Is It Write OR Sit Exam?

English Boo

I will write the exam.✖️
I'm writing exam.✖️
I wrote the exam.✖️

Most people, including English Linguists are always tempted to use these popular expressions:
I will write the exam.
I'm writing exam.
I wrote the exam.

Note: these expressions are wrong when using them to refer to the duty of the examinee.

The examinee takes exam, does exam, and sits for exam.
So that rewriting the above examples, we could have:

I will take the exam
I'm taking exam
I took the exam

Or

I will do the exam
I'm doing exam
I did the exam

Or

I will sit for the exam
I'm sitting for exam
I sat for the exam.

However, it is right to say:
He writes or sets the exam.
Only when referring to the duty of the examiner.

SIMILARLY,
Most scholars usually use the expressions:
Students offering Maths 202 should see the course lecturer on Tuesdays.
If you're offering my course, do well to see me.
Virtually all students use the expression:
I am not offering that course.
These usages are wrong.
Note: Candidates or Students can't or don't offer a course or subject, rather, they take or do a course or subject offered by the institution or school.
Therefore, the school offers the course and
The students take or do a course.

Please let's write and say it right.