It is worth noting, in my opinion, that my optimisation example illustrates a general exam strategy that I believe is under-utilised, which is:
Keep your eye on your goal.
In this question, my goal was the ratio
, and while that can be found by finding
and
and then dividing them, I am not actually required to find
or
.
In forming equation (2), I recognised that I was planning to use it to eliminate
or
from equation (1). Thus, I expressed (2) in the form that suited simplifying (1), rather than making
the subject and adding an extra line of algebra into the substitution step to get to the equation linking
to
.
As I showed later, rearranging equation (2) gave me a form for
where the only variable present was
.
Thus, I worked with the stationary point being at
. I knew that I could take the cube root if I needed
but recognised also that knowing
was likely to be sufficient. This also told me that using equation (2) to back-substitute and find an exact form for
was likely to be unnecessary.
In other words, I didn't stop to find an explicit form for
or
as neither of them was my goal.
In doing so, I avoided:
This is a strategy that can save you time and possibly also avoid losing marks from mistakes in working that isn't actually needed anyway.