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Re: HSC 2015 3U Marathon True. It was from a math tournament.

Re: HSC 2015 3U Marathon Yea I think I do. I wouldn't be able to come up with that in an exam though. Which part didn't you understand?

Re: HSC 2015 3U Marathon I think you can choose any card as long as it meets the conditions to be flipped.

Re: HSC 2015 3U Marathon A one-player card game is played by placing 13 cards (Ace through King in that order) in a circle. Initially all the cards are face-up and the objective of the game is to flip them face-down. However, a card can only be flipped face-down if another card that is '3...

Would that be a raw mark of ~75/105?

Re: HSC 2015 3U Marathon You've made a mistake in the bold part. Perhaps you have incorrectly substituted?

Re: HSC 2015 3U Marathon $Evaluate $\int^2_0 \left (\sqrt{\frac{4-x}{x}}-\sqrt{\frac{x}{4-x}} \right )~\mathrm{d}x$ using the substitution $u=4x-x^2$ or $x=4\sin^2{\theta}.

Ah okay. Thanks for the clarifications!

So then would you say f(x) is decreasing for x≤1? Which would mean at x=1, f'(x) is both increasing and decreasing, but not strictly doing either? Or does this just depend on what direction you approach x=1 from (1+ vs. 1-)?

Why x greater than or equal to 1 and not just x greater than 1? The f'(x) graph BlueGas posted has a hole at x=1.

If you draw a graph you should easily be able to figure out both the domain and range. If you don't have one here you go: Domain: what possible x-values can be subbed in to the function? Range: what possible y-values are outputted once these x-values are subbed in? Now to know where f(x) is...

Read this: http://community.boredofstudies.org/829/module-b-critical-study-texts/334678/excelling-critical-study-speeches-2015-2020-99-atar-hsc-graduate.html

Re: 2015 permutation X2 marathon Yep that's the correct answer. I'm guessing the 0.1 is if it lands on the island he is on. Can you explain the second part?

Re: 2015 permutation X2 marathon Fred lives on one of 10 islands sitting in a vast lake. One day a package drops uniformly at random on one of the ten islands. Fred can't swim and has no boat, but luckily there is a teleporter on each island. Each teleporter teleports to only one of the other...

Re: HSC 2015 3U Marathon The answer is 1/3. I can't explain why your answer is wrong though.

Re: HSC 2015 3U Marathon Twenty guests sit at twenty seats around a round table according to the following process. One guest, who is selected uniformly at random from the unseated guests, selects an empty seat uniformly at random and sits in that seat. This process repeats...

Re: HSC 2015 3U Marathon \begin{align*}u&=\ln{(\ln{(\ln{x})})} \\\frac{\mathrm{d}u}{\mathrm{d}x}&=\frac{1}{\ln{(\ln{x})}} \times\ \frac{\mathrm{d}}{\mathrm{d}x}\ln{(\ln{x})} \\&=\frac{1}{\ln{(\ln{x})}} \times\ \frac{1}{\ln{x}} \times \frac{\mathrm{d}}{\mathrm{d}x}\ln{x}...

Re: HSC 2015 3U Marathon Yep.

Re: HSC 2015 3U Marathon Well I drew the segment AC. Since CD is perpendicular to AB, angle CDA is equal to 90 degrees. One of the circle geometry theorems is "In a circle, the perpendicular bisector of a chord passes through the center of the circle." So if we have chord AB and center C, the...

Re: HSC 2015 3U Marathon I think that's the circle passing through A and B with center C, not passing through A, B, C.