The end of the world cometh - 4 boney dudes on horseback spotted by Daily Mail readers...

GCSE's getting harder causes Paul Dacre's head to explode.
or
"Slightly hard" GCSE Maths Question causes outrage...
http://www.bbc.co.uk/news/education-33017299
The actual question was:
Hannah has 6 orange sweets and some yellow sweets. Overall, she has n sweets. The probability of her taking 2 orange sweets is 1/3.
Prove that: n^2-n-90=0
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On 05/06/15 15:01, Tim Watts wrote:

I should add, that is a paraphrased version (as are all of them as they've been typed from memory).
For the avoidence of doubt, Hannah takes a sweet and it is orange. She eats it and takes another, which is also orange.
The probability of her managing to do this is stated as being 1/3.
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On 05/06/15 15:04, Tim Watts wrote:

which is odd, because as stated it is clearly 100%.. ;-)

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Ah but which has the most calories and can she see the colours? Also if she can, she could be colour blind in which case.. Brian
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For n = -9 or n = 10, easy enough to do in one's head.
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On 05/06/15 15:19, Tim Streater wrote:

https://twitter.com/hashtag/edexcelmaths
makes depressing reading...
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wrote:

That's a solution
not a proof
tim
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At the time I wrote that, I hadn't seen/heard the full question. All I heard was the equation part as reported on the Today prog.
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wrote:

Neither had/have I.
but there's enough information in what you posted to tell you that working out in you head that:
n, will not get you full marks (or even close)
(unless maths exams have been really dummed down in the past 40 years since I took mine)
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Indeed. But at the time of listening to Today, all I had was that it involved Hannah and some sweeties, and the equation. That's all.
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On 06/06/2015 11:15, tim..... wrote:

Correct, it is not a proof - neither was my answer earlier.
This is, though: 6/n x 5/n-1 = 1/3
--> 30/n^2-n = 1/3
--> 90 = n^2-n --> 0 = n^2-n-90
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wrote:

but it's still not a proof in the context of a maths question, which is
prove that n = 10 (from the information in the question, not from the equation)
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He's using the information in the question:
6/n x 5/(n-1) = 1/3
This is the information in the question.
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On 06/06/2015 19:07, tim..... wrote:

It didn't ask me to solve for n - but I have done. I formed the equation from the information in the question - thereby proving it. And, in my previous reply, I derived that n from the equation.
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wrote:

you're right sorry

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On 07/06/2015 11:12, tim..... wrote:

That's ok, I appreciate your reply.
It's a confusing issue, and I think the problem could have been put in a less confusing way. At first I simply found n - which was not the question, as you quite rightly pointed out.
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On 06/06/2015 19:07, tim..... wrote:

There is no requirement to "prove" n (and finding that n would be finding a solution, not providing a proof)
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wrote:

You are misunderstanding the way that "proof" in mathematics works.
You have been asked for a proof, so in order to get the marks you first have to find something that you can "prove".
Simply using the equation to solve n isn't it, because that is not a proof.
And as the equation resolved down to n the thing that you have, that can be proved, is that n is, in fact, the solution to the narrative part of the question.
Thus there becomes a requirement to prove that n solves the sweet problem, because that's all you have that you can use as the result of a mathematical proof.

Correct, so it's can't be the solution to the question that gets you the marks
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On 07/06/2015 11:20, tim..... wrote:

Well actually that was the accusation I was levelling at you[1] ;-) Although I suspect we are both singing from the same hymn sheet - but something has been lost in translation.
[1] Due to your response suggesting that one needs to prove n = 10

Indeed.
Farmer Giles correctly provided a proof IMHO - i.e. derived the required equation algebraically from the source equations extracted from the problem description.

Agreed.

Not really - you can make the proof without ever finding n (which can also be -9, a valid solution to the equation, although makes no sense in the context of the problem)

I am not sure about that - you can't prove that n = 10, since its not the only valid answer. The best you can say about 10 is that it is one possible solution for n.
Finding any number of solutions is not usually an adequate mathematical proof (unless proving a negative of course! I suspect that Andrew Wiles may be a tad upset if you can find integer values for a, b, & c where a^3 = b^3 + c^3 )

Which is what I was saying!
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GCSE's getting harder causes Paul Dacre's head to explode.

There are six orange sweets and n sweets overall. If she takes one, there is a 6/n chance of getting and orange sweet. When she takes one, there is one less orange sweet and one less sweet overall.
If she took another orange sweet, the probability would be (6-1)/(n-1)=5/n-1. Now, you have to find the probability if she gets two orange sweets so you simply times the two fractions: 6/n * 5/n-1 = 30/n^2-n.
It tells us the probability of two orange sweets is 1/3 which means 1/30/n^2-n.
We need to make the denominators the same so simply times 1/3 by 30/30 which would equal 30/90. if 30/90 = 30/n^2-n, then n^2-n. if n^2-n then n^2-n-90 will equal zero.
Mike (with a little help from Google)
Which being in the real 2015 world is exactly what I would do if this were a real problem, so who need to pass the exam?
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