We highly recommend you have your Corolla's ignition timing fault fixed and have a smog check retest administered. The correct ignition timing may fix the engine speed fault as well as reduce HC. This should be the first course of diagnosing the high HC fault. If after the timing correction, HC is still high or RPM is out of range or both, you may then begin diagnosing other faults which could cause high HC. Follow the link below for a list of problems which can cause a vehicle to fail the smog test due to high HC.
What Causes High HC?