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Struttura della prova e syllabus

TOLC-B structure

The TOLC-B structure consists of 50 questions divided into 4 sections. The sections are: Basic mathematics, Biology, Physics, Chemistry.
At the end of the TOLC-B there is an English Proficiency Test section with 30 questions.



The result of each TOLC-B, apart from the section English Proficiency Test, is determined by the number of questions answered correctly, incorrectly or unanswered which make up the total score as follows: 1 point for each correct answer, 0 points for each unanswered question and a penalty of 0.25 points for each incorrect answer.
There is no penalty for incorrect answers for the section English Proficiency Test and the score is determined as follows: 1 point for each correct answer and 0 points for each incorrect answer and unanswered question.


TOLC-B syllabus

Basic ​Mathematics section
This module aims to test the student’s overall basic knowledge required for all scientific degree courses, even those that have little mathematics in their program. To answer the questions in this module the basic mathematical knowledge usually studied during the first three or four years in all secondary schools is sufficient. This knowledge is briefly described below, divided into topics, with some considerations related to reciprocal links and to some types of reasoning, procedures and actions.
More than one mathematical concept and term here listed under different subjects may appear in a single question; to understand questions and answers it may also be necessary to refer to different kinds of mathematical knowledge, graphic representations and reasoning and to make careful use of common language. This peculiarity of the questions, which can result difficult even though the mathematical concepts involved are relatively elementary, is the reason for the name of the module. We take this opportunity to observe that it can often be difficult to immediately use student responses to determine specific knowledge deficiencies, as the reasons for a wrong answer can be multiple and go beyond the mere ignorance of a specific concept.

List of topics

  1. Numbers – Prime numbers, decomposition into prime factors. Greatest common divisor and least common multiple. Integer division with remainder. Powers, roots, logarithms. Decimal numbers. Fractions. Percentages. Arithmetic mean.
  2. Algebra – Manipulation of algebraic expressions. The concept of solution and “set of solutions” of an equation, an inequality, a system of equations and/or inequalities. First and second degree equations and inequalities. Linear systems.
  3. Geometry – Most common plane figures and their fundamental properties. Pythagorean theorem. Properties of similar triangles. Sine, cosine and tangent of an angle obtained from the relationship between the sides of a right-angled triangle. Perimeter and area of the most common plane figures. Incidence, parallelism, perpendicularity between straight lines in a plane. Main figures in space (lines, planes, parallelepipeds, prisms, pyramids, cylinders, cones, spheres). Volume of most common solids. Cartesian coordinates in the plane. Line equation from two points. Equation of a line through a point and parallel or perpendicular to a given line. Slope and intersections with the axes of a given straight line. Condition of perpendicularity between two lines. Distance between two points.
  4. Functions, graphs, relations – Basic functions terminology. Injective, surjective, bijective (or biunivocal correspondence) functions. Compound functions, invertible functions and reverse function. Graph of a function. Functions: power, root, absolute value, first and second degree polynomials, 1/x, and their graphs. Exponential and logarithmic functions base 2 and 10 and their graphs. Sine x and cosine x functions and their graphs. Simple equations and inequalities built with these functions.
  5. Combinatorial and probability –Representation and counting of various types of sets. Calculation of the probability of an event in a simple situation.
  6. Logic and language – In a certain situation and given certain premises, determine whether a statement is true or false (deduction). Deny an assertion. Interpret the terms “necessary condition”, “sufficient condition” and “necessary and sufficient condition”.
  7. Modeling, understanding, representation, problem solving – Formulate a situation or problem in mathematical terms. Understand texts that use different languages and representations. Represent data, relationships and functions with formulas, tables, bar charts, and other graphical modes. Solve a problem by adopting simple strategies, combining different knowledge and skills, making logical deductions and simple calculations.

Please note: All questions contain text with numbers, formulas and figures that the student should be familiar with.
The terms and symbols used vary between those most frequently used in secondary school and first year university lessons. In particular, you can find elementary notations from the language of sets, such as element, belong, subset, union, intersection, difference, complement, Cartesian product as well as expressions such as for each, all, none, some, at least one.
Notably, it may be necessary to switch from describing a situation in words (for example, a relation between quantities) to its algebraic formalization or to its graphic representation, and vice versa. For some questions this kind of ability may be more important than the knowledge of the mathematical concepts involved.
For all questions, with varying degrees of complexity, you will need to make logical deductions (for example, you may be asked to determine whether a certain statement, or its negation, is a logical consequence of other statements).
No calculators of any kind are allowed during the test. All required calculations can be done mentally, or with pen and paper. Some questions are formulated in such a way that the ability to make simple calculations quickly is very useful, and sometimes essential, for their solution.

