When writing discussions with physics, is it necessary to write up the whole formula using words? Or is it acceptable to just write it out using the symbols as it is written on the formula sheet?

There is no need to write the formula using words. I recommend writing any relevant equation in your answer, and ensuring you refer to each term in the equation (maybe even ticking each term off as you go). Remembering to state that one of the quantities ‘stays the same’ can be very important in earning maximum credit for your answer.

Here is an example that might help.