How does the Crimsora AP Calculus BC tutor work?

Crimsora teaches AP Calculus BC one concept at a time with a voice-first AI tutor, then reinforces it with practice, FRQs, and targeted review of your weak spots.

What does AP Calculus BC cover?

All 10 College Board units across 80 lessons, each mapped to the official CED learning objectives.

Can I try AP Calculus BC for free?

Yes — start a free trial lesson with no signup. You only create an account once you finish your first concept and want to save your progress.

AP Calculus BC

Master AP Calculus BC across all 10 College Board units with a voice-first AI tutor: limits, derivatives, integrals, series, and personalized gap-filling.

80 lessons · 10 College Board units

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Unit 1

U1.1 Introducing Calculus: Can Change Occur at an Instant?
AP-CALCBC-1.1
U1.2 Defining Limits and Using Limit Notation
AP-CALCBC-1.2
U1.3 Estimating Limits from Graphs and Tables
AP-CALCBC-1.3-1.4
U1.5 Determining Limits Using Algebraic Properties
AP-CALCBC-1.5
U1.6 Determining Limits Using Algebraic Manipulation
AP-CALCBC-1.6
U1.7 Selecting Procedures for Determining Limits
AP-CALCBC-1.7
U1.8 Determining Limits Using the Squeeze Theorem
AP-CALCBC-1.8
U1.9 Connecting Multiple Representations of Limits
AP-CALCBC-1.9
U1.10 Exploring Types of Discontinuities
AP-CALCBC-1.10
U1.11 Defining Continuity at a Point and Over an Interval
AP-CALCBC-1.11-1.12
U1.13 Removing Discontinuities
AP-CALCBC-1.13
U1.14 Infinite Limits and Vertical Asymptotes
AP-CALCBC-1.14
U1.15 Limits at Infinity and Horizontal Asymptotes
AP-CALCBC-1.15
U1.16 The Intermediate Value Theorem
AP-CALCBC-1.16
U1 FRQ Practice
AP-CALCBC-1-FRQ

Unit 2

U2.1 The Derivative — Definition and Notation
AP-CALCBC-2.1-2.2
U2.3 Estimating Derivatives at a Point
AP-CALCBC-2.3
U2.4 Connecting Differentiability and Continuity
AP-CALCBC-2.4
U2.5 The Power Rule and Linearity of the Derivative
AP-CALCBC-2.5-2.6
U2.7 Derivatives of sin, cos, e^x, and ln x
AP-CALCBC-2.7
U2.8 The Product Rule
AP-CALCBC-2.8
U2.9 The Quotient Rule and Derivatives of tan, cot, sec, csc
AP-CALCBC-2.9-2.10
U2 FRQ Practice
AP-CALCBC-2-FRQ

Unit 3

U3.1 The Chain Rule
AP-CALCBC-3.1
U3.2 Implicit Differentiation
AP-CALCBC-3.2
U3.3 Derivatives of Inverse Functions
AP-CALCBC-3.3-3.4
U3.5 Selecting Procedures and Higher-Order Derivatives
AP-CALCBC-3.5-3.6
U3 FRQ Practice
AP-CALCBC-3-FRQ

Unit 4

U4.1 Interpreting the Derivative in Context
AP-CALCBC-4.1-4.3
U4.2 Straight-Line Motion
AP-CALCBC-4.2
U4.4 Related Rates
AP-CALCBC-4.4-4.5
U4.6 Linearization (Local Linear Approximation)
AP-CALCBC-4.6
U4.7 L'Hôpital's Rule
AP-CALCBC-4.7
U4 FRQ Practice
AP-CALCBC-4-FRQ

Unit 5

U5.1 Mean Value Theorem and Extreme Value Theorem
AP-CALCBC-5.1-5.2
U5.3 First Derivative Analysis: Increasing/Decreasing and Local Extrema
AP-CALCBC-5.3-5.5
U5.6 Concavity and the Second Derivative Test
AP-CALCBC-5.6-5.7
U5.8 Connecting f, f', f'' through Graphs
AP-CALCBC-5.8-5.9
U5.10 Optimization Problems
AP-CALCBC-5.10-5.11
U5.12 Exploring Behaviors of Implicit Relations
AP-CALCBC-5.12
U5 FRQ Practice
AP-CALCBC-5-FRQ

