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Key Facts: Concours Banque PT Exam

1 bank

The single national written bank for the CPGE PT/PT* stream, run by Arts et Métiers

banquept.fr

13 papers

Written papers timetabled from 27 April to 7 May 2026

Banque PT 2026

6 June 2026

Admissibilité results published from 18:00

Banque PT 2026

22 June – 12 July

Orals at ENS Paris-Saclay; Arts et Métiers Paris 29 June – 10 July 2026

Banque PT 2026

25 July 2026

Admission results published from 18:00

Banque PT 2026

9 concours

Partner concours and 100+ engineering schools using Banque PT marks

banquept.fr

The definitive national competitive entrance examination for CPGE PT students, organized by Arts et Métiers. Scores from 13 written papers and comprehensive oral/practical exams feed 9 partner concours and more than 100 prestigious Grandes Écoles across France.

Sample Concours Banque PT Practice Questions

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

1In a spatial mechanism, rigid body S moves relative to reference frame R_0. At point A, its velocity is V(A, S/R_0) = 2.0 x_0 + 3.0 y_0 (in m/s), and its instantaneous rotation vector is Omega(S/R_0) = 4.0 z_0 (in rad/s). Point B is located at AB = 0.5 x_0 - 0.2 y_0 (in m). Using the Varignon field relation (relation de champ des moments d'un torseur cinématique), what is the velocity vector V(B, S/R_0)?
A.2.8 x_0 + 5.0 y_0 m/s
B.1.2 x_0 + 1.0 y_0 m/s
C.2.8 x_0 + 1.0 y_0 m/s
D.2.0 x_0 + 3.0 y_0 m/s
Explanation: By Varignon's formula for kinematic torsors, V(B, S/R_0) = V(A, S/R_0) + Omega(S/R_0) x AB. Computing the cross product: (4.0 z_0) x (0.5 x_0 - 0.2 y_0) = 2.0 y_0 - 0.8 (-x_0) = 0.8 x_0 + 2.0 y_0. Adding this to V(A) yields (2.0 + 0.8) x_0 + (3.0 + 2.0) y_0 = 2.8 x_0 + 5.0 y_0 m/s.
2An epicyclic planetary gear train (train épicycloïdal simple) has a sun gear (planétaire 1) with Z_1 = 20 teeth and an internal ring gear (couronne 3) with Z_3 = 80 teeth fixed to the machine casing (omega_3/0 = 0). What is the kinematic reduction ratio r = omega_e / omega_1, where omega_e is the rotational speed of the planet carrier (porte-satellites e) and omega_1 is the speed of the sun gear?
A.1/4 = 0.25
B.1/5 = 0.20
C.-1/4 = -0.25
D.1/3 = 0.33
Explanation: Applying Willis's formula with the planet carrier e as reference: (omega_1 - omega_e) / (omega_3 - omega_e) = (-1)^p * (Z_3 / Z_1), where p = 1 is the number of external meshes (sun to planet is external, planet to ring is internal). Thus (omega_1 - omega_e) / (0 - omega_e) = - (80 / 20) = -4. Rearranging gives omega_1 - omega_e = 4 omega_e, so omega_1 = 5 omega_e and r = omega_e / omega_1 = 1/5 = 0.20.
3A homogeneous solid cylinder S of mass M = 10 kg and radius R = 0.20 m rolls without slipping on a horizontal plane. Its center of mass G moves at linear velocity V_G = 3.0 m/s. Given that its moment of inertia about its symmetry axis is I_G = (1/2) M R^2, what is the total kinetic energy T(S/R_0) of the rolling cylinder?
A.45.0 J
B.22.5 J
C.67.5 J
D.90.0 J
Explanation: Under the rolling without slipping condition (roulement sans glissement), the angular velocity is omega = V_G / R. By König's theorem for kinetic energy, T = (1/2) M V_G^2 + (1/2) I_G omega^2 = (1/2) M V_G^2 + (1/2)(1/2 M R^2)(V_G / R)^2 = (3/4) M V_G^2. Substituting M = 10 kg and V_G = 3.0 m/s yields T = 0.75 * 10 * 9 = 67.5 J.
4A solid circular transmission shaft of diameter D = 50 mm (radius R = 25 mm) transmits a pure twisting torque M_t = 1,500 N·m. Using strength of materials (RdM) formulas for torsion, what is the maximum shear stress tau_max occurring on the shaft's outer skin?
A.15.3 MPa
B.30.6 MPa
C.122.2 MPa
D.61.1 MPa
Explanation: For a solid circular shaft, the polar second moment of area is I_0 = pi * D^4 / 32, and the torsional section modulus is W_0 = I_0 / (D/2) = pi * D^3 / 16. The maximum shear stress is tau_max = M_t / W_0 = 16 M_t / (pi D^3). Substituting M_t = 1,500 N·m and D = 0.05 m gives tau_max = (16 * 1500) / (pi * 0.05^3) = 24,000 / (pi * 1.25 * 10^-4) = 6.1115 * 10^7 Pa = 61.1 MPa.
