AP Calculus BC Unit Tests
Pick a unit to drill it head-on. Each unit has 4 different test variations so you can keep retaking until you master it.
Unit 1: Limits and Continuity
Limits from graphs, tables, and algebra; squeeze theorem; asymptotes; continuity and the IVT.
12 questions · ~18 min
Unit 2: Differentiation: Definition and Fundamental Properties
The limit definition, differentiability, and the power, product, quotient, trig, exponential, and log rules.
12 questions · ~18 min
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
The chain rule, implicit differentiation, inverse and inverse trig derivatives, and higher-order derivatives.
12 questions · ~18 min
Unit 4: Contextual Applications of Differentiation
Derivatives in context, straight-line motion, related rates, local linearity, and L’Hospital’s rule.
12 questions · ~18 min
Unit 5: Analytical Applications of Differentiation
The MVT and EVT, increasing and decreasing intervals, extrema, concavity, curve sketching, and optimization.
12 questions · ~18 min
Unit 6: Integration and Accumulation of Change
Riemann sums, the FTC, u-substitution, integration by parts, partial fractions, and improper integrals.
12 questions · ~18 min
Unit 7: Differential Equations
Slope fields, Euler’s method, separation of variables, exponential models, and logistic growth.
12 questions · ~18 min
Unit 8: Applications of Integration
Average value, motion, area between curves, volumes by cross sections, discs, and washers, and arc length.
12 questions · ~18 min
Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions
Derivatives and integrals of parametric, polar, and vector-valued functions; motion in the plane; polar area.
12 questions · ~18 min
Unit 10: Infinite Sequences and Series
Convergence tests, alternating series, power series, Taylor and Maclaurin series, and error bounds.
12 questions · ~18 min
How unit tests work
- Focused on a single AP unit, between a single-topic quiz and the full diagnostic.
- 4 variations per unit — pick a fresh variation any time you retake.
- Roughly 90 seconds per question — the same pacing as the AP exam.
- You'll get a unit-level score, recommended topics to review, and a question-by-question explanation.
About the AP Calculus BC exam
AP Calculus BC includes everything in Calculus AB and then extends it with a substantial body of additional material, making it equivalent to roughly two semesters of college calculus. Beyond AB's limits, derivatives, and integrals, BC adds advanced integration techniques such as integration by parts and partial fractions, improper integrals, logistic and other differential equations, parametric and polar functions, vector-valued functions, and—most distinctively—infinite sequences and series. The series unit is what truly separates BC from AB: students must master convergence tests (nth-term, integral, comparison, ratio, alternating series), Taylor and Maclaurin series, power series and intervals of convergence, and error bounds via the Lagrange and alternating series remainder. Integration and accumulation of change and infinite sequences and series are the two most heavily weighted units, together accounting for roughly a third of the exam. Students who already understand AB material well often find that their BC outcome hinges almost entirely on how confidently they handle series and parametric/polar topics, which demand pattern recognition and careful bookkeeping rather than the geometric intuition of earlier units. Effective preparation means treating series as its own discipline—drilling which convergence test fits which series and practicing Taylor expansions until they are automatic—while also keeping AB fundamentals sharp, since AB-level questions still make up much of the exam. Because BC reports an AB subscore, even students who struggle with the BC-only content can demonstrate mastery of core calculus. Timed practice on released free-response and disciplined justification writing remain essential.
Exam structure
Two equally weighted sections totaling 3 hours 15 minutes: Section I is 45 multiple-choice questions in 1 hour 45 minutes (30 no-calculator, 15 calculator), and Section II is 6 free-response questions in 1 hour 30 minutes (2 calculator, 4 no-calculator). Each section is 50% of the score, and the exam also reports an AB subscore.
Scoring
Weighted multiple-choice and free-response points form a composite converted to a 1-5 AP score (3 is passing); a separate AB subscore (1-5) is also reported.
Common mistakes
- Choosing the wrong convergence test or misapplying the ratio/comparison tests on series questions
- Forgetting to check endpoints when finding the interval of convergence of a power series
- Mishandling Lagrange error bound and alternating series error estimation
- Errors with parametric and polar derivatives (e.g., dy/dx = (dy/dt)/(dx/dt)) and polar area formulas
- Neglecting AB fundamentals while over-focusing on series, since AB-level content still dominates the exam