Everyone loves an 'impossible maths exam' story

[noblegiraffe]

The latest country to have an exam that has left students in tears is New Zealand. www.theguardian.com/world/2017/nov/22/impossible-new-zealand-maths-exam-even-flummoxes-teachers

Here's one of the questions if anyone fancies a go. I'm pretty sure there must be a more elegant solution than the one I came up with!

That's fab, Atia.
Spotting that DEG is equilateral is key, isn't it?

I'm not sure where your two right angles are coming from, calamity?

I can't take the credit, it was just cobbling together bits from above and ds saying x was twice the side angles. But yes, really quite simple when one stops panicking about the question and starts thinking about what one does know.

crikey, now that is elegant!

It is hard for most kids but that is the way exam should be.

I’ve done it slightly differently to larry and atia.

If you draw in line BG as well, then it bisects both angle x and G.

The top angle of triangle BEG is half of 60.
And if one of the base angles is half of x then the sum of both base angles is x.

So 180 - 30 = 150.

150 is correct and it took me about 2 minutes once I had found a pencil and paper.

The confusion in some previous answers is because some people have assumed that angles GDB and GEB are right angles which they are not. A triangle where the longest side is the whole diameter of a circle will have a right angle at any point on the circumference but these triangles are just the radius so are isoceles.

As soon as you label GE as radius r and GH as r/2 it is obvious that angle EGH is 60 and so EGB must be 30.

For an isoceles triangle with one angle=30 the other two must be 75

So x must be 150

Any maths teacher flummoxed by this should resign immediately.

Sorry forgot to post my image.

I like the last part but ‘it is obvious’ is not a proof. You may know a right angle triangle with a ratio of 1:2 has an angle of 60 degrees but you need trig to prove it (or drawing the line across and forming the equilateral triangle).

Or is there something that I am missing?

It isn’t a proof Larry, but is it asking for a proof?

And how about that swing problem on the page linked with other exam questions?

ah never mind, further googling suggests that there was actually more information - like the equation!! I was trying to figure out how to solve it with no heights...

kitten it said 'Justify your answer with clear geometric reasoning' so I'm not sure 'it's obvious' would wash!.

Answer: x=150
Proof: trivial

that teaches me to read properly, I had read Larry’s comment not noticing the speech marks and inserting an extra ‘is’ into ‘but ‘it is obvious’ is not a proof’.

Shouldn’t be allowed by ipad before 8:30 am!

I'm still confused by GE, GB and GD all being equal if the shape is a kite
Please explain

That's in the question, see top of image.

It's partly an optical illusion that GB doesn't look like GE and GD. Draw a sketch and then tip the diagram so that DB is horizontal, and you will be able to see that GB and GD do look equal.

Ah 'trivial' that mainstay of 'I don't know how to prove this but it must be true'

I would not have liked to have met that question in an exam as a 15 year old, even though the Geometry is basic. I would have found it a good homework question at that age.

I would have enjoyed it in an exam aged 15.

Now, I enjoy it as an internet problem. If I see the answer I post; if not, I lurk and read someone else’s solution!

‘It trivially follows...’, always seemed to work for the lecturers at uni but I was never given credit for using it (because I could not link the two pieces of my proof....).

It depends how much time you have in the exam. If the exam is purely based on reasoning they may be quite liberal with the time given for the paper because some questions need time spent on it.

Wouldn’t like to have met it in a GCSE though.

I wonder what would happen if you gave it to year 6/7 classes who heave had quite a lot of experience with reasoning activities? Might it be easier if you aren’t looking for a complex solution?

Rafals,

I would be surprised and seriously impressed if many (more than 1%) of year 6 or 7 students could access that kind of problem.

I think it might be slightly more than that. Purely because if your knowledge is limited to the angle properties of triangles and you are used to solving geometry problems by experimenting with drawing additional lines into diagrams that’s probably where you are going to expect the answer to be.

But if you are 15 and have a knowledge of trig, you are probably expecting the answer to be more difficult.

Doesn’t solve the issue of it being difficult to see the equal lines as being equal though.

can anyone help me with this?

In order for the equilateral triangle answer to work, you have to know that DE = DG (=GB).

But how do you know that?

oh sorry ignore me I see it

DE = GB = GD