For the question about the circle being wholly inside the other, did anyone else get 0<r<√45 - 5? Most people got 0<r<2, but I thought that this may not be right
I got this, as did most other people at my school who managed to answer it.
Does anyone remember the actual last question though?
Wasn't it something like y=4x^2+a/x+5 and y has a stationary point at which the y coordinate = 32.
I differentiated to find 8x-a/x^2 and then equated to 0. Then said that 8x^3-a=0 therefore 8x^3=a.
Plug that back into the original equation to get 32=4x^2+8x^2+5 (32 is the y coordinate we were given).
Solving that to get x= 0 and + or - 3/2. Then plugging that back in to the original equation gave a=0, not possible or a negative solution when it asked for the positive solution so solving that eventually gave 27.
I hope that makes sense? Think it's correct (I BLOODY HOPE SO!)
It is wrong as if you use k as -5 or -6 it will not intersect the curve, I checked it at the end.
He's right, you're wrong. b^2-4ac when K<-7.5 was a number less than zero. Above -7.5 it gave a positive number, so when K<-7.5 ether are no real roots to the equation and the lines do not cross, you probably subbed it in wrong.
For the question about the circle being wholly inside the other, did anyone else get 0<r<√45 - 5? Most people got 0<r<2, but I thought that this may not be right
I got that! I said the radius was 3√5 whereas lots thought it was 2√5.
Thing is on that question the distance from Centre to 0,0 was 5 therefore the radius couldn't have been 2√5 so I quickly changed that!
Wasn't it something like y=4x^2+a/x+5 and y has a stationary point at which the y coordinate = 32.
I differentiated to find 8x-a/x^2 and then equated to 0. Then said that 8x^3-a=0 therefore 8x^3=a.
Plug that back into the original equation to get 32=4x^2+8x^2+5 (32 is the y coordinate we were given).
Solving that to get x= 0 and + or - 3/2. Then plugging that back in to the original equation gave a=0, not possible or a negative solution when it asked for the positive solution so solving that eventually gave 27.
I hope that makes sense? Think it's correct (I BLOODY HOPE SO!)
With the indice questions, was it 2^-6 for part (i) and 2^13/3 for (ii)?
I got 2^-6 but was worrying cos all I remember from the exam is 2^5 divided by 2^7 which gives ¼ so there must've been something else I can't remember.