Mathematics Weblog

Stretching Question 2

Friday 13 October 2006 at 3:14 pm | In Articles | 3 Comments

In Stretching Question I wondered how students would cope with a type of question they wouldn’t have seen before:

If calculate and

The examiners’ report is now out and it says (edited to show context)

Attempts at calculating were rarely completely successful. Many candidates found that was the identity matrix but then went on to say that must also be the identity matrix. Others gave the value of or gave the correct answer without any indication as to their reason for doing so, or with incomplete reasoning.

How disappointing that so few managed to complete the question successfully. The lack of reasoning doesn’t tell us whether students guessed or found it too easy to bother putting down the working. It might have helped if students were taught that if and are integers then there exist integers and with such that but these fundamental ideas seemed to have been lost to A level. In the first AS exam the examiners comment that

When asked to use the Factor Theorem or Remainder Theorem, no marks can be earned for using long division.

which means

British students haven’t a clue how to do long division of polynomials so we’ve made it easier for you, so don’t try and pretend you know best. (See A Level Exam Questions).