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Further mathematics
In further maths, from A-level to AP-style courses, everything rests on precise statements and well-sorted cases. Lumi quizzes you on theorems, formulas and criteria until you can produce them without notes.
How to turn this subject into cards
On an advanced course the chapters pile up fast, so one card per result beats one card per chapter. Write the theorem, its exact conditions and one example where it does not apply. Conditions are what you forget first and what exams test the most. Lumi asks for a complete statement, then lets you correct it when it deliberately gets a condition wrong, which forces you to really know it. Studying with the aim of teaching has been shown to improve recall (Nestojko et al., 2014). Lumi handles the recall routine, not the thinking. It helps you memorise definitions, theorems, formulas and sequences of steps.
Example card
Try it, Lumi turns it into fill in the blank questions in your browser.
Further mathematics · teach this card to Lumi
De Moivre’s theorem says that the n-th power of cos theta plus i sin theta is cos n theta plus i sin n theta. A square matrix has an inverse only if its determinant is not zero. The eigenvalues of a matrix A satisfy det of A minus lambda I equals zero. The sum to infinity of a geometric series is a over 1 minus r, provided the modulus of r is less than 1.
Lumi’s question
_____ says that the n-th power of cos theta plus i sin theta is cos n theta plus i sin n theta.
Pick the missing word
Answer right to light Lumi up
Its lamp fades when a fact slips away.
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Teach this to Lumi
Give Lumi your further mathematics notes, it gives them back as questions at the right moment.