Mathematics MPSI (Engineering Prep) Revision Sheets
Mathematics in MPSI is the core subject: 12 hours of lectures weekly, over half of the coefficient at engineering school concours (X, ENS, Mines, Centrale). The curriculum covers algebra, analysis and probability.
Mathematics curriculum in MPSI (Engineering Prep)
The MPSI mathematics curriculum is organized into three areas. Algebra covers complex numbers, trigonometry, linear algebra (vector spaces, linear maps, matrices, determinants), arithmetic and polynomials. Analysis covers real numbers, sequences, single-variable functions (continuity, differentiability, integration), series and asymptotic analysis. Probability (introduced in 2013) covers combinatorics, random variables and joint distributions.
How to study mathematics in MPSI (Engineering Prep)?
3 simple steps for effective mathematics revision.
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Tips to succeed in mathematics MPSI (Engineering Prep)
Learn classical proofs of fundamental theorems (IVT, mean value, Rolle) — they appear in oral exams
Do at least 5 exercises per chapter before each colle: mastery comes through practice, not reading
Master basic calculations (derivatives, antiderivatives, equivalents) to 30-second speed: this frees time for hard questions
Use Anki with FSRS for memorizable formulas (trigonometry, usual integrals, reference series)
FAQ — Mathematics MPSI (Engineering Prep)
Which MPSI math chapters matter most for concours?
Three chapters concentrate ~60% of concours points: linear algebra (vector spaces, linear maps, matrices, eigenvalues in MP) which is foundational, analysis (sequences, series, integrals) structuring long papers, and probability (counting, random variables) which weighs heavily since the 2013 reform. Master these three pillars before tackling more technical chapters (arithmetic, polynomials).
How do I prepare math colles in MPSI?
A colle (weekly 1-hour oral exam) tests both lecture and exercises. Prepare by revising 4-5 major chapter proofs, doing 3-4 application exercises, and practicing clear board presentation (notation, logical articulation). Examiners value clarity and formal rigor over raw speed. 2-3 hours of prep per colle is enough with regular work.
Should I do exercises or learn the lecture first in MPSI?
Both alternating, never one without the other. Read the lecture to grasp the logic, then do 2-3 simple exercises to anchor definitions. Return to the lecture for theorems, then chain concours-style exercises. This 30-45 minute alternation is more effective than 3 hours of reading followed by 3 hours of exercises. It's deliberate practice applied to math.
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