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HSC 2015 Maths Marathon (archive) (1 Viewer)

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Trebla

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Post any questions within the scope and level of Mathematics (2 unit). Once a question is posted, it needs to be answered before the next question is raised.

I encourage all current students in particular to participate in this marathon.

To get the ball rolling:

 

Sy123

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Re: HSC 2015 2U Marathon

For those who haven't started series yet, and are still doing differentiation and integration

TOPIC: Integration

 

jkerr138

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Re: HSC 2015 2U Marathon

Is the volume solution 20pi/21 units ^3
 

jkerr138

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Re: HSC 2015 2U Marathon

Yeah, I did, I just used the minus, and multiplied by the area by 2 for it being symmetrical, and got 8pi/21. Thanks.
 

InteGrand

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Re: HSC 2015 2U Marathon

TOPIC: Maxima and Minima


Let the total available length of fencing be L. Let the dimensions of a rectangular paddock built from this fencing be x and y, so that 2x+2y = L (perimeter), i.e. x+y = L/2, or y = L/2 - x.

Now, the area of the paddock is A = xy = x(L/2 - x).

This represents a concave down parabola, so its turning point will give a max., and the turning point occurs midway between the two roots, which is when x = (L/2)/2 = L/4, so y = L/4 too (as y = L/2 - x). Hence for max. area, dimensions are equal, i.e. the rectangle is a square.
 
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Fiction

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Re: HSC 2015 2U Marathon

For those who haven't started series yet, and are still doing differentiation and integration

TOPIC: Integration

Can someone walk me through this question? I'm getting either pie/4 or pie/6 lol
//crappy maths
 

Axio

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Re: HSC 2015 2U Marathon

Just a quicker method that isn't very obvious:

Cancel out the denominators where we can and then add/subtract 2:









Sub in our known values now.
Good method. But shouldn't the fractions in the first line be a^2/b and b^2/a?

I just went:





And then subbing in values from there I got =-76.
 
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Fizzy_Cyst

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Re: HSC 2015 2U Marathon

Solve for x:

sin^2(x) - 3sin(x)cos(x) + 2cos^2(x) = 0 where 0<=x<=2(Pi)
 

Fiction

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