The entire AP Calculus BC course, rebuilt around visuals you can actually move — drag a curve, sweep an area, watch a series close in on its limit. Each idea is something you see and do, not just a formula to memorize.
Each is a complete guide — interactive lessons, a full exam-style practice set, and a one-page cheat sheet.
What a limit is, computing limits algebraically, the Squeeze Theorem, continuity and its failures, and asymptotes with the Intermediate Value Theorem — the foundation everything else is built on.
The derivative as the limit of a difference quotient, differentiability vs. continuity, the power and basic rules, derivatives of the key functions, and the product & quotient rules — where the derivative arrives and becomes a toolkit.
The chain rule, implicit differentiation, derivatives of inverse & inverse-trig functions, selecting the right procedure, and higher-order derivatives — where differentiation becomes reading structure.
Interpreting derivatives as rates in context, straight‑line motion, related rates, linear approximation, and L’Hôpital’s rule — the derivative put to work as a rate of change.
The Mean Value & Extreme Value Theorems, the first- and second-derivative tests, connecting f to f′ and f″, and optimization — reading a curve from its slope and bend, and pinning down the exact best.
Riemann sums, the Fundamental Theorem, the antiderivative toolkit, parts & partial fractions, and improper integrals — accumulation built from rectangles up.
Slope fields, Euler’s method, separable equations, and exponential & logistic models — reading an equation of change four different ways.
Area between curves, volumes by cross‑section and revolution, and arc length — integration put to work on real shapes.
Curves driven by a parameter — motion in the plane and a whole second coordinate system. The showcase for manipulable visuals.
When do infinitely many terms add to something finite? Convergence tests, power series, and Taylor approximations — made tangible.
All ten College Board units, in order — now all ten are live, every one built with the same visual, manipulable treatment.
This started as my own way through BC — the formulas were easy to memorize and impossible to picture. So I rebuilt each idea into something you can move, take apart, and actually see. If it helps one more person finally get it, that’s the whole point.
Every lesson is built around a visual you can actually move. Drag the slider — watch a plain polynomial bend, one term at a time, until it becomes the sine curve. That moment is the lesson; a textbook can only describe it.
Drag the slider, move the point, change the bounds. The visuals respond in real time, so you build intuition by playing — not by staring at a fixed diagram.
Every lesson explains where a formula comes from and which one to reach for — then names the exact mistake each tempting wrong answer represents.
Each unit ends with authentic AP-style multiple choice and free response, plus a printable cheat sheet that pairs every formula with the “which setup?” logic.