Biology section
List of topics

  1. Biological molecules – The importance of water in biology. Knowledge of the chemical composition of organisms: carbohydrates, lipids, proteins and nucleic acids. Polymers and monomers. Structure and function of macromolecules.
  • Water and its characteristics.
  • Hydrophilic and hydrophobic substances.
  • Chemical composition, structure and function of the main biological molecules: carbohydrates, lipids, amino acids and proteins, nucleotides and nucleic acids.
  1. The organization of cells– The fundamental differences between prokaryotic and eukaryotic cells; the structure and basic functions of the plasma membrane and the main organelles of the eukaryotic cell; identification through schematic drawings. The fundamental differences between animal cells and plant cells. Theories explaining the origin of the eukaryotic cell, with particular reference to endosymbiotic theory for mitochondria and chloroplasts.
  • Organization of the prokaryotic cells.
  • Organization of the eukaryotic cells.
  • Difference between animal cells and plant cells.
  • Structure and function of: plasma membrane, cell wall, nucleus, cytoplasm, mitochondria, chloroplasts, ribosomes, endoplasmic reticulum, Golgi apparat, lysosomes, vacuoles, cytoskeleton.
  • Evolution of the eukaryotic cells
  1. Fundamentals of genetics – Transmission and expression of hereditary characters in prokaryotic and eukaryotic cells, in individuals and populations. The structure of the genetic material and its levels of organization in microbial, plant and animal systems, including humans. Regulation of gene expression and mechanisms of mutagenesis.
  • Chromosomes.
  • Mendelian genetics.
  • Conservation of genetic information and its expression.
  • Genetic code.
  • DNA and genes.
  • Transcription and translation.
  1. Cell basis of reproduction and heredity. Reproduction and development. Vital cycles.
    – Cell division in prokaryotes. Cell division in unicellular and multicellular eukaryotic organisms. Mitosis and cell duplication. Meiosis and sexual reproduction. Gametes and zygote formation. The main stages of embryonic development. Differences in the life cycle of animals (diplontic) and plants (hapodiplontic).
  • Cell division. Mitosis and meiosis. Cytodieresis
  • Gametes, fertilization and some knowledge on embryonic development.
  • Reproduction and life cycles in animals.
  • Reproduction and life cycles in plants.
  1. Anatomy and physiology of animals and humans – Hierarchical organization of multicellular organisms: cells, tissues, organs and systems.
  • Structure and functions of the main tissues. Structure of body systems and their fundamental functions in animals and humans. Main structure and functions of animal tissues (epithelial, connective, muscular and nervous)
  • General organization of human digestive, respiratory, circulatory, skeletal muscle, excretory, reproductive, immune, nervous and endocrine systems. The sense organs.
  • Vital functions in animals and humans. Nutrition and digestion. Respiration. Circulation. Excretion. Nervous and chemical communication. Protection, support and movement. Immunity. Reproduction.
  1. Plant anatomy and physiology– Basic knowledge of the structure and function of the main plant tissues and organs. Basic knowledge of photosynthesis, to convert light energy into chemical energy for the production of organic molecules. The importance of plant organisms in ecosystems for the nutrition of other organisms as well as for the production of oxygen and the consumption of carbon dioxide that occur during the photosynthetic process. The importance of roots for land plants, their help in anchoring them to the ground and means to absorb water and mineral nutrients.
  • Structure and function of plant tissues and organs: leaf, root, stem, flower. Fruits and seeds.
  • Growth.
  • Photosynthesis.
  • Mineral nutrition.
  • Water absorption and transpiration.
  1. Biodiversity, classification, evolution – A general outline of the evolution of living beings and their classification into domains and kingdoms. Recognizing biodiversity: general characteristics of bacteria, protists, fungi, plants, animals. Viruses. Classification of biodiversity: general concepts of classification and phylogenesis, homology and analogy. The mechanisms of evolution: genetic variability, natural selection, adaptation, speciation and extinction.
  • Bacteria
  • Viruses
  • Protists
  • Fungi
  • General characteristics of the main plant phyla (mosses, ferns, gymnosperms, angiosperms)
  • General characteristics of the main animal phyla (Porifera, Cnidaria, Platyhelminthes, Nematoda, Mollusca, Annelida, Arthropoda, Echinodermata, Chordata)
  • Classification and phylogenesis, homology and analogy.
  • Evolution: genetic variability, natural selection, adaptation, speciation, extinction.
  1. Bioenergetics – The main metabolic processes through which cells convert, store, use and exchange energy. A general outline of photosynthesis, aerobic and anaerobic respiration, glycolysis and fermentation. Understanding of the differences between catabolism and anabolism. Definitions of autotrophic and heterotrophic metabolism. Basic knowledge on enzymatic catalysis. Basic knowledge on human nutrition – nutrients and other substances in foods that play a role in human nourishment, growth, reproduction, and health.
  • Energy flow and biological significance of photosynthesis, aerobic and anaerobic respiration, glycolysis, fermentation.
  • Catabolism and anabolism.
  • Autotrophic and heterotrophic metabolism.
  • Enzymatic catalysis.
  • Some knowledge of nutrition in humans
  1. Ecology – Basic knowledge of a) interactions between organisms and between organisms and the environment, at different levels of biological hierarchy: individuals, populations (groups of organisms of the same species that colonize a given territory), communities (structured sets of populations) and ecosystems (communities with their physical and chemical environment), (b) energy flows and material cycles that allow ecosystem functions to be maintained, (c) the factors determining the abundance and distribution of organisms and biodiversity.
  • Individuals, populations, communities, and ecosystems
  • Trophic chains
  • Habitat and ecological niche
  • Biotic interactions
  1. Biotechnology– Basic knowledge of techniques used for the production of goods and services, whose applications range from the pharmaceutical to the food industry and may also have important applications in the medical field.
  • Genetic engineering, GMO
  • Animal and plant biotechnology
  • Microbial biotechnology

