Free Practice Questions for Maturità Scientifico

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Key Facts: Maturità Scientifico Exam

60 / 100

Minimum passing score

D.Lgs. 62/2017 & MIM Guidelines

40 points

Maximum school credit (credito scolastico)

MIM Ordinanza Ministeriale n. 54

6 hours

Allotted time for Prima Prova (Italian)

MIM Esami di Stato Framework

6 hours

Allotted time for Seconda Prova (Math/Physics)

MIM Quadri di Riferimento

1 problem + 4 quesiti

Seconda Prova required answers

Out of 2 problems and 8 questions

€12.09

Statutory state examination fee

Agenzia delle Entrate / MIM

20 points each

Maximum score per exam component

Prima Prova, Seconda Prova, Colloquio

Scientific / Graphic

Permitted calculators (non-CAS)

MIM Annual Calculator Directive

The Italian Maturità for Liceo Scientifico evaluates candidates across school credit (max 40 points) and three exam phases (20 points each: Italian essay, 6-hour Mathematics/Physics open-response test, and multidisciplinary oral colloquio). A minimum composite score of 60/100 points is required to pass.

Sample Maturità Scientifico Practice Questions

Try these sample questions to review concepts for the Maturità Scientifico exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 95+ question experience with AI tutoring.

1Evaluate the trigonometric limit: lim_{x -> 0} (sin(3x) / (2x)).

A.3/2

B.0

C.1

D.2/3

Explanation: Using the standard fundamental limit lim_{u -> 0} (sin(u)/u) = 1 with u = 3x, we rewrite the expression as (3/2) * (sin(3x)/(3x)). As x approaches 0, the ratio sin(3x)/(3x) approaches 1, leaving (3/2) * 1 = 3/2.

2Evaluate the limit: lim_{x -> 0} (1 - cos(4x)) / (3x²).

A.4/3

B.8/3

C.16/3

D.2/3

Explanation: Using the Taylor expansion 1 - cos(u) = u²/2 + o(u²) as u -> 0 with u = 4x, the numerator becomes (4x)² / 2 = 16x² / 2 = 8x². Dividing by 3x² yields lim_{x -> 0} (8x² / 3x²) = 8/3. Alternatively, applying de l'Hôpital's rule twice yields the same result.

3Evaluate the limit involving Euler's number: lim_{x -> +∞} ((x + 3) / (x - 1))^x.

A.e²

B.e³

C.e⁴

D.e

Explanation: Rewrite the base as (x + 3)/(x - 1) = 1 + 4/(x - 1). The limit takes the standard form lim_{t -> ∞} (1 + k/t)^t = e^k with k = 4. Therefore, lim_{x -> +∞} (1 + 4/(x - 1))^x = e⁴.

4Using Taylor series or de l'Hôpital's rule, compute: lim_{x -> 0} (e^x - 1 - x - x²/2) / x³.

A.1/2

B.1/3

C.1/6

D.0

Explanation: The Taylor series expansion of e^x at x = 0 is e^x = 1 + x + x²/2! + x³/3! + o(x³) = 1 + x + x²/2 + x³/6 + o(x³). Subtracting 1 + x + x²/2 leaves x³/6 + o(x³). Dividing by x³ and taking the limit gives 1/6.

5Find the equation of the oblique asymptote y = mx + q as x -> +∞ for the rational function f(x) = (2x² - 3x + 5) / (x + 1).

A.y = 2x - 3

B.y = 2x - 5

C.y = 2x + 1

D.y = 2x + 5

Explanation: Performing polynomial division of 2x² - 3x + 5 by x + 1 gives 2x - 5 with a remainder of 10, so f(x) = 2x - 5 + 10/(x + 1). As x -> +∞, 10/(x + 1) -> 0, so the oblique asymptote is y = 2x - 5.

6Consider the function f(x) = (x² - 9) / (x - 3) for x ≠ 3, and f(3) = 5. What type of discontinuity does f have at x = 3?

A.Removable discontinuity (punto di singolarità eliminabile)

B.Jump discontinuity (salto / prima specie)

C.Essential discontinuity (seconda specie)

D.The function is continuous at x = 3

Explanation: Factoring the numerator gives (x - 3)(x + 3)/(x - 3) = x + 3 for x ≠ 3. The two-sided limit as x -> 3 is lim_{x -> 3} (x + 3) = 6. Because the finite limit exists but does not equal the defined value f(3) = 5, x = 3 is a removable discontinuity.

