In the public exam

[Xinfu]

Expected answer: In the public English exam, we had a text by Shakespeare; we had a reading paper, and listening and writing and speaking.

1. Are my sentences natural English?

2. How should I phrase the question that should lead to the expected answer? Would this do?:

- What did you do in the public English exam?

[poli]

I think so, but perhaps it would be more precise to say: What did the Public English Test consist of?

[Xinfu]

Thank you~

But which one is better/correct: the public English exam/English public exam

[Rusty]

"The public English exam" designates that an English exam (a test about the English language) can be taken publicly.
"The English public exam" designates that the public exam is written in English.

Both are correct. Neither one is better, because they mean different things.