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Man if u want 2 use scales do general... this subject is about getting the core concept right now some shitty little detail like that

b^2 - 4ac = -32i = 32 i^3 therefore x = -b +-sqrt (32i^3)/2i .... x= 1+ i(1+-sqrt(32i))/ i can proably be simplified but i cant be bothered :)

Not really for 1/f(x) its needed because that looks pretty different anyway...but for something like y^2=f(x) I would draw the original function because then u can show how for values -1<f(x)< 1 the curve is bigger and for x>1 and x<-1 the curve is smaller than the original curve...

For the second part of the question, sub r + sqrt (d) or whatever it is into the equation. You get a rational part + an irrational part = 0 with correct factorising. Now, just like equating imaginary parts in complex numbers, equate the irrational part and u get the expression for that = 0. Also...

So what does monotonic actually mean?

118 for SGS is quite impressive... i got 112 in that paper 1st off i think (nice question 8)... 2003 was aight also...about ur projectile thing: they can put in whatever they want...anyway projectile isnt hard, just apply the conditions and be ready to manipualte ur heart out. Monotonic...

You've got to admit it looks rather pretty... Im a fan of SGS 2001 question 8 ... so elegant in that u use all parts together like a big happy family...

See thats what I hate about financial maths... learning formulas is just like what we try to escape in doing maths : regurgitating useless information - which is basically the whole HSC course anyway

I dont think you'd have 2 bother? But im a lazy man... :) And yes telescoping series is exactly what I used...

Yeh it comes under harder 3 unit...this question doesnt do anything new anyway, u just have to play around with the expression...

I can't use compasses...they always slip on me...I've just 2 oversized circles whcih i can draw around as well as a mathaid...

Yeh... but then they say that finiancial mathematics is harder 2 unit in 3 unit and thus harder 3 unit in 4 unit... lol im just stirring the pot...but it could happen

U_n+1 = U_n(1+U_n) Let u_n = n (for my typing sake) 1/n - 1/(N+1) = 1/n - 1/n(1+n) = 1+ n -1/ (n(1+n)) 1/ 1+n now..... sum to infinity of 1/1+n = 1/1+U-1+ 1/1+u_2+..... = (1/u_1 - 1/u_2) + (1/u_2 - 1/U-3) +..... = 1/U_1 = 1/(1/3) = 3

Lol...it is pretty doubtful but if it happens you'll thank me :)

I dont think you can do this without a lead in... its like finding the limit to infinity of the fibonnaci series say... find 2 experssions for the same thing, let lim n app infinity = lim n app infinity + 1...then etc

You could also tackle it graphically...just drawing what the curves are like for values up to n... might be quicker than other methods?

Could this be the year when they put a bitch financial maths question - eg superannuation - into the 4 unit paper...they are at liberty to do so?

for this question to be answered im assuming they've given u a lead-in...ie some other expression for u_n. If this is the case, which I'm sure it is, then the limit as n approaches infinity is equal to (theoritically) the limit as n approaches infinity plus one. Let the limit = M say and...

Conics can be messy but can also be very elegant. The number one topic for elegance would have to be harder 3 unit... followed closley by complex numbers. I detest probability...

haha its kool man...the whole arrogance thing is just a way of preparation...if u go in there thinking ur better than the paper than u own it...gl 2 all this monday