How to Study Maths for the Brevet: Exercises, Mental Math and Geometry

# How to Study Maths for the Brevet: Exercises, Mental Math and Geometry

Studying maths for the brevet is not about re-reading your notes and answer keys. It is about redoing past exercises with the solution hidden, automating your basic calculations (fractions, powers, percentages, proportionality), and instantly recognizing which geometry tool to use (the intercept theorem, Pythagoras, trigonometry). The brevet is the French national exam taken at the end of middle school (around age 14-15), and its maths paper is not designed to trap you. It tests topics you have already seen, but it rewards students with solid reflexes who do not waste time. That is exactly what you can build in a few weeks.

TL;DR: The brevet maths paper lasts 2 hours, calculators are allowed, and it contains several independent exercises (often one open-ended "complex task" and sometimes a bit of block-based coding similar to Scratch). You gain the most points by redoing past papers without the answer key (active recall), drilling your mental-math automatisms, and quickly recognizing the right geometry theorem. Re-reading worked solutions gives the illusion of knowing but does not build real skill.

If you already feel like you "understand in class but mess up on test day," that is normal and fixable. The problem is almost never intelligence, it is the revision method. Cognitive science has shown for years that re-reading and highlighting are among the least effective techniques, while testing yourself is one of the most powerful (Dunlosky et al., 2013). In maths there is an extra twist: mixing problem types instead of practicing them in blocks clearly improves learning (Rohrer & Taylor, 2007). We will lean on both of these levers throughout.

What does the brevet maths paper actually look like?

Before revising, you need to know what is coming. The paper lasts 2 hours, the calculator is allowed (just make sure it supports exam mode if required). The paper is split into several independent exercises: if you get stuck on one, you can move to the next without losing anything. That is strategic information, more on it below.

You almost always find the same big families of exercises:

The complex task is often worth many points and scares students. In reality, even if you do not finish, everything correct you write earns marks. The scoring rewards the reasoning, not just the final answer.

Why is redoing exercises better than re-reading solutions?

This is the most important tip in the article, so read it twice. When you re-read a worked solution, your brain recognizes the steps and tells you "yes, I can do this." That is a trap, called the illusion of mastery. You recognize, but you cannot reproduce it alone.

The real test is to take an exercise, completely cover the solution, and try to solve it to the end. Struggling? Good, that means your brain is working. This mechanism is the testing effect: Roediger and Karpicke (2006) showed that testing yourself produces about 50% more retention than simply re-reading. In maths the effect is even stronger because you memorize a procedure, not just a fact.

Here is the routine to apply to each past-paper exercise:

1. Read the question and try to solve it alone, with no help, on paper.
2. If you are stuck for more than 5 minutes, look only at the first step of the solution, then cover it and continue alone.
3. Once done, compare with the solution and pinpoint exactly where it went wrong: missing knowledge, poorly applied method, or a simple calculation slip.
4. Redo the same type of exercise two days later, from memory.

That last step (returning to it a few days later) relies on distributed practice: spreading revision over time anchors learning far better than one big session (Cepeda et al., 2006). If you use Wizidoo, you do not have to manage this by hand: take a photo of your notes or import the PDF, the AI generates quizzes, and the topics you miss (fewer than two correct answers in a row) come back automatically in later quizzes. You work, the app tracks your weak spots.

How do you build mental math and automatisms?

The calculator is allowed, but it will not save you without automatisms. Why? Because spending 30 seconds typing each fraction wastes precious time on a 2-hour paper, and above all a bad automatism makes you set up a wrong calculation from the start.

The automatisms you need at your fingertips are always the same:

The best way to anchor them is to practice in small daily doses rather than one big weekly session. Five to ten minutes of daily mental math beat one hour on Sunday. Again, that is distributed practice talking (Cepeda et al., 2006). You can set yourself quick question series, alone or with someone, aiming for speed as much as accuracy.

One often-neglected point: reading the question. Before diving into a calculation, re-read what is being asked and figure out exactly what is expected. Many marks are lost simply by answering the wrong thing or forgetting the requested unit.

How do you stop picking the wrong geometry theorem?

Geometry on the brevet is rarely a calculation problem. It is a recognition problem: knowing which tool to use for which figure. Once you have the right reflex, the rest almost follows by itself.

Here is the decision grid to keep in mind:

• You see a right triangle and the question is about side lengths: think Pythagoras.
• You see a right triangle and angles are involved (or one is given): think trigonometry (sine, cosine, tangent).
• You see two parallel lines cut by transversals forming nested triangles: think the intercept theorem (Thales' theorem).
• You are asked for the image of a figure after a movement: think transformations (translation, rotation, symmetry).

The mnemonic for trigonometry still helps: "SOH-CAH-TOA" (Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent). Learn it by heart, it saves seconds on exam day.

To practice smartly, do not do ten intercept-theorem exercises in a row. Mix them. Do one intercept theorem, then a Pythagoras, then a trigonometry, then back to the intercept theorem. This mixing (interleaving) forces your brain to choose the right tool each time, exactly like on exam day. Rohrer and Taylor (2007) proved that this simple change in how you organize exercises improves maths results, even though it feels harder at the time. It is uncomfortable, but it works. If you want to understand how to unlock maths topics that still resist you, we wrote a full guide on really understanding maths.

