The exams you cited are part of a transparent admissions sytem (the Irish Leaving Cert, the French Bac, and the Swiss Matura are similar).

All these exams expect students to synthesize knowledge from a (mostly) standardized curriculum and aren't based on memorization (an example of a test of memorized information is the AP US History exam).

Sample A-level English literature question:

Analyse (Emily) BrontŽís presentation of Nelly Dean, Joseph and Zillah in Wuthering Heights and analyse their importance in the novel as a whole.

Sample question, Irish Leaving Certificate, Higher Level Maths:

NOTE from Val: most of this stuff is in vector notation, which I can't reproduce here.

2. (a) Find the value of s and the value of t that satisfy the equation
         s(i - 4j) + t(2i + 3j)= 4i - 27j

    (b) OP = 3i - 4j and OQ = 5(OP) where O is the origin.

       (i) Find OQ in terms of i and j.

       (ii) Find cos|angleOPQ| in surd form.

     (c) (I have omitted a proof using a triangle diagram)

Sorry, but you just don't see stuff like this on the SAT, because it a) can't be graded with a Scantron-like device or by a $10 per hour grader in two minutes or less (ideally much less), and b) is quite simply asking too much of American students and their schools.

The purpose of these exams is to identify students who are capable of college-level work. They're hard, and they require those "critical thinking skills" that get lip service but not much else in American schools. In many countries, secondary school exams are the sole gatekeepers of university admissions. No one at Trinity College, Dublin or University College, Cork cares about what you do after school is out. They care about your academic ability.

Last edited by Val; 09/16/14 10:33 AM. Reason: Clarity