Engine malfunction at 800ft

I had quite an educational session this morning, during my flight lesson. I had my first engine malfunction. I solo'd last week, but my instructor wanted to do another dual instruction before the next solo. In hindsight that was a good thing... otherwise I would have had the malfunction without an instructor onboard. So what happened? At 800ft, just after take off, the engine would not throttle down. The engine was stuck at 4000rpm. You can fly an airplane with 4000rpm but not land it. We informed the tower, and killed the engine mid-air, to glide back onto runway 12.

The lesson may have been more educational if it happened during a solo. I knew that killing the engine was the thing to do, but I would probably have declared a PAN PAN PAN over the radio, or if I panic'ed more, maybe even a MAYDAY. However, in aviation terminology, an event like this is not a 'forced landing' but a 'precautionary landing'. Another thing I learned: a broken throttle cable will open up the carburetor, not close it, as it would in a car or motorcycle. That makes sense of course, when you think about it.

The rotax engine in my plane is a 4 cylinder, with dual carburetors. With one broken cable, a closed throttle will result in one bank of cylinders fully fueled, and one bank of cylinders on idle fuel. This results in a rough running engine, that cannot go below 4000rpm.