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Key Facts: Concours Avenir Exam

7 Schools

Grandes Écoles

Concours Avenir

Total Exam Time

Association Concours Avenir

120 €

Standard Exam Fee

Concours Avenir (30 € for boursiers)

+3 / -1 / 0

Marking Scheme

Official QCM Rules

60%

Written Exam Weight

Selection Ratio (40% Dossier / 60% Exam)

No Calculator

Tool Policy

Written Test Regulations

Concours Avenir selects top students for 7 premier French engineering Grandes Écoles (ECE, EPF, ESILV, ESIGELEC, ESTACA, BUILDERS, and EIGSI) via a composite score of 40% high school academic record and 60% written QCM testing Mathématiques (1h30), Sciences (1h00), and Anglais (30 min) with negative marking (+3 for correct, -1 for wrong, 0 for omit). The official papers are in French; this bank is an English-language MCQ study adaptation.

Sample Concours Avenir Practice Questions

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

1What is the value of the limit lim (x -> 0) (e^x - 1) / x?

A.0

B.1

C.+infinity

D.e

Explanation: The expression (e^x - 1)/x represents the difference quotient of the exponential function at x = 0, namely (exp(x) - exp(0))/(x - 0). Since the derivative of exp(x) is exp(x) and exp(0) = 1, the limit is exp'(0) = 1. Alternatively, using L'Hôpital's rule or the first-order Taylor expansion e^x = 1 + x + o(x) yields 1.

2For all x > 0, what is the derivative of the function f(x) = x * ln(x)?

A.1 / x

B.ln(x) + 1

C.ln(x)

D.x + ln(x)

Explanation: Applying the product rule (uv)' = u'v + uv' with u(x) = x and v(x) = ln(x) gives u'(x) = 1 and v'(x) = 1/x. Thus, f'(x) = 1 * ln(x) + x * (1/x) = ln(x) + 1.

3What is the limit lim (x -> 0) ln(1 + 2x) / x?

A.0

B.1

C.2

D.ln(2)

Explanation: Using the standard limit lim (u -> 0) ln(1 + u)/u = 1 with substitution u = 2x, we have ln(1 + 2x)/x = 2 * (ln(1 + 2x)/(2x)). As x -> 0, u -> 0, so the limit is 2 * 1 = 2. This also corresponds to the definition of the derivative of g(x) = ln(1 + 2x) at 0, where g'(0) = 2/(1 + 0) = 2.

4Let f be a continuous function on [0, 2] such that f(0) = -1 and f(2) = 3. According to the Intermediate Value Theorem (théorème des valeurs intermédiaires), which statement is guaranteed to be true?

A.f is strictly increasing on [0, 2]

B.There exists at least one c in (0, 2) such that f(c) = 0

C.f(1) must equal 1

D.f is differentiable on (0, 2)

Explanation: By the Intermediate Value Theorem, if a function f is continuous on a closed interval [a, b] and 0 lies between f(a) and f(b), then there exists at least one real number c in (a, b) such that f(c) = 0. Here, f(0) = -1 < 0 < 3 = f(2), guaranteeing at least one root.

5What is the derivative of f(x) = exp(3x^2 - 1)?

A.6x * exp(3x^2 - 1)

B.3x * exp(3x^2 - 1)

C.(6x - 1) * exp(3x^2 - 1)

D.exp(6x)

Explanation: Using the chain rule (exp(u(x)))' = u'(x) * exp(u(x)) where u(x) = 3x^2 - 1, the derivative of u is u'(x) = 6x. Multiplying by exp(u(x)) yields f'(x) = 6x * exp(3x^2 - 1).

6What is the value of the limit lim (x -> 0) (cos(x) - 1) / x^2?

A.0

B.-1/2

C.1/2

D.-1

Explanation: Recall the Taylor expansion cos(x) = 1 - x^2/2 + o(x^2) as x -> 0. Substituting this into the expression gives (1 - x^2/2 + o(x^2) - 1)/x^2 = -1/2 + o(1), which converges to -1/2. Alternatively, applying L'Hôpital's rule twice: lim (-sin(x))/(2x) = lim (-cos(x))/2 = -1/2.

7Evaluate the definite integral I = int_0^1 x * exp(2x) dx.

A.(e^2 + 1) / 4

B.(e^2 - 1) / 2

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

D.e^2 / 2

Explanation: Use integration by parts: let u = x => u' = 1, and v' = exp(2x) => v = exp(2x)/2. Then I = [x * exp(2x) / 2]_0^1 - int_0^1 exp(2x)/2 dx = (1 * e^2 / 2 - 0) - [exp(2x) / 4]_0^1 = e^2 / 2 - (e^2 / 4 - 1 / 4) = e^2 / 4 + 1 / 4 = (e^2 + 1) / 4.

