The Mathematics exam in the PAU

1The two modalities

In the second year of baccalaureate there are two mathematics subjects depending on the modality, and each has its own PAU exam:

• Mathematics — science and technology modality. Taken by those heading to engineering, sciences, mathematics, physics, etc.
• Applied Mathematics for the Social Sciences (CCSS) — social sciences modality (economics, business, law, etc.).

They are different exams, with their own syllabus and focus, although they share the same general philosophy of the 2025 PAU.

2Exam structure

Since the 2025 model, each exam has a single version (you no longer choose between two separate papers) and consists of 4 compulsory exercises of 2.5 points each. There may be some internal optionality within an exercise.

Mathematics (science)

• Ex. 1Analysis (limits, continuity, derivatives, integrals).2.5 pts
• Ex. 2Linear algebra and geometry (matrices, systems, vectors, lines and planes).2.5 pts
• Ex. 3Probability (1.5 pts) combined with another block (1 pt).2.5 pts
• Ex. 4Two options to choose, 4A or 4B, from any part of the syllabus except Probability.2.5 pts

Applied Mathematics CCSS

• Ex. 1-3Cover all the blocks of the subject (algebra and linear programming, analysis, probability and statistics).2.5 pts ea.
• Ex. 4Cross-cutting problem with two options, A or B; you answer only one.2.5 pts

3Length and calculator

Each exam lasts 1 hour and 30 minutes. You may use a scientific calculator, but graphing, programmable or CAS calculators are not allowed, nor any device capable of storing, transmitting or receiving information.

4How it is marked

• You must justify your reasoning: a correct result without explaining the process can score 0.
• The answer must be written with coherence, correctness and clarity, using the appropriate mathematical notation and vocabulary.
• Spelling, presentation and coherence of discourse can deduct up to 10% of the mark.

5Syllabus by blocks

These are the main blocks covered. On the problems by topic page you can practise each one with real, solved PAU problems.

Mathematics (science)

• Analysis: limits and continuity, derivatives and applications, integrals.
• Linear algebra: matrices, determinants, systems of equations.
• Geometry: vectors, lines and planes in space.
• Probability and statistics: probability, distributions (binomial, normal).

Applied Mathematics CCSS

• Algebra: matrices and linear programming.
• Analysis: functions, derivatives and their applications, integrals.
• Probability and statistics: probability, distributions (binomial, normal) and statistical inference.

6Sittings

The PAU is held in two sittings a year: June (ordinary) and September (resit). The exact dates are published each year by the Canal Universitats.

7Official documents

The information on this page summarises the official guidance. Always check the original source for the definitive dates and details: