The first-year courses may appear to start from scratch. Fundamental concepts are carefully defined, ideas that may have seemed familiar from school are revisited, and the formal language of university-level mathematics is introduced.
This impression can be misleading, however. Although the theory may be developed from the foundations, successfully following the courses requires a reasonable degree of confidence with algebraic calculations, equations and inequalities, functions, graphs, trigonometry, basic geometry and formula manipulation.
The Preparatory Course is therefore intended not only to review and consolidate this knowledge, but also to develop fluency, speed and confidence in using it.
Preparatory Course 2026/27
The Preparatory Course is primarily intended for students about to begin the Bachelor’s Degree in Mathematics, but students from other Degree Programmes or from later years are also very welcome if they wish to review or consolidate their basic prerequisites.
| When | 14–18 September 2026 |
| Where | Room G, Polo Fibonacci |
| Time | 14:00–18:00 |
Test format
Students of the University of Pisa are invited to join the Precorso Matematica Team using the code wvo2p63.
Once they have joined, they can open the Preparatory Course Team directly for announcements, communications and course materials.
Programme
The Preparatory Course reviews and consolidates the main prerequisites in elementary mathematics: fractions and powers, polynomials, equations and inequalities, exponentials and logarithms, functions and graphs, trigonometry, Euclidean geometry and analytic geometry. Particular attention is paid not only to understanding the concepts, but also to being able to use them quickly and confidently when solving exercises.
The Preparatory Course Syllabus provides a detailed description of the topics and skills that students are expected to have mastered before the beginning of the courses.
Initial Knowledge Assessment Test
At the end of the Preparatory Course, an assessment test is organised. The test can also be taken by students who have not attended the Preparatory Course.
When and where
- Tuesday, 22 September 2026, at 9:00;
- Rooms E1 and G, Polo Fibonacci.
Test format
- 24 multiple-choice questions;
- 5 possible answers for each question;
- only one correct answer;
- 60 minutes.
Scoring
- 5 points for each correct answer;
- 2 points for each unanswered question;
- 0 points for each incorrect answer.
OFA threshold
- The OFA are fulfilled with a score of at least 85 points.
Practical information
- No registration is required;
- bring a photographic ID;
- bring paper for rough work;
- during the test, books, notes, calculators and communication devices are not allowed.
Have you already fulfilled the OFA? Take the test anyway
The test serves two different purposes. If you have not yet fulfilled the OFA, a score of at least 85 points will fulfil them. But the score also provides a concrete indication of how solid your basic knowledge is as you begin the first-year courses.
For this reason, we recommend that students take the test even if they have already fulfilled the OFA through the TOLC-S or TOLC-I. If the result highlights some difficulties, it is much better to identify them at this stage and address them immediately than to discover them during the first assessments in Mathematical Analysis 1, Arithmetic or Geometry 1.
What does the test really tell us?
The results for the previous cohort show a strong relationship between the score obtained in the test and performance in the main first-year examinations. In particular, students in the lower score ranges encounter substantially greater difficulties in passing Mathematical Analysis 1, Arithmetic and Geometry 1.
The administrative OFA threshold should therefore not be interpreted as a threshold for being “safely prepared”: the test score provides much more information than that.
| Preparatory Course | N | MA1 | Arithmetic | Geo 1 | ≥1 of the 3 | ≥2 of the 3 | All 3 |
|---|---|---|---|---|---|---|---|
| <85 | 21 | 0% · — | 0% · — | 0% · — | 0% | 0% | 0% |
| 85–89 | 4 | 0% · — | 0% · — | 0% · — | 0% | 0% | 0% |
| 90–94 | 4 | 0% · — | 0% · — | 0% · — | 0% | 0% | 0% |
| 95–99 | 2 | 0% · — | 50% · 21,0 | 0% · — | 50% | 0% | 0% |
| 100–109 | 11 | 27% · 20,7 | 36% · 21,5 | 45% · 22,6 | 64% | 36% | 9% |
| 110–119 | 18 | 22% · 23,0 | 50% · 24,3 | 61% · 25,2 | 72% | 50% | 11% |
| 120 | 11 | 91% · 27,7 | 82% · 26,0 | 73% · 27,8 | 91% | 91% | 64% |
How to read the table. In the columns for the individual examinations, the percentage indicates the proportion of students who passed the examination, followed by the average grade among those who passed. A grade of 30 cum laude is counted as 33. The examination results are updated to 31 August 2026.
Interpret with caution. The data concern a single cohort and do not, on their own, demonstrate a causal relationship. However, the differences are substantial enough to make the test useful even for students who have already formally fulfilled the OFA.