# Infinite area, finite volume of revolution. Another example of a poor mark scheme?

Discussion in 'Mathematics' started by begbiesan, Feb 27, 2012.

1. ### begbiesan

In a Further maths paper, a question required an answer to a definite integral: from x=1 to x=4 of the function (x/(x-1))^(1/2), using the substitution x=cosh^2 u
This gave a rather nasty, but finite result.
It cheated a little, because cosh-1 x has a domain for x>1, and x<-1.
Hence, the volume of revolution (requiring no such 'illegal' substitution) was infinite
(as expected).
I am not aware of any marks available for the valid comment concerning the validity, or otherwise, of the given substitution.

In another paper, GCSE, I have seen a trig question concerning the ratio of angles in a triangle of 2:3:5, and the students were encouraged to use trig to show that the sides were not in the same ratio as the angles.
No marks in the scheme for the obvious answer: "if the sides WERE 2:3:5, then there wouldn't BE a triangle" !!
Any other examples of such mark scheme bloopers?

(another question asked students to match the units to a type of measurement. the measurement was "weight", and students were expected to match this to 'grams'. as other matches were length to metres, area to hectare, and so on. "Newtons" was not a given option.)

2. ### NazardNew commenter

I am very happy to castigate examiners who set incorrect papers, but I don't think it is necessarily fair to call these 'mark scheme bloopers'.

Back in the day, when I marked public exam papers, the mark schemes were produced and printed before the first markers' meetings. this was before any papers had been marked and, amongst the information we were given was a statement to the effect that "these are draft mark schemes and are not exhaustive. Other answers and partial answers may gain some credit. contact your team leader if you are unsure."

Assuming that the markers are competent, then other correct answers should be referred up the food chain to someone who makes a ruling from on high.

The mark schemes were then published without any changes being made. I assume this was to save money.

Anyone else experience this too?