How hard are the AMC competitions?

Harder than school math tests by design. The MAA says its problems are more complex than those in routine math courses but connected to school standards, so a strong student can reach them with practice.

AMC 8	25 problems in 40 minutes, grade 8 and below
AMC 10	25 problems in 75 minutes, grade 10 and below
AMC 12	25 problems in 75 minutes, grade 12 and below
Calculators	Not allowed on any of them

Why the problems feel hard

Each one needs an idea, not just a method: a clever count, a hidden right triangle, a pattern in the last digits.
There is no calculator, so the arithmetic has to be organized.
Five answer choices are given, and the wrong ones are usually the results of common slips.

AMC 8, AMC 10 or AMC 12

The AMC 8 covers middle school topics. The AMC 10 covers elementary algebra, basic geometry, area and volume formulas, elementary number theory and elementary probability, and leaves out trigonometry, advanced algebra and advanced geometry. The AMC 12 covers the whole high school curriculum, including trigonometry, advanced algebra and advanced geometry, but no calculus. A student cannot take the AMC 10 and the AMC 12 on the same day.

How to get better at them

Work by area: arithmetic and proportional reasoning, algebra, geometry, number theory, and counting and probability. Learn the handful of ideas that recur in each, then sit full timed practice competitions so the pace feels normal by competition day.

Try 3 problems

Problem 1AMC 8

The product $1 \cdot 2 \cdot 3 \cdots 40$ of the integers from $1$ to $40$ is written out in full. How many zeros are at the end of this number?

Problem 2AMC 10

For how many integers $k$ does the equation $x^2 + kx + 36$ $= 0$ have two different integer solutions?

Problem 3AMC 12

A circle has center $O$ and radius $5$ . Point $P$ is $13$ units from $O$ . The two lines through $P$ tangent to the circle touch it at $A$ and $B$ . What is the length of chord $AB$ ?

Next step

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The MAA's American Mathematics Competitions page

Questions people ask

What is the difference between the AMC 10 and the AMC 12?

The AMC 12 covers more topics, including trigonometry and advanced algebra, which the AMC 10 leaves out. Both have 25 problems in 75 minutes.

Does the AMC use calculus?

No. The MAA says calculus is excluded from the AMC 12, and the AMC 8 and AMC 10 stop well before it.