After a dual check the pilot's instructor briefed the pilot to carry out two circuits, each with a full stop landing. Following the first circuit and landing, the pilot applied power to commence the take-off without bringing the aircraft to a stop. The aircraft veered sharply to the left, became airborne momentarily, before settling back onto the ground outside the flight strip. Flaps were selected fully down and the aircraft continued under full power across a storm water drain for another 38 metres before coming to rest. This was the pilot's second solo exercise. Following the loss of directional control it appears that the pilot became confused and did not apply the correct control inputs to bring the aircraft to a stop.