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Key Facts: Concours Geipi Polytech Exam

The Concours Geipi Polytech provides access to 35 public engineering schools across metropolitan France and overseas departments.

It offers over 3,800 places annually for high school graduates entering 5-year integrated engineering programmes.

Registration is managed through Parcoursup, with an application fee of 60 € (free for boursiers).

The written examination lasts 3 hours: 1 mandatory hour of Mathematics and two 1-hour science subjects.

All participating schools award the Diplôme d'Ingénieur accredited by the Commission des Titres d'Ingénieur (CTI).

The syllabus is aligned with the French Terminale Spécialité curricula in mathematics, physics-chemistry, computer science, and engineering sciences.

A unified competitive gateway to 35 public engineering schools across France (including the 15 Polytech network institutes), combining Parcoursup dossier evaluation with a rigorous 3-hour written examination (1-hour mandatory core Mathematics QCM plus two 1-hour scientific electives).

Sample Concours Geipi Polytech Practice Questions

Try these sample questions to review concepts for the Concours Geipi Polytech exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1What is the limit of f(x) = (e^(2x) - 1) / x as x approaches 0?

A.0

B.1

C.2

D.The limit does not exist

Explanation: By recognizing the definition of the derivative of g(u) = e^u at u = 0, or by using the standard limit lim_{u -> 0} (e^u - 1)/u = 1 with u = 2x, we have (e^(2x) - 1)/x = 2 * (e^(2x) - 1)/(2x) -> 2 * 1 = 2. Alternatively, L'Hôpital's rule gives 2e^(2x)/1 -> 2.

2What is the derivative f'(x) of the function f(x) = (3x - 1) e^(-2x) on R?

A.f'(x) = 3 e^(-2x)

B.f'(x) = (-6x + 5) e^(-2x)

C.f'(x) = (6x - 5) e^(-2x)

D.f'(x) = (-6x + 2) e^(-2x)

Explanation: Applying the product rule (uv)' = u'v + uv' with u(x) = 3x - 1 (so u'(x) = 3) and v(x) = e^(-2x) (so v'(x) = -2e^(-2x)), we get f'(x) = 3 e^(-2x) + (3x - 1)(-2 e^(-2x)) = (3 - 6x + 2) e^(-2x) = (-6x + 5) e^(-2x).

3Which function is the unique solution to the differential equation y' + 2y = 6 satisfying the initial condition y(0) = 5?

A.y(x) = 2 e^(-2x) + 3

B.y(x) = 5 e^(-2x)

C.y(x) = 3 e^(-2x) + 2

D.y(x) = 2 e^(2x) + 3

Explanation: The first-order linear differential equation y' + ay = b has general solution y(x) = C e^(-ax) + b/a. Here a = 2 and b = 6, giving the constant particular solution y_p = 6/2 = 3, so y(x) = C e^(-2x) + 3. The initial condition y(0) = 5 implies C + 3 = 5, thus C = 2, yielding y(x) = 2 e^(-2x) + 3.

4What is the value of the definite integral I = \int_0^1 (2x + 1) e^x dx?

A.2e - 1

B.3e - 3

C.e + 1

D.2e + 1

Explanation: Using integration by parts with u(x) = 2x + 1 (u'(x) = 2) and v'(x) = e^x (v(x) = e^x): I = [(2x + 1)e^x]_0^1 - \int_0^1 2e^x dx = (3e - 1) - [2e^x]_0^1 = (3e - 1) - (2e - 2) = e + 1.

5What is the limit of f(x) = ln(1 + 3x) / x as x approaches 0?

A.0

B.1

C.3

D.+inf

Explanation: Since lim_{u -> 0} ln(1 + u)/u = 1 (the derivative of ln(1+u) at u=0), we can rewrite the expression as 3 * ln(1 + 3x)/(3x). As x -> 0, u = 3x -> 0, so the limit is 3 * 1 = 3.

6What is the equation of the oblique asymptote (asymptote oblique) to the curve of f(x) = (2x^2 + 3x - 1) / (x + 1) as x approaches +inf?

A.y = 2x + 3

B.y = 2x + 1

C.y = 2x - 1

D.y = 2x

Explanation: Performing polynomial division of 2x^2 + 3x - 1 by x + 1 gives 2x^2 + 3x - 1 = (x + 1)(2x + 1) - 2. Therefore, f(x) = 2x + 1 - 2/(x + 1). As x -> +inf, -2/(x + 1) -> 0, which proves that the line y = 2x + 1 is the oblique asymptote.

