no rule, just a handy factorisation
Commerce (Finance) / Science (Advanced Mathematics) (Quantitative Risk) @ UNSW
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
Last edited by lolokay; 5 Aug 2009 at 9:39 PM.
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.
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
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.
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
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.
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
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,
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
Therefore there are 500 factors of 10 in 2008! and hence 2008! ends in 500 zeros.
Good luck everyone for the competition today =)
Last edited by kurt.physics; 6 Aug 2009 at 7:23 AM.
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.
lol u mad son?
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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?
Why does the chicken cross the street?
Because a chicken in motion stays in motion.
HD every year so far but probably wont this year =(
HSC '09
B Science (Adv. Mathematics) @ UNSW
The School of Mathematics Prize for Level 1 Mathematics
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.
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.
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?
HSC 2010
Mathematics - 99 || MX1 - 98
HSC 2011
Physics - 96 || Chemistry - 95
MX2 - 96
Eng Adv - 92
ATAR: 99.85
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.
22, 23, 26, 27
Did you do Senior paper too?
HSC 2010
Mathematics - 99 || MX1 - 98
HSC 2011
Physics - 96 || Chemistry - 95
MX2 - 96
Eng Adv - 92
ATAR: 99.85
i dont even remember the question any moree..
BCom/BSc (Adv Math) - '16
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