designing server side database to store user-specific data
There are 2 scenarios to consider. The first is when you have the user take 1 or more questions without a meaningful context such an exam or formal quiz. In which case you solution works. However, the second scenario is about when the user takes a question as part of a formal session. In this case you have the following rules:


A user takes zero, one or more quizes
A quiz contains 1 or more questions
A user provides an answer for zero,1 or more specific question on a specific quiz


Note:

Table names may be different in the solution than from this diagram

A1 = Standard answer for question 1

UA1 = User provided answer for question 1