ad-lib — If you ad-lib something in a play or a speech, you say something which has not been planned or written beforehand.
off-the-cuff — with little or no preparation; extemporaneous; impromptu: a speaker with a good off-the-cuff delivery.
impromptu — made or done without previous preparation: an impromptu address to the unexpected crowds.
unrehearsed — to practice (a musical composition, a play, a speech, etc.) in private prior to a public presentation.
spontaneous — coming or resulting from a natural impulse or tendency; without effort or premeditation; natural and unconstrained; unplanned: a spontaneous burst of applause.
offhand — cavalierly, curtly, or brusquely: to reply offhand.
adverb extempore
off the top of one's head — the upper part of the body in humans, joined to the trunk by the neck, containing the brain, eyes, ears, nose, and mouth.