8What is the exact value of the integral J = int_1^e ln(x) dx?

A.e

B.1

C.e - 1

D.0

Explanation: An antiderivative of ln(x) obtained by integration by parts is F(x) = x * ln(x) - x. Evaluating from 1 to e gives F(e) - F(1) = (e * ln(e) - e) - (1 * ln(1) - 1) = (e * 1 - e) - (0 - 1) = 0 - (-1) = 1.

9What is the equation of the tangent line to the curve y = ln(x) at the point with abscissa x = 1?

A.y = x - 1

B.y = x + 1

C.y = x

D.y = 2x - 2

Explanation: The tangent line equation at x = a is y = f'(a)(x - a) + f(a). Here, f(x) = ln(x), so f'(x) = 1/x. At a = 1, f(1) = ln(1) = 0 and f'(1) = 1/1 = 1. The equation is y = 1*(x - 1) + 0, which simplifies to y = x - 1.

10At which x-coordinate does the cubic function f(x) = x^3 - 6x^2 + 9x + 2 possess an inflection point (point d'inflexion)?

A.x = 1

B.x = 2

C.x = 3

D.x = 4

Explanation: An inflection point occurs where the second derivative changes sign. First, f'(x) = 3x^2 - 12x + 9. Second, f''(x) = 6x - 12. Setting f''(x) = 0 gives 6x - 12 = 0, so x = 2. Since f'' is a linear function with non-zero slope 6, it changes sign at x = 2, confirming an inflection point.

About the Concours Avenir Exam

Concours Avenir is the leading private engineering school joint competitive entrance examination in France, recruiting high school seniors (Terminale) directly into 7 premier CTI-accredited Grandes Écoles d'Ingénieurs: ECE (Paris, Lyon, Bordeaux), EPF (Cachan, Troyes, Montpellier, Saint-Nazaire), ESILV (Paris-La Défense, Nantes), ESIGELEC (Rouen, Poitiers), ESTACA (Saint-Quentin-en-Yvelines, Laval, Bordeaux), BUILDERS École d'ingénieurs (Caen, Lyon), and EIGSI (La Rochelle, Casablanca). The selection combines an academic dossier review (40%) and a rigorous one-day multiple-choice exam (60%) testing advanced mathematics, physical sciences, and technical English under strict negative marking (+3/-1/0).

Exam sponsor: Association Concours Avenir. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Written QCU examination sat on one national date: Mathématiques (45 questions to answer among about 60 proposed, 1h30, coefficient 6), Sciences in the candidate's second scientific spécialité — Physique-Chimie, SVT, NSI or SI (30 questions to answer among about 40 proposed, 1h00, coefficient 4), Anglais (45 questions, 30 min, coefficient 2). Scoring: +3 correct, -1 incorrect, 0 blank.

Time Limit

3 hours total

Passing Score

Competitive composite ranking (40% academic dossier + 60% written QCM examination). Official scoring applies +3 points per correct answer, -1 point per incorrect answer, and 0 for blank.

Exam / Certification Fees

120 € (30 € for boursiers du gouvernement français) for the Terminale générale maths + science profile; 75 € (15 € for boursiers) for other profiles and Terminale STI2D

Exam sponsor website

Reported exam pass rate: Competitive admission ranking based on applicant quota per school. 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%

Calculus and Complex Functions

Limits, derivatives, exponential and logarithmic functions, continuity, the intermediate value theorem, and integration by parts.

15%

Sequences and Discrete Mathematics

Recurrence relations, arithmetic-geometric sequences, monotonicity, limits, convergence, and mathematical induction.

15%

Probability and Statistics

Binomial distributions, expectation, variance, conditional probability, Bayes' theorem, and total probability law.

10%

Three-Dimensional Geometry

Cartesian coordinates, dot product, normal vectors, Cartesian equations of planes, and parametric representations of lines.

15%

Applied Physics and Chemistry

Newton's laws of motion, work-energy theorem, capacitor charging and discharging in RC circuits, harmonic oscillators, and acid-base pH titrations.

15%

Engineering English Comprehension

Technical English vocabulary, grammar in engineering contexts, cause-and-effect connectors, sentence structure, and technical reading comprehension.

