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Thread: Cambridge HSC MX1 Textbook Marathon/Q&A

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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread







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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    37 metres and 43'' I dont quite get.

    I get a value of -410.36 instead of 37 metres

    With the time part , I went (e-2) x 60 (remembering these units were initially in minutes)= which gave me approximately 8 seconds
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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    ^^^ Don't worry I sorted it out , with my scientific calculator I needed to type 'e1' for it to read it as 'e'
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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread













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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    I get it now, the initial conditions set , if you want to treat the top of the building as the origin, t=0, v=25, g=10, x=0.

    All good
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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Yea - I noticed in your 1st post: x = -120 instead of 0.
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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    http://prntscr.com/b0363w

    How can you work backwards from factorial? Thanks.

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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by si2136 View Post
    http://prntscr.com/b0363w

    How can you work backwards from factorial? Thanks.
    Inspection.


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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by InteGrand View Post
    Inspection.

    Is there another way without inspection? And is there a technique used in inspection in which you can notice it straight away?

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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by si2136 View Post
    Is there another way without inspection? And is there a technique used in inspection in which you can notice it straight away?
    If you know your early factorials, it's easy to recognise that 5! = 120. You'll probably recognise early factorials if you do lots of perms and combs Q's.

    In the above method, the only inspection comes about when at the stage (8-r)! = 120.

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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    A curve is given y = x^x where x > 0. Find the gradient function of the curve y = x^x.

    How do I manage to differentiate it using Logarithmic Functions? Thanks.

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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by si2136 View Post
    A curve is given y = x^x where x > 0. Find the gradient function of the curve y = x^x.

    How do I manage to differentiate it using Logarithmic Functions? Thanks.


    Last edited by InteGrand; 4 May 2016 at 9:34 PM.

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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by InteGrand View Post


    Since it's implicit differentiating, do you need to include dy/dx? in the answer?

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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by si2136 View Post
    Since it's implicit differentiating, do you need to include dy/dx? in the answer?
    The y' is the dy/dx.

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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by InteGrand View Post
    The y' is the dy/dx.
    Yes, but I mean for example you're differentiating f(x) = g^2

    Your answer wouldn't be 2g, but rather 2g dy/dx

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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by si2136 View Post
    Yes, but I mean for example you're differentiating f(x) = g^2

    Your answer wouldn't be 2g, but rather 2g dy/dx

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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Screen Shot 2016-05-23 at 8.43.39 PM.png
    Screen Shot 2016-05-23 at 8.44.33 PM.png

    Can someone please help me with this question?? I'm really bad at reasoning with geometry!
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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Similar Triangles. Circular Geo.

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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by si2136 View Post
    Similar Triangles. Circular Geo.
    Oh haha its not circle geo, its only 2U geometry. I want to see how good reasoning would look like.
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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    a)

    In triangles DEG and DFC:

    - angle EDG = angle FDC (same angle)

    - DE/DF = DG/DC = 1/2

    .: triangles DEG and DFC are similar. (pair of sides proportional and included angles equal)

    .: angle DGE = angle DCF (corresp angles of similar triangles)

    But these are corresponding angles

    .: EG // FC (and .: AC)


    b)

    angle ABC (= angle EBG) = Angle ACB (AB = AC)

    But angle DGE (= angle BGE) = angle ACB

    .: for triangle EBG, angle EBG = angle BGE

    .: EB = EG

    Now EG/FC = DE/DF = 1/2

    .: FC = 2 x EG = 2 x EB



    QED
    Last edited by Drongoski; 29 May 2016 at 6:41 PM.
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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Thank you so much!!
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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread









    The part I wasn't sure about in the question was it said "verify the result on the third column of the Pascal triangle."
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    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Bump


    "verify the result on the third column of the Pascal triangle." Does anyone have any idea on this? Or is my answer shown above good enough ?
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