Exams and olympiads

Learn for the exam. And beyond it.

NodeStudy follows what you want to learn: languages, university subjects, a question sparked by curiosity or exam preparation. These examples are starting points, not an exhaustive list of supported subjects.

Exams and entrance tests

Bring the question you got wrong, and the tutor locates the first step that failed.

MathsPhysicsChemistryProgrammingEntrance tests and olympiads

Every assistant will mark a question. The difference is what runs behind each step of this one.

“I differentiated y = sin(x²) and got cos(x²). Is that right?”

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The first step that failed

NodeStudy · illustrative answer

It is not, and the error sits in one step. You differentiated sin(u) correctly and stopped before differentiating u itself. Here u = x², so the derivative of sin(u) is cos(u)·u′, with u′ = 2x. The answer is 2x·cos(x²).

The principle: the chain rule does not disappear when the inner function is simple. It disappears when you treat the inner function as though it were x itself.

What runs behind it

The wrong step is not the model’s impression. A deterministic checker refutes the transition, and only a refutation counts: one point of disagreement proves inequality, while agreeing at several proves nothing.
The notebook inherits the turn’s evidence: verified when a checker refuted something there, provisional when the diagnosis was the model’s. The refutation covers the turn, not each sentence: the page claims the correction locates the step that failed, not that every line was proved by a tool.
The drill order is the server’s, not the model’s: blocks of different topics alternate where they can, and the faded pair stays together on purpose, because the worked example has to still be fresh when the next problem blanks its key step.

Challenge

A line through (0, 2) is tangent to the curve y = x³ − 3x. Find the point of tangency and justify why there is no other.

University and curiosity

Bring your course notation, ask for a simpler example, or go deeper than the lecture did. You do not need an exam booked.

“My course notes define the derivative as a limit and I cannot see what that means. Draw the tangent line and show me where the limit appears.”

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The definition, and the figure that explains it

Derivative: the limit of the average rates of change as the interval gets smaller and smaller.

$f'(x)=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}$

The figure is the same statement drawn: the tangent line touches the parabola at (1, 1) with slope 2, the value those average rates converge to.

Illustrative figure: the derivative f′(1) = 2 determines the tangent slope.

Paper search, with a question in mind

“Find studies on active recall and rereading. Compare the experimental conditions, the results and the limitations, with links to the papers.”

A reference to explore: Roediger & Karpicke (2006), Test-Enhanced Learning. The paper distinguishes immediate performance from delayed retention. That difference helps frame a more useful comparison than simply asking which technique “wins”.

Languages, classical ones included

Conversation by text, corrections that carry their reason, and analysis of form, including languages nobody speaks any more.

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Latin

“In rosā, with the long a, which case and number are possible? Explain how the quantity mark changes the analysis.”

The long vowel is the only thing separating the nominative rosa from the ablative rosā. Without the mark, which is how the text usually arrives, the form is ambiguous and the syntax of the sentence decides the case.

French

“Why does allée end in -e in this sentence? Explain the choice of auxiliary and the participle agreement, then ask me for the same sentence in the masculine.”

Aller takes être, and with être the participle agrees with the subject. The final -e is what says the speaker is a woman.

Japanese

“Do 昨日は勉強していました and 昨日は勉強しました describe the same thing? Explain the difference and give me a context where only one of them fits.”

しました presents the studying as a completed fact; していました presents it as an activity under way across an interval. It is the difference between “I studied yesterday” and “I was studying yesterday”.

Vocabulary you want to keep becomes a flashcard in the same gesture, and comes back at the right interval.

A hobby, treated as a subject

Bring a skill you want to get unstuck on and it becomes a track with the same structure: the notation first, then the practice, with a criterion for getting it right.

“I want to learn Square-1 from scratch. Explain the notation, teach me how to get back to a cube, and give me three shape drills to practise today.”

See an example

Square-1, from scratch

The track has the same shape as a school subject: the notation first, then the shape phase, then the permutation phase, each with drills to repeat until it comes out without looking. In a lesson the tutor also draws the intermediate shapes (scallop, kite, paw) and runs the sequence in code before claiming that it works.

Top layerBottom layer

The two layers of a solved Square-1. Four 60° corners and four 30° edges close each layer's 360°: the pieces are not the same size, which is why the layer leaves the square shape as soon as you slice. In a lesson the tutor also draws the intermediate shapes (scallop, kite, paw) and runs the sequence in code before claiming that it works.

It works for an instrument, for chess, or for a process at work. What the tutor asks for is a criterion for success: without one, it cannot tell you whether you managed it.

After the studying: the plan and the document

The four cases above end in the same place. What you studied becomes a dated plan, and becomes a file you can take out of the product.

From the goal to the planner

“I have two weeks to revise derivatives and integrals. I can study 40 minutes a day, except Sundays. I struggle with the chain rule. Build a plan with exercises and reviews and show it to me before scheduling.”

The tutor proposes sessions from your goal and your availability. Once you have reviewed the proposal, you ask for it to be scheduled: a proposed plan is not in the calendar yet.

NodeStudy / PlannerIllustrative example

TodayQueueCalendar

Week of 15 to 21 · 1 h planned of 3 h available

Today15
40 min / 1 h
The chain rule
Tue16
20 min / 1 h
Derivative exercises
Wed17
nothing due

Now

The chain rule

20 min · Calculus

Done when: you redo the derivative without looking at the solution.

Start session

Today1

Unaided review20 min

Summaries, handouts and mock exams, in the format you will actually use

An explanation becomes a PDF to revise from, a Word document to edit with your own notes, or a PowerPoint deck. When the answer carries a table, it also comes out as an Excel sheet.

“Build me a revision PDF on the chain rule, with definitions, two worked examples and exercises with answers at the end.”

Each format appears when it can carry the content: slides when the formulas fit on a slide, a sheet when there is a table to take away. A file that loses the explanation is not offered.

Your study, connected to your routine

Google Calendar

Send planner tasks and exams to your calendar, reviewing the changes before you sync.

GitHub

Study programming with your project in context: ask about a snippet, or turn the question into an exercise.

Anki

Your decks go both ways. The importer reads the file Anki itself exports, with a preview before anything is written.

Reminders

By email or in the browser, to pick up pending tasks and reviews. You choose the channels in settings.

Frequently asked

Do I need an exam coming up?

No. You can study a language, explore a new topic, work through a university subject or prepare a presentation. Start with what you want to understand.

Can I bring my own questions?

Yes. Share your question and your attempt, or upload your study material. Ask for hints, a worked explanation or another question to try independently.

Can I choose how much help I receive?

Yes. Ask for a small hint, a step-by-step explanation or a deeper discussion. You can then test your understanding without looking at the solution.

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