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Are GCSE’s getting harder – An answer

OK so that title is misleading. I am not going to say if I think for sure GCSEs are getting harder, though I do think the maths exams of the last couple of years are making more demands of Students.

But I will give the answer to the question I posted two days ago.

 

I think what is interesting about this question is that its unlikely the student has seen a question quite like this before.

 

Its hard to know how to prepare for the question. What it is looking for is a ‘feel’ for the situation. I think the new 9-1 exams are designed so that this ‘feel’ is required to get top grades.

So how do we answer it?  Well, we are given the common factorisation of a2 – b2.   We are told for the values of a and b this is a prime number.

But we also are given a multiply sum (a + b)(a – b) with this as the answer.  And what is the only multiply sum that has a given prime number p as the answer?

Its p x 1 !   So either a + b = 1 or a – b = 1.  A + b can’t = 1 because we can’t have two positive whole numbers adding up to 1.

so a – b = 1,  or a = b + 1. In other words they are consecutive numbers, as the question says.

And that’s it – It is only two marks after all. A knowledge of what prime numbers are, but in an unfamiliar context, is what is required for these marks.

And that’s what I mean by, an ability, a confidence, of recognising skills and facts learnt when seen in unfamiliar surroundings is what is required to get an 8 or 9 in the new GCSE. It will reward true understanding.

 

 

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