A problem from the PISA assessment relevant to calculus

Abstract

In this paper, one of the multiple choice tasks from the PISA test is considered. This particular task deals with the relation between a water tank, in which water is poured at a constant rate, and the given graphs of functions showing how the height of water in that tank changes in time. For the purpose of better understanding the types of tasks that resemble this one, a few similar tasks have been considered. These tasks could be used on various levels of education. We also hope that our paper could exemplify the case of a research project to be assigned to the best students and that the paper can also be useful for all those who teach introductory calculus.