1. ## Re: How did people go in the maths comp today?

Originally Posted by Official
For the map question I got the option where the 3rd letter is W. Besides that I can't remember
Yeh, that (E).

2. ## Re: How did people go in the maths comp today?

Originally Posted by kurt.physics
Yeh, that (E).

3. ## Re: How did people go in the maths comp today?

Originally Posted by Official
same! That question was annoying! I looked at the clock and i was like, theres no way i am going to be folding paper when i have 9 questions left, so i just folded the paper in my head =)

4. ## Re: How did people go in the maths comp today?

i just used the second picture
labelled it and drew some arrows
i got e too

5. ## Re: How did people go in the maths comp today?

I thought that question number 15 (intermediate) was a bit hard for a question 15, it was

$What is the last digit of\,\,6 \times 8^{2009}$

I got it only using modular arithmetic, but compared to last year q 15 its pretty hard. There is also the pattern of the question 21 in the intermediate papers being ridiculous and completely irrelevant (last years was Farmer Taylor blah blah) and this years was the map =Z

6. ## Re: How did people go in the maths comp today?

i was surprised at the position of the map question..

7. ## Re: How did people go in the maths comp today?

Originally Posted by kurt.physics
I thought that question number 15 (intermediate) was a bit hard for a question 15, it was

$What is the last digit of\,\,6 \times 8^{2009}$

I got it only using modular arithmetic, but compared to last year q 15 its pretty hard. There is also the pattern of the question 21 in the intermediate papers being ridiculous and completely irrelevant (last years was Farmer Taylor blah blah) and this years was the map =Z
I would have done it by finding a pattern since I don't know any advanced method

Corresponding last digits of various powers to 8
8^1 = 8
8^2 = 4
8^3 = 2
8^4 = 6
8^5 = 8

By this, we find that the last digit repeats every 4 powers
8^2009 = 8

And 8 * 6 = 8

8. ## Re: How did people go in the maths comp today?

map question was Q20. 4 marks

Were any of the questions from Q21-25, (c) by any chance? (from the senior paper)
I guessed (c)for a lot them.

9. ## Re: How did people go in the maths comp today?

Originally Posted by nerdsforever
map question was Q20. 4 marks

Were any of the questions from Q21-25, (c) by any chance? (from the senior paper)
I guessed (c)for a lot them.
Q. 23 was definitely 4, I'm not sure if that is (c) or (d)

10. ## Re: How did people go in the maths comp today?

what do you think 60 points would get me?

11. ## Re: How did people go in the maths comp today?

Official, what did you (or anyone else doing the Senior paper) get for the question with n-fold composites?

12. ## Re: How did people go in the maths comp today?

yay! I put 4 for Q23. It was (d). but were there any answers that were (c) by any chance?

13. ## Re: How did people go in the maths comp today?

Originally Posted by gurmies
Official, what did you (or anyone else doing the Senior paper) get for the question with n-fold composites?
Eh, which question is that? Can't remember

14. ## Re: How did people go in the maths comp today?

Originally Posted by Official
I would have done it by finding a pattern since I don't know any advanced method

Corresponding last digits of various powers to 8
8^1 = 8
8^2 = 4
8^3 = 2
8^4 = 6
8^5 = 8

By this, we find that the last digit repeats every 4 powers
8^2007 = 8
8^2008 = 4
8^2009 = 2

And 2 * 6 = 2

So I'm guessing its 2, am I correct?
Sorry, its 8. I can show you my solution if you want.

15. ## Re: How did people go in the maths comp today?

Originally Posted by kurt.physics
Sorry, its 8. I can show you my solution if you want.
Oh ok, my mistake then. What did you do to get 8?

Edit: My bad, made an error in the working lol, it is now corrected. Yeah, it is 8

16. ## Re: How did people go in the maths comp today?

It was like: Let f(x) = (x+6)/x and fn(x) = f(f(...

17. ## Re: How did people go in the maths comp today?

Originally Posted by nerdsforever
yay! I put 4 for Q23. It was (d). but were there any answers that were (c) by any chance?
Can't remember, I remember guessing C for 25 or something though lol
Originally Posted by nerdsforever
what do you think 60 points would get me?
Probably Distinction, or if the test was hard you can scrape in a High Distinction . Last year, I remember the HD cut off being 64 in the Intermediate Division.

18. ## Re: How did people go in the maths comp today?

I paid for it, and completely forgot about it! Argh.

19. ## Re: How did people go in the maths comp today?

Originally Posted by gurmies
It was like: Let f(x) = (x+6)/x and fn(x) = f(f(...
Oh I didn't get that one, I guess (c) though. Was that one of the questions 24 or 25?

20. ## Re: How did people go in the maths comp today?

anyone know the answer to 28,29 or 30?

21. ## Re: How did people go in the maths comp today?

I was tossing up between 2n and 2^n but went with 2n instead.

22. ## Re: How did people go in the maths comp today?

Originally Posted by Timothy.Siu
anyone know the answer to 28,29 or 30?
Not here, we weren't allowed to take the test papers home =[. How do you think you went?

not well.

24. ## Re: How did u go in the Australian Maths Competition?

Originally Posted by kurt.physics
Here is my solution to 26 for ya =)

$Question 26: What is the smallest positive integer which, when divided by each of 2,3,4,5,6 and 7, will give in each case a remainder that is one less than its divisor?$

$Let the smallest number be x, then$

$x \equiv 1 \mod 2$

$x \equiv 2 \mod 3$
.
.
.
$x \equiv 6 \mod 7$

$Note that each of these equations can be expressed as follows,$

$x \equiv -1 \mod 2$

$x \equiv -1 \mod 3$
.
.
.
$x \equiv -1 \mod 7$

$Hence\,\, x + 1\,\, is a multiple of \,\,2,3,4,5,6,7$

$\therefore x + 1\,\, is a multiple of\,\,LCM[2,3,4,5,6,7] = 420$

$As 420 is the smallest multiple of 420$

$\implies x + 1 = 420$

$\therefore x = \boxed{419}$
Arghh!!! I feel bad! I never knew there were people with strong maths out there. I probably got the last 4 questions wrong.

25. ## Re: How did people go in the maths comp today?

Lol, same. I came into the test room expecting an easier test. I got blown away by every question after 15

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