# Thread: Australian Mathematics Competition

1. ## Re: Westpac Maths Comp marathon

no rule, just a handy factorisation

2. ## Re: Westpac Maths Comp marathon

Originally Posted by kurt.physics
Problem 5

The sum of three numbers is 4, the sum of their squares is 10 and the sum of their
cubes is 22. What is the sum of their fourth powers?
is the answer to this 50?

figure out my notation; )

$\\ \alpha =4\\ \alpha ^2 = 10\\ \alpha ^3 = 22\\ \alpha ^4=???\\ \\ 1) (\alpha ^2)^2=\alpha ^4+2\alpha ^2\beta ^2=100\\ 2) (\alpha )(\alpha ^2)=\alpha ^3+\alpha \beta ^2=40\\ 3) (\alpha )(\alpha ^3)=\alpha ^4+\alpha\beta ^3=88\\ 4) (\alpha)^3=\alpha ^3+3\alpha \beta ^2+6\alpha \beta \gamma =64\\ 5) (\alpha )(\alpha \beta ^2)=2(\alpha \beta \gamma)(\alpha )+\alpha\beta ^3+2\alpha ^2\beta ^2 \\ \\ 2)->\alpha \beta ^2=18\\ 4)->\alpha \beta \gamma =-2\\ 1)+3),5) ->2\alpha ^4+(\alpha )(\alpha \beta ^2)-2(\alpha \beta \gamma)(\alpha )=188\\ 2\alpha ^4 = 188 - 4*18+2*-2*4\\ 2\alpha ^4 = 100\\ \alpha ^4 = 50$

3. ## Re: Westpac Maths Comp marathon

Originally Posted by lolokay
is the answer to this 50?

figure out my notation; )

$\\ \alpha =4\\ \alpha ^2 = 10\\ \alpha ^3 = 22\\ \alpha ^4=???\\ \\ 1) (\alpha ^2)^2=\alpha ^4+2\alpha ^2\beta ^2=100\\ 2) (\alpha )(\alpha ^2)=\alpha ^3+\alpha \beta ^2=40\\ 3) (\alpha )(\alpha ^3)=\alpha ^4+\alpha\beta ^3=88\\ 4) (\alpha)^3=\alpha ^3+3\alpha \beta ^2+6\alpha \beta \gamma =64\\ 5) (\alpha )(\alpha \beta ^2)=2(\alpha \beta \gamma)(\alpha )+\alpha\beta ^3+2\alpha ^2\beta ^2 \\ \\ 2)->\alpha \beta ^2=18\\ 4)->\alpha \beta \gamma =-2\\ 1)+3),5) ->2\alpha ^4+(\alpha )(\alpha \beta ^2)-2(\alpha \beta \gamma)(\alpha )=188\\ 2\alpha ^4 = 188 - 4*18+2*-2*4\\ 2\alpha ^4 = 100\\ \alpha ^4 = 50$
Yes, you are right =)

Would you like to post a new question?

4. ## Re: Westpac Maths Comp marathon

A rectangular prism 77 x 81 x 100 is cut into cubes of edge 1 by
planes parallel to the faces of the prism. A given internal diagonal
pierces how many of these cubes?
(A) 255 (B) 256 (C) 257 (D) 258 (E) 259

+ty kurt for the link to the papers. I'm gonna do them all eventually. just tried one, made a few silly errors and one question i wasn't sure about

5. ## Re: Australian Mathematics Competition

Does the Australian Maths Competition only have stuff from the 4 unit Maths course or does it have any stuff from Uni maths?

6. ## Re: Australian Mathematics Competition

Originally Posted by Dragonmaster262
Does the Australian Maths Competition only have stuff from the 4 unit Maths course or does it have any stuff from Uni maths?
The AMC is generally a problem solving exam. You will see that the first 10 questions are rudimentary. The next 5 will be more problem solving, the last 15 will be problem solving although knowledge of both number theory and combinatorics and a solid understanding of geometry and algebra would certainly make the last few questions 5 times easier.

