Available brain time in prépa

Text of the pre-term preparatory course at Lycée Saliège, August 2026. First part: method, attention, and what you can reasonably ask an AI. Second part: the prompt box.

Every year, during the pre-term course, the same question comes back in different forms. "When I go back over a lesson on my own, it takes me longer than the lesson itself." "I work eight hours a day and I have no sense of making progress." "I reread, I redo my summary sheets, and in the DS (the in-class test) nothing comes back."

These are three versions of the same problem. Working time is not the scarce resource in prépa (the two-year intensive course that prepares for the competitive entrance exams to the grandes écoles). Everyone has roughly the same amount of it. The scarce resource is the time during which the brain is actually doing something useful, and that time is far shorter than people think. The phrase "available brain time" was an ugly line from a television executive talking about advertising. I am turning it around: your brain has a limited working capacity per day, far more limited than the number of hours available. The question is not how to find more hours. It is how not to waste the ones where the brain is actually present.

Time is not the problem

Let us do the arithmetic. A week in Spé (the second year; the first is Sup) is something like 30 to 35 hours of lectures, tutorials and lab work, plus khôlles (the weekly individual oral examination), plus a DS on Saturday. Once you subtract sleep, meals and travel, there is something like 30 hours of possible personal work left. That is not nothing. And yet everybody is short of time.

If it takes you three hours to go back over a two-hour lesson, you do not have a time problem. You have a method problem. In class, the teacher does invisible work: he chooses the order, he carves the material up, he insists on three points and moves quickly over ten others, he produces the example at the right moment. You are following a marked path, which takes an hour because somebody decided it would take an hour. Alone in front of the poly (the printed course handout), you no longer have that guide. You read everything with the same weight, you stop on a piece of notation, you redo an intermediate calculation that does not matter. You are rebuilding the path at the same time as you walk it. It is bound to take longer.

But that is not the real problem. The real problem is that rereading is the wrong activity, whatever its duration. When the lesson is in front of your eyes, everything looks clear. You recognise every line. That feeling of clarity is not mastery, it is familiarity. On the day of the DS the poly is no longer there, and all that remains is what you are able to reconstruct from memory. Rereading does not train that. It trains recognition. The lesson goes blurry again the moment you close the notebook, so you reread it a second time. You have spent three hours on it.

A review of the literature that has become a classic (Dunlosky et al., 2013) ranked a dozen learning techniques by measured effectiveness. Rereading, highlighting and summarising sit right at the bottom. And yet they are the most widely used techniques, in prépa included, and among the hardest workers included. If you feel you are spending a great deal of time for very little result, the odds are that you are spending that time at the bottom of the ranking.

What going back over a lesson means

Going back over a lesson does not mean doing it again. The lesson in class is an hour of somebody else's thinking, organised for you. Going back over it means checking what is left of it in your head, and repairing the holes. There is no reason for that to take the same amount of time.

Concretely, the same evening, with the notebook closed, you take a blank sheet for fifteen minutes. You write down what you remember: the definitions, the statements with their hypotheses, the idea of each proof in one line, the methods. Then you open the notebook. You compare. What is missing, you read, only that, and you add it to the sheet. What was wrong, you correct in red. That comes to twenty-five minutes in total, and you know exactly what needs more work.

This is called free recall, or the testing effect (Roediger & Karpicke, 2006). For equal time, testing yourself produces more durable learning than restudying. An experiment published in Science (Karpicke & Blunt, 2011) compared recalling a text from memory with building a concept map with the text in front of you. A week later, the group that had recalled from memory did better, including on inference questions. The detail that matters: the students had predicted the opposite. The feeling of having worked well measures nothing.

The mechanism is counter-intuitive but well described (Bjork & Bjork, 1992): information retrieved without effort is not reinforced. Information you had to search for, with a gap of a few seconds, comes back stronger. So you have to put yourself deliberately in situations where you find out that you have forgotten. The blank in your memory during revision is not an accident along the way, it is the moment when the learning happens. Rereading prevents that blank from ever appearing, since everything is in front of your eyes.

People sometimes object that fifteen minutes is not enough to retrieve everything. That is correct, and that is the point. What you do not retrieve is what counts. The rest, you already had.

The same day

When you go back over a lesson matters as much as how. A lesson revisited the same evening takes fifteen minutes. The same lesson revisited a week later, the night before the khôlle, takes two hours, because almost nothing is left and everything has to be rebuilt. Everyone knows this, and everyone postpones anyway, because on the evening itself there is the DM (the homework assignment), and the DM is urgent.

