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Thread: First Year Mathematics B (Integration, Series, Discrete Maths & Modelling)

  1. #376
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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by Flop21 View Post
    I've become stuck on this again

    [3x + 2]/[(x^2+2x+2)(x-1)] = 1/(x-1) + (bx+c)/(x^2+2x+2).


    So I go 3x+2 = A(x^2+2x+2) + (bx+c)(x-1)... right?

    A is 1 like they already give us. But I can't seem to find an x value that will allow me to find bx+c?
    Sub. x = 0, which easily lets us find C. Then we can find B by subbing (say) x = 2.
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    Supreme Member Flop21's Avatar
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    Re: MATH1231/1241/1251 SOS Thread

    When doing first order linear differential equations...

    How did this turn into this?

    2015 HSC: English Adv, Mathematics, Business Studies, Biology, Multimedia.

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    Supreme Member Flop21's Avatar
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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by InteGrand View Post
    Sub. x = 0, which easily lets us find C. Then we can find B by subbing (say) x = 2.
    Oh thanks, silly me was getting confused when I was getting c = 0 for some reason. But that's the answer.
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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by Flop21 View Post
    When doing first order linear differential equations...

    How did this turn into this?

    Product rule.

  5. #380
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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by leehuan View Post
    Actually, whilst I can't deny the reduced difficulty of the HSC exams over the years, if it were to appear now I would be thoroughly displeased at that as well.

    I don't know what the HSC was like in 2003 to speak for back then



    Thanks for that proof though; that I'll show him as well.
    Can you recall whether there have been any contradiction proofs in the HSC more recently than 2003? Surely there should've been (though I can't remember any off the top of my head)?
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  6. #381
    Ancient Orator leehuan's Avatar
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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by InteGrand View Post
    Can you recall whether there have been any contradiction proofs in the HSC more recently than 2003? Surely there should've been (though I can't remember any off the top of my head)?
    Couldn't really off my head either

  7. #382
    Supreme Member Flop21's Avatar
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    Re: MATH1231/1241/1251 SOS Thread

    2 questions about marking.

    1. Will I lose marks if I just write down the limit in questions asking for 'does this series converge, if so find its limit'?

    2. Will I lose marks if I don't show fully working when row reducing in questions where it's just a step, e.g. finding eigenvectors I can just sometimes do it my head and will just write the final form.
    2015 HSC: English Adv, Mathematics, Business Studies, Biology, Multimedia.

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  8. #383
    Ancient Orator leehuan's Avatar
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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by Flop21 View Post
    2 questions about marking.

    1. Will I lose marks if I just write down the limit in questions asking for 'does this series converge, if so find its limit'?

    2. Will I lose marks if I don't show fully working when row reducing in questions where it's just a step, e.g. finding eigenvectors I can just sometimes do it my head and will just write the final form.
    Well if you want to find the limit of a series, unless it's that obvious how do you plan to do it by inspection though

    But with 2 I also skip row reductions if it's that obvious. I think my tutor does as well.
    I work around it by saying matrix*x = 0 therefore x = my answer
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    Ancient Orator leehuan's Avatar
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    Re: MATH1231/1241/1251 SOS Thread

    Good thing is that they're like we WANT to give you marks. So they don't have mark allocations like in the HSC so that they aren't limiting themselves.

    So I reckon if you jumped some steps but didn't jump too excessively to get the right answer you'd get it. (But of course if you jumped too many steps only to get the wrong answer well that's another story)

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    Ancient Orator leehuan's Avatar
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    Re: MATH1231/1241/1251 SOS Thread

    (for the same linearly independence qn)

    Another friend wants to know if there's fault in what he did and I can't really communicate anything

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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by leehuan View Post
    (for the same linearly independence qn)

    Another friend wants to know if there's fault in what he did and I can't really communicate anything
    Yeah that's correct.

  12. #387
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    Re: MATH1231/1241/1251 SOS Thread

    I could probably research it up but I feel as though InteGrand's answers are more comprehensible...


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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by leehuan View Post
    I could probably research it up but I feel as though InteGrand's answers are more comprehensible...





    Last edited by InteGrand; 7 Nov 2016 at 1:42 AM.
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    Loquacious One Drsoccerball's Avatar
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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by leehuan View Post
    I could probably research it up but I feel as though InteGrand's answers are more comprehensible...

    Spending too much time on mathematical memes ?
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  15. #390
    New Member FritzTheCat's Avatar
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    Re: First Year Mathematics B (Integration, Series, Discrete Maths & Modelling)

    Is everyone still doing this? I'd very much like to participate.

    Here's a problem I've been stuck on for a little while. Any takers?

    Last edited by FritzTheCat; 16 Jul 2017 at 10:08 PM.

  16. #391
    Senior Member sida1049's Avatar
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    Re: First Year Mathematics B (Integration, Series, Discrete Maths & Modelling)

    Consider the equation \lambda_1.v_1 + ... \lambda_m.v_m = 0. We need to show that all coefficients are zero. To do this, take the dot product of v_i to both sides to show that for arbitrary i = 1, 2, ... , m, \lambda_i = 0 (by the property of orthogonality). And we're done.
    Last edited by sida1049; 16 Jul 2017 at 10:21 PM.

    Bachelor of Science (Advanced Mathematics)/Bachelor of Arts III, USYD

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