Intermediate (AMC 10-12)

Strengthen problem-solving depth with multi-step AIME-style techniques, including functional equations, inequalities, advanced counting, and richer geometry.
This stage is about speed plus rigor: solve accurately under time pressure.

This section is currently under development. The content you see here is filler for now.

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Advanced Algebra

0/11

Quadratics, systems, and polynomial identities for AMC 10/12.

Advanced Algebra

Quadratics, systems, and polynomial identities for AMC 10/12.
Updated: 5 days ago

Higher-Power Factorizations

Difference of powers and odd-power sums.
Updated: 5 days ago

Sophie Germain Identity

Factoring

x^4 + 4y^4

using a hidden difference of squares.
Updated: 5 days ago

Newton's Sums

Recurrences that compute power sums from coefficients.
Updated: 5 days ago

Symmetric Polynomials

symmetric polynomials constructions, even symmetric polynomials, and their application.
Updated: 5 days ago

Symmetric Cubic Identity

The identity behind

x^3+y^3+z^3-3xyz

.
Updated: 5 days ago

Sum Formulas for Powers

Common power sums used in algebra and counting.
Updated: 5 days ago

Functional Equations

0/3

Standard substitutions and symmetry-based approaches.

Functional Equations (Intro)

Substitution and pattern-spotting in simple functional equations.
Updated: 5 days ago

Counting & Casework

0/2

Multi-step counting with careful case analysis.

Advanced Counting and Casework

Stars and bars, inclusion-exclusion, and structured casework.
Updated: 5 days ago

Probability

0/2

Conditional probability, geometric probability, and expected value.

Probability (Intermediate)

Conditional probability, expected value, and multi-stage experiments.
Updated: 5 days ago

Geometric Probability

A tool to deal with infinite probability problems using geometry
Updated: 5 days ago

Number Theory

0/2

Modular arithmetic, CRT, and divisibility techniques.

Modular Arithmetic

A powerful tool useful in solving problems involving remainders and divisibility.
Updated: 5 days ago

Number Theory (Intermediate)

Modular arithmetic, Diophantine basics, and residues for AMC 12.
Updated: 5 days ago

Chinese Remainder Theorem

Solving basic systems of linear congruences with pairwise coprime moduli and computing modular inverses.
Updated: 5 days ago

Euclidean Geometry

0/2

Circle theorems, power of a point, and cyclic quadrilaterals.

Euclidean Geometry

Power of a Point

Secants, tangents, and equal power products.
Updated: 5 days ago

Cyclic Quadrilaterals

Opposite angles and Ptolemy's theorem.
Updated: 5 days ago

Tangent Lines

Tangent-radius perpendicularity and equal tangents.
Updated: 5 days ago

Tangent Circles

External and internal tangency distances.
Updated: 5 days ago

Arc and Chord Relations

Chord length and arc length from central angle.
Updated: 5 days ago

Coordinate Geometry

0/2

Analytic methods, Shoelace formula, and coordinate-based proofs.

Coordinate Geometry

Slopes, distance, midpoints, and analytic geometry setups.
Updated: 5 days ago

Shoelace Formula

Fast area computation for polygons with coordinates.
Updated: 5 days ago

Inequalities

0/2

Algebraic and geometric inequality techniques for AMC/AIME.

Inequalities

AM-GM, Cauchy, and algebraic bounding for AMC 10/12.
Updated: 5 days ago

Sequences & Series

0/2

Convergence, recursive formulas, and summation methods.

Sequences and Series

Arithmetic and geometric sequences, recursion, and telescoping sums.
Updated: 5 days ago

Trigonometry

Unit circle, identities, and trig equations for contest math.

Unit Circle and Angle Measurement

Degrees vs. radians, special angles, and unit circle values.
Updated: 5 days ago

Fundamental Trig Identities

Pythagorean, even-odd, and cofunction identities.
Updated: 5 days ago

Angle Addition and Double/Half Angles

Sum, difference, double-angle, and half-angle formulas.
Updated: 5 days ago

Product-to-Sum and Sum-to-Product

Convert products into sums and vice versa.
Updated: 5 days ago

Trig Equations and Quadratics

Solve basic and quadratic trig equations in a full cycle.
Updated: 5 days ago

Inverse Trig Functions

Principal values and composition traps.
Updated: 5 days ago

Trig in Triangles

Law of sines, law of cosines, and area formulas.
Updated: 5 days ago

Trig Contest Patterns

Hidden special angles and auxiliary angle tricks.
Updated: 5 days ago

Complex Numbers

Complex arithmetic, polar form, roots of unity, and geometry.

Complex Basics

Definitions,

i

powers, the rectangular form, algebra with linear equations, and conjugates.
Updated: 5 days ago

The Complex Plane

Magnitude, distance, and loci in the plane.
Updated: 5 days ago

Polar Form and De Moivre

Use

re^{i\theta}

for powers and products.
Updated: 5 days ago

Geometry with Complex Numbers

Rotations, distances, and polygon criteria.
Updated: 5 days ago

Roots of Unity

Geometry and sums of

n

th roots.
Updated: 5 days ago

Roots of Unity (Advanced)

Cyclotomic facts and power-sum filters.
Updated: 5 days ago

Complex Numbers and Trig

Use

e^{i\theta}

to simplify trig products.
Updated: 5 days ago

Geometry Extensions

Regular polygons and three-dimensional geometry.

Regular Polygons

Angle and area formulas for regular

n

-gons.
Updated: 5 days ago

3D Geometry Essentials

Volumes of pyramids and tetrahedra.
Updated: 5 days ago

Uncategorized

Auto-discovered modules not yet placed in a syllabus chapter.

Vieta Root Jumping

Vieta jumping or root flipping, application to problems, and proof
Updated: 5 days ago