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Interesting question from an Eton 1950's entrance exam. watch

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1. (Original post by Profesh)
You'd think so, wouldn't you?
2. wow, i know when i was 11/12/13 i could not have answered that... standards have fallen....

i keep hearing from older people how things in further maths used to be in GCSE, like matrix algebra or something... and how a lot of A Level maths was in the O Level before...
3. (Original post by neomilan)
wow, i know when i was 11/12/13 i could not have answered that... standards have fallen....

i keep hearing from older people how things in further maths used to be in GCSE, like matrix algebra or something... and how a lot of A Level maths was in the O Level before...
In the late 1970s, my mixed ability class did Pythagoras' Theorem at age 11 and we spent a ridiculous amount of time at age of 13 learning set notation to accompany our beautifully constructed Venn Diagrams.

When I did O Level at age 16 (just a few years before GCSEs started), it included matrices (only 2x2) and some very basic differentiation. The standard of algebra was a LOT higher than is expected now (roughly equivalent to a good student at the start of Year 13 now).

I also took AO Additional Mathematics which was an optional second O Level in mathematics. This extended differentiation (including differentiation from first principles), introduced topics such as integration, SUVAT equations, permutations and combinations and included plenty of stuff on complex numbers including finding the nth roots of unity etc.

On the other hand, we spent next to no time handling data so there was no cumulative frequency, box plots, stem and leaf etc. Times change.
4. (Original post by aKarma)
If I were an eleven year old presented with this question i would have drawn a drawing. To test the accuracy of this I did this to a scale of 1cm to 1m (m are the units in the question). This easily found x to be 0.16m, 9m. Obviously these are approximate given on my diagram they were .16cm and 9 cm. Checking these finds them reasonably accurate. While this isn't a mathematical solution I think it is probably better than breaking down and crying, and would show potential for an 11 year old...
you can't draw it to scale as you don't know the angles that the ladder makes to the ground and wall.
5. (Original post by Barry Chuckle)
you can't draw it to scale as you don't know the angles that the ladder makes to the ground and wall.
You can in fact. Remember the restriction that the ladder is 10 cm long to this scale and must touch one vertex of the square.
6. (Original post by Barry Chuckle)
you can't draw it to scale as you don't know the angles that the ladder makes to the ground and wall.
You can. Draw the box first then extend its left and bottom sides. Fix the 0 on the ruler on the left line and the 10 on the bottom line and then slide up/left on the two ends of the ruler until the upper-right corner of the box touches.
7. how about if you did:
by similar triangles the side lengths are 1+x and 1+1/x
let tan(a) = 1/(1/x) => x = tan(a)
=> sin(a)= (x+1)/10 = (tan(a) +1)/10
=> tan(a)=10sin(a)-1=x

then checked your trig value tables to get a. (linear interpolation on the range would get a more accurate value)
well I guess it kinda works :/ and could be done at that age at the time.

This question is really easy to solve numerically if you have a calculator, (rearrangement method).
8. using trig tables (which go up 1 degree steps) and a bit tweaking I get 8.94 (without a calculator) and the correct answer is 8.937993689
9. (Original post by Erdős)
Arguably the quartic method should be reasonably accessible. All 11 year-old school children should be aware (at least) of the equation for the solution of quadratic equations.
Sadly this is far from the truth. I suspect fewer than 1% of 11 year old schoolchildren nationally will have heard of quadratic equations less alone be able to solve one.

Half of the students in this country leave school without EVER being shown quadratics. It is a grade B topic at GCSE and only appears on the Higher specification. I suspect plans may be afoot to make it a Grade A topic in due course.

In the revised National Strategy framework for teaching mathematics (released 2008) the following appears as an EXTENSION Learning Objective for able Year 11 students:

"solve quadratic equations by factorisation, completing the square and using the quadratic formula, including those in which the coefficient of the quadratic term is greater than 1".

I was working at a national level recently with some primary colleagues and this subject came up. Despite having responsibility for affecting the direction of UK mathematics education in the primary phase, the person I was working with did not understand how to factorise and solve a simple quadratic with integer solutions. I tried not to look suprised when she commented "That's why I teach primary and you teach secondary".
10. (Original post by Mr M)
I was working at a national level recently with some primary colleagues and this subject came up. Despite having responsibility for affecting the direction of UK mathematics education in the primary phase, the person I was working with did not understand how to factorise and solve a simple quadratic with integer solutions. I tried not to look suprised when she commented "That's why I teach primary and you teach secondary".
Does this mean that we need not blame the government for trying to dumb schooling down but teachers?
11. (Original post by Mr M)
I was working at a national level recently with some primary colleagues and this subject came up. Despite having responsibility for affecting the direction of UK mathematics education in the primary phase, the person I was working with did not understand how to factorise and solve a simple quadratic with integer solutions. I tried not to look suprised when she commented "That's why I teach primary and you teach secondary".
Is this common among prmiary teachers?
12. (Original post by SimonM)
Does this mean that we need not blame the government for trying to dumb schooling down but teachers?
Well the Government holds ultimate responsibility as you would not believe the pressure they apply on others in the clamour to produce continual "improvements" in the GCSE pass rates year-on-year. The easiest way to engineer an increased pass rate are to lower grade boundaries or decrease the difficulty of the exams.