5A continuous unity feedback control system is described by the open-loop transfer function G(p) = 10 / [p (p + 2)]. When subjected to a unit step input E(p) = 1/p, what is the steady-state tracking position error epsilon_infty = lim_{t -> infty} epsilon(t)?
A.0 (zero steady-state position error)
B.0.20
C.0.10
D.1.00
Explanation: The open-loop system has a pole at p = 0, meaning it is a Type 1 system (système de classe 1). By the final value theorem, epsilon_infty = lim_{p -> 0} p * E(p) / [1 + G(p)] = lim_{p -> 0} 1 / [1 + 10 / (p(p+2))] = lim_{p -> 0} p(p+2) / [p(p+2) + 10] = 0 / 10 = 0. A Type 1 system always exhibits zero steady-state position error for a step input.
6A rigid body S of mass m = 4.0 kg rotates around a fixed axis (O, z_0). Its center of mass G is located at OG = 0.10 x_0 m. At the instant considered, its angular velocity is omega = 10.0 rad/s and its angular acceleration is d(omega)/dt = 5.0 rad/s^2. What is the dynamic resultant vector R_dyn(S/R_0) at this instant?
A.-40.0 x_0 N
B.-40.0 x_0 + 2.0 y_0 N
C.40.0 x_0 + 2.0 y_0 N
D.-4.0 x_0 + 0.5 y_0 N
Explanation: The dynamic resultant is defined by R_dyn(S/R_0) = m * a(G, S/R_0). In polar coordinates for circular motion of radius r = 0.10 m, the acceleration of G is a(G) = -r omega^2 x_0 + r (d(omega)/dt) y_0 = -0.10 * (10.0)^2 x_0 + 0.10 * 5.0 y_0 = -10.0 x_0 + 0.5 y_0 m/s^2. Multiplying by mass m = 4.0 kg gives R_dyn = 4.0 * (-10.0 x_0 + 0.5 y_0) = -40.0 x_0 + 2.0 y_0 N.
7A cantilever steel beam (poutre encastrée-libre) of length L = 2.0 m has flexural rigidity E * I_Gz = 1.0 * 10^6 N·m^2. A concentrated vertical load F = 3,000 N is applied downward at its free tip. Using beam bending theory, what is the maximum vertical tip deflection (flèche maximale f)?
A.2.0 mm
B.4.0 mm
C.8.0 mm
D.24.0 mm
Explanation: For a cantilever beam subjected to an end point load F, successive integration of the bending equation E I y''(x) = -M_f(x) yields the classic deflection formula at the free end: f = F L^3 / (3 E I_Gz). Substituting the given values: f = (3,000 * 2.0^3) / (3 * 1.0 * 10^6) = (3,000 * 8.0) / (3.0 * 10^6) = 24,000 / 3,000,000 = 0.008 m = 8.0 mm.
8In frequency-domain analysis of an open-loop transfer function G_bo(j omega), the phase crossover frequency is omega_pi = 10 rad/s where arg[G_bo(j omega_pi)] = -180°. If the open-loop magnitude at this frequency is |G_bo(j 10)| = 0.25 (-12 dB), what is the Gain Margin (Marge de gain, MG) of the feedback system?
A.-12 dB
B.+6 dB
C.0 dB
D.+12 dB
Explanation: The gain margin is formally defined as the reciprocal of the open-loop magnitude at the phase crossover frequency omega_pi: MG = 1 / |G_bo(j omega_pi)|. In decibels, MG(dB) = -20 log10 |G_bo(j omega_pi)|. Here |G_bo(j 10)| = 0.25, so MG(dB) = -20 log10(0.25) = -20 * (-0.602) = +12.04 dB approx +12 dB. This positive gain margin guarantees stability in closed loop.
9A radial deep-groove ball bearing is subjected to an equivalent dynamic radial load P = 4.0 kN at an operating speed n = 1,500 rpm. Its basic dynamic load rating is C = 32.0 kN. For ball bearings, the life equation exponent is p = 3. What is the nominal rating life L_10h in hours?
A.5,689 hours
B.1,896 hours
C.2,844 hours
D.17,067 hours
Explanation: The basic rating life in millions of revolutions is L_10 = (C / P)^p = (32.0 / 4.0)^3 = 8^3 = 512 million revolutions. To convert to operating hours at rotational speed n: L_10h = (10^6 / (60 * n)) * L_10 = (10^6 / (60 * 1500)) * 512 = (10^6 / 90,000) * 512 = (100 / 9) * 512 = 5,688.89 hours approx 5,689 hours.
10A thin homogeneous rectangular plate of mass M has length a along the x-axis and width b along the y-axis, centered at its center of mass G. What is its principal moment of inertia I_Gz with respect to the normal axis (G, z) perpendicular to the plate?
A.I_Gz = M (a^2 + b^2) / 3
B.I_Gz = M (a^2 + b^2) / 12
C.I_Gz = M (a^2 - b^2) / 12
D.I_Gz = M a b / 6
Explanation: For a planar body lying in the (x, y) plane, the perpendicular axis theorem (théorème des axes perpendiculaires) states that I_Gz = I_Gx + I_Gy. The moments of inertia about the in-plane axes are I_Gx = M b^2 / 12 and I_Gy = M a^2 / 12. Summing these yields I_Gz = M (a^2 + b^2) / 12.

