HSC 2013 Maths Marathon (archive) (1 Viewer)

[andybandy]

Re: HSC 2013 2U Marathon

You found the positive area under the curve. When you integrate, anything below the x-axis becomes negative

Oh i get it! so would it be

<a href="http://www.codecogs.com/eqnedit.php?latex=\frac{\pi&space;(-1)^{2}}{4}&space;&plus;&space;\frac{1}{2}.1.1&space;&plus;&space;3.(-1)" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\frac{\pi&space;(-1)^{2}}{4}&space;&plus;&space;\frac{1}{2}.1.1&space;&plus;&space;3.(-1)" title="\frac{\pi (-1)^{2}}{4} + \frac{1}{2}.1.1 + 3.(-1)" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex=\frac{\pi}{4}&space;&plus;&space;\frac{1}{2}&space;&plus;&space;-3" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\frac{\pi}{4}&space;&plus;&space;\frac{1}{2}&space;&plus;&space;-3" title="\frac{\pi}{4} + \frac{1}{2} + -3" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex==&space;\frac{\pi&space;-&space;10}{4}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?=&space;\frac{\pi&space;-&space;10}{4}" title="= \frac{\pi - 10}{4}" /></a>

?

 

[andybandy]

Re: HSC 2013 2U Marathon

ok im not sure, how do you do it?

<a href="http://www.codecogs.com/eqnedit.php?latex=y&space;=&space;5^{x}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?y&space;=&space;5^{x}" title="y = 5^{x}" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex=\log_{5}y&space;=&space;x" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\log_{5}y&space;=&space;x" title="\log_{5}y = x" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex=\frac{\ln&space;y}{\ln&space;5}&space;=&space;x" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\frac{\ln&space;y}{\ln&space;5}&space;=&space;x" title="\frac{\ln y}{\ln 5} = x" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex=\ln&space;y&space;=&space;x.\ln&space;5" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\ln&space;y&space;=&space;x.\ln&space;5" title="\ln y = x.\ln 5" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex=y&space;=&space;e^{x.\ln&space;5}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?y&space;=&space;e^{x.\ln&space;5}" title="y = e^{x.\ln 5}" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex={y}'&space;=&space;\ln&space;5.e^{x.\ln&space;5}&space;=&space;\ln&space;5.e^{\ln&space;5^{x}}&space;=&space;\ln&space;5.5^{x}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?{y}'&space;=&space;\ln&space;5.e^{x.\ln&space;5}&space;=&space;\ln&space;5.e^{\ln&space;5^{x}}&space;=&space;\ln&space;5.5^{x}" title="{y}' = \ln 5.e^{x.\ln 5} = \ln 5.e^{\ln 5^{x}} = \ln 5.5^{x}" /></a>


Though if they dont ask for working, you can go straight from


<a href="http://www.codecogs.com/eqnedit.php?latex=y&space;=&space;5^{x}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?y&space;=&space;5^{x}" title="y = 5^{x}" /></a>

to

<a href="http://www.codecogs.com/eqnedit.php?latex={y}'&space;=&space;\1n&space;5.5^{x}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?{y}'&space;=&space;\1n&space;5.5^{x}" title="{y}' = \1n 5.5^{x}" /></a>


as a general rule

 

[girlworld_club]

Re: HSC 2013 2U Marathon

you must leave spaces between '<' for it to show

thanks

 

[Menomaths]

Re: HSC 2013 2U Marathon

Oh i get it! so would it be

<a href="http://www.codecogs.com/eqnedit.php?latex=\frac{\pi&space;(-1)^{2}}{4}&space;+&space;\frac{1}{2}.1.1&space;+&space;3.(-1)" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\frac{\pi&space;(-1)^{2}}{4}&space;+&space;\frac{1}{2}.1.1&space;+&space;3.(-1)" title="\frac{\pi (-1)^{2}}{4} + \frac{1}{2}.1.1 + 3.(-1)" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex=\frac{\pi}{4}&space;+&space;\frac{1}{2}&space;+&space;-3" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\frac{\pi}{4}&space;+&space;\frac{1}{2}&space;+&space;-3" title="\frac{\pi}{4} + \frac{1}{2} + -3" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex==&space;\frac{\pi&space;-&space;10}{4}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?=&space;\frac{\pi&space;-&space;10}{4}" title="= \frac{\pi - 10}{4}" /></a>

?

