Code Scholars Tutoring · AP Calculus BC

AP Calculus BC Course Outline

Explore all ten BC units, including the shared AB foundation, BC integration and differential-equation extensions, parametric and polar calculus, and infinite series.

Expand a unit to view its topics. BC-only topics are marked so students can identify the additional scope beyond AB. Percentages show the unit’s weighting in the multiple-choice section of the AP exam.

Unit 1: Limits and Continuity5–10% of MCQ · 16 topics

Unit 1 study guide →Unit MCQ practice Unit FRQ practice

1.1Change over shrinking intervals
Study lesson
1.2One-sided and two-sided limit notation
Study lesson
1.3Limits read from graphs
Study lesson
1.4Limits estimated from tables
Study lesson
1.5Limit laws and substitution
Study lesson
1.6Algebraic simplification of limits
Study lesson
1.7Choosing a limit method
Study lesson
1.8Bounding a function with the squeeze theorem
Study lesson
1.9Switching among limit representations
Study lesson
1.10Removable, jump, and infinite discontinuities
Study lesson
1.11Continuity at a point
Study lesson
1.12Continuity over intervals
Study lesson
1.13Repairing a removable discontinuity
Study lesson
1.14Unbounded behavior near a vertical asymptote
Study lesson
1.15End behavior and horizontal asymptotes
Study lesson
1.16Intermediate values and existence
Study lesson

Unit 2: Differentiation: Definition and Fundamental Properties5–10% of MCQ · 10 topics

Unit 2 study guide →Unit MCQ practice Unit FRQ practice

2.1Secant and tangent slopes
Study lesson
2.2Derivative definitions and notation
Study lesson
2.3Numerical estimates of derivatives
Study lesson
2.4Continuity versus differentiability
Study lesson
2.5The power rule
Study lesson
2.6Linearity of differentiation
Study lesson
2.7Basic trigonometric, exponential, and logarithmic derivatives
Study lesson
2.8Products of functions
Study lesson
2.9Quotients of functions
Study lesson
2.10Other trigonometric derivatives
Study lesson

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions5–10% of MCQ · 6 topics

Unit 3 study guide →Unit MCQ practice Unit FRQ practice

3.1Nested functions and the chain rule
Study lesson
3.2Implicit derivatives
Study lesson
3.3Derivatives of inverse functions
Study lesson
3.4Inverse trigonometric derivatives
Study lesson
3.5Selecting and combining derivative rules
Study lesson
3.6Higher derivatives
Study lesson

Unit 4: Contextual Applications of Differentiation5–10% of MCQ · 7 topics

Unit 4 study guide →Unit MCQ practice Unit FRQ practice

4.1Interpreting a derivative and its units
Study lesson
4.2Position, velocity, acceleration, and speed
Study lesson
4.3Rates in scientific and economic models
Study lesson
4.4Building a related-rates equation
Study lesson
4.5Solving related-rates questions
Study lesson
4.6Tangent-line estimates and local error
Study lesson
4.7Indeterminate forms and L’Hospital’s rule
Study lesson

Unit 5: Analytical Applications of Differentiation10–15% of MCQ · 12 topics

Unit 5 study guide →Unit MCQ practice Unit FRQ practice

5.1Mean Value Theorem hypotheses and conclusions
Study lesson
5.2Existence of extrema and critical points
Study lesson
5.3Increasing and decreasing intervals
Study lesson
5.4Sign changes and the first derivative test
Study lesson
5.5Absolute extrema by candidate comparison
Study lesson
5.6Concavity and inflection points
Study lesson
5.7Second derivative tests
Study lesson
5.8Graphing from derivative evidence
Study lesson
5.9Connecting graphs of a function and its derivatives
Study lesson
5.10Constructing an optimization model
Study lesson
5.11Solving and justifying optimization
Study lesson
5.12Analyzing implicit curves
Study lesson