7. ## Re: Australian Maths Competition

How about the solution of:
The number 2008! (factorial 2008) means the product of all the integers 1,2,3,4,...,2007,2008. With how many zeroes does 2008! end?

Tomorrow's the competition, and I need to know the solution of this wuestions, please? Thanks

8. ## Re: Australian Mathematics Competition

Yeah, I usually bomb these Maths Comps. Usually a combination of me not giving a damn and I also suck at problem solving. Never ever get HDs, but I usually do ok in school maths, so heh.

9. ## Re: Australian Maths Competition

Originally Posted by sharin_3
How about the solution of:
The number 2008! (factorial 2008) means the product of all the integers 1,2,3,4,...,2007,2008. With how many zeroes does 2008! end?

Tomorrow's the competition, and I need to know the solution of this wuestions, please? Thanks
The amount of zeros a number ends in is the amount of 10s that are in the prime factorization. Now 10 = 2 x 5. And so when we prime factorize 2008! we need to count the amount of 2s and the amount of 5s.

Now there is clearly going to be more 2s than 5s, so to determine how many factors of 10 there are in the prime factorization of 2008! we must only find how many 5s are in the prime factorization.

Now clearly finding the prime factorization of 2008! would be a torturous task, so we will "look" at each term of 2008! ie 1, 2, 3, 4, 5, 6, . . . ,2007, 2008.

So how many multiples 5s are there between 1 and 2008, well

$5m < 2008$

$m <401.6$

As m is an integer then there are 401.

Now some terms in the prime factorization will have 25 as a factor, and hence that terms will have 2 factors of 5. So we must count how many terms are multiples of 25. Now we already have counted 1 of those factors of 5 (out of those numbers that are multiples of 5^2), and so when we determine how many factors are multiples of 5^2, they will add 1 extra multiple of 5 into our count.

$25n < 2008$

$\therefore n < 80.32$

As n is an integer then there are 80.

But some of the factors of 2008! will be multiples of 5^3 = 125, so when we count these by the same logic as before they will contribute an extra 1 multiple of 5 into our count, so

$125p < 2008$

$p< 16.064$

As p is an integer then there are 16.

But some of the factors of 2008! will be multiples of 5^4 = 625, and so these will add an extra 1 multiple of 5 into our count. So,

$625j < 2008$

$\therefore j < 3.2128$

As j is an integer there are 3 of these.

As 5^5 is greater than 2008, then there are no multiples of 5^5 up to 2008.

So in total the amount of factors of 5 in 2008! are

$401 + 80 + 16 + 3 = 500$

Therefore there are 500 factors of 10 in 2008! and hence 2008! ends in 500 zeros.

Good luck everyone for the competition today =)

10. ## How did u go in the Australian Maths Competition?

today (6-8-09) i did my intermediate AMC test.This is just a thread to see which question u were stuck on ...q26-30:@ i need help on dem,, and ye just a general chat on how u went in the AMC test.

11. ## 回复: Re: Australian Mathematics Competition

Originally Posted by Aerath
Yeah, I usually bomb these Maths Comps. Usually a combination of me not giving a damn and I also suck at problem solving. Never ever get HDs, but I usually do ok in school maths, so heh.
some guy in my school got HD and does general math.... so yea the comp... doesnt mean anything lol

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

Arghhh i reckon this year's paper was harder than last years :S. The senior paper is anyway...i guessed like 10 questions.
Question 27 looked really interesting...but I didn't have time to finish it -_-
So how did you all go?

13. ## Re: 回复: Re: Australian Mathematics Competition

Originally Posted by shuning
some guy in my school got HD and does general math.... so yea the comp... doesnt mean anything lol
Thats soo amazing ....but i fail to believe it...:mad1:

14. ## Re: Australian Mathematics Competition

HD every year so far but probably wont this year =(

15. ## Re: Australian Mathematics Competition

This was the first time I ever competed and oh boy... it was the hardest test I ever took... by far!
Are these tests usually consistent in difficulty each year? What kinds of raw marks get HD's, D's and credits? I did the senior exam btw.

