9 core topics + 91 prerequisite topics taught as needed · approximately 26 hours of instruction including spaced review · premium unlock $39.99
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.
| Symmetric Systems [H] | Never solve for x and y — combine the symmetric pieces. |
| Polynomial Root Play [H] | Vieta for cubics: coefficients are symmetric functions of roots. |
| Counting Probability [H] | Count with combinations; flip to the complement. |
| AMC Number Theory [H] | Divisor counts from exponents; lcm from gcd. |
| AMC Geometry [H] | Areas scale with the square; coordinates give areas for free. |
| Logs & Exponents on the AMC [H] | Move exponents through logs; match bases. |
| Telescoping & Series [H] | Collapse the sum before computing it. |
| Functional Equations [H] | Plug in smart values; iterate carefully. |
| Complex Numbers on the AMC [H] | Powers of i cycle; moduli multiply. |
| 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. |
| 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. |
| Fractions ↔ Decimals | Converting between the two notations. |
| Percent of a Number | Percent means per hundred. |
| Percent Increase & Decrease | Applying a percent change to a quantity. |
| Ratios & Proportions | Two quantities that scale together. |
| 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. |
| Two-Step Equations | Undo addition/subtraction first, then multiplication. |
| Multi-Step Equations | Equations needing distribution or variables on both sides. |
| Linear Inequalities | Solving with <, >, ≤, ≥. |
| The Coordinate Plane | Locating points with (x, y) pairs. |
| Slope of a Line | Rise over run between two points. |
| Slope-Intercept Form | y = mx + b describes a whole line. |
| Systems of Equations (Substitution) | Two equations, two unknowns. |
| 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 Quadratics by Factoring | Zero-product property: if a·b = 0 then a = 0 or b = 0. |
| 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. |
| Product Rule for Exponents | Multiplying powers of the same base adds the exponents. |
| Quotient & Power Rules | Dividing powers subtracts exponents; a power of a power multiplies them. |
| Zero & Negative Exponents | Anything (nonzero) to the 0 power is 1; a negative exponent flips to a reciprocal. |
| Simplifying Radicals | Pulling perfect-square factors out of a square root. |
| Rational Exponents | Fractional exponents are roots: x^(p/q) is the q-th root of x, raised to the p. |
| Exponential Growth & Decay | Quantities that multiply by the same factor each time step: y = a·bᵗ. |
| Angle Relationships | Vertical, complementary, and supplementary angle pairs. |
| Parallel Lines & Transversals | Angle pairs formed when a transversal crosses parallel lines. |
| Triangle Angle Sum | The three angles of a triangle always add to 180°. |
| The Pythagorean Theorem | In a right triangle, a² + b² = c². |
| Similar Triangles | Same shape, different size: corresponding sides are proportional. |
| Perimeter & Area | Measuring around and inside basic shapes. |
| Circles: Area & Circumference | C = 2πr and A = πr². |
| Special Right Triangles | The 45-45-90 and 30-60-90 side ratios. |
| Function Notation & Evaluation | Reading f(x) notation and plugging in inputs. |
| Function Composition | Feeding one function's output into another: f(g(x)). |
| Piecewise Functions | Functions defined by different rules on different intervals. |
| Nonlinear Systems | Where a line meets a parabola: set the two formulas equal. |
| Complex Numbers | The imaginary unit i = √(−1) and numbers of the form a + bi. |
| Operations with Complex Numbers | Multiplying complex numbers with FOIL and i² = −1. |
| Polynomial Division | Dividing a polynomial by (x − a) with long or synthetic division. |
| Remainder & Factor Theorems | The remainder when p(x) is divided by (x − a) is simply p(a). |
| Zeros of Polynomials | Finding all the roots of a cubic by factoring it down. |
| End Behavior of Polynomials | Far from the origin, only the leading term matters. |
| Simplifying Rational Expressions | Factor top and bottom, then cancel the common factor. |
| Logarithms | log_b(x) asks: to what power must b be raised to get x? |
| Properties of Logarithms | Logs turn products into sums, quotients into differences, powers into multiples. |
| Exponential & Log Equations | Matching bases and rewriting between exponential and log form. |
| Arithmetic Sequences | Sequences that grow by a constant difference each step. |
| Geometric Sequences | Sequences that grow by a constant ratio each step. |
| Degrees & Radians | Two ways to measure the same angle: 180° equals π radians. |
| The Unit Circle | Exact sine, cosine, and tangent values at the special angles. |
| Asymptotes of Rational Functions | Where rational functions blow up and where they level off. |
| Limits: Graphical & Numerical | What value a function approaches — which need not be the value it takes. |
| One-Sided Limits | Approaching from the left or right — and when the two disagree. |
| Infinite Limits & Vertical Asymptotes | Where a function blows up: reading the sign of an infinite limit. |
| Limits at Infinity | End behavior of rational functions: compare the degrees. |
| Convergence of Sequences (BC) | A sequence converges if aₙ approaches a limit. |
| Geometric Series (BC) | Σarⁿ = a/(1−r) when |r| < 1. |
| Modular Arithmetic | Working with remainders directly. |
| Counting Divisors | Divisor count from the prime factorization. |
| Permutations | Ordered arrangements. |
| Combinations | Unordered selections: n choose k. |
| Counting & Probability | Favorable outcomes over total outcomes. |
| Vieta's Formulas | Relating roots to coefficients without solving. |
| Telescoping Sums | A sum that collapses to its endpoints. |
| Complex Arithmetic | Multiply out, use i² = −1. |
| Polar Form & Euler's Formula | z = re^{iθ}: modulus and angle instead of real and imaginary parts. |
| Quadratic Tricks | Complete the square; work with sums and products of roots. |
| Angle Chasing | Push known angles through triangles and polygons. |
| Grid Paths & Selections | Shortest paths are just choices in disguise. |
| Divisibility Duels | Factor counts, trailing zeros, digit sums. |
| Logarithm Puzzles | Chain rule for logs: bases cancel. |