Probability of first sweet being orange = 6/n
Probability of second sweet being orange = 5/(n-1)
Combined probability = 6/n x 5/(n-1)= 1/3

30/(n^2 - n)= 1/3

n^2 - n - 90 = 0

Thousands of GCSE candidates complaining that it was too hard?

baffled me !

A 10 year old should be able to solve that!

M&Ms,
they have the six different coloured sweets in a pack needed for the equation.

But Brian, we have the advantage of being edumificated.

There are people out there who aren't aware that 30% = 3 out of 10; who can't calculate how many square meters of flooring slabs are required to cover a 2 by 3 meter area; who can't divide £2.70 by 3...

Dats cozz yoo pay too pownd seventie conatliss init bruv.

Bloody forum auto correct spoils my fun sometimes.

I realise that, Neil, but I was trying to think in the context of GCSEs. If you are studying maths and have reached the end of the academic year (4 or 5?), my feeling is that this question ought to be pretty straightforward to answer.

My inclination is to suggest that the reason why it was found difficult might have been that it wasn't included in the preparation schedule. No-one actually showed them in advance how to do it.

Don't joke!!

I teach Science and Computer Science, and absolutely despair at how 14/15/16 year olds are unable to think through and solve any problems.

Yesterday, I asked my year 10 (15 year olds) Computer Science class to write down in English the steps needed to take a list of numbers and find out the highest number in the list.

It was like drawing teeth.

I personally blame it on allowing the use of calculators.

If a few complain that this was too hard, they obviously didn't study enough.
If thousands complain that this was too hard, then questions should be asked of the teachers and not the students.
I'm shocked that this is not the case.

Not in all cases, but in this one, it is a potentially valid point. Assuming that probability and quadratic equations are both on the maths syllabus, and the teachers have attempted to teach pupils how to abstract solutions using combined techniques, then yes.

It does make me wonder though. If most schools did not tackle this area, hence thousands of pupils complaining, it suggests a gap in the syllabus which could be a teaching fault but also an exam board fault.

Nevertheless, I stand by the point that the ability to abstract has been lost over the few generations.

Just out of interest (and the above does baffle me)
1. what is the ^ for
2. is the / sign here in place of the horizontal "over" symbol?
3. is it a question or a statement which needs explanation?

I'm assuming n is "any number".

Its a 'proof' question I believe.

Something like prove that the probability of picking two orange sweets equals the stated quadratic equation.

1. The little hat sign means 'to the power of' so n squared
2. You are right / means divided by

I've ranted on this before.

The problem is neither the pupils, the examination, nor, I think, the teaching: it is the ridiculous concept that a syllabus should be taught which encompasses the entire range of abilities, instead of sensibly streaming pupils by ability.

The result is a paper which has to be intelligible to someone who will never progress beyond basic arithmetic while providing challenging for those who are ready for calculus and more abstract mathematics.

These are two different subjects: arithmetic, which anyone should be able to do, and mathematics, which is a sophisticated and advanced study of symbolic manipulation. As different subjects, they should be different examinations and, significantly, different courses throughout the school.

The reader is invited to google for old examination papers and compare them with current 'equivalents'. They will find that, for example, an O-level paper from the 1970s or 1980s is *significantly* more advanced than the modern equivalent (and no, this is not 'it was harder in my day' speaking). When my generation was at school it was expected that arithmetic was understood *before* the O-level course was begun.

But then, I am of the generation that believes that a person who cannot manage basic arithmetic and basic spelling and grammar of his native tongue (absent medical reasons) upon leaving school is not yet human; at best he is an ape that has learned to dress himself.

I agree mostly with the above, although at many schools, there will be a differentiated syllabus with pupils streamed by ability.

I know from experience though that the syllabus may not be sufficiently different across classes to avoid this situation, and depending on the school, the variation in ability within each class may be so broad that it is impossible for the teacher to prepare and teach a lesson to that level of individuality.

It sounds like i come from the same era as Mr B above, where arithmetic was sorted at primary and algebra pretty much started in what is now year 7.

I observed a year 10 maths class a few weeks ago (15 year olds one year off GCSEs). The topic was linear equations leading to quadratics, and given this is almost the end of that year, it was shocking to see that this was only being taught now, and the lack of ability and engagement in the problem solving process!

But nobody's worked out how many sweets were in the bag, or that the remaining colours are indeed yellow! I've got my doubts what value for money Hannah got with that bag of sweets. Let's face it, when 60% of your bag is one colour there's QA issues afoot.

