Mine revs high and bounces between 1200 and 2200 on cold starts until the engine is completely warm. From what I've read, a bad intake manifold gasket is a common problem with the 9th and 10th gen Corollas. The gasket shrinks and seals improperly when cold, allowing unmetered air to enter the...
Sorry, I don't have a solution for you, but my 2009 Corolla S (manual transmission) did the exact same thing to me. I was on the way to work one morning and just as I shifted into second, I lost power and got a check engine light. I could barely even keep the car moving, but I pulled onto a...