática.

Yes, often you can.

• não consigo terminar a ficha = I can't finish the worksheet
• não consigo acabar a ficha = I can't finish the worksheet

Both are natural. In many contexts, terminar and acabar overlap.

That said, terminar is often a very straightforward choice for to finish in this kind of sentence.

Yes, it adds an important nuance.

Compare:

• Não termino a ficha. = I don't finish the worksheet / I'm not finishing the worksheet
• Não consigo terminar a ficha. = I can't manage to finish the worksheet

With conseguir, the idea is not just that the action does not happen, but that the speaker is unable to complete it.

So não consigo terminar is the better match for I can't finish.

Yes. A very natural alternative is:

• Não consigo terminar a ficha de matemática sem a calculadora.

This means exactly the same thing.

The version with Sem a calculadora at the beginning gives more emphasis to the condition:

• Without the calculator, I can't finish the maths worksheet.

The version with sem a calculadora at the end sounds a bit more neutral.

A broad European Portuguese pronunciation would sound roughly like:

• Sem a calculadora, não consigo terminar a ficha de matemática.
• Approximate English-style guide: sẽ-muh cal-cu-la-DO-ra, nãw cõ-SI-gu ter-mi-NAR uh FEE-shuh d(uh) ma-te-MA-ti-kuh

A few useful points:

• não has a nasal sound, not a clear now
• consigo has stress on si
• terminar has stress on the last syllable
• ficha sounds like FEE-sha
• In European Portuguese, unstressed vowels are often reduced, so some vowels sound less clear than in writing

The sentence is correct and understandable in both European and Brazilian Portuguese. However, a few things may differ:

1. Pronunciation is quite different.
2. Fixa de matemática? No — it is still ficha de matemática, but pronunciation changes.
3. In Brazil, ficha can still be understood, but in some contexts folha de exercícios, lista, or atividade might also be common depending on the region and school context.

So the sentence is perfectly fine, but ficha feels especially familiar in a European Portuguese school context.