Free Practice Questions for Concours ENS Tunis

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Key Facts: Concours ENS Tunis Exam

110 places

Admission quota across eight specialties in the 2026 notice

MESRS decision of 23 March 2026, article 2

20 TND

Application postal money order specified in the signed notice

MESRS decision of 23 March 2026, article 9

Age no greater than 24

Age limit at the date of the competition

MESRS decision of 23 March 2026, article 7

2–4 July 2026

Scheduled written-paper dates; oral admission follows

MESRS decision of 23 March 2026, articles 4 and 5

Use these 60 independent MCQs to review selected topics for your ENS Tunis specialty. Official admission uses written and oral tests, with 110 places and a 20 TND application fee in 2026. The bank's 30% science, 30% humanities and 40% language allocation is editorial study coverage, not an official blueprint or a common paper that every candidate takes.

Sample Concours ENS Tunis Practice Questions

Try these sample questions to review concepts for the Concours ENS Tunis exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 60+ question experience with AI tutoring.

1Let u be an endomorphism of a six-dimensional real vector space, with u^3 = 0 and rank(u^2) = 1. Which statement gives all possible values of rank(u)?

A.Only 2

B.Only 3

C.Either 2 or 3

D.Either 3 or 4

Explanation: Every nilpotent Jordan block has size at most three, and rank(u^2) = 1 requires exactly one block of size three. The remaining three dimensions can form blocks of sizes 1+1+1 or 2+1. These give total ranks 2 and 3 respectively, so the hypotheses do not determine a unique rank.

2For the real symmetric matrix A = [[0,2],[2,0]], which spectral description is correct? Let v = (1,1)/sqrt(2) and w = (1,-1)/sqrt(2).

A.v and w are orthonormal eigenvectors with eigenvalues 2 and -2 respectively.

B.v and w are orthonormal eigenvectors and both eigenvalues are 2.

C.The coordinate vectors (1,0) and (0,1) are eigenvectors with eigenvalues 2 and -2.

D.The eigenvalues are 2i and -2i, so no real eigenbasis exists.

Explanation: Multiplication gives Av = 2v and Aw = -2w. The two vectors have unit length and zero inner product, so they form an orthonormal eigenbasis. This illustrates the real spectral theorem without incorrectly assuming positive eigenvalues.

3For A = [[2, 1], [0, 2]], which pair gives the minimal polynomial and the dimension of the eigenspace for eigenvalue 2?

A.X - 2; dimension 2

B.(X - 2)^2; dimension 2

C.X - 2; dimension 1

D.(X - 2)^2; dimension 1

Explanation: A - 2I is nonzero, but its square is zero, so the minimal polynomial is (X - 2)^2. Solving (A - 2I)(x,y) = 0 gives y = 0, leaving a one-dimensional eigenspace. The matrix therefore lacks a basis of eigenvectors.

4For f_n(x) = x^n/(1+x^n) on [0,1], which statement describes its pointwise limit and uniform convergence?

A.The limit is zero everywhere, and convergence is uniform.

B.The limit is zero on [0,1) and 1/2 at 1, and convergence is not uniform.

C.The limit is zero on [0,1) and 1/2 at 1, and convergence is uniform.

D.The limit is 1/2 everywhere, and convergence is not uniform.

Explanation: For x < 1, x^n tends to zero; at x = 1 every term equals 1/2. Thus the pointwise limit is discontinuous at 1. Uniform convergence of these continuous functions would preserve continuity, so convergence on the whole interval is not uniform.

5For a complex variable z, consider the power series sum from n = 1 to infinity of [n!/(2n)!] z^(2n). What is its radius of convergence in z?

A.0

B.sqrt(2)

C.Infinity

D.2

Explanation: For fixed nonzero z, the ratio of successive term magnitudes is [(n+1)/((2n+2)(2n+1))]|z|^2 = |z|^2/[2(2n+1)]. This tends to zero for every finite z, so the ratio test gives absolute convergence throughout the complex plane. At z = 0 convergence is immediate, and the radius is infinite.

6Which function is a particular solution of y'' + 4y = cos(2x)?

