dude, i bet you surprise yourself. 95 is still very good man. I'm hoping for 100+, but i dunno, i might have been a bit vague in some explanations and lost a mark here and there. 95 will scale pretty high bro, the majority of state would have found it quite difficult
P'(x)=24x^2-24x+6
P'(x)>0 for increasing values
24x^2-24x+6>0
4x^2-6x+1>0
x=[6+-sqrt(36-16)]/8 (quadratic formula)
=(6+-2rt5)/8
So they are the values (sorry i dont have a calculator in hand)
then set up on a number line:
<-------A-------B------->
Test points for each section ie. <A...
1e)
int(pi/4-->0) cos@sin^2@ d@
Let u=sin@
du=cos@ d@
Change limits: when @=pi/4, u=1/rt2 when @=0, u=0
int(1/rt2-->0) u^2 du
|(1/3)u^3| (1/rt2-->0)
|(1/3)(1/2rt2)|-0
(1/6)rt2
Alternatively: This can just be done via inspection,
|(1/3)sin^3@| (pi/4-->0)
get the same answer
Q3aii)...
hey, the answer is no, it doesn't require proof, might benefit you seeing the proof once though just to help with understanding, but it's not testable to my understanding.
"A man shooter usually hits a bulls-eye 80% of the time. how many times must he fire his pistol in order that the probability of getting at least one bulls-eye exceeds 0.999?"P(bullseye)=0.8P(atleast one bullseye) = 1-P(no bullseye)therefore 1-(0.2)^n=0.999(0.2)^n=(1-0.999)n=ln(1-0.999)/ln(0.2)...
lol good one namu!Yeah i would agree with what namu said, i would say 2003 being the hardest. I think Q 10b) of 2000 was pretty hard also, put works out nicely once you get the idea of the q.2007 was also a pretty easy exam.
1. Find the volume of the solid generated by rotating the region bounded by the curves y^2=x and y=x^2 about the line y=x.
2. Use the method of slicing to find the volume of the solid obtained by rotating the region enclosed within the circle (x-1)^2+y^2=1 about the y-axis.