Physics section
The syllabus of the Physics module is deliberately limited to what can be found in high school texts and the topics listed do not require additional study. On the other hand, those relating to the modelling of physical phenomena are considered as indispensable mathematical skills and, in particular:

  • The use of graphical representations and functional models related at least to direct and inverse proportionality, linear dependence, increasing and decreasing quadratic proportionality, sinusoidal, exponential and logarithmic dependence
  • Recognising proportional relationships between the quantities used in a law, both in numerical and symbolic exercises

It is also essential to know how to use: the units of measurement of the International System, including prefixes, and the practical units most commonly used in science, scientific notation, the concept of order of magnitude, vector calculation limited to the composition and decomposition of vectors, scalar and vector product.

List of topics

  1. Kinematics and dynamics of the material point– Description of motion: velocity and acceleration, graph of time law, angular and peripheral velocity, angular acceleration, simple harmonic motion. Rectilinear motion, acceleration of gravity, free fall of bodies. Two-dimensional curvilinear motion, for example motion of a projectile and uniform circular motion, acceleration and centripetal force. Galilean principle of relativity and fictitious force: velocity and acceleration in reference frames in uniform or accelerated relative motion. The three laws of dynamics. Equilibrium of an extended rigid body (resulting from forces and moments of forces) with applications: inclined plane, lever, pulley, winch. Hooke’s law. Forces of friction. Barycentre motion of a rigid body. Momentum and impulse, Newton’s second law as a change in momentum. Work. Power. Kinetic energy. Conservative forces. Gravitational potential energy, elastic potential energy. Conservation laws. Elastic and inelastic collisions (special cases: central collision, collision against a rigid wall). Universal gravitation, gravitational potential energy and force, acceleration of gravity on a planet, motion of satellites and planets.
  2. Fluid mechanics– Quantities: density, pressure (in liquids and gases), flux, flow rate. Fluid statics: Pascal’s principle, Stevin’s law, Archimedes’ principle. Continuity equation. Torricelli’s principle, Bernoulli’s equation.
  3. Kinetic theory of gases and thermodynamics –Perfect gas law. Perfect gas equation of state Pressure and internal energy of a perfect monatomic gas. Absolute temperature. Heat, specific heat and heat capacity. Changes of state and latent heat. First law of thermodynamics. Efficiency of a thermal machine (Carnot cycle), reversible and irreversible cycles.
  4. Electrostatica and electric currents–Electrical charge. Coulomb’s law and electric field. Electric field flow and Gauss’s theorem (e.g. point charge, sphere charge and uniformly charged plane). Motion of charged particles in uniform electric fields. Conductors and electrostatic induction. Electrostatic potential, equipotential surfaces, potential difference. Potential energy for a uniform field and two point charges. Charge distribution, field and potential for a conductor in electrostatic equilibrium. Condenser capacity, equivalent capacity of condensers in series and in parallel. Electrostatic energy of a uniform field. Electric current, motion of charges, Ohm’s laws, electrical resistance, equivalent resistance for resistors in series and in parallel. Electromotive force and generator internal resistance. Joule effect.
  5. Oscillations, waves and optics– Simple harmonic motion: period, pulse, amplitude. Waves: amplitude, frequency, wavelength, velocity. Superposition principle and interference of harmonic waves. Standing waves. Energy transport: energy density and intensity of a wave, attenuation with the distance from a point source for a spherical wave. Interference. Diffraction. Reflection and refraction, Snell’s law and refractive index, total internal reflection. Plane and spherical mirrors: image formation and conjugated points. Thin lenses: image formation and conjugated points. Chromatic dispersion.
  6. Magnetism –Magnetic dipole, permanent magnets. Lorentz force: motion of point charges in uniform magnetic fields. Ampère’s circuital law, Biot-Savart law. Magnetic field of a wire and in an undefined solenoid. Force exerted by a magnetic field on an electric current, forces between current carrying wires (straight and parallel).
  7. Electromagnetic field –Faraday-Neumann-Lenz law. Electromagnetic waves. The electromagnetic spectrum and the nature of light.
  8. Modern physics –The structure of the atom and the nucleus, radioactive decay. Special relativity: constant of C, length contraction and time expansion, relativistic energy, conservation law. Photon, energy and frequency, photoelectric effect. Wave-particle dualism, Young’s double-slit experiment. Uncertainty principle.

