In January 2023, new Aprendizagens Essenciais (AE, Portugal's official "essential learning" syllabus) for secondary-school maths were approved by Despacho n.º 702/2023. For Matemática A they gradually replace the 2018 AE. For students now in secondary school, and for their parents, this means new topics, a different order and an exam in transition.
When they apply
| School year | New AE in force from |
|---|---|
| Year 10 (10.º ano) | 2024/2025 |
| Year 11 (11.º ano) | 2025/2026 |
| Year 12 (12.º ano) | 2026/2027 |
Some schools brought the new AE in early, in 2023/2024. In 2026/2027, all three years of Matemática A run on the new Aprendizagens Essenciais in every school for the first time.
What is studied each year
Year 10
Two "maths for citizenship" topics, Mathematical Models for Citizenship (models for elections, fair division and finance) and Statistics (univariate and bivariate data), alongside synthetic plane Geometry (notable points of the triangle, the Euler line, the nine-point circle), Functions (general properties, polynomial functions of degree at most 2, piecewise functions) and analytic Geometry in the plane and in space, with vectors.
Year 11
Geometry (trigonometry and the dot product), Discrete Mathematics (counting, sequences, arithmetic and geometric progressions) and Functions (cubic and quartic functions, operations on functions, rational functions and differential calculus).
Year 12
Complex Numbers (algebraic and trigonometric form), Probability (random experiments, probability, conditional probability, probability models on finite spaces, the normal model) and Functions (exponential, inverse, logarithmic and composite functions, derivatives, continuous and differentiable functions, approximate solution of equations).
Year 12 also has three optional topics: Introduction to Statistical Inference, Basic Antiderivatives and Definite Integrals, and Matrices. One is chosen per class, and the choice can differ from class to class. If time allows, more than one can be covered.
The DGE documents suggest one possible time allocation: five 50-minute lessons a week in Years 10 and 11, and six 45-minute lessons in Year 12, over 28 reference weeks.
What changed from the 2018 AE
The most objective way to see the difference is the table IAVE/EduQA used in the 2026 exam to separate the content exclusive to each syllabus:
| Only in the 2018 AE | Only in the 2023 AE |
|---|---|
| Parity of a function | Mathematical models for elections |
| De Morgan's laws for sets | Mathematical models for fair division |
| Monotonicity and limits of sequences | Mathematical models for finance |
| Limit of the sequence (1 + x/n)ⁿ | Synthetic geometry |
| Trigonometric equations | Sum of all terms of a geometric progression with |r| < 1 |
| Pascal's triangle and the binomial theorem | Probability distributions and the normal model |
| Trigonometric sum, difference and double-angle formulas | Numerical solution of equations |
Beyond content, the new AE put more weight on four ideas: maths for citizenship (elections, finance, statistical literacy), computational thinking and programming, systematic use of technology (spreadsheets, dynamic geometry, the graphing calculator) and project work. Years 10 and 11 each explicitly include at least one project.
And the national exam?
In 2026 the Matemática A exam (635) had to serve students from both syllabuses. It mainly assessed the shared content (geometry, functions, statistics, probability, combinatorics, sequences and complex numbers) and included three pairs of alternative questions, one from each syllabus, of which the student answered only one. As an exception, it did not assess the three optional Year 12 topics.
For 2027, the first year in which Year 12 runs on the new AE in every school, the exam rules will only be known from the 2027 Informação-Prova (the official exam specification), not yet published on 5 October 2026. This guide will be updated when it comes out.
The AE documents published by the DGE carry a revision dated 31 August 2026. Always check the version in force on the DGE website. This guide describes the organisation of topics set out in those documents.
What this means for students and parents
- Textbooks, worksheets and past papers may include content that is no longer on the syllabus, or leave out new topics. It is worth checking against the table above before studying from them.
- Topics such as finance, elections and the normal model call for interpretation and context, not just calculation.
- In Year 12, it pays to find out early which optional topic the class will cover.
- The graphing calculator and technology are part of what is learnt, not an extra.
Common questions
When do the new Matemática A Aprendizagens Essenciais take effect?
In Year 10 in 2024/2025, Year 11 in 2025/2026 and Year 12 in 2026/2027, according to the DGE. Some schools brought them in early, in 2023/2024.
What are the Year 12 optional topics?
Introduction to Statistical Inference, Basic Antiderivatives and Definite Integrals, and Matrices. At least one is covered per class.
Is the binomial theorem still part of Matemática A?
In the 2026 exam table, Pascal's triangle and the binomial theorem appear as content exclusive to the 2018 AE, meaning they are not in the new AE.
Do the new AE change the national exam?
In 2026 the exam assessed the content shared by both syllabuses and gave alternative questions for the content exclusive to each. The 2027 rules depend on the 2027 Informação-Prova, not yet published.
