One of the distinguishing features of a good mathematician is the ability to successfully tackle novel problems. Hence, to identify our best mathematics students in high school, we need assessment that distinguishes students who are successful at this.
A 'novel problem' at a high school level could be defined as using a familiar technique in an unfamiliar setting, where the decision of which technique is required is not obvious, or it could consist of combining two or more familiar techniques in an unfamiliar way.
I am interested in knowing if the AP Calculus exam contains such questions. If so, could someone please post a few examples of such questions from past papers?