'applied to a university' is a correct term and can be used in written English.
For example: I have applied to a university in hopes of furthering my studies.
Issy Sampson Despite having applied to a university largely populated by ducks, I arrived at uni anticipating drunken misadventures.
He was asked to disclose the cautions – even though they were spent under the Rehabilitation of Offenders Act 1974 – when he applied for a job at a football club at the age of 17 and when he applied to a university sports studies course.
I applied to a university and I got rejected.
Online applied to a university hospital-based cohort of Taiwanese breast cancer patients showed that the calculated predictions by Adjuvant!
Sun G, Haining R, Lin H ,Oreskovic NM, He J. Comparing the perception with the reality of walking in a hilly environment: an accessibility method applied to a University campus in Hong Kong.
When I was 18 I applied to a University in Tehran.
With that in mind, here's how you can help your sixth-former to find and apply to a university that's right for them.
The concurring opinion also cautioned that the requirement of neutrality did not apply to a university's own speech, as exemplified by curriculum choices.
There are, however, some practical concerns and students applying to a university late often find themselves at the bottom of the pile for accommodation.
