The AP Calculus BC curriculum is one of the most rigorous offered by the College Board. It encompasses all 8 units of the AP Calculus AB syllabus (Calculus I) and adds two massive, conceptually challenging units—plus several advanced topics scattered throughout the earlier units—to complete the equivalent of a college Calculus II course.
To succeed in this course, students must maintain an aggressive pace. You cannot afford to fall behind, because the hardest material (Infinite Series) sits at the very end of the syllabus. Below is the complete 10-unit breakdown, including the exam weightings and the specific BC-only topics you must master.
The 10 Units of AP Calculus BC
Limits, Continuity, and Differentiation Rules
Exam Weight: 11-19%
- Unit 1: Limits and Continuity (4-7%). Asymptotic behavior, L'Hôpital's Rule, and the formal definition of limits.
- Unit 2: Differentiation: Definition and Basic Rules (4-7%). Power, product, quotient rules, and defining the derivative.
- Unit 3: Differentiation: Composite, Implicit, and Inverse Functions (4-7%). Chain rule and inverse trigonometric derivatives.
Contextual & Analytical Applications of Derivatives
Exam Weight: 12-19%
- Unit 4: Contextual Applications (6-9%). Related rates, straight-line particle motion, and linear approximations.
- Unit 5: Analytical Applications (8-11%). Mean Value Theorem (MVT), Extreme Value Theorem (EVT), concavity, and curve sketching.
Integration and Accumulation of Change
Exam Weight: 17-20%
- Riemann Sums and Definite Integrals.
- The Fundamental Theorem of Calculus (Parts I & II).
- U-Substitution (AB topic).
- BC EXCLUSIVE: Integration by Parts and Linear Partial Fractions.
- BC EXCLUSIVE: Evaluating Improper Integrals (limits at infinity or vertical asymptotes).
Differential Equations and Applications of Integration
Exam Weight: 12-17%
- Unit 7: Differential Equations (6-9%). Slope fields and separable differential equations.
- BC EXCLUSIVE (Unit 7): Euler's Method for numerical approximation and Logistic Growth Models.
- Unit 8: Applications of Integration (6-9%). Area between curves, volume with cross-sections, and Disc/Washer methods.
- BC EXCLUSIVE (Unit 8): Arc Length of a smooth, planar curve and distance traveled by a particle.
Parametric, Polar, and Vector-Valued Functions
Exam Weight: 11-12%
- Calculating derivatives of parametric equations (dy/dx and d²y/dx²).
- Vector-valued functions: Position, velocity, and acceleration vectors.
- Calculating the area enclosed by a polar curve using integrals.
- Finding points of horizontal and vertical tangency on polar curves.
Infinite Sequences and Series
Exam Weight: 17-18%
- Convergence Tests: Geometric, nth Term, Integral, p-series, Comparison, Limit Comparison, Alternating, and Ratio tests.
- Radius and Interval of Convergence.
- Taylor and Maclaurin Polynomials/Series.
- Alternating Series Error Bound and Lagrange Error Bound.
Overwhelmed by the BC Syllabus?
EduQuest's structured AP Calculus BC curriculum ensures you stay on pace, master the BC-exclusives, and crush the May exam.
The BC-Exclusive Topics Masterlist
If you are transitioning from AP Calculus AB or self-studying, it is critical to know exactly which topics are NOT tested on the AB exam. The following topics make up roughly 40% of the BC exam and differentiate a Calculus I student from a Calculus II student:
Advanced Integration (Unit 6)
Integration by Parts (∫u dv = uv - ∫v du), Integration using Linear Partial Fractions, and evaluating Improper Integrals using limits.
Advanced Differential Equations (Unit 7)
Euler's Method for approximating solutions, and understanding the Logistics Differential Equation (dP/dt = kP(1 - P/K)).
Arc Length (Unit 8)
Using the integral formula L = ∫√(1 + (dy/dx)²) dx to find the length of a curve.
Parametric, Polar, and Vectors (Unit 9)
All of Unit 9 is exclusive to BC. You must calculate derivatives, arc lengths, and polar areas, as well as analyze 2D vector motion.
Infinite Series (Unit 10)
All of Unit 10 is exclusive to BC. This includes all convergence tests, power series, Taylor/Maclaurin series, and error bound calculations.
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Match UniversitiesStrategic Pacing Guide for Teachers & Self-Studiers
| Timeframe | Units to Cover | Primary Focus | Milestone Target |
|---|---|---|---|
| August - Mid October | Units 1, 2, 3, 4 | Rapid review of limits, core derivatives, and related rates. | Master the Chain Rule completely. |
| Late Oct - December | Units 5, 6 | Optimization, FTC, and all advanced integration techniques (By Parts/Partial Fractions). | Finish all integration before winter break. |
| January | Units 7, 8 | Differential equations, Euler's Method, and Volume. | Strong grasp of setting up Volume integrals. |
| February | Unit 9 | Parametric equations, Vectors, and Polar area. | Master graphing calculator use for Polar/Parametrics. |
| March - Early April | Unit 10 | Convergence tests, Taylor series, and Error Bounds. | Memorize the 4 core Maclaurin series. |
| Mid April - May | Review | Full-length timed practice tests and FRQ rubric drilling. | Score consistently >65% raw on practice exams. |
Exam Weighting and The 'AB Subscore'
- Ignoring the AB Foundation Approximately 60% of the BC exam covers AB topics (Units 1-8). If you rush through limits and basic derivatives to get to Taylor series, you will lose massive points on the easiest parts of the exam.
