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Key Facts: Concours Advance Exam

Concours Advance is a common entrance exam for four CTI-accredited Grandes Écoles: EPITA, ESME, IPSA, and Sup'Biotech.

Registration is managed through the national Parcoursup platform.

The examination includes written QCM papers in Mathématiques (1h30, coeff 4) and Anglais (30 min, coeff 3), plus an oral interview (coeff 7).

Calculators of any type are strictly prohibited in the written examination.

Registration fee is 75 €, waived completely for French state scholarship holders (boursiers).

Concours Advance selects candidates via Parcoursup for 4 leading engineering Grandes Écoles — EPITA, ESME, IPSA, and Sup'Biotech — using academic dossier evaluation, written QCM tests in Mathematics and English without calculator, and an oral interview.

Sample Concours Advance Practice Questions

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

1Without a calculator, evaluate the limit: lim (x -> 0) (e^(2x) - 1) / x.

A.0

B.1

C.2

D.e^2

Explanation: Recognizing the difference quotient for the function f(t) = e^(2t) at t = 0, the limit is f'(0). Since f'(t) = 2 e^(2t), we find f'(0) = 2 * e^0 = 2.

2Let f(x) = (3x + 1) e^(-x) for all real x. What is the expression of the derivative f'(x)?

A.(2 - 3x) e^(-x)

B.(3 - 3x) e^(-x)

C.3 e^(-x)

D.(-3x - 4) e^(-x)

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

3Which function solves the first-order differential equation y' + 2y = 0 subject to the initial condition y(0) = 5?

A.y(x) = 5 e^(2x)

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

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

D.y(x) = e^(-2x) + 4

Explanation: The homogeneous linear differential equation y' + ay = 0 has general solution y(x) = C e^(-ax). Here a = 2, so y(x) = C e^(-2x). Applying y(0) = 5 yields C = 5, giving y(x) = 5 e^(-2x).

4By growth hierarchy (croissances comparées), what is lim (x -> +inf) (x^2 + 3x) / e^x?

A.+inf

B.1

C.3

D.0

Explanation: According to standard growth hierarchy theorems in the French Terminale curriculum, the exponential function dominates any polynomial power at +infinity. Therefore, lim (x -> +inf) x^n / e^x = 0 for any positive integer n, meaning lim (x -> +inf) (x^2 + 3x)/e^x = 0.

5Simplify the exact value: A = ln(24) - 3 ln(2) + ln(9).

A.ln(27)

B.ln(18)

C.ln(36)

D.3

Explanation: Using logarithm identities: 3 ln(2) = ln(2^3) = ln(8). Then ln(24) - ln(8) = ln(24 / 8) = ln(3). Finally, ln(3) + ln(9) = ln(3 * 9) = ln(27) = 3 ln(3).

6Calculate the definite integral: I = int (0 to 1) (2x + 3) dx.

A.3

B.4

C.5

D.6

Explanation: An antiderivative of 2x + 3 is F(x) = x^2 + 3x. Evaluating between 0 and 1 gives F(1) - F(0) = (1^2 + 3 * 1) - 0 = 4.

7Determine the inflection point (point d'inflexion) of the cubic function f(x) = x^3 - 6x^2 + 9x + 2.

A.(1, 6)

B.(2, 4)

C.(3, 2)

D.(0, 2)

Explanation: The first derivative is f'(x) = 3x^2 - 12x + 9, so the second derivative is f''(x) = 6x - 12. Setting f''(x) = 0 yields x = 2. Since f''(x) changes sign at x = 2, an inflection point occurs at x = 2. Evaluating f(2) = 2^3 - 6(2^2) + 9(2) + 2 = 8 - 24 + 18 + 2 = 4, so the point is (2, 4).

8What is the Cartesian 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

C.y = x + 1

D.y = 2x - 2

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

9Find the unique antiderivative F(x) of f(x) = 2x / (x^2 + 1) on R such that F(0) = 3.

A.F(x) = ln(x^2 + 1) + 3

B.F(x) = ln(x^2 + 1)

C.F(x) = 2 ln(x^2 + 1) + 3

D.F(x) = 1 / (x^2 + 1)^2 + 2

Explanation: f(x) matches the pattern u'(x)/u(x) where u(x) = x^2 + 1 > 0. The general antiderivative is F(x) = ln(x^2 + 1) + C. Imposing F(0) = ln(1) + C = C = 3 yields F(x) = ln(x^2 + 1) + 3.

10Calculate the derivative of the function g(x) = ln(x^2 + 4) defined on R.

A.g'(x) = 2x / (x^2 + 4)

B.g'(x) = 1 / (x^2 + 4)

C.g'(x) = x / (x^2 + 4)

D.g'(x) = 2 / (x^2 + 4)

Explanation: For a composite function ln(u(x)), the chain rule gives [ln(u(x))]' = u'(x) / u(x). Here u(x) = x^2 + 4, so u'(x) = 2x. Thus g'(x) = 2x / (x^2 + 4).

