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Creating exercises: Types of questions

I always have trouble creating problem sheets so I’m trying to classify the types of exercises and problems I can use:

  1. Routine exercises. A routine exercise is usually a calculation or follows some given worked example. Good way to start a sheet.
  2. Problems. Solutions to these require more than just regurgitating some worked example or simply applying a theorem.
  3. Extend the theory. Prove a theorem that there has not been time for. Usually done via a set-by-step process.
  4. True/False or Always, Sometimes, Never. See previous post.
  5. Generalise a statement. Give a more general statement than in the notes say. Is it true or false?
  6. Create examples. Give an example of some mathematical object.
  7. Counter examples. Create counter examples to statements.
  8. Challenges. These are hardest to create but should be on the problem sheet for the strong students.

What other types of questions are there? Please leave comments below. If I get quite a few, I’ll describe them in another post.

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