It admits students based only on their scores on the Specialized High Schools Admissions Test (commonly referred to as the SHSAT).

QHSSYC is a member of the National Consortium for Specialized Secondary Schools of Mathematics, Science and Technology (NCSSSMST).

The curriculum is centered about the Regents and Advanced Placement exams; the school generates some of the highest test scores in the country.

Dr. Marmor left after the 2012–13 school year and the position was then held by Lenneen Gibson as Principal until October 2016, where she was then temporarily replaced by B.D.

On Monday, March 7, 2022, an anonymous caller sent a bomb threat to York College, which the high school's campus resides on.