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Key Facts: Concours Puissance Alpha Exam

Concours Puissance Alpha provides admissions pathway to 19 CTI-accredited French engineering schools with 35+ campuses nationwide.

Admission score is split evenly: 50% continuous academic dossier on Parcoursup + 50% written examination.

The written test session lasts 3h15: Mathématiques (1h30), Sciences appliquées (1h00), and Anglais (45 min).

Calculators are strictly forbidden; all mathematical and physical calculations must be carried out manually.

Standard registration fee is 130 €, reduced to 15 € for French government scholarship recipients (boursiers).

Scoring features negative marking: +1 point for a correct answer, -0.5 points per incorrect answer, and 0 for an omitted answer.

On Parcoursup, selecting Concours Puissance Alpha counts as 1 single vœu, allowing candidates to rank multiple member schools without consuming extra vœux.

Common entrance exam for 19 CTI-accredited engineering schools (35+ campuses across France), evaluated 50% on academic dossier and 50% on a 3h15 written QCM test (Maths, Applied Sciences, English) with negative marking (+1 / -0.5 / 0).

Sample Concours Puissance Alpha Practice Questions

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

1What is the equation of the tangent line to the curve of the function f(x) = x^3 - 3x + 2 at the point where x = 2?

A.y = 9x - 14

B.y = 9x + 4

C.y = 6x - 8

D.y = 3x - 2

Explanation: The value of the function at x = 2 is f(2) = 2^3 - 3(2) + 2 = 8 - 6 + 2 = 4. The derivative is f'(x) = 3x^2 - 3, yielding slope f'(2) = 3(4) - 3 = 9. Applying the tangent formula y = f'(2)(x - 2) + f(2) gives y = 9(x - 2) + 4 = 9x - 14.

2Let f be the function defined on R by f(x) = (2x + 1) e^(-x). Which expression represents its derivative f'(x)?

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

B.f'(x) = -(2x + 1) e^(-x)

C.f'(x) = (1 - 2x) e^(-x)

D.f'(x) = (2x - 1) e^(-x)

Explanation: Using the product rule (uv)' = u'v + uv' with u(x) = 2x + 1 (u'(x) = 2) and v(x) = e^(-x) (v'(x) = -e^(-x)), we obtain f'(x) = 2 e^(-x) + (2x + 1)(-e^(-x)) = [2 - (2x + 1)] e^(-x) = (1 - 2x) e^(-x).

3Determine the limit of the rational function f(x) = (3x^2 - 5x + 1) / (2x^2 + 7) as x approaches +infinity.

A.0

B.3/2

C.+infinity

D.1/7

Explanation: At infinity, the limit of a rational function equals the ratio of its highest-degree terms: lim_{x -> +inf} (3x^2) / (2x^2) = 3/2.

4Consider the equation x^3 + 2x - 5 = 0 on the interval [1, 2]. According to the Intermediate Value Theorem corollary (théorème de bijection), how many real solutions does this equation have on [1, 2]?

A.No real solutions

B.Infinitely many solutions

C.Exactly two distinct solutions

D.Exactly one unique solution

Explanation: Let f(x) = x^3 + 2x - 5. The derivative is f'(x) = 3x^2 + 2 > 0 for all real x, so f is strictly increasing and continuous. Calculating boundary values yields f(1) = 1 + 2 - 5 = -2 < 0 and f(2) = 8 + 4 - 5 = 7 > 0. Since 0 is strictly between f(1) and f(2), the bijection corollary guarantees exactly one unique solution in ]1, 2[.

5Find the coordinates of the inflection point (point d'inflexion) of the curve y = x^3 - 6x^2 + 9x + 1.

A.(2, 3)

B.(2, -1)

C.(1, 5)

D.(3, 1)

Explanation: The first derivative is y' = 3x^2 - 12x + 9, and the second derivative is y'' = 6x - 12. Setting y'' = 0 yields 6x = 12, so x = 2. Since y'' changes sign from negative to positive at x = 2, an inflection point occurs. Computing the y-coordinate gives y(2) = 2^3 - 6(2^2) + 9(2) + 1 = 8 - 24 + 18 + 1 = 3.

6What is the limit of x * ln(x) as x approaches 0 from the right (x -> 0^+)?

A.-infinity

B.1

C.0

D.-1

Explanation: By the fundamental theorem of comparative growths (croissances comparées) in the French Terminale curriculum, power functions dominate the natural logarithm at 0: lim_{x -> 0^+} x^n ln(x) = 0 for all n > 0. Thus, the limit is 0.

7Solve the first-order differential equation y' + 2y = 6 with the initial condition y(0) = 5.

