How to Get an A* in A-Level Maths

From the previous post, the possible answers were:

a) 4π cm²
b) 8π cm²
c) 16 cm²
d) 16π cm²
e) 32π cm²

Did you figure it out? Here's the correct answer:

The pi values seem to suggest that the answer might be something to do with a circle.
And then the cm² clearly suggests that the answer is representing the area of something.

So we might immediately think about the area of a circle, πr² - so we'd usually expect a square multiple of pi. Either 4π or 16π fit the bill.

If 4π cm² is the correct answer to the area of a circle, then r = 2
And if r = 2 then we can get to 4π by calculating either the area of a circle, πr², or the circumference of the circle... 2πr
This makes it a poor correct answer as it doesn't distinguish between people who remember how to calculate the area of a circle and those who have gotten it confused with the circumference (hopefully a rare error amongst A-level students, but still!)

If 16π cm² is the correct answer to the area of a circle, then r = 4
If r = 4 then if we make the circumference mistake - we'll get 8π... and we'll get the answer wrong.
Also if we forget to stick the π on the end we'll get 16... and get the answer wrong.
If we forget to square the 4, we'll get 4π... and get the answer wrong.
Or if we get confused and calculate 2πr² (it's been done before!) then we'l get 32π
This seems like a good correct answer - if we make a mistake getting to the correct answer, we're likely to fall into one of the trap wrong answers.

You might argue that the question could be based on the area of a circle with r = 2√2 for answer 8π cm². That would be a pretty cool alternative... however if the question is therefore testing your ability to square 2√2, you'd expect to see trap answers with the square root symbol. So I think we can rule this out.

I'm going to suggest the correct answer must be d) 16π cm². I might be wrong, and I couldn't be sure without seeing the question, but I'd be pretty confident.

Our logic here was entirely based on the fact that somebody else wrote the question in order to catch people out - using this tiny extra piece of information about someone else's behaviour to give us a big advantage.

For more on 'game theory' in real situations, check out The Art of Strategy by Dixit and Nalebuff. Highly recommended!

Here at How to Get an A* at A-level Maths, we'd advise you to always read the question before making a guess!