Politecnico di Milano

Technology, creativity and culture

Content details of the Test On Line (TOL) - Engineering


English questions are aimed at verifying comprehension of written English at an elementary level.

Logic, Mathematics and Statistics

  1. Logic: know how to work with sets. Recognise the hypothesis and thesis of a theorem. Recognize whether a given condition is necessary or sufficient. Correct use of expressions with a logical value ("if … then…"; "for each …"; "there is at least one …"; etc.). Analyse texts, identifying possible logical errors. Analyse the logical correctness of an argument. Recognise similarities and differences in various structures.
  2. Arithmetic: represent a natural number in a base other than ten. Perform calculations with fractions. Recognise whether two fractions are equivalent and be able to compare them. Work with inequalities. Perform calculations with powers and roots. Estimate the magnitude of results of numerical methods. Calculate percentages.
  3. Algebra: work with algebraic, rational, fractional, numerical or literal expressions. Transform an expression into another equivalent expression. Know how to add, multiply and factor polynomials. Simplify or transform an equation or inequality into an equivalent form. Solve first degree, second degree, rational and radical algebraic equations and inequalities. Recognise solvability of equations and inequalities in special cases. Solve first and second degree algebraic systems.
  4. Geometry: know how to create elementary geometric constructions. Calculate perimeters, areas and volumes of elementary plane and spatial figures. Geometrically interpret first and second degree algebraic systems. Know the equations of simple geometric loci. Know how to analytically translate simple geometric problems.
  5. Trigonometry: convert measurements of angles from degrees to radians and vice versa. Know the relationships between the elements (sides, angles) of a triangle. Use the main trigonometric formulas to solve simple geometric problems.
  6. Functions: know the graphical shape and main properties of the basic functions (powers, exponentials, logarithms, sine, cosine, etc.), also using information technology graphical display tools. Solve exponential, logarithmic and trigonometric equations and inequalities.
  7. Statistics: know how to solve simple counting problems (permutations, combinations, etc.). Know how to calculate the mean, variance and absolute and relative frequency of a given data set. Know how to interpret frequency diagrams and histograms.

Verbal comprehension

Verbal comprehension questions are designed to assess the ability of analysis and understanding developed in high school. They do not require, therefore, specific preparation in advance. 


  1. Mechanics: scalar and vector magnitudes, international system of measurement; definition of fundamental physical magnitudes (displacement, velocity, acceleration, mass, momentum, force, work, power) and their units of measure; law of inertia, fundamental law of dynamics and action and reaction principle. Motion of masses and projectiles. Newton's universal law of gravitation. Kepler's laws.
  2. Thermodynamics: concepts of temperature, heat, specific heat, expansion of bodies; ideal gas equations of state. First and second law of thermodynamics. Carnot cycle. Absolute temperature. Absolute zero.
  3. Electromagnetism: Electrostatics: Coulomb's law, electrostatic field, capacitors, electrostatic induction. Current intensity, Ohm's law. Magnetostatics: magnetic field, Lorentz force, motion of a charge in a magnetic field, magnetic field generated by a straight wire. Faraday's law of electromagnetic induction and induced currents.
  4. Waves and their propagation: wavelength, frequency and velocity of a wave. Interference phenomena. Optics: refractive index, light reflection, Snell's law.
  5. Structure of matter: basic knowledge on the constituents of the atom and the nucleus. Isotopes. Quantisation of energy. Photons.

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