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

Originally Posted by maths94
today (6-8-09) i did my intermediate AMC test.This is just a thread to see which question u were stuck on ...q26-30:@ i need help on dem,, and ye just a general chat on how u went in the AMC test.
I did the intermediate paper too. I thought the first 20 were easy (except i am a bit apprehensive about 17). Question 21 was stupid! I put (E), what bout yous?

Questions 22, 23 and 24 were pretty easy and 25 was a bit hard. Question 26 was easy the answer is 419, i didnt have enough time to work on 27, 28. I got 231 for 29 and didnt do 30.

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

I had to do the Senior Paper although I'm in yr 10 (accelerant). This is what I think I got:
1 - 10: 30 marks
11-20: 24 marks (Really hard for some reason =/)
21 - 30: 10 + 13 marks

= 77 marks.

What does this become around?

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

I thought the first 20 were easy (except i am a bit apprehensive about 17). Question 21 was stupid! I put (E), what bout yous?

Questions 22, 23 and 24 were pretty easy and 25 was a bit hard. Question 26 was easy the answer is 419, i didnt have enough time to work on 27, 28. I got 231 for 29 and didnt do 30.

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

Originally Posted by kurt.physics
I did the intermediate paper too. I thought the first 20 were easy (except i am a bit apprehensive about 17). Question 21 was stupid! I put (E), what bout yous?

Questions 22, 23 and 24 were pretty easy and 25 was a bit hard. Question 26 was easy the answer is 419, i didnt have enough time to work on 27, 28. I got 231 for 29 and didnt do 30.

wow 1-20 ye dey were oriite...wat did u get for the magic rabbit ones?

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

Originally Posted by Official
I had to do the Senior Paper although I'm in yr 10 (accelerant). This is what I think I got:
1 - 10: 30 marks
11-20: 24 marks (Really hard for some reason =/)
21 - 30: 10 + 13 marks

= 77 marks.

What does this become around?
Which questions of the 21 - 30 do you think you got?

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

22, 23, 26, 27

Did you do Senior paper too?

22. ## Re: Australian Mathematics Competition

Originally Posted by Puttah
This was the first time I ever competed and oh boy... it was the hardest test I ever took... by far!
Are these tests usually consistent in difficulty each year? What kinds of raw marks get HD's, D's and credits? I did the senior exam btw.
yeah consistently the same difficulty
probably 80-90 for HD for yr 12.
less for yr 11

23. ## Re: Westpac Maths Comp marathon

Originally Posted by lolokay
is the answer to this 50?

figure out my notation; )

$\\ \alpha =4\\ \alpha ^2 = 10\\ \alpha ^3 = 22\\ \alpha ^4=???\\ \\ 1) (\alpha ^2)^2=\alpha ^4+2\alpha ^2\beta ^2=100\\ 2) (\alpha )(\alpha ^2)=\alpha ^3+\alpha \beta ^2=40\\ 3) (\alpha )(\alpha ^3)=\alpha ^4+\alpha\beta ^3=88\\ 4) (\alpha)^3=\alpha ^3+3\alpha \beta ^2+6\alpha \beta \gamma =64\\ 5) (\alpha )(\alpha \beta ^2)=2(\alpha \beta \gamma)(\alpha )+\alpha\beta ^3+2\alpha ^2\beta ^2 \\ \\ 2)->\alpha \beta ^2=18\\ 4)->\alpha \beta \gamma =-2\\ 1)+3),5) ->2\alpha ^4+(\alpha )(\alpha \beta ^2)-2(\alpha \beta \gamma)(\alpha )=188\\ 2\alpha ^4 = 188 - 4*18+2*-2*4\\ 2\alpha ^4 = 100\\ \alpha ^4 = 50$
Lol wow, what a beast

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

Originally Posted by Official
22, 23, 26, 27

Did you do Senior paper too?
No ;P

Could you post them possibly? (some of them could be the same so perhaps you could just kinda explain which ones or something)

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

i dont even remember the question any moree..

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