Biology section
List of topics

  1. Macroscopic properties of matter – The macroscopic properties of matter are the observable properties of matter itself. Understanding the behaviour of materials is useful for interpreting situations you may encounter in everyday life. It is also important to understand the difference between physical and chemical changes in materials.
  • State of matter and physical changes.
  • Particle model of matter on a macroscopic scale.
  • Macroscopic properties of gases, liquids and solids (kinetic theory, fixed points, phase transitions).
  • Homogeneous and heterogeneous mixtures (suspensions, colloids, dispersions).
  • Separation of mixtures.
  • Chemical transformations.
  • Fundamental laws in chemistry (Lavoisier, Proust, Gay-Lussac, Avogadro).
  1. Microscopic properties of matter and composition of substances –Understanding the particle model of matter is important to explain the properties of materials, their interactions and their uses. The structure of the matter can be defined through particles called atoms composed of protons, neutrons and electrons. The study of the atomic structure, the electron configuration and the theories of binding allows a better understanding of the properties of metals, ionic substances, covalent solid compounds and covalent molecular structures.
  • Particle model of matter on a macroscopic scale.
  • Simple substances, compounds and ions.
  • The structure of the atom. Atomic mass and relative atomic mass (Ar), relative molecular mass (Mr).
  • Types of chemical bond: ionic, covalent and metallic.
  • Lewis structures (electron dot structures).
  • Intermolecular forces and hydrogen bonds
  • Polarity of the chemical bond.
  • Oxidation number and atomic valence.
  • Molecular geometry (VSEPR theory) and hybridization.
  1. Chemical reactions and stoichiometry – It is very important to acquire the ability to read, write and interpret reaction patterns correctly, as well as being able to work with the necessary units of measurement to determine the quantities of substances used in a chemical process or transformation. Stoichiometry calculates the proportions between atoms in molecules and between reagents and the products in chemical reactions. This information is used to balance chemical reaction patterns. The study of how the fundamental laws of chemistry were formulated helps to understand and apply the particle model of matter on a microscopic scale.
  • Balancing of chemical reactions.
  • Definition of the concept of mole and the Avogadro constant.
  • Units of measurement for concentration (mol dm-3, g dm-3, percentage composition) and their calculations
  • Mass to mole conversions.
  • Concepts of limiting reagent and theoretical yield.
  • Relationship between the number of moles (chemical amount) and mass in the reaction patterns.
  1. Periodic trends and atomic structure –Many properties of simple substances and atoms show a periodic trend. The electronic configuration of the atom of an element determines both its position in the periodic table and its reactivity to the other atoms of the table. Periodic trends can be used to predict atomic properties.
  • Periods and groups.
  • Atomic models.
  • Quantum numbers.
  • Electronic configuration of atoms: Aufbau principle and the Pauli exclusion principle.
  1. Compounds, properties and nomenclature of compounds. Solutions and Solution Properties – Acquiring the correct terminology and knowing how to classify compounds and ions is essential to the understand and discuss chemistry. Despite this premise, this knowledge can be achieved step by step while learning the basic chemical principles and understanding the various chemical reactions.
  • Formulas of substances and compounds.
  • Nomenclature of substances and compounds (IUPAC and traditional).
  • Properties of the main inorganic compounds (carbonates, sulphates, oxides, hydroxides):
  • Chemical properties of metals.
  • Electrolytes.
  • Properties of solutions, solubility.
  • Colligative properties of solutions.
