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Course: Math for fun and glory>Unit 3

Lesson 1: 2013 AMC 10 A

2013 AMC 10 A #25

Video by Art of Problem Solving.  Problem from the MAA American Mathematics Competitions. Created by Art of Problem Solving.

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• In comparison to the AMC8, how much harder are the AMC10? I am an 8th grader taking geometry and these problems seem quite challenging so I was wondering how much I need to study and learn.
• The AMC 10 is more about analysis and "abuse" of the various laws and properties of any number of things, which is seemingly unrelated. The AMC 10 has a bit more algebra than the AMC 8, would, but it's otherwise pretty similar: lot of analysis.
• Thankyou sir.I think the methods of solving these problems seem to be based on assumptions.Can you guide me with better shortcut methods?
• Thankyou sir.I think the methods of solving these problems seem to be based on assumptions.Can you guide me with better shortcut methods?
• I am in fifth grade and trying to learn about factorials. Can someone help?
• Exactly but the thing is by definition 0!=1 which has a lot of math to prove it. Now n!=n(n-1).... goes on till zero but not zero because if you multiply anything by zero the answer is zero.
So 1!=1, 2!=2(2-1)=2(1)=2, 3!=3*2*1=6 and it goes on. Hope that helped.
(1 vote)
• here's a problem.
cos 1+cos 2+cos 3+.....cos 178+cos 179=?
• At , wouldn't finding out if the three lines really did intersect be useless because in real tests you would use rulers and other tools?
• How do you do this please? I'm good at maths too but this is way too complicated SO MUCH WORKING OUT!! Can someone help me please??
(1 vote)
• on what question are you talking about m8
(1 vote)
• How did you get that
This is helping me a lot and but can help me
(1 vote)
• This only saves about 50 seconds as opposed to the drawing out and counting method, I would recommened you do that if you are good at art and can do it quickly. It's a good strategy though.
(1 vote)
• Simple factorial issue. Takes under 1 min to solve.
(1 vote)
• it was kinda confusing to me but know i see how many triangles can go into a octagon and add up how many isosceles triangles there to get 49 as your answer. Tricky question. Easy answer
(1 vote)
• Yes, after you do it for the first time it's much easier. Good luck
(1 vote)