From the experience of both of my kids, Scranton's math and science classes are quite rigorous. Yes, you will take a math placement test and you are correct in that you cannot use a calculator for that test. And, unless they have changed it, you cannot use a calculator on a test in at least certain math classes - I don't know about all of them.
If you score well enough on the placement test to be placed in calc. 1, you will still need to be prepared to work and study. It is not a piece of cake. I am not aware of any particularly "easy" math professors there. Unless you have a very strong aptitude for math, I would be careful thinking you "just want to get by in math with an A- or better". It could be harder than you think.
The same can be said for their chemistry and physics classes and professors. There a lot of students looking to go on to medical school, so the classes must be rigorous to prepare them.