Esami di maturità

The Italian news has been filled lately with discussion of the annual esami di maturità: that is, exams of maturity. (Similar reference here, but in English, and more general.) These constitute a sort of "final exam" for students who want a high school diploma. A number of European nations administer such exams every year. Our closest parallel, I think, are the exams required by the No Child Left Behind act.

There's a controversy on the language exam this year. Apparently, a question about Dante had incorrect references. Ouch.

While browsing there, I took a gander at the exams for mathematics in the liceo scientifico. This is a high school for those who wish to specialize in the sciences. I found some sample questions and solutions. You can find them here if you're interested. Some of the questions are surprisingly familiar; others are not, but I like them all the same. One of my favorites translates roughly as,

Consider the following statement: "The function tan x takes values with opposite signs on the interval I = [π/4,3π/4], yet there is no x = I such that f(x) = 0." Is this statement true or false? Why?

The correct response must appeal to the Intermediate Value Theorem (although the solution provided refers to it as the "Theorem of Zeroes"). However, instead of using the Intermediate Value Theorem to say what the Theorem "ordinarily" says ("such a value x exists"), the respondent must use it to explain why no such value exists: a hypothesis of the theorem is violated.

An excellent question. Not the sort of thing you can test for on a multiple choice test.

The application problems are nice, too. It's obvious that someone graduating from this program has to know calculus. Again, this is the liceo scientifico. Other licei would expect much less mathematical background, I'd think.