History Teacher Murder Mystery

On the first day of school, someone murdered a history teacher. There were four people at the school that the police suspected had done it: the landscaper, a math teacher, a basketball coach, and the principal. These were their alibis:

The landscaper said he was outside mowing the lawn.
The math teacher said he was giving a mid-year test.
The basketball coach said he was running practice drills with his players.
The principal said she was in her office.

After giving their alibies, Detective Mehul arrested the killer immediately. Who killed the history teacher and how did the police know?

The math teacher killed the history teacher. He claimed that he was giving a mid-year test, but it was the first day of school. The math teacher killed the history teacher. He claimed that he was giving a mid-year test, but it was the first day of school.