The DM is urgent. Going back over the lesson is important. Prépa is a machine for putting the urgent ahead of the important, and the people who come through are the ones who have found a way to protect the important. The simplest way: the fifteen minutes of recall happen before the DM, not after. They are short, they are not up for negotiation, and they make the DM faster, because you have just put the lesson back in your head.

The evening recall is only the first step. Four hours of revision the night before a DS work for the next day and leave almost nothing a month later. Four times one hour spread over three weeks is less pleasant and far more effective for the competitive exams (Cepeda et al., 2006, a meta-analysis over several hundred experiments). You go back to the recall sheet three days later, then a week later, ten minutes each time. For the material you need by heart, a spaced repetition program such as Anki does the arithmetic for you and presents each card just before you would forget it. Count on fifteen minutes a day, in the dead time.

The rest of the toolbox

Two other techniques have the same level of evidence behind them.

The first is interleaving. Do ten exercises from the same chapter one after another and you are no longer choosing the method, you are applying it. In the exam, nobody tells you that question 3 is a convexity exercise. Mixing chapters within a session is slower at the time and better in the end (Rohrer & Taylor, 2007), because you are also training yourself to recognise the type of problem.

The second is explaining. Teaching a piece of content forces you to reorganise it, to choose an order, to fill the holes you could not see (Fiorella & Mayer, 2013). You explain to a classmate, to a rubber duck, or, as we will come to, to an AI.

What these techniques have in common is that they are unpleasant. Robert Bjork speaks of desirable difficulties: conditions that slow immediate performance down and increase retention. If your revision session is comfortable, it is probably doing nothing.

Where the time goes

Let us move on to the second problem: "I work eight hours and I am not getting anywhere."

The first thing to know is that eight hours of useful work do not exist. Studies on deliberate practice, notably among high-level musicians (Ericsson et al., 1993), find a fairly stable ceiling: around four hours a day of genuinely effective work, in blocks, with rest in between. Beyond that you are present in front of the page, you are no longer learning. And it is precisely those hours that give the impression of working a lot.

Keep an honest account of your week for seven days. Write down not what you planned but what you actually did, in half-hour slots. Most people who do this discover two things.

The first: "working" time contains an enormous share of time spent sitting in front of the work without doing it. The lesson stays open, your gaze drifts, the phone appears in your hand without any decision on your part. One hour of real work in a three-hour evening is a common ratio. This is not laziness, it is what happens when the task is undefined and the phone is within reach.

The second: time is badly distributed across the day. The brain is not equally available at 8 a.m. and at 11 p.m. Work that requires thinking, a hard exercise, a proof to reconstruct, is done early, while the capacity is there. In the evening there is enough left to make Anki cards, to copy out a worked solution neatly, to draw up tomorrow's list. Doing the opposite, tackling an exercise at 11 p.m. and writing summary sheets at 8 a.m., is a guaranteed way to lose on both counts.

And then there is what eats into the four hours themselves.

There is the phone first, and not only when it rings. A rather striking experiment (Ward et al., 2017) showed that the mere presence of the phone on the desk, switched off, face down, reduces available working memory. The effect is stronger among those who report depending on it most. The practical conclusion is not "on aeroplane mode" or "face down": it is in another room. You do not have the willpower needed to ignore it, and neither do I, and it is not a question of willpower.

There is multitasking next, which does not exist. What goes by that name is rapid alternation between two tasks, and each switch costs a few seconds of getting back into context, plus the error that comes with it. Heavy media multitaskers are, contrary to what they believe, worse at filtering out distractions (Ophir, Nass & Wagner, 2009). Stick to one task, one medium, one window.

There is sleep last, which is not time taken away from work but half the work. Consolidation into long-term memory happens during the night: what was learned during the day is replayed and stabilised (Rasch & Born, 2013). A five-hour night after a day of revision means part of that day thrown away. The all-nighter before a DS removes what it claims to add. Nobody believes me about this in the first year. Everybody tells me so in the second.

Four rules

I do not like lists of advice, but this one is short.

Decide the night before. Every evening, write down precisely the list of what you will do tomorrow: "Exercise 4 from sheet 3, recall on chapter 7, Anki cards." Do not write "some maths". In the morning you are no longer deciding, you are executing. Deciding is what costs the brain most; you do it in the evening, when it is cheap. Motivation comes after starting, not before.

Put the phone in another room, for the reason given above. Dead time, the commute, the queue in the canteen, the ten minutes before a khôlle, is the one place where the phone is a revision tool: that is Anki time.

