Our math placement tests were paper - the school wanted to see the student’s work to assist in knowing how they came to an answer, whether incorrect ones were computational in nature, etc.
Totally agree about language placement. Our son had taken spanish k-9, including a 6 week exchange in Madrid with homestay, and was placed in spanish 1 when he entered BS in grade 10. We pushed back and asked him to be placed in spanish 2, and to be honest, it was a struggle for him. BS foreign language classes are very rigorous and hit the ground running in levels 2 and beyond. There is no catch up/review period.