Supposedly the QCA and the NAA are charged with maintaining standards but they are asleep on the job. You wouldn't give a toss either if you were treated the way their employees are. Example 1: earlier this year, all their staff in London were told they have to relocate to Leicester. Failure to do so would be treated as resignation from their posts. Example 2: when the KS3 National Tests were abolished recently, the majority of the staff working on them first heard about it on the BBC News.
13. (Original post by Mr M)
Well the Government holds ultimate responsibility as you would not believe the pressure they apply on others in the clamour to produce continual "improvements" in the GCSE pass rates year-on-year. The easiest way to engineer an increased pass rate are to lower grade boundaries or decrease the difficulty of the exams.

Supposedly the QCA and the NAA are charged with maintaining standards but they are asleep on the job. You wouldn't give a toss either if you were treated the way their employees are. Example 1: earlier this year, all their staff in London were told they have to relocate to Leicester. Failure to do so would be treated as resignation from their posts. Example 2: when the KS3 National Tests were abolished recently, the majority of the staff working on them first heard about it on the BBC News.
Gah, and to think that a few years ago Labour were saying Education, education, education. Its pretty shocking to be honest. It makes me think about the possibility of studying grade inflation as a topic. If we accept that it exists etc, it might be an interesting entity to study.
14. (Original post by Hancock orbital)
Is this common among prmiary teachers?
It wouldn't be fair for me to say. Primary teachers have an extremely difficult job as they are have to have a broad subject knowledge base (basically teach every subject). They only have to have Grade C or above in GCSE maths in order to teach it. My daughter's teacher got her nose put out of joint recently when I told her she was teaching the order of operations (BODMAS) incorrectly - she was just telling the children to read from left to right.

The Government has said that every primary school will eventually have at least one teacher who is qualified to a higher standard in mathematics or who will be invited to undertake some professional development training in the subject.
15. (Original post by Mr M)
Iy daughter's teacher got her nose put out of joint recently when I told her she was teaching the order of operations (BODMAS) incorrectly - she was just telling the children to read from left to right.
I sent a letter (email actually) of complain to Sky when they made the same mistake on a quiz show. Needless to say I await their response

The Government has said that every primary school will eventually have at least one teacher who is qualified to a higher standard in mathematics or who will be invited to undertake some professional development training in the subject.
A nice ambiguous statement enabling the government to manipulate the definitions in every word. I suspect they'll consider an E at A level a qualified to a higher standard?
16. (Original post by SimonM)
Gah, and to think that a few years ago Labour were saying Education, education, education. Its pretty shocking to be honest. It makes me think about the possibility of studying grade inflation as a topic. If we accept that it exists etc, it might be an interesting entity to study.
Robert Coe of Durham University has done a lot of research into this area. It is not widely reported (conspiracy theorists might like to speculate about why that might be).

Read this report Simon. It is guaranteed to annoy you.

http://www.reform.co.uk/documents/Th...athematics.pdf

A quote from the summary at the start:

"Reform has conducted an analysis of O-level/GCSE examinations over time. From 1951 to 1970 these were a rigorous test of thought and initiative in algebra, arithmetic and geometry. Students were required to think for themselves. By 1980 questions were becoming simpler. Following the introduction of the GCSE there was a sharp drop in difficulty, with questions leading pupils step by step to a solution. Pass marks were lowered throughout the period."

The example questions at the back of the report are extremely interesting.
17. (Original post by SimonM)
I sent a letter (email actually) of complain to Sky when they made the same mistake on a quiz show. Needless to say I await their response

A nice ambiguous statement enabling the government to manipulate the definitions in every word. I suspect they'll consider an E at A level a qualified to a higher standard?
Sadly, my understanding is that A Level maths will not be required at all. There are too few people with A Level maths working in the primary sector.
18. I think a big issue with maths teaching, and teaching in genereal, is that the money isn't sufficient to attract new people to the job. It needs to become much more competitive to get a job as a teacher, so teaching standards will rise and specifications won't have to be dumbed down further. The UK GCSE and A-level are at risk I believe of becoming a joke on the international stage.
19. Ok, I've read up to the end of chapter 2. I guess there is nothing in there that I hadn't already infered but it is good to see that there is rigorous proof that they are dumbing down exams. It makes me sick to see how bad the state of things are.

(Original post by ForGreatJustice)
I think a big issue with maths teaching, and teaching in genereal, is that the money isn't sufficient to attract new people to the job. It needs to become much more competitive to get a job as a teacher, so teaching standards will rise and specifications won't have to be dumbed down further.
And the NUT need to lose some of their power. Fixing prices across all subjects leads to a surplus of teachers in English and humanities and a serious shortage in maths and physics.

The UK GCSE and A-level are at risk I believe of becoming a joke on the international stage.
20. (Original post by SimonM)

even more so then

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