I'm looking at a sample math exam question for the 2025 University Entrance Exam (PAU) exam. Students are warned that when solving exercises, they must "model and solve everyday problems by linking and contextualizing mathematics to other areas of knowledge." They must "argue the suitability of the problem solutions to verify their validity." As an example, there's this case: "Juan finds among his grandfather's papers a sketch like the one in the attached figure, which describes an irrigated plot of land that he left as an inheritance to his father." And in the attached figure, we see the grandfather's plot of land. It's a kind of trapezoid but with one curved side. Like half an irregular ball, squared on one side. Students must calculate the coordinates of points P, Q, and R and the equation of line PR.
To do this as required, students will first have to consider whether the fact that it's the grandfather (and not the grandmother) who leaves the land to the father (is there no mother?), whom we assume he leaves to Juan, who we don't know is an only child, perpetuates sexist roles. Regarding irrigation, should we consider what he's planted? Fruit trees, a vineyard? Juan won't be able to irrigate much. Why isn't this specified in the era of climate change?
Let's leave aside the fact that Joan doesn't take anything away from the practical calculation of the coordinates requested in the exam. Let's get to the point. Students, above all, will have to answer the question by explaining that Joan's grandfather was a complete idiot. To move the tractor or plow with the horse, the land should be level. This goes beyond the "heroic viticulture" of Priorat. Turning around with the tractor would require constant maneuvering (it measures about eighty square meters). If Juan had to farm this land, which could be called Clos del Polinomio, he would spend the day walking back and forth, while all the other farmers would have been at the main festival for days, simply because they are heirs to rectangles and squares.
