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When it comes to writing examinations, there are two options I am considering.

The first is to write the entire exam originally (which will of course mean some well-known proofs, thereby technically not making it completely original)

The second is to use a ratio of 'original' questions and actual past paper questions.

My students have access to perhaps 50 past papers to practise from.

The theory I had behind using actual past paper questions was to encourage them to do more past papers. Perhaps not for the best of reasons (as I presume they'll be hoping that they'll get lucky and get a question in my exam that they've seen already) but motives aside, they may complete a larger volume of past papers.

I'd like to hear some thoughts regarding this. Is this a good idea, is this a terrible idea? I can imagine that a few students may get lucky but in terms of the majority of the cohort (around 60), it may boost overall past paper attempts.

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  • $\begingroup$ just to clarify, by "past papers" you are referring to exams you have administered in the past that students have been able to keep? $\endgroup$ – celeriko Mar 4 '15 at 16:45
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    $\begingroup$ Not necessarily exams that I have personally written, but indeed examinations that students have been able to keep and were provided with worked solutions sets. $\endgroup$ – Trogdor Mar 4 '15 at 16:46
  • $\begingroup$ ok cool, glad we are on the same page :) $\endgroup$ – celeriko Mar 4 '15 at 16:49
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    $\begingroup$ An advantage of reusing questions is that on questions that aren't just routine calculations, it can be difficult to judge in advance how difficult it will actually be for the students. Reusing questions makes it less likely that you will misjudge the level of difficulty. $\endgroup$ – Ben Crowell Mar 4 '15 at 17:29
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It depends on your goals for the examination. As you are mentioning proof, and using some well-known ones, it seems that you are aiming for more of a "show me that you've thought about all of these types of proofs" style.

As they have access to a large collection of examinations, I would, perhaps, pick a few exercises from those of the most important ideas and run with those with a few 'newer' style problems. As they have a large collection, you can perhaps place emphasis more "write down the core idea behind the proof of 'Big Theorem X'", or knowing how to prove a key lemma that is critical to a 'Big Theorem'. Other options are just having them prove an inductive step, if that is a tricky part, or a special case of some Big Theorem (or Large Lemma) or even a homework problem. The key point is that they can show you that they are familiar to the key proof strategies for the particular course you are teaching. While it sometimes boils down to "memorize this list of 100 proofs", hopefully, along the way, they pick up the proof strategies to simplify their list.

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