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Depends on the subject. In Ext 1/2 maths it is definitely a big deal. But surely the HSC is about getting into the course you want, not whether you get 5 minutes of fame for getting a state rank in one subject?

Re: HSC 2015 4U Marathon This is just bookwork - memorising a result.

4 marks behind top rank in Ext 2 Maths would leave practically no chance of getting a state rank.

So you state ranked with an HSC mark of 96.5 ?? Which subject was this?

What about a 3rd option .... asking your teacher for help ?

So .... you seem to be saying that you're not going to do OK in the HSC ???

Which goes to show it is not rank that is important - it is relative marks. He was probably one or at most two marks below first rank.

Re: HSC 2015 3U Marathon Having taught this a number of times, I can say that the reason people don't predict the answer well for this question is that they focus on themselves. That is, they imagine that THEY THEMSELVES (as part of the group) have to share a birthday with someone else in...

As I said, ½r²(θ-sinθ) where θ=7π/6. I'll let you work it out.

It seems your only means of "proving" this is to quote everyday experiences, and ASSERT that the principles that apply in your everyday life must apply everywhere and 'everytime'. The origin of the universe is an exception to everyday rules, WHICHEVER opinion you hold. The fact that it is such...

You've found the area of the major SECTOR. The formula for the area of a segment A=½r²(θ-sinθ) also works for major segments. Just sub in 7π/6.

Re: HSC 2015 4U Marathon This question from the 1950 Leaving Certificate.

Re: MX2 2015 Integration Marathon You have left out all the important working required to get that result ... ie. using the tan(A-B) result

Re: HSC 2015 3U Marathon No it's not.

Watch the demo at the top of this page: http://mathdemos.org/mathdemos/shellmethod/

1. Just substitute a large value of x to see which side it lies on. BTW, horizontal/oblique asymptotes CAN be crossed (though not in this question). 2. Confused, since you talk about a denominator of x+3, then use x^2 + 1

Either method is fine. See my solution for Cartesian coords:

Now ... can you explain the meaning of the last paragraph?

Alternatively: ab² - b³ = b²(a-b) > 0 since a>b & b²>0 ab² > b³

The first space shuttle disaster was basically caused by scientists extrapolating a line/curve beyond the last data point ... and getting it wrong.