FP2 unofficial MS
note : some answers may be wrong 1)
a) Show that
b) 0.00301
2)
a)
Line x=3
Circle, centre, 3,4 radius 5.
b)
Intersects line at 3+9i and 3-i
3)
a)
Cant remember
b)
4096
c)
r = 4th root 16 = 2
4theta = 2/3pi + 2kpi
theta = 1/6pi + 2kpi
+- (root(3) + i)
+- (1 - root(3)i)
4)
|(30 - 6w) / w| = |30 / w|
|30 - 6w| = |30|
let w = x + iy
|30 - 6x - 6iy| = |30|
(5-x)^2 + y^2 = 5^2
(x-5)^2 + y^2 = 5^2
5
a)
sin(3theta) = 0.5
3theta = 5/6pi, 1/6pi
theta = 5/18pi, 1/18pi
b)
![<br />A = \frac{1}{2} \int^{\frac{5\pi}{18}}_{\frac{\pi}{18}} [(1.5+sin(3\theta))^{2} - 4] d\theta](https://studentforums.biz/cgi-bin/mimetex.cgi?<br />A = \frac{1}{2} \int^{\frac{5\pi}{18}}_{\frac{\pi}{18}} [(1.5+sin(3\theta))^{2} - 4] d\theta)
Can't remember the exact value but its approximately 0.5 I think.
6
a)
Critical values -5, -3, -2
Value testing to give
-5>x>-3 or x>-2
b)
x>-2 only
7)
a)
Show that
b)
Don't really rember but something like,
y = (1/2 tan(2theta) + c^2cos(theta)^2
I think
8
a)
lambda = 3/10
b)
y = Acos(5theta) + (B+0.3x)sin(5theta)
c)
y = (1+0.3x)sin(5theta)
d)
Oscilating wave, period 0.4pi, increasing by the same amount each oscilation
