Edexcel Maths FP2 (New Spec)

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  1. JamesyB's Avatar
    1 08-04-2010  15:57
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    Edexcel Maths FP2 (New Spec)
    Hey Guys

    Found these threads really useful for C3 & C4 last year so I thought I'd make one for FP2. You know the drill, post the topics or specific questions you're having dificulties with and we'll try and help! I'll update this post with good bits of advice for each topic.

    June 2009 paper and Mark Scheme can be found here.

    Here are the topics including given formulas:

    Inequalities

    No Formulas Given

    Series

    No Formulas Given

    Complex Numbers

    Formulas:

    e^{i\theta} = cos\theta + isin\theta

    {r(cos\theta + isin\theta)}^{n} = {r^{n}(cosn\theta + isinn\theta)}

    The roots of z^{n} = 1 are given by z = e^{\frac{2\pi ki}{n}} k = 0, 1, 2, ..., n - 1.

    Differential Equations: First Order

    No Formulas Given

    Differential Equations: Second Order

    No Formulas Given

    Maclaurin & Taylor Series

    Formulas:

    f(x) = f(0) + xf'(0) + \frac{x^{2}}{2!}f''(0) + ... + \frac{x^{r}}{r!}f^{(r)}(0)...

    f(x) = f(a) + (x - a)f'(a) + \frac{(x - a)^{2}}{2!}f''(a) + ... + \frac{(x - a)^{r}}{r!}f^{(r)}(a)...

    f(a + x) = f(a) + xf'(a) + \frac{x^{2}}{2!}f''(a) +...+ \frac{x^{r}}{r!}f^{(r)}(a)...

    e^{x} = 1 + x + \frac{x^{2}}{2!} + ... + \frac{x^{r}}{r!}... for all x.

    ln(1 + x) = x - \frac{x^{2}}{2!} + \frac{x^{3}}{3!} - ... + (-1)^{r + 1} \frac{x^{r}}{r!} ... -1 < x \leq 1

    sin x = x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} - ... + (-1)^{r} \frac{x^{2r + 1}}{(2r + 1)!} ... for all x.

    cos x = 1 - \frac{x^{2}}{2!} + \frac{x^{4}}{4!} - ... + (-1)^{r} \frac{x^{2r}}{(2r)!} ... for all x.

    arctan x = x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} - ... + (-1)^{r} \frac{x^{2r + 1}}{2r + 1} ... -1 < x \leq 1

    Polar Coordinates

    Formulas:

    A = \frac{1}{2} \int r^{2} d\theta
  2. samir12's Avatar
    2 08-04-2010  16:24
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    Re: Edexcel FP2 June 29th Revision Thread!
    When it comes to finding the roots of complex numbers eg z^ 5 = 2i, when finding the angles, does it have to be between pie and minus pie or could you go above pie? Because in the book it only finds roots with angles between pie and minus pie, where as in exam papers, the markscheme just goes way above pie.
  3. JamesyB's Avatar
    3 09-04-2010  13:35
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    Re: Edexcel FP2 June 29th Revision Thread!
    (Original post by samir12)
    When it comes to finding the roots of complex numbers eg z^ 5 = 2i, when finding the angles, does it have to be between pie and minus pie or could you go above pie? Because in the book it only finds roots with angles between pie and minus pie, where as in exam papers, the markscheme just goes way above pie.
    It depends on the question, if there are limits placed on the angles in the question then stick to them (usually -\pi \leq \theta \leq \pi) otherwise I think they allow any correct angle, which can of course go way beyond pi.
  4. rbnphlp's Avatar
    4 10-04-2010  18:45
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    Re: Edexcel FP2 June 29th Revision Thread!
    anyone using a graphical calculator for polar coordinates?
  5. samir12's Avatar
    5 10-04-2010  18:51
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    Re: Edexcel FP2 June 29th Revision Thread!
    (Original post by rbnphlp)
    anyone using a graphical calculator for polar coordinates?
    I don't have one, but Im planning to get one especially for sketching polar coordinates.
  6. rbnphlp's Avatar
    6 10-04-2010  19:25
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    Re: Edexcel FP2 June 29th Revision Thread!
    (Original post by samir12)
    I don't have one, but Im planning to get one especially for sketching polar coordinates.
    I would recommend ti83 + ..dont fall into the trap of getting the pink one like I did
  7. Pheylan's Avatar
    7 10-04-2010  19:29
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    Re: Edexcel FP2 June 29th Revision Thread!
    it's on the 24th. i'm fairly confident, i love the differential equations
  8. rbnphlp's Avatar
    8 10-04-2010  19:36
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    Re: Edexcel FP2 June 29th Revision Thread!
    I hate those , so much to remember , dont like taylor mclaurian either ...
    Matrices is ok , integration with recurrence is lovely
  9. Pheylan's Avatar
    9 10-04-2010  19:50
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    Re: Edexcel FP2 June 29th Revision Thread!
    (Original post by rbnphlp)
    I hate those , so much to remember
    try this, probably the hardest question in chapter 5

    Use the substitution z = sinx to transform the differential equation

    cosx\frac{d^2y}{dx^2}+sinx\frac{ dy}{dx}-2ycos^3x=2cos^5x

    into the equation

    \frac{d^2y}{dz^2}-2y=2(1-z^2).

