The AP Calculus curriculum is divided into two distinct college-level courses managed by the College Board: AP Calculus AB and AP Calculus BC. AP Calculus AB covers the equivalent of a first-semester college calculus class, while AP Calculus BC covers the first two semesters, adding advanced integration techniques, polar coordinates, vectors, and infinite series.
The Unit Breakdown (AB vs. BC) The curriculum is organized into 10 core units. Calculus AB covers Units 1 through 8, while Calculus BC covers all 10 units.
Unit 1: Limits and Continuity (AB: 10–12% | BC: 4–7%) Concept of limits and finding limits algebraicly Continuity and the Intermediate Value Theorem Unit 2: Differentiation: Definition and Fundamental Properties (AB: 10–12% | BC: 4–7%) Defining the derivative via limits and average vs. instantaneous rate of change Derivative rules (Power, Product, Quotient, and Chain rules) Unit 3: Differentiation: Composite, Implicit, and Inverse Functions (AB: 9–13% | BC: 4–7%) Implicit differentiation and differentiating inverse functions Calculating higher-order derivatives Unit 4: Contextual Applications of Differentiation (AB: 10–15% | BC: 6–9%) Related rates, local linearity, and approximation Interpreting meaning of derivatives in real-world contexts Unit 5: Analytical Applications of Differentiation (AB: 15–18% | BC: 8–11%) Mean Value Theorem and Extreme Value Theorem Using first and second derivatives to graph functions (concavity, inflection points) Unit 6: Integration and Accumulation of Change (AB: 17–20% | BC: 17–20%) Riemann sums, definite integrals, and Fundamental Theorem of Calculus Anti-differentiation, integration by $u$-substitution, and integration by parts (BC only) Unit 7: Differential Equations (AB: 6–12% | BC: 6–9%) Slope fields, verifiable solutions, and separable differential equations Euler’s method and logistic models (BC only) Unit 8: Applications of Integration (AB: 10–15% | BC: 6–9%) Average value of a function and area between curves Volumes of solids via cross-sections, disc method, and washer method Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions (BC Only: 11–12%) Derivatives and integrals of parametric equations and vector functions Area and arc length in polar coordinates Unit 10: Infinite Sequences and Series (BC Only: 17–18%) Convergence and divergence tests (Ratio, $p$-series, Integral, Geometric) Taylor series, Maclaurin series, and power series intervals of convergence
Mathematical Practices Throughout either course, students must develop four foundational habits of mind:
1. Implementing Mathematical Processes: Determining expressions, limits, derivatives, and integrals. 2. Connecting Representations: Translating between numerical (tables), graphical, algebraic, and verbal data. 3. Justification: Explaining mathematical reasoning, theorems, and conclusions clearly. 4. Communication and Notation: Using standard, precise mathematical symbols and writing coherent arguments.
Exam Format Breakdown Both the [AP Calculus AB Exam] and the AP Calculus BC Exam follow an identical formatting timeline, running 3 hours and 15 minutes in total.
Section | Format | Timing | Calculator | Weight |
Section I: Part A | 30 Multiple-Choice Questions | 60 minutes | No | 33.3% | Section I: Part B | 15 Multiple-Choice Questions | 45 minutes | Yes (Graphing) | 16.7% | Section II: Part A | 2 Free-Response Questions | 30 minutes | Yes (Graphing) | 16.7% | Section II: Part B | 4 Free-Response Questions | 60 minutes | No | 33.3% |
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