Each of these three sentences is incorrect because of the should of/would of/could of construction:

I should of been better prepared for the exam.

I would of brought a jacket if I had known it would be cold.

I could of tried working harder.

How should these sentences be written instead? They should use could have, would have, and should have (or the contractions could’ve, would’ve, should’ve).

Because have (or the contraction form) sounds like of when spoken quickly, it’s common for writers to use the word of instead of have or its contraction. But it’s grammatically incorrect to use the could of/would of/should of construction.

Never, ever write could of, would of, or should of. I suggest staying away from the contraction form, too, and writing out both words instead—could have/would have/should have.