AMC 10
Competition
AMC 10 preparation: algebra, counting, number theory and geometry at contest depth, with full-length practice contests.
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Circles and Lines
Unit 1 · Circles & Lines
0 of 8 units complete
- 1Unit 1Circles & Lines5 parts · about 13 min
Circles and Lines
Coordinate geometry the AMC 10 way: the distance from a point to a line in one formula, the circle through three points, and the power of a point, which turns every chord, secant and tangent problem into one multiplication.
- 2Unit 2Algebra & Polynomials5 parts · about 12 min
Polynomials and Vieta
Know the roots without finding them. Read sums and products of roots straight off the coefficients, build symmetric expressions like x² + y² from x + y and xy, and solve symmetric systems in one move.
- 3Unit 3Counting: Inclusion–Exclusion & Stars and Bars5 parts · about 11 min
Inclusion–Exclusion and Stars and Bars
Two counting engines for the AMC 10. Inclusion–exclusion counts unions without double counting; stars and bars counts ways to share identical things. Then combine them to handle upper limits, and count arrangements with repeats.
- 4Unit 4Number Theory: Modular Arithmetic5 parts · about 12 min
Modular Arithmetic
Remainders are the AMC's secret weapon. Reduce huge powers mod n, glue remainders together with the Chinese Remainder Theorem to get last two digits, and prove equations impossible because the remainders never match.
- 5Unit 5Geometry: Power of a Point & Mass Points5 parts · about 10 min
Power of a Point and Mass Points
Two AMC 10 power tools: mass points turn ratio problems into seesaw balancing, and Ceva's theorem tells you when three cevians meet. Plus similar triangles for areas and the shoelace formula for any polygon on a grid.
- 6Unit 6Algebraic Weapons5 parts · about 11 min
Algebraic Weapons
The identities, inequalities and radical tricks that crack AMC algebra. Factor sums of cubes and Sophie Germain's identity, find minimums with AM–GM, and simplify nested square roots and conjugates.
- 7Unit 7Where the Formulas Come From5 parts · about 12 min
Where the Formulas Come From
Derive the quadratic formula by completing the square, the series sums by pairing and shifting, the power of a point from similar triangles, and AM–GM from the fact that squares are never negative. Rebuild them in the exam if your memory slips.
- 8Unit 8Identities and Techniques, Proved5 parts · about 12 min
Proofs by Counting
The cleanest proofs in combinatorics count one thing in two ways. Prove the handshake lemma, the hockey stick, the sum of squares, Vandermonde and the committee–chair identity, and see why inclusion–exclusion's signs alternate.