Skip to content
Wyatt's Notes — Qualifications

AP Calculus

AP Calculus

Comprehensive revision notes for AP Calculus AB/BC, aligned with the College Board Course and Exam Description.

These notes cover the full AP Calculus curriculum, from limits and continuity through to series and differential equations. Each topic page includes key theorems, worked examples, and step-by-step solutions to help you prepare for both the multiple-choice and free-response sections of the AP exam. The content follows the College Board’s course framework and mathematical practices.

Topics

Topics Covered

  • Limits and Continuity — evaluating limits algebraically and graphically, squeeze theorem, intermediate value theorem, infinite limits, limits at infinity
  • Derivatives — definition of the derivative, power/product/quotient/chain rules, implicit differentiation, related rates, optimisation, curve sketching
  • Integrals — Riemann sums, fundamental theorem of calculus, u-substitution, integration by parts, area between curves, volume of solids of revolution
  • Differential Equations — slope fields, separation of variables, exponential growth and decay, logistic models, Euler’s method
  • Sequences and Series — convergence tests (ratio, comparison, integral), Taylor and Maclaurin series, power series, radius and interval of convergence (BC only)

How to Use These Notes

  • Start with the topics you find most challenging and work through the notes systematically
  • Try to explain each concept back in your own words after reading a section
  • Use the topic links above to jump between related concepts when revising
  • Combine these notes with past paper practice for the best results

Study Tips

  • Show every step of your working; AP free-response questions award partial credit for correct intermediate steps even if the final answer is wrong
  • Practise justifying your answers — stating which theorem or test you are using is often required for full credit
  • Master your calculator skills (graphing, numerical integration, solver) for the calculator-active portions of the exam
  • Review common algebraic manipulations (partial fractions, long division, trigonometric identities) as they underpin most calculus techniques
  • BC students should pay particular attention to series convergence tests and parametric/polar functions, which are exclusive to the BC exam
  • Create a one-page summary sheet of all derivative and integral rules for quick reference during revision sessions
  • Time yourself when practising free-response questions — the exam is tight on time and pacing is a key skill
  • Keep a mistake log of questions you get wrong in practice and review it before the exam to avoid repeating the same errors
  • Review the AP Calculus mathematical practices alongside content — justification and communication are assessed throughout the exam

Summary

The key principles covered in this topic are linked in the sub-pages above. Focus on understanding the definitions, applying the formulas or frameworks, and evaluating strengths and limitations of each approach.

Worked Examples

Worked examples demonstrating the application of key concepts are covered in the detailed sub-pages linked above.

Common Pitfalls

  • Confusing terminology or concepts that appear similar but have distinct meanings.
  • Overlooking key assumptions or boundary conditions that limit applicability.