The AP Calculus exam in May rewards two kinds of preparation: fluency with procedures (differentiation rules, integration techniques, the fundamental theorem) and ability to read and interpret novel problems. These require different practice. Most students do only the first and then encounter the second on exam day without having built the relevant skill.
The exam structure
AP Calculus AB: 45 multiple choice (30 no-calculator, 15 with calculator) + 6 free response (2 with calculator, 4 without). 3 hours 15 minutes.
AP Calculus BC: same structure, plus additional topics: sequences and series, polar and parametric, and more integration techniques. Same time allocation.
Scores 1–5. A 3 earns credit at most universities; a 4 or 5 at selective institutions.
Topic weighting (AP Calculus AB)
Limits and continuity: 10–12% Differentiation — definition and basic rules: 10–12% Differentiation — composite, implicit, inverse: 9–13% Contextual applications of differentiation: 10–15% Applications of derivatives (mean value theorem, optimization): 15–18% Integration and accumulation of change: 17–20% Applications of integration: 6–12% Differential equations: 6–12%
Integration and accumulation is the highest-weighted single area. Students who shortchange integration practice in favour of differentiation routinely underperform relative to their ability.
A six-week plan
Weeks 1–2: Review every differentiation topic. Do not proceed until you can differentiate any function in under 60 seconds and handle implicit differentiation without referring to notes. The College Board's AP Classroom has free unit reviews.
Weeks 3–4: Integration — u-substitution, the fundamental theorem (both parts), integration by parts (BC only), and applications (area between curves, volume by disks and shells).
Week 5: Applications — related rates, optimization, differential equations, slope fields. These are the free-response question types that require both computation and written justification.
Week 6: Timed full past papers under exam conditions. Review errors by category, not by paper date.
The two calculator-paper mistakes
On the calculator-eligible sections, two habits distinguish students who score full marks from those who do not:
1. Storing intermediate values rather than rounding them. The AP exam rounds only the final answer. Students who round after each step accumulate error and sometimes land more than 0.001 away from the correct answer, which costs the point. Store every intermediate result in a calculator variable.
2. Showing the setup even when using a calculator. "I computed the integral" is not a justification. Write the setup (the integral expression, the limits, the integrand) before stating the calculator result. Free-response points are awarded for process, not just answers.
The written justification problem
Roughly a third of free-response marks are for mathematical justification — the reasoning that connects the setup to the conclusion. "The function is increasing because f'(x) > 0 on (1, 3)" earns a mark. "The function is increasing because I can see it" does not.
Practise writing justifications on every problem, not just the ones that explicitly ask for them. Justify every sign change, every extremum, every conclusion about concavity.
Frequently Asked Questions
How many past AP Calc papers should I do?
The College Board releases free-response questions going back to 1998. The most relevant are the last five years. Do not do older than 10 years for timing practice — the format changed. Use older papers for individual question practice without the time pressure.
Is AP Calculus BC significantly harder than AB?
BC covers all AB material plus: parametric equations, polar coordinates, vector-valued functions, series and sequences (including Taylor series), L'Hôpital's rule, and more integration techniques. The BC exam is longer but proportionally scored — students who do BC do not need a higher raw score to get a 5.