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since it's a poly over the ring of real numbers, the complex zeroes must come in conjugate pairs.. that will give you 2 of the factors which allows you to factor the quartic into 2 linear polynomials and 1 quadratic, which you can then further factorize ie 1+i is also a zero so you can...

My maxim: teachers are optional extras

try poly(phenyl-ethene) if you don't like styrene.. the benzene ring is the substituted group here.

back of fitzpatrick textbooks

All the notes you need could be found in textbooks... especially arnold/cambridge. rest is practice. You might want to have a look at the HSC tips in this forum

I believe getting just slightly ahead of class is a good practice. Atleast read ahead of class(this applies to every subject)

looks alright

orbital velocity - The speed at which a satellite orbit a central body at a particular distance. You can derive the formula of v can't you (using kepler's laws to find 2Pi*r/T) ? :D

If you hold an attitude that you are only going to study what's explicitly in the syllabus, you won't go far.

Do about 300 integration pratice problems.. you will eventually get the feel. :D involving squares a square roots -> some inverse trig sub. fractions -> probably some log substitution

more people becoming HSC examination machines

You will need some 90s and some mid-high 80s.. (assuming your school's papers aren't too difficult.

In short, space probes can gain speed by travelling close and around large planets

Maths is not like other subjects. notes do not help

Doesn't look pretty at all..

2d hmm check your question, I reckon you are confused

how do you know it doesn't work? You can't substitute arbitary values for d1, d2 they depend on each other. from your proof consider triangles OIE and ZJE. OE/OI = ZE/ZJ (r+d1)/r = (s + d2)/s 1 + d1/r = 1 + d2/s s*d1 = r*d2 and the result needed follows

It really depends on how good you want your motor to be. let's say each layer should be less than 2 mm thick. you use 3 plates for the commutator, with 2 brushes. and connect each plate with 2 coils

Well girraween is not like ruse and associates, I would say you can get top 5 with some effort

you need top 15% ish to get 90s