11 Plus Exams Forum

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:-

a=b[sq]
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?

I'm no bona-fide mathematician, but I do know that if you're told that two polynomials in x are equal for all values of x, then this implies that the corresponding coefficients are equal. (Don't know if that's in the GCSE syllabus, though.) In this case

x^2 + 12x + a = x^2 + 2bx + 36

implies 12 = 2b and a = 36. An alternative method (certainly within the GCSE syllabus) would be to plug in x=0, getting a=36, and then plug in x=1 to get

1 + 12 + 36 = 1 + 2b + 36

and thus b=6.

I might be over simplyfying things but isn't it a case of equating the co-efficients for each of the terms?