semi modals - I used to study at Cambridge School

I used to study at Cambridge School.

I am used to studying at Cambridge School.

If the verb is continuous tense, it need to be added "verb to be" before used to?

Answer

I used to study at Cambridge School.

This sentence discusses an action that happened entirely in the past.

I was studying at Cambridge School.

That would be past continuous.

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To be used to something is a special phrase that means being habituated. For example, "I am used to eating spicy foods, so this dish tastes bland."

Therefore,

I am used to studying at Cambridge School.

actually means, "I have a habit of studying at Cambridge School," which doesn't really make sense. It could make sense if you added some details: "I am used to studying at the Cambridge School library, which offers free Wi-Fi access to the academic journals I need. When I do my studying anywhere else, I find it very inconvenient."

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Incidentally, if you are talking about the University of Cambridge, you would usually just say "Cambridge":

I used to study at Cambridge. Now I teach at Oxford.