MAT - Paper 2018 - Q1H
Flashcards
Thinking past the geometry
What is it sometimes useful to think about when given a geometry question?
Trying to “see past the geometry” and think about constraints on variables instead.
What should you be doing with any geometric diagram?
Thinking about extreme cases.
Rearranging and minimising the expression
\[\frac{4s^2 + t^2}{5st}\]
How could you rearrange this into something potentially more useful?
\[\frac{4s}{5t} + \frac{t}{5s}\]
\[\frac{1}{5}(4\frac{s}{t} + \frac{t}{s})\]
What substitution could you make here?
\[u = \frac{s}{t}\]
\[\frac{1}{5}\left(4u + \frac{1}{u}\right)\]
How could you find the minimum value of this?
Differentiate and set to zero.