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Re: International Baccalaureate Marathon 2016 Well you should probably look at the populations of the countries too. I haven't searched up school-age populations, but in terms of overall populations (from memory), US is about 5 times that of UK (and about 60 times that of Australia). Edit...

Re: International Baccalaureate Marathon 2016 Do you mean the answer is obvious, or the question isn't of interest?

Unlikely, but someone posted a Q based on that on some marathon I think last year (iirc glittergal96). But yeah, error analysis isn't part of the HSC, so the most they could expect from you would be a hand-wavy answer (which is what the poster of the marathon Q said to avoid last year).

Re: International Baccalaureate Marathon 2016 Are you sure the IB is offered by most New South Wales schools? I thought it was relatively uncommon in NSW schools.

This is the best thread in a while. :p

Irrational (An irrational number is one that can't be expressed as the ratio of two integers.)

That was probably the whole point of the previous question.

Shuuya found it for you.

Well you'd better find it now then.

Did you find an expression for f-1 (x) earlier?

I think you missed the point. I know what the Q's mean, it's just they're technically not written right. If a function is only defined for x larger than 1, then it's meaningless to sub. in a value less than 1. What the Q's meant was something like treat f-inverse as the inverse of the function...

Why do you think I'm wrong and the answers aren't? (These are just technicalities that the HSC doesn't really pay attention to.)

Also I think you typoed Q. 2 a), because it's the same as the line above.

What the answers say have no impact on the statements I made.

$\noindent If $g$ has only been defined for $x\leq -1$, then both b) and c) will be undefined.$

$\noindent You know, technically speaking, b) and c) are undefined because the function $f$ hasn't been defined for $x < 1$.$

Yes, 1 g = 1000 mg.

A typical application of circles (and other conics) would be in Astrophysics. You can probably find more by researching online. E.g. An application of ellipses in celestial mechanics: the Hohmann Transfer Orbit (https://en.wikipedia.org/wiki/Hohmann_transfer_orbit). This is an elliptical orbit...

Yeah I meant all the Q's from 22 to 30 (so the ones in between too).

$\noindent I'm assuming the domain is all real $x$. In this case, as $x$ varies throughout the reals, $z$ just traces out a circle of radius 1 centred at $i$. So the range is $\left\{z \in \mathbb{C} : |z-i| = 1\right \}$.$