2 Unit Revising Marathon (2 Viewers)

SpiralFlex · Aug 9, 2011

Re: 2 Unit Revising Marathon HSC '10

powlmao said:
My school is only up to functions! (We have done barely anything)

Other than that I just know most of Trig, intergration, differeniation and probability

That's the 2U HSC course. You are more than ahead.

MrBrightside · Aug 9, 2011

Re: 2 Unit Revising Marathon HSC '10

powlmao said:
$4x^2-28x+49$
= $(2x-7)^2$

I find great difficulty in factorising these polynomials.

I watched this video: http://www.youtube.com/watch?v=9ETZbifO0fM&feature=relmfu

But he uses a simple example, in which every number can be factored out by 3.

I know that (2x-7)^2

= (2x-7)(2x-7)

=4x^2 -14x - 14x + 49

=4x^2 - 28x + 49

But factorising, I cannot find factors to fact this with. could you please show some easy-to-understand method that I can use for all these types of questions. Its pissing me off, since I can't get past the first stage of factorising this, yet I know everything else to find stationary points and inflexions etc.

I usually just use quadratic formula, because I'm really good with memorising formulas and it never fails, and I don't waste time trying to find factors. Can I just use the quadratic formula each time?

powlmao · Aug 9, 2011

Re: 2 Unit Revising Marathon HSC '10

SpiralFlex said:
That's the 2U HSC course. You are more than ahead.

I learnt all the trig, intergration stuff by myself.

SpiralFlex · Aug 9, 2011

Re: 2 Unit Revising Marathon HSC '10

powlmao said:
I learnt all the trig, intergration stuff by myself.

Good work.

MrBrightside said:
I find great difficulty in factorising these polynomials.

I watched this video: http://www.youtube.com/watch?v=9ETZbifO0fM&feature=relmfu

But he uses a simple example, in which every number can be factored out by 3.

I know that (2x-7)^2

= (2x-7)(2x-7)

=4x^2 -14x - 14x + 49

=4x^2 - 28x + 49

But factorising, I cannot find factors to fact this with. could you please show some easy-to-understand method that I can use for all these types of questions. Its pissing me off, since I can't get past the first stage of factorising this, yet I know everything else to find stationary points and inflexions etc.

I usually just use quadratic formula, because I'm really good with memorising formulas and it never fails, and I don't waste time trying to find factors. Can I just use the quadratic formula each time?

Practice. You will need to be able to recognise perfect squares instantly.

powlmao · Aug 9, 2011

Re: 2 Unit Revising Marathon HSC '10

MrBrightside said:
I find great difficulty in factorising these polynomials.

I watched this video: http://www.youtube.com/watch?v=9ETZbifO0fM&feature=relmfu

But he uses a simple example, in which every number can be factored out by 3.

I know that (2x-7)^2

= (2x-7)(2x-7)

=4x^2 -14x - 14x + 49

=4x^2 - 28x + 49

But factorising, I cannot find factors to fact this with. could you please show some easy-to-understand method that I can use for all these types of questions. Its pissing me off, since I can't get past the first stage of factorising this, yet I know everything else to find stationary points and inflexions etc.

I usually just use quadratic formula, because I'm really good with memorising formulas and it never fails, and I don't waste time trying to find factors. Can I just use the quadratic formula each time?

Yes, but it takes longer in most cases.

tambam · Aug 9, 2011

Re: 2 Unit Revising Marathon HSC '10

MrBrightside said:
I find great difficulty in factorising these polynomials.

I watched this video: http://www.youtube.com/watch?v=9ETZbifO0fM&feature=relmfu

But he uses a simple example, in which every number can be factored out by 3.

I know that (2x-7)^2

= (2x-7)(2x-7)

=4x^2 -14x - 14x + 49

=4x^2 - 28x + 49

But factorising, I cannot find factors to fact this with. could you please show some easy-to-understand method that I can use for all these types of questions. Its pissing me off, since I can't get past the first stage of factorising this, yet I know everything else to find stationary points and inflexions etc.

I usually just use quadratic formula, because I'm really good with memorising formulas and it never fails, and I don't waste time trying to find factors. Can I just use the quadratic formula each time?

Yeah just use the quadratic formula when its really large numbers that are harder to get your head around.
It will never fail

powlmao · Aug 9, 2011

Re: 2 Unit Revising Marathon HSC '10

Thanks Spiral. You inspired me to do the work ahead!

You made a real difference in my maths work!

SpiralFlex · Aug 9, 2011

Re: 2 Unit Revising Marathon HSC '10

powlmao said:
Thanks Spiral. You inspired me to do the work ahead! You made a real difference in my maths work!

Indeed. You had better have worked hard by the time you sit your HSC or Spiral will eat you.

powlmao · Aug 9, 2011

Re: 2 Unit Revising Marathon HSC '10

SpiralFlex said:
Indeed. You had better have worked hard by the time you sit your HSC or Spiral will eat you.

