1. ## Adoculus 2018 extension 2 mathematics competition

Well the trials are done so it is time to sharpen your Extension 2 skills with the annual Adoculus Extension 2 mathematics competition.

First prize is a beautiful new University of Sydney mug with a \$100 bonus for full marks.

Do not rush to your answers....but don't wait too long or you may be beaten to the punch. Working does not need to be shown.

Instructions are in the attachment.

The competition is only open to current high school students with a limit of one entry per student.
In the event of a tie, the first entry received will win.

Some of the questions look easy but are very hard, some look hard but are very easy. Think about each problem very carefully.

Truth is rarely pure and simple.

Good Luck

p.s.

Competition closes midnight October 24 2018.

Winner will be announced immediately after the final HSC examination. Only the winner will be notified of their mark.

If full marks are achieved complete solutions will be posted. Else only the winning mark will be released and the competition will run again in 2019.

Note that Questions 12 and 17 were amended slightly (19/09/18 10:30 pm) to remove some ambiguity

2. ## Re: Adoculus 2018 extension 2 mathematics competition

When is this due by?

3. ## Re: Adoculus 2018 extension 2 mathematics competition

Will we be notified of our mark even if we don't win the competition?

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4. ## Re: Adoculus 2018 extension 2 mathematics competition

For question 12 should "minimum" displacement be taken with respect to magnitude only or both sign and magnitude?

And for question 17 does "all directions" include every possible angle of projection of the water stream?

5. ## Re: Adoculus 2018 extension 2 mathematics competition

Yes it is ambiguous.

Calculate exactly, the maximum and minimum
distances traveled in any one second interval.

In Q17 the water does indeed travel in all possible directions

6. ## Re: Adoculus 2018 extension 2 mathematics competition

Originally Posted by peter ringout
In Q17 the water does indeed travel in all possible directions
Should we also assume that the brick wall is infinitely tall and wide?

Originally Posted by peter ringout

Calculate exactly, the maximum and minimum
distances traveled in any one second interval.
Just to clarify do you mean max/min (by magnitude only) displacements?

I think this would be different to max/min distances since the particle is clearly oscillating, e.g. 1m right and 3m left would be -2m displacement but 4m distance.

7. ## Re: Adoculus 2018 extension 2 mathematics competition

Thanks for the suggestions. Modified Q12 and 17 are clearer. Q12 is now slightly different. Fortunately there were no submissions at that point.

8. ## Re: Adoculus 2018 extension 2 mathematics competition

Will we get a mark once this is done?

9. ## Re: Adoculus 2018 extension 2 mathematics competition

Originally Posted by 1039213
Will we get a mark once this is done?
The OP states that only the winner will get their mark.

Also there aren't any problems with completing the answer sheet electronically, right? I can't remember the last time I had to print something out.

10. ## Re: Adoculus 2018 extension 2 mathematics competition

Question 5 does not make sense. There is no mention of characters on the green , red and yellow marbles.

11. ## Re: Adoculus 2018 extension 2 mathematics competition

Yes, electronic is OK.

12. ## Re: Adoculus 2018 extension 2 mathematics competition

There are no characters just colours.

14. ## Re: Adoculus 2018 extension 2 mathematics competition

Which questions?

15. ## Re: Adoculus 2018 extension 2 mathematics competition

5. Suppose that 2 identical green marbles, 2 identical red marbles and 2 identical yellow
marbles are arranged in a circle.
(As usual, two arrangements are deemed identical if one can be rotated to the other)
a) How many permutations exist with the two A’s positioned together?
b) How many permutations exist where no pair of identical characters sit together?
c) Hence or otherwise determine the total number of possible arrangements of the
six balls in a circle.
(Only 5c) needs to be recorded)
I believe he is referring to the previous parts.

16. ## Re: Adoculus 2018 extension 2 mathematics competition

My apologies! Q5 has been fixed. This question requires careful consideration.

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