A student gets 80% on a 25% weighted "token" homework component, 60% on a 25% "lab" component (due to copying large portions of someone else's report), and 30% on the 50% exam (there's always a few low apples). They pass with 50%.

The lecturer sees that the exam is too hard, and makes it easier the next year.

if your homework is 1/4 of your grade in the class, that class is a "pass me" class. in some math classes the prof refuses to acknowledge that homework actually has a measurable effect on your grade, but he will use its presence to round up instead of down (i.e. 89.5 becomes a 90 instead of an 89)

Cheating doesn't happen when there's virtually no incentive. I stand by my point that you can cheat in Math homework more easily than equivalent non-Math homework, if you want to.

If 400-level Math coures are really impossible to cheat on, but there are 400-level non-Math courses that are possible to cheat on, I'd just argue that this is because they aren't really equivalent.