There are many types of homework and undoubtedly some are not useful. These fall into the category which we often refer to as "busywork" - they are assigned for

There are many types of homework and undoubtedly some are not useful. These fall into the category which we often refer to as "busywork" - they are assigned for the sake of assigning homework because that's what instructors feel they should do. The useful kind of homework we can categorize as being helpful for the exam, and those which are useful even beyond the exam. In principle, they should be correlated, but there are also many ways to create useless exams too.