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AP Calculus BC

Advanced calculus with parametric equations, polar coordinates & infinite series

10
Total Units
8
AB Units Included
2
BC-Only Units
5
AP Exam Score

AP Calculus BC Overview

AP Calculus BC is equivalent to two semesters of college calculus. It includes all AP Calculus AB topicsplus additional advanced material: parametric and polar equations, vector-valued functions, and infinite series. BC students receive both a BC score and an AB subscore on the AP exam.

What's Included in AP Calculus BC

All AB Content (Units 1-8):

  • Limits and Continuity
  • Differentiation (Definition, Rules, Applications)
  • Integration and Accumulation
  • Differential Equations
  • Applications of Integration

BC-Only Content (Units 9-10):

  • Parametric Equations - Motion in the plane
  • Polar Coordinates - Curves in polar form
  • Vector-Valued Functions - Position, velocity, acceleration
  • Infinite Sequences - Convergence and divergence
  • Infinite Series - Taylor/Maclaurin series, power series
  • Convergence Tests - Ratio, root, comparison, alternating series

Important Note

AP Calculus BC covers all content from AP Calculus AB plus additional topics. If you're taking BC, you should first master all AB material (Units 1-8) before moving to BC-specific topics (Units 9-10). Start with the AP Calculus AB lessons below!

AP Calculus AB Lessons

Master Units 1-8: Limits, Derivatives, Integrals, and Differential Equations

Start with AB content

BC-Only Topics

Advanced topics: Parametric, Polar, Vectors & Series

Unit 9: Parametric, Polar & Vector Functions
Unit 10: Infinite Sequences and Series
Coming soon - full BC-only lessons

Complete Unit Breakdown

Units 1-8: AP Calculus AB Content

Available in the AP Calculus AB section

Unit 1: Limits and Continuity
Unit 2: Differentiation - Definition & Properties
Unit 3: Composite, Implicit & Inverse Functions
Unit 4: Contextual Applications of Differentiation
Unit 5: Analytical Applications of Differentiation
Unit 6: Integration and Accumulation
Unit 7: Differential Equations and Applications
Unit 8: Applications of Integration

Units 9-10: BC-Only Content

Advanced topics beyond AP Calculus AB

Unit 9: Parametric Equations, Polar Coordinates & Vector-Valued Functions
  • • Parametric equations for motion in the plane
  • • Derivatives and integrals of parametric curves
  • • Polar coordinate system and polar curves
  • • Area and arc length in polar coordinates
  • • Vector-valued functions for position, velocity, and acceleration
Unit 10: Infinite Sequences and Series
  • • Convergence and divergence of sequences
  • • Geometric series and telescoping series
  • • Convergence tests: Integral, Comparison, Limit Comparison, Ratio, Root
  • • Alternating series and absolute vs. conditional convergence
  • • Power series and radius/interval of convergence
  • • Taylor and Maclaurin series
  • • Applications of series approximations

AP Calculus BC Exam

The AP Calculus BC exam consists of 45 multiple-choice questions and 6 free-response questions. You'll receive both a BC score (1-5) and an AB subscore based on AB content only.

3 hours 15 min
Total Exam Time
50% / 50%
MCQ / FRQ Weight
~40%
BC-Only Content
BC Practice Exam
Full-length practice test
Study AB Content First
Master Units 1-8
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