A.y(x) = 5 e^(-2x) + 1

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

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

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

Explanation: The differential equation y' = -2y + 6 has general solutions of the form y(x) = C e^(-2x) - b/a = C e^(-2x) + 3, since -b/a = -(-6)/2 = 3. Using the initial condition y(0) = 5 gives C + 3 = 5, which implies C = 2. Thus, the unique solution is y(x) = 2 e^(-2x) + 3.

8Evaluate the definite integral I = int_{0}^{1} ((2x + 3) / (x^2 + 3x + 1)) dx.

A.ln(3)

B.5/4

C.ln(6) - ln(2)

D.ln(5)

Explanation: Recognize the form u'(x) / u(x) with u(x) = x^2 + 3x + 1. The derivative is u'(x) = 2x + 3. An antiderivative is ln|x^2 + 3x + 1|. Evaluating from 0 to 1 gives [ln(x^2 + 3x + 1)]_0^1 = ln(1 + 3 + 1) - ln(0 + 0 + 1) = ln(5) - ln(1) = ln(5).

9Calculate the definite integral J = int_{1}^{e} x ln(x) dx using integration by parts.

A.(e^2 + 1) / 4

B.(e^2 - 1) / 4

C.e^2 / 2

D.(3e^2 + 1) / 4

Explanation: Set u(x) = ln(x) (so u'(x) = 1/x) and v'(x) = x (so v(x) = x^2/2). By integration by parts, int_1^e x ln(x) dx = [(x^2/2) ln(x)]_1^e - int_1^e (x^2/2)(1/x) dx = (e^2/2 ln(e) - 0) - int_1^e (x/2) dx = e^2/2 - [x^2/4]_1^e = e^2/2 - (e^2/4 - 1/4) = e^2/4 + 1/4 = (e^2 + 1)/4.

10On which subset of R is the function f(x) = e^(2x) - x^2 strictly convex (convexe)?

A.R (convex on all of R)

B.]-infinity, 0]

C.[-ln(2)/2, +infinity[

D.[0, +infinity[

Explanation: Compute the derivatives: f'(x) = 2 e^(2x) - 2x, and f''(x) = 4 e^(2x) - 2. A twice-differentiable function is convex where f''(x) >= 0. Solving 4 e^(2x) - 2 >= 0 gives e^(2x) >= 1/2, so 2x >= ln(1/2) = -ln(2), which means x >= -ln(2)/2.

About the Concours Puissance Alpha Exam

Concours Puissance Alpha is the premier common entrance examination providing admission to 19 prestigious, CTI-accredited French engineering Grandes Écoles spanning more than 30 campuses across France (3iL Ingénieurs, CPE Lyon, EBI, EFREI, ELISA Aerospace, ESAIP, ESCOM Chimie, ESEO, ESIEA, ESIEE Paris, ESITC de Metz, ESITC Paris, ESTBB, ESTIA, ISEN Méditerranée, ISEN Ouest, ISEP, JUNIA — Programme HEI, and JUNIA — Programme ISEN). Open to high school seniors (Terminale générale with scientific specialties or Terminale STI2D) via the national Parcoursup platform, admission is determined by a balanced composite score: 50% evaluated from the academic dossier (school transcripts, Première/Terminale grades, teacher appraisals) and 50% determined by a rigorous written multi-choice examination (épreuves écrites). The written tests take place across authorized exam centers in mid-to-late April and evaluate Mathématiques (1h30), Sciences appliquées (1h00), and Anglais (45 min). The scoring utilizes negative marking (+1 for correct, -0.5 for incorrect, 0 for unanswered), rewarding precision and penalizing blind guessing.

Exam sponsor: Association Puissance Alpha. 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 15 minutes (Mathématiques 1h30, Sciences appliquées 1h00, Anglais 45 min)

Passing Score

Competitive composite ranking (50% academic dossier + 50% written QCM examination). Scoring on written QCM: +1 point per correct answer, -0.5 points per incorrect answer, 0 for blank.

Exam / Certification Fees

130 € (15 € for boursiers du gouvernement français), covering as many member programmes as the candidate selects

Exam sponsor website

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

Official sources

Association Puissance Alpha: 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 and Differential Equations

Derivatives, tangent lines, extrema, asymptotic behavior, exponential and logarithmic functions, integration techniques, area calculation, and first-order differential equations y' = ay + b.

15%

Numerical Sequences and Series

Arithmetic and geometric sequences, explicit and recurrence relations, monotonicity, boundedness, sandwich theorem, and convergence criteria.

15%

Probability and Stochastic Models

Tree diagrams, conditional probabilities, total probability formula, binomial distributions B(n, p), random variables, expectation, variance, and Chebychev inequalities.

