Design better tests. If you can "cheat" on a test by just googling things/looking at notes then the test isn't testing anything but rote memorization anyway.
It's also why I believe that in most cases multiple choice questions have no place in any well designed tests because it's extremely hard to create multiple choice questions that actually test the application of knowledge versus the regurgitation of rote learning.
When I was in university (grande école) in France, luckily all tests followed that format, they were open book, very few questions that needed deep detailed answers and were about interesting problems. Even finding tests from previous years and doing them was actually fun (tests were never reused).
I did an exchange in the US at RIT and most tests had very boring rote learning questions. For example in a computer graphics class: Which company were voting members of the OpenGL Architecture Review Board? Which year was the first OpenGl specification released?. I still remember those questions because I was shocked by how utterly stupid it was to have those on a test but, in general, 25 to 50% of the points of any tests was on those completely irrelevant, useless questions that anyone can google for.
Cheating is a problem for universities that never had proper testing standards. But that's a symptom of incompetence on the part of professors and of universities not making the choice to ensure that tests have to be well designed.
Although I also encountered a few where multiple answers were technically correct. Then you have to guess at which answer the professor thinks is "more correct" which kinda sucks.
It can be done decently but it's much easier to write and much more common to see bad multiple choice questions.
1. If you need to lookup stuff in your waste of material you won‘t be able to finish everything. The time constraint was very hard. 2. It was not just repeating former things, you had to have understood them. Everything was a transfer knowledge exercise.
Did you enjoy this exam? I am asking as I had a very similar experience in my undergrad:
Our university allowed some basic courses to be studied at different departments, if they were equivalent. This means that there was a CS Major Algebra 1, but also Math Major Algebra 1, and you can take either.
I took the Math Major Algebra 1, being a CS student, and I have passed everything up to the final exam, where I learned that the exam is literally what you describe. All the proofs and arguments needed follow from basic principles (as things in Algebra 1 tend to do), but there is a lot of questions and the time limit is strict.
Thus, you have no time to actually do any deliberate thinking, you have to memorize and understand the basics so well that you can develop the arguments essentially in real time.
(And it was not an open book exam, even, but as you describe, it would not have helped you too much.)
I hated that exam. I never took it out of principle, instead just quitting the course and doing it with a great grade a year later, in CS. I still dislike the idea of forcing knowledge acquisition through strict time limits. What if somebody is smart but has a slow start due to stress? Ugh.
Reminds me of my school days. Tests with hundreds of questions and less than a minute to solve each question. They were essentially testing the student's time management skills as well as their physical and mental fortitude in addition to their knowledge. Extremely exhausting and anxiety inducing.
The way some teachers solved this was a 1:1 oral complementary exam, where students were asked to explain a random set of their solutions. This is drastically more difficult to cheat in real time, and you will almost certainly look like an idiot if you come unprepared. It's a stupidly simple solution, disincentivizing cheating through shame. Doesn't need any proctoring rootkits and rectal cameras, a simple identity check is enough.
I see the same when I interview people online and I hear them frantically click their keyboard - but no help, I know before what Google returns.
[1] I don't ask API knowledge, if someone doesn't know some API I tell them just to invent the call they need.
(Then I spent an hour-ish talking to swardley about 3D printing and its future impact on IP law, etc. -- this was back in early 2007, before it was generally available. That was the weirdest non-technical interview I've had.)