Maths second paper practice tests.
Five complete papers built on the pattern of the real ministry papers: 2 problems and 8 questions, and you pick 1 + 4 as in the exam. You work on paper, and when you get stuck you reveal the guided solution one step at a time — every step explained the way I would explain it in a lesson, with graphs.
At the end you mark how much you managed on your own and get an estimated mark out of 20.
The maturità is Italy’s school-leaving exam; its second paper is the written test in the main subject of your school type, which for the scientific high school (liceo scientifico) is maths.
Test in ItalianThe questions of this simulator are in Italian, as in the real exam.
- Open the paper
Practice test 1
Rational function with a parameter · piecewise function · probability with dice
- Open the paper
Practice test 2
Exponential times a polynomial · absolute value · binomial and Bayes
- Open the paper
Practice test 3
Semicircle and integral function · logarithmic function · solid geometry
- Open the paper
Practice test 4
Family of cubics · trigonometric function · solids of revolution
- Open the paper
Practice test 5
Piecewise profile with a smooth join · homographic function and circle · applied questions
Frequently asked questions about the second paper.
What are these practice tests like?
Like the real ministry paper: 2 problems (you do 1) and 8 questions (you do 4), maximum time 6 hours. They are original papers built on the pattern of the real 2019–2025 papers: function studies with parameters, piecewise functions, areas and integrals in the problems; Euclidean and solid geometry, discrete probability, limits and optimisation in the questions.
How does the marking work?
The second paper is open-answer, so you work on paper as in the exam. For every problem and question you find the guided solution, which you reveal one step at a time — so you can get unstuck without having it all spoiled — and at the end you mark how much you had done on your own: the practice test estimates your mark out of 20 (problem 10 points, each question 2.5, as in the official grid).
Is a calculator allowed?
In the exam, yes, as long as it is scientific or graphic with no symbolic calculation (CAS) and no internet connection. It is best to practise with the same calculator you will bring to the exam.
Will the paper be a mix of maths and physics?
The mixed paper only came up in 2019. Since 2023 the scientific high school second paper has been maths only again, and it is confirmed that way for 2026 (19 June). The rumour of a mixed paper comes back every year: go by the ministry’s official announcements.
Shall we prepare for the maturità together?
If the practice test shows gaps in derivatives, integrals or function studies, have a look at the maths tutoring and the guides on derivatives, integrals and probability — or start with the free diagnostic call.