I’m going to echo a news story that appeared today in the main newspapers of Zaragoza. The story, available among other places at this link, tells us that the University acknowledged yesterday that one of the exercises in the mathematics exam for the university entrance exam exceeded the level of high school students. Therefore, it has been decided to evaluate the exam based on the three (out of four) exercises in which the student obtained the best score.
Was the difficulty of this exercise really excessive for a high school student? First, the exercise is solved briefly below for those who are interested.
The integral presented is the following:
The equation to be integrated can be decomposed into partial fractions, resulting in the following expression:
As can be seen, one of the roots of the equation is complex, so it is more convenient to express it as:
Finally, the integration is straightforward, and the solution to the exercise is:
From what I have read, some people think the solution was simple, while others, on the contrary, believe it indeed exceeded the level of a high school student. In my opinion, the mistake is being made of evaluating the difficulty of the integral from the knowledge of a university graduate.
We are not talking about whether it is easy for an engineer, a physicist, or a mathematician, but for a high school student. Personally, I believe the proposed integral clearly exceeds the high school level. Proof of this is the withdrawal of the exercise by the university, due to the fact that complex integrals were not included in the syllabus.
However, withdrawing the exercise presents a series of problems:
- If the exercise is eliminated, those who managed to solve it correctly despite its difficulty are not valued.
- If they consider the three out of four exercises with the best score, it represents a comparative advantage over other years.
- It also does not take into account that some people may have spent a significant amount of time (and morale) on this exercise, only to finally abandon it without a solution, affecting their performance on the rest of the exam.
In short, a huge blunder by the University of Zaragoza, for which the exam should be repeated, and accountability should be demanded from the person or persons who included the exercise.