7Find the first derivative f'(x) of the function f(x) = ln(x² + 1).

A.1 / (x² + 1)

B.2x / (x² + 1)

C.2 / (x² + 1)

D.x / (x² + 1)

Explanation: Applying the chain rule d/dx [ln(u(x))] = u'(x) / u(x) with u(x) = x² + 1 and u'(x) = 2x, we obtain f'(x) = 2x / (x² + 1).

8What is the equation of the line tangent to the curve y = x³ - 3x + 2 at the point where x = 2?

A.y = 9x - 14

B.y = 9x - 18

C.y = 3x - 2

D.y = 9x + 4

Explanation: The y-coordinate is y(2) = 2³ - 3(2) + 2 = 8 - 6 + 2 = 4. The derivative is y' = 3x² - 3, giving slope m = y'(2) = 3(4) - 3 = 9. The point-slope form is y - 4 = 9(x - 2), which simplifies to y = 9x - 14.

9Consider f(x) = x³ - 4x on the closed interval [-2, 2]. According to Rolle's theorem, there exists at least one point c in (-2, 2) such that f'(c) = 0. Which positive value of c satisfies this condition?

A.1

B.2√3 / 3

C.√2

D.4/3

Explanation: First, f(-2) = 0 and f(2) = 0, and f is a polynomial (continuous on [-2, 2] and differentiable on (-2, 2)). Setting f'(x) = 3x² - 4 = 0 gives x² = 4/3, so x = ± 2/√3 = ± 2√3 / 3. The positive solution is c = 2√3 / 3 ≈ 1.155, which lies within (-2, 2).

10For the function f(x) = x² - 2x on [0, 4], find the value of c guaranteed by the Mean Value Theorem (Lagrange's Theorem) such that f'(c) = (f(4) - f(0)) / (4 - 0).

A.1

B.2

C.3

D.√2

Explanation: Calculate f(4) = 4² - 2(4) = 8 and f(0) = 0. The average rate of change is (8 - 0)/(4 - 0) = 2. Differentiating gives f'(x) = 2x - 2. Setting 2c - 2 = 2 yields 2c = 4, so c = 2, which lies strictly inside the open interval (0, 4).

About the Maturità Scientifico Exam

The Liceo Scientifico Maturità combines the national Italian Prima Prova, the designated open-response Seconda Prova (Mathematics in 2026), and a multidisciplinary oral whose duration is set by the commission. The oral begins with a brief candidate reflection and covers four designated disciplines, civic education, formazione scuola-lavoro, and the written papers. This independent English-language MCQ bank targets concepts and calculations; it does not reproduce proofs, full open-response solutions, Italian writing, or oral performance.

Exam sponsor: Ministero dell'Istruzione e del Merito (MIM). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

The 2026 exam comprises School Credit (max 40), Prima Prova (Italian, 6 hours, max 20), Seconda Prova (Mathematics, 6 hours, max 20), and Colloquio Orale (max 20; duration set by the commission). The oral covers four designated disciplines, civic education, formazione scuola-lavoro, and the written papers. Minimum: 60/100.

Time Limit

Prima Prova 6 hours; Seconda Prova 6 hours; oral duration set by the commission

Passing Score

Minimum 60/100 points overall across school credit and all three examination components

Exam / Certification Fees

€12.09 (statutory state examination fee)

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.

35%

Mathematical Analysis & Functions

Limits, continuity, differential calculus, maxima and minima, curve sketching, asymptotes, integral calculus, Fundamental Theorem of Calculus, and differential equations.

20%

Analytic Geometry, Trigonometry & Solid Geometry

Conic sections, 3D Cartesian coordinates, planes and lines in space, polyhedra, surfaces and solids of revolution, and trigonometric equations and identities.

15%

Probability, Combinatorics & Statistics

Permutations, combinations, binomial coefficients, classical and conditional probability, Bayes' theorem, discrete random variables, and continuous distributions.

