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Key Facts: PoliTo TIL-I Exam

42 questions

Official test question count

PoliTo Bando di Concorso

90 minutes

Total test duration across 4 sections

PoliTo TIL Regulations

€50

Registration fee per TIL session

PoliTo Admission Call 2026

+1 / -0.25

Scoring: +1 correct, -0.25 wrong, 0 blank

PoliTo Scoring Regulations

4 sections

Math (16), Reading/Logic (10), Physics (10), Technical (6)

TIL-I Structure

LAIB Labs

In-person computer test on campus

Politecnico di Torino

The PoliTo TIL-I is the official 90-minute, 42-question computer-based entrance exam for undergraduate engineering programs at Politecnico di Torino. Delivered in university LAIB labs, it covers Mathematics (16 questions), Reading and Logic (10 questions), Physics (10 questions), and Technical Basics (6 questions). Each question is scored +1 for correct, -0.25 for incorrect, and 0 for unanswered, with a standard registration fee of €50.

Sample PoliTo TIL-I Practice Questions

Try these sample questions to review concepts for the PoliTo TIL-I exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 98+ question experience with AI tutoring.

1Solve the system of linear equations: 2x + 3y = 12 x - y = 1 What is the value of x + y?
A.4
B.5
C.6
D.7
Explanation: From the second equation, x = y + 1. Substituting into the first gives 2(y + 1) + 3y = 12, which simplifies to 5y + 2 = 12, yielding y = 2. Then x = 2 + 1 = 3. The requested sum is x + y = 3 + 2 = 5.
2According to the polynomial remainder theorem, what is the remainder when P(x) = 2x^3 - 3x^2 + 4x - 5 is divided by (x - 2)?
A.3
B.7
C.11
D.15
Explanation: By the polynomial remainder theorem, the remainder upon division by (x - 2) is equal to P(2). Evaluating the polynomial: P(2) = 2(2)^3 - 3(2)^2 + 4(2) - 5 = 2(8) - 3(4) + 8 - 5 = 16 - 12 + 8 - 5 = 7.
3What is the complete solution set to the rational inequality (x - 3) / (x + 2) <= 0?
A.(-2, 3]
B.[-2, 3]
C.(-infinity, -2) U [3, infinity)
D.[-2, 3)
Explanation: The critical points where the numerator and denominator vanish are x = 3 and x = -2. Testing the sign across intervals shows that the quotient is negative for -2 < x < 3 and zero at x = 3. Since x = -2 makes the denominator zero, it must be excluded, giving the interval (-2, 3].
4Simplify the expression: (8^(2/3) * 4^(3/2)) / 2^4.
A.1
B.2
C.4
D.8
Explanation: Convert each term to base 2: 8^(2/3) = (2^3)^(2/3) = 2^2 = 4, and 4^(3/2) = (2^2)^(3/2) = 2^3 = 8. The numerator is 4 * 8 = 32 = 2^5. Dividing by the denominator 2^4 yields 2^(5 - 4) = 2^1 = 2.
5Solve the logarithmic equation for real x: log_2(x) + log_2(x - 2) = 3.
A.x = 4
B.x = 2 and x = 4
C.x = -2 and x = 4
D.x = 8
Explanation: Combining the logarithms using the product property gives log_2(x(x - 2)) = 3. Exponentiating both sides yields x(x - 2) = 2^3 = 8, leading to x^2 - 2x - 8 = 0, which factors as (x - 4)(x + 2) = 0. The domain requires x > 2 for both logarithms to be defined, discarding x = -2 and leaving x = 4 as the only valid solution.
6If log_a(b) = 3, what is the exact value of log_b(a^2 * b^3)?
A.5/3
B.8/3
C.11/3
D.5
Explanation: Using logarithm rules, log_b(a^2 * b^3) = log_b(a^2) + log_b(b^3) = 2 log_b(a) + 3 log_b(b). Since log_a(b) = 3, the change-of-base reciprocal rule gives log_b(a) = 1 / log_a(b) = 1/3. Therefore, the expression evaluates to 2(1/3) + 3(1) = 2/3 + 3 = 11/3.
7What is the natural domain of the real-valued function f(x) = sqrt(4 - x^2)?
A.(-infinity, -2] U [2, infinity)
B.[-2, 2]
C.(-2, 2)
D.[0, 2]
Explanation: For a real square root to exist, the radicand must be non-negative: 4 - x^2 >= 0, which is equivalent to x^2 <= 4. Taking the square root gives |x| <= 2, meaning -2 <= x <= 2. Hence, the domain is the closed interval [-2, 2].
8Given the invertible function f(x) = (2x + 1) / (x - 3) for x != 3, find its inverse function f^(-1)(x).
A.f^(-1)(x) = (3x + 1) / (x - 2)
B.f^(-1)(x) = (x - 3) / (2x + 1)
C.f^(-1)(x) = (2x - 1) / (x + 3)
D.f^(-1)(x) = (3x - 1) / (x + 2)
Explanation: Set y = (2x + 1)/(x - 3) and solve for x: y(x - 3) = 2x + 1, expanding to yx - 3y = 2x + 1. Rearranging terms gives yx - 2x = 3y + 1, so x(y - 2) = 3y + 1, which yields x = (3y + 1)/(y - 2). Swapping variables gives f^(-1)(x) = (3x + 1)/(x - 2).
9If sin(theta) = 3/5 and theta lies in the first quadrant, what is the exact value of cos(2*theta)?
A.7/25
B.24/25
C.-7/25
D.16/25
Explanation: Using the double-angle formula cos(2*theta) = 1 - 2*sin^2(theta), substitute sin(theta) = 3/5 to obtain 1 - 2*(9/25) = 1 - 18/25 = 7/25.
10For 0 <= x < 2*pi, how many distinct real solutions exist for the equation 2*cos^2(x) - cos(x) - 1 = 0?
A.2
B.3
C.4
D.1
Explanation: Factoring the quadratic in cos(x) gives (2*cos(x) + 1)(cos(x) - 1) = 0. This gives two cases: cos(x) = 1 yields x = 0 (1 solution on [0, 2*pi)), and cos(x) = -1/2 yields x = 2*pi/3 and x = 4*pi/3 (2 solutions). Summing these produces exactly 3 distinct solutions.

