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Thread: Cambridge Prelim MX1 Textbook Marathon/Q&A

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by appleibeats View Post
    If v^2 = 24 - 6x -3x^2, find the acceleration of the particle at the particles greatest displacement from the origin.

    My answer:

    Greatest displacement at amplitude where v = 0

    When v = 0

    ( x - 2) (x + 4) = 0

    so x = 2 or x = -4

    Now acceleration = -3 -3x

    when x = -4 ( greatest displacement )

    acceleration = 9 m /s^2

    But the answers says Max displacement occurs when x = 2 so acceleration is -9m/s^2


    Why is it when x = 2 and not x = -4. Isn't the displacement from the origin greatest when x = -4 ??
    The distance from the origin is greatest at x = -4. The displacement includes the sign, so is greatest at x = +2.

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by Nailgun View Post
    what do you mean lel?
    When your identity is numerical, i.e there are no variables, you should be aiming to prove it without shifting anything.

    When your identity has variables, you can shift things around, maybe prove it using calculus.

    Or you could be me and do it by inspection.
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by InteGrand View Post
    The distance from the origin is greatest at x = -4. The displacement includes the sign, so is greatest at x = +2.
    So displacement can be either positive or negative?
    Whereas distance is positive or 0 only.

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by appleibeats View Post
    So displacement can be either positive or negative?
    Whereas distance is positive or 0 only.
    Distance is a scalar (magnitude only) whereas displacement is a vector (magnitude and direction)

    Therefore yes

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by appleibeats View Post
    If v^2 = 24 - 6x -3x^2, find the acceleration of the particle at the particles greatest displacement from the origin.

    My answer:

    Greatest displacement at amplitude where v = 0

    When v = 0

    ( x - 2) (x + 4) = 0

    so x = 2 or x = -4

    Now acceleration = -3 -3x

    when x = -4 ( greatest displacement )

    acceleration = 9 m /s^2

    But the answers says Max displacement occurs when x = 2 so acceleration is -9m/s^2


    Why is it when x = 2 and not x = -4. Isn't the displacement from the origin greatest when x = -4 ??
    Do you mind if I ask where you got that question from? Can't seem to find that in the Cambridge text book.
    | B Eng (Hons) | IB Mathematics SL | IB Mathematics HL | Australian Cricket | Casual University Statistics Tutor

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by davidgoes4wce View Post
    Do you mind if I ask where you got that question from? Can't seem to find that in the Cambridge text book.
    It's from the Grammar Trial 2015

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by appleibeats View Post
    It's from the Grammar Trial 2015
    Uhh

    Sorry for nitpicking but can you please leave this thread for the textbook questions

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    .

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread


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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by appleibeats View Post
    Have you learnt Implicit Differentiation?

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by si2136 View Post
    Have you learnt Implicit Differentiation?
    Yes, but the questions from the chapter about sums and products. So I think they want us to use that.

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by appleibeats View Post
    Yes, but the questions from the chapter about sums and products. So I think they want us to use that.
    equate both sides, you have a quartic equation

    α is a tangent, thus, a double root.

    The four roots are α,α,β,1 where β is some other root.

    Use the product and sum of roots formulae to determine the values of the roots.
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Is there a way to do this question without "equating coefficients"?
    http://pasteboard.co/C1Wjawh.png

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by Blitz_N7 View Post
    Is there a way to do this question without "equating coefficients"?
    http://pasteboard.co/C1Wjawh.png
    Yes, there is also a combinatorial proof that can be given. (Note that cj is just n choose j, from the Binomial Theorem.)





    Last edited by InteGrand; 2 May 2016 at 3:36 PM.

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Thank you Integrand!

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    polynomial.png
    induction.png

    Hey guys, need help with these questions on polynomials and induction

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Say roots are a and a2

    .: sum of roots: a + a2 = -m ==> m = -a(a+1)

    product of roots: a x a2 = a3 = n

    .: m3 = a3(-a3 - 3a2 - 3a -1)

    = n(-n +3m -1)

    = n(3m - n -1)
    Last edited by Drongoski; 2 May 2016 at 9:16 PM.
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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Screen Shot 2016-05-03 at 7.58.06 pm.png

    Not sure how to answer part b

    Do i get the cartisan form?

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by appleibeats View Post
    Screen Shot 2016-05-03 at 7.58.06 pm.png

    Not sure how to answer part b

    Do i get the cartisan form?



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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    For part c) Do i differentiate this equation in part b) in respects to T ? If so how do you find the derivate of x(T) squared ??

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by appleibeats View Post
    how do you find the derivate of x(T) squared ??

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by InteGrand View Post

    Found T to be 4, now how do I find max theta. Do I sub t = 4 into displacements of x and y and differentiate parametrically. I tried and got -cos(x)/sin(x) x for theta

    Answer says 30 degrees

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by appleibeats View Post
    Found T to be 4, now how do I find max theta. Do I sub t = 4 into displacements of x and y and differentiate parametrically. I tried and got -cos(x)/sin(x) x for theta

    Answer says 30 degrees
    appleibeats likes this.

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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread


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    Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

    Is it right for part b) to plug The new velocity and angle into part a max height and then equate it with part a) ?

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