Prosecution barrister Ruby Shrimpton said blood and urine samples from Corrigan indicated he had been drinking, and had used cocaine and cannabis.
But toxicologists could not say how much he had taken and drunk, or what the effects were at the time he met Algasim, she explained.
Pathologist Virginia Fitzpatrick-Swallow told the trial that Algasim suffered an 11.5cm-deep (4.5in) wound to his neck and a vital artery was cut.
Shrimpton told jurors that Algasim was dead within an hour of being stabbed.
Prosecutors said police found a high-vis hooded sweatshirt in a bin in close-by Vinter Terrace.
They said the weapon used, a silver kitchen knife with a 13cm-long (5in) blade, was found nearby.
Corrigan’s father Peter, who is in his early 50s and lives in Vinter Terrace, has admitted assisting an offender. He is also waiting to be sentenced.
EF International Language Campus, a Cambridge-based language school that teaches English to overseas students, previously said it was “deeply saddened” by the death of one of its students.