- Misunderstanding the Subscore The College Board provides an 'AB Subscore' (1-5) along with your BC score. This subscore is calculated ONLY from the questions testing Units 1-8. It acts as a safety net: if you bomb Unit 10 but ace the early units, you can still earn college credit for Calculus I.
- Failing to Practice FRQ 6 (Series) FRQ 6 is always an Infinite Series question. Because it's the last topic taught, students often run out of time to practice it. You must allocate specific time in April to drill past versions of FRQ 6.
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Check ProfileThe Most Heavily Tested Concepts
While everything in the CED is fair game, historical data shows that the College Board loves testing specific intersections of topics. On the BC exam, expect to see integration tested heavily through accumulation functions, and derivatives tested through contextual particle motion (now in 2D vector space).
“If you want to score a 5, you cannot ignore Error Bounds. Both the Alternating Series Error Bound and the Lagrange Error Bound routinely appear as 2-point sections on FRQ 6. Students often skip them because they look complicated, making them high-value differentiators for top scorers.”
How EduQuest Navigates the BC Syllabus
Aggressive, Supported Pacing
We ensure you never fall behind. By covering the AB topics efficiently, we carve out a full 6 weeks in the spring dedicated entirely to Unit 9 and Unit 10.
Visualizing Polar and Parametric
We use dynamic graphing tools to help you visualize what polar equations and vector paths actually look like, making the calculus intuitive rather than just formulaic.
The Convergence Flowchart
We teach Unit 10 using a proprietary flowchart method, ensuring you never guess which convergence test to apply on the exam.
A Note on Calculus Prerequisites
Calculus is just the application of limits to algebra, geometry, and trigonometry. The students who fail AP Calculus BC rarely fail because they don't understand the calculus concepts. They fail because their algebra is sloppy, their trig identities are forgotten, and they cannot manipulate fractions quickly.
— AP Math Department Chair
Before beginning the BC syllabus, you must ensure your Pre-Calculus foundation is rock solid. You should know the unit circle instantly, understand logarithmic properties, and be able to factor complex polynomials without a second thought. If you are weak in these areas, spend your summer reviewing Pre-Calculus before BC begins.
The AP Calculus BC Summer Prep Kit
Get ready for the hardest AP math course with our free summer prep kit—including a Pre-Calc diagnostic test, the essential trig identities cheat sheet, and a 4-week summer review schedule.
Final Thoughts
The BC syllabus is intimidating, but it is deeply rewarding. Mastering this curriculum not only earns you college credit but completely transforms your problem-solving abilities, preparing you for any STEM major you choose to pursue.
FAQs: AP Calculus BC Syllabus
Are Units 1-8 in BC exactly the same as in AB?
Mostly, yes. However, BC adds a few advanced topics into those early units. For example, Unit 6 adds Integration by Parts and Partial Fractions, Unit 7 adds Euler's Method and Logistic Growth, and Unit 8 adds Arc Length. But the core concepts of limits, derivatives, and basic integrals are identical.
How much of the exam is based on Unit 9 and Unit 10?
Units 9 (Parametric/Polar/Vectors) and Unit 10 (Infinite Series) together make up roughly 28% to 30% of the exam. However, because they are exclusively tested on the BC exam and feature heavily in the FRQs (specifically FRQ 2 and FRQ 6), they hold outsized importance.
Do I need to memorize all the convergence tests?
Yes, absolutely. You must know the conditions and conclusions for the Nth Term, Geometric, p-Series, Integral, Comparison, Limit Comparison, Alternating Series, and Ratio tests. You will not be provided with a formula sheet on the exam.
Is Multivariable Calculus (Calc III) on the BC syllabus?
No. AP Calculus BC covers Calculus I and Calculus II. It does not cover 3D planes, partial derivatives, or multiple integrals, which are topics reserved for Multivariable Calculus (often taken after completing BC).
What is a 'Logistic Growth Model'?
It is a differential equation of the form dP/dt = kP(1 - P/K) that models population growth where there is a carrying capacity (K). It is an exclusive BC topic (Unit 7) that frequently appears in the multiple-choice section.
Why is pacing so important in BC?
Because you are covering two semesters of college math in one high school year. If you spend too much time on basic derivatives in October, you will be forced to cram Infinite Series (the hardest topic) in April, which is a recipe for disaster on the exam.
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