Mathematics II: the exam that divides engineers

The Selectividad (Spain's university entrance exam) Maths II exam that divides engineers

An engineer has solved the Mathematics II exam from the Madrid Selectividad and declared it “enough to make you cry.” His final verdict—“I'm very sorry for the kids”—has peine the classic row that erupts every June. But the response is not unanimous even within the profession itself: several technicians have replied, with the paper in front of them, that the star exercise is a matrices problem solved in two steps. And that's where the mess begins.

What was actually asked in the Mathematics II exam?

The test consisted of four exercises, of which three offered an A or B alternative to choose from. According to the most repeated analysis in the thread, in each of those three one option was clearly manageable and the other manifestly difficult. The point of including an impossible option was not to punish the student, but to make them rule it out in two minutes of diagonal reading and go for the easy one. If both alternatives had been similarly difficult, the time lost deciding would have been lethal.

The exercise singled out as a scandal required expanding a third-order determinant with a parameter along a row with two zeros and then solving a homogeneous system of equations. No characteristic polynomial, no full diagonalisation. Those defending it sum it up like this: the method serves to obtain the eigenvalues, but it is explained in the question itself, step by step.

Is matrix diagonalisation part of the Bachillerato (Spain's upper secondary) syllabus?

Here the answer stops being binary. The Real Decreto 243/2022, de 5 de abril (a Spanish royal decree), which sets the minimum requirements for Bachillerato and was updated in March 2023, is the text cited to settle what should have been studied and what should not. Eigenvalues and eigenvectors are first-year university linear algebra material, but they appear in some science textbooks as an extension. In the Comunidad Valenciana, according to one account, they do not appear in the books or get explained in class.

The most repeated criticism is not that the concept is difficult, but how it was asked: some point out that a student can score on the section without having any idea what an endomorphism is. Many students can nail the numbers and have no idea what they have just done. That, they argue, is rote education, not mathematics.

The grievance between state and private schools

The most uncomfortable suspicion, raised by a forum user, suggests that certain first-year university material is taught in particular schools and excellence programmes, and that those questions end up slipping into the exam to give their students an advantage in choosing a degree. In schools in lower-income neighbourhoods, according to the same suspicion, there would be no room to extend the syllabus. The conclusion drawn is bitter: either you pay, or you live in the right area.

Add to that the weight of the academic record. According to this analysis, because the Bachillerato grade counts for 60 per cent of the access score, grade inflation is generated in schools and shady practices are hard to trace. The harshest calculation holds that the fairest thing would be for the exam to count for almost 100 per cent. And some warn about students who, with an average of 6, trust they can fix their grade with a 9 on the test.

The student who doesn't get frustrated: opens ChatGPT

A private tutor tells it bluntly: when his students can't do an exercise, they don't reread their notes, don't look for the formula, don't get stuck for five minutes. They give up and ask artificial intelligence to solve it. The tool is good; the shortcut is the problem: the ability to tolerate frustration is collapsing.

Places, selection and doctors: the debate that goes beyond the exam

The heart of the matter is not a determinant. If there are 100 physiotherapy places and 200 applicants, something has to discriminate. Those who defend the difficulty are clear: if there is no filtering, 95 per cent of students would end up enrolled on the same degrees, with Medicine and Computer Science at the top. The counterpoint comes from the other side: some argue that there is a shortage of doctors, that professionals trained abroad are hired and that the best are not paid enough, either in Medicine or Engineering.

Why does the same complaint repeat every year?

Because it serves a purpose. Some describe the noise every June as a preventive cry: public pressure to make the trinc week's marking more lenient. Through that lens, the catastrophist headline does not report an educational disaster; it negotiates down the marker's standard.

The exact point where the analysis gets stuck is this: defenders of the exam have not shown that the question was on the syllabus of all schools, and critics have not shown that it was impossible to solve with what was taught. No one will end up charged over it, nor does anyone need to be. The gap between what the regulation says and what reaches the classroom remains unquantified.