7At which value of x does the curve of f(x) = x^3 - 6x^2 + 9x + 2 have an inflection point (point d'inflexion)?

A.x = 1

B.x = 2

C.x = 3

D.x = 0

Explanation: An inflection point occurs where the second derivative vanishes and changes sign. The first derivative is f'(x) = 3x^2 - 12x + 9, and the second derivative is f''(x) = 6x - 12. Setting f''(x) = 0 yields 6x = 12, so x = 2. Since f''(x) changes from negative to positive at x = 2, this is an inflection point.

8What is the equation of the tangent line to the curve y = ln(2x - 1) at the point with abscissa x = 1?

A.y = 2x - 2

B.y = 2x - 1

C.y = x - 1

D.y = 2x

Explanation: At x = 1, y = ln(2(1) - 1) = ln(1) = 0. The derivative of f(x) = ln(2x - 1) is f'(x) = 2/(2x - 1). At x = 1, f'(1) = 2/1 = 2. The equation of the tangent is y = f'(1)(x - 1) + f(1) = 2(x - 1) + 0 = 2x - 2.

9What is the value of the integral J = \int_1^e (ln x) / x dx?

A.1

B.1/2

C.2

D.e - 1

Explanation: The integrand has the form u'(x) u(x) where u(x) = ln(x) and u'(x) = 1/x. An antiderivative of u' u is (1/2) u^2 = (1/2)(ln x)^2. Evaluating between 1 and e gives (1/2)(ln e)^2 - (1/2)(ln 1)^2 = (1/2)(1)^2 - 0 = 1/2.

10According to the growth hierarchy of functions (croissances comparées), what is the limit of f(x) = (x^2 + 1) e^(-x) as x approaches +inf?

A.+inf

B.1

C.0

D.-inf

Explanation: Rewriting f(x) as (x^2 + 1) / e^x = x^2/e^x + 1/e^x, the theorem of croissances comparées states that for any polynomial P(x), lim_{x -> +inf} P(x) e^(-x) = 0 because exponential growth dominates polynomial growth.

About the Concours Geipi Polytech Exam

The Concours Geipi Polytech is the premier joint competitive entrance examination in France for high school seniors (Terminale générale and technologique) seeking direct admission into 35 prestigious public engineering schools. The consortium encompasses all 15 university-affiliated schools in the Polytech Network (Angers, Clermont, Grenoble, Lille, Lyon, Marseille, Montpellier, Nancy, Nantes, Nice-Sophia, Orléans, Paris-Saclay, Sorbonne, Tours) alongside notable independent public engineering institutions such as ENIB (Brest), ENIM (Metz), ENISE (Saint-Étienne), ENSGSI (Nancy), ENSSAT (Lannion), ESISAR (Valence), ESIROI (La Réunion), IMT Nord Europe (ISIC), Télécom Saint-Étienne, and AgroSup Dijon. Candidates apply via the French national Parcoursup admissions platform. For the general track, the selection process combines a thorough academic file review (grades from Première and Terminale in mathematics, sciences, French, and English) with a comprehensive 3-hour written examination comprising a mandatory 1-hour Mathematics QCM (multiple-choice/short-answer paper) and two 1-hour scientific specialty tests chosen according to the candidate's Terminale focus (Physique-Chimie, Numérique et Sciences Informatiques - NSI, Sciences de l'Ingénieur - SI, or SVT/Biology). Admitted candidates enter a 5-year curriculum commencing with a 2-year integrated preparatory cycle (cycle préparatoire intégré), guaranteeing transition into engineering specializations without sitting the traditional CPGE concours.

Exam sponsor: Groupement d'Écoles d'Ingénieurs Publiques à Parcours Intégré (Geipi Polytech). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Question count not published by the exam provider

Time Limit

3 hours

Passing Score

Competitive ranking based on Parcoursup dossier and 3-hour written examination score; intake quotas per participating engineering school.

Exam / Certification Fees

60 € (free for boursiers du gouvernement français)

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Official sources

Groupement d'Écoles d'Ingénieurs Publiques à Parcours Intégré (Geipi Polytech): official exam information

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

25%

Calculus & Analysis

Limits, indeterminate forms, continuity, derivation rules, convexity, inflection points, exponential and natural logarithm functions, antiderivatives, integration techniques, and first-order differential equations.

