HSC Mathematics Marathon (1 Viewer)

cutemouse · Feb 8, 2011

Bored Of Fail 2 said:
^ in any first semester uni maths course, and I think it was in the four unit syllabus ( along time ago, I have seen it asked in some really old 4unit hsc exams papers, like from 1970's, I remember I have seen someone post up a ton of old 4unit exams )

I don't think L'Hopital's rule was ever in the Level 1 course... since my maths teacher (who did the Level 1 maths course) said he did it in uni.

jyu · Feb 8, 2011

jyu said:
14!

Still working on it.

jyu · Feb 8, 2011

30046464000?

jyu · Feb 8, 2011

Another approach
10973491200?

deterministic · Feb 9, 2011

jyu said:
Another approach
10973491200?

Correct! Explain how you got the answer.

jyu · Feb 9, 2011

deterministic said:
Correct! Explain how you got the answer.

Anchored a particular boy. Arrange the remaining 9 boys. There are 10 gaps between the boys. Place the 5 girls (at most one in a gap) in the gaps.

9!10P5 = 10973491200

Riproot · Feb 9, 2011

NewiJapper said:
if i = sqrt -1, find i^2.

$i^2=8$
IS THAT RIGHT?!

blackops23 · Feb 9, 2011

Riproot said:
$i^2=8$
IS THAT RIGHT?!

congratulations, you are correct, you're bound to get an E4 in 4 unit easily lolol how dumb do you have to be if you want to post that question anyway?

Riproot · Feb 9, 2011

blackops23 said:
congratulations, you are correct, you're bound to get an E4 in 4 unit easily lolol how dumb do you have to be if you want to post that question anyway?

I know, right? lol
My teacher tought the top ten kids that in year 7 or 8 lol

cutemouse · Feb 9, 2011

New question: Find the locus of z if arg ((z-1)/(z+1))= pi/4

Riproot · Feb 9, 2011

jm01 said:
New question: Find the locus of z if arg ((z-1)/(z+1))= pi/4

$((z-1)/(z+1))= pi/4$

ohexploitable · Feb 9, 2011

jm01 said:
New question: Find the locus of z if arg ((z-1)/(z+1))= pi/4

$\\x^2+(y-1)^2=2$

cutemouse · Feb 10, 2011

ohexploitable said:
$\\x^2+(y-1)^2=2$

Only the top arc... ie. y>0.

ohexploitable · Feb 11, 2011

Bored Of Fail 3 · Feb 11, 2011

ohexploitable said:
$\\\textbf{New Question:}\\\\\text{Solve }4x^4-12x^3-40x^2-14x-1=0.\\\text{HINT: express it as a difference of two squares.}$

hint cheat and use wolfram

NihaoMa · Feb 11, 2011

ohexploitable said:
$\\\textbf{New Question:}\\\\\text{Solve }4x^4-12x^3-40x^2-14x-1=0.\\\text{HINT: express it as a difference of two squares.}$

Wolfram or ask Vinh Nguyen (ie. ohexploitable) for the answer.

Bored Of Fail 3 · Feb 11, 2011

NihaoMa said:
k Vinh Nguyen (ie. ohexploitable) .

wtf, is that his name

Drongoski · Feb 11, 2011

ohexploitable said:
$\\\textbf{New Question:}\\\\\text{Solve }4x^4-12x^3-40x^2-14x-1=0.\\\text{HINT: express it as a difference of two squares.}$

$\therefore (4x^4 -12x^3+9x^2) - (49x^2+14x+1) = 0$

$i.e. (2x^2-3x)^2 - (7x+1)^2 = 0$

$i.e. (2x^2 -3x +7x+1)(2x^2-3x-7x-1) = 0$

$i.e. (2x^2+4x+1)(2x^2-10x-1) = 0$

Then solve the 2 quadratic eqns by formula.

jyu · Feb 13, 2011

New question:

Show
(sinx+sin3x+sin5x+sin7x+sin9x)/(cosx+cos3x+cos5x+cos7x+cos9x) = tan5x

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