Code Scholars Tutoring · AP Calculus BC
AP Calculus BC Study Guides
Learn the full BC course through detailed explanations, formulas with conditions, worked examples, and self-check problems with solutions.
Start with the unit you are studying. Each lesson connects the mathematical idea to its conditions, a worked example, and a problem you can try before revealing the reasoning. BC-only topics are marked throughout the guide.
Unit 1 · 5–10% of MCQ
Limits and Continuity
16 topics · 5 lessons
Unit 2 · 5–10% of MCQ
Differentiation: Definition and Fundamental Properties
10 topics · 4 lessons
Unit 3 · 5–10% of MCQ
Differentiation: Composite, Implicit, and Inverse Functions
6 topics · 3 lessons
Unit 4 · 5–10% of MCQ
Contextual Applications of Differentiation
7 topics · 4 lessons
Unit 5 · 10–15% of MCQ
Analytical Applications of Differentiation
12 topics · 5 lessons
Unit 6 · 15–20% of MCQ
Integration and Accumulation of Change
14 topics · 9 lessons
- Riemann sums, trapezoids, and signed area
- FTC for integral-defined functions
- Integral properties and the evaluation theorem
- Basic antiderivatives and substitution
- Algebraic rewriting before integration
- Integration by parts: choosing what to differentiateBC only
- Linear partial fractions and logarithmic antiderivativesBC only
- Improper integrals: limits before evaluationBC only
- Selecting and checking a BC integration method
Unit 7 · 5–10% of MCQ
Differential Equations
9 topics · 6 lessons
Unit 8 · 5–10% of MCQ
Applications of Integration
13 topics · 5 lessons
Unit 9 · 10–15% of MCQ
Parametric Equations, Polar Coordinates, and Vector-Valued Functions
9 topics · 9 lessons · BC only
- Parametric derivatives and tangent linesBC only
- Second derivatives of parametric curvesBC only
- Arc length and speed on a parametric curveBC only
- Vector-valued functions, velocity, and accelerationBC only
- Integrating vector functions and recovering positionBC only
- Planar motion: displacement, distance, and changing speedBC only
- Polar coordinates and Cartesian slopesBC only
- Area swept by one polar curveBC only
- Polar regions between curves and inside both curvesBC only
Unit 10 · 15–20% of MCQ
Infinite Sequences and Series
15 topics · 15 lessons · BC only
- Sequences, partial sums, and what a series meansBC only
- Geometric series and the correct first termBC only
- The nth-term divergence test and its limitsBC only
- The integral test and positive decreasing functionsBC only
- Harmonic series and the p-series thresholdBC only
- Direct and limit comparison for positive seriesBC only
- Alternating series: checking magnitudes and limitsBC only
- The ratio test: factorials, powers, and the inconclusive caseBC only
- Absolute versus conditional convergenceBC only
- Alternating-series error bounds and approximation intervalsBC only
- Taylor polynomials: matching derivatives at a centerBC only
- Lagrange error bounds for Taylor approximationsBC only
- Radius and interval of convergenceBC only
- Taylor and Maclaurin series for familiar functionsBC only
- Building new power series by substitution and integrationBC only