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The Big 2009 AEA Maths Thread! :)

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Thanks for everyone's input already!...Looks like this shall be a successful thread :smile: It's already turning out to be very useful for me, since I haven't yet done C4 differential equations (I'm not doing full further maths, just new syllabus FM AS privately!) so saw it as an opportune moment to get my textbook out and learn it! I think I really should get through c4 myself asap to really get to grips with the AEA questions, right?

Also, June 2005 Question 7 (attached)..parts a is pretty straight forward, part b is manageable, but I have no idea how to attempt part c...any ideas?


It's hard to see it there!, here's the direct link : http://s5.tinypic.com/df7waw.jpg
...

show;

ddxxn=nxn−1 \displaystyle \frac{d}{dx} x^n = nx^{n-1}
Reply 22
Avatar for Andylol
Andylol
14
My question, what's AEA? Never heard of that o.O
Reply 23
Avatar for Maebara
Maebara
Andylol
My question, what's AEA? Never heard of that o.O

http://en.wikipedia.org/wiki/Advanced_Extension_Award
Reply 24
Avatar for A.J.B
A.J.B
subscribed*
havent started solving papers for it though
... Providing; einx=cos(nx)+isin(nx)  and  i=−1 e^{inx} = cos(nx) + isin(nx) \; and \; i = \sqrt{-1} use the sub y=ekx y = e^{kx}

d2ydx2+4y=0 \displaystyle \frac{d^2y}{dx^2} +4y = 0

Hence obtain the function so;

d2ydx2+4y=sin(x) \displaystyle \frac{d^2y}{dx^2} +4y = sin(x)
1 Economic Historian
Thanks for everyone's input already!...Looks like this shall be a successful thread :smile: It's already turning out to be very useful for me, since I haven't yet done C4 differential equations (I'm not doing full further maths, just new syllabus FM AS privately!) so saw it as an opportune moment to get my textbook out and learn it! I think I really should get through c4 myself asap to really get to grips with the AEA questions, right?

Also, June 2005 Question 7 (attached)..parts a is pretty straight forward, part b is manageable, but I have no idea how to attempt part c...any ideas?


It's hard to see it there!, here's the direct link : http://s5.tinypic.com/df7waw.jpg


Expand out cos(2x) as 2cos⁡2x−12\cos^2 x - 1; now, can you make a substitution which'll enable you to use the result in (i)?
Glutamic Acid
Expand out cos(2x) as 2cos⁡2x−12\cos^2 x - 1; now, can you make a substitution which'll enable you to use the result in (i)?

Yeah I get it now, thanks! :smile:
(I think I better quickly learn how to use latex though, to actually start posting my working on here! :redface: )
8 Horizontal
Ok I'll start us off:

Solve the D.E.:

(dydx)2+sinx(cos2x)(dydx)−sin4x=0 \left( \frac{dy}{dx} \right)^2+sinx(cos^2x)\left( \frac{dy}{dx} \right)-sin^4x = 0

Spoiler


They can't ask diff eqs in the AEA. It's not C1-C4.
sohanshah
They can't ask diff eqs in the AEA. It's not C1-C4.


It is in the current C4 edexcel syllabus I quote from the specification:

"Analytical solution of simple first order differential equations with separable variables."

Furthermore, in the question not even this knowledge of separation of variable is needed all you need is the 'intuition' to try to factorise the expression and consider the expressions in the two brackets separately.
8 Horizontal
It is in the current C4 edexcel syllabus I quote from the specification:

"Analytical solution of simple first order differential equations with separable variables."

Furthermore, in the question not even this knowledge of separation of variable is needed all you need is the 'intuition' to try to factorise the expression and consider the expressions in the two brackets separately.

At the risk of sounding stupid, C4 differential equations are well...much much easier though :redface:
And I haven't found any questions like the one you posted in past papers as yet... :s-smilie:
Reply 31
Avatar for Mark13
Mark13
sohanshah
They can't ask diff eqs in the AEA. It's not C1-C4.


I'm pretty sure DEs are on C4. And to be fair, all you need to solve this question is:

Spoiler

1 Economic Historian
At the risk of sounding stupid, C4 differential equations are well...much much easier though :redface:
But AEA questions are supposed to be much harder than C4 ones.

And I haven't found any questions like the one you posted in past papers as yet... :s-smilie:
That, however, is a fair point. The people posting on this thread (and the 2009 STEP one) are not doing a great job of reproducing the examination style. Even in maths, real exam questions tend to be a little wordier than "solve {long complicated equation}".
Reply 33
Avatar for *MJ*
*MJ*
2
2X = 4

Find X...:ninja:
*MJ*
2X = 4

Find X...:ninja:


It is there... between 2 and the equation symbol *points*. :yep:
Reply 35
Avatar for *MJ*
*MJ*
2
(2Clever*0.5)^2
It is there... between 2 and the equation symbol *points*. :yep:


Go on...:smile:

This is better than the answer I was expecting...:tongue:

Solve 7 + 2 = 9...:ninja:

...:cool: :tongue:
Reply 36
Avatar for Mark13
Mark13
Given ln(x)=axln(x) = ax, where a is a constant, determine the values of a for which there is one solution to the equation.

EDIT: Maybe this is too hard for AEA? I'm not sure.
Mark13
Given ln(x)=axln(x) = ax, where a is a constant, determine the values of a for which there is one solution to the equation.

EDIT: Maybe this is too hard for AEA? I'm not sure.


... seems reasonable (Camb interview questions)

edit; you can even guess the correct answers from the graph.
Reply 38
Avatar for koki234
koki234
Mark13
Given ln(x)=axln(x) = ax, where a is a constant, determine the values of a for which there is one solution to the equation.

EDIT: Maybe this is too hard for AEA? I'm not sure.


Do you have the answer?
Consider values of a; a < 0

Spoiler

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