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AP Calculus BC syllabus: 10 units

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1

Unit 1: Limits and Continuity

4–7% of exam score

Limits from graphs, tables and algebra, squeeze theorem, continuity, removable and jump discontinuities, and the Intermediate Value Theorem.

Comprehensive Unit Scope:

Limits from graphs, tables and algebra, squeeze theorem, continuity, removable and jump discontinuities, and the Intermediate Value Theorem.

Sub-Topics & Theorems (4):
Estimating limits from graphs and tables
Squeeze theorem
Types of discontinuity
Intermediate Value Theorem
Core Formula Benchmark:
lim⁡x→cf(x)=f(c)  ⟺  f is continuous at c\lim_{x \to c} f(x) = f(c) \iff f \text{ is continuous at } c
Launch Unit 1: Limits and Continuity Studio
2

Unit 2: Differentiation: Definition and Fundamental Properties

4–7% of exam score

The derivative as a limit, differentiability versus continuity, and the power, product and quotient rules.

3

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

4–7% of exam score

The chain rule, implicit differentiation, derivatives of inverse and inverse trigonometric functions, and higher-order derivatives.

4

Unit 4: Contextual Applications of Differentiation

6–9% of exam score

Rates of change in context, straight-line motion, related rates, local linearization and L'Hôpital's rule.

5

Unit 5: Analytical Applications of Differentiation

8–11% of exam score

The Mean Value Theorem, Extreme Value Theorem, increasing and decreasing intervals, concavity, and optimization.

6

Unit 6: Integration and Accumulation of Change

17–20% of exam score

Riemann sums, the Fundamental Theorem of Calculus, substitution, and BC-only techniques: integration by parts, partial fractions and improper integrals.

7

Unit 7: Differential Equations

6–9% of exam score

Slope fields, separation of variables, exponential models, and BC-only Euler's method and logistic growth.

8

Unit 8: Applications of Integration

6–9% of exam score

Average value, motion using integrals, area between curves, volumes by cross-sections and revolution, and BC-only arc length.

9

Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions

11–12% of exam score

Derivatives and arc length of parametric curves, vector-valued motion, and area in polar coordinates.

10

Unit 10: Infinite Sequences and Series

17–18% of exam score

Convergence tests, power series, Taylor and Maclaurin series, radius and interval of convergence, and error bounds.