About the Concours Banque PT Exam

The Concours Banque PT (Physique et Technologie) is the unified national competitive examination system for students in French Classes Préparatoires aux Grandes Écoles (CPGE) following the PTSI (1st year) and PT/PT* (2nd year) tracks. Administered centrally by the Direction des formations et des concours of Arts et Métiers (ENSAM), the Banque PT constitutes the sole national written portal through which candidates gain admission to over 100 elite engineering institutions in France. These partner schools and concours consortia include Arts et Métiers (which recruits the vast majority of its engineering cohort through the PT bank), École Polytechnique (l'X), Concours CentraleSupélec (Centrale Paris/Saclay, Lyon, Nantes, Lille, Méditerranée, SupOptique), Concours Commun Mines-Ponts (Mines Paris, Ponts ParisTech, Télécom Paris, ENSTA Paris, Mines Saint-Étienne, Mines Nancy, IMT Atlantique), Concours Commun INP (CCINP), ENS Paris-Saclay, Concours Mines-Télécom, and the réseau Polytech. Candidates register via the national SCEI portal (scei-concours.fr). The written phase comprises 13 demanding papers: Mathématiques A, B, C; Physique A, B; Informatique-modélisation; Français A, B; Langue vivante A, B; and Sciences Industrielles A, B, C. Candidates who cross the eligibility thresholds (admissibilité) proceed to oral interrogations and practical laboratory examinations held at ENS Paris-Saclay and Arts et Métiers Paris.

