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HSC 2013 MX2 Marathon (archive) (6 Viewers)

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Sy123

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Re: HSC 2013 4U Marathon

Cbb checking haha but that is the correct idea.

As an addendum to your question, which I think I have asked before:

Prove that E has NO real roots if n is even.
I'll add it in the latex so people don't miss it
 

Sy123

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Re: HSC 2013 4U Marathon


















EDIT: I added another first part to make the question easier. It should be doable now.
 
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Sy123

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Re: HSC 2013 4U Marathon





Difficulty: Moderate

It would also be great if people could rate the difficulty of their own question as I have just done.
 
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Examine

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Re: HSC 2013 4U Marathon





Difficulty: Moderate

It would also be great if people could rate the difficulty of their own question as I have just done.
What does it mean by irrational numbers? (like (z-1)(z^4+z^3+z^2+z+1)) ?
 

Sy123

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Re: HSC 2013 4U Marathon

What does it mean by irrational numbers? (like (z-1)(z^4+z^3+z^2+z+1)) ?
HINT: Factorise into 1 linear factor, and 2 quadratic factors. The factorisation you have is among the integers, the one you should have among the irrationals which will be in the form of 1 linear and 2 quadratic factors will have irrational co-efficient

EDIT: I changed first one to show that.
 
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Examine

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Re: HSC 2013 4U Marathon

oops pls wait
 
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Sy123

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Re: HSC 2013 4U Marathon

isn't it subjective?
Yeah it is subjective but ask yourself where you would see it in an exam.

If Q1-3 then easy

Q4-6 moderate

Q7-8 hard.

Beyond HSC yet still in syllabus = Extreme (I guess?)
 

Sy123

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Re: HSC 2013 4U Marathon

Got up to iii, faced a problem:



Am I missing something here?


(Also I am very close to solving the last question)
 
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Examine

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Re: HSC 2013 4U Marathon





Difficulty: Moderate

It would also be great if people could rate the difficulty of their own question as I have just done.
for the first part

 
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Re: HSC 2013 4U Marathon

for your fourth and fifth lines, you can drop off the "cis" on RHS because you are talking about the arguments. Also you used z in the first part and suddenly you switched to x when factorising :p
 

Shadowdude

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Re: HSC 2013 4U Marathon

So I was reading some discussion on how this thread was just full of ridiculous questions 0.5% of the population can do, so how about we try something like...



(This is an easy-ish question... if you know "the trick to it")
 

Sy123

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Re: HSC 2013 4U Marathon

So I was reading some discussion on how this thread was just full of ridiculous questions 0.5% of the population can do, so how about we try something like...



(This is an easy-ish question... if you know "the trick to it")



Keep in mind my question is still unanswered (the second part) also people should be able to do the e is irrational one for those who know series, and the one on the previous page about E(x)
 

deswa1

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Re: HSC 2013 4U Marathon

Nice.



bit harder.
Ahh I like these sort of questions because you are using imaginary numbers to prove a 'real' result- I've always found that cool. I'll leave it for a current 4U student to solve it though
 

Shadowdude

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Re: HSC 2013 4U Marathon

Ahh I like these sort of questions because you are using imaginary numbers to prove a 'real' result- I've always found that cool. I'll leave it for a current 4U student to solve it though
True that. Especially for those who think "ugh complex numbers, why are we using imaginary numbers anyway - what's the point" - it's pretty awesome.

My lecturer for Complex Analysis shared the same feelings you have - and as an avid number theorist - and he gave us a question to do in class - you might want to try this one because it's not strictly in the syllabus, it just uses complex number ideas:




(hint: use complex numbers)

And the difficulty is... quite easy, you just have to know how to use the hint properly.
 

Sy123

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Re: HSC 2013 4U Marathon

True that. Especially for those who think "ugh complex numbers, why are we using imaginary numbers anyway - what's the point" - it's pretty awesome.

My lecturer for Complex Analysis shared the same feelings you have - and as an avid number theorist - and he gave us a question to do in class - you might want to try this one because it's not strictly in the syllabus, it just uses complex number ideas:




(hint: use complex numbers)

And the difficulty is... quite easy, you just have to know how to use the hint properly.





(still a question unanswered above)
 

Examine

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Re: HSC 2013 4U Marathon

for your fourth and fifth lines, you can drop off the "cis" on RHS because you are talking about the arguments. Also you used z in the first part and suddenly you switched to x when factorising :p
~oops~ and ty. (so you don't have to write cis for the 4th and 5th lines?)
 
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