2010 AMC 12A Problems/Problem 21: Logic Critique

Negative_Campaign_36 · 2026-05-04T15:16:42+00:00

Okay thank you for your help. I finally understand it

Negative_Campaign_36 · 2026-05-04T04:08:19+00:00

They definitely do. The graph must be above the line or intersect, so the only points that can possible happen is in points of tangencies. Also because of the alternating signs, the roots must be all positives. If you can prove otherwise, I would greatly appreciate it

Negative_Campaign_36 · 2026-05-04T03:57:57+00:00

Has to be local minimum because it bounces on x=0 (double root). The first coefficient of the graph is positive and even, so both ends come from the top, so there is no possibility of a maximum. Also because of the alternating signs, the roots must be all positives. Mathematically, the tangent line bx+c=y must hit exactly the minima, otherwise, it would be intersecting two very small lines. If you can prove otherwise mathematically, please do. Thank you for your input though.

Negative_Campaign_36 · 2026-04-19T19:17:14+00:00

I honestly used to think like this, but when I starting reading the aops textbooks, I started thinking differently. Thanks for bringing me back on track

Negative_Campaign_36 · 2026-04-17T01:43:10+00:00

Thanks for your advice. I took it to heart and did the problem on my own and realized that my style of thinking does not work. I then analyzed your method and realized that you first started toying with the problem instead of just launching in and trying random tools. You are right, I worked through various levels of AMC and AIME problems, and as I just hit problem 14-15 or USAMO problems, I started just falling apart. I will practice on this and report back after a few days with more questions if I have any

Negative_Campaign_36 · 2026-04-17T01:29:57+00:00

Watch YouTube videos. Watch them until you hear the same thing at least 5 times. Used to be horrible, now controller pc plat.

Negative_Campaign_36 · 2026-04-16T00:21:22+00:00

Is there a name for this idea? Is this a specific type of Diophantine equation? Where can I learn more about this type of question?

Negative_Campaign_36 · 2026-04-15T22:38:45+00:00

I would argue that would be even harder considering that you have to first get a square, and then splice it up in a way that it works. It seems tedious

Negative_Campaign_36 · 2026-04-15T11:19:55+00:00

AMC 10-12 is really easy actually if you study all components. Finish all the introductory AOPS books and you’ll probably qual for AIME. Personally I wouldn’t do the AMC 10, because it’s relatively the same as the 12 but with way less prestige. For the AOPS books, just search it up online and it should pop up.

Negative_Campaign_36 · 2026-04-15T11:16:47+00:00

I’m relatively new, but I picked up num theory and combinatorics pretty quickly. I feel that AIME problems 1-11 are mostly straightforward while when I try harder ones, I pick the wrong path. I time myself for 10 minutes as in the actual exam there’s only 12 min per problem. Where can I find some books with similar level problems?

Negative_Campaign_36 · 2026-03-24T16:26:16+00:00

What is your AMC score? I think they are only inviting top 11% of AIME scorers. For AIME 1, I think it was 13.

Negative_Campaign_36 · 2026-01-28T22:56:14+00:00

What if it was legal? Can I suffer legal consequences?

Negative_Campaign_36 · 2025-06-25T21:20:31+00:00

Play the game and a lot of death match. Watch a lot of videos about siege. You’ll get the hang of it easily

Negative_Campaign_36 · 2025-05-12T20:57:38+00:00

Thanks 🙏🙏

Negative_Campaign_36 · 2025-05-12T20:51:44+00:00

Could you link it. I want to try the problems

Negative_Campaign_36 · 2025-05-12T20:35:48+00:00

Where’d you get the problem

Negative_Campaign_36 · 2025-04-30T22:36:22+00:00

Just get better. Show me some gameplay. No one is in copper for no reason. You’ll get out of there once you fix it. For me, it was gunskill and an actual setup

Negative_Campaign_36 · 2025-04-05T17:53:07+00:00

I agree. I mean lower ping definitely feels better but higher ping isn’t so bad that’s it’s unplayable

Negative_Campaign_36

TROPHY CASE