UKMT Senior Individual Maths Challenge 2016 - Preparation and Tips

stalked the UKMT twitter and saw they tweeted a picture of a spreadsheet of previous grade boundaries

Chittesh14, I have PMed you now.

Everyone reading this, plz check out the 2002 SMC and just be glad we weren't sitting it then. It is insane compared to this

I've just done the SMC for the first time, as in Year 11, and pretty sure I got a score of 72 - does anyone know which certificate is that good enough for?

Here's a nice way to do it: Set up a coordinate system with the origin as the bottom left corner of the square, and let the side length of the square be 2, so that the midpoint of the bottom side is (1,0). Thus the circle is x^2+(y-2)^2=4, and the tangent line is y=m(x-1), where m is the gradient. Hence substitute to give x^2+(mx-m-2)^2=4 -> (1+m^2)x^2 - 2m(m+2)x + m^2 + 4m = 0. Now as the line is tangent, the quadratic should have only one solution (to give just one point of intersection), so using the discriminant, 4m^2(m+2)^2 - 4(1+m^2)(m^2+4m)=0 and by expanding and cancelling, this becomes 3m^2-4m=0, so as m is clearly non-zero, m = 4/3. Hence the ratio is 4:3.

I found it easier to just use the fact that the lengths of the 2 tangents from one point are equal and then pythagoras

Chittesh14, I have PMed you now.

1B 2D 3B 4C 5A 6D 7A 8B 9C 10B 11E 12C 13A 14D 15B 16D 17D 18E 19_ 20E 21_ 22C 23E 24_ 25_
Are these all correct if so is 109 enough for BMO qualifier?

Me as well, please.
Thanks

I'm pretty sure that I'm exactly the same as you (or thereabouts)! Those are the same four questions that I couldn't do. Anyway, 109 should quite easily be enough!

i got: 1B 2D 3B 4C 5A 6D 7A 8B 9C 10B 11E 12C 13A 14D 15B 16D 17D 18E 19D 20E 21C 22C 23E 24B 25D

I pretty much agree except with q9 where only two of the graphs work I believe.

I got 3 to work

X^2+y^2=1 and y=x anything else?