15%

Analytical Geometry in Space

Cartesian coordinates in R3, dot product, normal vectors, Cartesian equations of planes, parametric lines, orthogonal projections, and distances.

15%

Applied Physical Sciences

Newton's laws, uniform gravitational fields, projectile trajectories, orbital motion, RC and RLC circuit transient response, nuclear decay law, and chemical equilibrium.

15%

Academic and Technical English

Science and engineering terminology, grammatical error detection, structural syntax, scientific text comprehension, and pragmatic communication.

Preparing for the Concours Puissance Alpha Exam

What You Need to Know

Passing score: Competitive composite ranking (50% academic dossier + 50% written QCM examination). Scoring on written QCM: +1 point per correct answer, -0.5 points per incorrect answer, 0 for blank.
Assessment: Question count not published by the exam provider
Time limit: 3 hours 15 minutes (Mathématiques 1h30, Sciences appliquées 1h00, Anglais 45 min)
Exam / certification fees: 130 € (15 € for boursiers du gouvernement français), covering as many member programmes as the candidate selects Official sources

Using Our Practice Resources

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Concours Puissance Alpha: Suggested Study Strategy

1Master mental calculation and algebraic shortcuts: since calculators are banned, practice arithmetic manipulation, fractions, square roots, and logarithms without electronic assistance.

2Adopt a strict negative-marking strategy: if you cannot eliminate at least two plausible distractors or confirm your derivation, leave the answer blank to protect your score against the -0.5 penalty.

3Thoroughly review the Terminale Spécialité Mathématiques syllabus: differential equations (y' = ay + b), logarithmic and exponential properties, integration by parts, and spatial vector geometry are tested every single year.

4Practice selecting your exercises quickly: in the maths paper four exercises are compulsory, so scan the optional panel in the first three minutes and pick the four that match your Terminale options; in applied sciences you drop one of the seven exercises offered.

5Work past papers under strict exam timing: drill with 90-minute blocks for mathematics, 60-minute blocks for applied sciences, and 45-minute blocks for English to build endurance.

6Enhance technical English fluency: concentrate on scientific connectors, conditional structures, phrasal verbs, prefix/suffix transformations, and identifying subtle grammatical errors.

Frequently Asked Questions

What is Concours Puissance Alpha and which schools does it open access to?

Concours Puissance Alpha is a nationwide competitive entrance exam for French 5-year integrated engineering programmes (prepa intégrée). It provides access to 19 CTI-accredited engineering Grandes Écoles representing over 35 campuses across France, including CPE Lyon, EFREI Paris, ESIEE Paris, ISEP, ESEO, Junia HEI/ISEN, ESIEA, and ESCOM Chimie.

How is the final admission rank calculated for Puissance Alpha?

For general baccalaureate students with scientific specialties (Profil 2 Sciences), admission is calculated with equal weight: 50% from the candidate's academic dossier (Première and Terminale grades, French bac grades, teacher appraisals on Parcoursup) and 50% from the written QCM exams taken in April.

How does the negative marking (barème à points négatifs) work?

In the written QCM, questions generally award +1 point for a correct answer, deduct -0.5 points for an incorrect answer, and award 0 points for leaving a question blank. Therefore, candidates must avoid random guessing and only mark options when they can eliminate distractors with high confidence.

What is the format and duration of the written examination?

The written exam lasts a total of 3 hours and 15 minutes divided into three sequential sessions: Mathématiques (1 hour 30 minutes, 8 exercises of 4 questions each = 32 questions, of which 4 exercises are compulsory fundamentals and 4 are chosen freely from a panel matched to the candidate's Terminale options), Sciences appliquées (1 hour, 6 exercises to treat out of the 7 proposed in a single chosen subject among Physique-Chimie, SVT/biologie-écologie, NSI, SI or the science tronc commun), and Anglais (45 minutes, 25 MCQs covering grammar, vocabulary, and reading comprehension). For the 2026 session the written date was Saturday 25 April 2026.

Are calculators permitted in the written exams?

No. In general, calculators and personal electronic devices are strictly prohibited during the written exams of Concours Puissance Alpha. Calculations are designed to be completed by hand with mental arithmetic, estimation, and analytical simplification.

What registration process is required to sit for the exam?

Candidates register through the French national higher education portal Parcoursup between January and March. Selecting Concours Puissance Alpha counts as a single 'vœu multiple' with uncounted sub-wishes (sous-vœux non limités) for the participating engineering schools.

How should I manage my time during the Mathématiques paper?

With 1 hour 30 minutes for 8 exercises of 4 questions (32 questions in all), allocate roughly 11 minutes per exercise. Four exercises are compulsory fundamentals; read the optional panel early so you can pick the four remaining exercises that match your Terminale options and your strongest topics.