Pitfalls to avoid in maths for the brevet des collèges: Louise’s guide

Every year, in the exam hall, the same stories repeat themselves. A brilliant pupil, who had fully mastered his or her third-year course, loses three marks on a geometry exercise not because they did not know how to do it, but because they forgot to check a condition for use. Another changes a sign in the middle of a calculation and never realises it, convinced to the end that they are right. At Cabinet Ranelagh, I have seen these scripts pass across my desk since 2020, and I can assure you of this: the majority of marks lost in the maths brevet are not due to a lack of knowledge, but to recurring methodological pitfalls, almost always the same from one session to the next. This article is not a list of vague tips: it is a precise breakdown of the classic mistakes I correct week after week with my third-year pupils, so that you know exactly where to focus your attention in the weeks ahead.

The trap of order of operations and the disappearing sign

This is the most frequent and the most insidious mistake: it reveals no lack of understanding, only inattention. A pupil knows perfectly well that multiplication comes before addition, but under the pressure of the clock, they carry out the operations in the order in which they appear on the paper. The result: a calculation that is correct in its logic becomes wrong in absolute terms, and the error spreads through the rest of the exercise without the pupil noticing, since each subsequent step seems coherent with the previous one.

The disappearing sign follows the same mechanism. When expanding an expression such as minus open bracket, a minus b close bracket, one must distribute the minus sign across both terms, and it is precisely here that half of my third-year pupils stumble at the start of the year. My method at the practice is simple but extremely effective: I systematically ask them to rewrite the intermediate step, never to jump straight to the result, even if that seems quicker. A pupil who gets into the habit of writing out each sign distribution on their rough work, before copying it neatly, reduces their calculation error rate dramatically. It is a reflex built over several weeks, not the night before the exam, which is why I work on it from the very beginning of the year as part of the maths tuition.

Pythagoras and Thales: the conditions people forget to check

This is undoubtedly the most classic trap in the whole geometry paper, and the one that costs the most marks in written justification. Pythagoras’ theorem only applies in a right-angled triangle, and Thales’ theorem requires parallel lines and aligned points in a precise configuration. Yet, under pressure, many pupils apply the formula without ever stating, or even checking, that the conditions are met. The marker, for their part, cannot validate reasoning that does not justify its starting point, even if the final numerical answer is correct.

Last year I worked with a pupil, Camille, in third-year at a secondary school in the sixteenth arrondissement, who systematically obtained the correct answer on geometry exercises but lost two marks per exercise, session after session, on her blank practice papers. When I went through her papers with her, I identified the problem within minutes: she knew how to apply the formulas, but never wrote the justification sentence that should come before using them, such as triangle ABC is right-angled at A because, or the lines are parallel from the wording of the question, therefore. We then built together a writing framework which she repeated across around ten standard exercises, until that sentence became as automatic as the calculation itself. Three months later, she was no longer losing a single mark on this type of exercise. It is the perfect example of a trap invisible to the pupil, but perfectly identifiable to a trained outside eye.

Sloppy writing: when the right answer earns no marks

The maths brevet is not only a calculation paper, it is a proof paper. The official marking scheme rewards the method as much as the result, and this is precisely what many families overlook when they think revising maths simply means doing more practice exercises. A pupil who writes the final answer directly without showing the intermediate steps systematically loses marks, even when that answer is exact, because the marker can only assess what is written in black and white.

This trap affects particularly the quickest pupils, those who work things out mentally and find the answer in a few seconds. Paradoxically, these are often the ones who lose the most marks through overconfidence, because they see writing things down as a pointless waste of time. I always explain the same thing to them: the marker cannot read your mind, they can only mark what you have put on the page. At the practice, we therefore work on written expression as a discipline in its own right, with set phrases to memorise for introducing a calculation, a conclusion, a conjecture. This precision in writing, which also echoes the standards you find in a French lesson on clarity of expression, often makes the difference between a fairly good and a good mention.

Probability: the trap of misplaced equiprobability

Probability was introduced relatively late in the third-year syllabus, and it is a chapter in which even diligent pupils regularly fall into the same error: they assume an equiprobability that does not exist in the question. Typically, when faced with an exercise involving an urn containing balls of different colours in unequal quantities, some pupils calculate the probability by simply dividing by the number of colours, as if each colour were equally likely to be drawn, when one should divide by the total number of balls.

Another, more subtle, trap concerns complementary events and conditional probabilities disguised in a weighted tree diagram. The pupil multiplies the branches correctly, but forgets to add the paths leading to the same final event, or confuses the probability of a path with the total probability. I systematically ask them to draw the tree on rough paper before doing any calculation, even when the question does not explicitly request it, because the visual representation prevents most of these confusions. This method, simple in appearance, genuinely changes the picture: a pupil who visualises their tree before calculating makes two to three times fewer mistakes than one who launches straight into the fractions.

The calculator, a false friend on the big day

One might think the calculator eliminates all risk of error; in fact, the opposite too often happens. The first trap, almost comical in how often it returns each year, consists of entering a bracket or a negative sign incorrectly, producing a completely absurd result which the pupil accepts without question, simply because it came from the machine. A negative distance, a percentage above one hundred, an area larger than the plot it sits within: these inconsistencies should immediately raise the alarm, but many pupils never develop this instinct for checking through estimation.

The second trap concerns rounding. Many exercises ask for rounding to the nearest tenth or hundredth, and a correct answer that is poorly rounded, or rounded too early in the calculation rather than at the end, can cost a mark that seemed guaranteed. I always stress one simple rule to my pupils: never round an intermediate result, only the final result, and always reread the rounding instruction before handing in the paper. This vigilance, which may seem trivial, actually represents several marks accumulated across the paper, and it is exactly the kind of detail one works on properly through regular private tutoring rather than in a last-minute revision session.

Time management: the invisible trap that costs the most marks

People talk a great deal about calculation and method errors, but often forget the most decisive trap: managing time across the whole paper. The maths brevet lasts two hours and contains several independent exercises of varying length and difficulty. A pupil who spends fifteen minutes wrestling with an exercise worth only three marks, while an easier one awaits further on in the paper, often sacrifices easy points for an uncertain gain.

I systematically recommend that my pupils scan the entire paper within the first five minutes, identifying the exercises they can do straight away, before even putting down a single calculation. This strategic reading first secures the easy marks, then allows the remaining time to be devoted to the more complex exercises, particularly geometry ones which often require several stages of written reasoning. One of my pupils, Adam, in third-year, used to get stuck on the first difficult exercise he came across, wasting precious time out of pride and a desire to solve it before moving on. We worked together on a very simple protocol: if an exercise resists for more than three minutes without a clear lead, circle it and move to the next one, returning to it only at the end. This change in attitude, purely strategic, allowed him to gain nearly four additional marks in his next mock brevet, without having learnt a single new topic.

A method that is built over time

What these traps have in common is that they are never corrected in a single intensive revision session the night before the exam. They require repeated work over several weeks, where the pupil encounters the same type of mistake enough times to develop a reflex of vigilance that becomes automatic on the day. That is exactly the philosophy we have applied at Cabinet Ranelagh since 2020: supporting each pupil not by giving them answers, but by identifying their precise personal traps, the ones that recur in their own papers, in order to build a bespoke method rather than a generic lesson.

If your child is approaching the brevet and you feel the knowledge is there, but the marks keep slipping away inexplicably from one paper to the next, it is probably time to look more closely at those papers together. That is precisely the point of the support I offer on lescoursdelouise.com: sessions at the practice or by video call, built around what the pupil actually writes, not what one assumes they know. The traps of the brevet are not inevitable; they are simply habits we have not yet had the chance to correct.