30%

Advanced Physics

Electromagnetism, electromagnetic induction, Maxwell's equations, special relativity, quantum phenomena (photoelectric effect, de Broglie wavelength), and thermodynamics.

Preparing for the Maturità Scientifico Exam

What You Need to Know

Passing score: Minimum 60/100 points overall across school credit and all three examination components
Assessment: The 2026 exam comprises School Credit (max 40), Prima Prova (Italian, 6 hours, max 20), Seconda Prova (Mathematics, 6 hours, max 20), and Colloquio Orale (max 20; duration set by the commission). The oral covers four designated disciplines, civic education, formazione scuola-lavoro, and the written papers. Minimum: 60/100.
Time limit: Prima Prova 6 hours; Seconda Prova 6 hours; oral duration set by the commission
Exam / certification fees: €12.09 (statutory state examination fee) Official sources

Using Our Practice Resources

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Maturità Scientifico: Suggested Study Strategy

1Master calculus foundations: focus on limits involving indeterminate forms (de l'Hôpital's rule, Taylor/Maclaurin series), derivative rules, extreme value problems, and inflection points.

2Work extensively with integral calculus: practice integration by parts, substitution, partial fractions, and definite integrals applied to area between curves and volumes of solids of revolution.

3Strengthen 3D spatial geometry: drill vector dot and cross products, parametric equations of lines in space, Cartesian equations of planes, and distance formulas from points to planes.

4Review trigonometric relationships: be fluent with addition/subtraction formulas, double-angle identities, and solving trigonometric equations with boundary constraints.

5Internalize probability theorems: practice Bayes' theorem with tree diagrams, independent vs. dependent events, binomial distributions, and expected value calculations.

6Review Maxwell's equations and induction: understand Faraday-Neumann-Lenz law, self-inductance, LC and RLC circuit dynamics, and magnetic flux variations.

7Master special relativity kinematics: calculate Lorentz factor gamma, relativistic time dilation, length contraction, relativistic momentum, and total energy relationships.

8Grasp modern physics foundations: solve photoelectric effect work function problems, photon energy-frequency relations, and de Broglie matter wavelength calculations.

9Practice multi-step algebraic precision without relying on symbolic computer algebra systems (CAS), reflecting exam conditions.

10Prepare for the multidisciplinary oral colloquium by connecting scientific concepts (e.g. thermodynamics, relativity, entropy) with philosophy, history, and literature.

Frequently Asked Questions

What is the Esame di Stato (Maturità) for Liceo Scientifico and how is it structured?

The Maturità Scientifica is Italy's national secondary school-leaving examination for the scientific high school pathway. It consists of Prima Prova (Italian, 6 hours), the current year's designated open-response Seconda Prova (Mathematics in 2026, 6 hours), and a multidisciplinary Colloquio Orale whose duration is set by the commission.

What is the format of the Seconda Prova for Liceo Scientifico?

Under the ministerial Quadri di Riferimento and Ordinanza Ministeriale n. 54 del 26 marzo 2026, the Seconda Prova provides two comprehensive multi-part problems (problemi) and eight focused analytical questions (quesiti) in Mathematics and/or Physics. Each candidate chooses and solves exactly one problem and four questions within the 6-hour allotted time.

How is the Maturità scored and what is the passing score?

The total maximum score is 100 points: up to 40 points awarded for school credit (credito scolastico) accumulated during years 3, 4, and 5; up to 20 points for Prima Prova; up to 20 points for Seconda Prova; and up to 20 points for the Colloquio Orale. The minimum passing threshold is 60/100 points across the combined components. Candidates with maximum credit and top performance may be awarded honors (lode).

Are calculators permitted during the Seconda Prova?

Yes. Candidates are permitted to use non-programmable, non-graphing scientific calculators or approved non-CAS graphical calculators that lack internet connectivity or external communications capabilities, in accordance with the annual MIM permitted calculator list.

Are these practice questions official MIM examination materials?

No. These practice questions are an independent study resource developed by OpenExamPrep. They are not affiliated with, endorsed by, or administered by the Ministero dell'Istruzione e del Merito (MIM). The bank adapts key concepts, calculus techniques, and physics laws from the official Quadri di Riferimento into four-option multiple-choice questions to reinforce foundational principles and quantitative problem-solving.

Free Practice Questions for Maturità Scientifico

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