I will get a band 6!

SpiralFlex · Aug 9, 2011

Re: 2 Unit Revising Marathon HSC '10

powlmao said:
I will get a band 6!

I was kidding, I will eat you either way. I haven't had dinner yet.

powlmao · Aug 9, 2011

Re: 2 Unit Revising Marathon HSC '10

SpiralFlex said:
I was kidding, I will eat you either way. I haven't had dinner yet.

lol

I better hide!

MrBrightside · Aug 9, 2011

Re: 2 Unit Revising Marathon HSC '10

SpiralFlex said:
Good work.

Practice. You will need to be able to recognise perfect squares instantly.

Does that mean you can just write the perfect square down and that would get you 2 marks?

No working out required to be shown?

SpiralFlex · Aug 9, 2011

Re: 2 Unit Revising Marathon HSC '10

MrBrightside said:
Does that mean you can just write the perfect square down and that would get you 2 marks?

No working out required to be shown?

Questions won't be that easy. If they choose to put it down, it would probably be a one marker. But I suggest you learn how to factorise quickly for the sake of time management.

Haemolymph · Aug 9, 2011

MrBrightside said:
correct, you know this question on maths online, is taught the incorrect way. I saw it today and was like woah that's the wrong way, and its up there on maths online. They changed +- on the end number. Like you did.

I prefer this though:

x-5 = 3
OR

-(x-5) = 3

x = 8
OR

-x + 5 = 3
-x = -2
x = 2

Therefore x = 2 or x = 8

Both ways work, but I've been told that doing it the way I did it solves confusion when people do the other way.

They're exactly the same you are just moving the negative side to the other side. How you don't see that straight away is beyond me.

-(x+5) = 3
Take the negative to the other side
x+5 = -3

That's like saying
-x = 1 is the same as x = -1

But you're saying they're different which they aren't. You're just making the working simpler by doing in powlmao's way.

powlmao · Aug 9, 2011

Haemolymph said:
They're exactly the same you are just moving the negative side to the other side. How you don't see that straight away is beyond me.

-(x+5) = 3
Take the negative to the other side
x+5 = -3

That's like saying
-x = 1 is the same as x = -1

But you're saying they're different which they aren't. You're just making the working simpler by doing in powlmao's way.

I have always been told put the negetive on the side which is easier and simple.

Infidel · Aug 9, 2011

Re: 2 Unit Revising Marathon HSC '10

SpiralFlex said:
Calculate the exact volume formed by the curve $y=\ln x$ bounded by the lines $y=0$ and $y=\ln 3$ .

Come on dumbasses , do this one , its easy as shit.

See Q10 of 2008HSC for a hint if you are too stupid.

Also spiralflex the noob hasn't stated what axis is rotating about, I would assume the x axis.

nightweaver066 · Aug 9, 2011

Re: 2 Unit Revising Marathon HSC '10

Infidel said:
Come on dumbasses , do this one , its easy as shit.

See Q10 of 2008HSC for a hint if you are too stupid.

Also spiralflex the noob hasn't stated what axis is rotating about, I would assume the x axis.

You mean y-axis? If there are limits on the y-axis, then you should be rotating about y-axis. Anyways..

$y = \ln x$
$x = e^y$
Volume of bounded region rotated about y-axis: $\pi \int_{0}^{ln3} e^{2y}dy$
$=\frac{\pi}{2}[e^{2y}]_{0}^{\ln3}$
$=\frac{\pi}{2}(e^{2ln3}-1)$
$=\frac{8\pi}{2}$
$=4\pi units^3$
Question:

MrBrightside · Aug 9, 2011

Haemolymph said:
They're exactly the same you are just moving the negative side to the other side. How you don't see that straight away is beyond me.

-(x+5) = 3
Take the negative to the other side
x+5 = -3

That's like saying
-x = 1 is the same as x = -1

But you're saying they're different which they aren't. You're just making the working simpler by doing in powlmao's way.

Eh, I said they were different methods, and I do see that its basically doing the same thing.

SpiralFlex · Aug 9, 2011

Re: 2 Unit Revising Marathon HSC '10

nightweaver066 said:
You mean y-axis? If there are limits on the y-axis, then you should be rotating about y-axis. Anyways..

$y = \ln x$
$x = e^y$
Volume of bounded region rotated about y-axis: $\pi \int_{0}^{ln3} e^{2y}dy$
$=\frac{\pi}{2}[e^{2y}]_{0}^{\ln3}$
$=\frac{\pi}{2}(e^{2ln3}-e^{0})$
$=\frac{9\pi}{2}units^3$

Question:

A tiny bit of a mistake there nightweaver. Check it again.

Islam1 · Aug 9, 2011

Re: 2 Unit Revising Marathon HSC '10

HAHA e^0 is not zero newbs.

Also , it is assumed around the x axis , which makes it harder. you can just cheat and take the easy way.

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