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FP2 (Not MEI) - Thursday June 14 2012, AM

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    How are people finding this? How are past papers going? Enjoying hyperbolics?

    I've just got one more topic to learn and then revision can begin. y2=f(x) is the last topic, but it'll probably be done by Wednesday as the teacher's really good.

    I really like the integration stuff and the hyperbolics, but the numerical methods aren't my thing.
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    Instead of spamming the C4 thread, thought I'd post here instead

    Still got to finish reduction formulae (nearly there) and then chapter 12
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    (Original post by wibletg)
    Instead of spamming the C4 thread, thought I'd post here instead

    Still got to finish reduction formulae (nearly there) and then chapter 12
    How are you finding the reduction formulae? We've just done the 'extra tricks' section, I'll complete that exercise before Tuesday (so, tomorrow) and then chapter 12'll be done on Tues and Wednesday.

    What bits would you say you find the hardest?
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    (Original post by Contrad!ction.)
    How are you finding the reduction formulae? We've just done the 'extra tricks' section, I'll complete that exercise before Tuesday (so, tomorrow) and then chapter 12'll be done on Tues and Wednesday.

    What bits would you say you find the hardest?
    Not too bad, you've just got to be careful when solving sometimes...
    Constructing the formulae is easy, it's putting the numbers in that I tend to cock up on
    We've got the extra tricks bit to do* (i.e. trig) and that's it.

    The hardest part has to have been the chapter on integrating awkward things... but once you get your head around it it's not so bad seems they usually give you the substitution if it's something ridiculously complex.
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    (Original post by wibletg)
    Not too bad, you've just got to be careful when solving sometimes...
    Constructing the formulae is easy, it's putting the numbers in that I tend to cock up on
    We've got the extra tricks bit to do* (i.e. trig) and that's it.

    The hardest part has to have been the chapter on integrating awkward things... but once you get your head around it it's not so bad seems they usually give you the substitution if it's something ridiculously complex.
    The extra bits thing is pretty cool, although it requires a bit of initiative.

    I quite like that chapter, I probably find the polar chapter hardest as sometimes I need to visualise stuff, which I'm crap at.
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    (Original post by Contrad!ction.)
    The extra bits thing is pretty cool, although it requires a bit of initiative.

    I quite like that chapter, I probably find the polar chapter hardest as sometimes I need to visualise stuff, which I'm crap at.
    Naah, polar is fine, especially if you have snazzy polar graph paper
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    (Original post by wibletg)
    Naah, polar is fine, especially if you have snazzy polar graph paper
    We spent a lesson coming up with funky looking graphs. r=sin2(2θ) is a nice one.
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    (Original post by Contrad!ction.)
    We spent a lesson coming up with funky looking graphs. r=sin2(2θ) is a nice one.
    Argh.

    Got any tips for reduction formulae?

    We're finished the course and doing various bits of revision (Revision exercises, mock tests) but one thing that always gets me is reduction formulae!

    I can usually get In-2 but it's multiplied by a function of x that's not always in the original integral and I can never seem to extract it.

    Also, for anyone else, if you have the Jan 12 paper and MS I'd appreciate it?
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    Now FP3 is out of the way, how's everyone doing in FP2?

    Quick question on graph questions - Do you always sketch the y = f(x) graph and then sketch the y^2 = f(x) graph, or do you simply visualise and work out the y = f(x) graph in your head then go straight to the y^2 = f(x) sketch?

    EDIT - Also, is there a specific method for finding the gradient when y = 0 and f'(x) = 0 (e.g. the gradient at the origin)?
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    (Original post by Anon 17)
    Now FP3 is out of the way, how's everyone doing in FP2?

    Quick question on graph questions - Do you always sketch the y = f(x) graph and then sketch the y^2 = f(x) graph, or do you simply visualise and work out the y = f(x) graph in your head then go straight to the y^2 = f(x) sketch?

    EDIT - Also, is there a specific method for finding the gradient when y = 0 and f'(x) = 0 (e.g. the gradient at the origin)?
    I tend to sketch the y=f(x) graph first then work around that with a 'rejection region' and then work out which bits are elliptical

    Your second question though - what? are you on about with y^2=f(x) graphs or aymptotes or what? sorry, having a slow day
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    Yeah, y2 = f(x) graphs. I've been asked to work out the gradient at the origin, but as this particular graph has f'(x) being zero at the origin, I can't work out the gradient through differentiating the equation implicitly or finding dx/dy...
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    (Original post by Anon 17)
    Yeah, y2 = f(x) graphs. I've been asked to work out the gradient at the origin, but as this particular graph has f'(x) being zero at the origin, I can't work out the gradient through differentiating the equation implicitly or finding dx/dy...
    If you're talking about the point where the graph of y^2=f(x) crosses the x axis then the gradient is infinite at that point as it crosses the x axis at a right angle
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    The textbook explains very well about when f'(x) = 0.
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    No, I'm not on about that and of course I've read the textbook first =P

    y = 0, f'(x) = 0 - What do? All the textbook says here is how both the methods of finding the gradient (2y dy/dx = f'(x) or 2y = f'(x) dx/dy) both produce 0. An example is question 6 of exercise 12 in the textbook. Maybe I'm just being stupid, but I can't see how they got sqrt(6) as the answer. I am only just learning this chapter now, so yeah...
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    Hi guys, anyone got the mark scheme for Jan 2007? I really need it at the moment, could someone kindly post it here? thanks~
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    (Original post by lilipop)
    Hi guys, anyone got the mark scheme for Jan 2007? I really need it at the moment, could someone kindly post it here? thanks~
    http://www.xtremepapers.com/papers/O..._MS_Jan_07.pdf

    In here
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    Thx X
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     \int \! \sqrt{4x^2 - 1} \, \mathrm{d} x.

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    x=\frac{1}{2}\cosh{u}

\int \! \sqrt{\cosh^2{u} - 1} \, \frac{dx}{du} \mathrm{d} u.
    \frac{dx}{du} = \frac{1}{2}\sinh{u}
    \frac{1}{2} \int \! \sinh^2{u} \, \mathrm{d} u.
    \frac{1}{2} \int \! \cosh{2u} - 1 \, \mathrm{d} u.
    \frac{1}{2}(\frac{1}{2}\sinh{2u} - u)




    That is all well and good, but what would this change to when substituting back in? I can't get the answer in the mark scheme.

    \frac{1}{2}x\sqrt{4x^2-1}-\frac{1}{4}\cosh^{-1}{2x} + c

    Also does anyone have a good way of explaining sums of series and integrals? I understand myself about the rectangles but can't really explain too well in an exam situation.
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    Has anyone got the January 2012 paper?
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    (Original post by ihategeography)
    Has anyone got the January 2012 paper?
    I've got it, but not in PDF though...

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