AQA June 2016 Further Pure 2 Unofficial Mark Scheme

thank god! i panicked so much

what would 61/75 be? A?

Did anyone else get this for 7c? Haven't seen anyone else with this answer yet

Did anyone else get this for 7c? Haven't seen anyone else with this answer yet

Angle was 5pi/6

No the argument was $\dfrac{5\pi}{6}$.

Not too bad compared to some past papers, De Moivre's wasn't too bad but think a lot of people will have tripped up withs signs on the last 8 marks maybe

Proof by induction was hardest I've seen

Most questions could be checked with a calculator so that was nice

Literally used 5 different functions on my calculator to check my answers, it's great.

I used the series evaluator, cubic equation solver, definite integration button, derivative (at a point) button and complex number mode.

So I was pretty convinced I got everything right by the end! XD

Feel sorry for anyone with a standard calculator lol, I got the wrong argument for 7c and struggled with proof by induction but think I got the rest of the marks

Angle was 5pi/6, then when cube rooting you get 5pi/18.

Adding this to the unofficial ms thread too, since it seems like it'd be useful here:

If anyone wants to know how the induction went:$(1+p)^1 \geq 1+p$ obviously, so base case established.Assume $(1+p)^k \geq 1+kp$. Clearly we need to multiply by $1+p$ and we can do so without changing the sign of the inequality because $p\geq -1\Rightarrow 1+p \geq 0$.

Therefore $(1+p)^{k+1} \geq (1+kp)(1+p)=1+p+kp+kp^2=1+(k+1)p+kp^2 \geq 1+(k+1)p$, since $p^2 \geq 0$, $k \geq 1 \Rightarrow kp^2 \geq 0$.

Therefore result holds for $n=k+1$ and by induction we have result.

I stupidly didn't divide by the coefficient of 3z^3 to find gamma but the continued to p and q with the right method, would they ecf?

Sorry if this is a little irrelevant, but how has STEP gone for you? Did well in I and II?

for the question just before the hyperbolic integration, what did people get for the x value of the stationary point?

i got x = ln(root34-5/3)

that's definitely wrong, right?

These are my answers to todays FP2 exam. Not all of them are necassarily correct, please feel free to correct me on any you think are wrong. Not sure about the question numbers.
FP2 June 2016
1.
a) $A=4$
b) $\frac{50}{609}$
2.
a) i) B=1-2i
ii) ab = 5
b) Gamma is 1/3
c) p=-5 q=-7
3. a) Show that s is the required integral
b) ln7-3/4
4. a) (sqrt(3)/2)/(1+3x)sqrt(x)
b) (sqrt3)pi/18
5. Induction Q.
Trivial in the case n=1 since clearly 1+p >= 1+p
Assume true for n=k
(1+p)^k+1 = (1+p)^k(1+p) = (1+kp)(1+p)
= 1 + kp + p + kp^2 >= 1 + (k+1)p as kp^2>=0
Thus true for n=k+1 so true for all positive integers n by induction.

6.a) Show that Q
b) 6sqrt3 + 3arcosh2 + 5
7. a) 8
b)i) Sketch with a circle with centre -4root3 + 4i radius 4
ii) 2pi/3
c) Roots are 2e^i(xpi/18) where x=-7,5,17
8. a) Show that Q
b) Roots were itan(xpi) where x= 1,3,5,7
c) i) 1
ii) 6