  1. Thermodynamics and kinetics –Particle motions explain the properties of gases. The motion of atoms and molecules, as well as kinetics, allows a connection with chemical balances. Relationship between matter and energy. In a chemical reaction the energy can be absorbed or released. The rate of a chemical reactions of atoms and molecules depends on the frequency with which they collide. The number of these impacts is a function of the concentration, temperature and pressure of the reactive species. Catalysts can be used to change the rate of a chemical reaction. Under certain conditions, a reaction can reach equilibrium. To define the properties of covalent substances it is important to have understood the concepts of intermolecular forces, hydrogen bond, dipole-dipole interaction and dispersion forces.
  • Ideal gas laws (Boyle, Charles, Gay Lussac).
  • Partial pressure.
  • Laws of thermodynamics: internal energy, enthalpy, entropy and Gibbs free energy.
  • Exothermic and endothermic reactions.
  • Dynamic chemical balance (equilibrium constant and reaction quotient).
  • Reaction rate: factors that affect the reaction rate.
  • Activation energy and catalysis.
  1. Acids and Bases –Acids and bases have particular characteristics and are chemical products that can easily be found in any home. Acid-base theory and the use of indicators can be used to understand the acidic and basic properties of saline solutions, the balances in solution, as well as providing useful links to practical applications.
  • Definitions of acids and bases.
  • Common acids and bases.
  • Strength of acids and bases.
  • pH calculation.
  • Neutralization reactions and salt formation.
  • Acid-base reactions and use of pH indicators.
  • Buffer solutions
  1. Oxidations and reductions – reduction oxidations (redox) are reactions in which the atoms change their oxidation state. These reactions are characterised by the transfer of electrons between chemical species. These reactions play an important role in many phenomena of everyday life.
  • Redox reactions and interpretive models.
  • Identification of the oxidant and the reducing agent in a simple chemical redox transformation or in a reaction pattern.
  • Balancing simple redox reaction patterns.
  • Galvanic and electrolytic cells.
  • Scale of redox potentials.
  1. Organic chemistry – Organic chemistry studies carbon compounds other than carbon monoxide, carbon dioxide, and carbonates. Hydrocarbons, compounds containing only carbon and hydrogen, undergo specific reactions such as substitution reaction, combustion and addition reaction. Many organic compounds are characterised by the presence of functional groups. The student should be able to identify these functional groups, to assign them the correct nomenclature and the type of reactivity.
  • Origin and characteristics of hydrocarbons.
  • Carbon hybridization.
  • Organic compounds: structure and nomenclature. Isomerism, relationship between structure and property.
  • Alkanes, alkenes, alkynes, cycloalkanes.
  • Benzene and aromatic compounds.
  • Alcohols, aldehydes, ketones and carboxylic acids.
  • Nucleophiles and electrophiles: substitution and addition reactions.
  • Combustion reactions.
  • Oxidation and reduction reactions.
  1. Applied chemistry –Scientific measurements and their reliability are essential in the study of chemical processes. Understanding chemical processes can be used to describe, explain and predict biological, environmental and industrial processes.
  • Measurements and units of measurement.
  • Uncertainties in experimental measures, average and errors.
  • Chemical transformations in daily life.
  • Correct reading of commercial product labels (beverages, food, chemicals).
  • Main environmental issues (acid rain, greenhouse effect, smog…)
  • Safety regulations.


English section

Depending on the result obtained in the test, the grid below shows the initial preparation level and how to improve your results, if necessary.

≤ 6 Take a beginner English course (A1*)
 7 – 16 Take a first level English course (A2*)
 17 – 23 Take an intermediate English course (B1*)
 24 – 30 Take the B1* level English exam with no need to take a course