A.x sin(2x)/4

B.cos(2x)/4

C.x cos(2x)/4

D.x sin(2x)/2

Explanation: The forcing frequency coincides with that of the homogeneous equation, so an ordinary sine-cosine trial must be multiplied by x. For y = A x sin(2x), substitution gives y'' + 4y = 4A cos(2x). Matching the forcing term gives A = 1/4.

7Define f(x,y) = x^3 y/(x^4+y^2) away from the origin and f(0,0) = 0. Which statement holds at the origin?

A.f is discontinuous but has both partial derivatives.

B.f is differentiable with gradient (0,0).

C.f is continuous but has no directional derivative along the x-axis.

D.f is continuous and has zero directional derivative in every direction, but is not differentiable.

Explanation: The bound |f(x,y)| <= |x|/2 proves continuity. Along a fixed direction (h,k), f(th,tk)/t = t h^3 k/(t^2 h^4+k^2) tends to zero when k is nonzero, and the expression is identically zero when k = 0. Yet along x > 0 and y = x^2, f(x,x^2)/sqrt(x^2+x^4) tends to 1/2, contradicting differentiability with zero derivative.

8A particle moves under the sole force associated with the time-independent central potential V(r) = -k/r, with k > 0. Which pair is conserved?

A.Linear momentum and kinetic energy

B.Total mechanical energy and angular momentum about the force center

C.Linear momentum and angular momentum about the force center

D.Kinetic energy and potential energy separately

Explanation: The central force produces zero torque about its center, conserving angular momentum about that point. The time-independent conservative potential also conserves the sum of kinetic and potential energy. Neither the momentum vector nor the two energy terms separately must remain constant.

9An ideal gas with constant heat-capacity ratio gamma = 1.4 expands reversibly and adiabatically to twice its initial volume. What is T_2/T_1?

A.1.000

B.1.320

C.0.758

D.0.500

Explanation: For this process, T V^(gamma-1) is constant. Hence T_2/T_1 = (1/2)^0.4, approximately 0.758. The decrease reflects energy transferred as work without heat input.

10A series RLC circuit has R > 0 and ideal inductive and capacitive elements. At angular frequency omega = 1/sqrt(LC), what are its impedance magnitude and the current-voltage phase difference?

A.R; pi/2

B.sqrt(R^2 + (omega L)^2); 0

C.0; 0

D.R; 0

Explanation: The impedance is R + j(omega L - 1/(omega C)). At resonance the two reactances cancel, leaving the positive resistance R. The current and applied voltage are consequently in phase.

About the Concours ENS Tunis Exam

The Concours ENS Tunis admits élèves normaliens to the École normale supérieure. The 2026 session offers 110 places across Arabic, French, English, history, geography, philosophy, mathematics and physics specialties. This is an independent English-language MCQ study adaptation, not an official translation, an official-format simulation, or a substitute for extended writing, translation and oral practice. Arabic and French text is retained when integral to the skill being tested.

Exam sponsor: École normale supérieure de Tunis, Université de Tunis, under the Ministère de l'Enseignement supérieur et de la Recherche scientifique (MESRS). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Written admissibility papers on 2, 3 and 4 July 2026, followed by oral admission tests. Language specialties use a composition, grammatical study and translation; history and geography combine subject compositions and document/text commentary; philosophy combines general philosophy, commentary and a language test. Science specialties combine mathematical, physical or chemical problem papers with French and English tests. The governing orders also provide oral text explanation or subject presentations and discussion, including scientific culture presentations for science candidates. These are separate specialties, not a single common paper covering every subject.

Time Limit

2–4 hours per written paper over three days; oral timing varies by test and specialty

Passing Score

Under Decree 97-449, a mark below 7/20 in any test eliminates the candidate; written admissibility requires an average of at least 10/20, and final admission or waiting-list placement requires an overall average of at least 10/20 plus ranking within the available places

Exam / Certification Fees

20 TND by postal money order payable to the ENS accountant, as stated in article 9 of the signed 2026 notice

Exam sponsor website

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

Official sources

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% of this bank

Fundamental Sciences

18 questions: seven mathematics, six physics and five chemistry items. These are selected topics across the two science specialties, not an official paper weighting.

30% of this bank

Human Sciences

18 questions: eight philosophy, five history and five geography items. Study the subjects and paper requirements of your chosen specialty.

