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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]
No way they are scoring 30+ points on the Mathcounts state round with just Algebra I + school coaching.  If a kid truly did that, then the kid is a math prodigy with parents who severely dropped the ball.  
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You don't have to be a math prodigy for 30+.  Take a look at the state round.  It is easy to see how someone gets to 30+.

25 of the first 26 sprint and #28 are doable, as well as all the targets.  
That would be a score of 42, leaving plenty of room to get 30+.
The geometry that is needed is largely picked up in practices or self study.  ES Math Olympiad covers many of the geometry topics, though usually not circles like target #4.[/quote]

Here's problem 28:
Suppose x and y are real numbers for which 2xy + 16 = x^2 and 2xy + 9 = 4y^2
If y > 0, what is the value of x + y? Express your answer as a decimal to the nearest tenth.

You really think that's doable for a kid in Algebra I?

All of the targets are doable?  You really think a kid in Algebra I has any chance at all to solve #4?  
https://www.mathcounts.org/sites/default/files/2023%20State%20Competition%20Target%20Round.pdf

Any kids in Algebra I who can self-study and glean enough from their school club to solve problems like this are truly remarkable kids.  It's far outside of the norm.[/quote]

#28 is clever algebraic manipulation. Definitely Algebra 1. I solved the main idea in my head, but needed to write notes to finish the calculation. It's complicated and hard,but doesn't require any knowledge beyond Algebra 1. Algebra 2 won't help at all. An average non-mathlete AP Calculus student would not be able to solve it. What will help is Mathcounts Trainer to see similar problems, or the Art of Problem Solving book.

#4 is definition and area of a circle, Pythagorean theorem, and angle dissection with congruent triangles angles . It's geometry, but the simple parts. AMC 10 and AIME have much harder Geometry. Public schools don't teqch it until Geometry class because the public middle schools stupidly separate algebra from geometry across separate years. (RSM Geometry is merged with PreAlg/Alg/Alg2 over 3 years). Beast Academy and AoPS free Prealgebra website teach this level, as does amctrivial.com. Again, the problem is complicated and hard, but not advanced. You don't need more theory to solve these problems, you need creativity or exposure to similar problems.
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