# MAT - Paper 2018 - Q1H

> Source: https://ollybritton.com/notes/maths/problems/mat/2018/q1h/ · Updated: 2024-08-24 · Tags: mat, notes, maths

## Flashcards
### 2021-10-27
##### 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.

##### $$\frac{4s^t + t^2}{5st}$$ 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.

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