31 core topics
+ 16 prerequisite topics taught
as needed · approximately 12 hours of instruction
including spaced review
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.
| Evaluating Expressions
[M] |
Substituting a value for a variable. |
| Combining Like Terms
[M] |
Adding the coefficients of matching variable parts. |
| The Distributive Property
[M] |
Multiplying across a sum. |
| One-Step Equations
[M] |
Undoing a single operation. |
| Two-Step Equations
[M] |
Undo addition/subtraction first, then multiplication. |
| Multi-Step Equations
[H] |
Equations needing distribution or variables on both sides. |
| Linear Inequalities
[M] |
Solving with <, >, ≤, ≥. |
| The Coordinate Plane
[M] |
Locating points with (x, y) pairs. |
| Slope of a Line
[M] |
Rise over run between two points. |
| Slope-Intercept Form
[M] |
y = mx + b describes a whole line. |
| Finding a Line from Points
[H] |
Reconstructing y = mx + b from data. |
| Systems of Equations (Substitution)
[H] |
Two equations, two unknowns. |
| Elimination: A First Look
[H] |
Add or subtract equations so one variable cancels. |
| Systems: Word Problems
[H] |
Translating two facts into two equations. |
| Absolute Value Equations
[H] |
Distance equations have two answers. |
| Arithmetic Sequences
[H] |
Add the same amount each step. |
| Geometric Sequences
[H] |
Multiply by the same ratio each step. |
| 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. |