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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by leehuan View Post
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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by jathu123 View Post
    Note that arctan(t) + arctan(1/t) is only equal to pi/2 if t := a/b > 0. If t < 0, then it's -pi/2. The result in the question in the case t < 0 is similar, but with a minus sign in front of one of the trig. functions.
    Last edited by InteGrand; 17 Jan 2017 at 6:03 AM.
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    Re: HSC 2017 MX1 Marathon

    The inspiration of that question was actually just the fact

    a sin(x) + b cos(x) = b cos(x) + a sin(x)

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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by leehuan View Post
    The inspiration of that question was actually just the fact

    a sin(x) + b cos(x) = b cos(x) + a sin(x)
    Auxiliary! wow thats clever
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    Re: HSC 2017 MX1 Marathon




    This was the solution:


    I had my own solution. With geometry proofs Im aware that there are multiple ways you can go about explaining step by step.









    Just want to check if my working out is right.
    Last edited by davidgoes4wce; 6 Feb 2017 at 2:13 PM.
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    Re: HSC 2017 MX1 Marathon

    - a quick inverse trig question
    Q. let f(x) = sin^(-1) (x)
    a) for what values of m does the line y = mx cut y = f(x) at three points
    b) Investigate the concavity of the curve and find the coordinates of the point of intersection

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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by JackPatel View Post
    - a quick inverse trig question
    Q. let f(x) = sin^(-1) (x)
    a) for what values of m does the line y = mx cut y = f(x) at three points
    b) Investigate the concavity of the curve and find the coordinates of the point of intersection
    a)
    because is an odd function. So to find all possible lines we have to make sure that it passes through the origin, which it always does, and one point on the first quadrant (x,y). and by oddness of , the line also passes through (-x,-y) as well. therefore

    But at x=0 the tangent has a slope of 1 therefore
    m > 1

    b) Well, just take the second derivative and the intersection points are :
    Mahan Ghobadi

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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by davidgoes4wce View Post



    This was the solution:


    I had my own solution. With geometry proofs Im aware that there are multiple ways you can go about explaining step by step.









    Just want to check if my working out is right.
    The solution is correct. But your solution is exactly the same as the other one:
    In the textbook's solution, they subtracted two angles one at a time, meaning:

    But you subtracted the sum in one go, meaning:
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    Re: HSC 2017 MX1 Marathon









    Last edited by Mahan1; 6 Mar 2017 at 7:21 PM.
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    Re: HSC 2017 MX1 Marathon

    If you have trouble with Mathematical Induction, can you always expand the equation? It works, but it's just really slow.

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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by si2136 View Post
    If you have trouble with Mathematical Induction, can you always expand the equation? It works, but it's just really slow.
    Expand what equation? Do you have an example?
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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by pikachu975 View Post
    Expand what equation? Do you have an example?
    Well just say you're solving an equation and you're at the RTP step.

    You have to prove LHS = RHS, which is

    k/6 (k+1)(2k+1) + (k+1)^2 = (k+1)/6 (k+2)(2k+3)

    Can you simplify and expand left hand side, then simplify and expand the right hand side, so they're equal?

    I'm not moving the equation to the other side, but just simplifying it. It works if you can't figure out how to manipulate the factors. Is it possible to do that though?

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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by si2136 View Post
    Well just say you're solving an equation and you're at the RTP step.

    You have to prove LHS = RHS, which is

    k/6 (k+1)(2k+1) + (k+1)^2 = (k+1)/6 (k+2)(2k+3)

    Can you simplify and expand left hand side, then simplify and expand the right hand side, so they're equal?

    I'm not moving the equation to the other side, but just simplifying it. It works if you can't figure out how to manipulate the factors. Is it possible to do that though?
    Yeah, you can. But better to just factor k+1 from the LHS and go from there (saves you from having to expand so much).

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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by Mahan1 View Post








    By relation, I suppose you mean a single equation...

    a²=ab+c²
    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: HSC 2017 MX1 Marathon

    Prove the following statement using mathematical induction


    The last term on the L.H.S has n-digits

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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by wu345 View Post
    Prove the following statement using mathematical induction


    The last term on the L.H.S has n-digits


















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    Re: HSC 2017 MX1 Marathon



    Just need a quick 'yes' or 'no. Would it be correct to say

    ?

    ?

    I want to get perfect with my reasoning in congruency of triangles.
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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by davidgoes4wce View Post


    Just need a quick 'yes' or 'no. Would it be correct to say

    ?

    ?

    I want to get perfect with my reasoning in congruency of triangles.
    Yup, I don't see anything wrong in that and that's the exact way I would do it too.
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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by davidgoes4wce View Post


    Just need a quick 'yes' or 'no. Would it be correct to say

    ?

    ?

    I want to get perfect with my reasoning in congruency of triangles.
    Yep it's perfect and it's also nice that you took into account the order in which you named the angles, as you named them correspondingly for each triangle while the book just did any order.
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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by pikachu975 View Post
    Yep it's perfect and it's also nice that you took into account the order in which you named the angles, as you named them correspondingly for each triangle while the book just did any order.
    Different books do it slightly differently for some reason. I did all of the Year 10 5.3 Questions (Congruency triangles & Circle Geometry) from Cambridge text book and they did it in the a chronological order.

    I also had a look at the Oxford textbook and their method of reasoning and the way they write it , I noticed it is slightly different to the Cambridge text.I have a personal preference towards the way they write in Cambridge.
    Last edited by davidgoes4wce; 20 Jun 2017 at 3:30 PM.
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    Re: HSC 2017 MX1 Marathon

    I also do notice a huge overlap in 5.3 Maths Year 10 and Year 11 Prelim Extension 1 maths. (Trig, Circle Geometry, Polynomials in particular)
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    Re: HSC 2017 MX1 Marathon

    Consider the five functions:



    How many are even functions and how many are odd functions?

    I was a bit unsure about ?
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    Re: HSC 2017 MX1 Marathon

    Quote Originally Posted by davidgoes4wce View Post
    Consider the five functions:



    How many are even functions and how many are odd functions?

    I was a bit unsure about ?
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    Re: HSC 2017 MX1 Marathon

    http://prntscr.com/grt308

    Part ii please
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    Re: HSC 2017 MX1 Marathon

    Last edited by kawaiipotato; 1 Oct 2017 at 6:29 PM.
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