DS (good mathematician) is will be taking GCSE maths this summer and I thought I would share the following question from one of the OCR Jan 2008 paper which I thought was a poor question:-
Q10. Given that:-
x[squared] + 12x + a = (x + b)[sq] find the value of a & b
The answers given (on the OCR web site) are:-
a=6 & b=36
Candidates are expected multiply out the equation on the RHS to get:-
x[sq] +2bx + b[sq] (1 mark)
and then assume that as you have 2 quadratic on either side of the equals sign that:-
and 12=2b therefore b=6 (1 mark) and a=36 (1 mark)
My son had great difficultly (as I did) with the assumption above that when 2 quadratic equations are equal that the corresponding terms are therefore equal. He refused to accept (without a rigorous proof) that you were allowed to make this assumption.
I would be interested to hear the views of bone-fide mathematicians - is it reasonable that GCSE candidates should make that assumptions?