HSC Mathematics Marathon (5 Viewers)

[largarithmic]

Nice, I did pretty much the same thing ^^ I think you can motivate it by (1) knowing you want to somehow telescope, and (2) after computing a few values you guess that it goes to 3. Which would make sense as one on a third, so you try telescoping with 1/un.

Telescoping means that technique to sum a sequence: if you want to find sum un, you find some sequence sn s.t. un = s_(n-1) - s_n, then when you add them up, sum (1 to n) u_k = s_0 - s_n, which is often easy to compute.

 

[apollo1]

so is this an olympiad question?

 

[largarithmic]

so is this an olympiad question?

It could possibly be an easy olympiad question. The difference between easy olympiad questions and hard "harder 3U" questions is almost nil though. The entire circle geometry topic, entire probability topic, most induction questions (probably not those involving trig functions), definitely all 'inequalities' and most miscellaneous 'sequence' questions like this could be considered as 'olympiad questions'

 

[hup]

using a telescoping sum.

yea i was stuck and just tried that
the previous part is irrelevant though

 

[apollo1]

so telescoping is like a collapsing sum.

 

[hup]

so telescoping is like a collapsing sum.

havent you tried last years q8

 

[apollo1]

can someone help me with part 7 a (ii) i keep getting a different result.

http://4unitmaths.com/kings2009.pdf

 

[cutemouse]

And why is it a stupid question, because it's unconventional?

No, because firstly, in that year many students who were involved with various maths clubs had seen that question before and therefore could do it easily. Whilst those who hadn't seen it before couldn't do it.

And it doesn't really test the course IMO.

 

[hup]

can someone help me with part (ii) i keep getting a different result.

you need x in it somewhere so the obvious choice is to put dv = dx

 

[apollo1]

you need x in it somewhere so the obvious choice is to put dv = dx

wheres the x? its a complex vectors question.

 

[hup]

wheres the x? its a complex vectors question.

i thought you were talking about q8 2010

 

[apollo1]

i thought you were talking about q8 2010

lol no. i havent done any hsc papers yet. im saving them until the first week of october. doing independent trials atm.

 

[hup]

lol no. i havent done any hsc papers yet. im saving them until the first week of october. doing independent trials atm.

if you look theres solutions at the back but it is wrong
x by vector = rotate anticlockwise not clockwise

 

[apollo1]

if you look theres solutions at the back but it is wrong
x by vector = rotate anticlockwise not clockwise

ooh didnt no there was solutions. the solutions look right. wat do u think is wrong wit it?

 

[hup]

ooh didnt no there was solutions. the solutions look right. wat do u think is wrong wit it?

they are saying that CA = wCB, which is wrong
eg
if you have p=iq, then p =cis(pi/2)q so you are rotating vector q 90 deg anti clockwise
so it should be CB = wCA

 

[apollo1]

wat if you produced vector CA at C. then if you rotated vector BC 120 degrees anticlockwise it would turn into vector CA giving you desired result. is this valid?

 

[hup]

wat if you produced vector CA at C. then if you rotated vector BC 120 degrees anticlockwise it would turn into vector CA giving you desired result. is this valid?

actually its my bad I thought it was pi/3 not 2pi/3 yes solution is valid

 

[apollo1]

actually its my bad I thought it was pi/3 not 2pi/3 yes solution is valid

cool tnx 4 ur help.

 

[hup]

 

[artosis]

haha good question. Baulko 2011 trial?
took me quite awhile to get it out