AMC 12
Competition
AMC 12 preparation: everything in AMC 10 plus trigonometry, logarithms, complex numbers and harder geometry.
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Circles, Lines and Conics
Unit 1 · Circles & Lines
0 of 7 units complete
- 1Unit 1Circles & Lines5 parts · about 12 min
Circles, Lines and Conics
The AMC 12 analytic geometry kit: distances to lines, angle bisectors as equal distances, power of a point for secants and tangents, where circles meet parabolas, and the focus properties that define ellipses and parabolas.
- 2Unit 2Trigonometry & Complex Numbers5 parts · about 12 min
Trigonometry and Complex Numbers
The identities that turn AMC 12 trig into arithmetic, complex numbers as points you can rotate and stretch, and De Moivre's theorem with roots of unity, where the sums cancel to zero like magic.
- 3Unit 3Advanced Algebra5 parts · about 12 min
Advanced Algebra
Logarithms that collapse, inequalities that pin down maximums, and functional equations solved by plugging in the right values. Three favourite AMC 12 themes, each with a trick that makes it quick.
- 4Unit 4Sequences, Series & Recursion5 parts · about 11 min
Sequences, Series and Recursion
Standard sums you should know cold, telescoping series that collapse to two terms, infinite geometric series, and recursions that secretly repeat, so the 2026th term is just the 2nd in disguise.
- 5Unit 5Logs & Complex Numbers5 parts · about 10 min
Logs and Complex Numbers at Work
Two toolkits that make "impossible" AMC 12 problems routine: logarithms that unwrap nested expressions and count digits, and roots of unity that pick out every third binomial coefficient in one line.
- 6Unit 6Proofs and Derivations5 parts · about 12 min
Proofs and Derivations
Rebuild the AMC 12 formulas from scratch: the angle-addition identities from a distance on the unit circle, the binomial theorem by counting, the log rules from exponent rules, and the law of cosines from coordinates.
- 7Unit 7Identities 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.