Notice the sector of the circle is under the curve? So it's -pi/4

 

[RealiseNothing]

Re: HSC 2013 2U Marathon

Oh i get it! so would it be

<a href="http://www.codecogs.com/eqnedit.php?latex=\frac{\pi&space;(-1)^{2}}{4}&space;+&space;\frac{1}{2}.1.1&space;+&space;3.(-1)" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\frac{\pi&space;(-1)^{2}}{4}&space;+&space;\frac{1}{2}.1.1&space;+&space;3.(-1)" title="\frac{\pi (-1)^{2}}{4} + \frac{1}{2}.1.1 + 3.(-1)" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex=\frac{\pi}{4}&space;+&space;\frac{1}{2}&space;+&space;-3" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\frac{\pi}{4}&space;+&space;\frac{1}{2}&space;+&space;-3" title="\frac{\pi}{4} + \frac{1}{2} + -3" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex==&space;\frac{\pi&space;-&space;10}{4}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?=&space;\frac{\pi&space;-&space;10}{4}" title="= \frac{\pi - 10}{4}" /></a>

?

It's

Remember that the circle is beneath the x-axis and so it is negative.

 

[superSAIyan2]

Re: HSC 2013 2U Marathon

Two dice are rolled. You know that at least one of the dice is a 5. What is probability of getting a total of 8?

 

[andybandy]

Re: HSC 2013 2U Marathon

It's

Remember that the circle is beneath the x-axis and so it is negative.

My bad, but thanks for the help people!

 

[andybandy]

Re: HSC 2013 2U Marathon

Two dice are rolled. You know that at least one of the dice is a 5. What is probability of getting a total of 8?

1/6 ?

 

[Menomaths]

Re: HSC 2013 2U Marathon

Two dice are rolled. You know that at least one of the dice is a 5. What is probability of getting a total of 8?

1/6

 

[Menomaths]

Re: HSC 2013 2U Marathon

Find the exact value of sinx = 1/2 with full working (I forgot how to LOL)

 

[andybandy]

Re: HSC 2013 2U Marathon

Find the exact value of sinx = 1/2 with full working (I forgot how to LOL)

is their a limit such as 0 < x < 2pi?

 

[Menomaths]

Re: HSC 2013 2U Marathon

yeah

 

[andybandy]

Re: HSC 2013 2U Marathon

<a href="http://www.codecogs.com/eqnedit.php?latex=\sin&space;x&space;=&space;\frac{1}{2}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\sin&space;x&space;=&space;\frac{1}{2}" title="\sin x = \frac{1}{2}" /></a>

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

<a href="http://www.codecogs.com/eqnedit.php?latex=x&space;=&space;\frac{\pi}{6}&space;,&space;\pi&space;-&space;\frac{\pi}{6}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?x&space;=&space;\frac{\pi}{6}&space;,&space;\pi&space;-&space;\frac{\pi}{6}" title="x = \frac{\pi}{6} , \pi - \frac{\pi}{6}" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex=x&space;=&space;\frac{\pi}{6}&space;,&space;\frac{5\pi}{6}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?x&space;=&space;\frac{\pi}{6}&space;,&space;\frac{5\pi}{6}" title="x = \frac{\pi}{6} , \frac{5\pi}{6}" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex=\textup{for&space;}&space;0&space;<&space;x&space;<&space;2\pi" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\textup{for&space;}&space;0&space;<&space;x&space;<&space;2\pi" title="\textup{for } 0 < x < 2\pi" /></a>

 

[spanky125]

Re: HSC 2013 2U Marathon

is it in the 10th hour? i'm so bad at visualising.

It is a trick question, when the tide rises it raises the boat as well, so it will never reach the fifth rung.
Bit of lateral thinking required haha

 

[superSAIyan2]

Re: HSC 2013 2U Marathon

1/6

Lol, thats what i thought at first. But the answer says it 2/11.
Since you know at least one dice is definitely a 5, the total possible outcomes are : 1,5 2,5 3,5 4,5 5,5 5,6 and 5,1 5,2 5,3 5,4 5,6(dont count 5,5 again)
Since only 2 outcomes are favourable the probability is 2/11

 

[Youi_]

Re: HSC 2013 2U Marathon

 

[andybandy]

Re: HSC 2013 2U Marathon

x=0.207614169

 

[Menomaths]

Re: HSC 2013 2U Marathon

is it in the 10th hour? i'm so bad at visualising.

Can someone help me with this question:

Find the exact area enclosed by the curve y=sinx and the line y=1/2 for 0 < x < 2pi

So, y = sinx and y = 1/2
sinx = 1/2
x = pi/6 and 5pi/6
Those are the boundaries

Integrate(sinx-1/2) bounded by pi/6 and 5pi/6
you get: (-cosx-x/2) bounded by pi/6 and 5pi/6
now sub in
(-cos(5pi/6) - 5pi/12) - (-cos(pi/6)-pi/12)

(sqrt3)/2 - 5pi/12 + (sqrt3)/2 + pi/12

sqrt(3) - pi/3

 

[Youi_]

Re: HSC 2013 2U Marathon

x=0.207614169

Working out? Or did you just guess the decimals by some random stroke of luck

 

[spanky125]

Re: HSC 2013 2U Marathon

Working out? Or did you just guess the decimals by some random stroke of luck

I guessed the decimals, and yes I do work out a little bit thanks for noticing.