A (Exclam.)

Situations

S1: When seeing his mother back home from the market, the child exclaims:

A! Mẹ đã về!
(Oh! Mom is back!)

In this situation, the child expresses his joy.

S2: Lan's husband usually comes home late on Saturday. But today he arrives home early. Lan says:

A, hôm nay anh về sớm quá!
(Oh, you are home early today!)

In this situation, Lan expresses her surprise.

S3: Nam made an appointment with Bình to return his money. At the coffee shop, they talked a lot. He didn't remember to return the money until he was about to leave. He said:

A! Tôi quên, tôi chưa trả tiền cho anh.
(Oh! I forgot. I didn't return your money yet.)

In this situation, a is used to indicate that the speaker remembers something.

Definition

A, as an exclamatory word, is used at the beginning of the sentence to show joy, surprise, or to indicate that the speaker remembers something.

A! is an exclamatory sentence in S1 and S3, and a used at the beginning of the sentence is an exclamatory word in S2.

Both a and à, used interchangeably, express that the speaker is surprised or just figures out something. However, a is not used to express joy.

[1] — À, mẹ về!
(Yeah! Mom is back!)

We use thảo nào / hèn chi / hèn gì to express surprise when we suddenly remember or realize something. But thảo nào is used to express a conclusion or new discovery about something. Cf:

Hoa tells Lan that Mrs. Ba has just won the lottery. Lan says:

[2] Thảo nào dạo này trông bà ấy trẻ ra.
(That is why she looks younger these days.)

Lan suddenly remembers that Mrs. Ba still owes her money. Lan asks:

[3] À, chị có nghe bà ấy nói khi nào bà ấy trả tiền cho tôi không?
(Oh, did you hear her say when she will return my money?)

Combinations

À, ra vậy! (Cf. thảo nào), is used to express that we realize or understand something after hearing some news or an explanation. This expression is like a conclusion.

John speaks Vietnamese very well. Hà tells Nam that John's mother is Vietnamese. Nam says:

[1] — À, ra vậy!
(Oh, now I understand!)

À is also used in combination with thảo nào / hèn chi / hèn gì to express surprise and sudden understanding.

[2] — À, thảo nào!
(Oh, that is why!)