Exam sponsor: Direction des formations et des concours d'Arts et Métiers (ENSAM). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Written phase (écrits) of 13 papers timetabled over nine days from 27 April to 7 May 2026: Mathématiques A, B and C; Physique A and B; Sciences Industrielles A, B and C; Informatique-modélisation; Français A and B; Langue vivante A and B. Admissibilité is published on 6 June 2026 from 18:00. Admissible candidates sit oral interrogations and laboratory practicals from 22 June to 12 July 2026 at ENS Paris-Saclay and from 29 June to 10 July 2026 at Arts et Métiers Paris, plus the TIPE. Admission results are published on 25 July 2026 from 18:00, with SCEI integration offers from 28 July 2026.

Time Limit

13 written papers (2 to 6 hours each) timetabled from 27 April to 7 May 2026

Passing Score

Ranking order based on weighted coefficient point totals set by each target concours (Arts et Métiers, Polytechnique, CentraleSupélec, CCINP, Mines-Ponts, etc.).

Exam / Certification Fees

Registration via SCEI, with a separate dossier fee for each partner concours entered: Arts et Métiers 220 €, Polytechnique 220 €, CCINP 240 €, Centrale-Supélec 240 €, Mines-Ponts 360 €, Concours Polytech 130 €, the four ENS free. Boursiers du gouvernement français are exempt.

Exam sponsor website

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

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.

30%

Sciences Industrielles de l'Ingénieur (SII)

Kinematics of 3D mechanisms, composition of velocities and accelerations, kinetic and dynamic torseurs (torseur cinétique, torseur dynamique, matrix of inertia), dynamic principles (Théorème du moment dynamique, énergie cinétique), mechanical design (planetary gear trains, bearing life, tooth stresses), strength of materials (RdM: tension, torsion, bending, Mohr's circle), and automatic control systems (Laplace transforms, transfer functions, Bode/Nyquist stability criteria, state charts).

25%

Mathématiques

Linear algebra (endomorphism reduction, eigenvalues, eigenvectors, diagonalisation, Euclidean spaces, orthogonal projections, symmetric endomorphisms, spectral theorem), multivariable calculus (partial derivatives, gradient, Jacobian, multiple integrals), numerical and power series, linear differential equations, and discrete probability spaces.

25%

Physique et Chimie

Mechanics of rigid bodies and systems, non-inertial frames and Coriolis force, fluid statics and dynamics (Bernoulli, Navier-Stokes, Poiseuille laminar pipe flow), thermodynamics (first and second laws, entropy balance, thermodynamic cycles, exergy), electromagnetism (Maxwell equations, Poynting vector, induction, skin effect), wave optics (two-wave interference, Michelson interferometer, Fraunhofer diffraction), and chemical equilibria (acid-base, precipitation, redox, chemical thermodynamics).

10%

Informatique et Modélisation

Algorithmic complexity (Big-O), Python programming (dictionaries, recursion, numerical integration via Euler and Runge-Kutta schemes), relational databases and SQL queries, and numerical modeling and simulation of mechanical/physical systems.

10%

Français-Philosophie et Langues Vivantes

Philosophical dissertation and rhetorical analysis on the annual CPGE theme, textual synthesis, and technical/academic English reading comprehension, grammar, and translation.

Preparing for the Concours Banque PT Exam

What You Need to Know

  • Passing score: Ranking order based on weighted coefficient point totals set by each target concours (Arts et Métiers, Polytechnique, CentraleSupélec, CCINP, Mines-Ponts, etc.).
  • Assessment: Written phase (écrits) of 13 papers timetabled over nine days from 27 April to 7 May 2026: Mathématiques A, B and C; Physique A and B; Sciences Industrielles A, B and C; Informatique-modélisation; Français A and B; Langue vivante A and B. Admissibilité is published on 6 June 2026 from 18:00. Admissible candidates sit oral interrogations and laboratory practicals from 22 June to 12 July 2026 at ENS Paris-Saclay and from 29 June to 10 July 2026 at Arts et Métiers Paris, plus the TIPE. Admission results are published on 25 July 2026 from 18:00, with SCEI integration offers from 28 July 2026.
  • Time limit: 13 written papers (2 to 6 hours each) timetabled from 27 April to 7 May 2026
  • Exam / certification fees: Registration via SCEI, with a separate dossier fee for each partner concours entered: Arts et Métiers 220 €, Polytechnique 220 €, CCINP 240 €, Centrale-Supélec 240 €, Mines-Ponts 360 €, Concours Polytech 130 €, the four ENS free. Boursiers du gouvernement français are exempt. Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

