Mistake Master
All 10 units of the AP Calculus BC course framework, with exam weighting and topic counts. Units 1 through 8 are shared with AP Calculus AB. Units 9 and 10 are BC only, as are six topics inside units 6, 7, and 8: integration by parts, linear partial fractions, improper integrals, Euler's method, logistic models, and arc length. Weightings are from the College Board Course and Exam Description (see also the reference sheet).
What a limit is and how to read one from a graph, a table, or algebra. The Squeeze Theorem, the three kinds of discontinuity, continuity at a point and over an interval, infinite limits and asymptotes, and the Intermediate Value Theorem.
Average versus instantaneous rate of change, the derivative as a limit of difference quotients, when a derivative fails to exist, and the power, product, and quotient rules plus the basic trigonometric, exponential, and logarithmic derivatives.
The chain rule, implicit differentiation, derivatives of inverse and inverse trigonometric functions, choosing a procedure when several could work, and higher-order derivatives.
Interpreting a derivative in context with correct units, straight-line motion including the difference between speed and velocity, related rates, linear approximation, and L'Hospital's Rule.
The Mean Value and Extreme Value Theorems, increasing and decreasing intervals, the first and second derivative tests, concavity and points of inflection, reading f, f prime, and f double prime against each other, and optimization.
Riemann sums and the definite integral, accumulation functions, both parts of the Fundamental Theorem of Calculus, antiderivatives, and u-substitution. BC adds integration by parts, linear partial fractions, and improper integrals.
Modeling with differential equations, slope fields, separation of variables, general versus particular solutions, and exponential models. BC adds Euler's method and logistic growth.
Average value of a function, position from velocity, accumulation in applied contexts, area between curves, volumes by cross section, and solids of revolution by discs and washers. BC adds arc length.
Differentiating and integrating parametric and vector-valued functions, motion in the plane, parametric arc length, derivatives in polar form, and the area bounded by one or two polar curves.
Convergence and divergence, geometric and p-series, the nth term, integral, comparison, alternating series, and ratio tests, absolute versus conditional convergence, error bounds, and Taylor and Maclaurin series with radius and interval of convergence.
Everything above, mixed together. Work the open-ended challenge bank, sit a 45-question run that matches the length of the real BC multiple-choice section and mirrors its unit weighting — series and parametric/polar carry the BC-specific weight, exactly as they do on exam day — or blast all ten units' misconceptions in the arcade. The challenge bank runs the full 600 problems, units 1 through 10.
All of it is live: every unit above carries a topic page, a full lesson, a ten-scenario skill check, a ten-item diagnostic, targeted drills keyed to the misconceptions that diagnostic finds, and a cumulative unit exam.