About the PoliTo TIL-I Exam

The TIL-I (Test in Laib – Ingegneria) is the mandatory entrance examination for undergraduate engineering degree programmes (Corsi di Laurea in Ingegneria) at Politecnico di Torino. Administered as an in-person, computer-based test in the university's LAIB computer laboratories, the official exam consists of 42 five-option multiple-choice questions delivered in 90 minutes across four timed sections: Mathematics (16 questions, 36 min), Reading Comprehension and Logic (10 questions, 20 min), Physics (10 questions, 22 min), and Basic Technical Sciences (6 questions, 12 min). Scoring applies +1 point for correct answers, -0.25 points for incorrect answers, and 0 for unattempted questions. This question bank is an independent practice tool developed by OpenExamPrep featuring 100 high-yield questions with detailed explanations. It is an English-language study adaptation designed to strengthen theoretical mastery and problem-solving speed, and is not affiliated with or endorsed by Politecnico di Torino.

Exam sponsor: Politecnico di Torino. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

42 multiple-choice questions delivered in 90 minutes across 4 timed sections: Mathematics (16 questions, 36 min), Reading Comprehension and Logic (10 questions, 20 min), Physics (10 questions, 22 min), and Basic Technical Sciences (6 questions, 12 min). Scoring: +1 correct, -0.25 wrong, 0 blank.

Time Limit

90 minutes (Mathematics: 36 min, Reading and Logic: 20 min, Physics: 22 min, Basic Technical Sciences: 12 min)

Passing Score

Scoring is +1/-0.25/0; admission outcomes follow the current call and ranking

Exam / Certification Fees

€50

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.