Work in blocks that have a beginning and an end. Count fifty minutes of work, ten minutes of break, and a timer. During the block, you do one thing only. Pomodoro (25 and 5) has nothing magical about it, but it imposes exactly that, and it is useful for starting when you cannot: 25 minutes is something you can negotiate with yourself. The break means standing up and drinking a glass of water, not opening a tab: five minutes of a feed rests nothing and puts the brain back into switching mode. A finished block is a finished block, even if the exercise is not.

Sleep seven hours minimum, eight if possible.

Holding out for two hours

The rules above are for daily life. The competitive exams ask for something else: four hours in a row on one paper, with no break decided by anybody but you. That cannot be improvised.

The concentration window is trained like endurance in running. Do blocks of 25 minutes in the first week, then of 35, 45, 60 and 90 minutes. You only move up if the previous block was held without interruption. The two-hour block must have been done several times before the written papers, not discovered on the day. Once a week, sit a complete paper under real conditions: duration, silence, paper, watch. Thirty blocks of 25 minutes do not teach you to hold one of 120. They teach you to hold one of 25.

You also have to plan for the moment your head comes up. You have been in it for an hour, a question ends, you look up. Your gaze goes off to the room, to the clock, and when you come back there is nothing left. That moment is normal: finishing a sub-task releases attention, which settles on the first thing that comes along. What costs is not the second of pause, it is the return. There are two defences. The first is to write the next step in the margin before stopping, so that you come back to a note and not to a void. The second is to set yourself in advance a rule of the form "if... then...", which fires almost effortlessly when the moment comes (Gollwitzer, 1999): "if I look up, then I reread the last line I wrote before anything else". You move from one question to the next by reading the next one, never by looking around the room. You look at the clock at moments decided in advance, not when the urge strikes. And you allow yourself a thirty-second micro-break, eyes closed, a mouthful of water, every 45 to 60 minutes, also decided in advance.

What you do not do

Available brain time is also won by removing things.

You do not reread. You do not copy out summary sheets from the open lesson. You do not redo an exercise you have already got right. You do not read a worked solution before having searched, nor after searching for five minutes: a solution read before searching is a reread lesson; the same solution read after twenty minutes of being stuck is corrected free recall. You do not ask an AI for the solution to a DM exercise at midnight; you note that you are stuck, you move on, and you come back to it in the morning, where it often comes out on its own.

You do not do the whole DM. You will find that outrageous. A DM that you finish by spending six hours on it, three of them stuck to no purpose, costs more than it returns. A DM of which you do three quarters in three hours, with the sticking points noted and gone over afterwards with the worked solution, returns more. The DM is a tool for learning, not a goal. If you confuse it with a goal, it is the DM that will eat the recall of the lesson, the sleep, and the rest.

You do not revise everything at the same level. The material to be known by heart, theorems and hypotheses, is the common bedrock for every competitive exam; it is maintained daily and is not negotiable. The rest, endurance on long papers, unguided exercises, exploration, is distributed according to the exams you are aiming at (CCINP, Centrale, Mines and X-ENS, the main exam banks, roughly in increasing order of selectivity). CCINP is largely prepared through the course material and the classic exercises; Centrale through endurance; Mines through fast recognition of the right tool and command of the hypotheses; X-ENS through independence. A revision plan that treats every chapter and every exam equally is a plan that does not choose.

You do not work eight hours on a Sunday. Four full hours, in blocks, are worth more than eight diluted ones, and the four hours left over serve to do something else, which is not wasted time. The brain also consolidates while you walk.

And where does AI fit in

You can no longer talk about study methods without talking about it, so let us talk about it frankly.

An AI that solves your exercises, writes your summary sheets or explains the chapter to you makes you lose time, for the reason described above: everything it does in your place, you do not learn. The only serious randomised trial on the question (Bastani et al., 2025, close to a thousand secondary school students in mathematics) finds exactly that: with unrestricted access to ChatGPT during practice, results go up sharply; in the exam, without AI, those students do worse than the ones who never had access to it. The interesting point is that the version of the tool constrained to give hints and never the solution does not produce that effect. The problem is not the tool. It is asking for the answer.

There are, in fact, results in the other direction: an AI tutor designed to make the student work, rather than to answer for them, produced learning gains in physics greater than a class taught with active learning (Kestin et al., 2025). It is the same tool, with the opposite use and the opposite result.

In 1987 Jacques Rancière wrote a book called Le Maître ignorant (The Ignorant Schoolmaster). In it he tells the story of Joseph Jacotot, who taught French to Flemish students without speaking a word of Flemish. His thesis is that you do not need a master who explains. You need a master who demands, who checks that you are searching, and who does not let go. An AI that explains everything is the explaining master: it makes you dependent. An AI that questions you and sends you back to your own work is the ignorant master. It is not the model that makes the difference, it is what you ask of it.

