HSC Mathematics Marathon (3 Viewers)

[Deep Blue]

I'm not sure how much use this will be to anyone but I created separate pdfs for the 2000-2010 q7's and 8's that I thought someone body might like.

http://www.mediafire.com/?ajcqsa8fhaxqw2h

http://www.mediafire.com/?9rwm6vmlrrjd35d

 

[math man]

lets get this starting again...

Determine all the values of:



btw i made this up so enjoy

 

[artosis]

lets get this starting again...

Determine all the values of:



btw i made this up so enjoy

1/2(1+i^2n)?

 

[muzeikchun852]

lets get this starting again...

Determine all the values of:



btw i made this up so enjoy

1 if n is even.
0 if n is odd.

?

 

[K4M1N3]

lets get this starting again...

Determine all the values of:



btw i made this up so enjoy

For n is even: Sum = 1

for n is odd: Sum = 0


Next Question: Find the set of values of x for which the limiting sum exists for the series:

 

[math man]

1 if n is even.
0 if n is odd.

?

correct

 

[muzeikchun852]

For n is even: Sum = 1

for n is odd: Sum = 0


Next Question: Find the set of values of x for which the limiting sum exists for the series:

3/2 < x < 4 ?

 

[K4M1N3]

3/2 < x < 4 ?

OOO very very very close....have a look back at your working for a mistake.

 

[muzeikchun852]

OOO very very very close....have a look back at your working for a mistake.

3/2 =< x =< 4 ? haha

 

[K4M1N3]

3/2 =< x =< 4 ? haha

XD nah i got 2/3 < x < 4

EDIT: Woah my bad....actually bad teacher, got soln wrong. Sorry about that, yeah your soln is correct.

 

[Trebla]

Suppose that



Use the results



and



to show that

 

[hup]

Suppose that



Use the results



and



to show that

intredasting

 

[apollo1]

XD nah i got 2/3 < x < 4

EDIT: Woah my bad....actually bad teacher, got soln wrong. Sorry about that, yeah your soln is correct.

no it is 2/3 < x < 4. u teacher was right.

 

[math man]

no it is 2/3 < x < 4. u teacher was right.

this is correct

 

[muzeikchun852]

no it is 2/3 < x < 4. u teacher was right.

yeah 2/3 not 3/2.

 

[math man]

here is another good one:

 

[roryclifford]

here is another good one:

View attachment 23295

That was a cool one
If I get time I'll post up my solution if anyone wants, idk

 

[math man]

That was a cool one
If I get time I'll post up my solution if anyone wants, idk

post your solution to the last part if you dont mind

 

[apollo1]

for that last part is this a valid proof:

let angle NMB = x
therefore angle LMA = x
(vertically opposite angles equal)
angle PMA = 90
therefore angle PML = 90-x (complementary angles)
angle PMB = 90
(angles on a straight line supplementary)
therefore angle PMN = 90+x
since angle PMN + angle PML = 180
LN is a straight line (angles on a straight line supplementary)
therefore L, M and N are collinear

 

[math man]

for that last part is this a valid proof:

let angle NMB = x
therefore angle LMA = x
(vertically opposite angles equal)
angle PMA = 90
therefore angle PML = 90-x (complementary angles)
angle PMB = 90
(angles on a straight line supplementary)
therefore angle PMN = 90+x
since angle PMN + angle PML = 180
LN is a straight line (angles on a straight line supplementary)
therefore L, M and N are collinear

yep thats right