Exam-style questions, checked like a proof.

Original practice for the four IB Mathematics courses, analysis and approaches and applications and interpretation, at Standard and Higher Level. Every question is mapped to the official subject guide[1], calibrated on recent official papers[2] and marked in IB conventions[3].

  1. [1]IB subject guides, Mathematics: analysis and approaches; applications and interpretation.
  2. [2]Ten recent official SL papers, 800 marks, measured.
  3. [3]IB command terms; markscheme notation M, A, R, AG, FT.
  4. [4]TI-Nspire CX II guidebook; NumWorks software 23.

the method

How to use Hence.

Five steps, notion by notion. The first three are documents you download from your course tab; the last two are played on the site.

  1. Read the course

    The course of each sub-notion, with the notation the markscheme expects.

    course tab · PDF
  2. Study a marked example

    An exam-style question solved line by line, with the mark each line earns.

    course tab · PDF
  3. Do the exercise under it

    A similar question, on paper, then more practice.

    course tab · PDF
  4. Mark it

    Predict the marks of a question, write each line, and check it.

    Mark it · on the site
  5. Train the calculator

    The Paper 2 moves, key by key, on the NumWorks and the TI-Nspire[4].

    GDC training · on the site

what a marked example looks like

3.[Maximum mark: 6]

Let $f(x)=x\,\mathrm{e}^{-x}$, for $x\ge 0$.

(a)Show that $f'(x)=(1-x)\,\mathrm{e}^{-x}$.[2]
(b)Hence find the coordinates of the maximum point.[3]
(c)Write down the range of $f$.[1]
(b)  $f'(x)=0$M1
     $x=1$A1
     $\left(1,\ \mathrm{e}^{-1}\right)$A1
  • AG

    Show that gives the answer away: the marks are for the working, and the markscheme writes AG, answer given.

  • ⇒

    Hence asks you to use what you have just shown. The parts of a question lean on each other, as in the real papers, and that is where the name comes from.

  • [3]

    Three marks, three steps: a method mark, then two accuracy marks.

Why it is original. Each question starts from a syllabus point and an invented context, never from a past paper, a textbook or another website, and its origin is recorded.

one pack per course

Choose your pack.

Packs are bought per course, AA SL, AA HL, AI SL or AI HL, and open the same levels in its exam papers, in Mark it and in GDC training.

Free

Try it

  • A few examples in a few notions of every course
  • Mark it on those questions
  • The first moves of GDC training
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Premium

Every sub-notion

  • An example and a similar exercise in every sub-notion
  • Mark it: one question in every sub-notion
  • The first moves of GDC training
December 2026

Excellence

Everything

  • Several examples in every sub-notion
  • Mark it: every question
  • The full Paper 2 GDC trainer
December 2026

Bought by a parent, with an account for the student. Prices announced at launch; tell me if you want to be told.

I am Lenny Gastineau.

I teach mathematics in Switzerland, in three systems at once: the IB Diploma, the French baccalauréat and the British curriculum. Writing exercises for my classes is a weekly habit; Hence is where I do it for everyone, in my own time and separately from my school.

I use AI to draft and to check, and I say so. What makes a question good enough to publish, I decide, and the last check is mine.

Lenny

P.S. Found a mistake? Tell me at [email protected]: it is corrected within 72 hours, for everyone.

LG
Lenny, in class
in short
  • teachesIB Mathematics: analysis and approaches, both years of the course
  • also teachesthe French baccalauréat and the British curriculum
  • supervisesInternal Assessments and Extended Essays
  • correctionswithin 72 hours, to every buyer