AMC 10 & 12 — prep map (unofficial)

The American Mathematics Competitions AMC 10 and AMC 12 are multiple-choice contests that feed into AIME qualification for high scorers. Official rules, dates, and problems come from the Mathematical Association of America (MAA) — use maa.org and official AMC resources for the real thing.

This page is not affiliated with the MAA. It is an unofficial topic map and a bridge to what you practice in First Principles (graphs, slopes, function behavior) — not a substitute for past papers or a coach.

AMC 10 vs AMC 12 (high level)

	AMC 10	AMC 12
Typical audience	Grades ≤ 10 (eligibility rules on MAA site)	Grades ≤ 12
Difficulty / ceiling	Strong middle/high-school contest	Harder tail; more “late-precalculus” flavor
Calculus on the official syllabus?	No — problems are intended without calculus	No — same intent; calculus is never required
Still useful to know?	Graph intuition (monotonicity, max/min mood) parallels thinking like (f’) even when you solve with algebra	Logs, trig, exponentials show up more; a calculus course can be a shortcut on a few items after you know the contest baseline

Takeaway: prepare with official AMC topics first; treat calculus as enrichment and intuition — see also our Competition math stage ((\ln), concavity) and Math concepts index.

Topic buckets that show up constantly

Algebra & functions

Linear / quadratic / polynomial fluency; factoring; sensible substitution.
Exponentials and logarithms (especially AMC 12): laws of logs, solving (a^x = b), (\log) equations with domain checks.
Functional equations “light” — plug values, hunt symmetry, periodicity mood.
Piecewise and absolute value — case splits (mirrors kinks you see on graphs).

Geometry & counting (not the game’s main focus)

Triangles, circles, 3D; similarity; coordinate bash when allowed.
Combinatorics (count carefully, bijections, PIE mood); probability with clean sample spaces.

Number theory

Divisibility, gcd/lcm, modular arithmetic, Fermat/Euler mood for small cases — not the core of First Principles, but standard AMC bread.

Where calculus thinking still helps (unofficial)

Even when problems are designed for elementary methods:

“Where is the expression smallest/largest?” — matches optimization instincts (vertex, boundary, AM–GM).
Increasing / decreasing — matches sign of slope without naming a derivative.
Concave / convex mood — links to (\ln), tangents/chords, and our Competition math in-game stage.
Area / Riemann intuition from area / Riemann levels supports discrete → continuous metaphors (sums vs integrals) when you study series bounds later.

Game levels that echo AMC-friendly graphs (no exam claims)

Use the game for visual slope / domain / log / trig / absolute value gut checks — not for timed AMC drill:

Absolute Path, parabola / cubic stages — shape & extrema.
Trig (sine, cosine, tan window) — identities show up more on paper, but graphs build fluency.
(\ln) / (\sqrt{\cdot}) BC-style levels — domain discipline like contest log problems.
Competition math: ln, concavity & bound tricks — explicit contest lens.

Study pairing (official-first)

MAA competition hub + recent AMC 10/12 papers (timed practice).
Error log by bucket: logs, geo, NT, combo — not only “graph stages.”
AIME path: if you qualify, add longer algebra and careful arithmetic training; First Principles stays a calculus graph supplement.

Competition math — contest style, (\ln) stage, bounds & concavity.
AP Calculus BC — prep — formal calculus syllabus map (overlaps skills, not AMC format).
Math concepts & snippets — in-game curriculum glossary.

Unofficial · not affiliated with the MAA · First Principles is proprietary.