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In QCAA Maths Methods, there are a number of Internal Assessments, or IAs. Each one of them count towards your mark and has been created to be consistent with other assignments across Queensland. This includes assignments and also exams.
The PSMT, which is a Problem Solving and Modelling Task, is a written assignment which is usually quite a bit different to other things that they've done before, where they have to apply what they've learned to real-life scenarios. In Year 12, it is typically the first Internal Assessment, IA1 and is worth 20% (see 2025 syllabus here).
It typically extends over a few weeks and has a few hours of class time dedicated to it.
The PSMT can be quite different to what students have been learning in class. It often involves is creating a whole series of graphs which connect smoothly to each other as a way of representing how that works in real life.
This can be a bit of a trouble area for some students because they haven't done this sort of thing before, but if they play around with it and use an online graphing tool like Desmos or something like that, they kind of get the idea and they can start working towards it.
Then they need apply some principles of Calculus to help ensure that the connection between each graph is smooth. Here's an example:
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