In practice, this means turning the tool around. You produce, it questions. You write, it corrects. You get stuck, it asks a question, not a solution.

One prerequisite, before any prompt: give it your lesson. Photograph the pages of the chapter, or the poly, and send them as your first message. Without that, the AI works on what it thinks it knows about the syllabus, with the notation of some other book, a theorem in a form you have never seen, and every so often a false statement. With the photographs, it questions you on what was done in class, with the hypotheses exactly as your teacher wrote them, and you can hold it to account for any departure. The instruction fits in one sentence, to be put at the head of every prompt that follows:

Three examples are enough to give the idea.

The first is for being put through a khôlle (the colleur is the examiner who runs it; PC*, PC and PSI are science tracks):

The second is for getting unstuck without being handed the answer:

The third teaches you to be suspicious, because it writes false theorems with the same confidence as true ones:

These three prompts have the same structure: you work before it intervenes, the instruction explicitly forbids it to give the answer, and a trace is left that you can go back over three days later. Before opening an AI, three questions: have I already tried? Am I asking it to do, or to make me do? Will I be able to check what it tells me? If all three answers are yes, go ahead. Otherwise, close the tab.

The second part of this piece is a complete prompt box, sorted by revision goal, with the unyielding colleur, the oral examination panel, the fake lesson and the rest.

To finish

Let us go back to the original question. The two-hour lesson: you go back over it the same evening, fifteen minutes from memory, plus ten of comparison. You keep the sheet. You go back to it three days later and a week later, ten minutes each time. You never reread it in full again. You do this before the DM, not after. You put your phone in the corridor, and you sleep.

Four full hours in a day are worth eight diluted ones. This is not a consolation for those who work less. It is a description of what works.

Part two: the prompt box

The prompts below are sorted by revision goal. Copy them as they are, change the chapter and the level. They are written for maths but work in physics, chemistry and computer science with the adaptations indicated. A good prompt always has the same shape: a character ("You are..."), a task for you, a prohibition for it, and what it has to produce at the end. And always, as the first message, you send the photographs of your lesson with the instruction to work from them alone.

1. Knowing what you do not know

Checked free recall

This exercise comes before all the others, on every chapter. You write down from memory everything you know: definitions, theorems with hypotheses, methods, examples. Count ten to twenty minutes. Then you launch the prompt:

The missing content you go and find in the lesson yourself. The AI only points. Do it again a week later without looking at the first list.

The inventory of shaky points

This prompt turns one session into a programme for the next:

2. Getting khôlled

This is the central use. The khôlle is the format that forces recall without any support, out loud, in front of somebody who does not accept approximation.

The course khôlle

Do it out loud if your app accepts dictation. Otherwise switch to writing, but without copying and pasting the lesson: type it from memory.

The exercise khôlle

The proof khôlle

In physics, the first sentence becomes "I am going to present [model / experiment] to you, with the modelling hypotheses and the orders of magnitude." In chemistry, it becomes "I am going to present [mechanism / titration] to you, with the hypotheses and the conditions."

The unyielding colleur

To stop being afraid of the khôlle, you have to expose yourself to something harder than the real exam. The most demanding colleur in your school is less demanding than this one, and this one you can close with a click.

The instruction "telling me precisely what is wrong" is what makes the exercise useful rather than merely painful: you do not start again in a void, you start again knowing what to work on. Without it, you can circle a single word ten times without finding it, and that is brain time thrown away.

The oral version is for those who fall apart at the board:

The rapid-fire version works on speed in writing:

Here are two others at the same level, so as not to get used to a single examiner style. The first is the physics teacher who cannot stand recited formulas:

The second is the marker who reads only what is written, not what you meant:

At that level of demand, ten minutes is enough, and it is better to stop before you have had enough. The point is not to suffer, it is to make the real khôlle a situation you already know.

After a week of this regime, Thursday's khôlle is a friendly conversation. What is stressful in an oral is the unknown, and there is no unknown left once you have heard "Start again" two hundred times.

The oral examination panel

This exercise is harder than the khôlle. The panel is looking for your limit, not for confirmation.

3. Getting unstuck without being handed the answer

The single question

A hint about the method is already half the question. You allow yourself two questions at most. Beyond that, you go back to the lesson and come back the next day: being stuck overnight is one of the best moments for learning.

Diagnosing the block

This one is for when you do not even know why you are stuck:

The step back

This is Pólya's method. There is nothing more to say about it: stating it is often enough.

