I think it is a matter of culture to a large extent.
Now I really don't want to create an illusion that our school system is totally useless, but at least in former Czechoslovakia, mild Form of cheating is culturally acceptable. Especially at primary school and high school.
Most students have used some form of cheating at least several times and they openly talk about best cheating methods with their classmates, sometimes even parents talk about their favourite cheating stories.
It is difficult to explain just how much cheating is acceptable, because obviously, it depends on the subject, it's difficulty, importance and whether students believe the information you need to learn by heart is something useful, or something completely useless that teacher assess just because they need to give you some grade.
If I had to put some general rules, it is acceptable to write a formula on your hand. Or a couple of most difficult words when studying a foreign language.
It is also acceptable to gain access to test questions in advance, but in that case, you need to share that info in advance with your classmates or you will be considered selfish.
Of course, it is not considered OK to cheat every time. There is some unspoken limit that most students agree with.
At the university level, there is a smaller amount of cheating during the tests because if you study something, most people actually want to learn what is necessary for them to get a job. E. g. I used to cheat at HS, in subjects that I considered of no value to me. But once I got to Uni, I did not cheat at all, because I really wanted to gain knowledge in subjects that I chose myself.
At my university, academical honesty in essays and final thesis was very important and you had to make proper references every time. There are programs that check originality of each important piece of writing. If they discover you cheated in your thesis, you have a serious problem.
To sum up, helping yourself remember a physical formula - OK, copying someone's original piece of work - not OK.
Anything in between depends on many variables.
I really can't imagine giving students a home test. There is absolutely 0 chance that people would not use Internet, textbook or help each other. No one would consider that cheating, not even the most honest students. Anyway, no teacher would even give such a test! :D
I think it would be very interesting to make a study about attitudes towards cheating in various cultures.