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Original poster

Everyone loves an 'impossible maths exam' story

84 replies

noblegiraffe · 22/11/2017 18:54

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!

Everyone loves an 'impossible maths exam' story
OP posts:
larrygrylls · 23/11/2017 06:28

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?

yowerohotesies · 23/11/2017 04:21

Sorry forgot to post my image.

Everyone loves an 'impossible maths exam' story
yowerohotesies · 23/11/2017 04:20

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.

HarveySchlumpfenburger · 23/11/2017 00:57

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.

GHGN · 22/11/2017 22:17

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

OhYouBadBadKitten · 22/11/2017 22:03

crikey, now that is elegant!

AtiaoftheJulii · 22/11/2017 22:00

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.

Original poster
noblegiraffe · 22/11/2017 21:42

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

OP posts:
Original poster
noblegiraffe · 22/11/2017 21:33

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

OP posts:
AtiaoftheJulii · 22/11/2017 21:31

Ok, here's my (inspired by ds just now) contender for nice and neat:

Bottom angle (can't remember letters or type while looking at picture) is 60 because equilateral.

x is twice the side angle because isosceles.

Therefore 2x = 300, x = 150

TheFrendo · 22/11/2017 21:24

let side of square = 1 (so, DG=GB=EG=1 also)
sin(FDG) = FG / DG = 1/2 => FDG = 30
BGD = FDG = 30 (alternate angles)
GDB = GBD = GBE = GEB (two identical isosceles triangles)
x = GBD + GBE = 180 - 30 = 150

I think.

EllenJanethickerknickers · 22/11/2017 21:14

Bugger, I cocked up but i just showed it to DS3 in Y11 and he got it in about 3 minutes. Smile Hope for him yet.

calamityjam · 22/11/2017 21:10

Why am I so utterly shit at maths? I'm not thick but I just don't get it. I dissected the kite and it gave me 2 right angles which I halved to get 45 degrees. Same on the other side so added together 90degrees. Now I know this is wrong because it looks wrong and its an obtuse angle and tbf, looks about 150. Where am I going wrong??

HarveySchlumpfenburger · 22/11/2017 21:05

I had the same problem seeing triangle DEG as equilateral, noble.

Info in the question makes it equilateral. Brain is seeing it as isosceles.

OhYouBadBadKitten · 22/11/2017 20:58

thanks pingoose!

Cheeseandcucumber · 22/11/2017 20:51

You are all ridiculously smart. If my DD brought me this I'd fake a heart attack, it's the only logical way out.

pingoose · 22/11/2017 20:51

This page has the exam in its entirety, if anyone is interested:
www.stuff.co.nz/national/education/99106862/you-do-the-math-ncea-releases-exam-paper-teachers-students-complained-about
Students are also assessed internally throughout the year, so doesn't necessarily cover the whole year 11 curriculum.

It does seem that the maths exam gets complained about every year!

OhYouBadBadKitten · 22/11/2017 20:42

Larry, I liked your solution. Very elegant :)

TeenTimesTwo · 22/11/2017 20:39

Nice solution larry

OhYouBadBadKitten · 22/11/2017 20:38

but yes, Looking at the thread I used trig, not geometry, so it is cheating.

larrygrylls · 22/11/2017 20:38

Noble,

Thanks for sharing it. Good for a ‘problem of the week’!

OhYouBadBadKitten · 22/11/2017 20:37

I liked it but for me, not for an exam. I’m beginning to develop a love for geometry. Make square side length 2, then BEG is an isosceles triangle with main side lengths 2.

EGH is a triangle with side lengths 1,2, root 3 so angle egh is 60 degrees. That makes EGB 30. As it’s an isosceles EBG must be 75 degrees, Double that to get DGE.

Original poster
noblegiraffe · 22/11/2017 20:33

Yes criss, you were right! Grin Unbelievable!

OP posts:
Original poster
noblegiraffe · 22/11/2017 20:32

Oh nice, larry. Yes, that's the sort of answer I was expecting for 'geometrical reasoning'.

My brain was really struggling to see the triangle BEG as isosceles, it just looks wrong!

OP posts:
crisscrosscranky · 22/11/2017 20:22

So it is 150!?

My reasoning would have been:

More than 90 but less than 180, the two small angles look significantly less than 45 degrees and there's two of them so I guessed they were around 15 degrees.

I don't understand the actual answer Blush