IMC Key Stage 3 · 5. Inequalities, extreme values and the floor function
Find extreme values with squares, AM–GM and distances, always showing where equality happens, and solve floor-function equations by trapping the integer part.
IMC Key Stage 3 – Selected topics
Use $A^2\ge0$ and completing the square to find minima and maxima.
Apply AM–GM and check that the equality case is possible.
Interpret square roots as distances and minimise a path by reflection.
Solve equations with the integer and fractional parts by trapping the integer part.