How often do they change the nation's citizenship quiz?
Every few decades. The list of questions used today dates back to the last large-scale amnesty for illegal immigrants in 1986. Before then, the process wasn't nearly as standardized as it is today. Each immigration officer could ask whatever questions (and however many) he deemed appropriate during a naturalization interview. This loosey-goosey system wasn't equipped to handle the large number of naturalizations that resulted from the 1986 amnesty. So, a pair of officers at the INS got together and came up with the standard questions used today.
The new list didn't make the test predictable. Individual officers could still decide exactly which questions to ask, and they sometimes strayed from the samples. As late as the 1990s, testers were still inconsistent in the way they administered the test: Some might ask 10 questions, for example, and others 12.