The TOL consists of two parts:
- TENG (Test of English): to test your knowledge of the English language
- TEST: to test your knowledge of Reasoning, Mathematics and Statistics; Verbal Comprehension; Physics.
The questions are formulated by taking into account upper secondary schools’ ministerial curricula.
The TOL, held in Italian language, is carried out remotely and consists of 65 multiple choice questions, to be answered in 1 hour and 40 minutes (100 minutes). The subjects covered by the entrance test are:
Reasoning, mathematics and statistics: 25 questions in 65 minutes
Reasoning: Ability to work with sets. Recognise hypotheses and theses of a theorem. Recognise whether a given condition is necessary or sufficient. Properly use locutions of the Italian language with logical value (“se… allora…”;“per ogni…”; “esiste almeno un…”; etc.). Analyse the correctness of an inference by identifying possible errors in reasoning. Know how to negate a proposition and understand an argumentum ad absurdum.
Arithmetic: Break up an integer into its prime factors. Represent an integer in a base other than decimal. Know the difference between rational and irrational numbers. Perform calculations with recurring decimals and fractions. Recognise when two fractions are equal and be able to compare them. Deal with inequalities. Know the properties and be able to perform calculations with powers and roots. Know how to use the standard rounding rules on decimal numbers and make estimates of the results of numerical calculations. Calculate percentages.
Algebra: Work with algebraic or rational fractional, numerical or literal expressions. Transform an expression into an equation. Know how to add, multiply, divide, factor polynomials. Find the greatest common divisor and the least common multiple of polynomials. Know and be able to use the relation between factoring a polynomial and finding its roots. Simplify or transform an equation or inequality into an equivalent one. Solve linear algebraic equations and inequalities, quadratic equations, rational functions and fun ctions with radicals. Recognise how to solve equations and inequalities in particular cases. Solve linear and quadratic functions. Know how to work with absolute values of numbers or algebraic expressions.
Geometry: Know the fundamental concepts of synthetic geometry of the plane and space (parallelism, orthogonality, similarity, polygons and polyhedra, circumference and circle, sphere, etc.). Know how to draw basic geometric constructions. Calculate perimeters, areas, surfaces and volumes of basic shapes in the plane and space. Know the fundamentals of analytical geometry of the plane and space. Geometrically interpret linear and quadratic algebraic equations and functions. Know the equations or inequalities that define simple geometric loci (circumference, circle, ellipse, parabola, hyperbola, sphere, etc.). Know how to analytically interpret simple geometric properties and problems.
Trigonometry: Convert angle measurements from degrees to radians and vice versa. Know the relations between the elements (sides, angles) of a triangle. Know and be able to use the main trigonometric formulae to solve simple geometric problems.
Functions: Know the definition, graphical progression and main properties of basic functions (powers, exponentials, logarithms, sine, cosine, etc.). Solve exponential, logarithmic, trigonometric equations and inequalities.
Statistics: Solve simple counting problems (permutations, combinations, etc.) and calculate probabilities through counting. Calculate mean, mode, median, variance, standard deviation, relative and absolute frequencies of a given data set. Know how to convert percentages into relative frequencies, and vice versa. Know how to interpret frequency diagrams and histograms.
Verbal comprehension: 5 questions in 10 minutes
The questions are intended to ascertain the ability to understand a text, i.e., to be able to extract from it the opinions or information proposed by the author, regardless of any prior knowledge the student has on the subject matter. No specific preparation is therefore necessary.
Physics: 5 questions in 10 minutes
Mechanics: Scalar and vector quantities. The International System of Units Definition of fundamental physical quantities (displacement, velocity, acceleration, mass, momentum, force, work and power) and their units of measurement. Law of Inertia Fundamental Principle of Dynamics and Principle of Action and Reaction. Falling bodies and projectile motion Elastic force: oscillatory motion. Kinetic and potential energy; conservation of mechanical energy. Newton's law of universal gravitation. Kepler's laws. Fluids: pressure and Archimedes' principle.
Thermodynamics: Temperature, heat, specific heat, latent heat. Thermal balance. Ideal gases and equation of state. First and second laws of thermodynamics. Thermodynamic cycles; efficiency of a thermal machine. Absolute temperature. Absolute zero.
