Australian Maths Comp

[brightsky]

do you have prior knowledge of theorems to do successful in maths comp?
cant you jst sit there and work out no. patterns? actually... thats probably why i had no clue with most of the q.s 

some theorems would help a shit load, just by looking @ Q 29 i reckon you should know some properties of monic polynomials and the fundamental theorem of algebra would almost lead you to the answer, i cant be bothered with the details atm but thinking about that Q in my head knowing fta would help heapsss

Lol, best I can do is do a logical guess at the degree and fiddle around with numbers...but knowing theorems and stuff would significantly decrease the amount of time you spend on the question..

[TrueTears]

yeh, ahh i miss these high school maths, Q 30 looks like a fun graph theory question... lol if only i had time now i would attempt most of these

[Mulan]

how do you learn theorems? how come i havent come across any at school? do you do it in methods/further/specialist? or is it a self learning process?

[TrueTears]

u dont rly do proof-y stuff in vce maths, if you are passionate about maths and love problem solving you can begin by reading art and craft of problem solving, rly good to get started etc

competition maths is quite different from vce maths.

basically just read ALOT

[Mulan]

oh ok then. i think ill jst focus on normal yr 10 maths atm
one day...one day...

[luken93]

Okay here goes my answers, feel free to differ, just seeing how I went.
1 D
2 A
3 A
4 C
5 A
6 B
7 E
8 E
9 A? Cant remember exactly (If anyone wants to clear that up go ahead)
10 B
11 D
12 B
13 C
14 A
15 D
16 D
17 D ?
18 E
19 E ?
20 C
21 C ? No Idea never done them before
22 E ?
23 E ?
24 C ?
25 B
26 968
27 No idea
28 50
29 166
30 ?

Feel free to add some answers to my ? aha

[simonhu81292]

Q1-Q15...
everything seems right except..
Q10.B
Q11.D
looks like you will get a distinction+ for sure... 

[InitialDRulz]

Question 11 for people who can't see (which i agree, it is blurry)

For all values of x, the expression (7^3x + 7^2x) / (7^2x + 7^x) is equal to
A) 49
B) 7^2x
C) 7
D) 7^x
E) 1

[kamil9876]

i didnt do that q. looked too long and dint have time...
wat about this one?

How many whole no.s less than 2010 have exactly three factors?

THe numbers that have exactly three factors are exactly those that are the square of some prime.

e.g: 2^2=4, 3^2=9, 5^2=25...

In general one way to work out how many factors a number has is to use unique prime factorisation like this:

2^100 * 3^100 has how many factors?

well i can chose any number of the form 2^a * 3^b with a and b between 0 and 100. Thus there are 101*101 factors of this number. It follows from this method that only the squares of a prime have exactly 3 factors.


so i guess you just have to list all the prime numbers until u find one whose square is larger than 2010. (this last prime will be less than 50 because 2010<50^2, if that makes u feel any better).

[Hutchoo]

Oh from memory:

D
A
A
C
A
B
E
NO FUCKING IDEA
B
D
12,13 can't remember
A
C If 1 isn't a prime
16,17 can't remember
E
...
25 was B
I remember 26 and 28 to be what I posted. Rest I don't remember.

Q8..E
Q12.B
Q13.c
Q15...i got D . .
and WHAT....Q9 is B???damn ..chose A
my consecutive is gone~~~

http://en.wikipedia.org/wiki/List_of_prime_numbers
1 is not a prime number according to that...
Therefore 15 D

according to convention, 1 is not a prime. If it were, it would make a lot of theorems very annoying...

Terry Tao ftw

[TrueTears]

i didnt do that q. looked too long and dint have time...
wat about this one?

How many whole no.s less than 2010 have exactly three factors?

THe numbers that have exactly three factors are exactly those that are the square of some prime.

e.g: 2^2=4, 3^2=9, 5^2=25...

In general one way to work out how many factors a number has is to use unique prime factorisation like this:

2^100 * 3^100 has how many factors?

well i can chose any number of the form 2^a * 3^b with a and b between 0 and 100. Thus there are 100*100 factors of this number. It follows from this method that only the squares of a prime have exactly 3 factors.


so i guess you just have to list all the prime numbers until u find one whose square is larger than 2010. (this last prime will be less than 50 because 2010<50^2, if that makes u feel any better).

this was exactly my thinking when i showed mulan through pm hahaha just cudn't be bothered finishing it lol

Oh from memory:

D
A
A
C
A
B
E
NO FUCKING IDEA
B
D
12,13 can't remember
A
C If 1 isn't a prime
16,17 can't remember
E
...
25 was B
I remember 26 and 28 to be what I posted. Rest I don't remember.

Q8..E
Q12.B
Q13.c
Q15...i got D . .
and WHAT....Q9 is B???damn ..chose A
my consecutive is gone~~~

http://en.wikipedia.org/wiki/List_of_prime_numbers
1 is not a prime number according to that...
Therefore 15 D

according to convention, 1 is not a prime. If it were, it would make a lot of theorems very annoying...

Terry Tao ftw

did someone just mentioned my god.....?

[Mulan]

i didnt do that q. looked too long and dint have time...
wat about this one?

How many whole no.s less than 2010 have exactly three factors?

THe numbers that have exactly three factors are exactly those that are the square of some prime.

e.g: 2^2=4, 3^2=9, 5^2=25...

In general one way to work out how many factors a number has is to use unique prime factorisation like this:

2^100 * 3^100 has how many factors?

well i can chose any number of the form 2^a * 3^b with a and b between 0 and 100. Thus there are 100*100 factors of this number. It follows from this method that only the squares of a prime have exactly 3 factors.


so i guess you just have to list all the prime numbers until u find one whose square is larger than 2010. (this last prime will be less than 50 because 2010<50^2, if that makes u feel any better).

LOL thanks. listing...up to 50...
how on earth do they expect us to work this out in 75 minutes along with 29 other difficult questions? RIDICULOUS!

[Mulan]

ZOMG JST REALIZED IM NOT A VN NEWBIEE ANYMORE!
YAHOOOO! >.<

[AzureBlue]

I thought the questions were much more interesting this year..but Fermat's little theorem for q.8 is a bit over the top...

LOL I used Euler's phi function, could've used Fermat's but oh well... didn't take much time either way.

[AzureBlue]

Lol, best I can do is do a logical guess at the degree and fiddle around with numbers...but knowing theorems and stuff would significantly decrease the amount of time you spend on the question..

Definitely. Well, at least for the last digit thing Fermat's/Euler's Theorem would help though sometimes not essential. I have seen questions where Menelaus' Theorem has been applied and it saves a lot of effort and time. I've even seen Ptolemy's Theorem once I think! Though it must've been a while ago...

u dont rly do proof-y stuff in vce maths, if you are passionate about maths and love problem solving you can begin by reading art and craft of problem solving, rly good to get started etc
competition maths is quite different from vce maths.
basically just read ALOT

YES. I also recommend the Andreescu books and the Engel one, they are awesome! I personally have taken chapters/chunks from a lot of books to learn the theory