UK GCSE maths question caused indignation

qweerty

QPeople across the channel getting very exercised by a question on a GCSE (junior cert equivalent) maths question.


http://www.theguardian.com/education/2015/jun/05/students-protest-gcse-math-question-viral-trending-twitter

http://www.bbc.com/news/education-33017299

http://www.mirror.co.uk/news/uk-news/gcse-maths-question-row-can-5826816


Here it is:







Answer:

Probability of first sweet being orange = [latex]\frac{6}{n}[/latex]
Probability of first and second sweets being orange = [latex]\frac{6}{n} . \frac{5}{(n-1)}[/latex]
[latex]\frac{6}{n} . \frac{5}{(n-1)} = \frac{1}{3} [/latex]
[latex]n^2 - n -90 = 0[/latex]


While it is definitely not easy for those at that level of their maths education - i.e. probably 15 y/o's - it is definitely not excessively difficult either. It's likely there would have been no uproar had that appeared on an Irish exam because, as well as the fact that JC/LC maths has traditionally stood up very well in comparison with their GCSE/ALevel counterparts, there has long been a question on the junior cert requiring that students form an equation from verbal information. For my money, the one below from 2007 was the hardest:

The distance from town A to town B is half the distance from town B to town C. The total journey from town A to town C, through town B, is 60 km. A car travels at x km/h from town A to town B. It increases its speed by 20 km/h on the journey from town B to town C. The total time for the journey is 50 minutes. Find the value of x.



To mods: while the topic doesn't deal with LC directly, I think it would be of interest to those who read the LC forum.

Kremin

There are n sweets in a bag. Six of the sweets are orange. The rest are yellow. Someone takes two sweets from the bag. The probability both were orange is 1/3. Show that n^2-n-90=0

I'm sure some of you have seen this on FB but its an interesting little probability question.

Magnate

Kremin wrote: »

There are n sweets in a bag. Six of the sweets are orange. The rest are yellow. Someone takes two sweets from the bag. The probability both were orange is 1/3. Show that n^2-n-90=0

I'm sure some of you have seen this on FB but its an interesting little probability question.

It's a tricky one but I don't see how the outrage is justified. There's even a campaign for them to lower the grade boundary now.

OMGeary

Kremin wrote: »

There are n sweets in a bag. Six of the sweets are orange. The rest are yellow. Someone takes two sweets from the bag. The probability both were orange is 1/3. Show that n^2-n-90=0

I'm sure some of you have seen this on FB but its an interesting little probability question.

Sure just work backwords n is obviously 10, then just use that fact to prove the equation.

Kremin

OMGeary wrote: »

Sure just work backwords n is obviously 10, then just use that fact to prove the equation.

What if they didn't give you the equation though ?

The correct way to do it is
6/n (probability the first sweet is orange) x (5/n-1) (5 as one sweet is removed, n-1 as again, one sweet is removed) = 1/3

Multiple top and bottom of fraction....

30/n^2-n=1/3

Cross multiply....
90=n^2-n
0=n^2-n-90

Now.. according to facebook it took 4 accountants 4 hours to solve that, I don't know how true that is but I doubt anything like this will appear on Monday. More than likely any probability will be on Bernoulli

OMGeary

Kremin wrote: »

What if they didn't give you the equation though ?

The correct way to do it is
6/n (probability the first sweet is orange) x (5/n-1) (5 as one sweet is removed, n-1 as again, one sweet is removed) = 1/3

Multiple top and bottom of fraction....

30/n^2-n=1/3

Cross multiply....
90=n^2-n
0=n^2-n-90

Now.. according to facebook it took 4 accountants 4 hours to solve that, I don't know how true that is but I doubt anything like this will appear on Monday. More than likely any probability will be on Bernoulli

'Spose, but if they give you the equation, just cheat the system and work backwards

Fiona G

Kremin wrote:

Now.. according to facebook it took 4 accountants 4 hours to solve that, I don't know how true that is but I doubt anything like this will appear on Monday. More than likely any probability will be on Bernoulli

That's ridiculous, it's basic probability with some basic algebra??? Then again accountants are probably too used to Excel

Peregrine

Junior Cert HL would bite your hand off if you offered that as a question on Monday! :P

I don't know the GCSE syllabus but I guess it's a difficult question if you're not used to formulating equations from word problems which is something that's taught in Ireland from Junior Cert.

Derby1

qweerty wrote: »

The distance from town A to town B is half the distance from town B to town C. The total journey from town A to town C, through town B, is 60 km. A car travels at x km/h from town A to town B. It increases its speed by 20 km/h on the journey from town B to town C. The total time for the journey is 50 minutes. Find the value of x.

60 ?

qweerty

Derby1 wrote: »

60 ?

From memory*, yeah.


*Been a few years.