Electromagnetism: Electrostatics: Coulomb's law, electrostatic field, electric potential. Conductors in an electrostatic field: electrostatic induction, capacitors. Current intensity, Ohm's law. Magnetostatics: magnetic field, Lorentz force; magnetic field generated by a straight wire. Motion of charged particles in a magnetic field and an electric field.
Waves: Wavelength, frequency, speed of a wave. Intensity associated with a wave. Interference phenomena. Diffraction (basics). Reflection and refraction of waves.
Fundamentals of the structure of matter: the components of the atom Atomic structure: energy levels, quantum numbers, orbitals. Quantisation of energy. Photons.
English: 30 questions in 15 minutes
The questions are designed to test comprehension of written texts mainly in everyday language such as descriptions of events, feelings, desires.
Politecnico di Milano requires students to be proficient in English. You must take the TENG English test even if you already hold external certificates proving your English language skills. If you do not pass the TENG, i.e. if you answer correctly fewer than 24 questions out of 30, you will be assigned an OFA, an Additional Training Obligation (Obbligo Formativo Aggiuntivo) which will restrict your university career and that will have to be fulfiled after the enrolment.
How to prepare
The Politest (only in Italian)
To prepare for the Engineering TOL test, you can download the "Politest - The Engineering Test at Politecnico di Milano", an exercise book written by our lecturers and designed specifically to prepare prepare for the TOL:
Mathematics
Full volume
Physics
Full volume
Texts, questions and solutions 1 - 5
Texts, questions and solutions 6 - 10
Texts, questions and solutions 11 - 15
Texts, questions and solutions 16 - 20
Verbal comprehension
Full volume
Texts, questions and solutions1 - 5
Texts, questions and solutions 6 - 10
Texts, questions and solutions 11 - 15
Texts, questions and solutions 16 - 20
You can also purchase it at Poliprint, at the Milano Leonardo Campus (Via Bonardi, 9, Building 12, floor -1. Opening times: 08:30-18:30 Monday to Friday) and at Offical Merchandise and PoliPrint at the Milano Bovisa Campus (Via Candiani, 72, building B4, mezzanine floor. Opening times: 09:00-18:30 Monday to Friday).
DOL - Online Demo
When you take the test, you will have set times to answer the questions in the various sections. You can familiarise yourself with this format by practising the DOL (Demo Online), a shortened version of the TOL (Test Online).
MOOCS
MOOCs (Massive Open Online Courses) are free online courses, open to all and free to attend.
These courses are particularly useful to help you to consolidate the basic knowledge that will be assessed during the test.
To participate, simply register on the www.pok.polimi.it portal.
Each module includes lectures, tutorials and self-assessment quizzes.
MOOCs are aimed at different kinds of users. Those most useful for TOL preparation are:
- Introduction to university maths: Pre-Calculus (courses in Italian)
- Introduction to Experimental Physics: mechanics, thermodynamics (courses in Italian)
- Introduction to Experimental Physics: electromagnetism, optics, modern physics (courses in Italian)
Self-assessment tests
You can test yourself with two self-assessment tests which include questions on English, Mathematical Reasoning and Statistics, Verbal Comprehension and Physics.
In the respective excel file where you enter your answers: you can immediately see if you have answered correctly or not; at the end, the spreadsheet will give you your score, as if you had actually taken the test.
SELF-ASSESSMENT TEST 1
Self-assessment test n. 1
Score calculation - Self-assessment test n. 1
SELF-ASSESSMENT TEST 2
Self-assessment test n. 2
Score calculation - Self-assessment test n. 2
What to do beforethe test TOL - Demo TOL
To avoid technical problems when taking the test, we recommend you do a technical test with the test simulations that can be found in the REMOTE DEMO TOL section in your Online Services.
The demo will allow you to check that your internet connection is stable, that your computer for taking the test and your smart phone/tablet for accessing the virtual classroom are suitable for the test and to download and install the SEB software correctly.
You can repeat the Demo TOL remotely several times after you have registered for the test and only 7 days before the date of the test you are registered for.
On the days and at the times when the tests take place, you will not be able to use the Demo.
Check the calendar (in Italian only) of dates when you can take the remote TOL Demo with support.
The remote Demo TOL is available from Monday to Sunday from 14:00 to 23:59.
Remote Demo TOL with support is available Monday - Friday 14:00 to 18:00.
By trying out the remote Demo TOL with support, you can ask for help via chat for any problems you encounter.
Download the Remote test guide. (in Italian only). The guide 2025 will be available soon.