HSC 2015 MX2 Marathon (archive) (1 Viewer)

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Trebla

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Post any questions within the scope and level of Mathematics Extension 2. Once a question is posted, it needs to be answered before the next question is raised.

This thread is mainly targeting Q1-15 difficulty in the HSC. Any questions of Q16 difficulty or harder should be posted in this thread:
http://community.boredofstudies.org...1666/hsc-2015-4u-marathon-advanced-level.html

I encourage all current students in particular to participate in this marathon.

To start off:

 
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Soulful

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Re: HSC 2015 4U Marathon


















ok wow 1st time latex user (it isnt as scary as I thought haha) so I spent more time working out how this thing actually works than the question itself so I might have added some superfluous steps :'(

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(this is a complex numbers question)
 
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Axio

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Re: HSC 2015 4U Marathon

















ok wow 1st time latex user (it isnt as scary as I thought haha) so I spent more time working out how this thing actually works than the question itself so I might have added some superfluous steps :'(

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(this is a complex numbers question)








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FrankXie

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Re: HSC 2015 4U Marathon





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NEXT QUESTION

 
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Joshmosh2

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Re: HSC 2015 4U Marathon

part one is a well done. part two was a lot confusing: make sure you understand the definition of the argument of a complex number

Note: both part one and two can be solved from a geometric point of view
I think i misread the locus on my 1st attempt
My 2nd attempt (not the most elegant approach..): http://imgur.com/NTfoHbn
 

turntaker

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Re: HSC 2015 4U Marathon

Does anyone know how to find roots using Euler's
 

Axio

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Re: HSC 2015 4U Marathon

Here's my attempt:
http://imgur.com/OsVeIMC

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Find the number of real roots of the equation x^4 + 2x^3 + 8x + 15 = 0 and find the integral values of x between each
let equation = P(x)
P'(x)=4x^3+6x^2+8
P'(x)=(x+2)(4x^2-2x+4)
Therefore x=-2, y=-1 is the only stationary point and thus 2 real roots exist, with one root being between -3 and -2 and the other being between -2 and -1.
 
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