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HSC 2017-2019 MX2 Marathon ADVANCED (1 Viewer)

dan964

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Post any questions within the scope and level of Mathematics Extension 2 mainly targeting Q16 difficulty in the HSC.

Any questions beyond the scope of the HSC syllabus should be posted in the Extracurricular Topics forum:
http://community.boredofstudies.org/14/mathematics-extension-2/360463/14/mathematics-extension-2/360463/14/mathematics-extension-2/360463/14/mathematics-extension-2/360463/14/mathematics-extension-2/360463/14/mathematics-extension-2/360463/...icular-topics/

Once a question is posted, it needs to be answered before the next question is raised.

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

To get the ball-rolling

Question:
Using MX2 methods & complex numbers, find an expression for (degrees)


Edit 6/3/17: I have moved some of the advanced questions to this forum...
 
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Kingom

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HSC 2017 MX2 Marathon ADVANCED

A nice question
 

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seanieg89

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Re: HSC 2017 MX2 Marathon

Haha that was my suspicion.
 

Kingom

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Re: HSC 2017 MX2 Marathon

I believe it's accessible to the extension 2 student so i put it on the marathon
 

seanieg89

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Re: HSC 2017 MX2 Marathon

I believe it's accessible to the extension 2 student so i put it on the marathon
Yeah fair enough, they were a lot easier back in the day.

Still should probably put questions like it in the advanced thread (Dan only created it today I believe, but for the last couple of years we have usually split the questions into two marathons, one for routine stuff and one for questions at HSC Q16 difficulty or above. As long as it is still within syllabus of course).
 

Kingom

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Re: HSC 2017 MX2 Marathon

Yeah fair enough, they were a lot easier back in the day.

Still should probably put questions like it in the advanced thread (Dan only created it today I believe, but for the last couple of years we have usually split the questions into two marathons, one for routine stuff and one for questions at HSC Q16 difficulty or above. As long as it is still within syllabus of course).
Yeh i wanted to put this in the advanced marathon, but none existed at the time it was posted so
 

frog1944

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Re: HSC 2017 MX2 Marathon ADVANCED

Post any questions within the scope and level of Mathematics Extension 2 mainly targeting Q16 difficulty in the HSC.

Any questions beyond the scope of the HSC syllabus should be posted in the Extracurricular Topics forum:
http://community.boredofstudies.org/14/mathematics-extension-2/360463/14/mathematics-extension-2/360463/...icular-topics/

Once a question is posted, it needs to be answered before the next question is raised.

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

To get the ball-rolling

Question:
Using MX2 methods & complex numbers, find an expression for the cos 36.
Note that . Consider whose roots are . Thus the roots of are . Note that are the conjugates of respectively.

By comparison of coefficients for we get:
and
These are the sum of roots and product of roots of the quadratic equation; .
, but . Thus
 

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Re: HSC 2017 MX2 Marathon ADVANCED

A square pyramid has height exactly half it's base side length, a. Find the volume of the pyramid.
 

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