**Syllabus of Required Knowledge TOLC-I**

SECTIONS | NUMBER OF QUESTIONS | TIME AVAILABLE |

MATHEMATICS | 20 QUESTIONS | 50 MINUTES |

LOGIC | 10 QUESTIONS | 20 MINUTES |

SCIENCE | 10 QUESTIONS | 20 MINUTES |

VERBAL COMPREHENSION | 10 QUESTIONS | 20 MINUTES |

TOTAL | 50 QUESTIONS | 110 MINUTES |

ENGLISH | 30 QUESTIONS | 15 MINUTES |

TOTAL WITH ENGLISH | 80 QUESTIONS | 125 MINUTES |

Logic and Verbal Comprehension – The Logic and Verbal Comprehension questions are designed to test the candidates’ aptitude rather than ascertaining acquisitions achieved in higher education. They do not, therefore, require specific preliminary preparation.

**Mathematics:**

**Arithmetic and algebra **– Properties and operations on numbers (integers, rationals, reals). Absolute value. Powers and roots. Logarithms and exponentials. Literal calculus. Polynomials (operations, factorization). Algebraic equations and inequalities of the first and second degree or reducible to them. Systems of first degree equations. Rational, fractional and radical equations and inequalities. Geometry Segments and angles; their measure and properties. Lines and planes. Notable geometric loci. Properties of the main plane geometric figures (triangles, circumferences, circles, regular polygons, etc.) and their lengths and areas. Properties of the main solid geometric figures (spheres, cones, cylinders, prisms, parallelepipeds, pyramids, etc.) and their volumes and surface areas.

Analytical geometry and numerical functions – Cartesian coordinates. The concept of function. Equations of lines and simple geometric loci (circles, ellipses, parabolas, etc.). Graphs and properties of elementary functions (powers, logarithms, exponentials, etc.). Calculations using logarithms. Logarithmic and exponential equations and inequalities.

**Trigonometry **– Graphs and properties of the sine, cosine and tangent functions. The main trigonometric formulas (addition, subtraction, duplication, bisection). Trigonometric equations and inequalities. Relations between elements of a triangle.

**Statistics **– Knowledge of basic statistics (permutations, combinations, mean, variance and frequency) is assumed. Basic knowledge of interpretation of frequency diagrams and histograms.

**Science:**

Mechanics – Knowledge of scalar and vector quantities, the concept of measurement of a physical quantity and of a system of units of measurement is assumed; the definition of fundamental physical quantities (displacement, velocity, acceleration, mass, momentum, force, weight, work and power); knowledge of the law of inertia, Newton’s law and the principle of action and reaction, elements of fluid mechanics.

**Optics **– The principles of geometric optics; reflection, refraction; refractive index; prisms; concave and convex mirrors and lenses; elementary notions of lens systems and the devices that use them.

**Thermodynamics **– The concepts of temperature, heat, specific heat, expansion of bodies and the equation of state of ideal gases are assumed to be known. Elementary knowledge of the principles of thermodynamics is required.

**Electromagnetism **– Knowledge of basic notions of electrostatics (Coulomb’s law, electrostatic field and capacitors) and magnetostatics (current intensity, Ohm’s law and magnetostatic field) is assumed. Some basic notions are also required regarding electromagnetic radiation and its propagation.

**Chemistry and structure of matter** – Qualitative knowledge of the structure of atoms and molecules is required. In particular, elementary notions of the constituents of the atom and the periodic table of elements are assumed. Furthermore, the distinction between compounds formed by ions and those formed by molecules and knowledge of the relative physical characteristics are assumed, in particular of the most common compounds existing in nature, such as water and the constituents of the atmosphere.

**Chemical Symbols** – Knowledge of chemical symbols is assumed and the meaning of chemical formulas and equations is assumed to be known.

**Stoichiometry **– The concept of mole and its applications must be known; the ability to perform simple stoichiometric calculations is assumed.