40% of this bank

Languages and Literature

24 questions: nine Arabic, eight French and seven English literature or language items. This selection does not replace composition, translation or oral text explanation.

Preparing for the Concours ENS Tunis Exam

What You Need to Know

Passing score: Under Decree 97-449, a mark below 7/20 in any test eliminates the candidate; written admissibility requires an average of at least 10/20, and final admission or waiting-list placement requires an overall average of at least 10/20 plus ranking within the available places
Assessment: Written admissibility papers on 2, 3 and 4 July 2026, followed by oral admission tests. Language specialties use a composition, grammatical study and translation; history and geography combine subject compositions and document/text commentary; philosophy combines general philosophy, commentary and a language test. Science specialties combine mathematical, physical or chemical problem papers with French and English tests. The governing orders also provide oral text explanation or subject presentations and discussion, including scientific culture presentations for science candidates. These are separate specialties, not a single common paper covering every subject.
Time limit: 2–4 hours per written paper over three days; oral timing varies by test and specialty
Exam / certification fees: 20 TND by postal money order payable to the ENS accountant, as stated in article 9 of the signed 2026 notice Official sources

Using Our Practice Resources

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Concours ENS Tunis: Suggested Study Strategy

1Identify your specialty first and use its current ENS subject program and paper coefficients to plan study; the bank combines topics that different candidates take.

2For mathematics and science, write full solutions with assumptions, units and reasoning before using the MCQ options to check your result.

3For humanities, develop a thesis and supporting evidence, and practice sustained commentary on primary texts or geographic documents.

4For language specialties, practice grammatical analysis and translation using the actual Arabic, French or English text; an English explanation does not test full language production.

5Prepare oral presentations and discussion separately. Recognizing a correct explanation in an MCQ does not demonstrate that you can produce and defend it aloud.

Frequently Asked Questions

What is the official assessment format?

It is a competition with written admissibility and oral admission tests. The specialties have different papers and coefficients. Language candidates complete composition, grammatical and translation work; science candidates solve subject problems and take language tests. The notice does not list compulsory coursework, a portfolio or a separate practical examination for entry; oral subject and scientific-culture work still needs direct preparation.

Which languages are used in the official competition?

Arabic, French and English are confirmed in the official paper and translation requirements. Humanities rules include Arabic and French written work; science timetables include French and English language papers. Other language choices may be permitted for specific language tests, so these confirmed languages are not a claim that every paper offers all three or that the list is exhaustive.

How many places are available in 2026?

The signed MESRS notice allocates 15 places to Arabic, 15 to French, 20 to English, 10 each to history, geography and philosophy, and 15 each to mathematics and physics, totaling 110. Places are admission quotas, not topic weights.

Who can apply?

The 2026 notice requires Tunisian nationality and age no greater than 24 on the examination date. It specifies second-year national licence routes in the listed subjects, with eligibility to progress to year three, and second-year preparatory routes in humanities/literature or MP/PC sciences. Check the notice for the success documents required for your route; no general 14/20 written-test exemption is established by these sources.

What is the application fee?

Article 9 of the signed 23 March 2026 notice specifies a postal money order of twenty (20) Tunisian dinars payable to the ENS accountant. The notice's fee is 20 TND.

What are the dates and durations?

Applications ran from 18 May to 12 June 2026. Written papers were scheduled for 2–4 July 2026 and last 2, 3 or 4 hours depending on the paper. The notice says the oral schedule is announced after the written results; it is not one continuous timed test.

Does this bank reproduce the official syllabus distribution?

No common percentage blueprint applies across all eight specialties. The 2026 timetable gives separate paper coefficients, while the governing 1997 orders specify scientific subject programs and first-cycle subject scope for letters and humanities. Our 30/30/40 split is a selected cross-specialty study allocation. Use the current ENS subject program for your own specialty, including any annual reading requirements; this bank does not claim complete coverage of those requirements.

Can these MCQs replace written or oral preparation?

No. This English-language MCQ study adaptation supports concept review and error diagnosis. It is independent practice by OpenExamPrep, not an official translation or a simulation of the official format or language environment. Practice full proofs, essays, grammatical analysis, translation and spoken explanations in the languages and formats required for your specialty.