How do you revise statistics and probability?

This is often the most rewarding part, because the topics are few and come back nearly every year. You must master without hesitation:

• The mean (sum of values divided by their count) and the weighted mean (with frequencies).
• The median (the middle value once data is ordered) and never confuse it with the mean.
• The range (max value minus min value).
• Simple probability (number of favorable cases divided by number of possible cases).

The classic trap is mixing up mean and median. Keep a simple image in mind: the mean gets "dragged" by extreme values, the median does not. If a class has one student at 20 and all the others at 5, the mean climbs but the median stays at 5. On exam day, this kind of reflex earns you points without much thinking.

How do you manage your 2 hours on exam day?

You have revised, now you have to convert. Time management often makes the difference between two students of the same level.

First, since the exercises are independent, start with the ones you are most comfortable with. You secure points and build confidence before tackling the harder ones. Nothing forces you to do the paper in order.

Next, keep an eye on the clock. In 2 hours, aim to leave at least 10 minutes at the end to re-read, check your units and negative signs. A quick re-read often recovers a point or two lost carelessly.

Finally, on the complex task, never leave a blank page. Write what you know: the data, the formula you think applies, a diagram. Every correct element counts, even if you do not reach the end. The marker rewards the reasoning.

For a complete revision plan over the final weeks, you can follow our method to revise the brevet effectively, which applies to every subject, not just maths.

How can Wizidoo help you study maths?

The most time-consuming part of revising is building your tools: copying out sheets, making your own questions, finding what you are weak at. Wizidoo automates all of it. You import your maths notes as a photo or PDF, the AI turns them into quizzes and summary sheets, and all you have to do is test yourself.

The real advantage for maths is the automatic tracking of your weak spots. A topic you miss comes back on its own in later quizzes until you validate it (two correct answers in a row), and you see a mastery percentage per chapter. So you know precisely whether your geometry is solid or your probability is lagging. Progression happens in layers, from fundamentals to details, which fits the logic of maths perfectly, where each topic builds on the previous one.

Try Wizidoo for free at wizidoo.com

Frequently asked questions

How long does it take to revise maths for the brevet?

If you spread it over three to four weeks at 20 to 30 minutes of maths per day, you have plenty of time to cover the essentials. The secret is not the number of hours but regularity: small daily sessions (distributed practice) anchor automatisms far better than one big block the night before (Cepeda et al., 2006). For other subjects and an overall schedule, see our brevet revision FAQ.

I understand in class but fail tests, what should I do?

That is a sign you are confusing "understanding" with "being able to redo it." Understanding a solution is passive, redoing it alone is active. The fix is simple: close all your answer keys and redo the exercises from scratch on paper. Until you can reproduce an exercise without help, you have not truly mastered it. That is exactly what the testing effect measures (Roediger & Karpicke, 2006).

Do I need to memorize formulas for the brevet maths paper?

Yes for the essentials (Pythagoras, the intercept theorem, trigonometry SOH-CAH-TOA, common areas and volumes, the mean formula). Some volume formulas are sometimes recalled on the paper, but do not count on it. The best way is to anchor them through use: by redoing exercises repeatedly, you retain them without having to recite them. A summary sheet per chapter also helps keep them in view while you revise.

How do you revise the algorithmics (Scratch) part?

It is worth few points but very accessible. The key is reading a script block by block and predicting what it outputs, in the exact order of execution. Practice on two or three past papers: you will quickly see the questions are similar (movements, loops, variables that increment). A few exercises are enough to secure those points.

Is mental math useful if calculators are allowed?

Yes, very much. The calculator does not fix faulty reasoning, and typing every operation slows you down on a 2-hour paper. Good automatisms (fractions, percentages, order of operations) help you set up the right calculation first time and leave you time to re-read. Five minutes of mental math a day is enough to make the difference.

References

• Cepeda, N. J., Pashler, H., Vul, E., Wixted, J. T., & Rohrer, D. (2006). Distributed practice in verbal recall tasks: a review and quantitative synthesis. Psychological Bulletin, 132(3), 354-380.
• Dunlosky, J., Rawson, K. A., Marsh, E. J., Nathan, M. J., & Willingham, D. T. (2013). Improving students' learning with effective learning techniques. Psychological Science in the Public Interest, 14(1), 4-58.
• Roediger, H. L., & Karpicke, J. D. (2006). Test-enhanced learning: taking memory tests improves long-term retention. Psychological Science, 17(3), 249-255.
• Rohrer, D., & Taylor, K. (2007). The shuffling of mathematics problems improves learning. Instructional Science, 35(6), 481-498.

Further reading

• Revise the brevet effectively: the complete method
• FAQ: revising the brevet 2026
• Revise brevet history-geography in 30 days
• Understanding maths and unlocking your blocks
• Active recall: the memorization technique that works
• Spaced repetition for lasting memorization
• Last-minute study plan: 2 weeks
• How to revise the bac 2026: complete method