HSC 2012 MX2 Marathon (archive) (1 Viewer)

barbernator · May 5, 2012

Re: 2012 HSC MX2 Marathon

post questions once you answer guys

nightweaver066 · May 5, 2012

Re: 2012 HSC MX2 Marathon

$$P is any point on the ellipse $ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1~,~ (a > b); $ A, A' are the ends of the major axis; AP meets the minor axis at Q. Prove that the line through Q parallel to A'P is a tangent to one of the parabolas $ ay^2 \pm 4b^2x = 0.$

karnbmx · May 5, 2012

Re: 2012 HSC MX2 Marathon

Hmmm.....

$integrate: \int \frac{1}{1 + \sqrt{x}} \, dx$

nightweaver066 · May 5, 2012

Re: 2012 HSC MX2 Marathon

karnbmx said:
Hmmm.....

Find the indefinite integral of 1/1+squareroot(x)

$\int \frac{1}{1 + \sqrt{x}}dx$

$Let~u^2 = x$

$2udu = dx$

$\therefore \int \frac{2u}{1 + u}du$

$= \int 2 - \frac{2}{1 + u}du$

$= 2u - 2ln|1 + u|$

$= 2\sqrt{x} - 2ln|1 + \sqrt{x}| + c$

barbernator · May 5, 2012

Re: 2012 HSC MX2 Marathon

here is a nice graphs question. Graph the function <a href="http://www.codecogs.com/eqnedit.php?latex=y^2=x^3(x-2)" target="_blank"><img src="http://latex.codecogs.com/gif.latex?y^2=x^3(x-2)" title="y^2=x^3(x-2)" /></a> noting the behaviour of the curve near its intercepts. (you dont need to mark inflection points) (don't cheat and use wolfram)

also, nightweavers question takes ages fuuuuuuuuuuuu

nightweaver066 · May 5, 2012

Re: 2012 HSC MX2 Marathon

barbernator said:
here is a nice graphs question. Graph the function <a href="http://www.codecogs.com/eqnedit.php?latex=y^2=x^3(x-2)" target="_blank"><img src="http://latex.codecogs.com/gif.latex?y^2=x^3(x-2)" title="y^2=x^3(x-2)" /></a> noting the behaviour of the curve near its intercepts. (you dont need to mark inflection points) (don't cheat and use wolfram)

also, nightweavers question takes ages fuuuuuuuuuuuu

Have you finished it?

barbernator · May 5, 2012

Re: 2012 HSC MX2 Marathon

nightweaver066 said:
Have you finished it?

yes, im definitely not scripting the solution though haha. I used cartesian co-ordinates, parametric might have made it easier.

barbernator · May 6, 2012

Re: 2012 HSC MX2 Marathon

<a href="http://www.codecogs.com/eqnedit.php?latex=\int \frac{x^2}{\sqrt{1-x^2}}dx" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\int \frac{x^2}{\sqrt{1-x^2}}dx" title="\int \frac{x^2}{\sqrt{1-x^2}}dx" /></a>

juantheron · May 6, 2012

Re: 2012 HSC MX2 Marathon

$\hspace{-16}\bf{\int \frac{x^2}{\sqrt{1-x^2}}dx}$\\\\\\ Put $\bf{x =\sin \theta \Leftrightarrow dx=\cos \theta d\theta}$\\\\\\ $\bf{=\int \frac{\sin^2 \theta.\cos \theta.d\theta}{\cos\theta}=\frac{1}{2}\int 2\sin ^2 \theta d\theta }$\\\\\\ $\bf{=\frac{1}{2}\int \left(1+\cos 2\theta\right)d\theta}$\\\\\\ $\bf{=\frac{1}{2}\left(\theta+\frac{\sin 2\theta}{2}\right)+\mathbb{C}}$\\\\\\ $\bf{=\frac{1}{2}\sin^{-1}(x)+\frac{1}{2}.x.\sqrt{1-x^2}+\mathbb{C}}$$

juantheron · May 6, 2012

Re: 2012 HSC MX2 Marathon

$\hspace{-16}\bf{\int \frac{(4x^5+5x^4)}{(x^5+x+1)^2}dx}$

smartalec · May 6, 2012

Re: 2012 HSC MX2 Marathon

hey guys,
so this is totally an easy question for all of you, but I figured this would be the best place to get the quickest response. Its a measly prelim yr 11 mathematics questions. Its about domain nd range and I'm a bit confused :S

f(x) Square root 2x -6

smartalec · May 6, 2012

Re: 2012 HSC MX2 Marathon

rep for best answer!!

SpiralFlex · May 6, 2012

Re: 2012 HSC MX2 Marathon

$f(x) =\sqrt{2x -6}$

We know that the expression inside square root is always positive, (can be equal to zero too)

$\therefore 2x-6 \geq 0$

$x\geq 3$

And for f(x)

$f(x) \geq 0$

As it is always positive (can be equal to zero)

smartalec · May 6, 2012

Re: 2012 HSC MX2 Marathon

SpiralFlex said:
$f(x) =\sqrt{2x -6}$

We know that the expression inside square root is always positive, (can be equal to zero too)

$\therefore 2x-6 \geq 0$

thanks for the answer spiral! I should have mentioned I got that far, but I am not sure how to determine the domain and function and how i would d

$x\geq 3$

And for f(x)

$f(x) \geq 0$

As it is always positive (can be equal to zero)

And how would I determine the domain and range and draw it on a graph?

barbernator · May 6, 2012

Re: 2012 HSC MX2 Marathon

smartalec said:
And how would I determine the domain and range and draw it on a graph?

he just solved for domain and range, x=>3, y=>0. the graph is the positive axis of a sideways parabola

smartalec · May 6, 2012

Re: 2012 HSC MX2 Marathon

smartalec said:
And how would I determine the domain and range and draw it on a graph?

ohhh ok! thanks so much!

smartalec · May 6, 2012

Re: 2012 HSC MX2 Marathon

What is the congruent of 2 root 3 + 3 root 7?
Thanks so much guys!! Sorry for the stupid questions!

Carrotsticks · May 6, 2012

Re: 2012 HSC MX2 Marathon

smartalec said:
What is the congruent of 2 root 3 + 3 root 7?
Thanks so much guys!! Sorry for the stupid questions!

This thread is for MX2 questions.

If you have your own, make your own thread so you can ask as many questions as you like. Best not to hijack this one.

smartalec · May 6, 2012

Re: 2012 HSC MX2 Marathon

Carrotsticks said:
This thread is for MX2 questions.

If you have your own, make your own thread so you can ask as many questions as you like. Best not to hijack this one.

its my last question

haha

SpiralFlex · May 6, 2012

Re: 2012 HSC MX2 Marathon

Congruent? Lol

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