Mistake Master
All 8 units of the AP Calculus AB course framework, with exam weighting and topic counts. All eight units are on the AP Calculus AB exam. Six topics that live inside units 6, 7, and 8 are BC only and are not counted here: 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.
Total units
8
Total topics
81
Heaviest
Units 5 and 6
On the exam
Units 1-8
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.
Unit pages are being built one unit at a time. Each one ships with a lesson, a ten-item diagnostic, targeted drills, and a cumulative exam for every topic in the unit. Cards light up here as their unit goes live.