Unit 6: Integration and Accumulation of Change15–20% of MCQ · 14 topics

Unit 6 study guide →Unit MCQ practice Unit FRQ practice

6.1Signed accumulation from rates
Study lesson
6.2Rectangular and trapezoidal approximations
Study lesson
6.3Riemann sums and definite integrals
Study lesson
6.4Derivatives of accumulation functions
Study lesson
6.5Behavior of integral-defined functions
Study lesson
6.6Properties of definite integrals
Study lesson
6.7Evaluating definite integrals by antiderivatives
Study lesson
6.8Antiderivatives and constants
Study lesson
6.9Substitution and changed bounds
Study lesson
6.10Polynomial division and completing the square
Study lesson
6.11Integrating Using Integration by Parts
Study lessonBC only
6.12Integrating Using Linear Partial Fractions
Study lessonBC only
6.13Evaluating Improper Integrals
Study lessonBC only
6.14Choosing an AB integration method
Study lesson

Unit 7: Differential Equations5–10% of MCQ · 9 topics

Unit 7 study guide →Unit MCQ practice Unit FRQ practice

7.1Differential equations as models
Study lesson
7.2Checking a proposed solution
Study lesson
7.3Slope fields from a rate law
Study lesson
7.4Qualitative reasoning from slope fields
Study lesson
7.5Approximating Solutions Using Euler’s Method
Study lessonBC only
7.6Separation of variables
Study lesson
7.7Initial-value problems and solution domains
Study lesson
7.8Exponential growth and decay
Study lesson
7.9Logistic Models with Differential Equations
Study lessonBC only

Unit 8: Applications of Integration5–10% of MCQ · 13 topics

Unit 8 study guide →Unit MCQ practice Unit FRQ practice

8.1Average value over an interval
Study lesson
8.2Displacement and total distance
Study lesson
8.3Net change and contextual accumulation
Study lesson
8.4Area between curves with vertical slices
Study lesson
8.5Area between curves with horizontal slices
Study lesson
8.6Splitting area at multiple intersections
Study lesson
8.7Volumes with square or rectangular sections
Study lesson
8.8Volumes with triangular or semicircular sections
Study lesson
8.9Disks around a coordinate axis
Study lesson
8.10Disks around shifted axes
Study lesson
8.11Washers around a coordinate axis
Study lesson
8.12Washers around shifted axes
Study lesson
8.13The Arc Length of a Smooth, Planar Curve and Distance Traveled
Study lessonBC only

Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions10–15% of MCQ · 9 topics · BC only

Unit 9 study guide →Unit MCQ practice Unit FRQ practice

9.1Defining and Differentiating Parametric Equations
Study lessonBC only
9.2Second Derivatives of Parametric Equations
Study lessonBC only
9.3Finding Arc Lengths of Curves Given by Parametric Equations
Study lessonBC only
9.4Defining and Differentiating Vector-Valued Functions
Study lessonBC only
9.5Integrating Vector-Valued Functions
Study lessonBC only
9.6Solving Motion Problems Using Parametric and Vector-Valued Functions
Study lessonBC only
9.7Defining Polar Coordinates and Differentiating in Polar Form
Study lessonBC only
9.8Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve
Study lessonBC only
9.9Finding the Area of the Region Bounded by Two Polar Curves
Study lessonBC only

Unit 10: Infinite Sequences and Series15–20% of MCQ · 15 topics · BC only

Unit 10 study guide →Unit MCQ practice Unit FRQ practice

10.1Defining Convergent and Divergent Infinite Series
Study lessonBC only
10.2Working with Geometric Series
Study lessonBC only
10.3The nth Term Test for Divergence
Study lessonBC only
10.4Integral Test for Convergence
Study lessonBC only
10.5Harmonic Series and p-Series
Study lessonBC only
10.6Comparison Tests for Convergence
Study lessonBC only
10.7Alternating Series Test for Convergence
Study lessonBC only
10.8Ratio Test for Convergence
Study lessonBC only
10.9Determining Absolute or Conditional Convergence
Study lessonBC only
10.10Alternating Series Error Bound
Study lessonBC only
10.11Finding Taylor Polynomial Approximations of Functions
Study lessonBC only
10.12Lagrange Error Bound
Study lessonBC only
10.13Radius and Interval of Convergence of Power Series
Study lessonBC only
10.14Finding Taylor or Maclaurin Series for a Function
Study lessonBC only
10.15Representing Functions as Power Series
Study lessonBC only