AMC 10/12 and AIME preparation.
Polynomial roots, Vieta's formulas, and sequences.
Factorization tricks, rational expressions, and complex fractions.
Permutations, PIE, and expected value.
Roots of polynomials, factor theorem, and symmetric sums.
Triangle centers, similar figures, and circle theorems.
Arithmetic/geometric progressions, telescoping sums, and infinite series.
Log rules, radical conjugates, and exponential equations.
Domain/range, inverse functions, and basic functional equations.
De Moivre's theorem, complex plane geometry, and roots of unity.
AM-GM, Cauchy-Schwarz, and optimization techniques.
Permutations, combinations, and constructive counting.
Venn diagrams, derangements, and overlapping sets.
Distributing identical/distinct objects into urns.
Linear recurrences, characteristic equations, and formal series.
Geometric probability, conditional probability, and expected states.
Similar figures, Law of Sines/Cosines, and triangle centers.
Radical axes, inscribed angles, and tangent properties.
Cyclic quadrilaterals, Ptolemy's theorem, and regular polygons.
Shoelace formula, distance to lines, and conic sections.
Surface area, cross-sections, and inscribed spheres.
Barycentric coordinates and center of mass techniques for geometry.
Prime factorization, GCD/LCM, and Euclidean algorithm.
Congruences, remainder rules, and modular inverses.
Euler's totient function, Fermat's Little Theorem, and Wilson's theorem.
Finding integer solutions to linear and non-linear equations.
Base conversion, digit sums, and palindromic numbers.
Tau (divisors), Sigma (sum of divisors), and Phi functions.