Unit 6

U6.1 Riemann Sums and Definite Integral Notation
AP-CALCBC-6.1-6.3
U6.4 The Fundamental Theorem of Calculus
AP-CALCBC-6.4-6.7
U6.6 Properties of Definite Integrals
AP-CALCBC-6.6
U6.8 Basic Antiderivatives and Indefinite Integrals
AP-CALCBC-6.8
U6.9 Integration by Substitution
AP-CALCBC-6.9
U6.10 Integration Using Long Division and Completing the Square
AP-CALCBC-6.10
U6.11 Integration by Parts
AP-CALCBC-6.11
U6.12 Integration Using Partial Fractions
AP-CALCBC-6.12
U6.13 Improper Integrals
AP-CALCBC-6.13
U6.14 Selecting Techniques for Antidifferentiation
AP-CALCBC-6.14
U6 FRQ Practice
AP-CALCBC-6-FRQ

Unit 7

U7.1 Modeling and Verifying Differential Equations
AP-CALCBC-7.1-7.2
U7.3 Slope Fields
AP-CALCBC-7.3-7.4
U7.5 Euler's Method
AP-CALCBC-7.5
U7.6 Separation of Variables
AP-CALCBC-7.6-7.7
U7.8 Exponential Models
AP-CALCBC-7.8
U7.9 Logistic Models
AP-CALCBC-7.9
U7 FRQ Practice
AP-CALCBC-7-FRQ

Unit 8

U8.1 Average Value, Motion, and Accumulation Applications
AP-CALCBC-8.1-8.3
U8.4 Area Between Curves
AP-CALCBC-8.4-8.6
U8.7 Volumes with Known Cross Sections
AP-CALCBC-8.7-8.8
U8.9 Volumes of Revolution: Disc and Washer Methods
AP-CALCBC-8.9-8.11
U8.12 Washer Method: Revolving Around Other Axes
AP-CALCBC-8.12
U8.13 Arc Length
AP-CALCBC-8.13
U8 FRQ Practice
AP-CALCBC-8-FRQ

Unit 9

U9.1 Parametric Equations and Differentiation
AP-CALCBC-9.1-9.2
U9.3 Arc Length of Parametric Curves
AP-CALCBC-9.3
U9.4 Vector-Valued Functions and 2D Motion
AP-CALCBC-9.4-9.6
U9.7 Polar Coordinates and Differentiation
AP-CALCBC-9.7
U9.8 Area in Polar Coordinates
AP-CALCBC-9.8-9.9
U9 FRQ Practice
AP-CALCBC-9-FRQ

Unit 10

U10.1 Series, Sequences, and Geometric Series
AP-CALCBC-10.1-10.2
U10.3 Integral Test, p-Series, and Comparison Tests
AP-CALCBC-10.3-10.6
U10.7 Alternating Series and Error Bound
AP-CALCBC-10.7-10.10
U10.8 Ratio Test, Absolute and Conditional Convergence
AP-CALCBC-10.8-10.9
U10.11 Taylor Polynomials and Lagrange Error Bound
AP-CALCBC-10.11-10.12
U10.13 Power Series — Radius and Interval of Convergence
AP-CALCBC-10.13
U10.14 Common Maclaurin Series and Manipulation
AP-CALCBC-10.14-10.15
U10 FRQ Practice
AP-CALCBC-10-FRQ

Frequently asked questions

How does the Crimsora AP Calculus BC tutor work?: Crimsora teaches AP Calculus BC one concept at a time with a voice-first AI tutor, then reinforces it with practice, FRQs, and targeted review of your weak spots.
What does AP Calculus BC cover?: All 10 College Board units across 80 lessons, each mapped to the official CED learning objectives.
Can I try AP Calculus BC for free?: Yes — start a free trial lesson with no signup. You only create an account once you finish your first concept and want to save your progress.

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