**Organic Chemistry** – The structure of the simplest carbon compounds must be known.

**Solutions **– The definition of acid–base systems and pH must be known.

**Oxidation–reduction** – The concept of oxidation and reduction must be possessed. Elementary notions of combustion reactions are assumed

** TOLC-E Structure Test structure and syllabus**

SECTIONS | NUMBER OF QUESTIONS | TIME AVAILABLE |

LOGIC | 13 QUESTIONS | 30 MINUTES |

VERBAL COMPREHENSION | 10 QUESTIONS | 30 MINUTES |

MATHEMATICS | 13 QUESTIONS | 30 MINUTES |

TOTAL | 36 QUESTIONS | 90 MINUTES |

ENGLISH | 30 QUESTIONS | 15 MINUTES |

TOTAL WITH ENGLISH | 66 QUESTIONS | 105 MINUTES |

**TOLC-E knowledge syllabus**

**Logic and Verbal Comprehension**The Logic and Verbal Comprehension questions are designed to test the candidates’ aptitude rather than ascertaining achievements in higher education. They do not, therefore, require specific preliminary preparation.

**Mathematics**Properties and operations on numbers (integers, rational, real). Calculating percentages. Absolute value. Powers, roots and their properties. Exponentials, logarithms and their properties. Polynomials (operations, factorization, division with remainder, principle of identity). Rational fractional expressions. Algebraic equations and inequalities of the first and second degree or reducible to them. Resolution of simple linear systems. Rational fractional, irrational, logarithmic and exponential equations and inequalities. Literal calculus. Analytic geometry: Cartesian coordinates, equation of a straight line and simple geometric loci (parabola, circumference, hyperbola, ellipse), solution of simple problems of analytical geometry. Geometry: segments, polygons, circles, perimeters and areas; notable solids, surfaces and volumes. Elementary functions: graphs and domains.

**TOLC-F Structure Test structure and syllabus**

SECTIONS | NUMBER OF QUESTIONS | TIME AVAILABLE |

BIOLOGY | 15 QUESTIONS | 20 MINUTES |

CHEMISTRY | 15 QUESTIONS | 20 MINUTES |

MATHEMATICS | 7 QUESTIONS | 12 MINUTES |

PHYSICS | 7 QUESTIONS | 12 MINUTES |

LOGIC | 6 QUESTIONS | 8 MINUTES |

TOTAL | 50 QUESTIONS | 72 MINUTES |

ENGLISH | 30 QUESTIONS | 15 MINUTES |

TOTAL WITH ENGLISH | 80 QUESTIONS | 87 MINUTES |

TOLC-F required knowledge syllabus

Premise

The syllabi were created by a working group of teachers and researchers from the academic communities that over time have dealt with access to the study courses in the areas of Pharmacy and CTF. The Syllabi indicate the knowledge required to take the entrance test.

This refers to an active and conscious “knowledge”, linked to operational skills and the solution of problematic situations. In particular, the ability to recognize and set problems, selecting the appropriate information, identifying the most suitable tools and, where necessary, schematizing and representing data and situations, is a transversal ability common to all the topics indicated in the syllabi.

The syllabi are deliberately limited to giving essential indications, as the purpose of the entrance tests is to allow an overall assessment of the knowledge of basic topics of the various scientific disciplines and not to analytically measure the knowledge and skills of the students. If the test gives a student a negative signal for a certain discipline, specific activities must be carried out aimed at diagnosing the deficiencies more precisely and identifying the appropriate study strategies. These activities are necessary because, although it is true that to successfully follow the scientific degree courses it is not essential to know all the topics of the syllabi in advance, it is however important that the student who does not know some (or many) of them is aware of them and is able to master them quickly.

In the entrance test the use of calculators of any kind is not permitted; this does not mean, however, that it is not important to know how to use calculation tools. In many university study and work situations it may be appropriate to use pocket calculators, spreadsheets, geometric software and specific software for numerical and symbolic calculation or for statistics.

It would therefore be a serious mistake if high school students were to focus all their preparation on passing the entrance test and limit their knowledge to the requirements contained in the syllabi.

The starting point was the ministerial programs of these subjects for high school students.

**BIOLOGY**

Chemical composition of living organisms

Bioelements. The properties of water. Molecules/macromolecules of biological interest. Structure of carbohydrate monomers, lipid molecules, amino acids and nucleotides. Structure and functions of macromolecules: polysaccharides, nucleic acids and proteins. The properties of enzymes.

Elements of Biodiversity

Diversity and levels of organization of living organisms. Domains and kingdoms of living organisms. Bacteria, Protists, Fungi, Plants, Animals. Viruses.

Biology of the cell

Cellular organization. Morpho-functional characteristics of prokaryotic and eukaryotic cells. Main cellular constituents: cell membranes, cell walls, cytoplasm, mitochondria, plastids, ribosomes, endoplasmic reticulum, Golgi apparatus, lysosomes, nucleus, nucleolus.

