AP Calculus turns the big ideas of calculus into a year-long course with a high-stakes May exam scored 1–5. A 3, 4, or 5 can earn college credit. The two courses — AB and BC — share a spine; BC simply goes further. Here's how to prepare for either well.
AB vs BC — which is which
- AP Calculus AB ≈ a first semester (and a bit) of college calculus: limits, derivatives, integrals, and the Fundamental Theorem.
- AP Calculus BC = all of AB plus more techniques, parametric/polar/vector functions, and infinite series. BC also reports an "AB subscore."
If you're confident and want the strongest signal for STEM, BC is the better target — but only on a solid AB foundation.
Exam format at a glance
| Section I | Multiple choice — a no-calculator part and a calculator part |
| Section II | Free response — a calculator part and a no-calculator part |
| Length | ~3 hours 15 minutes total |
| Score | 1–5 (3+ often earns credit) |
Confirm the current year's exact timings and question counts on the College Board site — the structure above is stable, the fine print updates.
Unit checklist
Shared (AB & BC)
- Limits & continuity (incl. one-sided limits, asymptotes, IVT)
- Differentiation: definition & rules (power, product, quotient, chain)
- Differentiation: implicit, inverse, and composite; related rates
- Applications of derivatives (extrema, the Mean Value Theorem, concavity, optimisation, motion, L'Hôpital)
- Integration & the Fundamental Theorem of Calculus (Riemann sums, substitution, accumulation)
- Applications of integration (area between curves, volumes of revolution, average value, motion)
- Differential equations (slope fields, separation of variables, exponential models)
BC only (in addition)
- Integration by parts, partial fractions, improper integrals
- Parametric, polar, and vector-valued functions (and their calculus)
- Infinite sequences & series — convergence tests, power series, Taylor & Maclaurin series, error bounds
- Logistic growth
How to earn the 4s and 5s
- Master limits and the derivative definition first — everything builds on them.
- Practise both modes: the no-calculator sections reward clean algebra and exact values; the calculator sections reward knowing when and how to use it (and showing the set-up, not just the answer).
- Free-response discipline: label your work, show the integral/derivative you're evaluating, include units, and justify with the right theorem ("because changes sign…").
- For BC, drill series relentlessly — convergence tests and Taylor series are where BC points are won and lost.
- Time yourself. Pacing is a skill; practise full sections under the clock.
Common pitfalls
- Forgetting the chain rule's inner derivative (the single most common slip).
- Dropping the +C and mishandling definite-integral limits.
- On FRQs, giving the right number with no justification — the rubric wants the reasoning.
- BC: applying a convergence test without checking its hypotheses.
How IvyfordMath helps
IvyfordMath covers AP Calculus with hand-curated questions and a worked solution on every miss, plus reasoning drills that target exactly the justification skills AP free-response rewards — including the chain-rule and FTC steps students most often get wrong.
— Mike Vuu, Oxford Mathematics graduate and founder of IvyfordMath.