If you have a failed subject to make up in maths (in Italian, a debito) and the exam is at the end of August or in the first days of September, the first thing to do — before you even open the book — is to understand what is really waiting for you. It is not just any test: it has a precise format, precise timing, and precise consequences if it goes badly.
Every summer I work with students in your situation, so before telling you what to revise there is one thing worth doing: try the free practice test for the maths catch-up exam for your year. In about an hour you find out, with a real score, where you stand and which topics are your weak points, and you get the step-by-step solutions to every exercise. From there the rest of this article becomes a tailored plan, not a blind revision of the whole syllabus.
How the September exam really works
The failed subject in maths, technically a “suspended judgement” (sospensione del giudizio; OM 92/2007, DM 80/2007 — the Italian ministerial rules), must be checked by 31 August, but in practice almost all schools set the exam in the very first days of September, just before the school year starts — when your head is already elsewhere and the holidays that are over seem to have ended far too quickly.
The typical format:
- A written exam of 90-120 minutes, with 5-8 exercises.
- Often without a calculator, so hand calculation — factorisations, simplifications, systems — has to be fluent, not just “you could do it if you took your time”.
- Sometimes a short oral follows, which starts from a discussion of the written paper: they ask you to explain a step or justify a method you used.
- An extra 30 minutes for students with a specific learning disorder (DSA) (Italian law 170/2010), to be requested at the school office if you are entitled to it.
A pass (6/10) does not require virtuosity: basic theory stated correctly + application in simple contexts, with at most a few calculation errors. About 80% of the exam is pure technique — factorisations, equations, inequalities, systems — and the remaining 20% is an applied problem or a theory question. The difficulty is that of textbook exercises, not of a maths competition: there is nothing you haven’t already seen during the year.
What happens next depends on the result: if the exam goes well, the failed subject is cleared and promotion becomes final. If it goes badly, the class council decides — and in the most serious cases you may not be admitted to the next year. This is not meant to scare you: it is meant to make you see that three weeks well used now are worth more than any regret in October.
Why people end up failing maths
The failed subject almost never comes from “not being a maths person”. It comes from a gap that has built up: a concept not consolidated in October or November that then made everything built on top of it incomprehensible. Maths is cumulative — if you don’t master factorisation, you can’t simplify rational inequalities; if you don’t master quadratic equations, analytic geometry becomes a mystery.
The most common method mistakes that lead to failing are always the same three: studying theory without doing exercises (maths is learned by solving, not reading), studying in bursts instead of steadily (patterns are lost if you don’t repeat them), and never going back to the missing concept, piling “patches” on a hole that keeps widening. If you want to work on these three points calmly after the catch-up, I have written a broader guide on how to study maths without stress — it applies here too, but with three weeks available you need a more targeted approach, which is what follows.
What to revise, year by year
Your school’s exam syllabus is the most important document you have — more than the textbook — because it almost always matches what was actually covered in class, not the full table of contents. But if you have not received it yet, here are the topics that come up almost every time for each year.
Year 1 of high school
- Algebra and special products, for example .
- Factorisation (common factor, difference of squares, special trinomial).
- First-degree equations, also with simple parameters.
- Basic Euclidean geometry: triangles, congruence criteria, parallelograms.
To train on the Year 1 syllabus: maths catch-up, Year 1, 20 questions on algebra and equations with the correct answers by email.
Year 2 of high school
- Radicals: simplification, rationalisation, operations.
- Quadratic equations and inequalities, with the formula and the study of the sign.
- Systems of equations, linear and simple non-linear.
- The line in the Cartesian plane: equation, slope, parallel and perpendicular lines.
To train on the Year 2 syllabus: maths catch-up, Year 2, with radicals, quadratics and inequalities.
Year 3 of high school
- Equations and inequalities with absolute values and with radicals.
- Analytic geometry: line, parabola, circle, and often a first look at the ellipse and hyperbola.
- Functions: domain, study of the sign, first properties (even/odd, increasing/decreasing).
To train on the Year 3 syllabus: maths catch-up, Year 3, with absolute value, functions and conic sections.
Year 4 of high school
- Trigonometry: fundamental identities, trigonometric equations, solving triangles.