Cell cycle, reproduction, heredity

Cellular reproduction: mitosis and meiosis. Chromosome set. Reproduction and Heredity. Life cycles. Sexual and asexual reproduction. Mendelian genetics. Classical genetics: chromosomal theory of inheritance; sex chromosomes. Molecular genetics: DNA and genes; genetic code and its translation; protein synthesis. The DNA of prokaryotes. The chromosome of eukaryotes. Human genetics: transmission of mono- and polyfactorial characters; hereditary diseases. Mutations.

Elements of bioenergetics

Energy flow and biological significance of photosynthesis, glycolysis, aerobic respiration and fermentation; autotrophic and heterotrophic metabolism.

Elements of ecology

Components of the ecosystem. Food chains. Producers; consumers; decomposers. Interactions between species: competition, mutualism and parasitism.

Basics of human anatomy

Anatomy of the human organism: musculoskeletal system. Systems: digestive, respiratory, circulatory, excretory, immune, endocrine, nervous, reproductive.

Basics of Physiology

Physiology of the human organism: functions of support and movement, nutrition, respiration, circulation, excretion; immune, endocrine and nervous functions, reproductive function.

**CHEMISTRY**

The constitution of matter. The structure of the atom. The periodic table of elements

The structure of the atom: elementary particles; atomic number and mass number, isotopes, electronic structure of the atoms of the various elements.

The periodic table of elements: groups and periods; transition elements; periodic properties of the elements: atomic radius, ionization potential, electronic affinity; metals and nonmetals; relationships between electronic structure, position in the periodic table and properties. The chemical bond: ionic bond, covalent bond; polarity of bonds; electronegativity.

Fundamentals of general and inorganic chemistry. Inorganic compounds

Fundamentals of inorganic chemistry: nomenclature and main properties of inorganic compounds: oxides, hydroxides, acids, salts; position in the periodic table.

Chemical reactions. Oxidation-reduction

Chemical reactions and stoichiometry: atomic and molecular weight, Avogadro’s number, concept of mole, conversion from grams to moles and vice versa, elementary stoichiometric calculations, balancing simple reactions, various types of chemical reactions. Oxidation and reduction: oxidation number, concept of oxidant and reductant.

Solutions. Acids and bases

Solvent properties of water; solubility; main ways of expressing the concentration of solutions. Acids and bases: concepts of acid and base; acidity, neutrality, basicity of aqueous solutions; pH.

Organic chemistry

Fundamentals of organic chemistry: the chemistry of living things; bonds between carbon atoms; crude, structural and rational formulas; concept of isomerism; aliphatic, alicyclic and aromatic hydrocarbons; functional groups: alcohols, ethers, amines, aldehydes, ketones, carboxylic acids, esters, amides.

**MATHEMATICS**

Numerical sets

Numerical sets and their properties, elementary operations, ordering and comparison. Absolute value. Prime numbers, prime factorization. Greatest common divisor and least common multiple. Division with remainder between integers. Ratios, proportions and percentages, powers and roots.

Algebraic expressions

Basic algebra. Algebraic expressions. Operations with monomials and polynomials, notable products, factorization of a polynomial. Division between polynomials and Ruffini’s Theorem.

Equations and inequalities

Equations and inequalities of the first and second degree or reducible to them. Equations and inequalities with absolute value, exponential and logarithmic. Systems of linear or second degree equations.

Trigonometry

Measurements in degrees and radians. Basic trigonometric functions: sine, cosine, tangent, cotangent of an angle. Fundamental trigonometric relations.

Functions

Definition of function. Domain, image and counterimage of an element. Fundamental properties of functions: monotony, boundedness, periodicity. Composition of functions. Invertible functions and inverse function. Qualitative graphs of elementary functions: power functions, first and second degree polynomials, root, absolute value, exponential and logarithm, 1/x function, trigonometric functions.

Plane geometry

Principal plane figures and their elementary properties. Pythagorean theorem. Properties of similar triangles. Criteria for the congruence of triangles. Perimeter and area of principal plane figures (triangles, quadrilaterals, regular polygons and circles). Incidence, parallelism and perpendicularity between lines in the plane.

