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9:06am on Monday, 2nd September, 2024:

Anecdote

Sometimes, some of my exam questions are effectively multi-choice. I'll say something like "Here are four categories and ten situations. Associate each of the situations with the category that best describes it.".

Some exams, particularly involving first-year undergraduates, are all multi-choice. This is because marking 300 papers is a lot easier if a computer does it for you.

To pass a module, students need to get an aggregate of 40% or more across exams and coursework, with at least 30% in both. Because coursework marks are generally a lot higher than 40%, this means that candidates often only need 30% in the exam to pass.

If it's a multi-choice exam, though, you're going to get some questions right just by guessing. So ... how many questions do you need to get right to meet the minimum needed to pass?

Let's say you need to get at least Q% questions right, chosen from R options, and the pass mark is P%. In general:

Q + (100-Q)/R = P

so Q=(RP-100)/(R-1)

Plugging in the numbers:

R P% Q%

4 30 6.67

4 40 20

5 30 12.5

5 40 25

So if there are 50 ABCD questions and a pass mark of 30%, you only need to get 4 questions right and you've passed. OK, so luck plays a part (that (100-Q)/R is an average), but if you can rule out one of the answers then that increases your chances. That said, I have seen candidates score less than 25% on a 4-option mutli-choice exam.

Anyway, switching from R=4 to R=5 makes quite a difference, at least for a pass mark of 30%. So, should I give my multi-choice questions 4 options or 5?

Well, I know all this and I usually give them 4 options. That's because I am aware of what's coming in the rest of the question (that isn't mult-choice) and I don't want to have to mark a lot of resits.

I'll only ask multi-choice questions at most once per paper, and the section will be worth either 8, 10 or 12 marks (out of 100). If my whole paper was multi-choice, I'd want 5 options (the blank forms don't allow more).

Some lecturers ask questions that are binary, yes/no.

R P% Q%

2 30 -40

2 40 -20

A coin is going to pass those.

Still, if it pays its £9,250 per term, the university doesn't care.

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