Question

1. I am a good cook, amn't I?
2. I am a good cook, aren't I?
3. I am a good cook, ain't I?
4. I am a good cook, am I not?
(Which one is commonly used? Which one is used in written forms?)
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5. I amn't a good cook.
6. I aren't a good cook.
7. I ain't a good cook.
(Are the three all incorrect? Which contracted form can we use?)
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8. Amn't I a good cook?
9. Aren't I a good cook?
10. Ain't I a good cook?
11. Am I not a good cook?
(Which one is grammatically correct? Which one is correct in written forms?)

Answer 1

1-4 -- only 4 is correct, although the others are used by some people.

5 - 7 -- all are wrong.
The correct way to say this is
I'm not a good cook.

8 - 11 -- only 11 is correct.