GCSE questions
June 5th, 2015 at 11:35:32 AM
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There's been an item in today's news ( http://www.bbc.co.uk/news/education-33017299 , http://www.bbc.co.uk/news/education-33025782) about the questions in recent maths exams being harder. Like many here I passed my A-level maths and went onto to university, so could see the answer. Anyway here's the question, aimed for 16-year olds, that caused the stink (other questions at the bbc site).
n sweets in the bag, 6 are orange. p(1st sweet=orange) = 6/n.
now (n-1) sweets in bag, 5 are orange. p(2nd sweet=orange) = 5 / (n-1).
P(both) = 6/n * 5/(n-1) = 30 / (n (n-1)). Also given it = 1/3.
So 1 / 3 = 30 / (n (n-1) )
n (n-1) = 90
n^2 - n - 90 = 0.
This is also (n+9)(n-10)=0. So the solution is the bag has ten sweets.
Double check (6/10) * (5/9) = 30/90 = 1/3.
Quote: edexcelQ19.
There are n sweets in a bag.
6 of the sweets are orange.
The rest of the sweets are yellow.
Hannah takes at random a sweet from the bag.
She eats the sweet.
Hannah then takes at random another sweet from the nag.
She eats the sweet.
The probability that Hannah eats two orange sweets is 1/3.
(a) Show that n^2 - n - 90 = 0.
n sweets in the bag, 6 are orange. p(1st sweet=orange) = 6/n.
now (n-1) sweets in bag, 5 are orange. p(2nd sweet=orange) = 5 / (n-1).
P(both) = 6/n * 5/(n-1) = 30 / (n (n-1)). Also given it = 1/3.
So 1 / 3 = 30 / (n (n-1) )
n (n-1) = 90
n^2 - n - 90 = 0.
This is also (n+9)(n-10)=0. So the solution is the bag has ten sweets.
Double check (6/10) * (5/9) = 30/90 = 1/3.
June 5th, 2015 at 12:03:40 PM
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Well, from this I don't know, just to say 16-year-old doesn't mean it wasn't aimed at advanced students who in fact have had the suitable math background from taking advanced classes.
If it was aimed at a typical such, and you are telling me this is the math level that all such students all over the country are getting at that age, I am going to find that hard to swallow. I might buy that there are some questions nobody was supposed to get except a handful, and this question was the hardest.
If it was aimed at a typical such, and you are telling me this is the math level that all such students all over the country are getting at that age, I am going to find that hard to swallow. I might buy that there are some questions nobody was supposed to get except a handful, and this question was the hardest.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
June 5th, 2015 at 12:55:46 PM
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Combin(6,2)/Combin(n,2) = 1/3 Ie Combin(6,2) is Result and Combin(n,2) is population
15/Combin(n,2) = 1/3
Combin(n,2) = 45
n!/2*(n-2)! = 45
n!/(n-2)! = 90 And n! can be written as (n-2)!*(n-1)*n canceling the (n-2)!
(n-1)*n = 90
n^2 - n - 90 =0
Tough question for that level.
15/Combin(n,2) = 1/3
Combin(n,2) = 45
n!/2*(n-2)! = 45
n!/(n-2)! = 90 And n! can be written as (n-2)!*(n-1)*n canceling the (n-2)!
(n-1)*n = 90
n^2 - n - 90 =0
Tough question for that level.
June 5th, 2015 at 6:56:05 PM
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From my understanding, these are 11th graders? I’m trying to remember what I had known then. I do remember touching on a little probability—which I do believe included independent events/multiplication rule.
I definitely had the algebra though.
But maybe the probability combined with the algebra makes this too difficult of a question. But tests do need these kinds of questions…right?
I don’t know…I think I’m leaning towards this question being fair game.
I definitely had the algebra though.
But maybe the probability combined with the algebra makes this too difficult of a question. But tests do need these kinds of questions…right?
I don’t know…I think I’m leaning towards this question being fair game.
June 5th, 2015 at 7:02:51 PM
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Now, if…
Were replaced with…
Then that would have caused chaos ;).
Quote:The probability that Hannah eats two orange sweets is 1/3.
Were replaced with…
Quote:The probability that Hannah eats two yellow sweets given that she eats at least one yellow sweet is 1/5.
Then that would have caused chaos ;).
