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So is calculating infinity/infinity --> 1, which is also wrong.

Coming from the girl that thinks that infinity/infinity --> 1 :rolleyes:

Just use the fact that roots will satisfy the polynomial equations and add them. Or you could use: \alpha^3 + \beta^3 + \gamma^3 = (\alpha + \beta + \gamma)^3 - (\alpha\beta + \beta\gamma + \alpha\gamma) (I think this is the formula, I haven't done this in a while so I could be wrong).

Let P(x)=ax^4+bx^3+cx^2+dx+e Constant term is 4, thus e=4 P(x) is monic, thus a=1 P(x)=x^4+bx^3+cx^2+dx+4 If one zero is \sqrt2 then 4+2\sqrt2b+2c+\sqrt2d+4=0 \\ 2\sqrt2b+2c+\sqrt2d+8=0 As P(x) has rational (integer) coeff, then -\sqrt2 is also a zero. Thus we have...

It's a basic rule. If a polynomial, say, P(x)=ax^3+bx^2+cx+d has a rational root, then it is of the form x=r/s where r|d and s|a and where r and s are relatively prime.

Let the rational root be of form r/s where r|3 and s|2 and r and s are relatively prime. Thus possible rational roots are: 1/1, 3/1, 1/2 and 3/2. etc

It depends on the school. But you should get it. But really you should know the rules listed on them by now anyway.

Thanks. It was an interesting read. What are i, j and k vectors? I think I'm about to do them for Physics in university. Also, for f(x): \ R \ \to \ R \ : \ x \ \to \ x^3 ... what does the R \ \to \ R denote?

Our school apparently did it under *some* circumstances.

Well your school could 'lie' for you under extenuating circumstances...

Buchanan, what do you think about the proposed syllabus changes?

Yeah well... everyone's different. It's more concise if you make your own notes I think.

MIF isn't too bad for Curve Sketching I don't think... but yeah for other topics it could be better.

Nothing beats Coroneos :D

Well when we write ln[f(x)] we assume that the domain of the function is f(x)>0. To emphaise this domain you can use absolute values. But it's not really necessary.

Just sub the points into the equations.

But generally Band 6 in General Mathematics isn't that impressive since in most years they cap the HSC aligned mark at around 92 to prevent people from 'dumbing down'.

I dunno how you'd do the sugar bit. Perhaps distillation? In both cases you weight the liquid and then remove the CO2 by shaking or stirring it. Then I'd boil it to get rid of the water. You'd be left with the sugar. Then weigh that.

Yep. That works.

I didn't spend an hour every night systematically on Mathematics. But then again... I only did get band E4 for Ext 1 and Ext 2.