[deserteagle]

do you remeber the question on how to find the stationary points . I couldnt get the derivative equal to zero does anyone know how many marks that question was?

[Oromis263]

(Original post by foolscap)
Umm correction: I was pretty sure part 8a was to use de moivre's theorem to show that z^n + 1/(z^n) = 2cos(n theta), you've missed it out, then part b was to expand the z stuff.

Yeah, it was, cheers, I was just putting down things I remembered.

[Brister]

(Original post by Z1G)
I did it the exact same way

Cool

[Brister]

(Original post by 05hassay)
btw how did you guys mark the smaller arc on the argand diagram, is it okay to just make it bold?

That should almost certainly be fine. It is what they do in the mark schemes

[Crazypaving]

(Original post by 05hassay)
btw how did you guys mark the smaller arc on the argand diagram, is it okay to just make it bold?

I hope so, thats all i did. Couldn't really think of another way of showing it without messing up the diagram... But yeh i think bold is fine.

[linnet18]

Anyone got a copy of the questions or the paper?

[Dan*]

(Original post by chris669)
For the trig functions question, how many marks was part a worth?

Think it was 7

[Dan*]

(Original post by chris669)
On the argand diagram, I drew it to scale and wrote down the point of intersection with im(z), but forgot to mark on the diagram the co-ordinates of two points and the centre, will I lose marks for this?

almost definitely :/ unlucky mate, but i guess this means . . . Chris can't do it!

[chris669]

oh no, your back

[Quexx]

(Original post by Oromis263)
FP2 - 31st May 2012 Unofficial Mark Scheme

Well, here is what I remember:

Question 1 - hyperbolics, finding solutions
a) Draw the graph, pretty standard question, mark on the point of intersection
b) Solving gets + and - ln3

Question 2 - Loci
Circle, centre (2,3) touching the y-axis.
Line bisector between the two points (2,0) and (-3,1)? (not so sure about the second coordinate, but the idea is right)
c) Mark on the graph the part which satisfies both of the equations given. You had to mark the arc of the circle on the left of the bisecting line.

Question 3 - Summation of Series
a) Show that stuff, etc
b) Should rearrange to 2^26 - 1

Question 4 - Roots of Polynomials (Not sure what order these answers are in)
a) a+b+y = 0
b) Show that, using the cubic, rearrange after subbing the roots in, summing should bring you to the answer (similar to June 2011 paper)
c) y = -8, b = 4-7i
d) p = 1, q = 520
e) 520x^3 + x^2 + 1 = 0

Question 5 - Inverse functions
a) A core 3 rearrangement. State that secx = 1/cosx, then swap y and x, rearrange for y, thus it is shown.
b) Chain rule after swapping for cos^-1x.

Question 6 - Hyperbolic stuff again
Last part pi/256(128ln2 + 495)

Question 7 - Proof by induction
a) Prove it, as long as your method reaches what it is meant to and you lay out your proof correctly and logically
b) n = 316 (although some people have got n = 140? Will need to see paper for confirmation)

Question 8 - Hyperbolic stuff AGAIN
a) Expand the z stuff
b) Find the double angle representation of cos^4(2x)
c) Find the solutions between 0 and pi, k = 1/12, 5/12, 7/12 and 11/12
d) Show that it = 3pi/16. Integrate the double angle representation, sub pi/2 into the sin parts, they go to 0, leaving you with the answer.

I know this is very poorly structured and doesn't have all the answers. If you remember anymore/disagree/remember the structure better than I, quote here and I'll correct it.

Yep, got most of that. I didn't do the bit with n=316 (I said I would come back to it, then ran out of time xD).
However I'm pretty sure the equation in 4)e) is wrong, cos aren't you meant to get 520x^3 + 520x^2 + 1 = 0
Correct me if I'm wrong =P

[Oromis263]

(Original post by Quexx)
Yep, got most of that. I didn't do the bit with n=316 (I said I would come back to it, then ran out of time xD).
However I'm pretty sure the equation in 4)e) is wrong, cos aren't you meant to get 520x^3 + 520x^2 + 1 = 0
Correct me if I'm wrong =P

By using substitution method that X = 1/x, sub in 1/X for what you just found for the quadratic (which was x^3 +x + 520 = 0), to get (1/X)^3 + (1/X) + 520 = 0. Multiply through my X^3 to get the new cubic, which came out as 520X^3 + X^2 + 1 = 0. Roots of the previous equation were -8, 4+7i and 4-7i. By checking the new cubic I found with polysimult on the graphical calculator, it confirmed to be the same as 1/ each of the roots.

[Quexx]

(Original post by Oromis263)
By using substitution method that X = 1/x, sub in 1/X for what you just found for the quadratic (which was x^3 +x + 520 = 0), to get (1/X)^3 + (1/X) + 520 = 0. Multiply through my X^3 to get the new cubic, which came out as 520X^3 + X^2 + 1 = 0. Roots of the previous equation were -8, 4+7i and 4-7i. By checking the new cubic I found with polysimult on the graphical calculator, it confirmed to be the same as 1/ each of the roots.

Oh right... i didnt check with the roots... ah well -.-

[05hassay]

Also another thing, on the argand diagram i didn't label the centre point and the two other points. HOWEVER i did put a scale on the axis... will i lose marks or not?

