AMC 8 (Middle School)

28 core topics + 31 prerequisite topics taught as needed · approximately 15 hours of instruction including spaced review · premium unlock $24.99

How the course runs

An adaptive diagnostic (up to 40 questions) places the student on the course's knowledge graph — topics already known are credited, and instruction begins exactly at the learning frontier. Every topic is taught with a worked-example lesson and auto-graded practice; a topic is mastered at 75%+ and then maintained through spaced reviews on an expanding schedule. A cumulative quiz follows every 6 lessons. Prerequisite gaps below the course are detected and taught rather than skipped, so completion certifies the whole tower, not just the top.

Core curriculum

Geometry · 14 topics

Angle Relationships [E]	Vertical, complementary, and supplementary angle pairs.
Parallel Lines & Transversals [E]	Angle pairs formed when a transversal crosses parallel lines.
Triangle Angle Sum [E]	The three angles of a triangle always add to 180°.
The Pythagorean Theorem [M]	In a right triangle, a² + b² = c².
Distance & Midpoint [M]	Measuring segments in the coordinate plane.
Similar Triangles [M]	Same shape, different size: corresponding sides are proportional.
Perimeter & Area [E]	Measuring around and inside basic shapes.
Circles: Area & Circumference [M]	C = 2πr and A = πr².
Composite Areas [H]	Adding and subtracting simple shapes to measure a complicated one.
Volume: Prisms & Cylinders [M]	Volume = base area × height.
Volume: Cones, Pyramids & Spheres [M]	Pointed solids hold one third of the matching prism; spheres use 4/3 πr³.
Surface Area [M]	The total area of all the faces of a solid.
Special Right Triangles [H]	The 45-45-90 and 30-60-90 side ratios.
Arc Length & Sector Area [H]	A central angle takes the same fraction of the circumference and the area.

Math Olympiad: MOEMS & AMC 8 · 14 topics

Modular Arithmetic [M]	Working with remainders directly.
Counting Divisors [M]	Divisor count from the prime factorization.
GCD & LCM Relationships [M]	The identity gcd(a,b) · lcm(a,b) = a · b.
Digit Problems [M]	Reasoning about the digits of a number.
Units Digit of Powers [M]	Combine last-digit cycles, then add.
Permutations [M]	Ordered arrangements.
Combinations [M]	Unordered selections: n choose k.
The Pigeonhole Principle [M]	Guaranteeing a repeat.
Complementary Counting [M]	Count the opposite, then subtract.
Counting & Probability [H]	Favorable outcomes over total outcomes.
Vieta's Formulas [H]	Relating roots to coefficients without solving.
Telescoping Sums [H]	A sum that collapses to its endpoints.
Sums, Parity & Invariants [M]	Elegant closed forms and even/odd reasoning.
Recursion & Sequences [M]	Each term built from earlier ones.

Prerequisite material — taught automatically when the diagnostic finds gaps

Arithmetic Foundations · 8 topics

Adding & Subtracting Whole Numbers	Multi-digit addition and subtraction.
Multiplication	Multiplying whole numbers.
Division	Dividing whole numbers.
Order of Operations	Parentheses first, then multiplication/division, then addition/subtraction.
Negative Numbers: Adding & Subtracting	Working with numbers below zero on the number line.
Negative Numbers: Multiplying & Dividing	Sign rules for products and quotients.
Exponents	Repeated multiplication in shorthand.
Square Roots	Undoing a square.

Fractions · 6 topics

Equivalent Fractions	Different fractions can name the same amount.
Simplifying Fractions	Reducing a fraction to lowest terms.
Adding Fractions (Like Denominators)	Same-denominator addition.
Adding Fractions (Unlike Denominators)	Rewrite over a common denominator first.
Multiplying Fractions	Multiply straight across.
Dividing Fractions	Multiply by the reciprocal.

Decimals, Percents & Ratios · 1 topics

Ratios & Proportions

Two quantities that scale together.

Expressions & Equations · 4 topics

Evaluating Expressions	Substituting a value for a variable.
Combining Like Terms	Adding the coefficients of matching variable parts.
The Distributive Property	Multiplying across a sum.
One-Step Equations	Undoing a single operation.

Linear Functions · 1 topics

The Coordinate Plane

Locating points with (x, y) pairs.

Quadratics & Polynomials · 8 topics

Adding & Subtracting Polynomials	Combining polynomials by collecting like terms.
Multiplying Binomials (FOIL)	Expanding products of binomials.
Factoring Out the GCF	Undoing the distributive property.
Factoring Trinomials	Reversing FOIL: finding two numbers that multiply to c and add to b.
Special Factoring Patterns	Difference of squares and perfect-square trinomials.
Solving x² = k	Taking square roots of both sides — remembering ±.
Completing the Square	Turning any quadratic into a perfect square plus a constant.
The Quadratic Formula	x = (−b ± √(b² − 4ac)) / 2a solves any quadratic.

Radicals & Exponentials · 1 topics

Simplifying Radicals

Pulling perfect-square factors out of a square root.

Math Kangaroo: Benjamin & Cadet · 2 topics

Systematic Counting	Counting without missing or double-counting.
Number Patterns	Finding the rule behind a sequence.

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