exams or essays

Exams without unseen elements, i.e. that ask you to regurgitate stuff from the lectures, are the easiest in the sense that you can prepare for them. But it takes a lot of effort to memorize things, especially if you don't have any interest in them.

One should not be getting these types of questions at master's level though!

In my final year as an undergrad student we had exams in which we had to write essays as well.

I think OP meant exams or coursework.Of course,you have to write essays for exams,at GCSE never mind A-Level or University, but coursework essays,generally have to be a lot longer.

From what I gather these type of questions are common in mathematics and physics, but the lectures are so hard that it already is a challenge to understand them, let alone remember them. In fact theoretical questions like these seem to be more common in advanced classes where computations become unimportant. How you are assessed it very subject-dependent to be honest.

Route learning/bookwork only makes up ~30% of a question in maths/physics. The rest is usually a problem solving aspect where you have to apply what you know to an unfamiliar problem. This is the hard part.

Are the two not one and the same for a majority of the population?

My exams have been essays for the past three years.

Route learning/bookwork only makes up ~30% of a question in maths/physics. The rest is usually a problem solving aspect where you have to apply what you know to an unfamiliar problem. This is the hard part.

It is more like above 50% of lecture material so that you can pass just knowing what was presented in class and seminars and the rest is an application to a familiar, but previously unseen, problem. That being said the very last part may be very challenging and different from what has previously been seen. Having a look at the past Cambridge exams available online confirm this is the structure used there and at lesser universities I suspect the part of rote learning is even larger. Some graduate courses where it is just too difficult to come up with a reasonable problem and/or problems are unimportant even have exams that just ask for statements and proofs of theorems. But the difficulty of these questions is not to be understated as the material can be very, very difficult.