- Exponentials and logarithms: properties, equations, inequalities.
- Combinatorics and basic probability.
To train on the Year 4 syllabus: maths catch-up, Year 4, with trigonometry, exponentials and logarithms.
If you are not sure which topics were really covered in class, ask your teacher or get the exam syllabus from a classmate before losing hours on chapters your class never even tackled.
The plan for the last 2-3 weeks
With little time available, revising “by chapters” — I open the book and reread the theory from start to finish — is the slowest and least effective way to prepare. It gives a false sense of security: while you read, everything seems clear; faced with a real exercise, it doesn’t.
The revision that works is “by exercises”: take 4-5 exercises for each topic in the exam syllabus, solve them with the book closed, and classify each mistake. Didn’t you know the theory? Did you make a calculation error? Did you misunderstand what the exercise was asking? They are three different problems, with three different fixes — and telling them apart is more useful than saying vaguely “I need to revise more”.
Your mistakes become your main study material, not a scrap to correct and forget. If you have already done the free practice test, you already have the list of your weak points by topic: start from there instead of guessing what to revise. The typical scheme I use: week 1 on the topics where the practice test (or the first round of exercises) showed the most gaps, week 2 on the rest of the syllabus, the last days of week 3 devoted to a full timed practice test plus targeted review of the mistakes that emerged there.
Typical mistakes on exam day
Even with good preparation, points are lost on the day for reasons that have nothing to do with maths itself:
- Diving into the first exercise without reading the whole paper. The first minutes should be spent reading everything and estimating the difficulty, not starting to write.
- Not checking the conditions of existence. Solving an equation with radicals or a system without checking the domain is the most common and most costly mistake: a mathematically correct but unacceptable solution is worth zero.
- Getting stuck on one exercise for too long. If after 5 minutes you have no approach in mind, move on to the next. You come back with a clearer head, often with the right idea.
- Skipping the theory question because it is “worth little”. It is worth more than you think, and they are easy points if you have studied the definitions precisely — much easier than the points of the applied exercise.
- Not simplifying before calculating. Diving into the quotient formula or a complicated system without first simplifying the expression wastes time and increases the risk of calculation errors.
If the block you feel on exam day is not lack of preparation but real test anxiety, it is worth tackling that side too: I have written a guide with concrete techniques for managing test anxiety in maths and physics.
On the method side I have written the routine for practising against the clock, how to build a real study plan, the five maths mistakes that look right and the prof’s translations, all of which read well before the exam. Even once the exam is passed, the high school maths tests by year and topic help you avoid falling back into a failed subject in January.
Realistic timescales
With a single failed subject in maths, 6-8 lessons spread over 3-4 weeks are usually enough, provided you also practise on your own between lessons — lessons are there to fill the real gaps and correct your method, not to replace daily study. If the failed subject is in more than one subject, or you are starting from far behind, plan for 10-12 lessons in total and start as early as possible: the last weeks of August go faster than they seem.
If you also failed physics, I have written a twin guide on how to prepare for the physics catch-up exam: the underlying method — revise by exercises, not by chapters — is the same.
How we work in lessons
The first meeting is a diagnosis. If you have already taken the free practice test, we start from there: we look together at the weak points that emerged by topic and build the plan on those, without wasting time revising things you already master. If you haven’t taken it yet, the first lesson is exactly for that. From there we build a course on the real topics of your exam, with targeted exercises and at least one timed practice test under conditions as close as possible to the real ones, before exam day.
Lessons are online, one-to-one: the rates (single lesson or 10-hour package) are always on the pricing page — the package is good value if you expect to need several sessions, which, for a failed subject to recover in a few weeks, is often the case. My students’ average grade is 8.2/10, with over 215 students tutored and 97% of tests and exams passed: numbers that come from working on the points where a student really gets stuck, not from redoing theory they already know.
If you want to understand where to start with your specific case, the quickest route is to try the free catch-up practice test first and then book a free 30-minute introductory call via the contact page: you tell me the exam syllabus and how many weeks you have, and I tell you honestly how many lessons you need. You can also find the full programme of maths tutoring if you want to see how I structure the course across all the high school topics.