About the Concours Advance Exam

Concours Advance is a common competitive entrance examination organized by IONIS Education Group for admission into four prestigious CTI-accredited private engineering Grandes Écoles in France: EPITA (specialized in computer science, cybersecurity, artificial intelligence, and software engineering), ESME (multidisciplinary engineering covering energy, electronics, robotics, and connected systems), IPSA (dedicated to aerospace, aeronautics, and space systems engineering), and Sup'Biotech (specialized in biotechnology applied to healthcare, environment, agrifood, and cosmetics). Open primarily to Terminale students via the Parcoursup platform, selection is based on a composite score combining the candidate's academic school dossier, timed written multiple-choice tests (QCM) in Mathematics (1 hour 30 minutes, coefficient 4) and English (30 minutes, coefficient 3) taken strictly without calculator, and an individual oral interview (coefficient 7). This practice bank offers an English-language MCQ study adaptation designed to hone mental mathematical agility, analytical reasoning, and specialized technical English communication.

Exam sponsor: Concours Advance (IONIS Education Group). 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

2 hours written (Mathématiques 1h30, Anglais 30 min) plus 30 min oral interview

Passing Score

Competitive composite ranking based on Parcoursup dossier, written QCM tests (Mathématiques coefficient 4, Anglais coefficient 3), and oral interview (coefficient 7).

Exam / Certification Fees

75 € (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

Concours Advance (IONIS Education Group): 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.

30%

Calculus & Mathematical Analysis

Core calculus topics including limits, differential calculus, antiderivatives, integration properties, exponential and logarithmic functions, and differential equations.

20%

Sequences & Mathematical Induction

Arithmetic and geometric progressions, explicit and recursive formulas, proofs by mathematical induction, limits of sequences, and convergence criteria.

20%

Probability & Combinatorial Analysis

Counting techniques (permutations, combinations, k-tuples), Pascal's identity, Bernoulli trials, binomial distribution, conditional probability, and total probability theorem.

10%

Spatial Vector Geometry

Vector operations in 3D Euclidean space, dot product, orthogonality, normal vectors, Cartesian plane equations, parametric equations of lines, and relative positioning.

20%

Engineering English & Communication

Grammatical precision, sentence syntax, conditionals, prepositions, cohesive devices, and technical vocabulary relevant to computer science, aerospace, biotechnology, and electronics.

Preparing for the Concours Advance Exam

What You Need to Know

Passing score: Competitive composite ranking based on Parcoursup dossier, written QCM tests (Mathématiques coefficient 4, Anglais coefficient 3), and oral interview (coefficient 7).
Assessment: Question count not published by the exam provider
Time limit: 2 hours written (Mathématiques 1h30, Anglais 30 min) plus 30 min oral interview
Exam / certification fees: 75 € (free for boursiers du gouvernement français) Official sources

Using Our Practice Resources

Work through all 100 available questions
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Concours Advance: Suggested Study Strategy

1Train mental arithmetic and rapid algebraic simplifications daily, as calculators are strictly forbidden during the written test.

2Master the standard growth hierarchies (croissances comparées) for exponential, polynomial, and logarithmic limits to resolve indeterminate forms instantly.

3Review spatial geometry fundamentals: finding normal vectors from cross products or Cartesian equations, and checking whether points belong to planes or lines.

4Memorize binomial distribution formulas: P(X=k) = C(n,k) p^k (1-p)^(n-k), E(X)=np, and V(X)=np(1-p).

5Read technical articles in English on computer science, aviation, robotics, and biology to build lexical fluency for the Anglais paper.

Frequently Asked Questions

What Grandes Écoles are accessible through Concours Advance?

Concours Advance provides entry to 4 CTI-accredited private engineering schools: EPITA (computer science and software engineering), ESME (multidisciplinary systems and energy), IPSA (aeronautics and space), and Sup'Biotech (biotechnologies).

How is the overall Concours Advance score calculated?

Candidates are ranked using a composite grade combining their Parcoursup academic record (première and terminale marks and appréciations), the written QCM exams (Mathématiques with coefficient 4, Anglais with coefficient 3), and an oral interview (coefficient 7).

Are calculators allowed in the Concours Advance written tests?

No. The use of calculators is strictly prohibited during the written QCM examination. Speed, mental calculation accuracy, and rapid elimination of implausible answers are essential skills.

What is the format of the written test in Concours Advance?

The written exam consists of timed multiple-choice questions (QCM): 1 hour 30 minutes for Mathematics and 30 minutes for English. Depending on the test year, questions may carry negative marking for incorrect answers or neutral scoring for blank answers.

How does this practice bank adapt the official exam?

This bank provides 100 high-yield multiple-choice questions structured into 4 options with exact mathematical reasoning, fully worked calculations without calculator, and specialized engineering English practice to simulate the pace and standard of Concours Advance.