15%

Sequences & Induction

Arithmetic and geometric progressions, mathematical induction (raisonnement par récurrence), bounds, limits of sequences, monotone convergence theorem, and arithmetic-geometric recursive models.

15%

Probability & Combinatorics

Counting techniques, permutations, combinations, Pascal's triangle, conditional probability, Bayes' rule, tree diagrams, independence, and the binomial distribution B(n, p).

15%

Spatial Geometry & Vectors

3D Cartesian coordinate systems, scalar product (dot product), orthogonality, distance from point to plane, parametric equations of lines, and Cartesian equations of planes.

15%

Physics & Chemistry Fundamentals

Newtonian dynamics, projectile kinematics, work and kinetic energy, mechanical wave propagation, interference and diffraction, pH, acid-base equivalence titrations, and chemical kinetics.

15%

Digital Logic & Engineering

Algorithmic thinking in Python, conditional branches, loops, list comprehensions, binary numbers, Boolean algebra, logic gates, and engineering block representations.

Preparing for the Concours Geipi Polytech Exam

What You Need to Know

Passing score: Competitive ranking based on Parcoursup dossier and 3-hour written examination score; intake quotas per participating engineering school.
Assessment: Question count not published by the exam provider
Time limit: 3 hours
Exam / certification fees: 60 € (free for boursiers du gouvernement français) Official sources

Using Our Practice Resources

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Concours Geipi Polytech: Suggested Study Strategy

1Master the core Terminale Spécialité Mathématiques syllabus: exponential and logarithm properties, derivation, integration by substitution or parts, and sequence convergence.

2Practice speed and precision on short-answer and multiple-choice questions (QCM): eliminate obvious distractors and check edge cases quickly.

3Solidify 3D geometry calculations: practice extracting normal vectors from plane equations (ax + by + cz + d = 0) and computing dot products to determine orthogonality.

4Review binomial probabilities B(n, p) and combinatorics formulas (n choose k), especially calculation of expectations, variances, and complementary event probabilities.

5For physics-chemistry, memorize fundamental formulas: Newton's second law (sum F = ma), kinetic energy (0.5 m v^2), Snell-Descartes law, diffraction angle (theta = lambda / a), and titration equivalence (c_A V_A = c_B V_B).

6Trace Python code mentally: understand how loop indices behave, recursive base cases, and dichotomy search iterations.

Frequently Asked Questions

What is the Concours Geipi Polytech and which schools participate?

The Concours Geipi Polytech is a joint competitive entrance exam that recruits high school students into 35 French public engineering schools. These include all 15 schools of the Polytech network (such as Polytech Sorbonne, Paris-Saclay, Lyon, Nantes, Lille, etc.) and 20 affiliated public engineering schools (such as ENIM, ENIB, ENISE, ESISAR, and Télécom Saint-Étienne).

How is the written examination structured for general baccalaureate candidates?

The written exam lasts a total of 3 hours and is composed of three consecutive 1-hour parts: a mandatory 1-hour Mathematics QCM/short-answer section based on the Terminale Spécialité Mathématiques curriculum, followed by two 1-hour science subjects chosen by the candidate from Physics-Chemistry, NSI (Computer Science), SI (Engineering Sciences), or SVT (Life and Earth Sciences).

How are candidates ranked and admitted?

Admission is governed by a combined score derived from the candidate's Parcoursup academic file (grades in mathematics, sciences, French, and modern languages from Première and Terminale) and performance on the written examination (or an interview for the highest-ranked dossier candidates). Each participating school has a specific quota of places.

What is the registration fee for the Concours Geipi Polytech?

The application fee is 60 €, payable through the Parcoursup platform. Registration is completely free for French government scholarship holders (boursiers de l'État).

Are calculators allowed during the written examination?

Calculator regulations depend on the specific subject instructions published each year by the Geipi Polytech examination committee. For the Mathematics QCM, calculators are typically either strictly forbidden or strictly limited to mode examen (silent and cleared of external memory).

What is an integrated preparatory cycle (cycle préparatoire intégré)?

An integrated prep cycle is a 2-year post-baccalaureate university-level foundation course taught directly within or affiliated with the engineering school network. Students who successfully validate their two years of continuous assessment transition directly into their 3-year cycle d'ingénieur without having to take national CPGE competitive exams.