Mathematics
This section covers the mathematics syllabus for the École Polytechnique FUI exam and provides useful resources and exercises for preparation.
Syllabus / Topics
The mathematics exam covers the following main areas.
1Algebra
Topics include polynomial equations, exponentials and logarithms, complex numbers, sequences and recurrence relations, and other fundamental algebraic techniques.
2Functions and Equations
Study transformations of functions, graphs, and the solution of standard algebraic and transcendental equations.
3Inequalities
Work on standard inequality techniques, estimation, absolute values, and clean algebraic reasoning.
Courses
Resources will be added soon.
4Sequences and Series
Cover arithmetic and geometric sequences, recurrence thinking, and standard finite-sum manipulation.
Courses
Resources will be added soon.
5Trigonometry
Review identities, transformations, trigonometric equations, and applications to geometry and modeling.
Courses
Resources will be added soon.
6Geometry
Classical Euclidean geometry, circle relations, angle chasing, and geometric proof habits.
Courses
Resources will be added soon.
7Coordinate Geometry
Lines, circles, conics, and analytic geometry tools that connect algebra with geometry.
Courses
Resources will be added soon.
8Combinatorics and Probability
Elementary counting, binomial reasoning, probability models, and careful case analysis.
Courses
Resources will be added soon.
9Mathematical Reasoning and Proofs
Develop clear written and oral mathematical explanations, with attention to definitions and logical structure.
Courses
Resources will be added soon.
Note: The exact emphasis may vary slightly from year to year. Always refer to past exams.
Tips & Strategy
- Build fluency in definitions and standard techniques before chasing speed.
- Explain one solution aloud each week as preparation for oral-style reasoning.
- Use past problems to identify weak topics and update your checklist regularly.