Going from memory again, YMMV:
Carol: "He's going to catch up to us and when he does the only thing that's gonna stop him destroying this ship is me so you'd better let me talk to him!"
Kirk: "Relax, we're at warp, he can't catch us."
Carol: "Yes he can! He's been designing a ship with Mark Four capabilities including--"
Sulu: "Captain... I'm getting a reading here I don't understand..."
Could be another scene I don't recall where someone mentions an advanced warp drive, but I can't imagine what it would be. Khan later mentions that the Vengeance has "twice the size, three times the speed" but that's it (his comment "If you think you're safe at warp, you're wrong" is what sent Carol running in the first place).
When else would Carol have mentioned an advanced warp drive?