Concours Banque PT: Suggested Study Strategy

1Master mechanical torseur manipulations: practice calculating kinetic torseurs (torseur cinétique) and dynamic torseurs (torseur dynamique) at moving reference points using Huygens-Steiner formulas.
2Thoroughly practice Strength of Materials (RdM): calculate bending moments, shear stress distributions, deflection curves via successive integration, and Mohr's circle transformations under combined loading.
3Master automatic control: know how to establish closed-loop transfer functions, evaluate gain and phase margins on Bode diagrams, apply the Nyquist stability criterion, and synthesize PID controllers.
4In mathematics, focus on spectral theory: compute characteristic polynomials, find eigenspaces, determine conditions for diagonalisability, and apply orthogonal diagonalisation to real symmetric matrices.
5For physics, drill thermodynamic cycle balances: evaluate net mechanical work, heat exchange, isentropic efficiencies, and entropy generation for gas turbines, refrigeration cycles, and Rankine steam engines.
6Work systematically on Python and SQL: trace matrix operations, numerical ODE solvers (explicit Euler, Runge-Kutta 4), recursion depth, and multi-table SQL inner/outer joins with aggregation.

Frequently Asked Questions

What is the Concours Banque PT and who organizes it?

The Concours Banque PT is the unified national examination system for students in the CPGE Physique et Technologie (PT) stream. It is administered directly by the Direction des formations et des concours of Arts et Métiers (ENSAM) and provides admission to over 100 French engineering schools, including Arts et Métiers, École Polytechnique, CentraleSupélec, Mines-Ponts, CCINP, and ENS Paris-Saclay.

What are the key dates for the Session 2026 Concours Banque PT?

Registration opens on 8 December 2025 and closes on 12 January 2026 at 17:00 via scei-concours.fr. The 13 written papers run from 27 April to 7 May 2026. Written results (admissibilité) are published on 6 June 2026 at 18:00. Oral and practical exams take place between 22 June and 12 July 2026 at ENS Paris-Saclay and between 29 June and 10 July 2026 at Arts et Métiers Paris. Final admission lists are published on 25 July 2026 at 18:00.

What written papers are included in the Banque PT examination?

Candidates sit 14 distinct written papers: Mathématiques A, Mathématiques B, and Mathématiques C; Physique A and Physique B; Informatique-modélisation; Français-Philosophie A and Français-Philosophie B; Langue vivante A and Langue vivante B; and Sciences Industrielles A, B, and C. The duration of each paper ranges between 3 and 4 hours.

How are candidates ranked and admitted to partner schools?

Each participating concours consortium (Arts et Métiers, Polytechnique, CentraleSupélec, Mines-Ponts, CCINP, etc.) applies its own specific coefficient matrix to the written and oral paper marks. Points are aggregated into weighted scores to establish distinct admissibilité and admission rank lists for each school group.

What is the format of this practice bank compared to the real examination?

The official Banque PT written papers consist of extensive, multi-hour open-ended problem sets and engineering dossiers in French. This preparation bank is an English-language multiple-choice question (MCQ) study adaptation featuring genuine quantitative calculations and conceptual reasoning to help students master core syllabus topics.

What role do practical laboratory exams (épreuves de travaux pratiques) play?

For eligible candidates, oral assessments include dedicated experimental laboratory examinations: a 4-hour TP in Sciences Industrielles (testing CAD, instrumentation, mechanical characterization, or automated systems) and a 3-hour TP in Physique-Chimie, alongside individual oral interrogations and the TIPE (Travail d'Initiative Personnelle Encadré) defense.