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    Re: HSC 2017 Maths (Advanced) Marathon

    To add onto the marathon, here's a new question:

    Capture.PNG

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    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by athena13 View Post
    To add onto the marathon, here's a new question:

    Capture.PNG
    http://imgur.com/YqJJwLA
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    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by athena13 View Post
    To add onto the marathon, here's a new question:

    Capture.PNG
    Oh my god the number of times \quad is used in that TEX code... anyways, is that picture from the MIF textbook?

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    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by InteGrand View Post





    Last edited by 1729; 29 Jan 2017 at 1:59 AM.

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    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by 1729 View Post
    Excuse my notation, but here we go (correct me if I am wrong InteGrand)




    Last edited by InteGrand; 28 Jan 2017 at 5:36 PM.

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    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by InteGrand View Post





    Last edited by 1729; 29 Jan 2017 at 2:00 AM.

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    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by 1729 View Post
    Okay, I am going to use different greek letters for different weights, although not sure if this is reasonable notation. Now correct me if this is wrong.. although I am fairly confident that I got it.. this took ages to type my apologies






    Well done.

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    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by 1729 View Post
    Okay, I am going to use different greek letters for different weights, although not sure if this is reasonable notation. Now correct me if this is wrong.. although I am fairly confident that I got it.. this took ages to type my apologies






    This is HSC maths??

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    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by boredofstudiesuser1 View Post
    This is HSC maths??
    It can be done using only high school algebra as 1729 did, but admittedly it probably wouldn't come up in a HSC paper (not without any guidance anway).

    You can find out more about weighted averages at the Wikipedia article for it: https://en.wikipedia.org/wiki/Weighted_arithmetic_mean .
    Last edited by InteGrand; 28 Jan 2017 at 7:41 PM.

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    Re: HSC 2017 Maths (Advanced) Marathon

    I came across a question in the Cambridge textbook today and I haven't looked at the answer yet.



    I'm assuming its a constant of 1 next to the dx when we integrate it? Somebody could confirm
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    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by davidgoes4wce View Post
    I came across a question in the Cambridge textbook today and I haven't looked at the answer yet.



    I'm assuming its a constant of 1 next to the dx when we integrate it? Somebody could confirm
    Yes, that's right (it's common practice to drop the '1' and write it like they've written it).
    davidgoes4wce and frog1944 like this.

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    Re: HSC 2017 Maths (Advanced) Marathon

    Congruency test

    I came across this question tonight and wanted to clear a couple of things up. At times could we use either RHS test or SAS test to explain parts (b) and (f)? They are exactly the same shape as one can see and the Cambridge textbook gives 2 solutions:



    The answer for part (b) was RHS in the textbook

    The answer for part (f) was SAS in the text book
    Last edited by davidgoes4wce; 8 Feb 2017 at 12:59 AM.
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    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by davidgoes4wce View Post
    Congruency test

    I came across this question tonight and wanted to clear a couple of things up. At times could we use either RHS test or SAS test to explain parts (b) and (d)? They are exactly the same shape as one can see and the Cambridge textbook gives 2 solutions:



    The answer for part (b) was RHS in the textbook

    The answer for part (f) was SAS in the text book
    I would say no (may be wrong).

    In (b), the angle is not included within the two sides marked and therefore can only be RHS (SAS is side, included angle, side)

    On the other hand, in (f) it is SAS as they are giving you two sides and an included angle but the hypotenuse is not one of the sides. Therefore it is directly SAS and I would say, indirectly RHS.
    davidgoes4wce likes this.

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    Re: HSC 2017 Maths (Advanced) Marathon

    ^^ I can see it now . It's something that I never really looked into specifically.

    SO I take it, if they give the hypotenuse length and a right angle, we can conclude its a RHS . (also one of the adjacent or opposite lengths)

    If we are given a right angle, adjacent and an opposite length, then its a SAS.
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    Re: HSC 2017 Maths (Advanced) Marathon

    I was also looking to compare (b) v (f)....................earlier I mentioned (b) v (d)
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    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by davidgoes4wce View Post
    I was also looking to compare (b) v (f)....................earlier I mentioned (b) v (d)
    Yeah, I just assumed so since d had no angle marked or hypotenuse

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    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by boredofstudiesuser1 View Post
    Yeah, I just assumed so since d had no angle marked or hypotenuse
    I learnt something new I guess, I always had the assumption that with congruency tests, that if there was a right angle in there, it was always RHS.

    Not sure if the majority of HSC and prelim students knew that in the back of their mind. (And I'm not afraid to say this was from a Year 9 Maths textbook )
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    Re: HSC 2017 Maths (Advanced) Marathon

    Show that x^3 - 8 has only one linear factor over the real number field,

    What is the real number field?

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    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by 19KANguy View Post
    Show that x^3 - 8 has only one linear factor over the real number field,

    What is the real number field?
    To solve it in a different way, we can look at the roots, since is a cubic polynomial then there are three roots, .Obviously one of the roots is 2,so let
    then sum and product of the roots imply

    then

    which implies

    and no real number satisfies above equality, hence there is only one linear factor
    Last edited by Mahan1; 17 Feb 2017 at 11:26 PM.
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    Re: HSC 2017 Maths (Advanced) Marathon

    Hey guys,
    I've got little to no idea about how to solve the logarithmic equation questions I've come across in the past hsc papers.

    Can someone help me solve: 2lnx=ln(5+4x) AND 2log(base5)^3=log(base5)^x-log(base5)^6

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    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by dragon658 View Post
    Hey guys,
    I've got little to no idea about how to solve the logarithmic equation questions I've come across in the past hsc papers.

    Can someone help me solve: 2lnx=ln(5+4x) AND 2log(base5)^3=log(base5)^x-log(base5)^6
    Last edited by 1729; 25 Feb 2017 at 12:18 AM.

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    Re: HSC 2017 Maths (Advanced) Marathon

    Herooo, Pls help with this
    Capture1.PNG
    HSC 2017- 90.85
    Goal: get 90s in all subjects... rip
    English Adv: 85
    Math Adv: 89
    Biology: 86
    Chemistry: 81
    Economics: 86
    Business Stud: 91

  23. #48
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    Re: HSC 2017 Maths (Advanced) Marathon

    Quote Originally Posted by Mathew587 View Post
    Herooo, Pls help with this
    Capture1.PNG

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    Re: HSC 2017 Maths (Advanced) Marathon



    edit: My bad, didn't see there was an answer already

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    Re: HSC 2017 Maths (Advanced) Marathon

    Oh you can do that? My teachers a bit weird and would want us to actually write the whole solution out. How could you prove Tn = Sn - Sn-1?? ^^D
    HSC 2017- 90.85
    Goal: get 90s in all subjects... rip
    English Adv: 85
    Math Adv: 89
    Biology: 86
    Chemistry: 81
    Economics: 86
    Business Stud: 91

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