Thank you for that.
So I understand that ^ is the accepted alternative for 'squared', where the small '2' might not be found on some keyboards.
And that the first statement seems to mean that the probablity of picking orange is 6 times out of the number of sweets available? Assuming that n is 'any' number....
I would have thought it more likely to be a percentage...

Original post included most of the solution hence it is obvious n=10.
Expanding on Wombat's post above, the challenge in the exam was to take some information and produce the equations shown then simplify. That's the bit some people struggled with.

Well it's obvious to those who are familiar with the format....



As with the 'senior' previous contributors to this thread, I was directed first through arithmetic then algebra before geometry - "Ordinary" Maths. It was calculus that closed the door firmly for me and the need to deal in such formulae and the ability to retain them. I don't find my mind works well in that manner or with pattern - however rather surprisingly to me I can still remember the notes of Bach-Busoni's Chaconne (about 15 minutes duration) which I last performed 43 years ago, and many other similar ones. Memory and its routes are fascinating, but I'm nearly straying off topic.

Maths in my experience has the reputation for having the "worst" teachers and the association of private tutors to help pupils pass exams - I wonder if that's a bit harsh and if because of people's varying ways of learning whether it needs be taught to far smaller numbers of pupils at any one time. Like two.

Yeah, absolutely didn't mean that to come across as derogatory. Trying to point out (admittedly much less concisely than Wombat) that the solution is presented at start of this thread and therefore the problem posed in the exam needed more thought than simply figuring out the value of n.
When mathematics gets complicated I do agree the teacher and in particular their particular methods can make a huge difference. Living in the age of the internet must be great for more motivated students.

Not sure I agree, I believe fully understanding the question involves knowing n. Okay they're not asking for n, but at the same time you do need to construct then rearrange the formula to prove the statement. Once you're there it's not much more to solve n. With that information you can check your own work to see if you had the right approach. This was possibly the best bit of advice I ever received in the subject.

That's what I'm saying. For the masses, here is the question as it appeared on the paper:

Going back to a point that seems to have sunk out of sight, but which I still think is relevant, to me it seems likely that contrary to the established practice this question was not explicitly 'worked through' during preparation for the exam. The pupils are used to everything being worked out for them. That's why they complained. If you read the original article again, I think you'll find some fairly explicit references to that fact.

Quite interested in this. It is possible that previous exam papers have not covered this type of question, and as mentioned, probability, and separately, quadratic equations are on the syllabus, but no-one predicted or thought that a problem involving both would appear as a question on an exam paper.

I have quite limited experience as not been at the teaching game for long, but having prepared students for science and computer science for a couple of years, it is not general practice, or even possible, to prepare students for every type of question that comes up. I'll give a computer science example - the exam board cannot predict what languages schools teach, so to ask code related questions, they use a form of pseudocode for which a guide is available. I prepared my students by ensuring they practiced using the guide, and also looked at the few prior papers to see what typical questions have come up in the past. This year, I was spot on, and the extra practice in those areas paid off. In science, which is a much broader church, I followed a similar strategy, but was not so lucky.

So strategically, whether good or bad, yes, teachers will try and pre-empt questions or question areas, but every year, in every topic, the exam boards stay one jump ahead.

This maths question might have been a jump too far!!

Oh and on the question itself, us elderly folk would always double check our answers by working out n, but the question does not actually require this as it is a proof. Basically prove that the probability can be represented by the given quadratic equation. Don't need to work out n for that, just need to abstract until the cows come home!!! n is a figment of your mind!!

I wonder how much of the issue is that there are two questions disguised as one. The second part, of course, really means 'prove that n = 10' but you don't see that until you've solved the quadratic.

n^2 - n - 90 = 0
n^2 - n = 90
n^2 = 90 + n ... hmm, you could use the quadratic equation solver, but on the other hand, I can't believe that kids don't know squares up to 10...
So, n = 10.

Now, knowing that, you know that Hannah chooses two sweets from 6 orange and 4 yellow. If the probability that both are orange is 1/3, then you have proved the thesis.

The probability of the first sweet being orange is 6/10; and *if it is orange* then the probability of the second being orange is 5/9; combined probability of both is 6*5/10*9 = 30/90 = 1/3.

QED.

@ Enforcer, your point seems to be that most kids have limited or no intellect. Bit harsh!

This is a lot clearer than the OP!

I seem to have forgotten to provide a link!!