Algebra
- Matrices, inverses, AX = B
- Parameter systems and consistency
- Geometric reading when asked
PAU Mathematics exam (Catalonia)
The Catalonia PAU maths paper mixes algebra, calculus, geometry and probability. Marks come from a short justified method, not from a lone final number.
Catalonia’s science-maths PAU rewards a short justified method, not forty proofs by heart. These four blocks come back every sitting.
Typical paper structure
- Independent questions (often a/b/c) adding up to 10 marks.
- Common blocks: systems and matrices, derivatives and integrals, 3-D geometry, probability.
- Working is marked. An unjustified result may score zero.
- Science maths and social-science maths share a format but not the same syllabus.
What actually appears on the paper
Calculus
- Domain, extrema, optimisation from a worded prompt
- Antiderivatives and definite-integral area
3-D geometry
- Dot/cross product
- Line and plane, distances
- Relative position
Probability
- Tree diagrams, total probability, Bayes
- Independence vs mutually exclusive events
Worked example: derivative and extrema
Let f(x) = x³ − 6x² + 9x. Find f′(x) and the relative extrema.
- f′(x) = 3x² − 12x + 9.
- 3x² − 12x + 9 = 0 → x = 1 and x = 3.
- f′′(x) = 6x − 12. f′′(1) < 0 (local max), f′′(3) > 0 (local min).
- f(1) = 4, f(3) = 0.
Local maximum at (1, 4) and local minimum at (3, 0).
Worked example: definite integral and area
Area between y = x² − 2x and the x-axis on [0, 3].
- Roots at 0 and 2; the graph is below the axis on [0, 2] and above on [2, 3].
- Area = ∫₀² (2x − x²) dx + ∫₂³ (x² − 2x) dx = 4/3 + 4/3 = 8/3.
Area = 8/3 square units.
Common mark-losers
- Missing domain or units.
- Not checking a system (especially with parameters).
- Mixing up f′ = 0 and f′′ = 0.
- Inventing an antiderivative in a definite integral.
How scripts are marked
- An unjustified final number can score zero.
- If (a) fails, carry a stated assumption into (b).
- Name the test for a max/min. A sketch saves geometry marks.
Eight-week plan
One block a week, a timed past paper, and an error log. That is the Tortosa intensive rhythm.
Weeks 1–2
Matrices and parameter systems.
Weeks 3–4
Derivatives and optimisation.
Week 5
Integrals and area.
Week 6
3-D geometry with a sketch every time.
Week 7
Probability plus a full mock.
Week 8
Only collected mistakes. Sleep.
How LETSE Academy teaches this
- Groups of 6 in Tortosa or live online.
- Weekly past-paper slice with spoken mark schemes.
- Personal error log before the next block.
FAQ
Do I need proofs by heart?
You need methods you can apply under time pressure.
Which calculator?
Only models allowed for that Catalonia sitting.
How do you prepare this at LETSE?
Groups of 6 in Tortosa, mocks with feedback, and online classes.
Science maths or social-science maths?
Different papers. Do not mix the syllabus.
Official past papers?
Use the Catalonia PAU archive, not random Telegram PDFs.
Want marked practice?
PAU prep in Tortosa and online. You can also estimate your access grade.