Answers to 2008 AMC (1 Viewer)

[PC]

Courtesy of Australian Mathematics Trust.

 

[buchanan]

Ta.

I've attached a solution to Q30.

Perhaps others may wish to add to this thread with complete solutions to all the other questions + alternative methods.

e.g., I know of at least 4 other ways to solve Q30.

 

[PC]

Whoever wrote the question is twisted and evil.

Remember that the cosine rule states that a² = b² + c² – 2bc cos A.

So each of the three things under the square root signs can be manipulated using the cosine rule.

Also remember that cos 45° = 1/√2 but 1/√2 is equal to √2/2, so the √2 in the expressions is 2 x √2/2 = 2 x 1/√2 = 2 cos 45°, and then everything else falls into place.

 

[buchanan]

Yep. You are right. Cosine rule method works.

Here it is:

 

[lookoutastroboy]

hey buchanan,

just looking back at your posts, how are you so good at the AMC and is there any ways I can improve to be able to solve most of the problems like you?












thanks lookoutastroboy

 

[buchanan]

I don't know if you can say I'm good at AMC. I only did one question! But it'd be good to put up solutions here to the others.

You might also like to look at mathlinks.ro for other competition level questions.

 

[PC]

Yep. You are right. Cosine rule method works.

Here it is:

Actually, after days of looking at that question, it was when I was looking at your first solution that the cosine thing clicked with me. More of a "why didn't I see that before" headache really.

 

[jyu]

Q28 http://itute.com/board/viewtopic.php?t=339


Q29 http://itute.com/board/viewtopic.php?p=746#746

 

[bored of sc]

WOW! I guessed B for Q21-25 (of Senior Category). So I get 10 points (2 correct) based on pure chance! Yay!

 

[jyu]

Q27 http://itute.com/board/viewtopic.php?p=751#751

 

[bored of sc]

You guys wouldn't happen to have a copy of the entire paper(s) would you?

Thanks for the answers by the way.

 

[x.Exhaust.x]

When will the awards be given out to the schools so us students can know what we achieved (credit, distinction etc.) Thanks.