    Hence solve the equation cosx\frac{d^2y}{dx^2}+sinx\frac{ dy}{dx}-2ycos^3x=2cos^5x, giving y in terms of x.
  10. JamesyB's Avatar
    10 10-04-2010  19:56
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    Re: Edexcel FP2 June 29th Revision Thread!
    (Original post by Pheylan)
    it's on the 24th. i'm fairly confident, i love the differential equations
    You're right it is, dunno where 29th came from haha do you know if it's possible to change the title??
  11. Pheylan's Avatar
    11 10-04-2010  20:00
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    Re: Edexcel FP2 June 29th Revision Thread!
    (Original post by JamesyB)
    You're right it is, dunno where 29th came from haha do you know if it's possible to change the title??
    yep, just put the mouse on the black bit and double click:

  12. rbnphlp's Avatar
    12 10-04-2010  20:18
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    Re: Edexcel FP2 June 29th Revision Thread!
    (Original post by Pheylan)
    try this, probably the hardest question in chapter 5

    Use the substitution z = sinx to transform the differential equation

    cosx\frac{d^2y}{dx^2}+sinx\frac{ dy}{dx}-2ycos^3x=2cos^5x

    into the equation

    \frac{d^2y}{dz^2}-2y=2(1-z^2).

    Hence solve the equation cosx\frac{d^2y}{dx^2}+sinx\frac{ dy}{dx}-2ycos^3x=2cos^5x, giving y in terms of x.
    not too bad..
  13. kosy91's Avatar
    13 10-04-2010  20:27
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    Re: Edexcel FP2 June 29th Revision Thread!
    hey you guys....i am sitting that paper as well!!
  14. Roxalana's Avatar
    14 10-04-2010  20:46
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    Re: Edexcel FP2 June 29th Revision Thread!
    (Original post by Pheylan)
    try this, probably the hardest question in chapter 5

    Use the substitution z = sinx to transform the differential equation

    cosx\frac{d^2y}{dx^2}+sinx\frac{ dy}{dx}-2ycos^3x=2cos^5x

    into the equation

    \frac{d^2y}{dz^2}-2y=2(1-z^2).

    Hence solve the equation cosx\frac{d^2y}{dx^2}+sinx\frac{ dy}{dx}-2ycos^3x=2cos^5x, giving y in terms of x.
    oh my god... i got mixed up, how the heell do you do it

    what do u make the f(x) equal to?
  15. rbnphlp's Avatar
    15 10-04-2010  20:53
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    Re: Edexcel FP2 June 29th Revision Thread!
    (Original post by Roxalana)
    oh my god... i got mixed up, how the heell do you do it

    what do u make the f(x) equal to?
    if you have done the transformation ,notice that this is a function of z i.e f(z), and its a quadratic, so something of the form (A+Bz+Cz^2) will suffice
  16. Roxalana's Avatar
    16 10-04-2010  23:15
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    Re: Edexcel FP2 June 29th Revision Thread!
    (Original post by rbnphlp)
    if you have done the transformation ,notice that this is a function of z i.e f(z), and its a quadratic, so something of the form (A+Bz+Cz^2) will suffice
    sorry could u just remind me the method for this specific particular integral..please
  17. KeineHeldenMehr's Avatar
    17 11-04-2010  19:31
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    Re: Edexcel FP2 June 24th Revision Thread!
    ah this paper would be ok if it didnt have series.

    Maclaurin & Taylor Series and method of differences are a nightmare, doesn't help that the green book has so many mistakes.

    for maclaurin series, how do you find the r th derivative ?

    is the only way to find it by observing previous derivatives of a lower order?
  18. kosy91's Avatar
    18 11-04-2010  20:15
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    Re: Edexcel FP2 June 24th Revision Thread!
    the edexcel book has just too many mistakes in it. especially in complex numbers. doesnt anything like proof-reading exist in this word???
  19. Roxalana's Avatar
    19 11-04-2010  20:17
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    Re: Edexcel FP2 June 24th Revision Thread!
    (Original post by kosy91)
    the edexcel book has just too many mistakes in it. especially in complex numbers. doesnt anything like proof-reading exist in this word???
    It does...? where...
  20. Pheylan's Avatar
    20 11-04-2010  20:23
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    Re: Edexcel FP2 June 24th Revision Thread!
    from page 44:

    |(x-6)+iy|^2=2^2|(x+6)+i(y-9)|^2

    (x-6)^2+y^2=4[(x+6)^2+(y-9)^2]

    i don't understand what happened there. why does the i just disappear?
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