How to deal with problems and questions

Maturità 2025, all the tips to arrive ready for the maths test

The proposed topics do not only relate to mathematical analysis (function study, differential and integral calculus) but also to topics from previous years.

by Carmine Fiore

4' min read

4' min read

Once again this year, Ministerial Decree No. 13 of 28 January 2025 established the subject of Mathematics as the second test of the state examination for the scientific high schools. The second test will be prepared by the ministry and will take place on 19 June.

The test consists of solving one of the two proposed problems and answering four questions out of the eight indicated; the time available is 6 hours. It should be noted that only the required number of problems and questions need to be completed. The test will be awarded up to 20 points. In addition, the MIM memo prot.no. 10961/2025 contains the updated list of calculators that can be used. Having said a few reminders on how the second test will be conducted, let us move on to give some simple and useful advice to students.

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Founding nuclei of the second test

Candidates' preparation for the second test must focus on reinforcing the knowledge acquired throughout high school and not only on the topics addressed in the final year. In fact, the topics proposed do not only relate to mathematical analysis (function study, differential and integral calculus) but also to the topics of previous years. Analysis of tests from previous years reveals the constant presence of questions relating to Euclidean geometry, analytical geometry in space, optimisation problems, probability and combinatorial calculus. Naturally, since the discipline identified is Mathematics, there will be no links or arguments from Physics.

How to choose the problem and the questions to be answered?

Do not panic and get anxious if at first reading the questions seem 'difficult'. To make your choice, read the text of both problems carefully so as to interpret and understand every detail; highlight the data provided, not only the numerical data, but also the conditions and constraints imposed by the outline. Identify the topics to which the problem refers and outline the procedure to be followed and the strategy to be applied in solving it. Careful reading will make the problem less complicated than it appears. Same procedure for the choice of questions. Don't be afraid if this analysis will take some time, it is better to make a careful and decisive choice than to start an exercise hastily and realise, during its execution, that it is more difficult than expected. This is a useless and risky waste of time.

Which exercise to start with

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Once you have chosen the problem and the questions, start with the ones you find easiest and most within your grasp, so that you can calm down and gain more confidence. If you feel it is appropriate to tackle the questions first because they are easier for you, go ahead; you will tackle the problem with more determination and peace of mind.

Usually, the two problems are structured in several points and each point is independent of the next. Often, the next point provides the solution of the previous one so that the candidate can still proceed with the task. Therefore, if one encounters difficulties in solving one point of the problem, proceed with the following points and, with greater peace of mind and determination, go back at a later point.

Use of calculator

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A correct use of the graphing calculator can help you in checking the correctness of the chosen procedure, in plotting a graph and having a counter-check on the accuracy of the calculations performed and the compatibility of the expected result. Of course, you need to familiarise yourself with the use of the calculator a few weeks before the test as, sometimes, many commands are not immediate and you cannot improvise their use on the day of the exam.

Mode of delivery

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After finishing the problem or question, carefully review the procedure and calculations performed, in order to avoid transcription errors, typos or calculation errors. Take care also of the form and the way of presenting the work. Fundamental, then, is to argue the choices made, specify the steps you take, recall the theorems used. Be clear and rigorous in your explanations and present your reasoning in a way that is comprehensible to the grader; these shortcomings could penalise you and lower your grade.

Time Management

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Time management is crucial. Organise your time by deciding how much to devote to the problem and how much to the questions; consider that each question should not take less than 30-45 minutes. In this organisation, consider the time needed to copy, revise and check all the work in order to present it in a clear and orderly manner. Of course, if you find that a question or problem point takes longer than the set time, move on to the next one and perhaps return to it later. Take breaks between questions in order to rest your brain or distract yourself from articulated reasoning. Drink and munch on some snacks.

How to prepare for the test

In order to arrive calmly at the test, it is necessary to organise a revision programme of the main topics covered during the five-year period. Dedicating three to four days to revision before the exam only serves to confuse you and increase your anxiety. Instead, start a few weeks earlier by deciding which topics to revise in the various weeks; organise summary and synthesis sheets. Review and revise previous years' exams and mock exams carried out during the fifth year.

Outline the typology and structure of the various problems proposed and identify the techniques for solving them (e.g. how to deal with problems involving a family of parameter-dependent functions; i.e. problems requiring the analysis of the graphs of a function in order to deduce the representative analytical expression or derive the graph of its derivative or integral function, etc.).

It is better if the practice exercises for the test are carried out together with some classmates, the comparison is always useful and fruitful to measure one's preparation. Avoid, therefore, the intense study of the day before: it is tiring and useless, better to break away and arrive at the test with serenity and determination. Best wishes to all!

Teacher Mathematics Liceo scientifico Isacco Newton Rome

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