A calma ajuda a resolver o problema.

Here a is the feminine singular definite article, meaning the.

Portuguese often uses the definite article with abstract nouns in general statements, where English usually uses no article. So:

• A calma ajuda... = literally Calmness helps...
• Natural English would usually just say Calmness helps... or Being calm helps...

So the article is normal in Portuguese, even though it may feel unnecessary to an English speaker.

Here calma is a noun: calmness, calm, or composure.

You can tell because it comes after the article a, forming a calma.

Compare:

• A calma ajuda. → calma is a noun: calmness
• Ela está calma. → calma is an adjective: calm

So in this sentence, a calma means the state or quality of being calm.

Ajuda is the third-person singular present tense of the verb ajudar (to help).

It matches the subject a calma, which is singular:

• a calma → singular subject
• ajuda → singular verb

So the structure is:

• A calma = subject
• ajuda = verb
• a resolver o problema = complement

That second a is not an article. It is a preposition.

In this sentence, ajudar is followed by a + infinitive:

• ajudar a resolver
• literally to help to solve

So:

• first A = article in A calma
• second a = preposition before resolver

Even though both words are written a, they do different jobs.

Yes, you may hear that, especially in Brazilian Portuguese, but ajuda a resolver is a very standard and natural form.

In practice:

• ajuda a resolver = very common, clear, standard
• ajuda resolver = also heard, especially in speech

For a learner, ajudar a + infinitive is a safe pattern to use.

Because it expresses the action that is being helped.

After ajuda a, Portuguese normally uses the infinitive:

• ajuda a resolver
• ajuda a entender
• ajuda a melhorar

This is similar to English helps to solve, helps to understand, helps to improve.

So resolver stays in its base form because it is not the main conjugated verb of the sentence. The main conjugated verb is ajuda.

O is the masculine singular definite article, meaning the.

Portuguese usually uses an article with singular countable nouns more often than English does. So resolver o problema is the normal way to say solve the problem.

It can also suggest that the problem is:

• specific
• already known from context
• the one under discussion

If you said resolver problemas, that would mean solve problems in a more general sense.

Because not all Portuguese nouns ending in -a are feminine.

Problema is one of several masculine nouns of Greek origin that end in -ma. So it takes masculine articles and adjectives:

• o problema
• um problema
• problema sério

Other common examples:

• o sistema
• o tema
• o programa
• o idioma

So even though problema ends in -a, it is masculine.

It can do either, depending on context, but by itself it sounds very much like a general truth or general principle.

That is because:

• a calma can mean calmness in a broad, generic sense
• the present tense ajuda often expresses something generally true

So the sentence naturally reads like:

• Calmness helps solve the problem
• Being calm helps when solving the problem

Even though o problema is singular, it may still refer to the problem at hand or the problem being discussed.

They are different structures, and all can be natural depending on what you want to emphasize.

• A calma ajuda a resolver o problema.
  Focuses on calmness as an idea or quality.

• Ter calma ajuda a resolver o problema.
  Means Being calm helps solve the problem. This is also very natural.

• Manter a calma ajuda a resolver o problema.
  Means Keeping calm helps solve the problem. This sounds especially natural when someone is under pressure.

So the original sentence is correct and natural, but in everyday Brazilian Portuguese, ter calma or manter a calma may sound a little more conversational in some contexts.