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Advanced Higher Maths 2011-2012 : Discussion and Help

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2010 paper analysis tomorrow.
Original post by Mr Dangermouse
My take on the 2009 paper
...


Might go do this when I've done the 2009 paper. Less than a week now, AHH!
Argh, nearly midday and I haven't even started 2010 yet.
2010 is absolutely brutal. I've had to take a break halfway through to avoid breaking things.
Can someone remind me how a go about scaling a matrix? Say for example I wanted a scale factor of 2.
Original post by Quintro
Can someone remind me how a go about scaling a matrix? Say for example I wanted a scale factor of 2.


Multiply all of its elements by 2.
Original post by ukdragon37
Multiply all of its elements by 2.

It's that simple? Wow, lol.
Reply 1107
Avatar for PaulB
PaulB
Does anyone have any idea if the AH course was different 2003 and before? Apart from the obvious changes (mechanics/stats sections in the same paper) was there any difference to the Unit 1/2 course since there is some stuff in the 2002 paper that I had to look up the techniques for. From looking them up, I don't remember being taught them.
Original post by PaulB
From looking them up, I don't remember being taught them.


Like what?
Original post by PaulB
Does anyone have any idea if the AH course was different 2003 and before? Apart from the obvious changes (mechanics/stats sections in the same paper) was there any difference to the Unit 1/2 course since there is some stuff in the 2002 paper that I had to look up the techniques for. From looking them up, I don't remember being taught them.


Are there any questions in particular that you are talking about? I can't really see anything in the 2002 paper that isn't in the current syllabus.
Reply 1110
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PaulB
Original post by TheUnbeliever
Like what?


Original post by Quintro
Are there any questions in particular that you are talking about? I can't really see anything in the 2002 paper that isn't in the current syllabus.


The one about integrating ln(1+x). I looked up how to do it online and I don't remember doing anything like that.
Original post by PaulB
The one about integrating ln(1+x). I looked up how to do it online and I don't remember doing anything like that.


That's easy. 1/(1+x)
Original post by PaulB
The one about integrating ln(1+x). I looked up how to do it online and I don't remember doing anything like that.

You should have covered that during integration by parts.


Original post by Mr Dangermouse
That's easy. 1/(1+x)

He said integrating.
Original post by PaulB
The one about integrating ln(1+x). I looked up how to do it online and I don't remember doing anything like that.


There isn't really any extra content there, you just have to know the 'multiply by one and proceed by parts' trick. That question was in our prelim my year, presumably to make sure we did.
Original post by Quintro
You should have covered that during integration by parts.



He said integrating.



My bad. You would do integration by parts and use 1 as the dummy variable.


ie. "integral sign" 1.ln(1+x)dx


u = ln(1+x)
du = (1/(1+x))dx

dv = 1dx
v = x

xln(1+x) - "integral" (x/(1+x))dx

xln(1+x) - xln(1+x)

= 0
Original post by Mr Dangermouse
My bad. You would do integration by parts and use 1 as the dummy variable.


ie. "integral sign" 1.ln(1+x)dx


u = ln(1+x)
du = (1/(1+x))dx

dv = 1dx
v = x

xln(1+x) - "integral" (x/(1+x))dx

xln(1+x) - xln(1+x)

= 0


:lolwut:

You know something is clearly wrong when you integrate to get 0
Original post by ukdragon37
:lolwut:

You know something is clearly wrong when you integrate to get 0


True, what did I do wrong?
Original post by Mr Dangermouse
True, what did I do wrong?


You've sort of "half-integrated" the 1/(1+x) part in x/(1+x). Instead:

∫xdx1+x=∫(1−11+x)dx=x−ln⁡(1+x)+C\displaystyle\int\dfrac{xdx}{1+x} = \displaystyle\int\left(1 - \dfrac{1}{1+x}\right)dx = x - \ln\left(1+x\right) + C


Pretty sure that's right

Edit: typical ukd: posting the right answer just before anyone else. :tongue:
(edited 11 years ago)
I don't understand that at all.

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