Solid geometry

Lines and planes. Characteristics of principal solid figures (parallelepipeds, prisms, pyramids, cylinders, cones and spheres).

Analytical geometry

Cartesian coordinates in the plane. Distance between two points and midpoint of a segment. Equations of lines. Angular coefficient. Equation of a line given one of its points and the angular coefficient. Equation of a line given two of its points. Conditions of parallelism and perpendicularity. Incident, parallel and coincident lines. Finding the point of intersection of two incident lines. Parabola with axis of symmetry parallel to the ordinate axis: equation, properties, coordinates of the vertex. Circumference: equation, properties, coordinates of the center and length of the radius.

Combinatorics, probability and statistics

Factorial of a number and binomial coefficient. Arrangements, combinations and permutations. Probability of events as a ratio between favorable cases and possible cases. Probability of events that are exclusive, conditioned and independent. Probability of the complementary event of a given event. Arithmetic mean.

**PHYSICS**

Measurements

Ability to formalize and quantify phenomena with a scientific approach. Ability to observe physical phenomena in everyday reality and relate them to the knowledge acquired. Direct and indirect measurements. Fundamental and derived quantities. Physical dimensions of quantities. Dimensionless quantities, angles, vector quantities. Units of measurement, systems of units of measurement (CGS, International). Names and relationships between fundamental and derived units. Order of magnitude, multiples and submultiples (names and values). Conversion between units of measurement. Experimental uncertainties, compatibility between measurements. Significant figures. Approximation and truncation. Scientific notation. Arithmetic mean. Relative and absolute errors. Experimental sensitivity. Precision and accuracy of measurements. Representation of results. Scaling laws, direct and inverse proportionality.

Kinematics and dynamics

Vectors and operations on vectors. Kinematic quantities: displacement, velocity and acceleration (average and instantaneous, scalar and vector). Description of motions in space (trajectory) and time (time equation). Various motions with particular regard to uniform rectilinear motion, uniformly accelerated motion, and uniform circular motion. [For all motions: definition and relationships between the related kinematic quantities, graphical representation]. Concept of frequency and period.

Forces

Concept of mass. Concept of force. The three laws of dynamics. Vector composition of forces, resultant. Law of universal gravitation and gravitational acceleration. Concept of weight. Other examples of forces: friction, elastic, electric. Vector composition of forces, resultant. Work. Kinetic energy. Conservative forces and potential energies. Principle of conservation of mechanical energy. Concept of momentum.

Fluid mechanics

The states of aggregation of matter. Fluids. Density. Pressure and its units of measurement (not only in the SI system). Stevin’s law. Pascal’s principle. Hydrostatic thrust (Archimedes’ principle). Flow, flow rate. Conservation of energy for fluids in motion.

Thermology, kinetic theory of gases, thermodynamics

Temperature, thermal equilibrium (zeroth law). Thermometric scales. Gases and ideal gases. Mole, Avogadro’s number, atomic mass. Internal energy of monatomic gases. Heat. Specific heat, heat capacity. Changes of state and latent heats. Kinetic theory of gases. Concept of equation of state, gas laws and equation of state of ideal gases. Adiabatic, isochore, isobaric, isothermal transformations. First, second, and third law of thermodynamics. Definition of entropy. State functions. Thermal expansion. Mechanisms of heat propagation: conduction, convection, radiation. Joule effect.

Electrostatics, electric currents, magnetism

Electric charge, induction. Coulomb’s law. Concept of electric field. Direct current. Electric potential, electrical resistance, resistivity, Ohm’s laws. Magnetic phenomena. Magnetic dipole. Concept of magnetic field. Magnetic field produced by an infinitely long wire carrying a current. Lorenz force. Faraday-Lenz law and induced currents.

Wave phenomena, geometric optics

General characteristics of waves, wavelength. Wave propagation (qualitatively), speed. Types of waves. Interference and diffraction phenomena. Sound waves. Notes on electromagnetic waves and the nature of light. Spectrum of light, dispersion. Reflection, refraction. Total reflection. Optical path. Mirrors. Diopters. Thin lenses. Optical focus. Images. Magnification.

**LOGIC**

Logic and Language

Logic of propositions. Concept of necessary or sufficient condition. Interpretation of various types of graphic representations and tables. Reasoning on elementary mathematical concepts.

**English Section**

Based on the result obtained in the test, the grid below provides indications on the initial level of preparation and the consequent actions.