[Mikeyyy!]

Hated the paper aswell! lost so many stupid marks and some questions just didn't do well for me :/

And WHY did I put n=315 when I got the answer as 315.2?! I'm such an idiot and should have read the question properly

[jc092]

(Original post by 05hassay)
btw how did you guys mark the smaller arc on the argand diagram, is it okay to just make it bold?

How many marks for this part? I drew the whole segment

[Dangerous Theory]

(Original post by jc092)
How many marks for this part? I drew the whole segment

1. Fortunate for you, but I was disappointed. They've never given a measly mark for satisfying two conditions before


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[Dan*]

(Original post by f1mad)
That's because it was. Having thought about it, I believe 140 is a valid answer.

I think there are two ways of doing that question.

yeah, the right way and the wrong way. You did it the wrong way.

[Dan*]

(Original post by Oromis263)
FP2 - 31st May 2012 Unofficial Mark Scheme

Well, here is what I remember:

Question 1 - hyperbolics, finding solutions
a) Draw the graph, pretty standard question, mark on the point of intersection
b) Solving gets + and - ln3

Question 2 - Loci
Circle, centre (2,3) touching the y-axis.
Line bisector between the two points (2,0) and (-3,1)? (not so sure about the second coordinate, but the idea is right)
c) Mark on the graph the part which satisfies both of the equations given. You had to mark the arc of the circle on the left of the bisecting line.

Question 3 - Summation of Series
a) Show that stuff, etc
b) Should rearrange to 2^26 - 1

Question 4 - Roots of Polynomials (Not sure what order these answers are in)
a) a+b+y = 0
b) Show that, using the cubic, rearrange after subbing the roots in, summing should bring you to the answer (similar to June 2011 paper)
c) y = -8, b = 4-7i
d) p = 1, q = 520
e) 520x^3 + x^2 + 1 = 0

Question 5 - Inverse functions
a) A core 3 rearrangement. State that secx = 1/cosx, then swap y and x, rearrange for y, thus it is shown.
b) Chain rule after swapping for cos^-1x.

Question 6 - Hyperbolic stuff again
Last part pi/256(128ln2 + 495)

Question 7 - Proof by induction
a) Prove it, as long as your method reaches what it is meant to and you lay out your proof correctly and logically
b) n = 316

Question 8 - Hyperbolic stuff AGAIN
a) Show that z^n + z^-n = 2cosntheta
b) Expand the z stuff
c) Find the double angle representation of cos^4(2x)
d) Find the solutions between 0 and pi, k = 1/12, 5/12, 7/12 and 11/12
e) Show that it = 3pi/16. Integrate the double angle representation, sub pi/2 into the sin parts, they go to 0, leaving you with the answer.

I know this is very poorly structured and doesn't have all the answers. If you remember anymore/disagree/remember the structure better than I, quote here and I'll correct it.

nerd.

[Oromis263]

(Original post by Dan*)
nerd.

Thank you for your input

[kirstyy93]

(Original post by Oromis263)
FP2 - 31st May 2012 Unofficial Mark Scheme

Well, here is what I remember:

Question 1 - hyperbolics, finding solutions
a) Draw the graph, pretty standard question, mark on the point of intersection
b) Solving gets + and - ln3

Question 2 - Loci
Circle, centre (2,3) touching the y-axis.
Line bisector between the two points (2,0) and (-3,1)? (not so sure about the second coordinate, but the idea is right)
c) Mark on the graph the part which satisfies both of the equations given. You had to mark the arc of the circle on the left of the bisecting line.

Question 3 - Summation of Series
a) Show that stuff, etc
b) Should rearrange to 2^26 - 1

Question 4 - Roots of Polynomials (Not sure what order these answers are in)
a) a+b+y = 0
b) Show that, using the cubic, rearrange after subbing the roots in, summing should bring you to the answer (similar to June 2011 paper)
c) y = -8, b = 4-7i
d) p = 1, q = 520
e) 520x^3 + x^2 + 1 = 0

Question 5 - Inverse functions
a) A core 3 rearrangement. State that secx = 1/cosx, then swap y and x, rearrange for y, thus it is shown.
b) Chain rule after swapping for cos^-1x.

Question 6 - Hyperbolic stuff again
Last part pi/256(128ln2 + 495)

Question 7 - Proof by induction
a) Prove it, as long as your method reaches what it is meant to and you lay out your proof correctly and logically
b) n = 316

Question 8 - Hyperbolic stuff AGAIN
a) Show that z^n + z^-n = 2cosntheta
b) Expand the z stuff
c) Find the double angle representation of cos^4(2x)
d) Find the solutions between 0 and pi, k = 1/12, 5/12, 7/12 and 11/12
e) Show that it = 3pi/16. Integrate the double angle representation, sub pi/2 into the sin parts, they go to 0, leaving you with the answer.

I know this is very poorly structured and doesn't have all the answers. If you remember anymore/disagree/remember the structure better than I, quote here and I'll correct it.

Do you remember how many marks question 4e was worth? I think I must have missed it out by mistake as I don't remember them asking for an equation :/ how silly of me


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