act up vs carry on

act up and carry on both are verbs.

Word	Noun	Adjective	Verb	Adverb
act up	No	No	Yes	No
carry on	No	No	Yes	No

As verbs, act up and carry on are synonyms defined as:

act up (verb)	carry on (verb)
make itself felt as a recurring pain	continue talking
misbehave badly; act in a silly or improper way	direct the course of; manage or control
	misbehave badly; act in a silly or improper way
	keep or maintain in unaltered condition; cause to remain or last