I’ve been doing preparation for the Oxford MAT exam with a couple of my Year 13s and in the 2008 paper I came across this very nice question about the Trapezium Rule.
I really like this question as to answer it you need to have more understanding about how the trapezium rule actually works than standard A-Level questions on this subject. Invariably they are just pure “plug some numbers in and crunch them” questions which lead to the wide perception that numerical methods are boring. Of course being a numerical analyst I really don’t agree with this perception, but agree that their presentation in the current A-Level course doesn’t help with this.
The above question is nice in that it combines knowledge of the performance of the trapezium rule with graph transformations.
I will leave you to work out the answer, the small Geogebra file I have written may help you visualise what is happening… 