38%

Mathematics

Arithmetic, algebra, functions, equations and inequalities, coordinate geometry, trigonometry, limits, basic calculus, and probability/statistics

24%

Physics

Mechanics, kinematics, dynamics, work and energy, fluid mechanics, thermodynamics, electromagnetism, and optics

24%

Reading Comprehension and Logic

Text analysis, deductive and propositional logic, conditional statements, syllogisms, and critical reasoning

14%

Basic Technical Sciences

Elementary mechanics, electrical circuits, properties of materials, technical representations, and fundamental chemistry

Preparing for the PoliTo TIL-I Exam

What You Need to Know

  • Passing score: Scoring is +1/-0.25/0; admission outcomes follow the current call and ranking
  • Assessment: 42 multiple-choice questions delivered in 90 minutes across 4 timed sections: Mathematics (16 questions, 36 min), Reading Comprehension and Logic (10 questions, 20 min), Physics (10 questions, 22 min), and Basic Technical Sciences (6 questions, 12 min). Scoring: +1 correct, -0.25 wrong, 0 blank.
  • Time limit: 90 minutes (Mathematics: 36 min, Reading and Logic: 20 min, Physics: 22 min, Basic Technical Sciences: 12 min)
  • Exam / certification fees: €50 Official sources

Using Our Practice Resources

  • Work through all 98 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

PoliTo TIL-I: Suggested Study Strategy

1Understand the negative marking formula: with -0.25 points for a wrong answer and +1.0 for a correct answer, only make an educated guess if you can confidently eliminate at least one incorrect option.
2Practice non-calculator calculations: calculators and digital tools are strictly prohibited during the TIL-I, so train mental arithmetic, fraction simplification, and order-of-magnitude estimations.
3Manage section time strictly: each section has an independent countdown timer (e.g., 36 minutes for 16 math questions gives you 2.25 minutes per question), and unused time cannot be carried over to subsequent sections.
4Prioritize mathematics and physics fundamentals: together they account for over 60% of the exam, focusing especially on functions, trigonometric identities, Newtonian kinematics/dynamics, and DC circuit analysis.
5Master logical deductions and conditional equivalences: logic questions can be answered rapidly and with high accuracy once you master truth tables, contrapositives, and syllogistic structures.

Frequently Asked Questions

What is the TIL-I and which degree courses require it?

The TIL-I (Test in Laib – Ingegneria) is the standardized admission exam required for all undergraduate bachelor's degree programmes (Corsi di Laurea Triennale) in Engineering offered by Politecnico di Torino.

How is the official TIL-I structured and timed?

The official TIL-I consists of 42 multiple-choice questions to be completed in 90 minutes across four strictly timed sections: Mathematics (16 questions in 36 minutes), Reading Comprehension and Logic (10 questions in 20 minutes), Physics (10 questions in 22 minutes), and Basic Technical Sciences (6 questions in 12 minutes).

How is the TIL-I scored and what penalty applies to incorrect answers?

Each correct response earns +1 point, unattempted questions receive 0 points, and incorrect responses deduct -0.25 points. The raw score is normalized to a 100-point scale for ranking purposes.

What score guarantees admission to Politecnico di Torino engineering courses?

Politecnico di Torino publishes admission thresholds, ranking rules, and any score-based guarantees in the annual call. Candidates must use the current call rather than relying on a typical or historic 60/100 figure.

Are these practice questions an official Politecnico di Torino exam?

No. This question bank is an independent educational prep resource developed by OpenExamPrep. It is not endorsed, sponsored, or certified by Politecnico di Torino. Questions are presented in English with four options as a high-yield study adaptation to help students build core analytical and technical skills.

Where is the TIL-I taken?

The TIL-I is administered in person on campus in Politecnico di Torino's specialized computer laboratories, known as LAIB (Laboratori di Informatica di Base).