There is no (multiple choice) standardized testing in the Finnish school system and I cannot imagine passing the math tests based on rote learning. I have to assume she took the test somewhere else.
EDIT: The exams at the end of high school can be considered standardized tests, but they are taken at your own school, graded by your own teacher and only verified by the national test organisation. They are not multiple-choice tests.
These are not tests generated from patterns. You may be asked e.g. to solve an applied problem you've never heard of or to sketch a proof to a given (simple) lemma you've never proved before.
OTOH, you are not supposed to solve every problem in the exam, so perhaps you can get the best grade even if you skip all the problems where there's no pattern to apply. In that case, that's a loop hole which the exam creators should plug.
I cannot seem to access that link outside finland.
That is indeed a tough proof to solve sight unseen. Any reason you say that students are seeing that question for the first time in the test. Seems like a famous questions, even chatgpt got the proof correctly .
I think the pressing question here is what the Anki cards contained w.r.t. these problems :-)
The high school curriculum and the text books are not focused on proofs or famous questions. Further, the goal of the exam is to find out your position in the normal distribution of your peers' math skills. You are not supposed to be able to beat everyone else by rote learning (so if you can do it, it's quite a hack!).
I don't think ChatGPT is a good comparison, because it has obviously memorized much more than a human could, and a test to poke its strengths and weaknesses would look different.
EDIT: The exams at the end of high school can be considered standardized tests, but they are taken at your own school, graded by your own teacher and only verified by the national test organisation. They are not multiple-choice tests.