Spain
Selectividad Mathematics
Mathematics II paper of the Spanish university entrance exam (PAU, still widely called Selectividad, EBAU or EvAU): analysis, linear algebra, geometry in space, and probability, on a structure set by each region.
Exam Format
Questions
One paper per region with compulsory questions plus a choice between options. For 2027, Madrid and Andalucía both ask for five answers worth 2 points each: three compulsory questions and two chosen from pairs (Andalucía requires two Analysis answers and one each of Algebra, Geometry, and Statistics and Probability). Catalonia uses four compulsory 2.5-point exercises with a free choice in the fourth.
Duration
90 minutes, fixed nationally by Real Decreto 534/2024 for every PAU exam, with at least 30 minutes of rest between consecutive exams.
Scoring
Graded 0-10 with two decimals. The access phase averages four exams (five in regions with a co-official language) and needs at least 4; it counts 40% of the access grade next to 60% from the Bachillerato average, and access requires 5. Universities add weighted subject grades for admission.
Calculator
Set by each region. Andalucía bans programmable, graphing, and data-storing calculators; Madrid also bans models that solve equations, work with matrices or determinants, or compute derivatives and integrals; Catalonia bans calculators with stored information or transmission.
Study Strategies
- 1Start from your own region's official 2026-2027 model and guidelines: the number of questions, the choices, and the calculator list differ between regions, and Andalucía changes its format for 2027.
- 2Give analysis the most time: limits and continuity, derivatives with optimization and curve sketching, and integrals by parts and substitution with areas appear in every regional paper, and Andalucía requires two analysis answers out of five.
- 3Turn linear algebra into reliable points: rank and discussion of systems with a parameter (Rouché-Frobenius), inverse matrices, and matrix equations follow repeatable procedures that reward practice.
- 4Prepare probability in full, since it now appears in the Madrid, Andalucía and Catalonia papers: conditional probability, total probability and Bayes, and the binomial distribution. Andalucía's syllabus also includes the normal distribution with the table.
- 5Justify every step in writing: answers without reasoning lose marks, Andalucía reserves part of each exercise for correct mathematical language, and Catalonia can deduct up to 0.25 points per problem for poor writing, notation, or presentation.
How Math Zen Helps
Math Zen covers the core of Matemáticas II: matrices and determinants, limits, derivatives, integrals, vectors and planes in space, and probability including Bayes' theorem and the binomial distribution. As Selectividad-specific templates are added, you will be able to practice the multi-part, fully justified problem style of the PAU.
Topics Covered
Matrices
7 subtopics, 14 templates
Sequences & Series
7 subtopics, 17 templates
Limits
6 subtopics, 12 templates
Derivatives
12 subtopics, 24 templates
Functions
5 subtopics, 10 templates
Logarithms
4 subtopics, 9 templates
Integrals
19 subtopics, 22 templates
Vectors
5 subtopics, 13 templates
Geometry
12 subtopics, 29 templates
Probability
7 subtopics, 16 templates