# Struttura della prova e syllabus

**TOLC-S structure**

The **TOLC-S** structure consists of **50** questions divided into 4 sections. The sections are: **Basic mathematics**, **Logic and problems**, **Reading comprehension** and **Basic science**.

At the end of the TOLC-S there is an **English Proficiency Test section with 30 questions**.

SECIONS |
NUMBER OF QUESTIONS |
TIME ALLOTTED |

BASIC MATHEMATICS | 20 QUESTIONS | 50 MINUTES |

LOGIC AND PROBLEMS | 10 QUESTIONS | 20 MINUTES |

READING COMPREHENSION | 10 QUESTIONS | 20 MINUTES |

BASIC SCIENCE | 10 QUESTIONS | 20 MINUTES |

TOTAL |
50 QUESTIONS |
110 MINUTES |

ENGLISH | 30 QUESTIONS | 15 MINUTES |

TOTAL INCLUDING ENGLISH |
80 QUESTIONS |
125 MINUTES |

The result of each TOLC-S, 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.

The **Reading Comprehension section** is composed of a text and 10 questions. The first 5 questions are related to the text itself, while each of the other 5 questions is independent and does not refer to other texts.

TOLC-S syllabus

**Basic Mathematics section**

The *Basic Mathematics* 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. Please find below a summary of the required knowledge divided into topics. A single question may contain concepts that in the syllabus are mentioned in different topics. In order to understand a question, it may be necessary to use different mathematical skills at the same time, as well as graphic representations and logic of various kinds. In particular, 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. 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 and functions, and terms such as: *element, belong, subset, union, intersection, for each, all, none, some, at least one, if… then*.

**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.

**Algebra** – Manipulation of algebraic expressions. 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.

**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 passing 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.

**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 and their graphs. Sine x and cosine x functions and their graphs. Simple equations and inequalities built with these functions.

**Combinatorial and probability** – Representation and counting of finite sets. Calculation of the probability of an event in a simple situation.

**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”.

**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.

**Logic and problems section****
**The section contains problems that require to connect data and knowledge in non-immediate ways and to make logical deductions of some complexity. For example, you may be asked to determine whether a certain statement, or its negation, is a logical consequence of other statements, in which the following terms are used:

*if, then, all, none, some, at least one*. This type of question can be placed in a mathematical context or in a context of common daily knowledge. The mathematical knowledge covered in the first four years of secondary schools of all kinds is sufficient to answer these questions.

**Reading comprehension section****
**The section assesses the ability to understand short texts, in particular on scientific subjects. The questions and the choice of answers may contain tables, charts and simple mathematical formulas. Depending on the context, basic scientific and mathematical terms may be encountered in the questions.

To answer the questions it is necessary to understand the logical and syntactic structure of the question and the choice of answers, to use natural language, mathematical language and different types of graphic representations, translating from one language to another.

**Basic science section**

The section aims to test the ability to do various types of reasoning in the science field, combining fundamental physical, chemical, geological and astronomical knowledge and using different languages and representations. In addition, knowledge of the main units of measurement of the International System is required.

**Mechanics**– Vector addition and decomposition. Balances of forces. Uniform linear motion and uniform circular motion. Time law of motion, speed, acceleration. Newton’s law of gravitational force. Newton’s law*F=ma*. Mass and weight. Gravitational acceleration. Falling bodies and uniformly accelerated motion. Kinetic energy, work, power. Conservation of energy. Potential energy. Simple harmonic motion: period, pulsatance and amplitude. Density, pressure. Laws of fluid statics. Archimedes’ principle

**Waves**– Amplitude, frequency, wavelength, velocity; reflection and refraction; attenuation of intensity with distance.

**Thermodynamics**– Heat, thermal equilibrium, temperature, heat capacity. Ideal gas laws. Change of status.

**Electricity and magnetism**– Electric charge. Coulomb’s law and electric field. Motion of charged particles in uniform electric fields. Conductors and electrostatic induction. Electrostatic potential, equipotential surfaces, potential difference. Qualitative charge distribution, field and potential for a conductor in electrostatic equilibrium. Electric current, Ohm’s law, electrical resistance, equivalent resistance for resistors in series and parallel. Magnetic field generated by a magnet and a straight wire through which flows current.- CHEMISTRY

**Macroscopic and microscopic properties of matter. Properties and nomenclature of compounds and solutions***–*States of matter and physical transformations. The particle model of matter. Macroscopic properties of liquids, solids and gases. Homogeneous and heterogeneous mixtures. Properties of solutions. Chemical transformations. Fundamental laws of chemistry. Simple substances, compounds and ions. The structure of the atom. Properties and formulas of the principal inorganic compounds. Periodic properties. Atomic models.

**Chemical reactions and stoichiometry. Acids and bases. Oxidations and reductions**– Concentration unit of measurement (mol/dm3, g/dm3), percentage composition. Definition of acids and bases and acid-base reactions. Redox reactions and interpretive models. Balancing of chemical reactions. Origin and characteristics of hydrocarbons. Structure and nomenclature of the main organic compounds.

**Thermodynamics, kinetics, chemical bond and applied chemistry**– Types of chemical bonds: ionic, covalent and metallic. Lewis structures (electron dot structures). Intermolecular forces and hydrogen bonds. Oxidation number and atomic valence. Ideal gas laws. Reaction rate, activation energy and catalysis. Measurements, units of measurement and uncertainties in experimental measurements. Chemistry and chemical transformations in daily life. Main environmental issues (acid rain, greenhouse effect, smog…). Safety regulations. - EARTH SCIENCE

**Exogenous dynamics of the Earth**–Global relief model; marine and continental hydrosphere; the cryosphere; composition, layers and extent of the atmosphere; atmospheric pressure; atmospheric circulation; humidity, precipitation and disturbance; the geographic distribution of climates and climate change.

**Endogenous evolution and dynamics of the Earth**–Minerals; the lithogenetic cycle; rocks; fossils and their meaning in rocks; the deformation of rocks; volcanic activity, its products and forms; Earth’s concentric shell structure; structure and composition of the Earth’s crust; Earth’s internal heat flux; Earth’s magnetic field; the definition of earthquake; elastic-rebound theory; the seismic cycle; types of seismic waves and their propagation and registration; macroseismic intensity and magnitude; volcanic and seismic phenomena and their geographical distribution in the dynamics of the Earth; Wegener’s continental drift hypothesis; tectonic plates theory; the seismic and volcanic risk; types of plate margins; formation and evolution of mountain ranges.

**The Earth in space**– The Earth in the solar system; the principal motions of the Earth; the shape of the Earth; orientation and measurement of time.

**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.

POINTS |
RECOMMENDED ENGLISH COURSE |

≤ 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 |