# e is irrational (1 Viewer)

#### buchanan

##### .
The method only uses 3 unit. Can you do a 3 unit proof for the irrationality of &pi;?

That looks way too complicated to bother trying to understand, nor do I know about irrationality of pi by 3u...

Does anyone know where I can get a copy of the Independent 4u 07 paper?

#### buchanan

##### .
It's a lot easier than the methods in past HSC exams.

#### Captain Gh3y

##### Rhinorhondothackasaurus
buchanan said:
The method only uses 3 unit. Can you do a 3 unit proof for the irrationality of &pi;?
taylor series aren't in 3 unit

#### buchanan

##### .
I think the Taylors series method is the best one for e.

But that's not the method in the Ind. paper. Their method uses no calculus whatsoever.

Here's the question in the paper:

<img src=http://www.geocities.com/threeunitnotes/e1.gif width=750>

Solution:

<img src=http://www.geocities.com/threeunitnotes/e2.gif width=750>

Last edited:
G

#### gaoOO

##### Guest
god i hate these proof. Whenever i see one of these questions in the past papers, i tell myself, what are the chances they'll ask us again? I'll be screwed if they ask one of these irrational proofs.

btw, what was the actual question for the independent paper? Surely they didn't launch straight into "prove that e is irrational."

#### buchanan

##### .
buchanan said:
Here's the question in the paper:

<img src=http://www.geocities.com/threeunitnotes/e1.gif width=750>
Again I say it's a lot easier than the methods in past HSC exams.

#### tutor01

##### Member
I agree that the method of the proof of irrationality of e that is implied by the latest Ind. trial paper is easier than the methods implied by earlier HSC questions. However, I think that the earlier HSC questions on the irrationality of e (in particular the 1993 HSC question on this topic) provided a much better test of the Extension 2 syllabus than does the Ind trial paper.

Any news on the HSC Maths syllabus development? Are the BoS still insisting on including the CLT without the necessary recourse to Fourier transforms or characteristic functions?

#### buchanan

##### .
There is also a syllabus mapping attached to the Ind. paper and it says it's testing Harder Ext. 1 Inequalities in this question. So I'm satisfied that it is adequately testing the syllabus.

I also think it's good to have a variety of methods. So even though the others in HSC exams are harder, they should nevertheless also be done by students.

As for the new syllabus, the CLT and other things more generally, well I think a Mickey Mouse approach is unacceptable. There will be presentations on it at the MANSW conference in a few days from now. Are you going?

#### MeOverYou

##### Banned
buchanan said:
NO YOU

Obligatory lower case text.