That last question

[pi]

This question would have required some great/lucky mathematical insight. Good question.

Again it seems methods will be much harder than spesh.

[Stevensmay]

I was so close to that... I did that... and then I thought, 'what point is getting 'x''?

oh god

why

I did the exact same thing mate ;(.

That feel when you realise how close you were, yet still down 8 marks.

[bafron]

First part is just gradient of the curve.









We know from earlier.



And we know the gradient is negative thus

 
TOO BAD I COULDN'T DO IT IN THE FKN EXAM.
think there might be an error in there.

you can simplify by taking a 2 out of the sqrt which cancels the twos giving

[Stevensmay]

Doubt you lost 8 marks, VCAA will be giving out consequential marks like candy I reckon

Can't get consequential for a blank question.

[Lejn]

Can't get consequential for a blank question.

Nice to know someone else is my painful boat. But I neglected checking my MC because of this, and I've lost A LOT there as well, god. I was a wonderful representative for my school as top of SACs, jeez I still hope I can get mid 30s.

[ngabe]

Did it slightly differently,

I did y=mx+c
Sub (0,k) and you get y=mx+k

and then equate y to g(x)

Hence, mx+k = 4 - 1/4x^2 (or whatever g(x) was)

rearranged it, and then... I ended up w a quadratic.

Used discriminant = 0 because it's a tangent.


Man, I wasted about 20-30 minutes on this... Didn't check...

Not sure if this 8 marks was worth it....

& was it me or the multiple choice was not as easy as previous years?

[P0ppinfr3sh]

I figured out one expression for the gradient, thought i could do nothing with it and so rubbed it out. Then i figured out the other expression for the gradient, thought i could do nothing with it and was running out of time so just left it there.
If only i had just made the connection.....

[friedchicken]

Oh wow. I left the gradient as positive, and kept trying to d/dx the equation when it was k... very annoyed since I think I would've gotten the minimum area otherwise.

[chuck981996]

I got the gradient, but it took me a good 10 minutes of scrambling around so I had barely enough time to finish, leading to me putting the max. and min. areas the wrong way around.

[jeff.]

I used the discriminant.

So first function (16-x^2)/4=mx + k

=> 16x - x^2 -4mx - 4k = 0

- x^2 + (16 - 4m) x - 4K = 0

sqrt((16 - 4m)^2 - 4(-1)(-4k)) = 0

I think that was it. Ended up with m = - sqrt(k-4).