Advanced Topics
Logs, trig, inequalities and complex numbers for AMC 12 and AIME.
- 39Floor and Ceiling FunctionsreadyRound down, round up, keep what is left: turn floors into inequalities, split x into integer and fractional parts, and count where a line meets a staircase.
0% - 40InequalitiesreadySquares are never negative, averages beat geometric means, and dot products never beat lengths: three inequalities that find every maximum and minimum on the AMC.
0% - 41LogarithmsreadyLogarithms turn powers into multiplication and products into sums. Learn the definition, the log rules and the base change formula that unlock AMC 12 and AIME log problems (this topic is mainly relevant for the AMC 12).
0% - 42Algebraic TrigonometryreadyMainly for the AMC 12 (and a shortcut on some AMC 10 problems): the six trig ratios, the unit circle, the big identities, and counting solutions with graphs.
0% - 43Geometric TrigonometryreadyThree formulas turn any triangle into numbers: half ab sin C for area, the Law of Sines with its circumradius 2R, and the Law of Cosines, the Pythagorean Theorem with a correction term.
0% - 44Complex NumbersreadyPut a second axis through the number line and arithmetic turns into geometry: multiplying rotates, De Moivre powers spiral, and roots of unity make regular polygons.
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