HSC 2013 MX2 Marathon (archive) (5 Viewers)

[Sy123]

Re: HSC 2014 4U Marathon

 

[seanieg89]

Re: HSC 2014 4U Marathon

Question:

This is not true as stated. It is true iff w is a PRIMITIVE n-th root of unity.

 

[Sy123]

Re: HSC 2014 4U Marathon

 

[Sy123]

Re: HSC 2014 4U Marathon

 

[seanieg89]

Re: HSC 2014 4U Marathon

It's a shame more polynomial questions of this sort aren't asked in the HSC.

 

[seanieg89]

Re: HSC 2014 4U Marathon

One that I've asked a couple of times before:

Prove that any real polynomial is non-negative if and only if it is the sum of the squares of two real polynomials.

 

[Sy123]

Re: HSC 2014 4U Marathon



The above 4 questions are able to be done with only Complex Numbers and Polynomials knowledge.

 

[dunjaaa]

Re: HSC 2014 4U Marathon

Solution attached

 

[dunjaaa]

Re: HSC 2014 4U Marathon

what is a primitive nth root of unity?

 

[dunjaaa]

Re: HSC 2014 4U Marathon

I don't know if this is correct

 

[anomalousdecay]

Re: HSC 2014 4U Marathon

That compared to the inequalities we post is like comparing general maths to first year.

Just saying that dunjaa needs to learn something from the beginning. I'm assuming they haven't started inequalities.

 

[Fizzy_Cyst]

Re: HSC 2014 4U Marathon

I wonder how many HSC 2014 students are posting in this thread! Some of the questions are insane for students who have done 1 term of Ext 2 Maths! LoL

OGs remember that we all began somewhere! LoL

 

[dunjaaa]

Re: HSC 2014 4U Marathon

I can develop some of the basic inequality results that come up in harder 3u but some of those inequality proofs posted previously, absolutely no clue

 

[Sy123]

Re: HSC 2014 4U Marathon

I can develop some of the basic inequality results that come up in harder 3u but some of those inequality proofs posted previously, absolutely no clue

Well done on the first solution is correct, but, are you sure that your result for the limit is correct? I am getting a different result

Also the inqeualities posted are way too hard for HSC level inequalities, HSC level is easy

 

[anomalousdecay]

Re: HSC 2014 4U Marathon

Also the inqeualities posted are way too hard for HSC level inequalities, HSC level is easy

I can vouch for the ones found in the actual HSC exam, but some others which are found in textbooks I found highly challenging.

 

[dunjaaa]

Re: HSC 2014 4U Marathon

Can you share your result, Idk what I'm doing wrong

 

[Sy123]

Re: HSC 2014 4U Marathon

Can you share your result, Idk what I'm doing wrong

Actually I made a mistake in my working, the limit does not exist, my bad

 

[Sy123]

Re: HSC 2014 4U Marathon

This can fall under graphs

 

[dunjaaa]

Re: HSC 2014 4U Marathon

Not sure about my inequality result, but I think my solution is wrong

 

[nikitasuitsrevenge]

Re: HSC 2014 4U Marathon

It is given that "N" is a positive real number and z1, z2 are complex numbers. Show that the points representing z1, z2 and (z1-iNz2)/1-iN form the vertices of a right angled triangle.