4. Working on hypotheses, and staying suspicious

Competitive exams are full of almost-theorems: the statement you think you remember, true up to one hypothesis. The AI produces them too, without being asked. The exercises below train the reflex you need in front of everything it writes.

Almost-theorems

Hunting the hypothesis

In physics, you work on the conditions for applying a law (Ohm, Bernoulli, ideal gas, the quasi-static approximation). In chemistry, it is the hypotheses of a model (dilute solution, complete reaction, steady state).

The fake lesson

Reading a lesson while hunting for the error means checking every line. What you do not find is what you would have copied out without batting an eyelid.

Devil's advocate

The last sentence matters. Without it, the AI approves out of politeness.

5. Marking without producing

The exam script

The timed mock paper

Take a real watch, put the phone on aeroplane mode and use paper. The "time against marks" feedback is the one you never get in class.

The student to mark

Marking a script forces you to know better than the person who wrote it.

6. Explaining in order to learn

The ignorant student

The ten-year-old

If the explanation does not come all the way down to a simple image, the notion is not understood. The exercise lasts ten minutes, no more.

The sceptical classmate

Looking for what a result is good for means remembering the context in which to reach for it. It is useful at the end of the day, when there is no energy left for an exercise.

The order-of-magnitude physicist

7. Maintenance: spacing and interleaving

Anki cards built with the AI

You reread every card before importing it: that is already a first revision. You delete the silly cards and correct the wrong ones: that too is revision. Then Anki takes care of the spacing.

Spaced recall on the shaky points

This is Anki with open questions, to be done at D+1, D+3 and D+7.

Mixing chapters

In the exam, nobody tells you which chapter the question comes from. That is exactly what you never train for when you work chapter by chapter.

8. Computer science

The rule is the same: the code first, on paper, then at the keyboard, then the AI.

The silent debugger

You have to trace the execution yourself. That is exactly what the written paper asks for.

Complexity

Tracing

The algorithm from memory

9. Organising

This is the one use where the AI produces something in your place: a schedule, not content.

Redo it every Sunday with the updated list.

What not to do

• "Solve this exercise for me." You read, you nod, you have learned nothing.
• "Make me a summary sheet on [chapter]." That is rereading, on a text you did not even write.
• "Explain this chapter to me." If the lesson is not understood, go and see the teacher, a classmate, the poly. The AI comes last, and in questions, not in exposition.
• Asking three times over for "just give me a hint" until you get the answer. You ask two questions, then you come back tomorrow.
• Trusting a statement it produces without checking it. A theorem whose hypotheses you cannot reconstruct is not part of your course material, whoever wrote it.

A typical week with AI

Every day there is Anki: 15 minutes, with cards generated by the AI and reread by you.

Further reading

• Dunlosky, Rawson, Marsh, Nathan, Willingham (2013). Improving Students' Learning With Effective Learning Techniques. Psychological Science in the Public Interest, 14(1).
• Roediger & Karpicke (2006). Test-Enhanced Learning. Psychological Science, 17(3).
• Karpicke & Blunt (2011). Retrieval Practice Produces More Learning than Elaborative Studying with Concept Mapping. Science, 331.
• Bjork & Bjork (1992). A new theory of disuse and an old theory of stimulus fluctuation.
• Cepeda, Pashler, Vul, Wixted, Rohrer (2006). Distributed practice in verbal recall tasks. Psychological Bulletin, 132(3).
• Rohrer & Taylor (2007). The shuffling of mathematics problems improves learning. Instructional Science, 35.
• Fiorella & Mayer (2013). The relative benefits of learning by teaching and teaching expectancy. Contemporary Educational Psychology, 38.
• Ericsson, Krampe, Tesch-Römer (1993). The role of deliberate practice in the acquisition of expert performance. Psychological Review, 100(3).
• Ward, Duke, Gneezy, Bos (2017). Brain Drain: The Mere Presence of One's Own Smartphone Reduces Available Cognitive Capacity. Journal of the Association for Consumer Research, 2(2).
• Ophir, Nass, Wagner (2009). Cognitive control in media multitaskers. PNAS, 106(37).
• Rasch & Born (2013). About sleep's role in memory. Physiological Reviews, 93(2).
• Gollwitzer (1999). Implementation intentions: Strong effects of simple plans. American Psychologist, 54(7).
• Bastani et al. (2025). Generative AI without guardrails can harm learning. PNAS, 122(26).
• Kestin et al. (2025). AI tutoring outperforms in-class active learning. Scientific Reports, 15.
• Rancière (1987). Le Maître ignorant (The Ignorant Schoolmaster). Fayard.