Non-selective test

Basic mathematical knowledge will be tested at the beginning of the academic year (as stipulated in Art. 6 of M.D. 270/04) with a compulsory but non-selective test, success in which is not conditional on admission to the degree course. Failure to reach the threshold set by the degree course, as specified in the Didactic Regulations, entails the allocation of specific additional training obligations (OFAs) that must be met within the first year of the course.
All students enrolling in the first-cycle Degree Course in Nature and Environmental Sciences are required to take a (non-selective) initial knowledge assessment test, which usually takes place before classes begin.
In the 2021/2022 academic year, the test took place on 10 September 2021, starting at 9.30 a.m., in online mode. 
To take the test, students must register online by 7.9.2021 using the form available on the degree course website. It is not necessary to be already enrolled in the degree course. When registering for the test, students with disabilities will be able to apply for auxiliary aids and/or additional time to take the test, through the university's 'Le Eli-Che' support centre for vulnerable groups, students with disabilities and students with specific learning disorders. 
At the end of registration each student registered for the test will receive an e-mail with instructions on how to take the test.
The following are exempt from taking the test students enrolling in the Degree Course having already obtained a technical-scientific degree; students transferring from another Degree Course of our or another University having already passed a mathematics examination; students who have successfully taken an advance mathematics knowledge test in the year 2020 and 2021 (Test TOLC) TOLC with a passing threshold of 6, provided that they present documentation proving that they have passed the test to be sent by e-mail to the Degree Course President Prof. Donato A. M. Donato A. Grasso (
The test will consist of 15 questions to be answered in 60 minutes and will cover mathematics topics relating to the secondary school syllabuses listed below. Each correct answer will give one point, there will be no penalty for wrong answers. 
- Basic concepts of set theory. Intersection, union, difference and complementary; Cartesian product.
- Numerical sets. Natural integers, relative integers, rational and real numbers; finite and periodic decimals. Graphical representation on an oriented line. Fraction operations and sorting. Decimal representation. Algebraic operations and inequalities. Absolute value. Properties of powers. Power with positive base and rational exponent. Powers with a real exponent. Exponentials and their properties. Logarithms and their properties.
- Elementary plane geometry. Elementary properties of points, segments, half lines, straight lines. Elementary properties of triangles and polygons. Regular polygons. Elementary properties of circumference and circle.
- Algebraic calculus. Polynomial expressions; remarkable products (square and cube of a binomial, difference of squares); decomposition of the trinomial of the second degree. Algebraic transformations of expressions. Polynomials in one variable: simple decompositions.
- Equations and inequalities. Equations and systems of the first degree. Equations of the second degree. Rational equations. Irrational equations. Equations with absolute value. 
- Exponential equations. Logarithmic equations. Sign of the trinomial of the second degree. Disequations of the first and second degree. Rational Disequations. Irrational Disequations. Disequations with absolute value. Exponential equations. Logarithmic Disequations. Systems of inequalities.
- Analytical geometry. Cartesian plane: abscissas, ordinates and representation of points. Distance between two points. Cartesian equation of a straight line. Meaning of the angular coefficient. Parable. Link with inequalities of the second degree. Equation of a circumference.
- Trigonometry. Rectangular triangles and their properties. Pythagoras' Theorem. Sine and cosine of an angle and their elementary properties. Trigonometric equations and inequalities.
- Functions. General notion of function. Injective, suriective and bijective functions. Inverse function. Graph of a real function of real variable.
Those who do not exceed the thresholds defined by the Course Council will be allocated OFAs (Additional Training Obligations) to be completed as described below:
For scores from 0 to 4, it will be MANDATORY to attend the remedial course scheduled in the two weeks following the test, and to take another test at the end of that course. 
If the debt is not settled, the Course Council will assess the student's position and decide on other possible measures (such as, for example, not allowing enrolment in the second year if the mathematics examination is not passed within the first year).
For scores of 5 to 7, no OFAs will be awarded, but it will still be STRONGLY RECOMMENDED to take the remedial course.
For scores from 8 to 15 the course is not compulsory, but students may attend it if they wish.


- Concetti base di teoria degli insiemi. Intersezione, unione, differenza e complementare; prodotto cartesiano.

- Insiemi numerici. Interi naturali, interi relativi, numeri razionali e numeri reali; decimali finiti e periodici. Rappresentazione grafica su una retta orientata. Operazioni fra frazioni e ordinamento. Rappresentazione decimale. Operazioni algebriche e disuguaglianze. Valore assoluto. Proprietà delle potenze. Potenza con base positiva ed esponente razionale. Potenze con esponente reale. Esponenziali e loro proprietà. Logaritmi e loro proprietà.

- Geometria elementare del piano. Proprietà elementari di punti, segmenti, semirette, rette. Proprietà elementari di triangoli e poligoni. Poligoni regolari. Proprietà elementari di circonferenza e cerchio.

- Calcolo algebrico. Espressioni polinomiali; prodotti notevoli (quadrato e cubo di un binomio, differenza di quadrati); decomposizione del trinomio di secondo grado. Trasformazioni algebriche di espressioni. Polinomi in una variabile: semplici decomposizioni.

- Equazioni e disequazioni. Equazioni e sistemi di primo grado. Equazioni di secondo grado. Equazioni razionali. Equazioni irrazionali. Equazioni con il valore assoluto. 

- Equazioni esponenziali. Equazioni logaritmiche. Segno del trinomio di secondo grado. Disequazioni di primo e di secondo grado. Disequazioni razionali. Disequazioni irrazionali. Disequazioni con il valore assoluto. Disequazioni esponenziali. Disequazioni logaritmiche. Sistemi di disequazioni.

- Geometria analitica. Piano cartesiano: ascisse, ordinate e rappresentazione dei punti. Distanza fra due punti. Equazione cartesiana di una retta. Significato del coefficiente angolare. Parabola. Legame con le disequazioni di secondo grado. Equazione di una circonferenza.

- Trigonometria. Triangoli rettangoli e loro proprietà. Teorema di Pitagora. Seno e coseno di un angolo e loro proprietà elementari. Equazioni e disequazioni trigonometriche.

- Funzioni. Nozione generale di funzione. Funzioni iniettive, suriettive e biiettive. Funzione inversa. Grafico di una funzione reale di variabile reale.


Please be reminded that attendance to the course is compulsory for students who didn’t sit the initial preparation self-assessment test or who took it but obtained a grade lower than 5 and that it is strongly recommended to students who have obtained a mark between 5 and 7. However, also students who have obtained a higher grade can attend the course.

As all course units in the a.y. 2022/23, classes will take place only in person and not remotely. Recordings and other materials will be made available to students who cannot attend classes.

The remedial course will take place from 9 am to 1 pm from 12 to 16 September 2022 in room A, Earth Sciences Complex.

At the end of the course, a new test will be made available for those students who didn’t take the self-assessment test or who got a grade lower than 5; students failing to pass the test will be assigned additional training obbligations by the Course Council.