PAU 2026 — Mathematics (Series 1)
University entrance examination, Mathematics for the science and technology track of Bachillerato. Step-by-step solutions to the four exercises (exercise 4 with both options, A and B).
Questions
Each card opens the corresponding solution.
Piecewise-defined function — continuity, area and tangent line
Find the values of $m$ that make the function continuous, compute an area with integrals for $m=-2$ and find a tangent line of slope $-2$.
System of three planes — discussion and geometric interpretation
Discuss the system according to the parameter $m$, interpret the three planes geometrically and solve the case $m=1$; then a fourth equation with a given solution.
Probability and optimisation — Tickets for a concert
Total and conditional probability with a tree of cases, and the study of a cubic function to find when 100 decibels are exceeded.
Optimisation (Option A) · Geometry in space (Option B)
Option A: minimise the sum of the areas of a circle and a square with a fixed total perimeter. Option B: plane through three points, area of the triangle and tetrahedron of volume 1. Both solved.
In exercise 4 you must choose a single option (A or B). On this site you will find both worked out: Option A at P4 and Option B at P4 · Option B.