As an OU student you have to make several TMAs for each course you do. TMA stands for Tutor Marked Assignment. A TMA consists of assignments covering all the booklets you studied in the period prior to the cutoff date of the TMA. The cutoff date is the latest date the work has to be received by your Tutor. This is a period of cutoff dates. Usually you'll find a lot of blog, forum, twitter or facebook posts about TMAs that have been done. Completing a TMA is just part of the study process but for an OU student it's somewhat of an event. Not like an exam, but sending it out gives a feeling of relief, achievement perhaps. Completing a TMA is not something most people do in a few hours, some TMAs take weeks if not months to complete.
The average result of the TMA ( after some formula has been applied to it ), is the maximum result you can get from the course because the final result of the course is the minimum of the exam result and the average TMA score. Also, a minimum TMA score is required to be eligible for taking the exam. For example.
TMA result: 15/100 not eligible for exam.
TMA result: 65/100. Exam result: 100/100. Course result 65/100.
TMA result: 100/100. Exam result: 15/100. Course result 15/100 and thus a FAIL.
Completing all the TMAs on time, requires regular study, and regular study enhances the chance on a good exam result significantly. I suppose that's the thought behind it all. The second example may seem rather undesirable, but it just is not a realistic scenario. A student with a 100% exam score usually has no problems with the TMAs.
Personally, the TMAs are no longer my 'major math challenge'. Slowly but steady I am working on my own mathematical projects. I still need to study, of course, but I am an OU student mainly to justify the time I spend on mathematics to the other stakeholders in my time.  When you say you study mathematics as a hobby, people accept it ( at best ), but explaining that, in fact, you are involved in your own mathematical research is worse than telling that you apply the tools of Scientology in your life. So... I am an OU Student, if you know what I mean. ;)
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(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)
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