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vwee hee hee.

Haha cheers. Yeah my list isn't exactly ordered but the top two are definitely my favourite two games ever. I also loved GE but the customisability of PD multiplayer wins out for me, there was an insane amount of content in that game. FF6 is just beautiful, an absolute masterpiece. Yep, I enjoy...

1. Final Fantasy 6 on the SNES. 2. Perfect Dark 64 3. Any incarnation of Smash Bros. (favourite is probably 64 for the sheer rape factor.) 4. Majora's Mask 5. SC1: Brood War

Re: 2012 HSC MX2 Marathon Not quite, the polynomial does not contain only even powers...some justification would be needed to say that the sum of the nonconstant terms can never be -1. (I also do not understand what you are saying about limits.) A hint: One way to do it is by induction.

Re: 2012 HSC MX2 Marathon Might as well bring this back to life. Prove that the polynomial p(x)=\sum_{k=0}^{2n} \frac{x^k}{k!} has no real roots. (Where n is a non-negative integer.)

Herstein's "Topics in Algebra" is an absolute classic and contains all you learn during this course (I think).

LHS-RHS=\frac{1}{2}(a+b+c)((a-b)^2+(a-c)^2+(b-c)^2). From this the result is immediate.

Its more ugly mathematics than cheap. "Fake" proofs by contradiction aren't pretty.

How is it not proving anything? Showing that LHS-RHS is non-negative or non-positive is precisely a proof of the claim the quesiton makes. You are not making any unjustified assumptions.

Nearly every inequality in the MX2 course can be deduced as a consequence from (a-b)^2 \geq 0. The only exceptions I can think of that I have seen are the inequalities that come from the use of calculus.

Projectile motion.

Write the numerator as the sum of two polynomials, one with a factor of (x^2-1), another with a factor of (x^2+1). It falls apart from there.

(I know it is trivial from expanding (x-y)^2, but it is also a consequence of two dimensional C-S by taking the dot product of (x,y) with (y,x). Perhaps that is what he meant.)

The question also uses differentiation under the integral to obtain an expression for B'(t), out of syllabus and not always valid.

happy to do a couple of questions if you need something to compare with. not going to write full solutions to everything though.

(The bottom expression is x times the derivative of the top one.)

By the way, this question can also be done by differentiation of the geometric series.

This is correct. The question is just using the sine rule and then solving a quadratic.

Of course you can, I am not saying otherwise. I am merely saying that I think it is easier to pass every university subject in a year of an undergraduate degree than it is to meet the atar cutoffs required by typical high school students.

I know what you mean because I set high standards for myself (as I am guessing you do). In my experience post-graduation though, your actual marks aren't particularly important unless you are heading into a particularly competitive profession or academia. Ie marks are unimportant to the majority...