Past events are easy to hide - simply follow the steps in the Calendars app:
Edit the calendar in which you would like to hide past events.
Navigate to the second step 'Content'.
To hide them uncheck the box 'Display past events'.
Once you've done this, the change will be instant and you can change it back whenever you'd like.
FAQs:
Q. If I check "Display past events" what will my students see on my public events calendar?
A. In 'list' layout: they will see all bookable and non-bookable events from last month up to one year ahead.
A. In 'calendar' layout: they will see all bookable and non-bookable events in all past and future months.
Q. If I uncheck "Display past events" what will my students see on my public events calendar?
A. In 'list' layout: they will see all bookable and non-bookable events from today up to one year ahead.
A. In 'calendar' layout: all bookable and non-bookable events from today forward.