French Math Exams paper is called “Composition”, it is unlike English Math paper solving different independent questions. In fact “Composition” is made up of many inter-dependent smaller questions, they together step-by-step lead to proving some Math theorems or corollary.
Before every Math composition, the French Math professor would tell the students the test scope covers all Math they learn thus far from primary school till today. Quite similar to sitting for any English language Composition, the scope of vocaburary and grammar covers everything we learn since day 1 in primary school. Math is, after all, a “language” of science and logic.
Look at this year Ecole Polytchnique (and Ecole Normales Supérieures) Math Composition below:
[Note: My next few blogs will contain the English translation, and hopefully the solution contributed from the comments by blog readers. ]
It is notoriously famous for being very tough. It needs 2 years of preparation after Baccalaureat (A-level) in the Classes Préparatoires (Maths Supérieures, Maths Spéciales), located not in universities but in few prestigious ancient Lycées (High Schools) selected by Napoléon eg. Lycée Louis Le Grand (Paris), Lycée Henri IV, Lycée Pierre de Fermat (Toulous), Lycée Du Park (Lyon)… taking in only the brightest Baccalaureat high-school students in Math (only 7.5% of each year High-school cohorts from Baccalaureat).
200 years ago the 19th century Math genius (father of Group Theory and Modern Algebra) Evariste Galois failed this Ecole Polytechnique “Composition” Exams twice because he was too good for the Examiners to understand him. The inventor of Topology Henri Poincaré topped in this Exams, while Charles Hermite (Galois’s 15 years junior from the same professor Richard of Lycée Louis Le Grand) was in the last position, almost failed!
Note: Ecole Normales Supérieures and Ecole Polytechnique combine their Concours entrance exams together in recent years.