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Thread: IB Maths Marathon

  1. #51
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    Re: International Baccalaureate Marathon 2016

    Quote Originally Posted by davidgoes4wce View Post
    this is what I did based on your advice:







    Im guessing that we have to break that double again down again ?
    Yep.

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    Re: International Baccalaureate Marathon 2016

    Curious little fact about negative numbers mentioned in the book

    "In Europe, it took until the 17th century for negative numbers to be accepted."

    An Indian mathematician Brahmagupta , who's name comes up fairly frequently was the first to introduce the idea.
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    Re: International Baccalaureate Marathon 2016

    Quote Originally Posted by davidgoes4wce View Post




















    That's my final simplified step.
    Sign errors all over the place.
    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: International Baccalaureate Marathon 2016

    Ahhh I made a mistake
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    Re: International Baccalaureate Marathon 2016

    I had a go again:



























    That's my final simplified step.
    Last edited by davidgoes4wce; 26 Jun 2016 at 10:28 PM.
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    Re: International Baccalaureate Marathon 2016

    To the above working out, you can verify the solution by plugging in x = pi/2. RHS yields 20 which exceeds the range of the sine function. So you probably made a small error somewhere

    pi/2 because sin(pi/2) is easily calculated
    Clue 1: 121 112
    Who am I?

    ( ͡° ͜ʖ ͡°) ( ͡° ͜ʖ ͡°)Clue 2

    Clue 0: Clockwise

    Clue 3: Are you watching closely? ∃ a clue every now and then
    Clue 4: 99 115
    Clue 5: |℘(S)| = 15^2 + 31

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    Re: International Baccalaureate Marathon 2016




























    Think I found it
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  8. #58
    Junior Member parad0xica's Avatar
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    Re: International Baccalaureate Marathon 2016

    This:



    To this:



    But it should be:



    Also, your final result is still wrong because substituting x = pi/2 yields 20.
    Clue 1: 121 112
    Who am I?

    ( ͡° ͜ʖ ͡°) ( ͡° ͜ʖ ͡°)Clue 2

    Clue 0: Clockwise

    Clue 3: Are you watching closely? ∃ a clue every now and then
    Clue 4: 99 115
    Clue 5: |℘(S)| = 15^2 + 31

  9. #59
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    Re: International Baccalaureate Marathon 2016

    OK Thanks I see it try to fix it again
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    Re: International Baccalaureate Marathon 2016



























    Is that right?
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    Re: International Baccalaureate Marathon 2016

    Quote Originally Posted by davidgoes4wce View Post


























    Is that right?
    If we sub. in x = pi/2 to the final answer, since sin(pi/2) = 1, we get -32 + 72 -24 + 5 = 21, which is outside the range of the LHS, which is sin(5x), which is between -1 and 1 always.

    This is the check that parad0xica mentioned in an earlier comment.
    Last edited by InteGrand; 26 Jun 2016 at 11:28 PM.

  12. #62
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    Re: International Baccalaureate Marathon 2016

    Quote Originally Posted by davidgoes4wce View Post


























    Is that right?
    Not possible, sin5x is a polynomial in sinx of degree 5.

    Some power in there is broken.
    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: International Baccalaureate Marathon 2016

    Im not sure about this question, is my expansion and simplification right?
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    Re: International Baccalaureate Marathon 2016

    Quote Originally Posted by davidgoes4wce View Post













    Looking at the first term only when going from line 5 to line 6, you did this:



    I think it was an issue of focus, not of lack of knowledge
    Last edited by parad0xica; 27 Jun 2016 at 12:20 AM.
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    Clue 1: 121 112
    Who am I?

    ( ͡° ͜ʖ ͡°) ( ͡° ͜ʖ ͡°)Clue 2

    Clue 0: Clockwise

    Clue 3: Are you watching closely? ∃ a clue every now and then
    Clue 4: 99 115
    Clue 5: |℘(S)| = 15^2 + 31

  15. #65
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    Re: International Baccalaureate Marathon 2016

    I'll try it again after watching a bit of the Euro 2016 action
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    Re: International Baccalaureate Marathon 2016



















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    Re: International Baccalaureate Marathon 2016

    Maths HL Introductory Problem:



    My thinking was to integrate the circumference of a circle in order to get the area of a circle.
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    Re: International Baccalaureate Marathon 2016

    Quote Originally Posted by davidgoes4wce View Post
    Maths HL Introductory Problem:



    My thinking was to integrate the circumference of a circle in order to get the area of a circle.
    Yeah that's essentially one way to do it. The typical HSC method would be to do something like integrate sqrt(r^2 - x^2) between 0 and r (this getting the area of the quarter-disk), and then multiplying by 4. The integration would be carried out using a trig. substitution (or you could use integration by parts but for that definite integral, trig. sub. is nicer).

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    Re: International Baccalaureate Marathon 2016

    Something like

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    Re: International Baccalaureate Marathon 2016

    Quote Originally Posted by davidgoes4wce View Post
    Something like

    Pretty much. And the area of a circle of radius 0 is 0, which makes C = 0. Not sure how rigorous you are required to be though with regards to explaining the integral.

    Here's a paper discussing when the perimeter of a shape will be the derivative of its area, or area the derivative of volume: https://www.math.byu.edu/~mdorff/docs/DorffPaper07.pdf .
    Last edited by InteGrand; 27 Jun 2016 at 10:23 PM.
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    Re: International Baccalaureate Marathon 2016



    I was a bit confused on this Introductory Question in Maths HL on Differentiation page 527 of Cambridge.

    Im thinking the function is



    We have to use differentiation and set to some value to solve for v.

    Anyone with any ideas to get a kick start to this question?
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    Re: International Baccalaureate Marathon 2016

    Quote Originally Posted by davidgoes4wce View Post


    I was a bit confused on this Introductory Question in Maths HL on Differentiation page 527 of Cambridge.

    Im thinking the function is



    We have to use differentiation and set to some value to solve for v.

    Anyone with any ideas to get a kick start to this question?
    davidgoes4wce likes this.

  23. #73
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    Re: International Baccalaureate Marathon 2016

    I totally didn't see it like that, after you explained that I got it.
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    Re: International Baccalaureate Marathon 2016

    Quote Originally Posted by InteGrand View Post
    I had a go at finishing off this question















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    Re: International Baccalaureate Marathon 2016



    Intro Problem Chapter 16
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