Preparing for the Concours Avenir Exam

What You Need to Know

Passing score: Competitive composite ranking (40% academic dossier + 60% written QCM examination). Official scoring applies +3 points per correct answer, -1 point per incorrect answer, and 0 for blank.
Assessment: Written QCU examination sat on one national date: Mathématiques (45 questions to answer among about 60 proposed, 1h30, coefficient 6), Sciences in the candidate's second scientific spécialité — Physique-Chimie, SVT, NSI or SI (30 questions to answer among about 40 proposed, 1h00, coefficient 4), Anglais (45 questions, 30 min, coefficient 2). Scoring: +3 correct, -1 incorrect, 0 blank.
Time limit: 3 hours total
Exam / certification fees: 120 € (30 € for boursiers du gouvernement français) for the Terminale générale maths + science profile; 75 € (15 € for boursiers) for other profiles and Terminale STI2D Official sources

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Concours Avenir: Suggested Study Strategy

1Master the +3/-1/0 scoring rule: an incorrect guess costs -1 point, so only guess if you can eliminate at least two plausible options.

2Practice without a calculator: all Concours Avenir math and physics calculations are designed for fast mental or scratch-paper arithmetic.

3Memorize standard derivative and antiderivative formulas, especially exponential composites, logarithmic derivatives, and integration by parts.

4Review first-order recurrence sequences: practice finding the fixed-point limit L = aL + b and expressing the explicit general term un = C*a^n + L.

5Be confident in 3D analytic geometry: practice writing Cartesian plane equations ax + by + cz + d = 0 and determining orthogonal projections onto lines and planes.

6Drill binomial probability and Bayes' formula: know E(X) = np, V(X) = np(1-p), and P(A|B) = P(B|A)P(A)/P(B) without hesitation.

7Review fundamental physics relationships: Newton's second law, kinetic/potential energy conservation, RC circuit time constants (tau = RC), and pH = -log[H3O+].

8Sharpen engineering English: focus on technical prepositions, conditional clauses, false friends (faux amis), and cause-effect discourse markers.

Frequently Asked Questions

What is Concours Avenir and which Grandes Écoles does it admit to?

Concours Avenir is a unified competitive examination system in France granting admission to 7 renowned CTI-accredited private engineering Grandes Écoles: ECE, EPF, ESILV, ESIGELEC, ESTACA, BUILDERS École d'ingénieurs, and EIGSI. Through a single application on Parcoursup, candidates can apply to all participating schools and their various campuses.

How does the negative marking scoring system work in Concours Avenir?

Concours Avenir uses a strict scoring scheme to reward genuine mastery and deter random guessing: each correct answer scores +3 points, an unanswered question scores 0 points, and an incorrect answer penalizes the candidate by -1 point. As a result, calculating the expected value of guessing is vital; candidates should omit questions where they cannot rule out multiple distractors.

What is the weight distribution between high school grades and the written exam?

The final ranking is determined by a composite score: the academic dossier (transcripts of Première and Terminale, covering Mathématiques, science specialties, and modern languages) accounts for 40%, while the centralized written QCM examination accounts for 60%. Highly ranked applicants based on academic records may be designated 'Grands Classés' and exempted from sitting the written tests.

What subjects and time allocations comprise the written examination?

The written test consists of three independent multiple-choice papers taken on a single Saturday: Mathématiques (45 questions to answer among about 60 proposed, 1 hour 30 minutes, coefficient 6), Sciences (30 questions to answer among about 40 proposed, in the candidate's second scientific spécialité — Physique-Chimie, SVT, NSI or SI — 1 hour, coefficient 4), and Anglais (45 questions testing grammar, vocabulary, and reading comprehension, 30 minutes, coefficient 2). For the 2026 session the written date was Saturday 2 May 2026.

Are calculators permitted during the Concours Avenir written tests?

Historically, electronic calculators of any type (including programmable calculators in exam mode) are strictly forbidden in the Concours Avenir written examinations. Questions are intentionally engineered so that mental arithmetic, algebraic simplification, and scientific estimation suffice.

Who is eligible to take the Concours Avenir (Avenir Bac)?

Eligible candidates are students currently in their final year of secondary school (Terminale générale) who have chosen scientific specialties (specifically Mathématiques plus another science specialty such as Physique-Chimie, NSI, or SI), as well as students enrolled in the Terminale STI2D stream.

What is the difference between Concours Avenir Bac and Concours Avenir Plus?

Concours Avenir Bac is specifically tailored for high school seniors aiming to enter directly into the first year of integrated 5-year engineering programs. Concours Avenir Plus is an admissions contest intended for university students (holding or pursuing a Bac+1, Bac+2, Bac+3, or Bac+4 such as BTS, BUT, or Licence) who wish to enter in the 2nd, 3rd, or 4th year.

How should I structure my preparation for the multiple-choice format?

Successful candidates practice extensively with past papers (annales) under strict time pressure without a calculator. They develop speed in standard algebraic manipulations, memorize essential trigonometric and calculus formulas, and master strategic decision-making regarding when to leave an uncertain question blank to avoid the -1 penalty.